feat: add gzip and new headers

1 files changed, 341 insertions, 0 deletions

diff --git a/lib/libm/j0f.c b/lib/libm/j0f.c
new file mode 100644
index 00000000..5c7ffcbc
--- /dev/null
+++ b/lib/libm/j0f.c
@@ -0,0 +1,341 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_j0f.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.
+ * ====================================================
+ */
+
+#define _GNU_SOURCE
+#include "libm.h"
+
+static float pzerof(float), qzerof(float);
+
+static const float invsqrtpi = 5.6418961287e-01, /* 0x3f106ebb */
+	tpi = 6.3661974669e-01;			 /* 0x3f22f983 */
+
+static float common(uint32_t ix, float x, int y0)
+{
+	float z, s, c, ss, cc;
+	/*
+	 * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
+	 * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
+	 */
+	s = sinf(x);
+	c = cosf(x);
+	if (y0)
+		c = -c;
+	cc = s + c;
+	if (ix < 0x7f000000) {
+		ss = s - c;
+		z = -cosf(2 * x);
+		if (s * c < 0)
+			cc = z / ss;
+		else
+			ss = z / cc;
+		if (ix < 0x58800000) {
+			if (y0)
+				ss = -ss;
+			cc = pzerof(x) * cc - qzerof(x) * ss;
+		}
+	}
+	return invsqrtpi * cc / sqrtf(x);
+}
+
+/* R0/S0 on [0, 2.00] */
+static const float R02 = 1.5625000000e-02, /* 0x3c800000 */
+	R03 = -1.8997929874e-04,	   /* 0xb947352e */
+	R04 = 1.8295404516e-06,		   /* 0x35f58e88 */
+	R05 = -4.6183270541e-09,	   /* 0xb19eaf3c */
+	S01 = 1.5619102865e-02,		   /* 0x3c7fe744 */
+	S02 = 1.1692678527e-04,		   /* 0x38f53697 */
+	S03 = 5.1354652442e-07,		   /* 0x3509daa6 */
+	S04 = 1.1661400734e-09;		   /* 0x30a045e8 */
+
+float j0f(float x)
+{
+	float z, r, s;
+	uint32_t ix;
+
+	GET_FLOAT_WORD(ix, x);
+	ix &= 0x7fffffff;
+	if (ix >= 0x7f800000)
+		return 1 / (x * x);
+	x = fabsf(x);
+
+	if (ix >= 0x40000000) { /* |x| >= 2 */
+		/* large ulp error near zeros */
+		return common(ix, x, 0);
+	}
+	if (ix >= 0x3a000000) { /* |x| >= 2**-11 */
+		/* up to 4ulp error near 2 */
+		z = x * x;
+		r = z * (R02 + z * (R03 + z * (R04 + z * R05)));
+		s = 1 + z * (S01 + z * (S02 + z * (S03 + z * S04)));
+		return (1 + x / 2) * (1 - x / 2) + z * (r / s);
+	}
+	if (ix >= 0x21800000) /* |x| >= 2**-60 */
+		x = 0.25f * x * x;
+	return 1 - x;
+}
+
+static const float u00 = -7.3804296553e-02, /* 0xbd9726b5 */
+	u01 = 1.7666645348e-01,		    /* 0x3e34e80d */
+	u02 = -1.3818567619e-02,	    /* 0xbc626746 */
+	u03 = 3.4745343146e-04,		    /* 0x39b62a69 */
+	u04 = -3.8140706238e-06,	    /* 0xb67ff53c */
+	u05 = 1.9559013964e-08,		    /* 0x32a802ba */
+	u06 = -3.9820518410e-11,	    /* 0xae2f21eb */
+	v01 = 1.2730483897e-02,		    /* 0x3c509385 */
+	v02 = 7.6006865129e-05,		    /* 0x389f65e0 */
+	v03 = 2.5915085189e-07,		    /* 0x348b216c */
+	v04 = 4.4111031494e-10;		    /* 0x2ff280c2 */
+
+float y0f(float x)
+{
+	float z, u, v;
+	uint32_t ix;
+
+	GET_FLOAT_WORD(ix, x);
+	if ((ix & 0x7fffffff) == 0)
+		return -1 / 0.0f;
+	if (ix >> 31)
+		return 0 / 0.0f;
+	if (ix >= 0x7f800000)
+		return 1 / x;
+	if (ix >= 0x40000000) { /* |x| >= 2.0 */
+		/* large ulp error near zeros */
+		return common(ix, x, 1);
+	}
+	if (ix >= 0x39000000) { /* x >= 2**-13 */
+		/* large ulp error at x ~= 0.89 */
+		z = x * x;
+		u = u00 +
+		    z * (u01 +
+			 z * (u02 +
+			      z * (u03 + z * (u04 + z * (u05 + z * u06)))));
+		v = 1 + z * (v01 + z * (v02 + z * (v03 + z * v04)));
+		return u / v + tpi * (j0f(x) * logf(x));
+	}
+	return u00 + tpi * logf(x);
+}
+
+/* The asymptotic expansions of pzero is
+ *      1 - 9/128 s^2 + 11025/98304 s^4 - ...,  where s = 1/x.
