1996-03-05 21:41:30 +00:00
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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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1997-07-22 00:10:33 +00:00
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* software is freely granted, provided that this notice
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1996-03-05 21:41:30 +00:00
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* is preserved.
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* ====================================================
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*/
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#if defined(LIBM_SCCS) && !defined(lint)
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static char rcsid[] = "$NetBSD: e_log10.c,v 1.9 1995/05/10 20:45:51 jtc 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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1997-07-22 00:10:33 +00:00
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*
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1996-03-05 21:41:30 +00:00
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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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1997-07-22 00:10:33 +00:00
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* n = ilogb(x),
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1996-03-05 21:41:30 +00:00
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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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1997-07-22 00:10:33 +00:00
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* To guarantee log10(10**n)=n, where 10**n is normal, the rounding
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1996-03-05 21:41:30 +00:00
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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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1997-07-22 00:10:33 +00:00
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* log10(x) is NaN with signal if x < 0;
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1996-03-05 21:41:30 +00:00
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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 __ieee754_log10(double x)
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#else
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double __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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1997-07-22 00:10:33 +00:00
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if (hx < 0x00100000) { /* x < 2**-1022 */
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1996-03-05 21:41:30 +00:00
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if (((hx&0x7fffffff)|lx)==0)
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1997-07-22 00:10:33 +00:00
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return -two54/(x-x); /* log(+-0)=-inf */
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if (hx<0) return (x-x)/(x-x); /* log(-#) = NaN */
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1996-03-05 21:41:30 +00:00
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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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}
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