1 /* 2 * This file is part of the MicroPython project, http://micropython.org/ 3 * 4 * These math functions are taken from newlib-nano-2, the newlib/libm/math 5 * directory, available from https://github.com/32bitmicro/newlib-nano-2. 6 * 7 * Appropriate copyright headers are reproduced below. 8 */ 9 10 /* erf_lgamma.c -- float version of er_lgamma.c. 11 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. 12 */ 13 14 /* 15 * ==================================================== 16 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 17 * 18 * Developed at SunPro, a Sun Microsystems, Inc. business. 19 * Permission to use, copy, modify, and distribute this 20 * software is freely granted, provided that this notice 21 * is preserved. 22 * ==================================================== 23 * 24 */ 25 26 #include "fdlibm.h" 27 28 #define __ieee754_logf logf 29 30 #ifdef __STDC__ 31 static const float 32 #else 33 static float 34 #endif 35 two23= 8.3886080000e+06f, /* 0x4b000000 */ 36 half= 5.0000000000e-01f, /* 0x3f000000 */ 37 one = 1.0000000000e+00f, /* 0x3f800000 */ 38 pi = 3.1415927410e+00f, /* 0x40490fdb */ 39 a0 = 7.7215664089e-02f, /* 0x3d9e233f */ 40 a1 = 3.2246702909e-01f, /* 0x3ea51a66 */ 41 a2 = 6.7352302372e-02f, /* 0x3d89f001 */ 42 a3 = 2.0580807701e-02f, /* 0x3ca89915 */ 43 a4 = 7.3855509982e-03f, /* 0x3bf2027e */ 44 a5 = 2.8905137442e-03f, /* 0x3b3d6ec6 */ 45 a6 = 1.1927076848e-03f, /* 0x3a9c54a1 */ 46 a7 = 5.1006977446e-04f, /* 0x3a05b634 */ 47 a8 = 2.2086278477e-04f, /* 0x39679767 */ 48 a9 = 1.0801156895e-04f, /* 0x38e28445 */ 49 a10 = 2.5214456400e-05f, /* 0x37d383a2 */ 50 a11 = 4.4864096708e-05f, /* 0x383c2c75 */ 51 tc = 1.4616321325e+00f, /* 0x3fbb16c3 */ 52 tf = -1.2148628384e-01f, /* 0xbdf8cdcd */ 53 /* tt = -(tail of tf) */ 54 tt = 6.6971006518e-09f, /* 0x31e61c52 */ 55 t0 = 4.8383611441e-01f, /* 0x3ef7b95e */ 56 t1 = -1.4758771658e-01f, /* 0xbe17213c */ 57 t2 = 6.4624942839e-02f, /* 0x3d845a15 */ 58 t3 = -3.2788541168e-02f, /* 0xbd064d47 */ 59 t4 = 1.7970675603e-02f, /* 0x3c93373d */ 60 t5 = -1.0314224288e-02f, /* 0xbc28fcfe */ 61 t6 = 6.1005386524e-03f, /* 0x3bc7e707 */ 62 t7 = -3.6845202558e-03f, /* 0xbb7177fe */ 63 t8 = 2.2596477065e-03f, /* 0x3b141699 */ 64 t9 = -1.4034647029e-03f, /* 0xbab7f476 */ 65 t10 = 8.8108185446e-04f, /* 0x3a66f867 */ 66 t11 = -5.3859531181e-04f, /* 0xba0d3085 */ 67 t12 = 3.1563205994e-04f, /* 0x39a57b6b */ 68 t13 = -3.1275415677e-04f, /* 0xb9a3f927 */ 69 t14 = 3.3552918467e-04f, /* 0x39afe9f7 */ 70 u0 = -7.7215664089e-02f, /* 0xbd9e233f */ 71 u1 = 6.3282704353e-01f, /* 0x3f2200f4 */ 72 u2 = 1.4549225569e+00f, /* 0x3fba3ae7 */ 73 u3 = 9.7771751881e-01f, /* 0x3f7a4bb2 */ 74 u4 = 2.2896373272e-01f, /* 0x3e6a7578 */ 75 u5 = 1.3381091878e-02f, /* 