mirror of
https://sourceware.org/git/glibc.git
synced 2024-11-15 01:21:06 +00:00
129 lines
4.1 KiB
C
129 lines
4.1 KiB
C
/* Adapted for log2 by Ulrich Drepper <drepper@cygnus.com>. */
|
|
/*
|
|
* ====================================================
|
|
* 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_log2(x)
|
|
* Return the logarithm to base 2 of x
|
|
*
|
|
* Method :
|
|
* 1. Argument Reduction: find k and f such that
|
|
* x = 2^k * (1+f),
|
|
* where sqrt(2)/2 < 1+f < sqrt(2) .
|
|
*
|
|
* 2. Approximation of log(1+f).
|
|
* Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
|
|
* = 2s + 2/3 s**3 + 2/5 s**5 + .....,
|
|
* = 2s + s*R
|
|
* We use a special Reme algorithm on [0,0.1716] to generate
|
|
* a polynomial of degree 14 to approximate R The maximum error
|
|
* of this polynomial approximation is bounded by 2**-58.45. In
|
|
* other words,
|
|
* 2 4 6 8 10 12 14
|
|
* R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s
|
|
* (the values of Lg1 to Lg7 are listed in the program)
|
|
* and
|
|
* | 2 14 | -58.45
|
|
* | Lg1*s +...+Lg7*s - R(z) | <= 2
|
|
* | |
|
|
* Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
|
|
* In order to guarantee error in log below 1ulp, we compute log
|
|
* by
|
|
* log(1+f) = f - s*(f - R) (if f is not too large)
|
|
* log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy)
|
|
*
|
|
* 3. Finally, log(x) = k + log(1+f).
|
|
* = k+(f-(hfsq-(s*(hfsq+R))))
|
|
*
|
|
* Special cases:
|
|
* log2(x) is NaN with signal if x < 0 (including -INF) ;
|
|
* log2(+INF) is +INF; log(0) is -INF with signal;
|
|
* log2(NaN) is that NaN with no signal.
|
|
*
|
|
* 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 ln2 = 0.69314718055994530942;
|
|
static const double two54 = 1.80143985094819840000e+16; /* 43500000 00000000 */
|
|
static const double Lg1 = 6.666666666666735130e-01; /* 3FE55555 55555593 */
|
|
static const double Lg2 = 3.999999999940941908e-01; /* 3FD99999 9997FA04 */
|
|
static const double Lg3 = 2.857142874366239149e-01; /* 3FD24924 94229359 */
|
|
static const double Lg4 = 2.222219843214978396e-01; /* 3FCC71C5 1D8E78AF */
|
|
static const double Lg5 = 1.818357216161805012e-01; /* 3FC74664 96CB03DE */
|
|
static const double Lg6 = 1.531383769920937332e-01; /* 3FC39A09 D078C69F */
|
|
static const double Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
|
|
|
|
static const double zero = 0.0;
|
|
|
|
double
|
|
__ieee754_log2 (double x)
|
|
{
|
|
double hfsq, f, s, z, R, w, t1, t2, dk;
|
|
int32_t k, hx, i, j;
|
|
u_int32_t lx;
|
|
|
|
EXTRACT_WORDS (hx, lx, x);
|
|
|
|
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 */
|
|
GET_HIGH_WORD (hx, x);
|
|
}
|
|
if (__builtin_expect (hx >= 0x7ff00000, 0))
|
|
return x + x;
|
|
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);
|
|
dk = (double) k;
|
|
f = x - 1.0;
|
|
if ((0x000fffff & (2 + hx)) < 3)
|
|
{ /* |f| < 2**-20 */
|
|
if (f == zero)
|
|
return dk;
|
|
R = f * f * (0.5 - 0.33333333333333333 * f);
|
|
return dk - (R - f) / ln2;
|
|
}
|
|
s = f / (2.0 + f);
|
|
z = s * s;
|
|
i = hx - 0x6147a;
|
|
w = z * z;
|
|
j = 0x6b851 - hx;
|
|
t1 = w * (Lg2 + w * (Lg4 + w * Lg6));
|
|
t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7)));
|
|
i |= j;
|
|
R = t2 + t1;
|
|
if (i > 0)
|
|
{
|
|
hfsq = 0.5 * f * f;
|
|
return dk - ((hfsq - (s * (hfsq + R))) - f) / ln2;
|
|
}
|
|
else
|
|
{
|
|
return dk - ((s * (f - R)) - f) / ln2;
|
|
}
|
|
}
|
|
|
|
strong_alias (__ieee754_log2, __log2_finite)
|