/* @(#)e_log10.c 1.3 95/01/18 */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunSoft, 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("$FreeBSD$");
/* * Return the base 2 logarithm of x. See e_log.c and k_log.h for most * comments. * * This reduces x to {k, 1+f} exactly as in e_log.c, then calls the kernel, * then does the combining and scaling steps * log2(x) = (f - 0.5*f*f + k_log1p(f)) / ln2 + k * in not-quite-routine extra precision.
*/
k=0; if (hx < 0x00100000) { /* x < 2**-1022 */ if (((hx&0x7fffffff)|lx)==0) return -two54/vzero; /* log(+-0)=-inf */ if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
k -= 54; x *= two54; /* subnormal number, scale up x */
GET_HIGH_WORD(hx,x);
} if (hx >= 0x7ff00000) return x+x; if (hx == 0x3ff00000 && lx == 0) return zero; /* log(1) = +0 */
k += (hx>>20)-1023;
hx &= 0x000fffff;
i = (hx+0x95f64)&0x100000;
SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */
k += (i>>20);
y = (double)k;
f = x - 1.0;
hfsq = 0.5*f*f;
r = k_log1p(f);
/* * f-hfsq must (for args near 1) be evaluated in extra precision * to avoid a large cancellation when x is near sqrt(2) or 1/sqrt(2). * This is fairly efficient since f-hfsq only depends on f, so can * be evaluated in parallel with R. Not combining hfsq with R also * keeps R small (though not as small as a true `lo' term would be), * so that extra precision is not needed for terms involving R. * * Compiler bugs involving extra precision used to break Dekker's * theorem for spitting f-hfsq as hi+lo, unless double_t was used * or the multi-precision calculations were avoided when double_t * has extra precision. These problems are now automatically * avoided as a side effect of the optimization of combining the * Dekker splitting step with the clear-low-bits step. * * y must (for args near sqrt(2) and 1/sqrt(2)) be added in extra * precision to avoid a very large cancellation when x is very near * these values. Unlike the above cancellations, this problem is * specific to base 2. It is strange that adding +-1 is so much * harder than adding +-ln2 or +-log10_2. * * This uses Dekker's theorem to normalize y+val_hi, so the * compiler bugs are back in some configurations, sigh. And I * don't want to used double_t to avoid them, since that gives a * pessimization and the support for avoiding the pessimization * is not yet available. * * The multi-precision calculations for the multiplications are * routine.
*/
hi = f - hfsq;
SET_LOW_WORD(hi,0);
lo = (f - hi) - hfsq + r;
val_hi = hi*ivln2hi;
val_lo = (lo+hi)*ivln2lo + lo*ivln2hi;
/* spadd(val_hi, val_lo, y), except for not using double_t: */
w = y + val_hi;
val_lo += (y - w) + val_hi;
val_hi = w;
return val_lo + val_hi;
}
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