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/* 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.
*/
use super::atan;
use super::fabs;
const PI: f64 = 3.1415926535897931160E+00; /* 0x400921FB, 0x54442D18 */
const PI_LO: f64 = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
/// Arctangent of y/x (f64)
///
/// Computes the inverse tangent (arc tangent) of `y/x`.
/// Produces the correct result even for angles near pi/2 or -pi/2 (that is, when `x` is near 0).
/// Returns a value in radians, in the range of -pi to pi.
#[inline]
#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
pub fn atan2(y: f64, x: f64) -> f64 {
if x.is_nan() || y.is_nan() {
return x + y;
}
let mut ix = (x.to_bits() >> 32) as u32;
let lx = x.to_bits() as u32;
let mut iy = (y.to_bits() >> 32) as u32;
let ly = y.to_bits() as u32;
if ((ix.wrapping_sub(0x3ff00000)) | lx) == 0 {
/* x = 1.0 */
return atan(y);
}
let m = ((iy >> 31) & 1) | ((ix >> 30) & 2); /* 2*sign(x)+sign(y) */
ix &= 0x7fffffff;
iy &= 0x7fffffff;
/* when y = 0 */
if (iy | ly) == 0 {
return match m {
0 | 1 => y, /* atan(+-0,+anything)=+-0 */
2 => PI, /* atan(+0,-anything) = PI */
_ => -PI, /* atan(-0,-anything) =-PI */
};
}
/* when x = 0 */
if (ix | lx) == 0 {
return if m & 1 != 0 { -PI / 2.0 } else { PI / 2.0 };
}
/* when x is INF */
if ix == 0x7ff00000 {
if iy == 0x7ff00000 {
return match m {
0 => PI / 4.0, /* atan(+INF,+INF) */
1 => -PI / 4.0, /* atan(-INF,+INF) */
2 => 3.0 * PI / 4.0, /* atan(+INF,-INF) */
_ => -3.0 * PI / 4.0, /* atan(-INF,-INF) */
};
} else {
return match m {
0 => 0.0, /* atan(+...,+INF) */
1 => -0.0, /* atan(-...,+INF) */
2 => PI, /* atan(+...,-INF) */
_ => -PI, /* atan(-...,-INF) */
};
}
}
/* |y/x| > 0x1p64 */
if ix.wrapping_add(64 << 20) < iy || iy == 0x7ff00000 {
return if m & 1 != 0 { -PI / 2.0 } else { PI / 2.0 };
}
/* z = atan(|y/x|) without spurious underflow */
let z = if (m & 2 != 0) && iy.wrapping_add(64 << 20) < ix {
/* |y/x| < 0x1p-64, x<0 */
0.0
} else {
atan(fabs(y / x))
};
match m {
0 => z, /* atan(+,+) */
1 => -z, /* atan(-,+) */
2 => PI - (z - PI_LO), /* atan(+,-) */
_ => (z - PI_LO) - PI, /* atan(-,-) */
}
}
#[test]
fn sanity_check() {
assert_eq!(atan2(0.0, 1.0), 0.0);
assert_eq!(atan2(0.0, -1.0), PI);
assert_eq!(atan2(-0.0, -1.0), -PI);
assert_eq!(atan2(3.0, 2.0), atan(3.0 / 2.0));
assert_eq!(atan2(2.0, -1.0), atan(2.0 / -1.0) + PI);
assert_eq!(atan2(-2.0, -1.0), atan(-2.0 / -1.0) - PI);
}
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