| /* 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. |
| #[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); |
| } |
