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+
+/* @(#)e_log10.c 1.3 95/01/18 */
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ */
+
+/* log10(x)
+ * Return the base 10 logarithm of x
+ *
+ * Method :
+ * Let log10_2hi = leading 40 bits of log10(2) and
+ * log10_2lo = log10(2) - log10_2hi,
+ * ivln10 = 1/log(10) rounded.
+ * Then
+ * n = ilogb(x),
+ * if(n<0) n = n+1;
+ * x = scalbn(x,-n);
+ * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
+ *
+ * Note 1:
+ * To guarantee log10(10**n)=n, where 10**n is normal, the rounding
+ * mode must set to Round-to-Nearest.
+ * Note 2:
+ * [1/log(10)] rounded to 53 bits has error .198 ulps;
+ * log10 is monotonic at all binary break points.
+ *
+ * Special cases:
+ * log10(x) is NaN with signal if x < 0;
+ * log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
+ * log10(NaN) is that NaN with no signal;
+ * log10(10**N) = N for N=0,1,...,22.
+ *
+ * Constants:
+ * The hexadecimal values are the intended ones for the following constants.
+ * The decimal values may be used, provided that the compiler will convert
+ * from decimal to binary accurately enough to produce the hexadecimal values
+ * shown.
+ */
+
+#include <math.h>
+#include "math_private.h"
+
+static const double
+two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
+ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
+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 y,z;
+ 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 */
+ k -= 54; x *= two54; /* subnormal number, scale up x */
+ GET_HIGH_WORD(hx,x);
+ }
+ if (hx >= 0x7ff00000) return x+x;
+ k += (hx>>20)-1023;
+ i = ((uint32_t)k&0x80000000)>>31;
+ hx = (hx&0x000fffff)|((0x3ff-i)<<20);
+ y = (double)(k+i);
+ SET_HIGH_WORD(x,hx);
+ z = y*log10_2lo + ivln10*log(x);
+ return z+y*log10_2hi;
+}