cosmopolitan/libc/tinymath/atan2.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.                                   │
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│  Permission is hereby granted, free of charge, to any person obtaining       │
│  a copy of this software and associated documentation files (the             │
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│  distribute, sublicense, and/or sell copies of the Software, and to          │
│  permit persons to whom the Software is furnished to do so, subject to       │
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│  The above copyright notice and this permission notice shall be              │
│  included in all copies or substantial portions of the Software.             │
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│  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,             │
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╚─────────────────────────────────────────────────────────────────────────────*/
#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_atan2.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.
 * ====================================================
 *
 */
/* atan2(y,x)
 * Method :
 *      1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
 *      2. Reduce x to positive by (if x and y are unexceptional):
 *              ARG (x+iy) = arctan(y/x)           ... if x > 0,
 *              ARG (x+iy) = pi - arctan[y/(-x)]   ... if x < 0,
 *
 * Special cases:
 *
 *      ATAN2((anything), NaN ) is NaN;
 *      ATAN2(NAN , (anything) ) is NaN;
 *      ATAN2(+-0, +(anything but NaN)) is +-0  ;
 *      ATAN2(+-0, -(anything but NaN)) is +-pi ;
 *      ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
 *      ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
 *      ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
 *      ATAN2(+-INF,+INF ) is +-pi/4 ;
 *      ATAN2(+-INF,-INF ) is +-3pi/4;
 *      ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
 *
 * Constants:
 * The hexadecimal values are the intended ones for the following
 * constants. The decimal values may be used, provided that the
 * compiler will convert from decimal to binary accurately enough
 * to produce the hexadecimal values shown.
 */

static const double
pi     = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
pi_lo  = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */

/**
 * Returns arc tangent of 𝑦/𝑥.
 * @note the greatest of all libm functions
 */
double atan2(double y, double x)
{
	double z;
	uint32_t m,lx,ly,ix,iy;

	if (isnan(x) || isnan(y))
		return x+y;
	EXTRACT_WORDS(ix, lx, x);
	EXTRACT_WORDS(iy, ly, y);
	if ((ix-0x3ff00000 | lx) == 0)  /* x = 1.0 */
		return atan(y);
	m = ((iy>>31)&1) | ((ix>>30)&2);  /* 2*sign(x)+sign(y) */
	ix = ix & 0x7fffffff;
	iy = iy & 0x7fffffff;

	/* when y = 0 */
	if ((iy|ly) == 0) {
		switch(m) {
		case 0:
		case 1: return y;   /* atan(+-0,+anything)=+-0 */
		case 2: return  pi; /* atan(+0,-anything) = pi */
		case 3: return -pi; /* atan(-0,-anything) =-pi */
		}
	}
	/* when x = 0 */
	if ((ix|lx) == 0)
		return m&1 ? -pi/2 : pi/2;
	/* when x is INF */
	if (ix == 0x7ff00000) {
		if (iy == 0x7ff00000) {
			switch(m) {
			case 0: return  pi/4;   /* atan(+INF,+INF) */
			case 1: return -pi/4;   /* atan(-INF,+INF) */
			case 2: return  3*pi/4; /* atan(+INF,-INF) */
			case 3: return -3*pi/4; /* atan(-INF,-INF) */
			}
		} else {
			switch(m) {
			case 0: return  0.0; /* atan(+...,+INF) */
			case 1: return -0.0; /* atan(-...,+INF) */
			case 2: return  pi;  /* atan(+...,-INF) */
			case 3: return -pi;  /* atan(-...,-INF) */
			}
		}
	}
	/* |y/x| > 0x1p64 */
	if (ix+(64<<20) < iy || iy == 0x7ff00000)
		return m&1 ? -pi/2 : pi/2;

	/* z = atan(|y/x|) without spurious underflow */
	if ((m&2) && iy+(64<<20) < ix)  /* |y/x| < 0x1p-64, x<0 */
		z = 0;
	else
		z = atan(fabs(y/x));
	switch (m) {
	case 0: return z;              /* atan(+,+) */
	case 1: return -z;             /* atan(-,+) */
	case 2: return pi - (z-pi_lo); /* atan(+,-) */
	default: /* case 3 */
		return (z-pi_lo) - pi; /* atan(-,-) */
	}
}