URL
https://opencores.org/ocsvn/openrisc/openrisc/trunk
Subversion Repositories openrisc
Compare Revisions
- This comparison shows the changes necessary to convert path
/openrisc/trunk/rtos/ecos-2.0/packages/language/c/libm/v2_0/src/double/ieee754-core
- from Rev 27 to Rev 174
- ↔ Reverse comparison
Rev 27 → Rev 174
/e_asin.c
0,0 → 1,173
//=========================================================================== |
// |
// e_asin.c |
// |
// Part of the standard mathematical function library |
// |
//=========================================================================== |
//####ECOSGPLCOPYRIGHTBEGIN#### |
// ------------------------------------------- |
// This file is part of eCos, the Embedded Configurable Operating System. |
// Copyright (C) 1998, 1999, 2000, 2001, 2002 Red Hat, Inc. |
// |
// eCos is free software; you can redistribute it and/or modify it under |
// the terms of the GNU General Public License as published by the Free |
// Software Foundation; either version 2 or (at your option) any later version. |
// |
// eCos is distributed in the hope that it will be useful, but WITHOUT ANY |
// WARRANTY; without even the implied warranty of MERCHANTABILITY or |
// FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
// for more details. |
// |
// You should have received a copy of the GNU General Public License along |
// with eCos; if not, write to the Free Software Foundation, Inc., |
// 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA. |
// |
// As a special exception, if other files instantiate templates or use macros |
// or inline functions from this file, or you compile this file and link it |
// with other works to produce a work based on this file, this file does not |
// by itself cause the resulting work to be covered by the GNU General Public |
// License. However the source code for this file must still be made available |
// in accordance with section (3) of the GNU General Public License. |
// |
// This exception does not invalidate any other reasons why a work based on |
// this file might be covered by the GNU General Public License. |
// |
// Alternative licenses for eCos may be arranged by contacting Red Hat, Inc. |
// at http://sources.redhat.com/ecos/ecos-license/ |
// ------------------------------------------- |
//####ECOSGPLCOPYRIGHTEND#### |
//=========================================================================== |
//#####DESCRIPTIONBEGIN#### |
// |
// Author(s): jlarmour |
// Contributors: jlarmour |
// Date: 1998-02-13 |
// Purpose: |
// Description: |
// Usage: |
// |
//####DESCRIPTIONEND#### |
// |
//=========================================================================== |
|
// CONFIGURATION |
|
#include <pkgconf/libm.h> // Configuration header |
|
// Include the Math library? |
#ifdef CYGPKG_LIBM |
|
// Derived from code with the following copyright |
|
|
/* @(#)e_asin.c 1.3 95/01/18 */ |
/* |
* ==================================================== |
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
* |
* Developed at SunSoft, 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 "mathincl/fdlibm.h" |
|
static const double |
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 */ |
|
double __ieee754_asin(double x) |
{ |
double t,w,p,q,c,r,s; |
int hx,ix; |
|
hx = CYG_LIBM_HI(x); |
ix = hx&0x7fffffff; |
if(ix>= 0x3ff00000) { /* |x|>= 1 */ |
if(((ix-0x3ff00000)|CYG_LIBM_LO(x))==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 = 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; |
CYG_LIBM_LO(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 // ifdef CYGPKG_LIBM |
|
// EOF e_asin.c |
/e_atanh.c
0,0 → 1,125
//=========================================================================== |
// |
// e_atanh.c |
// |
// Part of the standard mathematical function library |
// |
//=========================================================================== |
//####ECOSGPLCOPYRIGHTBEGIN#### |
// ------------------------------------------- |
// This file is part of eCos, the Embedded Configurable Operating System. |
// Copyright (C) 1998, 1999, 2000, 2001, 2002 Red Hat, Inc. |
// |
// eCos is free software; you can redistribute it and/or modify it under |
// the terms of the GNU General Public License as published by the Free |
// Software Foundation; either version 2 or (at your option) any later version. |
// |
// eCos is distributed in the hope that it will be useful, but WITHOUT ANY |
// WARRANTY; without even the implied warranty of MERCHANTABILITY or |
// FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
// for more details. |
// |
// You should have received a copy of the GNU General Public License along |
// with eCos; if not, write to the Free Software Foundation, Inc., |
// 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA. |
// |
// As a special exception, if other files instantiate templates or use macros |
// or inline functions from this file, or you compile this file and link it |
// with other works to produce a work based on this file, this file does not |
// by itself cause the resulting work to be covered by the GNU General Public |
// License. However the source code for this file must still be made available |
// in accordance with section (3) of the GNU General Public License. |
// |
// This exception does not invalidate any other reasons why a work based on |
// this file might be covered by the GNU General Public License. |
// |
// Alternative licenses for eCos may be arranged by contacting Red Hat, Inc. |
// at http://sources.redhat.com/ecos/ecos-license/ |
// ------------------------------------------- |
//####ECOSGPLCOPYRIGHTEND#### |
//=========================================================================== |
//#####DESCRIPTIONBEGIN#### |
// |
// Author(s): jlarmour |
// Contributors: jlarmour |
// Date: 1998-02-13 |
// Purpose: |
// Description: |
// Usage: |
// |
//####DESCRIPTIONEND#### |
// |
//=========================================================================== |
|
// CONFIGURATION |
|
#include <pkgconf/libm.h> // Configuration header |
|
// Include the Math library? |
#ifdef CYGPKG_LIBM |
|
// Derived from code with the following copyright |
|
|
/* @(#)e_atanh.c 1.3 95/01/18 */ |
/* |
* ==================================================== |
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
* |
* Developed at SunSoft, 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 "mathincl/fdlibm.h" |
|
static const double one = 1.0, huge = 1e300; |
|
static double zero = 0.0; |
|
double __ieee754_atanh(double x) |
{ |
double t; |
int hx,ix; |
unsigned lx; |
hx = CYG_LIBM_HI(x); /* high word */ |
lx = CYG_LIBM_LO(x); /* low word */ |
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 */ |
CYG_LIBM_HI(x) = ix; /* x <- |x| */ |
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 // ifdef CYGPKG_LIBM |
|
// EOF e_atanh.c |
/e_cosh.c
0,0 → 1,146
//=========================================================================== |
// |
// e_cosh.c |
// |
// Part of the standard mathematical function library |
// |
//=========================================================================== |
//####ECOSGPLCOPYRIGHTBEGIN#### |
// ------------------------------------------- |
// This file is part of eCos, the Embedded Configurable Operating System. |
// Copyright (C) 1998, 1999, 2000, 2001, 2002 Red Hat, Inc. |
// |
// eCos is free software; you can redistribute it and/or modify it under |
// the terms of the GNU General Public License as published by the Free |
// Software Foundation; either version 2 or (at your option) any later version. |
// |
// eCos is distributed in the hope that it will be useful, but WITHOUT ANY |
// WARRANTY; without even the implied warranty of MERCHANTABILITY or |
// FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
// for more details. |
// |
// You should have received a copy of the GNU General Public License along |
// with eCos; if not, write to the Free Software Foundation, Inc., |
// 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA. |
// |
// As a special exception, if other files instantiate templates or use macros |
// or inline functions from this file, or you compile this file and link it |
// with other works to produce a work based on this file, this file does not |
// by itself cause the resulting work to be covered by the GNU General Public |
// License. However the source code for this file must still be made available |
// in accordance with section (3) of the GNU General Public License. |
// |
// This exception does not invalidate any other reasons why a work based on |
// this file might be covered by the GNU General Public License. |
// |
// Alternative licenses for eCos may be arranged by contacting Red Hat, Inc. |
// at http://sources.redhat.com/ecos/ecos-license/ |
// ------------------------------------------- |
//####ECOSGPLCOPYRIGHTEND#### |
//=========================================================================== |
//#####DESCRIPTIONBEGIN#### |
// |
// Author(s): jlarmour |
// Contributors: jlarmour |
// Date: 1998-02-13 |
// Purpose: |
// Description: |
// Usage: |
// |
//####DESCRIPTIONEND#### |
// |
//=========================================================================== |
|
// CONFIGURATION |
|
#include <pkgconf/libm.h> // Configuration header |
|
// Include the Math library? |
#ifdef CYGPKG_LIBM |
|
// Derived from code with the following copyright |
|
|
/* @(#)e_cosh.c 1.3 95/01/18 */ |
/* |
* ==================================================== |
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
* |
* Developed at SunSoft, 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 "mathincl/fdlibm.h" |
|
static const double one = 1.0, half=0.5, huge = 1.0e300; |
|
double __ieee754_cosh(double x) |
{ |
double t,w; |
int ix; |
unsigned lx; |
|
/* High word of |x|. */ |
ix = CYG_LIBM_HI(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] */ |
lx = *( (((*(unsigned*)&one)>>29)) + (unsigned*)&x); |
if (ix<0x408633CE || |
((ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d))) { |
w = __ieee754_exp(half*fabs(x)); |
t = half*w; |
return t*w; |
} |
|
/* |x| > overflowthresold, cosh(x) overflow */ |
return huge*huge; |
} |
|
#endif // ifdef CYGPKG_LIBM |
|
// EOF e_cosh.c |
/e_exp.c
0,0 → 1,218
//=========================================================================== |
// |
// e_exp.c |
// |
// Part of the standard mathematical function library |
// |
//=========================================================================== |
//####ECOSGPLCOPYRIGHTBEGIN#### |
// ------------------------------------------- |
// This file is part of eCos, the Embedded Configurable Operating System. |
// Copyright (C) 1998, 1999, 2000, 2001, 2002 Red Hat, Inc. |
// |
// eCos is free software; you can redistribute it and/or modify it under |
// the terms of the GNU General Public License as published by the Free |
// Software Foundation; either version 2 or (at your option) any later version. |
// |
