/** @file | |
Compute the base 10 logrithm of x. | |
Copyright (c) 2010 - 2011, Intel Corporation. All rights reserved.<BR> | |
This program and the accompanying materials are licensed and made available under | |
the terms and conditions of the BSD License that accompanies this distribution. | |
The full text of the license may be found at | |
http://opensource.org/licenses/bsd-license. | |
THE PROGRAM IS DISTRIBUTED UNDER THE BSD LICENSE ON AN "AS IS" BASIS, | |
WITHOUT WARRANTIES OR REPRESENTATIONS OF ANY KIND, EITHER EXPRESS OR IMPLIED. | |
* ==================================================== | |
* 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 | |
* software is freely granted, provided that this notice | |
* is preserved. | |
* ==================================================== | |
e_log10.c 5.1 93/09/24 | |
NetBSD: e_log10.c,v 1.12 2002/05/26 22:01:51 wiz Exp | |
**/ | |
#include <LibConfig.h> | |
#include <sys/EfiCdefs.h> | |
/* __ieee754_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" | |
#include <errno.h> | |
#if defined(_MSC_VER) /* Handle Microsoft VC++ compiler specifics. */ | |
// potential divide by 0 -- near line 80, (x-x)/zero is on purpose | |
#pragma warning ( disable : 4723 ) | |
#endif | |
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 | |
__ieee754_log10(double x) | |
{ | |
double y,z; | |
int32_t i,k,hx; | |
u_int32_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) { | |
errno = EDOM; | |
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 = ((u_int32_t)k&0x80000000)>>31; | |
hx = (hx&0x000fffff)|((0x3ff-i)<<20); | |
y = (double)(k+i); | |
SET_HIGH_WORD(x,hx); | |
z = y*log10_2lo + ivln10*__ieee754_log(x); | |
return z+y*log10_2hi; | |
} |