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 * Conversion to float fixed By Steven G. Kargl. 4 */ 5 6 /* 7 * ==================================================== 8 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 9 * 10 * Developed at SunPro, a Sun Microsystems, Inc. business. 11 * Permission to use, copy, modify, and distribute this 12 * software is freely granted, provided that this notice 13 * is preserved. 14 * ==================================================== 15 */ 16 17 #include <sys/cdefs.h> 18 __FBSDID("$FreeBSD$"); 19 20 #include "math.h" 21 #include "math_private.h" 22 23 static const volatile float vzero = 0; 24 25 static const float 26 zero= 0, 27 half= 0.5, 28 one = 1, 29 pi = 3.1415927410e+00, /* 0x40490fdb */ 30 /* 31 * Domain y in [0x1p-27, 0.27], range ~[-3.4599e-10, 3.4590e-10]: 32 * |(lgamma(2 - y) + 0.5 * y) / y - a(y)| < 2**-31.4 33 */ 34 a0 = 7.72156641e-02, /* 0x3d9e233f */ 35 a1 = 3.22467119e-01, /* 0x3ea51a69 */ 36 a2 = 6.73484802e-02, /* 0x3d89ee00 */ 37 a3 = 2.06395667e-02, /* 0x3ca9144f */ 38 a4 = 6.98275631e-03, /* 0x3be4cf9b */ 39 a5 = 4.11768444e-03, /* 0x3b86eda4 */ 40 /* 41 * Domain x in [tc-0.24, tc+0.28], range ~[-5.6577e-10, 5.5677e-10]: 42 * |(lgamma(x) - tf) - t(x - tc)| < 2**-30.8. 43 */ 44 tc = 1.46163213e+00, /* 0x3fbb16c3 */ 45 tf = -1.21486291e-01, /* 0xbdf8cdce */ 46 t0 = -2.94064460e-11, /* 0xae0154b7 */ 47 t1 = -2.35939837e-08, /* 0xb2caabb8 */ 48 t2 = 4.83836412e-01, /* 0x3ef7b968 */ 49 t3 = -1.47586212e-01, /* 0xbe1720d7 */ 50 t4 = 6.46013096e-02, /* 0x3d844db1 */ 51 t5 = -3.28450352e-02, /* 0xbd068884 */ 52 t6 = 1.86483748e-02, /* 0x3c98c47a */ 53 t7 = -9.89206228e-03, /* 0xbc221251 */ 54 /* 55 * Domain y in [-0.1, 0.232], range ~[-8.4931e-10, 8.7794e-10]: 56 * |(lgamma(1 + y) + 0.5 * y) / y - u(y) / v(y)| < 2**-31.2 57 */ 58 u0 = -7.72156641e-02, /* 0xbd9e233f */ 59 u1 = 7.36789703e-01, /* 0x3f3c9e40 */ 60 u2 = 4.95649040e-01, /* 0x3efdc5b6 */ 61 v1 = 1.10958421e+00, /* 0x3f8e06db */ 62 v2 = 2.10598111e-01, /* 0x3e57a708 */ 63 v3 = -1.02995494e-02, /* 0xbc28bf71 */ 64 /* 65 * Domain x in (2, 3], range ~[-5.5189e-11, 5.2317e-11]: 66 * |(lgamma(y+2) - 0.5 * y) / y - s(y)/r(y)| < 2**-35.0 67 * with y = x - 2. 68 */ 69 s0 = -7.72156641e-02, /* 0xbd9e233f */ 70 s1 = 2.69987404e-01, /* 0x3e8a3bca */ 71 s2 = 1.42851010e-01, /* 0x3e124789 */ 72 s3 = 1.19389519e-02, /* 0x3c439b98 */ 73 r1 = 6.79650068e-01, /* 0x3f2dfd8c */ 74 r2 = 1.16058730e-01, /* 0x3dedb033 */ 75 r3 = 3.75673687e-03, /* 0x3b763396 */ 76 /* 77 * Domain z in [8, 0x1p24], range ~[-1.2640e-09, 1.2640e-09]: 78 * |lgamma(x) - (x - 0.5) * (log(x) - 1) - w(1/x)| < 2**-29.6. 