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;
+}