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/* origin: FreeBSD /usr/src/lib/msun/src/e_logf.c */
/*
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@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.
* ====================================================
*/
#include "libm.h"
static const float
ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
two25 = 3.355443200e+07, /* 0x4c000000 */
/* |(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 */
static const float zero = 0.0;
float logf(float x)
{
float hfsq,f,s,z,R,w,t1,t2,dk;
int32_t k,ix,i,j;
GET_FLOAT_WORD(ix, x);
k = 0;
if (ix < 0x00800000) { /* x < 2**-126 */
if ((ix & 0x7fffffff) == 0)
return -two25/zero; /* log(+-0)=-inf */
if (ix < 0)
return (x-x)/zero; /* log(-#) = NaN */
/* subnormal number, scale up x */
k -= 25;
x *= two25;
GET_FLOAT_WORD(ix, x);
}
if (ix >= 0x7f800000)
return x+x;
k += (ix>>23) - 127;
ix &= 0x007fffff;
i = (ix + (0x95f64<<3)) & 0x800000;
SET_FLOAT_WORD(x, ix|(i^0x3f800000)); /* normalize x or x/2 */
k += i>>23;
f = x - 1.0f;
if ((0x007fffff & (0x8000 + ix)) < 0xc000) { /* -2**-9 <= f < 2**-9 */
if (f == zero) {
if (k == 0)
return zero;
dk = (float)k;
return dk*ln2_hi + dk*ln2_lo;
}
R = f*f*(0.5f - 0.33333333333333333f*f);
if (k == 0)
return f-R;
dk = (float)k;
return dk*ln2_hi - ((R-dk*ln2_lo)-f);
}
s = f/(2.0f + f);
dk = (float)k;
z = s*s;
i = ix-(0x6147a<<3);
w = z*z;
j = (0x6b851<<3)-ix;
t1= w*(Lg2+w*Lg4);
t2= z*(Lg1+w*Lg3);
i |= j;
R = t2 + t1;
if (i > 0) {
hfsq = 0.5f * f * f;
if (k == 0)
return f - (hfsq-s*(hfsq+R));
return dk*ln2_hi - ((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
} else {
if (k == 0)
return f - s*(f-R);
return dk*ln2_hi - ((s*(f-R)-dk*ln2_lo)-f);
}
}
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