| /* e_lgammaf_r.c -- float version of e_lgamma_r.c. |
| * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. |
| * Conversion to float fixed By Steven G. Kargl. |
| */ |
| |
| /* |
| * ==================================================== |
| * 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 <sys/cdefs.h> |
| __FBSDID("$FreeBSD$"); |
| |
| #include "math.h" |
| #include "math_private.h" |
| |
| static const volatile float vzero = 0; |
| |
| static const float |
| zero= 0, |
| half= 0.5, |
| one = 1, |
| pi = 3.1415927410e+00, /* 0x40490fdb */ |
| /* |
| * Domain y in [0x1p-27, 0.27], range ~[-3.4599e-10, 3.4590e-10]: |
| * |(lgamma(2 - y) + 0.5 * y) / y - a(y)| < 2**-31.4 |
| */ |
| a0 = 7.72156641e-02, /* 0x3d9e233f */ |
| a1 = 3.22467119e-01, /* 0x3ea51a69 */ |
| a2 = 6.73484802e-02, /* 0x3d89ee00 */ |
| a3 = 2.06395667e-02, /* 0x3ca9144f */ |
| a4 = 6.98275631e-03, /* 0x3be4cf9b */ |
| a5 = 4.11768444e-03, /* 0x3b86eda4 */ |
| /* |
| * Domain x in [tc-0.24, tc+0.28], range ~[-5.6577e-10, 5.5677e-10]: |
| * |(lgamma(x) - tf) - t(x - tc)| < 2**-30.8. |
| */ |
| tc = 1.46163213e+00, /* 0x3fbb16c3 */ |
| tf = -1.21486291e-01, /* 0xbdf8cdce */ |
| t0 = -2.94064460e-11, /* 0xae0154b7 */ |
| t1 = -2.35939837e-08, /* 0xb2caabb8 */ |
| t2 = 4.83836412e-01, /* 0x3ef7b968 */ |
| t3 = -1.47586212e-01, /* 0xbe1720d7 */ |
| t4 = 6.46013096e-02, /* 0x3d844db1 */ |
| t5 = -3.28450352e-02, /* 0xbd068884 */ |
| t6 = 1.86483748e-02, /* 0x3c98c47a */ |
| t7 = -9.89206228e-03, /* 0xbc221251 */ |
| /* |
| * Domain y in [-0.1, 0.232], range ~[-8.4931e-10, 8.7794e-10]: |
| * |(lgamma(1 + y) + 0.5 * y) / y - u(y) / v(y)| < 2**-31.2 |
| */ |
| u0 = -7.72156641e-02, /* 0xbd9e233f */ |
| u1 = 7.36789703e-01, /* 0x3f3c9e40 */ |
| u2 = 4.95649040e-01, /* 0x3efdc5b6 */ |
| v1 = 1.10958421e+00, /* 0x3f8e06db */ |
| v2 = 2.10598111e-01, /* 0x3e57a708 */ |
| v3 = -1.02995494e-02, /* 0xbc28bf71 */ |
| /* |
| * Domain x in (2, 3], range ~[-5.5189e-11, 5.2317e-11]: |
| * |(lgamma(y+2) - 0.5 * y) / y - s(y)/r(y)| < 2**-35.0 |
| * with y = x - 2. |
| */ |
| s0 = -7.72156641e-02, /* 0xbd9e233f */ |
| s1 = 2.69987404e-01, /* 0x3e8a3bca */ |
| s2 = 1.42851010e-01, /* 0x3e124789 */ |
| s3 = 1.19389519e-02, /* 0x3c439b98 */ |
| r1 = 6.79650068e-01, /* 0x3f2dfd8c */ |
| r2 = 1.16058730e-01, /* 0x3dedb033 */ |
| r3 = 3.75673687e-03, /* 0x3b763396 */ |
| /* |
| * Domain z in [8, 0x1p24], range ~[-1.2640e-09, 1.2640e-09]: |
| * |lgamma(x) - (x - 0.5) * (log(x) - 1) - w(1/x)| < 2**-29.6. |
| */ |
| w0 = 4.18938547e-01, /* 0x3ed67f1d */ |
| w1 = 8.33332464e-02, /* 0x3daaaa9f */ |
| w2 = -2.76129087e-03; /* 0xbb34f6c6 */ |
| |
| static float |
| sin_pif(float x) |
| { |
| volatile float vz; |
| float y,z; |
| int n; |
| |
| y = -x; |
| |
| vz = y+0x1p23F; /* depend on 0 <= y < 0x1p23 */ |
