Static search trees: 40x faster than binary search
1 Introduction1.1 Problem statement1.2 Motivation1.3 Recommended reading1.4 Binary search and Eytzinger layout1.5 Hugepages1.6 A note on benchmarking1.7 Cache lines1.8 S-trees and B-trees2 Optimizing find2.1 Linear2.2 Auto-vectorization2.3 Trailing zeros2.4 Popcount2.5 Manual SIMD3 Optimizing the search3.1 Batching3.2 Prefetching3.3 Pointer arithmetic3.3.1 Up-front splat3.3.2 Byte-based pointers3.
Sub-pixel Distance Transform — Acko.net
This page includes diagrams in WebGPU, which has limited browser support. For the full experience, use Chrome on Windows or Mac, or a developer build on other platforms. In this post I will describe Use.GPU's text rendering, which uses a bespoke approach to Signed Distance Fields (SDFs). This was borne out of necessity: while SDF text is pretty common on GPUs, some of the established practice on g
Smoothed-particle hydrodynamics - Wikipedia
Schematic view of an SPH convolution Flow around cylinder with free surface modelled with SPH. See[1] for similar simulations. Smoothed-particle hydrodynamics (SPH) is a computational method used for simulating the mechanics of continuum media, such as solid mechanics and fluid flows. It was developed by Gingold and Monaghan[2] and Lucy[3] in 1977, initially for astrophysical problems. It has been
Designing a Tree Diff Algorithm Using Dynamic Programming and A* - Tristan Hume
During my internship at Jane Street1, one of my projects was a config editing tool that at first sounded straightforward but culminated in me designing a custom tree diffing algorithm using dynamic programming, relentlessly optimizing it and then transforming it into an A* accelerated path finding algorithm. This post is the story of the design and optimization of the algorithm, of interest to any
malloc.c ã‚’èªã‚€ (malloc / free)
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FFT:NTT
2020/07/13 HCPC 2020/07/13 HCPC /46 !2 2020/07/13 HCPC /46 f(x) n − 1 ζn 1 n ð’ª(n2 ) ð’ª(n log n) !3 Ì‚ f(t) = n−1 ∑ i=0 f(ζi n)ti 2020/07/13 HCPC /46 !4 2020/07/13 HCPC /46 (x + x2 + x4 )(x3 + x6 + x10 + x15 )[x7 ] = 2 f(x)[xa ] := xa !5 2020/07/13 HCPC /46 f(x), g(x) n m f(x)g(x) n + m − 1 f(x) = (1 + 2x) g(x) = (3 + x + 4x2 ) f(x)g(x) = 3 + 7x + 6x2 + 8x3 !6 2020/07/13 HCPC /46 !7 f(x), g(x) n m
NTT(数論変æ›)ã®ã‚„ã•ã—ã„解説 - Senã®ç«¶æŠ€ãƒ—ãƒã‚°ãƒ©ãƒŸãƒ³ã‚°å‚™å¿˜éŒ²
ã“ã®è¨˜äº‹ã¯ã€é«˜é€Ÿãƒ•ãƒ¼ãƒªã‚¨å¤‰æ›ã®1ã¤ã®ãƒãƒªã‚¨ãƒ¼ã‚·ãƒ§ãƒ³ã§ã‚ã‚‹ã€Numeric Theory Translation(数論変æ›)ã®è©³ã—ã„解説記事ã§ã™ã€‚ ã‚ã¾ã‚Šãªã‹ã£ãŸã®ã§æ›¸ãã¾ã—ãŸã€‚ 数論変æ›ã«ã‚ã‚ŠãŒã¡ãª ãªã‚“ã§$ 10 ^ 9 + 7 $ã˜ã‚ƒãƒ€ãƒ¡ãªã®ã‹ åŽŸå§‹æ ¹ã£ã¦ä½•ï¼Ÿ ã¨ã‹ã«ã¤ã„ã¦ã‚‚ã“れを見れã°ã‚ã‹ã‚Šã¾ã™ã€‚ å‰æ知è˜ã¨ã—ã¦ã¯ã€Fast Fourier Translation(高速フーリエ変æ›)ãŒå¿…è¦ã§ã™ã€‚ kaage大先生ã®Qiita記事ã¨ã‹ã¯ä¸é«˜ç”Ÿã«ã‚‚ã‚ã‹ã‚Šã‚„ã™ã書ã‹ã‚Œã¦ã„ã¾ã™ã€‚ 下ã«ä¸€å¿œè‡ªåˆ†ã®å‹‰å¼·ãƒŽãƒ¼ãƒˆã‚’載ã›ã¾ã™ã€‚(上ã®è¨˜äº‹ã®è¡Œé–“を埋ã‚ãŸæ„Ÿã˜ã§ã™) ã§ã¯ã€æ•°è«–変æ›ã«ã¤ã„ã¦èª¬æ˜Žã—ãŸã„ã¨æ€ã„ã¾ã™ã€‚ 高速フーリエ変æ›ã®å¼±ç‚¹ 高速フーリエ変æ›ã¯æ£ã—ã„ã§ã™ãŒã€å¼±ç‚¹ã¨ã—ã¦ç²¾åº¦ãŒè¶³ã‚Šãªã„ã¨ã„ã†ã®ãŒã‚ã‚Šã¾ã™ã€‚ ãªãœãªã‚‰ã°ã€è¤‡ç´ æ•°ã®1ã®$ 2 ^ m $ä¹—æ ¹ã¯è¨ˆç®—上ã§ã¯ã‚Œã£ãã¨ã—ãŸ64bitå€ç²¾åº¦æµ®å‹•å°æ•°ç‚¹
You (Probably) Shouldn't use a Lookup Table - Speculative Branches