0x3c5b3c5e */ 76 v1 = 2.4559779167e+00f, /* 0x401d2ebe */ 77 v2 = 2.1284897327e+00f, /* 0x4008392d */ 78 v3 = 7.6928514242e-01f, /* 0x3f44efdf */ 79 v4 = 1.0422264785e-01f, /* 0x3dd572af */ 80 v5 = 3.2170924824e-03f, /* 0x3b52d5db */ 81 s0 = -7.7215664089e-02f, /* 0xbd9e233f */ 82 s1 = 2.1498242021e-01f, /* 0x3e5c245a */ 83 s2 = 3.2577878237e-01f, /* 0x3ea6cc7a */ 84 s3 = 1.4635047317e-01f, /* 0x3e15dce6 */ 85 s4 = 2.6642270386e-02f, /* 0x3cda40e4 */ 86 s5 = 1.8402845599e-03f, /* 0x3af135b4 */ 87 s6 = 3.1947532989e-05f, /* 0x3805ff67 */ 88 r1 = 1.3920053244e+00f, /* 0x3fb22d3b */ 89 r2 = 7.2193557024e-01f, /* 0x3f38d0c5 */ 90 r3 = 1.7193385959e-01f, /* 0x3e300f6e */ 91 r4 = 1.8645919859e-02f, /* 0x3c98bf54 */ 92 r5 = 7.7794247773e-04f, /* 0x3a4beed6 */ 93 r6 = 7.3266842264e-06f, /* 0x36f5d7bd */ 94 w0 = 4.1893854737e-01f, /* 0x3ed67f1d */ 95 w1 = 8.3333335817e-02f, /* 0x3daaaaab */ 96 w2 = -2.7777778450e-03f, /* 0xbb360b61 */ 97 w3 = 7.9365057172e-04f, /* 0x3a500cfd */ 98 w4 = -5.9518753551e-04f, /* 0xba1c065c */ 99 w5 = 8.3633989561e-04f, /* 0x3a5b3dd2 */ 100 w6 = -1.6309292987e-03f; /* 0xbad5c4e8 */ 101 102 #ifdef __STDC__ 103 static const float zero= 0.0000000000e+00f; 104 #else 105 static float zero= 0.0000000000e+00f; 106 #endif 107 108 #ifdef __STDC__ sin_pif(float x)109 static float sin_pif(float x) 110 #else 111 static float sin_pif(x) 112 float x; 113 #endif 114 { 115 float y,z; 116 __int32_t n,ix; 117 118 GET_FLOAT_WORD(ix,x); 119 ix &= 0x7fffffff; 120 121 if(ix<0x3e800000) return __kernel_sinf(pi*x,zero,0); 122 y = -x; /* x is assume negative */ 123 124 /* 125 * argument reduction, make sure inexact flag not raised if input 126 * is an integer 127 */ 128 z = floorf(y); 129 if(z!=y) { /* inexact anyway */ 130 y *= (float)0.5; 131 y = (float)2.0*(y - floorf(y)); /* y = |x| mod 2.0 */ 132 n = (__int32_t) (y*(float)4.0); 133 } else { 134 if(ix>=0x4b800000) { 135 y = zero; n = 0; /* y must be even */ 136 } else { 137 if(ix<0x4b000000) z = y+two23; /* exact */ 138 GET_FLOAT_WORD(n,z); 139 n &= 1; 140 y = n; 141 n<<= 2; 142 } 143 } 144 switch (n) { 145 case 0: y = __kernel_sinf(pi*y,zero,0); break; 146 case 1: 147 case 2: y = __kernel_cosf(pi*((float)0.5-y),zero); break; 148 case 3: 149 case 4: y = __kernel_sinf(pi*(one-y),zero,0); break; 150 case 5: 151 case 6: y = -__kernel_cosf(pi*(y-(float)1.5),zero); break; 152 default: y = __kernel_sinf(pi*(y-(float)2.0),zero,0); break; 153 } 154 return -y; 155 } 156 157 158 #ifdef __STDC__ __ieee754_lgammaf_r(float x,int * signgamp)159 float __ieee754_lgammaf_r(float x, int *signgamp) 160 #else 161 float __ieee754_lgammaf_r(x,signgamp) 162 float x; int *signgamp; 163 #endif 164 { 165 float t,y,z,nadj = 0.0,p,p1,p2,p3,q,r,w; 166 __int32_t i,hx,ix; 