fn cbrt64(x: f64) f64x: f6466
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120fn cbrt64(x: f64) f64 {
const B1: u32 = 715094163; // (1023 - 1023 / 3 - 0.03306235651 * 2^20
const B2: u32 = 696219795; // (1023 - 1023 / 3 - 54 / 3 - 0.03306235651 * 2^20
// |1 / cbrt(x) - p(x)| < 2^(23.5)
const P0: f64 = 1.87595182427177009643;
const P1: f64 = -1.88497979543377169875;
const P2: f64 = 1.621429720105354466140;
const P3: f64 = -0.758397934778766047437;
const P4: f64 = 0.145996192886612446982;
var u = @as(u64, @bitCast(x));
var hx = @as(u32, @intCast(u >> 32)) & 0x7FFFFFFF;
// cbrt(nan, inf) = itself
if (hx >= 0x7FF00000) {
return x + x;
}
// cbrt to ~5bits
if (hx < 0x00100000) {
u = @as(u64, @bitCast(x * 0x1.0p54));
hx = @as(u32, @intCast(u >> 32)) & 0x7FFFFFFF;
// cbrt(+-0) = itself
if (hx == 0) {
return x;
}
hx = hx / 3 + B2;
} else {
hx = hx / 3 + B1;
}
u &= 1 << 63;
u |= @as(u64, hx) << 32;
var t = @as(f64, @bitCast(u));
// cbrt to 23 bits
// cbrt(x) = t * cbrt(x / t^3) ~= t * P(t^3 / x)
const r = (t * t) * (t / x);
t = t * ((P0 + r * (P1 + r * P2)) + ((r * r) * r) * (P3 + r * P4));
// Round t away from 0 to 23 bits
u = @as(u64, @bitCast(t));
u = (u + 0x80000000) & 0xFFFFFFFFC0000000;
t = @as(f64, @bitCast(u));
// one step newton to 53 bits
const s = t * t;
var q = x / s;
const w = t + t;
q = (q - t) / (w + q);
return t + t * q;
}