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    /or1k/trunk/newlib-1.10.0/newlib/libm/math
    from Rev 1010 to Rev 1765
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  •

Rev 1010 → Rev 1765

/w_cabs.c
0,0 → 1,20
/*
* cabs() wrapper for hypot().
*
* Written by J.T. Conklin, <jtc@wimsey.com>
* Placed into the Public Domain, 1994.
*/
 
#include "fdlibm.h"
 
struct complex {
double x;
double y;
};
 
double
cabs(z)
struct complex z;
{
return hypot(z.x, z.y);
}
/wf_hypot.c
0,0 → 1,79
/* wf_hypot.c -- float version of w_hypot.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
* wrapper hypotf(x,y)
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifdef __STDC__
float hypotf(float x, float y) /* wrapper hypotf */
#else
float hypotf(x,y) /* wrapper hypotf */
float x,y;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_hypotf(x,y);
#else
float z;
struct exception exc;
z = __ieee754_hypotf(x,y);
if(_LIB_VERSION == _IEEE_) return z;
if((!finitef(z))&&finitef(x)&&finitef(y)) {
/* hypotf(finite,finite) overflow */
#ifndef HUGE_VAL
#define HUGE_VAL inf
double inf = 0.0;
 
SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */
#endif
exc.type = OVERFLOW;
exc.name = "hypotf";
exc.err = 0;
exc.arg1 = (double)x;
exc.arg2 = (double)y;
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
if (exc.err != 0)
errno = exc.err;
return (float)exc.retval;
} else
return z;
#endif
}
 
#ifdef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double hypot(double x, double y)
#else
double hypot(x,y)
double x,y;
#endif
{
return (double) hypotf((float) x, (float) y);
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/sf_isinf.c
0,0 → 1,33
/*
* isinff(x) returns 1 if x is +-infinity, else 0;
* Added by Cygnus Support.
*/
 
#include "fdlibm.h"
 
#ifdef __STDC__
int isinff(float x)
#else
int isinff(x)
float x;
#endif
{
__int32_t ix;
GET_FLOAT_WORD(ix,x);
ix &= 0x7fffffff;
return FLT_UWORD_IS_INFINITE(ix);
}
 
#ifdef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
int isinf(double x)
#else
int isinf(x)
double x;
#endif
{
return isinff((float) x);
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/e_exp.c
0,0 → 1,167
 
/* @(#)e_exp.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/* __ieee754_exp(x)
* Returns the exponential of x.
*
* Method
* 1. Argument reduction:
* Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658.
* Given x, find r and integer k such that
*
* x = k*ln2 + r, |r| <= 0.5*ln2.
*
* Here r will be represented as r = hi-lo for better
* accuracy.
*
* 2. Approximation of exp(r) by a special rational function on
* the interval [0,0.34658]:
* Write
* R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ...
* We use a special Reme algorithm on [0,0.34658] to generate
* a polynomial of degree 5 to approximate R. The maximum error
* of this polynomial approximation is bounded by 2**-59. In
* other words,
* R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5
* (where z=r*r, and the values of P1 to P5 are listed below)
* and
* | 5 | -59
* | 2.0+P1*z+...+P5*z - R(z) | <= 2
* | |
* The computation of exp(r) thus becomes
* 2*r
* exp(r) = 1 + -------
* R - r
* r*R1(r)
* = 1 + r + ----------- (for better accuracy)
* 2 - R1(r)
* where
* 2 4 10
* R1(r) = r - (P1*r + P2*r + ... + P5*r ).
*
* 3. Scale back to obtain exp(x):
* From step 1, we have
* exp(x) = 2^k * exp(r)
*
* Special cases:
* exp(INF) is INF, exp(NaN) is NaN;
* exp(-INF) is 0, and
* for finite argument, only exp(0)=1 is exact.
*
* Accuracy:
* according to an error analysis, the error is always less than
* 1 ulp (unit in the last place).
*
* Misc. info.
* For IEEE double
* if x > 7.09782712893383973096e+02 then exp(x) overflow
* if x < -7.45133219101941108420e+02 then exp(x) underflow
*
* Constants:
* The hexadecimal values are the intended ones for the following
* constants. The decimal values may be used, provided that the
* compiler will convert from decimal to binary accurately enough
* to produce the hexadecimal values shown.
*/
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
static const double
#else
static double
#endif
one = 1.0,
halF[2] = {0.5,-0.5,},
huge = 1.0e+300,
twom1000= 9.33263618503218878990e-302, /* 2**-1000=0x01700000,0*/
o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */
u_threshold= -7.45133219101941108420e+02, /* 0xc0874910, 0xD52D3051 */
ln2HI[2] ={ 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */
-6.93147180369123816490e-01,},/* 0xbfe62e42, 0xfee00000 */
ln2LO[2] ={ 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */
-1.90821492927058770002e-10,},/* 0xbdea39ef, 0x35793c76 */
invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */
P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */
 
 
#ifdef __STDC__
double __ieee754_exp(double x) /* default IEEE double exp */
#else
double __ieee754_exp(x) /* default IEEE double exp */
double x;
#endif
{
double y,hi,lo,c,t;
__int32_t k,xsb;
__uint32_t hx;
 
GET_HIGH_WORD(hx,x);
xsb = (hx>>31)&1; /* sign bit of x */
hx &= 0x7fffffff; /* high word of |x| */
 
/* filter out non-finite argument */
if(hx >= 0x40862E42) { /* if |x|>=709.78... */
if(hx>=0x7ff00000) {
__uint32_t lx;
GET_LOW_WORD(lx,x);
if(((hx&0xfffff)|lx)!=0)
return x+x; /* NaN */
else return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */
}
if(x > o_threshold) return huge*huge; /* overflow */
if(x < u_threshold) return twom1000*twom1000; /* underflow */
}
 
/* argument reduction */
if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */
hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
} else {
k = invln2*x+halF[xsb];
t = k;
hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
lo = t*ln2LO[0];
}
x = hi - lo;
}
else if(hx < 0x3e300000) { /* when |x|<2**-28 */
if(huge+x>one) return one+x;/* trigger inexact */
}
else k = 0;
 
/* x is now in primary range */
t = x*x;
c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
if(k==0) return one-((x*c)/(c-2.0)-x);
else y = one-((lo-(x*c)/(2.0-c))-hi);
if(k >= -1021) {
__uint32_t hy;
GET_HIGH_WORD(hy,y);
SET_HIGH_WORD(y,hy+(k<<20)); /* add k to y's exponent */
return y;
} else {
__uint32_t hy;
GET_HIGH_WORD(hy,y);
SET_HIGH_WORD(y,hy+((k+1000)<<20)); /* add k to y's exponent */
return y*twom1000;
}
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/s_floor.c
0,0 → 1,134
 
/* @(#)s_floor.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
FUNCTION
<<floor>>, <<floorf>>, <<ceil>>, <<ceilf>>---floor and ceiling
INDEX
floor
INDEX
floorf
INDEX
ceil
INDEX
ceilf
 
ANSI_SYNOPSIS
#include <math.h>
double floor(double <[x]>);
float floorf(float <[x]>);
double ceil(double <[x]>);
float ceilf(float <[x]>);
 
TRAD_SYNOPSIS
#include <math.h>
double floor(<[x]>)
double <[x]>;
float floorf(<[x]>)
float <[x]>;
double ceil(<[x]>)
double <[x]>;
float ceilf(<[x]>)
float <[x]>;
 
DESCRIPTION
<<floor>> and <<floorf>> find
@tex
$\lfloor x \rfloor$,
@end tex
the nearest integer less than or equal to <[x]>.
<<ceil>> and <<ceilf>> find
@tex
$\lceil x\rceil$,
@end tex
the nearest integer greater than or equal to <[x]>.
 
RETURNS
<<floor>> and <<ceil>> return the integer result as a double.
<<floorf>> and <<ceilf>> return the integer result as a float.
 
PORTABILITY
<<floor>> and <<ceil>> are ANSI.
<<floorf>> and <<ceilf>> are extensions.
 
 
*/
 
/*
* floor(x)
* Return x rounded toward -inf to integral value
* Method:
* Bit twiddling.
* Exception:
* Inexact flag raised if x not equal to floor(x).
*/
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
static const double huge = 1.0e300;
#else
static double huge = 1.0e300;
#endif
 
#ifdef __STDC__
double floor(double x)
#else
double floor(x)
double x;
#endif
{
__int32_t i0,i1,j0;
__uint32_t i,j;
EXTRACT_WORDS(i0,i1,x);
j0 = ((i0>>20)&0x7ff)-0x3ff;
if(j0<20) {
if(j0<0) { /* raise inexact if x != 0 */
if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */
if(i0>=0) {i0=i1=0;}
else if(((i0&0x7fffffff)|i1)!=0)
{ i0=0xbff00000;i1=0;}
}
} else {
i = (0x000fffff)>>j0;
if(((i0&i)|i1)==0) return x; /* x is integral */
if(huge+x>0.0) { /* raise inexact flag */
if(i0<0) i0 += (0x00100000)>>j0;
i0 &= (~i); i1=0;
}
}
} else if (j0>51) {
if(j0==0x400) return x+x; /* inf or NaN */
else return x; /* x is integral */
} else {
i = ((__uint32_t)(0xffffffff))>>(j0-20);
if((i1&i)==0) return x; /* x is integral */
if(huge+x>0.0) { /* raise inexact flag */
if(i0<0) {
if(j0==20) i0+=1;
else {
j = i1+(1<<(52-j0));
if(j<i1) i0 +=1 ; /* got a carry */
i1=j;
}
}
i1 &= (~i);
}
}
INSERT_WORDS(x,i0,i1);
return x;
}
 
#endif /* _DOUBLE_IS_32BITS */
/sf_erf.c
0,0 → 1,246
/* sf_erf.c -- float version of s_erf.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
#include "fdlibm.h"
 
#ifdef __v810__
#define const
#endif
 
#ifdef __STDC__
static const float
#else
static float
#endif
tiny = 1e-30,
half= 5.0000000000e-01, /* 0x3F000000 */
one = 1.0000000000e+00, /* 0x3F800000 */
two = 2.0000000000e+00, /* 0x40000000 */
/* c = (subfloat)0.84506291151 */
erx = 8.4506291151e-01, /* 0x3f58560b */
/*
* Coefficients for approximation to erf on [0,0.84375]
*/
efx = 1.2837916613e-01, /* 0x3e0375d4 */
efx8= 1.0270333290e+00, /* 0x3f8375d4 */
pp0 = 1.2837916613e-01, /* 0x3e0375d4 */
pp1 = -3.2504209876e-01, /* 0xbea66beb */
pp2 = -2.8481749818e-02, /* 0xbce9528f */
pp3 = -5.7702702470e-03, /* 0xbbbd1489 */
pp4 = -2.3763017452e-05, /* 0xb7c756b1 */
qq1 = 3.9791721106e-01, /* 0x3ecbbbce */
qq2 = 6.5022252500e-02, /* 0x3d852a63 */
qq3 = 5.0813062117e-03, /* 0x3ba68116 */
qq4 = 1.3249473704e-04, /* 0x390aee49 */
qq5 = -3.9602282413e-06, /* 0xb684e21a */
/*
* Coefficients for approximation to erf in [0.84375,1.25]
*/
pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */
pa1 = 4.1485610604e-01, /* 0x3ed46805 */
pa2 = -3.7220788002e-01, /* 0xbebe9208 */
pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */
pa4 = -1.1089469492e-01, /* 0xbde31cc2 */
pa5 = 3.5478305072e-02, /* 0x3d1151b3 */
pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */
qa1 = 1.0642088205e-01, /* 0x3dd9f331 */
qa2 = 5.4039794207e-01, /* 0x3f0a5785 */
qa3 = 7.1828655899e-02, /* 0x3d931ae7 */
qa4 = 1.2617121637e-01, /* 0x3e013307 */
qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */
qa6 = 1.1984500103e-02, /* 0x3c445aa3 */
/*
* Coefficients for approximation to erfc in [1.25,1/0.35]
*/
ra0 = -9.8649440333e-03, /* 0xbc21a093 */
ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */
ra2 = -1.0558626175e+01, /* 0xc128f022 */
ra3 = -6.2375331879e+01, /* 0xc2798057 */
ra4 = -1.6239666748e+02, /* 0xc322658c */
ra5 = -1.8460508728e+02, /* 0xc3389ae7 */
ra6 = -8.1287437439e+01, /* 0xc2a2932b */
ra7 = -9.8143291473e+00, /* 0xc11d077e */
sa1 = 1.9651271820e+01, /* 0x419d35ce */
sa2 = 1.3765776062e+02, /* 0x4309a863 */
sa3 = 4.3456588745e+02, /* 0x43d9486f */
sa4 = 6.4538726807e+02, /* 0x442158c9 */
sa5 = 4.2900814819e+02, /* 0x43d6810b */
sa6 = 1.0863500214e+02, /* 0x42d9451f */
sa7 = 6.5702495575e+00, /* 0x40d23f7c */
sa8 = -6.0424413532e-02, /* 0xbd777f97 */
/*
* Coefficients for approximation to erfc in [1/.35,28]
*/
rb0 = -9.8649431020e-03, /* 0xbc21a092 */
rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */
rb2 = -1.7757955551e+01, /* 0xc18e104b */
rb3 = -1.6063638306e+02, /* 0xc320a2ea */
rb4 = -6.3756646729e+02, /* 0xc41f6441 */
rb5 = -1.0250950928e+03, /* 0xc480230b */
rb6 = -4.8351919556e+02, /* 0xc3f1c275 */
sb1 = 3.0338060379e+01, /* 0x41f2b459 */
sb2 = 3.2579251099e+02, /* 0x43a2e571 */
sb3 = 1.5367296143e+03, /* 0x44c01759 */
sb4 = 3.1998581543e+03, /* 0x4547fdbb */
sb5 = 2.5530502930e+03, /* 0x451f90ce */
sb6 = 4.7452853394e+02, /* 0x43ed43a7 */
sb7 = -2.2440952301e+01; /* 0xc1b38712 */
 
#ifdef __STDC__
float erff(float x)
#else
float erff(x)
float x;
#endif
{
__int32_t hx,ix,i;
float R,S,P,Q,s,y,z,r;
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
if(!FLT_UWORD_IS_FINITE(ix)) { /* erf(nan)=nan */
i = ((__uint32_t)hx>>31)<<1;
return (float)(1-i)+one/x; /* erf(+-inf)=+-1 */
}
 
if(ix < 0x3f580000) { /* |x|<0.84375 */
if(ix < 0x31800000) { /* |x|<2**-28 */
if (ix < 0x04000000)
/*avoid underflow */
return (float)0.125*((float)8.0*x+efx8*x);
return x + efx*x;
}
z = x*x;
r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
y = r/s;
return x + x*y;
}
if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
s = fabsf(x)-one;
P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
if(hx>=0) return erx + P/Q; else return -erx - P/Q;
}
if (ix >= 0x40c00000) { /* inf>|x|>=6 */
if(hx>=0) return one-tiny; else return tiny-one;
}
x = fabsf(x);
s = one/(x*x);
if(ix< 0x4036DB6E) { /* |x| < 1/0.35 */
R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
ra5+s*(ra6+s*ra7))))));
S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
sa5+s*(sa6+s*(sa7+s*sa8)))))));
} else { /* |x| >= 1/0.35 */
R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
rb5+s*rb6)))));
S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
sb5+s*(sb6+s*sb7))))));
}
GET_FLOAT_WORD(ix,x);
SET_FLOAT_WORD(z,ix&0xfffff000);
r = __ieee754_expf(-z*z-(float)0.5625)*__ieee754_expf((z-x)*(z+x)+R/S);
if(hx>=0) return one-r/x; else return r/x-one;
}
 
#ifdef __STDC__
float erfcf(float x)
#else
float erfcf(x)
float x;
#endif
{
__int32_t hx,ix;
float R,S,P,Q,s,y,z,r;
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
if(!FLT_UWORD_IS_FINITE(ix)) { /* erfc(nan)=nan */
/* erfc(+-inf)=0,2 */
return (float)(((__uint32_t)hx>>31)<<1)+one/x;
}
 
if(ix < 0x3f580000) { /* |x|<0.84375 */
if(ix < 0x23800000) /* |x|<2**-56 */
return one-x;
z = x*x;
r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
y = r/s;
if(hx < 0x3e800000) { /* x<1/4 */
return one-(x+x*y);
} else {
r = x*y;
r += (x-half);
return half - r ;
}
}
if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
s = fabsf(x)-one;
P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
if(hx>=0) {
z = one-erx; return z - P/Q;
} else {
z = erx+P/Q; return one+z;
}
}
if (ix < 0x41e00000) { /* |x|<28 */
x = fabsf(x);
s = one/(x*x);
if(ix< 0x4036DB6D) { /* |x| < 1/.35 ~ 2.857143*/
R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
ra5+s*(ra6+s*ra7))))));
S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
sa5+s*(sa6+s*(sa7+s*sa8)))))));
} else { /* |x| >= 1/.35 ~ 2.857143 */
if(hx<0&&ix>=0x40c00000) return two-tiny;/* x < -6 */
R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
rb5+s*rb6)))));
S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
sb5+s*(sb6+s*sb7))))));
}
GET_FLOAT_WORD(ix,x);
SET_FLOAT_WORD(z,ix&0xfffff000);
r = __ieee754_expf(-z*z-(float)0.5625)*
__ieee754_expf((z-x)*(z+x)+R/S);
if(hx>0) return r/x; else return two-r/x;
} else {
if(hx>0) return tiny*tiny; else return two-tiny;
}
}
 
#ifdef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double erf(double x)
#else
double erf(x)
double x;
#endif
{
return (double) erff((float) x);
}
 
#ifdef __STDC__
double erfc(double x)
#else
double erfc(x)
double x;
#endif
{
return (double) erfcf((float) x);
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/e_sinh.c
0,0 → 1,86
 
/* @(#)e_sinh.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/* __ieee754_sinh(x)
* Method :
* mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
* 1. Replace x by |x| (sinh(-x) = -sinh(x)).
* 2.
* E + E/(E+1)
* 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x)
* 2
*
* 22 <= x <= lnovft : sinh(x) := exp(x)/2
* lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2)
* ln2ovft < x : sinh(x) := x*shuge (overflow)
*
* Special cases:
* sinh(x) is |x| if x is +INF, -INF, or NaN.
* only sinh(0)=0 is exact for finite x.
*/
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
static const double one = 1.0, shuge = 1.0e307;
#else
static double one = 1.0, shuge = 1.0e307;
#endif
 
#ifdef __STDC__
double __ieee754_sinh(double x)
#else
double __ieee754_sinh(x)
double x;
#endif
{
double t,w,h;
__int32_t ix,jx;
__uint32_t lx;
 
/* High word of |x|. */
GET_HIGH_WORD(jx,x);
ix = jx&0x7fffffff;
 
/* x is INF or NaN */
if(ix>=0x7ff00000) return x+x;
 
h = 0.5;
if (jx<0) h = -h;
/* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
if (ix < 0x40360000) { /* |x|<22 */
if (ix<0x3e300000) /* |x|<2**-28 */
if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
t = expm1(fabs(x));
if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one));
return h*(t+t/(t+one));
}
 
/* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
if (ix < 0x40862E42) return h*__ieee754_exp(fabs(x));
 
/* |x| in [log(maxdouble), overflowthresold] */
GET_LOW_WORD(lx,x);
if (ix<0x408633CE || (ix==0x408633ce && lx<=(__uint32_t)0x8fb9f87d)) {
w = __ieee754_exp(0.5*fabs(x));
t = h*w;
return t*w;
}
 
/* |x| > overflowthresold, sinh(x) overflow */
return x*shuge;
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/wr_lgamma.c
0,0 → 1,77
 
/* @(#)wr_lgamma.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
* wrapper double lgamma_r(double x, int *signgamp)
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double lgamma_r(double x, int *signgamp) /* wrapper lgamma_r */
#else
double lgamma_r(x,signgamp) /* wrapper lgamma_r */
double x; int *signgamp;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_lgamma_r(x,signgamp);
#else
double y;
struct exception exc;
y = __ieee754_lgamma_r(x,signgamp);
if(_LIB_VERSION == _IEEE_) return y;
if(!finite(y)&&finite(x)) {
#ifndef HUGE_VAL
#define HUGE_VAL inf
double inf = 0.0;
 
SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */
#endif
exc.name = "lgamma";
exc.err = 0;
exc.arg1 = exc.arg2 = (double)x;
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if(floor(x)==x&&x<=0.0) {
/* lgamma(-integer) */
exc.type = SING;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
 
} else {
/* lgamma(finite) overflow */
exc.type = OVERFLOW;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
} else
return y;
#endif
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/w_fmod.c
0,0 → 1,107
 
/* @(#)w_fmod.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
FUNCTION
<<fmod>>, <<fmodf>>---floating-point remainder (modulo)
 
INDEX
fmod
INDEX
fmodf
 
ANSI_SYNOPSIS
#include <math.h>
double fmod(double <[x]>, double <[y]>)
float fmodf(float <[x]>, float <[y]>)
 
TRAD_SYNOPSIS
#include <math.h>
double fmod(<[x]>, <[y]>)
double (<[x]>, <[y]>);
 
float fmodf(<[x]>, <[y]>)
float (<[x]>, <[y]>);
 
DESCRIPTION
The <<fmod>> and <<fmodf>> functions compute the floating-point
remainder of <[x]>/<[y]> (<[x]> modulo <[y]>).
 
RETURNS
The <<fmod>> function returns the value
@ifinfo
<[x]>-<[i]>*<[y]>,
@end ifinfo
@tex
$x-i\times y$,
@end tex
for the largest integer <[i]> such that, if <[y]> is nonzero, the
result has the same sign as <[x]> and magnitude less than the
magnitude of <[y]>.
 
<<fmod(<[x]>,0)>> returns NaN, and sets <<errno>> to <<EDOM>>.
 
You can modify error treatment for these functions using <<matherr>>.
 
PORTABILITY
<<fmod>> is ANSI C. <<fmodf>> is an extension.
*/
 
/*
* wrapper fmod(x,y)
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double fmod(double x, double y) /* wrapper fmod */
#else
double fmod(x,y) /* wrapper fmod */
double x,y;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_fmod(x,y);
#else
double z;
struct exception exc;
z = __ieee754_fmod(x,y);
if(_LIB_VERSION == _IEEE_ ||isnan(y)||isnan(x)) return z;
if(y==0.0) {
/* fmod(x,0) */
exc.type = DOMAIN;
exc.name = "fmod";
exc.arg1 = x;
exc.arg2 = y;
exc.err = 0;
if (_LIB_VERSION == _SVID_)
exc.retval = x;
else
exc.retval = 0.0/0.0;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
} else
return z;
#endif
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/e_j0.c
0,0 → 1,487
 
/* @(#)e_j0.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/* __ieee754_j0(x), __ieee754_y0(x)
* Bessel function of the first and second kinds of order zero.
* Method -- j0(x):
* 1. For tiny x, we use j0(x) = 1 - x^2/4 + x^4/64 - ...
* 2. Reduce x to |x| since j0(x)=j0(-x), and
* for x in (0,2)
* j0(x) = 1-z/4+ z^2*R0/S0, where z = x*x;
* (precision: |j0-1+z/4-z^2R0/S0 |<2**-63.67 )
* for x in (2,inf)
* j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0))
* where x0 = x-pi/4. It is better to compute sin(x0),cos(x0)
* as follow:
* cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
* = 1/sqrt(2) * (cos(x) + sin(x))
* sin(x0) = sin(x)cos(pi/4)-cos(x)sin(pi/4)
* = 1/sqrt(2) * (sin(x) - cos(x))
* (To avoid cancellation, use
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
* to compute the worse one.)
*
* 3 Special cases
* j0(nan)= nan
* j0(0) = 1
* j0(inf) = 0
*
* Method -- y0(x):
* 1. For x<2.
* Since
* y0(x) = 2/pi*(j0(x)*(ln(x/2)+Euler) + x^2/4 - ...)
* therefore y0(x)-2/pi*j0(x)*ln(x) is an even function.
* We use the following function to approximate y0,
* y0(x) = U(z)/V(z) + (2/pi)*(j0(x)*ln(x)), z= x^2
* where
* U(z) = u00 + u01*z + ... + u06*z^6
* V(z) = 1 + v01*z + ... + v04*z^4
* with absolute approximation error bounded by 2**-72.
* Note: For tiny x, U/V = u0 and j0(x)~1, hence
* y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27)
* 2. For x>=2.
* y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0))
* where x0 = x-pi/4. It is better to compute sin(x0),cos(x0)
* by the method mentioned above.
* 3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0.
*/
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
static double pzero(double), qzero(double);
#else
static double pzero(), qzero();
#endif
 
#ifdef __STDC__
static const double
#else
static double
#endif
huge = 1e300,
one = 1.0,
invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */
tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
/* R0/S0 on [0, 2.00] */
R02 = 1.56249999999999947958e-02, /* 0x3F8FFFFF, 0xFFFFFFFD */
R03 = -1.89979294238854721751e-04, /* 0xBF28E6A5, 0xB61AC6E9 */
R04 = 1.82954049532700665670e-06, /* 0x3EBEB1D1, 0x0C503919 */
R05 = -4.61832688532103189199e-09, /* 0xBE33D5E7, 0x73D63FCE */
S01 = 1.56191029464890010492e-02, /* 0x3F8FFCE8, 0x82C8C2A4 */
S02 = 1.16926784663337450260e-04, /* 0x3F1EA6D2, 0xDD57DBF4 */
S03 = 5.13546550207318111446e-07, /* 0x3EA13B54, 0xCE84D5A9 */
S04 = 1.16614003333790000205e-09; /* 0x3E1408BC, 0xF4745D8F */
 
#ifdef __STDC__
static const double zero = 0.0;
#else
static double zero = 0.0;
#endif
 
#ifdef __STDC__
double __ieee754_j0(double x)
#else
double __ieee754_j0(x)
double x;
#endif
{
double z, s,c,ss,cc,r,u,v;
__int32_t hx,ix;
 
GET_HIGH_WORD(hx,x);
ix = hx&0x7fffffff;
if(ix>=0x7ff00000) return one/(x*x);
x = fabs(x);
if(ix >= 0x40000000) { /* |x| >= 2.0 */
s = sin(x);
c = cos(x);
ss = s-c;
cc = s+c;
if(ix<0x7fe00000) { /* make sure x+x not overflow */
z = -cos(x+x);
if ((s*c)<zero) cc = z/ss;
else ss = z/cc;
}
/*
* j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
* y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
*/
if(ix>0x48000000) z = (invsqrtpi*cc)/__ieee754_sqrt(x);
else {
u = pzero(x); v = qzero(x);
z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrt(x);
}
return z;
}
if(ix<0x3f200000) { /* |x| < 2**-13 */
if(huge+x>one) { /* raise inexact if x != 0 */
if(ix<0x3e400000) return one; /* |x|<2**-27 */
else return one - 0.25*x*x;
}
}
z = x*x;
r = z*(R02+z*(R03+z*(R04+z*R05)));
s = one+z*(S01+z*(S02+z*(S03+z*S04)));
if(ix < 0x3FF00000) { /* |x| < 1.00 */
return one + z*(-0.25+(r/s));
} else {
u = 0.5*x;
return((one+u)*(one-u)+z*(r/s));
}
}
 
#ifdef __STDC__
static const double
#else
static double
#endif
u00 = -7.38042951086872317523e-02, /* 0xBFB2E4D6, 0x99CBD01F */
u01 = 1.76666452509181115538e-01, /* 0x3FC69D01, 0x9DE9E3FC */
u02 = -1.38185671945596898896e-02, /* 0xBF8C4CE8, 0xB16CFA97 */
u03 = 3.47453432093683650238e-04, /* 0x3F36C54D, 0x20B29B6B */
u04 = -3.81407053724364161125e-06, /* 0xBECFFEA7, 0x73D25CAD */
u05 = 1.95590137035022920206e-08, /* 0x3E550057, 0x3B4EABD4 */
u06 = -3.98205194132103398453e-11, /* 0xBDC5E43D, 0x693FB3C8 */
v01 = 1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */
v02 = 7.60068627350353253702e-05, /* 0x3F13ECBB, 0xF578C6C1 */
v03 = 2.59150851840457805467e-07, /* 0x3E91642D, 0x7FF202FD */
v04 = 4.41110311332675467403e-10; /* 0x3DFE5018, 0x3BD6D9EF */
 
#ifdef __STDC__
double __ieee754_y0(double x)
#else
double __ieee754_y0(x)
double x;
#endif
{
double z, s,c,ss,cc,u,v;
__int32_t hx,ix,lx;
 
EXTRACT_WORDS(hx,lx,x);
ix = 0x7fffffff&hx;
/* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */
if(ix>=0x7ff00000) return one/(x+x*x);
if((ix|lx)==0) return -one/zero;
if(hx<0) return zero/zero;
if(ix >= 0x40000000) { /* |x| >= 2.0 */
/* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0))
* where x0 = x-pi/4
* Better formula:
* cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
* = 1/sqrt(2) * (sin(x) + cos(x))
* sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
* = 1/sqrt(2) * (sin(x) - cos(x))
* To avoid cancellation, use
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
* to compute the worse one.
*/
s = sin(x);
c = cos(x);
ss = s-c;
cc = s+c;
/*
* j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
* y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
*/
if(ix<0x7fe00000) { /* make sure x+x not overflow */
z = -cos(x+x);
if ((s*c)<zero) cc = z/ss;
else ss = z/cc;
}
if(ix>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrt(x);
else {
u = pzero(x); v = qzero(x);
z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrt(x);
}
return z;
}
if(ix<=0x3e400000) { /* x < 2**-27 */
return(u00 + tpi*__ieee754_log(x));
}
z = x*x;
u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06)))));
v = one+z*(v01+z*(v02+z*(v03+z*v04)));
return(u/v + tpi*(__ieee754_j0(x)*__ieee754_log(x)));
}
 
/* The asymptotic expansions of pzero is
* 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x.
* For x >= 2, We approximate pzero by
* pzero(x) = 1 + (R/S)
* where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10
* S = 1 + pS0*s^2 + ... + pS4*s^10
* and
* | pzero(x)-1-R/S | <= 2 ** ( -60.26)
*/
#ifdef __STDC__
static const double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
#else
static double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
#endif
0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
-7.03124999999900357484e-02, /* 0xBFB1FFFF, 0xFFFFFD32 */
-8.08167041275349795626e+00, /* 0xC02029D0, 0xB44FA779 */
-2.57063105679704847262e+02, /* 0xC0701102, 0x7B19E863 */
-2.48521641009428822144e+03, /* 0xC0A36A6E, 0xCD4DCAFC */
-5.25304380490729545272e+03, /* 0xC0B4850B, 0x36CC643D */
};
#ifdef __STDC__
static const double pS8[5] = {
#else
static double pS8[5] = {
#endif
1.16534364619668181717e+02, /* 0x405D2233, 0x07A96751 */
3.83374475364121826715e+03, /* 0x40ADF37D, 0x50596938 */
4.05978572648472545552e+04, /* 0x40E3D2BB, 0x6EB6B05F */
1.16752972564375915681e+05, /* 0x40FC810F, 0x8F9FA9BD */
4.76277284146730962675e+04, /* 0x40E74177, 0x4F2C49DC */
};
 
#ifdef __STDC__
static const double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
#else
static double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
#endif
-1.14125464691894502584e-11, /* 0xBDA918B1, 0x47E495CC */
-7.03124940873599280078e-02, /* 0xBFB1FFFF, 0xE69AFBC6 */
-4.15961064470587782438e+00, /* 0xC010A370, 0xF90C6BBF */
-6.76747652265167261021e+01, /* 0xC050EB2F, 0x5A7D1783 */
-3.31231299649172967747e+02, /* 0xC074B3B3, 0x6742CC63 */
-3.46433388365604912451e+02, /* 0xC075A6EF, 0x28A38BD7 */
};
#ifdef __STDC__
static const double pS5[5] = {
#else
static double pS5[5] = {
#endif
6.07539382692300335975e+01, /* 0x404E6081, 0x0C98C5DE */
1.05125230595704579173e+03, /* 0x40906D02, 0x5C7E2864 */
5.97897094333855784498e+03, /* 0x40B75AF8, 0x8FBE1D60 */
9.62544514357774460223e+03, /* 0x40C2CCB8, 0xFA76FA38 */
2.40605815922939109441e+03, /* 0x40A2CC1D, 0xC70BE864 */
};
 
#ifdef __STDC__
static const double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
#else
static double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
#endif
-2.54704601771951915620e-09, /* 0xBE25E103, 0x6FE1AA86 */
-7.03119616381481654654e-02, /* 0xBFB1FFF6, 0xF7C0E24B */
-2.40903221549529611423e+00, /* 0xC00345B2, 0xAEA48074 */
-2.19659774734883086467e+01, /* 0xC035F74A, 0x4CB94E14 */
-5.80791704701737572236e+01, /* 0xC04D0A22, 0x420A1A45 */
-3.14479470594888503854e+01, /* 0xC03F72AC, 0xA892D80F */
};
#ifdef __STDC__
static const double pS3[5] = {
#else
static double pS3[5] = {
#endif
3.58560338055209726349e+01, /* 0x4041ED92, 0x84077DD3 */
3.61513983050303863820e+02, /* 0x40769839, 0x464A7C0E */
1.19360783792111533330e+03, /* 0x4092A66E, 0x6D1061D6 */
1.12799679856907414432e+03, /* 0x40919FFC, 0xB8C39B7E */
1.73580930813335754692e+02, /* 0x4065B296, 0xFC379081 */
};
 
#ifdef __STDC__
static const double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
#else
static double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
#endif
-8.87534333032526411254e-08, /* 0xBE77D316, 0xE927026D */
-7.03030995483624743247e-02, /* 0xBFB1FF62, 0x495E1E42 */
-1.45073846780952986357e+00, /* 0xBFF73639, 0x8A24A843 */
-7.63569613823527770791e+00, /* 0xC01E8AF3, 0xEDAFA7F3 */
-1.11931668860356747786e+01, /* 0xC02662E6, 0xC5246303 */
-3.23364579351335335033e+00, /* 0xC009DE81, 0xAF8FE70F */
};
#ifdef __STDC__
static const double pS2[5] = {
#else
static double pS2[5] = {
#endif
2.22202997532088808441e+01, /* 0x40363865, 0x908B5959 */
1.36206794218215208048e+02, /* 0x4061069E, 0x0EE8878F */
2.70470278658083486789e+02, /* 0x4070E786, 0x42EA079B */
1.53875394208320329881e+02, /* 0x40633C03, 0x3AB6FAFF */
1.46576176948256193810e+01, /* 0x402D50B3, 0x44391809 */
};
 
#ifdef __STDC__
static double pzero(double x)
#else
static double pzero(x)
double x;
#endif
{
#ifdef __STDC__
const double *p,*q;
#else
double *p,*q;
#endif
double z,r,s;
__int32_t ix;
GET_HIGH_WORD(ix,x);
ix &= 0x7fffffff;
if(ix>=0x40200000) {p = pR8; q= pS8;}
else if(ix>=0x40122E8B){p = pR5; q= pS5;}
else if(ix>=0x4006DB6D){p = pR3; q= pS3;}
else {p = pR2; q= pS2;}
z = one/(x*x);
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
return one+ r/s;
}
 
/* For x >= 8, the asymptotic expansions of qzero is
* -1/8 s + 75/1024 s^3 - ..., where s = 1/x.
* We approximate qzero by
* qzero(x) = s*(-1.25 + (R/S))
* where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10
* S = 1 + qS0*s^2 + ... + qS5*s^12
* and
* | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22)
*/
#ifdef __STDC__
static const double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
#else
static double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
#endif
0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
7.32421874999935051953e-02, /* 0x3FB2BFFF, 0xFFFFFE2C */
1.17682064682252693899e+01, /* 0x40278952, 0x5BB334D6 */
5.57673380256401856059e+02, /* 0x40816D63, 0x15301825 */
8.85919720756468632317e+03, /* 0x40C14D99, 0x3E18F46D */
3.70146267776887834771e+04, /* 0x40E212D4, 0x0E901566 */
};
#ifdef __STDC__
static const double qS8[6] = {
#else
static double qS8[6] = {
#endif
1.63776026895689824414e+02, /* 0x406478D5, 0x365B39BC */
8.09834494656449805916e+03, /* 0x40BFA258, 0x4E6B0563 */
1.42538291419120476348e+05, /* 0x41016652, 0x54D38C3F */
8.03309257119514397345e+05, /* 0x412883DA, 0x83A52B43 */
8.40501579819060512818e+05, /* 0x4129A66B, 0x28DE0B3D */
-3.43899293537866615225e+05, /* 0xC114FD6D, 0x2C9530C5 */
};
 
#ifdef __STDC__
static const double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
#else
static double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
#endif
1.84085963594515531381e-11, /* 0x3DB43D8F, 0x29CC8CD9 */
7.32421766612684765896e-02, /* 0x3FB2BFFF, 0xD172B04C */
5.83563508962056953777e+00, /* 0x401757B0, 0xB9953DD3 */
1.35111577286449829671e+02, /* 0x4060E392, 0x0A8788E9 */
1.02724376596164097464e+03, /* 0x40900CF9, 0x9DC8C481 */
1.98997785864605384631e+03, /* 0x409F17E9, 0x53C6E3A6 */
};
#ifdef __STDC__
static const double qS5[6] = {
#else
static double qS5[6] = {
#endif
8.27766102236537761883e+01, /* 0x4054B1B3, 0xFB5E1543 */
2.07781416421392987104e+03, /* 0x40A03BA0, 0xDA21C0CE */
1.88472887785718085070e+04, /* 0x40D267D2, 0x7B591E6D */
5.67511122894947329769e+04, /* 0x40EBB5E3, 0x97E02372 */
3.59767538425114471465e+04, /* 0x40E19118, 0x1F7A54A0 */
-5.35434275601944773371e+03, /* 0xC0B4EA57, 0xBEDBC609 */
};
 
#ifdef __STDC__
static const double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
#else
static double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
#endif
4.37741014089738620906e-09, /* 0x3E32CD03, 0x6ADECB82 */
7.32411180042911447163e-02, /* 0x3FB2BFEE, 0x0E8D0842 */
3.34423137516170720929e+00, /* 0x400AC0FC, 0x61149CF5 */
4.26218440745412650017e+01, /* 0x40454F98, 0x962DAEDD */
1.70808091340565596283e+02, /* 0x406559DB, 0xE25EFD1F */
1.66733948696651168575e+02, /* 0x4064D77C, 0x81FA21E0 */
};
#ifdef __STDC__
static const double qS3[6] = {
#else
static double qS3[6] = {
#endif
4.87588729724587182091e+01, /* 0x40486122, 0xBFE343A6 */
7.09689221056606015736e+02, /* 0x40862D83, 0x86544EB3 */
3.70414822620111362994e+03, /* 0x40ACF04B, 0xE44DFC63 */
6.46042516752568917582e+03, /* 0x40B93C6C, 0xD7C76A28 */
2.51633368920368957333e+03, /* 0x40A3A8AA, 0xD94FB1C0 */
-1.49247451836156386662e+02, /* 0xC062A7EB, 0x201CF40F */
};
 
#ifdef __STDC__
static const double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
#else
static double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
#endif
1.50444444886983272379e-07, /* 0x3E84313B, 0x54F76BDB */
7.32234265963079278272e-02, /* 0x3FB2BEC5, 0x3E883E34 */
1.99819174093815998816e+00, /* 0x3FFFF897, 0xE727779C */
1.44956029347885735348e+01, /* 0x402CFDBF, 0xAAF96FE5 */
3.16662317504781540833e+01, /* 0x403FAA8E, 0x29FBDC4A */
1.62527075710929267416e+01, /* 0x403040B1, 0x71814BB4 */
};
#ifdef __STDC__
static const double qS2[6] = {
#else
static double qS2[6] = {
#endif
3.03655848355219184498e+01, /* 0x403E5D96, 0xF7C07AED */
2.69348118608049844624e+02, /* 0x4070D591, 0xE4D14B40 */
8.44783757595320139444e+02, /* 0x408A6645, 0x22B3BF22 */
8.82935845112488550512e+02, /* 0x408B977C, 0x9C5CC214 */
2.12666388511798828631e+02, /* 0x406A9553, 0x0E001365 */
-5.31095493882666946917e+00, /* 0xC0153E6A, 0xF8B32931 */
};
 
#ifdef __STDC__
static double qzero(double x)
#else
static double qzero(x)
double x;
#endif
{
#ifdef __STDC__
const double *p,*q;
#else
double *p,*q;
#endif
double s,r,z;
__int32_t ix;
GET_HIGH_WORD(ix,x);
ix &= 0x7fffffff;
if(ix>=0x40200000) {p = qR8; q= qS8;}
else if(ix>=0x40122E8B){p = qR5; q= qS5;}
else if(ix>=0x4006DB6D){p = qR3; q= qS3;}
else {p = qR2; q= qS2;}
z = one/(x*x);
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
return (-.125 + r/s)/x;
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/wf_gamma.c
0,0 → 1,93
/* wf_gamma.c -- float version of w_gamma.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
 
#include "fdlibm.h"
#include <reent.h>
#include <errno.h>
 
#ifdef __STDC__
float gammaf(float x)
#else
float gammaf(x)
float x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_gammaf_r(x,&(_REENT->_new._reent._gamma_signgam));
#else
float y;
struct exception exc;
y = __ieee754_gammaf_r(x,&(_REENT->_new._reent._gamma_signgam));
if(_LIB_VERSION == _IEEE_) return y;
if(!finitef(y)&&finitef(x)) {
#ifndef HUGE_VAL
#define HUGE_VAL inf
double inf = 0.0;
 
SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */
#endif
if(floorf(x)==x&&x<=(float)0.0) {
/* gammaf(-integer) or gammaf(0) */
exc.type = SING;
exc.name = "gammaf";
exc.err = 0;
exc.arg1 = exc.arg2 = (double)x;
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
} else {
/* gammaf(finite) overflow */
exc.type = OVERFLOW;
exc.name = "gammaf";
exc.err = 0;
exc.arg1 = exc.arg2 = (double)x;
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
}
if (exc.err != 0)
errno = exc.err;
return (float)exc.retval;
} else
return y;
#endif
}
 
#ifdef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double gamma(double x)
#else
double gamma(x)
double x;
#endif
{
return (double) gammaf((float) x);
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/erf_gamma.c
0,0 → 1,34
/* erf_gamma.c -- float version of er_gamma.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
 
/* __ieee754_gammaf_r(x, signgamp)
* Reentrant version of the logarithm of the Gamma function
* with user provide pointer for the sign of Gamma(x).
*
* Method: See __ieee754_lgammaf_r
*/
 
#include "fdlibm.h"
 
#ifdef __STDC__
float __ieee754_gammaf_r(float x, int *signgamp)
#else
float __ieee754_gammaf_r(x,signgamp)
float x; int *signgamp;
#endif
{
return __ieee754_lgammaf_r(x,signgamp);
}
/ef_j1.c
0,0 → 1,439
/* ef_j1.c -- float version of e_j1.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
#include "fdlibm.h"
 
#ifdef __STDC__
static float ponef(float), qonef(float);
#else
static float ponef(), qonef();
#endif
 
#ifdef __STDC__
static const float
#else
static float
#endif
huge = 1e30,
one = 1.0,
invsqrtpi= 5.6418961287e-01, /* 0x3f106ebb */
tpi = 6.3661974669e-01, /* 0x3f22f983 */
/* R0/S0 on [0,2] */
r00 = -6.2500000000e-02, /* 0xbd800000 */
r01 = 1.4070566976e-03, /* 0x3ab86cfd */
r02 = -1.5995563444e-05, /* 0xb7862e36 */
r03 = 4.9672799207e-08, /* 0x335557d2 */
s01 = 1.9153760746e-02, /* 0x3c9ce859 */
s02 = 1.8594678841e-04, /* 0x3942fab6 */
s03 = 1.1771846857e-06, /* 0x359dffc2 */
s04 = 5.0463624390e-09, /* 0x31ad6446 */
s05 = 1.2354227016e-11; /* 0x2d59567e */
 
#ifdef __STDC__
static const float zero = 0.0;
#else
static float zero = 0.0;
#endif
 
#ifdef __STDC__
float __ieee754_j1f(float x)
#else
float __ieee754_j1f(x)
float x;
#endif
{
float z, s,c,ss,cc,r,u,v,y;
__int32_t hx,ix;
 
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
if(!FLT_UWORD_IS_FINITE(ix)) return one/x;
y = fabsf(x);
if(ix >= 0x40000000) { /* |x| >= 2.0 */
s = sinf(y);
c = cosf(y);
ss = -s-c;
cc = s-c;
if(ix<=FLT_UWORD_HALF_MAX) { /* make sure y+y not overflow */
z = cosf(y+y);
if ((s*c)>zero) cc = z/ss;
else ss = z/cc;
}
/*
* j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x)
* y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x)
*/
if(ix>0x80000000) z = (invsqrtpi*cc)/__ieee754_sqrtf(y);
else {
u = ponef(y); v = qonef(y);
z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrtf(y);
}
if(hx<0) return -z;
else return z;
}
if(ix<0x32000000) { /* |x|<2**-27 */
if(huge+x>one) return (float)0.5*x;/* inexact if x!=0 necessary */
}
z = x*x;
r = z*(r00+z*(r01+z*(r02+z*r03)));
s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05))));
r *= x;
return(x*(float)0.5+r/s);
}
 
#ifdef __STDC__
static const float U0[5] = {
#else
static float U0[5] = {
#endif
-1.9605709612e-01, /* 0xbe48c331 */
5.0443872809e-02, /* 0x3d4e9e3c */
-1.9125689287e-03, /* 0xbafaaf2a */
2.3525259166e-05, /* 0x37c5581c */
-9.1909917899e-08, /* 0xb3c56003 */
};
#ifdef __STDC__
static const float V0[5] = {
#else
static float V0[5] = {
#endif
1.9916731864e-02, /* 0x3ca3286a */
2.0255257550e-04, /* 0x3954644b */
1.3560879779e-06, /* 0x35b602d4 */
6.2274145840e-09, /* 0x31d5f8eb */
1.6655924903e-11, /* 0x2d9281cf */
};
 
#ifdef __STDC__
float __ieee754_y1f(float x)
#else
float __ieee754_y1f(x)
float x;
#endif
{
float z, s,c,ss,cc,u,v;
__int32_t hx,ix;
 
GET_FLOAT_WORD(hx,x);
ix = 0x7fffffff&hx;
/* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */
if(!FLT_UWORD_IS_FINITE(ix)) return one/(x+x*x);
if(FLT_UWORD_IS_ZERO(ix)) return -one/zero;
if(hx<0) return zero/zero;
if(ix >= 0x40000000) { /* |x| >= 2.0 */
s = sinf(x);
c = cosf(x);
ss = -s-c;
cc = s-c;
if(ix<=FLT_UWORD_HALF_MAX) { /* make sure x+x not overflow */
z = cosf(x+x);
if ((s*c)>zero) cc = z/ss;
else ss = z/cc;
}
/* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0))
* where x0 = x-3pi/4
* Better formula:
* cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
* = 1/sqrt(2) * (sin(x) - cos(x))
* sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
* = -1/sqrt(2) * (cos(x) + sin(x))
* To avoid cancellation, use
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
* to compute the worse one.
*/
if(ix>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrtf(x);
else {
u = ponef(x); v = qonef(x);
z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrtf(x);
}
return z;
}
if(ix<=0x24800000) { /* x < 2**-54 */
return(-tpi/x);
}
z = x*x;
u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4])));
v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4]))));
return(x*(u/v) + tpi*(__ieee754_j1f(x)*__ieee754_logf(x)-one/x));
}
 
/* For x >= 8, the asymptotic expansions of pone is
* 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x.
* We approximate pone by
* pone(x) = 1 + (R/S)
* where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10
* S = 1 + ps0*s^2 + ... + ps4*s^10
* and
* | pone(x)-1-R/S | <= 2 ** ( -60.06)
*/
 
#ifdef __STDC__
static const float pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
#else
static float pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
#endif
0.0000000000e+00, /* 0x00000000 */
1.1718750000e-01, /* 0x3df00000 */
1.3239480972e+01, /* 0x4153d4ea */
4.1205184937e+02, /* 0x43ce06a3 */
3.8747453613e+03, /* 0x45722bed */
7.9144794922e+03, /* 0x45f753d6 */
};
#ifdef __STDC__
static const float ps8[5] = {
#else
static float ps8[5] = {
#endif
1.1420736694e+02, /* 0x42e46a2c */
3.6509309082e+03, /* 0x45642ee5 */
3.6956207031e+04, /* 0x47105c35 */
9.7602796875e+04, /* 0x47bea166 */
3.0804271484e+04, /* 0x46f0a88b */
};
 
#ifdef __STDC__
static const float pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
#else
static float pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
#endif
1.3199052094e-11, /* 0x2d68333f */
1.1718749255e-01, /* 0x3defffff */
6.8027510643e+00, /* 0x40d9b023 */
1.0830818176e+02, /* 0x42d89dca */
5.1763616943e+02, /* 0x440168b7 */
5.2871520996e+02, /* 0x44042dc6 */
};
#ifdef __STDC__
static const float ps5[5] = {
#else
static float ps5[5] = {
#endif
5.9280597687e+01, /* 0x426d1f55 */
9.9140142822e+02, /* 0x4477d9b1 */
5.3532670898e+03, /* 0x45a74a23 */
7.8446904297e+03, /* 0x45f52586 */
1.5040468750e+03, /* 0x44bc0180 */
};
 
#ifdef __STDC__
static const float pr3[6] = {
#else
static float pr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
#endif
3.0250391081e-09, /* 0x314fe10d */
1.1718686670e-01, /* 0x3defffab */
3.9329774380e+00, /* 0x407bb5e7 */
3.5119403839e+01, /* 0x420c7a45 */
9.1055007935e+01, /* 0x42b61c2a */
4.8559066772e+01, /* 0x42423c7c */
};
#ifdef __STDC__
static const float ps3[5] = {
#else
static float ps3[5] = {
#endif
3.4791309357e+01, /* 0x420b2a4d */
3.3676245117e+02, /* 0x43a86198 */
1.0468714600e+03, /* 0x4482dbe3 */
8.9081134033e+02, /* 0x445eb3ed */
1.0378793335e+02, /* 0x42cf936c */
};
 
#ifdef __STDC__
static const float pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
#else
static float pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
#endif
1.0771083225e-07, /* 0x33e74ea8 */
1.1717621982e-01, /* 0x3deffa16 */
2.3685150146e+00, /* 0x401795c0 */
1.2242610931e+01, /* 0x4143e1bc */
1.7693971634e+01, /* 0x418d8d41 */
5.0735230446e+00, /* 0x40a25a4d */
};
#ifdef __STDC__
static const float ps2[5] = {
#else
static float ps2[5] = {
#endif
2.1436485291e+01, /* 0x41ab7dec */
1.2529022980e+02, /* 0x42fa9499 */
2.3227647400e+02, /* 0x436846c7 */
1.1767937469e+02, /* 0x42eb5bd7 */
8.3646392822e+00, /* 0x4105d590 */
};
 
#ifdef __STDC__
static float ponef(float x)
#else
static float ponef(x)
float x;
#endif
{
#ifdef __STDC__
const float *p,*q;
#else
float *p,*q;
#endif
float z,r,s;
__int32_t ix;
GET_FLOAT_WORD(ix,x);
ix &= 0x7fffffff;
if(ix>=0x41000000) {p = pr8; q= ps8;}
else if(ix>=0x40f71c58){p = pr5; q= ps5;}
else if(ix>=0x4036db68){p = pr3; q= ps3;}
else {p = pr2; q= ps2;}
z = one/(x*x);
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
return one+ r/s;
}
 
/* For x >= 8, the asymptotic expansions of qone is
* 3/8 s - 105/1024 s^3 - ..., where s = 1/x.
* We approximate qone by
* qone(x) = s*(0.375 + (R/S))
* where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10
* S = 1 + qs1*s^2 + ... + qs6*s^12
* and
* | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13)
*/
 
#ifdef __STDC__
static const float qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
#else
static float qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
#endif
0.0000000000e+00, /* 0x00000000 */
-1.0253906250e-01, /* 0xbdd20000 */
-1.6271753311e+01, /* 0xc1822c8d */
-7.5960174561e+02, /* 0xc43de683 */
-1.1849806641e+04, /* 0xc639273a */
-4.8438511719e+04, /* 0xc73d3683 */
};
#ifdef __STDC__
static const float qs8[6] = {
#else
static float qs8[6] = {
#endif
1.6139537048e+02, /* 0x43216537 */
7.8253862305e+03, /* 0x45f48b17 */
1.3387534375e+05, /* 0x4802bcd6 */
7.1965775000e+05, /* 0x492fb29c */
6.6660125000e+05, /* 0x4922be94 */
-2.9449025000e+05, /* 0xc88fcb48 */
};
 
#ifdef __STDC__
static const float qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
#else
static float qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
#endif
-2.0897993405e-11, /* 0xadb7d219 */
-1.0253904760e-01, /* 0xbdd1fffe */
-8.0564479828e+00, /* 0xc100e736 */
-1.8366960144e+02, /* 0xc337ab6b */
-1.3731937256e+03, /* 0xc4aba633 */
-2.6124443359e+03, /* 0xc523471c */
};
#ifdef __STDC__
static const float qs5[6] = {
#else
static float qs5[6] = {
#endif
8.1276550293e+01, /* 0x42a28d98 */
1.9917987061e+03, /* 0x44f8f98f */
1.7468484375e+04, /* 0x468878f8 */
4.9851425781e+04, /* 0x4742bb6d */
2.7948074219e+04, /* 0x46da5826 */
-4.7191835938e+03, /* 0xc5937978 */
};
 
#ifdef __STDC__
static const float qr3[6] = {
#else
static float qr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
#endif
-5.0783124372e-09, /* 0xb1ae7d4f */
-1.0253783315e-01, /* 0xbdd1ff5b */
-4.6101160049e+00, /* 0xc0938612 */
-5.7847221375e+01, /* 0xc267638e */
-2.2824453735e+02, /* 0xc3643e9a */
-2.1921012878e+02, /* 0xc35b35cb */
};
#ifdef __STDC__
static const float qs3[6] = {
#else
static float qs3[6] = {
#endif
4.7665153503e+01, /* 0x423ea91e */
6.7386511230e+02, /* 0x4428775e */
3.3801528320e+03, /* 0x45534272 */
5.5477290039e+03, /* 0x45ad5dd5 */
1.9031191406e+03, /* 0x44ede3d0 */
-1.3520118713e+02, /* 0xc3073381 */
};
 
#ifdef __STDC__
static const float qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
#else
static float qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
#endif
-1.7838172539e-07, /* 0xb43f8932 */
-1.0251704603e-01, /* 0xbdd1f475 */
-2.7522056103e+00, /* 0xc0302423 */
-1.9663616180e+01, /* 0xc19d4f16 */
-4.2325313568e+01, /* 0xc2294d1f */
-2.1371921539e+01, /* 0xc1aaf9b2 */
};
#ifdef __STDC__
static const float qs2[6] = {
#else
static float qs2[6] = {
#endif
2.9533363342e+01, /* 0x41ec4454 */
2.5298155212e+02, /* 0x437cfb47 */
7.5750280762e+02, /* 0x443d602e */
7.3939318848e+02, /* 0x4438d92a */
1.5594900513e+02, /* 0x431bf2f2 */
-4.9594988823e+00, /* 0xc09eb437 */
};
 
