musl/src/math/log10.c

/* origin: FreeBSD /usr/src/lib/msun/src/e_log10.c */
/*
 * ====================================================
 * 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.
 * ====================================================
 */
/*
 * 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.
 */

#include "libm.h"
#include "__log1p.h"

static const double
two54     = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
ivln10hi  = 4.34294481878168880939e-01, /* 0x3fdbcb7b, 0x15200000 */
ivln10lo  = 2.50829467116452752298e-11, /* 0x3dbb9438, 0xca9aadd5 */
log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */

double log10(double x)
{
	double f,hfsq,hi,lo,r,val_hi,val_lo,w,y,y2;
	int32_t i,k,hx;
	uint32_t lx;

	EXTRACT_WORDS(hx, lx, x);

	k = 0;
	if (hx < 0x00100000) {  /* x < 2**-1022  */
		if (((hx&0x7fffffff)|lx) == 0)
			return -two54/0.0;  /* log(+-0)=-inf */
		if (hx<0)
			return (x-x)/0.0;   /* log(-#) = NaN */
		/* subnormal number, scale up x */
		k -= 54;
		x *= two54;
		GET_HIGH_WORD(hx, x);
	}
	if (hx >= 0x7ff00000)
		return x+x;
	if (hx == 0x3ff00000 && lx == 0)
		return 0.0;  /* 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 = __log1p(f);

	/* See log2.c for 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;
}