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MATH ∩ PROGRAMMING

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FEATURED POSTS

#featured  #mathematics  #programming 
2011-06-20
My next book will be Practical Math for Programmers
Searching for Riemann Hypothesis Counterexamples
Linear Programming and Healthy Diets
Hybrid Images
Bezier Curves and Picasso
Correcting Errors in Data

 * Unusual Tips for Parenting Toddlers
   2024-04-01
   #april cools 
   It’s April Cools! Last year I wrote about friendship bracelets and the year
   before about cocktails. This year it’s parenting. Parenting articles are a
   dime a dozen and always bury the lede behind a long story. I’ll skip that.
   How to think about your child and your role as a parent These are framing
   devices. Concrete things to do to work toward these are in the next section.
   I will refer to the numbers for each action to show what principle it is
   applying.
 * Tabletop Games Based on Math Problems
   2024-03-08
   #tabletop games  #mathematics  #set  #card games 
   There’s a family of tabletop games that are based directly on a nontrivial
   mathematics problem. As a casual and fun way to inaugurate my new blog
   (migrated from Wordpress to Hugo, after my work on getting better LaTeX
   mathmode support in Hugo), I thought I’d write a short listicle about them,
   so that I have a place to add more as I find them, as well as give the
   shortest canonical description of the associated math problem.
 * MLIR — A Global Optimization and Dataflow Analysis
   2023-11-15
   #compilers  #heir  #mathematics  #mlir  #optimization  #primer  #programming 
   Table of Contents In this article we’ll implement a global optimization pass,
   and show how to use the dataflow analysis framework to verify the results of
   our optimization. The code for this article is in this pull request, and as
   usual the commits are organized to be read in order. The noisy arithmetic
   problem This demonstration is based on a simplified model of computation
   relevant to the HEIR project. You don’t need to be familiar with that project
   to follow this article, but if you’re wondering why someone would ever want
   the kind of optimization I’m going to write, that project is why.
 * MLIR — Lowering through LLVM
   2023-11-01
   #compilers  #heir  #llvm  #mathematics  #mlir  #primer  #programming 
   Table of Contents In the last article we lowered our custom poly dialect to
   standard MLIR dialects. In this article we’ll continue lowering it to LLVM
   IR, exporting it out of MLIR to LLVM, and then compiling to x86 machine code.
   The code for this article is in this pull request, and as usual the commits
   are organized to be read in order. Defining a Pipeline The first step in
   lowering to machine code is to lower to an “exit dialect.
 * MLIR — Dialect Conversion
   2023-10-23
   #cryptography  #heir  #mathematics  #mlir  #polynomial ring  #polynomials 
   #primer  #programming 
   Table of Contents In previous articles we defined a dialect, and wrote
   various passes to optimize and canonicalize a program using that dialect.
   However, one of the main tenets of MLIR is “incremental lowering,” the idea
   that there are lots of levels of IR granularity, and you incrementally lower
   different parts of the IR, only discarding information when it’s no longer
   useful for optimizations. In this article we’ll see the first step of that:
   lowering the poly dialect to a combination of standard MLIR dialects, using
   the so-called dialect conversion infrastructure to accomplish it.
 * Socks, a matching game based on an additive combinatorics problem
   2023-10-14
   #additive combinatorics  #board games  #card game  #games  #Group Theory 
   #mathematics 
   Can you find a set of cards among these six, such that the socks on the
   chosen cards can be grouped into matching pairs? (Duplicate pairs of the same
   sock are OK) Spoilers: If the cards are indexed as 1 2 3 4 5 6 Then the
   following three subsets work: {1,2,4,5,6}, {2,3,6}, and {1,3,4,5}.
 * MLIR — Canonicalizers and Declarative Rewrite Patterns
   2023-09-20
   #c++  #canonicalization  #compilers  #complex numbers  #mathematics  #mlir 
   #polynomials  #primer  #programming 
   Table of Contents In a previous article we defined folding functions, and
   used them to enable some canonicalization and the sccp constant propagation
   pass for the poly dialect. This time we’ll see how to add more general
   canonicalization patterns. The code for this article is in this pull request,
   and as usual the commits are organized to be read in order. Why is
   Canonicalization Needed? MLIR provides folding as a mechanism to simplify an
   IR, which can result in simpler, more efficient ops (e.
 * Encoding Schemes in FHE
   2023-09-18
   #complex numbers  #cryptography  #encoding  #fhe  #fully homomorphic
   encryption  #learning with errors  #lwe  #mathematics  #Number Theory 
   #programming  #residue number system  #rlwe 
   In cryptography, we need a distinction between a cleartext and a plaintext. A
   cleartext is a message in its natural form. A plaintext is a cleartext that
   is represented in a specific way to prepare it for encryption in a specific
   scheme. The process of taking a cleartext and turning it into a plaintext is
   called encoding, and the reverse is called decoding. In homomorphic
   encryption, the distinction matters. Cleartexts are generally all integers,
   though the bit width of allowed integers can be restricted (e.
 * MLIR — Verifiers
   2023-09-13
   #c++  #compilers  #mathematics  #mlir  #primer  #programming 
   Table of Contents Last time we defined folders and used them to enable some
   canonicalization and the sccp constant propagation pass for the poly dialect.
   This time we’ll add some additional safety checks to the dialect in the form
   of verifiers. The code for this article is in this pull request, and as usual
   the commits are organized to be read in order. Purpose of a verifier
   Verifiers ensure the types and operations in a concrete MLIR program are
   well-formed.
 * MLIR — Folders and Constant Propagation
   2023-09-11
   #c++  #compilers  #folding  #heir  #mathematics  #mlir  #programming 
   Table of Contents Last time we saw how to use pre-defined MLIR traits to
   enable upstream MLIR passes like loop-invariant-code-motion to apply to poly
   programs. We left out -sccp (sparse conditional constant propagation), and so
   this time we’ll add what is needed to make that pass work. It requires the
   concept of folding. The code for this article is in this pull request, and as
   usual the commits are organized to be read in order.