    // 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/log1pf.c

    // https://git.musl-libc.org/cgit/musl/tree/src/math/log1p.c

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

    /// Returns the natural logarithm of 1 + x with greater accuracy when x is near zero.
    ///
    /// Special Cases:
    ///  - log1p(+inf)  = +inf
    ///  - log1p(+-0)   = +-0
    ///  - log1p(-1)    = -inf
    ///  - log1p(x)     = nan if x < -1
    ///  - log1p(nan)   = nan
    pub fn log1p(x: anytype) @TypeOf(x) {
        const T = @TypeOf(x);
        return switch (T) {
            f32 => log1p_32(x),
            f64 => log1p_64(x),
            else => @compileError("log1p not implemented for " ++ @typeName(T)),
        };
    }

    fn log1p_32(x: f32) f32 {
        const ln2_hi = 6.9313812256e-01;
        const ln2_lo = 9.0580006145e-06;
        const Lg1: f32 = 0xaaaaaa.0p-24;
        const Lg2: f32 = 0xccce13.0p-25;
        const Lg3: f32 = 0x91e9ee.0p-25;
        const Lg4: f32 = 0xf89e26.0p-26;

        const u = @bitCast(u32, x);
        var ix = u;
        var k: i32 = 1;
        var f: f32 = undefined;
        var c: f32 = undefined;

        // 1 + x < sqrt(2)+

        if (ix < 0x3ED413D0 or ix >> 31 != 0) {
            // x <= -1.0

            if (ix >= 0xBF800000) {
                // log1p(-1) = -inf

                if (x == -1.0) {
                    return -math.inf(f32);
                }
                // log1p(x < -1) = nan

                else {
                    return math.nan(f32);
                }
            }
            // |x| < 2^(-24)

            if ((ix << 1) < (0x33800000 << 1)) {
                // underflow if subnormal

                if (ix & 0x7F800000 == 0) {
                    math.doNotOptimizeAway(x * x);
                }
                return x;
            }
            // sqrt(2) / 2- <= 1 + x < sqrt(2)+

            if (ix <= 0xBE95F619) {
                k = 0;
                c = 0;
                f = x;
            }
        } else if (ix >= 0x7F800000) {
            return x;
        }

        if (k != 0) {
            const uf = 1 + x;
            var iu = @bitCast(u32, uf);
            iu += 0x3F800000 - 0x3F3504F3;
            k = @intCast(i32, iu >> 23) - 0x7F;

            // correction to avoid underflow in c / u

            if (k < 25) {
                c = if (k >= 2) 1 - (uf - x) else x - (uf - 1);
                c /= uf;
            } else {
                c = 0;
            }

            // u into [sqrt(2)/2, sqrt(2)]

            iu = (iu & 0x007FFFFF) + 0x3F3504F3;
            f = @bitCast(f32, iu) - 1;
        }

        const s = f / (2.0 + f);
        const z = s * s;
        const w = z * z;
        const t1 = w * (Lg2 + w * Lg4);
        const t2 = z * (Lg1 + w * Lg3);
        const R = t2 + t1;
        const hfsq = 0.5 * f * f;
        const dk = @intToFloat(f32, k);

        return s * (hfsq + R) + (dk * ln2_lo + c) - hfsq + f + dk * ln2_hi;
    }

    fn log1p_64(x: f64) f64 {
        const ln2_hi: f64 = 6.93147180369123816490e-01;
        const ln2_lo: f64 = 1.90821492927058770002e-10;
        const Lg1: f64 = 6.666666666666735130e-01;
        const Lg2: f64 = 3.999999999940941908e-01;
        const Lg3: f64 = 2.857142874366239149e-01;
        const Lg4: f64 = 2.222219843214978396e-01;
        const Lg5: f64 = 1.818357216161805012e-01;
        const Lg6: f64 = 1.531383769920937332e-01;
        const Lg7: f64 = 1.479819860511658591e-01;

        var ix = @bitCast(u64, x);
        var hx = @intCast(u32, ix >> 32);
        var k: i32 = 1;
        var c: f64 = undefined;
        var f: f64 = undefined;

