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| 1 /* origin: FreeBSD /usr/src/lib/msun/src/s_log1pf.c */ |
| 2 /* |
| 3 * ==================================================== |
| 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| 5 * |
| 6 * Developed at SunPro, a Sun Microsystems, Inc. business. |
| 7 * Permission to use, copy, modify, and distribute this |
| 8 * software is freely granted, provided that this notice |
| 9 * is preserved. |
| 10 * ==================================================== |
| 11 */ |
| 12 |
| 13 #include "libm.h" |
| 14 |
| 15 static const float |
| 16 ln2_hi = 6.9313812256e-01, /* 0x3f317180 */ |
| 17 ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */ |
| 18 /* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */ |
| 19 Lg1 = 0xaaaaaa.0p-24, /* 0.66666662693 */ |
| 20 Lg2 = 0xccce13.0p-25, /* 0.40000972152 */ |
| 21 Lg3 = 0x91e9ee.0p-25, /* 0.28498786688 */ |
| 22 Lg4 = 0xf89e26.0p-26; /* 0.24279078841 */ |
| 23 |
| 24 float log1pf(float x) |
| 25 { |
| 26 union {float f; uint32_t i;} u = {x}; |
| 27 float_t hfsq,f,c,s,z,R,w,t1,t2,dk; |
| 28 uint32_t ix,iu; |
| 29 int k; |
| 30 |
| 31 ix = u.i; |
| 32 k = 1; |
| 33 if (ix < 0x3ed413d0 || ix>>31) { /* 1+x < sqrt(2)+ */ |
| 34 if (ix >= 0xbf800000) { /* x <= -1.0 */ |
| 35 if (x == -1) |
| 36 return x/0.0f; /* log1p(-1)=+inf */ |
| 37 return (x-x)/0.0f; /* log1p(x<-1)=NaN */ |
| 38 } |
| 39 if (ix<<1 < 0x33800000<<1) { /* |x| < 2**-24 */ |
| 40 /* underflow if subnormal */ |
| 41 if ((ix&0x7f800000) == 0) |
| 42 FORCE_EVAL(x*x); |
| 43 return x; |
| 44 } |
| 45 if (ix <= 0xbe95f619) { /* sqrt(2)/2- <= 1+x < sqrt(2)+ */ |
| 46 k = 0; |
| 47 c = 0; |
| 48 f = x; |
| 49 } |
| 50 } else if (ix >= 0x7f800000) |
| 51 return x; |
| 52 if (k) { |
| 53 u.f = 1 + x; |
| 54 iu = u.i; |
| 55 iu += 0x3f800000 - 0x3f3504f3; |
| 56 k = (int)(iu>>23) - 0x7f; |
| 57 /* correction term ~ log(1+x)-log(u), avoid underflow in c/u */ |
| 58 if (k < 25) { |
| 59 c = k >= 2 ? 1-(u.f-x) : x-(u.f-1); |
| 60 c /= u.f; |
| 61 } else |
| 62 c = 0; |
| 63 /* reduce u into [sqrt(2)/2, sqrt(2)] */ |
| 64 iu = (iu&0x007fffff) + 0x3f3504f3; |
| 65 u.i = iu; |
| 66 f = u.f - 1; |
| 67 } |
| 68 s = f/(2.0f + f); |
| 69 z = s*s; |
| 70 w = z*z; |
| 71 t1= w*(Lg2+w*Lg4); |
| 72 t2= z*(Lg1+w*Lg3); |
| 73 R = t2 + t1; |
| 74 hfsq = 0.5f*f*f; |
| 75 dk = k; |
| 76 return s*(hfsq+R) + (dk*ln2_lo+c) - hfsq + f + dk*ln2_hi; |
| 77 } |
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