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, 84 insertions, 0 deletions

diff --git a/src/math/log10.c b/src/math/log10.c
new file mode 100644
index 00000000..5422599a
--- /dev/null
+++ b/src/math/log10.c
@@ -0,0 +1,84 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_log10.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 10 logarithm of x.  See e_log.c and k_log.h for most
+ * comments.
+ *
+ *    log10(x) = (f - 0.5*f*f + k_log1p(f)) / ln10 + k * log10(2)
+ * in not-quite-routine extra precision.
+ */
+
+#include "libm.h"
+#include "__log1p.h"
+
+static const double
+two54     = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
+ivln10hi  = 4.34294481878168880939e-01, /* 0x3fdbcb7b, 0x15200000 */
+ivln10lo  = 2.50829467116452752298e-11, /* 0x3dbb9438, 0xca9aadd5 */
+log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
+log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
+
+static const double zero = 0.0;
+
+double log10(double x)
+{
+	double f,hfsq,hi,lo,r,val_hi,val_lo,w,y,y2;
+	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);
+
+	/* See log2.c for details. */
+	hi = f - hfsq;
+	SET_LOW_WORD(hi, 0);
+	lo = (f - hi) - hfsq + r;
+	val_hi = hi*ivln10hi;
+	y2 = y*log10_2hi;
+	val_lo = y*log10_2lo + (lo+hi)*ivln10lo + lo*ivln10hi;
+
+	/*
+	 * Extra precision in for adding y*log10_2hi is not strictly needed
+	 * since there is no very large cancellation near x = sqrt(2) or
+	 * x = 1/sqrt(2), but we do it anyway since it costs little on CPUs
+	 * with some parallelism and it reduces the error for many args.
+	 */
+	w = y2 + val_hi;
+	val_lo += (y2 - w) + val_hi;
+	val_hi = w;
+
+	return val_lo + val_hi;
+}