79 */ 80 w0 = 4.18938547e-01, /* 0x3ed67f1d */ 81 w1 = 8.33332464e-02, /* 0x3daaaa9f */ 82 w2 = -2.76129087e-03; /* 0xbb34f6c6 */ 83 84 static float 85 sin_pif(float x) 86 { 87 volatile float vz; 88 float y,z; 89 int n; 90 91 y = -x; 92 93 vz = y+0x1p23F; /* depend on 0 <= y < 0x1p23 */ 94 z = vz-0x1p23F; /* rintf(y) for the above range */ 95 if (z == y) 96 return zero; 97 98 vz = y+0x1p21F; 99 GET_FLOAT_WORD(n,vz); /* bits for rounded y (units 0.25) */ 100 z = vz-0x1p21F; /* y rounded to a multiple of 0.25 */ 101 if (z > y) { 102 z -= 0.25F; /* adjust to round down */ 103 n--; 104 } 105 n &= 7; /* octant of y mod 2 */ 106 y = y - z + n * 0.25F; /* y mod 2 */ 107 108 switch (n) { 109 case 0: y = __kernel_sindf(pi*y); break; 110 case 1: 111 case 2: y = __kernel_cosdf(pi*((float)0.5-y)); break; 112 case 3: 113 case 4: y = __kernel_sindf(pi*(one-y)); break; 114 case 5: 115 case 6: y = -__kernel_cosdf(pi*(y-(float)1.5)); break; 116 default: y = __kernel_sindf(pi*(y-(float)2.0)); break; 117 } 118 return -y; 119 } 120 121 122 float 123 lgammaf_r(float x, int *signgamp) 124 { 125 float nadj,p,p1,p2,q,r,t,w,y,z; 126 int32_t hx; 127 int i,ix; 128 129 GET_FLOAT_WORD(hx,x); 130 131 /* purge +-Inf and NaNs */ 132 *signgamp = 1; 133 ix = hx&0x7fffffff; 134 if(ix>=0x7f800000) return x*x; 135 136 /* purge +-0 and tiny arguments */ 137 *signgamp = 1-2*((uint32_t)hx>>31); 138 if(ix<0x32000000) { /* |x|<2**-27, return -log(|x|) */ 139 if(ix==0) 140 return one/vzero; 141 return -logf(fabsf(x)); 142 } 143 144 /* purge negative integers and start evaluation for other x < 0 */ 145 if(hx<0) { 146 *signgamp = 1; 147 if(ix>=0x4b000000) /* |x|>=2**23, must be -integer */ 148 return one/vzero; 149 t = sin_pif(x); 150 if(t==zero) return one/vzero; /* -integer */ 151 nadj = logf(pi/fabsf(t*x)); 152 if(t<zero) *signgamp = -1; 153 x = -x; 154 } 155 156 /* purge 1 and 2 */ 157 if (ix==0x3f800000||ix==0x40000000) r = 0; 158 /* for x < 2.0 */ 159 else if(ix<0x40000000) { 160 if(ix<=0x3f666666) { /* lgamma(x) = lgamma(x+1)-log(x) */ 161 r = -logf(x); 162 if(ix>=0x3f3b4a20) {y = one-x; i= 0;} 163 else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;} 164 else {y = x; i=2;} 165 } else { 166 r = zero; 167 if(ix>=0x3fdda618) {y=2-x;i=0;} /* [1.7316,2] */ 168 else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */ 169 else {y=x-one;i=2;} 170 } 171 switch(i) { 172 case 0: 173 z = y*y; 174 p1 = a0+z*(a2+z*a4); 175 p2 = z*(a1+z*(a3+z*a5)); 176 p = y*p1+p2; 177 r += p-y/2; break; 178 case 1: 179 p = t0+y*t1+y*y*(t2+y*(t3+y*(t4+y*(t5+y*(t6+y*t7))))); 180 r += tf + p; break; 181 case 2: 182 p1 = y*(u0+y*(u1+y*u2)); 183 p2 = one+y*(v1+y*(v2+y*v3)); 184 r += p1/p2-y/2; 185 } 186 } 187 /* x < 8.0 */ 188 else if(ix<0x41000000) { 189 i = x; 190 y = x-i; 191 p = y*(s0+y*(s1+y*(s2+y*s3))); 192 q = one+y*(r1+y*(r2+y*r3)); 193 r = y/2+p/q; 194 z = one; /* lgamma(1+s) = log(s) + lgamma(s) */ 195 switch(i) { 196 case 7: z *= (y+6); /* FALLTHRU */ 197 case 6: z *= (y+5); /* FALLTHRU */ 198 case 5: z *= (y+4); /* FALLTHRU */ 199 case 4: z *= (y+3); /* FALLTHRU */ 200 case 3: z *= (y+2); /* FALLTHRU */ 201 r += logf(z); break; 202 } 203 /* 8.0 <= x < 2**27 */ 204 } else if (ix < 0x4d000000) { 205 t = logf(x); 206 z = one/x; 207 y = z*z; 208 w = w0+z*(w1+y*w2); 209 r = (x-half)*(t-one)+w; 210 } else 211 /* 2**27 <= x <= inf */ 212 r = x*(logf(x)-one); 213 if(hx<0) r = nadj - r; 214 return r; 215 } 216