Finite Field Assembly:Emulate GPU on CPU
Finite Field Assembly (FF-asm) is a low-level programming language that emulates GPU-like parallel computing capabilities on CPUs through recursive computing and finite field mathematics, without requiring actual GPU hardware or traditional parallelization methods.
https://leetarxiv.substack.com/p/emulating-a-gpu-on-a-cpu-using-finite?ref=aipure
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Updated:Jul 16, 2025
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What is Finite Field Assembly:Emulate GPU on CPU
Finite Field Assembly (FF-asm) is an extension of C that enables GPU-like parallel computations on regular CPUs through mathematical constructs called finite fields. Founded on the thesis that 'math is mostly invented, rarely discovered', FF-asm empowers programmers to create their own mathematical systems to solve computational problems. It provides a unique approach to parallel computing by implementing recursive computing - performing calculations inside other calculations - rather than relying on traditional SIMD vectorization or OpenMP parallelization routines.
Key Features of Finite Field Assembly:Emulate GPU on CPU
Finite Field Assembly (FF-asm) is a programming language that enables GPU-like parallel computations on regular CPUs without using traditional SIMD or OpenMP parallelization. It uses recursive computing and finite field mathematics to perform multiple calculations simultaneously within a single computation. The language extends C and allows programmers to create custom mathematical systems using congruences and prime number theory to achieve parallel processing capabilities.
Recursive Computing: Performs calculations inside other calculations recursively, enabling parallel processing without traditional parallelization techniques
Custom Mathematical Systems: Allows programmers to create their own mathematical structures using finite fields to solve specific problems
C Language Extension: Built as an extension to C, providing low-level control while maintaining familiar syntax and memory management
Finite Field Operations: Supports basic arithmetic operations (addition, multiplication) in finite fields with customizable field orders
Use Cases of Finite Field Assembly:Emulate GPU on CPU
High Performance Computing: Enables parallel processing capabilities on systems without GPU hardware for scientific computations
Cryptography: Implements finite field arithmetic operations essential for cryptographic algorithms and secure communications
Matrix Operations: Performs efficient matrix calculations using finite field arithmetic for applications in linear algebra and data processing
Pros
Enables parallel processing without specialized hardware
Provides high-level mathematical abstractions
Integrates seamlessly with existing C codebases
Cons
Requires understanding of finite field mathematics
Limited to specific types of computational problems
May have performance overhead compared to native GPU implementations
How to Use Finite Field Assembly:Emulate GPU on CPU
Install Prerequisites: Install GNU MP Bignum library (libgmp) and obtain ff_asm_runtime.h and ff_asm_primes.h files from the official GitHub repository
Set Up Project Directory: Create a new directory and place ff_asm_runtime.h and ff_asm_primes.h files in it. This will be your working directory.
Create Hello World Program: Create a file named 01_HelloWorld.c that initializes an 8-bit unsigned integer finite field. Include the required headers and write code to allocate memory, set field order, append data and print the field.
Compile and Run: Compile using command: gcc 01_HelloWorld.c -lgmp -lm -o m.o && ./m.o
Implement Addition: Create a new file for recursive addition operations using ff_asmAdd() function. This allows performing multiple additions simultaneously through recursive computing.
Implement Multiplication: Create another file to implement multiplication using ff_asmMultiply() function. Make sure to increase field order to accommodate larger results.
Memory Management: Always use ff_asmMalloc() to allocate memory for fields and ff_asmFreeField() to free memory when done.
Debug and Print: Use ff_asmDataDebug() to prepare data for printing and ff_asmPrintField() to display the field contents and verify results.
Optimize Field Orders: Adjust field orders in fieldOrder array based on your computation needs - larger orders allow for bigger numbers but use more memory.
Finite Field Assembly:Emulate GPU on CPU FAQs
FF-asm is a programming language founded on the idea that math is mostly invented rather than discovered. It's an extension of C that enables programmers to create their own mathematical systems using finite fields as the basic data structure. Its main feature is recursive computing - performing calculations inside other calculations.
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