cosmopolitan/libc/tinymath/atan2f.c

/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8   -*-│
│ vi: set noet ft=c ts=8 sw=8 fenc=utf-8                                   :vi │
╚──────────────────────────────────────────────────────────────────────────────╝
│                                                                              │
│ FreeBSD lib/msun/src/s_asinhl.c                                              │
│ Converted to ldbl by David Schultz <das@FreeBSD.ORG> and Bruce D. Evans.     │
│                                                                              │
│ 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.                                                                │
│                                                                              │
│ Copyright (c) 1992-2023 The FreeBSD Project.                                 │
│                                                                              │
│ Redistribution and use in source and binary forms, with or without           │
│ modification, are permitted provided that the following conditions           │
│ are met:                                                                     │
│ 1. Redistributions of source code must retain the above copyright            │
│    notice, this list of conditions and the following disclaimer.             │
│ 2. Redistributions in binary form must reproduce the above copyright         │
│    notice, this list of conditions and the following disclaimer in the       │
│    documentation and/or other materials provided with the distribution.      │
│                                                                              │
│ THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND       │
│ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE        │
│ IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE   │
│ ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE      │
│ FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL   │
│ DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS      │
│ OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)        │
│ HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT   │
│ LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY    │
│ OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF       │
│ SUCH DAMAGE.                                                                 │
│                                                                              │
╚─────────────────────────────────────────────────────────────────────────────*/
#include "libc/tinymath/freebsd.internal.h"
__static_yoink("freebsd_libm_notice");
__static_yoink("fdlibm_notice");

static volatile float
tiny  = 1.0e-30;
static const float
zero  = 0.0,
pi_o_4  = 7.8539818525e-01, /* 0x3f490fdb */
pi_o_2  = 1.5707963705e+00, /* 0x3fc90fdb */
pi      = 3.1415927410e+00; /* 0x40490fdb */
static volatile float
pi_lo   = -8.7422776573e-08; /* 0xb3bbbd2e */

/**
 * Returns arc tangent of 𝑦/𝑥.
 */
float
atan2f(float y, float x)
{
	float z;
	int32_t k,m,hx,hy,ix,iy;

	GET_FLOAT_WORD(hx,x);
	ix = hx&0x7fffffff;
	GET_FLOAT_WORD(hy,y);
	iy = hy&0x7fffffff;
	if((ix>0x7f800000)||
	   (iy>0x7f800000))	/* x or y is NaN */
	    return nan_mix(x, y);
	if(hx==0x3f800000) return atanf(y);   /* x=1.0 */
	m = ((hy>>31)&1)|((hx>>30)&2);	/* 2*sign(x)+sign(y) */

    /* when y = 0 */
	if(iy==0) {
	    switch(m) {
		case 0:
		case 1: return y; 	/* atan(+-0,+anything)=+-0 */
		case 2: return  pi+tiny;/* atan(+0,-anything) = pi */
		case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
	    }
	}
    /* when x = 0 */
	if(ix==0) return (hy<0)?  -pi_o_2-tiny: pi_o_2+tiny;

    /* when x is INF */
	if(ix==0x7f800000) {
	    if(iy==0x7f800000) {
		switch(m) {
		    case 0: return  pi_o_4+tiny;/* atan(+INF,+INF) */
		    case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
		    case 2: return  (float)3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
		    case 3: return (float)-3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
		}
	    } else {
		switch(m) {
		    case 0: return  zero  ;	/* atan(+...,+INF) */
		    case 1: return -zero  ;	/* atan(-...,+INF) */
		    case 2: return  pi+tiny  ;	/* atan(+...,-INF) */
		    case 3: return -pi-tiny  ;	/* atan(-...,-INF) */
		}
	    }
	}
    /* when y is INF */
	if(iy==0x7f800000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;

    /* compute y/x */
	k = (iy-ix)>>23;
	if(k > 26) {			/* |y/x| >  2**26 */
	    z=pi_o_2+(float)0.5*pi_lo;
	    m&=1;
	}
	else if(k<-26&&hx<0) z=0.0; 	/* 0 > |y|/x > -2**-26 */
	else z=atanf(fabsf(y/x));	/* safe to do 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(-,-) */
	}
}