1 /* e_lgammaf_r.c -- float version of e_lgamma_r.c. 2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. 3 */ 4 5 /* 6 * ==================================================== 7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 8 * 9 * Developed at SunPro, a Sun Microsystems, Inc. business. 10 * Permission to use, copy, modify, and distribute this 11 * software is freely granted, provided that this notice 12 * is preserved. 13 * ==================================================== 14 */ 15 16 #include <sys/cdefs.h> 17 __FBSDID("$FreeBSD$"); 18 19 #include "math.h" 20 #include "math_private.h" 21 22 static const float 23 two23= 8.3886080000e+06, /* 0x4b000000 */ 24 half= 5.0000000000e-01, /* 0x3f000000 */ 25 one = 1.0000000000e+00, /* 0x3f800000 */ 26 pi = 3.1415927410e+00, /* 0x40490fdb */ 27 a0 = 7.7215664089e-02, /* 0x3d9e233f */ 28 a1 = 3.2246702909e-01, /* 0x3ea51a66 */ 29 a2 = 6.7352302372e-02, /* 0x3d89f001 */ 30 a3 = 2.0580807701e-02, /* 0x3ca89915 */ 31 a4 = 7.3855509982e-03, /* 0x3bf2027e */ 32 a5 = 2.8905137442e-03, /* 0x3b3d6ec6 */ 33 a6 = 1.1927076848e-03, /* 0x3a9c54a1 */ 34 a7 = 5.1006977446e-04, /* 0x3a05b634 */ 35 a8 = 2.2086278477e-04, /* 0x39679767 */ 36 a9 = 1.0801156895e-04, /* 0x38e28445 */ 37 a10 = 2.5214456400e-05, /* 0x37d383a2 */ 38 a11 = 4.4864096708e-05, /* 0x383c2c75 */ 39 tc = 1.4616321325e+00, /* 0x3fbb16c3 */ 40 tf = -1.2148628384e-01, /* 0xbdf8cdcd */ 41 /* tt = -(tail of tf) */ 42 tt = 6.6971006518e-09, /* 0x31e61c52 */ 43 t0 = 4.8383611441e-01, /* 0x3ef7b95e */ 44 t1 = -1.4758771658e-01, /* 0xbe17213c */ 45 t2 = 6.4624942839e-02, /* 0x3d845a15 */ 46 t3 = -3.2788541168e-02, /* 0xbd064d47 */ 47 t4 = 1.7970675603e-02, /* 0x3c93373d */ 48 t5 = -1.0314224288e-02, /* 0xbc28fcfe */ 49 t6 = 6.1005386524e-03, /* 0x3bc7e707 */ 50 t7 = -3.6845202558e-03, /* 0xbb7177fe */ 51 t8 = 2.2596477065e-03, /* 0x3b141699 */ 52 t9 = -1.4034647029e-03, /* 0xbab7f476 */ 53 t10 = 8.8108185446e-04, /* 0x3a66f867 */ 54 t11 = -5.3859531181e-04, /* 0xba0d3085 */ 55 t12 = 3.1563205994e-04, /* 0x39a57b6b */ 56 t13 = -3.1275415677e-04, /* 0xb9a3f927 */ 57 t14 = 3.3552918467e-04, /* 0x39afe9f7 */ 58 u0 = -7.7215664089e-02, /* 0xbd9e233f */ 59 u1 = 6.3282704353e-01, /* 0x3f2200f4 */ 60 u2 = 1.4549225569e+00, /* 0x3fba3ae7 */ 61 u3 = 9.7771751881e-01, /* 0x3f7a4bb2 */ 62 u4 = 2.2896373272e-01, /* 0x3e6a7578 */ 63 u5 = 1.3381091878e-02, /* 0x3c5b3c5e */ 64 v1 = 2.4559779167e+00, /* 0x401d2ebe */ 65 v2 = 2.1284897327e+00, /* 0x4008392d */ 66 v3 = 7.6928514242e-01, /* 0x3f44efdf */ 67 v4 = 1.0422264785e-01, /* 0x3dd572af */ 68 v5 = 3.2170924824e-03, /* 0x3b52d5db */ 69 s0 = -7.7215664089e-02, /* 0xbd9e233f */ 70 s1 = 2.1498242021e-01, /* 0x3e5c245a */ 71 s2 = 3.2577878237e-01, /* 0x3ea6cc7a */ 72 s3 = 1.4635047317e-01, /* 0x3e15dce6 */ 73 s4 = 2.6642270386e-02, /* 0x3cda40e4 */ 74 s5 = 1.8402845599e-03, /* 0x3af135b4 */ 75 s6 = 3.1947532989e-05, /* 0x3805ff67 */ 76 r1 = 1.3920053244e+00, /* 0x3fb22d3b */ 77 r2 = 7.2193557024e-01, /* 0x3f38d0c5 */ 78 r3 = 1.7193385959e-01, /* 0x3e300f6e */ 79 r4 = 1.8645919859e-02, /* 0x3c98bf54 */ 80 r5 = 7.7794247773e-04, /* 0x3a4beed6 */ 81 r6 = 7.3266842264e-06, /* 0x36f5d7bd */ 82 w0 = 4.1893854737e-01, /* 0x3ed67f1d */ 83 w1 = 8.3333335817e-02, /* 0x3daaaaab */ 84 w2 = -2.7777778450e-03, /* 0xbb360b61 */ 85 w3 = 7.9365057172e-04, /* 0x3a500cfd */ 86 w4 = -5.9518753551e-04, /* 0xba1c065c */ 87 w5 = 8.3633989561e-04, /* 0x3a5b3dd2 */ 88 w6 = -1.6309292987e-03; /* 0xbad5c4e8 */ 89 90 static const float zero= 0.0000000000e+00; 91 92 static float sin_pif(float x) 93 { 94 float y,z; 95 int n,ix; 96 97 GET_FLOAT_WORD(ix,x); 98 ix &= 0x7fffffff; 99 100 if(ix<0x3e800000) return __kernel_sindf(pi*x); 101 y = -x; /* x is assume negative */ 102 103 /* 104 * argument reduction, make sure inexact flag not raised if input 105 * is an integer 106 */ 107 z = floorf(y); 108 if(z!