+ * For x >= 2, We approximate pzero by
+ *      pzero(x) = 1 + (R/S)
+ * where  R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10
+ *        S = 1 + pS0*s^2 + ... + pS4*s^10
+ * and
+ *      | pzero(x)-1-R/S | <= 2  ** ( -60.26)
+ */
+static const float pR8[6] = {
+	/* for x in [inf, 8]=1/[0,0.125] */
+	0.0000000000e+00,  /* 0x00000000 */
+	-7.0312500000e-02, /* 0xbd900000 */
+	-8.0816707611e+00, /* 0xc1014e86 */
+	-2.5706311035e+02, /* 0xc3808814 */
+	-2.4852163086e+03, /* 0xc51b5376 */
+	-5.2530439453e+03, /* 0xc5a4285a */
+};
+static const float pS8[5] = {
+	1.1653436279e+02, /* 0x42e91198 */
+	3.8337448730e+03, /* 0x456f9beb */
+	4.0597855469e+04, /* 0x471e95db */
+	1.1675296875e+05, /* 0x47e4087c */
+	4.7627726562e+04, /* 0x473a0bba */
+};
+static const float pR5[6] = {
+	/* for x in [8,4.5454]=1/[0.125,0.22001] */
+	-1.1412546255e-11, /* 0xad48c58a */
+	-7.0312492549e-02, /* 0xbd8fffff */
+	-4.1596107483e+00, /* 0xc0851b88 */
+	-6.7674766541e+01, /* 0xc287597b */
+	-3.3123129272e+02, /* 0xc3a59d9b */
+	-3.4643338013e+02, /* 0xc3ad3779 */
+};
+static const float pS5[5] = {
+	6.0753936768e+01, /* 0x42730408 */
+	1.0512523193e+03, /* 0x44836813 */
+	5.9789707031e+03, /* 0x45bad7c4 */
+	9.6254453125e+03, /* 0x461665c8 */
+	2.4060581055e+03, /* 0x451660ee */
+};
+
+static const float pR3[6] = {
+	/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
+	-2.5470459075e-09, /* 0xb12f081b */
+	-7.0311963558e-02, /* 0xbd8fffb8 */
+	-2.4090321064e+00, /* 0xc01a2d95 */
+	-2.1965976715e+01, /* 0xc1afba52 */
+	-5.8079170227e+01, /* 0xc2685112 */
+	-3.1447946548e+01, /* 0xc1fb9565 */
+};
+static const float pS3[5] = {
+	3.5856033325e+01, /* 0x420f6c94 */
+	3.6151397705e+02, /* 0x43b4c1ca */
+	1.1936077881e+03, /* 0x44953373 */
+	1.1279968262e+03, /* 0x448cffe6 */
+	1.7358093262e+02, /* 0x432d94b8 */
+};
+
+static const float pR2[6] = {
+	/* for x in [2.8570,2]=1/[0.3499,0.5] */
+	-8.8753431271e-08, /* 0xb3be98b7 */
+	-7.0303097367e-02, /* 0xbd8ffb12 */
+	-1.4507384300e+00, /* 0xbfb9b1cc */
+	-7.6356959343e+00, /* 0xc0f4579f */
+	-1.1193166733e+01, /* 0xc1331736 */
+	-3.2336456776e+00, /* 0xc04ef40d */
+};
+static const float pS2[5] = {
+	2.2220300674e+01, /* 0x41b1c32d */
+	1.3620678711e+02, /* 0x430834f0 */
+	2.7047027588e+02, /* 0x43873c32 */
+	1.5387539673e+02, /* 0x4319e01a */
+	1.4657617569e+01, /* 0x416a859a */
+};
+
+static float pzerof(float x)
+{
+	const float *p, *q;
+	float_t z, r, s;
+	uint32_t ix;
+
+	GET_FLOAT_WORD(ix, x);
+	ix &= 0x7fffffff;
+	if (ix >= 0x41000000) {
+		p = pR8;
+		q = pS8;
+	} else if (ix >= 0x409173eb) {
+		p = pR5;
+		q = pS5;
+	} else if (ix >= 0x4036d917) {
+		p = pR3;
+		q = pS3;
+	} else /*ix >= 0x40000000*/ {
+		p = pR2;
+		q = pS2;
+	}
+	z = 1.0f / (x * x);
+	r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5]))));
+	s = 1.0f + z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * q[4]))));
+	return 1.0f + r / s;
+}
+
+/* For x >= 8, the asymptotic expansions of qzero is
+ *      -1/8 s + 75/1024 s^3 - ..., where s = 1/x.
