12116Sjkh/* e_lgammaf_r.c -- float version of e_lgamma_r.c. 22116Sjkh * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. 32116Sjkh */ 42116Sjkh 52116Sjkh/* 62116Sjkh * ==================================================== 72116Sjkh * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 82116Sjkh * 92116Sjkh * Developed at SunPro, a Sun Microsystems, Inc. business. 102116Sjkh * Permission to use, copy, modify, and distribute this 118870Srgrimes * software is freely granted, provided that this notice 122116Sjkh * is preserved. 132116Sjkh * ==================================================== 142116Sjkh */ 152116Sjkh 16176451Sdas#include <sys/cdefs.h> 17176451Sdas__FBSDID("$FreeBSD$"); 182116Sjkh 192116Sjkh#include "math.h" 202116Sjkh#include "math_private.h" 212116Sjkh 22271779Stijlstatic const volatile float vzero = 0; 23271779Stijl 248870Srgrimesstatic const float 25271779Stijlzero= 0.0000000000e+00, 262116Sjkhhalf= 5.0000000000e-01, /* 0x3f000000 */ 272116Sjkhone = 1.0000000000e+00, /* 0x3f800000 */ 282116Sjkhpi = 3.1415927410e+00, /* 0x40490fdb */ 292116Sjkha0 = 7.7215664089e-02, /* 0x3d9e233f */ 302116Sjkha1 = 3.2246702909e-01, /* 0x3ea51a66 */ 312116Sjkha2 = 6.7352302372e-02, /* 0x3d89f001 */ 322116Sjkha3 = 2.0580807701e-02, /* 0x3ca89915 */ 332116Sjkha4 = 7.3855509982e-03, /* 0x3bf2027e */ 342116Sjkha5 = 2.8905137442e-03, /* 0x3b3d6ec6 */ 352116Sjkha6 = 1.1927076848e-03, /* 0x3a9c54a1 */ 362116Sjkha7 = 5.1006977446e-04, /* 0x3a05b634 */ 372116Sjkha8 = 2.2086278477e-04, /* 0x39679767 */ 382116Sjkha9 = 1.0801156895e-04, /* 0x38e28445 */ 392116Sjkha10 = 2.5214456400e-05, /* 0x37d383a2 */ 402116Sjkha11 = 4.4864096708e-05, /* 0x383c2c75 */ 412116Sjkhtc = 1.4616321325e+00, /* 0x3fbb16c3 */ 422116Sjkhtf = -1.2148628384e-01, /* 0xbdf8cdcd */ 432116Sjkh/* tt = -(tail of tf) */ 442116Sjkhtt = 6.6971006518e-09, /* 0x31e61c52 */ 452116Sjkht0 = 4.8383611441e-01, /* 0x3ef7b95e */ 462116Sjkht1 = -1.4758771658e-01, /* 0xbe17213c */ 472116Sjkht2 = 6.4624942839e-02, /* 0x3d845a15 */ 482116Sjkht3 = -3.2788541168e-02, /* 0xbd064d47 */ 492116Sjkht4 = 1.7970675603e-02, /* 0x3c93373d */ 502116Sjkht5 = -1.0314224288e-02, /* 0xbc28fcfe */ 512116Sjkht6 = 6.1005386524e-03, /* 0x3bc7e707 */ 522116Sjkht7 = -3.6845202558e-03, /* 0xbb7177fe */ 532116Sjkht8 = 2.2596477065e-03, /* 0x3b141699 */ 542116Sjkht9 = -1.4034647029e-03, /* 0xbab7f476 */ 552116Sjkht10 = 8.8108185446e-04, /* 0x3a66f867 */ 562116Sjkht11 = -5.3859531181e-04, /* 0xba0d3085 */ 572116Sjkht12 = 3.1563205994e-04, /* 0x39a57b6b */ 582116Sjkht13 = -3.1275415677e-04, /* 0xb9a3f927 */ 592116Sjkht14 = 3.3552918467e-04, /* 0x39afe9f7 */ 602116Sjkhu0 = -7.7215664089e-02, /* 0xbd9e233f */ 612116Sjkhu1 = 6.3282704353e-01, /* 0x3f2200f4 */ 622116Sjkhu2 = 1.4549225569e+00, /* 0x3fba3ae7 */ 632116Sjkhu3 = 9.7771751881e-01, /* 0x3f7a4bb2 */ 642116Sjkhu4 = 2.2896373272e-01, /* 0x3e6a7578 */ 652116Sjkhu5 = 1.3381091878e-02, /* 0x3c5b3c5e */ 662116Sjkhv1 = 2.4559779167e+00, /* 0x401d2ebe */ 672116Sjkhv2 = 2.1284897327e+00, /* 0x4008392d */ 682116Sjkhv3 = 