#ifdef __STDC__
static float qonef(float x)
#else
static float qonef(x)
float x;
#endif
{
#ifdef __STDC__
const float *p,*q;
#else
float *p,*q;
#endif
float s,r,z;
__int32_t ix;
GET_FLOAT_WORD(ix,x);
ix &= 0x7fffffff;
if(ix>=0x40200000) {p = qr8; q= qs8;}
else if(ix>=0x40f71c58){p = qr5; q= qs5;}
else if(ix>=0x4036db68){p = qr3; q= qs3;}
else {p = qr2; q= qs2;}
z = one/(x*x);
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
return ((float).375 + r/s)/x;
}
/e_log10.c
0,0 → 1,98
 
/* @(#)e_log10.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/* __ieee754_log10(x)
* Return the base 10 logarithm of x
*
* Method :
* Let log10_2hi = leading 40 bits of log10(2) and
* log10_2lo = log10(2) - log10_2hi,
* ivln10 = 1/log(10) rounded.
* Then
* n = ilogb(x),
* if(n<0) n = n+1;
* x = scalbn(x,-n);
* log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
*
* Note 1:
* To guarantee log10(10**n)=n, where 10**n is normal, the rounding
* mode must set to Round-to-Nearest.
* Note 2:
* [1/log(10)] rounded to 53 bits has error .198 ulps;
* log10 is monotonic at all binary break points.
*
* Special cases:
* log10(x) is NaN with signal if x < 0;
* log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
* log10(NaN) is that NaN with no signal;
* log10(10**N) = N for N=0,1,...,22.
*
* Constants:
* The hexadecimal values are the intended ones for the following constants.
* The decimal values may be used, provided that the compiler will convert
* from decimal to binary accurately enough to produce the hexadecimal values
* shown.
*/
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
static const double
#else
static double
#endif
two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
 
#ifdef __STDC__
static const double zero = 0.0;
#else
static double zero = 0.0;
#endif
 
#ifdef __STDC__
double __ieee754_log10(double x)
#else
double __ieee754_log10(x)
double x;
#endif
{
double y,z;
__int32_t i,k,hx;
__uint32_t lx;
 
EXTRACT_WORDS(hx,lx,x);
 
k=0;
if (hx < 0x00100000) { /* x < 2**-1022 */
if (((hx&0x7fffffff)|lx)==0)
return -two54/zero; /* log(+-0)=-inf */
if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
k -= 54; x *= two54; /* subnormal number, scale up x */
GET_HIGH_WORD(hx,x);
}
if (hx >= 0x7ff00000) return x+x;
k += (hx>>20)-1023;
i = ((__uint32_t)k&0x80000000)>>31;
hx = (hx&0x000fffff)|((0x3ff-i)<<20);
y = (double)(k+i);
SET_HIGH_WORD(x,hx);
z = y*log10_2lo + ivln10*__ieee754_log(x);
return z+y*log10_2hi;
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/wr_gamma.c
0,0 → 1,76
 
/* @(#)wr_gamma.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
* wrapper double gamma_r(double x, int *signgamp)
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double gamma_r(double x, int *signgamp) /* wrapper lgamma_r */
#else
double gamma_r(x,signgamp) /* wrapper lgamma_r */
double x; int *signgamp;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_gamma_r(x,signgamp);
#else
double y;
struct exception exc;
y = __ieee754_gamma_r(x,signgamp);
if(_LIB_VERSION == _IEEE_) return y;
if(!finite(y)&&finite(x)) {
#ifndef HUGE_VAL
#define HUGE_VAL inf
double inf = 0.0;
 
SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */
#endif
exc.name = "gamma";
exc.err = 0;
exc.arg1 = exc.arg2 = (double)x;
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if(floor(x)==x&&x<=0.0) {
/* gamma(-integer) or gamma(0) */
exc.type = SING;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
} else {
/* gamma(finite) overflow */
exc.type = OVERFLOW;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
} else
return y;
#endif
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/ef_log10.c
0,0 → 1,62
/* ef_log10.c -- float version of e_log10.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
#include "fdlibm.h"
 
#ifdef __STDC__
static const float
#else
static float
#endif
two25 = 3.3554432000e+07, /* 0x4c000000 */
ivln10 = 4.3429449201e-01, /* 0x3ede5bd9 */
log10_2hi = 3.0102920532e-01, /* 0x3e9a2080 */
log10_2lo = 7.9034151668e-07; /* 0x355427db */
 
#ifdef __STDC__
static const float zero = 0.0;
#else
static float zero = 0.0;
#endif
 
#ifdef __STDC__
float __ieee754_log10f(float x)
#else
float __ieee754_log10f(x)
float x;
#endif
{
float y,z;
__int32_t i,k,hx;
 
GET_FLOAT_WORD(hx,x);
 
k=0;
if (FLT_UWORD_IS_ZERO(hx&0x7fffffff))
return -two25/zero; /* log(+-0)=-inf */
if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
if (!FLT_UWORD_IS_FINITE(hx)) return x+x;
if (FLT_UWORD_IS_SUBNORMAL(hx)) {
k -= 25; x *= two25; /* subnormal number, scale up x */
GET_FLOAT_WORD(hx,x);
}
k += (hx>>23)-127;
i = ((__uint32_t)k&0x80000000)>>31;
hx = (hx&0x007fffff)|((0x7f-i)<<23);
y = (float)(k+i);
SET_FLOAT_WORD(x,hx);
z = y*log10_2lo + ivln10*__ieee754_logf(x);
return z+y*log10_2hi;
}
/w_jn.c
0,0 → 1,141
 
/* @(#)w_jn.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
* wrapper jn(int n, double x), yn(int n, double x)
* floating point Bessel's function of the 1st and 2nd kind
* of order n
*
* Special cases:
* y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal;
* y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal.
* Note 2. About jn(n,x), yn(n,x)
* For n=0, j0(x) is called,
* for n=1, j1(x) is called,
* for n<x, forward recursion us used starting
* from values of j0(x) and j1(x).
* for n>x, a continued fraction approximation to
* j(n,x)/j(n-1,x) is evaluated and then backward
* recursion is used starting from a supposed value
* for j(n,x). The resulting value of j(0,x) is
* compared with the actual value to correct the
* supposed value of j(n,x).
*
* yn(n,x) is similar in all respects, except
* that forward recursion is used for all
* values of n>1.
*
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double jn(int n, double x) /* wrapper jn */
#else
double jn(n,x) /* wrapper jn */
double x; int n;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_jn(n,x);
#else
double z;
struct exception exc;
z = __ieee754_jn(n,x);
if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z;
if(fabs(x)>X_TLOSS) {
/* jn(|x|>X_TLOSS) */
exc.type = TLOSS;
exc.name = "jn";
exc.err = 0;
exc.arg1 = n;
exc.arg2 = x;
exc.retval = 0.0;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
} else
return z;
#endif
}
 
#ifdef __STDC__
double yn(int n, double x) /* wrapper yn */
#else
double yn(n,x) /* wrapper yn */
double x; int n;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_yn(n,x);
#else
double z;
struct exception exc;
z = __ieee754_yn(n,x);
if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z;
if(x <= 0.0){
/* yn(n,0) = -inf or yn(x<0) = NaN */
#ifndef HUGE_VAL
#define HUGE_VAL inf
double inf = 0.0;
 
SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */
#endif
exc.type = DOMAIN; /* should be SING for IEEE */
exc.name = "yn";
exc.err = 0;
exc.arg1 = n;
exc.arg2 = x;
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
}
if(x>X_TLOSS) {
/* yn(x>X_TLOSS) */
exc.type = TLOSS;
exc.name = "yn";
exc.err = 0;
exc.arg1 = n;
exc.arg2 = x;
exc.retval = 0.0;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
} else
return z;
#endif
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/ef_acos.c
0,0 → 1,84
/* ef_acos.c -- float version of e_acos.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
#include "fdlibm.h"
 
#ifdef __STDC__
static const float
#else
static float
#endif
one = 1.0000000000e+00, /* 0x3F800000 */
pi = 3.1415925026e+00, /* 0x40490fda */
pio2_hi = 1.5707962513e+00, /* 0x3fc90fda */
pio2_lo = 7.5497894159e-08, /* 0x33a22168 */
pS0 = 1.6666667163e-01, /* 0x3e2aaaab */
pS1 = -3.2556581497e-01, /* 0xbea6b090 */
pS2 = 2.0121252537e-01, /* 0x3e4e0aa8 */
pS3 = -4.0055535734e-02, /* 0xbd241146 */
pS4 = 7.9153501429e-04, /* 0x3a4f7f04 */
pS5 = 3.4793309169e-05, /* 0x3811ef08 */
qS1 = -2.4033949375e+00, /* 0xc019d139 */
qS2 = 2.0209457874e+00, /* 0x4001572d */
qS3 = -6.8828397989e-01, /* 0xbf303361 */
qS4 = 7.7038154006e-02; /* 0x3d9dc62e */
 
#ifdef __STDC__
float __ieee754_acosf(float x)
#else
float __ieee754_acosf(x)
float x;
#endif
{
float z,p,q,r,w,s,c,df;
__int32_t hx,ix;
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
if(ix==0x3f800000) { /* |x|==1 */
if(hx>0) return 0.0; /* acos(1) = 0 */
else return pi+(float)2.0*pio2_lo; /* acos(-1)= pi */
} else if(ix>0x3f800000) { /* |x| >= 1 */
return (x-x)/(x-x); /* acos(|x|>1) is NaN */
}
if(ix<0x3f000000) { /* |x| < 0.5 */
if(ix<=0x23000000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
z = x*x;
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
r = p/q;
return pio2_hi - (x - (pio2_lo-x*r));
} else if (hx<0) { /* x < -0.5 */
z = (one+x)*(float)0.5;
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
s = __ieee754_sqrtf(z);
r = p/q;
w = r*s-pio2_lo;
return pi - (float)2.0*(s+w);
} else { /* x > 0.5 */
__int32_t idf;
z = (one-x)*(float)0.5;
s = __ieee754_sqrtf(z);
df = s;
GET_FLOAT_WORD(idf,df);
SET_FLOAT_WORD(df,idf&0xfffff000);
c = (z-df*df)/(s+df);
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
r = p/q;
w = r*s+c;
return (float)2.0*(df+w);
}
}
/kf_tan.c
0,0 → 1,96
/* kf_tan.c -- float version of k_tan.c
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
#include "fdlibm.h"
#ifdef __STDC__
static const float
#else
static float
#endif
one = 1.0000000000e+00, /* 0x3f800000 */
pio4 = 7.8539812565e-01, /* 0x3f490fda */
pio4lo= 3.7748947079e-08, /* 0x33222168 */
T[] = {
3.3333334327e-01, /* 0x3eaaaaab */
1.3333334029e-01, /* 0x3e088889 */
5.3968254477e-02, /* 0x3d5d0dd1 */
2.1869488060e-02, /* 0x3cb327a4 */
8.8632395491e-03, /* 0x3c11371f */
3.5920790397e-03, /* 0x3b6b6916 */
1.4562094584e-03, /* 0x3abede48 */
5.8804126456e-04, /* 0x3a1a26c8 */
2.4646313977e-04, /* 0x398137b9 */
7.8179444245e-05, /* 0x38a3f445 */
7.1407252108e-05, /* 0x3895c07a */
-1.8558637748e-05, /* 0xb79bae5f */
2.5907305826e-05, /* 0x37d95384 */
};
 
#ifdef __STDC__
float __kernel_tanf(float x, float y, int iy)
#else
float __kernel_tanf(x, y, iy)
float x,y; int iy;
#endif
{
float z,r,v,w,s;
__int32_t ix,hx;
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff; /* high word of |x| */
if(ix<0x31800000) /* x < 2**-28 */
{if((int)x==0) { /* generate inexact */
if((ix|(iy+1))==0) return one/fabsf(x);
else return (iy==1)? x: -one/x;
}
}
if(ix>=0x3f2ca140) { /* |x|>=0.6744 */
if(hx<0) {x = -x; y = -y;}
z = pio4-x;
w = pio4lo-y;
x = z+w; y = 0.0;
}
z = x*x;
w = z*z;
/* Break x^5*(T[1]+x^2*T[2]+...) into
* x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
* x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
*/
r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));
v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));
s = z*x;
r = y + z*(s*(r+v)+y);
r += T[0]*s;
w = x+r;
if(ix>=0x3f2ca140) {
v = (float)iy;
return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r)));
}
if(iy==1) return w;
else { /* if allow error up to 2 ulp,
simply return -1.0/(x+r) here */
/* compute -1.0/(x+r) accurately */
float a,t;
__int32_t i;
z = w;
GET_FLOAT_WORD(i,z);
SET_FLOAT_WORD(z,i&0xfffff000);
v = r-(z - x); /* z+v = r+x */
t = a = -(float)1.0/w; /* a = -1.0/w */
GET_FLOAT_WORD(i,t);
SET_FLOAT_WORD(t,i&0xfffff000);
s = (float)1.0+t*z;
return t+a*(s+t*v);
}
}
/wf_remainder.c
0,0 → 1,74
/* wf_remainder.c -- float version of w_remainder.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
* wrapper remainderf(x,p)
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifdef __STDC__
float remainderf(float x, float y) /* wrapper remainder */
#else
float remainderf(x,y) /* wrapper remainder */
float x,y;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_remainderf(x,y);
#else
float z;
struct exception exc;
z = __ieee754_remainderf(x,y);
if(_LIB_VERSION == _IEEE_ || isnanf(y)) return z;
if(y==(float)0.0) {
/* remainderf(x,0) */
exc.type = DOMAIN;
exc.name = "remainderf";
exc.err = 0;
exc.arg1 = (double)x;
exc.arg2 = (double)y;
exc.retval = 0.0/0.0;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
if (exc.err != 0)
errno = exc.err;
return (float)exc.retval;
} else
return z;
#endif
}
 
#ifdef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double remainder(double x, double y)
#else
double remainder(x,y)
double x,y;
#endif
{
return (double) remainderf((float) x, (float) y);
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
 
 
 
 
/wf_jn.c
0,0 → 1,138
/* wf_jn.c -- float version of w_jn.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
#include "fdlibm.h"
#include <errno.h>
 
 
#ifdef __STDC__
float jnf(int n, float x) /* wrapper jnf */
#else
float jnf(n,x) /* wrapper jnf */
float x; int n;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_jnf(n,x);
#else
float z;
struct exception exc;
z = __ieee754_jnf(n,x);
if(_LIB_VERSION == _IEEE_ || isnanf(x) ) return z;
if(fabsf(x)>(float)X_TLOSS) {
/* jnf(|x|>X_TLOSS) */
exc.type = TLOSS;
exc.name = "jnf";
exc.err = 0;
exc.arg1 = (double)n;
exc.arg2 = (double)x;
exc.retval = 0.0;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
} else
return z;
#endif
}
 
#ifdef __STDC__
float ynf(int n, float x) /* wrapper ynf */
#else
float ynf(n,x) /* wrapper ynf */
float x; int n;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_ynf(n,x);
#else
float z;
struct exception exc;
z = __ieee754_ynf(n,x);
if(_LIB_VERSION == _IEEE_ || isnanf(x) ) return z;
if(x <= (float)0.0){
/* ynf(n,0) = -inf or ynf(x<0) = NaN */
#ifndef HUGE_VAL
#define HUGE_VAL inf
double inf = 0.0;
 
SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */
#endif
exc.type = DOMAIN; /* should be SING for IEEE */
exc.name = "ynf";
exc.err = 0;
exc.arg1 = (double)n;
exc.arg2 = (double)x;
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
if (exc.err != 0)
errno = exc.err;
return (float)exc.retval;
}
if(x>(float)X_TLOSS) {
/* ynf(x>X_TLOSS) */
exc.type = TLOSS;
exc.name = "ynf";
exc.err = 0;
exc.arg1 = (double)n;
exc.arg2 = (double)x;
exc.retval = 0.0;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
if (exc.err != 0)
errno = exc.err;
return (float)exc.retval;
} else
return z;
#endif
}
 
#ifdef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double jn(int n, double x)
#else
double jn(n,x)
double x; int n;
#endif
{
return (double) jnf(n, (float) x);
}
 
#ifdef __STDC__
double yn(int n, double x)
#else
double yn(n,x)
double x; int n;
#endif
{
return (double) ynf(n, (float) x);
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/sf_ldexp.c
0,0 → 1,44
/* sf_ldexp.c -- float version of s_ldexp.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifdef __STDC__
float ldexpf(float value, int exp)
#else
float ldexpf(value, exp)
float value; int exp;
#endif
{
if(!finitef(value)||value==(float)0.0) return value;
value = scalbnf(value,exp);
if(!finitef(value)||value==(float)0.0) errno = ERANGE;
return value;
}
 
#ifdef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double ldexp(double value, int exp)
#else
double ldexp(value, exp)
double value; int exp;
#endif
{
return (double) ldexpf((float) value, exp);
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/kf_cos.c
0,0 → 1,59
/* kf_cos.c -- float version of k_cos.c
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
#include "fdlibm.h"
 
#ifdef __STDC__
static const float
#else
static float
#endif
one = 1.0000000000e+00, /* 0x3f800000 */
C1 = 4.1666667908e-02, /* 0x3d2aaaab */
C2 = -1.3888889225e-03, /* 0xbab60b61 */
C3 = 2.4801587642e-05, /* 0x37d00d01 */
C4 = -2.7557314297e-07, /* 0xb493f27c */
C5 = 2.0875723372e-09, /* 0x310f74f6 */
C6 = -1.1359647598e-11; /* 0xad47d74e */
 
#ifdef __STDC__
float __kernel_cosf(float x, float y)
#else
float __kernel_cosf(x, y)
float x,y;
#endif
{
float a,hz,z,r,qx;
__int32_t ix;
GET_FLOAT_WORD(ix,x);
ix &= 0x7fffffff; /* ix = |x|'s high word*/
if(ix<0x32000000) { /* if x < 2**27 */
if(((int)x)==0) return one; /* generate inexact */
}
z = x*x;
r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
if(ix < 0x3e99999a) /* if |x| < 0.3 */
return one - ((float)0.5*z - (z*r - x*y));
else {
if(ix > 0x3f480000) { /* x > 0.78125 */
qx = (float)0.28125;
} else {
SET_FLOAT_WORD(qx,ix-0x01000000); /* x/4 */
}
hz = (float)0.5*z-qx;
a = one-qx;
return a - (hz - (z*r-x*y));
}
}
/s_atan.c
0,0 → 1,181
 
/* @(#)s_atan.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
 
/*
FUNCTION
<<atan>>, <<atanf>>---arc tangent
 
INDEX
atan
INDEX
atanf
 
ANSI_SYNOPSIS
#include <math.h>
double atan(double <[x]>);
float atanf(float <[x]>);
 
TRAD_SYNOPSIS
#include <math.h>
double atan(<[x]>);
double <[x]>;
 
float atanf(<[x]>);
float <[x]>;
 
DESCRIPTION
 
<<atan>> computes the inverse tangent (arc tangent) of the input value.
 
<<atanf>> is identical to <<atan>>, save that it operates on <<floats>>.
 
RETURNS
@ifinfo
<<atan>> returns a value in radians, in the range of -pi/2 to pi/2.
@end ifinfo
@tex
<<atan>> returns a value in radians, in the range of $-\pi/2$ to $\pi/2$.
@end tex
 
PORTABILITY
<<atan>> is ANSI C. <<atanf>> is an extension.
 
*/
 
/* atan(x)
* Method
* 1. Reduce x to positive by atan(x) = -atan(-x).
* 2. According to the integer k=4t+0.25 chopped, t=x, the argument
* is further reduced to one of the following intervals and the
* arctangent of t is evaluated by the corresponding formula:
*
* [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
* [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
* [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
* [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
* [39/16,INF] atan(x) = atan(INF) + atan( -1/t )
*
* Constants:
* The hexadecimal values are the intended ones for the following
* constants. The decimal values may be used, provided that the
* compiler will convert from decimal to binary accurately enough
* to produce the hexadecimal values shown.
*/
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
static const double atanhi[] = {
#else
static double atanhi[] = {
#endif
4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
};
 
#ifdef __STDC__
static const double atanlo[] = {
#else
static double atanlo[] = {
#endif
2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
};
 
#ifdef __STDC__
static const double aT[] = {
#else
static double aT[] = {
#endif
3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
-1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
-1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
-7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
-5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
-3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
};
 
#ifdef __STDC__
static const double
#else
static double
#endif
one = 1.0,
huge = 1.0e300;
 
#ifdef __STDC__
double atan(double x)
#else
double atan(x)
double x;
#endif
{
double w,s1,s2,z;
__int32_t ix,hx,id;
 
GET_HIGH_WORD(hx,x);
ix = hx&0x7fffffff;
if(ix>=0x44100000) { /* if |x| >= 2^66 */
__uint32_t low;
GET_LOW_WORD(low,x);
if(ix>0x7ff00000||
(ix==0x7ff00000&&(low!=0)))
return x+x; /* NaN */
if(hx>0) return atanhi[3]+atanlo[3];
else return -atanhi[3]-atanlo[3];
} if (ix < 0x3fdc0000) { /* |x| < 0.4375 */
if (ix < 0x3e200000) { /* |x| < 2^-29 */
if(huge+x>one) return x; /* raise inexact */
}
id = -1;
} else {
x = fabs(x);
if (ix < 0x3ff30000) { /* |x| < 1.1875 */
if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */
id = 0; x = (2.0*x-one)/(2.0+x);
} else { /* 11/16<=|x|< 19/16 */
id = 1; x = (x-one)/(x+one);
}
} else {
if (ix < 0x40038000) { /* |x| < 2.4375 */
id = 2; x = (x-1.5)/(one+1.5*x);
} else { /* 2.4375 <= |x| < 2^66 */
id = 3; x = -1.0/x;
}
}}
/* end of argument reduction */
z = x*x;
w = z*z;
/* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
if (id<0) return x - x*(s1+s2);
else {
z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
return (hx<0)? -z:z;
}
}
 
#endif /* _DOUBLE_IS_32BITS */
/ef_cosh.c
0,0 → 1,71
/* ef_cosh.c -- float version of e_cosh.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
#include "fdlibm.h"
 
#ifdef __v810__
#define const
#endif
 
#ifdef __STDC__
static const float one = 1.0, half=0.5, huge = 1.0e30;
#else
static float one = 1.0, half=0.5, huge = 1.0e30;
#endif
 
#ifdef __STDC__
float __ieee754_coshf(float x)
#else
float __ieee754_coshf(x)
float x;
#endif
{
float t,w;
__int32_t ix;
 
GET_FLOAT_WORD(ix,x);
ix &= 0x7fffffff;
 
/* x is INF or NaN */
if(!FLT_UWORD_IS_FINITE(ix)) return x*x;
 
/* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
if(ix<0x3eb17218) {
t = expm1f(fabsf(x));
w = one+t;
if (ix<0x24000000) return w; /* cosh(tiny) = 1 */
return one+(t*t)/(w+w);
}
 
/* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
if (ix < 0x41b00000) {
t = __ieee754_expf(fabsf(x));
return half*t+half/t;
}
 
/* |x| in [22, log(maxdouble)] return half*exp(|x|) */
if (ix <= FLT_UWORD_LOG_MAX)
return half*__ieee754_expf(fabsf(x));
 
/* |x| in [log(maxdouble), overflowthresold] */
if (ix <= FLT_UWORD_LOG_2MAX) {
w = __ieee754_expf(half*fabsf(x));
t = half*w;
return t*w;
}
 
/* |x| > overflowthresold, cosh(x) overflow */
return huge*huge;
}
/sf_signif.c
0,0 → 1,40
/* sf_signif.c -- float version of s_signif.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
#include "fdlibm.h"
 
#ifdef __STDC__
float significandf(float x)
#else
float significandf(x)
float x;
#endif
{
return __ieee754_scalbf(x,(float) -ilogbf(x));
}
 
#ifdef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double significand(double x)
#else
double significand(x)
double x;
#endif
{
return (double) significandf((float) x);
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/w_log10.c
0,0 → 1,115
 
/* @(#)w_log10.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
FUNCTION
<<log10>>, <<log10f>>---base 10 logarithms
 
INDEX
log10
INDEX
log10f
 
ANSI_SYNOPSIS
#include <math.h>
double log10(double <[x]>);
float log10f(float <[x]>);
 
TRAD_SYNOPSIS
#include <math.h>
double log10(<[x]>)
double <[x]>;
 
float log10f(<[x]>)
float <[x]>;
 
DESCRIPTION
<<log10>> returns the base 10 logarithm of <[x]>.
It is implemented as <<log(<[x]>) / log(10)>>.
 
<<log10f>> is identical, save that it takes and returns <<float>> values.
 
RETURNS
<<log10>> and <<log10f>> return the calculated value.
 
See the description of <<log>> for information on errors.
 
PORTABILITY
<<log10>> is ANSI C. <<log10f>> is an extension.
 
*/
 
/*
* wrapper log10(X)
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double log10(double x) /* wrapper log10 */
#else
double log10(x) /* wrapper log10 */
double x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_log10(x);
#else
double z;
struct exception exc;
z = __ieee754_log10(x);
if(_LIB_VERSION == _IEEE_ || isnan(x)) return z;
if(x<=0.0) {
#ifndef HUGE_VAL
#define HUGE_VAL inf
double inf = 0.0;
 
SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */
#endif
exc.name = "log10";
exc.err = 0;
exc.arg1 = x;
exc.arg2 = x;
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if(x==0.0) {
/* log10(0) */
exc.type = SING;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = EDOM;
}
} else {
/* log10(x<0) */
exc.type = DOMAIN;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
} else
return z;
#endif
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/sf_tan.c
0,0 → 1,57
/* sf_tan.c -- float version of s_tan.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
#include "fdlibm.h"
 
#ifdef __STDC__
float tanf(float x)
#else
float tanf(x)
float x;
#endif
{
float y[2],z=0.0;
__int32_t n,ix;
 
GET_FLOAT_WORD(ix,x);
 
/* |x| ~< pi/4 */
ix &= 0x7fffffff;
if(ix <= 0x3f490fda) return __kernel_tanf(x,z,1);
 
/* tan(Inf or NaN) is NaN */
else if (!FLT_UWORD_IS_FINITE(ix)) return x-x; /* NaN */
 
/* argument reduction needed */
else {
n = __ieee754_rem_pio2f(x,y);
return __kernel_tanf(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even
-1 -- n odd */
}
}
 
#ifdef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double tan(double x)
#else
double tan(x)
double x;
#endif
{
return (double) tanf((float) x);
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/sf_atan.c
0,0 → 1,129
/* sf_atan.c -- float version of s_atan.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
 
#include "fdlibm.h"
 
#ifdef __STDC__
static const float atanhi[] = {
#else
static float atanhi[] = {
#endif
4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */
7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */
9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */
1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */
};
 
#ifdef __STDC__
static const float atanlo[] = {
#else
static float atanlo[] = {
#endif
5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */
3.7748947079e-08, /* atan(1.0)lo 0x33222168 */
3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */
7.5497894159e-08, /* atan(inf)lo 0x33a22168 */
};
 
#ifdef __STDC__
static const float aT[] = {
#else
static float aT[] = {
#endif
3.3333334327e-01, /* 0x3eaaaaaa */
-2.0000000298e-01, /* 0xbe4ccccd */
1.4285714924e-01, /* 0x3e124925 */
-1.1111110449e-01, /* 0xbde38e38 */
9.0908870101e-02, /* 0x3dba2e6e */
-7.6918758452e-02, /* 0xbd9d8795 */
6.6610731184e-02, /* 0x3d886b35 */
-5.8335702866e-02, /* 0xbd6ef16b */
4.9768779427e-02, /* 0x3d4bda59 */
-3.6531571299e-02, /* 0xbd15a221 */
1.6285819933e-02, /* 0x3c8569d7 */
};
 
#ifdef __STDC__
static const float
#else
static float
#endif
one = 1.0,
huge = 1.0e30;
 
#ifdef __STDC__
float atanf(float x)
#else
float atanf(x)
float x;
#endif
{
float w,s1,s2,z;
__int32_t ix,hx,id;
 
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
if(ix>=0x50800000) { /* if |x| >= 2^34 */
if(FLT_UWORD_IS_NAN(ix))
return x+x; /* NaN */
if(hx>0) return atanhi[3]+atanlo[3];
else return -atanhi[3]-atanlo[3];
} if (ix < 0x3ee00000) { /* |x| < 0.4375 */
if (ix < 0x31000000) { /* |x| < 2^-29 */
if(huge+x>one) return x; /* raise inexact */
}
id = -1;
} else {
x = fabsf(x);
if (ix < 0x3f980000) { /* |x| < 1.1875 */
if (ix < 0x3f300000) { /* 7/16 <=|x|<11/16 */
id = 0; x = ((float)2.0*x-one)/((float)2.0+x);
} else { /* 11/16<=|x|< 19/16 */
id = 1; x = (x-one)/(x+one);
}
} else {
if (ix < 0x401c0000) { /* |x| < 2.4375 */
id = 2; x = (x-(float)1.5)/(one+(float)1.5*x);
} else { /* 2.4375 <= |x| < 2^66 */
id = 3; x = -(float)1.0/x;
}
}}
/* end of argument reduction */
z = x*x;
w = z*z;
/* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
if (id<0) return x - x*(s1+s2);
else {
z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
return (hx<0)? -z:z;
}
}
 
#ifdef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double atan(double x)
#else
double atan(x)
double x;
#endif
{
return (double) atanf((float) x);
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/sf_cos.c
0,0 → 1,68
/* sf_cos.c -- float version of s_cos.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
#include "fdlibm.h"
 
#ifdef __STDC__
static const float one=1.0;
#else
static float one=1.0;
#endif
 
#ifdef __STDC__
float cosf(float x)
#else
float cosf(x)
float x;
#endif
{
float y[2],z=0.0;
__int32_t n,ix;
 
GET_FLOAT_WORD(ix,x);
 
/* |x| ~< pi/4 */
ix &= 0x7fffffff;
if(ix <= 0x3f490fd8) return __kernel_cosf(x,z);
 
/* cos(Inf or NaN) is NaN */
else if (!FLT_UWORD_IS_FINITE(ix)) return x-x;
 
/* argument reduction needed */
else {
n = __ieee754_rem_pio2f(x,y);
switch(n&3) {
case 0: return __kernel_cosf(y[0],y[1]);
case 1: return -__kernel_sinf(y[0],y[1],1);
case 2: return -__kernel_cosf(y[0],y[1]);
default:
return __kernel_sinf(y[0],y[1],1);
}
}
}
 
#ifdef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double cos(double x)
#else
double cos(x)
double x;
#endif
{
return (double) cosf((float) x);
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/wf_log.c
0,0 → 1,85
/* wf_log.c -- float version of w_log.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
* wrapper logf(x)
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifdef __STDC__
float logf(float x) /* wrapper logf */
#else
float logf(x) /* wrapper logf */
float x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_logf(x);
#else
float z;
struct exception exc;
z = __ieee754_logf(x);
if(_LIB_VERSION == _IEEE_ || isnanf(x) || x > (float)0.0) return z;
#ifndef HUGE_VAL
#define HUGE_VAL inf
double inf = 0.0;
 
SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */
#endif
exc.name = "logf";
exc.err = 0;
exc.arg1 = exc.arg2 = (double)x;
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if(x==(float)0.0) {
/* logf(0) */
exc.type = SING;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = EDOM;
}
} else {
/* logf(x<0) */
exc.type = DOMAIN;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
}
if (exc.err != 0)
errno = exc.err;
return (float)exc.retval;
#endif
}
 
#ifdef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double log(double x)
#else
double log(x)
double x;
#endif
{
return (double) logf((float) x);
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/w_asin.c
0,0 → 1,121
 
/* @(#)w_asin.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
 
/*
FUNCTION
<<asin>>, <<asinf>>---arc sine
 
INDEX
asin
INDEX
asinf
 
ANSI_SYNOPSIS
#include <math.h>
double asin(double <[x]>);
float asinf(float <[x]>);
 
TRAD_SYNOPSIS
#include <math.h>
double asin(<[x]>)
double <[x]>;
 
float asinf(<[x]>)
float <[x]>;
 
 
DESCRIPTION
 
<<asin>> computes the inverse sine (arc sine) of the argument <[x]>.
Arguments to <<asin>> must be in the range @minus{}1 to 1.
 
<<asinf>> is identical to <<asin>>, other than taking and
returning floats.
 
You can modify error handling for these routines using <<matherr>>.
 
RETURNS
@ifinfo
<<asin>> returns values in radians, in the range of -pi/2 to pi/2.
@end ifinfo
@tex
<<asin>> returns values in radians, in the range of $-\pi/2$ to $\pi/2$.
@end tex
 
If <[x]> is not in the range @minus{}1 to 1, <<asin>> and <<asinf>>
return NaN (not a number), set the global variable <<errno>> to
<<EDOM>>, and issue a <<DOMAIN error>> message.
 
You can change this error treatment using <<matherr>>.
 
QUICKREF ANSI SVID POSIX RENTRANT
asin y,y,y,m
asinf n,n,n,m
 
MATHREF
asin, -1<=arg<=1, asin(arg),,,
asin, NAN, arg,EDOM, DOMAIN
 
MATHREF
asinf, -1<=arg<=1, asin(arg),,,
asinf, NAN, arg,EDOM, DOMAIN
 
 
*/
 
/*
* wrapper asin(x)
*/
 
 
#include "fdlibm.h"
#include <errno.h>
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double asin(double x) /* wrapper asin */
#else
double asin(x) /* wrapper asin */
double x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_asin(x);
#else
double z;
struct exception exc;
z = __ieee754_asin(x);
if(_LIB_VERSION == _IEEE_ || isnan(x)) return z;
if(fabs(x)>1.0) {
/* asin(|x|>1) */
exc.type = DOMAIN;
exc.name = "asin";
exc.err = 0;
exc.arg1 = exc.arg2 = x;
exc.retval = 0.0;
if(_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
} else
return z;
#endif
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/wf_scalb.c
0,0 → 1,118
/* wf_scalb.c -- float version of w_scalb.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
* wrapper scalbf(float x, float fn) is provide for
* passing various standard test suite. One
* should use scalbn() instead.
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifdef __STDC__
#ifdef _SCALB_INT
float scalbf(float x, int fn) /* wrapper scalbf */
#else
float scalbf(float x, float fn) /* wrapper scalbf */
#endif
#else
float scalbf(x,fn) /* wrapper scalbf */
#ifdef _SCALB_INT
float x; int fn;
#else
float x,fn;
#endif
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_scalbf(x,fn);
#else
float z;
#ifndef HUGE_VAL
#define HUGE_VAL inf
double inf = 0.0;
 
SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */
#endif
struct exception exc;
z = __ieee754_scalbf(x,fn);
if(_LIB_VERSION == _IEEE_) return z;
if(!(finitef(z)||isnanf(z))&&finitef(x)) {
/* scalbf overflow; SVID also returns +-HUGE_VAL */
exc.type = OVERFLOW;
exc.name = "scalbf";
exc.err = 0;
exc.arg1 = (double)x;
exc.arg2 = (double)fn;
exc.retval = x > 0.0 ? HUGE_VAL : -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
}
if(z==(float)0.0&&z!=x) {
/* scalbf underflow */
exc.type = UNDERFLOW;
exc.name = "scalbf";
exc.err = 0;
exc.arg1 = (double)x;
exc.arg2 = (double)fn;
exc.retval = copysign(0.0,x);
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
}
#ifndef _SCALB_INT
if(!finitef(fn)) errno = ERANGE;
#endif
return z;
#endif
}
 
#ifdef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
#ifdef _SCALB_INT
double scalb(double x, int fn)
#else
double scalb(double x, double fn)
#endif
#else
double scalb(x, fn)
#ifdef _SCALB_INT
double x; int fn;
#else
double x,fn;
#endif
#endif
{
#ifdef _SCALB_INT
return (double) scalbf((float) x, fn);
#else
return (double) scalbf((float) x, (float) fn);
#endif
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/wf_acos.c
0,0 → 1,69
/* wf_acos.c -- float version of w_acos.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
* wrap_acosf(x)
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifdef _HAVE_STDC
float acosf(float x) /* wrapper acosf */
#else
float acosf(x) /* wrapper acosf */
float x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_acosf(x);
#else
float z;
struct exception exc;
z = __ieee754_acosf(x);
if(_LIB_VERSION == _IEEE_ || isnanf(x)) return z;
if(fabsf(x)>(float)1.0) {
/* acosf(|x|>1) */
exc.type = DOMAIN;
exc.name = "acosf";
exc.err = 0;
exc.arg1 = exc.arg2 = (double)x;
exc.retval = 0.0;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
if (exc.err != 0)
errno = exc.err;
return (float)exc.retval;
} else
return z;
#endif
}
 
#ifdef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double acos(double x)
#else
double acos(x)
double x;
#endif
{
return (double) acosf((float) x);
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/wf_cosh.c
0,0 → 1,78
/* wf_cosh.c -- float version of w_cosh.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
* wrapper coshf(x)
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifdef __STDC__
float coshf(float x) /* wrapper coshf */
#else
float coshf(x) /* wrapper coshf */
float x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_coshf(x);
#else
float z;
struct exception exc;
z = __ieee754_coshf(x);
if(_LIB_VERSION == _IEEE_ || isnanf(x)) return z;
if(fabsf(x)>(float)8.9415985107e+01) {
/* coshf(finite) overflow */
#ifndef HUGE_VAL
#define HUGE_VAL inf
double inf = 0.0;
 
SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */
#endif
exc.type = OVERFLOW;
exc.name = "coshf";
exc.err = 0;
exc.arg1 = exc.arg2 = (double)x;
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
if (exc.err != 0)
errno = exc.err;
return (float)exc.retval;
} else
return z;
#endif
}
 
#ifdef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double cosh(double x)
#else
double cosh(x)
double x;
#endif
{
return (double) coshf((float) x);
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/e_fmod.c
0,0 → 1,140
 
/* @(#)e_fmod.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
* __ieee754_fmod(x,y)
* Return x mod y in exact arithmetic
* Method: shift and subtract
*/
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
static const double one = 1.0, Zero[] = {0.0, -0.0,};
#else
static double one = 1.0, Zero[] = {0.0, -0.0,};
#endif
 
#ifdef __STDC__
double __ieee754_fmod(double x, double y)
#else
double __ieee754_fmod(x,y)
double x,y ;
#endif
{
__int32_t n,hx,hy,hz,ix,iy,sx,i;
__uint32_t lx,ly,lz;
 
EXTRACT_WORDS(hx,lx,x);
EXTRACT_WORDS(hy,ly,y);
sx = hx&0x80000000; /* sign of x */
hx ^=sx; /* |x| */
hy &= 0x7fffffff; /* |y| */
 
/* purge off exception values */
if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */
((hy|((ly|-ly)>>31))>0x7ff00000)) /* or y is NaN */
return (x*y)/(x*y);
if(hx<=hy) {
if((hx<hy)||(lx<ly)) return x; /* |x|<|y| return x */
if(lx==ly)
return Zero[(__uint32_t)sx>>31]; /* |x|=|y| return x*0*/
}
 
/* determine ix = ilogb(x) */
if(hx<0x00100000) { /* subnormal x */
if(hx==0) {
for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
} else {
for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
}
} else ix = (hx>>20)-1023;
 
/* determine iy = ilogb(y) */
if(hy<0x00100000) { /* subnormal y */
if(hy==0) {
for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
} else {
for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
}
} else iy = (hy>>20)-1023;
 
/* set up {hx,lx}, {hy,ly} and align y to x */
if(ix >= -1022)
hx = 0x00100000|(0x000fffff&hx);
else { /* subnormal x, shift x to normal */
n = -1022-ix;
if(n<=31) {
hx = (hx<<n)|(lx>>(32-n));
lx <<= n;
} else {
hx = lx<<(n-32);
lx = 0;
}
}
if(iy >= -1022)
hy = 0x00100000|(0x000fffff&hy);
else { /* subnormal y, shift y to normal */
n = -1022-iy;
if(n<=31) {
hy = (hy<<n)|(ly>>(32-n));
ly <<= n;
} else {
hy = ly<<(n-32);
ly = 0;
}
}
 
/* fix point fmod */
n = ix - iy;
while(n--) {
hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;}
else {
if((hz|lz)==0) /* return sign(x)*0 */
return Zero[(__uint32_t)sx>>31];
hx = hz+hz+(lz>>31); lx = lz+lz;
}
}
hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
if(hz>=0) {hx=hz;lx=lz;}
 
/* convert back to floating value and restore the sign */
if((hx|lx)==0) /* return sign(x)*0 */
return Zero[(__uint32_t)sx>>31];
while(hx<0x00100000) { /* normalize x */
hx = hx+hx+(lx>>31); lx = lx+lx;
iy -= 1;
}
if(iy>= -1022) { /* normalize output */
hx = ((hx-0x00100000)|((iy+1023)<<20));
INSERT_WORDS(x,hx|sx,lx);
} else { /* subnormal output */
n = -1022 - iy;
if(n<=20) {
lx = (lx>>n)|((__uint32_t)hx<<(32-n));
hx >>= n;
} else if (n<=31) {
lx = (hx<<(32-n))|(lx>>n); hx = sx;
} else {
lx = hx>>(n-32); hx = sx;
}
INSERT_WORDS(x,hx|sx,lx);
x *= one; /* create necessary signal */
}
return x; /* exact output */
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/s_isinf.c
0,0 → 1,26
/*
* isinf(x) returns 1 if x is infinity, else 0;
* no branching!
* Added by Cygnus Support.
*/
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
int isinf(double x)
#else
int isinf(x)
double x;
#endif
{
__int32_t hx,lx;
EXTRACT_WORDS(hx,lx,x);
hx &= 0x7fffffff;
hx |= (__uint32_t)(lx|(-lx))>>31;
hx = 0x7ff00000 - hx;
return 1 - (int)((__uint32_t)(hx|(-hx))>>31);
}
 
#endif /* _DOUBLE_IS_32BITS */
/e_atanh.c
0,0 → 1,75
 
/* @(#)e_atanh.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
 
/* __ieee754_atanh(x)
* Method :
* 1.Reduced x to positive by atanh(-x) = -atanh(x)
* 2.For x>=0.5
* 1 2x x
* atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
* 2 1 - x 1 - x
*
* For x<0.5
* atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
*
* Special cases:
* atanh(x) is NaN if |x| > 1 with signal;
* atanh(NaN) is that NaN with no signal;
* atanh(+-1) is +-INF with signal.
*
*/
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
static const double one = 1.0, huge = 1e300;
#else
static double one = 1.0, huge = 1e300;
#endif
 
#ifdef __STDC__
static const double zero = 0.0;
#else
static double zero = 0.0;
#endif
 
#ifdef __STDC__
double __ieee754_atanh(double x)
#else
double __ieee754_atanh(x)
double x;
#endif
{
double t;
__int32_t hx,ix;
__uint32_t lx;
EXTRACT_WORDS(hx,lx,x);
ix = hx&0x7fffffff;
if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
return (x-x)/(x-x);
if(ix==0x3ff00000)
return x/zero;
if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */
SET_HIGH_WORD(x,ix);
if(ix<0x3fe00000) { /* x < 0.5 */
t = x+x;
t = 0.5*log1p(t+t*x/(one-x));
} else
t = 0.5*log1p((x+x)/(one-x));
if(hx>=0) return t; else return -t;
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/wf_pow.c
0,0 → 1,179
/* wf_pow.c -- float version of w_pow.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
* wrapper powf(x,y) return x**y
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifdef __STDC__
float powf(float x, float y) /* wrapper powf */
#else
float powf(x,y) /* wrapper powf */
float x,y;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_powf(x,y);
#else
float z;
struct exception exc;
z=__ieee754_powf(x,y);
if(_LIB_VERSION == _IEEE_|| isnanf(y)) return z;
if(isnanf(x)) {
if(y==(float)0.0) {
/* powf(NaN,0.0) */
/* error only if _LIB_VERSION == _SVID_ & _XOPEN_ */
exc.type = DOMAIN;
exc.name = "powf";
exc.err = 0;
exc.arg1 = (double)x;
exc.arg2 = (double)y;
exc.retval = x;
if (_LIB_VERSION == _IEEE_ ||
_LIB_VERSION == _POSIX_) exc.retval = 1.0;
else if (!matherr(&exc)) {
errno = EDOM;
}
if (exc.err != 0)
errno = exc.err;
return (float)exc.retval;
} else
return z;
}
if(x==(float)0.0){
if(y==(float)0.0) {
/* powf(0.0,0.0) */
/* error only if _LIB_VERSION == _SVID_ */
exc.type = DOMAIN;
exc.name = "powf";
exc.err = 0;
exc.arg1 = (double)x;
exc.arg2 = (double)y;
exc.retval = 0.0;
if (_LIB_VERSION != _SVID_) exc.retval = 1.0;
else if (!matherr(&exc)) {
errno = EDOM;
}
if (exc.err != 0)
errno = exc.err;
return (float)exc.retval;
}
if(finitef(y)&&y<(float)0.0) {
/* 0**neg */
exc.type = DOMAIN;
exc.name = "powf";
exc.err = 0;
exc.arg1 = (double)x;
exc.arg2 = (double)y;
if (_LIB_VERSION == _SVID_)
exc.retval = 0.0;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
if (exc.err != 0)
errno = exc.err;
return (float)exc.retval;
}
return z;
}
if(!finitef(z)) {
if(finitef(x)&&finitef(y)) {
if(isnanf(z)) {
/* neg**non-integral */
exc.type = DOMAIN;
exc.name = "powf";
exc.err = 0;
exc.arg1 = (double)x;
exc.arg2 = (double)y;
if (_LIB_VERSION == _SVID_)
exc.retval = 0.0;
else
exc.retval = 0.0/0.0; /* X/Open allow NaN */
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
if (exc.err != 0)
errno = exc.err;
return (float)exc.retval;
} else {
/* powf(x,y) overflow */
exc.type = OVERFLOW;
exc.name = "powf";
exc.err = 0;
exc.arg1 = (double)x;
exc.arg2 = (double)y;
if (_LIB_VERSION == _SVID_) {
exc.retval = HUGE;
y *= 0.5;
if(x<0.0&&rint(y)!=y) exc.retval = -HUGE;
} else {
exc.retval = HUGE_VAL;
y *= 0.5;
if(x<0.0&&rint(y)!=y) exc.retval = -HUGE_VAL;
}
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
if (exc.err != 0)
errno = exc.err;
return (float)exc.retval;
}
}
}
if(z==(float)0.0&&finitef(x)&&finitef(y)) {
/* powf(x,y) underflow */
exc.type = UNDERFLOW;
exc.name = "powf";
exc.err = 0;
exc.arg1 = (double)x;
exc.arg2 = (double)y;
exc.retval = 0.0;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
if (exc.err != 0)
errno = exc.err;
return (float)exc.retval;
}
return z;
#endif
}
 
#ifdef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double pow(double x, double y)
#else
double pow(x,y)
double x,y;
#endif
{
return (double) powf((float) x, (float) y);
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/ef_atanh.c
0,0 → 1,54
/* ef_atanh.c -- float version of e_atanh.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
 
#include "fdlibm.h"
 
#ifdef __STDC__
static const float one = 1.0, huge = 1e30;
#else
static float one = 1.0, huge = 1e30;
#endif
 
#ifdef __STDC__
static const float zero = 0.0;
#else
static float zero = 0.0;
#endif
 
#ifdef __STDC__
float __ieee754_atanhf(float x)
#else
float __ieee754_atanhf(x)
float x;
#endif
{
float t;
__int32_t hx,ix;
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
if (ix>0x3f800000) /* |x|>1 */
return (x-x)/(x-x);
if(ix==0x3f800000)
return x/zero;
if(ix<0x31800000&&(huge+x)>zero) return x; /* x<2**-28 */
SET_FLOAT_WORD(x,ix);
if(ix<0x3f000000) { /* x < 0.5 */
t = x+x;
t = (float)0.5*log1pf(t+t*x/(one-x));
} else
t = (float)0.5*log1pf((x+x)/(one-x));
if(hx>=0) return t; else return -t;
}
/ef_sinh.c
0,0 → 1,63
/* ef_sinh.c -- float version of e_sinh.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
#include "fdlibm.h"
 
#ifdef __STDC__
static const float one = 1.0, shuge = 1.0e37;
#else
static float one = 1.0, shuge = 1.0e37;
#endif
 
#ifdef __STDC__
float __ieee754_sinhf(float x)
#else
float __ieee754_sinhf(x)
float x;
#endif
{
float t,w,h;
__int32_t ix,jx;
 
GET_FLOAT_WORD(jx,x);
ix = jx&0x7fffffff;
 
/* x is INF or NaN */
if(!FLT_UWORD_IS_FINITE(ix)) return x+x;
 
h = 0.5;
if (jx<0) h = -h;
/* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
if (ix < 0x41b00000) { /* |x|<22 */
if (ix<0x31800000) /* |x|<2**-28 */
if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
t = expm1f(fabsf(x));
if(ix<0x3f800000) return h*((float)2.0*t-t*t/(t+one));
return h*(t+t/(t+one));
}
 
/* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
if (ix<=FLT_UWORD_LOG_MAX) return h*__ieee754_expf(fabsf(x));
 
/* |x| in [log(maxdouble), overflowthresold] */
if (ix<=FLT_UWORD_LOG_2MAX) {
w = __ieee754_expf((float)0.5*fabsf(x));
t = h*w;
return t*w;
}
 
/* |x| > overflowthresold, sinh(x) overflow */
return x*shuge;
}
/wrf_lgamma.c
0,0 → 1,75
/* wrf_lgamma.c -- float version of wr_lgamma.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
* wrapper float lgammaf_r(float x, int *signgamp)
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifdef __STDC__
float lgammaf_r(float x, int *signgamp) /* wrapper lgammaf_r */
#else
float lgammaf_r(x,signgamp) /* wrapper lgammaf_r */
float x; int *signgamp;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_lgammaf_r(x,signgamp);
#else
float y;
struct exception exc;
y = __ieee754_lgammaf_r(x,signgamp);
if(_LIB_VERSION == _IEEE_) return y;
if(!finitef(y)&&finitef(x)) {
#ifndef HUGE_VAL
#define HUGE_VAL inf
double inf = 0.0;
 
SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */
#endif
exc.name = "lgammaf";
exc.err = 0;
exc.arg1 = exc.arg2 = (double)x;
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if(floorf(x)==x&&x<=(float)0.0) {
/* lgammaf(-integer) or lgamma(0) */
exc.type = SING;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
 
} else {
/* lgammaf(finite) overflow */
exc.type = OVERFLOW;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
}
if (exc.err != 0)
errno = exc.err;
return (float)exc.retval;
} else
return y;
#endif
}
/e_j1.c
0,0 → 1,486
 
/* @(#)e_j1.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/* __ieee754_j1(x), __ieee754_y1(x)
* Bessel function of the first and second kinds of order zero.
* Method -- j1(x):
* 1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ...
* 2. Reduce x to |x| since j1(x)=-j1(-x), and
* for x in (0,2)
* j1(x) = x/2 + x*z*R0/S0, where z = x*x;
* (precision: |j1/x - 1/2 - R0/S0 |<2**-61.51 )
* for x in (2,inf)
* j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1))
* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1))
* where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1)
* as follow:
* cos(x1) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
* = 1/sqrt(2) * (sin(x) - cos(x))
* sin(x1) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
* = -1/sqrt(2) * (sin(x) + cos(x))
* (To avoid cancellation, use
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
* to compute the worse one.)
*
* 3 Special cases
* j1(nan)= nan
* j1(0) = 0
* j1(inf) = 0
*
* Method -- y1(x):
* 1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN
* 2. For x<2.
* Since
* y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...)
* therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function.
* We use the following function to approximate y1,
* y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2
* where for x in [0,2] (abs err less than 2**-65.89)
* U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4
* V(z) = 1 + v0[0]*z + ... + v0[4]*z^5
* Note: For tiny x, 1/x dominate y1 and hence
* y1(tiny) = -2/pi/tiny, (choose tiny<2**-54)
* 3. For x>=2.
* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1))
* where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1)
* by method mentioned above.
*/
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
static double pone(double), qone(double);
#else
static double pone(), qone();
#endif
 
#ifdef __STDC__
static const double
#else
static double
#endif
huge = 1e300,
one = 1.0,
invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */
tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
/* R0/S0 on [0,2] */
r00 = -6.25000000000000000000e-02, /* 0xBFB00000, 0x00000000 */
r01 = 1.40705666955189706048e-03, /* 0x3F570D9F, 0x98472C61 */
r02 = -1.59955631084035597520e-05, /* 0xBEF0C5C6, 0xBA169668 */
r03 = 4.96727999609584448412e-08, /* 0x3E6AAAFA, 0x46CA0BD9 */
s01 = 1.91537599538363460805e-02, /* 0x3F939D0B, 0x12637E53 */
s02 = 1.85946785588630915560e-04, /* 0x3F285F56, 0xB9CDF664 */
s03 = 1.17718464042623683263e-06, /* 0x3EB3BFF8, 0x333F8498 */
s04 = 5.04636257076217042715e-09, /* 0x3E35AC88, 0xC97DFF2C */
s05 = 1.23542274426137913908e-11; /* 0x3DAB2ACF, 0xCFB97ED8 */
 
#ifdef __STDC__
static const double zero = 0.0;
#else
static double zero = 0.0;
#endif
 
#ifdef __STDC__
double __ieee754_j1(double x)
#else
double __ieee754_j1(x)
double x;
#endif
{
double z, s,c,ss,cc,r,u,v,y;
__int32_t hx,ix;
 
GET_HIGH_WORD(hx,x);
ix = hx&0x7fffffff;
if(ix>=0x7ff00000) return one/x;
y = fabs(x);
if(ix >= 0x40000000) { /* |x| >= 2.0 */
s = sin(y);
c = cos(y);
ss = -s-c;
cc = s-c;
if(ix<0x7fe00000) { /* make sure y+y not overflow */
z = cos(y+y);
if ((s*c)>zero) cc = z/ss;
else ss = z/cc;
}
/*
* j1(x) = 1/__ieee754_sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / __ieee754_sqrt(x)
* y1(x) = 1/__ieee754_sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / __ieee754_sqrt(x)
*/
if(ix>0x48000000) z = (invsqrtpi*cc)/__ieee754_sqrt(y);
else {
u = pone(y); v = qone(y);
z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrt(y);
}
if(hx<0) return -z;
else return z;
}
if(ix<0x3e400000) { /* |x|<2**-27 */
if(huge+x>one) return 0.5*x;/* inexact if x!=0 necessary */
}
z = x*x;
r = z*(r00+z*(r01+z*(r02+z*r03)));
s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05))));
r *= x;
return(x*0.5+r/s);
}
 
#ifdef __STDC__
static const double U0[5] = {
#else
static double U0[5] = {
#endif
-1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */
5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */
-1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */
2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */
-9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */
};
#ifdef __STDC__
static const double V0[5] = {
#else
static double V0[5] = {
#endif
1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */
2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */
1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */
6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */
1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */
};
 
#ifdef __STDC__
double __ieee754_y1(double x)
#else
double __ieee754_y1(x)
double x;
#endif
{
double z, s,c,ss,cc,u,v;
__int32_t hx,ix,lx;
 
