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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.
* ====================================================
*/
//#include <sys/cdefs.h>
//__FBSDID("$FreeBSD$");
/*
* Return the base 10 logarithm of x. See e_log.c and k_log.h for most
* comments.
*
* log10(x) = (f - 0.5*f*f + k_log1p(f)) / ln10 + k * log10(2)
* in not-quite-routine extra precision.
*/
#include <float.h>
#include "math_private.h"
#include "k_log.h"
static const double
two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
ivln10hi = 4.34294481878168880939e-01, /* 0x3fdbcb7b, 0x15200000 */
ivln10lo = 2.50829467116452752298e-11, /* 0x3dbb9438, 0xca9aadd5 */
log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
static const double zero = 0.0;
static volatile double vzero = 0.0;
double
__ieee754_log10(double x)
{
double f,hfsq,hi,lo,r,val_hi,val_lo,w,y,y2;
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/vzero; /* 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;
if (hx == 0x3ff00000 && lx == 0)
return zero; /* log(1) = +0 */
k += (hx>>20)-1023;
hx &= 0x000fffff;
i = (hx+0x95f64)&0x100000;
SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */
k += (i>>20);
y = (double)k;
f = x - 1.0;
hfsq = 0.5*f*f;
r = k_log1p(f);
/* See e_log2.c for most details. */
hi = f - hfsq;
SET_LOW_WORD(hi,0);
lo = (f - hi) - hfsq + r;
val_hi = hi*ivln10hi;
y2 = y*log10_2hi;
val_lo = y*log10_2lo + (lo+hi)*ivln10lo + lo*ivln10hi;
/*
* Extra precision in for adding y*log10_2hi is not strictly needed
* since there is no very large cancellation near x = sqrt(2) or
* x = 1/sqrt(2), but we do it anyway since it costs little on CPUs
* with some parallelism and it reduces the error for many args.
*/
w = y2 + val_hi;
val_lo += (y2 - w) + val_hi;
val_hi = w;
return val_lo + val_hi;
}