feat: add gzip and new headers

1 files changed, 104 insertions, 0 deletions

diff --git a/lib/libm/__cosl.c b/lib/libm/__cosl.c
new file mode 100644
index 00000000..09d42d6b
--- /dev/null
+++ b/lib/libm/__cosl.c
@@ -0,0 +1,104 @@
+/* origin: FreeBSD /usr/src/lib/msun/ld80/k_cosl.c */
+/* origin: FreeBSD /usr/src/lib/msun/ld128/k_cosl.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
+ *
+ * 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.
+ * ====================================================
+ */
+
+#include "libm.h"
+
+#if (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
+#if LDBL_MANT_DIG == 64
+/*
+ * ld80 version of __cos.c.  See __cos.c for most comments.
+ */
+/*
+ * Domain [-0.7854, 0.7854], range ~[-2.43e-23, 2.425e-23]:
+ * |cos(x) - c(x)| < 2**-75.1
+ *
+ * The coefficients of c(x) were generated by a pari-gp script using
+ * a Remez algorithm that searches for the best higher coefficients
+ * after rounding leading coefficients to a specified precision.
+ *
+ * Simpler methods like Chebyshev or basic Remez barely suffice for
+ * cos() in 64-bit precision, because we want the coefficient of x^2
+ * to be precisely -0.5 so that multiplying by it is exact, and plain
+ * rounding of the coefficients of a good polynomial approximation only
+ * gives this up to about 64-bit precision.  Plain rounding also gives
+ * a mediocre approximation for the coefficient of x^4, but a rounding
+ * error of 0.5 ulps for this coefficient would only contribute ~0.01
+ * ulps to the final error, so this is unimportant.  Rounding errors in
+ * higher coefficients are even less important.
+ *
+ * In fact, coefficients above the x^4 one only need to have 53-bit
+ * precision, and this is more efficient.  We get this optimization
+ * almost for free from the complications needed to search for the best
+ * higher coefficients.
+ */
+static const long double C1 = 0.0416666666666666666136L; /*  0xaaaaaaaaaaaaaa9b.0p-68
+							  */
+static const double C2 = -0.0013888888888888874, /* -0x16c16c16c16c10.0p-62 */
+	C3 = 0.000024801587301571716,		 /*  0x1a01a01a018e22.0p-68 */
+	C4 = -0.00000027557319215507120,	 /* -0x127e4fb7602f22.0p-74 */
+	C5 = 0.0000000020876754400407278,	 /*  0x11eed8caaeccf1.0p-81 */
+	C6 = -1.1470297442401303e-11,		 /* -0x19393412bd1529.0p-89 */
+	C7 = 4.7383039476436467e-14;		 /*  0x1aac9d9af5c43e.0p-97 */
+#define POLY(z) \
+	(z *    \
+	 (C1 + z * (C2 + z * (C3 + z * (C4 + z * (C5 + z * (C6 + z * C7)))))))
+#elif LDBL_MANT_DIG == 113
+/*
+ * ld128 version of __cos.c.  See __cos.c for most comments.
+ */
+/*
+ * Domain [-0.7854, 0.7854], range ~[-1.80e-37, 1.79e-37]:
+ * |cos(x) - c(x))| < 2**-122.0
+ *
+ * 113-bit precision requires more care than 64-bit precision, since
+ * simple methods give a minimax polynomial with coefficient for x^2
+ * that is 1 ulp below 0.5, but we want it to be precisely 0.5.  See
+ * above for more details.
+ */
+static const long double C1 = 0.04166666666666666666666666666666658424671L,
+			 C2 = -0.001388888888888888888888888888863490893732L,
+			 C3 = 0.00002480158730158730158730158600795304914210L,
+			 C4 = -0.2755731922398589065255474947078934284324e-6L,
+			 C5 = 0.2087675698786809897659225313136400793948e-8L,
+			 C6 = -0.1147074559772972315817149986812031204775e-10L,
+			 C7 = 0.4779477332386808976875457937252120293400e-13L;
+static const double C8 = -0.1561920696721507929516718307820958119868e-15,
+		    C9 = 0.4110317413744594971475941557607804508039e-18,
+		    C10 = -0.8896592467191938803288521958313920156409e-21,
+		    C11 = 0.1601061435794535138244346256065192782581e-23;
+#define POLY(z)                                                   \
+	(z *                                                      \
+	 (C1 +                                                    \
+	  z * (C2 +                                               \
+	       z * (C3 +                                          \
+		    z * (C4 +                                     \
+			 z * (C5 +                                \
+			      z * (C6 +                           \
+				   z * (C7 +                      \
+					z * (C8 +                 \
+					     z * (C9 + z * (C10 + \
+							    z * C11)))))))))))
+#endif
+
+long double __cosl(long double x, long double y)
+{
+	long double hz, z, r, w;
+
+	z = x * x;
+	r = POLY(z);
+	hz = 0.5 * z;
+	w = 1.0 - hz;
+	return w + (((1.0 - w) - hz) + (z * r - x * y));
+}
+#endif