| z = vz-0x1p23F; /* rintf(y) for the above range */ |
| if (z == y) |
| return zero; |
| |
| vz = y+0x1p21F; |
| GET_FLOAT_WORD(n,vz); /* bits for rounded y (units 0.25) */ |
| z = vz-0x1p21F; /* y rounded to a multiple of 0.25 */ |
| if (z > y) { |
| z -= 0.25F; /* adjust to round down */ |
| n--; |
| } |
| n &= 7; /* octant of y mod 2 */ |
| y = y - z + n * 0.25F; /* y mod 2 */ |
| |
| switch (n) { |
| case 0: y = __kernel_sindf(pi*y); break; |
| case 1: |
| case 2: y = __kernel_cosdf(pi*((float)0.5-y)); break; |
| case 3: |
| case 4: y = __kernel_sindf(pi*(one-y)); break; |
| case 5: |
| case 6: y = -__kernel_cosdf(pi*(y-(float)1.5)); break; |
| default: y = __kernel_sindf(pi*(y-(float)2.0)); break; |
| } |
| return -y; |
| } |
| |
| |
| float |
| __ieee754_lgammaf_r(float x, int *signgamp) |
| { |
| float nadj,p,p1,p2,q,r,t,w,y,z; |
| int32_t hx; |
| int i,ix; |
| |
| GET_FLOAT_WORD(hx,x); |
| |
| /* purge +-Inf and NaNs */ |
| *signgamp = 1; |
| ix = hx&0x7fffffff; |
| if(ix>=0x7f800000) return x*x; |
| |
| /* purge +-0 and tiny arguments */ |
| *signgamp = 1-2*((uint32_t)hx>>31); |
| if(ix<0x32000000) { /* |x|<2**-27, return -log(|x|) */ |
| if(ix==0) |
| return one/vzero; |
| return -__ieee754_logf(fabsf(x)); |
| } |
| |
| /* purge negative integers and start evaluation for other x < 0 */ |
| if(hx<0) { |
| *signgamp = 1; |
| if(ix>=0x4b000000) /* |x|>=2**23, must be -integer */ |
| return one/vzero; |
| t = sin_pif(x); |
| if(t==zero) return one/vzero; /* -integer */ |
| nadj = __ieee754_logf(pi/fabsf(t*x)); |
| if(t<zero) *signgamp = -1; |
| x = -x; |
| } |
| |
| /* purge 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 = -__ieee754_logf(x); |
| if(ix>=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=2-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); |
| p2 = z*(a1+z*(a3+z*a5)); |
| p = y*p1+p2; |
| r += p-y/2; break; |
| case 1: |
| p = t0+y*t1+y*y*(t2+y*(t3+y*(t4+y*(t5+y*(t6+y*t7))))); |
| r += tf + p; break; |
| case 2: |
| p1 = y*(u0+y*(u1+y*u2)); |
| p2 = one+y*(v1+y*(v2+y*v3)); |
| r += p1/p2-y/2; |
| } |
| } |
| /* x < 8.0 */ |
| else if(ix<0x41000000) { |
| i = x; |
| y = x-i; |
| p = y*(s0+y*(s1+y*(s2+y*s3))); |
| q = one+y*(r1+y*(r2+y*r3)); |
| r = y/2+p/q; |
| z = one; /* lgamma(1+s) = log(s) + lgamma(s) */ |
| switch(i) { |
| case 7: z *= (y+6); /* FALLTHRU */ |
| case 6: z *= (y+5); /* FALLTHRU */ |
| case 5: z *= (y+4); /* FALLTHRU */ |
| case 4: z *= (y+3); /* FALLTHRU */ |
| case 3: z *= (y+2); /* FALLTHRU */ |
| r += __ieee754_logf(z); break; |
| } |
| /* 8.0 <= x < 2**27 */ |
| } else if (ix < 0x4d000000) { |
| t = __ieee754_logf(x); |
| z = one/x; |
| y = z*z; |
| w = w0+z*(w1+y*w2); |
| r = (x-half)*(t-one)+w; |
| } else |
| /* 2**27 <= x <= inf */ |
| r = x*(__ieee754_logf(x)-one); |
| if(hx<0) r = nadj - r; |
| return r; |
| } |