xref: /aosp_15_r20/external/musl/src/math/atan2.c (revision c9945492fdd68bbe62686c5b452b4dc1be3f8453)
1*c9945492SAndroid Build Coastguard Worker /* origin: FreeBSD /usr/src/lib/msun/src/e_atan2.c */
2*c9945492SAndroid Build Coastguard Worker /*
3*c9945492SAndroid Build Coastguard Worker  * ====================================================
4*c9945492SAndroid Build Coastguard Worker  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5*c9945492SAndroid Build Coastguard Worker  *
6*c9945492SAndroid Build Coastguard Worker  * Developed at SunSoft, a Sun Microsystems, Inc. business.
7*c9945492SAndroid Build Coastguard Worker  * Permission to use, copy, modify, and distribute this
8*c9945492SAndroid Build Coastguard Worker  * software is freely granted, provided that this notice
9*c9945492SAndroid Build Coastguard Worker  * is preserved.
10*c9945492SAndroid Build Coastguard Worker  * ====================================================
11*c9945492SAndroid Build Coastguard Worker  *
12*c9945492SAndroid Build Coastguard Worker  */
13*c9945492SAndroid Build Coastguard Worker /* atan2(y,x)
14*c9945492SAndroid Build Coastguard Worker  * Method :
15*c9945492SAndroid Build Coastguard Worker  *      1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
16*c9945492SAndroid Build Coastguard Worker  *      2. Reduce x to positive by (if x and y are unexceptional):
17*c9945492SAndroid Build Coastguard Worker  *              ARG (x+iy) = arctan(y/x)           ... if x > 0,
18*c9945492SAndroid Build Coastguard Worker  *              ARG (x+iy) = pi - arctan[y/(-x)]   ... if x < 0,
19*c9945492SAndroid Build Coastguard Worker  *
20*c9945492SAndroid Build Coastguard Worker  * Special cases:
21*c9945492SAndroid Build Coastguard Worker  *
22*c9945492SAndroid Build Coastguard Worker  *      ATAN2((anything), NaN ) is NaN;
23*c9945492SAndroid Build Coastguard Worker  *      ATAN2(NAN , (anything) ) is NaN;
24*c9945492SAndroid Build Coastguard Worker  *      ATAN2(+-0, +(anything but NaN)) is +-0  ;
25*c9945492SAndroid Build Coastguard Worker  *      ATAN2(+-0, -(anything but NaN)) is +-pi ;
26*c9945492SAndroid Build Coastguard Worker  *      ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
27*c9945492SAndroid Build Coastguard Worker  *      ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
28*c9945492SAndroid Build Coastguard Worker  *      ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
29*c9945492SAndroid Build Coastguard Worker  *      ATAN2(+-INF,+INF ) is +-pi/4 ;
30*c9945492SAndroid Build Coastguard Worker  *      ATAN2(+-INF,-INF ) is +-3pi/4;
31*c9945492SAndroid Build Coastguard Worker  *      ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
32*c9945492SAndroid Build Coastguard Worker  *
33*c9945492SAndroid Build Coastguard Worker  * Constants:
34*c9945492SAndroid Build Coastguard Worker  * The hexadecimal values are the intended ones for the following
35*c9945492SAndroid Build Coastguard Worker  * constants. The decimal values may be used, provided that the
36*c9945492SAndroid Build Coastguard Worker  * compiler will convert from decimal to binary accurately enough
37*c9945492SAndroid Build Coastguard Worker  * to produce the hexadecimal values shown.
