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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/* __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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2012-03-09 19:29:16 +00:00
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#include <math.h>
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#include <math_private.h>
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1996-03-05 21:41:30 +00:00
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2012-05-14 19:49:42 +00:00
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static const double two54 = 1.80143985094819840000e+16; /* 0x43500000, 0x00000000 */
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static const double ivln10 = 4.34294481903251816668e-01; /* 0x3FDBCB7B, 0x1526E50E */
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static const double log10_2hi = 3.01029995663611771306e-01; /* 0x3FD34413, 0x509F6000 */
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static const double log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
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1996-03-05 21:41:30 +00:00
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2011-10-12 15:27:51 +00:00
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double
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2012-05-14 19:49:42 +00:00
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__ieee754_log10 (double x)
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1996-03-05 21:41:30 +00:00
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{
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2012-05-14 19:49:42 +00:00
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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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1996-03-05 21:41:30 +00:00
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2012-05-14 19:49:42 +00:00
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EXTRACT_WORDS (hx, lx, x);
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1996-03-05 21:41:30 +00:00
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2012-05-14 19:49:42 +00:00
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k = 0;
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if (hx < 0x00100000)
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{ /* x < 2**-1022 */
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if (__builtin_expect (((hx & 0x7fffffff) | lx) == 0, 0))
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return -two54 / (x - x); /* log(+-0)=-inf */
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if (__builtin_expect (hx < 0, 0))
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return (x - x) / (x - x); /* log(-#) = NaN */
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k -= 54;
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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 (__builtin_expect (hx >= 0x7ff00000, 0))
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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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1996-03-05 21:41:30 +00:00
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}
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2012-05-14 19:49:42 +00:00
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2011-10-12 15:27:51 +00:00
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strong_alias (__ieee754_log10, __log10_finite)
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