atan2.rs - source
Description: Source of the Rust file `/Users/erlendbasso/.cargo/registry/src/github.com-1ecc6299db9ec823/libm-0.2.6/src/math/atan2.rs`.
Keywords: rust, rustlang, rust-lang

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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.
    #[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);
    }