117 lines
3.7 KiB
C
117 lines
3.7 KiB
C
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/* @(#)e_log10.c 1.3 95/01/18 */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunSoft, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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#include "cdefs-compat.h"
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//__FBSDID("$FreeBSD: src/lib/msun/src/e_log2.c,v 1.4 2011/10/15 05:23:28 das Exp $");
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/*
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* Return the base 2 logarithm of x. See e_log.c and k_log.h for most
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* comments.
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*
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* This reduces x to {k, 1+f} exactly as in e_log.c, then calls the kernel,
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* then does the combining and scaling steps
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* log2(x) = (f - 0.5*f*f + k_log1p(f)) / ln2 + k
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* in not-quite-routine extra precision.
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*/
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#include <float.h>
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#include <openlibm_math.h>
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#include "math_private.h"
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#include "k_log.h"
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static const double
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two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
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ivln2hi = 1.44269504072144627571e+00, /* 0x3ff71547, 0x65200000 */
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ivln2lo = 1.67517131648865118353e-10; /* 0x3de705fc, 0x2eefa200 */
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static const double zero = 0.0;
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OLM_DLLEXPORT double
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__ieee754_log2(double x)
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{
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double f,hfsq,hi,lo,r,val_hi,val_lo,w,y;
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int32_t i,k,hx;
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u_int32_t lx;
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EXTRACT_WORDS(hx,lx,x);
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k=0;
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if (hx < 0x00100000) { /* x < 2**-1022 */
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if (((hx&0x7fffffff)|lx)==0)
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return -two54/zero; /* log(+-0)=-inf */
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if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
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k -= 54; x *= two54; /* subnormal number, scale up x */
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GET_HIGH_WORD(hx,x);
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}
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if (hx >= 0x7ff00000) return x+x;
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if (hx == 0x3ff00000 && lx == 0)
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return zero; /* log(1) = +0 */
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k += (hx>>20)-1023;
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hx &= 0x000fffff;
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i = (hx+0x95f64)&0x100000;
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SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */
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k += (i>>20);
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y = (double)k;
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f = x - 1.0;
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hfsq = 0.5*f*f;
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r = k_log1p(f);
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/*
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* f-hfsq must (for args near 1) be evaluated in extra precision
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* to avoid a large cancellation when x is near sqrt(2) or 1/sqrt(2).
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* This is fairly efficient since f-hfsq only depends on f, so can
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* be evaluated in parallel with R. Not combining hfsq with R also
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* keeps R small (though not as small as a true `lo' term would be),
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* so that extra precision is not needed for terms involving R.
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*
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* Compiler bugs involving extra precision used to break Dekker's
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* theorem for spitting f-hfsq as hi+lo, unless double_t was used
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* or the multi-precision calculations were avoided when double_t
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* has extra precision. These problems are now automatically
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* avoided as a side effect of the optimization of combining the
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* Dekker splitting step with the clear-low-bits step.
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*
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* y must (for args near sqrt(2) and 1/sqrt(2)) be added in extra
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* precision to avoid a very large cancellation when x is very near
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* these values. Unlike the above cancellations, this problem is
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* specific to base 2. It is strange that adding +-1 is so much
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* harder than adding +-ln2 or +-log10_2.
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*
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* This uses Dekker's theorem to normalize y+val_hi, so the
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* compiler bugs are back in some configurations, sigh. And I
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* don't want to used double_t to avoid them, since that gives a
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* pessimization and the support for avoiding the pessimization
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* is not yet available.
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*
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* The multi-precision calculations for the multiplications are
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* routine.
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*/
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hi = f - hfsq;
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SET_LOW_WORD(hi,0);
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lo = (f - hi) - hfsq + r;
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val_hi = hi*ivln2hi;
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val_lo = (lo+hi)*ivln2lo + lo*ivln2hi;
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/* spadd(val_hi, val_lo, y), except for not using double_t: */
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w = y + val_hi;
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val_lo += (y - w) + val_hi;
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val_hi = w;
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return val_lo + val_hi;
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}
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#if (LDBL_MANT_DIG == 53)
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openlibm_weak_reference(log2, log2l);
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#endif
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