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📄 catrig.c(18.56 KB)
📄 catrigf.c(9.27 KB)
📄 catrigl.c(10.37 KB)
📄 e_acos.c(3.38 KB)
📄 e_acosf.c(1.99 KB)
📄 e_acosh.c(1.63 KB)
📄 e_acoshf.c(1.27 KB)
📄 e_acoshl.c(2.19 KB)
📄 e_acosl.c(2.16 KB)
📄 e_asin.c(3.55 KB)
📄 e_asinf.c(1.58 KB)
📄 e_asinl.c(1.85 KB)
📄 e_atan2.c(3.74 KB)
📄 e_atan2f.c(2.63 KB)
📄 e_atan2l.c(3.42 KB)
📄 e_atanh.c(1.64 KB)
📄 e_atanhf.c(1.12 KB)
📄 e_atanhl.c(1.76 KB)
📄 e_cosh.c(2.21 KB)
📄 e_coshf.c(1.45 KB)
📄 e_coshl.c(4 KB)
📄 e_exp.c(5.07 KB)
📄 e_expf.c(2.7 KB)
📄 e_fmod.c(3.34 KB)
📄 e_fmodf.c(2.59 KB)
📄 e_fmodl.c(3.77 KB)
📄 e_gamma.c(725 B)
📄 e_gamma_r.c(801 B)
📄 e_gammaf.c(814 B)
📄 e_gammaf_r.c(890 B)
📄 e_hypot.c(3.22 KB)
📄 e_hypotf.c(2.15 KB)
📄 e_hypotl.c(3.16 KB)
📄 e_j0.c(14.39 KB)
📄 e_j0f.c(10.31 KB)
📄 e_j1.c(14.12 KB)
📄 e_j1f.c(9.98 KB)
📄 e_jn.c(7.08 KB)
📄 e_jnf.c(4.75 KB)
📄 e_lgamma.c(819 B)
📄 e_lgamma_r.c(10.7 KB)
📄 e_lgammaf.c(820 B)
📄 e_lgammaf_r.c(5.82 KB)
📄 e_lgammal.c(599 B)
📄 e_log.c(4.42 KB)
📄 e_log10.c(2.5 KB)
📄 e_log10f.c(1.93 KB)
📄 e_log2.c(3.64 KB)
📄 e_log2f.c(2.37 KB)
📄 e_logf.c(2.36 KB)
📄 e_pow.c(9.84 KB)
📄 e_powf.c(7.34 KB)
📄 e_rem_pio2.c(4.7 KB)
📄 e_rem_pio2f.c(1.96 KB)
📄 e_remainder.c(1.75 KB)
📄 e_remainderf.c(1.41 KB)
📄 e_remainderl.c(1.55 KB)
📄 e_scalb.c(1.07 KB)
📄 e_scalbf.c(1.06 KB)
📄 e_sinh.c(2.03 KB)
📄 e_sinhf.c(1.43 KB)
📄 e_sinhl.c(4.12 KB)
📄 e_sqrt.c(14.12 KB)
📄 e_sqrtf.c(1.91 KB)
📄 e_sqrtl.c(4.28 KB)
📄 fenv-softfloat.h(4.96 KB)
📄 imprecise.c(2.08 KB)
📄 k_cos.c(2.75 KB)
📄 k_cosf.c(1.23 KB)
📄 k_exp.c(3.55 KB)
📄 k_expf.c(2.67 KB)
📄 k_log.h(3.34 KB)
📄 k_logf.h(992 B)
📄 k_rem_pio2.c(15.51 KB)
📄 k_sin.c(2.27 KB)
📄 k_sincos.h(1.7 KB)
