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, 127 insertions, 0 deletions

diff --git a/src/math/expl.c b/src/math/expl.c
new file mode 100644
index 00000000..898cf1a5
--- /dev/null
+++ b/src/math/expl.c
@@ -0,0 +1,127 @@
+/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_expl.c */
+/*
+ * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
+ *
+ * Permission to use, copy, modify, and distribute this software for any
+ * purpose with or without fee is hereby granted, provided that the above
+ * copyright notice and this permission notice appear in all copies.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
+ * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
+ * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
+ * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
+ * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
+ * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
+ * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
+ */
+/*
+ *      Exponential function, long double precision
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, expl();
+ *
+ * y = expl( x );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns e (2.71828...) raised to the x power.
+ *
+ * Range reduction is accomplished by separating the argument
+ * into an integer k and fraction f such that
+ *
+ *     x    k  f
+ *    e  = 2  e.
+ *
+ * A Pade' form of degree 2/3 is used to approximate exp(f) - 1
+ * in the basic range [-0.5 ln 2, 0.5 ln 2].
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      +-10000     50000       1.12e-19    2.81e-20
+ *
+ *
+ * Error amplification in the exponential function can be
+ * a serious matter.  The error propagation involves
+ * exp( X(1+delta) ) = exp(X) ( 1 + X*delta + ... ),
+ * which shows that a 1 lsb error in representing X produces
+ * a relative error of X times 1 lsb in the function.
+ * While the routine gives an accurate result for arguments
+ * that are exactly represented by a long double precision
+ * computer number, the result contains amplified roundoff
+ * error for large arguments not exactly represented.
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * exp underflow    x < MINLOG         0.0
+ * exp overflow     x > MAXLOG         MAXNUM
+ *
+ */
+
+#include "libm.h"
+
+#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
+long double expl(long double x)
+{
+	return exp(x);
+}
+#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
+
+static long double P[3] = {
+ 1.2617719307481059087798E-4L,
+ 3.0299440770744196129956E-2L,
+ 9.9999999999999999991025E-1L,
+};
+static long double Q[4] = {
+ 3.0019850513866445504159E-6L,
+ 2.5244834034968410419224E-3L,
+ 2.2726554820815502876593E-1L,
+ 2.0000000000000000000897E0L,
+};
+static const long double
+C1 = 6.9314575195312500000000E-1L,
+C2 = 1.4286068203094172321215E-6L,
+MAXLOGL = 1.1356523406294143949492E4L,
+MINLOGL = -1.13994985314888605586758E4L,
+LOG2EL = 1.4426950408889634073599E0L;
+
+long double expl(long double x)
+{
+	long double px, xx;
+	int n;
+
+	if (isnan(x))
+		return x;
+	if (x > MAXLOGL)
+		return INFINITY;
+	if (x < MINLOGL)
+		return 0.0L;
+
+	/* Express e**x = e**g 2**n
+	 *   = e**g e**(n loge(2))
+	 *   = e**(g + n loge(2))
+	 */
+	px = floorl(LOG2EL * x + 0.5L); /* floor() truncates toward -infinity. */
+	n = px;
+	x -= px * C1;
+	x -= px * C2;
+
+	/* rational approximation for exponential
+	 * of the fractional part:
+	 * e**x =  1 + 2x P(x**2)/(Q(x**2) - P(x**2))
+	 */
+	xx = x * x;
+	px = x * __polevll(xx, P, 2);
+	x =  px/(__polevll(xx, Q, 3) - px);
+	x = 1.0L + ldexpl(x, 1);
+	x = ldexpl(x, n);
+	return x;
+}
+#endif