logf.c

/* 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);
	}
}