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/* @(#)e_log10.c 5.1 93/09/24 */
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/*
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 * ====================================================
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 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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 *
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 * Developed at SunPro, a Sun Microsystems, Inc. business.
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 * Permission to use, copy, modify, and distribute this
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 * software is freely granted, provided that this notice
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 * is preserved.
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 * ====================================================
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 */
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#ifndef lint
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static char rcsid[] = "$\Id: e_log10.c,v 1.3.6.1 1997/02/23 11:03:06 joerg Exp $";
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#endif
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/* __ieee754_log10(x)
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 * Return the base 10 logarithm of x
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 *
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 * Method :
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 *      Let log10_2hi = leading 40 bits of log10(2) and
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 *          log10_2lo = log10(2) - log10_2hi,
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 *          ivln10   = 1/log(10) rounded.
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 *      Then
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 *              n = ilogb(x),
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 *              if(n<0)  n = n+1;
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 *              x = scalbn(x,-n);
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 *              log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
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 *
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 * Note 1:
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 *      To guarantee log10(10**n)=n, where 10**n is normal, the rounding
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 *      mode must set to Round-to-Nearest.
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 * Note 2:
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 *      [1/log(10)] rounded to 53 bits has error  .198   ulps;
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 *      log10 is monotonic at all binary break points.
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 *
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 * Special cases:
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 *      log10(x) is NaN with signal if x < 0;
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 *      log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
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 *      log10(NaN) is that NaN with no signal;
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 *      log10(10**N) = N  for N=0,1,...,22.
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 *
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 * Constants:
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 * The hexadecimal values are the intended ones for the following constants.
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 * The decimal values may be used, provided that the compiler will convert
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 * from decimal to binary accurately enough to produce the hexadecimal values
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 * shown.
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 */
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#include "math.h"
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#include "math_private.h"
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#ifdef __STDC__
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static const double
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#else
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static double
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#endif
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two54      =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
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ivln10     =  4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
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log10_2hi  =  3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
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log10_2lo  =  3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
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#ifdef __STDC__
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static const double zero   =  0.0;
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#else
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static double zero   =  0.0;
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#endif
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#ifdef __STDC__
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        double __generic___ieee754_log10(double x)
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#else
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        double __generic___ieee754_log10(x)
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        double x;
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#endif
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{
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        double y,z;
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        int32_t i,k,hx;
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        u_int32_t lx;
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        EXTRACT_WORDS(hx,lx,x);
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        k=0;
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        if (hx < 0x00100000) {                  /* x < 2**-1022  */
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            if (((hx&0x7fffffff)|lx)==0)
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                return -two54/zero;             /* log(+-0)=-inf */
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            if (hx<0) return (x-x)/zero;        /* log(-#) = NaN */
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            k -= 54; x *= two54; /* subnormal number, scale up x */
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            GET_HIGH_WORD(hx,x);
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        }
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        if (hx >= 0x7ff00000) return x+x;
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        k += (hx>>20)-1023;
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        i  = ((u_int32_t)k&0x80000000)>>31;
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        hx = (hx&0x000fffff)|((0x3ff-i)<<20);
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        y  = (double)(k+i);
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        SET_HIGH_WORD(x,hx);
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        z  = y*log10_2lo + ivln10*__ieee754_log(x);
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        return  z+y*log10_2hi;
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}