first commit of the new libm!

thanks to the hard work of Szabolcs Nagy (nsz), identifying the best
(from correctness and license standpoint) implementations from freebsd
and openbsd and cleaning them up! musl should now fully support c99
float and long double math functions, and has near-complete complex
math support. tgmath should also work (fully on gcc-compatible
compilers, and mostly on any c99 compiler).

based largely on commit 0376d44a890fea261506f1fc63833e7a686dca19 from
nsz's libm git repo, with some additions (dummy versions of a few
missing long double complex functions, etc.) by me.

various cleanups still need to be made, including re-adding (if
they're correct) some asm functions that were dropped.

1 files changed, 76 insertions, 0 deletions

diff --git a/src/math/__cosl.c b/src/math/__cosl.c
new file mode 100644
index 00000000..9ea51ecf
--- /dev/null
+++ b/src/math/__cosl.c
@@ -0,0 +1,76 @@
+/* origin: FreeBSD /usr/src/lib/msun/ld80/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_MAX_EXP == 16384
+/*
+ * 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 double one = 1.0;
+
+// FIXME
+/* Long double constants are slow on these arches, and broken on i386. */
+static const volatile double
+C1hi = 0.041666666666666664,            /*  0x15555555555555.0p-57 */
+C1lo = 2.2598839032744733e-18;          /*  0x14d80000000000.0p-111 */
+#define C1      ((long double)C1hi + C1lo)
+
+#if 0
+static const long double
+C1 =  0.0416666666666666666136L;        /*  0xaaaaaaaaaaaaaa9b.0p-68 */
+#endif
+
+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 */
+
+long double __cosl(long double x, long double y)
+{
+	long double hz,z,r,w;
+
+	z  = x*x;
+	r  = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*(C6+z*C7))))));
+	hz = 0.5*z;
+	w  = one-hz;
+	return w + (((one-w)-hz) + (z*r-x*y));
+}
+#endif