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| 3362 | Serge | 1 | /* erf_lgamma.c -- float version of er_lgamma.c. |
| 2 | * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. |
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| 3 | */ |
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| 4 | |||
| 5 | /* |
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| 6 | * ==================================================== |
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| 7 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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| 8 | * |
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| 9 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
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| 10 | * Permission to use, copy, modify, and distribute this |
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| 11 | * software is freely granted, provided that this notice |
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| 12 | * is preserved. |
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| 13 | * ==================================================== |
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| 14 | * |
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| 15 | */ |
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| 16 | |||
| 17 | #include "fdlibm.h" |
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| 18 | |||
| 19 | #ifdef __STDC__ |
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| 20 | static const float |
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| 21 | #else |
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| 22 | static float |
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| 23 | #endif |
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| 24 | two23= 8.3886080000e+06, /* 0x4b000000 */ |
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| 25 | half= 5.0000000000e-01, /* 0x3f000000 */ |
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| 26 | one = 1.0000000000e+00, /* 0x3f800000 */ |
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| 27 | pi = 3.1415927410e+00, /* 0x40490fdb */ |
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| 28 | a0 = 7.7215664089e-02, /* 0x3d9e233f */ |
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| 29 | a1 = 3.2246702909e-01, /* 0x3ea51a66 */ |
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| 30 | a2 = 6.7352302372e-02, /* 0x3d89f001 */ |
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| 31 | a3 = 2.0580807701e-02, /* 0x3ca89915 */ |
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| 32 | a4 = 7.3855509982e-03, /* 0x3bf2027e */ |
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| 33 | a5 = 2.8905137442e-03, /* 0x3b3d6ec6 */ |
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| 34 | a6 = 1.1927076848e-03, /* 0x3a9c54a1 */ |
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| 35 | a7 = 5.1006977446e-04, /* 0x3a05b634 */ |
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| 36 | a8 = 2.2086278477e-04, /* 0x39679767 */ |
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| 37 | a9 = 1.0801156895e-04, /* 0x38e28445 */ |
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| 38 | a10 = 2.5214456400e-05, /* 0x37d383a2 */ |
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| 39 | a11 = 4.4864096708e-05, /* 0x383c2c75 */ |
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| 40 | tc = 1.4616321325e+00, /* 0x3fbb16c3 */ |
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| 41 | tf = -1.2148628384e-01, /* 0xbdf8cdcd */ |
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| 42 | /* tt = -(tail of tf) */ |
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| 43 | tt = 6.6971006518e-09, /* 0x31e61c52 */ |
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| 44 | t0 = 4.8383611441e-01, /* 0x3ef7b95e */ |
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| 45 | t1 = -1.4758771658e-01, /* 0xbe17213c */ |
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| 46 | t2 = 6.4624942839e-02, /* 0x3d845a15 */ |
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| 47 | t3 = -3.2788541168e-02, /* 0xbd064d47 */ |
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| 48 | t4 = 1.7970675603e-02, /* 0x3c93373d */ |
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| 49 | t5 = -1.0314224288e-02, /* 0xbc28fcfe */ |
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| 50 | t6 = 6.1005386524e-03, /* 0x3bc7e707 */ |
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| 51 | t7 = -3.6845202558e-03, /* 0xbb7177fe */ |
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| 52 | t8 = 2.2596477065e-03, /* 0x3b141699 */ |
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| 53 | t9 = -1.4034647029e-03, /* 0xbab7f476 */ |
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| 54 | t10 = 8.8108185446e-04, /* 0x3a66f867 */ |
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| 55 | t11 = -5.3859531181e-04, /* 0xba0d3085 */ |
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| 56 | t12 = 3.1563205994e-04, /* 0x39a57b6b */ |
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| 57 | t13 = -3.1275415677e-04, /* 0xb9a3f927 */ |
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| 58 | t14 = 3.3552918467e-04, /* 0x39afe9f7 */ |
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| 59 | u0 = -7.7215664089e-02, /* 0xbd9e233f */ |
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| 60 | u1 = 6.3282704353e-01, /* 0x3f2200f4 */ |
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| 61 | u2 = 1.4549225569e+00, /* 0x3fba3ae7 */ |
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| 62 | u3 = 9.7771751881e-01, /* 0x3f7a4bb2 */ |
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| 63 | u4 = 2.2896373272e-01, /* 0x3e6a7578 */ |
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| 64 | u5 = 1.3381091878e-02, /* 0x3c5b3c5e */ |
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| 65 | v1 = 2.4559779167e+00, /* 0x401d2ebe */ |
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| 66 | v2 = 2.1284897327e+00, /* 0x4008392d */ |
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| 67 | v3 = 7.6928514242e-01, /* 0x3f44efdf */ |
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| 68 | v4 = 1.0422264785e-01, /* 0x3dd572af */ |
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| 69 | v5 = 3.2170924824e-03, /* 0x3b52d5db */ |
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| 70 | s0 = -7.7215664089e-02, /* 0xbd9e233f */ |
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| 71 | s1 = 2.1498242021e-01, /* 0x3e5c245a */ |
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| 72 | s2 = 3.2577878237e-01, /* 0x3ea6cc7a */ |
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| 73 | s3 = 1.4635047317e-01, /* 0x3e15dce6 */ |
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| 74 | s4 = 2.6642270386e-02, /* 0x3cda40e4 */ |
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| 75 | s5 = 1.8402845599e-03, /* 0x3af135b4 */ |
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| 76 | s6 = 3.1947532989e-05, /* 0x3805ff67 */ |
