    // 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/tanhf.c

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

    const std = @import("../std.zig");
    const math = std.math;
    const expect = std.testing.expect;
    const expo2 = @import("expo2.zig").expo2;
    const maxInt = std.math.maxInt;

    /// Returns the hyperbolic tangent of x.
    ///
    /// Special Cases:
    ///  - sinh(+-0)   = +-0
    ///  - sinh(+-inf) = +-1
    ///  - sinh(nan)   = nan
    pub fn tanh(x: anytype) @TypeOf(x) {
        const T = @TypeOf(x);
        return switch (T) {
            f32 => tanh32(x),
            f64 => tanh64(x),
            else => @compileError("tanh not implemented for " ++ @typeName(T)),
        };
    }

    // tanh(x) = (exp(x) - exp(-x)) / (exp(x) + exp(-x))

    //         = (exp(2x) - 1) / (exp(2x) - 1 + 2)

    //         = (1 - exp(-2x)) / (exp(-2x) - 1 + 2)

    fn tanh32(x: f32) f32 {
        const u = @bitCast(u32, x);
        const ux = u & 0x7FFFFFFF;
        const ax = @bitCast(f32, ux);
        const sign = (u >> 31) != 0;

        var t: f32 = undefined;

        // |x| < log(3) / 2 ~= 0.5493 or nan

        if (ux > 0x3F0C9F54) {
            // |x| > 10

            if (ux > 0x41200000) {
                t = 1.0 + 0 / x;
            } else {
                t = math.expm1(2 * ax);
                t = 1 - 2 / (t + 2);
            }
        }
        // |x| > log(5 / 3) / 2 ~= 0.2554

        else if (ux > 0x3E82C578) {
            t = math.expm1(2 * ax);
            t = t / (t + 2);
        }
        // |x| >= 0x1.0p-126

        else if (ux >= 0x00800000) {
            t = math.expm1(-2 * ax);
            t = -t / (t + 2);
        }
        // |x| is subnormal

        else {
            math.doNotOptimizeAway(ax * ax);
            t = ax;
        }

        return if (sign) -t else t;
    }

    fn tanh64(x: f64) f64 {
        const u = @bitCast(u64, x);
        const ux = u & 0x7FFFFFFFFFFFFFFF;
        const w = @intCast(u32, ux >> 32);
        const ax = @bitCast(f64, ux);
        const sign = (u >> 63) != 0;

        var t: f64 = undefined;

        // |x| < log(3) / 2 ~= 0.5493 or nan

        if (w > 0x3FE193EA) {
            // |x| > 20 or nan

            if (w > 0x40340000) {
                t = 1.0 - 0 / ax;
            } else {
                t = math.expm1(2 * ax);
                t = 1 - 2 / (t + 2);
            }
        }
        // |x| > log(5 / 3) / 2 ~= 0.2554

        else if (w > 0x3FD058AE) {
            t = math.expm1(2 * ax);
            t = t / (t + 2);
        }
        // |x| >= 0x1.0p-1022

        else if (w >= 0x00100000) {
            t = math.expm1(-2 * ax);
            t = -t / (t + 2);
        }
        // |x| is subnormal

        else {
            math.doNotOptimizeAway(@floatCast(f32, ax));
            t = ax;
        }

        return if (sign) -t else t;
    }

    test "math.tanh" {
        try expect(tanh(@as(f32, 1.5)) == tanh32(1.5));
        try expect(tanh(@as(f64, 1.5)) == tanh64(1.5));
    }

    test "math.tanh32" {
        const epsilon = 0.000001;

        try expect(math.approxEqAbs(f32, tanh32(0.0), 0.0, epsilon));
        try expect(math.approxEqAbs(f32, tanh32(0.2), 0.197375, epsilon));
        try expect(math.approxEqAbs(f32, tanh32(0.8923), 0.712528, epsilon));
        try expect(math.approxEqAbs(f32, tanh32(1.5), 0.905148, epsilon));
        try expect(math.approxEqAbs(f32, tanh32(37.45), 1.0, epsilon));
        try expect(math.approxEqAbs(f32, tanh32(-0.8923), -0.712528, epsilon));
        try expect(math.approxEqAbs(f32, tanh32(-1.5), -0.905148, epsilon));
        try expect(math.approxEqAbs(f32, tanh32(-37.45), -1.0, epsilon));
    }

    test "math.tanh64" {
        const epsilon = 0.000001;

        try expect(math.approxEqAbs(f64, tanh64(0.0), 0.0, epsilon));
        try expect(math.approxEqAbs(f64, tanh64(0.2), 0.197375, epsilon));
        try expect(math.approxEqAbs(f64, tanh64(0.8923), 0.712528, epsilon));
        try expect(math.approxEqAbs(f64, tanh64(1.5), 0.905148, epsilon));
        try expect(math.approxEqAbs(f64, tanh64(37.45), 1.0, epsilon));
        try expect(math.approxEqAbs(f64, tanh64(-0.8923), -0.712528, epsilon));
        try expect(math.approxEqAbs(f64, tanh64(-1.5), -0.905148, epsilon));
        try expect(math.approxEqAbs(f64, tanh64(-37.45), -1.0, epsilon));
    }

    test "math.tanh32.special" {
        try expect(tanh32(0.0) == 0.0);
        try expect(tanh32(-0.0) == -0.0);
        try expect(tanh32(math.inf(f32)) == 1.0);
        try expect(tanh32(-math.inf(f32)) == -1.0);
        try expect(math.isNan(tanh32(math.nan(f32))));
    }

    test "math.tanh64.special" {
        try expect(tanh64(0.0) == 0.0);
        try expect(tanh64(-0.0) == -0.0);
        try expect(tanh64(math.inf(f64)) == 1.0);
        try expect(tanh64(-math.inf(f64)) == -1.0);
        try expect(math.isNan(tanh64(math.nan(f64))));
    }