📄 k_sincosf.h(1.38 KB)
📄 k_sincosl.h(4.82 KB)
📄 k_sinf.c(1.21 KB)
📄 k_tan.c(3.93 KB)
📄 k_tanf.c(1.97 KB)
📄 math.h(13.92 KB)
📄 math_private.h(24.72 KB)
📄 s_asinh.c(1.64 KB)
📄 s_asinhf.c(1.32 KB)
📄 s_asinhl.c(2.41 KB)
📄 s_atan.c(4.08 KB)
📄 s_atanf.c(2.42 KB)
📄 s_atanl.c(2.32 KB)
📄 s_carg.c(1.55 KB)
📄 s_cargf.c(1.55 KB)
📄 s_cargl.c(1.57 KB)
📄 s_cbrt.c(4.03 KB)
📄 s_cbrtf.c(1.85 KB)
📄 s_cbrtl.c(3.34 KB)
📄 s_ccosh.c(5.01 KB)
📄 s_ccoshf.c(3.08 KB)
📄 s_ceil.c(1.73 KB)
📄 s_ceilf.c(1.24 KB)
📄 s_ceill.c(2.38 KB)
📄 s_cexp.c(2.88 KB)
📄 s_cexpf.c(2.85 KB)
📄 s_cimag.c(1.53 KB)
📄 s_cimagf.c(1.53 KB)
📄 s_cimagl.c(1.55 KB)
📄 s_clog.c(5.06 KB)
📄 s_clogf.c(5.01 KB)
📄 s_clogl.c(5.49 KB)
📄 s_conj.c(1.51 KB)
📄 s_conjf.c(1.52 KB)
📄 s_conjl.c(1.53 KB)
📄 s_copysign.c(808 B)
📄 s_copysignf.c(905 B)
📄 s_copysignl.c(1.57 KB)
📄 s_cos.c(2.19 KB)
📄 s_cosf.c(2.2 KB)
📄 s_cosl.c(2.55 KB)
📄 s_cpow.c(1.8 KB)
📄 s_cpowf.c(1.79 KB)
📄 s_cpowl.c(1.83 KB)
📄 s_cproj.c(1.74 KB)
📄 s_cprojf.c(1.66 KB)
📄 s_cprojl.c(1.68 KB)
📄 s_creal.c(1.45 KB)
📄 s_crealf.c(1.45 KB)
📄 s_creall.c(1.46 KB)
📄 s_csinh.c(5.01 KB)
📄 s_csinhf.c(3.06 KB)
📄 s_csqrt.c(3.29 KB)
📄 s_csqrtf.c(2.65 KB)
📄 s_csqrtl.c(3.78 KB)
📄 s_ctanh.c(4.32 KB)
📄 s_ctanhf.c(2.45 KB)
📄 s_erf.c(11 KB)
📄 s_erff.c(5.11 KB)
📄 s_exp2.c(14.03 KB)
📄 s_exp2f.c(4.14 KB)
📄 s_expm1.c(7.18 KB)
📄 s_expm1f.c(3.41 KB)
📄 s_fabs.c(677 B)
📄 s_fabsf.c(765 B)
📄 s_fabsl.c(1.68 KB)
📄 s_fdim.c(1.7 KB)
📄 s_finite.c(700 B)
📄 s_finitef.c(796 B)
📄 s_floor.c(1.74 KB)
📄 s_floorf.c(1.41 KB)
📄 s_floorl.c(2.38 KB)
📄 s_fma.c(7.92 KB)
📄 s_fmaf.c(2.57 KB)
📄 s_fmal.c(7.38 KB)
📄 s_fmax.c(2.01 KB)
📄 s_fmaxf.c(1.88 KB)
📄 s_fmaxl.c(1.98 KB)
