    // 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/atanhf.c

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

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

    /// Returns the hyperbolic arc-tangent of x.
    ///
    /// Special Cases:
    ///  - atanh(+-1) = +-inf with signal
    ///  - atanh(x)   = nan if |x| > 1 with signal
    ///  - atanh(nan) = nan
    pub fn atanh(x: anytype) @TypeOf(x) {
        const T = @TypeOf(x);
        return switch (T) {
            f32 => atanh_32(x),
            f64 => atanh_64(x),
            else => @compileError("atanh not implemented for " ++ @typeName(T)),
        };
    }

    // atanh(x) = log((1 + x) / (1 - x)) / 2 = log1p(2x / (1 - x)) / 2 ~= x + x^3 / 3 + o(x^5)

    fn atanh_32(x: f32) f32 {
        const u = @bitCast(u32, x);
        const i = u & 0x7FFFFFFF;
        const s = u >> 31;

        var y = @bitCast(f32, i); // |x|

        if (y == 1.0) {
            return math.copysign(math.inf(f32), x);
        }

        if (u < 0x3F800000 - (1 << 23)) {
            if (u < 0x3F800000 - (32 << 23)) {
                // underflow

                if (u < (1 << 23)) {
                    math.doNotOptimizeAway(y * y);
                }
            }
            // |x| < 0.5

            else {
                y = 0.5 * math.log1p(2 * y + 2 * y * y / (1 - y));
            }
        } else {
            y = 0.5 * math.log1p(2 * (y / (1 - y)));
        }

        return if (s != 0) -y else y;
    }

    fn atanh_64(x: f64) f64 {
        const u = @bitCast(u64, x);
        const e = (u >> 52) & 0x7FF;
        const s = u >> 63;

        var y = @bitCast(f64, u & (maxInt(u64) >> 1)); // |x|

        if (y == 1.0) {
            return math.copysign(math.inf(f64), x);
        }

        if (e < 0x3FF - 1) {
            if (e < 0x3FF - 32) {
                // underflow

                if (e == 0) {
                    math.doNotOptimizeAway(@floatCast(f32, y));
                }
            }
            // |x| < 0.5

            else {
                y = 0.5 * math.log1p(2 * y + 2 * y * y / (1 - y));
            }
        } else {
            y = 0.5 * math.log1p(2 * (y / (1 - y)));
        }

        return if (s != 0) -y else y;
    }

    test "math.atanh" {
        try expect(atanh(@as(f32, 0.0)) == atanh_32(0.0));
        try expect(atanh(@as(f64, 0.0)) == atanh_64(0.0));
    }

    test "math.atanh_32" {
        const epsilon = 0.000001;

        try expect(math.approxEqAbs(f32, atanh_32(0.0), 0.0, epsilon));
        try expect(math.approxEqAbs(f32, atanh_32(0.2), 0.202733, epsilon));
        try expect(math.approxEqAbs(f32, atanh_32(0.8923), 1.433099, epsilon));
    }

    test "math.atanh_64" {
        const epsilon = 0.000001;

        try expect(math.approxEqAbs(f64, atanh_64(0.0), 0.0, epsilon));
        try expect(math.approxEqAbs(f64, atanh_64(0.2), 0.202733, epsilon));
        try expect(math.approxEqAbs(f64, atanh_64(0.8923), 1.433099, epsilon));
    }

    test "math.atanh32.special" {
        try expect(math.isPositiveInf(atanh_32(1)));
        try expect(math.isNegativeInf(atanh_32(-1)));
        try expect(math.isSignalNan(atanh_32(1.5)));
        try expect(math.isSignalNan(atanh_32(-1.5)));
        try expect(math.isNan(atanh_32(math.nan(f32))));
    }

    test "math.atanh64.special" {
        try expect(math.isPositiveInf(atanh_64(1)));
        try expect(math.isNegativeInf(atanh_64(-1)));
        try expect(math.isSignalNan(atanh_64(1.5)));
        try expect(math.isSignalNan(atanh_64(-1.5)));
        try expect(math.isNan(atanh_64(math.nan(f64))));
    }