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, 107 insertions, 0 deletions

diff --git a/src/math/log2.c b/src/math/log2.c
new file mode 100644
index 00000000..a5b8abdd
--- /dev/null
+++ b/src/math/log2.c
@@ -0,0 +1,107 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_log2.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * 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.
+ * ====================================================
+ */
+/*
+ * Return the base 2 logarithm of x.  See log.c and __log1p.h for most
+ * comments.
+ *
+ * This reduces x to {k, 1+f} exactly as in e_log.c, then calls the kernel,
+ * then does the combining and scaling steps
+ *    log2(x) = (f - 0.5*f*f + k_log1p(f)) / ln2 + k
+ * in not-quite-routine extra precision.
+ */
+
+#include "libm.h"
+#include "__log1p.h"
+
+static const double
+two54   = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
+ivln2hi = 1.44269504072144627571e+00, /* 0x3ff71547, 0x65200000 */
+ivln2lo = 1.67517131648865118353e-10; /* 0x3de705fc, 0x2eefa200 */
+
+static const double zero = 0.0;
+
+double log2(double x)
+{
+	double f,hfsq,hi,lo,r,val_hi,val_lo,w,y;
+	int32_t i,k,hx;
+	uint32_t lx;
+
+	EXTRACT_WORDS(hx, lx, x);
+
+	k = 0;
+	if (hx < 0x00100000) {  /* x < 2**-1022  */
+		if (((hx&0x7fffffff)|lx) == 0)
+			return -two54/zero;  /* log(+-0)=-inf */
+		if (hx < 0)
+			return (x-x)/zero;   /* log(-#) = NaN */
+		/* subnormal number, scale up x */
+		k -= 54;
+		x *= two54;
+		GET_HIGH_WORD(hx, x);
+	}
+	if (hx >= 0x7ff00000)
+		return x+x;
+	if (hx == 0x3ff00000 && lx == 0)
+		return zero;  /* log(1) = +0 */
+	k += (hx>>20) - 1023;
+	hx &= 0x000fffff;
+	i = (hx+0x95f64) & 0x100000;
+	SET_HIGH_WORD(x, hx|(i^0x3ff00000));  /* normalize x or x/2 */
+	k += i>>20;
+	y = (double)k;
+	f = x - 1.0;
+	hfsq = 0.5*f*f;
+	r = __log1p(f);
+
+	/*
+	 * f-hfsq must (for args near 1) be evaluated in extra precision
+	 * to avoid a large cancellation when x is near sqrt(2) or 1/sqrt(2).
+	 * This is fairly efficient since f-hfsq only depends on f, so can
+	 * be evaluated in parallel with R.  Not combining hfsq with R also
+	 * keeps R small (though not as small as a true `lo' term would be),
+	 * so that extra precision is not needed for terms involving R.
+	 *
+	 * Compiler bugs involving extra precision used to break Dekker's
+	 * theorem for spitting f-hfsq as hi+lo, unless double_t was used
+	 * or the multi-precision calculations were avoided when double_t
+	 * has extra precision.  These problems are now automatically
+	 * avoided as a side effect of the optimization of combining the
+	 * Dekker splitting step with the clear-low-bits step.
+	 *
+	 * y must (for args near sqrt(2) and 1/sqrt(2)) be added in extra
+	 * precision to avoid a very large cancellation when x is very near
+	 * these values.  Unlike the above cancellations, this problem is
+	 * specific to base 2.  It is strange that adding +-1 is so much
+	 * harder than adding +-ln2 or +-log10_2.
+	 *
+	 * This uses Dekker's theorem to normalize y+val_hi, so the
+	 * compiler bugs are back in some configurations, sigh.  And I
+	 * don't want to used double_t to avoid them, since that gives a
+	 * pessimization and the support for avoiding the pessimization
+	 * is not yet available.
+	 *
+	 * The multi-precision calculations for the multiplications are
+	 * routine.
+	 */
+	hi = f - hfsq;
+	SET_LOW_WORD(hi, 0);
+	lo = (f - hi) - hfsq + r;
+	val_hi = hi*ivln2hi;
+	val_lo = (lo+hi)*ivln2lo + lo*ivln2hi;
+
+	/* spadd(val_hi, val_lo, y), except for not using double_t: */
+	w = y + val_hi;
+	val_lo += (y - w) + val_hi;
+	val_hi = w;
+
+	return val_lo + val_hi;
+}