📄 s_fmin.c(2.01 KB)
📄 s_fminf.c(1.88 KB)
📄 s_fminl.c(1.98 KB)
📄 s_frexp.c(1.31 KB)
📄 s_frexpf.c(1.02 KB)
📄 s_frexpl.c(2 KB)
📄 s_ilogb.c(1.14 KB)
📄 s_ilogbf.c(976 B)
📄 s_ilogbl.c(1.21 KB)
📄 s_isfinite.c(1.72 KB)
📄 s_isnan.c(2.1 KB)
📄 s_isnormal.c(1.78 KB)
📄 s_llrint.c(156 B)
📄 s_llrintf.c(157 B)
📄 s_llrintl.c(163 B)
📄 s_llround.c(215 B)
📄 s_llroundf.c(216 B)
📄 s_llroundl.c(222 B)
📄 s_log1p.c(5.6 KB)
📄 s_log1pf.c(3.14 KB)
📄 s_logb.c(1.13 KB)
📄 s_logbf.c(1023 B)
📄 s_logbl.c(1.24 KB)
📄 s_lrint.c(2.1 KB)
📄 s_lrintf.c(151 B)
📄 s_lrintl.c(157 B)
📄 s_lround.c(2.45 KB)
📄 s_lroundf.c(208 B)
📄 s_lroundl.c(214 B)
📄 s_modf.c(1.88 KB)
📄 s_modff.c(1.39 KB)
📄 s_modfl.c(3.41 KB)
📄 s_nan.c(3.32 KB)
📄 s_nearbyint.c(2.29 KB)
📄 s_nextafter.c(2.03 KB)
📄 s_nextafterf.c(1.61 KB)
📄 s_nextafterl.c(2.02 KB)
📄 s_nexttoward.c(1.75 KB)
📄 s_nexttowardf.c(1.42 KB)
📄 s_remquo.c(3.86 KB)
📄 s_remquof.c(3.02 KB)
📄 s_remquol.c(4.42 KB)
📄 s_rint.c(2.33 KB)
📄 s_rintf.c(1.22 KB)
📄 s_rintl.c(2.77 KB)
📄 s_round.c(1.83 KB)
📄 s_roundf.c(1.74 KB)
📄 s_roundl.c(1.84 KB)
📄 s_scalbln.c(1.82 KB)
📄 s_scalbn.c(1.9 KB)
📄 s_scalbnf.c(1.67 KB)
📄 s_scalbnl.c(1.9 KB)
📄 s_signbit.c(1.7 KB)
📄 s_signgam.c(61 B)
📄 s_significand.c(727 B)
📄 s_significandf.c(691 B)
📄 s_sin.c(2.18 KB)
📄 s_sincos.c(1.6 KB)
📄 s_sincosf.c(2.57 KB)
📄 s_sincosl.c(2.67 KB)
📄 s_sinf.c(2.18 KB)
📄 s_sinl.c(2.49 KB)
📄 s_tan.c(2.02 KB)
📄 s_tanf.c(1.97 KB)
📄 s_tanh.c(2.02 KB)
📄 s_tanhf.c(1.39 KB)
📄 s_tanhl.c(5.09 KB)
📄 s_tanl.c(2.6 KB)
📄 s_tgammaf.c(1.75 KB)
📄 s_trunc.c(1.5 KB)
📄 s_truncf.c(1.21 KB)
📄 s_truncl.c(1.61 KB)
📄 w_cabs.c(365 B)
📄 w_cabsf.c(350 B)
📄 w_cabsl.c(357 B)
📄 w_drem.c(211 B)
📄 w_dremf.c(254 B)