// eCos is distributed in the hope that it will be useful, but WITHOUT ANY |
// WARRANTY; without even the implied warranty of MERCHANTABILITY or |
// FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
// for more details. |
// |
// You should have received a copy of the GNU General Public License along |
// with eCos; if not, write to the Free Software Foundation, Inc., |
// 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA. |
// |
// As a special exception, if other files instantiate templates or use macros |
// or inline functions from this file, or you compile this file and link it |
// with other works to produce a work based on this file, this file does not |
// by itself cause the resulting work to be covered by the GNU General Public |
// License. However the source code for this file must still be made available |
// in accordance with section (3) of the GNU General Public License. |
// |
// This exception does not invalidate any other reasons why a work based on |
// this file might be covered by the GNU General Public License. |
// |
// Alternative licenses for eCos may be arranged by contacting Red Hat, Inc. |
// at http://sources.redhat.com/ecos/ecos-license/ |
// ------------------------------------------- |
//####ECOSGPLCOPYRIGHTEND#### |
//=========================================================================== |
//#####DESCRIPTIONBEGIN#### |
// |
// Author(s): jlarmour |
// Contributors: jlarmour |
// Date: 1998-02-13 |
// Purpose: |
// Description: |
// Usage: |
// |
//####DESCRIPTIONEND#### |
// |
//=========================================================================== |
|
// CONFIGURATION |
|
#include <pkgconf/libm.h> // Configuration header |
|
// Include the Math library? |
#ifdef CYGPKG_LIBM |
|
// Derived from code with the following copyright |
|
|
/* @(#)e_exp.c 1.3 95/01/18 */ |
/* |
* ==================================================== |
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
* |
* Developed at SunSoft, 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 "mathincl/fdlibm.h" |
|
static const double |
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 */ |
|
|
double __ieee754_exp(double x) /* default IEEE double exp */ |
{ |
double y,hi,lo,c,t; |
int k,xsb; |
unsigned hx; |
|
hi=lo=0.0; /* to placate compiler */ |
hx = CYG_LIBM_HI(x); /* high word of 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) { |
if(((hx&0xfffff)|CYG_LIBM_LO(x))!=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; |
} |
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) { |
CYG_LIBM_HI(y) += (k<<20); /* add k to y's exponent */ |
return y; |
} else { |
CYG_LIBM_HI(y) += ((k+1000)<<20);/* add k to y's exponent */ |
return y*twom1000; |
} |
} |
|
#endif // ifdef CYGPKG_LIBM |
|
// EOF e_exp.c |
/e_acosh.c
0,0 → 1,122
//=========================================================================== |
// |
// e_acosh.c |
// |
// Part of the standard mathematical function library |
// |
//=========================================================================== |
//####ECOSGPLCOPYRIGHTBEGIN#### |
// ------------------------------------------- |
// This file is part of eCos, the Embedded Configurable Operating System. |
// Copyright (C) 1998, 1999, 2000, 2001, 2002 Red Hat, Inc. |
// |
// eCos is free software; you can redistribute it and/or modify it under |
// the terms of the GNU General Public License as published by the Free |
// Software Foundation; either version 2 or (at your option) any later version. |
// |
// eCos is distributed in the hope that it will be useful, but WITHOUT ANY |
// WARRANTY; without even the implied warranty of MERCHANTABILITY or |
// FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
// for more details. |
// |
// You should have received a copy of the GNU General Public License along |
// with eCos; if not, write to the Free Software Foundation, Inc., |
// 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA. |
// |
// As a special exception, if other files instantiate templates or use macros |
// or inline functions from this file, or you compile this file and link it |
// with other works to produce a work based on this file, this file does not |
// by itself cause the resulting work to be covered by the GNU General Public |
// License. However the source code for this file must still be made available |
// in accordance with section (3) of the GNU General Public License. |
// |
// This exception does not invalidate any other reasons why a work based on |
// this file might be covered by the GNU General Public License. |
// |
// Alternative licenses for eCos may be arranged by contacting Red Hat, Inc. |
// at http://sources.redhat.com/ecos/ecos-license/ |
// ------------------------------------------- |
//####ECOSGPLCOPYRIGHTEND#### |
//=========================================================================== |
//#####DESCRIPTIONBEGIN#### |
// |
// Author(s): jlarmour |
// Contributors: jlarmour |
// Date: 1998-02-13 |
// Purpose: |
// Description: |
// Usage: |
// |
//####DESCRIPTIONEND#### |
// |
//=========================================================================== |
|
// CONFIGURATION |
|
#include <pkgconf/libm.h> // Configuration header |
|
// Include the Math library? |
#ifdef CYGPKG_LIBM |
|
// Derived from code with the following copyright |
|
|
/* @(#)e_acosh.c 1.3 95/01/18 */ |
/* |
* ==================================================== |
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
* |
* Developed at SunSoft, 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 "mathincl/fdlibm.h" |
|
static const double |
one = 1.0, |
ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ |
|
double __ieee754_acosh(double x) |
{ |
double t; |
int hx; |
hx = CYG_LIBM_HI(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)|CYG_LIBM_LO(x))==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+sqrt(t-one))); |
} else { /* 1<x<2 */ |
t = x-one; |
return log1p(t+sqrt(2.0*t+t*t)); |
} |
} |
|
#endif // ifdef CYGPKG_LIBM |
|
// EOF e_acosh.c |
/e_lgamma.c
0,0 → 1,94
//=========================================================================== |
// |
// e_lgamma.c |
// |
// Part of the standard mathematical function library |
// |
//=========================================================================== |
//####ECOSGPLCOPYRIGHTBEGIN#### |
// ------------------------------------------- |
// This file is part of eCos, the Embedded Configurable Operating System. |
// Copyright (C) 1998, 1999, 2000, 2001, 2002 Red Hat, Inc. |
// |
// eCos is free software; you can redistribute it and/or modify it under |
// the terms of the GNU General Public License as published by the Free |
// Software Foundation; either version 2 or (at your option) any later version. |
// |
// eCos is distributed in the hope that it will be useful, but WITHOUT ANY |
// WARRANTY; without even the implied warranty of MERCHANTABILITY or |
// FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
// for more details. |
// |
// You should have received a copy of the GNU General Public License along |
// with eCos; if not, write to the Free Software Foundation, Inc., |
// 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA. |
// |
// As a special exception, if other files instantiate templates or use macros |
// or inline functions from this file, or you compile this file and link it |
// with other works to produce a work based on this file, this file does not |
// by itself cause the resulting work to be covered by the GNU General Public |
// License. However the source code for this file must still be made available |
// in accordance with section (3) of the GNU General Public License. |
// |
// This exception does not invalidate any other reasons why a work based on |
// this file might be covered by the GNU General Public License. |
// |
// Alternative licenses for eCos may be arranged by contacting Red Hat, Inc. |
// at http://sources.redhat.com/ecos/ecos-license/ |
// ------------------------------------------- |
//####ECOSGPLCOPYRIGHTEND#### |
//=========================================================================== |
//#####DESCRIPTIONBEGIN#### |
// |
// Author(s): jlarmour |
// Contributors: jlarmour |
// Date: 1998-02-13 |
// Purpose: |
// Description: |
// Usage: |
// |
//####DESCRIPTIONEND#### |
// |
//=========================================================================== |
|
// CONFIGURATION |
|
#include <pkgconf/libm.h> // Configuration header |
|
// Include the Math library? |
#ifdef CYGPKG_LIBM |
|
// Derived from code with the following copyright |
|
|
/* @(#)e_lgamma.c 1.3 95/01/18 */ |
/* |
* ==================================================== |
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
* |
* Developed at SunSoft, 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(x) |
* Return the logarithm of the Gamma function of x. |
* |
* Method: call __ieee754_lgamma_r |
*/ |
|
#include <math.h> |
#include "mathincl/fdlibm.h" |
|
double |
__ieee754_lgamma(double x) |
{ |
return __ieee754_lgamma_r(x,&signgam); |
} |
|
#endif // ifdef CYGPKG_LIBM |
|
// EOF e_lgamma.c |
/e_sinh.c
0,0 → 1,139
//=========================================================================== |
// |
// e_sinh.c |
// |
// Part of the standard mathematical function library |
// |
//=========================================================================== |
//####ECOSGPLCOPYRIGHTBEGIN#### |
// ------------------------------------------- |
// This file is part of eCos, the Embedded Configurable Operating System. |
// Copyright (C) 1998, 1999, 2000, 2001, 2002 Red Hat, Inc. |
// |
// eCos is free software; you can redistribute it and/or modify it under |
// the terms of the GNU General Public License as published by the Free |
// Software Foundation; either version 2 or (at your option) any later version. |
// |
// eCos is distributed in the hope that it will be useful, but WITHOUT ANY |
// WARRANTY; without even the implied warranty of MERCHANTABILITY or |
// FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
// for more details. |
// |
// You should have received a copy of the GNU General Public License along |
// with eCos; if not, write to the Free Software Foundation, Inc., |
// 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA. |
// |
// As a special exception, if other files instantiate templates or use macros |
// or inline functions from this file, or you compile this file and link it |
// with other works to produce a work based on this file, this file does not |
// by itself cause the resulting work to be covered by the GNU General Public |
// License. However the source code for this file must still be made available |
// in accordance with section (3) of the GNU General Public License. |
// |
// This exception does not invalidate any other reasons why a work based on |
// this file might be covered by the GNU General Public License. |
// |
// Alternative licenses for eCos may be arranged by contacting Red Hat, Inc. |
// at http://sources.redhat.com/ecos/ecos-license/ |
