feat: add gzip and new headers

1 files changed, 248 insertions, 0 deletions

diff --git a/lib/libm/lgammaf_r.c b/lib/libm/lgammaf_r.c
new file mode 100644
index 00000000..4b63298e
--- /dev/null
+++ b/lib/libm/lgammaf_r.c
@@ -0,0 +1,248 @@
+/* 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"
+
+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);