cosmopolitan/libc/tinymath/asinf.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\
fdlibm (fdlibm license)\\n\
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
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_asinf.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 double
pio2 = 1.570796326794896558e+00;

static const float
/* coefficients for R(x^2) */
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 sine of 𝑥.
 */
float asinf(float x)
{
	double s;
	float z;
	uint32_t hx,ix;

	GET_FLOAT_WORD(hx, x);
	ix = hx & 0x7fffffff;
	if (ix >= 0x3f800000) {  /* |x| >= 1 */
		if (ix == 0x3f800000)  /* |x| == 1 */
			return x*pio2 + 0x1p-120f;  /* asin(+-1) = +-pi/2 with inexact */
		return 0/(x-x);  /* asin(|x|>1) is NaN */
	}
	if (ix < 0x3f000000) {  /* |x| < 0.5 */
		/* if 0x1p-126 <= |x| < 0x1p-12, avoid raising underflow */
		if (ix < 0x39800000 && ix >= 0x00800000)
			return x;
		return x + x*R(x*x);
	}
	/* 1 > |x| >= 0.5 */
	z = (1 - fabsf(x))*0.5f;
	s = sqrt(z);
	x = pio2 - 2*(s+s*R(z));
	if (hx >> 31)
		return -x;
	return x;
}