    // 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/acoshf.c

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

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

    /// Returns the hyperbolic arc-cosine of x.
    ///
    /// Special cases:
    ///  - acosh(x)   = snan if x < 1
    ///  - acosh(nan) = nan
    pub fn acosh(x: anytype) @TypeOf(x) {
        const T = @TypeOf(x);
        return switch (T) {
            f32 => acosh32(x),
            f64 => acosh64(x),
            else => @compileError("acosh not implemented for " ++ @typeName(T)),
        };
    }

    // acosh(x) = log(x + sqrt(x * x - 1))

    fn acosh32(x: f32) f32 {
        const u = @bitCast(u32, x);
        const i = u & 0x7FFFFFFF;

        // |x| < 2, invalid if x < 1 or nan

        if (i < 0x3F800000 + (1 << 23)) {
            return math.log1p(x - 1 + @sqrt((x - 1) * (x - 1) + 2 * (x - 1)));
        }
        // |x| < 0x1p12

        else if (i < 0x3F800000 + (12 << 23)) {
            return @log(2 * x - 1 / (x + @sqrt(x * x - 1)));
        }
        // |x| >= 0x1p12

        else {
            return @log(x) + 0.693147180559945309417232121458176568;
        }
    }

    fn acosh64(x: f64) f64 {
        const u = @bitCast(u64, x);
        const e = (u >> 52) & 0x7FF;

        // |x| < 2, invalid if x < 1 or nan

        if (e < 0x3FF + 1) {
            return math.log1p(x - 1 + @sqrt((x - 1) * (x - 1) + 2 * (x - 1)));
        }
        // |x| < 0x1p26

        else if (e < 0x3FF + 26) {
            return @log(2 * x - 1 / (x + @sqrt(x * x - 1)));
        }
        // |x| >= 0x1p26 or nan

        else {
            return @log(x) + 0.693147180559945309417232121458176568;
        }
    }

    test "math.acosh" {
        try expect(acosh(@as(f32, 1.5)) == acosh32(1.5));
        try expect(acosh(@as(f64, 1.5)) == acosh64(1.5));
    }

    test "math.acosh32" {
        const epsilon = 0.000001;

        try expect(math.approxEqAbs(f32, acosh32(1.5), 0.962424, epsilon));
        try expect(math.approxEqAbs(f32, acosh32(37.45), 4.315976, epsilon));
        try expect(math.approxEqAbs(f32, acosh32(89.123), 5.183133, epsilon));
        try expect(math.approxEqAbs(f32, acosh32(123123.234375), 12.414088, epsilon));
    }

    test "math.acosh64" {
        const epsilon = 0.000001;

        try expect(math.approxEqAbs(f64, acosh64(1.5), 0.962424, epsilon));
        try expect(math.approxEqAbs(f64, acosh64(37.45), 4.315976, epsilon));
        try expect(math.approxEqAbs(f64, acosh64(89.123), 5.183133, epsilon));
        try expect(math.approxEqAbs(f64, acosh64(123123.234375), 12.414088, epsilon));
    }

    test "math.acosh32.special" {
        try expect(math.isNan(acosh32(math.nan(f32))));
        try expect(math.isSignalNan(acosh32(0.5)));
    }

    test "math.acosh64.special" {
        try expect(math.isNan(acosh64(math.nan(f64))));
        try expect(math.isSignalNan(acosh64(0.5)));
    }