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/* origin: FreeBSD /usr/src/lib/msun/src/e_log10f.c */
/*
* ====================================================
* 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.
* ====================================================
*/
/*
* See comments in log10.c.
*/
#include <math.h>
#include <stdint.h>
static const float ivln10hi = 4.3432617188e-01, /* 0x3ede6000 */
ivln10lo = -3.1689971365e-05, /* 0xb804ead9 */
log10_2hi = 3.0102920532e-01, /* 0x3e9a2080 */
log10_2lo = 7.9034151668e-07, /* 0x355427db */
/* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]).
*/
Lg1 = 0xaaaaaa.0p-24, /* 0.66666662693 */
Lg2 = 0xccce13.0p-25, /* 0.40000972152 */
Lg3 = 0x91e9ee.0p-25, /* 0.28498786688 */
Lg4 = 0xf89e26.0p-26; /* 0.24279078841 */
float log10f(float x)
{
union {
float f;
uint32_t i;
} u = { x };
float_t hfsq, f, s, z, R, w, t1, t2, dk, hi, lo;
uint32_t ix;
int k;
ix = u.i;
k = 0;
if (ix < 0x00800000 || ix >> 31) { /* x < 2**-126 */
if (ix << 1 == 0)
return -1 / (x * x); /* log(+-0)=-inf */
if (ix >> 31)
return (x - x) / 0.0f; /* log(-#) = NaN */
/* subnormal number, scale up x */
k -= 25;
x *= 0x1p25f;
u.f = x;
ix = u.i;
} else if (ix >= 0x7f800000) {
return x;
} else if (ix == 0x3f800000)
return 0;
/* reduce x into [sqrt(2)/2, sqrt(2)] */
ix += 0x3f800000 - 0x3f3504f3;
k += (int)(ix >> 23) - 0x7f;
ix = (ix & 0x007fffff) + 0x3f3504f3;
u.i = ix;
x = u.f;
f = x - 1.0f;
s = f / (2.0f + f);
z = s * s;
w = z * z;
t1 = w * (Lg2 + w * Lg4);
t2 = z * (Lg1 + w * Lg3);
R = t2 + t1;
hfsq = 0.5f * f * f;
hi = f - hfsq;
u.f = hi;
u.i &= 0xfffff000;
hi = u.f;
lo = f - hi - hfsq + s * (hfsq + R);
dk = k;
return dk * log10_2lo + (lo + hi) * ivln10lo + lo * ivln10hi +
hi * ivln10hi + dk * log10_2hi;
}
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