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/* e_lgammaf_r.c -- float version of e_lgamma_r.c. |
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* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. |
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*/ |
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/* |
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* ==================================================== |
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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* |
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* Developed at SunPro, a Sun Microsystems, Inc. business. |
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* Permission to use, copy, modify, and distribute this |
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* software is freely granted, provided that this notice |
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* is preserved. |
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* ==================================================== |
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*/ |
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#include "math.h" |
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#include "math_private.h" |
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static const float |
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two23= 8.3886080000e+06, /* 0x4b000000 */ |
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half= 5.0000000000e-01, /* 0x3f000000 */ |
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one = 1.0000000000e+00, /* 0x3f800000 */ |
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pi = 3.1415927410e+00, /* 0x40490fdb */ |
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a0 = 7.7215664089e-02, /* 0x3d9e233f */ |
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a1 = 3.2246702909e-01, /* 0x3ea51a66 */ |
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a2 = 6.7352302372e-02, /* 0x3d89f001 */ |
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a3 = 2.0580807701e-02, /* 0x3ca89915 */ |
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a4 = 7.3855509982e-03, /* 0x3bf2027e */ |
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a5 = 2.8905137442e-03, /* 0x3b3d6ec6 */ |
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a6 = 1.1927076848e-03, /* 0x3a9c54a1 */ |
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a7 = 5.1006977446e-04, /* 0x3a05b634 */ |
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a8 = 2.2086278477e-04, /* 0x39679767 */ |
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a9 = 1.0801156895e-04, /* 0x38e28445 */ |
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a10 = 2.5214456400e-05, /* 0x37d383a2 */ |
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a11 = 4.4864096708e-05, /* 0x383c2c75 */ |
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tc = 1.4616321325e+00, /* 0x3fbb16c3 */ |
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tf = -1.2148628384e-01, /* 0xbdf8cdcd */ |
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/* tt = -(tail of tf) */ |
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tt = 6.6971006518e-09, /* 0x31e61c52 */ |
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t0 = 4.8383611441e-01, /* 0x3ef7b95e */ |
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t1 = -1.4758771658e-01, /* 0xbe17213c */ |
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t2 = 6.4624942839e-02, /* 0x3d845a15 */ |
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t3 = -3.2788541168e-02, /* 0xbd064d47 */ |
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t4 = 1.7970675603e-02, /* 0x3c93373d */ |
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t5 = -1.0314224288e-02, /* 0xbc28fcfe */ |
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t6 = 6.1005386524e-03, /* 0x3bc7e707 */ |
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t7 = -3.6845202558e-03, /* 0xbb7177fe */ |
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t8 = 2.2596477065e-03, /* 0x3b141699 */ |
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t9 = -1.4034647029e-03, /* 0xbab7f476 */ |
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t10 = 8.8108185446e-04, /* 0x3a66f867 */ |
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t11 = -5.3859531181e-04, /* 0xba0d3085 */ |
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t12 = 3.1563205994e-04, /* 0x39a57b6b */ |
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t13 = -3.1275415677e-04, /* 0xb9a3f927 */ |
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t14 = 3.3552918467e-04, /* 0x39afe9f7 */ |
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u0 = -7.7215664089e-02, /* 0xbd9e233f */ |
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u1 = 6.3282704353e-01, /* 0x3f2200f4 */ |
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u2 = 1.4549225569e+00, /* 0x3fba3ae7 */ |
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u3 = 9.7771751881e-01, /* 0x3f7a4bb2 */ |
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u4 = 2.2896373272e-01, /* 0x3e6a7578 */ |
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u5 = 1.3381091878e-02, /* 0x3c5b3c5e */ |
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v1 = 2.4559779167e+00, /* 0x401d2ebe */ |
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v2 = 2.1284897327e+00, /* 0x4008392d */ |
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v3 = 7.6928514242e-01, /* 0x3f44efdf */ |
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v4 = 1.0422264785e-01, /* 0x3dd572af */ |
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v5 = 3.2170924824e-03, /* 0x3b52d5db */ |
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s0 = -7.7215664089e-02, /* 0xbd9e233f */ |
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s1 = 2.1498242021e-01, /* 0x3e5c245a */ |
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s2 = 3.2577878237e-01, /* 0x3ea6cc7a */ |
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s3 = 1.4635047317e-01, /* 0x3e15dce6 */ |
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s4 = 2.6642270386e-02, /* 0x3cda40e4 */ |
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s5 = 1.8402845599e-03, /* 0x3af135b4 */ |
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s6 = 3.1947532989e-05, /* 0x3805ff67 */ |
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r1 = 1.3920053244e+00, /* 0x3fb22d3b */ |
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r2 = 7.2193557024e-01, /* 0x3f38d0c5 */ |
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r3 = 1.7193385959e-01, /* 0x3e300f6e */ |
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r4 = 1.8645919859e-02, /* 0x3c98bf54 */ |
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r5 = 7.7794247773e-04, /* 0x3a4beed6 */ |
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r6 = 7.3266842264e-06, /* 0x36f5d7bd */ |
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w0 = 4.1893854737e-01, /* 0x3ed67f1d */ |
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w1 = 8.3333335817e-02, /* 0x3daaaaab */ |
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w2 = -2.7777778450e-03, /* 0xbb360b61 */ |
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w3 = 7.9365057172e-04, /* 0x3a500cfd */ |
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w4 = -5.9518753551e-04, /* 0xba1c065c */ |
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w5 = 8.3633989561e-04, /* 0x3a5b3dd2 */ |
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w6 = -1.6309292987e-03; /* 0xbad5c4e8 */ |
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static const float zero= 0.0000000000e+00; |
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static float |
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sin_pif(float x) |
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{ |
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float y,z; |
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int n,ix; |
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GET_FLOAT_WORD(ix,x); |
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ix &= 0x7fffffff; |
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if(ix<0x3e800000) return __kernel_sinf(pi*x,zero,0); |
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y = -x; /* x is assume negative */ |
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/* |
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* argument reduction, make sure inexact flag not raised if input |
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* is an integer |
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*/ |
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z = floorf(y); |
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if(z!=y) { /* inexact anyway */ |
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y *= (float)0.5; |
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y = (float)2.0*(y - floorf(y)); /* y = |x| mod 2.0 */ |
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n = (int) (y*(float)4.0); |
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} else { |
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if(ix>=0x4b800000) { |
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y = zero; n = 0; /* y must be even */ |
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} else { |
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if(ix<0x4b000000) z = y+two23; /* exact */ |
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GET_FLOAT_WORD(n,z); |
