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Pseudo Random Numbers

An app-note describes how to generate random numbers using the CRC instruction, and how to generate real random numbers [xmosrandom]. In short, a pseudo random sequence can be generated using the CRC instruction and a suitable polynomial.

For specific purposes, random numbers may need to have a specific distribution. As an example, we show here how to make a pseudo random number generator that generates random values with a Triangular Probability Density Function (TPDF), used in, for example, audio dithering.

Below is the code to generate those numbers. It generates a 32-bit pseudo random number, takes the bottom and top bits, sums those, and normalises it around 0. It generates random numbers in the range $[1..2^{2B}-1]$, with a PDF $P\left(x\right)=2^{-B}-2^{-2B}|x-2^B+1|$:

#define POLYNOMIAL 0xEDB88320
#define B 8

unsigned int seed = 0xffffffff;

int tpdf() {
  int value1, value2;

  crc32(seed, ~0, POLYNOMIAL);
  value1 = seed >> (32-B);
  value2 = seed & ((1<<B)-1);
  return value1 + value2 + 1;
}

The value from this random number geneator can, for example, be used to initialise the accumulator prior to performing a series of multiply accumulate operations.

[xmosrandom]

Random numbers on the XS1-L1, http://www.xmos.com/published/randoman