// ------------------------------------------- |
//####ECOSGPLCOPYRIGHTEND#### |
//=========================================================================== |
//#####DESCRIPTIONBEGIN#### |
// |
// Author(s): jlarmour |
// Contributors: jlarmour |
// Date: 1998-02-13 |
// Purpose: |
// Description: |
// Usage: |
// |
//####DESCRIPTIONEND#### |
// |
//=========================================================================== |
|
// CONFIGURATION |
|
#include <pkgconf/libm.h> // Configuration header |
|
// Include the Math library? |
#ifdef CYGPKG_LIBM |
|
// Derived from code with the following copyright |
|
|
/* @(#)e_sinh.c 1.3 95/01/18 */ |
/* |
* ==================================================== |
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
* |
* Developed at SunSoft, 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 "mathincl/fdlibm.h" |
|
static const double one = 1.0, shuge = 1.0e307; |
|
double __ieee754_sinh(double x) |
{ |
double t,w,h; |
int ix,jx; |
unsigned lx; |
|
/* High word of |x|. */ |
jx = CYG_LIBM_HI(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] */ |
lx = *( (((*(unsigned*)&one)>>29)) + (unsigned*)&x); |
if (ix<0x408633CE || ((ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d))) { |
w = __ieee754_exp(0.5*fabs(x)); |
t = h*w; |
return t*w; |
} |
|
/* |x| > overflowthresold, sinh(x) overflow */ |
return x*shuge; |
} |
|
#endif // ifdef CYGPKG_LIBM |
|
// EOF e_sinh.c |
/e_gamma_r.c
0,0 → 1,93
//=========================================================================== |
// |
// e_gamma_r.c |
// |
// Part of the standard mathematical function library |
// |
//=========================================================================== |
//####ECOSGPLCOPYRIGHTBEGIN#### |
// ------------------------------------------- |
// This file is part of eCos, the Embedded Configurable Operating System. |
// Copyright (C) 1998, 1999, 2000, 2001, 2002 Red Hat, Inc. |
// |
// eCos is free software; you can redistribute it and/or modify it under |
// the terms of the GNU General Public License as published by the Free |
// Software Foundation; either version 2 or (at your option) any later version. |
// |
// eCos is distributed in the hope that it will be useful, but WITHOUT ANY |
// WARRANTY; without even the implied warranty of MERCHANTABILITY or |
// FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
// for more details. |
// |
// You should have received a copy of the GNU General Public License along |
// with eCos; if not, write to the Free Software Foundation, Inc., |
// 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA. |
// |
// As a special exception, if other files instantiate templates or use macros |
// or inline functions from this file, or you compile this file and link it |
// with other works to produce a work based on this file, this file does not |
// by itself cause the resulting work to be covered by the GNU General Public |
// License. However the source code for this file must still be made available |
// in accordance with section (3) of the GNU General Public License. |
// |
// This exception does not invalidate any other reasons why a work based on |
// this file might be covered by the GNU General Public License. |
// |
// Alternative licenses for eCos may be arranged by contacting Red Hat, Inc. |
// at http://sources.redhat.com/ecos/ecos-license/ |
// ------------------------------------------- |
//####ECOSGPLCOPYRIGHTEND#### |
//=========================================================================== |
//#####DESCRIPTIONBEGIN#### |
// |
// Author(s): jlarmour |
// Contributors: jlarmour |
// Date: 1998-02-13 |
// Purpose: |
// Description: |
// Usage: |
// |
//####DESCRIPTIONEND#### |
// |
//=========================================================================== |
|
// CONFIGURATION |
|
#include <pkgconf/libm.h> // Configuration header |
|
// Include the Math library? |
#ifdef CYGPKG_LIBM |
|
// Derived from code with the following copyright |
|
|
/* @(#)e_gamma_r.c 1.3 95/01/18 */ |
/* |
* ==================================================== |
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
* |
* Developed at SunSoft, 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 "mathincl/fdlibm.h" |
|
double __ieee754_gamma_r(double x, int *signgamp) |
{ |
return __ieee754_lgamma_r(x,signgamp); |
} |
|
#endif // ifdef CYGPKG_LIBM |
|
// EOF e_gamma_r.c |
/e_hypot.c
0,0 → 1,176
//=========================================================================== |
// |
// e_hypot.c |
// |
// Part of the standard mathematical function library |
// |
//=========================================================================== |
//####ECOSGPLCOPYRIGHTBEGIN#### |
// ------------------------------------------- |
// This file is part of eCos, the Embedded Configurable Operating System. |
// Copyright (C) 1998, 1999, 2000, 2001, 2002 Red Hat, Inc. |
// |
// eCos is free software; you can redistribute it and/or modify it under |
// the terms of the GNU General Public License as published by the Free |
// Software Foundation; either version 2 or (at your option) any later version. |
// |
// eCos is distributed in the hope that it will be useful, but WITHOUT ANY |
// WARRANTY; without even the implied warranty of MERCHANTABILITY or |
// FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
// for more details. |
// |
// You should have received a copy of the GNU General Public License along |
// with eCos; if not, write to the Free Software Foundation, Inc., |
// 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA. |
// |
// As a special exception, if other files instantiate templates or use macros |
// or inline functions from this file, or you compile this file and link it |
// with other works to produce a work based on this file, this file does not |
// by itself cause the resulting work to be covered by the GNU General Public |
// License. However the source code for this file must still be made available |
// in accordance with section (3) of the GNU General Public License. |
// |
// This exception does not invalidate any other reasons why a work based on |
// this file might be covered by the GNU General Public License. |
// |
// Alternative licenses for eCos may be arranged by contacting Red Hat, Inc. |
// at http://sources.redhat.com/ecos/ecos-license/ |
// ------------------------------------------- |
//####ECOSGPLCOPYRIGHTEND#### |
//=========================================================================== |
//#####DESCRIPTIONBEGIN#### |
// |
// Author(s): jlarmour |
// Contributors: jlarmour |
// Date: 1998-02-13 |
// Purpose: |
// Description: |
// Usage: |
// |
//####DESCRIPTIONEND#### |
// |
//=========================================================================== |
|
// CONFIGURATION |
|
#include <pkgconf/libm.h> // Configuration header |
|
// Include the Math library? |
#ifdef CYGPKG_LIBM |
|
// Derived from code with the following copyright |
|
|
/* @(#)e_hypot.c 1.3 95/01/18 */ |
/* |
* ==================================================== |
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
* |
* Developed at SunSoft, 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 "mathincl/fdlibm.h" |
|
double __ieee754_hypot(double x, double y) |
{ |
double a=x,b=y,t1,t2,y1,y2,w; |
int j,k,ha,hb; |
|
ha = CYG_LIBM_HI(x)&0x7fffffff; /* high word of x */ |
hb = CYG_LIBM_HI(y)&0x7fffffff; /* high word of y */ |
if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} |
CYG_LIBM_HI(a) = ha; /* a <- |a| */ |
CYG_LIBM_HI(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 */ |
w = a+b; /* for sNaN */ |
if(((ha&0xfffff)|CYG_LIBM_LO(a))==0) w = a; |
if(((hb^0x7ff00000)|CYG_LIBM_LO(b))==0) w = b; |
return w; |
} |
/* scale a and b by 2**-600 */ |
ha -= 0x25800000; hb -= 0x25800000; k += 600; |
CYG_LIBM_HI(a) = ha; |
CYG_LIBM_HI(b) = hb; |
} |
if(hb < 0x20b00000) { /* b < 2**-500 */ |
if(hb <= 0x000fffff) { /* subnormal b or 0 */ |
if((hb|(CYG_LIBM_LO(b)))==0) return a; |
t1=0; |
CYG_LIBM_HI(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; |
CYG_LIBM_HI(a) = ha; |
CYG_LIBM_HI(b) = hb; |
} |
} |
/* medium size a and b */ |
w = a-b; |
if (w>b) { |
t1 = 0; |
CYG_LIBM_HI(t1) = ha; |
t2 = a-t1; |
w = sqrt(t1*t1-(b*(-b)-t2*(a+t1))); |
} else { |
a = a+a; |
y1 = 0; |
CYG_LIBM_HI(y1) = hb; |
y2 = b - y1; |
t1 = 0; |
CYG_LIBM_HI(t1) = ha+0x00100000; |
t2 = a - t1; |
w = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b))); |
} |
if(k!=0) { |
t1 = 1.0; |
CYG_LIBM_HI(t1) += (k<<20); |
return t1*w; |
} else return w; |
} |
|
#endif // ifdef CYGPKG_LIBM |
|
// EOF e_hypot.c |
/e_pow.c
0,0 → 1,371
//======================================================================== |
// |
// e_pow.c |
// |
// Part of the standard mathematical function library |
// |
//======================================================================== |
//####ECOSGPLCOPYRIGHTBEGIN#### |
// ------------------------------------------- |
// This file is part of eCos, the Embedded Configurable Operating System. |
// Copyright (C) 1998, 1999, 2000, 2001, 2002 Red Hat, Inc. |
// |
// eCos is free software; you can redistribute it and/or modify it under |
// the terms of the GNU General Public License as published by the Free |
// Software Foundation; either version 2 or (at your option) any later version. |
// |
// eCos is distributed in the hope that it will be useful, but WITHOUT ANY |
// WARRANTY; without even the implied warranty of MERCHANTABILITY or |
// FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
// for more details. |
// |
// You should have received a copy of the GNU General Public License along |
// with eCos; if not, write to the Free Software Foundation, Inc., |
// 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA. |
// |
// As a special exception, if other files instantiate templates or use macros |
// or inline functions from this file, or you compile this file and link it |
// with other works to produce a work based on this file, this file does not |
// by itself cause the resulting work to be covered by the GNU General Public |
// License. However the source code for this file must still be made available |
// in accordance with section (3) of the GNU General Public License. |
// |
// This exception does not invalidate any other reasons why a work based on |
// this file might be covered by the GNU General Public License. |
// |
// Alternative licenses for eCos may be arranged by contacting Red Hat, Inc. |
// at http://sources.redhat.com/ecos/ecos-license/ |
// ------------------------------------------- |
//####ECOSGPLCOPYRIGHTEND#### |
//======================================================================== |
//#####DESCRIPTIONBEGIN#### |
// |
// Author(s): jlarmour |
// Contributors: |
// Date: 2001-07-20 |
// Purpose: |
// Description: |
// Usage: |
// |
//####DESCRIPTIONEND#### |
// |
//======================================================================== |
|
// CONFIGURATION |
|
