/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*
* ***** BEGIN LICENSE BLOCK *****
* Version: MPL 1.1/GPL 2.0/LGPL 2.1
*
* The contents of this file are subject to the Mozilla Public License Version
* 1.1 (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
* http://www.mozilla.org/MPL/
*
* Software distributed under the License is distributed on an "AS IS" basis,
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
* for the specific language governing rights and limitations under the
* License.
*
* The Original Code is Mozilla Communicator client code, released
* March 31, 1998.
*
* The Initial Developer of the Original Code is
* Sun Microsystems, Inc.
* Portions created by the Initial Developer are Copyright (C) 1998
* the Initial Developer. All Rights Reserved.
*
* Contributor(s):
*
* Alternatively, the contents of this file may be used under the terms of
* either of the GNU General Public License Version 2 or later (the "GPL"),
* or the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
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/* @(#)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.
* ====================================================
*/
/* __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 "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
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 double zero = 0.0;
#ifdef __STDC__
double __ieee754_log10(double x)
#else
double __ieee754_log10(x)
double x;
#endif
{
fd_twoints u;
double y,z;
int i,k,hx;
unsigned lx;
u.d = x;
hx = __HI(u); /* high word of x */
lx = __LO(u); /* low word of 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 */
u.d = x;
hx = __HI(u); /* high word of x */
}
if (hx >= 0x7ff00000) return x+x;
k += (hx>>20)-1023;
i = ((unsigned)k&0x80000000)>>31;
hx = (hx&0x000fffff)|((0x3ff-i)<<20);
y = (double)(k+i);
u.d = x;
__HI(u) = hx;
x = u.d;
z = y*log10_2lo + ivln10*__ieee754_log(x);
return z+y*log10_2hi;
}