public static float[] RadixSort(this float[] array)
{
    // temporary array and the array of converted floats to ints
    int[] t = new int[array.Length];
    int[] a = new int[array.Length];
    for (int i = 0; i < array.Length; i++)
        a[i] = BitConverter.ToInt32(BitConverter.GetBytes(array[i]), 0);

    // set the group length to 1, 2, 4, 8 or 16
    // and see which one is quicker
    int groupLength = 4;
    int bitLength = 32;

    // counting and prefix arrays
    // (dimension is 2^r, the number of possible values of a r-bit number)
    int[] count = new int[1 << groupLength];
    int[] pref = new int[1 << groupLength];
    int groups = bitLength / groupLength;
    int mask = (1 << groupLength) - 1;
    int negatives = 0, positives = 0;

    for (int c = 0, shift = 0; c < groups; c++, shift += groupLength)
    {
        // reset count array
        for (int j = 0; j < count.Length; j++)
            count[j] = 0;

        // counting elements of the c-th group
        for (int i = 0; i < a.Length; i++)
        {
            count[(a[i] >> shift) & mask]++;

            // additionally count all negative
            // values in first round
            if (c == 0 && a[i] < 0)
                negatives++;
        }
        if (c == 0) positives = a.Length - negatives;

        // calculating prefixes
        pref[0] = 0;
        for (int i = 1; i < count.Length; i++)
            pref[i] = pref[i - 1] + count[i - 1];

        // from a[] to t[] elements ordered by c-th group
        for (int i = 0; i < a.Length; i++){
            // Get the right index to sort the number in
            int index = pref[(a[i] >> shift) & mask]++;

            if (c == groups - 1)
            {
                // We're in the last (most significant) group, if the
                // number is negative, order them inversely in front
                // of the array, pushing positive ones back.
                if (a[i] < 0)
                    index = positives - (index - negatives) - 1;
                else
                    index += negatives;
            }
            t[index] = a[i];
        }

        // a[]=t[] and start again until the last group
        t.CopyTo(a, 0);
    }

    // Convert back the ints to the float array
    float[] ret = new float[a.Length];
    for (int i = 0; i < a.Length; i++)
        ret[i] = BitConverter.ToSingle(BitConverter.GetBytes(a[i]), 0);

    return ret;
}

ret[i] = BitConverter.ToSingle(BitConverter.GetBytes(a[i]), 0);

ret[a.Length - i - 1] = BitConverter.ToSingle(BitConverter.GetBytes(a[i]), 0);

NaN -> -Inf -> Min -> Negative Nums -> 0 -> Positive Nums -> Max -> +Inf

float[] test = new float[10000000];
Random rnd = new Random();
for (int i = 0; i < test.Length; i++)
{
    byte[] buffer = new byte[4];
    rnd.NextBytes(buffer);
    float rndfloat = BitConverter.ToSingle(buffer, 0);
    switch(i){
        case 0: { test[i] = float.MaxValue; break; }
        case 1: { test[i] = float.MinValue; break; }
        case 2: { test[i] = float.NaN; break; }
        case 3: { test[i] = float.NegativeInfinity; break; }
        case 4: { test[i] = float.PositiveInfinity; break; }
        case 5: { test[i] = 0f; break; }
        default: { test[i] = test[i] = rndfloat; break; }
    }
}

Stopwatch sw = new Stopwatch();
sw.Start();

float[] sorted1 = test.RadixSort();

sw.Stop();
Console.WriteLine(string.Format("RadixSort: {0}", sw.Elapsed));
sw.Reset();
sw.Start();

float[] sorted2 = test.OrderBy(x => x).ToArray();

sw.Stop();
Console.WriteLine(string.Format("Linq OrderBy: {0}", sw.Elapsed));
sw.Reset();
sw.Start();

Array.Sort(test);
float[] sorted3 = test;

sw.Stop();
Console.WriteLine(string.Format("Array.Sort: {0}", sw.Elapsed));

RadixSort: 00:00:03.9902332
Linq OrderBy: 00:00:17.4983272
Array.Sort: 00:00:03.1536785

RadixSort: 00:00:00.0012944
Linq OrderBy: 00:00:00.0072271
Array.Sort: 00:00:00.0002979

static public void RadixSortFloat(this float[] array, int arrayLen = -1)
        {
            // Some use cases have an array that is longer as the filled part which we want to sort
            if (arrayLen < 0) arrayLen = array.Length;
            // Cast our original array as long
            Span<float> asFloat = array;
            Span<int> t = MemoryMarshal.Cast<float, int>(asFloat);
            // Create a temp array
            Span<int> a = new Span<int>(new int[arrayLen]);

            // set the group length to 1, 2, 4, 8 or 16
            // and see which one is quicker
            int groupLength = 16;
            int bitLength = 32;

            // counting and prefix arrays
            // (dimension is 2^r, the number of possible values of a r-bit number)
            var dim = 1 << groupLength;
            var count = new int[dim];
            var pref = new int[dim];
            int groups = bitLength / groupLength;
            int mask = (dim) - 1;
            int negatives = 0, positives = 0;

            for (int c = 0, shift = 0; c < groups; c++, shift += groupLength)
            {
                // reset count array
                for (int j = 0; j < dim; j++) count[j] = 0;

                // counting elements of the c-th group
                for (int i = 0; i < arrayLen; i++)
                {
                    count[(a[i] >> shift) & mask]++;

                    // additionally count all negative
                    // values in first round
                    if (c == 0 && a[i] < 0)
                        negatives++;
                }
                if (c == 0) positives = a.Length - negatives;

                // calculating prefixes
                pref[0] = 0;
                for (int i = 1; i < dim; i++) pref[i] = pref[i - 1] + count[i - 1];

                // from a[] to t[] elements ordered by c-th group
                for (int i = 0; i < a.Length; i++)
                {
                    // Get the right index to sort the number in
                    int index = pref[(a[i] >> shift) & mask]++;

                    if (c == groups - 1)
                    {
                        // We're in the last (most significant) group, if the
                        // number is negative, order them inversely in front
                        // of the array, pushing positive ones back.
                        if (a[i] < 0)
                            index = positives - (index - negatives) - 1;
                        else
                            index += negatives;
                    }
                    t[index] = a[i];
                }

                // swap the arrays and start again until the last group
                var temp = a;
                a = t;
                t = temp;
            }

            // Convert back the ints to the float array if we did an uneven number of copy swap runs
            if (groups % 2 != 0)
            {
                asFloat = MemoryMarshal.Cast<int, float>(a);
                for (int i = 0; i < arrayLen; i++) array[i] = asFloat[i];
            }
        }