7.6928514242e-01, /* 0x3f44efdf */ 692116Sjkhv4 = 1.0422264785e-01, /* 0x3dd572af */ 702116Sjkhv5 = 3.2170924824e-03, /* 0x3b52d5db */ 712116Sjkhs0 = -7.7215664089e-02, /* 0xbd9e233f */ 722116Sjkhs1 = 2.1498242021e-01, /* 0x3e5c245a */ 732116Sjkhs2 = 3.2577878237e-01, /* 0x3ea6cc7a */ 742116Sjkhs3 = 1.4635047317e-01, /* 0x3e15dce6 */ 752116Sjkhs4 = 2.6642270386e-02, /* 0x3cda40e4 */ 762116Sjkhs5 = 1.8402845599e-03, /* 0x3af135b4 */ 772116Sjkhs6 = 3.1947532989e-05, /* 0x3805ff67 */ 782116Sjkhr1 = 1.3920053244e+00, /* 0x3fb22d3b */ 792116Sjkhr2 = 7.2193557024e-01, /* 0x3f38d0c5 */ 802116Sjkhr3 = 1.7193385959e-01, /* 0x3e300f6e */ 812116Sjkhr4 = 1.8645919859e-02, /* 0x3c98bf54 */ 822116Sjkhr5 = 7.7794247773e-04, /* 0x3a4beed6 */ 832116Sjkhr6 = 7.3266842264e-06, /* 0x36f5d7bd */ 842116Sjkhw0 = 4.1893854737e-01, /* 0x3ed67f1d */ 852116Sjkhw1 = 8.3333335817e-02, /* 0x3daaaaab */ 862116Sjkhw2 = -2.7777778450e-03, /* 0xbb360b61 */ 872116Sjkhw3 = 7.9365057172e-04, /* 0x3a500cfd */ 882116Sjkhw4 = -5.9518753551e-04, /* 0xba1c065c */ 892116Sjkhw5 = 8.3633989561e-04, /* 0x3a5b3dd2 */ 902116Sjkhw6 = -1.6309292987e-03; /* 0xbad5c4e8 */ 912116Sjkh 92271779Stijlstatic float 93271779Stijlsin_pif(float x) 942116Sjkh{ 95271779Stijl volatile float vz; 962116Sjkh float y,z; 97271779Stijl int n; 982116Sjkh 99271779Stijl y = -x; 1002116Sjkh 101271779Stijl vz = y+0x1p23F; /* depend on 0 <= y < 0x1p23 */ 102271779Stijl z = vz-0x1p23F; /* rintf(y) for the above range */ 103271779Stijl if (z == y) 104271779Stijl return zero; 1052116Sjkh 106271779Stijl vz = y+0x1p21F; 107271779Stijl GET_FLOAT_WORD(n,vz); /* bits for rounded y (units 0.25) */ 108271779Stijl z = vz-0x1p21F; /* y rounded to a multiple of 0.25 */ 109271779Stijl if (z > y) { 110271779Stijl z -= 0.25F; /* adjust to round down */ 111271779Stijl n--; 112271779Stijl } 113271779Stijl n &= 7; /* octant of y mod 2 */ 114271779Stijl y = y - z + n * 0.25F; /* y mod 2 */ 115271779Stijl 1162116Sjkh switch (n) { 117152869Sbde case 0: y = __kernel_sindf(pi*y); break; 1188870Srgrimes case 1: 119152869Sbde case 2: y = __kernel_cosdf(pi*((float)0.5-y)); break; 1208870Srgrimes case 3: 121152869Sbde case 4: y = __kernel_sindf(pi*(one-y)); break; 1222116Sjkh case 5: 123152869Sbde case 6: y = -__kernel_cosdf(pi*(y-(float)1.5)); break; 124152869Sbde default: y = __kernel_sindf(pi*(y-(float)2.0)); break; 1252116Sjkh } 1262116Sjkh return -y; 1272116Sjkh} 1282116Sjkh 1292116Sjkh 13097413Salfredfloat 13197413Salfred__ieee754_lgammaf_r(float x, int *signgamp) 1322116Sjkh{ 1332116Sjkh float t,y,z,nadj,p,p1,p2,p3,q,r,w; 134169220Sbde int32_t hx; 135169220Sbde int i,ix; 1362116Sjkh 1372116Sjkh GET_FLOAT_WORD(hx,x); 1382116Sjkh 139169220Sbde /* purge off +-inf, NaN, +-0, tiny and negative arguments */ 1402116Sjkh *signgamp = 1; 1412116Sjkh ix = hx&0x7fffffff; 1422116Sjkh if(ix>=0x7f800000) return x*x; 143271779Stijl if(ix==0) return one/vzero; 144152878Sbde if(ix<0x35000000) { /* |x|<2**-21, return -log(|x|) */ 1452116Sjkh if(hx<0) { 1462116Sjkh *signgamp = -1; 1472116Sjkh return -__ieee754_logf(-x); 1482116Sjkh } else return -__ieee754_logf(x); 1492116Sjkh } 1502116Sjkh if(hx<0) { 1512116Sjkh if(ix>=0x4b000000) /* |x|>=2**23, must be -integer */ 152271779Stijl return one/vzero; 1532116Sjkh t = sin_pif(x); 154271779Stijl if(t==zero) return one/vzero; /* -integer */ 1552116Sjkh nadj = __ieee754_logf(pi/fabsf(t*x)); 1562116Sjkh if(t<zero) *signgamp = -1; 1572116Sjkh x = -x; 1582116Sjkh } 1592116Sjkh 1602116Sjkh /* purge off 1 and 2 */ 1612116Sjkh if (ix==0x3f800000||ix==0x40000000) r = 0; 1622116Sjkh /* for x < 2.0 */ 1632116Sjkh else if(ix<0x40000000) { 1642116Sjkh if(ix<=0x3f666666) { /* lgamma(x) = lgamma(x+1)-log(x) */ 1652116Sjkh r = -__ieee754_logf(x); 1662116Sjkh if(ix>=0x3f3b4a20) {y = one-x; i= 0;} 1672116Sjkh else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;} 1682116Sjkh else {y = x; i=2;} 1692116Sjkh } else { 1702116Sjkh r = zero; 1712116Sjkh if(ix>=0x3fdda618) {y=(float)2.0-x;i=0;} /* [1.7316,2] */ 1722116Sjkh else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */ 1732116Sjkh else {y=x-one;i=2;} 1742116Sjkh } 1752116Sjkh switch(i) { 1762116Sjkh case 0: 1772116Sjkh z = y*y; 1782116Sjkh p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10)))); 1792116Sjkh p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11))))); 1802116Sjkh p = y*p1+p2; 1812116Sjkh r += (p-(float)0.5*y); break; 1822116Sjkh case 1: 1832116Sjkh z = y*y; 1842116Sjkh w = z*y; 1852116Sjkh p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */ 1862116Sjkh p2 = t1+w*(t4+w*(t7+w*(t10+w*t13))); 1872116Sjkh p3 = t2+w*(t5+w*(t8+w*(t11+w*t14))); 1882116Sjkh p = z*p1-(tt-w*(p2+y*p3)); 1892116Sjkh r += (tf + p); break; 1908870Srgrimes case 2: 1912116Sjkh p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5))))); 1922116Sjkh p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5)))); 1932116Sjkh r += (-(float)0.5*y + p1/p2); 1942116Sjkh } 1952116Sjkh } 1962116Sjkh else if(ix<0x41000000) { /* x < 8.0 */ 1972116Sjkh i = (int)x; 1982116Sjkh y = x-(float)i; 1992116Sjkh p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6)))))); 2002116Sjkh q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6))))); 2012116Sjkh r = half*y+p/q; 2022116Sjkh z = one; /* lgamma(1+s) = log(s) + lgamma(s) */ 2032116Sjkh switch(i) { 2042116Sjkh case 7: z *= (y+(float)6.0); /* FALLTHRU */ 2052116Sjkh case 6: z *= (y+(float)5.0); /* FALLTHRU */ 2062116Sjkh case 5: z *= (y+(float)4.0); /* FALLTHRU */ 2072116Sjkh case 4: z *= (y+(float)3.0); /* FALLTHRU */ 2082116Sjkh case 3: z *= (y+(float)2.0); /* FALLTHRU */ 2092116Sjkh r += __ieee754_logf(z); break; 2102116Sjkh } 2112116Sjkh /* 8.0 <= x < 2**58 */ 2122116Sjkh } else if (ix < 0x5c800000) { 2132116Sjkh t = __ieee754_logf(x); 2142116Sjkh z = one/x; 2152116Sjkh y = z*z; 2162116Sjkh w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6))))); 2172116Sjkh r = (x-half)*(t-one)+w; 2188870Srgrimes } else 2192116Sjkh /* 2**58 <= x <= inf */ 2202116Sjkh r = x*(__ieee754_logf(x)-one); 2212116Sjkh if(hx<0) r = nadj - r; 2222116Sjkh return r; 2232116Sjkh} 224