#include <pkgconf/libm.h> // Configuration header |
|
|
/* @(#)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 "mathincl/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) */ |
|
// EOF e_pow.c |
/e_atan2.c
0,0 → 1,180
//=========================================================================== |
// |
// e_atan2.c |
// |
// Part of the standard mathematical function library |
// |
//=========================================================================== |
//####ECOSGPLCOPYRIGHTBEGIN#### |
// ------------------------------------------- |
// This file is part of eCos, the Embedded Configurable Operating System. |
// Copyright (C) 1998, 1999, 2000, 2001, 2002 Red Hat, Inc. |
// |
// eCos is free software; you can redistribute it and/or modify it under |
// the terms of the GNU General Public License as published by the Free |
// Software Foundation; either version 2 or (at your option) any later version. |
// |
// eCos is distributed in the hope that it will be useful, but WITHOUT ANY |
// WARRANTY; without even the implied warranty of MERCHANTABILITY or |
// FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
// for more details. |
// |
// You should have received a copy of the GNU General Public License along |
// with eCos; if not, write to the Free Software Foundation, Inc., |
// 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA. |
// |
// As a special exception, if other files instantiate templates or use macros |
// or inline functions from this file, or you compile this file and link it |
// with other works to produce a work based on this file, this file does not |
// by itself cause the resulting work to be covered by the GNU General Public |
// License. However the source code for this file must still be made available |
// in accordance with section (3) of the GNU General Public License. |
// |
// This exception does not invalidate any other reasons why a work based on |
// this file might be covered by the GNU General Public License. |
// |
// Alternative licenses for eCos may be arranged by contacting Red Hat, Inc. |
// at http://sources.redhat.com/ecos/ecos-license/ |
// ------------------------------------------- |
//####ECOSGPLCOPYRIGHTEND#### |
//=========================================================================== |
//#####DESCRIPTIONBEGIN#### |
// |
// Author(s): jlarmour |
// Contributors: jlarmour |
// Date: 1998-02-13 |
// Purpose: |
// Description: |
// Usage: |
// |
//####DESCRIPTIONEND#### |
// |
//=========================================================================== |
|
// CONFIGURATION |
|
#include <pkgconf/libm.h> // Configuration header |
|
// Include the Math library? |
#ifdef CYGPKG_LIBM |
|
// Derived from code with the following copyright |
|
|
/* @(#)e_atan2.c 1.3 95/01/18 */ |
/* |
* ==================================================== |
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
* |
* Developed at SunSoft, 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 "mathincl/fdlibm.h" |
|
static const double |
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 */ |
|
double __ieee754_atan2(double y, double x) |
{ |
double z; |
int k,m,hx,hy,ix,iy; |
unsigned lx,ly; |
|
hx = CYG_LIBM_HI(x); ix = hx&0x7fffffff; |
lx = CYG_LIBM_LO(x); |
hy = CYG_LIBM_HI(y); iy = hy&0x7fffffff; |
ly = CYG_LIBM_LO(y); |
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: CYG_LIBM_HI(z) ^= 0x80000000; |
return z ; /* atan(-,+) */ |
case 2: return pi-(z-pi_lo);/* atan(+,-) */ |
default: /* case 3 */ |
return (z-pi_lo)-pi;/* atan(-,-) */ |
} |
} |
|
#endif // ifdef CYGPKG_LIBM |
|
// EOF e_atan2.c |
/e_remainder.c
0,0 → 1,134
//=========================================================================== |
// |
// e_remainder.c |
// |
// Part of the standard mathematical function library |
// |
//=========================================================================== |
//####ECOSGPLCOPYRIGHTBEGIN#### |
// ------------------------------------------- |
// This file is part of eCos, the Embedded Configurable Operating System. |
// Copyright (C) 1998, 1999, 2000, 2001, 2002 Red Hat, Inc. |
// |
// eCos is free software; you can redistribute it and/or modify it under |
// the terms of the GNU General Public License as published by the Free |
// Software Foundation; either version 2 or (at your option) any later version. |
// |
// eCos is distributed in the hope that it will be useful, but WITHOUT ANY |
// WARRANTY; without even the implied warranty of MERCHANTABILITY or |
// FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
// for more details. |
// |
// You should have received a copy of the GNU General Public License along |
// with eCos; if not, write to the Free Software Foundation, Inc., |
// 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA. |
// |
// As a special exception, if other files instantiate templates or use macros |
// or inline functions from this file, or you compile this file and link it |
// with other works to produce a work based on this file, this file does not |
// by itself cause the resulting work to be covered by the GNU General Public |
// License. However the source code for this file must still be made available |
// in accordance with section (3) of the GNU General Public License. |
// |
// This exception does not invalidate any other reasons why a work based on |
// this file might be covered by the GNU General Public License. |
// |
// Alternative licenses for eCos may be arranged by contacting Red Hat, Inc. |
// at http://sources.redhat.com/ecos/ecos-license/ |
// ------------------------------------------- |
//####ECOSGPLCOPYRIGHTEND#### |
//=========================================================================== |
//#####DESCRIPTIONBEGIN#### |
// |
// Author(s): jlarmour |
// Contributors: jlarmour |
// Date: 1998-02-13 |
// Purpose: |
// Description: |
// Usage: |
// |
//####DESCRIPTIONEND#### |
// |
//=========================================================================== |
|
// CONFIGURATION |
|
#include <pkgconf/libm.h> // Configuration header |
|
// Include the Math library? |
#ifdef CYGPKG_LIBM |
|
// Derived from code with the following copyright |
|
|
/* @(#)e_remainder.c 1.3 95/01/18 */ |
/* |
* ==================================================== |
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
* |
* Developed at SunSoft, 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 "mathincl/fdlibm.h" |
|
static const double zero = 0.0; |
|
|
double __ieee754_remainder(double x, double p) |
{ |
int hx,hp; |
unsigned sx,lx,lp; |
double p_half; |
|
hx = CYG_LIBM_HI(x); /* high word of x */ |
lx = CYG_LIBM_LO(x); /* low word of x */ |
hp = CYG_LIBM_HI(p); /* high word of p */ |
lp = CYG_LIBM_LO(p); /* low word of 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; |
} |
} |
CYG_LIBM_HI(x) ^= sx; |
return x; |
} |
|
#endif // ifdef CYGPKG_LIBM |
|
// EOF e_remainder.c |
/e_jn.c
0,0 → 1,328
//=========================================================================== |
// |
// e_jn.c |
// |
// Part of the standard mathematical function library |
// |
//=========================================================================== |
//####ECOSGPLCOPYRIGHTBEGIN#### |
// ------------------------------------------- |
// This file is part of eCos, the Embedded Configurable Operating System. |
// Copyright (C) 1998, 1999, 2000, 2001, 2002 Red Hat, Inc. |
// |
// eCos is free software; you can redistribute it and/or modify it under |
// the terms of the GNU General Public License as published by the Free |
// Software Foundation; either version 2 or (at your option) any later version. |
// |
// eCos is distributed in the hope that it will be useful, but WITHOUT ANY |
// WARRANTY; without even the implied warranty of MERCHANTABILITY or |
// FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
// for more details. |
// |
// You should have received a copy of the GNU General Public License along |
// with eCos; if not, write to the Free Software Foundation, Inc., |
// 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA. |
// |
// As a special exception, if other files instantiate templates or use macros |
// or inline functions from this file, or you compile this file and link it |
// with other works to produce a work based on this file, this file does not |
// by itself cause the resulting work to be covered by the GNU General Public |
// License. However the source code for this file must still be made available |
// in accordance with section (3) of the GNU General Public License. |
// |
// This exception does not invalidate any other reasons why a work based on |
// this file might be covered by the GNU General Public License. |
// |
// Alternative licenses for eCos may be arranged by contacting Red Hat, Inc. |
// at http://sources.redhat.com/ecos/ecos-license/ |
// ------------------------------------------- |
//####ECOSGPLCOPYRIGHTEND#### |
//=========================================================================== |
//#####DESCRIPTIONBEGIN#### |
// |
// Author(s): jlarmour |
// Contributors: jlarmour |
// Date: 1998-02-13 |
// Purpose: |
// Description: |
// Usage: |
// |
//####DESCRIPTIONEND#### |
// |
//=========================================================================== |
|
// CONFIGURATION |
|
#include <pkgconf/libm.h> // Configuration header |
|
// Include the Math library? |
#ifdef CYGPKG_LIBM |
|
// Derived from code with the following copyright |
|
|
/* @(#)e_jn.c 1.4 95/01/18 */ |
/* |
* ==================================================== |
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
* |
* Developed at SunSoft, 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 "mathincl/fdlibm.h" |
|
static const double |
invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ |
two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */ |
one = 1.00000000000000000000e+00; /* 0x3FF00000, 0x00000000 */ |
|
static double zero = 0.00000000000000000000e+00; |
|
double __ieee754_jn(int n, double x) |
{ |
int 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) |
*/ |
hx = CYG_LIBM_HI(x); |
ix = 0x7fffffff&hx; |
lx = CYG_LIBM_LO(x); |
/* if J(n,NaN) is NaN */ |
if((ix|((unsigned)(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; |
default: temp = 0.0; break; /* not used - purely to |
* placate compiler */ |
} |
b = invsqrtpi*temp/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; int 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; |
} |
|
double __ieee754_yn(int n, double x) |
{ |
int i,hx,ix,lx; |
int sign; |
double a, b, temp; |
|
hx = CYG_LIBM_HI(x); |
ix = 0x7fffffff&hx; |
lx = CYG_LIBM_LO(x); |
/* if Y(n,NaN) is NaN */ |
if((ix|((unsigned)(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; |
default: temp = 0.0; break; /* not used - purely to |
* placate compiler */ |
} |
b = invsqrtpi*temp/sqrt(x); |
} else { |
a = __ieee754_y0(x); |
b = __ieee754_y1(x); |
/* quit if b is -inf */ |
for(i=1;i<n&&((unsigned)CYG_LIBM_HI(b) != 0xfff00000);i++){ |
temp = b; |
b = ((double)(i+i)/x)*b - a; |
