Comments on the Avalanche Effect

A quick overview of what "Avalanche Effect" properties are, why they can be used to test and search for PRNGs and overview of how to convert the property into a comparision measurement.

Some comments on approximately equal FP comparisons

In which I point to some other peoples blog posts and make some minor comments.

Measuring ULP distance

Some code for measuring the ULP distance between floats with comments.

Floating point division with known divisor

A small note on division removal

posit: thin triangle other tricks (REVEALED!)

First post in breaking down why the posits presentations are egregiously disingenuous.

An empirical testing point set on sphere and caps

Code for incrementally generating a spherical Fibonacci point set on a spherical cap

Solving for quaternion rotation from a vector viewpoint

A short description of solving a quaternion rotation using vectors

Volume element of SO(3) and average uniform random rotation angle

Find the expression of a volume element of rotations.

Basic XOR-rotates and their inverse

Simplified description of bijections formed only from XORs and bit rotations.

Table of basic reversible integer operations

A table and some comments on integer bijections.

PRNS with 32 bits of state

A multistream low complexity random access PRNG/permutation generator.

Integer multiplicative inverse via Newton's method

A short note on computing the modular multiplicative inverse of an odd integer.

Linear Congruential Sequences

A small list of properties of full-period sequences for reference.

On quaternion/rotation matrix conversions and errors

Skims the math of quaternions to rotations matrices and back with empirical errors including small angle special case.

Hopf coordinate conversion and torque minimal factorization

Gives a mile-high overview of the Hopf map from geometry perspective.

Quaternion quantization: part 1

An overview of full-range context-free quantization of quaternions into fixed bit package.

Converting to Euler & Tait-Bryan

A note on reducing errors when converting to Euler angles or Tait-Bryan paramerters.

Uniform random 3D rotations

a brief note on generating random rotations in 3D