        // 1 + x < sqrt(2)

        if (hx < 0x3FDA827A or hx >> 31 != 0) {
            // x <= -1.0

            if (hx >= 0xBFF00000) {
                // log1p(-1) = -inf

                if (x == -1.0) {
                    return -math.inf(f64);
                }
                // log1p(x < -1) = nan

                else {
                    return math.nan(f64);
                }
            }
            // |x| < 2^(-53)

            if ((hx << 1) < (0x3CA00000 << 1)) {
                if ((hx & 0x7FF00000) == 0) {
                    math.raiseUnderflow();
                }
                return x;
            }
            // sqrt(2) / 2- <= 1 + x < sqrt(2)+

            if (hx <= 0xBFD2BEC4) {
                k = 0;
                c = 0;
                f = x;
            }
        } else if (hx >= 0x7FF00000) {
            return x;
        }

        if (k != 0) {
            const uf = 1 + x;
            const hu = @bitCast(u64, uf);
            var iu = @intCast(u32, hu >> 32);
            iu += 0x3FF00000 - 0x3FE6A09E;
            k = @intCast(i32, iu >> 20) - 0x3FF;

            // correction to avoid underflow in c / u

            if (k < 54) {
                c = if (k >= 2) 1 - (uf - x) else x - (uf - 1);
                c /= uf;
            } else {
                c = 0;
            }

            // u into [sqrt(2)/2, sqrt(2)]

            iu = (iu & 0x000FFFFF) + 0x3FE6A09E;
            const iq = (@as(u64, iu) << 32) | (hu & 0xFFFFFFFF);
            f = @bitCast(f64, iq) - 1;
        }

        const hfsq = 0.5 * f * f;
        const s = f / (2.0 + f);
        const z = s * s;
        const w = z * z;
        const t1 = w * (Lg2 + w * (Lg4 + w * Lg6));
        const t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7)));
        const R = t2 + t1;
        const dk = @intToFloat(f64, k);

        return s * (hfsq + R) + (dk * ln2_lo + c) - hfsq + f + dk * ln2_hi;
    }

    test "math.log1p" {
        try expect(log1p(@as(f32, 0.0)) == log1p_32(0.0));
        try expect(log1p(@as(f64, 0.0)) == log1p_64(0.0));
    }

    test "math.log1p_32" {
        const epsilon = 0.000001;

        try expect(math.approxEqAbs(f32, log1p_32(0.0), 0.0, epsilon));
        try expect(math.approxEqAbs(f32, log1p_32(0.2), 0.182322, epsilon));
        try expect(math.approxEqAbs(f32, log1p_32(0.8923), 0.637793, epsilon));
        try expect(math.approxEqAbs(f32, log1p_32(1.5), 0.916291, epsilon));
        try expect(math.approxEqAbs(f32, log1p_32(37.45), 3.649359, epsilon));
        try expect(math.approxEqAbs(f32, log1p_32(89.123), 4.501175, epsilon));
        try expect(math.approxEqAbs(f32, log1p_32(123123.234375), 11.720949, epsilon));
    }

    test "math.log1p_64" {
        const epsilon = 0.000001;

        try expect(math.approxEqAbs(f64, log1p_64(0.0), 0.0, epsilon));
        try expect(math.approxEqAbs(f64, log1p_64(0.2), 0.182322, epsilon));
        try expect(math.approxEqAbs(f64, log1p_64(0.8923), 0.637793, epsilon));
        try expect(math.approxEqAbs(f64, log1p_64(1.5), 0.916291, epsilon));
        try expect(math.approxEqAbs(f64, log1p_64(37.45), 3.649359, epsilon));
        try expect(math.approxEqAbs(f64, log1p_64(89.123), 4.501175, epsilon));
        try expect(math.approxEqAbs(f64, log1p_64(123123.234375), 11.720949, epsilon));
    }

    test "math.log1p_32.special" {
        try expect(math.isPositiveInf(log1p_32(math.inf(f32))));
        try expect(log1p_32(0.0) == 0.0);
        try expect(log1p_32(-0.0) == -0.0);
        try expect(math.isNegativeInf(log1p_32(-1.0)));
        try expect(math.isNan(log1p_32(-2.0)));
        try expect(math.isNan(log1p_32(math.nan(f32))));
    }

    test "math.log1p_64.special" {
        try expect(math.isPositiveInf(log1p_64(math.inf(f64))));
        try expect(log1p_64(0.0) == 0.0);
        try expect(log1p_64(-0.0) == -0.0);
        try expect(math.isNegativeInf(log1p_64(-1.0)));
        try expect(math.isNan(log1p_64(-2.0)));
        try expect(math.isNan(log1p_64(math.nan(f64))));
    }