1 files changed, 285 insertions, 0 deletions
diff --git a/lib/mlibc/options/ansi/musl-generic-math/lgamma_r.c b/lib/mlibc/options/ansi/musl-generic-math/lgamma_r.c
new file mode 100644
index 0000000..84596a3
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+++ b/lib/mlibc/options/ansi/musl-generic-math/lgamma_r.c
@@ -0,0 +1,285 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_lgamma_r.c */
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ *
+ */
+/* 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 "libm.h"
+#include "weak_alias.h"
+//#include "libc.h"
+
+static const double
+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 */
+
+/* sin(pi*x) assuming x > 2^-100, if sin(pi*x)==0 the sign is arbitrary */
+static double sin_pi(double x)
+{
+	int n;
+
+	/* spurious inexact if odd int */
+	x = 2.0*(x*0.5 - floor(x*0.5));  /* x mod 2.0 */
+
+	n = (int)(x*4.0);
+	n = (n+1)/2;
+	x -= n*0.5f;
+	x *= pi;
+
+	switch (n) {
+	default: /* case 4: */
+	case 0: return __sin(x, 0.0, 0);
+	case 1: return __cos(x, 0.0);
+	case 2: return __sin(-x, 0.0, 0);
+	case 3: return -__cos(x, 0.0);
+	}
+}
+
+double __lgamma_r(double x, int *signgamp)
+{
+	union {double f; uint64_t i;} u = {x};
+	double_t t,y,z,nadj,p,p1,p2,p3,q,r,w;
+	uint32_t ix;
+	int sign,i;
+
+	/* purge off +-inf, NaN, +-0, tiny and negative arguments */
+	*signgamp = 1;
+	sign = u.i>>63;
+	ix = u.i>>32 & 0x7fffffff;
+	if (ix >= 0x7ff00000)
+		return x*x;
+	if (ix < (0x3ff-70)<<20) {  /* |x|<2**-70, return -log(|x|) */
+		if(sign) {
+			x = -x;
+			*signgamp = -1;
+		}
+		return -log(x);
+	}
+	if (sign) {
+		x = -x;
+		t = sin_pi(x);
+		if (t == 0.0) /* -integer */
+			return 1.0/(x-x);
+		if (t > 0.0)
+			*signgamp = -1;
+		else
+			t = -t;
+		nadj = log(pi/(t*x));
+	}
+
+	/* purge off 1 and 2 */
+	if ((ix == 0x3ff00000 || ix == 0x40000000) && (uint32_t)u.i == 0)
+		r = 0;
+	/* for x < 2.0 */
+	else if (ix < 0x40000000) {
+		if (ix <= 0x3feccccc) {   /* lgamma(x) = lgamma(x+1)-log(x) */
+			r = -log(x);
+			if (ix >= 0x3FE76944) {
+				y = 1.0 - x;
+				i = 0;
+			} else if (ix >= 0x3FCDA661) {
+				y = x - (tc-1.0);
+				i = 1;
+			} else {
+				y = x;
+				i = 2;
+			}
+		} else {
+			r = 0.0;
+			if (ix >= 0x3FFBB4C3) {  /* [1.7316,2] */
+				y = 2.0 - x;
+				i = 0;
+			} else if(ix >= 0x3FF3B4C4) {  /* [1.23,1.73] */
+				y = x - tc;
+				i = 1;
+			} else {
+				y = x - 1.0;
+				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-0.5*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 = 1.0+y*(v1+y*(v2+y*(v3+y*(v4+y*v5))));
+			r += -0.5*y + p1/p2;
+		}
+	} else if (ix < 0x40200000) {  /* x < 8.0 */
+		i = (int)x;
+		y = x - (double)i;
+		p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6))))));
+		q = 1.0+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6)))));
+		r = 0.5*y+p/q;
+		z = 1.0;    /* lgamma(1+s) = log(s) + lgamma(s) */
+		switch (i) {
+		case 7: z *= y + 6.0;  /* FALLTHRU */
+		case 6: z *= y + 5.0;  /* FALLTHRU */
+		case 5: z *= y + 4.0;  /* FALLTHRU */
+		case 4: z *= y + 3.0;  /* FALLTHRU */
+		case 3: z *= y + 2.0;  /* FALLTHRU */
+			r += log(z);
+			break;
+		}
+	} else if (ix < 0x43900000) {  /* 8.0 <= x < 2**58 */
+		t = log(x);
+		z = 1.0/x;
+		y = z*z;
+		w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6)))));
+		r = (x-0.5)*(t-1.0)+w;
+	} else                         /* 2**58 <= x <= inf */
+		r =  x*(log(x)-1.0);
+	if (sign)
+		r = nadj - r;
+	return r;
+}
+
+weak_alias(__lgamma_r, lgamma_r);