Fast Cube Root ( < 2^32 ), part 2

/*
The mean time to take a cube root from a 32 bits uint was: < 13 ns
                                            new mean time: < 12 ns

It is a bit faster, especially for large values, because variables are initialized properly.
       
       |--------------------------------|
       |         cro32(x)               |       
       |-----|-----||------------|------|       
       |   x |  ns ||          x |   ns |       
       |-----|-----||------------|------|
       |   0 | 3,0 ||        511 |  4,6 |       
       |   1 | 2,3 ||       1023 |  5,3 |       
       |   3 | 2,3 ||       2047 |  5,6 |               ___
       |   7 | 2,3 ||       4095 |  5,0 |           \3 /                
       |  15 | 3,3 ||      32768 |  7,6 |            \/  x = y          
       |  31 | 2,6 ||    1048576 |  9,0 |          
       |  63 | 2,6 ||  268435456 | 11,0 |           Input: 0 <= x < 2^32
       |  64 | 5,0 ||  536870912 | 11,3 |          Output: y, such that y^3 <= x < (y+1)^3
       |  65 | 5,0 || 1070599167 | 13,0 |       
       | 100 | 5,0 || 1070599168 | 13,0 |
       | 127 | 5,0 || 1073741824 | 11,3 |
       | 128 | 5,3 || 1073774592 | 11,3 |
       | 255 | 4,6 || 2147483648 | 11,0 |
       | 256 | 4,6 || 4294967295 | 11,7 |
       |-----|-----||------------|------|
       
       4294967295 roots in 50686 ms, mean time 11,80 ns (before 12,55 ns)
       
Another way to find roots is using a look-up table. Below "fill_cubes" fills a "cubes" array,
"cro32t" does a binary search for a root. Mean time: 30 ns.
I have not tried to optimize it further, I see no reason why it should be much faster.
*/

using System;
using System.Diagnostics;
class cube_root
{
    private static uint cro32(uint x)
    {
        uint y = 4u, z = 16u, b = 61u << 21;
        if (x < 1u << 24)
            if (x < 1u << 12)
                if (x < 1u << 06)
                    if (x < 1u << 03)
                        return x == 0u ? 0u : 1u;
                    else
                        return x < 27u ? 2u : 3u;
                else
                    if (x < 1u << 09) goto L8; else goto L7;
            else
                if (x < 1u << 18)
                    if (x < 1u << 15) goto L6; else goto L5;
                else
                    if (x < 1u << 21) goto L4; else goto L3;
        else
            if (x < 1u << 30)
                if (x < 1u << 27) goto L2;
                else
                {
                    if (x >= 27u << 24) { x -= 27u << 24; z = 36u; y = 6u; b = 127u << 21; }
                    else { x -= 1u << 27; }
                }
            else
            {
                if (x >= 27u << 27) { x -= 27u << 27; z = 144u; y = 12u; b = 469u << 21; }
                else
                {
                    if (x >= 125u << 24) { x -= 125u << 24; z = 100u; y = 10u; b = 331u << 21; }
                    else { x -= 1u << 30; z = 64u; y = 8u; b = 217u << 21; }
                }
            }
        goto M1;

    L2: if (x >= 27u << 21) { x -= 27u << 21; z = 36u; y = 6u; } else { x -= 1u << 24; } goto M2;
    L3: if (x >= 27u << 18) { x -= 27u << 18; z = 36u; y = 6u; } else { x -= 1u << 21; } goto M3;
    L4: if (x >= 27u << 15) { x -= 27u << 15; z = 36u; y = 6u; } else { x -= 1u << 18; } goto M4;
    L5: if (x >= 27u << 12) { x -= 27u << 12; z = 36u; y = 6u; } else { x -= 1u << 15; } goto M5;
    L6: if (x >= 27u << 09) { x -= 27u << 09; z = 36u; y = 6u; } else { x -= 1u << 12; } goto M6;
    L7: if (x >= 27u << 06) { x -= 27u << 06; z = 36u; y = 6u; } else { x -= 1u << 09; } goto M7;
    L8: if (x >= 27u << 03) { x -= 27u << 03; z = 36u; y = 6u; } else { x -= 1u << 06; } goto M8;

    M1: if (x >= b) { x -= b; z += y * 2 + 1u; y += 1u; } y *= 2; z *= 4;
    M2: b = (y + z) * 3 + 1u << 18; if (x >= b) { x -= b; z += y * 2 + 1u; y += 1u; } y *= 2; z *= 4;
    M3: b = (y + z) * 3 + 1u << 15; if (x >= b) { x -= b; z += y * 2 + 1u; y += 1u; } y *= 2; z *= 4;
    M4: b = (y + z) * 3 + 1u << 12; if (x >= b) { x -= b; z += y * 2 + 1u; y += 1u; } y *= 2; z *= 4;
    M5: b = (y + z) * 3 + 1u << 09; if (x >= b) { x -= b; z += y * 2 + 1u; y += 1u; } y *= 2; z *= 4;
    M6: b = (y + z) * 3 + 1u << 06; if (x >= b) { x -= b; z += y * 2 + 1u; y += 1u; } y *= 2; z *= 4;
    M7: b = (y + z) * 3 + 1u << 03; if (x >= b) { x -= b; z += y * 2 + 1u; y += 1u; } y *= 2; z *= 4;
    M8: return x <= (y + z) * 3 ? y : y + 1u;
    }

    private static uint[] cubes = new uint[2048];
    private static void fill_cubes()
    {
        int i = 0; uint a = 0u, b = 1u, c = 6u;
        do
        {
            cubes[i++] = a;
            a += b; b += c; c += 6u;
        }
        while (i < 1626);
        do cubes[i++] = ~0u;
        while (i < 2048);
    }
    private static uint cro32t(uint x)
    {
        uint i = 1u << 10, j = 1u << 9, u = 1u << 30;
        for (; j > 0; j >>= 1)
        {
            if (x < u) i -= j;
            else if (x > u) i += j;
            else return i < 1625u ? i : 1625u;
            u = cubes[i];
        }
        return x < u ? i - 1 : i;
    }

    private static Stopwatch sw = new Stopwatch();
    static void Main(string[] args)
    {
        cro32_all();        // ~1 minute, comment out "cro32t" , uint[] cubes, etc.
                            //  Or try seperate executables.

        fill_cubes();
        cro32t_all();       // ~2 minutes
        Console.ReadLine();
    }
    private static void cro32_all()
    {
        uint x; double t;
        cro32(~0u);
        sw.Restart();
        for (x = 0; x < ~0u; x++) cro32(x);
        sw.Stop();
        t = sw.ElapsedMilliseconds;
        sw.Restart();
        for (x = 0; x < ~0u; x++) ; // nada
        sw.Stop();
        t -= sw.ElapsedMilliseconds;
        Console.Write(x + " roots in " + t + " ms, ");
        Console.WriteLine("mean time {0:.00} ns", t * 1000000 / x);
        // 4294967295 roots in 50686 ms, mean time 11,80 ns
    }
    private static void cro32t_all()
    {
        uint x; double t;
        cro32t(~0u);
        sw.Restart();
        for (x = 0; x < ~0u; x++) cro32t(x);
        sw.Stop();
        t = sw.ElapsedMilliseconds;
        sw.Restart();
        for (x = 0; x < ~0u; x++) ; // nada
        sw.Stop();
        t -= sw.ElapsedMilliseconds;
        Console.Write(x + " roots in " + t + " ms, ");
        Console.WriteLine("mean time {0:.00} ns", t * 1000000 / x);
        // 4294967295 roots in 129254 ms, mean time 30,09 ns
    }
}