Tag
floating-point
- Oct 24, 2026 Conditioning, Tolerances, and the Digits a Reproduction Can Demand How the condition number sets the width of the interval a computed result actually occupies, and how that interval determines which differences between two runs are meaningful. scientific computing
- Oct 22, 2026 Ray-Triangle Intersection and the Watertight Edge Test How the ray-triangle test is derived from Cramer rule, why shared edges produce pinhole artifacts, and what a watertight edge function buys and costs. computer graphics
- Oct 16, 2026 Choosing Between fp16 and bf16: Exponent Range and Mantissa Budget Both formats are 16 bits, but they split those bits differently. The split decides whether a training run needs loss scaling and how much precision each weight update retains. deep learning
- Jun 9, 2026 Delta-of-Delta Timestamps and XOR Float Encoding on Disk How a time series block compresses to roughly two bytes per sample using a predictable timestamp pattern and the leading zeros of consecutive floats. observability
- Feb 7, 2026 Relay Arithmetic and the Floating-Point Word in the Zuse Z3 How a two-register stack machine with a 22-bit floating-point word ran at a few hertz, why it had no conditional branch, and what that costs in program length. computing history
- Sep 25, 2025 Exact Geometric Predicates and Adaptive Precision Why the sign of a determinant is the fragile part of computational geometry, how error bounds let a fast float path stay exact, and when exact arithmetic becomes unavoidable. algorithms
- Aug 28, 2025 Tree Reductions and Floating-Point Summation Order Why a pairwise tree sum is not the same number as a linear sum, how much error the tree removes, and how shuffle-based and shared-memory reduction stages compose. gpu computing
- Jun 26, 2025 The Slab Test for Boxes and the Inverse-Direction Shortcut How the ray-box test becomes three interval intersections, why precomputed reciprocals turn axis-parallel rays into NaN, and what the IEEE comparison rules do with it. computer graphics
- Feb 21, 2025 Reversed-Z: Using Floating-Point Depth Without Wasting It Standard depth mapping spends almost all of a floating-point buffer near the near plane; reversing it to 1 at the near plane and 0 at the far plane redistributes precision where it is needed. computer graphics
- Nov 8, 2024 Reduction Trees and What Associativity Buys Why a reduction needs an associative operator to be reordered, how tree shape changes floating-point results, and what error bounds the shapes imply. algorithms
- Sep 29, 2024 Solving Quadratic Ray Intersections Without Losing the Far Root Why the textbook quadratic formula fails for distant spheres, how the stable form differs by an addition of magnitudes, and what the determinant sign means geometrically. computer graphics
- Oct 17, 2023 Constant Folding and Algebraic Rewrites on a Fixed Graph How a compiler evaluates constant subgraphs at build time, which algebraic identities survive floating-point arithmetic, and why rewrite order determines the result. inference systems
- Jul 28, 2022 Floating-Point ABI Variants and the Linker Errors They Cause Soft, softfp, and hard float on 32-bit ARM decide where arguments travel rather than what arithmetic runs, and only the static linker notices when a build mixes them. systems programming