| /* origin: FreeBSD /usr/src/lib/msun/src/e_lgammaf_r.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 "libm.h" |
| #include "libc.h" |
| |
| static const float |
| 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 */ |
| |
| /* sin(pi*x) assuming x > 2^-100, if sin(pi*x)==0 the sign is arbitrary */ |
| static float sin_pi(float x) |
| { |
| double_t y; |
| int n; |
| |
| /* spurious inexact if odd int */ |
| x = 2*(x*0.5f - floorf(x*0.5f)); /* x mod 2.0 */ |
| |
| n = (int)(x*4); |
| n = (n+1)/2; |
| y = x - n*0.5f; |
| y *= 3.14159265358979323846; |
| switch (n) { |
| default: /* case 4: */ |
| case 0: return __sindf(y); |
| case 1: return __cosdf(y); |
| case 2: return __sindf(-y); |
| case 3: return -__cosdf(y); |
| } |
| } |
| |
| float __lgammaf_r(float x, int *signgamp) |
| { |
| union {float f; uint32_t i;} u = {x}; |
| float t,y,z,nadj,p,p1,p2,p3,q,r,w; |
| uint32_t ix; |
| int i,sign; |
| |
| /* purge off +-inf, NaN, +-0, tiny and negative arguments */ |
| *signgamp = 1; |
| sign = u.i>>31; |
| ix = u.i & 0x7fffffff; |
| if (ix >= 0x7f800000) |
| return x*x; |
| if (ix < 0x35000000) { /* |x| < 2**-21, return -log(|x|) */ |
| if (sign) { |
| *signgamp = -1; |
| x = -x; |
| } |
| return -logf(x); |
| } |
| if (sign) { |
| x = -x; |
| t = sin_pi(x); |
| if (t == 0.0f) /* -integer */ |
| return 1.0f/(x-x); |
| if (t > 0.0f) |
| *signgamp = -1; |
| else |
| t = -t; |
| nadj = logf(pi/(t*x)); |
| } |
| |
| /* purge off 1 and 2 */ |
| if (ix == 0x3f800000 || ix == 0x40000000) |
| r = 0; |
| /* for x < 2.0 */ |
| else if (ix < 0x40000000) { |
| if (ix <= 0x3f666666) { /* lgamma(x) = lgamma(x+1)-log(x) */ |
| r = -logf(x); |
| if (ix >= 0x3f3b4a20) { |
| y = 1.0f - x; |
| i = 0; |
| } else if (ix >= 0x3e6d3308) { |
| y = x - (tc-1.0f); |
| i = 1; |
| } else { |
| y = x; |
| i = 2; |
| } |
| } else { |
| r = 0.0f; |
| if (ix >= 0x3fdda618) { /* [1.7316,2] */ |
| y = 2.0f - x; |
| i = 0; |
| } else if (ix >= 0x3F9da620) { /* [1.23,1.73] */ |
| y = x - tc; |
| i = 1; |
| } else { |
| y = x - 1.0f; |
| 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 - 0.5f*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 = 1.0f+y*(v1+y*(v2+y*(v3+y*(v4+y*v5)))); |
| r += -0.5f*y + p1/p2; |
| } |
| } else if (ix < 0x41000000) { /* x < 8.0 */ |
| i = (int)x; |
| y = x - (float)i; |
| p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6)))))); |
| q = 1.0f+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6))))); |
| r = 0.5f*y+p/q; |
| z = 1.0f; /* lgamma(1+s) = log(s) + lgamma(s) */ |
| switch (i) { |
| case 7: z *= y + 6.0f; /* FALLTHRU */ |
| case 6: z *= y + 5.0f; /* FALLTHRU */ |
| case 5: z *= y + 4.0f; /* FALLTHRU */ |
| case 4: z *= y + 3.0f; /* FALLTHRU */ |
| case 3: z *= y + 2.0f; /* FALLTHRU */ |
| r += logf(z); |
| break; |
| } |
| } else if (ix < 0x5c800000) { /* 8.0 <= x < 2**58 */ |
| t = logf(x); |
| z = 1.0f/x; |
| y = z*z; |
| w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6))))); |
| r = (x-0.5f)*(t-1.0f)+w; |
| } else /* 2**58 <= x <= inf */ |
| r = x*(logf(x)-1.0f); |
| if (sign) |
| r = nadj - r; |
| return r; |
| } |
| |
| weak_alias(__lgammaf_r, lgammaf_r); |