a = temp; |
} |
} |
if(sign>0) return b; else return -b; |
} |
|
#endif // ifdef CYGPKG_LIBM |
|
// EOF e_jn.c |
/e_j0.c
0,0 → 1,440
//=========================================================================== |
// |
// e_j0.c |
// |
// Part of the standard mathematical function library |
// |
//=========================================================================== |
//####ECOSGPLCOPYRIGHTBEGIN#### |
// ------------------------------------------- |
// This file is part of eCos, the Embedded Configurable Operating System. |
// Copyright (C) 1998, 1999, 2000, 2001, 2002 Red Hat, Inc. |
// |
// eCos is free software; you can redistribute it and/or modify it under |
// the terms of the GNU General Public License as published by the Free |
// Software Foundation; either version 2 or (at your option) any later version. |
// |
// eCos is distributed in the hope that it will be useful, but WITHOUT ANY |
// WARRANTY; without even the implied warranty of MERCHANTABILITY or |
// FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
// for more details. |
// |
// You should have received a copy of the GNU General Public License along |
// with eCos; if not, write to the Free Software Foundation, Inc., |
// 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA. |
// |
// As a special exception, if other files instantiate templates or use macros |
// or inline functions from this file, or you compile this file and link it |
// with other works to produce a work based on this file, this file does not |
// by itself cause the resulting work to be covered by the GNU General Public |
// License. However the source code for this file must still be made available |
// in accordance with section (3) of the GNU General Public License. |
// |
// This exception does not invalidate any other reasons why a work based on |
// this file might be covered by the GNU General Public License. |
// |
// Alternative licenses for eCos may be arranged by contacting Red Hat, Inc. |
// at http://sources.redhat.com/ecos/ecos-license/ |
// ------------------------------------------- |
//####ECOSGPLCOPYRIGHTEND#### |
//=========================================================================== |
//#####DESCRIPTIONBEGIN#### |
// |
// Author(s): jlarmour |
// Contributors: jlarmour |
// Date: 1998-02-13 |
// Purpose: |
// Description: |
// Usage: |
// |
//####DESCRIPTIONEND#### |
// |
//=========================================================================== |
|
// CONFIGURATION |
|
#include <pkgconf/libm.h> // Configuration header |
|
// Include the Math library? |
#ifdef CYGPKG_LIBM |
|
// Derived from code with the following copyright |
|
|
/* @(#)e_j0.c 1.3 95/01/18 */ |
/* |
* ==================================================== |
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
* |
* Developed at SunSoft, 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 "mathincl/fdlibm.h" |
|
static double pzero(double), qzero(double); |
|
static const double |
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 */ |
|
static double zero = 0.0; |
|
double __ieee754_j0(double x) |
{ |
double z, s,c,ss,cc,r,u,v; |
int hx,ix; |
|
hx = CYG_LIBM_HI(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)/sqrt(x); |
else { |
u = pzero(x); v = qzero(x); |
z = invsqrtpi*(u*cc-v*ss)/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)); |
} |
} |
|
static const double |
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 */ |
|
double __ieee754_y0(double x) |
{ |
double z, s,c,ss,cc,u,v; |
int hx,ix,lx; |
|
hx = CYG_LIBM_HI(x); |
ix = 0x7fffffff&hx; |
lx = CYG_LIBM_LO(x); |
/* 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)/sqrt(x); |
else { |
u = pzero(x); v = qzero(x); |
z = invsqrtpi*(u*ss+v*cc)/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) |
*/ |
static const double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ |
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 */ |
}; |
static const double pS8[5] = { |
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 */ |
}; |
|
static const double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
-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 */ |
}; |
static const double pS5[5] = { |
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 */ |
}; |
|
static const double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ |
-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 */ |
}; |
static const double pS3[5] = { |
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 */ |
}; |
|
static const double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
-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 */ |
}; |
static const double pS2[5] = { |
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 */ |
}; |
|
static double pzero(double x) |
{ |
const double *p,*q; |
double z,r,s; |
int ix; |
ix = 0x7fffffff&CYG_LIBM_HI(x); |
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;} /*if (ix>=0x40000000) */ |
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 pzero 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) |
*/ |
static const double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ |
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 */ |
}; |
static const double qS8[6] = { |
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 */ |
}; |
|
static const double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
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 */ |
}; |
static const double qS5[6] = { |
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 */ |
}; |
|
static const double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ |
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 */ |
}; |
static const double qS3[6] = { |
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 */ |
}; |
|
static const double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
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 */ |
}; |
static const double qS2[6] = { |
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 */ |
}; |
|
static double qzero(double x) |
{ |
const double *p,*q; |
double s,r,z; |
int ix; |
ix = 0x7fffffff&CYG_LIBM_HI(x); |
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;} /* if(ix>=0x40000000) */ |
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 // ifdef CYGPKG_LIBM |
|
// EOF e_j0.c |
/e_j1.c
0,0 → 1,435
//=========================================================================== |
// |
// e_j1.c |
// |
// Part of the standard mathematical function library |
// |
//=========================================================================== |
//####ECOSGPLCOPYRIGHTBEGIN#### |
// ------------------------------------------- |
// This file is part of eCos, the Embedded Configurable Operating System. |
// Copyright (C) 1998, 1999, 2000, 2001, 2002 Red Hat, Inc. |
// |
// eCos is free software; you can redistribute it and/or modify it under |
// the terms of the GNU General Public License as published by the Free |
// Software Foundation; either version 2 or (at your option) any later version. |
// |
// eCos is distributed in the hope that it will be useful, but WITHOUT ANY |
// WARRANTY; without even the implied warranty of MERCHANTABILITY or |
// FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
// for more details. |
// |
// You should have received a copy of the GNU General Public License along |
// with eCos; if not, write to the Free Software Foundation, Inc., |
// 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA. |
// |
// As a special exception, if other files instantiate templates or use macros |
// or inline functions from this file, or you compile this file and link it |
// with other works to produce a work based on this file, this file does not |
// by itself cause the resulting work to be covered by the GNU General Public |
// License. However the source code for this file must still be made available |
// in accordance with section (3) of the GNU General Public License. |
// |
// This exception does not invalidate any other reasons why a work based on |
// this file might be covered by the GNU General Public License. |
// |
// Alternative licenses for eCos may be arranged by contacting Red Hat, Inc. |
// at http://sources.redhat.com/ecos/ecos-license/ |
// ------------------------------------------- |
//####ECOSGPLCOPYRIGHTEND#### |
//=========================================================================== |
//#####DESCRIPTIONBEGIN#### |
// |
// Author(s): jlarmour |
// Contributors: jlarmour |
// Date: 1998-02-13 |
// Purpose: |
// Description: |
// Usage: |
// |
//####DESCRIPTIONEND#### |
// |
//=========================================================================== |
|
// CONFIGURATION |
|
#include <pkgconf/libm.h> // Configuration header |
|
// Include the Math library? |
#ifdef CYGPKG_LIBM |
|
// Derived from code with the following copyright |
|
|
/* @(#)e_j1.c 1.3 95/01/18 */ |
/* |
* ==================================================== |
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
* |
* Developed at SunSoft, 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 "mathincl/fdlibm.h" |
|
static double pone(double), qone(double); |
|
static const double |
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 */ |
|
static double zero = 0.0; |
|
double __ieee754_j1(double x) |
{ |
double z, s,c,ss,cc,r,u,v,y; |
int hx,ix; |
|
hx = CYG_LIBM_HI(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/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>0x48000000) z = (invsqrtpi*cc)/sqrt(y); |
else { |
u = pone(y); v = qone(y); |
z = invsqrtpi*(u*cc-v*ss)/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); |
} |
|
static const double U0[5] = { |
-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 */ |
}; |
static const double V0[5] = { |
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 */ |
}; |
|
double __ieee754_y1(double x) |
{ |
double z, s,c,ss,cc,u,v; |
int hx,ix,lx; |
|
hx = CYG_LIBM_HI(x); |
ix = 0x7fffffff&hx; |
lx = CYG_LIBM_LO(x); |
/* 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)/sqrt(x); |
else { |
u = pone(x); v = qone(x); |
z = invsqrtpi*(u*ss+v*cc)/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) |
*/ |
|
static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ |
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 */ |
}; |
static const double ps8[5] = { |
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 */ |
}; |
|
static const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
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 */ |
}; |
static const double ps5[5] = { |
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 */ |
}; |
|
static const double pr3[6] = { |
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 */ |
}; |
static const double ps3[5] = { |
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 */ |
}; |
|
static const double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
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 */ |
}; |
static const double ps2[5] = { |
