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 } 78