e_lgammaf_r.c revision 152869
1251881Speter/* e_lgammaf_r.c -- float version of e_lgamma_r.c. 2251881Speter * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. 3251881Speter */ 4251881Speter 5251881Speter/* 6251881Speter * ==================================================== 7251881Speter * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 8251881Speter * 9251881Speter * Developed at SunPro, a Sun Microsystems, Inc. business. 10251881Speter * Permission to use, copy, modify, and distribute this 11251881Speter * software is freely granted, provided that this notice 12251881Speter * is preserved. 13251881Speter * ==================================================== 14251881Speter */ 15251881Speter 16251881Speter#ifndef lint 17251881Speterstatic char rcsid[] = "$FreeBSD: head/lib/msun/src/e_lgammaf_r.c 152869 2005-11-28 04:58:57Z bde $"; 18251881Speter#endif 19251881Speter 20251881Speter#include "math.h" 21251881Speter#include "math_private.h" 22251881Speter 23251881Speterstatic const float 24251881Spetertwo23= 8.3886080000e+06, /* 0x4b000000 */ 25251881Speterhalf= 5.0000000000e-01, /* 0x3f000000 */ 26251881Speterone = 1.0000000000e+00, /* 0x3f800000 */ 27251881Speterpi = 3.1415927410e+00, /* 0x40490fdb */ 28251881Spetera0 = 7.7215664089e-02, /* 0x3d9e233f */ 29251881Spetera1 = 3.2246702909e-01, /* 0x3ea51a66 */ 30251881Spetera2 = 6.7352302372e-02, /* 0x3d89f001 */ 31251881Spetera3 = 2.0580807701e-02, /* 0x3ca89915 */ 32251881Spetera4 = 7.3855509982e-03, /* 0x3bf2027e */ 33251881Spetera5 = 2.8905137442e-03, /* 0x3b3d6ec6 */ 34251881Spetera6 = 1.1927076848e-03, /* 0x3a9c54a1 */ 35251881Spetera7 = 5.1006977446e-04, /* 0x3a05b634 */ 36251881Spetera8 = 2.2086278477e-04, /* 0x39679767 */ 37251881Spetera9 = 1.0801156895e-04, /* 0x38e28445 */ 38251881Spetera10 = 2.5214456400e-05, /* 0x37d383a2 */ 39251881Spetera11 = 4.4864096708e-05, /* 0x383c2c75 */ 40251881Spetertc = 1.4616321325e+00, /* 0x3fbb16c3 */ 41251881Spetertf = -1.2148628384e-01, /* 0xbdf8cdcd */ 42251881Speter/* tt = -(tail of tf) */ 43251881Spetertt = 6.6971006518e-09, /* 0x31e61c52 */ 44251881Spetert0 = 4.8383611441e-01, /* 0x3ef7b95e */ 45251881Spetert1 = -1.4758771658e-01, /* 0xbe17213c */ 46251881Spetert2 = 6.4624942839e-02, /* 0x3d845a15 */ 47251881Spetert3 = -3.2788541168e-02, /* 0xbd064d47 */ 48251881Spetert4 = 1.7970675603e-02, /* 0x3c93373d */ 49251881Spetert5 = -1.0314224288e-02, /* 0xbc28fcfe */ 50251881Spetert6 = 6.1005386524e-03, /* 0x3bc7e707 */ 51251881Spetert7 = -3.6845202558e-03, /* 0xbb7177fe */ 52251881Spetert8 = 2.2596477065e-03, /* 0x3b141699 */ 53251881Spetert9 = -1.4034647029e-03, /* 0xbab7f476 */ 54251881Spetert10 = 8.8108185446e-04, /* 0x3a66f867 */ 55251881Spetert11 = -5.3859531181e-04, /* 0xba0d3085 */ 56251881Spetert12 = 3.1563205994e-04, /* 0x39a57b6b */ 57251881Spetert13 = -3.1275415677e-04, /* 0xb9a3f927 */ 58251881Spetert14 = 3.3552918467e-04, /* 0x39afe9f7 */ 59251881Speteru0 = -7.7215664089e-02, /* 0xbd9e233f */ 60251881Speteru1 = 6.3282704353e-01, /* 0x3f2200f4 */ 61251881Speteru2 = 1.4549225569e+00, /* 0x3fba3ae7 */ 62251881Speteru3 = 9.7771751881e-01, /* 0x3f7a4bb2 */ 63251881Speteru4 = 2.2896373272e-01, /* 0x3e6a7578 */ 64251881Speteru5 = 1.3381091878e-02, /* 0x3c5b3c5e */ 65251881Speterv1 = 2.4559779167e+00, /* 0x401d2ebe */ 66251881Speterv2 = 2.1284897327e+00, /* 0x4008392d */ 67251881Speterv3 = 7.6928514242e-01, /* 0x3f44efdf */ 68251881Speterv4 = 