EXTRACT_WORDS(hx,lx,x);
ix = 0x7fffffff&hx;
/* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */
if(ix>=0x7ff00000) return one/(x+x*x);
if((ix|lx)==0) return -one/zero;
if(hx<0) return zero/zero;
if(ix >= 0x40000000) { /* |x| >= 2.0 */
s = sin(x);
c = cos(x);
ss = -s-c;
cc = s-c;
if(ix<0x7fe00000) { /* make sure x+x not overflow */
z = cos(x+x);
if ((s*c)>zero) cc = z/ss;
else ss = z/cc;
}
/* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0))
* where x0 = x-3pi/4
* Better formula:
* cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
* = 1/sqrt(2) * (sin(x) - cos(x))
* sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
* = -1/sqrt(2) * (cos(x) + sin(x))
* To avoid cancellation, use
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
* to compute the worse one.
*/
if(ix>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrt(x);
else {
u = pone(x); v = qone(x);
z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrt(x);
}
return z;
}
if(ix<=0x3c900000) { /* x < 2**-54 */
return(-tpi/x);
}
z = x*x;
u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4])));
v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4]))));
return(x*(u/v) + tpi*(__ieee754_j1(x)*__ieee754_log(x)-one/x));
}
 
/* For x >= 8, the asymptotic expansions of pone is
* 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x.
* We approximate pone by
* pone(x) = 1 + (R/S)
* where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10
* S = 1 + ps0*s^2 + ... + ps4*s^10
* and
* | pone(x)-1-R/S | <= 2 ** ( -60.06)
*/
 
#ifdef __STDC__
static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
#else
static double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
#endif
0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */
1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */
4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */
3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */
7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */
};
#ifdef __STDC__
static const double ps8[5] = {
#else
static double ps8[5] = {
#endif
1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */
3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */
3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */
9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */
3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */
};
 
#ifdef __STDC__
static const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
#else
static double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
#endif
1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */
1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */
6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */
1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */
5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */
5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */
};
#ifdef __STDC__
static const double ps5[5] = {
#else
static double ps5[5] = {
#endif
5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */
9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */
5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */
7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */
1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */
};
 
#ifdef __STDC__
static const double pr3[6] = {
#else
static double pr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
#endif
3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */
1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */
3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */
3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */
9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */
4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */
};
#ifdef __STDC__
static const double ps3[5] = {
#else
static double ps3[5] = {
#endif
3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */
3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */
1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */
8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */
1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */
};
 
#ifdef __STDC__
static const double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
#else
static double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
#endif
1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */
1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */
2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */
1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */
1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */
5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */
};
#ifdef __STDC__
static const double ps2[5] = {
#else
static double ps2[5] = {
#endif
2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */
1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */
2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */
1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */
8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */
};
 
#ifdef __STDC__
static double pone(double x)
#else
static double pone(x)
double x;
#endif
{
#ifdef __STDC__
const double *p,*q;
#else
double *p,*q;
#endif
double z,r,s;
__int32_t ix;
GET_HIGH_WORD(ix,x);
ix &= 0x7fffffff;
if(ix>=0x40200000) {p = pr8; q= ps8;}
else if(ix>=0x40122E8B){p = pr5; q= ps5;}
else if(ix>=0x4006DB6D){p = pr3; q= ps3;}
else {p = pr2; q= ps2;}
z = one/(x*x);
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
return one+ r/s;
}
 
/* For x >= 8, the asymptotic expansions of qone is
* 3/8 s - 105/1024 s^3 - ..., where s = 1/x.
* We approximate qone by
* qone(x) = s*(0.375 + (R/S))
* where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10
* S = 1 + qs1*s^2 + ... + qs6*s^12
* and
* | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13)
*/
 
#ifdef __STDC__
static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
#else
static double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
#endif
0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
-1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */
-1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */
-7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */
-1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */
-4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */
};
#ifdef __STDC__
static const double qs8[6] = {
#else
static double qs8[6] = {
#endif
1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */
7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */
1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */
7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */
6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */
-2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */
};
 
#ifdef __STDC__
static const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
#else
static double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
#endif
-2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */
-1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */
-8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */
-1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */
-1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */
-2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */
};
#ifdef __STDC__
static const double qs5[6] = {
#else
static double qs5[6] = {
#endif
8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */
1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */
1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */
4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */
2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */
-4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */
};
 
#ifdef __STDC__
static const double qr3[6] = {
#else
static double qr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
#endif
-5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */
-1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */
-4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */
-5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */
-2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */
-2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */
};
#ifdef __STDC__
static const double qs3[6] = {
#else
static double qs3[6] = {
#endif
4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */
6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */
3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */
5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */
1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */
-1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */
};
 
#ifdef __STDC__
static const double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
#else
static double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
#endif
-1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */
-1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */
-2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */
-1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */
-4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */
-2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */
};
#ifdef __STDC__
static const double qs2[6] = {
#else
static double qs2[6] = {
#endif
2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */
2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */
7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */
7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */
1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */
-4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */
};
 
#ifdef __STDC__
static double qone(double x)
#else
static double qone(x)
double x;
#endif
{
#ifdef __STDC__
const double *p,*q;
#else
double *p,*q;
#endif
double s,r,z;
__int32_t ix;
GET_HIGH_WORD(ix,x);
ix &= 0x7fffffff;
if(ix>=0x40200000) {p = qr8; q= qs8;}
else if(ix>=0x40122E8B){p = qr5; q= qs5;}
else if(ix>=0x4006DB6D){p = qr3; q= qs3;}
else {p = qr2; q= qs2;}
z = one/(x*x);
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
return (.375 + r/s)/x;
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/e_rem_pio2.c
0,0 → 1,185
 
/* @(#)e_rem_pio2.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
 
/* __ieee754_rem_pio2(x,y)
*
* return the remainder of x rem pi/2 in y[0]+y[1]
* use __kernel_rem_pio2()
*/
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
/*
* Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
*/
#ifdef __STDC__
static const __int32_t two_over_pi[] = {
#else
static __int32_t two_over_pi[] = {
#endif
0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
};
 
#ifdef __STDC__
static const __int32_t npio2_hw[] = {
#else
static __int32_t npio2_hw[] = {
#endif
0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
0x404858EB, 0x404921FB,
};
 
/*
* invpio2: 53 bits of 2/pi
* pio2_1: first 33 bit of pi/2
* pio2_1t: pi/2 - pio2_1
* pio2_2: second 33 bit of pi/2
* pio2_2t: pi/2 - (pio2_1+pio2_2)
* pio2_3: third 33 bit of pi/2
* pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
*/
 
#ifdef __STDC__
static const double
#else
static double
#endif
zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
 
#ifdef __STDC__
__int32_t __ieee754_rem_pio2(double x, double *y)
#else
__int32_t __ieee754_rem_pio2(x,y)
double x,y[];
#endif
{
double z,w,t,r,fn;
double tx[3];
__int32_t i,j,n,ix,hx;
int e0,nx;
__uint32_t low;
 
GET_HIGH_WORD(hx,x); /* high word of x */
ix = hx&0x7fffffff;
if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */
{y[0] = x; y[1] = 0; return 0;}
if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */
if(hx>0) {
z = x - pio2_1;
if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
y[0] = z - pio2_1t;
y[1] = (z-y[0])-pio2_1t;
} else { /* near pi/2, use 33+33+53 bit pi */
z -= pio2_2;
y[0] = z - pio2_2t;
y[1] = (z-y[0])-pio2_2t;
}
return 1;
} else { /* negative x */
z = x + pio2_1;
if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
y[0] = z + pio2_1t;
y[1] = (z-y[0])+pio2_1t;
} else { /* near pi/2, use 33+33+53 bit pi */
z += pio2_2;
y[0] = z + pio2_2t;
y[1] = (z-y[0])+pio2_2t;
}
return -1;
}
}
if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
t = fabs(x);
n = (__int32_t) (t*invpio2+half);
fn = (double)n;
r = t-fn*pio2_1;
w = fn*pio2_1t; /* 1st round good to 85 bit */
if(n<32&&ix!=npio2_hw[n-1]) {
y[0] = r-w; /* quick check no cancellation */
} else {
__uint32_t high;
j = ix>>20;
y[0] = r-w;
GET_HIGH_WORD(high,y[0]);
i = j-((high>>20)&0x7ff);
if(i>16) { /* 2nd iteration needed, good to 118 */
t = r;
w = fn*pio2_2;
r = t-w;
w = fn*pio2_2t-((t-r)-w);
y[0] = r-w;
GET_HIGH_WORD(high,y[0]);
i = j-((high>>20)&0x7ff);
if(i>49) { /* 3rd iteration need, 151 bits acc */
t = r; /* will cover all possible cases */
w = fn*pio2_3;
r = t-w;
w = fn*pio2_3t-((t-r)-w);
y[0] = r-w;
}
}
}
y[1] = (r-y[0])-w;
if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
else return n;
}
/*
* all other (large) arguments
*/
if(ix>=0x7ff00000) { /* x is inf or NaN */
y[0]=y[1]=x-x; return 0;
}
/* set z = scalbn(|x|,ilogb(x)-23) */
GET_LOW_WORD(low,x);
SET_LOW_WORD(z,low);
e0 = (int)((ix>>20)-1046); /* e0 = ilogb(z)-23; */
SET_HIGH_WORD(z, ix - ((__int32_t)e0<<20));
for(i=0;i<2;i++) {
tx[i] = (double)((__int32_t)(z));
z = (z-tx[i])*two24;
}
tx[2] = z;
nx = 3;
while(tx[nx-1]==zero) nx--; /* skip zero term */
n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi);
if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
return n;
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/w_atanh.c
0,0 → 1,140
 
/* @(#)w_atanh.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
FUNCTION
<<atanh>>, <<atanhf>>---inverse hyperbolic tangent
 
INDEX
atanh
INDEX
atanhf
 
ANSI_SYNOPSIS
#include <math.h>
double atanh(double <[x]>);
float atanhf(float <[x]>);
 
TRAD_SYNOPSIS
#include <math.h>
double atanh(<[x]>)
double <[x]>;
 
float atanhf(<[x]>)
float <[x]>;
 
DESCRIPTION
<<atanh>> calculates the inverse hyperbolic tangent of <[x]>.
 
<<atanhf>> is identical, other than taking and returning
<<float>> values.
 
RETURNS
<<atanh>> and <<atanhf>> return the calculated value.
 
If
@ifinfo
|<[x]>|
@end ifinfo
@tex
$|x|$
@end tex
is greater than 1, the global <<errno>> is set to <<EDOM>> and
the result is a NaN. A <<DOMAIN error>> is reported.
 
If
@ifinfo
|<[x]>|
@end ifinfo
@tex
$|x|$
@end tex
is 1, the global <<errno>> is set to <<EDOM>>; and the result is
infinity with the same sign as <<x>>. A <<SING error>> is reported.
 
You can modify the error handling for these routines using
<<matherr>>.
 
PORTABILITY
Neither <<atanh>> nor <<atanhf>> are ANSI C.
 
QUICKREF
atanh - pure
atanhf - pure
 
 
*/
 
/*
* wrapper atanh(x)
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double atanh(double x) /* wrapper atanh */
#else
double atanh(x) /* wrapper atanh */
double x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_atanh(x);
#else
double z,y;
struct exception exc;
z = __ieee754_atanh(x);
if(_LIB_VERSION == _IEEE_ || isnan(x)) return z;
y = fabs(x);
if(y>=1.0) {
if(y>1.0) {
/* atanh(|x|>1) */
exc.type = DOMAIN;
exc.name = "atanh";
exc.err = 0;
exc.arg1 = exc.arg2 = x;
exc.retval = 0.0/0.0;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
} else {
/* atanh(|x|=1) */
exc.type = SING;
exc.name = "atanh";
exc.err = 0;
exc.arg1 = exc.arg2 = x;
exc.retval = x/0.0; /* sign(x)*inf */
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
} else
return z;
#endif
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
 
 
 
 
/wf_drem.c
0,0 → 1,19
/*
* dremf() wrapper for remainderf().
*
* Written by J.T. Conklin, <jtc@wimsey.com>
* Placed into the Public Domain, 1994.
*/
 
#include "fdlibm.h"
 
float
#ifdef __STDC__
dremf(float x, float y)
#else
dremf(x, y)
float x, y;
#endif
{
return remainderf(x, y);
}
/wf_exp.c
0,0 → 1,103
/* wf_exp.c -- float version of w_exp.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
* wrapper expf(x)
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifdef __STDC__
static const float
#else
static float
#endif
o_threshold= 8.8721679688e+01, /* 0x42b17180 */
u_threshold= -1.0397208405e+02; /* 0xc2cff1b5 */
 
#ifdef __STDC__
float expf(float x) /* wrapper expf */
#else
float expf(x) /* wrapper expf */
float x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_expf(x);
#else
float z;
struct exception exc;
z = __ieee754_expf(x);
if(_LIB_VERSION == _IEEE_) return z;
if(finitef(x)) {
if(x>o_threshold) {
/* expf(finite) overflow */
#ifndef HUGE_VAL
#define HUGE_VAL inf
double inf = 0.0;
 
SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */
#endif
exc.type = OVERFLOW;
exc.name = "expf";
exc.err = 0;
exc.arg1 = exc.arg2 = (double)x;
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
} else if(x<u_threshold) {
/* expf(finite) underflow */
exc.type = UNDERFLOW;
exc.name = "expf";
exc.err = 0;
exc.arg1 = exc.arg2 = (double)x;
exc.retval = 0.0;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
}
}
return z;
#endif
}
 
#ifdef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double exp(double x)
#else
double exp(x)
double x;
#endif
{
return (double) expf((float) x);
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/ef_log.c
0,0 → 1,92
/* ef_log.c -- float version of e_log.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
#include "fdlibm.h"
 
#ifdef __STDC__
static const float
#else
static float
#endif
ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
two25 = 3.355443200e+07, /* 0x4c000000 */
Lg1 = 6.6666668653e-01, /* 3F2AAAAB */
Lg2 = 4.0000000596e-01, /* 3ECCCCCD */
Lg3 = 2.8571429849e-01, /* 3E924925 */
Lg4 = 2.2222198546e-01, /* 3E638E29 */
Lg5 = 1.8183572590e-01, /* 3E3A3325 */
Lg6 = 1.5313838422e-01, /* 3E1CD04F */
Lg7 = 1.4798198640e-01; /* 3E178897 */
 
#ifdef __STDC__
static const float zero = 0.0;
#else
static float zero = 0.0;
#endif
 
#ifdef __STDC__
float __ieee754_logf(float x)
#else
float __ieee754_logf(x)
float x;
#endif
{
float hfsq,f,s,z,R,w,t1,t2,dk;
__int32_t k,ix,i,j;
 
GET_FLOAT_WORD(ix,x);
 
k=0;
if (FLT_UWORD_IS_ZERO(ix&0x7fffffff))
return -two25/zero; /* log(+-0)=-inf */
if (ix<0) return (x-x)/zero; /* log(-#) = NaN */
if (!FLT_UWORD_IS_FINITE(ix)) return x+x;
if (FLT_UWORD_IS_SUBNORMAL(ix)) {
k -= 25; x *= two25; /* subnormal number, scale up x */
GET_FLOAT_WORD(ix,x);
}
k += (ix>>23)-127;
ix &= 0x007fffff;
i = (ix+(0x95f64<<3))&0x800000;
SET_FLOAT_WORD(x,ix|(i^0x3f800000)); /* normalize x or x/2 */
k += (i>>23);
f = x-(float)1.0;
if((0x007fffff&(15+ix))<16) { /* |f| < 2**-20 */
if(f==zero) { if(k==0) return zero; else {dk=(float)k;
return dk*ln2_hi+dk*ln2_lo;}}
R = f*f*((float)0.5-(float)0.33333333333333333*f);
if(k==0) return f-R; else {dk=(float)k;
return dk*ln2_hi-((R-dk*ln2_lo)-f);}
}
s = f/((float)2.0+f);
dk = (float)k;
z = s*s;
i = ix-(0x6147a<<3);
w = z*z;
j = (0x6b851<<3)-ix;
t1= w*(Lg2+w*(Lg4+w*Lg6));
t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
i |= j;
R = t2+t1;
if(i>0) {
hfsq=(float)0.5*f*f;
if(k==0) return f-(hfsq-s*(hfsq+R)); else
return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
} else {
if(k==0) return f-s*(f-R); else
return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
}
}
/s_fabs.c
0,0 → 1,73
 
/* @(#)s_fabs.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
FUNCTION
<<fabs>>, <<fabsf>>---absolute value (magnitude)
INDEX
fabs
INDEX
fabsf
 
ANSI_SYNOPSIS
#include <math.h>
double fabs(double <[x]>);
float fabsf(float <[x]>);
 
TRAD_SYNOPSIS
#include <math.h>
double fabs(<[x]>)
double <[x]>;
 
float fabsf(<[x]>)
float <[x]>;
 
DESCRIPTION
<<fabs>> and <<fabsf>> calculate
@tex
$|x|$,
@end tex
the absolute value (magnitude) of the argument <[x]>, by direct
manipulation of the bit representation of <[x]>.
 
RETURNS
The calculated value is returned. No errors are detected.
 
PORTABILITY
<<fabs>> is ANSI.
<<fabsf>> is an extension.
 
*/
 
/*
* fabs(x) returns the absolute value of x.
*/
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double fabs(double x)
#else
double fabs(x)
double x;
#endif
{
__uint32_t high;
GET_HIGH_WORD(high,x);
SET_HIGH_WORD(x,high&0x7fffffff);
return x;
}
 
#endif /* _DOUBLE_IS_32BITS */
/wf_sinh.c
0,0 → 1,78
/* wf_sinh.c -- float version of w_sinh.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
* wrapper sinhf(x)
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifdef __STDC__
float sinhf(float x) /* wrapper sinhf */
#else
float sinhf(x) /* wrapper sinhf */
float x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_sinhf(x);
#else
float z;
struct exception exc;
z = __ieee754_sinhf(x);
if(_LIB_VERSION == _IEEE_) return z;
if(!finitef(z)&&finitef(x)) {
/* sinhf(finite) overflow */
#ifndef HUGE_VAL
#define HUGE_VAL inf
double inf = 0.0;
SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */
#endif
exc.type = OVERFLOW;
exc.name = "sinhf";
exc.err = 0;
exc.arg1 = exc.arg2 = (double)x;
if (_LIB_VERSION == _SVID_)
exc.retval = ( (x>0.0) ? HUGE : -HUGE);
else
exc.retval = ( (x>0.0) ? HUGE_VAL : -HUGE_VAL);
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
if (exc.err != 0)
errno = exc.err;
return (float)exc.retval;
} else
return z;
#endif
}
 
#ifdef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double sinh(double x)
#else
double sinh(x)
double x;
#endif
{
return (double) sinhf((float) x);
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/s_ldexp.c
0,0 → 1,81
 
/* @(#)s_ldexp.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
FUNCTION
<<ldexp>>, <<ldexpf>>---load exponent
 
INDEX
ldexp
INDEX
ldexpf
 
ANSI_SYNOPSIS
#include <math.h>
double ldexp(double <[val]>, int <[exp]>);
float ldexpf(float <[val]>, int <[exp]>);
 
TRAD_SYNOPSIS
#include <math.h>
 
double ldexp(<[val]>, <[exp]>)
double <[val]>;
int <[exp]>;
 
float ldexpf(<[val]>, <[exp]>)
float <[val]>;
int <[exp]>;
 
 
DESCRIPTION
<<ldexp>> calculates the value
@ifinfo
<[val]> times 2 to the power <[exp]>.
@end ifinfo
@tex
$val\times 2^{exp}$.
@end tex
<<ldexpf>> is identical, save that it takes and returns <<float>>
rather than <<double>> values.
 
RETURNS
<<ldexp>> returns the calculated value.
 
Underflow and overflow both set <<errno>> to <<ERANGE>>.
On underflow, <<ldexp>> and <<ldexpf>> return 0.0.
On overflow, <<ldexp>> returns plus or minus <<HUGE_VAL>>.
 
PORTABILITY
<<ldexp>> is ANSI, <<ldexpf>> is an extension.
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double ldexp(double value, int exp)
#else
double ldexp(value, exp)
double value; int exp;
#endif
{
if(!finite(value)||value==0.0) return value;
value = scalbn(value,exp);
if(!finite(value)||value==0.0) errno = ERANGE;
return value;
}
 
#endif /* _DOUBLE_IS_32BITS */
/e_asin.c
0,0 → 1,121
 
/* @(#)e_asin.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/* __ieee754_asin(x)
* Method :
* Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
* we approximate asin(x) on [0,0.5] by
* asin(x) = x + x*x^2*R(x^2)
* where
* R(x^2) is a rational approximation of (asin(x)-x)/x^3
* and its remez error is bounded by
* |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
*
* For x in [0.5,1]
* asin(x) = pi/2-2*asin(sqrt((1-x)/2))
* Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
* then for x>0.98
* asin(x) = pi/2 - 2*(s+s*z*R(z))
* = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
* For x<=0.98, let pio4_hi = pio2_hi/2, then
* f = hi part of s;
* c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z)
* and
* asin(x) = pi/2 - 2*(s+s*z*R(z))
* = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
* = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
*
* Special cases:
* if x is NaN, return x itself;
* if |x|>1, return NaN with invalid signal.
*
*/
 
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
static const double
#else
static double
#endif
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
huge = 1.000e+300,
pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
/* coefficient for R(x^2) */
pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
 
#ifdef __STDC__
double __ieee754_asin(double x)
#else
double __ieee754_asin(x)
double x;
#endif
{
double t,w,p,q,c,r,s;
__int32_t hx,ix;
GET_HIGH_WORD(hx,x);
ix = hx&0x7fffffff;
if(ix>= 0x3ff00000) { /* |x|>= 1 */
__uint32_t lx;
GET_LOW_WORD(lx,x);
if(((ix-0x3ff00000)|lx)==0)
/* asin(1)=+-pi/2 with inexact */
return x*pio2_hi+x*pio2_lo;
return (x-x)/(x-x); /* asin(|x|>1) is NaN */
} else if (ix<0x3fe00000) { /* |x|<0.5 */
if(ix<0x3e400000) { /* if |x| < 2**-27 */
if(huge+x>one) return x;/* return x with inexact if x!=0*/
} else {
t = x*x;
p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
w = p/q;
return x+x*w;
}
}
/* 1> |x|>= 0.5 */
w = one-fabs(x);
t = w*0.5;
p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
s = __ieee754_sqrt(t);
if(ix>=0x3FEF3333) { /* if |x| > 0.975 */
w = p/q;
t = pio2_hi-(2.0*(s+s*w)-pio2_lo);
} else {
w = s;
SET_LOW_WORD(w,0);
c = (t-w*w)/(s+w);
r = p/q;
p = 2.0*s*r-(pio2_lo-2.0*c);
q = pio4_hi-2.0*w;
t = pio4_hi-(p-q);
}
if(hx>0) return t; else return -t;
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/s_ceil.c
0,0 → 1,80
 
/* @(#)s_ceil.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
* ceil(x)
* Return x rounded toward -inf to integral value
* Method:
* Bit twiddling.
* Exception:
* Inexact flag raised if x not equal to ceil(x).
*/
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
static const double huge = 1.0e300;
#else
static double huge = 1.0e300;
#endif
 
#ifdef __STDC__
double ceil(double x)
#else
double ceil(x)
double x;
#endif
{
__int32_t i0,i1,j0;
__uint32_t i,j;
EXTRACT_WORDS(i0,i1,x);
j0 = ((i0>>20)&0x7ff)-0x3ff;
if(j0<20) {
if(j0<0) { /* raise inexact if x != 0 */
if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */
if(i0<0) {i0=0x80000000;i1=0;}
else if((i0|i1)!=0) { i0=0x3ff00000;i1=0;}
}
} else {
i = (0x000fffff)>>j0;
if(((i0&i)|i1)==0) return x; /* x is integral */
if(huge+x>0.0) { /* raise inexact flag */
if(i0>0) i0 += (0x00100000)>>j0;
i0 &= (~i); i1=0;
}
}
} else if (j0>51) {
if(j0==0x400) return x+x; /* inf or NaN */
else return x; /* x is integral */
} else {
i = ((__uint32_t)(0xffffffff))>>(j0-20);
if((i1&i)==0) return x; /* x is integral */
if(huge+x>0.0) { /* raise inexact flag */
if(i0>0) {
if(j0==20) i0+=1;
else {
j = i1 + (1<<(52-j0));
if(j<i1) i0+=1; /* got a carry */
i1 = j;
}
}
i1 &= (~i);
}
}
INSERT_WORDS(x,i0,i1);
return x;
}
 
#endif /* _DOUBLE_IS_32BITS */
/w_j0.c
0,0 → 1,229
 
/* @(#)w_j0.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
FUNCTION
<<jN>>,<<jNf>>,<<yN>>,<<yNf>>---Bessel functions
 
INDEX
j0
INDEX
j0f
INDEX
j1
INDEX
j1f
INDEX
jn
INDEX
jnf
INDEX
y0
INDEX
y0f
INDEX
y1
INDEX
y1f
INDEX
yn
INDEX
ynf
 
ANSI_SYNOPSIS
#include <math.h>
double j0(double <[x]>);
float j0f(float <[x]>);
double j1(double <[x]>);
float j1f(float <[x]>);
double jn(int <[n]>, double <[x]>);
float jnf(int <[n]>, float <[x]>);
double y0(double <[x]>);
float y0f(float <[x]>);
double y1(double <[x]>);
float y1f(float <[x]>);
double yn(int <[n]>, double <[x]>);
float ynf(int <[n]>, float <[x]>);
 
TRAD_SYNOPSIS
#include <math.h>
 
double j0(<[x]>)
double <[x]>;
float j0f(<[x]>)
float <[x]>;
double j1(<[x]>)
double <[x]>;
float j1f(<[x]>)
float <[x]>;
double jn(<[n]>, <[x]>)
int <[n]>;
double <[x]>;
float jnf(<[n]>, <[x]>)
int <[n]>;
float <[x]>;
 
double y0(<[x]>)
double <[x]>;
float y0f(<[x]>)
float <[x]>;
double y1(<[x]>)
double <[x]>;
float y1f(<[x]>)
float <[x]>;
double yn(<[n]>, <[x]>)
int <[n]>;
double <[x]>;
float ynf(<[n]>, <[x]>)
int <[n]>;
float <[x]>;
 
DESCRIPTION
The Bessel functions are a family of functions that solve the
differential equation
@ifinfo
. 2 2 2
. x y'' + xy' + (x - p )y = 0
@end ifinfo
@tex
$$x^2{d^2y\over dx^2} + x{dy\over dx} + (x^2-p^2)y = 0$$
@end tex
These functions have many applications in engineering and physics.
 
<<jn>> calculates the Bessel function of the first kind of order
<[n]>. <<j0>> and <<j1>> are special cases for order 0 and order
1 respectively.
 
Similarly, <<yn>> calculates the Bessel function of the second kind of
order <[n]>, and <<y0>> and <<y1>> are special cases for order 0 and
1.
 
<<jnf>>, <<j0f>>, <<j1f>>, <<ynf>>, <<y0f>>, and <<y1f>> perform the
same calculations, but on <<float>> rather than <<double>> values.
 
RETURNS
The value of each Bessel function at <[x]> is returned.
 
PORTABILITY
None of the Bessel functions are in ANSI C.
*/
 
/*
* wrapper j0(double x), y0(double x)
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double j0(double x) /* wrapper j0 */
#else
double j0(x) /* wrapper j0 */
double x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_j0(x);
#else
struct exception exc;
double z = __ieee754_j0(x);
if(_LIB_VERSION == _IEEE_ || isnan(x)) return z;
if(fabs(x)>X_TLOSS) {
/* j0(|x|>X_TLOSS) */
exc.type = TLOSS;
exc.name = "j0";
exc.err = 0;
exc.arg1 = exc.arg2 = x;
exc.retval = 0.0;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
} else
return z;
#endif
}
 
#ifdef __STDC__
double y0(double x) /* wrapper y0 */
#else
double y0(x) /* wrapper y0 */
double x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_y0(x);
#else
double z;
struct exception exc;
z = __ieee754_y0(x);
if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z;
if(x <= 0.0){
#ifndef HUGE_VAL
#define HUGE_VAL inf
double inf = 0.0;
 
SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */
#endif
/* y0(0) = -inf or y0(x<0) = NaN */
exc.type = DOMAIN; /* should be SING for IEEE y0(0) */
exc.name = "y0";
exc.err = 0;
exc.arg1 = exc.arg2 = x;
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
}
if(x>X_TLOSS) {
/* y0(x>X_TLOSS) */
exc.type = TLOSS;
exc.name = "y0";
exc.err = 0;
exc.arg1 = exc.arg2 = x;
exc.retval = 0.0;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
} else
return z;
#endif
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
 
 
 
 
 
 
 
/sf_fabs.c
0,0 → 1,47
/* sf_fabs.c -- float version of s_fabs.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
* fabsf(x) returns the absolute value of x.
*/
 
#include "fdlibm.h"
 
#ifdef __STDC__
float fabsf(float x)
#else
float fabsf(x)
float x;
#endif
{
__uint32_t ix;
GET_FLOAT_WORD(ix,x);
SET_FLOAT_WORD(x,ix&0x7fffffff);
return x;
}
 
#ifdef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double fabs(double x)
#else
double fabs(x)
double x;
#endif
{
return (double) fabsf((float) x);
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/k_sin.c
0,0 → 1,79
 
/* @(#)k_sin.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/* __kernel_sin( x, y, iy)
* kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
* Input x is assumed to be bounded by ~pi/4 in magnitude.
* Input y is the tail of x.
* Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
*
* Algorithm
* 1. Since sin(-x) = -sin(x), we need only to consider positive x.
* 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
* 3. sin(x) is approximated by a polynomial of degree 13 on
* [0,pi/4]
* 3 13
* sin(x) ~ x + S1*x + ... + S6*x
* where
*
* |sin(x) 2 4 6 8 10 12 | -58
* |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2
* | x |
*
* 4. sin(x+y) = sin(x) + sin'(x')*y
* ~ sin(x) + (1-x*x/2)*y
* For better accuracy, let
* 3 2 2 2 2
* r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
* then 3 2
* sin(x) = x + (S1*x + (x *(r-y/2)+y))
*/
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
static const double
#else
static double
#endif
half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
 
#ifdef __STDC__
double __kernel_sin(double x, double y, int iy)
#else
double __kernel_sin(x, y, iy)
double x,y; int iy; /* iy=0 if y is zero */
#endif
{
double z,r,v;
__int32_t ix;
GET_HIGH_WORD(ix,x);
ix &= 0x7fffffff; /* high word of x */
if(ix<0x3e400000) /* |x| < 2**-27 */
{if((int)x==0) return x;} /* generate inexact */
z = x*x;
v = z*x;
r = S2+z*(S3+z*(S4+z*(S5+z*S6)));
if(iy==0) return x+v*(S1+z*r);
else return x-((z*(half*y-v*r)-y)-v*S1);
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/sf_ceil.c
0,0 → 1,70
/* sf_ceil.c -- float version of s_ceil.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
#include "fdlibm.h"
 
#ifdef __STDC__
static const float huge = 1.0e30;
#else
static float huge = 1.0e30;
#endif
 
#ifdef __STDC__
float ceilf(float x)
#else
float ceilf(x)
float x;
#endif
{
__int32_t i0,j0;
__uint32_t i,ix;
GET_FLOAT_WORD(i0,x);
ix = (i0&0x7fffffff);
j0 = (ix>>23)-0x7f;
if(j0<23) {
if(j0<0) { /* raise inexact if x != 0 */
if(huge+x>(float)0.0) {/* return 0*sign(x) if |x|<1 */
if(i0<0) {i0=0x80000000;}
else if(!FLT_UWORD_IS_ZERO(ix)) { i0=0x3f800000;}
}
} else {
i = (0x007fffff)>>j0;
if((i0&i)==0) return x; /* x is integral */
if(huge+x>(float)0.0) { /* raise inexact flag */
if(i0>0) i0 += (0x00800000)>>j0;
i0 &= (~i);
}
}
} else {
if(!FLT_UWORD_IS_FINITE(ix)) return x+x; /* inf or NaN */
else return x; /* x is integral */
}
SET_FLOAT_WORD(x,i0);
return x;
}
 
#ifdef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double ceil(double x)
#else
double ceil(x)
double x;
#endif
{
return (double) ceilf((float) x);
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/wf_j0.c
0,0 → 1,137
/* wf_j0.c -- float version of w_j0.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
* wrapper j0f(float x), y0f(float x)
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifdef __STDC__
float j0f(float x) /* wrapper j0f */
#else
float j0f(x) /* wrapper j0f */
float x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_j0f(x);
#else
struct exception exc;
float z = __ieee754_j0f(x);
if(_LIB_VERSION == _IEEE_ || isnanf(x)) return z;
if(fabsf(x)>(float)X_TLOSS) {
/* j0f(|x|>X_TLOSS) */
exc.type = TLOSS;
exc.name = "j0f";
exc.err = 0;
exc.arg1 = exc.arg2 = (double)x;
exc.retval = 0.0;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
if (exc.err != 0)
errno = exc.err;
return (float)exc.retval;
} else
return z;
#endif
}
 
#ifdef __STDC__
float y0f(float x) /* wrapper y0f */
#else
float y0f(x) /* wrapper y0f */
float x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_y0f(x);
#else
float z;
struct exception exc;
z = __ieee754_y0f(x);
if(_LIB_VERSION == _IEEE_ || isnanf(x) ) return z;
if(x <= (float)0.0){
#ifndef HUGE_VAL
#define HUGE_VAL inf
double inf = 0.0;
 
SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */
#endif
/* y0f(0) = -inf or y0f(x<0) = NaN */
exc.type = DOMAIN; /* should be SING for IEEE y0f(0) */
exc.name = "y0f";
exc.err = 0;
exc.arg1 = exc.arg2 = (double)x;
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
if (exc.err != 0)
errno = exc.err;
return (float)exc.retval;
}
if(x>(float)X_TLOSS) {
/* y0f(x>X_TLOSS) */
exc.type = TLOSS;
exc.name = "y0f";
exc.err = 0;
exc.arg1 = exc.arg2 = (double)x;
exc.retval = 0.0;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
if (exc.err != 0)
errno = exc.err;
return (float)exc.retval;
} else
return z;
#endif
}
 
#ifdef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double j0(double x)
#else
double j0(x)
double x;
#endif
{
return (double) j0f((float) x);
}
 
#ifdef __STDC__
double y0(double x)
#else
double y0(x)
double x;
#endif
{
return (double) y0f((float) x);
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/w_log.c
0,0 → 1,115
 
/* @(#)w_log.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
FUNCTION
<<log>>, <<logf>>---natural logarithms
 
INDEX
log
INDEX
logf
 
ANSI_SYNOPSIS
#include <math.h>
double log(double <[x]>);
float logf(float <[x]>);
 
TRAD_SYNOPSIS
#include <math.h>
double log(<[x]>);
double <[x]>;
 
float logf(<[x]>);
float <[x]>;
 
DESCRIPTION
Return the natural logarithm of <[x]>, that is, its logarithm base e
(where e is the base of the natural system of logarithms, 2.71828@dots{}).
<<log>> and <<logf>> are identical save for the return and argument types.
 
You can use the (non-ANSI) function <<matherr>> to specify error
handling for these functions.
 
RETURNS
Normally, returns the calculated value. When <[x]> is zero, the
returned value is <<-HUGE_VAL>> and <<errno>> is set to <<ERANGE>>.
When <[x]> is negative, the returned value is <<-HUGE_VAL>> and
<<errno>> is set to <<EDOM>>. You can control the error behavior via
<<matherr>>.
 
PORTABILITY
<<log>> is ANSI, <<logf>> is an extension.
*/
 
/*
* wrapper log(x)
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double log(double x) /* wrapper log */
#else
double log(x) /* wrapper log */
double x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_log(x);
#else
double z;
struct exception exc;
z = __ieee754_log(x);
if(_LIB_VERSION == _IEEE_ || isnan(x) || x > 0.0) return z;
#ifndef HUGE_VAL
#define HUGE_VAL inf
double inf = 0.0;
 
SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */
#endif
exc.name = "log";
exc.err = 0;
exc.arg1 = x;
exc.arg2 = x;
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if(x==0.0) {
/* log(0) */
exc.type = SING;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = EDOM;
}
} else {
/* log(x<0) */
exc.type = DOMAIN;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
#endif
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/s_sin.c
0,0 → 1,132
 
/* @(#)s_sin.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
FUNCTION
<<sin>>, <<sinf>>, <<cos>>, <<cosf>>---sine or cosine
INDEX
sin
INDEX
sinf
INDEX
cos
INDEX
cosf
ANSI_SYNOPSIS
#include <math.h>
double sin(double <[x]>);
float sinf(float <[x]>);
double cos(double <[x]>);
float cosf(float <[x]>);
 
TRAD_SYNOPSIS
#include <math.h>
double sin(<[x]>)
double <[x]>;
float sinf(<[x]>)
float <[x]>;
 
double cos(<[x]>)
double <[x]>;
float cosf(<[x]>)
float <[x]>;
 
DESCRIPTION
<<sin>> and <<cos>> compute (respectively) the sine and cosine
of the argument <[x]>. Angles are specified in radians.
 
<<sinf>> and <<cosf>> are identical, save that they take and
return <<float>> values.
 
 
RETURNS
The sine or cosine of <[x]> is returned.
 
PORTABILITY
<<sin>> and <<cos>> are ANSI C.
<<sinf>> and <<cosf>> are extensions.
 
QUICKREF
sin ansi pure
sinf - pure
*/
 
/* sin(x)
* Return sine function of x.
*
* kernel function:
* __kernel_sin ... sine function on [-pi/4,pi/4]
* __kernel_cos ... cose function on [-pi/4,pi/4]
* __ieee754_rem_pio2 ... argument reduction routine
*
* Method.
* Let S,C and T denote the sin, cos and tan respectively on
* [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
* in [-pi/4 , +pi/4], and let n = k mod 4.
* We have
*
* n sin(x) cos(x) tan(x)
* ----------------------------------------------------------
* 0 S C T
* 1 C -S -1/T
* 2 -S -C T
* 3 -C S -1/T
* ----------------------------------------------------------
*
* Special cases:
* Let trig be any of sin, cos, or tan.
* trig(+-INF) is NaN, with signals;
* trig(NaN) is that NaN;
*
* Accuracy:
* TRIG(x) returns trig(x) nearly rounded
*/
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double sin(double x)
#else
double sin(x)
double x;
#endif
{
double y[2],z=0.0;
__int32_t n,ix;
 
/* High word of x. */
GET_HIGH_WORD(ix,x);
 
/* |x| ~< pi/4 */
ix &= 0x7fffffff;
if(ix <= 0x3fe921fb) return __kernel_sin(x,z,0);
 
/* sin(Inf or NaN) is NaN */
else if (ix>=0x7ff00000) return x-x;
 
/* argument reduction needed */
else {
n = __ieee754_rem_pio2(x,y);
switch(n&3) {
case 0: return __kernel_sin(y[0],y[1],1);
case 1: return __kernel_cos(y[0],y[1]);
case 2: return -__kernel_sin(y[0],y[1],1);
default:
return -__kernel_cos(y[0],y[1]);
}
}
}
 
#endif /* _DOUBLE_IS_32BITS */
/sf_frexp.c
0,0 → 1,61
/* sf_frexp.c -- float version of s_frexp.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
#include "fdlibm.h"
 
#ifdef __STDC__
static const float
#else
static float
#endif
two25 = 3.3554432000e+07; /* 0x4c000000 */
 
#ifdef __STDC__
float frexpf(float x, int *eptr)
#else
float frexpf(x, eptr)
float x; int *eptr;
#endif
{
__int32_t hx, ix;
GET_FLOAT_WORD(hx,x);
ix = 0x7fffffff&hx;
*eptr = 0;
if(!FLT_UWORD_IS_FINITE(ix)||FLT_UWORD_IS_ZERO(ix)) return x; /* 0,inf,nan */
if (FLT_UWORD_IS_SUBNORMAL(ix)) { /* subnormal */
x *= two25;
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
*eptr = -25;
}
*eptr += (ix>>23)-126;
hx = (hx&0x807fffff)|0x3f000000;
SET_FLOAT_WORD(x,hx);
return x;
}
 
#ifdef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double frexp(double x, int *eptr)
#else
double frexp(x, eptr)
double x; int *eptr;
#endif
{
return (double) frexpf((float) x, eptr);
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/wf_log10.c
0,0 → 1,88
/* wf_log10.c -- float version of w_log10.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
* wrapper log10f(X)
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifdef __STDC__
float log10f(float x) /* wrapper log10f */
#else
float log10f(x) /* wrapper log10f */
float x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_log10f(x);
#else
float z;
struct exception exc;
z = __ieee754_log10f(x);
if(_LIB_VERSION == _IEEE_ || isnanf(x)) return z;
if(x<=(float)0.0) {
#ifndef HUGE_VAL
#define HUGE_VAL inf
double inf = 0.0;
 
SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */
#endif
exc.name = "log10f";
exc.err = 0;
exc.arg1 = exc.arg2 = (double)x;
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if(x==(float)0.0) {
/* log10f(0) */
exc.type = SING;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = EDOM;
}
} else {
/* log10f(x<0) */
exc.type = DOMAIN;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
}
if (exc.err != 0)
errno = exc.err;
return (float)exc.retval;
} else
return z;
#endif
}
 
#ifdef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double log10(double x)
#else
double log10(x)
double x;
#endif
{
return (double) log10f((float) x);
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/w_sqrt.c
0,0 → 1,93
 
/* @(#)w_sqrt.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
FUNCTION
<<sqrt>>, <<sqrtf>>---positive square root
 
INDEX
sqrt
INDEX
sqrtf
 
ANSI_SYNOPSIS
#include <math.h>
double sqrt(double <[x]>);
float sqrtf(float <[x]>);
 
TRAD_SYNOPSIS
#include <math.h>
double sqrt(<[x]>);
float sqrtf(<[x]>);
 
DESCRIPTION
<<sqrt>> computes the positive square root of the argument.
You can modify error handling for this function with
<<matherr>>.
 
RETURNS
On success, the square root is returned. If <[x]> is real and
positive, then the result is positive. If <[x]> is real and
negative, the global value <<errno>> is set to <<EDOM>> (domain error).
 
 
PORTABILITY
<<sqrt>> is ANSI C. <<sqrtf>> is an extension.
*/
 
/*
* wrapper sqrt(x)
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double sqrt(double x) /* wrapper sqrt */
#else
double sqrt(x) /* wrapper sqrt */
double x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_sqrt(x);
#else
struct exception exc;
double z;
z = __ieee754_sqrt(x);
if(_LIB_VERSION == _IEEE_ || isnan(x)) return z;
if(x<0.0) {
exc.type = DOMAIN;
exc.name = "sqrt";
exc.err = 0;
exc.arg1 = exc.arg2 = x;
if (_LIB_VERSION == _SVID_)
exc.retval = 0.0;
else
exc.retval = 0.0/0.0;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
} else
return z;
#endif
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/ef_pow.c
0,0 → 1,253
/* ef_pow.c -- float version of e_pow.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
#include "fdlibm.h"
 
#ifdef __v810__
#define const
#endif
 
#ifdef __STDC__
static const float
#else
static float
#endif
bp[] = {1.0, 1.5,},
dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */
dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */
zero = 0.0,
one = 1.0,
two = 2.0,
two24 = 16777216.0, /* 0x4b800000 */
huge = 1.0e30,
tiny = 1.0e-30,
/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
L1 = 6.0000002384e-01, /* 0x3f19999a */
L2 = 4.2857143283e-01, /* 0x3edb6db7 */
L3 = 3.3333334327e-01, /* 0x3eaaaaab */
L4 = 2.7272811532e-01, /* 0x3e8ba305 */
L5 = 2.3066075146e-01, /* 0x3e6c3255 */
L6 = 2.0697501302e-01, /* 0x3e53f142 */
P1 = 1.6666667163e-01, /* 0x3e2aaaab */
P2 = -2.7777778450e-03, /* 0xbb360b61 */
P3 = 6.6137559770e-05, /* 0x388ab355 */
P4 = -1.6533901999e-06, /* 0xb5ddea0e */
P5 = 4.1381369442e-08, /* 0x3331bb4c */
lg2 = 6.9314718246e-01, /* 0x3f317218 */
lg2_h = 6.93145752e-01, /* 0x3f317200 */
lg2_l = 1.42860654e-06, /* 0x35bfbe8c */
ovt = 4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */
cp = 9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */
cp_h = 9.6179199219e-01, /* 0x3f763800 =head of cp */
cp_l = 4.7017383622e-06, /* 0x369dc3a0 =tail of cp_h */
ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
ivln2_h = 1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/
ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
 
#ifdef __STDC__
float __ieee754_powf(float x, float y)
#else
float __ieee754_powf(x,y)
float x, y;
#endif
{
float z,ax,z_h,z_l,p_h,p_l;
float y1,t1,t2,r,s,t,u,v,w;
__int32_t i,j,k,yisint,n;
__int32_t hx,hy,ix,iy,is;
 
GET_FLOAT_WORD(hx,x);
GET_FLOAT_WORD(hy,y);
ix = hx&0x7fffffff; iy = hy&0x7fffffff;
 
/* y==zero: x**0 = 1 */
if(FLT_UWORD_IS_ZERO(iy)) return one;
 
/* +-NaN return x+y */
if(FLT_UWORD_IS_NAN(ix) ||
FLT_UWORD_IS_NAN(iy))
return x+y;
 
/* determine if y is an odd int when x < 0
* yisint = 0 ... y is not an integer
* yisint = 1 ... y is an odd int
* yisint = 2 ... y is an even int
*/
yisint = 0;
if(hx<0) {
if(iy>=0x4b800000) yisint = 2; /* even integer y */
else if(iy>=0x3f800000) {
k = (iy>>23)-0x7f; /* exponent */
j = iy>>(23-k);
if((j<<(23-k))==iy) yisint = 2-(j&1);
}
}
 
/* special value of y */
if (FLT_UWORD_IS_INFINITE(iy)) { /* y is +-inf */
if (ix==0x3f800000)
return y - y; /* inf**+-1 is NaN */
else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */
return (hy>=0)? y: zero;
else /* (|x|<1)**-,+inf = inf,0 */
return (hy<0)?-y: zero;
}
if(iy==0x3f800000) { /* y is +-1 */
if(hy<0) return one/x; else return x;
}
if(hy==0x40000000) return x*x; /* y is 2 */
if(hy==0x3f000000) { /* y is 0.5 */
if(hx>=0) /* x >= +0 */
return __ieee754_sqrtf(x);
}
 
ax = fabsf(x);
/* special value of x */
if(FLT_UWORD_IS_INFINITE(ix)||FLT_UWORD_IS_ZERO(ix)||ix==0x3f800000){
z = ax; /*x is +-0,+-inf,+-1*/
if(hy<0) z = one/z; /* z = (1/|x|) */
if(hx<0) {
if(((ix-0x3f800000)|yisint)==0) {
z = (z-z)/(z-z); /* (-1)**non-int is NaN */
} else if(yisint==1)
z = -z; /* (x<0)**odd = -(|x|**odd) */
}
return z;
}
/* (x<0)**(non-int) is NaN */
if(((((__uint32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x);
 
/* |y| is huge */
if(iy>0x4d000000) { /* if |y| > 2**27 */
/* over/underflow if x is not close to one */
if(ix<0x3f7ffff8) return (hy<0)? huge*huge:tiny*tiny;
if(ix>0x3f800007) return (hy>0)? huge*huge:tiny*tiny;
/* now |1-x| is tiny <= 2**-20, suffice to compute
log(x) by x-x^2/2+x^3/3-x^4/4 */
t = x-1; /* t has 20 trailing zeros */
w = (t*t)*((float)0.5-t*((float)0.333333333333-t*(float)0.25));
u = ivln2_h*t; /* ivln2_h has 16 sig. bits */
v = t*ivln2_l-w*ivln2;
t1 = u+v;
GET_FLOAT_WORD(is,t1);
SET_FLOAT_WORD(t1,is&0xfffff000);
t2 = v-(t1-u);
} else {
float s2,s_h,s_l,t_h,t_l;
n = 0;
/* take care subnormal number */
if(FLT_UWORD_IS_SUBNORMAL(ix))
{ax *= two24; n -= 24; GET_FLOAT_WORD(ix,ax); }
n += ((ix)>>23)-0x7f;
j = ix&0x007fffff;
/* determine interval */
ix = j|0x3f800000; /* normalize ix */
if(j<=0x1cc471) k=0; /* |x|<sqrt(3/2) */
else if(j<0x5db3d7) k=1; /* |x|<sqrt(3) */
else {k=0;n+=1;ix -= 0x00800000;}
SET_FLOAT_WORD(ax,ix);
 
/* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
v = one/(ax+bp[k]);
s = u*v;
s_h = s;
GET_FLOAT_WORD(is,s_h);
SET_FLOAT_WORD(s_h,is&0xfffff000);
/* t_h=ax+bp[k] High */
SET_FLOAT_WORD(t_h,((ix>>1)|0x20000000)+0x0040000+(k<<21));
t_l = ax - (t_h-bp[k]);
s_l = v*((u-s_h*t_h)-s_h*t_l);
/* compute log(ax) */
s2 = s*s;
r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
r += s_l*(s_h+s);
s2 = s_h*s_h;
t_h = (float)3.0+s2+r;
GET_FLOAT_WORD(is,t_h);
SET_FLOAT_WORD(t_h,is&0xfffff000);
t_l = r-((t_h-(float)3.0)-s2);
/* u+v = s*(1+...) */
u = s_h*t_h;
v = s_l*t_h+t_l*s;
/* 2/(3log2)*(s+...) */
p_h = u+v;
GET_FLOAT_WORD(is,p_h);
SET_FLOAT_WORD(p_h,is&0xfffff000);
p_l = v-(p_h-u);
z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
z_l = cp_l*p_h+p_l*cp+dp_l[k];
/* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
t = (float)n;
t1 = (((z_h+z_l)+dp_h[k])+t);
GET_FLOAT_WORD(is,t1);
SET_FLOAT_WORD(t1,is&0xfffff000);
t2 = z_l-(((t1-t)-dp_h[k])-z_h);
}
 
s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
if(((((__uint32_t)hx>>31)-1)|(yisint-1))==0)
s = -one; /* (-ve)**(odd int) */
 
/* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
GET_FLOAT_WORD(is,y);
SET_FLOAT_WORD(y1,is&0xfffff000);
p_l = (y-y1)*t1+y*t2;
p_h = y1*t1;
z = p_l+p_h;
GET_FLOAT_WORD(j,z);
i = j&0x7fffffff;
if (j>0) {
if (i>FLT_UWORD_EXP_MAX)
return s*huge*huge; /* overflow */
else if (i==FLT_UWORD_EXP_MAX)
if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */
} else {
if (i>FLT_UWORD_EXP_MIN)
return s*tiny*tiny; /* underflow */
else if (i==FLT_UWORD_EXP_MIN)
if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */
}
/*
* compute 2**(p_h+p_l)
*/
k = (i>>23)-0x7f;
n = 0;
if(i>0x3f000000) { /* if |z| > 0.5, set n = [z+0.5] */
n = j+(0x00800000>>(k+1));
k = ((n&0x7fffffff)>>23)-0x7f; /* new k for n */
SET_FLOAT_WORD(t,n&~(0x007fffff>>k));
n = ((n&0x007fffff)|0x00800000)>>(23-k);
if(j<0) n = -n;
p_h -= t;
}
t = p_l+p_h;
GET_FLOAT_WORD(is,t);
SET_FLOAT_WORD(t,is&0xfffff000);
u = t*lg2_h;
v = (p_l-(t-p_h))*lg2+t*lg2_l;
z = u+v;
w = v-(z-u);
t = z*z;
t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
r = (z*t1)/(t1-two)-(w+z*w);
z = one-(r-z);
GET_FLOAT_WORD(j,z);
j += (n<<23);
if((j>>23)<=0) z = scalbnf(z,(int)n); /* subnormal output */
else SET_FLOAT_WORD(z,j);
return s*z;
}
/w_lgamma.c
0,0 → 1,89
 
/* @(#)w_lgamma.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
 
/* double lgamma(double x)
* Return the logarithm of the Gamma function of x.
*
* Method: call __ieee754_lgamma_r
*/
 
#include "fdlibm.h"
#include <reent.h>
#include <errno.h>
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double lgamma(double x)
#else
double lgamma(x)
double x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_lgamma_r(x,&(_REENT->_new._reent._gamma_signgam));
#else
double y;
struct exception exc;
y = __ieee754_lgamma_r(x,&(_REENT->_new._reent._gamma_signgam));
if(_LIB_VERSION == _IEEE_) return y;
if(!finite(y)&&finite(x)) {
#ifndef HUGE_VAL
#define HUGE_VAL inf
double inf = 0.0;
 
SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */
#endif
exc.name = "lgamma";
exc.err = 0;
exc.arg1 = x;
exc.arg2 = x;
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if(floor(x)==x&&x<=0.0) {
/* lgamma(-integer) */
exc.type = SING;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
 
} else {
/* lgamma(finite) overflow */
exc.type = OVERFLOW;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
} else
return y;
#endif
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
 
 
 
 
 
 
 
/er_lgamma.c
0,0 → 1,309
 
/* @(#)er_lgamma.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
 
/* __ieee754_lgamma_r(x, signgamp)
* Reentrant version of the logarithm of the Gamma function
* with user provide pointer for the sign of Gamma(x).
*
* Method:
* 1. Argument Reduction for 0 < x <= 8
* Since gamma(1+s)=s*gamma(s), for x in [0,8], we may
* reduce x to a number in [1.5,2.5] by
* lgamma(1+s) = log(s) + lgamma(s)
* for example,
* lgamma(7.3) = log(6.3) + lgamma(6.3)
* = log(6.3*5.3) + lgamma(5.3)
* = log(6.3*5.3*4.3*3.3*2.3) + lgamma(2.3)
* 2. Polynomial approximation of lgamma around its
* minimun ymin=1.461632144968362245 to maintain monotonicity.
* On [ymin-0.23, ymin+0.27] (i.e., [1.23164,1.73163]), use
* Let z = x-ymin;
* lgamma(x) = -1.214862905358496078218 + z^2*poly(z)
* where
* poly(z) is a 14 degree polynomial.
* 2. Rational approximation in the primary interval [2,3]
* We use the following approximation:
* s = x-2.0;
* lgamma(x) = 0.5*s + s*P(s)/Q(s)
* with accuracy
* |P/Q - (lgamma(x)-0.5s)| < 2**-61.71
* Our algorithms are based on the following observation
*
* zeta(2)-1 2 zeta(3)-1 3
* lgamma(2+s) = s*(1-Euler) + --------- * s - --------- * s + ...
* 2 3
*
* where Euler = 0.5771... is the Euler constant, which is very
* close to 0.5.
*
* 3. For x>=8, we have
* lgamma(x)~(x-0.5)log(x)-x+0.5*log(2pi)+1/(12x)-1/(360x**3)+....
* (better formula:
* lgamma(x)~(x-0.5)*(log(x)-1)-.5*(log(2pi)-1) + ...)
* Let z = 1/x, then we approximation
* f(z) = lgamma(x) - (x-0.5)(log(x)-1)
* by
* 3 5 11
* w = w0 + w1*z + w2*z + w3*z + ... + w6*z
* where
* |w - f(z)| < 2**-58.74
*
* 4. For negative x, since (G is gamma function)
* -x*G(-x)*G(x) = pi/sin(pi*x),
* we have
* G(x) = pi/(sin(pi*x)*(-x)*G(-x))
* since G(-x) is positive, sign(G(x)) = sign(sin(pi*x)) for x<0
* Hence, for x<0, signgam = sign(sin(pi*x)) and
* lgamma(x) = log(|Gamma(x)|)
* = log(pi/(|x*sin(pi*x)|)) - lgamma(-x);
* Note: one should avoid compute pi*(-x) directly in the
* computation of sin(pi*(-x)).
*
* 5. Special Cases
* lgamma(2+s) ~ s*(1-Euler) for tiny s
* lgamma(1)=lgamma(2)=0
* lgamma(x) ~ -log(x) for tiny x
* lgamma(0) = lgamma(inf) = inf
* lgamma(-integer) = +-inf
*
*/
 
