/* @(#)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;
}
