atan2_64

fn atan2_64(y: f64, x: f64) f64 {
    const pi: f64 = 3.1415926535897931160E+00;
    const pi_lo: f64 = 1.2246467991473531772E-16;

    if (math.isNan(x) or math.isNan(y)) {
        return x + y;
    }

    const ux: u64 = @bitCast(x);
    var ix: u32 = @intCast(ux >> 32);
    const lx: u32 = @intCast(ux & 0xFFFFFFFF);

    const uy: u64 = @bitCast(y);
    var iy: u32 = @intCast(uy >> 32);
    const ly: u32 = @intCast(uy & 0xFFFFFFFF);

    // x = 1.0
    if ((ix -% 0x3FF00000) | lx == 0) {
        return math.atan(y);
    }

    // 2 * sign(x) + sign(y)
    const m = ((iy >> 31) & 1) | ((ix >> 30) & 2);
    ix &= 0x7FFFFFFF;
    iy &= 0x7FFFFFFF;

    if (iy | ly == 0) {
        switch (m) {
            0, 1 => return y, // atan(+-0, +...)
            2 => return pi, // atan(+0, -...)
            3 => return -pi, // atan(-0, -...)
            else => unreachable,
        }
    }

    if (ix | lx == 0) {
        if (m & 1 != 0) {
            return -pi / 2;
        } else {
            return pi / 2;
        }
    }

    if (ix == 0x7FF00000) {
        if (iy == 0x7FF00000) {
            switch (m) {
                0 => return pi / 4, // atan(+inf, +inf)
                1 => return -pi / 4, // atan(-inf, +inf)
                2 => return 3 * pi / 4, // atan(+inf, -inf)
                3 => return -3 * pi / 4, // atan(-inf, -inf)
                else => unreachable,
            }
        } else {
            switch (m) {
                0 => return 0.0, // atan(+..., +inf)
                1 => return -0.0, // atan(-..., +inf)
                2 => return pi, // atan(+..., -inf)
                3 => return -pi, // atan(-...f, -inf)
                else => unreachable,
            }
        }
    }

    // |y / x| > 0x1p64
    if (ix +% (64 << 20) < iy or iy == 0x7FF00000) {
        if (m & 1 != 0) {
            return -pi / 2;
        } else {
            return pi / 2;
        }
    }

    // z = atan(|y / x|) with correct underflow
    const z = z: {
        if ((m & 2) != 0 and iy +% (64 << 20) < ix) {
            break :z 0.0;
        } else {
            break :z math.atan(@abs(y / x));
        }
    };

    switch (m) {
        0 => return z, // atan(+, +)
        1 => return -z, // atan(-, +)
        2 => return pi - (z - pi_lo), // atan(+, -)
        3 => return (z - pi_lo) - pi, // atan(-, -)
        else => unreachable,
    }
}