/* erf_lgamma.c -- float version of er_lgamma.c. * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== * */ #include "fdlibm.h" #ifdef __STDC__ static const float #else static float #endif two23= 8.3886080000e+06, /* 0x4b000000 */ half= 5.0000000000e-01, /* 0x3f000000 */ one = 1.0000000000e+00, /* 0x3f800000 */ pi = 3.1415927410e+00, /* 0x40490fdb */ a0 = 7.7215664089e-02, /* 0x3d9e233f */ a1 = 3.2246702909e-01, /* 0x3ea51a66 */ a2 = 6.7352302372e-02, /* 0x3d89f001 */ a3 = 2.0580807701e-02, /* 0x3ca89915 */ a4 = 7.3855509982e-03, /* 0x3bf2027e */ a5 = 2.8905137442e-03, /* 0x3b3d6ec6 */ a6 = 1.1927076848e-03, /* 0x3a9c54a1 */ a7 = 5.1006977446e-04, /* 0x3a05b634 */ a8 = 2.2086278477e-04, /* 0x39679767 */ a9 = 1.0801156895e-04, /* 0x38e28445 */ a10 = 2.5214456400e-05, /* 0x37d383a2 */ a11 = 4.4864096708e-05, /* 0x383c2c75 */ tc = 1.4616321325e+00, /* 0x3fbb16c3 */ tf = -1.2148628384e-01, /* 0xbdf8cdcd */ /* tt = -(tail of tf) */ tt = 6.6971006518e-09, /* 0x31e61c52 */ t0 = 4.8383611441e-01, /* 0x3ef7b95e */ t1 = -1.4758771658e-01, /* 0xbe17213c */ t2 = 6.4624942839e-02, /* 0x3d845a15 */ t3 = -3.2788541168e-02, /* 0xbd064d47 */ t4 = 1.7970675603e-02, /* 0x3c93373d */ t5 = -1.0314224288e-02, /* 0xbc28fcfe */ t6 = 6.1005386524e-03, /* 0x3bc7e707 */ t7 = -3.6845202558e-03, /* 0xbb7177fe */ t8 = 2.2596477065e-03, /* 0x3b141699 */ t9 = -1.4034647029e-03, /* 0xbab7f476 */ t10 = 8.8108185446e-04, /* 0x3a66f867 */ t11 = -5.3859531181e-04, /* 0xba0d3085 */ t12 = 3.1563205994e-04, /* 0x39a57b6b */ t13 = -3.1275415677e-04, /* 0xb9a3f927 */ t14 = 3.3552918467e-04, /* 0x39afe9f7 */ u0 = -7.7215664089e-02, /* 0xbd9e233f */ u1 = 6.3282704353e-01, /* 0x3f2200f4 */ u2 = 1.4549225569e+00, /* 0x3fba3ae7 */ u3 = 9.7771751881e-01, /* 0x3f7a4bb2 */ u4 = 2.2896373272e-01, /* 0x3e6a7578 */ u5 = 1.3381091878e-02, /* 0x3c5b3c5e */ v1 = 2.4559779167e+00, /* 0x401d2ebe */ v2 = 2.1284897327e+00, /* 0x4008392d */ v3 = 7.6928514242e-01, /* 0x3f44efdf */ v4 = 1.0422264785e-01, /* 0x3dd572af */ v5 = 3.2170924824e-03, /* 0x3b52d5db */ s0 = -7.7215664089e-02, /* 0xbd9e233f */ s1 = 2.1498242021e-01, /* 0x3e5c245a */ s2 = 3.2577878237e-01, /* 0x3ea6cc7a */ s3 = 1.4635047317e-01, /* 0x3e15dce6 */ s4 = 2.6642270386e-02, /* 0x3cda40e4 */ s5 = 1.8402845599e-03, /* 0x3af135b4 */ s6 = 3.1947532989e-05, /* 0x3805ff67 */ r1 = 1.3920053244e+00, /* 0x3fb22d3b */ r2 = 7.2193557024e-01, /* 0x3f38d0c5 */ r3 = 1.7193385959e-01, /* 0x3e300f6e */ r4 = 1.8645919859e-02, /* 0x3c98bf54 */ r5 = 7.7794247773e-04, /* 0x3a4beed6 */ r6 = 7.3266842264e-06, /* 0x36f5d7bd */ w0 = 4.1893854737e-01, /* 0x3ed67f1d */ w1 = 8.3333335817e-02, /* 0x3daaaaab */ w2 = -2.7777778450e-03, /* 0xbb360b61 */ w3 = 7.9365057172e-04, /* 0x3a500cfd */ w4 = -5.9518753551e-04, /* 0xba1c065c */ w5 = 8.3633989561e-04, /* 0x3a5b3dd2 */ w6 = -1.6309292987e-03; /* 0xbad5c4e8 */ #ifdef __STDC__ static const float zero= 0.0000000000e+00; #else static float zero= 0.0000000000e+00; #endif #ifdef __STDC__ static float sin_pif(float x) #else static float sin_pif(x) float x; #endif { float y,z; __int32_t n,ix; GET_FLOAT_WORD(ix,x); ix &= 0x7fffffff; if(ix<0x3e800000) return __kernel_sinf(pi*x,zero,0); y = -x; /* x is assume negative */ /* * argument reduction, make sure inexact flag not raised if input * is an integer */ z = floorf(y); if(z!