Finalize work on the math library. It's time to do this monster

commit, and deal with problems (if any) in tree.

Note that this adds the following functions.  Ports with hacks might
need adjustments.

nexttoward(3), fma(3), nexttowardf(3), fmaf(3), acoshl(3), asinhl(3),
atanhl(3), coshl(3), sinhl(3), tanhl(3), expl(3), expm1l(3), logl(3),
log10l(3), log1pl(3), log2l(3), modfl(3), cbrtl(3), hypotl(3),
powl(3), erfl(3), erfcl(3), lgammal(3), tgammal(3), ceill(3),
floorl(3), lrintl(3), llrintl(3), roundl(3), lroundl(3), llroundl(3),
truncl(3), fmodl(3), remainderl(3), remquol(3), nextafterl(3),
nexttowardl(3), fmal(3).

With this commit, our library implements all functionality required
by C99.  Documentation bits will follow.

1 files changed, 145 insertions, 0 deletions

diff --git a/lib/libm/src/ld128/e_expl.c b/lib/libm/src/ld128/e_expl.c
new file mode 100644
index 00000000000..6ef65e83a04
--- /dev/null
+++ b/lib/libm/src/ld128/e_expl.c
@@ -0,0 +1,145 @@
+/*	$OpenBSD: e_expl.c,v 1.1 2011/07/06 00:02:42 martynas Exp $	*/
+
+/*
+ * 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.
+ */
+
+/*							expl.c
+ *
+ *	Exponential function, 128-bit 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      +-MAXLOG    100,000     2.6e-34     8.6e-35
+ *
+ *
+ * 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
+ *
+ */
+
+/*	Exponential function	*/
+
+#include <float.h>
+#include <math.h>
+
+/* Pade' coefficients for exp(x) - 1
+   Theoretical peak relative error = 2.2e-37,
+   relative peak error spread = 9.2e-38
+ */
+static long double P[5] = {
+ 3.279723985560247033712687707263393506266E-10L,
+ 6.141506007208645008909088812338454698548E-7L,
+ 2.708775201978218837374512615596512792224E-4L,
+ 3.508710990737834361215404761139478627390E-2L,
+ 9.999999999999999999999999999999999998502E-1L
+};
+static long double Q[6] = {
+ 2.980756652081995192255342779918052538681E-12L,
+ 1.771372078166251484503904874657985291164E-8L,
+ 1.504792651814944826817779302637284053660E-5L,
+ 3.611828913847589925056132680618007270344E-3L,
+ 2.368408864814233538909747618894558968880E-1L,
+ 2.000000000000000000000000000000000000150E0L
+};
+/* C1 + C2 = ln 2 */
+static long double C1 = -6.93145751953125E-1L;
+static long double C2 = -1.428606820309417232121458176568075500134E-6L;
+
+static long double LOG2EL = 1.442695040888963407359924681001892137426646L;
+static long double MAXLOGL = 1.1356523406294143949491931077970764891253E4L;
+static long double MINLOGL = -1.143276959615573793352782661133116431383730e4L;
+static const long double huge = 0x1p10000L;
+#if 0 /* XXX Prevent gcc from erroneously constant folding this. */
+static const long double twom10000 = 0x1p-10000L;
+#else
+static volatile long double twom10000 = 0x1p-10000L;
+#endif
+
+extern long double __polevll(long double, void *, int);
+
+long double
+expl(long double x)
+{
+long double px, xx;
+int n;
+
+if( x > MAXLOGL)
+	return (huge*huge);		/* overflow */
+
+if( x < MINLOGL )
+	return (twom10000*twom10000);	/* underflow */
+
+/* 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, 4 );
+xx = __polevll( xx, Q, 5 );
+x =  px/( xx - px );
+x = 1.0L + x + x;
+
+x = ldexpl( x, n );
+return(x);
+}