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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);
+}