Popcount walks: next, previous, toward and nearest

Informal (and by-example) derivation of walking adjacent integers with the same population count as the input.

A fast path floating point underflow test elision from absorption

A sketch of a fast path filter to avoid explicit underflow checking following an addition or subtraction.

Stable look-at rotations

Derives stable look-at computations for Yaw/Pitch, swing-twist and quaternions

Weighted function approximation: angle trisection

Example of a weighted sum of functions approximation: trisect an angle

An evil and odious map (partition into even/odd parity in increasing order)

Presents a map that paritions integers into the even and odd parity subsets where each are in increasing order

A fast perfect shuffle for n≤64

Describes a perfect shuffle using a bitset and the original pencil-and-paper Fisher-Yates method.

Quaternion swing twist decomposition

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.

Random number draws with fixed parity

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

A cheap normal distribution approximation

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

Error growth of composing rotations

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

Basic uniform random floating-point values

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.

Solve power-of-two LCG for constants

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

A design and implementation of sincospi in binary32

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

Generating the log of a uniform random float

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.

FMA: extended precision addition and multiplication by constant

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

Tau and the art of Windmill jousting

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

Got Gamma?

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

A slerp by half

Some notes computing the rotation half away between two inputs