Thoughts on software, hardware, performance, math, and similar topics I have been working on another post recently, also related to division, but I wanted to address a comment I got from several people on the previous division article. This comment invariably follows a lot of articles on using math to do things with chars and shorts. It is: “why are you doing all of this when you can just use a lo
githublog/2024/5/10/cordic.md at main · francisrstokes/githublog
This post is an adaptation of a twitter thread I put together a few days ago. CORDIC is an algorithm for computing trig functions like sin, cos, tan etc on low powered hardware, without an FPU (i.e. no floating point) or expensive lookup tables. In fact, it reduces these complex functions to simple additions and bit shifts. I'll cut right to the chase and tell you why I love this algorithm so much
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将棋AIã§ç”¨ã„ã¦ã„る詰将棋ルーãƒãƒ³ã«df-pnã¨ã„ã†ã‚¢ãƒ«ã‚´ãƒªã‚ºãƒ ãŒã‚る。 ã“ã‚Œã¯ã€proof number(証明数)ã€disproof number(éžè¨¼æ˜Žæ•°)を用ã„ã¦åŠ¹çŽ‡çš„ã«æŽ¢ç´¢ã‚’è¡Œã„ã€ãã®å±€é¢ãŒè©°ã‚€ã‹ã€è©°ã¾ãªã„ã‹ã‚’判定ã§ãã‚‹ã¨ã¦ã‚‚強力ãªã‚¢ãƒ«ã‚´ãƒªã‚ºãƒ ã§ã‚る。 将棋ファンãªã‚‰ã€Žè„Šå°¾è©°ã€ã¨è¨€ã†ã€ŒãƒŸã‚¯ãƒã‚³ã‚¹ãƒ¢ã‚¹ã€(1525手詰)を解ã詰将棋専用ソフトã«ã¤ã„ã¦ä¸€åº¦ãらã„ã¯èžã„ãŸã“ã¨ãらã„ã‚ã‚‹ã ã‚ã†ã€‚ã“ã‚Œã¯ã€è„Šå°¾ã•ã‚“ãŒå¤§å¦æ™‚代ã«ä½œæˆã•ã‚ŒãŸãƒ—ãƒã‚°ãƒ©ãƒ ã§ã‚る。ãã“ã«ä½¿ã‚ã‚Œã¦ã„ãŸã®ãŒè„Šå°¾ã•ã‚“ãŒè€ƒæ¡ˆã•ã‚ŒãŸdf-pnã¨ã„ã†ã‚¢ãƒ«ã‚´ãƒªã‚ºãƒ ã§ã‚る。 df-pnã«é–¢ã—ã¦ã¯ã€è„Šå°¾ã•ã‚“自身ã®è«–æ–‡(1998å¹´)ãŒã‚ã‚‹ã‚‚ã®ã®ã€è¦ç‚¹ã—ã‹æ›¸ã‹ã‚Œã¦ãŠã‚‰ãšã€ã„ã¾ã®ã‚ˆã†ã«GitHubã«ã‚½ãƒ¼ã‚¹ã‚³ãƒ¼ãƒ‰ãŒã‚ã‚‹ã‚ã‘ã§ã‚‚ãªãã€ãã®è©³ç´°ã«ã¤ã„ã¦ã¯é•·ã‚‰ã謎ã«åŒ…ã¾ã‚ŒãŸã¾ã¾ã§ã‚ã£ãŸã€‚(ã“ã®è„Šå°¾ã•ã‚“ã®è«–æ–‡ã§ã¯ã€è¨¼æ˜Žæ•°ã®ã¿ã‚’用ã„ã¦ãŠã‚Šã€éžè¨¼æ˜Žæ•°ã¯é™½ã«ã¯å‡º
Beyond A*: Better Planning with Transformers via Search Dynamics Bootstrapping
While Transformers have enabled tremendous progress in various application settings, such architectures still trail behind traditional symbolic planners for solving complex decision making tasks. In this work, we demonstrate how to train Transformers to solve complex planning tasks. This is accomplished by training an encoder-decoder Transformer model to predict the search dynamics of the $A^*$ se
Arithmetic–geometric mean - Wikipedia
This article is about the particular type of mean. For the similarly named inequality, see Inequality of arithmetic and geometric means. Plot of the arithmetic–geometric mean among several generalized means. In mathematics, the arithmetic–geometric mean (AGM or agM[1]) of two positive real numbers x and y is the mutual limit of a sequence of arithmetic means and a sequence of geometric means. The
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Interval parsing grammars for file format parsing (2023) | Hacker News
A brief introduction to interval arithmetic
GitHub - facebookresearch/searchformer: Official codebase for the paper "Beyond A* Better Planning with Transformers via Search Dynamics Bootstrapping".
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https://cr.yp.to/arith/logagm-20030717-retypeset20220327.pdf
https://cr.yp.to/lineartime/multapps-20080515.pdf
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