Editing: e_lgamma_r.c

/* @(#)e_lgamma_r.c 1.3 95/01/18 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunSoft, 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("$FreeBSD$");

/* __ieee754_lgamma_r(x, signgamp)
 * Reentrant version of the logarithm of the Gamma function
 * with user provide pointer for the sign of Gamma(x).
 *
 * Method:
 *   1. Argument Reduction for 0 < x <= 8
 * 	Since gamma(1+s)=s*gamma(s), for x in [0,8], we may
 * 	reduce x to a number in [1.5,2.5] by
 * 		lgamma(1+s) = log(s) + lgamma(s)
 *	for example,
 *		lgamma(7.3) = log(6.3) + lgamma(6.3)
 *			    = log(6.3*5.3) + lgamma(5.3)
 *			    = log(6.3*5.3*4.3*3.3*2.3) + lgamma(2.3)
 *   2. Polynomial approximation of lgamma around its
 *	minimun ymin=1.461632144968362245 to maintain monotonicity.
 *	On [ymin-0.23, ymin+0.27] (i.e., [1.23164,1.73163]), use
 *		Let z = x-ymin;
 *		lgamma(x) = -1.214862905358496078218 + z^2*poly(z)
 *	where
 *		poly(z) is a 14 degree polynomial.
 *   2. Rational approximation in the primary interval [2,3]
 *	We use the following approximation:
 *		s = x-2.0;
 *		lgamma(x) = 0.5*s + s*P(s)/Q(s)
 *	with accuracy
 *		|P/Q - (lgamma(x)-0.5s)| < 2**-61.71
 *	Our algorithms are based on the following observation
 *
 *                             zeta(2)-1    2    zeta(3)-1    3
 * lgamma(2+s) = s*(1-Euler) + --------- * s  -  --------- * s  + ...
 *                                 2                 3
 *
 *	where Euler = 0.5771... is the Euler constant, which is very
 *	close to 0.5.
 *
 *   3. For x>=8, we have
 *	lgamma(x)~(x-0.5)log(x)-x+0.5*log(2pi)+1/(12x)-1/(360x**3)+....
 *	(better formula:
 *	   lgamma(x)~(x-0.5)*(log(x)-1)-.5*(log(2pi)-1) + ...)
 *	Let z = 1/x, then we approximation
 *		f(z) = lgamma(x) - (x-0.5)(log(x)-1)
 *	by
 *	  			    3       5             11
 *		w = w0 + w1*z + w2*z  + w3*z  + ... + w6*z
 *	where
 *		|w - f(z)| < 2**-58.74
 *
 *   4. For negative x, since (G is gamma function)
 *		-x*G(-x)*G(x) = pi/sin(pi*x),
 * 	we have
 * 		G(x) = pi/(sin(pi*x)*(-x)*G(-x))
 *	since G(-x) is positive, sign(G(x)) = sign(sin(pi*x)) for x<0
 *	Hence, for x<0, signgam = sign(sin(pi*x)) and
 *		lgamma(x) = log(|Gamma(x)|)
 *			  = log(pi/(|x*sin(pi*x)|)) - lgamma(-x);
 *	Note: one should avoid compute pi*(-x) directly in the
 *	      computation of sin(pi*(-x)).
 *
 *   5. Special Cases
 *		lgamma(2+s) ~ s*(1-Euler) for tiny s
 *		lgamma(1) = lgamma(2) = 0
 *		lgamma(x) ~ -log(|x|) for tiny x
 *		lgamma(0) = lgamma(neg.integer) = inf and raise divide-by-zero
 *		lgamma(inf) = inf
 *		lgamma(-inf) = inf (bug for bug compatible with C99!?)
 */

#include <float.h>

#include "math.h"
#include "math_private.h"

static const volatile double vzero = 0;