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| 77 | r1 = 1.3920053244e+00, /* 0x3fb22d3b */ |
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| 78 | r2 = 7.2193557024e-01, /* 0x3f38d0c5 */ |
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| 79 | r3 = 1.7193385959e-01, /* 0x3e300f6e */ |
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| 80 | r4 = 1.8645919859e-02, /* 0x3c98bf54 */ |
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| 81 | r5 = 7.7794247773e-04, /* 0x3a4beed6 */ |
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| 82 | r6 = 7.3266842264e-06, /* 0x36f5d7bd */ |
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| 83 | w0 = 4.1893854737e-01, /* 0x3ed67f1d */ |
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| 84 | w1 = 8.3333335817e-02, /* 0x3daaaaab */ |
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| 85 | w2 = -2.7777778450e-03, /* 0xbb360b61 */ |
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| 86 | w3 = 7.9365057172e-04, /* 0x3a500cfd */ |
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| 87 | w4 = -5.9518753551e-04, /* 0xba1c065c */ |
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| 88 | w5 = 8.3633989561e-04, /* 0x3a5b3dd2 */ |
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| 89 | w6 = -1.6309292987e-03; /* 0xbad5c4e8 */ |
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| 90 | |||
| 91 | #ifdef __STDC__ |
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| 92 | static const float zero= 0.0000000000e+00; |
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| 93 | #else |
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| 94 | static float zero= 0.0000000000e+00; |
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| 95 | #endif |
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| 96 | |||
| 97 | #ifdef __STDC__ |
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| 98 | static float sin_pif(float x) |
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| 99 | #else |
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| 100 | static float sin_pif(x) |
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| 101 | float x; |
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| 102 | #endif |
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| 103 | { |
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| 104 | float y,z; |
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| 105 | __int32_t n,ix; |
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| 106 | |||
| 107 | GET_FLOAT_WORD(ix,x); |
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| 108 | ix &= 0x7fffffff; |
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| 109 | |||
| 110 | if(ix<0x3e800000) return __kernel_sinf(pi*x,zero,0); |
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| 111 | y = -x; /* x is assume negative */ |
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| 112 | |||
| 113 | /* |
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| 114 | * argument reduction, make sure inexact flag not raised if input |
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| 115 | * is an integer |
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| 116 | */ |
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| 117 | z = floorf(y); |
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| 118 | if(z!=y) { /* inexact anyway */ |
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| 119 | y *= (float)0.5; |
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| 120 | y = (float)2.0*(y - floorf(y)); /* y = |x| mod 2.0 */ |
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| 121 | n = (__int32_t) (y*(float)4.0); |
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| 122 | } else { |
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| 123 | if(ix>=0x4b800000) { |
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| 124 | y = zero; n = 0; /* y must be even */ |
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| 125 | } else { |
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| 126 | if(ix<0x4b000000) z = y+two23; /* exact */ |
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| 127 | GET_FLOAT_WORD(n,z); |
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| 128 | n &= 1; |
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| 129 | y = n; |
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| 130 | n<<= 2; |
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| 131 | } |
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| 132 | } |
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| 133 | switch (n) { |
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| 134 | case 0: y = __kernel_sinf(pi*y,zero,0); break; |
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| 135 | case 1: |
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| 136 | case 2: y = __kernel_cosf(pi*((float)0.5-y),zero); break; |
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| 137 | case 3: |
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| 138 | case 4: y = __kernel_sinf(pi*(one-y),zero,0); break; |
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| 139 | case 5: |
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| 140 | case 6: y = -__kernel_cosf(pi*(y-(float)1.5),zero); break; |
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| 141 | default: y = __kernel_sinf(pi*(y-(float)2.0),zero,0); break; |
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| 142 | } |
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| 143 | return -y; |
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| 144 | } |
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| 145 | |||
| 146 | |||
| 147 | #ifdef __STDC__ |
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| 148 | float __ieee754_lgammaf_r(float x, int *signgamp) |
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| 149 | #else |
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| 150 | float __ieee754_lgammaf_r(x,signgamp) |
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| 151 | float x; int *signgamp; |
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| 152 | #endif |
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| 153 | { |
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| 154 | float t,y,z,nadj = 0.0,p,p1,p2,p3,q,r,w; |
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| 155 | __int32_t i,hx,ix; |
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| 156 | |||
| 157 | GET_FLOAT_WORD(hx,x); |
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| 158 | |||
| 159 | /* purge off +-inf, NaN, +-0, and negative arguments */ |
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| 160 | *signgamp = 1; |
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| 161 | ix = hx&0x7fffffff; |
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| 162 | if(ix>=0x7f800000) return x*x; |
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| 163 | if(ix==0) return one/zero; |
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| 164 | if(ix<0x1c800000) { /* |x|<2**-70, return -log(|x|) */ |
