MBR blog-a-like http://marc-b-reynolds.github.io Special cased quaternion log and exp Describes efficient implementations of scaled quaternion log and exp. Sat, 10 Oct 2026 00:00:00 +0000 http://marc-b-reynolds.github.io/quaternions/2026/10/10/QuatExpMap.html http://marc-b-reynolds.github.io/quaternions/2026/10/10/QuatExpMap.html Moving integer division to floating-point is trivial Shows that floating point trunc(x/y) equals integer x/y provided the integers fit in the floating point format. Mon, 10 Aug 2026 00:00:00 +0000 http://marc-b-reynolds.github.io/math/2026/08/10/IntDivByFP.html http://marc-b-reynolds.github.io/math/2026/08/10/IntDivByFP.html A normal/twist transform for TBN representation Covers a transform that converts the tangent and bitangent of a 3D frame to a point on the unit circle. Wed, 06 May 2026 00:00:00 +0000 http://marc-b-reynolds.github.io/math/2026/05/06/NormalTwist.html http://marc-b-reynolds.github.io/math/2026/05/06/NormalTwist.html Item weights vs. the Paradox of Rarity This post describes using item weights to define the relative frequency of drop rates. Wed, 01 Jan 2025 00:00:00 +0000 http://marc-b-reynolds.github.io/math/2025/01/01/Rarity.html http://marc-b-reynolds.github.io/math/2025/01/01/Rarity.html Comments on parameterized SplitMix and PCG style generators Builds up a rational for a presented method for generating the additive constant of a LCG or Weyl sequence based PRNG. Wed, 11 Dec 2024 00:00:00 +0000 http://marc-b-reynolds.github.io/math/2024/12/11/LCGAddConst.html http://marc-b-reynolds.github.io/math/2024/12/11/LCGAddConst.html Popcount walks: next, previous, toward and nearest Informal (and by-example) derivation of walking adjacent integers with the same population count as the input. Thu, 09 Nov 2023 00:00:00 +0000 http://marc-b-reynolds.github.io/math/2023/11/09/PopNextPrev.html http://marc-b-reynolds.github.io/math/2023/11/09/PopNextPrev.html 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. Wed, 12 Jul 2023 00:00:00 +0000 http://marc-b-reynolds.github.io/math/2023/07/12/FpAbsorbUnderflow.html http://marc-b-reynolds.github.io/math/2023/07/12/FpAbsorbUnderflow.html Stable look-at rotations Derives stable look-at computations for Yaw/Pitch, swing-twist and quaternions Thu, 15 Jun 2023 00:00:00 +0000 http://marc-b-reynolds.github.io/math/2023/06/15/LookAt.html http://marc-b-reynolds.github.io/math/2023/06/15/LookAt.html Weighted function approximation: angle trisection Example of a weighted sum of functions approximation: trisect an angle Sat, 21 Jan 2023 00:00:00 +0000 http://marc-b-reynolds.github.io/math/2023/01/21/Trisect.html http://marc-b-reynolds.github.io/math/2023/01/21/Trisect.html 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 Fri, 16 Dec 2022 00:00:00 +0000 http://marc-b-reynolds.github.io/math/2022/12/16/ParityWalks.html http://marc-b-reynolds.github.io/math/2022/12/16/ParityWalks.html