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/* @(#)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
* 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 <math.h>
#include <math_private.h>
#include <stdint.h>
static const double two54 = 1.80143985094819840000e+16; /* 0x4350000000000000 */
static const double ivln10 = 4.34294481903251816668e-01; /* 0x3FDBCB7B1526E50E */
static const double log10_2hi = 3.01029995663611771306e-01; /* 0x3FD34413509F6000 */
static const double log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF311F12B36 */
double
__ieee754_log10 (double x)
{
double y, z;
int64_t i, hx;
int32_t k;
EXTRACT_WORDS64 (hx, x);
k = 0;
if (hx < INT64_C(0x0010000000000000))
{ /* x < 2**-1022 */
if (__glibc_unlikely ((hx & UINT64_C(0x7fffffffffffffff)) == 0))
return -two54 / fabs (x); /* log(+-0)=-inf */
if (__glibc_unlikely (hx < 0))
return (x - x) / (x - x); /* log(-#) = NaN */
k -= 54;
x *= two54; /* subnormal number, scale up x */
EXTRACT_WORDS64 (hx, x);
}
/* scale up resulted in a NaN number */
if (__glibc_unlikely (hx >= UINT64_C(0x7ff0000000000000)))
return x + x;
k += (hx >> 52) - 1023;
i = ((uint64_t) k & UINT64_C(0x8000000000000000)) >> 63;
hx = (hx & UINT64_C(0x000fffffffffffff)) | ((0x3ff - i) << 52);
y = (double) (k + i);
INSERT_WORDS64 (x, hx);
z = y * log10_2lo + ivln10 * __ieee754_log (x);
return z + y * log10_2hi;
}
strong_alias (__ieee754_log10, __log10_finite)
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