e_lgammaf_r.c revision 176451
1170461Srrs/* e_lgammaf_r.c -- float version of e_lgamma_r.c. 2170461Srrs * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. 3224271Stuexen */ 4170461Srrs 5170461Srrs/* 6170461Srrs * ==================================================== 7170461Srrs * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 8170461Srrs * 9170461Srrs * Developed at SunPro, a Sun Microsystems, Inc. business. 10170461Srrs * Permission to use, copy, modify, and distribute this 11170461Srrs * software is freely granted, provided that this notice 12170461Srrs * is preserved. 13170461Srrs * ==================================================== 14170461Srrs */ 15170461Srrs 16170461Srrs#include <sys/cdefs.h> 17170461Srrs__FBSDID("$FreeBSD: head/lib/msun/src/e_lgammaf_r.c 176451 2008-02-22 02:30:36Z das $"); 18170461Srrs 19170461Srrs#include "math.h" 20170461Srrs#include "math_private.h" 21170461Srrs 22170461Srrsstatic const float 23170461Srrstwo23= 8.3886080000e+06, /* 0x4b000000 */ 24170461Srrshalf= 5.0000000000e-01, /* 0x3f000000 */ 25170461Srrsone = 1.0000000000e+00, /* 0x3f800000 */ 26170461Srrspi = 3.1415927410e+00, /* 0x40490fdb */ 27170461Srrsa0 = 7.7215664089e-02, /* 0x3d9e233f */ 28170461Srrsa1 = 3.2246702909e-01, /* 0x3ea51a66 */ 29170461Srrsa2 = 6.7352302372e-02, /* 0x3d89f001 */ 30170461Srrsa3 = 2.0580807701e-02, /* 0x3ca89915 */ 31170461Srrsa4 = 7.3855509982e-03, /* 0x3bf2027e */ 32170461Srrsa5 = 2.8905137442e-03, /* 0x3b3d6ec6 */ 33170461Srrsa6 = 1.1927076848e-03, /* 0x3a9c54a1 */ 34170461Srrsa7 = 5.1006977446e-04, /* 0x3a05b634 */ 35170461Srrsa8 = 2.2086278477e-04, /* 0x39679767 */ 36170461Srrsa9 = 1.0801156895e-04, /* 0x38e28445 */ 37170461Srrsa10 = 2.5214456400e-05, /* 0x37d383a2 */ 38170461Srrsa11 = 4.4864096708e-05, /* 0x383c2c75 */ 39170461Srrstc = 1.4616321325e+00, /* 0x3fbb16c3 */ 40170461Srrstf = -1.2148628384e-01, /* 0xbdf8cdcd */ 41170461Srrs/* tt = -(tail of tf) */ 42170461Srrstt = 6.6971006518e-09, /* 0x31e61c52 */ 43170461Srrst0 = 4.8383611441e-01, /* 0x3ef7b95e */ 44170461Srrst1 = -1.4758771658e-01, /* 0xbe17213c */ 45170461Srrst2 = 6.4624942839e-02, /* 0x3d845a15 */ 46170461Srrst3 = -3.2788541168e-02, /* 0xbd064d47 */ 47170461Srrst4 = 1.7970675603e-02, /* 0x3c93373d */ 48170461Srrst5 = -1.0314224288e-02, /* 0xbc28fcfe */ 49170461Srrst6 = 6.1005386524e-03, /* 0x3bc7e707 */ 50170461Srrst7 = -3.6845202558e-03, /* 0xbb7177fe */ 51170461Srrst8 = 2.2596477065e-03, /* 0x3b141699 */ 52170461Srrst9 = -1.4034647029e-03, /* 0xbab7f476 */ 53170461Srrst10 = 8.8108185446e-04, /* 0x3a66f867 */ 54170461Srrst11 = -5.3859531181e-04, /* 0xba0d3085 */ 55170461Srrst12 = 3.1563205994e-04, /* 0x39a57b6b */ 56200462Sdelphijt13 = -3.1275415677e-04, /* 0xb9a3f927 */ 57200462Sdelphijt14 = 3.3552918467e-04, /* 0x39afe9f7 */ 58170461Srrsu0 = -7.7215664089e-02, /* 0xbd9e233f */ 59170461Srrsu1 = 6.3282704353e-01, /* 0x3f2200f4 */ 60170461Srrsu2 = 1.4549225569e+00, /* 0x3fba3ae7 */ 61279122Smarcelu3 = 9.7771751881e-01, /* 0x3f7a4bb2 */ 62170461Srrsu4 = 2.2896373272e-01, /* 0x3e6a7578 */ 63200462Sdelphiju5 = 1.3381091878e-02, /* 0x3c5b3c5e */ 64170461Srrsv1 = 2.4559779167e+00, /* 0x401d2ebe */ 65279122Smarcelv2 = 2.1284897327e+00, /* 0x4008392d */ 66170461Srrsv3 = 7.6928514242e-01, /* 0x3f44efdf */ 67170461Srrsv4 = 1.0422264785e-01, /* 0x3dd572af */ 68170461Srrsv5 = 3.2170924824e-03, /* 