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 */ |
}; |
|
static double pone(double x) |
{ |
const double *p,*q; |
double z,r,s; |
int ix; |
ix = 0x7fffffff&CYG_LIBM_HI(x); |
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;} /* if(ix>=0x40000000) */ |
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 pone 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) |
*/ |
|
static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ |
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 */ |
}; |
static const double qs8[6] = { |
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 */ |
}; |
|
static const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
-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 */ |
}; |
static const double qs5[6] = { |
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 */ |
}; |
|
static const double qr3[6] = { |
-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 */ |
}; |
static const double qs3[6] = { |
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 */ |
}; |
|
static const double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
-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 */ |
}; |
static const double qs2[6] = { |
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 */ |
}; |
|
static double qone(double x) |
{ |
const double *p,*q; |
double s,r,z; |
int ix; |
ix = 0x7fffffff&CYG_LIBM_HI(x); |
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;} /* if(ix>=0x40000000) */ |
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 // ifdef CYGPKG_LIBM |
|
// EOF e_j1.c |
/e_rem_pio2.c
0,0 → 1,224
//=========================================================================== |
// |
// e_rem_pio2.c |
// |
// Part of the standard mathematical function library |
// |
//=========================================================================== |
//####ECOSGPLCOPYRIGHTBEGIN#### |
// ------------------------------------------- |
// This file is part of eCos, the Embedded Configurable Operating System. |
// Copyright (C) 1998, 1999, 2000, 2001, 2002 Red Hat, Inc. |
// |
// eCos is free software; you can redistribute it and/or modify it under |
// the terms of the GNU General Public License as published by the Free |
// Software Foundation; either version 2 or (at your option) any later version. |
// |
// eCos is distributed in the hope that it will be useful, but WITHOUT ANY |
// WARRANTY; without even the implied warranty of MERCHANTABILITY or |
// FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
// for more details. |
// |
// You should have received a copy of the GNU General Public License along |
// with eCos; if not, write to the Free Software Foundation, Inc., |
// 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA. |
// |
// As a special exception, if other files instantiate templates or use macros |
// or inline functions from this file, or you compile this file and link it |
// with other works to produce a work based on this file, this file does not |
// by itself cause the resulting work to be covered by the GNU General Public |
// License. However the source code for this file must still be made available |
// in accordance with section (3) of the GNU General Public License. |
// |
// This exception does not invalidate any other reasons why a work based on |
// this file might be covered by the GNU General Public License. |
// |
// Alternative licenses for eCos may be arranged by contacting Red Hat, Inc. |
// at http://sources.redhat.com/ecos/ecos-license/ |
// ------------------------------------------- |
//####ECOSGPLCOPYRIGHTEND#### |
//=========================================================================== |
//#####DESCRIPTIONBEGIN#### |
// |
// Author(s): jlarmour |
// Contributors: jlarmour |
// Date: 1998-02-13 |
// Purpose: |
// Description: |
// Usage: |
// |
//####DESCRIPTIONEND#### |
// |
//=========================================================================== |
|
// CONFIGURATION |
|
#include <pkgconf/libm.h> // Configuration header |
|
// Include the Math library? |
#ifdef CYGPKG_LIBM |
|
// Derived from code with the following copyright |
|
|
/* @(#)e_rem_pio2.c 1.4 95/01/18 */ |
/* |
* ==================================================== |
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
* |
* Developed at SunSoft, 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 "mathincl/fdlibm.h" |
|
/* |
* Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi |
*/ |
static const int two_over_pi[] = { |
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, |
}; |
|
static const int npio2_hw[] = { |
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) |
*/ |
|
static const double |
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 */ |
|
int __ieee754_rem_pio2(double x, double *y) |
{ |
double z,w,t,r,fn; |
double tx[3]; |
int e0,i,j,nx,n,ix,hx; |
|
hx = CYG_LIBM_HI(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 = (int) (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 { |
j = ix>>20; |
y[0] = r-w; |
i = j-(((CYG_LIBM_HI(y[0]))>>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; |
i = j-(((CYG_LIBM_HI(y[0]))>>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) */ |
CYG_LIBM_LO(z) = CYG_LIBM_LO(x); |
e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ |
CYG_LIBM_HI(z) = ix - (e0<<20); |
for(i=0;i<2;i++) { |
tx[i] = (double)((int)(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 // ifdef CYGPKG_LIBM |
|
// EOF e_rem_pio2.c |
/e_lgamma_r.c
0,0 → 1,357
//=========================================================================== |
// |
// e_lgamma_r.c |
// |
// Part of the standard mathematical function library |
// |
//=========================================================================== |
//####ECOSGPLCOPYRIGHTBEGIN#### |
// ------------------------------------------- |
// This file is part of eCos, the Embedded Configurable Operating System. |
// Copyright (C) 1998, 1999, 2000, 2001, 2002 Red Hat, Inc. |
// |
// eCos is free software; you can redistribute it and/or modify it under |
// the terms of the GNU General Public License as published by the Free |
// Software Foundation; either version 2 or (at your option) any later version. |
// |
// eCos is distributed in the hope that it will be useful, but WITHOUT ANY |
// WARRANTY; without even the implied warranty of MERCHANTABILITY or |
// FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
// for more details. |
// |
// You should have received a copy of the GNU General Public License along |
// with eCos; if not, write to the Free Software Foundation, Inc., |
// 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA. |
// |
// As a special exception, if other files instantiate templates or use macros |
// or inline functions from this file, or you compile this file and link it |
// with other works to produce a work based on this file, this file does not |
// by itself cause the resulting work to be covered by the GNU General Public |
// License. However the source code for this file must still be made available |
// in accordance with section (3) of the GNU General Public License. |
// |
// This exception does not invalidate any other reasons why a work based on |
// this file might be covered by the GNU General Public License. |
// |
// Alternative licenses for eCos may be arranged by contacting Red Hat, Inc. |
// at http://sources.redhat.com/ecos/ecos-license/ |
// ------------------------------------------- |
//####ECOSGPLCOPYRIGHTEND#### |
//=========================================================================== |
//#####DESCRIPTIONBEGIN#### |
// |
// Author(s): jlarmour |
// Contributors: jlarmour |
// Date: 1998-02-13 |
// Purpose: |
// Description: |
// Usage: |
// |
//####DESCRIPTIONEND#### |
// |
//=========================================================================== |
|
// CONFIGURATION |
|
#include <pkgconf/libm.h> // Configuration header |
|
// Include the Math library? |
#ifdef CYGPKG_LIBM |
|
// Derived from code with the following copyright |
|
|
/* @(#)e_lgamma_r.c 1.3 95/01/18 */ |
/* |
* ==================================================== |
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
* |
* Developed at SunSoft, 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 "mathincl/fdlibm.h" |
|
static const double |
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 */ |
|
static double zero= 0.00000000000000000000e+00; |
|
static double sin_pi(double x) |
{ |
double y,z; |
int n,ix; |
|
ix = 0x7fffffff&CYG_LIBM_HI(x); |
|
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 = (int) (y*4.0); |
} else { |
if(ix>=0x43400000) { |
y = zero; n = 0; /* y must be even */ |
} else { |
if(ix<0x43300000) z = y+two52; /* exact */ |
n = CYG_LIBM_LO(z)&1; /* lower word of z */ |
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; |
} |
|
|
double __ieee754_lgamma_r(double x, int *signgamp) |
{ |
double t,y,z,nadj,p,p1,p2,p3,q,r,w; |
int i,hx,lx,ix; |
|
nadj = 0.0; /* to placate compiler */ |
hx = CYG_LIBM_HI(x); |
lx = CYG_LIBM_LO(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 = (int)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; |
} |
|
#endif // ifdef CYGPKG_LIBM |
|
// EOF e_lgamma_r.c |
/e_log.c
0,0 → 1,204
//=========================================================================== |
// |
// e_log.c |
// |
// Part of the standard mathematical function library |
// |
//=========================================================================== |
//####ECOSGPLCOPYRIGHTBEGIN#### |
// ------------------------------------------- |
// This file is part of eCos, the Embedded Configurable Operating System. |
// Copyright (C) 1998, 1999, 2000, 2001, 2002 Red Hat, Inc. |
// |
// eCos is free software; you can redistribute it and/or modify it under |
// the terms of the GNU General Public License as published by the Free |
// Software Foundation; either version 2 or (at your option) any later version. |
// |
// eCos is distributed in the hope that it will be useful, but WITHOUT ANY |
// WARRANTY; without even the implied warranty of MERCHANTABILITY or |
// FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
// for more details. |
// |
// You should have received a copy of the GNU General Public License along |
// with eCos; if not, write to the Free Software Foundation, Inc., |
// 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA. |
// |
// As a special exception, if other files instantiate templates or use macros |
// or inline functions from this file, or you compile this file and link it |
// with other works to produce a work based on this file, this file does not |
// by itself cause the resulting work to be covered by the GNU General Public |
// License. However the source code for this file must still be made available |
// in accordance with section (3) of the GNU General Public License. |
// |
// This exception does not invalidate any other reasons why a work based on |
// this file might be covered by the GNU General Public License. |