#include "fdlibm.h"
 
#ifdef __STDC__
static const double
#else
static double
#endif
two52= 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */
half= 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
a0 = 7.72156649015328655494e-02, /* 0x3FB3C467, 0xE37DB0C8 */
a1 = 3.22467033424113591611e-01, /* 0x3FD4A34C, 0xC4A60FAD */
a2 = 6.73523010531292681824e-02, /* 0x3FB13E00, 0x1A5562A7 */
a3 = 2.05808084325167332806e-02, /* 0x3F951322, 0xAC92547B */
a4 = 7.38555086081402883957e-03, /* 0x3F7E404F, 0xB68FEFE8 */
a5 = 2.89051383673415629091e-03, /* 0x3F67ADD8, 0xCCB7926B */
a6 = 1.19270763183362067845e-03, /* 0x3F538A94, 0x116F3F5D */
a7 = 5.10069792153511336608e-04, /* 0x3F40B6C6, 0x89B99C00 */
a8 = 2.20862790713908385557e-04, /* 0x3F2CF2EC, 0xED10E54D */
a9 = 1.08011567247583939954e-04, /* 0x3F1C5088, 0x987DFB07 */
a10 = 2.52144565451257326939e-05, /* 0x3EFA7074, 0x428CFA52 */
a11 = 4.48640949618915160150e-05, /* 0x3F07858E, 0x90A45837 */
tc = 1.46163214496836224576e+00, /* 0x3FF762D8, 0x6356BE3F */
tf = -1.21486290535849611461e-01, /* 0xBFBF19B9, 0xBCC38A42 */
/* tt = -(tail of tf) */
tt = -3.63867699703950536541e-18, /* 0xBC50C7CA, 0xA48A971F */
t0 = 4.83836122723810047042e-01, /* 0x3FDEF72B, 0xC8EE38A2 */
t1 = -1.47587722994593911752e-01, /* 0xBFC2E427, 0x8DC6C509 */
t2 = 6.46249402391333854778e-02, /* 0x3FB08B42, 0x94D5419B */
t3 = -3.27885410759859649565e-02, /* 0xBFA0C9A8, 0xDF35B713 */
t4 = 1.79706750811820387126e-02, /* 0x3F9266E7, 0x970AF9EC */
t5 = -1.03142241298341437450e-02, /* 0xBF851F9F, 0xBA91EC6A */
t6 = 6.10053870246291332635e-03, /* 0x3F78FCE0, 0xE370E344 */
t7 = -3.68452016781138256760e-03, /* 0xBF6E2EFF, 0xB3E914D7 */
t8 = 2.25964780900612472250e-03, /* 0x3F6282D3, 0x2E15C915 */
t9 = -1.40346469989232843813e-03, /* 0xBF56FE8E, 0xBF2D1AF1 */
t10 = 8.81081882437654011382e-04, /* 0x3F4CDF0C, 0xEF61A8E9 */
t11 = -5.38595305356740546715e-04, /* 0xBF41A610, 0x9C73E0EC */
t12 = 3.15632070903625950361e-04, /* 0x3F34AF6D, 0x6C0EBBF7 */
t13 = -3.12754168375120860518e-04, /* 0xBF347F24, 0xECC38C38 */
t14 = 3.35529192635519073543e-04, /* 0x3F35FD3E, 0xE8C2D3F4 */
u0 = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */
u1 = 6.32827064025093366517e-01, /* 0x3FE4401E, 0x8B005DFF */
u2 = 1.45492250137234768737e+00, /* 0x3FF7475C, 0xD119BD6F */
u3 = 9.77717527963372745603e-01, /* 0x3FEF4976, 0x44EA8450 */
u4 = 2.28963728064692451092e-01, /* 0x3FCD4EAE, 0xF6010924 */
u5 = 1.33810918536787660377e-02, /* 0x3F8B678B, 0xBF2BAB09 */
v1 = 2.45597793713041134822e+00, /* 0x4003A5D7, 0xC2BD619C */
v2 = 2.12848976379893395361e+00, /* 0x40010725, 0xA42B18F5 */
v3 = 7.69285150456672783825e-01, /* 0x3FE89DFB, 0xE45050AF */
v4 = 1.04222645593369134254e-01, /* 0x3FBAAE55, 0xD6537C88 */
v5 = 3.21709242282423911810e-03, /* 0x3F6A5ABB, 0x57D0CF61 */
s0 = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */
s1 = 2.14982415960608852501e-01, /* 0x3FCB848B, 0x36E20878 */
s2 = 3.25778796408930981787e-01, /* 0x3FD4D98F, 0x4F139F59 */
s3 = 1.46350472652464452805e-01, /* 0x3FC2BB9C, 0xBEE5F2F7 */
s4 = 2.66422703033638609560e-02, /* 0x3F9B481C, 0x7E939961 */
s5 = 1.84028451407337715652e-03, /* 0x3F5E26B6, 0x7368F239 */
s6 = 3.19475326584100867617e-05, /* 0x3F00BFEC, 0xDD17E945 */
r1 = 1.39200533467621045958e+00, /* 0x3FF645A7, 0x62C4AB74 */
r2 = 7.21935547567138069525e-01, /* 0x3FE71A18, 0x93D3DCDC */
r3 = 1.71933865632803078993e-01, /* 0x3FC601ED, 0xCCFBDF27 */
r4 = 1.86459191715652901344e-02, /* 0x3F9317EA, 0x742ED475 */
r5 = 7.77942496381893596434e-04, /* 0x3F497DDA, 0xCA41A95B */
r6 = 7.32668430744625636189e-06, /* 0x3EDEBAF7, 0xA5B38140 */
w0 = 4.18938533204672725052e-01, /* 0x3FDACFE3, 0x90C97D69 */
w1 = 8.33333333333329678849e-02, /* 0x3FB55555, 0x5555553B */
w2 = -2.77777777728775536470e-03, /* 0xBF66C16C, 0x16B02E5C */
w3 = 7.93650558643019558500e-04, /* 0x3F4A019F, 0x98CF38B6 */
w4 = -5.95187557450339963135e-04, /* 0xBF4380CB, 0x8C0FE741 */
w5 = 8.36339918996282139126e-04, /* 0x3F4B67BA, 0x4CDAD5D1 */
w6 = -1.63092934096575273989e-03; /* 0xBF5AB89D, 0x0B9E43E4 */
 
#ifdef __STDC__
static const double zero= 0.00000000000000000000e+00;
#else
static double zero= 0.00000000000000000000e+00;
#endif
 
#ifdef __STDC__
static double sin_pi(double x)
#else
static double sin_pi(x)
double x;
#endif
{
double y,z;
__int32_t n,ix;
 
GET_HIGH_WORD(ix,x);
ix &= 0x7fffffff;
 
if(ix<0x3fd00000) return __kernel_sin(pi*x,zero,0);
y = -x; /* x is assume negative */
 
/*
* argument reduction, make sure inexact flag not raised if input
* is an integer
*/
z = floor(y);
if(z!=y) { /* inexact anyway */
y *= 0.5;
y = 2.0*(y - floor(y)); /* y = |x| mod 2.0 */
n = (__int32_t) (y*4.0);
} else {
if(ix>=0x43400000) {
y = zero; n = 0; /* y must be even */
} else {
if(ix<0x43300000) z = y+two52; /* exact */
GET_LOW_WORD(n,z);
n &= 1;
y = n;
n<<= 2;
}
}
switch (n) {
case 0: y = __kernel_sin(pi*y,zero,0); break;
case 1:
case 2: y = __kernel_cos(pi*(0.5-y),zero); break;
case 3:
case 4: y = __kernel_sin(pi*(one-y),zero,0); break;
case 5:
case 6: y = -__kernel_cos(pi*(y-1.5),zero); break;
default: y = __kernel_sin(pi*(y-2.0),zero,0); break;
}
return -y;
}
 
 
#ifdef __STDC__
double __ieee754_lgamma_r(double x, int *signgamp)
#else
double __ieee754_lgamma_r(x,signgamp)
double x; int *signgamp;
#endif
{
double t,y,z,nadj,p,p1,p2,p3,q,r,w;
__int32_t i,hx,lx,ix;
 
EXTRACT_WORDS(hx,lx,x);
 
/* purge off +-inf, NaN, +-0, and negative arguments */
*signgamp = 1;
ix = hx&0x7fffffff;
if(ix>=0x7ff00000) return x*x;
if((ix|lx)==0) return one/zero;
if(ix<0x3b900000) { /* |x|<2**-70, return -log(|x|) */
if(hx<0) {
*signgamp = -1;
return -__ieee754_log(-x);
} else return -__ieee754_log(x);
}
if(hx<0) {
if(ix>=0x43300000) /* |x|>=2**52, must be -integer */
return one/zero;
t = sin_pi(x);
if(t==zero) return one/zero; /* -integer */
nadj = __ieee754_log(pi/fabs(t*x));
if(t<zero) *signgamp = -1;
x = -x;
}
 
/* purge off 1 and 2 */
if((((ix-0x3ff00000)|lx)==0)||(((ix-0x40000000)|lx)==0)) r = 0;
/* for x < 2.0 */
else if(ix<0x40000000) {
if(ix<=0x3feccccc) { /* lgamma(x) = lgamma(x+1)-log(x) */
r = -__ieee754_log(x);
if(ix>=0x3FE76944) {y = one-x; i= 0;}
else if(ix>=0x3FCDA661) {y= x-(tc-one); i=1;}
else {y = x; i=2;}
} else {
r = zero;
if(ix>=0x3FFBB4C3) {y=2.0-x;i=0;} /* [1.7316,2] */
else if(ix>=0x3FF3B4C4) {y=x-tc;i=1;} /* [1.23,1.73] */
else {y=x-one;i=2;}
}
switch(i) {
case 0:
z = y*y;
p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10))));
p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11)))));
p = y*p1+p2;
r += (p-0.5*y); break;
case 1:
z = y*y;
w = z*y;
p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */
p2 = t1+w*(t4+w*(t7+w*(t10+w*t13)));
p3 = t2+w*(t5+w*(t8+w*(t11+w*t14)));
p = z*p1-(tt-w*(p2+y*p3));
r += (tf + p); break;
case 2:
p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5)))));
p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5))));
r += (-0.5*y + p1/p2);
}
}
else if(ix<0x40200000) { /* x < 8.0 */
i = (__int32_t)x;
t = zero;
y = x-(double)i;
p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6))))));
q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6)))));
r = half*y+p/q;
z = one; /* lgamma(1+s) = log(s) + lgamma(s) */
switch(i) {
case 7: z *= (y+6.0); /* FALLTHRU */
case 6: z *= (y+5.0); /* FALLTHRU */
case 5: z *= (y+4.0); /* FALLTHRU */
case 4: z *= (y+3.0); /* FALLTHRU */
case 3: z *= (y+2.0); /* FALLTHRU */
r += __ieee754_log(z); break;
}
/* 8.0 <= x < 2**58 */
} else if (ix < 0x43900000) {
t = __ieee754_log(x);
z = one/x;
y = z*z;
w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6)))));
r = (x-half)*(t-one)+w;
} else
/* 2**58 <= x <= inf */
r = x*(__ieee754_log(x)-one);
if(hx<0) r = nadj - r;
return r;
}
/Makefile.am
0,0 → 1,183
## Process this file with automake to generate Makefile.in
 
AUTOMAKE_OPTIONS = cygnus
 
INCLUDES = -I$(srcdir)/../common $(NEWLIB_CFLAGS) $(CROSS_CFLAGS) $(TARGET_CFLAGS)
 
src = k_standard.c k_rem_pio2.c \
k_cos.c k_sin.c k_tan.c \
e_acos.c e_acosh.c e_asin.c e_atan2.c \
e_atanh.c e_cosh.c e_exp.c e_fmod.c \
er_gamma.c e_hypot.c e_j0.c \
e_j1.c e_jn.c er_lgamma.c \
e_log.c e_log10.c e_pow.c e_rem_pio2.c e_remainder.c \
e_scalb.c e_sinh.c e_sqrt.c \
w_acos.c w_acosh.c w_asin.c w_atan2.c \
w_atanh.c w_cosh.c w_exp.c w_fmod.c \
w_gamma.c wr_gamma.c w_hypot.c w_j0.c \
w_j1.c w_jn.c w_lgamma.c wr_lgamma.c \
w_log.c w_log10.c w_pow.c w_remainder.c \
w_scalb.c w_sinh.c w_sqrt.c \
w_cabs.c w_drem.c \
s_asinh.c s_atan.c s_ceil.c \
s_cos.c s_erf.c s_fabs.c s_floor.c \
s_frexp.c s_isnan.c s_ldexp.c \
s_signif.c s_sin.c \
s_tan.c s_tanh.c \
s_isinf.c s_infconst.c
 
fsrc = kf_rem_pio2.c \
kf_cos.c kf_sin.c kf_tan.c \
ef_acos.c ef_acosh.c ef_asin.c ef_atan2.c \
ef_atanh.c ef_cosh.c ef_exp.c ef_fmod.c \
erf_gamma.c ef_hypot.c ef_j0.c \
ef_j1.c ef_jn.c erf_lgamma.c \
ef_log.c ef_log10.c ef_pow.c ef_rem_pio2.c ef_remainder.c \
ef_scalb.c ef_sinh.c ef_sqrt.c \
wf_acos.c wf_acosh.c wf_asin.c wf_atan2.c \
wf_atanh.c wf_cosh.c wf_exp.c wf_fmod.c \
wf_gamma.c wrf_gamma.c wf_hypot.c wf_j0.c \
wf_j1.c wf_jn.c wf_lgamma.c wrf_lgamma.c \
wf_log.c wf_log10.c wf_pow.c wf_remainder.c \
wf_scalb.c wf_sinh.c wf_sqrt.c \
wf_cabs.c wf_drem.c \
sf_asinh.c sf_atan.c sf_ceil.c \
sf_cos.c sf_erf.c sf_fabs.c sf_floor.c \
sf_frexp.c sf_isnan.c sf_ldexp.c \
sf_signif.c sf_sin.c \
sf_tan.c sf_tanh.c \
sf_isinf.c
 
libmath_la_LDFLAGS = -Xcompiler -nostdlib
 
if USE_LIBTOOL
noinst_LTLIBRARIES = libmath.la
libmath_la_SOURCES = $(src) $(fsrc)
noinst_DATA = objectlist.awk.in
else
noinst_LIBRARIES = lib.a
lib_a_SOURCES = $(src) $(fsrc)
noinst_DATA =
endif # USE_LIBTOOL
 
include $(srcdir)/../../Makefile.shared
 
chobj = wacos.def wacosh.def wasin.def sasinh.def \
satan.def watan2.def watanh.def wj0.def \
wcosh.def serf.def wexp.def \
sfabs.def sfloor.def wfmod.def sfrexp.def \
wgamma.def whypot.def sldexp.def wlog.def \
wlog10.def \
wpow.def wremainder.def ssin.def wsinh.def \
wsqrt.def stan.def stanh.def \
sisnan.def
 
SUFFIXES = .def
 
CHEW = ../../doc/makedoc -f $(srcdir)/../../doc/doc.str
 
.c.def:
$(CHEW) < $< > $*.def 2> $*.ref
touch stmp-def
 
TARGETDOC = ../tmp.texi
 
doc: $(chobj)
cat $(srcdir)/math.tex >> $(TARGETDOC)
 
CLEANFILES = $(chobj) *.ref
 
# Texinfo does not appear to support underscores in file names, so we
# name the .def files without underscores.
 
wacos.def: w_acos.c
$(CHEW) < $(srcdir)/w_acos.c >$@ 2>/dev/null
touch stmp-def
wacosh.def: w_acosh.c
$(CHEW) < $(srcdir)/w_acosh.c >$@ 2>/dev/null
touch stmp-def
wasin.def: w_asin.c
$(CHEW) < $(srcdir)/w_asin.c >$@ 2>/dev/null
touch stmp-def
sasinh.def: s_asinh.c
$(CHEW) < $(srcdir)/s_asinh.c >$@ 2>/dev/null
touch stmp-def
satan.def: s_atan.c
$(CHEW) < $(srcdir)/s_atan.c >$@ 2>/dev/null
touch stmp-def
watan2.def: w_atan2.c
$(CHEW) < $(srcdir)/w_atan2.c >$@ 2>/dev/null
touch stmp-def
watanh.def: w_atanh.c
$(CHEW) < $(srcdir)/w_atanh.c >$@ 2>/dev/null
touch stmp-def
wj0.def: w_j0.c
$(CHEW) < $(srcdir)/w_j0.c >$@ 2>/dev/null
touch stmp-def
scopysign.def: s_copysign.c
$(CHEW) < $(srcdir)/../common/s_copysign.c >$@ 2>/dev/null
touch stmp-def
wcosh.def: w_cosh.c
$(CHEW) < $(srcdir)/w_cosh.c >$@ 2>/dev/null
touch stmp-def
serf.def: s_erf.c
$(CHEW) < $(srcdir)/s_erf.c >$@ 2>/dev/null
touch stmp-def
wexp.def: w_exp.c
$(CHEW) < $(srcdir)/w_exp.c >$@ 2>/dev/null
touch stmp-def
sfabs.def: s_fabs.c
$(CHEW) < $(srcdir)/s_fabs.c >$@ 2>/dev/null
touch stmp-def
sfloor.def: s_floor.c
$(CHEW) < $(srcdir)/s_floor.c >$@ 2>/dev/null
touch stmp-def
wfmod.def: w_fmod.c
$(CHEW) < $(srcdir)/w_fmod.c >$@ 2>/dev/null
touch stmp-def
sfrexp.def: s_frexp.c
$(CHEW) < $(srcdir)/s_frexp.c >$@ 2>/dev/null
touch stmp-def
wgamma.def: w_gamma.c
$(CHEW) < $(srcdir)/w_gamma.c >$@ 2>/dev/null
touch stmp-def
whypot.def: w_hypot.c
$(CHEW) < $(srcdir)/w_hypot.c >$@ 2>/dev/null
touch stmp-def
sldexp.def: s_ldexp.c
$(CHEW) < $(srcdir)/s_ldexp.c >$@ 2>/dev/null
touch stmp-def
wlog.def: w_log.c
$(CHEW) < $(srcdir)/w_log.c >$@ 2>/dev/null
touch stmp-def
wlog10.def: w_log10.c
$(CHEW) < $(srcdir)/w_log10.c >$@ 2>/dev/null
touch stmp-def
wpow.def: w_pow.c
$(CHEW) < $(srcdir)/w_pow.c >$@ 2>/dev/null
touch stmp-def
wremainder.def: w_remainder.c
$(CHEW) < $(srcdir)/w_remainder.c >$@ 2>/dev/null
touch stmp-def
ssin.def: s_sin.c
$(CHEW) < $(srcdir)/s_sin.c >$@ 2>/dev/null
touch stmp-def
wsinh.def: w_sinh.c
$(CHEW) < $(srcdir)/w_sinh.c >$@ 2>/dev/null
touch stmp-def
wsqrt.def: w_sqrt.c
$(CHEW) < $(srcdir)/w_sqrt.c >$@ 2>/dev/null
touch stmp-def
stan.def: s_tan.c
$(CHEW) < $(srcdir)/s_tan.c >$@ 2>/dev/null
touch stmp-def
stanh.def: s_tanh.c
$(CHEW) < $(srcdir)/s_tanh.c >$@ 2>/dev/null
touch stmp-def
sisnan.def: s_isnan.c
$(CHEW) < $(srcdir)/s_isnan.c >$@ 2>/dev/null
touch stmp-def
 
# A partial dependency list.
 
$(lib_a_OBJECTS): $(srcdir)/../../libc/include/math.h $(srcdir)/../common/fdlibm.h
/wf_lgamma.c
0,0 → 1,87
/* wf_lgamma.c -- float version of w_lgamma.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
 
#include "fdlibm.h"
#include <reent.h>
#include <errno.h>
 
#ifdef __STDC__
float lgammaf(float x)
#else
float lgammaf(x)
float x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_lgammaf_r(x,&(_REENT->_new._reent._gamma_signgam));
#else
float y;
struct exception exc;
y = __ieee754_lgammaf_r(x,&(_REENT->_new._reent._gamma_signgam));
if(_LIB_VERSION == _IEEE_) return y;
if(!finitef(y)&&finitef(x)) {
#ifndef HUGE_VAL
#define HUGE_VAL inf
double inf = 0.0;
 
SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */
#endif
exc.name = "lgammaf";
exc.err = 0;
exc.arg1 = exc.arg2 = (double)x;
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if(floorf(x)==x&&x<=(float)0.0) {
/* lgammaf(-integer) */
exc.type = SING;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
 
} else {
/* lgammaf(finite) overflow */
exc.type = OVERFLOW;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
}
if (exc.err != 0)
errno = exc.err;
return (float)exc.retval;
} else
return y;
#endif
}
 
#ifdef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double lgamma(double x)
#else
double lgamma(x)
double x;
#endif
{
return (double) lgammaf((float) x);
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/sf_asinh.c
0,0 → 1,66
/* sf_asinh.c -- float version of s_asinh.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
#include "fdlibm.h"
 
#ifdef __STDC__
static const float
#else
static float
#endif
one = 1.0000000000e+00, /* 0x3F800000 */
ln2 = 6.9314718246e-01, /* 0x3f317218 */
huge= 1.0000000000e+30;
 
#ifdef __STDC__
float asinhf(float x)
#else
float asinhf(x)
float x;
#endif
{
float t,w;
__int32_t hx,ix;
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
if(!FLT_UWORD_IS_FINITE(ix)) return x+x; /* x is inf or NaN */
if(ix< 0x31800000) { /* |x|<2**-28 */
if(huge+x>one) return x; /* return x inexact except 0 */
}
if(ix>0x4d800000) { /* |x| > 2**28 */
w = __ieee754_logf(fabsf(x))+ln2;
} else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */
t = fabsf(x);
w = __ieee754_logf((float)2.0*t+one/(__ieee754_sqrtf(x*x+one)+t));
} else { /* 2.0 > |x| > 2**-28 */
t = x*x;
w =log1pf(fabsf(x)+t/(one+__ieee754_sqrtf(one+t)));
}
if(hx>0) return w; else return -w;
}
 
#ifdef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double asinh(double x)
#else
double asinh(x)
double x;
#endif
{
return (double) asinhf((float) x);
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/erf_lgamma.c
0,0 → 1,244
/* erf_lgamma.c -- float version of er_lgamma.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
 
#include "fdlibm.h"
 
#ifdef __STDC__
static const float
#else
static float
#endif
two23= 8.3886080000e+06, /* 0x4b000000 */
half= 5.0000000000e-01, /* 0x3f000000 */
one = 1.0000000000e+00, /* 0x3f800000 */
pi = 3.1415927410e+00, /* 0x40490fdb */
a0 = 7.7215664089e-02, /* 0x3d9e233f */
a1 = 3.2246702909e-01, /* 0x3ea51a66 */
a2 = 6.7352302372e-02, /* 0x3d89f001 */
a3 = 2.0580807701e-02, /* 0x3ca89915 */
a4 = 7.3855509982e-03, /* 0x3bf2027e */
a5 = 2.8905137442e-03, /* 0x3b3d6ec6 */
a6 = 1.1927076848e-03, /* 0x3a9c54a1 */
a7 = 5.1006977446e-04, /* 0x3a05b634 */
a8 = 2.2086278477e-04, /* 0x39679767 */
a9 = 1.0801156895e-04, /* 0x38e28445 */
a10 = 2.5214456400e-05, /* 0x37d383a2 */
a11 = 4.4864096708e-05, /* 0x383c2c75 */
tc = 1.4616321325e+00, /* 0x3fbb16c3 */
tf = -1.2148628384e-01, /* 0xbdf8cdcd */
/* tt = -(tail of tf) */
tt = 6.6971006518e-09, /* 0x31e61c52 */
t0 = 4.8383611441e-01, /* 0x3ef7b95e */
t1 = -1.4758771658e-01, /* 0xbe17213c */
t2 = 6.4624942839e-02, /* 0x3d845a15 */
t3 = -3.2788541168e-02, /* 0xbd064d47 */
t4 = 1.7970675603e-02, /* 0x3c93373d */
t5 = -1.0314224288e-02, /* 0xbc28fcfe */
t6 = 6.1005386524e-03, /* 0x3bc7e707 */
t7 = -3.6845202558e-03, /* 0xbb7177fe */
t8 = 2.2596477065e-03, /* 0x3b141699 */
t9 = -1.4034647029e-03, /* 0xbab7f476 */
t10 = 8.8108185446e-04, /* 0x3a66f867 */
t11 = -5.3859531181e-04, /* 0xba0d3085 */
t12 = 3.1563205994e-04, /* 0x39a57b6b */
t13 = -3.1275415677e-04, /* 0xb9a3f927 */
t14 = 3.3552918467e-04, /* 0x39afe9f7 */
u0 = -7.7215664089e-02, /* 0xbd9e233f */
u1 = 6.3282704353e-01, /* 0x3f2200f4 */
u2 = 1.4549225569e+00, /* 0x3fba3ae7 */
u3 = 9.7771751881e-01, /* 0x3f7a4bb2 */
u4 = 2.2896373272e-01, /* 0x3e6a7578 */
u5 = 1.3381091878e-02, /* 0x3c5b3c5e */
v1 = 2.4559779167e+00, /* 0x401d2ebe */
v2 = 2.1284897327e+00, /* 0x4008392d */
v3 = 7.6928514242e-01, /* 0x3f44efdf */
v4 = 1.0422264785e-01, /* 0x3dd572af */
v5 = 3.2170924824e-03, /* 0x3b52d5db */
s0 = -7.7215664089e-02, /* 0xbd9e233f */
s1 = 2.1498242021e-01, /* 0x3e5c245a */
s2 = 3.2577878237e-01, /* 0x3ea6cc7a */
s3 = 1.4635047317e-01, /* 0x3e15dce6 */
s4 = 2.6642270386e-02, /* 0x3cda40e4 */
s5 = 1.8402845599e-03, /* 0x3af135b4 */
s6 = 3.1947532989e-05, /* 0x3805ff67 */
r1 = 1.3920053244e+00, /* 0x3fb22d3b */
r2 = 7.2193557024e-01, /* 0x3f38d0c5 */
r3 = 1.7193385959e-01, /* 0x3e300f6e */
r4 = 1.8645919859e-02, /* 0x3c98bf54 */
r5 = 7.7794247773e-04, /* 0x3a4beed6 */
r6 = 7.3266842264e-06, /* 0x36f5d7bd */
w0 = 4.1893854737e-01, /* 0x3ed67f1d */
w1 = 8.3333335817e-02, /* 0x3daaaaab */
w2 = -2.7777778450e-03, /* 0xbb360b61 */
w3 = 7.9365057172e-04, /* 0x3a500cfd */
w4 = -5.9518753551e-04, /* 0xba1c065c */
w5 = 8.3633989561e-04, /* 0x3a5b3dd2 */
w6 = -1.6309292987e-03; /* 0xbad5c4e8 */
 
#ifdef __STDC__
static const float zero= 0.0000000000e+00;
#else
static float zero= 0.0000000000e+00;
#endif
 
#ifdef __STDC__
static float sin_pif(float x)
#else
static float sin_pif(x)
float x;
#endif
{
float y,z;
__int32_t n,ix;
 
GET_FLOAT_WORD(ix,x);
ix &= 0x7fffffff;
 
if(ix<0x3e800000) return __kernel_sinf(pi*x,zero,0);
y = -x; /* x is assume negative */
 
/*
* argument reduction, make sure inexact flag not raised if input
* is an integer
*/
z = floorf(y);
if(z!=y) { /* inexact anyway */
y *= (float)0.5;
y = (float)2.0*(y - floorf(y)); /* y = |x| mod 2.0 */
n = (__int32_t) (y*(float)4.0);
} else {
if(ix>=0x4b800000) {
y = zero; n = 0; /* y must be even */
} else {
if(ix<0x4b000000) z = y+two23; /* exact */
GET_FLOAT_WORD(n,z);
n &= 1;
y = n;
n<<= 2;
}
}
switch (n) {
case 0: y = __kernel_sinf(pi*y,zero,0); break;
case 1:
case 2: y = __kernel_cosf(pi*((float)0.5-y),zero); break;
case 3:
case 4: y = __kernel_sinf(pi*(one-y),zero,0); break;
case 5:
case 6: y = -__kernel_cosf(pi*(y-(float)1.5),zero); break;
default: y = __kernel_sinf(pi*(y-(float)2.0),zero,0); break;
}
return -y;
}
 
 
#ifdef __STDC__
float __ieee754_lgammaf_r(float x, int *signgamp)
#else
float __ieee754_lgammaf_r(x,signgamp)
float x; int *signgamp;
#endif
{
float t,y,z,nadj,p,p1,p2,p3,q,r,w;
__int32_t i,hx,ix;
 
GET_FLOAT_WORD(hx,x);
 
/* purge off +-inf, NaN, +-0, and negative arguments */
*signgamp = 1;
ix = hx&0x7fffffff;
if(ix>=0x7f800000) return x*x;
if(ix==0) return one/zero;
if(ix<0x1c800000) { /* |x|<2**-70, return -log(|x|) */
if(hx<0) {
*signgamp = -1;
return -__ieee754_logf(-x);
} else return -__ieee754_logf(x);
}
if(hx<0) {
if(ix>=0x4b000000) /* |x|>=2**23, must be -integer */
return one/zero;
t = sin_pif(x);
if(t==zero) return one/zero; /* -integer */
nadj = __ieee754_logf(pi/fabsf(t*x));
if(t<zero) *signgamp = -1;
x = -x;
}
 
/* purge off 1 and 2 */
if (ix==0x3f800000||ix==0x40000000) r = 0;
/* for x < 2.0 */
else if(ix<0x40000000) {
if(ix<=0x3f666666) { /* lgamma(x) = lgamma(x+1)-log(x) */
r = -__ieee754_logf(x);
if(ix>=0x3f3b4a20) {y = one-x; i= 0;}
else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;}
else {y = x; i=2;}
} else {
r = zero;
if(ix>=0x3fdda618) {y=(float)2.0-x;i=0;} /* [1.7316,2] */
else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */
else {y=x-one;i=2;}
}
switch(i) {
case 0:
z = y*y;
p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10))));
p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11)))));
p = y*p1+p2;
r += (p-(float)0.5*y); break;
case 1:
z = y*y;
w = z*y;
p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */
p2 = t1+w*(t4+w*(t7+w*(t10+w*t13)));
p3 = t2+w*(t5+w*(t8+w*(t11+w*t14)));
p = z*p1-(tt-w*(p2+y*p3));
r += (tf + p); break;
case 2:
p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5)))));
p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5))));
r += (-(float)0.5*y + p1/p2);
}
}
else if(ix<0x41000000) { /* x < 8.0 */
i = (__int32_t)x;
t = zero;
y = x-(float)i;
p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6))))));
q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6)))));
r = half*y+p/q;
z = one; /* lgamma(1+s) = log(s) + lgamma(s) */
switch(i) {
case 7: z *= (y+(float)6.0); /* FALLTHRU */
case 6: z *= (y+(float)5.0); /* FALLTHRU */
case 5: z *= (y+(float)4.0); /* FALLTHRU */
case 4: z *= (y+(float)3.0); /* FALLTHRU */
case 3: z *= (y+(float)2.0); /* FALLTHRU */
r += __ieee754_logf(z); break;
}
/* 8.0 <= x < 2**58 */
} else if (ix < 0x5c800000) {
t = __ieee754_logf(x);
z = one/x;
y = z*z;
w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6)))));
r = (x-half)*(t-one)+w;
} else
/* 2**58 <= x <= inf */
r = x*(__ieee754_logf(x)-one);
if(hx<0) r = nadj - r;
return r;
}
/w_pow.c
0,0 → 1,231
 
 
/* @(#)w_pow.c 5.2 93/10/01 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
FUNCTION
<<pow>>, <<powf>>---x to the power y
INDEX
pow
INDEX
powf
 
 
ANSI_SYNOPSIS
#include <math.h>
double pow(double <[x]>, double <[y]>);
float pow(float <[x]>, float <[y]>);
 
TRAD_SYNOPSIS
#include <math.h>
double pow(<[x]>, <[y]>);
double <[x]>, <[y]>;
 
float pow(<[x]>, <[y]>);
float <[x]>, <[y]>;
 
DESCRIPTION
<<pow>> and <<powf>> calculate <[x]> raised to the exp1.0nt <[y]>.
@tex
(That is, $x^y$.)
@end tex
 
RETURNS
On success, <<pow>> and <<powf>> return the value calculated.
 
When the argument values would produce overflow, <<pow>>
returns <<HUGE_VAL>> and set <<errno>> to <<ERANGE>>. If the
argument <[x]> passed to <<pow>> or <<powf>> is a negative
noninteger, and <[y]> is also not an integer, then <<errno>>
is set to <<EDOM>>. If <[x]> and <[y]> are both 0, then
<<pow>> and <<powf>> return <<1>>.
 
You can modify error handling for these functions using <<matherr>>.
 
PORTABILITY
<<pow>> is ANSI C. <<powf>> is an extension. */
 
/*
* wrapper pow(x,y) return x**y
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double pow(double x, double y) /* wrapper pow */
#else
double pow(x,y) /* wrapper pow */
double x,y;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_pow(x,y);
#else
double z;
#ifndef HUGE_VAL
#define HUGE_VAL inf
double inf = 0.0;
 
SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */
#endif
struct exception exc;
z=__ieee754_pow(x,y);
if(_LIB_VERSION == _IEEE_|| isnan(y)) return z;
if(isnan(x)) {
if(y==0.0) {
/* pow(NaN,0.0) */
/* error only if _LIB_VERSION == _SVID_ & _XOPEN_ */
exc.type = DOMAIN;
exc.name = "pow";
exc.err = 0;
exc.arg1 = x;
exc.arg2 = y;
exc.retval = x;
if (_LIB_VERSION == _IEEE_ ||
_LIB_VERSION == _POSIX_) exc.retval = 1.0;
else if (!matherr(&exc)) {
errno = EDOM;
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
} else
return z;
}
if(x==0.0){
if(y==0.0) {
/* pow(0.0,0.0) */
/* error only if _LIB_VERSION == _SVID_ */
exc.type = DOMAIN;
exc.name = "pow";
exc.err = 0;
exc.arg1 = x;
exc.arg2 = y;
exc.retval = 0.0;
if (_LIB_VERSION != _SVID_) exc.retval = 1.0;
else if (!matherr(&exc)) {
errno = EDOM;
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
}
if(finite(y)&&y<0.0) {
/* 0**neg */
exc.type = DOMAIN;
exc.name = "pow";
exc.err = 0;
exc.arg1 = x;
exc.arg2 = y;
if (_LIB_VERSION == _SVID_)
exc.retval = 0.0;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
}
return z;
}
if(!finite(z)) {
if(finite(x)&&finite(y)) {
if(isnan(z)) {
/* neg**non-integral */
exc.type = DOMAIN;
exc.name = "pow";
exc.err = 0;
exc.arg1 = x;
exc.arg2 = y;
if (_LIB_VERSION == _SVID_)
exc.retval = 0.0;
else
exc.retval = 0.0/0.0; /* X/Open allow NaN */
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
} else {
/* pow(x,y) overflow */
exc.type = OVERFLOW;
exc.name = "pow";
exc.err = 0;
exc.arg1 = x;
exc.arg2 = y;
if (_LIB_VERSION == _SVID_) {
exc.retval = HUGE;
y *= 0.5;
if(x<0.0&&rint(y)!=y) exc.retval = -HUGE;
} else {
exc.retval = HUGE_VAL;
y *= 0.5;
if(x<0.0&&rint(y)!=y) exc.retval = -HUGE_VAL;
}
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
}
}
}
if(z==0.0&&finite(x)&&finite(y)) {
/* pow(x,y) underflow */
exc.type = UNDERFLOW;
exc.name = "pow";
exc.err = 0;
exc.arg1 = x;
exc.arg2 = y;
exc.retval = 0.0;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
}
return z;
#endif
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
 
 
 
 
 
 
 
 
 
 
 
 
 
 
/ef_fmod.c
0,0 → 1,113
/* ef_fmod.c -- float version of e_fmod.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
* __ieee754_fmodf(x,y)
* Return x mod y in exact arithmetic
* Method: shift and subtract
*/
 
#include "fdlibm.h"
 
#ifdef __STDC__
static const float one = 1.0, Zero[] = {0.0, -0.0,};
#else
static float one = 1.0, Zero[] = {0.0, -0.0,};
#endif
 
#ifdef __STDC__
float __ieee754_fmodf(float x, float y)
#else
float __ieee754_fmodf(x,y)
float x,y ;
#endif
{
__int32_t n,hx,hy,hz,ix,iy,sx,i;
 
GET_FLOAT_WORD(hx,x);
GET_FLOAT_WORD(hy,y);
sx = hx&0x80000000; /* sign of x */
hx ^=sx; /* |x| */
hy &= 0x7fffffff; /* |y| */
 
/* purge off exception values */
if(FLT_UWORD_IS_ZERO(hy)||
!FLT_UWORD_IS_FINITE(hx)||
FLT_UWORD_IS_NAN(hy))
return (x*y)/(x*y);
if(hx<hy) return x; /* |x|<|y| return x */
if(hx==hy)
return Zero[(__uint32_t)sx>>31]; /* |x|=|y| return x*0*/
 
/* Note: y cannot be zero if we reach here. */
 
/* determine ix = ilogb(x) */
if(FLT_UWORD_IS_SUBNORMAL(hx)) { /* subnormal x */
for (ix = -126,i=(hx<<8); i>0; i<<=1) ix -=1;
} else ix = (hx>>23)-127;
 
/* determine iy = ilogb(y) */
if(FLT_UWORD_IS_SUBNORMAL(hy)) { /* subnormal y */
for (iy = -126,i=(hy<<8); i>=0; i<<=1) iy -=1;
} else iy = (hy>>23)-127;
 
/* set up {hx,lx}, {hy,ly} and align y to x */
if(ix >= -126)
hx = 0x00800000|(0x007fffff&hx);
else { /* subnormal x, shift x to normal */
n = -126-ix;
hx = hx<<n;
}
if(iy >= -126)
hy = 0x00800000|(0x007fffff&hy);
else { /* subnormal y, shift y to normal */
n = -126-iy;
hy = hy<<n;
}
 
/* fix point fmod */
n = ix - iy;
while(n--) {
hz=hx-hy;
if(hz<0){hx = hx+hx;}
else {
if(hz==0) /* return sign(x)*0 */
return Zero[(__uint32_t)sx>>31];
hx = hz+hz;
}
}
hz=hx-hy;
if(hz>=0) {hx=hz;}
 
/* convert back to floating value and restore the sign */
if(hx==0) /* return sign(x)*0 */
return Zero[(__uint32_t)sx>>31];
while(hx<0x00800000) { /* normalize x */
hx = hx+hx;
iy -= 1;
}
if(iy>= -126) { /* normalize output */
hx = ((hx-0x00800000)|((iy+127)<<23));
SET_FLOAT_WORD(x,hx|sx);
} else { /* subnormal output */
/* If denormals are not supported, this code will generate a
zero representation. */
n = -126 - iy;
hx >>= n;
SET_FLOAT_WORD(x,hx|sx);
x *= one; /* create necessary signal */
}
return x; /* exact output */
}
/e_acosh.c
0,0 → 1,70
 
/* @(#)e_acosh.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
 
/* __ieee754_acosh(x)
* Method :
* Based on
* acosh(x) = log [ x + sqrt(x*x-1) ]
* we have
* acosh(x) := log(x)+ln2, if x is large; else
* acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
* acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
*
* Special cases:
* acosh(x) is NaN with signal if x<1.
* acosh(NaN) is NaN without signal.
*/
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
static const double
#else
static double
#endif
one = 1.0,
ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */
 
#ifdef __STDC__
double __ieee754_acosh(double x)
#else
double __ieee754_acosh(x)
double x;
#endif
{
double t;
__int32_t hx;
__uint32_t lx;
EXTRACT_WORDS(hx,lx,x);
if(hx<0x3ff00000) { /* x < 1 */
return (x-x)/(x-x);
} else if(hx >=0x41b00000) { /* x > 2**28 */
if(hx >=0x7ff00000) { /* x is inf of NaN */
return x+x;
} else
return __ieee754_log(x)+ln2; /* acosh(huge)=log(2x) */
} else if(((hx-0x3ff00000)|lx)==0) {
return 0.0; /* acosh(1) = 0 */
} else if (hx > 0x40000000) { /* 2**28 > x > 2 */
t=x*x;
return __ieee754_log(2.0*x-one/(x+__ieee754_sqrt(t-one)));
} else { /* 1<x<2 */
t = x-one;
return log1p(t+__ieee754_sqrt(2.0*t+t*t));
}
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/Makefile.in
0,0 → 1,564
# Makefile.in generated automatically by automake 1.4 from Makefile.am
 
# Copyright (C) 1994, 1995-8, 1999 Free Software Foundation, Inc.
# This Makefile.in is free software; the Free Software Foundation
# gives unlimited permission to copy and/or distribute it,
# with or without modifications, as long as this notice is preserved.
 
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY, to the extent permitted by law; without
# even the implied warranty of MERCHANTABILITY or FITNESS FOR A
# PARTICULAR PURPOSE.
 
 
 
SHELL = @SHELL@
 
srcdir = @srcdir@
top_srcdir = @top_srcdir@
VPATH = @srcdir@
prefix = @prefix@
exec_prefix = @exec_prefix@
 
bindir = @bindir@
sbindir = @sbindir@
libexecdir = @libexecdir@
datadir = @datadir@
sysconfdir = @sysconfdir@
sharedstatedir = @sharedstatedir@
localstatedir = @localstatedir@
libdir = @libdir@
infodir = @infodir@
mandir = @mandir@
includedir = @includedir@
oldincludedir = /usr/include
 
DESTDIR =
 
pkgdatadir = $(datadir)/@PACKAGE@
pkglibdir = $(libdir)/@PACKAGE@
pkgincludedir = $(includedir)/@PACKAGE@
 
top_builddir = ..
 
ACLOCAL = @ACLOCAL@
AUTOCONF = @AUTOCONF@
AUTOMAKE = @AUTOMAKE@
AUTOHEADER = @AUTOHEADER@
 
INSTALL = @INSTALL@
INSTALL_PROGRAM = @INSTALL_PROGRAM@ $(AM_INSTALL_PROGRAM_FLAGS)
INSTALL_DATA = @INSTALL_DATA@
INSTALL_SCRIPT = @INSTALL_SCRIPT@
transform = @program_transform_name@
 
NORMAL_INSTALL = :
PRE_INSTALL = :
POST_INSTALL = :
NORMAL_UNINSTALL = :
PRE_UNINSTALL = :
POST_UNINSTALL = :
host_alias = @host_alias@
host_triplet = @host@
AR = @AR@
AS = @AS@
CC = @CC@
CPP = @CPP@
DLLTOOL = @DLLTOOL@
EXEEXT = @EXEEXT@
LDFLAGS = @LDFLAGS@
LIBM_MACHINE_LIB = @LIBM_MACHINE_LIB@
LIBTOOL = @LIBTOOL@
LN_S = @LN_S@
MAINT = @MAINT@
MAKEINFO = @MAKEINFO@
NEWLIB_CFLAGS = @NEWLIB_CFLAGS@
OBJDUMP = @OBJDUMP@
PACKAGE = @PACKAGE@
RANLIB = @RANLIB@
VERSION = @VERSION@
aext = @aext@
libm_machine_dir = @libm_machine_dir@
machine_dir = @machine_dir@
newlib_basedir = @newlib_basedir@
oext = @oext@
sys_dir = @sys_dir@
 
AUTOMAKE_OPTIONS = cygnus
 
INCLUDES = -I$(srcdir)/../common $(NEWLIB_CFLAGS) $(CROSS_CFLAGS) $(TARGET_CFLAGS)
 
src = k_standard.c k_rem_pio2.c \
k_cos.c k_sin.c k_tan.c \
e_acos.c e_acosh.c e_asin.c e_atan2.c \
e_atanh.c e_cosh.c e_exp.c e_fmod.c \
er_gamma.c e_hypot.c e_j0.c \
e_j1.c e_jn.c er_lgamma.c \
e_log.c e_log10.c e_pow.c e_rem_pio2.c e_remainder.c \
e_scalb.c e_sinh.c e_sqrt.c \
w_acos.c w_acosh.c w_asin.c w_atan2.c \
w_atanh.c w_cosh.c w_exp.c w_fmod.c \
w_gamma.c wr_gamma.c w_hypot.c w_j0.c \
w_j1.c w_jn.c w_lgamma.c wr_lgamma.c \
w_log.c w_log10.c w_pow.c w_remainder.c \
w_scalb.c w_sinh.c w_sqrt.c \
w_cabs.c w_drem.c \
s_asinh.c s_atan.c s_ceil.c \
s_cos.c s_erf.c s_fabs.c s_floor.c \
s_frexp.c s_isnan.c s_ldexp.c \
s_signif.c s_sin.c \
s_tan.c s_tanh.c \
s_isinf.c s_infconst.c
 
 
fsrc = kf_rem_pio2.c \
kf_cos.c kf_sin.c kf_tan.c \
ef_acos.c ef_acosh.c ef_asin.c ef_atan2.c \
ef_atanh.c ef_cosh.c ef_exp.c ef_fmod.c \
erf_gamma.c ef_hypot.c ef_j0.c \
ef_j1.c ef_jn.c erf_lgamma.c \
ef_log.c ef_log10.c ef_pow.c ef_rem_pio2.c ef_remainder.c \
ef_scalb.c ef_sinh.c ef_sqrt.c \
wf_acos.c wf_acosh.c wf_asin.c wf_atan2.c \
wf_atanh.c wf_cosh.c wf_exp.c wf_fmod.c \
wf_gamma.c wrf_gamma.c wf_hypot.c wf_j0.c \
wf_j1.c wf_jn.c wf_lgamma.c wrf_lgamma.c \
wf_log.c wf_log10.c wf_pow.c wf_remainder.c \
wf_scalb.c wf_sinh.c wf_sqrt.c \
wf_cabs.c wf_drem.c \
sf_asinh.c sf_atan.c sf_ceil.c \
sf_cos.c sf_erf.c sf_fabs.c sf_floor.c \
sf_frexp.c sf_isnan.c sf_ldexp.c \
sf_signif.c sf_sin.c \
sf_tan.c sf_tanh.c \
sf_isinf.c
 
 
libmath_la_LDFLAGS = -Xcompiler -nostdlib
 
@USE_LIBTOOL_TRUE@noinst_LTLIBRARIES = @USE_LIBTOOL_TRUE@libmath.la
@USE_LIBTOOL_TRUE@libmath_la_SOURCES = @USE_LIBTOOL_TRUE@$(src) $(fsrc)
@USE_LIBTOOL_TRUE@noinst_DATA = @USE_LIBTOOL_TRUE@objectlist.awk.in
@USE_LIBTOOL_FALSE@noinst_DATA =
@USE_LIBTOOL_FALSE@noinst_LIBRARIES = @USE_LIBTOOL_FALSE@lib.a
@USE_LIBTOOL_FALSE@lib_a_SOURCES = @USE_LIBTOOL_FALSE@$(src) $(fsrc)
 
chobj = wacos.def wacosh.def wasin.def sasinh.def \
satan.def watan2.def watanh.def wj0.def \
wcosh.def serf.def wexp.def \
sfabs.def sfloor.def wfmod.def sfrexp.def \
wgamma.def whypot.def sldexp.def wlog.def \
wlog10.def \
wpow.def wremainder.def ssin.def wsinh.def \
wsqrt.def stan.def stanh.def \
sisnan.def
 
 
SUFFIXES = .def
 
CHEW = ../../doc/makedoc -f $(srcdir)/../../doc/doc.str
 
TARGETDOC = ../tmp.texi
 
CLEANFILES = $(chobj) *.ref
mkinstalldirs = $(SHELL) $(top_srcdir)/../../mkinstalldirs
CONFIG_CLEAN_FILES =
LIBRARIES = $(noinst_LIBRARIES)
 
 
DEFS = @DEFS@ -I. -I$(srcdir)
CPPFLAGS = @CPPFLAGS@
LIBS = @LIBS@
lib_a_LIBADD =
@USE_LIBTOOL_FALSE@lib_a_OBJECTS = k_standard.o k_rem_pio2.o k_cos.o \
@USE_LIBTOOL_FALSE@k_sin.o k_tan.o e_acos.o e_acosh.o e_asin.o \
@USE_LIBTOOL_FALSE@e_atan2.o e_atanh.o e_cosh.o e_exp.o e_fmod.o \
@USE_LIBTOOL_FALSE@er_gamma.o e_hypot.o e_j0.o e_j1.o e_jn.o \
@USE_LIBTOOL_FALSE@er_lgamma.o e_log.o e_log10.o e_pow.o e_rem_pio2.o \
@USE_LIBTOOL_FALSE@e_remainder.o e_scalb.o e_sinh.o e_sqrt.o w_acos.o \
@USE_LIBTOOL_FALSE@w_acosh.o w_asin.o w_atan2.o w_atanh.o w_cosh.o \
@USE_LIBTOOL_FALSE@w_exp.o w_fmod.o w_gamma.o wr_gamma.o w_hypot.o \
@USE_LIBTOOL_FALSE@w_j0.o w_j1.o w_jn.o w_lgamma.o wr_lgamma.o w_log.o \
@USE_LIBTOOL_FALSE@w_log10.o w_pow.o w_remainder.o w_scalb.o w_sinh.o \
@USE_LIBTOOL_FALSE@w_sqrt.o w_cabs.o w_drem.o s_asinh.o s_atan.o \
@USE_LIBTOOL_FALSE@s_ceil.o s_cos.o s_erf.o s_fabs.o s_floor.o \
@USE_LIBTOOL_FALSE@s_frexp.o s_isnan.o s_ldexp.o s_signif.o s_sin.o \
@USE_LIBTOOL_FALSE@s_tan.o s_tanh.o s_isinf.o s_infconst.o \
@USE_LIBTOOL_FALSE@kf_rem_pio2.o kf_cos.o kf_sin.o kf_tan.o ef_acos.o \
@USE_LIBTOOL_FALSE@ef_acosh.o ef_asin.o ef_atan2.o ef_atanh.o ef_cosh.o \
@USE_LIBTOOL_FALSE@ef_exp.o ef_fmod.o erf_gamma.o ef_hypot.o ef_j0.o \
@USE_LIBTOOL_FALSE@ef_j1.o ef_jn.o erf_lgamma.o ef_log.o ef_log10.o \
@USE_LIBTOOL_FALSE@ef_pow.o ef_rem_pio2.o ef_remainder.o ef_scalb.o \
@USE_LIBTOOL_FALSE@ef_sinh.o ef_sqrt.o wf_acos.o wf_acosh.o wf_asin.o \
@USE_LIBTOOL_FALSE@wf_atan2.o wf_atanh.o wf_cosh.o wf_exp.o wf_fmod.o \
@USE_LIBTOOL_FALSE@wf_gamma.o wrf_gamma.o wf_hypot.o wf_j0.o wf_j1.o \
@USE_LIBTOOL_FALSE@wf_jn.o wf_lgamma.o wrf_lgamma.o wf_log.o wf_log10.o \
@USE_LIBTOOL_FALSE@wf_pow.o wf_remainder.o wf_scalb.o wf_sinh.o \
@USE_LIBTOOL_FALSE@wf_sqrt.o wf_cabs.o wf_drem.o sf_asinh.o sf_atan.o \
@USE_LIBTOOL_FALSE@sf_ceil.o sf_cos.o sf_erf.o sf_fabs.o sf_floor.o \
@USE_LIBTOOL_FALSE@sf_frexp.o sf_isnan.o sf_ldexp.o sf_signif.o \
@USE_LIBTOOL_FALSE@sf_sin.o sf_tan.o sf_tanh.o sf_isinf.o
LTLIBRARIES = $(noinst_LTLIBRARIES)
 
libmath_la_LIBADD =
@USE_LIBTOOL_TRUE@libmath_la_OBJECTS = k_standard.lo k_rem_pio2.lo \
@USE_LIBTOOL_TRUE@k_cos.lo k_sin.lo k_tan.lo e_acos.lo e_acosh.lo \
@USE_LIBTOOL_TRUE@e_asin.lo e_atan2.lo e_atanh.lo e_cosh.lo e_exp.lo \
@USE_LIBTOOL_TRUE@e_fmod.lo er_gamma.lo e_hypot.lo e_j0.lo e_j1.lo \
@USE_LIBTOOL_TRUE@e_jn.lo er_lgamma.lo e_log.lo e_log10.lo e_pow.lo \
@USE_LIBTOOL_TRUE@e_rem_pio2.lo e_remainder.lo e_scalb.lo e_sinh.lo \
@USE_LIBTOOL_TRUE@e_sqrt.lo w_acos.lo w_acosh.lo w_asin.lo w_atan2.lo \
@USE_LIBTOOL_TRUE@w_atanh.lo w_cosh.lo w_exp.lo w_fmod.lo w_gamma.lo \
@USE_LIBTOOL_TRUE@wr_gamma.lo w_hypot.lo w_j0.lo w_j1.lo w_jn.lo \
@USE_LIBTOOL_TRUE@w_lgamma.lo wr_lgamma.lo w_log.lo w_log10.lo w_pow.lo \
@USE_LIBTOOL_TRUE@w_remainder.lo w_scalb.lo w_sinh.lo w_sqrt.lo \
@USE_LIBTOOL_TRUE@w_cabs.lo w_drem.lo s_asinh.lo s_atan.lo s_ceil.lo \
@USE_LIBTOOL_TRUE@s_cos.lo s_erf.lo s_fabs.lo s_floor.lo s_frexp.lo \
@USE_LIBTOOL_TRUE@s_isnan.lo s_ldexp.lo s_signif.lo s_sin.lo s_tan.lo \
@USE_LIBTOOL_TRUE@s_tanh.lo s_isinf.lo s_infconst.lo kf_rem_pio2.lo \
@USE_LIBTOOL_TRUE@kf_cos.lo kf_sin.lo kf_tan.lo ef_acos.lo ef_acosh.lo \
@USE_LIBTOOL_TRUE@ef_asin.lo ef_atan2.lo ef_atanh.lo ef_cosh.lo \
@USE_LIBTOOL_TRUE@ef_exp.lo ef_fmod.lo erf_gamma.lo ef_hypot.lo \
@USE_LIBTOOL_TRUE@ef_j0.lo ef_j1.lo ef_jn.lo erf_lgamma.lo ef_log.lo \
@USE_LIBTOOL_TRUE@ef_log10.lo ef_pow.lo ef_rem_pio2.lo ef_remainder.lo \
@USE_LIBTOOL_TRUE@ef_scalb.lo ef_sinh.lo ef_sqrt.lo wf_acos.lo \
@USE_LIBTOOL_TRUE@wf_acosh.lo wf_asin.lo wf_atan2.lo wf_atanh.lo \
@USE_LIBTOOL_TRUE@wf_cosh.lo wf_exp.lo wf_fmod.lo wf_gamma.lo \
@USE_LIBTOOL_TRUE@wrf_gamma.lo wf_hypot.lo wf_j0.lo wf_j1.lo wf_jn.lo \
@USE_LIBTOOL_TRUE@wf_lgamma.lo wrf_lgamma.lo wf_log.lo wf_log10.lo \
@USE_LIBTOOL_TRUE@wf_pow.lo wf_remainder.lo wf_scalb.lo wf_sinh.lo \
@USE_LIBTOOL_TRUE@wf_sqrt.lo wf_cabs.lo wf_drem.lo sf_asinh.lo \
@USE_LIBTOOL_TRUE@sf_atan.lo sf_ceil.lo sf_cos.lo sf_erf.lo sf_fabs.lo \
@USE_LIBTOOL_TRUE@sf_floor.lo sf_frexp.lo sf_isnan.lo sf_ldexp.lo \
@USE_LIBTOOL_TRUE@sf_signif.lo sf_sin.lo sf_tan.lo sf_tanh.lo \
@USE_LIBTOOL_TRUE@sf_isinf.lo
CFLAGS = @CFLAGS@
COMPILE = $(CC) $(DEFS) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(AM_CFLAGS) $(CFLAGS)
LTCOMPILE = $(LIBTOOL) --mode=compile $(CC) $(DEFS) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(AM_CFLAGS) $(CFLAGS)
CCLD = $(CC)
LINK = $(LIBTOOL) --mode=link $(CCLD) $(AM_CFLAGS) $(CFLAGS) $(LDFLAGS) -o $@
DATA = $(noinst_DATA)
 
