feat: add gzip and new headers

1 files changed, 128 insertions, 0 deletions

diff --git a/lib/libm/cbrtl.c b/lib/libm/cbrtl.c
new file mode 100644
index 00000000..12c82f03
--- /dev/null
+++ b/lib/libm/cbrtl.c
@@ -0,0 +1,128 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_cbrtl.c */
+/*-
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ * Copyright (c) 2009-2011, Bruce D. Evans, Steven G. Kargl, David Schultz.
+ *
+ * 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.
+ * ====================================================
+ *
+ * The argument reduction and testing for exceptional cases was
+ * written by Steven G. Kargl with input from Bruce D. Evans
+ * and David A. Schultz.
+ */
+
+#include "libm.h"
+
+#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
+long double cbrtl(long double x)
+{
+	return cbrt(x);
+}
+#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
+static const unsigned B1 = 709958130; /* B1 = (127-127.0/3-0.03306235651)*2**23
+				       */
+
+long double cbrtl(long double x)
+{
+	union ldshape u = { x }, v;
+	union {
+		float f;
+		uint32_t i;
+	} uft;
+	long double r, s, t, w;
+	double_t dr, dt, dx;
+	float_t ft;
+	int e = u.i.se & 0x7fff;
+	int sign = u.i.se & 0x8000;
+
+	/*
+	 * If x = +-Inf, then cbrt(x) = +-Inf.
+	 * If x = NaN, then cbrt(x) = NaN.
+	 */
+	if (e == 0x7fff)
+		return x + x;
+	if (e == 0) {
+		/* Adjust subnormal numbers. */
+		u.f *= 0x1p120;
+		e = u.i.se & 0x7fff;
+		/* If x = +-0, then cbrt(x) = +-0. */
+		if (e == 0)
+			return x;
+		e -= 120;
+	}
+	e -= 0x3fff;
+	u.i.se = 0x3fff;
+	x = u.f;
+	switch (e % 3) {
+	case 1:
+	case -2:
+		x *= 2;
+		e--;
+		break;
+	case 2:
+	case -1:
+		x *= 4;
+		e -= 2;
+		break;
+	}
+	v.f = 1.0;
+	v.i.se = sign | (0x3fff + e / 3);
+
+	/*
+	 * The following is the guts of s_cbrtf, with the handling of
+	 * special values removed and extra care for accuracy not taken,
+	 * but with most of the extra accuracy not discarded.
+	 */
+
+	/* ~5-bit estimate: */
+	uft.f = x;
+	uft.i = (uft.i & 0x7fffffff) / 3 + B1;
+	ft = uft.f;
+
+	/* ~16-bit estimate: */
+	dx = x;
+	dt = ft;
+	dr = dt * dt * dt;
+	dt = dt * (dx + dx + dr) / (dx + dr + dr);
+
+	/* ~47-bit estimate: */
+	dr = dt * dt * dt;
+	dt = dt * (dx + dx + dr) / (dx + dr + dr);
+
+#if LDBL_MANT_DIG == 64
+	/*
+	 * dt is cbrtl(x) to ~47 bits (after x has been reduced to 1 <= x < 8).
+	 * Round it away from zero to 32 bits (32 so that t*t is exact, and
+	 * away from zero for technical reasons).
+	 */
+	t = dt + (0x1.0p32L + 0x1.0p-31L) - 0x1.0p32;
+#elif LDBL_MANT_DIG == 113
+	/*
+	 * Round dt away from zero to 47 bits.  Since we don't trust the 47,
+	 * add 2 47-bit ulps instead of 1 to round up.  Rounding is slow and
+	 * might be avoidable in this case, since on most machines dt will
+	 * have been evaluated in 53-bit precision and the technical reasons
+	 * for rounding up might not apply to either case in cbrtl() since
+	 * dt is much more accurate than needed.
+	 */
+	t = dt + 0x2.0p-46 + 0x1.0p60L - 0x1.0p60;
+#endif
+
+	/*
+	 * Final step Newton iteration to 64 or 113 bits with
+	 * error < 0.667 ulps
+	 */
+	s = t * t;	       /* t*t is exact */
+	r = x / s;	       /* error <= 0.5 ulps; |r| < |t| */
+	w = t + t;	       /* t+t is exact */
+	r = (r - t) / (w + r); /* r-t is exact; w+r ~= 3*t */
+	t = t + t * r;	       /* error <= 0.5 + 0.5/3 + epsilon */
+
+	t *= v.f;
+	return t;
+}
+#endif