=y) { /* inexact anyway */ y *= (float)0.5; y = (float)2.0*(y - floorf(y)); /* y = |x| mod 2.0 */ n = (__int32_t) (y*(float)4.0); } else { if(ix>=0x4b800000) { y = zero; n = 0; /* y must be even */ } else { if(ix<0x4b000000) z = y+two23; /* exact */ GET_FLOAT_WORD(n,z); n &= 1; y = n; n<<= 2; } } switch (n) { case 0: y = __kernel_sinf(pi*y,zero,0); break; case 1: case 2: y = __kernel_cosf(pi*((float)0.5-y),zero); break; case 3: case 4: y = __kernel_sinf(pi*(one-y),zero,0); break; case 5: case 6: y = -__kernel_cosf(pi*(y-(float)1.5),zero); break; default: y = __kernel_sinf(pi*(y-(float)2.0),zero,0); break; } return -y; } #ifdef __STDC__ float __ieee754_lgammaf_r(float x, int *signgamp) #else float __ieee754_lgammaf_r(x, signgamp) float x; int *signgamp; #endif { float t,y,z,nadj = 0.0,p,p1,p2,p3,q,r,w; __int32_t i,hx,ix; GET_FLOAT_WORD(hx,x); /* purge off +-inf, NaN, +-0, and negative arguments */ *signgamp = 1; ix = hx&0x7fffffff; if(ix>=0x7f800000) { return x*x; } if(ix==0) { if(hx<0) *signgamp = -1; return one/(x-x); } if(ix<0x30800000) { /* |x|<2**-30, return -log(|x|) */ if(hx<0) { *signgamp = -1; return -__ieee754_logf(-x); } else return -__ieee754_logf(x); } if(hx<0) { if(ix>=0x4b000000) { /* |x|>=2**23, must be -integer */ return one/(x-x); } t = sin_pif(x); if(t==zero) { /* tgamma wants NaN instead of INFINITY */ return one/(x-x); /* -integer */ } nadj = __ieee754_logf(pi/fabsf(t*x)); if(t=0x3f3b4a20) {y = one-x; i= 0;} else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;} else {y = x; i=2;} } else { r = zero; if(ix>=0x3fdda618) {y=(float)2.0-x;i=0;} /* [1.7316,2] */ else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */ else {y=x-one;i=2;} } switch(i) { case 0: z = y*y; p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10)))); p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11))))); p = y*p1+p2; r += (p-(float)0.5*y); break; case 1: z = y*y; w = z*y; p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */ p2 = t1+w*(t4+w*(t7+w*(t10+w*t13))); p3 = t2+w*(t5+w*(t8+w*(t11+w*t14))); p = z*p1-(tt-w*(p2+y*p3)); r += (tf + p); break; case 2: p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5))))); p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5)))); r += (-(float)0.5*y + p1/p2); } } else if(ix<0x41000000) { /* x < 8.0 */ i = (__int32_t)x; t = zero; y = x-(float)i; p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6)))))); q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6))))); r = half*y+p/q; z = one; /* lgamma(1+s) = log(s) + lgamma(s) */ switch(i) { case 7: z *= (y+(float)6.0); /* FALLTHRU */ case 6: z *= (y+(float)5.0); /* FALLTHRU */ case 5: z *= (y+(float)4.0); /* FALLTHRU */ case 4: z *= (y+(float)3.0); /* FALLTHRU */ case 3: z *= (y+(float)2.0); /* FALLTHRU */ r += __ieee754_logf(z); break; } /* 8.0 <= x < 2**58 */ } else if (ix < 0x5c800000) { t = __ieee754_logf(x); z = one/x; y = z*z; w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6))))); r = (x-half)*(t-one)+w; } else /* 2**58 <= x <= inf */ r = x*(__ieee754_logf(x)-one); if(hx<0) r = nadj - r; return r; }