0x3b52d5db */ 69170461Srrss0 = -7.7215664089e-02, /* 0xbd9e233f */ 70170461Srrss1 = 2.1498242021e-01, /* 0x3e5c245a */ 71175061Sobriens2 = 3.2577878237e-01, /* 0x3ea6cc7a */ 72175061Sobriens3 = 1.4635047317e-01, /* 0x3e15dce6 */ 73175061Sobriens4 = 2.6642270386e-02, /* 0x3cda40e4 */ 74175061Sobriens5 = 1.8402845599e-03, /* 0x3af135b4 */ 75175061Sobriens6 = 3.1947532989e-05, /* 0x3805ff67 */ 76175061Sobrienr1 = 1.3920053244e+00, /* 0x3fb22d3b */ 77175061Sobrienr2 = 7.2193557024e-01, /* 0x3f38d0c5 */ 78175061Sobrienr3 = 1.7193385959e-01, /* 0x3e300f6e */ 79175061Sobrienr4 = 1.8645919859e-02, /* 0x3c98bf54 */ 80175061Sobrienr5 = 7.7794247773e-04, /* 0x3a4beed6 */ 81170461Srrsr6 = 7.3266842264e-06, /* 0x36f5d7bd */ 82287351Shrsw0 = 4.1893854737e-01, /* 0x3ed67f1d */ 83170461Srrsw1 = 8.3333335817e-02, /* 0x3daaaaab */ 84170461Srrsw2 = -2.7777778450e-03, /* 0xbb360b61 */ 85175061Sobrienw3 = 7.9365057172e-04, /* 0x3a500cfd */ 86175061Sobrienw4 = -5.9518753551e-04, /* 0xba1c065c */ 87175061Sobrienw5 = 8.3633989561e-04, /* 0x3a5b3dd2 */ 88175061Sobrienw6 = -1.6309292987e-03; /* 0xbad5c4e8 */ 89170461Srrs 90170461Srrsstatic const float zero= 0.0000000000e+00; 91170461Srrs 92170461Srrs static float sin_pif(float x) 93170461Srrs{ 94170461Srrs float y,z; 95287351Shrs int n,ix; 96170461Srrs 97170461Srrs GET_FLOAT_WORD(ix,x); 98170461Srrs ix &= 0x7fffffff; 99170461Srrs 100170461Srrs if(ix<0x3e800000) return __kernel_sindf(pi*x); 101287351Shrs y = -x; /* x is assume negative */ 102170461Srrs 103279122Smarcel /* 104279122Smarcel * argument reduction, make sure inexact flag not raised if input 105170461Srrs * is an integer 106170461Srrs */ 107238514Stuexen z = floorf(y); 108303267Stuexen if(z!=y) { /* inexact anyway */ 109303267Stuexen y *= (float)0.5; 110238514Stuexen y = (float)2.0*(y - floorf(y)); /* y = |x| mod 2.0 */ 111224271Stuexen n = (int) (y*(float)4.0); 112224271Stuexen } else { 113303267Stuexen if(ix>=0x4b800000) { 114303267Stuexen y = zero; n = 0; /* y must be even */ 115224271Stuexen } else { 116224271Stuexen if(ix<0x4b000000) z = y+two23; /* exact */ 117224271Stuexen GET_FLOAT_WORD(n,z); 118279122Smarcel n &= 1; 119279122Smarcel y = n; 120224271Stuexen n<<= 2; 121224271Stuexen } 122224271Stuexen } 123224271Stuexen switch (n) { 124224271Stuexen case 0: y = __kernel_sindf(pi*y); break; 125279122Smarcel case 1: 126279122Smarcel case 2: y = __kernel_cosdf(pi*((float)0.5-y)); break; 127279122Smarcel case 3: 128224271Stuexen case 4: y = __kernel_sindf(pi*(one-y)); break; 129238514Stuexen case 5: 130224271Stuexen case 6: y = -__kernel_cosdf(pi*(y-(float)1.5)); break; 131224271Stuexen default: y = __kernel_sindf(pi*(y-(float)2.0)); break; 132224271Stuexen } 133238514Stuexen return -y; 134224271Stuexen} 135224271Stuexen 136224271Stuexen 137224271Stuexenfloat 138224271Stuexen__ieee754_lgammaf_r(float x, int *signgamp) 139224271Stuexen{ 140224271Stuexen float t,y,z,nadj,p,p1,p2,p3,q,r,w; 141224271Stuexen int32_t hx; 142224271Stuexen int i,ix; 143229403Sed 144224271Stuexen GET_FLOAT_WORD(hx,x); 145224271Stuexen 146224271Stuexen /* purge off +-inf, NaN, +-0, tiny and negative arguments */ 147224271Stuexen *signgamp = 1; 148224271Stuexen ix = hx&0x7fffffff; 149224271Stuexen if(ix>=0x7f800000) return x*x; 150224271Stuexen if(ix==0) return one/zero; 151279122Smarcel if(ix<0x35000000) { /* |x|<2**-21, return -log(|x|) */ 152279122Smarcel if(hx<0) { 153279122Smarcel *signgamp = -1; 154279122Smarcel return -__ieee754_logf(-x); 155279122Smarcel } else return -__ieee754_logf(x); 156279122Smarcel } 157279122Smarcel if(hx<0) { 158279122Smarcel if(ix>=0x4b000000) /* |x|>=2**23, must be -integer */ 159224271Stuexen return one/zero; 160224271Stuexen t = sin_pif(x); 161170461Srrs if(t==zero) return one/zero; /* -integer */ 162170461Srrs nadj = __ieee754_logf(pi/fabsf(t*x)); 163170461Srrs if(t<zero) *signgamp = -1; 164170461Srrs x = -x; 165170461Srrs } 166170461Srrs 167170461Srrs /* purge off 1 and 2 */ 168170461Srrs if (ix==0x3f800000||ix==0x40000000) r = 0; 169170461Srrs /* for x < 2.0 */ 170170461Srrs else if(ix<0x40000000) { 171170461Srrs if(ix<=0x3f666666) { /* lgamma(x) = lgamma(x+1)-log(x) */ 172170461Srrs r = -__ieee754_logf(x); 173170461Srrs if(ix>=0x3f3b4a20) {y = one-x; i= 0;} 174170461Srrs else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;} 175175061Sobrien else {y = x; i=2;} 176170461Srrs } else { 177170461Srrs r = zero; 178170461Srrs if(ix>=0x3fdda618) {y=(float)2.0-x;i=0;} /* [1.7316,2] */ 179170461Srrs else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */ 180170461Srrs else {y=x-one;i=2;} 181170461Srrs } 182170461Srrs switch(i) { 183170461Srrs case 0: 184170461Srrs z = y*y; 185170461Srrs p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10)))); 186170461Srrs p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11))))); 187170461Srrs p = y*p1+p2; 188170461Srrs r += (p-(float)0.5*y); break; 189170461Srrs case 1: 190170461Srrs z = y*y; 191170461Srrs w = z*y; 192170461Srrs p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */ 193170461Srrs p2 = t1+w*(t4+w*(t7+w*(t10+w*t13))); 194170461Srrs p3 = t2+w*(t5+w*(t8+w*(t11+w*t14))); 195170461Srrs p = z*p1-(tt-w*(p2+y*p3)); 196170461Srrs r += (tf + p); break; 197170461Srrs case 2: 198170461Srrs p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5))))); 199170461Srrs p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5)))); 200170461Srrs r += (-(float)0.5*y + p1/p2); 201170461Srrs } 202170461Srrs } 203170461Srrs else if(ix<0x41000000) { /* x < 8.0 */ 204170461Srrs i = (int)x; 205170461Srrs t = zero; 206170461Srrs y = x-(float)i; 207170461Srrs p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6)))))); 208170461Srrs q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6))))); 209224271Stuexen r = half*y+p/q; 210170461Srrs z = one; /* lgamma(1+s) = log(s) + lgamma(s) */ 211170461Srrs switch(i) { 212170461Srrs case 7: z *= (y+(float)6.0); /* FALLTHRU */ 213170461Srrs case 6: z *= (y+(float)5.0); /* FALLTHRU */ 214170461Srrs case 5: z *= (y+(float)4.0); /* FALLTHRU */ 215170461Srrs case 4: z *= (y+(float)3.0); /* FALLTHRU */ 216170461Srrs case 3: z *= (y+(float)2.0); /* FALLTHRU */ 217170461Srrs r += __ieee754_logf(z); break; 218170461Srrs } 219170461Srrs /* 8.0 <= x < 2**58 */ 220170461Srrs } else if (ix < 0x5c800000) { 221170461Srrs t = __ieee754_logf(x); 222170461Srrs z = one/x; 223170461Srrs y = z*z; 224170461Srrs w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6))))); 225170461Srrs r = (x-half)*(t-one)+w; 226170461Srrs } else 227170461Srrs /* 2**58 <= x <= inf */ 228170461Srrs r = x*(__ieee754_logf(x)-one); 229170461Srrs if(hx<0) r = nadj - r; 230175061Sobrien return r; 231170461Srrs} 232170461Srrs