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