static const double
zero=  0.00000000000000000000e+00,
half=  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
pi  =  3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
a0  =  7.72156649015328655494e-02, /* 0x3FB3C467, 0xE37DB0C8 */
a1  =  3.22467033424113591611e-01, /* 0x3FD4A34C, 0xC4A60FAD */
a2  =  6.73523010531292681824e-02, /* 0x3FB13E00, 0x1A5562A7 */
a3  =  2.05808084325167332806e-02, /* 0x3F951322, 0xAC92547B */
a4  =  7.38555086081402883957e-03, /* 0x3F7E404F, 0xB68FEFE8 */
a5  =  2.89051383673415629091e-03, /* 0x3F67ADD8, 0xCCB7926B */
a6  =  1.19270763183362067845e-03, /* 0x3F538A94, 0x116F3F5D */
a7  =  5.10069792153511336608e-04, /* 0x3F40B6C6, 0x89B99C00 */
a8  =  2.20862790713908385557e-04, /* 0x3F2CF2EC, 0xED10E54D */
a9  =  1.08011567247583939954e-04, /* 0x3F1C5088, 0x987DFB07 */
a10 =  2.52144565451257326939e-05, /* 0x3EFA7074, 0x428CFA52 */
a11 =  4.48640949618915160150e-05, /* 0x3F07858E, 0x90A45837 */
tc  =  1.46163214496836224576e+00, /* 0x3FF762D8, 0x6356BE3F */
tf  = -1.21486290535849611461e-01, /* 0xBFBF19B9, 0xBCC38A42 */
/* tt = -(tail of tf) */
tt  = -3.63867699703950536541e-18, /* 0xBC50C7CA, 0xA48A971F */
t0  =  4.83836122723810047042e-01, /* 0x3FDEF72B, 0xC8EE38A2 */
t1  = -1.47587722994593911752e-01, /* 0xBFC2E427, 0x8DC6C509 */
t2  =  6.46249402391333854778e-02, /* 0x3FB08B42, 0x94D5419B */
t3  = -3.27885410759859649565e-02, /* 0xBFA0C9A8, 0xDF35B713 */
t4  =  1.79706750811820387126e-02, /* 0x3F9266E7, 0x970AF9EC */
t5  = -1.03142241298341437450e-02, /* 0xBF851F9F, 0xBA91EC6A */
t6  =  6.10053870246291332635e-03, /* 0x3F78FCE0, 0xE370E344 */
t7  = -3.68452016781138256760e-03, /* 0xBF6E2EFF, 0xB3E914D7 */
t8  =  2.25964780900612472250e-03, /* 0x3F6282D3, 0x2E15C915 */
t9  = -1.40346469989232843813e-03, /* 0xBF56FE8E, 0xBF2D1AF1 */
t10 =  8.81081882437654011382e-04, /* 0x3F4CDF0C, 0xEF61A8E9 */
t11 = -5.38595305356740546715e-04, /* 0xBF41A610, 0x9C73E0EC */
t12 =  3.15632070903625950361e-04, /* 0x3F34AF6D, 0x6C0EBBF7 */
t13 = -3.12754168375120860518e-04, /* 0xBF347F24, 0xECC38C38 */
t14 =  3.35529192635519073543e-04, /* 0x3F35FD3E, 0xE8C2D3F4 */
u0  = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */
u1  =  6.32827064025093366517e-01, /* 0x3FE4401E, 0x8B005DFF */
u2  =  1.45492250137234768737e+00, /* 0x3FF7475C, 0xD119BD6F */
u3  =  9.77717527963372745603e-01, /* 0x3FEF4976, 0x44EA8450 */
u4  =  2.28963728064692451092e-01, /* 0x3FCD4EAE, 0xF6010924 */
u5  =  1.33810918536787660377e-02, /* 0x3F8B678B, 0xBF2BAB09 */
v1  =  2.45597793713041134822e+00, /* 0x4003A5D7, 0xC2BD619C */
v2  =  2.12848976379893395361e+00, /* 0x40010725, 0xA42B18F5 */
v3  =  7.69285150456672783825e-01, /* 0x3FE89DFB, 0xE45050AF */
v4  =  1.04222645593369134254e-01, /* 0x3FBAAE55, 0xD6537C88 */
v5  =  3.21709242282423911810e-03, /* 0x3F6A5ABB, 0x57D0CF61 */
s0  = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */
s1  =  2.14982415960608852501e-01, /* 0x3FCB848B, 0x36E20878 */
s2  =  3.25778796408930981787e-01, /* 0x3FD4D98F, 0x4F139F59 */
s3  =  1.46350472652464452805e-01, /* 0x3FC2BB9C, 0xBEE5F2F7 */
s4  =  2.66422703033638609560e-02, /* 0x3F9B481C, 0x7E939961 */
s5  =  1.84028451407337715652e-03, /* 0x3F5E26B6, 0x7368F239 */
s6  =  3.19475326584100867617e-05, /* 0x3F00BFEC, 0xDD17E945 */
r1  =  1.39200533467621045958e+00, /* 0x3FF645A7, 0x62C4AB74 */
r2  =  7.21935547567138069525e-01, /* 0x3FE71A18, 0x93D3DCDC */
r3  =  1.71933865632803078993e-01, /* 0x3FC601ED, 0xCCFBDF27 */
r4  =  1.86459191715652901344e-02, /* 0x3F9317EA, 0x742ED475 */
r5  =  7.77942496381893596434e-04, /* 0x3F497DDA, 0xCA41A95B */
r6  =  7.32668430744625636189e-06, /* 0x3EDEBAF7, 0xA5B38140 */
w0  =  4.18938533204672725052e-01, /* 0x3FDACFE3, 0x90C97D69 */
w1  =  8.33333333333329678849e-02, /* 0x3FB55555, 0x5555553B */
w2  = -2.77777777728775536470e-03, /* 0xBF66C16C, 0x16B02E5C */
w3  =  7.93650558643019558500e-04, /* 0x3F4A019F, 0x98CF38B6 */
w4  = -5.95187557450339963135e-04, /* 0xBF4380CB, 0x8C0FE741 */
w5  =  8.36339918996282139126e-04, /* 0x3F4B67BA, 0x4CDAD5D1 */
w6  = -1.63092934096575273989e-03; /* 0xBF5AB89D, 0x0B9E43E4 */