DIST_COMMON = Makefile.am Makefile.in
 
 
DISTFILES = $(DIST_COMMON) $(SOURCES) $(HEADERS) $(TEXINFOS) $(EXTRA_DIST)
 
TAR = gtar
GZIP_ENV = --best
SOURCES = $(lib_a_SOURCES) $(libmath_la_SOURCES)
OBJECTS = $(lib_a_OBJECTS) $(libmath_la_OBJECTS)
 
all: all-redirect
.SUFFIXES:
.SUFFIXES: .S .c .def .lo .o .s
$(srcdir)/Makefile.in: @MAINTAINER_MODE_TRUE@ Makefile.am $(top_srcdir)/configure.in $(ACLOCAL_M4) $(srcdir)/../../Makefile.shared
cd $(top_srcdir) && $(AUTOMAKE) --cygnus math/Makefile
 
Makefile: $(srcdir)/Makefile.in $(top_builddir)/config.status
cd $(top_builddir) \
&& CONFIG_FILES=$(subdir)/$@ CONFIG_HEADERS= $(SHELL) ./config.status
 
 
mostlyclean-noinstLIBRARIES:
 
clean-noinstLIBRARIES:
-test -z "$(noinst_LIBRARIES)" || rm -f $(noinst_LIBRARIES)
 
distclean-noinstLIBRARIES:
 
maintainer-clean-noinstLIBRARIES:
 
.c.o:
$(COMPILE) -c $<
 
.s.o:
$(COMPILE) -c $<
 
.S.o:
$(COMPILE) -c $<
 
mostlyclean-compile:
-rm -f *.o core *.core
 
clean-compile:
 
distclean-compile:
-rm -f *.tab.c
 
maintainer-clean-compile:
 
.c.lo:
$(LIBTOOL) --mode=compile $(COMPILE) -c $<
 
.s.lo:
$(LIBTOOL) --mode=compile $(COMPILE) -c $<
 
.S.lo:
$(LIBTOOL) --mode=compile $(COMPILE) -c $<
 
mostlyclean-libtool:
-rm -f *.lo
 
clean-libtool:
-rm -rf .libs _libs
 
distclean-libtool:
 
maintainer-clean-libtool:
 
lib.a: $(lib_a_OBJECTS) $(lib_a_DEPENDENCIES)
-rm -f lib.a
$(AR) cru lib.a $(lib_a_OBJECTS) $(lib_a_LIBADD)
$(RANLIB) lib.a
 
mostlyclean-noinstLTLIBRARIES:
 
clean-noinstLTLIBRARIES:
-test -z "$(noinst_LTLIBRARIES)" || rm -f $(noinst_LTLIBRARIES)
 
distclean-noinstLTLIBRARIES:
 
maintainer-clean-noinstLTLIBRARIES:
 
libmath.la: $(libmath_la_OBJECTS) $(libmath_la_DEPENDENCIES)
$(LINK) $(libmath_la_LDFLAGS) $(libmath_la_OBJECTS) $(libmath_la_LIBADD) $(LIBS)
 
tags: TAGS
 
ID: $(HEADERS) $(SOURCES) $(LISP)
list='$(SOURCES) $(HEADERS)'; \
unique=`for i in $$list; do echo $$i; done | \
awk ' { files[$$0] = 1; } \
END { for (i in files) print i; }'`; \
here=`pwd` && cd $(srcdir) \
&& mkid -f$$here/ID $$unique $(LISP)
 
TAGS: $(HEADERS) $(SOURCES) $(TAGS_DEPENDENCIES) $(LISP)
tags=; \
here=`pwd`; \
list='$(SOURCES) $(HEADERS)'; \
unique=`for i in $$list; do echo $$i; done | \
awk ' { files[$$0] = 1; } \
END { for (i in files) print i; }'`; \
test -z "$(ETAGS_ARGS)$$unique$(LISP)$$tags" \
|| (cd $(srcdir) && etags $(ETAGS_ARGS) $$tags $$unique $(LISP) -o $$here/TAGS)
 
mostlyclean-tags:
 
clean-tags:
 
distclean-tags:
-rm -f TAGS ID
 
maintainer-clean-tags:
 
distdir = $(top_builddir)/$(PACKAGE)-$(VERSION)/$(subdir)
 
subdir = math
 
distdir: $(DISTFILES)
@for file in $(DISTFILES); do \
if test -f $$file; then d=.; else d=$(srcdir); fi; \
if test -d $$d/$$file; then \
cp -pr $$d/$$file $(distdir)/$$file; \
else \
test -f $(distdir)/$$file \
|| ln $$d/$$file $(distdir)/$$file 2> /dev/null \
|| cp -p $$d/$$file $(distdir)/$$file || :; \
fi; \
done
info-am:
info: info-am
dvi-am:
dvi: dvi-am
check-am:
check: check-am
installcheck-am:
installcheck: installcheck-am
install-info-am:
install-info: install-info-am
install-exec-am:
install-exec: install-exec-am
 
install-data-am:
install-data: install-data-am
 
install-am: all-am
@$(MAKE) $(AM_MAKEFLAGS) install-exec-am install-data-am
install: install-am
uninstall-am:
uninstall: uninstall-am
all-am: Makefile $(LIBRARIES) $(LTLIBRARIES) $(DATA)
all-redirect: all-am
install-strip:
$(MAKE) $(AM_MAKEFLAGS) AM_INSTALL_PROGRAM_FLAGS=-s install
installdirs:
 
 
mostlyclean-generic:
 
clean-generic:
-test -z "$(CLEANFILES)" || rm -f $(CLEANFILES)
 
distclean-generic:
-rm -f Makefile $(CONFIG_CLEAN_FILES)
-rm -f config.cache config.log stamp-h stamp-h[0-9]*
 
maintainer-clean-generic:
mostlyclean-am: mostlyclean-noinstLIBRARIES mostlyclean-compile \
mostlyclean-libtool mostlyclean-noinstLTLIBRARIES \
mostlyclean-tags mostlyclean-generic
 
mostlyclean: mostlyclean-am
 
clean-am: clean-noinstLIBRARIES clean-compile clean-libtool \
clean-noinstLTLIBRARIES clean-tags clean-generic \
mostlyclean-am
 
clean: clean-am
 
distclean-am: distclean-noinstLIBRARIES distclean-compile \
distclean-libtool distclean-noinstLTLIBRARIES \
distclean-tags distclean-generic clean-am
-rm -f libtool
 
distclean: distclean-am
 
maintainer-clean-am: maintainer-clean-noinstLIBRARIES \
maintainer-clean-compile maintainer-clean-libtool \
maintainer-clean-noinstLTLIBRARIES \
maintainer-clean-tags maintainer-clean-generic \
distclean-am
@echo "This command is intended for maintainers to use;"
@echo "it deletes files that may require special tools to rebuild."
 
maintainer-clean: maintainer-clean-am
 
.PHONY: mostlyclean-noinstLIBRARIES distclean-noinstLIBRARIES \
clean-noinstLIBRARIES maintainer-clean-noinstLIBRARIES \
mostlyclean-compile distclean-compile clean-compile \
maintainer-clean-compile mostlyclean-libtool distclean-libtool \
clean-libtool maintainer-clean-libtool mostlyclean-noinstLTLIBRARIES \
distclean-noinstLTLIBRARIES clean-noinstLTLIBRARIES \
maintainer-clean-noinstLTLIBRARIES tags mostlyclean-tags distclean-tags \
clean-tags maintainer-clean-tags distdir info-am info dvi-am dvi check \
check-am installcheck-am installcheck install-info-am install-info \
install-exec-am install-exec install-data-am install-data install-am \
install uninstall-am uninstall all-redirect all-am all installdirs \
mostlyclean-generic distclean-generic clean-generic \
maintainer-clean-generic clean mostlyclean distclean maintainer-clean
 
 
objectlist.awk.in: $(noinst_LTLIBRARIES)
-rm -f objectlist.awk.in
for i in `ls *.lo` ; \
do \
echo $$i `pwd`/$$i >> objectlist.awk.in ; \
done
 
.c.def:
$(CHEW) < $< > $*.def 2> $*.ref
touch stmp-def
 
doc: $(chobj)
cat $(srcdir)/math.tex >> $(TARGETDOC)
 
# Texinfo does not appear to support underscores in file names, so we
# name the .def files without underscores.
 
wacos.def: w_acos.c
$(CHEW) < $(srcdir)/w_acos.c >$@ 2>/dev/null
touch stmp-def
wacosh.def: w_acosh.c
$(CHEW) < $(srcdir)/w_acosh.c >$@ 2>/dev/null
touch stmp-def
wasin.def: w_asin.c
$(CHEW) < $(srcdir)/w_asin.c >$@ 2>/dev/null
touch stmp-def
sasinh.def: s_asinh.c
$(CHEW) < $(srcdir)/s_asinh.c >$@ 2>/dev/null
touch stmp-def
satan.def: s_atan.c
$(CHEW) < $(srcdir)/s_atan.c >$@ 2>/dev/null
touch stmp-def
watan2.def: w_atan2.c
$(CHEW) < $(srcdir)/w_atan2.c >$@ 2>/dev/null
touch stmp-def
watanh.def: w_atanh.c
$(CHEW) < $(srcdir)/w_atanh.c >$@ 2>/dev/null
touch stmp-def
wj0.def: w_j0.c
$(CHEW) < $(srcdir)/w_j0.c >$@ 2>/dev/null
touch stmp-def
scopysign.def: s_copysign.c
$(CHEW) < $(srcdir)/../common/s_copysign.c >$@ 2>/dev/null
touch stmp-def
wcosh.def: w_cosh.c
$(CHEW) < $(srcdir)/w_cosh.c >$@ 2>/dev/null
touch stmp-def
serf.def: s_erf.c
$(CHEW) < $(srcdir)/s_erf.c >$@ 2>/dev/null
touch stmp-def
wexp.def: w_exp.c
$(CHEW) < $(srcdir)/w_exp.c >$@ 2>/dev/null
touch stmp-def
sfabs.def: s_fabs.c
$(CHEW) < $(srcdir)/s_fabs.c >$@ 2>/dev/null
touch stmp-def
sfloor.def: s_floor.c
$(CHEW) < $(srcdir)/s_floor.c >$@ 2>/dev/null
touch stmp-def
wfmod.def: w_fmod.c
$(CHEW) < $(srcdir)/w_fmod.c >$@ 2>/dev/null
touch stmp-def
sfrexp.def: s_frexp.c
$(CHEW) < $(srcdir)/s_frexp.c >$@ 2>/dev/null
touch stmp-def
wgamma.def: w_gamma.c
$(CHEW) < $(srcdir)/w_gamma.c >$@ 2>/dev/null
touch stmp-def
whypot.def: w_hypot.c
$(CHEW) < $(srcdir)/w_hypot.c >$@ 2>/dev/null
touch stmp-def
sldexp.def: s_ldexp.c
$(CHEW) < $(srcdir)/s_ldexp.c >$@ 2>/dev/null
touch stmp-def
wlog.def: w_log.c
$(CHEW) < $(srcdir)/w_log.c >$@ 2>/dev/null
touch stmp-def
wlog10.def: w_log10.c
$(CHEW) < $(srcdir)/w_log10.c >$@ 2>/dev/null
touch stmp-def
wpow.def: w_pow.c
$(CHEW) < $(srcdir)/w_pow.c >$@ 2>/dev/null
touch stmp-def
wremainder.def: w_remainder.c
$(CHEW) < $(srcdir)/w_remainder.c >$@ 2>/dev/null
touch stmp-def
ssin.def: s_sin.c
$(CHEW) < $(srcdir)/s_sin.c >$@ 2>/dev/null
touch stmp-def
wsinh.def: w_sinh.c
$(CHEW) < $(srcdir)/w_sinh.c >$@ 2>/dev/null
touch stmp-def
wsqrt.def: w_sqrt.c
$(CHEW) < $(srcdir)/w_sqrt.c >$@ 2>/dev/null
touch stmp-def
stan.def: s_tan.c
$(CHEW) < $(srcdir)/s_tan.c >$@ 2>/dev/null
touch stmp-def
stanh.def: s_tanh.c
$(CHEW) < $(srcdir)/s_tanh.c >$@ 2>/dev/null
touch stmp-def
sisnan.def: s_isnan.c
$(CHEW) < $(srcdir)/s_isnan.c >$@ 2>/dev/null
touch stmp-def
 
# A partial dependency list.
 
$(lib_a_OBJECTS): $(srcdir)/../../libc/include/math.h $(srcdir)/../common/fdlibm.h
 
# Tell versions [3.59,3.63) of GNU make to not export all variables.
# Otherwise a system limit (for SysV at least) may be exceeded.
.NOEXPORT:
/wf_cabs.c
0,0 → 1,20
/*
* cabsf() wrapper for hypotf().
*
* Written by J.T. Conklin, <jtc@wimsey.com>
* Placed into the Public Domain, 1994.
*/
 
#include "fdlibm.h"
 
struct complex {
float x;
float y;
};
 
float
cabsf(z)
struct complex z;
{
return hypotf(z.x, z.y);
}
/s_infconst.c
0,0 → 1,15
/* Infinity as a constant value. This is used for HUGE_VAL.
* Added by Cygnus Support.
*/
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
#ifdef __IEEE_BIG_ENDIAN
const union __dmath __infinity[1] = {{{ 0x7ff00000, 0 }}};
#else
const union __dmath __infinity[1] = {{{ 0, 0x7ff00000 }}};
#endif
#else /* defined (_DOUBLE_IS_32BITS) */
const union __dmath __infinity[1] = {{{ 0x7f800000, 0 }}};
#endif /* defined (_DOUBLE_IS_32BITS) */
/ef_exp.c
0,0 → 1,100
/* ef_exp.c -- float version of e_exp.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
#include "fdlibm.h"
 
#ifdef __v810__
#define const
#endif
 
#ifdef __STDC__
static const float
#else
static float
#endif
one = 1.0,
halF[2] = {0.5,-0.5,},
huge = 1.0e+30,
twom100 = 7.8886090522e-31, /* 2**-100=0x0d800000 */
ln2HI[2] ={ 6.9313812256e-01, /* 0x3f317180 */
-6.9313812256e-01,}, /* 0xbf317180 */
ln2LO[2] ={ 9.0580006145e-06, /* 0x3717f7d1 */
-9.0580006145e-06,}, /* 0xb717f7d1 */
invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */
P1 = 1.6666667163e-01, /* 0x3e2aaaab */
P2 = -2.7777778450e-03, /* 0xbb360b61 */
P3 = 6.6137559770e-05, /* 0x388ab355 */
P4 = -1.6533901999e-06, /* 0xb5ddea0e */
P5 = 4.1381369442e-08; /* 0x3331bb4c */
 
#ifdef __STDC__
float __ieee754_expf(float x) /* default IEEE double exp */
#else
float __ieee754_expf(x) /* default IEEE double exp */
float x;
#endif
{
float y,hi,lo,c,t;
__int32_t k,xsb,sx;
__uint32_t hx;
 
GET_FLOAT_WORD(sx,x);
xsb = (sx>>31)&1; /* sign bit of x */
hx = sx & 0x7fffffff; /* high word of |x| */
 
/* filter out non-finite argument */
if(FLT_UWORD_IS_NAN(hx))
return x+x; /* NaN */
if(FLT_UWORD_IS_INFINITE(hx))
return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */
if(sx > FLT_UWORD_LOG_MAX)
return huge*huge; /* overflow */
if(sx < 0 && hx > FLT_UWORD_LOG_MIN)
return twom100*twom100; /* underflow */
/* argument reduction */
if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
} else {
k = invln2*x+halF[xsb];
t = k;
hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
lo = t*ln2LO[0];
}
x = hi - lo;
}
else if(hx < 0x31800000) { /* when |x|<2**-28 */
if(huge+x>one) return one+x;/* trigger inexact */
}
else k = 0;
 
/* x is now in primary range */
t = x*x;
c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
if(k==0) return one-((x*c)/(c-(float)2.0)-x);
else y = one-((lo-(x*c)/((float)2.0-c))-hi);
if(k >= -125) {
__uint32_t hy;
GET_FLOAT_WORD(hy,y);
SET_FLOAT_WORD(y,hy+(k<<23)); /* add k to y's exponent */
return y;
} else {
__uint32_t hy;
GET_FLOAT_WORD(hy,y);
SET_FLOAT_WORD(y,hy+((k+100)<<23)); /* add k to y's exponent */
return y*twom100;
}
}
/ef_acosh.c
0,0 → 1,53
/* ef_acosh.c -- float version of e_acosh.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
 
#include "fdlibm.h"
 
#ifdef __STDC__
static const float
#else
static float
#endif
one = 1.0,
ln2 = 6.9314718246e-01; /* 0x3f317218 */
 
#ifdef __STDC__
float __ieee754_acoshf(float x)
#else
float __ieee754_acoshf(x)
float x;
#endif
{
float t;
__int32_t hx;
GET_FLOAT_WORD(hx,x);
if(hx<0x3f800000) { /* x < 1 */
return (x-x)/(x-x);
} else if(hx >=0x4d800000) { /* x > 2**28 */
if(!FLT_UWORD_IS_FINITE(hx)) { /* x is inf of NaN */
return x+x;
} else
return __ieee754_logf(x)+ln2; /* acosh(huge)=log(2x) */
} else if (hx==0x3f800000) {
return 0.0; /* acosh(1) = 0 */
} else if (hx > 0x40000000) { /* 2**28 > x > 2 */
t=x*x;
return __ieee754_logf((float)2.0*x-one/(x+__ieee754_sqrtf(t-one)));
} else { /* 1<x<2 */
t = x-one;
return log1pf(t+__ieee754_sqrtf((float)2.0*t+t*t));
}
}
/e_atan2.c
0,0 → 1,131
 
/* @(#)e_atan2.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
 
/* __ieee754_atan2(y,x)
* Method :
* 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
* 2. Reduce x to positive by (if x and y are unexceptional):
* ARG (x+iy) = arctan(y/x) ... if x > 0,
* ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
*
* Special cases:
*
* ATAN2((anything), NaN ) is NaN;
* ATAN2(NAN , (anything) ) is NaN;
* ATAN2(+-0, +(anything but NaN)) is +-0 ;
* ATAN2(+-0, -(anything but NaN)) is +-pi ;
* ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
* ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
* ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
* ATAN2(+-INF,+INF ) is +-pi/4 ;
* ATAN2(+-INF,-INF ) is +-3pi/4;
* ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
*
* Constants:
* The hexadecimal values are the intended ones for the following
* constants. The decimal values may be used, provided that the
* compiler will convert from decimal to binary accurately enough
* to produce the hexadecimal values shown.
*/
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
static const double
#else
static double
#endif
tiny = 1.0e-300,
zero = 0.0,
pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
 
#ifdef __STDC__
double __ieee754_atan2(double y, double x)
#else
double __ieee754_atan2(y,x)
double y,x;
#endif
{
double z;
__int32_t k,m,hx,hy,ix,iy;
__uint32_t lx,ly;
 
EXTRACT_WORDS(hx,lx,x);
ix = hx&0x7fffffff;
EXTRACT_WORDS(hy,ly,y);
iy = hy&0x7fffffff;
if(((ix|((lx|-lx)>>31))>0x7ff00000)||
((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */
return x+y;
if((hx-0x3ff00000|lx)==0) return atan(y); /* x=1.0 */
m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */
 
/* when y = 0 */
if((iy|ly)==0) {
switch(m) {
case 0:
case 1: return y; /* atan(+-0,+anything)=+-0 */
case 2: return pi+tiny;/* atan(+0,-anything) = pi */
case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
}
}
/* when x = 0 */
if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
/* when x is INF */
if(ix==0x7ff00000) {
if(iy==0x7ff00000) {
switch(m) {
case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
}
} else {
switch(m) {
case 0: return zero ; /* atan(+...,+INF) */
case 1: return -zero ; /* atan(-...,+INF) */
case 2: return pi+tiny ; /* atan(+...,-INF) */
case 3: return -pi-tiny ; /* atan(-...,-INF) */
}
}
}
/* when y is INF */
if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
 
/* compute y/x */
k = (iy-ix)>>20;
if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */
else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */
else z=atan(fabs(y/x)); /* safe to do y/x */
switch (m) {
case 0: return z ; /* atan(+,+) */
case 1: {
__uint32_t zh;
GET_HIGH_WORD(zh,z);
SET_HIGH_WORD(z,zh ^ 0x80000000);
}
return z ; /* atan(-,+) */
case 2: return pi-(z-pi_lo);/* atan(+,-) */
default: /* case 3 */
return (z-pi_lo)-pi;/* atan(-,-) */
}
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/ef_atan2.c
0,0 → 1,101
/* ef_atan2.c -- float version of e_atan2.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
 
#include "fdlibm.h"
 
#ifdef __STDC__
static const float
#else
static float
#endif
tiny = 1.0e-30,
zero = 0.0,
pi_o_4 = 7.8539818525e-01, /* 0x3f490fdb */
pi_o_2 = 1.5707963705e+00, /* 0x3fc90fdb */
pi = 3.1415925026e+00, /* 0x40490fda */
pi_lo = 1.5099578832e-07; /* 0x34222168 */
 
#ifdef __STDC__
float __ieee754_atan2f(float y, float x)
#else
float __ieee754_atan2f(y,x)
float y,x;
#endif
{
float z;
__int32_t k,m,hx,hy,ix,iy;
 
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
GET_FLOAT_WORD(hy,y);
iy = hy&0x7fffffff;
if(FLT_UWORD_IS_NAN(ix)||
FLT_UWORD_IS_NAN(iy)) /* x or y is NaN */
return x+y;
if(hx==0x3f800000) return atanf(y); /* x=1.0 */
m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */
 
/* when y = 0 */
if(FLT_UWORD_IS_ZERO(iy)) {
switch(m) {
case 0:
case 1: return y; /* atan(+-0,+anything)=+-0 */
case 2: return pi+tiny;/* atan(+0,-anything) = pi */
case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
}
}
/* when x = 0 */
if(FLT_UWORD_IS_ZERO(ix)) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
/* when x is INF */
if(FLT_UWORD_IS_INFINITE(ix)) {
if(FLT_UWORD_IS_INFINITE(iy)) {
switch(m) {
case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
case 2: return (float)3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
case 3: return (float)-3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
}
} else {
switch(m) {
case 0: return zero ; /* atan(+...,+INF) */
case 1: return -zero ; /* atan(-...,+INF) */
case 2: return pi+tiny ; /* atan(+...,-INF) */
case 3: return -pi-tiny ; /* atan(-...,-INF) */
}
}
}
/* when y is INF */
if(FLT_UWORD_IS_INFINITE(iy)) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
 
/* compute y/x */
k = (iy-ix)>>23;
if(k > 60) z=pi_o_2+(float)0.5*pi_lo; /* |y/x| > 2**60 */
else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */
else z=atanf(fabsf(y/x)); /* safe to do y/x */
switch (m) {
case 0: return z ; /* atan(+,+) */
case 1: {
__uint32_t zh;
GET_FLOAT_WORD(zh,z);
SET_FLOAT_WORD(z,zh ^ 0x80000000);
}
return z ; /* atan(-,+) */
case 2: return pi-(z-pi_lo);/* atan(+,-) */
default: /* case 3 */
return (z-pi_lo)-pi;/* atan(-,-) */
}
}
/wf_fmod.c
0,0 → 1,73
/* wf_fmod.c -- float version of w_fmod.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
* wrapper fmodf(x,y)
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifdef __STDC__
float fmodf(float x, float y) /* wrapper fmodf */
#else
float fmodf(x,y) /* wrapper fmodf */
float x,y;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_fmodf(x,y);
#else
float z;
struct exception exc;
z = __ieee754_fmodf(x,y);
if(_LIB_VERSION == _IEEE_ ||isnanf(y)||isnanf(x)) return z;
if(y==(float)0.0) {
/* fmodf(x,0) */
exc.type = DOMAIN;
exc.name = "fmodf";
exc.err = 0;
exc.arg1 = (double)x;
exc.arg2 = (double)y;
if (_LIB_VERSION == _SVID_)
exc.retval = x;
else
exc.retval = 0.0/0.0;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
if (exc.err != 0)
errno = exc.err;
return (float)exc.retval;
} else
return z;
#endif
}
 
#ifdef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double fmod(double x, double y)
#else
double fmod(x,y)
double x,y;
#endif
{
return (double) fmodf((float) x, (float) y);
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/ef_jn.c
0,0 → 1,207
/* ef_jn.c -- float version of e_jn.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
#include "fdlibm.h"
 
#ifdef __STDC__
static const float
#else
static float
#endif
invsqrtpi= 5.6418961287e-01, /* 0x3f106ebb */
two = 2.0000000000e+00, /* 0x40000000 */
one = 1.0000000000e+00; /* 0x3F800000 */
 
#ifdef __STDC__
static const float zero = 0.0000000000e+00;
#else
static float zero = 0.0000000000e+00;
#endif
 
#ifdef __STDC__
float __ieee754_jnf(int n, float x)
#else
float __ieee754_jnf(n,x)
int n; float x;
#endif
{
__int32_t i,hx,ix, sgn;
float a, b, temp, di;
float z, w;
 
/* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
* Thus, J(-n,x) = J(n,-x)
*/
GET_FLOAT_WORD(hx,x);
ix = 0x7fffffff&hx;
/* if J(n,NaN) is NaN */
if(FLT_UWORD_IS_NAN(ix)) return x+x;
if(n<0){
n = -n;
x = -x;
hx ^= 0x80000000;
}
if(n==0) return(__ieee754_j0f(x));
if(n==1) return(__ieee754_j1f(x));
sgn = (n&1)&(hx>>31); /* even n -- 0, odd n -- sign(x) */
x = fabsf(x);
if(FLT_UWORD_IS_ZERO(ix)||FLT_UWORD_IS_INFINITE(ix))
b = zero;
else if((float)n<=x) {
/* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
a = __ieee754_j0f(x);
b = __ieee754_j1f(x);
for(i=1;i<n;i++){
temp = b;
b = b*((float)(i+i)/x) - a; /* avoid underflow */
a = temp;
}
} else {
if(ix<0x30800000) { /* x < 2**-29 */
/* x is tiny, return the first Taylor expansion of J(n,x)
* J(n,x) = 1/n!*(x/2)^n - ...
*/
if(n>33) /* underflow */
b = zero;
else {
temp = x*(float)0.5; b = temp;
for (a=one,i=2;i<=n;i++) {
a *= (float)i; /* a = n! */
b *= temp; /* b = (x/2)^n */
}
b = b/a;
}
} else {
/* use backward recurrence */
/* x x^2 x^2
* J(n,x)/J(n-1,x) = ---- ------ ------ .....
* 2n - 2(n+1) - 2(n+2)
*
* 1 1 1
* (for large x) = ---- ------ ------ .....
* 2n 2(n+1) 2(n+2)
* -- - ------ - ------ -
* x x x
*
* Let w = 2n/x and h=2/x, then the above quotient
* is equal to the continued fraction:
* 1
* = -----------------------
* 1
* w - -----------------
* 1
* w+h - ---------
* w+2h - ...
*
* To determine how many terms needed, let
* Q(0) = w, Q(1) = w(w+h) - 1,
* Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
* When Q(k) > 1e4 good for single
* When Q(k) > 1e9 good for double
* When Q(k) > 1e17 good for quadruple
*/
/* determine k */
float t,v;
float q0,q1,h,tmp; __int32_t k,m;
w = (n+n)/(float)x; h = (float)2.0/(float)x;
q0 = w; z = w+h; q1 = w*z - (float)1.0; k=1;
while(q1<(float)1.0e9) {
k += 1; z += h;
tmp = z*q1 - q0;
q0 = q1;
q1 = tmp;
}
m = n+n;
for(t=zero, i = 2*(n+k); i>=m; i -= 2) t = one/(i/x-t);
a = t;
b = one;
/* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
* Hence, if n*(log(2n/x)) > ...
* single 8.8722839355e+01
* double 7.09782712893383973096e+02
* long double 1.1356523406294143949491931077970765006170e+04
* then recurrent value may overflow and the result is
* likely underflow to zero
*/
tmp = n;
v = two/x;
tmp = tmp*__ieee754_logf(fabsf(v*tmp));
if(tmp<(float)8.8721679688e+01) {
for(i=n-1,di=(float)(i+i);i>0;i--){
temp = b;
b *= di;
b = b/x - a;
a = temp;
di -= two;
}
} else {
for(i=n-1,di=(float)(i+i);i>0;i--){
temp = b;
b *= di;
b = b/x - a;
a = temp;
di -= two;
/* scale b to avoid spurious overflow */
if(b>(float)1e10) {
a /= b;
t /= b;
b = one;
}
}
}
b = (t*__ieee754_j0f(x)/b);
}
}
if(sgn==1) return -b; else return b;
}
 
#ifdef __STDC__
float __ieee754_ynf(int n, float x)
#else
float __ieee754_ynf(n,x)
int n; float x;
#endif
{
__int32_t i,hx,ix,ib;
__int32_t sign;
float a, b, temp;
 
GET_FLOAT_WORD(hx,x);
ix = 0x7fffffff&hx;
/* if Y(n,NaN) is NaN */
if(FLT_UWORD_IS_NAN(ix)) return x+x;
if(FLT_UWORD_IS_ZERO(ix)) return -one/zero;
if(hx<0) return zero/zero;
sign = 1;
if(n<0){
n = -n;
sign = 1 - ((n&1)<<1);
}
if(n==0) return(__ieee754_y0f(x));
if(n==1) return(sign*__ieee754_y1f(x));
if(FLT_UWORD_IS_INFINITE(ix)) return zero;
 
a = __ieee754_y0f(x);
b = __ieee754_y1f(x);
/* quit if b is -inf */
GET_FLOAT_WORD(ib,b);
for(i=1;i<n&&ib!=0xff800000;i++){
temp = b;
b = ((float)(i+i)/x)*b - a;
GET_FLOAT_WORD(ib,b);
a = temp;
}
if(sign>0) return b; else return -b;
}
/w_exp.c
0,0 → 1,136
 
/* @(#)w_exp.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
FUNCTION
<<exp>>, <<expf>>---exponential
INDEX
exp
INDEX
expf
 
ANSI_SYNOPSIS
#include <math.h>
double exp(double <[x]>);
float expf(float <[x]>);
 
TRAD_SYNOPSIS
#include <math.h>
double exp(<[x]>);
double <[x]>;
 
float expf(<[x]>);
float <[x]>;
 
DESCRIPTION
<<exp>> and <<expf>> calculate the exponential of <[x]>, that is,
@ifinfo
e raised to the power <[x]> (where e
@end ifinfo
@tex
$e^x$ (where $e$
@end tex
is the base of the natural system of logarithms, approximately 2.71828).
 
You can use the (non-ANSI) function <<matherr>> to specify
error handling for these functions.
 
RETURNS
On success, <<exp>> and <<expf>> return the calculated value.
If the result underflows, the returned value is <<0>>. If the
result overflows, the returned value is <<HUGE_VAL>>. In
either case, <<errno>> is set to <<ERANGE>>.
 
PORTABILITY
<<exp>> is ANSI C. <<expf>> is an extension.
 
*/
 
/*
* wrapper exp(x)
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
static const double
#else
static double
#endif
o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */
u_threshold= -7.45133219101941108420e+02; /* 0xc0874910, 0xD52D3051 */
 
#ifdef __STDC__
double exp(double x) /* wrapper exp */
#else
double exp(x) /* wrapper exp */
double x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_exp(x);
#else
double z;
struct exception exc;
z = __ieee754_exp(x);
if(_LIB_VERSION == _IEEE_) return z;
if(finite(x)) {
if(x>o_threshold) {
/* exp(finite) overflow */
#ifndef HUGE_VAL
#define HUGE_VAL inf
double inf = 0.0;
 
SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */
#endif
exc.type = OVERFLOW;
exc.name = "exp";
exc.err = 0;
exc.arg1 = exc.arg2 = x;
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
} else if(x<u_threshold) {
/* exp(finite) underflow */
exc.type = UNDERFLOW;
exc.name = "exp";
exc.err = 0;
exc.arg1 = exc.arg2 = x;
exc.retval = 0.0;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
}
}
return z;
#endif
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/w_acosh.c
0,0 → 1,122
 
/* @(#)w_acosh.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
 
/*
FUNCTION
<<acosh>>, <<acoshf>>---inverse hyperbolic cosine
 
INDEX
acosh
INDEX
acoshf
 
ANSI_SYNOPSIS
#include <math.h>
double acosh(double <[x]>);
float acoshf(float <[x]>);
 
TRAD_SYNOPSIS
#include <math.h>
double acosh(<[x]>)
double <[x]>;
 
float acoshf(<[x]>)
float <[x]>;
 
DESCRIPTION
<<acosh>> calculates the inverse hyperbolic cosine of <[x]>.
<<acosh>> is defined as
@ifinfo
. log(<[x]> + sqrt(<[x]>*<[x]>-1))
@end ifinfo
@tex
$$ln\Bigl(x + \sqrt{x^2-1}\Bigr)$$
@end tex
 
<[x]> must be a number greater than or equal to 1.
 
<<acoshf>> is identical, other than taking and returning floats.
 
RETURNS
<<acosh>> and <<acoshf>> return the calculated value. If <[x]>
less than 1, the return value is NaN and <<errno>> is set to <<EDOM>>.
 
You can change the error-handling behavior with the non-ANSI
<<matherr>> function.
 
PORTABILITY
Neither <<acosh>> nor <<acoshf>> are ANSI C. They are not recommended
for portable programs.
 
 
QUICKREF ANSI SVID POSIX RENTRANT
acos n,n,n,m
acosf n,n,n,m
 
MATHREF
acosh, NAN, arg,DOMAIN,EDOM
acosh, < 1.0, NAN,DOMAIN,EDOM
acosh, >=1.0, acosh(arg),,,
 
MATHREF
acoshf, NAN, arg,DOMAIN,EDOM
acoshf, < 1.0, NAN,DOMAIN,EDOM
acoshf, >=1.0, acosh(arg),,,
 
*/
 
/*
* wrapper acosh(x)
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double acosh(double x) /* wrapper acosh */
#else
double acosh(x) /* wrapper acosh */
double x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_acosh(x);
#else
double z;
struct exception exc;
z = __ieee754_acosh(x);
if(_LIB_VERSION == _IEEE_ || isnan(x)) return z;
if(x<1.0) {
/* acosh(x<1) */
exc.type = DOMAIN;
exc.name = "acosh";
exc.err = 0;
exc.arg1 = exc.arg2 = x;
exc.retval = 0.0/0.0;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
} else
return z;
#endif
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/ef_rem_pio2.c
0,0 → 1,193
/* ef_rem_pio2.c -- float version of e_rem_pio2.c
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
 
/* __ieee754_rem_pio2f(x,y)
*
* return the remainder of x rem pi/2 in y[0]+y[1]
* use __kernel_rem_pio2f()
*/
 
#include "fdlibm.h"
 
/*
* Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
*/
#ifdef __STDC__
static const __int32_t two_over_pi[] = {
#else
static __int32_t two_over_pi[] = {
#endif
0xA2, 0xF9, 0x83, 0x6E, 0x4E, 0x44, 0x15, 0x29, 0xFC,
0x27, 0x57, 0xD1, 0xF5, 0x34, 0xDD, 0xC0, 0xDB, 0x62,
0x95, 0x99, 0x3C, 0x43, 0x90, 0x41, 0xFE, 0x51, 0x63,
0xAB, 0xDE, 0xBB, 0xC5, 0x61, 0xB7, 0x24, 0x6E, 0x3A,
0x42, 0x4D, 0xD2, 0xE0, 0x06, 0x49, 0x2E, 0xEA, 0x09,
0xD1, 0x92, 0x1C, 0xFE, 0x1D, 0xEB, 0x1C, 0xB1, 0x29,
0xA7, 0x3E, 0xE8, 0x82, 0x35, 0xF5, 0x2E, 0xBB, 0x44,
0x84, 0xE9, 0x9C, 0x70, 0x26, 0xB4, 0x5F, 0x7E, 0x41,
0x39, 0x91, 0xD6, 0x39, 0x83, 0x53, 0x39, 0xF4, 0x9C,
0x84, 0x5F, 0x8B, 0xBD, 0xF9, 0x28, 0x3B, 0x1F, 0xF8,
0x97, 0xFF, 0xDE, 0x05, 0x98, 0x0F, 0xEF, 0x2F, 0x11,
0x8B, 0x5A, 0x0A, 0x6D, 0x1F, 0x6D, 0x36, 0x7E, 0xCF,
0x27, 0xCB, 0x09, 0xB7, 0x4F, 0x46, 0x3F, 0x66, 0x9E,
0x5F, 0xEA, 0x2D, 0x75, 0x27, 0xBA, 0xC7, 0xEB, 0xE5,
0xF1, 0x7B, 0x3D, 0x07, 0x39, 0xF7, 0x8A, 0x52, 0x92,
0xEA, 0x6B, 0xFB, 0x5F, 0xB1, 0x1F, 0x8D, 0x5D, 0x08,
0x56, 0x03, 0x30, 0x46, 0xFC, 0x7B, 0x6B, 0xAB, 0xF0,
0xCF, 0xBC, 0x20, 0x9A, 0xF4, 0x36, 0x1D, 0xA9, 0xE3,
0x91, 0x61, 0x5E, 0xE6, 0x1B, 0x08, 0x65, 0x99, 0x85,
0x5F, 0x14, 0xA0, 0x68, 0x40, 0x8D, 0xFF, 0xD8, 0x80,
0x4D, 0x73, 0x27, 0x31, 0x06, 0x06, 0x15, 0x56, 0xCA,
0x73, 0xA8, 0xC9, 0x60, 0xE2, 0x7B, 0xC0, 0x8C, 0x6B,
};
 
/* This array is like the one in e_rem_pio2.c, but the numbers are
single precision and the last 8 bits are forced to 0. */
#ifdef __STDC__
static const __int32_t npio2_hw[] = {
#else
static __int32_t npio2_hw[] = {
#endif
0x3fc90f00, 0x40490f00, 0x4096cb00, 0x40c90f00, 0x40fb5300, 0x4116cb00,
0x412fed00, 0x41490f00, 0x41623100, 0x417b5300, 0x418a3a00, 0x4196cb00,
0x41a35c00, 0x41afed00, 0x41bc7e00, 0x41c90f00, 0x41d5a000, 0x41e23100,
0x41eec200, 0x41fb5300, 0x4203f200, 0x420a3a00, 0x42108300, 0x4216cb00,
0x421d1400, 0x42235c00, 0x4229a500, 0x422fed00, 0x42363600, 0x423c7e00,
0x4242c700, 0x42490f00
};
 
/*
* invpio2: 24 bits of 2/pi
* pio2_1: first 17 bit of pi/2
* pio2_1t: pi/2 - pio2_1
* pio2_2: second 17 bit of pi/2
* pio2_2t: pi/2 - (pio2_1+pio2_2)
* pio2_3: third 17 bit of pi/2
* pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
*/
 
#ifdef __STDC__
static const float
#else
static float
#endif
zero = 0.0000000000e+00, /* 0x00000000 */
half = 5.0000000000e-01, /* 0x3f000000 */
two8 = 2.5600000000e+02, /* 0x43800000 */
invpio2 = 6.3661980629e-01, /* 0x3f22f984 */
pio2_1 = 1.5707855225e+00, /* 0x3fc90f80 */
pio2_1t = 1.0804334124e-05, /* 0x37354443 */
pio2_2 = 1.0804273188e-05, /* 0x37354400 */
pio2_2t = 6.0770999344e-11, /* 0x2e85a308 */
pio2_3 = 6.0770943833e-11, /* 0x2e85a300 */
pio2_3t = 6.1232342629e-17; /* 0x248d3132 */
 
#ifdef __STDC__
__int32_t __ieee754_rem_pio2f(float x, float *y)
#else
__int32_t __ieee754_rem_pio2f(x,y)
float x,y[];
#endif
{
float z,w,t,r,fn;
float tx[3];
__int32_t i,j,n,ix,hx;
int e0,nx;
 
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
if(ix<=0x3f490fd8) /* |x| ~<= pi/4 , no need for reduction */
{y[0] = x; y[1] = 0; return 0;}
if(ix<0x4016cbe4) { /* |x| < 3pi/4, special case with n=+-1 */
if(hx>0) {
z = x - pio2_1;
if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */
y[0] = z - pio2_1t;
y[1] = (z-y[0])-pio2_1t;
} else { /* near pi/2, use 24+24+24 bit pi */
z -= pio2_2;
y[0] = z - pio2_2t;
y[1] = (z-y[0])-pio2_2t;
}
return 1;
} else { /* negative x */
z = x + pio2_1;
if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */
y[0] = z + pio2_1t;
y[1] = (z-y[0])+pio2_1t;
} else { /* near pi/2, use 24+24+24 bit pi */
z += pio2_2;
y[0] = z + pio2_2t;
y[1] = (z-y[0])+pio2_2t;
}
return -1;
}
}
if(ix<=0x43490f80) { /* |x| ~<= 2^7*(pi/2), medium size */
t = fabsf(x);
n = (__int32_t) (t*invpio2+half);
fn = (float)n;
r = t-fn*pio2_1;
w = fn*pio2_1t; /* 1st round good to 40 bit */
if(n<32&&(ix&0xffffff00)!=npio2_hw[n-1]) {
y[0] = r-w; /* quick check no cancellation */
} else {
__uint32_t high;
j = ix>>23;
y[0] = r-w;
GET_FLOAT_WORD(high,y[0]);
i = j-((high>>23)&0xff);
if(i>8) { /* 2nd iteration needed, good to 57 */
t = r;
w = fn*pio2_2;
r = t-w;
w = fn*pio2_2t-((t-r)-w);
y[0] = r-w;
GET_FLOAT_WORD(high,y[0]);
i = j-((high>>23)&0xff);
if(i>25) { /* 3rd iteration need, 74 bits acc */
t = r; /* will cover all possible cases */
w = fn*pio2_3;
r = t-w;
w = fn*pio2_3t-((t-r)-w);
y[0] = r-w;
}
}
}
y[1] = (r-y[0])-w;
if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
else return n;
}
/*
* all other (large) arguments
*/
if(!FLT_UWORD_IS_FINITE(ix)) {
y[0]=y[1]=x-x; return 0;
}
/* set z = scalbn(|x|,ilogb(x)-7) */
e0 = (int)((ix>>23)-134); /* e0 = ilogb(z)-7; */
SET_FLOAT_WORD(z, ix - ((__int32_t)e0<<23));
for(i=0;i<2;i++) {
tx[i] = (float)((__int32_t)(z));
z = (z-tx[i])*two8;
}
tx[2] = z;
nx = 3;
while(tx[nx-1]==zero) nx--; /* skip zero term */
n = __kernel_rem_pio2f(tx,y,e0,nx,2,two_over_pi);
if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
return n;
}
/k_rem_pio2.c
0,0 → 1,320
 
/* @(#)k_rem_pio2.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
* __kernel_rem_pio2(x,y,e0,nx,prec,ipio2)
* double x[],y[]; int e0,nx,prec; int ipio2[];
*
* __kernel_rem_pio2 return the last three digits of N with
* y = x - N*pi/2
* so that |y| < pi/2.
*
* The method is to compute the integer (mod 8) and fraction parts of
* (2/pi)*x without doing the full multiplication. In general we
* skip the part of the product that are known to be a huge integer (
* more accurately, = 0 mod 8 ). Thus the number of operations are
* independent of the exponent of the input.
*
* (2/pi) is represented by an array of 24-bit integers in ipio2[].
*
* Input parameters:
* x[] The input value (must be positive) is broken into nx
* pieces of 24-bit integers in double precision format.
* x[i] will be the i-th 24 bit of x. The scaled exponent
* of x[0] is given in input parameter e0 (i.e., x[0]*2^e0
* match x's up to 24 bits.
*
* Example of breaking a double positive z into x[0]+x[1]+x[2]:
* e0 = ilogb(z)-23
* z = scalbn(z,-e0)
* for i = 0,1,2
* x[i] = floor(z)
* z = (z-x[i])*2**24
*
*
* y[] ouput result in an array of double precision numbers.
* The dimension of y[] is:
* 24-bit precision 1
* 53-bit precision 2
* 64-bit precision 2
* 113-bit precision 3
* The actual value is the sum of them. Thus for 113-bit
* precison, one may have to do something like:
*
* long double t,w,r_head, r_tail;
* t = (long double)y[2] + (long double)y[1];
* w = (long double)y[0];
* r_head = t+w;
* r_tail = w - (r_head - t);
*
* e0 The exponent of x[0]
*
* nx dimension of x[]
*
* prec an integer indicating the precision:
* 0 24 bits (single)
* 1 53 bits (double)
* 2 64 bits (extended)
* 3 113 bits (quad)
*
* ipio2[]
* integer array, contains the (24*i)-th to (24*i+23)-th
* bit of 2/pi after binary point. The corresponding
* floating value is
*
* ipio2[i] * 2^(-24(i+1)).
*
* External function:
* double scalbn(), floor();
*
*
* Here is the description of some local variables:
*
* jk jk+1 is the initial number of terms of ipio2[] needed
* in the computation. The recommended value is 2,3,4,
* 6 for single, double, extended,and quad.
*
* jz local integer variable indicating the number of
* terms of ipio2[] used.
*
* jx nx - 1
*
* jv index for pointing to the suitable ipio2[] for the
* computation. In general, we want
* ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8
* is an integer. Thus
* e0-3-24*jv >= 0 or (e0-3)/24 >= jv
* Hence jv = max(0,(e0-3)/24).
*
* jp jp+1 is the number of terms in PIo2[] needed, jp = jk.
*
* q[] double array with integral value, representing the
* 24-bits chunk of the product of x and 2/pi.
*
* q0 the corresponding exponent of q[0]. Note that the
* exponent for q[i] would be q0-24*i.
*
* PIo2[] double precision array, obtained by cutting pi/2
* into 24 bits chunks.
*
* f[] ipio2[] in floating point
*
* iq[] integer array by breaking up q[] in 24-bits chunk.
*
* fq[] final product of x*(2/pi) in fq[0],..,fq[jk]
*
* ih integer. If >0 it indicates q[] is >= 0.5, hence
* it also indicates the *sign* of the result.
*
*/
 
 
/*
* Constants:
* The hexadecimal values are the intended ones for the following
* constants. The decimal values may be used, provided that the
* compiler will convert from decimal to binary accurately enough
* to produce the hexadecimal values shown.
*/
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
static const int init_jk[] = {2,3,4,6}; /* initial value for jk */
#else
static int init_jk[] = {2,3,4,6};
#endif
 
#ifdef __STDC__
static const double PIo2[] = {
#else
static double PIo2[] = {
#endif
1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */
7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */
5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */
3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */
1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */
1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */
2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */
2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */
};
 
#ifdef __STDC__
static const double
#else
static double
#endif
zero = 0.0,
one = 1.0,
two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */
 
#ifdef __STDC__
int __kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, const __int32_t *ipio2)
#else
int __kernel_rem_pio2(x,y,e0,nx,prec,ipio2)
double x[], y[]; int e0,nx,prec; __int32_t ipio2[];
#endif
{
__int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
double z,fw,f[20],fq[20],q[20];
 
/* initialize jk*/
jk = init_jk[prec];
jp = jk;
 
/* determine jx,jv,q0, note that 3>q0 */
jx = nx-1;
jv = (e0-3)/24; if(jv<0) jv=0;
q0 = e0-24*(jv+1);
 
/* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
j = jv-jx; m = jx+jk;
for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (double) ipio2[j];
 
/* compute q[0],q[1],...q[jk] */
for (i=0;i<=jk;i++) {
for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;
}
 
jz = jk;
recompute:
/* distill q[] into iq[] reversingly */
for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
fw = (double)((__int32_t)(twon24* z));
iq[i] = (__int32_t)(z-two24*fw);
z = q[j-1]+fw;
}
 
/* compute n */
z = scalbn(z,(int)q0); /* actual value of z */
z -= 8.0*floor(z*0.125); /* trim off integer >= 8 */
n = (__int32_t) z;
z -= (double)n;
ih = 0;
if(q0>0) { /* need iq[jz-1] to determine n */
i = (iq[jz-1]>>(24-q0)); n += i;
iq[jz-1] -= i<<(24-q0);
ih = iq[jz-1]>>(23-q0);
}
else if(q0==0) ih = iq[jz-1]>>23;
else if(z>=0.5) ih=2;
 
if(ih>0) { /* q > 0.5 */
n += 1; carry = 0;
for(i=0;i<jz ;i++) { /* compute 1-q */
j = iq[i];
if(carry==0) {
if(j!=0) {
carry = 1; iq[i] = 0x1000000- j;
}
} else iq[i] = 0xffffff - j;
}
if(q0>0) { /* rare case: chance is 1 in 12 */
switch(q0) {
case 1:
iq[jz-1] &= 0x7fffff; break;
case 2:
iq[jz-1] &= 0x3fffff; break;
}
}
if(ih==2) {
z = one - z;
if(carry!=0) z -= scalbn(one,(int)q0);
}
}
 
/* check if recomputation is needed */
if(z==zero) {
j = 0;
for (i=jz-1;i>=jk;i--) j |= iq[i];
if(j==0) { /* need recomputation */
for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */
 
for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */
f[jx+i] = (double) ipio2[jv+i];
for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
q[i] = fw;
}
jz += k;
goto recompute;
}
}
 
/* chop off zero terms */
if(z==0.0) {
jz -= 1; q0 -= 24;
while(iq[jz]==0) { jz--; q0-=24;}
} else { /* break z into 24-bit if necessary */
z = scalbn(z,-(int)q0);
if(z>=two24) {
fw = (double)((__int32_t)(twon24*z));
iq[jz] = (__int32_t)(z-two24*fw);
jz += 1; q0 += 24;
iq[jz] = (__int32_t) fw;
} else iq[jz] = (__int32_t) z ;
}
 
/* convert integer "bit" chunk to floating-point value */
fw = scalbn(one,(int)q0);
for(i=jz;i>=0;i--) {
q[i] = fw*(double)iq[i]; fw*=twon24;
}
 
/* compute PIo2[0,...,jp]*q[jz,...,0] */
for(i=jz;i>=0;i--) {
for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
fq[jz-i] = fw;
}
 
/* compress fq[] into y[] */
switch(prec) {
case 0:
fw = 0.0;
for (i=jz;i>=0;i--) fw += fq[i];
y[0] = (ih==0)? fw: -fw;
break;
case 1:
case 2:
fw = 0.0;
for (i=jz;i>=0;i--) fw += fq[i];
y[0] = (ih==0)? fw: -fw;
fw = fq[0]-fw;
for (i=1;i<=jz;i++) fw += fq[i];
y[1] = (ih==0)? fw: -fw;
break;
case 3: /* painful */
for (i=jz;i>0;i--) {
fw = fq[i-1]+fq[i];
fq[i] += fq[i-1]-fw;
fq[i-1] = fw;
}
for (i=jz;i>1;i--) {
fw = fq[i-1]+fq[i];
fq[i] += fq[i-1]-fw;
fq[i-1] = fw;
}
for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
if(ih==0) {
y[0] = fq[0]; y[1] = fq[1]; y[2] = fw;
} else {
y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
}
}
return n&7;
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/wf_atanh.c
0,0 → 1,83
/* wf_atanh.c -- float version of w_atanh.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
* wrapper atanhf(x)
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifdef __STDC__
float atanhf(float x) /* wrapper atanhf */
#else
float atanhf(x) /* wrapper atanhf */
float x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_atanhf(x);
#else
float z,y;
struct exception exc;
z = __ieee754_atanhf(x);
if(_LIB_VERSION == _IEEE_ || isnanf(x)) return z;
y = fabsf(x);
if(y>=(float)1.0) {
if(y>(float)1.0) {
/* atanhf(|x|>1) */
exc.type = DOMAIN;
exc.name = "atanhf";
exc.err = 0;
exc.arg1 = exc.arg2 = (double)x;
exc.retval = 0.0/0.0;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
} else {
/* atanhf(|x|=1) */
exc.type = SING;
exc.name = "atanhf";
exc.err = 0;
exc.arg1 = exc.arg2 = (double)x;
exc.retval = x/0.0; /* sign(x)*inf */
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
}
if (exc.err != 0)
errno = exc.err;
return (float)exc.retval;
} else
return z;
#endif
}
 
#ifdef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double atanh(double x)
#else
double atanh(x)
double x;
#endif
{
return (double) atanhf((float) x);
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/w_atan2.c
0,0 → 1,117
 
/* @(#)w_atan2.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
 
/*
FUNCTION
<<atan2>>, <<atan2f>>---arc tangent of y/x
 
INDEX
atan2
INDEX
atan2f
 
ANSI_SYNOPSIS
#include <math.h>
double atan2(double <[y]>,double <[x]>);
float atan2f(float <[y]>,float <[x]>);
 
TRAD_SYNOPSIS
#include <math.h>
double atan2(<[y]>,<[x]>);
double <[y]>;
double <[x]>;
 
float atan2f(<[y]>,<[x]>);
float <[y]>;
float <[x]>;
 
DESCRIPTION
 
<<atan2>> computes the inverse tangent (arc tangent) of <[y]>/<[x]>.
<<atan2>> produces the correct result even for angles near
@ifinfo
pi/2 or -pi/2
@end ifinfo
@tex
$\pi/2$ or $-\pi/2$
@end tex
(that is, when <[x]> is near 0).
 
