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/*
* ====================================================
* 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 <sys/cdefs.h>
__FBSDID("$FreeBSD$");
/*
* Float version of e_log2.c. See the latter for most comments.
*/
#include "math.h"
#include "math_private.h"
#include "k_logf.h"
static const float
two25 = 3.3554432000e+07, /* 0x4c000000 */
ivln2hi = 1.4428710938e+00, /* 0x3fb8b000 */
ivln2lo = -1.7605285393e-04; /* 0xb9389ad4 */
static const float zero = 0.0;
float
__ieee754_log2f(float x)
{
float f,hfsq,hi,lo,r,y;
int32_t i,k,hx;
GET_FLOAT_WORD(hx,x);
k=0;
if (hx < 0x00800000) { /* x < 2**-126 */
if ((hx&0x7fffffff)==0)
return -two25/zero; /* log(+-0)=-inf */
if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
k -= 25; x *= two25; /* subnormal number, scale up x */
GET_FLOAT_WORD(hx,x);
}
if (hx >= 0x7f800000) return x+x;
if (hx == 0x3f800000)
return zero; /* log(1) = +0 */
k += (hx>>23)-127;
hx &= 0x007fffff;
i = (hx+(0x4afb0d))&0x800000;
SET_FLOAT_WORD(x,hx|(i^0x3f800000)); /* normalize x or x/2 */
k += (i>>23);
y = (float)k;
f = x - (float)1.0;
hfsq = (float)0.5*f*f;
r = k_log1pf(f);
/*
* We no longer need to avoid falling into the multi-precision
* calculations due to compiler bugs breaking Dekker's theorem.
* Keep avoiding this as an optimization. See e_log2.c for more
* details (some details are here only because the optimization
* is not yet available in double precision).
*
* Another compiler bug turned up. With gcc on i386,
* (ivln2lo + ivln2hi) would be evaluated in float precision
* despite runtime evaluations using double precision. So we
* must cast one of its terms to float_t. This makes the whole
* expression have type float_t, so return is forced to waste
* time clobbering its extra precision.
*/
if (sizeof(float_t) > sizeof(float))
return (r - hfsq + f) * ((float_t)ivln2lo + ivln2hi) + y;
hi = f - hfsq;
GET_FLOAT_WORD(hx,hi);
SET_FLOAT_WORD(hi,hx&0xfffff000);
lo = (f - hi) - hfsq + r;
return (lo+hi)*ivln2lo + lo*ivln2hi + hi*ivln2hi + y;
}
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