38*c9945492SAndroid Build Coastguard Worker  */
39*c9945492SAndroid Build Coastguard Worker 
40*c9945492SAndroid Build Coastguard Worker #include "libm.h"
41*c9945492SAndroid Build Coastguard Worker 
42*c9945492SAndroid Build Coastguard Worker static const double
43*c9945492SAndroid Build Coastguard Worker pi     = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
44*c9945492SAndroid Build Coastguard Worker pi_lo  = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
45*c9945492SAndroid Build Coastguard Worker 
atan2(double y,double x)46*c9945492SAndroid Build Coastguard Worker double atan2(double y, double x)
47*c9945492SAndroid Build Coastguard Worker {
48*c9945492SAndroid Build Coastguard Worker 	double z;
49*c9945492SAndroid Build Coastguard Worker 	uint32_t m,lx,ly,ix,iy;
50*c9945492SAndroid Build Coastguard Worker 
51*c9945492SAndroid Build Coastguard Worker 	if (isnan(x) || isnan(y))
52*c9945492SAndroid Build Coastguard Worker 		return x+y;
53*c9945492SAndroid Build Coastguard Worker 	EXTRACT_WORDS(ix, lx, x);
54*c9945492SAndroid Build Coastguard Worker 	EXTRACT_WORDS(iy, ly, y);
55*c9945492SAndroid Build Coastguard Worker 	if ((ix-0x3ff00000 | lx) == 0)  /* x = 1.0 */
56*c9945492SAndroid Build Coastguard Worker 		return atan(y);
57*c9945492SAndroid Build Coastguard Worker 	m = ((iy>>31)&1) | ((ix>>30)&2);  /* 2*sign(x)+sign(y) */
58*c9945492SAndroid Build Coastguard Worker 	ix = ix & 0x7fffffff;
59*c9945492SAndroid Build Coastguard Worker 	iy = iy & 0x7fffffff;
60*c9945492SAndroid Build Coastguard Worker 
61*c9945492SAndroid Build Coastguard Worker 	/* when y = 0 */
62*c9945492SAndroid Build Coastguard Worker 	if ((iy|ly) == 0) {
63*c9945492SAndroid Build Coastguard Worker 		switch(m) {
64*c9945492SAndroid Build Coastguard Worker 		case 0:
65*c9945492SAndroid Build Coastguard Worker 		case 1: return y;   /* atan(+-0,+anything)=+-0 */
66*c9945492SAndroid Build Coastguard Worker 		case 2: return  pi; /* atan(+0,-anything) = pi */
67*c9945492SAndroid Build Coastguard Worker 		case 3: return -pi; /* atan(-0,-anything) =-pi */
68*c9945492SAndroid Build Coastguard Worker 		}
69*c9945492SAndroid Build Coastguard Worker 	}
70*c9945492SAndroid Build Coastguard Worker 	/* when x = 0 */
71*c9945492SAndroid Build Coastguard Worker 	if ((ix|lx) == 0)
72*c9945492SAndroid Build Coastguard Worker 		return m&1 ? -pi/2 : pi/2;
73*c9945492SAndroid Build Coastguard Worker 	/* when x is INF */
74*c9945492SAndroid Build Coastguard Worker 	if (ix == 0x7ff00000) {
75*c9945492SAndroid Build Coastguard Worker 		if (iy == 0x7ff00000) {
76*c9945492SAndroid Build Coastguard Worker 			switch(m) {
77*c9945492SAndroid Build Coastguard Worker 			case 0: return  pi/4;   /* atan(+INF,+INF) */
78*c9945492SAndroid Build Coastguard Worker 			case 1: return -pi/4;   /* atan(-INF,+INF) */
79*c9945492SAndroid Build Coastguard Worker 			case 2: return  3*pi/4; /* atan(+INF,-INF) */
80*c9945492SAndroid Build Coastguard Worker 			case 3: return -3*pi/4; /* atan(-INF,-INF) */
81*c9945492SAndroid Build Coastguard Worker 			}
82*c9945492SAndroid Build Coastguard Worker 		} else {
83*c9945492SAndroid Build Coastguard Worker 			switch(m) {
84*c9945492SAndroid Build Coastguard Worker 			case 0: return  0.0; /* atan(+...,+INF) */
85*c9945492SAndroid Build Coastguard Worker 			case 1: return -0.0; /* atan(-...,+INF) */
86*c9945492SAndroid Build Coastguard Worker 			case 2: return  pi;  /* atan(+...,-INF) */
87*c9945492SAndroid Build Coastguard Worker 			case 3: return -pi;  /* atan(-...,-INF) */
88*c9945492SAndroid Build Coastguard Worker 			}
89*c9945492SAndroid Build Coastguard Worker 		}
90*c9945492SAndroid Build Coastguard Worker 	}
91*c9945492SAndroid Build Coastguard Worker 	/* |y/x| > 0x1p64 */
92*c9945492SAndroid Build Coastguard Worker 	if (ix+(64<<20) < iy || iy == 0x7ff00000)
93*c9945492SAndroid Build Coastguard Worker 		return m&1 ? -pi/2 : pi/2;
94*c9945492SAndroid Build Coastguard Worker 
95*c9945492SAndroid Build Coastguard Worker 	/* z = atan(|y/x|) without spurious underflow */
96*c9945492SAndroid Build Coastguard Worker 	if ((m&2) && iy+(64<<20) < ix)  /* |y/x| < 0x1p-64, x<0 */
97*c9945492SAndroid Build Coastguard Worker 		z = 0;
98*c9945492SAndroid Build Coastguard Worker 	else
99*c9945492SAndroid Build Coastguard Worker 		z = atan(fabs(y/x));
100*c9945492SAndroid Build Coastguard Worker 	switch (m) {
101*c9945492SAndroid Build Coastguard Worker 	case 0: return z;              /* atan(+,+) */
102*c9945492SAndroid Build Coastguard Worker 	case 1: return -z;             /* atan(-,+) */
103*c9945492SAndroid Build Coastguard Worker 	case 2: return pi - (z-pi_lo); /* atan(+,-) */
104*c9945492SAndroid Build Coastguard Worker 	default: /* case 3 */
105*c9945492SAndroid Build Coastguard Worker 		return (z-pi_lo) - pi; /* atan(-,-) */
106*c9945492SAndroid Build Coastguard Worker 	}
107*c9945492SAndroid Build Coastguard Worker }
108