<<atan2f>> is identical to <<atan2>>, save that it takes and returns
<<float>>.
 
RETURNS
<<atan2>> and <<atan2f>> return a value in radians, in the range of
@ifinfo
-pi to pi.
@end ifinfo
@tex
$-\pi$ to $\pi$.
@end tex
 
If both <[x]> and <[y]> are 0.0, <<atan2>> causes a <<DOMAIN>> error.
 
You can modify error handling for these functions using <<matherr>>.
 
PORTABILITY
<<atan2>> is ANSI C. <<atan2f>> is an extension.
 
 
*/
 
/*
* wrapper atan2(y,x)
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double atan2(double y, double x) /* wrapper atan2 */
#else
double atan2(y,x) /* wrapper atan2 */
double y,x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_atan2(y,x);
#else
double z;
struct exception exc;
z = __ieee754_atan2(y,x);
if(_LIB_VERSION == _IEEE_||isnan(x)||isnan(y)) return z;
if(x==0.0&&y==0.0) {
/* atan2(+-0,+-0) */
exc.arg1 = y;
exc.arg2 = x;
exc.type = DOMAIN;
exc.name = "atan2";
exc.err = 0;
exc.retval = 0.0;
if(_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
} else
return z;
#endif
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/kf_rem_pio2.c
0,0 → 1,208
/* kf_rem_pio2.c -- float version of k_rem_pio2.c
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
#include "fdlibm.h"
 
/* In the float version, the input parameter x contains 8 bit
integers, not 24 bit integers. 113 bit precision is not supported. */
 
#ifdef __STDC__
static const int init_jk[] = {4,7,9}; /* initial value for jk */
#else
static int init_jk[] = {4,7,9};
#endif
 
#ifdef __STDC__
static const float PIo2[] = {
#else
static float PIo2[] = {
#endif
1.5703125000e+00, /* 0x3fc90000 */
4.5776367188e-04, /* 0x39f00000 */
2.5987625122e-05, /* 0x37da0000 */
7.5437128544e-08, /* 0x33a20000 */
6.0026650317e-11, /* 0x2e840000 */
7.3896444519e-13, /* 0x2b500000 */
5.3845816694e-15, /* 0x27c20000 */
5.6378512969e-18, /* 0x22d00000 */
8.3009228831e-20, /* 0x1fc40000 */
3.2756352257e-22, /* 0x1bc60000 */
6.3331015649e-25, /* 0x17440000 */
};
 
#ifdef __STDC__
static const float
#else
static float
#endif
zero = 0.0,
one = 1.0,
two8 = 2.5600000000e+02, /* 0x43800000 */
twon8 = 3.9062500000e-03; /* 0x3b800000 */
 
#ifdef __STDC__
int __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const __int32_t *ipio2)
#else
int __kernel_rem_pio2f(x,y,e0,nx,prec,ipio2)
float x[], y[]; int e0,nx,prec; __int32_t ipio2[];
#endif
{
__int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
float z,fw,f[20],fq[20],q[20];
 
/* initialize jk*/
jk = init_jk[prec];
jp = jk;
 
/* determine jx,jv,q0, note that 3>q0 */
jx = nx-1;
jv = (e0-3)/8; if(jv<0) jv=0;
q0 = e0-8*(jv+1);
 
/* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
j = jv-jx; m = jx+jk;
for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j];
 
/* compute q[0],q[1],...q[jk] */
for (i=0;i<=jk;i++) {
for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;
}
 
jz = jk;
recompute:
/* distill q[] into iq[] reversingly */
for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
fw = (float)((__int32_t)(twon8* z));
iq[i] = (__int32_t)(z-two8*fw);
z = q[j-1]+fw;
}
 
/* compute n */
z = scalbnf(z,(int)q0); /* actual value of z */
z -= (float)8.0*floorf(z*(float)0.125); /* trim off integer >= 8 */
n = (__int32_t) z;
z -= (float)n;
ih = 0;
if(q0>0) { /* need iq[jz-1] to determine n */
i = (iq[jz-1]>>(8-q0)); n += i;
iq[jz-1] -= i<<(8-q0);
ih = iq[jz-1]>>(7-q0);
}
else if(q0==0) ih = iq[jz-1]>>8;
else if(z>=(float)0.5) ih=2;
 
if(ih>0) { /* q > 0.5 */
n += 1; carry = 0;
for(i=0;i<jz ;i++) { /* compute 1-q */
j = iq[i];
if(carry==0) {
if(j!=0) {
carry = 1; iq[i] = 0x100- j;
}
} else iq[i] = 0xff - j;
}
if(q0>0) { /* rare case: chance is 1 in 12 */
switch(q0) {
case 1:
iq[jz-1] &= 0x7f; break;
case 2:
iq[jz-1] &= 0x3f; break;
}
}
if(ih==2) {
z = one - z;
if(carry!=0) z -= scalbnf(one,(int)q0);
}
}
 
/* check if recomputation is needed */
if(z==zero) {
j = 0;
for (i=jz-1;i>=jk;i--) j |= iq[i];
if(j==0) { /* need recomputation */
for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */
 
for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */
f[jx+i] = (float) ipio2[jv+i];
for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
q[i] = fw;
}
jz += k;
goto recompute;
}
}
 
/* chop off zero terms */
if(z==(float)0.0) {
jz -= 1; q0 -= 8;
while(iq[jz]==0) { jz--; q0-=8;}
} else { /* break z into 8-bit if necessary */
z = scalbnf(z,-(int)q0);
if(z>=two8) {
fw = (float)((__int32_t)(twon8*z));
iq[jz] = (__int32_t)(z-two8*fw);
jz += 1; q0 += 8;
iq[jz] = (__int32_t) fw;
} else iq[jz] = (__int32_t) z ;
}
 
/* convert integer "bit" chunk to floating-point value */
fw = scalbnf(one,(int)q0);
for(i=jz;i>=0;i--) {
q[i] = fw*(float)iq[i]; fw*=twon8;
}
 
/* compute PIo2[0,...,jp]*q[jz,...,0] */
for(i=jz;i>=0;i--) {
for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
fq[jz-i] = fw;
}
 
/* compress fq[] into y[] */
switch(prec) {
case 0:
fw = 0.0;
for (i=jz;i>=0;i--) fw += fq[i];
y[0] = (ih==0)? fw: -fw;
break;
case 1:
case 2:
fw = 0.0;
for (i=jz;i>=0;i--) fw += fq[i];
y[0] = (ih==0)? fw: -fw;
fw = fq[0]-fw;
for (i=1;i<=jz;i++) fw += fq[i];
y[1] = (ih==0)? fw: -fw;
break;
case 3: /* painful */
for (i=jz;i>0;i--) {
fw = fq[i-1]+fq[i];
fq[i] += fq[i-1]-fw;
fq[i-1] = fw;
}
for (i=jz;i>1;i--) {
fw = fq[i-1]+fq[i];
fq[i] += fq[i-1]-fw;
fq[i-1] = fw;
}
for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
if(ih==0) {
y[0] = fq[0]; y[1] = fq[1]; y[2] = fw;
} else {
y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
}
}
return n&7;
}
/e_sqrt.c
0,0 → 1,452
 
/* @(#)e_sqrt.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/* __ieee754_sqrt(x)
* Return correctly rounded sqrt.
* ------------------------------------------
* | Use the hardware sqrt if you have one |
* ------------------------------------------
* Method:
* Bit by bit method using integer arithmetic. (Slow, but portable)
* 1. Normalization
* Scale x to y in [1,4) with even powers of 2:
* find an integer k such that 1 <= (y=x*2^(2k)) < 4, then
* sqrt(x) = 2^k * sqrt(y)
* 2. Bit by bit computation
* Let q = sqrt(y) truncated to i bit after binary point (q = 1),
* i 0
* i+1 2
* s = 2*q , and y = 2 * ( y - q ). (1)
* i i i i
*
* To compute q from q , one checks whether
* i+1 i
*
* -(i+1) 2
* (q + 2 ) <= y. (2)
* i
* -(i+1)
* If (2) is false, then q = q ; otherwise q = q + 2 .
* i+1 i i+1 i
*
* With some algebric manipulation, it is not difficult to see
* that (2) is equivalent to
* -(i+1)
* s + 2 <= y (3)
* i i
*
* The advantage of (3) is that s and y can be computed by
* i i
* the following recurrence formula:
* if (3) is false
*
* s = s , y = y ; (4)
* i+1 i i+1 i
*
* otherwise,
* -i -(i+1)
* s = s + 2 , y = y - s - 2 (5)
* i+1 i i+1 i i
*
* One may easily use induction to prove (4) and (5).
* Note. Since the left hand side of (3) contain only i+2 bits,
* it does not necessary to do a full (53-bit) comparison
* in (3).
* 3. Final rounding
* After generating the 53 bits result, we compute one more bit.
* Together with the remainder, we can decide whether the
* result is exact, bigger than 1/2ulp, or less than 1/2ulp
* (it will never equal to 1/2ulp).
* The rounding mode can be detected by checking whether
* huge + tiny is equal to huge, and whether huge - tiny is
* equal to huge for some floating point number "huge" and "tiny".
*
* Special cases:
* sqrt(+-0) = +-0 ... exact
* sqrt(inf) = inf
* sqrt(-ve) = NaN ... with invalid signal
* sqrt(NaN) = NaN ... with invalid signal for signaling NaN
*
* Other methods : see the appended file at the end of the program below.
*---------------
*/
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
static const double one = 1.0, tiny=1.0e-300;
#else
static double one = 1.0, tiny=1.0e-300;
#endif
 
#ifdef __STDC__
double __ieee754_sqrt(double x)
#else
double __ieee754_sqrt(x)
double x;
#endif
{
double z;
__int32_t sign = (int)0x80000000;
__uint32_t r,t1,s1,ix1,q1;
__int32_t ix0,s0,q,m,t,i;
 
EXTRACT_WORDS(ix0,ix1,x);
 
/* take care of Inf and NaN */
if((ix0&0x7ff00000)==0x7ff00000) {
return x*x+x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf
sqrt(-inf)=sNaN */
}
/* take care of zero */
if(ix0<=0) {
if(((ix0&(~sign))|ix1)==0) return x;/* sqrt(+-0) = +-0 */
else if(ix0<0)
return (x-x)/(x-x); /* sqrt(-ve) = sNaN */
}
/* normalize x */
m = (ix0>>20);
if(m==0) { /* subnormal x */
while(ix0==0) {
m -= 21;
ix0 |= (ix1>>11); ix1 <<= 21;
}
for(i=0;(ix0&0x00100000)==0;i++) ix0<<=1;
m -= i-1;
ix0 |= (ix1>>(32-i));
ix1 <<= i;
}
m -= 1023; /* unbias exponent */
ix0 = (ix0&0x000fffff)|0x00100000;
if(m&1){ /* odd m, double x to make it even */
ix0 += ix0 + ((ix1&sign)>>31);
ix1 += ix1;
}
m >>= 1; /* m = [m/2] */
 
/* generate sqrt(x) bit by bit */
ix0 += ix0 + ((ix1&sign)>>31);
ix1 += ix1;
q = q1 = s0 = s1 = 0; /* [q,q1] = sqrt(x) */
r = 0x00200000; /* r = moving bit from right to left */
 
while(r!=0) {
t = s0+r;
if(t<=ix0) {
s0 = t+r;
ix0 -= t;
q += r;
}
ix0 += ix0 + ((ix1&sign)>>31);
ix1 += ix1;
r>>=1;
}
 
r = sign;
while(r!=0) {
t1 = s1+r;
t = s0;
if((t<ix0)||((t==ix0)&&(t1<=ix1))) {
s1 = t1+r;
if(((t1&sign)==sign)&&(s1&sign)==0) s0 += 1;
ix0 -= t;
if (ix1 < t1) ix0 -= 1;
ix1 -= t1;
q1 += r;
}
ix0 += ix0 + ((ix1&sign)>>31);
ix1 += ix1;
r>>=1;
}
 
/* use floating add to find out rounding direction */
if((ix0|ix1)!=0) {
z = one-tiny; /* trigger inexact flag */
if (z>=one) {
z = one+tiny;
if (q1==(__uint32_t)0xffffffff) { q1=0; q += 1;}
else if (z>one) {
if (q1==(__uint32_t)0xfffffffe) q+=1;
q1+=2;
} else
q1 += (q1&1);
}
}
ix0 = (q>>1)+0x3fe00000;
ix1 = q1>>1;
if ((q&1)==1) ix1 |= sign;
ix0 += (m <<20);
INSERT_WORDS(z,ix0,ix1);
return z;
}
#endif /* defined(_DOUBLE_IS_32BITS) */
 
/*
Other methods (use floating-point arithmetic)
-------------
(This is a copy of a drafted paper by Prof W. Kahan
and K.C. Ng, written in May, 1986)
 
Two algorithms are given here to implement sqrt(x)
(IEEE double precision arithmetic) in software.
Both supply sqrt(x) correctly rounded. The first algorithm (in
Section A) uses newton iterations and involves four divisions.
The second one uses reciproot iterations to avoid division, but
requires more multiplications. Both algorithms need the ability
to chop results of arithmetic operations instead of round them,
and the INEXACT flag to indicate when an arithmetic operation
is executed exactly with no roundoff error, all part of the
standard (IEEE 754-1985). The ability to perform shift, add,
subtract and logical AND operations upon 32-bit words is needed
too, though not part of the standard.
 
A. sqrt(x) by Newton Iteration
 
(1) Initial approximation
 
Let x0 and x1 be the leading and the trailing 32-bit words of
a floating point number x (in IEEE double format) respectively
 
1 11 52 ...widths
------------------------------------------------------
x: |s| e | f |
------------------------------------------------------
msb lsb msb lsb ...order
 
------------------------ ------------------------
x0: |s| e | f1 | x1: | f2 |
------------------------ ------------------------
 
By performing shifts and subtracts on x0 and x1 (both regarded
as integers), we obtain an 8-bit approximation of sqrt(x) as
follows.
 
k := (x0>>1) + 0x1ff80000;
y0 := k - T1[31&(k>>15)]. ... y ~ sqrt(x) to 8 bits
Here k is a 32-bit integer and T1[] is an integer array containing
correction terms. Now magically the floating value of y (y's
leading 32-bit word is y0, the value of its trailing word is 0)
approximates sqrt(x) to almost 8-bit.
 
Value of T1:
static int T1[32]= {
0, 1024, 3062, 5746, 9193, 13348, 18162, 23592,
29598, 36145, 43202, 50740, 58733, 67158, 75992, 85215,
83599, 71378, 60428, 50647, 41945, 34246, 27478, 21581,
16499, 12183, 8588, 5674, 3403, 1742, 661, 130,};
 
(2) Iterative refinement
 
Apply Heron's rule three times to y, we have y approximates
sqrt(x) to within 1 ulp (Unit in the Last Place):
 
y := (y+x/y)/2 ... almost 17 sig. bits
y := (y+x/y)/2 ... almost 35 sig. bits
y := y-(y-x/y)/2 ... within 1 ulp
 
 
Remark 1.
Another way to improve y to within 1 ulp is:
 
y := (y+x/y) ... almost 17 sig. bits to 2*sqrt(x)
y := y - 0x00100006 ... almost 18 sig. bits to sqrt(x)
 
2
(x-y )*y
y := y + 2* ---------- ...within 1 ulp
2
3y + x
 
 
This formula has one division fewer than the one above; however,
it requires more multiplications and additions. Also x must be
scaled in advance to avoid spurious overflow in evaluating the
expression 3y*y+x. Hence it is not recommended uless division
is slow. If division is very slow, then one should use the
reciproot algorithm given in section B.
 
(3) Final adjustment
 
By twiddling y's last bit it is possible to force y to be
correctly rounded according to the prevailing rounding mode
as follows. Let r and i be copies of the rounding mode and
inexact flag before entering the square root program. Also we
use the expression y+-ulp for the next representable floating
numbers (up and down) of y. Note that y+-ulp = either fixed
point y+-1, or multiply y by nextafter(1,+-inf) in chopped
mode.
 
I := FALSE; ... reset INEXACT flag I
R := RZ; ... set rounding mode to round-toward-zero
z := x/y; ... chopped quotient, possibly inexact
If(not I) then { ... if the quotient is exact
if(z=y) {
I := i; ... restore inexact flag
R := r; ... restore rounded mode
return sqrt(x):=y.
} else {
z := z - ulp; ... special rounding
}
}
i := TRUE; ... sqrt(x) is inexact
If (r=RN) then z=z+ulp ... rounded-to-nearest
If (r=RP) then { ... round-toward-+inf
y = y+ulp; z=z+ulp;
}
y := y+z; ... chopped sum
y0:=y0-0x00100000; ... y := y/2 is correctly rounded.
I := i; ... restore inexact flag
R := r; ... restore rounded mode
return sqrt(x):=y.
(4) Special cases
 
Square root of +inf, +-0, or NaN is itself;
Square root of a negative number is NaN with invalid signal.
 
 
B. sqrt(x) by Reciproot Iteration
 
(1) Initial approximation
 
Let x0 and x1 be the leading and the trailing 32-bit words of
a floating point number x (in IEEE double format) respectively
(see section A). By performing shifs and subtracts on x0 and y0,
we obtain a 7.8-bit approximation of 1/sqrt(x) as follows.
 
k := 0x5fe80000 - (x0>>1);
y0:= k - T2[63&(k>>14)]. ... y ~ 1/sqrt(x) to 7.8 bits
 
Here k is a 32-bit integer and T2[] is an integer array
containing correction terms. Now magically the floating
value of y (y's leading 32-bit word is y0, the value of
its trailing word y1 is set to zero) approximates 1/sqrt(x)
to almost 7.8-bit.
 
Value of T2:
static int T2[64]= {
0x1500, 0x2ef8, 0x4d67, 0x6b02, 0x87be, 0xa395, 0xbe7a, 0xd866,
0xf14a, 0x1091b,0x11fcd,0x13552,0x14999,0x15c98,0x16e34,0x17e5f,
0x18d03,0x19a01,0x1a545,0x1ae8a,0x1b5c4,0x1bb01,0x1bfde,0x1c28d,
0x1c2de,0x1c0db,0x1ba73,0x1b11c,0x1a4b5,0x1953d,0x18266,0x16be0,
0x1683e,0x179d8,0x18a4d,0x19992,0x1a789,0x1b445,0x1bf61,0x1c989,
0x1d16d,0x1d77b,0x1dddf,0x1e2ad,0x1e5bf,0x1e6e8,0x1e654,0x1e3cd,
0x1df2a,0x1d635,0x1cb16,0x1be2c,0x1ae4e,0x19bde,0x1868e,0x16e2e,
0x1527f,0x1334a,0x11051,0xe951, 0xbe01, 0x8e0d, 0x5924, 0x1edd,};
 
(2) Iterative refinement
 
Apply Reciproot iteration three times to y and multiply the
result by x to get an approximation z that matches sqrt(x)
to about 1 ulp. To be exact, we will have
-1ulp < sqrt(x)-z<1.0625ulp.
... set rounding mode to Round-to-nearest
y := y*(1.5-0.5*x*y*y) ... almost 15 sig. bits to 1/sqrt(x)
y := y*((1.5-2^-30)+0.5*x*y*y)... about 29 sig. bits to 1/sqrt(x)
... special arrangement for better accuracy
z := x*y ... 29 bits to sqrt(x), with z*y<1
z := z + 0.5*z*(1-z*y) ... about 1 ulp to sqrt(x)
 
Remark 2. The constant 1.5-2^-30 is chosen to bias the error so that
(a) the term z*y in the final iteration is always less than 1;
(b) the error in the final result is biased upward so that
-1 ulp < sqrt(x) - z < 1.0625 ulp
instead of |sqrt(x)-z|<1.03125ulp.
 
(3) Final adjustment
 
By twiddling y's last bit it is possible to force y to be
correctly rounded according to the prevailing rounding mode
as follows. Let r and i be copies of the rounding mode and
inexact flag before entering the square root program. Also we
use the expression y+-ulp for the next representable floating
numbers (up and down) of y. Note that y+-ulp = either fixed
point y+-1, or multiply y by nextafter(1,+-inf) in chopped
mode.
 
R := RZ; ... set rounding mode to round-toward-zero
switch(r) {
case RN: ... round-to-nearest
if(x<= z*(z-ulp)...chopped) z = z - ulp; else
if(x<= z*(z+ulp)...chopped) z = z; else z = z+ulp;
break;
case RZ:case RM: ... round-to-zero or round-to--inf
R:=RP; ... reset rounding mod to round-to-+inf
if(x<z*z ... rounded up) z = z - ulp; else
if(x>=(z+ulp)*(z+ulp) ...rounded up) z = z+ulp;
break;
case RP: ... round-to-+inf
if(x>(z+ulp)*(z+ulp)...chopped) z = z+2*ulp; else
if(x>z*z ...chopped) z = z+ulp;
break;
}
 
Remark 3. The above comparisons can be done in fixed point. For
example, to compare x and w=z*z chopped, it suffices to compare
x1 and w1 (the trailing parts of x and w), regarding them as
two's complement integers.
 
...Is z an exact square root?
To determine whether z is an exact square root of x, let z1 be the
trailing part of z, and also let x0 and x1 be the leading and
trailing parts of x.
 
If ((z1&0x03ffffff)!=0) ... not exact if trailing 26 bits of z!=0
I := 1; ... Raise Inexact flag: z is not exact
else {
j := 1 - [(x0>>20)&1] ... j = logb(x) mod 2
k := z1 >> 26; ... get z's 25-th and 26-th
fraction bits
I := i or (k&j) or ((k&(j+j+1))!=(x1&3));
}
R:= r ... restore rounded mode
return sqrt(x):=z.
 
If multiplication is cheaper then the foregoing red tape, the
Inexact flag can be evaluated by
 
I := i;
I := (z*z!=x) or I.
 
Note that z*z can overwrite I; this value must be sensed if it is
True.
 
Remark 4. If z*z = x exactly, then bit 25 to bit 0 of z1 must be
zero.
 
--------------------
z1: | f2 |
--------------------
bit 31 bit 0
 
Further more, bit 27 and 26 of z1, bit 0 and 1 of x1, and the odd
or even of logb(x) have the following relations:
 
-------------------------------------------------
bit 27,26 of z1 bit 1,0 of x1 logb(x)
-------------------------------------------------
00 00 odd and even
01 01 even
10 10 odd
10 00 even
11 01 even
-------------------------------------------------
 
(4) Special cases (see (4) of Section A).
*/
/w_j1.c
0,0 → 1,121
 
/* @(#)w_j1.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
* wrapper of j1,y1
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double j1(double x) /* wrapper j1 */
#else
double j1(x) /* wrapper j1 */
double x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_j1(x);
#else
double z;
struct exception exc;
z = __ieee754_j1(x);
if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z;
if(fabs(x)>X_TLOSS) {
/* j1(|x|>X_TLOSS) */
exc.type = TLOSS;
exc.name = "j1";
exc.err = 0;
exc.arg1 = exc.arg2 = x;
exc.retval = 0.0;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
} else
return z;
#endif
}
 
#ifdef __STDC__
double y1(double x) /* wrapper y1 */
#else
double y1(x) /* wrapper y1 */
double x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_y1(x);
#else
double z;
struct exception exc;
z = __ieee754_y1(x);
if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z;
if(x <= 0.0){
#ifndef HUGE_VAL
#define HUGE_VAL inf
double inf = 0.0;
 
SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */
#endif
/* y1(0) = -inf or y1(x<0) = NaN */
exc.type = DOMAIN; /* should be SING for IEEE */
exc.name = "y1";
exc.err = 0;
exc.arg1 = exc.arg2 = x;
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
}
if(x>X_TLOSS) {
/* y1(x>X_TLOSS) */
exc.type = TLOSS;
exc.name = "y1";
exc.err = 0;
exc.arg1 = exc.arg2 = x;
exc.retval = 0.0;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
} else
return z;
#endif
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
 
 
 
 
 
/sf_isnan.c
0,0 → 1,47
/* sf_isnan.c -- float version of s_isnan.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
* isnanf(x) returns 1 is x is nan, else 0;
*/
 
#include "fdlibm.h"
 
#ifdef __STDC__
int isnanf(float x)
#else
int isnanf(x)
float x;
#endif
{
__int32_t ix;
GET_FLOAT_WORD(ix,x);
ix &= 0x7fffffff;
return FLT_UWORD_IS_NAN(ix);
}
 
#ifdef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
int isnan(double x)
#else
int isnan(x)
double x;
#endif
{
return isnanf((float) x);
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/wrf_gamma.c
0,0 → 1,74
/* wrf_gamma.c -- float version of wr_gamma.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
* wrapper float gammaf_r(float x, int *signgamp)
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifdef __STDC__
float gammaf_r(float x, int *signgamp) /* wrapper lgammaf_r */
#else
float gammaf_r(x,signgamp) /* wrapper lgammaf_r */
float x; int *signgamp;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_gammaf_r(x,signgamp);
#else
float y;
struct exception exc;
y = __ieee754_gammaf_r(x,signgamp);
if(_LIB_VERSION == _IEEE_) return y;
if(!finitef(y)&&finitef(x)) {
#ifndef HUGE_VAL
#define HUGE_VAL inf
double inf = 0.0;
 
SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */
#endif
exc.name = "gammaf";
exc.err = 0;
exc.arg1 = exc.arg2 = (double)x;
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if(floorf(x)==x&&x<=(float)0.0) {
/* gammaf(-integer) or gamma(0) */
exc.type = SING;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
} else {
/* gammaf(finite) overflow */
exc.type = OVERFLOW;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
}
if (exc.err != 0)
errno = exc.err;
return (float)exc.retval;
} else
return y;
#endif
}
/s_signif.c
0,0 → 1,34
 
/* @(#)s_signif.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
* significand(x) computes just
* scalb(x, (double) -ilogb(x)),
* for exercising the fraction-part(F) IEEE 754-1985 test vector.
*/
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double significand(double x)
#else
double significand(x)
double x;
#endif
{
return __ieee754_scalb(x,(double) -ilogb(x));
}
 
#endif /* _DOUBLE_IS_32BITS */
/ef_asin.c
0,0 → 1,88
/* ef_asin.c -- float version of e_asin.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
#include "fdlibm.h"
 
#ifdef __STDC__
static const float
#else
static float
#endif
one = 1.0000000000e+00, /* 0x3F800000 */
huge = 1.000e+30,
pio2_hi = 1.57079637050628662109375f,
pio2_lo = -4.37113900018624283e-8f,
pio4_hi = 0.785398185253143310546875f,
/* coefficient for R(x^2) */
pS0 = 1.6666667163e-01, /* 0x3e2aaaab */
pS1 = -3.2556581497e-01, /* 0xbea6b090 */
pS2 = 2.0121252537e-01, /* 0x3e4e0aa8 */
pS3 = -4.0055535734e-02, /* 0xbd241146 */
pS4 = 7.9153501429e-04, /* 0x3a4f7f04 */
pS5 = 3.4793309169e-05, /* 0x3811ef08 */
qS1 = -2.4033949375e+00, /* 0xc019d139 */
qS2 = 2.0209457874e+00, /* 0x4001572d */
qS3 = -6.8828397989e-01, /* 0xbf303361 */
qS4 = 7.7038154006e-02; /* 0x3d9dc62e */
 
#ifdef __STDC__
float __ieee754_asinf(float x)
#else
float __ieee754_asinf(x)
float x;
#endif
{
float t,w,p,q,c,r,s;
__int32_t hx,ix;
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
if(ix==0x3f800000) {
/* asin(1)=+-pi/2 with inexact */
return x*pio2_hi+x*pio2_lo;
} else if(ix> 0x3f800000) { /* |x|>= 1 */
return (x-x)/(x-x); /* asin(|x|>1) is NaN */
} else if (ix<0x3f000000) { /* |x|<0.5 */
if(ix<0x32000000) { /* if |x| < 2**-27 */
if(huge+x>one) return x;/* return x with inexact if x!=0*/
} else {
t = x*x;
p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
w = p/q;
return x+x*w;
}
}
/* 1> |x|>= 0.5 */
w = one-fabsf(x);
t = w*(float)0.5;
p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
s = __ieee754_sqrtf(t);
if(ix>=0x3F79999A) { /* if |x| > 0.975 */
w = p/q;
t = pio2_hi-((float)2.0*(s+s*w)-pio2_lo);
} else {
__int32_t iw;
w = s;
GET_FLOAT_WORD(iw,w);
SET_FLOAT_WORD(w,iw&0xfffff000);
c = (t-w*w)/(s+w);
r = p/q;
p = (float)2.0*s*r-(pio2_lo-(float)2.0*c);
q = pio4_hi-(float)2.0*w;
t = pio4_hi-(p-q);
}
if(hx>0) return t; else return -t;
}
/wf_j1.c
0,0 → 1,139
/* wf_j1.c -- float version of w_j1.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
* wrapper of j1f,y1f
*/
 
#include "fdlibm.h"
#include <errno.h>
 
 
#ifdef __STDC__
float j1f(float x) /* wrapper j1f */
#else
float j1f(x) /* wrapper j1f */
float x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_j1f(x);
#else
float z;
struct exception exc;
z = __ieee754_j1f(x);
if(_LIB_VERSION == _IEEE_ || isnanf(x) ) return z;
if(fabsf(x)>(float)X_TLOSS) {
/* j1f(|x|>X_TLOSS) */
exc.type = TLOSS;
exc.name = "j1f";
exc.err = 0;
exc.arg1 = exc.arg2 = (double)x;
exc.retval = 0.0;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
} else
return z;
#endif
}
 
#ifdef __STDC__
float y1f(float x) /* wrapper y1f */
#else
float y1f(x) /* wrapper y1f */
float x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_y1f(x);
#else
float z;
struct exception exc;
z = __ieee754_y1f(x);
if(_LIB_VERSION == _IEEE_ || isnanf(x) ) return z;
if(x <= (float)0.0){
/* y1f(0) = -inf or y1f(x<0) = NaN */
#ifndef HUGE_VAL
#define HUGE_VAL inf
double inf = 0.0;
 
SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */
#endif
exc.type = DOMAIN; /* should be SING for IEEE */
exc.name = "y1f";
exc.err = 0;
exc.arg1 = exc.arg2 = (double)x;
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
if (exc.err != 0)
errno = exc.err;
return (float)exc.retval;
}
if(x>(float)X_TLOSS) {
/* y1f(x>X_TLOSS) */
exc.type = TLOSS;
exc.name = "y1f";
exc.err = 0;
exc.arg1 = exc.arg2 = (double)x;
exc.retval = 0.0;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
if (exc.err != 0)
errno = exc.err;
return (float)exc.retval;
} else
return z;
#endif
}
 
#ifdef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double j1(double x)
#else
double j1(x)
double x;
#endif
{
return (double) j1f((float) x);
}
 
#ifdef __STDC__
double y1(double x)
#else
double y1(x)
double x;
#endif
{
return (double) y1f((float) x);
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/s_frexp.c
0,0 → 1,114
 
/* @(#)s_frexp.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
FUNCTION
<<frexp>>, <<frexpf>>---split floating-point number
INDEX
frexp
INDEX
frexpf
 
ANSI_SYNOPSIS
#include <math.h>
double frexp(double <[val]>, int *<[exp]>);
float frexpf(float <[val]>, int *<[exp]>);
 
TRAD_SYNOPSIS
#include <math.h>
double frexp(<[val]>, <[exp]>)
double <[val]>;
int *<[exp]>;
 
float frexpf(<[val]>, <[exp]>)
float <[val]>;
int *<[exp]>;
 
 
DESCRIPTION
All non zero, normal numbers can be described as <[m]> * 2**<[p]>.
<<frexp>> represents the double <[val]> as a mantissa <[m]>
and a power of two <[p]>. The resulting mantissa will always
be greater than or equal to <<0.5>>, and less than <<1.0>> (as
long as <[val]> is nonzero). The power of two will be stored
in <<*>><[exp]>.
 
@ifinfo
<[m]> and <[p]> are calculated so that
<[val]> is <[m]> times <<2>> to the power <[p]>.
@end ifinfo
@tex
<[m]> and <[p]> are calculated so that
$ val = m \times 2^p $.
@end tex
 
<<frexpf>> is identical, other than taking and returning
floats rather than doubles.
 
RETURNS
<<frexp>> returns the mantissa <[m]>. If <[val]> is <<0>>, infinity,
or Nan, <<frexp>> will set <<*>><[exp]> to <<0>> and return <[val]>.
 
PORTABILITY
<<frexp>> is ANSI.
<<frexpf>> is an extension.
 
 
*/
 
/*
* for non-zero x
* x = frexp(arg,&exp);
* return a double fp quantity x such that 0.5 <= |x| <1.0
* and the corresponding binary exponent "exp". That is
* arg = x*2^exp.
* If arg is inf, 0.0, or NaN, then frexp(arg,&exp) returns arg
* with *exp=0.
*/
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
static const double
#else
static double
#endif
two54 = 1.80143985094819840000e+16; /* 0x43500000, 0x00000000 */
 
#ifdef __STDC__
double frexp(double x, int *eptr)
#else
double frexp(x, eptr)
double x; int *eptr;
#endif
{
__int32_t hx, ix, lx;
EXTRACT_WORDS(hx,lx,x);
ix = 0x7fffffff&hx;
*eptr = 0;
if(ix>=0x7ff00000||((ix|lx)==0)) return x; /* 0,inf,nan */
if (ix<0x00100000) { /* subnormal */
x *= two54;
GET_HIGH_WORD(hx,x);
ix = hx&0x7fffffff;
*eptr = -54;
}
*eptr += (ix>>20)-1022;
hx = (hx&0x800fffff)|0x3fe00000;
SET_HIGH_WORD(x,hx);
return x;
}
 
#endif /* _DOUBLE_IS_32BITS */
/e_hypot.c
0,0 → 1,128
 
/* @(#)e_hypot.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/* __ieee754_hypot(x,y)
*
* Method :
* If (assume round-to-nearest) z=x*x+y*y
* has error less than sqrt(2)/2 ulp, than
* sqrt(z) has error less than 1 ulp (exercise).
*
* So, compute sqrt(x*x+y*y) with some care as
* follows to get the error below 1 ulp:
*
* Assume x>y>0;
* (if possible, set rounding to round-to-nearest)
* 1. if x > 2y use
* x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
* where x1 = x with lower 32 bits cleared, x2 = x-x1; else
* 2. if x <= 2y use
* t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
* where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
* y1= y with lower 32 bits chopped, y2 = y-y1.
*
* NOTE: scaling may be necessary if some argument is too
* large or too tiny
*
* Special cases:
* hypot(x,y) is INF if x or y is +INF or -INF; else
* hypot(x,y) is NAN if x or y is NAN.
*
* Accuracy:
* hypot(x,y) returns sqrt(x^2+y^2) with error less
* than 1 ulps (units in the last place)
*/
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double __ieee754_hypot(double x, double y)
#else
double __ieee754_hypot(x,y)
double x, y;
#endif
{
double a=x,b=y,t1,t2,y1,y2,w;
__int32_t j,k,ha,hb;
 
GET_HIGH_WORD(ha,x);
ha &= 0x7fffffff;
GET_HIGH_WORD(hb,y);
hb &= 0x7fffffff;
if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
SET_HIGH_WORD(a,ha); /* a <- |a| */
SET_HIGH_WORD(b,hb); /* b <- |b| */
if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
k=0;
if(ha > 0x5f300000) { /* a>2**500 */
if(ha >= 0x7ff00000) { /* Inf or NaN */
__uint32_t low;
w = a+b; /* for sNaN */
GET_LOW_WORD(low,a);
if(((ha&0xfffff)|low)==0) w = a;
GET_LOW_WORD(low,b);
if(((hb^0x7ff00000)|low)==0) w = b;
return w;
}
/* scale a and b by 2**-600 */
ha -= 0x25800000; hb -= 0x25800000; k += 600;
SET_HIGH_WORD(a,ha);
SET_HIGH_WORD(b,hb);
}
if(hb < 0x20b00000) { /* b < 2**-500 */
if(hb <= 0x000fffff) { /* subnormal b or 0 */
__uint32_t low;
GET_LOW_WORD(low,b);
if((hb|low)==0) return a;
t1=0;
SET_HIGH_WORD(t1,0x7fd00000); /* t1=2^1022 */
b *= t1;
a *= t1;
k -= 1022;
} else { /* scale a and b by 2^600 */
ha += 0x25800000; /* a *= 2^600 */
hb += 0x25800000; /* b *= 2^600 */
k -= 600;
SET_HIGH_WORD(a,ha);
SET_HIGH_WORD(b,hb);
}
}
/* medium size a and b */
w = a-b;
if (w>b) {
t1 = 0;
SET_HIGH_WORD(t1,ha);
t2 = a-t1;
w = __ieee754_sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
} else {
a = a+a;
y1 = 0;
SET_HIGH_WORD(y1,hb);
y2 = b - y1;
t1 = 0;
SET_HIGH_WORD(t1,ha+0x00100000);
t2 = a - t1;
w = __ieee754_sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
}
if(k!=0) {
__uint32_t high;
t1 = 1.0;
GET_HIGH_WORD(high,t1);
SET_HIGH_WORD(t1,high+(k<<20));
return t1*w;
} else return w;
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/math.tex
0,0 → 1,199
@node Math
@chapter Mathematical Functions (@file{math.h})
 
This chapter groups a wide variety of mathematical functions. The
corresponding definitions and declarations are in @file{math.h}.
Two definitions from @file{math.h} are of particular interest.
 
@enumerate
@item
The representation of infinity as a @code{double} is defined as
@code{HUGE_VAL}; this number is returned on overflow by many functions.
 
@item
The structure @code{exception} is used when you write customized error
handlers for the mathematical functions. You can customize error
handling for most of these functions by defining your own version of
@code{matherr}; see the section on @code{matherr} for details.
@end enumerate
 
@cindex system calls
@cindex support subroutines
@cindex stubs
@cindex OS stubs
Since the error handling code calls @code{fputs}, the mathematical
subroutines require stubs or minimal implementations for the same list
of OS subroutines as @code{fputs}: @code{close}, @code{fstat},
@code{isatty}, @code{lseek}, @code{read}, @code{sbrk}, @code{write}.
@xref{syscalls,,System Calls, libc.info, The Cygnus C Support Library},
for a discussion and for sample minimal implementations of these support
subroutines.
 
Alternative declarations of the mathematical functions, which exploit
specific machine capabilities to operate faster---but generally have
less error checking and may reflect additional limitations on some
machines---are available when you include @file{fastmath.h} instead of
@file{math.h}.
 
@menu
* version:: Version of library
* acos:: Arccosine
* acosh:: Inverse hyperbolic cosine
* asin:: Arcsine
* asinh:: Inverse hyperbolic sine
* atan:: Arctangent
* atan2:: Arctangent of y/x
* atanh:: Inverse hyperbolic tangent
* jN:: Bessel functions (jN, yN)
* cbrt:: Cube root
* copysign:: Sign of Y, magnitude of X
* cosh:: Hyperbolic cosine
* erf:: Error function (erf, erfc)
* exp:: Exponential
* expm1:: Exponential of x, - 1
* fabs:: Absolute value (magnitude)
* floor:: Floor and ceiling (floor, ceil)
* fmod:: Floating-point remainder (modulo)
* frexp:: Split floating-point number
* gamma:: Logarithmic gamma function
* hypot:: Distance from origin
* ilogb:: Get exponent
* infinity:: Floating infinity
* isnan:: Check type of number
* ldexp:: Load exponent
* log:: Natural logarithms
* log10:: Base 10 logarithms
* log1p:: Log of 1 + X
* matherr:: Modifiable math error handler
* modf:: Split fractional and integer parts
* nan:: Floating Not a Number
* nextafter:: Get next representable number
* pow:: X to the power Y
* remainder:: remainder of X divided by Y
* scalbn:: scalbn
* sin:: Sine or cosine (sin, cos)
* sinh:: Hyperbolic sine
* sqrt:: Positive square root
* tan:: Tangent
* tanh:: Hyperbolic tangent
@end menu
 
@page
@node version
@section Version of library
 
There are four different versions of the math library routines: IEEE,
POSIX, X/Open, or SVID. The version may be selected at runtime by
setting the global variable @code{_LIB_VERSION}, defined in
@file{math.h}. It may be set to one of the following constants defined
in @file{math.h}: @code{_IEEE_}, @code{_POSIX_}, @code{_XOPEN_}, or
@code{_SVID_}. The @code{_LIB_VERSION} variable is not specific to any
thread, and changing it will affect all threads.
 
The versions of the library differ only in how errors are handled.
 
In IEEE mode, the @code{matherr} function is never called, no warning
messages are printed, and @code{errno} is never set.
 
In POSIX mode, @code{errno} is set correctly, but the @code{matherr}
function is never called and no warning messages are printed.
 
In X/Open mode, @code{errno} is set correctly, and @code{matherr} is
called, but warning message are not printed.
 
In SVID mode, functions which overflow return 3.40282346638528860e+38,
the maximum single precision floating point value, rather than infinity.
Also, @code{errno} is set correctly, @code{matherr} is called, and, if
@code{matherr} returns 0, warning messages are printed for some errors.
For example, by default @samp{log(-1.0)} writes this message on standard
error output:
 
@example
log: DOMAIN error
@end example
 
The library is set to X/Open mode by default.
 
@page
@include math/wacos.def
 
@page
@include math/wacosh.def
 
@page
@include math/wasin.def
 
@page
@include math/sasinh.def
 
@page
@include math/satan.def
 
@page
@include math/watan2.def
 
@page
@include math/watanh.def
 
@page
@include math/wj0.def
 
@page
@include math/wcosh.def
 
@page
@include math/serf.def
 
@page
@include math/wexp.def
 
@page
@include math/sfabs.def
 
@page
@include math/sfloor.def
 
@page
@include math/wfmod.def
 
@page
@include math/sfrexp.def
 
@page
@include math/wgamma.def
 
@page
@include math/whypot.def
 
@page
@include math/sisnan.def
 
@page
@include math/sldexp.def
 
@page
@include math/wlog.def
 
@page
@include math/wlog10.def
 
@page
@include math/wpow.def
 
@page
@include math/wremainder.def
 
@page
@include math/wsqrt.def
 
@page
@include math/ssin.def
 
@page
@include math/wsinh.def
 
@page
@include math/stan.def
 
@page
@include math/stanh.def
/kf_sin.c
0,0 → 1,49
/* kf_sin.c -- float version of k_sin.c
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
#include "fdlibm.h"
 
#ifdef __STDC__
static const float
#else
static float
#endif
half = 5.0000000000e-01,/* 0x3f000000 */
S1 = -1.6666667163e-01, /* 0xbe2aaaab */
S2 = 8.3333337680e-03, /* 0x3c088889 */
S3 = -1.9841270114e-04, /* 0xb9500d01 */
S4 = 2.7557314297e-06, /* 0x3638ef1b */
S5 = -2.5050759689e-08, /* 0xb2d72f34 */
S6 = 1.5896910177e-10; /* 0x2f2ec9d3 */
 
#ifdef __STDC__
float __kernel_sinf(float x, float y, int iy)
#else
float __kernel_sinf(x, y, iy)
float x,y; int iy; /* iy=0 if y is zero */
#endif
{
float z,r,v;
__int32_t ix;
GET_FLOAT_WORD(ix,x);
ix &= 0x7fffffff; /* high word of x */
if(ix<0x32000000) /* |x| < 2**-27 */
{if((int)x==0) return x;} /* generate inexact */
z = x*x;
v = z*x;
r = S2+z*(S3+z*(S4+z*(S5+z*S6)));
if(iy==0) return x+v*(S1+z*r);
else return x-((z*(half*y-v*r)-y)-v*S1);
}
/w_acos.c
0,0 → 1,118
 
/* @(#)w_acos.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
FUNCTION
<<acos>>, <<acosf>>---arc cosine
 
INDEX
acos
INDEX
acosf
 
ANSI_SYNOPSIS
#include <math.h>
double acos(double <[x]>);
float acosf(float <[x]>);
 
TRAD_SYNOPSIS
#include <math.h>
double acos(<[x]>)
double <[x]>;
 
float acosf(<[x]>)
float <[x]>;
 
 
 
DESCRIPTION
 
<<acos>> computes the inverse cosine (arc cosine) of the input value.
Arguments to <<acos>> must be in the range @minus{}1 to 1.
 
<<acosf>> is identical to <<acos>>, except that it performs
its calculations on <<floats>>.
 
RETURNS
@ifinfo
<<acos>> and <<acosf>> return values in radians, in the range of 0 to pi.
@end ifinfo
@tex
<<acos>> and <<acosf>> return values in radians, in the range of <<0>> to $\pi$.
@end tex
 
If <[x]> is not between @minus{}1 and 1, the returned value is NaN
(not a number) the global variable <<errno>> is set to <<EDOM>>, and a
<<DOMAIN error>> message is sent as standard error output.
 
You can modify error handling for these functions using <<matherr>>.
 
 
QUICKREF ANSI SVID POSIX RENTRANT
acos y,y,y,m
acosf n,n,n,m
 
MATHREF
acos, [-1,1], acos(arg),,,
acos, NAN, arg,DOMAIN,EDOM
 
MATHREF
acosf, [-1,1], acosf(arg),,,
acosf, NAN, argf,DOMAIN,EDOM
*/
 
/*
* wrap_acos(x)
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double acos(double x) /* wrapper acos */
#else
double acos(x) /* wrapper acos */
double x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_acos(x);
#else
double z;
struct exception exc;
z = __ieee754_acos(x);
if(_LIB_VERSION == _IEEE_ || isnan(x)) return z;
if(fabs(x)>1.0) {
/* acos(|x|>1) */
exc.type = DOMAIN;
exc.name = "acos";
exc.err = 0;
exc.arg1 = exc.arg2 = x;
exc.retval = 0.0;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
} else
return z;
#endif
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/ef_hypot.c
0,0 → 1,83
/* ef_hypot.c -- float version of e_hypot.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
#include "fdlibm.h"
 
#ifdef __STDC__
float __ieee754_hypotf(float x, float y)
#else
float __ieee754_hypotf(x,y)
float x, y;
#endif
{
float a=x,b=y,t1,t2,y1,y2,w;
__int32_t j,k,ha,hb;
 
GET_FLOAT_WORD(ha,x);
ha &= 0x7fffffffL;
GET_FLOAT_WORD(hb,y);
hb &= 0x7fffffffL;
if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
SET_FLOAT_WORD(a,ha); /* a <- |a| */
SET_FLOAT_WORD(b,hb); /* b <- |b| */
if((ha-hb)>0xf000000L) {return a+b;} /* x/y > 2**30 */
k=0;
if(ha > 0x58800000L) { /* a>2**50 */
if(!FLT_UWORD_IS_FINITE(ha)) { /* Inf or NaN */
w = a+b; /* for sNaN */
if(FLT_UWORD_IS_INFINITE(ha)) w = a;
if(FLT_UWORD_IS_INFINITE(hb)) w = b;
return w;
}
/* scale a and b by 2**-60 */
ha -= 0x5d800000L; hb -= 0x5d800000L; k += 60;
SET_FLOAT_WORD(a,ha);
SET_FLOAT_WORD(b,hb);
}
if(hb < 0x26800000L) { /* b < 2**-50 */
if(FLT_UWORD_IS_ZERO(hb)) {
return a;
} else if(FLT_UWORD_IS_SUBNORMAL(hb)) {
SET_FLOAT_WORD(t1,0x3f000000L); /* t1=2^126 */
b *= t1;
a *= t1;
k -= 126;
} else { /* scale a and b by 2^60 */
ha += 0x5d800000; /* a *= 2^60 */
hb += 0x5d800000; /* b *= 2^60 */
k -= 60;
SET_FLOAT_WORD(a,ha);
SET_FLOAT_WORD(b,hb);
}
}
/* medium size a and b */
w = a-b;
if (w>b) {
SET_FLOAT_WORD(t1,ha&0xfffff000L);
t2 = a-t1;
w = __ieee754_sqrtf(t1*t1-(b*(-b)-t2*(a+t1)));
} else {
a = a+a;
SET_FLOAT_WORD(y1,hb&0xfffff000L);
y2 = b - y1;
SET_FLOAT_WORD(t1,ha+0x00800000L);
t2 = a - t1;
w = __ieee754_sqrtf(t1*y1-(w*(-w)-(t1*y2+t2*b)));
}
if(k!=0) {
SET_FLOAT_WORD(t1,0x3f800000L+(k<<23));
return t1*w;
} else return w;
}
/sf_sin.c
0,0 → 1,62
/* sf_sin.c -- float version of s_sin.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
#include "fdlibm.h"
 
#ifdef __STDC__
float sinf(float x)
#else
float sinf(x)
float x;
#endif
{
float y[2],z=0.0;
__int32_t n,ix;
 
GET_FLOAT_WORD(ix,x);
 
/* |x| ~< pi/4 */
ix &= 0x7fffffff;
if(ix <= 0x3f490fd8) return __kernel_sinf(x,z,0);
 
/* sin(Inf or NaN) is NaN */
else if (!FLT_UWORD_IS_FINITE(ix)) return x-x;
 
/* argument reduction needed */
else {
n = __ieee754_rem_pio2f(x,y);
switch(n&3) {
case 0: return __kernel_sinf(y[0],y[1],1);
case 1: return __kernel_cosf(y[0],y[1]);
case 2: return -__kernel_sinf(y[0],y[1],1);
default:
return -__kernel_cosf(y[0],y[1]);
}
}
}
 
#ifdef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double sin(double x)
#else
double sin(x)
double x;
#endif
{
return (double) sinf((float) x);
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/w_cosh.c
0,0 → 1,116
 
/* @(#)w_cosh.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
 
FUNCTION
<<cosh>>, <<coshf>>---hyperbolic cosine
 
ANSI_SYNOPSIS
#include <math.h>
double cosh(double <[x]>);
float coshf(float <[x]>)
 
TRAD_SYNOPSIS
#include <math.h>
double cosh(<[x]>)
double <[x]>;
 
float coshf(<[x]>)
float <[x]>;
 
DESCRIPTION
 
<<cosh>> computes the hyperbolic cosine of the argument <[x]>.
<<cosh(<[x]>)>> is defined as
@ifinfo
. (exp(x) + exp(-x))/2
@end ifinfo
@tex
$${(e^x + e^{-x})} \over 2$$
@end tex
 
Angles are specified in radians.
<<coshf>> is identical, save that it takes and returns <<float>>.
 
RETURNS
The computed value is returned. When the correct value would create
an overflow, <<cosh>> returns the value <<HUGE_VAL>> with the
appropriate sign, and the global value <<errno>> is set to <<ERANGE>>.
 
You can modify error handling for these functions using the
function <<matherr>>.
 
PORTABILITY
<<cosh>> is ANSI.
<<coshf>> is an extension.
 
QUICKREF
cosh ansi pure
coshf - pure
*/
 
/*
* wrapper cosh(x)
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifndef _DOUBLE_IS_32BITS
#ifdef __STDC__
double cosh(double x) /* wrapper cosh */
#else
double cosh(x) /* wrapper cosh */
double x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_cosh(x);
#else
double z;
struct exception exc;
z = __ieee754_cosh(x);
if(_LIB_VERSION == _IEEE_ || isnan(x)) return z;
if(fabs(x)>7.10475860073943863426e+02) {
/* cosh(finite) overflow */
#ifndef HUGE_VAL
#define HUGE_VAL inf
double inf = 0.0;
 
SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */
#endif
exc.type = OVERFLOW;
exc.name = "cosh";
exc.err = 0;
exc.arg1 = exc.arg2 = x;
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
} else
return z;
#endif
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/s_asinh.c
0,0 → 1,107
 
/* @(#)s_asinh.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
FUNCTION
<<asinh>>, <<asinhf>>---inverse hyperbolic sine
 
INDEX
asinh
INDEX
asinhf
 
ANSI_SYNOPSIS
#include <math.h>
double asinh(double <[x]>);
float asinhf(float <[x]>);
 
TRAD_SYNOPSIS
#include <math.h>
double asinh(<[x]>)
double <[x]>;
 
float asinhf(<[x]>)
float <[x]>;
 
DESCRIPTION
<<asinh>> calculates the inverse hyperbolic sine of <[x]>.
<<asinh>> is defined as
@ifinfo
. sgn(<[x]>) * log(abs(<[x]>) + sqrt(1+<[x]>*<[x]>))
@end ifinfo
@tex
$$sign(x) \times ln\Bigl(|x| + \sqrt{1+x^2}\Bigr)$$
@end tex
 
<<asinhf>> is identical, other than taking and returning floats.
 
RETURNS
<<asinh>> and <<asinhf>> return the calculated value.
 
PORTABILITY
Neither <<asinh>> nor <<asinhf>> are ANSI C.
 
*/
 
/* asinh(x)
* Method :
* Based on
* asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
* we have
* asinh(x) := x if 1+x*x=1,
* := sign(x)*(log(x)+ln2)) for large |x|, else
* := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
* := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
*/
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
static const double
#else
static double
#endif
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
huge= 1.00000000000000000000e+300;
 
#ifdef __STDC__
double asinh(double x)
#else
double asinh(x)
double x;
#endif
{
double t,w;
__int32_t hx,ix;
GET_HIGH_WORD(hx,x);
ix = hx&0x7fffffff;
if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */
if(ix< 0x3e300000) { /* |x|<2**-28 */
if(huge+x>one) return x; /* return x inexact except 0 */
}
if(ix>0x41b00000) { /* |x| > 2**28 */
w = __ieee754_log(fabs(x))+ln2;
} else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */
t = fabs(x);
w = __ieee754_log(2.0*t+one/(__ieee754_sqrt(x*x+one)+t));
} else { /* 2.0 > |x| > 2**-28 */
t = x*x;
w =log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t)));
}
if(hx>0) return w; else return -w;
}
 
#endif /* _DOUBLE_IS_32BITS */
/wf_asin.c
0,0 → 1,71
/* wf_asin.c -- float version of w_asin.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
 
/*
* wrapper asinf(x)
*/
 
 
#include "fdlibm.h"
#include <errno.h>
 
#ifdef __STDC__
float asinf(float x) /* wrapper asinf */
#else
float asinf(x) /* wrapper asinf */
float x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_asinf(x);
#else
float z;
struct exception exc;
z = __ieee754_asinf(x);
if(_LIB_VERSION == _IEEE_ || isnanf(x)) return z;
if(fabsf(x)>(float)1.0) {
/* asinf(|x|>1) */
exc.type = DOMAIN;
exc.name = "asinf";
exc.err = 0;
exc.arg1 = exc.arg2 = (double)x;
exc.retval = 0.0;
if(_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
if (exc.err != 0)
errno = exc.err;
return (float)exc.retval;
} else
return z;
#endif
}
 
#ifdef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double asin(double x)
#else
double asin(x)
double x;
#endif
{
return (double) asinf((float) x);
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/w_hypot.c
0,0 → 1,109
 
/* @(#)w_hypot.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
FUNCTION
<<hypot>>, <<hypotf>>---distance from origin
INDEX
hypot
INDEX
hypotf
 
ANSI_SYNOPSIS
#include <math.h>
double hypot(double <[x]>, double <[y]>);
float hypotf(float <[x]>, float <[y]>);
 
TRAD_SYNOPSIS
double hypot(<[x]>, <[y]>)
double <[x]>, <[y]>;
 
float hypotf(<[x]>, <[y]>)
float <[x]>, <[y]>;
 
DESCRIPTION
<<hypot>> calculates the Euclidean distance
@tex
$\sqrt{x^2+y^2}$
@end tex
@ifinfo
<<sqrt(<[x]>*<[x]> + <[y]>*<[y]>)>>
@end ifinfo
between the origin (0,0) and a point represented by the
Cartesian coordinates (<[x]>,<[y]>). <<hypotf>> differs only
in the type of its arguments and result.
 