1.0422264785e-01, /* 0x3dd572af */ 69251881Speterv5 = 3.2170924824e-03, /* 0x3b52d5db */ 70251881Speters0 = -7.7215664089e-02, /* 0xbd9e233f */ 71251881Speters1 = 2.1498242021e-01, /* 0x3e5c245a */ 72251881Speters2 = 3.2577878237e-01, /* 0x3ea6cc7a */ 73251881Speters3 = 1.4635047317e-01, /* 0x3e15dce6 */ 74251881Speters4 = 2.6642270386e-02, /* 0x3cda40e4 */ 75251881Speters5 = 1.8402845599e-03, /* 0x3af135b4 */ 76251881Speters6 = 3.1947532989e-05, /* 0x3805ff67 */ 77251881Speterr1 = 1.3920053244e+00, /* 0x3fb22d3b */ 78251881Speterr2 = 7.2193557024e-01, /* 0x3f38d0c5 */ 79251881Speterr3 = 1.7193385959e-01, /* 0x3e300f6e */ 80251881Speterr4 = 1.8645919859e-02, /* 0x3c98bf54 */ 81251881Speterr5 = 7.7794247773e-04, /* 0x3a4beed6 */ 82251881Speterr6 = 7.3266842264e-06, /* 0x36f5d7bd */ 83251881Speterw0 = 4.1893854737e-01, /* 0x3ed67f1d */ 84251881Speterw1 = 8.3333335817e-02, /* 0x3daaaaab */ 85251881Speterw2 = -2.7777778450e-03, /* 0xbb360b61 */ 86251881Speterw3 = 7.9365057172e-04, /* 0x3a500cfd */ 87251881Speterw4 = -5.9518753551e-04, /* 0xba1c065c */ 88251881Speterw5 = 8.3633989561e-04, /* 0x3a5b3dd2 */ 89251881Speterw6 = -1.6309292987e-03; /* 0xbad5c4e8 */ 90251881Speter 91251881Speterstatic const float zero= 0.0000000000e+00; 92251881Speter 93251881Speter static float sin_pif(float x) 94251881Speter{ 95251881Speter float y,z; 96251881Speter int n,ix; 97251881Speter 98251881Speter GET_FLOAT_WORD(ix,x); 99251881Speter ix &= 0x7fffffff; 100251881Speter 101251881Speter if(ix<0x3e800000) return __kernel_sindf(pi*x); 102251881Speter y = -x; /* x is assume negative */ 103251881Speter 104251881Speter /* 105251881Speter * argument reduction, make sure inexact flag not raised if input 106251881Speter * is an integer 107251881Speter */ 108251881Speter z = floorf(y); 109251881Speter if(z!=y) { /* inexact anyway */ 110251881Speter y *= (float)0.5; 111251881Speter y = (float)2.0*(y - floorf(y)); /* y = |x| mod 2.0 */ 112251881Speter n = (int) (y*(float)4.0); 113251881Speter } else { 114251881Speter if(ix>=0x4b800000) { 115251881Speter y = zero; n = 0; /* y must be even */ 116251881Speter } else { 117251881Speter if(ix<0x4b000000) z = y+two23; /* exact */ 118251881Speter GET_FLOAT_WORD(n,z); 119251881Speter n &= 1; 120251881Speter y = n; 121251881Speter n<<= 2; 122251881Speter } 123251881Speter } 124251881Speter switch (n) { 125251881Speter case 0: y = __kernel_sindf(pi*y); break; 126251881Speter case 1: 127251881Speter case 2: y = __kernel_cosdf(pi*((float)0.5-y)); break; 128251881Speter case 3: 129251881Speter case 4: y = __kernel_sindf(pi*(one-y)); break; 130251881Speter case 5: 131251881Speter case 6: y = -__kernel_cosdf(pi*(y-(float)1.5)); break; 132251881Speter default: y = __kernel_sindf(pi*(y-(float)2.0)); break; 133251881Speter } 134251881Speter return -y; 135251881Speter} 136251881Speter 137251881Speter 138251881Speterfloat 139251881Speter__ieee754_lgammaf_r(float x, int *signgamp) 140251881Speter{ 141251881Speter float t,y,z,nadj,p,p1,p2,p3,q,r,w; 142251881Speter int i,hx,ix; 143251881Speter 144251881Speter GET_FLOAT_WORD(hx,x); 145251881Speter 146251881Speter /* purge off +-inf, NaN, +-0, and negative arguments */ 147251881Speter *signgamp = 1; 148251881Speter ix = hx&0x7fffffff; 149251881Speter if(ix>=0x7f800000) return x*x; 150251881Speter if(ix==0) return one/zero; 151251881Speter if(ix<0x1c800000) { /* |x|<2**-70, return -log(|x|) */ 152251881Speter if(hx<0) { 