    // Ported from musl, which is licensed under the MIT license:

    // https://git.musl-libc.org/cgit/musl/tree/COPYRIGHT

    //

    // https://git.musl-libc.org/cgit/musl/tree/src/math/atan2f.c

    // https://git.musl-libc.org/cgit/musl/tree/src/math/atan2.c

    const std = @import("../std.zig");
    const math = std.math;
    const expect = std.testing.expect;

    /// Returns the arc-tangent of y/x.
    ///
    /// Special Cases:
    ///  - atan2(y, nan)     = nan
    ///  - atan2(nan, x)     = nan
    ///  - atan2(+0, x>=0)   = +0
    ///  - atan2(-0, x>=0)   = -0
    ///  - atan2(+0, x<=-0)  = +pi
    ///  - atan2(-0, x<=-0)  = -pi
    ///  - atan2(y>0, 0)     = +pi/2
    ///  - atan2(y<0, 0)     = -pi/2
    ///  - atan2(+inf, +inf) = +pi/4
    ///  - atan2(-inf, +inf) = -pi/4
    ///  - atan2(+inf, -inf) = 3pi/4
    ///  - atan2(-inf, -inf) = -3pi/4
    ///  - atan2(y, +inf)    = 0
    ///  - atan2(y>0, -inf)  = +pi
    ///  - atan2(y<0, -inf)  = -pi
    ///  - atan2(+inf, x)    = +pi/2
    ///  - atan2(-inf, x)    = -pi/2
    pub fn atan2(comptime T: type, y: T, x: T) T {
        return switch (T) {
            f32 => atan2_32(y, x),
            f64 => atan2_64(y, x),
            else => @compileError("atan2 not implemented for " ++ @typeName(T)),
        };
    }

    fn atan2_32(y: f32, x: f32) f32 {
        const pi: f32 = 3.1415927410e+00;
        const pi_lo: f32 = -8.7422776573e-08;

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

        var ix = @as(u32, @bitCast(x));
        var iy = @as(u32, @bitCast(y));

        // x = 1.0

        if (ix == 0x3F800000) {
            return math.atan(y);
        }

        // 2 * sign(x) + sign(y)

        const m = ((iy >> 31) & 1) | ((ix >> 30) & 2);
        ix &= 0x7FFFFFFF;
        iy &= 0x7FFFFFFF;

        if (iy == 0) {
            switch (m) {
                0, 1 => return y, // atan(+-0, +...)

                2 => return pi, // atan(+0, -...)

                3 => return -pi, // atan(-0, -...)

                else => unreachable,
            }
        }

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

        if (ix == 0x7F800000) {
            if (iy == 0x7F800000) {
                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| > 0x1p26

        if (ix + (26 << 23) < iy or iy == 0x7F800000) {
            if (m & 1 != 0) {
                return -pi / 2;
            } else {
                return pi / 2;
            }
        }

        // z = atan(|y / x|) with correct underflow

        var z = z: {
            if ((m & 2) != 0 and iy + (26 << 23) < ix) {
                break :z 0.0;
            } else {
                break :z math.atan(@fabs(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,
        }
    }

    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;
        }

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

        var uy = @as(u64, @bitCast(y));
        var iy = @as(u32, @intCast(uy >> 32));
        var ly = @as(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

        var z = z: {
            if ((m & 2) != 0 and iy +% (64 << 20) < ix) {
                break :z 0.0;
            } else {
                break :z math.atan(@fabs(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,
        }
    }

    test "math.atan2" {
        try expect(atan2(f32, 0.2, 0.21) == atan2_32(0.2, 0.21));
        try expect(atan2(f64, 0.2, 0.21) == atan2_64(0.2, 0.21));
    }

    test "math.atan2_32" {
        const epsilon = 0.000001;

        try expect(math.approxEqAbs(f32, atan2_32(0.0, 0.0), 0.0, epsilon));
        try expect(math.approxEqAbs(f32, atan2_32(0.2, 0.2), 0.785398, epsilon));
        try expect(math.approxEqAbs(f32, atan2_32(-0.2, 0.2), -0.785398, epsilon));
        try expect(math.approxEqAbs(f32, atan2_32(0.2, -0.2), 2.356194, epsilon));
        try expect(math.approxEqAbs(f32, atan2_32(-0.2, -0.2), -2.356194, epsilon));
        try expect(math.approxEqAbs(f32, atan2_32(0.34, -0.4), 2.437099, epsilon));
        try expect(math.approxEqAbs(f32, atan2_32(0.34, 1.243), 0.267001, epsilon));
    }

    test "math.atan2_64" {
        const epsilon = 0.000001;

        try expect(math.approxEqAbs(f64, atan2_64(0.0, 0.0), 0.0, epsilon));
        try expect(math.approxEqAbs(f64, atan2_64(0.2, 0.2), 0.785398, epsilon));
        try expect(math.approxEqAbs(f64, atan2_64(-0.2, 0.2), -0.785398, epsilon));
        try expect(math.approxEqAbs(f64, atan2_64(0.2, -0.2), 2.356194, epsilon));
        try expect(math.approxEqAbs(f64, atan2_64(-0.2, -0.2), -2.356194, epsilon));
        try expect(math.approxEqAbs(f64, atan2_64(0.34, -0.4), 2.437099, epsilon));
        try expect(math.approxEqAbs(f64, atan2_64(0.34, 1.243), 0.267001, epsilon));
    }

