expm1_64

fn expm1_64(x_: f64) f64 {
    if (math.isNan(x_))
        return math.nan(f64);

    const o_threshold: f64 = 7.09782712893383973096e+02;
    const ln2_hi: f64 = 6.93147180369123816490e-01;
    const ln2_lo: f64 = 1.90821492927058770002e-10;
    const invln2: f64 = 1.44269504088896338700e+00;
    const Q1: f64 = -3.33333333333331316428e-02;
    const Q2: f64 = 1.58730158725481460165e-03;
    const Q3: f64 = -7.93650757867487942473e-05;
    const Q4: f64 = 4.00821782732936239552e-06;
    const Q5: f64 = -2.01099218183624371326e-07;

    var x = x_;
    const ux = @as(u64, @bitCast(x));
    const hx = @as(u32, @intCast(ux >> 32)) & 0x7FFFFFFF;
    const sign = ux >> 63;

    if (math.isNegativeInf(x)) {
        return -1.0;
    }

    // |x| >= 56 * ln2
    if (hx >= 0x4043687A) {
        // exp1md(nan) = nan
        if (hx > 0x7FF00000) {
            return x;
        }
        // exp1md(-ve) = -1
        if (sign != 0) {
            return -1;
        }
        if (x > o_threshold) {
            math.raiseOverflow();
            return math.inf(f64);
        }
    }

    var hi: f64 = undefined;
    var lo: f64 = undefined;
    var c: f64 = undefined;
    var k: i32 = undefined;

    // |x| > 0.5 * ln2
    if (hx > 0x3FD62E42) {
        // |x| < 1.5 * ln2
        if (hx < 0x3FF0A2B2) {
            if (sign == 0) {
                hi = x - ln2_hi;
                lo = ln2_lo;
                k = 1;
            } else {
                hi = x + ln2_hi;
                lo = -ln2_lo;
                k = -1;
            }
        } else {
            var kf = invln2 * x;
            if (sign != 0) {
                kf -= 0.5;
            } else {
                kf += 0.5;
            }

            k = @as(i32, @intFromFloat(kf));
            const t = @as(f64, @floatFromInt(k));
            hi = x - t * ln2_hi;
            lo = t * ln2_lo;
        }

        x = hi - lo;
        c = (hi - x) - lo;
    }
    // |x| < 2^(-54)
    else if (hx < 0x3C900000) {
        if (hx < 0x00100000) {
            mem.doNotOptimizeAway(@as(f32, @floatCast(x)));
        }
        return x;
    } else {
        k = 0;
    }

    const hfx = 0.5 * x;
    const hxs = x * hfx;
    const r1 = 1.0 + hxs * (Q1 + hxs * (Q2 + hxs * (Q3 + hxs * (Q4 + hxs * Q5))));
    const t = 3.0 - r1 * hfx;
    var e = hxs * ((r1 - t) / (6.0 - x * t));

    // c is 0
    if (k == 0) {
        return x - (x * e - hxs);
    }

    e = x * (e - c) - c;
    e -= hxs;

    // exp(x) ~ 2^k (x_reduced - e + 1)
    if (k == -1) {
        return 0.5 * (x - e) - 0.5;
    }
    if (k == 1) {
        if (x < -0.25) {
            return -2.0 * (e - (x + 0.5));
        } else {
            return 1.0 + 2.0 * (x - e);
        }
    }

    const twopk = @as(f64, @bitCast(@as(u64, @intCast(0x3FF +% k)) << 52));

    if (k < 0 or k > 56) {
        var y = x - e + 1.0;
        if (k == 1024) {
            y = y * 2.0 * 0x1.0p1023;
        } else {
            y = y * twopk;
        }

        return y - 1.0;
    }

    const uf = @as(f64, @bitCast(@as(u64, @intCast(0x3FF -% k)) << 52));
    if (k < 20) {
        return (x - e + (1 - uf)) * twopk;
    } else {
        return (x - (e + uf) + 1) * twopk;
    }
}