167 168 GET_FLOAT_WORD(hx,x); 169 170 /* purge off +-inf, NaN, +-0, and negative arguments */ 171 *signgamp = 1; 172 ix = hx&0x7fffffff; 173 if(ix>=0x7f800000) return x*x; 174 if(ix==0) return one/zero; 175 if(ix<0x1c800000) { /* |x|<2**-70, return -log(|x|) */ 176 if(hx<0) { 177 *signgamp = -1; 178 return -__ieee754_logf(-x); 179 } else return -__ieee754_logf(x); 180 } 181 if(hx<0) { 182 if(ix>=0x4b000000) /* |x|>=2**23, must be -integer */ 183 return one/zero; 184 t = sin_pif(x); 185 if(t==zero) return one/zero; /* -integer */ 186 nadj = __ieee754_logf(pi/fabsf(t*x)); 187 if(t<zero) *signgamp = -1; 188 x = -x; 189 } 190 191 /* purge off 1 and 2 */ 192 if (ix==0x3f800000||ix==0x40000000) r = 0; 193 /* for x < 2.0 */ 194 else if(ix<0x40000000) { 195 if(ix<=0x3f666666) { /* lgamma(x) = lgamma(x+1)-log(x) */ 196 r = -__ieee754_logf(x); 197 if(ix>=0x3f3b4a20) {y = one-x; i= 0;} 198 else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;} 199 else {y = x; i=2;} 200 } else { 201 r = zero; 202 if(ix>=0x3fdda618) {y=(float)2.0-x;i=0;} /* [1.7316,2] */ 203 else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */ 204 else {y=x-one;i=2;} 205 } 206 switch(i) { 207 case 0: 208 z = y*y; 209 p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10)))); 210 p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11))))); 211 p = y*p1+p2; 212 r += (p-(float)0.5*y); break; 213 case 1: 214 z = y*y; 215 w = z*y; 216 p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */ 217 p2 = t1+w*(t4+w*(t7+w*(t10+w*t13))); 218 p3 = t2+w*(t5+w*(t8+w*(t11+w*t14))); 219 p = z*p1-(tt-w*(p2+y*p3)); 220 r += (tf + p); break; 221 case 2: 222 p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5))))); 223 p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5)))); 224 r += (-(float)0.5*y + p1/p2); 225 } 226 } 227 else if(ix<0x41000000) { /* x < 8.0 */ 228 i = (__int32_t)x; 229 t = zero; 230 y = x-(float)i; 231 p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6)))))); 232 q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6))))); 233 r = half*y+p/q; 234 z = one; /* lgamma(1+s) = log(s) + lgamma(s) */ 235 switch(i) { 236 case 7: z *= (y+(float)6.0); /* FALLTHRU */ 237 case 6: z *= (y+(float)5.0); /* FALLTHRU */ 238 case 5: z *= (y+(float)4.0); /* FALLTHRU */ 239 case 4: z *= (y+(float)3.0); /* FALLTHRU */ 240 case 3: z *= (y+(float)2.0); /* FALLTHRU */ 241 r += __ieee754_logf(z); break; 242 } 243 /* 8.0 <= x < 2**58 */ 244 } else if (ix < 0x5c800000) { 245 t = __ieee754_logf(x); 246 z = one/x; 247 y = z*z; 248 w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6))))); 249 r = (x-half)*(t-one)+w; 250 } else 251 /* 2**58 <= x <= inf */ 252 r = x*(__ieee754_logf(x)-one); 253 if(hx<0) r = nadj - r; 254 return r; 255 } 256