// |
// Alternative licenses for eCos may be arranged by contacting Red Hat, Inc. |
// at http://sources.redhat.com/ecos/ecos-license/ |
// ------------------------------------------- |
//####ECOSGPLCOPYRIGHTEND#### |
//=========================================================================== |
//#####DESCRIPTIONBEGIN#### |
// |
// Author(s): jlarmour |
// Contributors: jlarmour |
// Date: 1998-02-13 |
// Purpose: |
// Description: |
// Usage: |
// |
//####DESCRIPTIONEND#### |
// |
//=========================================================================== |
|
// CONFIGURATION |
|
#include <pkgconf/libm.h> // Configuration header |
|
// Include the Math library? |
#ifdef CYGPKG_LIBM |
|
// Derived from code with the following copyright |
|
|
/* @(#)e_log.c 1.3 95/01/18 */ |
/* |
* ==================================================== |
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
* |
* Developed at SunSoft, 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 "mathincl/fdlibm.h" |
|
static const double |
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 */ |
|
static double zero = 0.0; |
|
double __ieee754_log(double x) |
{ |
double hfsq,f,s,z,R,w,t1,t2,dk; |
int k,hx,i,j; |
unsigned lx; |
|
hx = CYG_LIBM_HI(x); /* high word of x */ |
lx = CYG_LIBM_LO(x); /* low word of 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 */ |
hx = CYG_LIBM_HI(x); /* high word of x */ |
} |
if (hx >= 0x7ff00000) return x+x; |
k += (hx>>20)-1023; |
hx &= 0x000fffff; |
i = (hx+0x95f64)&0x100000; |
CYG_LIBM_HI(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 // ifdef CYGPKG_LIBM |
|
// EOF e_log.c |
/e_gamma.c
0,0 → 1,94
//=========================================================================== |
// |
// e_gamma.c |
// |
// Part of the standard mathematical function library |
// |
//=========================================================================== |
//####ECOSGPLCOPYRIGHTBEGIN#### |
// ------------------------------------------- |
// This file is part of eCos, the Embedded Configurable Operating System. |
// Copyright (C) 1998, 1999, 2000, 2001, 2002 Red Hat, Inc. |
// |
// eCos is free software; you can redistribute it and/or modify it under |
// the terms of the GNU General Public License as published by the Free |
// Software Foundation; either version 2 or (at your option) any later version. |
// |
// eCos is distributed in the hope that it will be useful, but WITHOUT ANY |
// WARRANTY; without even the implied warranty of MERCHANTABILITY or |
// FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
// for more details. |
// |
// You should have received a copy of the GNU General Public License along |
// with eCos; if not, write to the Free Software Foundation, Inc., |
// 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA. |
// |
// As a special exception, if other files instantiate templates or use macros |
// or inline functions from this file, or you compile this file and link it |
// with other works to produce a work based on this file, this file does not |
// by itself cause the resulting work to be covered by the GNU General Public |
// License. However the source code for this file must still be made available |
// in accordance with section (3) of the GNU General Public License. |
// |
// This exception does not invalidate any other reasons why a work based on |
// this file might be covered by the GNU General Public License. |
// |
// Alternative licenses for eCos may be arranged by contacting Red Hat, Inc. |
// at http://sources.redhat.com/ecos/ecos-license/ |
// ------------------------------------------- |
//####ECOSGPLCOPYRIGHTEND#### |
//=========================================================================== |
//#####DESCRIPTIONBEGIN#### |
// |
// Author(s): jlarmour |
// Contributors: jlarmour |
// Date: 1998-02-13 |
// Purpose: |
// Description: |
// Usage: |
// |
//####DESCRIPTIONEND#### |
// |
//=========================================================================== |
|
// CONFIGURATION |
|
#include <pkgconf/libm.h> // Configuration header |
|
// Include the Math library? |
#ifdef CYGPKG_LIBM |
|
// Derived from code with the following copyright |
|
|
/* @(#)e_gamma.c 1.3 95/01/18 */ |
/* |
* ==================================================== |
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
* |
* Developed at SunSoft, 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(x) |
* Return the logarithm of the Gamma function of x. |
* |
* Method: call __ieee754_gamma_r |
*/ |
|
#include <math.h> |
#include "mathincl/fdlibm.h" |
|
double |
__ieee754_gamma(double x) |
{ |
return __ieee754_gamma_r(x,&signgam); |
} |
|
#endif // ifdef CYGPKG_LIBM |
|
// EOF e_gamma.c |
/e_log10.c
0,0 → 1,148
//=========================================================================== |
// |
// e_log10.c |
// |
// Part of the standard mathematical function library |
// |
//=========================================================================== |
//####ECOSGPLCOPYRIGHTBEGIN#### |
// ------------------------------------------- |
// This file is part of eCos, the Embedded Configurable Operating System. |
// Copyright (C) 1998, 1999, 2000, 2001, 2002 Red Hat, Inc. |
// |
// eCos is free software; you can redistribute it and/or modify it under |
// the terms of the GNU General Public License as published by the Free |
// Software Foundation; either version 2 or (at your option) any later version. |
// |
// eCos is distributed in the hope that it will be useful, but WITHOUT ANY |
// WARRANTY; without even the implied warranty of MERCHANTABILITY or |
// FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
// for more details. |
// |
// You should have received a copy of the GNU General Public License along |
// with eCos; if not, write to the Free Software Foundation, Inc., |
// 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA. |
// |
// As a special exception, if other files instantiate templates or use macros |
// or inline functions from this file, or you compile this file and link it |
// with other works to produce a work based on this file, this file does not |
// by itself cause the resulting work to be covered by the GNU General Public |
// License. However the source code for this file must still be made available |
// in accordance with section (3) of the GNU General Public License. |
// |
// This exception does not invalidate any other reasons why a work based on |
// this file might be covered by the GNU General Public License. |
// |
// Alternative licenses for eCos may be arranged by contacting Red Hat, Inc. |
// at http://sources.redhat.com/ecos/ecos-license/ |
// ------------------------------------------- |
//####ECOSGPLCOPYRIGHTEND#### |
//=========================================================================== |
//#####DESCRIPTIONBEGIN#### |
// |
// Author(s): jlarmour |
// Contributors: jlarmour |
// Date: 1998-02-13 |
// Purpose: |
// Description: |
// Usage: |
// |
//####DESCRIPTIONEND#### |
// |
//=========================================================================== |
|
// CONFIGURATION |
|
#include <pkgconf/libm.h> // Configuration header |
|
// Include the Math library? |
#ifdef CYGPKG_LIBM |
|
// Derived from code with the following copyright |
|
|
/* @(#)e_log10.c 1.3 95/01/18 */ |
/* |
* ==================================================== |
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
* |
* Developed at SunSoft, 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 "mathincl/fdlibm.h" |
|
static const double |
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 */ |
|
static double zero = 0.0; |
|
double __ieee754_log10(double x) |
{ |
double y,z; |
int i,k,hx; |
unsigned lx; |
|
hx = CYG_LIBM_HI(x); /* high word of x */ |
lx = CYG_LIBM_LO(x); /* low word of 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 */ |
hx = CYG_LIBM_HI(x); /* high word of x */ |
} |
if (hx >= 0x7ff00000) return x+x; |
k += (hx>>20)-1023; |
i = ((unsigned)k&0x80000000)>>31; |
hx = (hx&0x000fffff)|((0x3ff-i)<<20); |
y = (double)(k+i); |
CYG_LIBM_HI(x) = hx; |
z = y*log10_2lo + ivln10*__ieee754_log(x); |
return z+y*log10_2hi; |
} |
|
#endif // ifdef CYGPKG_LIBM |
|
// EOF e_log10.c |
/e_scalb.c
0,0 → 1,107
//=========================================================================== |
// |
// e_scalb.c |
// |
// Part of the standard mathematical function library |
// |
//=========================================================================== |
//####ECOSGPLCOPYRIGHTBEGIN#### |
// ------------------------------------------- |
// This file is part of eCos, the Embedded Configurable Operating System. |
// Copyright (C) 1998, 1999, 2000, 2001, 2002 Red Hat, Inc. |
// |
// eCos is free software; you can redistribute it and/or modify it under |
// the terms of the GNU General Public License as published by the Free |
// Software Foundation; either version 2 or (at your option) any later version. |
// |
// eCos is distributed in the hope that it will be useful, but WITHOUT ANY |
// WARRANTY; without even the implied warranty of MERCHANTABILITY or |
// FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
// for more details. |
// |
// You should have received a copy of the GNU General Public License along |
// with eCos; if not, write to the Free Software Foundation, Inc., |
// 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA. |
// |
// As a special exception, if other files instantiate templates or use macros |
// or inline functions from this file, or you compile this file and link it |
// with other works to produce a work based on this file, this file does not |
// by itself cause the resulting work to be covered by the GNU General Public |
// License. However the source code for this file must still be made available |
// in accordance with section (3) of the GNU General Public License. |
// |
// This exception does not invalidate any other reasons why a work based on |
// this file might be covered by the GNU General Public License. |
// |
// Alternative licenses for eCos may be arranged by contacting Red Hat, Inc. |
// at http://sources.redhat.com/ecos/ecos-license/ |
// ------------------------------------------- |
//####ECOSGPLCOPYRIGHTEND#### |
//=========================================================================== |
//#####DESCRIPTIONBEGIN#### |
// |
// Author(s): jlarmour |
// Contributors: jlarmour |
// Date: 1998-02-13 |
// Purpose: |
// Description: |
// Usage: |
// |
//####DESCRIPTIONEND#### |
// |
//=========================================================================== |
|
// CONFIGURATION |
|
#include <pkgconf/libm.h> // Configuration header |
|
// Include the Math library? |
#ifdef CYGPKG_LIBM |
|
// Derived from code with the following copyright |
|
|
/* @(#)e_scalb.c 1.3 95/01/18 */ |
/* |
* ==================================================== |
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
* |
* Developed at SunSoft, 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 "mathincl/fdlibm.h" |
