Given a unit quaternion $Q$ factor into a pair such that $Q = Q_rQ_a$ where $a$ is a predefined axis and $r$ is an orthogonal axis. This is commonly called swing-twist decomposition.

Describes simple transforms to generate random numbers with a given parity and the math background.

A brief explaination and implementation of the standard normal distribution approximation "on the cheap".

Some quick-n-dirty empirical results to spitball the error growth on composing rotations

Micropost on unbiased uniform float generation on $\left(0,1\right]$, $\left[-1,1\right)$ and $\left[-1,1\right)$. The latter two have twice the number of samples as the standard method.

A quick derivation of solving for LCG constants (power-of-two modulus) given three sequential outputs of the generator.

Walks through constructing faithfully rounded $\sin\left(\pi x\right)$ and $\cos\left(\pi x\right)$.

Sketches out some possible implementations of taking the logarithm of a uniform floating point value.

Computing Weyl (additive recurrence) sequences in float-point has some gotchas.

Micro-post on title.

Brushstrokes using FMAs to compute: K+x and Kx with K in higher than native precision.

TLDR: Use tau if you want, but you need a good argument to say pi was a historic mistake.

A breakdown on my joke approximation of $x^{2.2}$

Some notes computing the rotation half away between two inputs

A feasibility study to determine if an involution can be competitive (quality and cost) bit mixer.

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.

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

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

A small note on division removal

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