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, 123 insertions, 0 deletions

diff --git a/src/math/expm1l.c b/src/math/expm1l.c
new file mode 100644
index 00000000..2f94dfa2
--- /dev/null
+++ b/src/math/expm1l.c
@@ -0,0 +1,123 @@
+/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_expm1l.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, minus 1
+ *      Long double precision
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, expm1l();
+ *
+ * y = expm1l( x );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns e (2.71828...) raised to the x power, minus 1.
+ *
+ * Range reduction is accomplished by separating the argument
+ * into an integer k and fraction f such that
+ *
+ *     x    k  f
+ *    e  = 2  e.
+ *
+ * An expansion x + .5 x^2 + x^3 R(x) approximates exp(f) - 1
+ * in the basic range [-0.5 ln 2, 0.5 ln 2].
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE    -45,+MAXLOG   200,000     1.2e-19     2.5e-20
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * expm1l overflow   x > MAXLOG         MAXNUM
+ *
+ */
+
+#include "libm.h"
+
+#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
+long double expm1l(long double x)
+{
+	return expm1(x);
+}
+#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
+static const long double MAXLOGL = 1.1356523406294143949492E4L;
+
+/* exp(x) - 1 = x + 0.5 x^2 + x^3 P(x)/Q(x)
+   -.5 ln 2  <  x  <  .5 ln 2
+   Theoretical peak relative error = 3.4e-22  */
+static const long double
+P0 = -1.586135578666346600772998894928250240826E4L,
+P1 =  2.642771505685952966904660652518429479531E3L,
+P2 = -3.423199068835684263987132888286791620673E2L,
+P3 =  1.800826371455042224581246202420972737840E1L,
+P4 = -5.238523121205561042771939008061958820811E-1L,
+Q0 = -9.516813471998079611319047060563358064497E4L,
+Q1 =  3.964866271411091674556850458227710004570E4L,
+Q2 = -7.207678383830091850230366618190187434796E3L,
+Q3 =  7.206038318724600171970199625081491823079E2L,
+Q4 = -4.002027679107076077238836622982900945173E1L,
+/* Q5 = 1.000000000000000000000000000000000000000E0 */
+/* C1 + C2 = ln 2 */
+C1 = 6.93145751953125E-1L,
+C2 = 1.428606820309417232121458176568075500134E-6L,
+/* ln 2^-65 */
+minarg = -4.5054566736396445112120088E1L,
+huge = 0x1p10000L;
+
+long double expm1l(long double x)
+{
+	long double px, qx, xx;
+	int k;
+
+	/* Overflow.  */
+	if (x > MAXLOGL)
+		return huge*huge;  /* overflow */
+	if (x == 0.0)
+		return x;
+	/* Minimum value.*/
+	if (x < minarg)
+		return -1.0L;
+
+	xx = C1 + C2;
+	/* Express x = ln 2 (k + remainder), remainder not exceeding 1/2. */
+	px = floorl (0.5 + x / xx);
+	k = px;
+	/* remainder times ln 2 */
+	x -= px * C1;
+	x -= px * C2;
+
+	/* Approximate exp(remainder ln 2).*/
+	px = (((( P4 * x + P3) * x + P2) * x + P1) * x + P0) * x;
+	qx = (((( x + Q4) * x + Q3) * x + Q2) * x + Q1) * x + Q0;
+	xx = x * x;
+	qx = x + (0.5 * xx + xx * px / qx);
+
+	/* exp(x) = exp(k ln 2) exp(remainder ln 2) = 2^k exp(remainder ln 2).
+	 We have qx = exp(remainder ln 2) - 1, so
+	 exp(x) - 1  =  2^k (qx + 1) - 1  =  2^k qx + 2^k - 1.  */
+	px = ldexpl(1.0L, k);
+	x = px * qx + (px - 1.0);
+	return x;
+}
+#endif