|
#ifdef CYGFUN_LIBM_SVID3_scalb |
double __ieee754_scalb(double x, double fn) |
#else |
double __ieee754_scalb(double x, int fn) |
#endif |
{ |
#ifdef CYGFUN_LIBM_SVID3_scalb |
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); |
#else |
return scalbn(x,fn); |
#endif |
} |
|
#endif // ifdef CYGPKG_LIBM |
|
// EOF e_scalb.c |
/e_fmod.c
0,0 → 1,197
//=========================================================================== |
// |
// e_fmod.c |
// |
// Part of the standard mathematical function library |
// |
//=========================================================================== |
//####ECOSGPLCOPYRIGHTBEGIN#### |
// ------------------------------------------- |
// This file is part of eCos, the Embedded Configurable Operating System. |
// Copyright (C) 1998, 1999, 2000, 2001, 2002 Red Hat, Inc. |
// |
// eCos is free software; you can redistribute it and/or modify it under |
// the terms of the GNU General Public License as published by the Free |
// Software Foundation; either version 2 or (at your option) any later version. |
// |
// eCos is distributed in the hope that it will be useful, but WITHOUT ANY |
// WARRANTY; without even the implied warranty of MERCHANTABILITY or |
// FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
// for more details. |
// |
// You should have received a copy of the GNU General Public License along |
// with eCos; if not, write to the Free Software Foundation, Inc., |
// 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA. |
// |
// As a special exception, if other files instantiate templates or use macros |
// or inline functions from this file, or you compile this file and link it |
// with other works to produce a work based on this file, this file does not |
// by itself cause the resulting work to be covered by the GNU General Public |
// License. However the source code for this file must still be made available |
// in accordance with section (3) of the GNU General Public License. |
// |
// This exception does not invalidate any other reasons why a work based on |
// this file might be covered by the GNU General Public License. |
// |
// Alternative licenses for eCos may be arranged by contacting Red Hat, Inc. |
// at http://sources.redhat.com/ecos/ecos-license/ |
// ------------------------------------------- |
//####ECOSGPLCOPYRIGHTEND#### |
//=========================================================================== |
//#####DESCRIPTIONBEGIN#### |
// |
// Author(s): jlarmour |
// Contributors: jlarmour |
// Date: 1998-02-13 |
// Purpose: |
// Description: |
// Usage: |
// |
//####DESCRIPTIONEND#### |
// |
//=========================================================================== |
|
// CONFIGURATION |
|
#include <pkgconf/libm.h> // Configuration header |
|
// Include the Math library? |
#ifdef CYGPKG_LIBM |
|
// Derived from code with the following copyright |
|
|
/* @(#)e_fmod.c 1.3 95/01/18 */ |
/* |
* ==================================================== |
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
* |
* Developed at SunSoft, 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 "mathincl/fdlibm.h" |
|
static const double one = 1.0, Zero[] = {0.0, -0.0,}; |
|
double __ieee754_fmod(double x, double y) |
{ |
int n,hx,hy,hz,ix,iy,sx,i; |
unsigned lx,ly,lz; |
|
hx = CYG_LIBM_HI(x); /* high word of x */ |
lx = CYG_LIBM_LO(x); /* low word of x */ |
hy = CYG_LIBM_HI(y); /* high word of y */ |
ly = CYG_LIBM_LO(y); /* low word of 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[(unsigned)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[(unsigned)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[(unsigned)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)); |
CYG_LIBM_HI(x) = hx|sx; |
CYG_LIBM_LO(x) = lx; |
} else { /* subnormal output */ |
n = -1022 - iy; |
if(n<=20) { |
lx = (lx>>n)|((unsigned)hx<<(32-n)); |
hx >>= n; |
} else if (n<=31) { |
lx = (hx<<(32-n))|(lx>>n); hx = sx; |
} else { |
lx = hx>>(n-32); hx = sx; |
} |
CYG_LIBM_HI(x) = hx|sx; |
CYG_LIBM_LO(x) = lx; |
x *= one; /* create necessary signal */ |
} |
return x; /* exact output */ |
} |
|
#endif // ifdef CYGPKG_LIBM |
|
// EOF e_fmod.c |
/e_acos.c
0,0 → 1,162
//=========================================================================== |
// |
// e_acos.c |
// |
// Part of the standard mathematical function library |
// |
//=========================================================================== |
//####ECOSGPLCOPYRIGHTBEGIN#### |
// ------------------------------------------- |
// This file is part of eCos, the Embedded Configurable Operating System. |
// Copyright (C) 1998, 1999, 2000, 2001, 2002 Red Hat, Inc. |
// |
// eCos is free software; you can redistribute it and/or modify it under |
// the terms of the GNU General Public License as published by the Free |
// Software Foundation; either version 2 or (at your option) any later version. |
// |
// eCos is distributed in the hope that it will be useful, but WITHOUT ANY |
// WARRANTY; without even the implied warranty of MERCHANTABILITY or |
// FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
// for more details. |
// |
// You should have received a copy of the GNU General Public License along |
// with eCos; if not, write to the Free Software Foundation, Inc., |
// 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA. |
// |
// As a special exception, if other files instantiate templates or use macros |
// or inline functions from this file, or you compile this file and link it |
// with other works to produce a work based on this file, this file does not |
// by itself cause the resulting work to be covered by the GNU General Public |
// License. However the source code for this file must still be made available |
// in accordance with section (3) of the GNU General Public License. |
// |
// This exception does not invalidate any other reasons why a work based on |
// this file might be covered by the GNU General Public License. |
// |
// Alternative licenses for eCos may be arranged by contacting Red Hat, Inc. |
// at http://sources.redhat.com/ecos/ecos-license/ |
// ------------------------------------------- |
//####ECOSGPLCOPYRIGHTEND#### |
//=========================================================================== |
//#####DESCRIPTIONBEGIN#### |
// |
// Author(s): jlarmour |
// Contributors: jlarmour |
// Date: 1998-02-13 |
// Purpose: |
// Description: |
// Usage: |
// |
//####DESCRIPTIONEND#### |
// |
//=========================================================================== |
|
// CONFIGURATION |
|
#include <pkgconf/libm.h> // Configuration header |
|
// Include the Math library? |
#ifdef CYGPKG_LIBM |
|
// Derived from code with the following copyright |
|
|
/* @(#)e_acos.c 1.3 95/01/18 */ |
/* |
* ==================================================== |
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
* |
* Developed at SunSoft, 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 "mathincl/fdlibm.h" |
|
static const double |
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 */ |
|
double __ieee754_acos(double x) |
{ |
double z,p,q,r,w,s,c,df; |
int hx,ix; |
hx = CYG_LIBM_HI(x); |
ix = hx&0x7fffffff; |
if(ix>=0x3ff00000) { /* |x| >= 1 */ |
if(((ix-0x3ff00000)|CYG_LIBM_LO(x))==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 = 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 = sqrt(z); |
df = s; |
CYG_LIBM_LO(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 // ifdef CYGPKG_LIBM |
|
// EOF e_acos.c |
/e_sqrt.c
0,0 → 1,507
//=========================================================================== |
// |
// e_sqrt.c |
// |
// Part of the standard mathematical function library |
// |
//=========================================================================== |
//####ECOSGPLCOPYRIGHTBEGIN#### |
// ------------------------------------------- |
// This file is part of eCos, the Embedded Configurable Operating System. |
// Copyright (C) 1998, 1999, 2000, 2001, 2002 Red Hat, Inc. |
// |
// eCos is free software; you can redistribute it and/or modify it under |
// the terms of the GNU General Public License as published by the Free |
// Software Foundation; either version 2 or (at your option) any later version. |
// |
// eCos is distributed in the hope that it will be useful, but WITHOUT ANY |
// WARRANTY; without even the implied warranty of MERCHANTABILITY or |
// FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
// for more details. |
// |
// You should have received a copy of the GNU General Public License along |
// with eCos; if not, write to the Free Software Foundation, Inc., |
// 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA. |
// |
// As a special exception, if other files instantiate templates or use macros |
// or inline functions from this file, or you compile this file and link it |
// with other works to produce a work based on this file, this file does not |
// by itself cause the resulting work to be covered by the GNU General Public |
// License. However the source code for this file must still be made available |
// in accordance with section (3) of the GNU General Public License. |
// |
// This exception does not invalidate any other reasons why a work based on |
// this file might be covered by the GNU General Public License. |
// |
// Alternative licenses for eCos may be arranged by contacting Red Hat, Inc. |
// at http://sources.redhat.com/ecos/ecos-license/ |
// ------------------------------------------- |
//####ECOSGPLCOPYRIGHTEND#### |
//=========================================================================== |
//#####DESCRIPTIONBEGIN#### |
// |
// Author(s): jlarmour |
// Contributors: jlarmour |
// Date: 1998-02-13 |
// Purpose: |
// Description: |
// Usage: |
// |
//####DESCRIPTIONEND#### |
// |
//=========================================================================== |
|
// CONFIGURATION |
|
#include <pkgconf/libm.h> // Configuration header |
|
// Include the Math library? |
#ifdef CYGPKG_LIBM |
|
// Derived from code with the following copyright |
|
/* @(#)e_sqrt.c 1.3 95/01/18 */ |
/* |
* ==================================================== |
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
* |
* Developed at SunSoft, 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 "mathincl/fdlibm.h" |
|
static const double one = 1.0, tiny=1.0e-300; |
|
double __ieee754_sqrt(double x) |
{ |
double z; |
int sign = (int)0x80000000; |
unsigned r,t1,s1,ix1,q1; |
int ix0,s0,q,m,t,i; |
|
ix0 = CYG_LIBM_HI(x); /* high word of x */ |
ix1 = CYG_LIBM_LO(x); /* low word of 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)==(unsigned)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==(unsigned)0xffffffff) { q1=0; q += 1;} |
else if (z>one) { |
if (q1==(unsigned)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); |
CYG_LIBM_HI(z) = ix0; |
CYG_LIBM_LO(z) = ix1; |
return z; |
} |
|
/* |
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). |
|
*/ |
|
|
#endif // ifdef CYGPKG_LIBM |
|
// EOF e_sqrt.c |