RETURNS
Normally, the distance value is returned. On overflow,
<<hypot>> returns <<HUGE_VAL>> and sets <<errno>> to
<<ERANGE>>.
 
You can change the error treatment with <<matherr>>.
 
PORTABILITY
<<hypot>> and <<hypotf>> are not ANSI C. */
 
/*
* wrapper hypot(x,y)
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double hypot(double x, double y)/* wrapper hypot */
#else
double hypot(x,y) /* wrapper hypot */
double x,y;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_hypot(x,y);
#else
double z;
struct exception exc;
z = __ieee754_hypot(x,y);
if(_LIB_VERSION == _IEEE_) return z;
if((!finite(z))&&finite(x)&&finite(y)) {
/* hypot(finite,finite) overflow */
#ifndef HUGE_VAL
#define HUGE_VAL inf
double inf = 0.0;
 
SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */
#endif
exc.type = OVERFLOW;
exc.name = "hypot";
exc.err = 0;
exc.arg1 = x;
exc.arg2 = y;
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
} else
return z;
#endif
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/s_erf.c
0,0 → 1,373
 
/* @(#)s_erf.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
FUNCTION
<<erf>>, <<erff>>, <<erfc>>, <<erfcf>>---error function
INDEX
erf
INDEX
erff
INDEX
erfc
INDEX
erfcf
 
ANSI_SYNOPSIS
#include <math.h>
double erf(double <[x]>);
float erff(float <[x]>);
double erfc(double <[x]>);
float erfcf(float <[x]>);
TRAD_SYNOPSIS
#include <math.h>
 
double erf(<[x]>)
double <[x]>;
 
float erff(<[x]>)
float <[x]>;
 
double erfc(<[x]>)
double <[x]>;
 
float erfcf(<[x]>)
float <[x]>;
 
DESCRIPTION
<<erf>> calculates an approximation to the ``error function'',
which estimates the probability that an observation will fall within
<[x]> standard deviations of the mean (assuming a normal
distribution).
@tex
The error function is defined as
$${2\over\sqrt\pi}\times\int_0^x e^{-t^2}dt$$
@end tex
 
<<erfc>> calculates the complementary probability; that is,
<<erfc(<[x]>)>> is <<1 - erf(<[x]>)>>. <<erfc>> is computed directly,
so that you can use it to avoid the loss of precision that would
result from subtracting large probabilities (on large <[x]>) from 1.
 
<<erff>> and <<erfcf>> differ from <<erf>> and <<erfc>> only in the
argument and result types.
 
RETURNS
For positive arguments, <<erf>> and all its variants return a
probability---a number between 0 and 1.
 
PORTABILITY
None of the variants of <<erf>> are ANSI C.
*/
 
/* double erf(double x)
* double erfc(double x)
* x
* 2 |\
* erf(x) = --------- | exp(-t*t)dt
* sqrt(pi) \|
* 0
*
* erfc(x) = 1-erf(x)
* Note that
* erf(-x) = -erf(x)
* erfc(-x) = 2 - erfc(x)
*
* Method:
* 1. For |x| in [0, 0.84375]
* erf(x) = x + x*R(x^2)
* erfc(x) = 1 - erf(x) if x in [-.84375,0.25]
* = 0.5 + ((0.5-x)-x*R) if x in [0.25,0.84375]
* where R = P/Q where P is an odd poly of degree 8 and
* Q is an odd poly of degree 10.
* -57.90
* | R - (erf(x)-x)/x | <= 2
*
*
* Remark. The formula is derived by noting
* erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....)
* and that
* 2/sqrt(pi) = 1.128379167095512573896158903121545171688
* is close to one. The interval is chosen because the fix
* point of erf(x) is near 0.6174 (i.e., erf(x)=x when x is
* near 0.6174), and by some experiment, 0.84375 is chosen to
* guarantee the error is less than one ulp for erf.
*
* 2. For |x| in [0.84375,1.25], let s = |x| - 1, and
* c = 0.84506291151 rounded to single (24 bits)
* erf(x) = sign(x) * (c + P1(s)/Q1(s))
* erfc(x) = (1-c) - P1(s)/Q1(s) if x > 0
* 1+(c+P1(s)/Q1(s)) if x < 0
* |P1/Q1 - (erf(|x|)-c)| <= 2**-59.06
* Remark: here we use the taylor series expansion at x=1.
* erf(1+s) = erf(1) + s*Poly(s)
* = 0.845.. + P1(s)/Q1(s)
* That is, we use rational approximation to approximate
* erf(1+s) - (c = (single)0.84506291151)
* Note that |P1/Q1|< 0.078 for x in [0.84375,1.25]
* where
* P1(s) = degree 6 poly in s
* Q1(s) = degree 6 poly in s
*
* 3. For x in [1.25,1/0.35(~2.857143)],
* erfc(x) = (1/x)*exp(-x*x-0.5625+R1/S1)
* erf(x) = 1 - erfc(x)
* where
* R1(z) = degree 7 poly in z, (z=1/x^2)
* S1(z) = degree 8 poly in z
*
* 4. For x in [1/0.35,28]
* erfc(x) = (1/x)*exp(-x*x-0.5625+R2/S2) if x > 0
* = 2.0 - (1/x)*exp(-x*x-0.5625+R2/S2) if -6<x<0
* = 2.0 - tiny (if x <= -6)
* erf(x) = sign(x)*(1.0 - erfc(x)) if x < 6, else
* erf(x) = sign(x)*(1.0 - tiny)
* where
* R2(z) = degree 6 poly in z, (z=1/x^2)
* S2(z) = degree 7 poly in z
*
* Note1:
* To compute exp(-x*x-0.5625+R/S), let s be a single
* precision number and s := x; then
* -x*x = -s*s + (s-x)*(s+x)
* exp(-x*x-0.5626+R/S) =
* exp(-s*s-0.5625)*exp((s-x)*(s+x)+R/S);
* Note2:
* Here 4 and 5 make use of the asymptotic series
* exp(-x*x)
* erfc(x) ~ ---------- * ( 1 + Poly(1/x^2) )
* x*sqrt(pi)
* We use rational approximation to approximate
* g(s)=f(1/x^2) = log(erfc(x)*x) - x*x + 0.5625
* Here is the error bound for R1/S1 and R2/S2
* |R1/S1 - f(x)| < 2**(-62.57)
* |R2/S2 - f(x)| < 2**(-61.52)
*
* 5. For inf > x >= 28
* erf(x) = sign(x) *(1 - tiny) (raise inexact)
* erfc(x) = tiny*tiny (raise underflow) if x > 0
* = 2 - tiny if x<0
*
* 7. Special case:
* erf(0) = 0, erf(inf) = 1, erf(-inf) = -1,
* erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2,
* erfc/erf(NaN) is NaN
*/
 
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
static const double
#else
static double
#endif
tiny = 1e-300,
half= 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */
/* c = (float)0.84506291151 */
erx = 8.45062911510467529297e-01, /* 0x3FEB0AC1, 0x60000000 */
/*
* Coefficients for approximation to erf on [0,0.84375]
*/
efx = 1.28379167095512586316e-01, /* 0x3FC06EBA, 0x8214DB69 */
efx8= 1.02703333676410069053e+00, /* 0x3FF06EBA, 0x8214DB69 */
pp0 = 1.28379167095512558561e-01, /* 0x3FC06EBA, 0x8214DB68 */
pp1 = -3.25042107247001499370e-01, /* 0xBFD4CD7D, 0x691CB913 */
pp2 = -2.84817495755985104766e-02, /* 0xBF9D2A51, 0xDBD7194F */
pp3 = -5.77027029648944159157e-03, /* 0xBF77A291, 0x236668E4 */
pp4 = -2.37630166566501626084e-05, /* 0xBEF8EAD6, 0x120016AC */
qq1 = 3.97917223959155352819e-01, /* 0x3FD97779, 0xCDDADC09 */
qq2 = 6.50222499887672944485e-02, /* 0x3FB0A54C, 0x5536CEBA */
qq3 = 5.08130628187576562776e-03, /* 0x3F74D022, 0xC4D36B0F */
qq4 = 1.32494738004321644526e-04, /* 0x3F215DC9, 0x221C1A10 */
qq5 = -3.96022827877536812320e-06, /* 0xBED09C43, 0x42A26120 */
/*
* Coefficients for approximation to erf in [0.84375,1.25]
*/
pa0 = -2.36211856075265944077e-03, /* 0xBF6359B8, 0xBEF77538 */
pa1 = 4.14856118683748331666e-01, /* 0x3FDA8D00, 0xAD92B34D */
pa2 = -3.72207876035701323847e-01, /* 0xBFD7D240, 0xFBB8C3F1 */
pa3 = 3.18346619901161753674e-01, /* 0x3FD45FCA, 0x805120E4 */
pa4 = -1.10894694282396677476e-01, /* 0xBFBC6398, 0x3D3E28EC */
pa5 = 3.54783043256182359371e-02, /* 0x3FA22A36, 0x599795EB */
pa6 = -2.16637559486879084300e-03, /* 0xBF61BF38, 0x0A96073F */
qa1 = 1.06420880400844228286e-01, /* 0x3FBB3E66, 0x18EEE323 */
qa2 = 5.40397917702171048937e-01, /* 0x3FE14AF0, 0x92EB6F33 */
qa3 = 7.18286544141962662868e-02, /* 0x3FB2635C, 0xD99FE9A7 */
qa4 = 1.26171219808761642112e-01, /* 0x3FC02660, 0xE763351F */
qa5 = 1.36370839120290507362e-02, /* 0x3F8BEDC2, 0x6B51DD1C */
qa6 = 1.19844998467991074170e-02, /* 0x3F888B54, 0x5735151D */
/*
* Coefficients for approximation to erfc in [1.25,1/0.35]
*/
ra0 = -9.86494403484714822705e-03, /* 0xBF843412, 0x600D6435 */
ra1 = -6.93858572707181764372e-01, /* 0xBFE63416, 0xE4BA7360 */
ra2 = -1.05586262253232909814e+01, /* 0xC0251E04, 0x41B0E726 */
ra3 = -6.23753324503260060396e+01, /* 0xC04F300A, 0xE4CBA38D */
ra4 = -1.62396669462573470355e+02, /* 0xC0644CB1, 0x84282266 */
ra5 = -1.84605092906711035994e+02, /* 0xC067135C, 0xEBCCABB2 */
ra6 = -8.12874355063065934246e+01, /* 0xC0545265, 0x57E4D2F2 */
ra7 = -9.81432934416914548592e+00, /* 0xC023A0EF, 0xC69AC25C */
sa1 = 1.96512716674392571292e+01, /* 0x4033A6B9, 0xBD707687 */
sa2 = 1.37657754143519042600e+02, /* 0x4061350C, 0x526AE721 */
sa3 = 4.34565877475229228821e+02, /* 0x407B290D, 0xD58A1A71 */
sa4 = 6.45387271733267880336e+02, /* 0x40842B19, 0x21EC2868 */
sa5 = 4.29008140027567833386e+02, /* 0x407AD021, 0x57700314 */
sa6 = 1.08635005541779435134e+02, /* 0x405B28A3, 0xEE48AE2C */
sa7 = 6.57024977031928170135e+00, /* 0x401A47EF, 0x8E484A93 */
sa8 = -6.04244152148580987438e-02, /* 0xBFAEEFF2, 0xEE749A62 */
/*
* Coefficients for approximation to erfc in [1/.35,28]
*/
rb0 = -9.86494292470009928597e-03, /* 0xBF843412, 0x39E86F4A */
rb1 = -7.99283237680523006574e-01, /* 0xBFE993BA, 0x70C285DE */
rb2 = -1.77579549177547519889e+01, /* 0xC031C209, 0x555F995A */
rb3 = -1.60636384855821916062e+02, /* 0xC064145D, 0x43C5ED98 */
rb4 = -6.37566443368389627722e+02, /* 0xC083EC88, 0x1375F228 */
rb5 = -1.02509513161107724954e+03, /* 0xC0900461, 0x6A2E5992 */
rb6 = -4.83519191608651397019e+02, /* 0xC07E384E, 0x9BDC383F */
sb1 = 3.03380607434824582924e+01, /* 0x403E568B, 0x261D5190 */
sb2 = 3.25792512996573918826e+02, /* 0x40745CAE, 0x221B9F0A */
sb3 = 1.53672958608443695994e+03, /* 0x409802EB, 0x189D5118 */
sb4 = 3.19985821950859553908e+03, /* 0x40A8FFB7, 0x688C246A */
sb5 = 2.55305040643316442583e+03, /* 0x40A3F219, 0xCEDF3BE6 */
sb6 = 4.74528541206955367215e+02, /* 0x407DA874, 0xE79FE763 */
sb7 = -2.24409524465858183362e+01; /* 0xC03670E2, 0x42712D62 */
 
#ifdef __STDC__
double erf(double x)
#else
double erf(x)
double x;
#endif
{
__int32_t hx,ix,i;
double R,S,P,Q,s,y,z,r;
GET_HIGH_WORD(hx,x);
ix = hx&0x7fffffff;
if(ix>=0x7ff00000) { /* erf(nan)=nan */
i = ((__uint32_t)hx>>31)<<1;
return (double)(1-i)+one/x; /* erf(+-inf)=+-1 */
}
 
if(ix < 0x3feb0000) { /* |x|<0.84375 */
if(ix < 0x3e300000) { /* |x|<2**-28 */
if (ix < 0x00800000)
return 0.125*(8.0*x+efx8*x); /*avoid underflow */
return x + efx*x;
}
z = x*x;
r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
y = r/s;
return x + x*y;
}
if(ix < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */
s = fabs(x)-one;
P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
if(hx>=0) return erx + P/Q; else return -erx - P/Q;
}
if (ix >= 0x40180000) { /* inf>|x|>=6 */
if(hx>=0) return one-tiny; else return tiny-one;
}
x = fabs(x);
s = one/(x*x);
if(ix< 0x4006DB6E) { /* |x| < 1/0.35 */
R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
ra5+s*(ra6+s*ra7))))));
S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
sa5+s*(sa6+s*(sa7+s*sa8)))))));
} else { /* |x| >= 1/0.35 */
R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
rb5+s*rb6)))));
S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
sb5+s*(sb6+s*sb7))))));
}
z = x;
SET_LOW_WORD(z,0);
r = __ieee754_exp(-z*z-0.5625)*__ieee754_exp((z-x)*(z+x)+R/S);
if(hx>=0) return one-r/x; else return r/x-one;
}
 
#ifdef __STDC__
double erfc(double x)
#else
double erfc(x)
double x;
#endif
{
__int32_t hx,ix;
double R,S,P,Q,s,y,z,r;
GET_HIGH_WORD(hx,x);
ix = hx&0x7fffffff;
if(ix>=0x7ff00000) { /* erfc(nan)=nan */
/* erfc(+-inf)=0,2 */
return (double)(((__uint32_t)hx>>31)<<1)+one/x;
}
 
if(ix < 0x3feb0000) { /* |x|<0.84375 */
if(ix < 0x3c700000) /* |x|<2**-56 */
return one-x;
z = x*x;
r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
y = r/s;
if(hx < 0x3fd00000) { /* x<1/4 */
return one-(x+x*y);
} else {
r = x*y;
r += (x-half);
return half - r ;
}
}
if(ix < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */
s = fabs(x)-one;
P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
if(hx>=0) {
z = one-erx; return z - P/Q;
} else {
z = erx+P/Q; return one+z;
}
}
if (ix < 0x403c0000) { /* |x|<28 */
x = fabs(x);
s = one/(x*x);
if(ix< 0x4006DB6D) { /* |x| < 1/.35 ~ 2.857143*/
R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
ra5+s*(ra6+s*ra7))))));
S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
sa5+s*(sa6+s*(sa7+s*sa8)))))));
} else { /* |x| >= 1/.35 ~ 2.857143 */
if(hx<0&&ix>=0x40180000) return two-tiny;/* x < -6 */
R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
rb5+s*rb6)))));
S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
sb5+s*(sb6+s*sb7))))));
}
z = x;
SET_LOW_WORD(z,0);
r = __ieee754_exp(-z*z-0.5625)*
__ieee754_exp((z-x)*(z+x)+R/S);
if(hx>0) return r/x; else return two-r/x;
} else {
if(hx>0) return tiny*tiny; else return two-tiny;
}
}
 
#endif /* _DOUBLE_IS_32BITS */
/w_gamma.c
0,0 → 1,193
 
/* @(#)w_gamma.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
 
/*
FUNCTION
<<gamma>>, <<gammaf>>, <<lgamma>>, <<lgammaf>>, <<gamma_r>>,
<<gammaf_r>>, <<lgamma_r>>, <<lgammaf_r>>---logarithmic gamma
function
INDEX
gamma
INDEX
gammaf
INDEX
lgamma
INDEX
lgammaf
INDEX
gamma_r
INDEX
gammaf_r
INDEX
lgamma_r
INDEX
lgammaf_r
 
ANSI_SYNOPSIS
#include <math.h>
double gamma(double <[x]>);
float gammaf(float <[x]>);
double lgamma(double <[x]>);
float lgammaf(float <[x]>);
double gamma_r(double <[x]>, int *<[signgamp]>);
float gammaf_r(float <[x]>, int *<[signgamp]>);
double lgamma_r(double <[x]>, int *<[signgamp]>);
float lgammaf_r(float <[x]>, int *<[signgamp]>);
 
TRAD_SYNOPSIS
#include <math.h>
double gamma(<[x]>)
double <[x]>;
float gammaf(<[x]>)
float <[x]>;
double lgamma(<[x]>)
double <[x]>;
float lgammaf(<[x]>)
float <[x]>;
double gamma_r(<[x]>, <[signgamp]>)
double <[x]>;
int <[signgamp]>;
float gammaf_r(<[x]>, <[signgamp]>)
float <[x]>;
int <[signgamp]>;
double lgamma_r(<[x]>, <[signgamp]>)
double <[x]>;
int <[signgamp]>;
float lgammaf_r(<[x]>, <[signgamp]>)
float <[x]>;
int <[signgamp]>;
 
DESCRIPTION
<<gamma>> calculates
@tex
$\mit ln\bigl(\Gamma(x)\bigr)$,
@end tex
the natural logarithm of the gamma function of <[x]>. The gamma function
(<<exp(gamma(<[x]>))>>) is a generalization of factorial, and retains
the property that
@ifinfo
<<exp(gamma(N))>> is equivalent to <<N*exp(gamma(N-1))>>.
@end ifinfo
@tex
$\mit \Gamma(N)\equiv N\times\Gamma(N-1)$.
@end tex
Accordingly, the results of the gamma function itself grow very
quickly. <<gamma>> is defined as
@tex
$\mit ln\bigl(\Gamma(x)\bigr)$ rather than simply $\mit \Gamma(x)$
@end tex
@ifinfo
the natural log of the gamma function, rather than the gamma function
itself,
@end ifinfo
to extend the useful range of results representable.
 
The sign of the result is returned in the global variable <<signgam>>,
which is declared in math.h.
 
<<gammaf>> performs the same calculation as <<gamma>>, but uses and
returns <<float>> values.
 
<<lgamma>> and <<lgammaf>> are alternate names for <<gamma>> and
<<gammaf>>. The use of <<lgamma>> instead of <<gamma>> is a reminder
that these functions compute the log of the gamma function, rather
than the gamma function itself.
 
The functions <<gamma_r>>, <<gammaf_r>>, <<lgamma_r>>, and
<<lgammaf_r>> are just like <<gamma>>, <<gammaf>>, <<lgamma>>, and
<<lgammaf>>, respectively, but take an additional argument. This
additional argument is a pointer to an integer. This additional
argument is used to return the sign of the result, and the global
variable <<signgam>> is not used. These functions may be used for
reentrant calls (but they will still set the global variable <<errno>>
if an error occurs).
 
RETURNS
Normally, the computed result is returned.
 
When <[x]> is a nonpositive integer, <<gamma>> returns <<HUGE_VAL>>
and <<errno>> is set to <<EDOM>>. If the result overflows, <<gamma>>
returns <<HUGE_VAL>> and <<errno>> is set to <<ERANGE>>.
 
You can modify this error treatment using <<matherr>>.
 
PORTABILITY
Neither <<gamma>> nor <<gammaf>> is ANSI C. */
 
/* double gamma(double x)
* Return the logarithm of the Gamma function of x.
*
* Method: call gamma_r
*/
 
#include "fdlibm.h"
#include <reent.h>
#include <errno.h>
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double gamma(double x)
#else
double gamma(x)
double x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_gamma_r(x,&(_REENT->_new._reent._gamma_signgam));
#else
double y;
struct exception exc;
y = __ieee754_gamma_r(x,&(_REENT->_new._reent._gamma_signgam));
if(_LIB_VERSION == _IEEE_) return y;
if(!finite(y)&&finite(x)) {
#ifndef HUGE_VAL
#define HUGE_VAL inf
double inf = 0.0;
 
SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */
#endif
exc.name = "gamma";
exc.err = 0;
exc.arg1 = exc.arg2 = x;
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if(floor(x)==x&&x<=0.0) {
/* gamma(-integer) or gamma(0) */
exc.type = SING;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
} else {
/* gamma(finite) overflow */
exc.type = OVERFLOW;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
} else
return y;
#endif
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/er_gamma.c
0,0 → 1,32
 
/* @(#)er_gamma.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
 
/* __ieee754_gamma_r(x, signgamp)
* Reentrant version of the logarithm of the Gamma function
* with user provide pointer for the sign of Gamma(x).
*
* Method: See __ieee754_lgamma_r
*/
 
#include "fdlibm.h"
 
#ifdef __STDC__
double __ieee754_gamma_r(double x, int *signgamp)
#else
double __ieee754_gamma_r(x,signgamp)
double x; int *signgamp;
#endif
{
return __ieee754_lgamma_r(x,signgamp);
}
/sf_floor.c
0,0 → 1,80
/* sf_floor.c -- float version of s_floor.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
* floorf(x)
* Return x rounded toward -inf to integral value
* Method:
* Bit twiddling.
* Exception:
* Inexact flag raised if x not equal to floorf(x).
*/
 
#include "fdlibm.h"
 
#ifdef __STDC__
static const float huge = 1.0e30;
#else
static float huge = 1.0e30;
#endif
 
#ifdef __STDC__
float floorf(float x)
#else
float floorf(x)
float x;
#endif
{
__int32_t i0,j0;
__uint32_t i,ix;
GET_FLOAT_WORD(i0,x);
ix = (i0&0x7fffffff);
j0 = (ix>>23)-0x7f;
if(j0<23) {
if(j0<0) { /* raise inexact if x != 0 */
if(huge+x>(float)0.0) {/* return 0*sign(x) if |x|<1 */
if(i0>=0) {i0=0;}
else if(!FLT_UWORD_IS_ZERO(ix))
{ i0=0xbf800000;}
}
} else {
i = (0x007fffff)>>j0;
if((i0&i)==0) return x; /* x is integral */
if(huge+x>(float)0.0) { /* raise inexact flag */
if(i0<0) i0 += (0x00800000)>>j0;
i0 &= (~i);
}
}
} else {
if(!FLT_UWORD_IS_FINITE(ix)) return x+x; /* inf or NaN */
else return x; /* x is integral */
}
SET_FLOAT_WORD(x,i0);
return x;
}
 
#ifdef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double floor(double x)
#else
double floor(x)
double x;
#endif
{
return (double) floorf((float) x);
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/e_remainder.c
0,0 → 1,80
 
/* @(#)e_remainder.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/* __ieee754_remainder(x,p)
* Return :
* returns x REM p = x - [x/p]*p as if in infinite
* precise arithmetic, where [x/p] is the (infinite bit)
* integer nearest x/p (in half way case choose the even one).
* Method :
* Based on fmod() return x-[x/p]chopped*p exactlp.
*/
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
static const double zero = 0.0;
#else
static double zero = 0.0;
#endif
 
 
#ifdef __STDC__
double __ieee754_remainder(double x, double p)
#else
double __ieee754_remainder(x,p)
double x,p;
#endif
{
__int32_t hx,hp;
__uint32_t sx,lx,lp;
double p_half;
 
EXTRACT_WORDS(hx,lx,x);
EXTRACT_WORDS(hp,lp,p);
sx = hx&0x80000000;
hp &= 0x7fffffff;
hx &= 0x7fffffff;
 
/* purge off exception values */
if((hp|lp)==0) return (x*p)/(x*p); /* p = 0 */
if((hx>=0x7ff00000)|| /* x not finite */
((hp>=0x7ff00000)&& /* p is NaN */
(((hp-0x7ff00000)|lp)!=0)))
return (x*p)/(x*p);
 
 
if (hp<=0x7fdfffff) x = __ieee754_fmod(x,p+p); /* now x < 2p */
if (((hx-hp)|(lx-lp))==0) return zero*x;
x = fabs(x);
p = fabs(p);
if (hp<0x00200000) {
if(x+x>p) {
x-=p;
if(x+x>=p) x -= p;
}
} else {
p_half = 0.5*p;
if(x>p_half) {
x-=p;
if(x>=p_half) x -= p;
}
}
GET_HIGH_WORD(hx,x);
SET_HIGH_WORD(x,hx^sx);
return x;
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/k_standard.c
0,0 → 1,784
 
/* @(#)k_standard.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifndef _USE_WRITE
#include <stdio.h> /* fputs(), stderr */
#define WRITE2(u,v) fputs(u, stderr)
#else /* !defined(_USE_WRITE) */
#include <unistd.h> /* write */
#define WRITE2(u,v) write(2, u, v)
#undef fflush
#endif /* !defined(_USE_WRITE) */
 
#ifdef __STDC__
static const double zero = 0.0; /* used as const */
#else
static double zero = 0.0; /* used as const */
#endif
 
/*
* Standard conformance (non-IEEE) on exception cases.
* Mapping:
* 1 -- acos(|x|>1)
* 2 -- asin(|x|>1)
* 3 -- atan2(+-0,+-0)
* 4 -- hypot overflow
* 5 -- cosh overflow
* 6 -- exp overflow
* 7 -- exp underflow
* 8 -- y0(0)
* 9 -- y0(-ve)
* 10-- y1(0)
* 11-- y1(-ve)
* 12-- yn(0)
* 13-- yn(-ve)
* 14-- lgamma(finite) overflow
* 15-- lgamma(-integer)
* 16-- log(0)
* 17-- log(x<0)
* 18-- log10(0)
* 19-- log10(x<0)
* 20-- pow(0.0,0.0)
* 21-- pow(x,y) overflow
* 22-- pow(x,y) underflow
* 23-- pow(0,negative)
* 24-- pow(neg,non-integral)
* 25-- sinh(finite) overflow
* 26-- sqrt(negative)
* 27-- fmod(x,0)
* 28-- remainder(x,0)
* 29-- acosh(x<1)
* 30-- atanh(|x|>1)
* 31-- atanh(|x|=1)
* 32-- scalb overflow
* 33-- scalb underflow
* 34-- j0(|x|>X_TLOSS)
* 35-- y0(x>X_TLOSS)
* 36-- j1(|x|>X_TLOSS)
* 37-- y1(x>X_TLOSS)
* 38-- jn(|x|>X_TLOSS, n)
* 39-- yn(x>X_TLOSS, n)
* 40-- gamma(finite) overflow
* 41-- gamma(-integer)
* 42-- pow(NaN,0.0)
*/
 
 
#ifdef __STDC__
double __kernel_standard(double x, double y, int type)
#else
double __kernel_standard(x,y,type)
double x,y; int type;
#endif
{
struct exception exc;
#ifndef HUGE_VAL /* this is the only routine that uses HUGE_VAL */
#define HUGE_VAL inf
double inf = 0.0;
 
SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */
#endif
 
#ifdef _USE_WRITE
/* (void) fflush(_stdout_r(p)); */
#endif
exc.arg1 = x;
exc.arg2 = y;
exc.err = 0;
switch(type) {
case 1:
case 101:
/* acos(|x|>1) */
exc.type = DOMAIN;
exc.name = type < 100 ? "acos" : "acosf";
exc.retval = zero;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
/* if(_LIB_VERSION == _SVID_) {
(void) WRITE2("acos: DOMAIN error\n", 19);
} */
errno = EDOM;
}
break;
case 2:
case 102:
/* asin(|x|>1) */
exc.type = DOMAIN;
exc.name = type < 100 ? "asin" : "asinf";
exc.retval = zero;
if(_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
/* if(_LIB_VERSION == _SVID_) {
(void) WRITE2("asin: DOMAIN error\n", 19);
} */
errno = EDOM;
}
break;
case 3:
case 103:
/* atan2(+-0,+-0) */
exc.arg1 = y;
exc.arg2 = x;
exc.type = DOMAIN;
exc.name = type < 100 ? "atan2" : "atan2f";
exc.retval = zero;
if(_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
/* if(_LIB_VERSION == _SVID_) {
(void) WRITE2("atan2: DOMAIN error\n", 20);
} */
errno = EDOM;
}
break;
case 4:
case 104:
/* hypot(finite,finite) overflow */
exc.type = OVERFLOW;
exc.name = type < 100 ? "hypot" : "hypotf";
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
break;
case 5:
case 105:
/* cosh(finite) overflow */
exc.type = OVERFLOW;
exc.name = type < 100 ? "cosh" : "coshf";
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
break;
case 6:
case 106:
/* exp(finite) overflow */
exc.type = OVERFLOW;
exc.name = type < 100 ? "exp" : "expf";
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
break;
case 7:
case 107:
/* exp(finite) underflow */
exc.type = UNDERFLOW;
exc.name = type < 100 ? "exp" : "expf";
exc.retval = zero;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
break;
case 8:
case 108:
/* y0(0) = -inf */
exc.type = DOMAIN; /* should be SING for IEEE */
exc.name = type < 100 ? "y0" : "y0f";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
/* if (_LIB_VERSION == _SVID_) {
(void) WRITE2("y0: DOMAIN error\n", 17);
} */
errno = EDOM;
}
break;
case 9:
case 109:
/* y0(x<0) = NaN */
exc.type = DOMAIN;
exc.name = type < 100 ? "y0" : "y0f";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
/*if (_LIB_VERSION == _SVID_) {
(void) WRITE2("y0: DOMAIN error\n", 17);
} */
errno = EDOM;
}
break;
case 10:
case 110:
/* y1(0) = -inf */
exc.type = DOMAIN; /* should be SING for IEEE */
exc.name = type < 100 ? "y1" : "y1f";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
/* if (_LIB_VERSION == _SVID_) {
(void) WRITE2("y1: DOMAIN error\n", 17);
} */
errno = EDOM;
}
break;
case 11:
case 111:
/* y1(x<0) = NaN */
exc.type = DOMAIN;
exc.name = type < 100 ? "y1" : "y1f";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
/* if (_LIB_VERSION == _SVID_) {
(void) WRITE2("y1: DOMAIN error\n", 17);
} */
errno = EDOM;
}
break;
case 12:
case 112:
/* yn(n,0) = -inf */
exc.type = DOMAIN; /* should be SING for IEEE */
exc.name = type < 100 ? "yn" : "ynf";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
/* if (_LIB_VERSION == _SVID_) {
(void) WRITE2("yn: DOMAIN error\n", 17);
} */
errno = EDOM;
}
break;
case 13:
case 113:
/* yn(x<0) = NaN */
exc.type = DOMAIN;
exc.name = type < 100 ? "yn" : "ynf";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
/* if (_LIB_VERSION == _SVID_) {
(void) WRITE2("yn: DOMAIN error\n", 17);
} */
errno = EDOM;
}
break;
case 14:
case 114:
/* lgamma(finite) overflow */
exc.type = OVERFLOW;
exc.name = type < 100 ? "lgamma" : "lgammaf";
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
break;
case 15:
case 115:
/* lgamma(-integer) or lgamma(0) */
exc.type = SING;
exc.name = type < 100 ? "lgamma" : "lgammaf";
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
/* if (_LIB_VERSION == _SVID_) {
(void) WRITE2("lgamma: SING error\n", 19);
} */
errno = EDOM;
}
break;
case 16:
case 116:
/* log(0) */
exc.type = SING;
exc.name = type < 100 ? "log" : "logf";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
/* if (_LIB_VERSION == _SVID_) {
(void) WRITE2("log: SING error\n", 16);
} */
errno = EDOM;
}
break;
case 17:
case 117:
/* log(x<0) */
exc.type = DOMAIN;
exc.name = type < 100 ? "log" : "logf";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
/* if (_LIB_VERSION == _SVID_) {
(void) WRITE2("log: DOMAIN error\n", 18);
} */
errno = EDOM;
}
break;
case 18:
case 118:
/* log10(0) */
exc.type = SING;
exc.name = type < 100 ? "log10" : "log10f";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
/* if (_LIB_VERSION == _SVID_) {
(void) WRITE2("log10: SING error\n", 18);
} */
errno = EDOM;
}
break;
case 19:
case 119:
/* log10(x<0) */
exc.type = DOMAIN;
exc.name = type < 100 ? "log10" : "log10f";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
/* if (_LIB_VERSION == _SVID_) {
(void) WRITE2("log10: DOMAIN error\n", 20);
} */
errno = EDOM;
}
break;
case 20:
case 120:
/* pow(0.0,0.0) */
/* error only if _LIB_VERSION == _SVID_ */
exc.type = DOMAIN;
exc.name = type < 100 ? "pow" : "powf";
exc.retval = zero;
if (_LIB_VERSION != _SVID_) exc.retval = 1.0;
else if (!matherr(&exc)) {
/* (void) WRITE2("pow(0,0): DOMAIN error\n", 23); */
errno = EDOM;
}
break;
case 21:
case 121:
/* pow(x,y) overflow */
exc.type = OVERFLOW;
exc.name = type < 100 ? "pow" : "powf";
if (_LIB_VERSION == _SVID_) {
exc.retval = HUGE;
y *= 0.5;
if(x<zero&&rint(y)!=y) exc.retval = -HUGE;
} else {
exc.retval = HUGE_VAL;
y *= 0.5;
if(x<zero&&rint(y)!=y) exc.retval = -HUGE_VAL;
}
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
break;
case 22:
case 122:
/* pow(x,y) underflow */
exc.type = UNDERFLOW;
exc.name = type < 100 ? "pow" : "powf";
exc.retval = zero;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
break;
case 23:
case 123:
/* 0**neg */
exc.type = DOMAIN;
exc.name = type < 100 ? "pow" : "powf";
if (_LIB_VERSION == _SVID_)
exc.retval = zero;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
/* if (_LIB_VERSION == _SVID_) {
(void) WRITE2("pow(0,neg): DOMAIN error\n", 25);
} */
errno = EDOM;
}
break;
case 24:
case 124:
/* neg**non-integral */
exc.type = DOMAIN;
exc.name = type < 100 ? "pow" : "powf";
if (_LIB_VERSION == _SVID_)
exc.retval = zero;
else
exc.retval = zero/zero; /* X/Open allow NaN */
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
/* if (_LIB_VERSION == _SVID_) {
(void) WRITE2("neg**non-integral: DOMAIN error\n", 32);
} */
errno = EDOM;
}
break;
case 25:
case 125:
/* sinh(finite) overflow */
exc.type = OVERFLOW;
exc.name = type < 100 ? "sinh" : "sinhf";
if (_LIB_VERSION == _SVID_)
exc.retval = ( (x>zero) ? HUGE : -HUGE);
else
exc.retval = ( (x>zero) ? HUGE_VAL : -HUGE_VAL);
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
break;
case 26:
case 126:
/* sqrt(x<0) */
exc.type = DOMAIN;
exc.name = type < 100 ? "sqrt" : "sqrtf";
if (_LIB_VERSION == _SVID_)
exc.retval = zero;
else
exc.retval = zero/zero;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
/* if (_LIB_VERSION == _SVID_) {
(void) WRITE2("sqrt: DOMAIN error\n", 19);
} */
errno = EDOM;
}
break;
case 27:
case 127:
/* fmod(x,0) */
exc.type = DOMAIN;
exc.name = type < 100 ? "fmod" : "fmodf";
if (_LIB_VERSION == _SVID_)
exc.retval = x;
else
exc.retval = zero/zero;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
/* if (_LIB_VERSION == _SVID_) {
(void) WRITE2("fmod: DOMAIN error\n", 20);
} */
errno = EDOM;
}
break;
case 28:
case 128:
/* remainder(x,0) */
exc.type = DOMAIN;
exc.name = type < 100 ? "remainder" : "remainderf";
exc.retval = zero/zero;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
/* if (_LIB_VERSION == _SVID_) {
(void) WRITE2("remainder: DOMAIN error\n", 24);
} */
errno = EDOM;
}
break;
case 29:
case 129:
/* acosh(x<1) */
exc.type = DOMAIN;
exc.name = type < 100 ? "acosh" : "acoshf";
exc.retval = zero/zero;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
/* if (_LIB_VERSION == _SVID_) {
(void) WRITE2("acosh: DOMAIN error\n", 20);
} */
errno = EDOM;
}
break;
case 30:
case 130:
/* atanh(|x|>1) */
exc.type = DOMAIN;
exc.name = type < 100 ? "atanh" : "atanhf";
exc.retval = zero/zero;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
/* if (_LIB_VERSION == _SVID_) {
(void) WRITE2("atanh: DOMAIN error\n", 20);
} */
errno = EDOM;
}
break;
case 31:
case 131:
/* atanh(|x|=1) */
exc.type = SING;
exc.name = type < 100 ? "atanh" : "atanhf";
exc.retval = x/zero; /* sign(x)*inf */
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
/* if (_LIB_VERSION == _SVID_) {
(void) WRITE2("atanh: SING error\n", 18);
} */
errno = EDOM;
}
break;
case 32:
case 132:
/* scalb overflow; SVID also returns +-HUGE_VAL */
exc.type = OVERFLOW;
exc.name = type < 100 ? "scalb" : "scalbf";
exc.retval = x > zero ? HUGE_VAL : -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
break;
case 33:
case 133:
/* scalb underflow */
exc.type = UNDERFLOW;
exc.name = type < 100 ? "scalb" : "scalbf";
exc.retval = copysign(zero,x);
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
break;
case 34:
case 134:
/* j0(|x|>X_TLOSS) */
exc.type = TLOSS;
exc.name = type < 100 ? "j0" : "j0f";
exc.retval = zero;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
/* if (_LIB_VERSION == _SVID_) {
(void) WRITE2(exc.name, 2);
(void) WRITE2(": TLOSS error\n", 14);
} */
errno = ERANGE;
}
break;
case 35:
case 135:
/* y0(x>X_TLOSS) */
exc.type = TLOSS;
exc.name = type < 100 ? "y0" : "y0f";
exc.retval = zero;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
/* if (_LIB_VERSION == _SVID_) {
(void) WRITE2(exc.name, 2);
(void) WRITE2(": TLOSS error\n", 14);
} */
errno = ERANGE;
}
break;
case 36:
case 136:
/* j1(|x|>X_TLOSS) */
exc.type = TLOSS;
exc.name = type < 100 ? "j1" : "j1f";
exc.retval = zero;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
/* if (_LIB_VERSION == _SVID_) {
(void) WRITE2(exc.name, 2);
(void) WRITE2(": TLOSS error\n", 14);
} */
errno = ERANGE;
}
break;
case 37:
case 137:
/* y1(x>X_TLOSS) */
exc.type = TLOSS;
exc.name = type < 100 ? "y1" : "y1f";
exc.retval = zero;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
/* if (_LIB_VERSION == _SVID_) {
(void) WRITE2(exc.name, 2);
(void) WRITE2(": TLOSS error\n", 14);
} */
errno = ERANGE;
}
break;
case 38:
case 138:
/* jn(|x|>X_TLOSS) */
exc.type = TLOSS;
exc.name = type < 100 ? "jn" : "jnf";
exc.retval = zero;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
/* if (_LIB_VERSION == _SVID_) {
(void) WRITE2(exc.name, 2);
(void) WRITE2(": TLOSS error\n", 14);
} */
errno = ERANGE;
}
break;
case 39:
case 139:
/* yn(x>X_TLOSS) */
exc.type = TLOSS;
exc.name = type < 100 ? "yn" : "ynf";
exc.retval = zero;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
/* if (_LIB_VERSION == _SVID_) {
(void) WRITE2(exc.name, 2);
(void) WRITE2(": TLOSS error\n", 14);
} */
errno = ERANGE;
}
break;
case 40:
case 140:
/* gamma(finite) overflow */
exc.type = OVERFLOW;
exc.name = type < 100 ? "gamma" : "gammaf";
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
break;
case 41:
case 141:
/* gamma(-integer) or gamma(0) */
exc.type = SING;
exc.name = type < 100 ? "gamma" : "gammaf";
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
/* if (_LIB_VERSION == _SVID_) {
(void) WRITE2("gamma: SING error\n", 18);
} */
errno = EDOM;
}
break;
case 42:
case 142:
/* pow(NaN,0.0) */
/* error only if _LIB_VERSION == _SVID_ & _XOPEN_ */
exc.type = DOMAIN;
exc.name = type < 100 ? "pow" : "powf";
exc.retval = x;
if (_LIB_VERSION == _IEEE_ ||
_LIB_VERSION == _POSIX_) exc.retval = 1.0;
else if (!matherr(&exc)) {
errno = EDOM;
}
break;
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
}
 
 
/e_jn.c
0,0 → 1,281
 
/* @(#)e_jn.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
* __ieee754_jn(n, x), __ieee754_yn(n, x)
* floating point Bessel's function of the 1st and 2nd kind
* of order n
*
* Special cases:
* y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal;
* y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal.
* Note 2. About jn(n,x), yn(n,x)
* For n=0, j0(x) is called,
* for n=1, j1(x) is called,
* for n<x, forward recursion us used starting
* from values of j0(x) and j1(x).
* for n>x, a continued fraction approximation to
* j(n,x)/j(n-1,x) is evaluated and then backward
* recursion is used starting from a supposed value
* for j(n,x). The resulting value of j(0,x) is
* compared with the actual value to correct the
* supposed value of j(n,x).
*
* yn(n,x) is similar in all respects, except
* that forward recursion is used for all
* values of n>1.
*
*/
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
static const double
#else
static double
#endif
invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */
two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */
one = 1.00000000000000000000e+00; /* 0x3FF00000, 0x00000000 */
 
#ifdef __STDC__
static const double zero = 0.00000000000000000000e+00;
#else
static double zero = 0.00000000000000000000e+00;
#endif
 
#ifdef __STDC__
double __ieee754_jn(int n, double x)
#else
double __ieee754_jn(n,x)
int n; double x;
#endif
{
__int32_t i,hx,ix,lx, sgn;
double a, b, temp, di;
double z, w;
 
/* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
* Thus, J(-n,x) = J(n,-x)
*/
EXTRACT_WORDS(hx,lx,x);
ix = 0x7fffffff&hx;
/* if J(n,NaN) is NaN */
if((ix|((__uint32_t)(lx|-lx))>>31)>0x7ff00000) return x+x;
if(n<0){
n = -n;
x = -x;
hx ^= 0x80000000;
}
if(n==0) return(__ieee754_j0(x));
if(n==1) return(__ieee754_j1(x));
sgn = (n&1)&(hx>>31); /* even n -- 0, odd n -- sign(x) */
x = fabs(x);
if((ix|lx)==0||ix>=0x7ff00000) /* if x is 0 or inf */
b = zero;
else if((double)n<=x) {
/* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
if(ix>=0x52D00000) { /* x > 2**302 */
/* (x >> n**2)
* Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
* Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
* Let s=sin(x), c=cos(x),
* xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
*
* n sin(xn)*sqt2 cos(xn)*sqt2
* ----------------------------------
* 0 s-c c+s
* 1 -s-c -c+s
* 2 -s+c -c-s
* 3 s+c c-s
*/
switch(n&3) {
case 0: temp = cos(x)+sin(x); break;
case 1: temp = -cos(x)+sin(x); break;
case 2: temp = -cos(x)-sin(x); break;
case 3: temp = cos(x)-sin(x); break;
}
b = invsqrtpi*temp/__ieee754_sqrt(x);
} else {
a = __ieee754_j0(x);
b = __ieee754_j1(x);
for(i=1;i<n;i++){
temp = b;
b = b*((double)(i+i)/x) - a; /* avoid underflow */
a = temp;
}
}
} else {
if(ix<0x3e100000) { /* x < 2**-29 */
/* x is tiny, return the first Taylor expansion of J(n,x)
* J(n,x) = 1/n!*(x/2)^n - ...
*/
if(n>33) /* underflow */
b = zero;
else {
temp = x*0.5; b = temp;
for (a=one,i=2;i<=n;i++) {
a *= (double)i; /* a = n! */
b *= temp; /* b = (x/2)^n */
}
b = b/a;
}
} else {
/* use backward recurrence */
/* x x^2 x^2
* J(n,x)/J(n-1,x) = ---- ------ ------ .....
* 2n - 2(n+1) - 2(n+2)
*
* 1 1 1
* (for large x) = ---- ------ ------ .....
* 2n 2(n+1) 2(n+2)
* -- - ------ - ------ -
* x x x
*
* Let w = 2n/x and h=2/x, then the above quotient
* is equal to the continued fraction:
* 1
* = -----------------------
* 1
* w - -----------------
* 1
* w+h - ---------
* w+2h - ...
*
* To determine how many terms needed, let
* Q(0) = w, Q(1) = w(w+h) - 1,
* Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
* When Q(k) > 1e4 good for single
* When Q(k) > 1e9 good for double
* When Q(k) > 1e17 good for quadruple
*/
/* determine k */
double t,v;
double q0,q1,h,tmp; __int32_t k,m;
w = (n+n)/(double)x; h = 2.0/(double)x;
q0 = w; z = w+h; q1 = w*z - 1.0; k=1;
while(q1<1.0e9) {
k += 1; z += h;
tmp = z*q1 - q0;
q0 = q1;
q1 = tmp;
}
m = n+n;
for(t=zero, i = 2*(n+k); i>=m; i -= 2) t = one/(i/x-t);
a = t;
b = one;
/* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
* Hence, if n*(log(2n/x)) > ...
* single 8.8722839355e+01
* double 7.09782712893383973096e+02
* long double 1.1356523406294143949491931077970765006170e+04
* then recurrent value may overflow and the result is
* likely underflow to zero
*/
tmp = n;
v = two/x;
tmp = tmp*__ieee754_log(fabs(v*tmp));
if(tmp<7.09782712893383973096e+02) {
for(i=n-1,di=(double)(i+i);i>0;i--){
temp = b;
b *= di;
b = b/x - a;
a = temp;
di -= two;
}
} else {
for(i=n-1,di=(double)(i+i);i>0;i--){
temp = b;
b *= di;
b = b/x - a;
a = temp;
di -= two;
/* scale b to avoid spurious overflow */
if(b>1e100) {
a /= b;
t /= b;
b = one;
}
}
}
b = (t*__ieee754_j0(x)/b);
}
}
if(sgn==1) return -b; else return b;
}
 
#ifdef __STDC__
double __ieee754_yn(int n, double x)
#else
double __ieee754_yn(n,x)
int n; double x;
#endif
{
__int32_t i,hx,ix,lx;
__int32_t sign;
double a, b, temp;
 
EXTRACT_WORDS(hx,lx,x);
ix = 0x7fffffff&hx;
/* if Y(n,NaN) is NaN */
if((ix|((__uint32_t)(lx|-lx))>>31)>0x7ff00000) return x+x;
if((ix|lx)==0) return -one/zero;
if(hx<0) return zero/zero;
sign = 1;
if(n<0){
n = -n;
sign = 1 - ((n&1)<<1);
}
if(n==0) return(__ieee754_y0(x));
if(n==1) return(sign*__ieee754_y1(x));
if(ix==0x7ff00000) return zero;
if(ix>=0x52D00000) { /* x > 2**302 */
/* (x >> n**2)
* Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
* Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
* Let s=sin(x), c=cos(x),
* xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
*
* n sin(xn)*sqt2 cos(xn)*sqt2
* ----------------------------------
* 0 s-c c+s
* 1 -s-c -c+s
* 2 -s+c -c-s
* 3 s+c c-s
*/
switch(n&3) {
case 0: temp = sin(x)-cos(x); break;
case 1: temp = -sin(x)-cos(x); break;
case 2: temp = -sin(x)+cos(x); break;
case 3: temp = sin(x)+cos(x); break;
}
b = invsqrtpi*temp/__ieee754_sqrt(x);
} else {
__uint32_t high;
a = __ieee754_y0(x);
b = __ieee754_y1(x);
/* quit if b is -inf */
GET_HIGH_WORD(high,b);
for(i=1;i<n&&high!=0xfff00000;i++){
temp = b;
b = ((double)(i+i)/x)*b - a;
GET_HIGH_WORD(high,b);
a = temp;
}
}
if(sign>0) return b; else return -b;
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/w_drem.c
0,0 → 1,15
/*
* drem() wrapper for remainder().
*
* Written by J.T. Conklin, <jtc@wimsey.com>
* Placed into the Public Domain, 1994.
*/
 
#include "fdlibm.h"
 
double
drem(x, y)
double x, y;
{
return remainder(x, y);
}
/ef_remainder.c
0,0 → 1,68
/* ef_remainder.c -- float version of e_remainder.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
#include "fdlibm.h"
 
#ifdef __STDC__
static const float zero = 0.0;
#else
static float zero = 0.0;
#endif
 
 
#ifdef __STDC__
float __ieee754_remainderf(float x, float p)
#else
float __ieee754_remainderf(x,p)
float x,p;
#endif
{
__int32_t hx,hp;
__uint32_t sx;
float p_half;
 
GET_FLOAT_WORD(hx,x);
GET_FLOAT_WORD(hp,p);
sx = hx&0x80000000;
hp &= 0x7fffffff;
hx &= 0x7fffffff;
 
/* purge off exception values */
if(FLT_UWORD_IS_ZERO(hp)||
!FLT_UWORD_IS_FINITE(hx)||
FLT_UWORD_IS_NAN(hp))
return (x*p)/(x*p);
 
 
if (hp<=FLT_UWORD_HALF_MAX) x = __ieee754_fmodf(x,p+p); /* now x < 2p */
if ((hx-hp)==0) return zero*x;
x = fabsf(x);
p = fabsf(p);
if (hp<0x01000000) {
if(x+x>p) {
x-=p;
if(x+x>=p) x -= p;
}
} else {
p_half = (float)0.5*p;
if(x>p_half) {
x-=p;
if(x>=p_half) x -= p;
}
}
GET_FLOAT_WORD(hx,x);
SET_FLOAT_WORD(x,hx^sx);
return x;
}
/ef_j0.c
0,0 → 1,439
/* ef_j0.c -- float version of e_j0.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
#include "fdlibm.h"
 
#ifdef __STDC__
static float pzerof(float), qzerof(float);
#else
static float pzerof(), qzerof();
#endif
 
#ifdef __STDC__
static const float
#else
static float
#endif
huge = 1e30,
one = 1.0,
invsqrtpi= 5.6418961287e-01, /* 0x3f106ebb */
tpi = 6.3661974669e-01, /* 0x3f22f983 */
/* R0/S0 on [0, 2.00] */
R02 = 1.5625000000e-02, /* 0x3c800000 */
R03 = -1.8997929874e-04, /* 0xb947352e */
R04 = 1.8295404516e-06, /* 0x35f58e88 */
R05 = -4.6183270541e-09, /* 0xb19eaf3c */
S01 = 1.5619102865e-02, /* 0x3c7fe744 */
S02 = 1.1692678527e-04, /* 0x38f53697 */
S03 = 5.1354652442e-07, /* 0x3509daa6 */
S04 = 1.1661400734e-09; /* 0x30a045e8 */
 
#ifdef __STDC__
static const float zero = 0.0;
#else
static float zero = 0.0;
#endif
 
#ifdef __STDC__
float __ieee754_j0f(float x)
#else
float __ieee754_j0f(x)
float x;
#endif
{
float z, s,c,ss,cc,r,u,v;
__int32_t hx,ix;
 
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
if(!FLT_UWORD_IS_FINITE(ix)) return one/(x*x);
x = fabsf(x);
if(ix >= 0x40000000) { /* |x| >= 2.0 */
s = sinf(x);
c = cosf(x);
ss = s-c;
cc = s+c;
if(ix<=FLT_UWORD_HALF_MAX) { /* make sure x+x not overflow */
z = -cosf(x+x);
if ((s*c)<zero) cc = z/ss;
else ss = z/cc;
}
/*
* j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
* y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
*/
if(ix>0x80000000) z = (invsqrtpi*cc)/__ieee754_sqrtf(x);
else {
u = pzerof(x); v = qzerof(x);
z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrtf(x);
}
return z;
}
if(ix<0x39000000) { /* |x| < 2**-13 */
if(huge+x>one) { /* raise inexact if x != 0 */
if(ix<0x32000000) return one; /* |x|<2**-27 */
else return one - (float)0.25*x*x;
}
}
z = x*x;
r = z*(R02+z*(R03+z*(R04+z*R05)));
s = one+z*(S01+z*(S02+z*(S03+z*S04)));
if(ix < 0x3F800000) { /* |x| < 1.00 */
return one + z*((float)-0.25+(r/s));
} else {
u = (float)0.5*x;
return((one+u)*(one-u)+z*(r/s));
}
}
 
#ifdef __STDC__
static const float
#else
static float
#endif
u00 = -7.3804296553e-02, /* 0xbd9726b5 */
u01 = 1.7666645348e-01, /* 0x3e34e80d */
u02 = -1.3818567619e-02, /* 0xbc626746 */
u03 = 3.4745343146e-04, /* 0x39b62a69 */
u04 = -3.8140706238e-06, /* 0xb67ff53c */
u05 = 1.9559013964e-08, /* 0x32a802ba */
u06 = -3.9820518410e-11, /* 0xae2f21eb */
v01 = 1.2730483897e-02, /* 0x3c509385 */
v02 = 7.6006865129e-05, /* 0x389f65e0 */
v03 = 2.5915085189e-07, /* 0x348b216c */
v04 = 4.4111031494e-10; /* 0x2ff280c2 */
 
#ifdef __STDC__
float __ieee754_y0f(float x)
#else
float __ieee754_y0f(x)
float x;
#endif
{
float z, s,c,ss,cc,u,v;
__int32_t hx,ix;
 
GET_FLOAT_WORD(hx,x);
ix = 0x7fffffff&hx;
/* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */
if(!FLT_UWORD_IS_FINITE(ix)) return one/(x+x*x);
if(FLT_UWORD_IS_ZERO(ix)) return -one/zero;
if(hx<0) return zero/zero;
if(ix >= 0x40000000) { /* |x| >= 2.0 */
/* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0))
* where x0 = x-pi/4
* Better formula:
* cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
* = 1/sqrt(2) * (sin(x) + cos(x))
* sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
* = 1/sqrt(2) * (sin(x) - cos(x))
* To avoid cancellation, use
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
* to compute the worse one.
*/
s = sinf(x);
c = cosf(x);
ss = s-c;
cc = s+c;
/*
* j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
* y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
*/
if(ix<=FLT_UWORD_HALF_MAX) { /* make sure x+x not overflow */
z = -cosf(x+x);
if ((s*c)<zero) cc = z/ss;
else ss = z/cc;
}
if(ix>0x80000000) z = (invsqrtpi*ss)/__ieee754_sqrtf(x);
else {
u = pzerof(x); v = qzerof(x);
z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrtf(x);
}
return z;
}
if(ix<=0x32000000) { /* x < 2**-27 */
return(u00 + tpi*__ieee754_logf(x));
}
z = x*x;
u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06)))));
v = one+z*(v01+z*(v02+z*(v03+z*v04)));
return(u/v + tpi*(__ieee754_j0f(x)*__ieee754_logf(x)));
}
 