/*
 * Compute sin(pi*x) without actually doing the pi*x multiplication.
 * sin_pi(x) is only called for x < 0 and |x| < 2**(p-1) where p is
 * the precision of x.
 */
static double
sin_pi(double x)
{
	volatile double vz;
	double y,z;
	int n;

y = -x;

vz = y+0x1p52;			/* depend on 0 <= y < 0x1p52 */
	z = vz-0x1p52;			/* rint(y) for the above range */
	if (z == y)
	    return zero;

vz = y+0x1p50;
	GET_LOW_WORD(n,vz);		/* bits for rounded y (units 0.25) */
	z = vz-0x1p50;			/* y rounded to a multiple of 0.25 */
	if (z > y) {
	    z -= 0.25;			/* adjust to round down */
	    n--;
	}
	n &= 7;				/* octant of y mod 2 */
	y = y - z + n * 0.25;		/* y mod 2 */

switch (n) {
	    case 0:   y =  __kernel_sin(pi*y,zero,0); break;
	    case 1:
	    case 2:   y =  __kernel_cos(pi*(0.5-y),zero); break;
	    case 3:
	    case 4:   y =  __kernel_sin(pi*(one-y),zero,0); break;
	    case 5:
	    case 6:   y = -__kernel_cos(pi*(y-1.5),zero); break;
	    default:  y =  __kernel_sin(pi*(y-2.0),zero,0); break;
	    }
	return -y;
}

double
__ieee754_lgamma_r(double x, int *signgamp)
{
	double nadj,p,p1,p2,p3,q,r,t,w,y,z;
	int32_t hx;
	int i,ix,lx;

EXTRACT_WORDS(hx,lx,x);

/* purge +-Inf and NaNs */
	*signgamp = 1;
	ix = hx&0x7fffffff;
	if(ix>=0x7ff00000) return x*x;

/* purge +-0 and tiny arguments */
	*signgamp = 1-2*((uint32_t)hx>>31);
	if(ix<0x3c700000) {	/* |x|<2**-56, return -log(|x|) */
	    if((ix|lx)==0)
	        return one/vzero;
	    return -__ieee754_log(fabs(x));
	}

/* purge negative integers and start evaluation for other x < 0 */
	if(hx<0) {
	    *signgamp = 1;
	    if(ix>=0x43300000) 	/* |x|>=2**52, must be -integer */
		return one/vzero;
	    t = sin_pi(x);
	    if(t==zero) return one/vzero; /* -integer */
	    nadj = __ieee754_log(pi/fabs(t*x));
	    if(t<zero) *signgamp = -1;
	    x = -x;
	}

/* purge 1 and 2 */
	if((((ix-0x3ff00000)|lx)==0)||(((ix-0x40000000)|lx)==0)) r = 0;
    /* for x < 2.0 */
	else if(ix<0x40000000) {
	    if(ix<=0x3feccccc) { 	/* lgamma(x) = lgamma(x+1)-log(x) */
		r = -__ieee754_log(x);
		if(ix>=0x3FE76944) {y = one-x; i= 0;}
		else if(ix>=0x3FCDA661) {y= x-(tc-one); i=1;}
	  	else {y = x; i=2;}
	    } else {
	  	r = zero;
	        if(ix>=0x3FFBB4C3) {y=2.0-x;i=0;} /* [1.7316,2] */
	        else if(ix>=0x3FF3B4C4) {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-y/2; 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 += p1/p2-y/2;
	    }
	}
    /* x < 8.0 */
	else if(ix<0x40200000) {
	    i = x;
	    y = x-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 = 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_log(z); break;
	    }
    /* 8.0 <= x < 2**56 */
	} else if (ix < 0x43700000) {
	    t = __ieee754_log(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**56 <= x <= inf */
	    r =  x*(__ieee754_log(x)-one);
	if(hx<0) r = nadj - r;
	return r;
}

#if (LDBL_MANT_DIG == 53)
__weak_reference(lgamma_r, lgammal_r);
#endif

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