working on it

05/musl-final/src/math/e_log10.c

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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;
+}