/* @(#)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 10 logarithm of x. See e_log.c and k_log.h for most * comments. * * log10(x) = (f - 0.5*f*f + k_log1p(f)) / ln10 + k * log10(2) * 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);
/* See e_log2.c for most details. */
hi = f - hfsq;
SET_LOW_WORD(hi,0);
lo = (f - hi) - hfsq + r;
val_hi = hi*ivln10hi;
y2 = y*log10_2hi;
val_lo = y*log10_2lo + (lo+hi)*ivln10lo + lo*ivln10hi;
/* * Extra precision in for adding y*log10_2hi is not strictly needed * since there is no very large cancellation near x = sqrt(2) or * x = 1/sqrt(2), but we do it anyway since it costs little on CPUs * with some parallelism and it reduces the error for many args.
*/
w = y2 + val_hi;
val_lo += (y2 - w) + val_hi;
val_hi = w;
return val_lo + val_hi;
}
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