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n &= 1; |
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y = n; |
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n<<= 2; |
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} |
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} |
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switch (n) { |
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case 0: y = __kernel_sinf(pi*y,zero,0); break; |
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case 1: |
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case 2: y = __kernel_cosf(pi*((float)0.5-y),zero); break; |
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case 3: |
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case 4: y = __kernel_sinf(pi*(one-y),zero,0); break; |
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case 5: |
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case 6: y = -__kernel_cosf(pi*(y-(float)1.5),zero); break; |
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default: y = __kernel_sinf(pi*(y-(float)2.0),zero,0); break; |
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} |
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return -y; |
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} |
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float |
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lgammaf_r(float x, int *signgamp) |
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{ |
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float t,y,z,nadj,p,p1,p2,p3,q,r,w; |
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int i,hx,ix; |
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GET_FLOAT_WORD(hx,x); |
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/* purge off +-inf, NaN, +-0, and negative arguments */ |
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*signgamp = 1; |
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ix = hx&0x7fffffff; |
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✓✓ |
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if(ix>=0x7f800000) return x*x; |
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✓✓ |
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if(ix==0) { |
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✓✓ |
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if(hx<0) |
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*signgamp = -1; |
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return one/zero; |
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} |
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✗✓ |
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if(ix<0x1c800000) { /* |x|<2**-70, return -log(|x|) */ |
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if(hx<0) { |
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*signgamp = -1; |
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return - logf(-x); |
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} else return - logf(x); |
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} |
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✗✓ |
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if(hx<0) { |
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if(ix>=0x4b000000) /* |x|>=2**23, must be -integer */ |
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return one/zero; |
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t = sin_pif(x); |
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if(t==zero) return one/zero; /* -integer */ |
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nadj = logf(pi/fabsf(t*x)); |
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if(t<zero) *signgamp = -1; |
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x = -x; |
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} |
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/* purge off 1 and 2 */ |
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✓✓ |
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if (ix==0x3f800000||ix==0x40000000) r = 0; |
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/* for x < 2.0 */ |
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✗✓ |
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else if(ix<0x40000000) { |
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if(ix<=0x3f666666) { /* lgamma(x) = lgamma(x+1)-log(x) */ |
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r = - logf(x); |
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if(ix>=0x3f3b4a20) {y = one-x; i= 0;} |
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else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;} |
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else {y = x; i=2;} |
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} else { |
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r = zero; |
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if(ix>=0x3fdda618) {y=(float)2.0-x;i=0;} /* [1.7316,2] */ |
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else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */ |
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else {y=x-one;i=2;} |
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} |
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switch(i) { |
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case 0: |
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z = y*y; |
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p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10)))); |
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p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11))))); |
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p = y*p1+p2; |
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r += (p-(float)0.5*y); break; |
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case 1: |
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z = y*y; |
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w = z*y; |
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p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */ |
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p2 = t1+w*(t4+w*(t7+w*(t10+w*t13))); |
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p3 = t2+w*(t5+w*(t8+w*(t11+w*t14))); |
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p = z*p1-(tt-w*(p2+y*p3)); |
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r += (tf + p); break; |
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case 2: |
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p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5))))); |
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p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5)))); |
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r += (-(float)0.5*y + p1/p2); |
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} |
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} |
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✓✗ |
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else if(ix<0x41000000) { /* x < 8.0 */ |
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i = (int)x; |
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t = zero; |
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y = x-(float)i; |
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p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6)))))); |
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q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6))))); |
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r = half*y+p/q; |
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z = one; /* lgamma(1+s) = log(s) + lgamma(s) */ |
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✗✗✗✗
✓✓ |
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switch(i) { |
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case 7: z *= (y+(float)6.0); /* FALLTHRU */ |
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case 6: z *= (y+(float)5.0); /* FALLTHRU */ |
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case 5: z *= (y+(float)4.0); /* FALLTHRU */ |
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case 4: z *= (y+(float)3.0); /* FALLTHRU */ |
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case 3: z *= (y+(float)2.0); /* FALLTHRU */ |
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r += logf(z); break; |
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} |
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/* 8.0 <= x < 2**58 */ |
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} else if (ix < 0x5c800000) { |
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t = logf(x); |
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z = one/x; |
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y = z*z; |
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w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6))))); |
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r = (x-half)*(t-one)+w; |
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} else |
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/* 2**58 <= x <= inf */ |
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r = x*(logf(x)-one); |
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✗✓ |
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if(hx<0) r = nadj - r; |
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return r; |
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} |
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DEF_NONSTD(lgammaf_r); |