Gea-Suan LinDec 10

https://blog.gslin.org/archives/2025/12/10/12779/compiler-%e5%b1%85%e7%84%b6%e6%9c%83%e7%9b%b4%e6%8e%a5%e6%8a%8a-loop-%e7%ae%97%e5%87%ba-closed-form-expression-%e5%85%ac%e5%bc%8f%e8%a7%a3/

Compiler 居然會直接把 loop 算出 closed-form expression (公式解)

#ClosedForm #compiler #expression #formula #loop #math #mathematics #optimization

Compiler 居然會直接把 loop 算出 closed-form expression (公式解)

在 Lobsters 上看到「Do Not Optimize Away」這篇，開頭這段提到有些 loop 在 compiler 的 optimization 會直接算出 closed-form expression (封閉形式，或是常說的公式解)，就不需要跑 loop 了，像是經典的 ： var total: u32 = 0; for (0..

Gea-Suan Lin's BLOG
Pustam | पुस्तम | পুস্তম🇳🇵Oct 4, 2024
A lattice sum with a surprising closed form:
\[\Large\displaystyle\sum_{\substack{(m,n)\in\mathbb Z^2\\(m,n)\neq0}}\dfrac{1}{(m+ni)^4}=\dfrac{\varpi^4}{15}=\dfrac{\Gamma^8\left(\frac14\right)}{960\pi^2}\]
#LatticeSum #ClosedForm #LemniscateConstant #Series #Sum #GammaFunction #Pi
Mohammad HajiaghayiFeb 16, 2023

Now (7pm ET) watch
https://youtu.be/IGGEbA7OF2A
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Lesson 7: Introduction to Algorithms by Mohammad Hajiaghayi: Making #Recursive Relations #ClosedForm using #Algebra and #induction
we also talk about #algorithmicthinking in our daily lives.

Lesson 7: Introduction to Algorithms by Mohammad Hajiaghayi: Making Recursive Relations Closed-Form

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