    // 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/sinhf.c

    // https://git.musl-libc.org/cgit/musl/tree/src/math/sinh.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 sine of x.
    ///
    /// Special Cases:
    ///  - sinh(+-0)   = +-0
    ///  - sinh(+-inf) = +-inf
    ///  - sinh(nan)   = nan
    pub fn sinh(x: anytype) @TypeOf(x) {
        const T = @TypeOf(x);
        return switch (T) {
            f32 => sinh32(x),
            f64 => sinh64(x),
            else => @compileError("sinh not implemented for " ++ @typeName(T)),
        };
    }

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

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

    //         = x + x^3 / 6 + o(x^5)

    fn sinh32(x: f32) f32 {
        const u = @bitCast(u32, x);
        const ux = u & 0x7FFFFFFF;
        const ax = @bitCast(f32, ux);

        if (x == 0.0 or math.isNan(x)) {
            return x;
        }

        var h: f32 = 0.5;
        if (u >> 31 != 0) {
            h = -h;
        }

        // |x| < log(FLT_MAX)

        if (ux < 0x42B17217) {
            const t = math.expm1(ax);
            if (ux < 0x3F800000) {
                if (ux < 0x3F800000 - (12 << 23)) {
                    return x;
                } else {
                    return h * (2 * t - t * t / (t + 1));
                }
            }
            return h * (t + t / (t + 1));
        }

        // |x| > log(FLT_MAX) or nan

        return 2 * h * expo2(ax);
    }

    fn sinh64(x: f64) f64 {
        const u = @bitCast(u64, x);
        const w = @intCast(u32, u >> 32) & (maxInt(u32) >> 1);
        const ax = @bitCast(f64, u & (maxInt(u64) >> 1));

        if (x == 0.0 or math.isNan(x)) {
            return x;
        }

        var h: f32 = 0.5;
        if (u >> 63 != 0) {
            h = -h;
        }

        // |x| < log(FLT_MAX)

        if (w < 0x40862E42) {
            const t = math.expm1(ax);
            if (w < 0x3FF00000) {
                if (w < 0x3FF00000 - (26 << 20)) {
                    return x;
                } else {
                    return h * (2 * t - t * t / (t + 1));
                }
            }
            // NOTE: |x| > log(0x1p26) + eps could be h * exp(x)

            return h * (t + t / (t + 1));
        }

        // |x| > log(DBL_MAX) or nan

        return 2 * h * expo2(ax);
    }

    test "math.sinh" {
        try expect(sinh(@as(f32, 1.5)) == sinh32(1.5));
        try expect(sinh(@as(f64, 1.5)) == sinh64(1.5));
    }

    test "math.sinh32" {
        const epsilon = 0.000001;

        try expect(math.approxEqAbs(f32, sinh32(0.0), 0.0, epsilon));
        try expect(math.approxEqAbs(f32, sinh32(0.2), 0.201336, epsilon));
        try expect(math.approxEqAbs(f32, sinh32(0.8923), 1.015512, epsilon));
        try expect(math.approxEqAbs(f32, sinh32(1.5), 2.129279, epsilon));
        try expect(math.approxEqAbs(f32, sinh32(-0.0), -0.0, epsilon));
        try expect(math.approxEqAbs(f32, sinh32(-0.2), -0.201336, epsilon));
        try expect(math.approxEqAbs(f32, sinh32(-0.8923), -1.015512, epsilon));
        try expect(math.approxEqAbs(f32, sinh32(-1.5), -2.129279, epsilon));
    }

    test "math.sinh64" {
        const epsilon = 0.000001;

        try expect(math.approxEqAbs(f64, sinh64(0.0), 0.0, epsilon));
        try expect(math.approxEqAbs(f64, sinh64(0.2), 0.201336, epsilon));
        try expect(math.approxEqAbs(f64, sinh64(0.8923), 1.015512, epsilon));
        try expect(math.approxEqAbs(f64, sinh64(1.5), 2.129279, epsilon));
        try expect(math.approxEqAbs(f64, sinh64(-0.0), -0.0, epsilon));
        try expect(math.approxEqAbs(f64, sinh64(-0.2), -0.201336, epsilon));
        try expect(math.approxEqAbs(f64, sinh64(-0.8923), -1.015512, epsilon));
        try expect(math.approxEqAbs(f64, sinh64(-1.5), -2.129279, epsilon));
    }

    test "math.sinh32.special" {
        try expect(sinh32(0.0) == 0.0);
        try expect(sinh32(-0.0) == -0.0);
        try expect(math.isPositiveInf(sinh32(math.inf(f32))));
        try expect(math.isNegativeInf(sinh32(-math.inf(f32))));
        try expect(math.isNan(sinh32(math.nan(f32))));
    }

    test "math.sinh64.special" {
        try expect(sinh64(0.0) == 0.0);
        try expect(sinh64(-0.0) == -0.0);
        try expect(math.isPositiveInf(sinh64(math.inf(f64))));
        try expect(math.isNegativeInf(sinh64(-math.inf(f64))));
        try expect(math.isNan(sinh64(math.nan(f64))));
    }