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, 182 insertions, 0 deletions

diff --git a/src/math/log2l.c b/src/math/log2l.c
new file mode 100644
index 00000000..cf08b0a4
--- /dev/null
+++ b/src/math/log2l.c
@@ -0,0 +1,182 @@
+/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_log2l.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.
+ */
+/*
+ *      Base 2 logarithm, long double precision
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, log2l();
+ *
+ * y = log2l( x );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the base 2 logarithm of x.
+ *
+ * The argument is separated into its exponent and fractional
+ * parts.  If the exponent is between -1 and +1, the (natural)
+ * logarithm of the fraction is approximated by
+ *
+ *     log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
+ *
+ * Otherwise, setting  z = 2(x-1)/x+1),
+ *
+ *     log(x) = z + z**3 P(z)/Q(z).
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      0.5, 2.0     30000      9.8e-20     2.7e-20
+ *    IEEE     exp(+-10000)  70000      5.4e-20     2.3e-20
+ *
+ * In the tests over the interval exp(+-10000), the logarithms
+ * of the random arguments were uniformly distributed over
+ * [-10000, +10000].
+ *
+ * ERROR MESSAGES:
+ *
+ * log singularity:  x = 0; returns -INFINITY
+ * log domain:       x < 0; returns NAN
+ */
+
+#include "libm.h"
+
+#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
+long double log2l(long double x)
+{
+	return log2(x);
+}
+#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
+/* Coefficients for ln(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
+ * 1/sqrt(2) <= x < sqrt(2)
+ * Theoretical peak relative error = 6.2e-22
+ */
+static long double P[] = {
+ 4.9962495940332550844739E-1L,
+ 1.0767376367209449010438E1L,
+ 7.7671073698359539859595E1L,
+ 2.5620629828144409632571E2L,
+ 4.2401812743503691187826E2L,
+ 3.4258224542413922935104E2L,
+ 1.0747524399916215149070E2L,
+};
+static long double Q[] = {
+/* 1.0000000000000000000000E0,*/
+ 2.3479774160285863271658E1L,
+ 1.9444210022760132894510E2L,
+ 7.7952888181207260646090E2L,
+ 1.6911722418503949084863E3L,
+ 2.0307734695595183428202E3L,
+ 1.2695660352705325274404E3L,
+ 3.2242573199748645407652E2L,
+};
+
+/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2),
+ * where z = 2(x-1)/(x+1)
+ * 1/sqrt(2) <= x < sqrt(2)
+ * Theoretical peak relative error = 6.16e-22
+ */
+static long double R[4] = {
+ 1.9757429581415468984296E-3L,
+-7.1990767473014147232598E-1L,
+ 1.0777257190312272158094E1L,
+-3.5717684488096787370998E1L,
+};
+static long double S[4] = {
+/* 1.00000000000000000000E0L,*/
+-2.6201045551331104417768E1L,
+ 1.9361891836232102174846E2L,
+-4.2861221385716144629696E2L,
+};
+/* log2(e) - 1 */
+#define LOG2EA 4.4269504088896340735992e-1L
+
+#define SQRTH 0.70710678118654752440L
+
+long double log2l(long double x)
+{
+	volatile long double z;
+	long double y;
+	int e;
+
+	if (isnan(x))
+		return x;
+	if (x == INFINITY)
+		return x;
+	if (x <= 0.0L) {
+		if (x == 0.0L)
+			return -INFINITY;
+		return NAN;
+	}
+
+	/* separate mantissa from exponent */
+	/* Note, frexp is used so that denormal numbers
+	 * will be handled properly.
+	 */
+	x = frexpl(x, &e);
+
+	/* logarithm using log(x) = z + z**3 P(z)/Q(z),
+	 * where z = 2(x-1)/x+1)
+	 */
+	if (e > 2 || e < -2) {
+		if (x < SQRTH) {  /* 2(2x-1)/(2x+1) */
+			e -= 1;
+			z = x - 0.5L;
+			y = 0.5L * z + 0.5L;
+		} else {  /*  2 (x-1)/(x+1)   */
+			z = x - 0.5L;
+			z -= 0.5L;
+			y = 0.5L * x  + 0.5L;
+		}
+		x = z / y;
+		z = x*x;
+		y = x * (z * __polevll(z, R, 3) / __p1evll(z, S, 3));
+		goto done;
+	}
+
+	/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
+	if (x < SQRTH) {
+		e -= 1;
+		x = ldexpl(x, 1) - 1.0L; /*  2x - 1  */
+	} else {
+		x = x - 1.0L;
+	}
+	z = x*x;
+	y = x * (z * __polevll(x, P, 6) / __p1evll(x, Q, 7));
+	y = y - ldexpl(z, -1);   /* -0.5x^2 + ... */
+
+done:
+	/* Multiply log of fraction by log2(e)
+	 * and base 2 exponent by 1
+	 *
+	 * ***CAUTION***
+	 *
+	 * This sequence of operations is critical and it may
+	 * be horribly defeated by some compiler optimizers.
+	 */
+	z = y * LOG2EA;
+	z += x * LOG2EA;
+	z += y;
+	z += x;
+	z += e;
+	return z;
+}
+#endif