/* origin: FreeBSD /usr/src/lib/msun/src/e_log10f.c */
/*
 * ====================================================
 * 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.
 * ====================================================
 */
/*
 * See comments in log10.c.
 */

#include <math.h>   // for float_t, log10f
#include <stdint.h> // for uint32_t

static const float ivln10hi = 4.3432617188e-01, /* 0x3ede6000 */
	ivln10lo = -3.1689971365e-05,		/* 0xb804ead9 */
	log10_2hi = 3.0102920532e-01,		/* 0x3e9a2080 */
	log10_2lo = 7.9034151668e-07,		/* 0x355427db */
	/* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]).
	 */
	Lg1 = 0xaaaaaa.0p-24, /* 0.66666662693 */
	Lg2 = 0xccce13.0p-25, /* 0.40000972152 */
	Lg3 = 0x91e9ee.0p-25, /* 0.28498786688 */
	Lg4 = 0xf89e26.0p-26; /* 0.24279078841 */

float log10f(float x)
{
	union {
		float f;
		uint32_t i;
	} u = { x };
	float_t hfsq, f, s, z, R, w, t1, t2, dk, hi, lo;
	uint32_t ix;
	int k;

	ix = u.i;
	k = 0;
	if (ix < 0x00800000 || ix >> 31) { /* x < 2**-126  */
		if (ix << 1 == 0)
			return -1 / (x * x); /* log(+-0)=-inf */
		if (ix >> 31)
			return (x - x) / 0.0f; /* log(-#) = NaN */
		/* subnormal number, scale up x */
		k -= 25;
		x *= 0x1p25f;
		u.f = x;
		ix = u.i;
	} else if (ix >= 0x7f800000) {
		return x;
	} else if (ix == 0x3f800000)
		return 0;

	/* reduce x into [sqrt(2)/2, sqrt(2)] */
	ix += 0x3f800000 - 0x3f3504f3;
	k += (int)(ix >> 23) - 0x7f;
	ix = (ix & 0x007fffff) + 0x3f3504f3;
	u.i = ix;
	x = u.f;

	f = x - 1.0f;
	s = f / (2.0f + f);
	z = s * s;
	w = z * z;
	t1 = w * (Lg2 + w * Lg4);
	t2 = z * (Lg1 + w * Lg3);
	R = t2 + t1;
	hfsq = 0.5f * f * f;

	hi = f - hfsq;
	u.f = hi;
	u.i &= 0xfffff000;
	hi = u.f;
	lo = f - hi - hfsq + s * (hfsq + R);
	dk = k;
	return dk * log10_2lo + (lo + hi) * ivln10lo + lo * ivln10hi +
	       hi * ivln10hi + dk * log10_2hi;
}