/* The asymptotic expansions of pzero is
* 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x.
* For x >= 2, We approximate pzero by
* pzero(x) = 1 + (R/S)
* where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10
* S = 1 + pS0*s^2 + ... + pS4*s^10
* and
* | pzero(x)-1-R/S | <= 2 ** ( -60.26)
*/
#ifdef __STDC__
static const float pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
#else
static float pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
#endif
0.0000000000e+00, /* 0x00000000 */
-7.0312500000e-02, /* 0xbd900000 */
-8.0816707611e+00, /* 0xc1014e86 */
-2.5706311035e+02, /* 0xc3808814 */
-2.4852163086e+03, /* 0xc51b5376 */
-5.2530439453e+03, /* 0xc5a4285a */
};
#ifdef __STDC__
static const float pS8[5] = {
#else
static float pS8[5] = {
#endif
1.1653436279e+02, /* 0x42e91198 */
3.8337448730e+03, /* 0x456f9beb */
4.0597855469e+04, /* 0x471e95db */
1.1675296875e+05, /* 0x47e4087c */
4.7627726562e+04, /* 0x473a0bba */
};
#ifdef __STDC__
static const float pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
#else
static float pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
#endif
-1.1412546255e-11, /* 0xad48c58a */
-7.0312492549e-02, /* 0xbd8fffff */
-4.1596107483e+00, /* 0xc0851b88 */
-6.7674766541e+01, /* 0xc287597b */
-3.3123129272e+02, /* 0xc3a59d9b */
-3.4643338013e+02, /* 0xc3ad3779 */
};
#ifdef __STDC__
static const float pS5[5] = {
#else
static float pS5[5] = {
#endif
6.0753936768e+01, /* 0x42730408 */
1.0512523193e+03, /* 0x44836813 */
5.9789707031e+03, /* 0x45bad7c4 */
9.6254453125e+03, /* 0x461665c8 */
2.4060581055e+03, /* 0x451660ee */
};
 
#ifdef __STDC__
static const float pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
#else
static float pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
#endif
-2.5470459075e-09, /* 0xb12f081b */
-7.0311963558e-02, /* 0xbd8fffb8 */
-2.4090321064e+00, /* 0xc01a2d95 */
-2.1965976715e+01, /* 0xc1afba52 */
-5.8079170227e+01, /* 0xc2685112 */
-3.1447946548e+01, /* 0xc1fb9565 */
};
#ifdef __STDC__
static const float pS3[5] = {
#else
static float pS3[5] = {
#endif
3.5856033325e+01, /* 0x420f6c94 */
3.6151397705e+02, /* 0x43b4c1ca */
1.1936077881e+03, /* 0x44953373 */
1.1279968262e+03, /* 0x448cffe6 */
1.7358093262e+02, /* 0x432d94b8 */
};
 
#ifdef __STDC__
static const float pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
#else
static float pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
#endif
-8.8753431271e-08, /* 0xb3be98b7 */
-7.0303097367e-02, /* 0xbd8ffb12 */
-1.4507384300e+00, /* 0xbfb9b1cc */
-7.6356959343e+00, /* 0xc0f4579f */
-1.1193166733e+01, /* 0xc1331736 */
-3.2336456776e+00, /* 0xc04ef40d */
};
#ifdef __STDC__
static const float pS2[5] = {
#else
static float pS2[5] = {
#endif
2.2220300674e+01, /* 0x41b1c32d */
1.3620678711e+02, /* 0x430834f0 */
2.7047027588e+02, /* 0x43873c32 */
1.5387539673e+02, /* 0x4319e01a */
1.4657617569e+01, /* 0x416a859a */
};
 
#ifdef __STDC__
static float pzerof(float x)
#else
static float pzerof(x)
float x;
#endif
{
#ifdef __STDC__
const float *p,*q;
#else
float *p,*q;
#endif
float z,r,s;
__int32_t ix;
GET_FLOAT_WORD(ix,x);
ix &= 0x7fffffff;
if(ix>=0x41000000) {p = pR8; q= pS8;}
else if(ix>=0x40f71c58){p = pR5; q= pS5;}
else if(ix>=0x4036db68){p = pR3; q= pS3;}
else {p = pR2; q= pS2;}
z = one/(x*x);
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
return one+ r/s;
}
 
/* For x >= 8, the asymptotic expansions of qzero is
* -1/8 s + 75/1024 s^3 - ..., where s = 1/x.
* We approximate qzero by
* qzero(x) = s*(-1.25 + (R/S))
* where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10
* S = 1 + qS0*s^2 + ... + qS5*s^12
* and
* | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22)
*/
#ifdef __STDC__
static const float qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
#else
static float qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
#endif
0.0000000000e+00, /* 0x00000000 */
7.3242187500e-02, /* 0x3d960000 */
1.1768206596e+01, /* 0x413c4a93 */
5.5767340088e+02, /* 0x440b6b19 */
8.8591972656e+03, /* 0x460a6cca */
3.7014625000e+04, /* 0x471096a0 */
};
#ifdef __STDC__
static const float qS8[6] = {
#else
static float qS8[6] = {
#endif
1.6377603149e+02, /* 0x4323c6aa */
8.0983447266e+03, /* 0x45fd12c2 */
1.4253829688e+05, /* 0x480b3293 */
8.0330925000e+05, /* 0x49441ed4 */
8.4050156250e+05, /* 0x494d3359 */
-3.4389928125e+05, /* 0xc8a7eb69 */
};
 
#ifdef __STDC__
static const float qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
#else
static float qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
#endif
1.8408595828e-11, /* 0x2da1ec79 */
7.3242180049e-02, /* 0x3d95ffff */
5.8356351852e+00, /* 0x40babd86 */
1.3511157227e+02, /* 0x43071c90 */
1.0272437744e+03, /* 0x448067cd */
1.9899779053e+03, /* 0x44f8bf4b */
};
#ifdef __STDC__
static const float qS5[6] = {
#else
static float qS5[6] = {
#endif
8.2776611328e+01, /* 0x42a58da0 */
2.0778142090e+03, /* 0x4501dd07 */
1.8847289062e+04, /* 0x46933e94 */
5.6751113281e+04, /* 0x475daf1d */
3.5976753906e+04, /* 0x470c88c1 */
-5.3543427734e+03, /* 0xc5a752be */
};
 
#ifdef __STDC__
static const float qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
#else
static float qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
#endif
4.3774099900e-09, /* 0x3196681b */
7.3241114616e-02, /* 0x3d95ff70 */
3.3442313671e+00, /* 0x405607e3 */
4.2621845245e+01, /* 0x422a7cc5 */
1.7080809021e+02, /* 0x432acedf */
1.6673394775e+02, /* 0x4326bbe4 */
};
#ifdef __STDC__
static const float qS3[6] = {
#else
static float qS3[6] = {
#endif
4.8758872986e+01, /* 0x42430916 */
7.0968920898e+02, /* 0x44316c1c */
3.7041481934e+03, /* 0x4567825f */
6.4604252930e+03, /* 0x45c9e367 */
2.5163337402e+03, /* 0x451d4557 */
-1.4924745178e+02, /* 0xc3153f59 */
};
 
#ifdef __STDC__
static const float qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
#else
static float qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
#endif
1.5044444979e-07, /* 0x342189db */
7.3223426938e-02, /* 0x3d95f62a */
1.9981917143e+00, /* 0x3fffc4bf */
1.4495602608e+01, /* 0x4167edfd */
3.1666231155e+01, /* 0x41fd5471 */
1.6252708435e+01, /* 0x4182058c */
};
#ifdef __STDC__
static const float qS2[6] = {
#else
static float qS2[6] = {
#endif
3.0365585327e+01, /* 0x41f2ecb8 */
2.6934811401e+02, /* 0x4386ac8f */
8.4478375244e+02, /* 0x44533229 */
8.8293585205e+02, /* 0x445cbbe5 */
2.1266638184e+02, /* 0x4354aa98 */
-5.3109550476e+00, /* 0xc0a9f358 */
};
 
#ifdef __STDC__
static float qzerof(float x)
#else
static float qzerof(x)
float x;
#endif
{
#ifdef __STDC__
const float *p,*q;
#else
float *p,*q;
#endif
float s,r,z;
__int32_t ix;
GET_FLOAT_WORD(ix,x);
ix &= 0x7fffffff;
if(ix>=0x41000000) {p = qR8; q= qS8;}
else if(ix>=0x40f71c58){p = qR5; q= qS5;}
else if(ix>=0x4036db68){p = qR3; q= qS3;}
else {p = qR2; q= qS2;}
z = one/(x*x);
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
return (-(float).125 + r/s)/x;
}
/e_log.c
0,0 → 1,146
 
/* @(#)e_log.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/* __ieee754_log(x)
* Return the logrithm of x
*
* Method :
* 1. Argument Reduction: find k and f such that
* x = 2^k * (1+f),
* where sqrt(2)/2 < 1+f < sqrt(2) .
*
* 2. Approximation of log(1+f).
* Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
* = 2s + 2/3 s**3 + 2/5 s**5 + .....,
* = 2s + s*R
* We use a special Reme algorithm on [0,0.1716] to generate
* a polynomial of degree 14 to approximate R The maximum error
* of this polynomial approximation is bounded by 2**-58.45. In
* other words,
* 2 4 6 8 10 12 14
* R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s
* (the values of Lg1 to Lg7 are listed in the program)
* and
* | 2 14 | -58.45
* | Lg1*s +...+Lg7*s - R(z) | <= 2
* | |
* Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
* In order to guarantee error in log below 1ulp, we compute log
* by
* log(1+f) = f - s*(f - R) (if f is not too large)
* log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy)
*
* 3. Finally, log(x) = k*ln2 + log(1+f).
* = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
* Here ln2 is split into two floating point number:
* ln2_hi + ln2_lo,
* where n*ln2_hi is always exact for |n| < 2000.
*
* Special cases:
* log(x) is NaN with signal if x < 0 (including -INF) ;
* log(+INF) is +INF; log(0) is -INF with signal;
* log(NaN) is that NaN with no signal.
*
* Accuracy:
* according to an error analysis, the error is always less than
* 1 ulp (unit in the last place).
*
* Constants:
* The hexadecimal values are the intended ones for the following
* constants. The decimal values may be used, provided that the
* compiler will convert from decimal to binary accurately enough
* to produce the hexadecimal values shown.
*/
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
static const double
#else
static double
#endif
ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */
ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */
two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */
Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
 
#ifdef __STDC__
static const double zero = 0.0;
#else
static double zero = 0.0;
#endif
 
#ifdef __STDC__
double __ieee754_log(double x)
#else
double __ieee754_log(x)
double x;
#endif
{
double hfsq,f,s,z,R,w,t1,t2,dk;
__int32_t k,hx,i,j;
__uint32_t lx;
 
EXTRACT_WORDS(hx,lx,x);
 
k=0;
if (hx < 0x00100000) { /* x < 2**-1022 */
if (((hx&0x7fffffff)|lx)==0)
return -two54/zero; /* log(+-0)=-inf */
if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
k -= 54; x *= two54; /* subnormal number, scale up x */
GET_HIGH_WORD(hx,x);
}
if (hx >= 0x7ff00000) return x+x;
k += (hx>>20)-1023;
hx &= 0x000fffff;
i = (hx+0x95f64)&0x100000;
SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */
k += (i>>20);
f = x-1.0;
if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */
if(f==zero) { if(k==0) return zero; else {dk=(double)k;
return dk*ln2_hi+dk*ln2_lo;}}
R = f*f*(0.5-0.33333333333333333*f);
if(k==0) return f-R; else {dk=(double)k;
return dk*ln2_hi-((R-dk*ln2_lo)-f);}
}
s = f/(2.0+f);
dk = (double)k;
z = s*s;
i = hx-0x6147a;
w = z*z;
j = 0x6b851-hx;
t1= w*(Lg2+w*(Lg4+w*Lg6));
t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
i |= j;
R = t2+t1;
if(i>0) {
hfsq=0.5*f*f;
if(k==0) return f-(hfsq-s*(hfsq+R)); else
return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
} else {
if(k==0) return f-s*(f-R); else
return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
}
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/w_sinh.c
0,0 → 1,120
 
/* @(#)w_sinh.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
 
/*
FUNCTION
<<sinh>>, <<sinhf>>---hyperbolic sine
 
INDEX
sinh
INDEX
sinhf
 
ANSI_SYNOPSIS
#include <math.h>
double sinh(double <[x]>);
float sinhf(float <[x]>);
 
TRAD_SYNOPSIS
#include <math.h>
double sinh(<[x]>)
double <[x]>;
 
float sinhf(<[x]>)
float <[x]>;
 
DESCRIPTION
<<sinh>> computes the hyperbolic sine of the argument <[x]>.
Angles are specified in radians. <<sinh>>(<[x]>) is defined as
@ifinfo
. (exp(<[x]>) - exp(-<[x]>))/2
@end ifinfo
@tex
$${e^x - e^{-x}}\over 2$$
@end tex
 
<<sinhf>> is identical, save that it takes and returns <<float>> values.
 
RETURNS
The hyperbolic sine of <[x]> is returned.
 
When the correct result is too large to be representable (an
overflow), <<sinh>> returns <<HUGE_VAL>> with the
appropriate sign, and sets the global value <<errno>> to
<<ERANGE>>.
 
You can modify error handling for these functions with <<matherr>>.
 
PORTABILITY
<<sinh>> is ANSI C.
<<sinhf>> is an extension.
 
QUICKREF
sinh ansi pure
sinhf - pure
*/
 
/*
* wrapper sinh(x)
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double sinh(double x) /* wrapper sinh */
#else
double sinh(x) /* wrapper sinh */
double x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_sinh(x);
#else
double z;
struct exception exc;
z = __ieee754_sinh(x);
if(_LIB_VERSION == _IEEE_) return z;
if(!finite(z)&&finite(x)) {
/* sinh(finite) overflow */
#ifndef HUGE_VAL
#define HUGE_VAL inf
double inf = 0.0;
SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */
#endif
exc.type = OVERFLOW;
exc.name = "sinh";
exc.err = 0;
exc.arg1 = exc.arg2 = x;
if (_LIB_VERSION == _SVID_)
exc.retval = ( (x>0.0) ? HUGE : -HUGE);
else
exc.retval = ( (x>0.0) ? HUGE_VAL : -HUGE_VAL);
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
} else
return z;
#endif
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/e_scalb.c
0,0 → 1,55
 
/* @(#)e_scalb.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
* __ieee754_scalb(x, fn) is provide for
* passing various standard test suite. One
* should use scalbn() instead.
*/
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef _SCALB_INT
#ifdef __STDC__
double __ieee754_scalb(double x, int fn)
#else
double __ieee754_scalb(x,fn)
double x; int fn;
#endif
#else
#ifdef __STDC__
double __ieee754_scalb(double x, double fn)
#else
double __ieee754_scalb(x,fn)
double x, fn;
#endif
#endif
{
#ifdef _SCALB_INT
return scalbn(x,fn);
#else
if (isnan(x)||isnan(fn)) return x*fn;
if (!finite(fn)) {
if(fn>0.0) return x*fn;
else return x/(-fn);
}
if (rint(fn)!=fn) return (fn-fn)/(fn-fn);
if ( fn > 65000.0) return scalbn(x, 65000);
if (-fn > 65000.0) return scalbn(x,-65000);
return scalbn(x,(int)fn);
#endif
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/wf_acosh.c
0,0 → 1,70
/* wf_acosh.c -- float version of w_acosh.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
 
/*
* wrapper acoshf(x)
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifdef __STDC__
float acoshf(float x) /* wrapper acoshf */
#else
float acoshf(x) /* wrapper acoshf */
float x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_acoshf(x);
#else
float z;
struct exception exc;
z = __ieee754_acoshf(x);
if(_LIB_VERSION == _IEEE_ || isnanf(x)) return z;
if(x<(float)1.0) {
/* acoshf(x<1) */
exc.type = DOMAIN;
exc.name = "acoshf";
exc.err = 0;
exc.arg1 = exc.arg2 = (double)x;
exc.retval = 0.0/0.0;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
if (exc.err != 0)
errno = exc.err;
return (float)exc.retval;
} else
return z;
#endif
}
 
#ifdef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double acosh(double x)
#else
double acosh(x)
double x;
#endif
{
return (double) acoshf((float) x);
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/e_acos.c
0,0 → 1,111
 
/* @(#)e_acos.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/* __ieee754_acos(x)
* Method :
* acos(x) = pi/2 - asin(x)
* acos(-x) = pi/2 + asin(x)
* For |x|<=0.5
* acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c)
* For x>0.5
* acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
* = 2asin(sqrt((1-x)/2))
* = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z)
* = 2f + (2c + 2s*z*R(z))
* where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
* for f so that f+c ~ sqrt(z).
* For x<-0.5
* acos(x) = pi - 2asin(sqrt((1-|x|)/2))
* = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
*
* Special cases:
* if x is NaN, return x itself;
* if |x|>1, return NaN with invalid signal.
*
* Function needed: sqrt
*/
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
static const double
#else
static double
#endif
one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
 
#ifdef __STDC__
double __ieee754_acos(double x)
#else
double __ieee754_acos(x)
double x;
#endif
{
double z,p,q,r,w,s,c,df;
__int32_t hx,ix;
GET_HIGH_WORD(hx,x);
ix = hx&0x7fffffff;
if(ix>=0x3ff00000) { /* |x| >= 1 */
__uint32_t lx;
GET_LOW_WORD(lx,x);
if(((ix-0x3ff00000)|lx)==0) { /* |x|==1 */
if(hx>0) return 0.0; /* acos(1) = 0 */
else return pi+2.0*pio2_lo; /* acos(-1)= pi */
}
return (x-x)/(x-x); /* acos(|x|>1) is NaN */
}
if(ix<0x3fe00000) { /* |x| < 0.5 */
if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
z = x*x;
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
r = p/q;
return pio2_hi - (x - (pio2_lo-x*r));
} else if (hx<0) { /* x < -0.5 */
z = (one+x)*0.5;
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
s = __ieee754_sqrt(z);
r = p/q;
w = r*s-pio2_lo;
return pi - 2.0*(s+w);
} else { /* x > 0.5 */
z = (one-x)*0.5;
s = __ieee754_sqrt(z);
df = s;
SET_LOW_WORD(df,0);
c = (z-df*df)/(s+df);
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
r = p/q;
w = r*s+c;
return 2.0*(df+w);
}
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/s_isnan.c
0,0 → 1,122
 
/* @(#)s_isnan.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
FUNCTION
<<isnan>>,<<isnanf>>,<<isinf>>,<<isinff>>,<<finite>>,<<finitef>>---test for exceptional numbers
 
INDEX
isnan
INDEX
isinf
INDEX
finite
 
INDEX
isnanf
INDEX
isinff
INDEX
finitef
 
ANSI_SYNOPSIS
#include <ieeefp.h>
int isnan(double <[arg]>);
int isinf(double <[arg]>);
int finite(double <[arg]>);
int isnanf(float <[arg]>);
int isinff(float <[arg]>);
int finitef(float <[arg]>);
 
TRAD_SYNOPSIS
#include <ieeefp.h>
int isnan(<[arg]>)
double <[arg]>;
int isinf(<[arg]>)
double <[arg]>;
int finite(<[arg]>);
double <[arg]>;
int isnanf(<[arg]>);
float <[arg]>;
int isinff(<[arg]>);
float <[arg]>;
int finitef(<[arg]>);
float <[arg]>;
 
 
DESCRIPTION
These functions provide information on the floating point
argument supplied.
 
There are five major number formats -
o+
o zero
a number which contains all zero bits.
o subnormal
Is used to represent number with a zero exponent, but a non zero fraction.
o normal
A number with an exponent, and a fraction
o infinity
A number with an all 1's exponent and a zero fraction.
o NAN
A number with an all 1's exponent and a non zero fraction.
 
o-
 
<<isnan>> returns 1 if the argument is a nan. <<isinf>>
returns 1 if the argument is infinity. <<finite>> returns 1 if the
argument is zero, subnormal or normal.
The <<isnanf>>, <<isinff>> and <<finitef>> perform the same
operations as their <<isnan>>, <<isinf>> and <<finite>>
counterparts, but on single precision floating point numbers.
 
QUICKREF
isnan - pure
QUICKREF
isinf - pure
QUICKREF
finite - pure
QUICKREF
isnan - pure
QUICKREF
isinf - pure
QUICKREF
finite - pure
*/
 
/*
* isnan(x) returns 1 is x is nan, else 0;
* no branching!
*/
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
int isnan(double x)
#else
int isnan(x)
double x;
#endif
{
__int32_t hx,lx;
EXTRACT_WORDS(hx,lx,x);
hx &= 0x7fffffff;
hx |= (__uint32_t)(lx|(-lx))>>31;
hx = 0x7ff00000 - hx;
return (int)(((__uint32_t)(hx))>>31);
}
 
#endif /* _DOUBLE_IS_32BITS */
/w_remainder.c
0,0 → 1,108
 
/* @(#)w_remainder.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
FUNCTION
<<remainder>>, <<remainderf>>---round and remainder
INDEX
remainder
INDEX
remainderf
 
ANSI_SYNOPSIS
#include <math.h>
double remainder(double <[x]>, double <[y]>);
float remainderf(float <[x]>, float <[y]>);
 
TRAD_SYNOPSIS
#include <math.h>
double remainder(<[x]>,<[y]>)
double <[x]>, <[y]>;
float remainderf(<[x]>,<[y]>)
float <[x]>, <[y]>;
 
DESCRIPTION
<<remainder>> and <<remainderf>> find the remainder of
<[x]>/<[y]>; this value is in the range -<[y]>/2 .. +<[y]>/2.
 
RETURNS
<<remainder>> returns the integer result as a double.
 
PORTABILITY
<<remainder>> is a System V release 4.
<<remainderf>> is an extension.
 
*/
 
/*
* wrapper remainder(x,p)
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double remainder(double x, double y) /* wrapper remainder */
#else
double remainder(x,y) /* wrapper remainder */
double x,y;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_remainder(x,y);
#else
double z;
struct exception exc;
z = __ieee754_remainder(x,y);
if(_LIB_VERSION == _IEEE_ || isnan(y)) return z;
if(y==0.0) {
/* remainder(x,0) */
exc.type = DOMAIN;
exc.name = "remainder";
exc.err = 0;
exc.arg1 = x;
exc.arg2 = y;
exc.retval = 0.0/0.0;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
} else
return z;
#endif
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
/k_tan.c
0,0 → 1,132
 
/* @(#)k_tan.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/* __kernel_tan( x, y, k )
* kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854
* Input x is assumed to be bounded by ~pi/4 in magnitude.
* Input y is the tail of x.
* Input k indicates whether tan (if k=1) or
* -1/tan (if k= -1) is returned.
*
* Algorithm
* 1. Since tan(-x) = -tan(x), we need only to consider positive x.
* 2. if x < 2^-28 (hx<0x3e300000 0), return x with inexact if x!=0.
* 3. tan(x) is approximated by a odd polynomial of degree 27 on
* [0,0.67434]
* 3 27
* tan(x) ~ x + T1*x + ... + T13*x
* where
*
* |tan(x) 2 4 26 | -59.2
* |----- - (1+T1*x +T2*x +.... +T13*x )| <= 2
* | x |
*
* Note: tan(x+y) = tan(x) + tan'(x)*y
* ~ tan(x) + (1+x*x)*y
* Therefore, for better accuracy in computing tan(x+y), let
* 3 2 2 2 2
* r = x *(T2+x *(T3+x *(...+x *(T12+x *T13))))
* then
* 3 2
* tan(x+y) = x + (T1*x + (x *(r+y)+y))
*
* 4. For x in [0.67434,pi/4], let y = pi/4 - x, then
* tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
* = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
*/
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
static const double
#else
static double
#endif
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
pio4 = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
pio4lo= 3.06161699786838301793e-17, /* 0x3C81A626, 0x33145C07 */
T[] = {
3.33333333333334091986e-01, /* 0x3FD55555, 0x55555563 */
1.33333333333201242699e-01, /* 0x3FC11111, 0x1110FE7A */
5.39682539762260521377e-02, /* 0x3FABA1BA, 0x1BB341FE */
2.18694882948595424599e-02, /* 0x3F9664F4, 0x8406D637 */
8.86323982359930005737e-03, /* 0x3F8226E3, 0xE96E8493 */
3.59207910759131235356e-03, /* 0x3F6D6D22, 0xC9560328 */
1.45620945432529025516e-03, /* 0x3F57DBC8, 0xFEE08315 */
5.88041240820264096874e-04, /* 0x3F4344D8, 0xF2F26501 */
2.46463134818469906812e-04, /* 0x3F3026F7, 0x1A8D1068 */
7.81794442939557092300e-05, /* 0x3F147E88, 0xA03792A6 */
7.14072491382608190305e-05, /* 0x3F12B80F, 0x32F0A7E9 */
-1.85586374855275456654e-05, /* 0xBEF375CB, 0xDB605373 */
2.59073051863633712884e-05, /* 0x3EFB2A70, 0x74BF7AD4 */
};
 
#ifdef __STDC__
double __kernel_tan(double x, double y, int iy)
#else
double __kernel_tan(x, y, iy)
double x,y; int iy;
#endif
{
double z,r,v,w,s;
__int32_t ix,hx;
GET_HIGH_WORD(hx,x);
ix = hx&0x7fffffff; /* high word of |x| */
if(ix<0x3e300000) /* x < 2**-28 */
{if((int)x==0) { /* generate inexact */
__uint32_t low;
GET_LOW_WORD(low,x);
if(((ix|low)|(iy+1))==0) return one/fabs(x);
else return (iy==1)? x: -one/x;
}
}
if(ix>=0x3FE59428) { /* |x|>=0.6744 */
if(hx<0) {x = -x; y = -y;}
z = pio4-x;
w = pio4lo-y;
x = z+w; y = 0.0;
}
z = x*x;
w = z*z;
/* Break x^5*(T[1]+x^2*T[2]+...) into
* x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
* x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
*/
r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));
v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));
s = z*x;
r = y + z*(s*(r+v)+y);
r += T[0]*s;
w = x+r;
if(ix>=0x3FE59428) {
v = (double)iy;
return (double)(1-((hx>>30)&2))*(v-2.0*(x-(w*w/(w+v)-r)));
}
if(iy==1) return w;
else { /* if allow error up to 2 ulp,
simply return -1.0/(x+r) here */
/* compute -1.0/(x+r) accurately */
double a,t;
z = w;
SET_LOW_WORD(z,0);
v = r-(z - x); /* z+v = r+x */
t = a = -1.0/w; /* a = -1.0/w */
SET_LOW_WORD(t,0);
s = 1.0+t*z;
return t+a*(s+t*v);
}
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/ef_scalb.c
0,0 → 1,53
/* ef_scalb.c -- float version of e_scalb.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
#include "fdlibm.h"
#include <limits.h>
 
#ifdef _SCALB_INT
#ifdef __STDC__
float __ieee754_scalbf(float x, int fn)
#else
float __ieee754_scalbf(x,fn)
float x; int fn;
#endif
#else
#ifdef __STDC__
float __ieee754_scalbf(float x, float fn)
#else
float __ieee754_scalbf(x,fn)
float x, fn;
#endif
#endif
{
#ifdef _SCALB_INT
return scalbnf(x,fn);
#else
if (isnanf(x)||isnanf(fn)) return x*fn;
if (!finitef(fn)) {
if(fn>(float)0.0) return x*fn;
else return x/(-fn);
}
if (rintf(fn)!=fn) return (fn-fn)/(fn-fn);
#if INT_MAX > 65000
if ( fn > (float)65000.0) return scalbnf(x, 65000);
if (-fn > (float)65000.0) return scalbnf(x,-65000);
#else
if ( fn > (float)32000.0) return scalbnf(x, 32000);
if (-fn > (float)32000.0) return scalbnf(x,-32000);
#endif
return scalbnf(x,(int)fn);
#endif
}
/k_cos.c
0,0 → 1,96
 
/* @(#)k_cos.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
* __kernel_cos( x, y )
* kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
* Input x is assumed to be bounded by ~pi/4 in magnitude.
* Input y is the tail of x.
*
* Algorithm
* 1. Since cos(-x) = cos(x), we need only to consider positive x.
* 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
* 3. cos(x) is approximated by a polynomial of degree 14 on
* [0,pi/4]
* 4 14
* cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
* where the remez error is
*
* | 2 4 6 8 10 12 14 | -58
* |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2
* | |
*
* 4 6 8 10 12 14
* 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then
* cos(x) = 1 - x*x/2 + r
* since cos(x+y) ~ cos(x) - sin(x)*y
* ~ cos(x) - x*y,
* a correction term is necessary in cos(x) and hence
* cos(x+y) = 1 - (x*x/2 - (r - x*y))
* For better accuracy when x > 0.3, let qx = |x|/4 with
* the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
* Then
* cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
* Note that 1-qx and (x*x/2-qx) is EXACT here, and the
* magnitude of the latter is at least a quarter of x*x/2,
* thus, reducing the rounding error in the subtraction.
*/
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
static const double
#else
static double
#endif
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
 
#ifdef __STDC__
double __kernel_cos(double x, double y)
#else
double __kernel_cos(x, y)
double x,y;
#endif
{
double a,hz,z,r,qx;
__int32_t ix;
GET_HIGH_WORD(ix,x);
ix &= 0x7fffffff; /* ix = |x|'s high word*/
if(ix<0x3e400000) { /* if x < 2**27 */
if(((int)x)==0) return one; /* generate inexact */
}
z = x*x;
r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
if(ix < 0x3FD33333) /* if |x| < 0.3 */
return one - (0.5*z - (z*r - x*y));
else {
if(ix > 0x3fe90000) { /* x > 0.78125 */
qx = 0.28125;
} else {
INSERT_WORDS(qx,ix-0x00200000,0); /* x/4 */
}
hz = 0.5*z-qx;
a = one-qx;
return a - (hz - (z*r-x*y));
}
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/e_cosh.c
0,0 → 1,93
 
/* @(#)e_cosh.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/* __ieee754_cosh(x)
* Method :
* mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
* 1. Replace x by |x| (cosh(x) = cosh(-x)).
* 2.
* [ exp(x) - 1 ]^2
* 0 <= x <= ln2/2 : cosh(x) := 1 + -------------------
* 2*exp(x)
*
* exp(x) + 1/exp(x)
* ln2/2 <= x <= 22 : cosh(x) := -------------------
* 2
* 22 <= x <= lnovft : cosh(x) := exp(x)/2
* lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2)
* ln2ovft < x : cosh(x) := huge*huge (overflow)
*
* Special cases:
* cosh(x) is |x| if x is +INF, -INF, or NaN.
* only cosh(0)=1 is exact for finite x.
*/
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
static const double one = 1.0, half=0.5, huge = 1.0e300;
#else
static double one = 1.0, half=0.5, huge = 1.0e300;
#endif
 
#ifdef __STDC__
double __ieee754_cosh(double x)
#else
double __ieee754_cosh(x)
double x;
#endif
{
double t,w;
__int32_t ix;
__uint32_t lx;
 
/* High word of |x|. */
GET_HIGH_WORD(ix,x);
ix &= 0x7fffffff;
 
/* x is INF or NaN */
if(ix>=0x7ff00000) return x*x;
 
/* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
if(ix<0x3fd62e43) {
t = expm1(fabs(x));
w = one+t;
if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */
return one+(t*t)/(w+w);
}
 
/* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
if (ix < 0x40360000) {
t = __ieee754_exp(fabs(x));
return half*t+half/t;
}
 
/* |x| in [22, log(maxdouble)] return half*exp(|x|) */
if (ix < 0x40862E42) return half*__ieee754_exp(fabs(x));
 
/* |x| in [log(maxdouble), overflowthresold] */
GET_LOW_WORD(lx,x);
if (ix<0x408633CE ||
(ix==0x408633ce && lx<=(__uint32_t)0x8fb9f87d)) {
w = __ieee754_exp(half*fabs(x));
t = half*w;
return t*w;
}
 
/* |x| > overflowthresold, cosh(x) overflow */
return huge*huge;
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/wf_atan2.c
0,0 → 1,71
/* wf_atan2.c -- float version of w_atan2.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
 
/*
* wrapper atan2f(y,x)
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifdef __STDC__
float atan2f(float y, float x) /* wrapper atan2f */
#else
float atan2f(y,x) /* wrapper atan2 */
float y,x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_atan2f(y,x);
#else
float z;
struct exception exc;
z = __ieee754_atan2f(y,x);
if(_LIB_VERSION == _IEEE_||isnanf(x)||isnanf(y)) return z;
if(x==(float)0.0&&y==(float)0.0) {
/* atan2f(+-0,+-0) */
exc.arg1 = y;
exc.arg2 = x;
exc.err = 0;
exc.type = DOMAIN;
exc.name = "atan2f";
exc.retval = 0.0;
if(_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
if (exc.err != 0)
errno = exc.err;
return (float)exc.retval;
} else
return z;
#endif
}
 
#ifdef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double atan2(double y, double x)
#else
double atan2(y,x)
double y,x;
#endif
{
return (double) atan2f((float) y, (float) x);
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/ef_sqrt.c
0,0 → 1,90
/* ef_sqrtf.c -- float version of e_sqrt.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
#include "fdlibm.h"
 
#ifdef __STDC__
static const float one = 1.0, tiny=1.0e-30;
#else
static float one = 1.0, tiny=1.0e-30;
#endif
 
#ifdef __STDC__
float __ieee754_sqrtf(float x)
#else
float __ieee754_sqrtf(x)
float x;
#endif
{
float z;
__int32_t sign = (__int32_t)0x80000000;
__uint32_t r,hx;
__int32_t ix,s,q,m,t,i;
 
GET_FLOAT_WORD(ix,x);
hx = ix&0x7fffffff;
 
/* take care of Inf and NaN */
if(!FLT_UWORD_IS_FINITE(hx))
return x*x+x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf
sqrt(-inf)=sNaN */
/* take care of zero and -ves */
if(FLT_UWORD_IS_ZERO(hx)) return x;/* sqrt(+-0) = +-0 */
if(ix<0) return (x-x)/(x-x); /* sqrt(-ve) = sNaN */
 
/* normalize x */
m = (ix>>23);
if(FLT_UWORD_IS_SUBNORMAL(hx)) { /* subnormal x */
for(i=0;(ix&0x00800000L)==0;i++) ix<<=1;
m -= i-1;
}
m -= 127; /* unbias exponent */
ix = (ix&0x007fffffL)|0x00800000L;
if(m&1) /* odd m, double x to make it even */
ix += ix;
m >>= 1; /* m = [m/2] */
 
/* generate sqrt(x) bit by bit */
ix += ix;
q = s = 0; /* q = sqrt(x) */
r = 0x01000000L; /* r = moving bit from right to left */
 
while(r!=0) {
t = s+r;
if(t<=ix) {
s = t+r;
ix -= t;
q += r;
}
ix += ix;
r>>=1;
}
 
/* use floating add to find out rounding direction */
if(ix!=0) {
z = one-tiny; /* trigger inexact flag */
if (z>=one) {
z = one+tiny;
if (z>one)
q += 2;
else
q += (q&1);
}
}
ix = (q>>1)+0x3f000000L;
ix += (m <<23);
SET_FLOAT_WORD(z,ix);
return z;
}
/s_tan.c
0,0 → 1,114
 
/* @(#)s_tan.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
 
/*
 
FUNCTION
<<tan>>, <<tanf>>---tangent
 
INDEX
tan
INDEX
tanf
 
ANSI_SYNOPSIS
#include <math.h>
double tan(double <[x]>);
float tanf(float <[x]>);
 
TRAD_SYNOPSIS
#include <math.h>
double tan(<[x]>)
double <[x]>;
 
float tanf(<[x]>)
float <[x]>;
 
 
DESCRIPTION
<<tan>> computes the tangent of the argument <[x]>.
Angles are specified in radians.
 
<<tanf>> is identical, save that it takes and returns <<float>> values.
 
RETURNS
The tangent of <[x]> is returned.
 
PORTABILITY
<<tan>> is ANSI. <<tanf>> is an extension.
*/
 
/* tan(x)
* Return tangent function of x.
*
* kernel function:
* __kernel_tan ... tangent function on [-pi/4,pi/4]
* __ieee754_rem_pio2 ... argument reduction routine
*
* Method.
* Let S,C and T denote the sin, cos and tan respectively on
* [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
* in [-pi/4 , +pi/4], and let n = k mod 4.
* We have
*
* n sin(x) cos(x) tan(x)
* ----------------------------------------------------------
* 0 S C T
* 1 C -S -1/T
* 2 -S -C T
* 3 -C S -1/T
* ----------------------------------------------------------
*
* Special cases:
* Let trig be any of sin, cos, or tan.
* trig(+-INF) is NaN, with signals;
* trig(NaN) is that NaN;
*
* Accuracy:
* TRIG(x) returns trig(x) nearly rounded
*/
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double tan(double x)
#else
double tan(x)
double x;
#endif
{
double y[2],z=0.0;
__int32_t n,ix;
 
/* High word of x. */
GET_HIGH_WORD(ix,x);
 
/* |x| ~< pi/4 */
ix &= 0x7fffffff;
if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);
 
/* tan(Inf or NaN) is NaN */
else if (ix>=0x7ff00000) return x-x; /* NaN */
 
/* argument reduction needed */
else {
n = __ieee754_rem_pio2(x,y);
return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even
-1 -- n odd */
}
}
 
#endif /* _DOUBLE_IS_32BITS */
/s_cos.c
0,0 → 1,82
 
/* @(#)s_cos.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/* cos(x)
* Return cosine function of x.
*
* kernel function:
* __kernel_sin ... sine function on [-pi/4,pi/4]
* __kernel_cos ... cosine function on [-pi/4,pi/4]
* __ieee754_rem_pio2 ... argument reduction routine
*
* Method.
* Let S,C and T denote the sin, cos and tan respectively on
* [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
* in [-pi/4 , +pi/4], and let n = k mod 4.
* We have
*
* n sin(x) cos(x) tan(x)
* ----------------------------------------------------------
* 0 S C T
* 1 C -S -1/T
* 2 -S -C T
* 3 -C S -1/T
* ----------------------------------------------------------
*
* Special cases:
* Let trig be any of sin, cos, or tan.
* trig(+-INF) is NaN, with signals;
* trig(NaN) is that NaN;
*
* Accuracy:
* TRIG(x) returns trig(x) nearly rounded
*/
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double cos(double x)
#else
double cos(x)
double x;
#endif
{
double y[2],z=0.0;
__int32_t n,ix;
 
/* High word of x. */
GET_HIGH_WORD(ix,x);
 
/* |x| ~< pi/4 */
ix &= 0x7fffffff;
if(ix <= 0x3fe921fb) return __kernel_cos(x,z);
 
/* cos(Inf or NaN) is NaN */
else if (ix>=0x7ff00000) return x-x;
 
/* argument reduction needed */
else {
n = __ieee754_rem_pio2(x,y);
switch(n&3) {
case 0: return __kernel_cos(y[0],y[1]);
case 1: return -__kernel_sin(y[0],y[1],1);
case 2: return -__kernel_cos(y[0],y[1]);
default:
return __kernel_sin(y[0],y[1],1);
}
}
}
 
#endif /* _DOUBLE_IS_32BITS */
/e_pow.c
0,0 → 1,312
 
/* @(#)e_pow.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/* __ieee754_pow(x,y) return x**y
*
* n
* Method: Let x = 2 * (1+f)
* 1. Compute and return log2(x) in two pieces:
* log2(x) = w1 + w2,
* where w1 has 53-24 = 29 bit trailing zeros.
* 2. Perform y*log2(x) = n+y' by simulating muti-precision
* arithmetic, where |y'|<=0.5.
* 3. Return x**y = 2**n*exp(y'*log2)
*
* Special cases:
* 1. (anything) ** 0 is 1
* 2. (anything) ** 1 is itself
* 3. (anything) ** NAN is NAN
* 4. NAN ** (anything except 0) is NAN
* 5. +-(|x| > 1) ** +INF is +INF
* 6. +-(|x| > 1) ** -INF is +0
* 7. +-(|x| < 1) ** +INF is +0
* 8. +-(|x| < 1) ** -INF is +INF
* 9. +-1 ** +-INF is NAN
* 10. +0 ** (+anything except 0, NAN) is +0
* 11. -0 ** (+anything except 0, NAN, odd integer) is +0
* 12. +0 ** (-anything except 0, NAN) is +INF
* 13. -0 ** (-anything except 0, NAN, odd integer) is +INF
* 14. -0 ** (odd integer) = -( +0 ** (odd integer) )
* 15. +INF ** (+anything except 0,NAN) is +INF
* 16. +INF ** (-anything except 0,NAN) is +0
* 17. -INF ** (anything) = -0 ** (-anything)
* 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
* 19. (-anything except 0 and inf) ** (non-integer) is NAN
*
* Accuracy:
* pow(x,y) returns x**y nearly rounded. In particular
* pow(integer,integer)
* always returns the correct integer provided it is
* representable.
*
* Constants :
* The hexadecimal values are the intended ones for the following
* constants. The decimal values may be used, provided that the
* compiler will convert from decimal to binary accurately enough
* to produce the hexadecimal values shown.
*/
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
static const double
#else
static double
#endif
bp[] = {1.0, 1.5,},
dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
zero = 0.0,
one = 1.0,
two = 2.0,
two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */
huge = 1.0e300,
tiny = 1.0e-300,
/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */
lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
 
#ifdef __STDC__
double __ieee754_pow(double x, double y)
#else
double __ieee754_pow(x,y)
double x, y;
#endif
{
double z,ax,z_h,z_l,p_h,p_l;
double y1,t1,t2,r,s,t,u,v,w;
__int32_t i,j,k,yisint,n;
__int32_t hx,hy,ix,iy;
__uint32_t lx,ly;
 
EXTRACT_WORDS(hx,lx,x);
EXTRACT_WORDS(hy,ly,y);
ix = hx&0x7fffffff; iy = hy&0x7fffffff;
 
/* y==zero: x**0 = 1 */
if((iy|ly)==0) return one;
 
/* +-NaN return x+y */
if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) ||
iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0)))
return x+y;
 
/* determine if y is an odd int when x < 0
* yisint = 0 ... y is not an integer
* yisint = 1 ... y is an odd int
* yisint = 2 ... y is an even int
*/
yisint = 0;
if(hx<0) {
if(iy>=0x43400000) yisint = 2; /* even integer y */
else if(iy>=0x3ff00000) {
k = (iy>>20)-0x3ff; /* exponent */
if(k>20) {
j = ly>>(52-k);
if((j<<(52-k))==ly) yisint = 2-(j&1);
} else if(ly==0) {
j = iy>>(20-k);
if((j<<(20-k))==iy) yisint = 2-(j&1);
}
}
}
 
/* special value of y */
if(ly==0) {
if (iy==0x7ff00000) { /* y is +-inf */
if(((ix-0x3ff00000)|lx)==0)
return y - y; /* inf**+-1 is NaN */
else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */
return (hy>=0)? y: zero;
else /* (|x|<1)**-,+inf = inf,0 */
return (hy<0)?-y: zero;
}
if(iy==0x3ff00000) { /* y is +-1 */
if(hy<0) return one/x; else return x;
}
if(hy==0x40000000) return x*x; /* y is 2 */
if(hy==0x3fe00000) { /* y is 0.5 */
if(hx>=0) /* x >= +0 */
return __ieee754_sqrt(x);
}
}
 
ax = fabs(x);
/* special value of x */
if(lx==0) {
if(ix==0x7ff00000||ix==0||ix==0x3ff00000){
z = ax; /*x is +-0,+-inf,+-1*/
if(hy<0) z = one/z; /* z = (1/|x|) */
if(hx<0) {
if(((ix-0x3ff00000)|yisint)==0) {
z = (z-z)/(z-z); /* (-1)**non-int is NaN */
} else if(yisint==1)
z = -z; /* (x<0)**odd = -(|x|**odd) */
}
return z;
}
}
/* (x<0)**(non-int) is NaN */
/* CYGNUS LOCAL: This used to be
if((((hx>>31)+1)|yisint)==0) return (x-x)/(x-x);
but ANSI C says a right shift of a signed negative quantity is
implementation defined. */
if(((((__uint32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x);
 
/* |y| is huge */
if(iy>0x41e00000) { /* if |y| > 2**31 */
if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */
if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
}
/* over/underflow if x is not close to one */
if(ix<0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
if(ix>0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
/* now |1-x| is tiny <= 2**-20, suffice to compute
log(x) by x-x^2/2+x^3/3-x^4/4 */
t = x-1; /* t has 20 trailing zeros */
w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25));
u = ivln2_h*t; /* ivln2_h has 21 sig. bits */
v = t*ivln2_l-w*ivln2;
t1 = u+v;
SET_LOW_WORD(t1,0);
t2 = v-(t1-u);
} else {
double s2,s_h,s_l,t_h,t_l;
n = 0;
/* take care subnormal number */
if(ix<0x00100000)
{ax *= two53; n -= 53; GET_HIGH_WORD(ix,ax); }
n += ((ix)>>20)-0x3ff;
j = ix&0x000fffff;
/* determine interval */
ix = j|0x3ff00000; /* normalize ix */
if(j<=0x3988E) k=0; /* |x|<sqrt(3/2) */
else if(j<0xBB67A) k=1; /* |x|<sqrt(3) */
else {k=0;n+=1;ix -= 0x00100000;}
SET_HIGH_WORD(ax,ix);
 
/* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
v = one/(ax+bp[k]);
s = u*v;
s_h = s;
SET_LOW_WORD(s_h,0);
/* t_h=ax+bp[k] High */
t_h = zero;
SET_HIGH_WORD(t_h,((ix>>1)|0x20000000)+0x00080000+(k<<18));
t_l = ax - (t_h-bp[k]);
s_l = v*((u-s_h*t_h)-s_h*t_l);
/* compute log(ax) */
s2 = s*s;
r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
r += s_l*(s_h+s);
s2 = s_h*s_h;
t_h = 3.0+s2+r;
SET_LOW_WORD(t_h,0);
t_l = r-((t_h-3.0)-s2);
/* u+v = s*(1+...) */
u = s_h*t_h;
v = s_l*t_h+t_l*s;
/* 2/(3log2)*(s+...) */
p_h = u+v;
SET_LOW_WORD(p_h,0);
p_l = v-(p_h-u);
z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
z_l = cp_l*p_h+p_l*cp+dp_l[k];
/* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
t = (double)n;
t1 = (((z_h+z_l)+dp_h[k])+t);
SET_LOW_WORD(t1,0);
t2 = z_l-(((t1-t)-dp_h[k])-z_h);
}
 
s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
if(((((__uint32_t)hx>>31)-1)|(yisint-1))==0)
s = -one;/* (-ve)**(odd int) */
 
/* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
y1 = y;
SET_LOW_WORD(y1,0);
p_l = (y-y1)*t1+y*t2;
p_h = y1*t1;
z = p_l+p_h;
EXTRACT_WORDS(j,i,z);
if (j>=0x40900000) { /* z >= 1024 */
if(((j-0x40900000)|i)!=0) /* if z > 1024 */
return s*huge*huge; /* overflow */
else {
if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */
}
} else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */
if(((j-0xc090cc00)|i)!=0) /* z < -1075 */
return s*tiny*tiny; /* underflow */
else {
if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */
}
}
/*
* compute 2**(p_h+p_l)
*/
i = j&0x7fffffff;
k = (i>>20)-0x3ff;
n = 0;
if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */
n = j+(0x00100000>>(k+1));
k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */
t = zero;
SET_HIGH_WORD(t,n&~(0x000fffff>>k));
n = ((n&0x000fffff)|0x00100000)>>(20-k);
if(j<0) n = -n;
p_h -= t;
}
t = p_l+p_h;
SET_LOW_WORD(t,0);
u = t*lg2_h;
v = (p_l-(t-p_h))*lg2+t*lg2_l;
z = u+v;
w = v-(z-u);
t = z*z;
t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
r = (z*t1)/(t1-two)-(w+z*w);
z = one-(r-z);
GET_HIGH_WORD(j,z);
j += (n<<20);
if((j>>20)<=0) z = scalbn(z,(int)n); /* subnormal output */
else SET_HIGH_WORD(z,j);
return s*z;
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/w_scalb.c
0,0 → 1,94
 
/* @(#)w_scalb.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
* wrapper scalb(double x, double fn) is provide for
* passing various standard test suite. One
* should use scalbn() instead.
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
#ifdef _SCALB_INT
double scalb(double x, int fn) /* wrapper scalb */
#else
double scalb(double x, double fn) /* wrapper scalb */
#endif
#else
double scalb(x,fn) /* wrapper scalb */
#ifdef _SCALB_INT
double x; int fn;
#else
double x,fn;
#endif
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_scalb(x,fn);
#else
double z;
#ifndef HUGE_VAL
#define HUGE_VAL inf
double inf = 0.0;
 
SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */
#endif
struct exception exc;
z = __ieee754_scalb(x,fn);
if(_LIB_VERSION == _IEEE_) return z;
if(!(finite(z)||isnan(z))&&finite(x)) {
/* scalb overflow; SVID also returns +-HUGE_VAL */
exc.type = OVERFLOW;
exc.name = "scalb";
exc.err = 0;
exc.arg1 = x;
exc.arg2 = fn;
exc.retval = x > 0.0 ? HUGE_VAL : -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
}
if(z==0.0&&z!=x) {
/* scalb underflow */
exc.type = UNDERFLOW;
exc.name = "scalb";
exc.err = 0;
exc.arg1 = x;
exc.arg2 = fn;
exc.retval = copysign(0.0,x);
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
if (exc.err != 0)
errno = exc.err;
return exc.retval;
}
#ifndef _SCALB_INT
if(!finite(fn)) errno = ERANGE;
#endif
return z;
#endif
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/s_tanh.c
0,0 → 1,128
 
/* @(#)s_tanh.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
 
FUNCTION
<<tanh>>, <<tanhf>>---hyperbolic tangent
 
INDEX
tanh
INDEX
tanhf
 
ANSI_SYNOPSIS
#include <math.h>
double tanh(double <[x]>);
float tanhf(float <[x]>);
 
TRAD_SYNOPSIS
#include <math.h>
double tanh(<[x]>)
double <[x]>;
 
float tanhf(<[x]>)
float <[x]>;
 
 
DESCRIPTION
 
<<tanh>> computes the hyperbolic tangent of
the argument <[x]>. Angles are specified in radians.
 
<<tanh(<[x]>)>> is defined as
. sinh(<[x]>)/cosh(<[x]>)
<<tanhf>> is identical, save that it takes and returns <<float>> values.
 
RETURNS
The hyperbolic tangent of <[x]> is returned.
 
PORTABILITY
<<tanh>> is ANSI C. <<tanhf>> is an extension.
 
*/
 
/* Tanh(x)
* Return the Hyperbolic Tangent of x
*
* Method :
* x -x
* e - e
* 0. tanh(x) is defined to be -----------
* x -x
* e + e
* 1. reduce x to non-negative by tanh(-x) = -tanh(x).
* 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x)
* -t
* 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x)
* t + 2
* 2
* 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x)
* t + 2
* 22.0 < x <= INF : tanh(x) := 1.
*
* Special cases:
* tanh(NaN) is NaN;
* only tanh(0)=0 is exact for finite argument.
*/
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
static const double one=1.0, two=2.0, tiny = 1.0e-300;
#else
static double one=1.0, two=2.0, tiny = 1.0e-300;
#endif
 
#ifdef __STDC__
double tanh(double x)
#else
double tanh(x)
double x;
#endif
{
double t,z;
__int32_t jx,ix;
 
/* High word of |x|. */
GET_HIGH_WORD(jx,x);
ix = jx&0x7fffffff;
 
/* x is INF or NaN */
if(ix>=0x7ff00000) {
if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */
else return one/x-one; /* tanh(NaN) = NaN */
}
 
/* |x| < 22 */
if (ix < 0x40360000) { /* |x|<22 */
if (ix<0x3c800000) /* |x|<2**-55 */
return x*(one+x); /* tanh(small) = small */
if (ix>=0x3ff00000) { /* |x|>=1 */
t = expm1(two*fabs(x));
z = one - two/(t+two);
} else {
t = expm1(-two*fabs(x));
z= -t/(t+two);
}
/* |x| > 22, return +-1 */
} else {
z = one - tiny; /* raised inexact flag */
}
return (jx>=0)? z: -z;
}
 
#endif /* _DOUBLE_IS_32BITS */
/sf_tanh.c
0,0 → 1,73
/* sf_tanh.c -- float version of s_tanh.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
#include "fdlibm.h"
 
#ifdef __STDC__
static const float one=1.0, two=2.0, tiny = 1.0e-30;
#else
static float one=1.0, two=2.0, tiny = 1.0e-30;
#endif
 
#ifdef __STDC__
float tanhf(float x)
#else
float tanhf(x)
float x;
#endif
{
float t,z;
__int32_t jx,ix;
 
GET_FLOAT_WORD(jx,x);
ix = jx&0x7fffffff;
 
/* x is INF or NaN */
if(!FLT_UWORD_IS_FINITE(ix)) {
if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */
else return one/x-one; /* tanh(NaN) = NaN */
}
 
/* |x| < 22 */
if (ix < 0x41b00000) { /* |x|<22 */
if (ix<0x24000000) /* |x|<2**-55 */
return x*(one+x); /* tanh(small) = small */
if (ix>=0x3f800000) { /* |x|>=1 */
t = expm1f(two*fabsf(x));
z = one - two/(t+two);
} else {
t = expm1f(-two*fabsf(x));
z= -t/(t+two);
}
/* |x| > 22, return +-1 */
} else {
z = one - tiny; /* raised inexact flag */
}
return (jx>=0)? z: -z;
}
 
#ifdef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double tanh(double x)
#else
double tanh(x)
double x;
#endif
{
return (double) tanhf((float) x);
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */
/wf_sqrt.c
0,0 → 1,72
/* wf_sqrt.c -- float version of w_sqrt.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
 
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
 
/*
* wrapper sqrtf(x)
*/
 
#include "fdlibm.h"
#include <errno.h>
 
#ifdef __STDC__
float sqrtf(float x) /* wrapper sqrtf */
#else
float sqrtf(x) /* wrapper sqrtf */
float x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_sqrtf(x);
#else
float z;
struct exception exc;
z = __ieee754_sqrtf(x);
if(_LIB_VERSION == _IEEE_ || isnanf(x)) return z;
if(x<(float)0.0) {
/* sqrtf(negative) */
exc.type = DOMAIN;
exc.name = "sqrtf";
exc.err = 0;
exc.arg1 = exc.arg2 = (double)x;
if (_LIB_VERSION == _SVID_)
exc.retval = 0.0;
else
exc.retval = 0.0/0.0;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
errno = EDOM;
}
if (exc.err != 0)
errno = exc.err;
return (float)exc.retval;
} else
return z;
#endif
}
 
#ifdef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
double sqrt(double x)
#else
double sqrt(x)
double x;
#endif
{
return (double) sqrtf((float) x);
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */

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