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cbrt32

cbrt.cbrt32

fn cbrt32(x: f32) f32

File

lib/std/math/cbrt.zig:26

Code

fn cbrt32(x: f32) f32 {
    const B1: u32 = 709958130; // (127 - 127.0 / 3 - 0.03306235651) * 2^23
    const B2: u32 = 642849266; // (127 - 127.0 / 3 - 24 / 3 - 0.03306235651) * 2^23

    var u = @as(u32, @bitCast(x));
    var hx = u & 0x7FFFFFFF;

    // cbrt(nan, inf) = itself
    if (hx >= 0x7F800000) {
        return x + x;
    }

    // cbrt to ~5bits
    if (hx < 0x00800000) {
        // cbrt(+-0) = itself
        if (hx == 0) {
            return x;
        }
        u = @as(u32, @bitCast(x * 0x1.0p24));
        hx = u & 0x7FFFFFFF;
        hx = hx / 3 + B2;
    } else {
        hx = hx / 3 + B1;
    }

    u &= 0x80000000;
    u |= hx;

    // first step newton to 16 bits
    var t: f64 = @as(f32, @bitCast(u));
    var r: f64 = t * t * t;
    t = t * (@as(f64, x) + x + r) / (x + r + r);

    // second step newton to 47 bits
    r = t * t * t;
    t = t * (@as(f64, x) + x + r) / (x + r + r);

    return @as(f32, @floatCast(t));
}