+ * We approximate pzero by
+ *      qzero(x) = s*(-1.25 + (R/S))
+ * where  R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10
+ *        S = 1 + qS0*s^2 + ... + qS5*s^12
+ * and
+ *      | qzero(x)/s +1.25-R/S | <= 2  ** ( -61.22)
+ */
+static const float qR8[6] = {
+	/* for x in [inf, 8]=1/[0,0.125] */
+	0.0000000000e+00, /* 0x00000000 */
+	7.3242187500e-02, /* 0x3d960000 */
+	1.1768206596e+01, /* 0x413c4a93 */
+	5.5767340088e+02, /* 0x440b6b19 */
+	8.8591972656e+03, /* 0x460a6cca */
+	3.7014625000e+04, /* 0x471096a0 */
+};
+static const float qS8[6] = {
+	1.6377603149e+02,  /* 0x4323c6aa */
+	8.0983447266e+03,  /* 0x45fd12c2 */
+	1.4253829688e+05,  /* 0x480b3293 */
+	8.0330925000e+05,  /* 0x49441ed4 */
+	8.4050156250e+05,  /* 0x494d3359 */
+	-3.4389928125e+05, /* 0xc8a7eb69 */
+};
+
+static const float qR5[6] = {
+	/* for x in [8,4.5454]=1/[0.125,0.22001] */
+	1.8408595828e-11, /* 0x2da1ec79 */
+	7.3242180049e-02, /* 0x3d95ffff */
+	5.8356351852e+00, /* 0x40babd86 */
+	1.3511157227e+02, /* 0x43071c90 */
+	1.0272437744e+03, /* 0x448067cd */
+	1.9899779053e+03, /* 0x44f8bf4b */
+};
+static const float qS5[6] = {
+	8.2776611328e+01,  /* 0x42a58da0 */
+	2.0778142090e+03,  /* 0x4501dd07 */
+	1.8847289062e+04,  /* 0x46933e94 */
+	5.6751113281e+04,  /* 0x475daf1d */
+	3.5976753906e+04,  /* 0x470c88c1 */
+	-5.3543427734e+03, /* 0xc5a752be */
+};
+
+static const float qR3[6] = {
+	/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
+	4.3774099900e-09, /* 0x3196681b */
+	7.3241114616e-02, /* 0x3d95ff70 */
+	3.3442313671e+00, /* 0x405607e3 */
+	4.2621845245e+01, /* 0x422a7cc5 */
+	1.7080809021e+02, /* 0x432acedf */
+	1.6673394775e+02, /* 0x4326bbe4 */
+};
+static const float qS3[6] = {
+	4.8758872986e+01,  /* 0x42430916 */
+	7.0968920898e+02,  /* 0x44316c1c */
+	3.7041481934e+03,  /* 0x4567825f */
+	6.4604252930e+03,  /* 0x45c9e367 */
+	2.5163337402e+03,  /* 0x451d4557 */
+	-1.4924745178e+02, /* 0xc3153f59 */
+};
+
+static const float qR2[6] = {
+	/* for x in [2.8570,2]=1/[0.3499,0.5] */
+	1.5044444979e-07, /* 0x342189db */
+	7.3223426938e-02, /* 0x3d95f62a */
+	1.9981917143e+00, /* 0x3fffc4bf */
+	1.4495602608e+01, /* 0x4167edfd */
+	3.1666231155e+01, /* 0x41fd5471 */
+	1.6252708435e+01, /* 0x4182058c */
+};
+static const float qS2[6] = {
+	3.0365585327e+01,  /* 0x41f2ecb8 */
+	2.6934811401e+02,  /* 0x4386ac8f */
+	8.4478375244e+02,  /* 0x44533229 */
+	8.8293585205e+02,  /* 0x445cbbe5 */
+	2.1266638184e+02,  /* 0x4354aa98 */
+	-5.3109550476e+00, /* 0xc0a9f358 */
+};
+
+static float qzerof(float x)
+{
+	const float *p, *q;
+	float_t s, r, z;
+	uint32_t ix;
+
+	GET_FLOAT_WORD(ix, x);
+	ix &= 0x7fffffff;
+	if (ix >= 0x41000000) {
+		p = qR8;
+		q = qS8;
+	} else if (ix >= 0x409173eb) {
+		p = qR5;
+		q = qS5;
+	} else if (ix >= 0x4036d917) {
+		p = qR3;
+		q = qS3;
+	} else /*ix >= 0x40000000*/ {
+		p = qR2;
+		q = qS2;
+	}
+	z = 1.0f / (x * x);
+	r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5]))));
+	s = 1.0f +
+	    z * (q[0] +
+		 z * (q[1] + z * (q[2] + z * (q[3] + z * (q[4] + z * q[5])))));
+	return (-.125f + r / s) / x;
+}