1996-03-05 21:41:30 +00:00
|
|
|
/* @(#)e_log10.c 5.1 93/09/24 */
|
|
|
|
|
/*
|
|
|
|
|
* ====================================================
|
|
|
|
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
|
|
|
|
*
|
|
|
|
|
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
|
|
|
|
* Permission to use, copy, modify, and distribute this
|
1997-07-22 00:10:33 +00:00
|
|
|
* software is freely granted, provided that this notice
|
1996-03-05 21:41:30 +00:00
|
|
|
* is preserved.
|
|
|
|
|
* ====================================================
|
|
|
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* __ieee754_log10(x)
|
|
|
|
|
* Return the base 10 logarithm of x
|
1997-07-22 00:10:33 +00:00
|
|
|
*
|
1996-03-05 21:41:30 +00:00
|
|
|
* Method :
|
|
|
|
|
* Let log10_2hi = leading 40 bits of log10(2) and
|
|
|
|
|
* log10_2lo = log10(2) - log10_2hi,
|
|
|
|
|
* ivln10 = 1/log(10) rounded.
|
|
|
|
|
* Then
|
1997-07-22 00:10:33 +00:00
|
|
|
* n = ilogb(x),
|
1996-03-05 21:41:30 +00:00
|
|
|
* if(n<0) n = n+1;
|
|
|
|
|
* x = scalbn(x,-n);
|
|
|
|
|
* log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
|
|
|
|
|
*
|
|
|
|
|
* Note 1:
|
1997-07-22 00:10:33 +00:00
|
|
|
* To guarantee log10(10**n)=n, where 10**n is normal, the rounding
|
1996-03-05 21:41:30 +00:00
|
|
|
* 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:
|
1997-07-22 00:10:33 +00:00
|
|
|
* log10(x) is NaN with signal if x < 0;
|
1996-03-05 21:41:30 +00:00
|
|
|
* 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;
|
|
|
|
|
|
2011-10-12 15:27:51 +00:00
|
|
|
double
|
|
|
|
|
__ieee754_log10(double x)
|
1996-03-05 21:41:30 +00:00
|
|
|
{
|
|
|
|
|
double y,z;
|
|
|
|
|
int32_t i,k,hx;
|
|
|
|
|
u_int32_t lx;
|
|
|
|
|
|
|
|
|
|
EXTRACT_WORDS(hx,lx,x);
|
|
|
|
|
|
2011-10-12 15:27:51 +00:00
|
|
|
k=0;
|
|
|
|
|
if (hx < 0x00100000) { /* x < 2**-1022 */
|
|
|
|
|
if (__builtin_expect(((hx&0x7fffffff)|lx)==0, 0))
|
|
|
|
|
return -two54/(x-x); /* log(+-0)=-inf */
|
|
|
|
|
if (__builtin_expect(hx<0, 0))
|
|
|
|
|
return (x-x)/(x-x); /* log(-#) = NaN */
|
|
|
|
|
k -= 54; x *= two54; /* subnormal number, scale up x */
|
1996-03-05 21:41:30 +00:00
|
|
|
GET_HIGH_WORD(hx,x);
|
2011-10-12 15:27:51 +00:00
|
|
|
}
|
|
|
|
|
if (__builtin_expect(hx >= 0x7ff00000, 0)) return x+x;
|
1996-03-05 21:41:30 +00:00
|
|
|
k += (hx>>20)-1023;
|
|
|
|
|
i = ((u_int32_t)k&0x80000000)>>31;
|
2011-10-12 15:27:51 +00:00
|
|
|
hx = (hx&0x000fffff)|((0x3ff-i)<<20);
|
|
|
|
|
y = (double)(k+i);
|
1996-03-05 21:41:30 +00:00
|
|
|
SET_HIGH_WORD(x,hx);
|
|
|
|
|
z = y*log10_2lo + ivln10*__ieee754_log(x);
|
|
|
|
|
return z+y*log10_2hi;
|
|
|
|
|
}
|
2011-10-12 15:27:51 +00:00
|
|
|
strong_alias (__ieee754_log10, __log10_finite)
|