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| 165 | if(hx<0) { |
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| 166 | *signgamp = -1; |
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| 167 | return -__ieee754_logf(-x); |
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| 168 | } else return -__ieee754_logf(x); |
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| 169 | } |
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| 170 | if(hx<0) { |
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| 171 | if(ix>=0x4b000000) /* |x|>=2**23, must be -integer */ |
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| 172 | return one/zero; |
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| 173 | t = sin_pif(x); |
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| 174 | if(t==zero) return one/zero; /* -integer */ |
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| 175 | nadj = __ieee754_logf(pi/fabsf(t*x)); |
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| 176 | if(t |
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| 177 | x = -x; |
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| 178 | } |
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| 179 | |||
| 180 | /* purge off 1 and 2 */ |
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| 181 | if (ix==0x3f800000||ix==0x40000000) r = 0; |
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| 182 | /* for x < 2.0 */ |
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| 183 | else if(ix<0x40000000) { |
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| 184 | if(ix<=0x3f666666) { /* lgamma(x) = lgamma(x+1)-log(x) */ |
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| 185 | r = -__ieee754_logf(x); |
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| 186 | if(ix>=0x3f3b4a20) {y = one-x; i= 0;} |
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| 187 | else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;} |
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| 188 | else {y = x; i=2;} |
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| 189 | } else { |
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| 190 | r = zero; |
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| 191 | if(ix>=0x3fdda618) {y=(float)2.0-x;i=0;} /* [1.7316,2] */ |
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| 192 | else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */ |
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| 193 | else {y=x-one;i=2;} |
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| 194 | } |
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| 195 | switch(i) { |
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| 196 | case 0: |
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| 197 | z = y*y; |
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| 198 | p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10)))); |
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| 199 | p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11))))); |
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| 200 | p = y*p1+p2; |
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| 201 | r += (p-(float)0.5*y); break; |
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| 202 | case 1: |
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| 203 | z = y*y; |
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| 204 | w = z*y; |
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| 205 | p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */ |
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| 206 | p2 = t1+w*(t4+w*(t7+w*(t10+w*t13))); |
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| 207 | p3 = t2+w*(t5+w*(t8+w*(t11+w*t14))); |
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| 208 | p = z*p1-(tt-w*(p2+y*p3)); |
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| 209 | r += (tf + p); break; |
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| 210 | case 2: |
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| 211 | p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5))))); |
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| 212 | p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5)))); |
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| 213 | r += (-(float)0.5*y + p1/p2); |
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| 214 | } |
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| 215 | } |
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| 216 | else if(ix<0x41000000) { /* x < 8.0 */ |
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| 217 | i = (__int32_t)x; |
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| 218 | t = zero; |
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| 219 | y = x-(float)i; |
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| 220 | p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6)))))); |
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| 221 | q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6))))); |
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| 222 | r = half*y+p/q; |
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| 223 | z = one; /* lgamma(1+s) = log(s) + lgamma(s) */ |
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| 224 | switch(i) { |
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| 225 | case 7: z *= (y+(float)6.0); /* FALLTHRU */ |
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| 226 | case 6: z *= (y+(float)5.0); /* FALLTHRU */ |
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| 227 | case 5: z *= (y+(float)4.0); /* FALLTHRU */ |
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| 228 | case 4: z *= (y+(float)3.0); /* FALLTHRU */ |
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| 229 | case 3: z *= (y+(float)2.0); /* FALLTHRU */ |
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| 230 | r += __ieee754_logf(z); break; |
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| 231 | } |
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| 232 | /* 8.0 <= x < 2**58 */ |
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| 233 | } else if (ix < 0x5c800000) { |
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| 234 | t = __ieee754_logf(x); |
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| 235 | z = one/x; |
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| 236 | y = z*z; |
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| 237 | w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6))))); |
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| 238 | r = (x-half)*(t-one)+w; |
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| 239 | } else |
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| 240 | /* 2**58 <= x <= inf */ |
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| 241 | r = x*(__ieee754_logf(x)-one); |
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| 242 | if(hx<0) r = nadj - r; |
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| 243 | return r; |
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| 244 | } |