| 1 |
39 |
lampret |
/* ef_exp.c -- float version of e_exp.c.
|
| 2 |
|
|
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
| 3 |
|
|
*/
|
| 4 |
|
|
|
| 5 |
|
|
/*
|
| 6 |
|
|
* ====================================================
|
| 7 |
|
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
| 8 |
|
|
*
|
| 9 |
|
|
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
| 10 |
|
|
* Permission to use, copy, modify, and distribute this
|
| 11 |
|
|
* software is freely granted, provided that this notice
|
| 12 |
|
|
* is preserved.
|
| 13 |
|
|
* ====================================================
|
| 14 |
|
|
*/
|
| 15 |
|
|
|
| 16 |
|
|
#include "fdlibm.h"
|
| 17 |
|
|
|
| 18 |
|
|
#ifdef __v810__
|
| 19 |
|
|
#define const
|
| 20 |
|
|
#endif
|
| 21 |
|
|
|
| 22 |
|
|
#ifdef __STDC__
|
| 23 |
|
|
static const float
|
| 24 |
|
|
#else
|
| 25 |
|
|
static float
|
| 26 |
|
|
#endif
|
| 27 |
|
|
one = 1.0,
|
| 28 |
|
|
halF[2] = {0.5,-0.5,},
|
| 29 |
|
|
huge = 1.0e+30,
|
| 30 |
|
|
twom100 = 7.8886090522e-31, /* 2**-100=0x0d800000 */
|
| 31 |
|
|
o_threshold= 8.8721679688e+01, /* 0x42b17180 */
|
| 32 |
|
|
u_threshold= -1.0397208405e+02, /* 0xc2cff1b5 */
|
| 33 |
|
|
ln2HI[2] ={ 6.9313812256e-01, /* 0x3f317180 */
|
| 34 |
|
|
-6.9313812256e-01,}, /* 0xbf317180 */
|
| 35 |
|
|
ln2LO[2] ={ 9.0580006145e-06, /* 0x3717f7d1 */
|
| 36 |
|
|
-9.0580006145e-06,}, /* 0xb717f7d1 */
|
| 37 |
|
|
invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */
|
| 38 |
|
|
P1 = 1.6666667163e-01, /* 0x3e2aaaab */
|
| 39 |
|
|
P2 = -2.7777778450e-03, /* 0xbb360b61 */
|
| 40 |
|
|
P3 = 6.6137559770e-05, /* 0x388ab355 */
|
| 41 |
|
|
P4 = -1.6533901999e-06, /* 0xb5ddea0e */
|
| 42 |
|
|
P5 = 4.1381369442e-08; /* 0x3331bb4c */
|
| 43 |
|
|
|
| 44 |
|
|
#ifdef __STDC__
|
| 45 |
|
|
float __ieee754_expf(float x) /* default IEEE double exp */
|
| 46 |
|
|
#else
|
| 47 |
|
|
float __ieee754_expf(x) /* default IEEE double exp */
|
| 48 |
|
|
float x;
|
| 49 |
|
|
#endif
|
| 50 |
|
|
{
|
| 51 |
|
|
float y,hi,lo,c,t;
|
| 52 |
|
|
__int32_t k,xsb;
|
| 53 |
|
|
__uint32_t hx;
|
| 54 |
|
|
|
| 55 |
|
|
GET_FLOAT_WORD(hx,x);
|
| 56 |
|
|
xsb = (hx>>31)&1; /* sign bit of x */
|
| 57 |
|
|
hx &= 0x7fffffff; /* high word of |x| */
|
| 58 |
|
|
|
| 59 |
|
|
/* filter out non-finite argument */
|
| 60 |
|
|
if(hx >= 0x42b17218) { /* if |x|>=88.721... */
|
| 61 |
|
|
if(hx>0x7f800000)
|
| 62 |
|
|
return x+x; /* NaN */
|
| 63 |
|
|
if(hx==0x7f800000)
|
| 64 |
|
|
return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */
|
| 65 |
|
|
if(x > o_threshold) return huge*huge; /* overflow */
|
| 66 |
|
|
if(x < u_threshold) return twom100*twom100; /* underflow */
|
| 67 |
|
|
}
|
| 68 |
|
|
|
| 69 |
|
|
/* argument reduction */
|
| 70 |
|
|
if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
|
| 71 |
|
|
if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
|
| 72 |
|
|
hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
|
| 73 |
|
|
} else {
|
| 74 |
|
|
k = invln2*x+halF[xsb];
|
| 75 |
|
|
t = k;
|
| 76 |
|
|
hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
|
| 77 |
|
|
lo = t*ln2LO[0];
|
| 78 |
|
|
}
|
| 79 |
|
|
x = hi - lo;
|
| 80 |
|
|
}
|
| 81 |
|
|
else if(hx < 0x31800000) { /* when |x|<2**-28 */
|
| 82 |
|
|
if(huge+x>one) return one+x;/* trigger inexact */
|
| 83 |
|
|
}
|
| 84 |
|
|
else k = 0;
|
| 85 |
|
|
|
| 86 |
|
|
/* x is now in primary range */
|
| 87 |
|
|
t = x*x;
|
| 88 |
|
|
c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
|
| 89 |
|
|
if(k==0) return one-((x*c)/(c-(float)2.0)-x);
|
| 90 |
|
|
else y = one-((lo-(x*c)/((float)2.0-c))-hi);
|
| 91 |
|
|
if(k >= -125) {
|
| 92 |
|
|
__uint32_t hy;
|
| 93 |
|
|
GET_FLOAT_WORD(hy,y);
|
| 94 |
|
|
SET_FLOAT_WORD(y,hy+(k<<23)); /* add k to y's exponent */
|
| 95 |
|
|
return y;
|
| 96 |
|
|
} else {
|
| 97 |
|
|
__uint32_t hy;
|
| 98 |
|
|
GET_FLOAT_WORD(hy,y);
|
| 99 |
|
|
SET_FLOAT_WORD(y,hy+((k+100)<<23)); /* add k to y's exponent */
|
| 100 |
|
|
return y*twom100;
|
| 101 |
|
|
}
|
| 102 |
|
|
}
|