    test "math.atan2_32.special" {
        const epsilon = 0.000001;

        try expect(math.isNan(atan2_32(1.0, math.nan(f32))));
        try expect(math.isNan(atan2_32(math.nan(f32), 1.0)));
        try expect(atan2_32(0.0, 5.0) == 0.0);
        try expect(atan2_32(-0.0, 5.0) == -0.0);
        try expect(math.approxEqAbs(f32, atan2_32(0.0, -5.0), math.pi, epsilon));
        //expect(math.approxEqAbs(f32, atan2_32(-0.0, -5.0), -math.pi, .{.rel=0,.abs=epsilon})); TODO support negative zero?

        try expect(math.approxEqAbs(f32, atan2_32(1.0, 0.0), math.pi / 2.0, epsilon));
        try expect(math.approxEqAbs(f32, atan2_32(1.0, -0.0), math.pi / 2.0, epsilon));
        try expect(math.approxEqAbs(f32, atan2_32(-1.0, 0.0), -math.pi / 2.0, epsilon));
        try expect(math.approxEqAbs(f32, atan2_32(-1.0, -0.0), -math.pi / 2.0, epsilon));
        try expect(math.approxEqAbs(f32, atan2_32(math.inf(f32), math.inf(f32)), math.pi / 4.0, epsilon));
        try expect(math.approxEqAbs(f32, atan2_32(-math.inf(f32), math.inf(f32)), -math.pi / 4.0, epsilon));
        try expect(math.approxEqAbs(f32, atan2_32(math.inf(f32), -math.inf(f32)), 3.0 * math.pi / 4.0, epsilon));
        try expect(math.approxEqAbs(f32, atan2_32(-math.inf(f32), -math.inf(f32)), -3.0 * math.pi / 4.0, epsilon));
        try expect(atan2_32(1.0, math.inf(f32)) == 0.0);
        try expect(math.approxEqAbs(f32, atan2_32(1.0, -math.inf(f32)), math.pi, epsilon));
        try expect(math.approxEqAbs(f32, atan2_32(-1.0, -math.inf(f32)), -math.pi, epsilon));
        try expect(math.approxEqAbs(f32, atan2_32(math.inf(f32), 1.0), math.pi / 2.0, epsilon));
        try expect(math.approxEqAbs(f32, atan2_32(-math.inf(f32), 1.0), -math.pi / 2.0, epsilon));
    }

    test "math.atan2_64.special" {
        const epsilon = 0.000001;

        try expect(math.isNan(atan2_64(1.0, math.nan(f64))));
        try expect(math.isNan(atan2_64(math.nan(f64), 1.0)));
        try expect(atan2_64(0.0, 5.0) == 0.0);
        try expect(atan2_64(-0.0, 5.0) == -0.0);
        try expect(math.approxEqAbs(f64, atan2_64(0.0, -5.0), math.pi, epsilon));
        //expect(math.approxEqAbs(f64, atan2_64(-0.0, -5.0), -math.pi, .{.rel=0,.abs=epsilon})); TODO support negative zero?

        try expect(math.approxEqAbs(f64, atan2_64(1.0, 0.0), math.pi / 2.0, epsilon));
        try expect(math.approxEqAbs(f64, atan2_64(1.0, -0.0), math.pi / 2.0, epsilon));
        try expect(math.approxEqAbs(f64, atan2_64(-1.0, 0.0), -math.pi / 2.0, epsilon));
        try expect(math.approxEqAbs(f64, atan2_64(-1.0, -0.0), -math.pi / 2.0, epsilon));
        try expect(math.approxEqAbs(f64, atan2_64(math.inf(f64), math.inf(f64)), math.pi / 4.0, epsilon));
        try expect(math.approxEqAbs(f64, atan2_64(-math.inf(f64), math.inf(f64)), -math.pi / 4.0, epsilon));
        try expect(math.approxEqAbs(f64, atan2_64(math.inf(f64), -math.inf(f64)), 3.0 * math.pi / 4.0, epsilon));
        try expect(math.approxEqAbs(f64, atan2_64(-math.inf(f64), -math.inf(f64)), -3.0 * math.pi / 4.0, epsilon));
        try expect(atan2_64(1.0, math.inf(f64)) == 0.0);
        try expect(math.approxEqAbs(f64, atan2_64(1.0, -math.inf(f64)), math.pi, epsilon));
        try expect(math.approxEqAbs(f64, atan2_64(-1.0, -math.inf(f64)), -math.pi, epsilon));
        try expect(math.approxEqAbs(f64, atan2_64(math.inf(f64), 1.0), math.pi / 2.0, epsilon));
        try expect(math.approxEqAbs(f64, atan2_64(-math.inf(f64), 1.0), -math.pi / 2.0, epsilon));
    }