153251881Speter *signgamp = -1; 154251881Speter return -__ieee754_logf(-x); 155251881Speter } else return -__ieee754_logf(x); 156251881Speter } 157251881Speter if(hx<0) { 158251881Speter if(ix>=0x4b000000) /* |x|>=2**23, must be -integer */ 159251881Speter return one/zero; 160251881Speter t = sin_pif(x); 161251881Speter if(t==zero) return one/zero; /* -integer */ 162251881Speter nadj = __ieee754_logf(pi/fabsf(t*x)); 163251881Speter if(t<zero) *signgamp = -1; 164251881Speter x = -x; 165251881Speter } 166251881Speter 167251881Speter /* purge off 1 and 2 */ 168251881Speter if (ix==0x3f800000||ix==0x40000000) r = 0; 169251881Speter /* for x < 2.0 */ 170251881Speter else if(ix<0x40000000) { 171251881Speter if(ix<=0x3f666666) { /* lgamma(x) = lgamma(x+1)-log(x) */ 172251881Speter r = -__ieee754_logf(x); 173251881Speter if(ix>=0x3f3b4a20) {y = one-x; i= 0;} 174251881Speter else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;} 175251881Speter else {y = x; i=2;} 176251881Speter } else { 177251881Speter r = zero; 178251881Speter if(ix>=0x3fdda618) {y=(float)2.0-x;i=0;} /* [1.7316,2] */ 179251881Speter else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */ 180251881Speter else {y=x-one;i=2;} 181251881Speter } 182251881Speter switch(i) { 183251881Speter case 0: 184251881Speter z = y*y; 185251881Speter p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10)))); 186251881Speter p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11))))); 187251881Speter p = y*p1+p2; 188251881Speter r += (p-(float)0.5*y); break; 189251881Speter case 1: 190251881Speter z = y*y; 191251881Speter w = z*y; 192251881Speter p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */ 193251881Speter p2 = t1+w*(t4+w*(t7+w*(t10+w*t13))); 194251881Speter p3 = t2+w*(t5+w*(t8+w*(t11+w*t14))); 195251881Speter p = z*p1-(tt-w*(p2+y*p3)); 196251881Speter r += (tf + p); break; 197251881Speter case 2: 198251881Speter p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5))))); 199251881Speter p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5)))); 200251881Speter r += (-(float)0.5*y + p1/p2); 201251881Speter } 202251881Speter } 203251881Speter else if(ix<0x41000000) { /* x < 8.0 */ 204251881Speter i = (int)x; 205251881Speter t = zero; 206251881Speter y = x-(float)i; 207251881Speter p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6)))))); 208251881Speter q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6))))); 209251881Speter r = half*y+p/q; 210251881Speter z = one; /* lgamma(1+s) = log(s) + lgamma(s) */ 211251881Speter switch(i) { 212251881Speter case 7: z *= (y+(float)6.0); /* FALLTHRU */ 213251881Speter case 6: z *= (y+(float)5.0); /* FALLTHRU */ 214251881Speter case 5: z *= (y+(float)4.0); /* FALLTHRU */ 215251881Speter case 4: z *= (y+(float)3.0); /* FALLTHRU */ 216251881Speter case 3: z *= (y+(float)2.0); /* FALLTHRU */ 217251881Speter r += __ieee754_logf(z); break; 218251881Speter } 219251881Speter /* 8.0 <= x < 2**58 */ 220251881Speter } else if (ix < 0x5c800000) { 221251881Speter t = __ieee754_logf(x); 222251881Speter z = one/x; 223251881Speter y = z*z; 224251881Speter w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6))))); 225251881Speter r = (x-half)*(t-one)+w; 226251881Speter } else 227251881Speter /* 2**58 <= x <= inf */ 228251881Speter r = x*(__ieee754_logf(x)-one); 229251881Speter if(hx<0) r = nadj - r; 230251881Speter return r; 231251881Speter} 232251881Speter