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glibc  2.9
e_log10.c
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00001 /* @(#)e_log10.c 5.1 93/09/24 */
00002 /*
00003  * ====================================================
00004  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
00005  *
00006  * Developed at SunPro, a Sun Microsystems, Inc. business.
00007  * Permission to use, copy, modify, and distribute this
00008  * software is freely granted, provided that this notice
00009  * is preserved.
00010  * ====================================================
00011  */
00012 
00013 #if defined(LIBM_SCCS) && !defined(lint)
00014 static char rcsid[] = "$NetBSD: e_log10.c,v 1.9 1995/05/10 20:45:51 jtc Exp $";
00015 #endif
00016 
00017 /* __ieee754_log10(x)
00018  * Return the base 10 logarithm of x
00019  *
00020  * Method :
00021  *     Let log10_2hi = leading 40 bits of log10(2) and
00022  *         log10_2lo = log10(2) - log10_2hi,
00023  *         ivln10   = 1/log(10) rounded.
00024  *     Then
00025  *            n = ilogb(x),
00026  *            if(n<0)  n = n+1;
00027  *            x = scalbn(x,-n);
00028  *            log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
00029  *
00030  * Note 1:
00031  *     To guarantee log10(10**n)=n, where 10**n is normal, the rounding
00032  *     mode must set to Round-to-Nearest.
00033  * Note 2:
00034  *     [1/log(10)] rounded to 53 bits has error  .198   ulps;
00035  *     log10 is monotonic at all binary break points.
00036  *
00037  * Special cases:
00038  *     log10(x) is NaN with signal if x < 0;
00039  *     log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
00040  *     log10(NaN) is that NaN with no signal;
00041  *     log10(10**N) = N  for N=0,1,...,22.
00042  *
00043  * Constants:
00044  * The hexadecimal values are the intended ones for the following constants.
00045  * The decimal values may be used, provided that the compiler will convert
00046  * from decimal to binary accurately enough to produce the hexadecimal values
00047  * shown.
00048  */
00049 
00050 #include "math.h"
00051 #include "math_private.h"
00052 
00053 #ifdef __STDC__
00054 static const double
00055 #else
00056 static double
00057 #endif
00058 two54      =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
00059 ivln10     =  4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
00060 log10_2hi  =  3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
00061 log10_2lo  =  3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
00062 
00063 #ifdef __STDC__
00064 static const double zero   =  0.0;
00065 #else
00066 static double zero   =  0.0;
00067 #endif
00068 
00069 #ifdef __STDC__
00070        double __ieee754_log10(double x)
00071 #else
00072        double __ieee754_log10(x)
00073        double x;
00074 #endif
00075 {
00076        double y,z;
00077        int32_t i,k,hx;
00078        u_int32_t lx;
00079 
00080        EXTRACT_WORDS(hx,lx,x);
00081 
00082         k=0;
00083         if (hx < 0x00100000) {                   /* x < 2**-1022  */
00084             if (((hx&0x7fffffff)|lx)==0)
00085                 return -two54/(x-x);             /* log(+-0)=-inf */
00086             if (hx<0) return (x-x)/(x-x); /* log(-#) = NaN */
00087             k -= 54; x *= two54; /* subnormal number, scale up x */
00088            GET_HIGH_WORD(hx,x);
00089         }
00090        if (hx >= 0x7ff00000) return x+x;
00091        k += (hx>>20)-1023;
00092        i  = ((u_int32_t)k&0x80000000)>>31;
00093         hx = (hx&0x000fffff)|((0x3ff-i)<<20);
00094         y  = (double)(k+i);
00095        SET_HIGH_WORD(x,hx);
00096        z  = y*log10_2lo + ivln10*__ieee754_log(x);
00097        return  z+y*log10_2hi;
00098 }