    // 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/complex/cexpf.c

    // https://git.musl-libc.org/cgit/musl/tree/src/complex/cexp.c

    const std = @import("../../std.zig");
    const testing = std.testing;
    const math = std.math;
    const cmath = math.complex;
    const Complex = cmath.Complex;

    const ldexp_cexp = @import("ldexp.zig").ldexp_cexp;

    /// Returns e raised to the power of z (e^z).
    pub fn exp(z: anytype) @TypeOf(z) {
        const T = @TypeOf(z.re);

        return switch (T) {
            f32 => exp32(z),
            f64 => exp64(z),
            else => @compileError("exp not implemented for " ++ @typeName(z)),
        };
    }

    fn exp32(z: Complex(f32)) Complex(f32) {
        const exp_overflow = 0x42b17218; // max_exp * ln2 ~= 88.72283955

        const cexp_overflow = 0x43400074; // (max_exp - min_denom_exp) * ln2

        const x = z.re;
        const y = z.im;

        const hy = @as(u32, @bitCast(y)) & 0x7fffffff;
        // cexp(x + i0) = exp(x) + i0

        if (hy == 0) {
            return Complex(f32).init(@exp(x), y);
        }

        const hx = @as(u32, @bitCast(x));
        // cexp(0 + iy) = cos(y) + isin(y)

        if ((hx & 0x7fffffff) == 0) {
            return Complex(f32).init(@cos(y), @sin(y));
        }

        if (hy >= 0x7f800000) {
            // cexp(finite|nan +- i inf|nan) = nan + i nan

            if ((hx & 0x7fffffff) != 0x7f800000) {
                return Complex(f32).init(y - y, y - y);
            } // cexp(-inf +- i inf|nan) = 0 + i0

            else if (hx & 0x80000000 != 0) {
                return Complex(f32).init(0, 0);
            } // cexp(+inf +- i inf|nan) = inf + i nan

            else {
                return Complex(f32).init(x, y - y);
            }
        }

        // 88.7 <= x <= 192 so must scale

        if (hx >= exp_overflow and hx <= cexp_overflow) {
            return ldexp_cexp(z, 0);
        } // - x < exp_overflow => exp(x) won't overflow (common)

        // - x > cexp_overflow, so exp(x) * s overflows for s > 0

        // - x = +-inf

        // - x = nan

        else {
            const exp_x = @exp(x);
            return Complex(f32).init(exp_x * @cos(y), exp_x * @sin(y));
        }
    }

    fn exp64(z: Complex(f64)) Complex(f64) {
        const exp_overflow = 0x40862e42; // high bits of max_exp * ln2 ~= 710

        const cexp_overflow = 0x4096b8e4; // (max_exp - min_denorm_exp) * ln2

        const x = z.re;
        const y = z.im;

        const fy: u64 = @bitCast(y);
        const hy: u32 = @intCast((fy >> 32) & 0x7fffffff);
        const ly: u32 = @truncate(fy);

        // cexp(x + i0) = exp(x) + i0

        if (hy | ly == 0) {
            return Complex(f64).init(@exp(x), y);
        }

        const fx: u64 = @bitCast(x);
        const hx: u32 = @intCast(fx >> 32);
        const lx: u32 = @truncate(fx);

        // cexp(0 + iy) = cos(y) + isin(y)

        if ((hx & 0x7fffffff) | lx == 0) {
            return Complex(f64).init(@cos(y), @sin(y));
        }

        if (hy >= 0x7ff00000) {
            // cexp(finite|nan +- i inf|nan) = nan + i nan

            if (lx != 0 or (hx & 0x7fffffff) != 0x7ff00000) {
                return Complex(f64).init(y - y, y - y);
            } // cexp(-inf +- i inf|nan) = 0 + i0

            else if (hx & 0x80000000 != 0) {
                return Complex(f64).init(0, 0);
            } // cexp(+inf +- i inf|nan) = inf + i nan

            else {
                return Complex(f64).init(x, y - y);
            }
        }

        // 709.7 <= x <= 1454.3 so must scale

        if (hx >= exp_overflow and hx <= cexp_overflow) {
            return ldexp_cexp(z, 0);
        } // - x < exp_overflow => exp(x) won't overflow (common)

        // - x > cexp_overflow, so exp(x) * s overflows for s > 0

        // - x = +-inf

        // - x = nan

        else {
            const exp_x = @exp(x);
            return Complex(f64).init(exp_x * @cos(y), exp_x * @sin(y));
        }
    }

    test "complex.cexp32" {
        const tolerance_f32 = @sqrt(math.floatEps(f32));

        {
            const a = Complex(f32).init(5, 3);
            const c = exp(a);

            try testing.expectApproxEqRel(@as(f32, -1.46927917e+02), c.re, tolerance_f32);
            try testing.expectApproxEqRel(@as(f32, 2.0944065e+01), c.im, tolerance_f32);
        }

        {
            const a = Complex(f32).init(88.8, 0x1p-149);
            const c = exp(a);

            try testing.expectApproxEqAbs(math.inf(f32), c.re, tolerance_f32);
            try testing.expectApproxEqAbs(@as(f32, 5.15088629e-07), c.im, tolerance_f32);
        }
    }

    test "complex.cexp64" {
        const tolerance_f64 = @sqrt(math.floatEps(f64));

        {
            const a = Complex(f64).init(5, 3);
            const c = exp(a);

            try testing.expectApproxEqRel(@as(f64, -1.469279139083189e+02), c.re, tolerance_f64);
            try testing.expectApproxEqRel(@as(f64, 2.094406620874596e+01), c.im, tolerance_f64);
        }

        {
            const a = Complex(f64).init(709.8, 0x1p-1074);
            const c = exp(a);

            try testing.expectApproxEqAbs(math.inf(f64), c.re, tolerance_f64);
            try testing.expectApproxEqAbs(@as(f64, 9.036659362159884e-16), c.im, tolerance_f64);
        }
    }