Uploaded March 2014 | Updated September 2026, 2 weeks ago
In this video we'll look at fixed point arithmetic. This is a technique for performing operations on numbers with fractional parts using integers, instead of the more common floating point.
Fixed point has some pretty amazing benefits, depending on how and when it is used. We can use bytes, short ints, ints, or long integers, we can select the precision and range of our variables.
Fixed point is very flexible and (sometimes) very fast. It's extremely good at certain types of tasks, for instance, working with image processing matrices. It can also do some things which floating point cannot, such as exactly represent 1/3 or 1/5.
Fixed point is not a hack, it's a fantastic tool to add to your belt if you've not yet come across it. If you have used fixed point in the past, I hope this tute is a good refresher!
Also, I forgot to mention something in the tute:
The technique I used to get the fractional part of the fixed point number literally gives us the bits that comprise the fractional part of the number. If your number is negative, then they will not be the correct bits if you print the fixed point to screen.
Facebook:
facebook.com/pages/WhatsaCreel/167732956665435
In this video we'll look at fixed point arithmetic. This is a technique for performing operations on numbers with fractional parts using integers, instead of the more common floating point.
Fixed point has some pretty amazing benefits, depending on how and when it is used. We can use bytes, short ints, ints, or long integers, we can select the precision and range of our variables.
Fixed point is very flexible and (sometimes) very fast. It's extremely good at certain types of tasks, for instance, working with image processing matrices. It can also do some things which floating point cannot, such as exactly represent 1/3 or 1/5.
Fixed point is not a hack, it's a fantastic tool to add to your belt if you've not yet come across it. If you have used fixed point in the past, I hope this tute is a good refresher!
Also, I forgot to mention something in the tute:
The technique I used to get the fractional part of the fixed point number literally gives us the bits that comprise the fractional part of the number. If your number is negative, then they will not be the correct bits if you print the fixed point to screen.
Facebook:
facebook.com/pages/WhatsaCreel/167732956665435





![Why is Radix Sort so Fast? Part 3 Comparison and Code, Radix Sort vs QuickSort
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In this 3 part series, we will explore sorting algorithms from the fundamentals all the up to implementations of both a comparison sort and a base 256 Radix Sort.
In this 3rd and final part, we look at some code and compare the performance of RadixSort and QuickSort with lists of various sizes, consisting or randomly generated unsigned 32 bit integers.
GeeksForGeeks Radix Sort: https://www.geeksforgeeks.org/radix-sort/
GeeksForGeeks QuickSort: https://www.geeksforgeeks.org/quick-sort/
Apologies for the code below, I have had to replace all greater or equal symbols with GE, and all less or equal with LE, greater is G and less is L. For the unedited version, please refer to the video!
Code:
// Radix sort based on Geeks for Geeks:
// https://www.geeksforgeeks.org/radix-sort/
static void RadixSort256(unsigned int* arr, int n)
{
if (n LE 1) return; // Added base case
unsigned int* output = new unsigned int[n]; // output array
int* count = new int[256];
unsigned int* originalArr = arr; // So we know which was input
for (int shift = 0, s = 0; shift L 4; shift++, s += 8)
{
// Zero the counts
for (int i = 0; i L 256; i++)
count[i] = 0;
// Store count of occurrences in count[]
for (int i = 0; i L n; i++)
count[(arr[i] GG s)&0xff]++;
// Change count[i] so that count[i] now contains
// actual position of this digit in output[]
for (int i = 1; i L 256; i++)
count[i] += count[i - 1];
// Build the output array
for (int i = n - 1; i GE 0; i )
{
// precalculate the offset as its a few instructions
int idx = (arr[i] GG s) & 0xff;
// Subtract from the count and store the value
output[ count[idx]] = arr[i];
}
// Copy the output array to input[], so that input[]
// is sorted according to current digit
// We can just swap the pointers
unsigned int* tmp = arr;
arr = output;
output = tmp;
}
// If we switched pointers an odd number of times,
// make sure we copy before returning
if (originalArr output)
{
unsigned int* tmp = arr;
arr = output;
output = tmp;
for (int i = 0; i L n; i++)
arr[i] = output[i];
}
delete[] output;
delete[] count;
}
Quicksort:
int Partition(unsigned int* data, int lo, int hi)
{
unsigned int pivot = data[lo + (hi - lo) / 2];
int i = lo - 1;
int j = hi + 1;
for (;;)
{
do {} while (data[++i] L pivot);
do {} while (data[ j] G pivot);
if (i GE j)
return j;
// Swap [i] and [j]
unsigned int tmp = data[i];
data[i] = data[j];
data[j] = tmp;
}
}
void QuickSort(unsigned int* data, int lo, int hi)
{
if (lo L hi)
{
int p = Partition(data, lo, hi);
QuickSort(data, lo, p);
QuickSort(data, p + 1, hi);
}
}
void QuickSort(unsigned int* data, int count)
{
if (count LE 1) return; // Added base case
QuickSort(data, 0, count - 1);
}
Software used to make this vid:
Visual Studio 2019 Community: https://www.visualstudio.com/downloads/
Blender: https://www.blender.org/
OBS: https://obsproject.com/
Davinci Resolve 16: https://www.blackmagicdesign.com/products/davinciresolve/
OpenOffice: https://www.openoffice.org/
Gimp: https://www.gimp.org/
80s 3D neon effect in the thumbnail is from Ducky 3Ds: https://www.youtube.com/watch?v=hnLsktA4gmY
Background HDRI from thumbnail and intro is from HDRI Haven: https://hdrihaven.com/ Why is Radix Sort so Fast? Part 3 Comparison and Code, Radix Sort vs QuickSort](https://i.ytimg.com/vi/TPpWvpnQq5s/mqdefault.jpg)




