cosmopolitan/libc/tinymath/acosf.c

/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8   -*-│
│vi: set et ft=c ts=8 tw=8 fenc=utf-8                                       :vi│
╚──────────────────────────────────────────────────────────────────────────────╝
│                                                                              │
│  Musl Libc                                                                   │
│  Copyright © 2005-2020 Rich Felker, et al.                                   │
│                                                                              │
│  Permission is hereby granted, free of charge, to any person obtaining       │
│  a copy of this software and associated documentation files (the             │
│  "Software"), to deal in the Software without restriction, including         │
│  without limitation the rights to use, copy, modify, merge, publish,         │
│  distribute, sublicense, and/or sell copies of the Software, and to          │
│  permit persons to whom the Software is furnished to do so, subject to       │
│  the following conditions:                                                   │
│                                                                              │
│  The above copyright notice and this permission notice shall be              │
│  included in all copies or substantial portions of the Software.             │
│                                                                              │
│  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,             │
│  EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF          │
│  MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.      │
│  IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY        │
│  CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,        │
│  TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE           │
│  SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                      │
│                                                                              │
╚─────────────────────────────────────────────────────────────────────────────*/
#include "libc/math.h"
#include "libc/tinymath/complex.internal.h"

asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
/* clang-format off */

/* origin: FreeBSD /usr/src/lib/msun/src/e_acosf.c */
/*
 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
 */
/*
 * ====================================================
 * 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.
 * ====================================================
 */

static const float
pio2_hi = 1.5707962513e+00, /* 0x3fc90fda */
pio2_lo = 7.5497894159e-08, /* 0x33a22168 */
pS0 =  1.6666586697e-01,
pS1 = -4.2743422091e-02,
pS2 = -8.6563630030e-03,
qS1 = -7.0662963390e-01;

static float R(float z)
{
	float_t p, q;
	p = z*(pS0+z*(pS1+z*pS2));
	q = 1.0f+z*qS1;
	return p/q;
}

/**
 * Returns arc cosine of 𝑥.
 */
float acosf(float x)
{
	float z,w,s,c,df;
	uint32_t hx,ix;

	GET_FLOAT_WORD(hx, x);
	ix = hx & 0x7fffffff;
	/* |x| >= 1 or nan */
	if (ix >= 0x3f800000) {
		if (ix == 0x3f800000) {
			if (hx >> 31)
				return 2*pio2_hi + 0x1p-120f;
			return 0;
		}
		return 0/(x-x);
	}
	/* |x| < 0.5 */
	if (ix < 0x3f000000) {
		if (ix <= 0x32800000) /* |x| < 2**-26 */
			return pio2_hi + 0x1p-120f;
		return pio2_hi - (x - (pio2_lo-x*R(x*x)));
	}
	/* x < -0.5 */
	if (hx >> 31) {
		z = (1+x)*0.5f;
		s = sqrtf(z);
		w = R(z)*s-pio2_lo;
		return 2*(pio2_hi - (s+w));
	}
	/* x > 0.5 */
	z = (1-x)*0.5f;
	s = sqrtf(z);
	GET_FLOAT_WORD(hx,s);
	SET_FLOAT_WORD(df,hx&0xfffff000);
	c = (z-df*df)/(s+df);
	w = R(z)*s+c;
	return 2*(df+w);
}