feat: add gzip and new headers

1 files changed, 314 insertions, 0 deletions

diff --git a/lib/libm/lgamma_r.c b/lib/libm/lgamma_r.c
new file mode 100644
index 00000000..00eeb27b
--- /dev/null
+++ b/lib/libm/lgamma_r.c
@@ -0,0 +1,314 @@
+/* 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"
+
+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);