=y) { /* inexact anyway */ 109 y *= (float)0.5; 110 y = (float)2.0*(y - floorf(y)); /* y = |x| mod 2.0 */ 111 n = (int) (y*(float)4.0); 112 } else { 113 if(ix>=0x4b800000) { 114 y = zero; n = 0; /* y must be even */ 115 } else { 116 if(ix<0x4b000000) z = y+two23; /* exact */ 117 GET_FLOAT_WORD(n,z); 118 n &= 1; 119 y = n; 120 n<<= 2; 121 } 122 } 123 switch (n) { 124 case 0: y = __kernel_sindf(pi*y); break; 125 case 1: 126 case 2: y = __kernel_cosdf(pi*((float)0.5-y)); break; 127 case 3: 128 case 4: y = __kernel_sindf(pi*(one-y)); break; 129 case 5: 130 case 6: y = -__kernel_cosdf(pi*(y-(float)1.5)); break; 131 default: y = __kernel_sindf(pi*(y-(float)2.0)); break; 132 } 133 return -y; 134 } 135 136 137 float 138 __ieee754_lgammaf_r(float x, int *signgamp) 139 { 140 float t,y,z,nadj,p,p1,p2,p3,q,r,w; 141 int32_t hx; 142 int i,ix; 143 144 GET_FLOAT_WORD(hx,x); 145 146 /* purge off +-inf, NaN, +-0, tiny and negative arguments */ 147 *signgamp = 1; 148 ix = hx&0x7fffffff; 149 if(ix>=0x7f800000) return x*x; 150 if(ix==0) return one/zero; 151 if(ix<0x35000000) { /* |x|<2**-21, return -log(|x|) */ 152 if(hx<0) { 153 *signgamp = -1; 154 return -__ieee754_logf(-x); 155 } else return -__ieee754_logf(x); 156 } 157 if(hx<0) { 158 if(ix>=0x4b000000) /* |x|>=2**23, must be -integer */ 159 return one/zero; 160 t = sin_pif(x); 161 if(t==zero) return one/zero; /* -integer */ 162 nadj = __ieee754_logf(pi/fabsf(t*x)); 163 if(t<zero) *signgamp = -1; 164 x = -x; 165 } 166 167 /* purge off 1 and 2 */ 168 if (ix==0x3f800000||ix==0x40000000) r = 0; 169 /* for x < 2.0 */ 170 else if(ix<0x40000000) { 171 if(ix<=0x3f666666) { /* lgamma(x) = lgamma(x+1)-log(x) */ 172 r = -__ieee754_logf(x); 173 if(ix>=0x3f3b4a20) {y = one-x; i= 0;} 174 else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;} 175 else {y = x; i=2;} 176 } else { 177 r = zero; 178 if(ix>=0x3fdda618) {y=(float)2.0-x;i=0;} /* [1.7316,2] */ 179 else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */ 180 else {y=x-one;i=2;} 181 } 182 switch(i) { 183 case 0: 184 z = y*y; 185 p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10)))); 186 p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11))))); 187 p = y*p1+p2; 188 r += (p-(float)0.5*y); break; 189 case 1: 190 z = y*y; 191 w = z*y; 192 p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */ 193 p2 = t1+w*(t4+w*(t7+w*(t10+w*t13))); 194 p3 = t2+w*(t5+w*(t8+w*(t11+w*t14))); 195 p = z*p1-(tt-w*(p2+y*p3)); 196 r += (tf + p); break; 197 case 2: 198 p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5))))); 199 p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5)))); 200 r += (-(float)0.5*y + p1/p2); 201 } 202 } 203 else if(ix<0x41000000) { /* x < 8.0 */ 204 i = (int)x; 205 y = x-(float)i; 206 p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6)))))); 207 q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6))))); 208 r = half*y+p/q; 209 z = one; /* lgamma(1+s) = log(s) + lgamma(s) */ 210 switch(i) { 211 case 7: z *= (y+(float)6.0); /* FALLTHRU */ 212 case 6: z *= (y+(float)5.0); /* FALLTHRU */ 213 case 5: z *= (y+(float)4.0); /* FALLTHRU */ 214 case 4: z *= (y+(float)3.0); /* FALLTHRU */ 215 case 3: z *= (y+(float)2.0); /* FALLTHRU */ 216 r += __ieee754_logf(z); break; 217 } 218 /* 8.0 <= x < 2**58 */ 219 } else if (ix < 0x5c800000) { 220 t = __ieee754_logf(x); 221 z = one/x; 222 y = z*z; 223 w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6))))); 224 r = (x-half)*(t-one)+w; 225 } else 226 /* 2**58 <= x <= inf */ 227 r = x*(__ieee754_logf(x)-one); 228 if(hx<0) r = nadj - r; 229 return r; 230 } 231