Finite Field Assembly:Emulate GPU on CPU Introduction

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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.
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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.

How does Finite Field Assembly:Emulate GPU on CPU work?

FF-asm works by leveraging the mathematical theory of congruences and primes to perform multiple calculations simultaneously through recursive computing. It uses custom finite fields that support operations like addition and multiplication using unsigned integers. The system represents data as elements in finite fields and performs operations on these fields using concepts from number theory. For example, when adding two arrays of numbers, instead of processing them sequentially or through traditional parallel methods, FF-asm converts the operations into a series of nested calculations within finite fields. This allows multiple computations to be performed simultaneously through mathematical properties rather than hardware parallelism. The language includes specialized functions for memory allocation (ff_asmMalloc), field operations (ff_asmAdd, ff_asmMultiply), and data management within these finite fields.

Benefits of Finite Field Assembly:Emulate GPU on CPU

The primary advantage of FF-asm is its ability to achieve parallel computing capabilities on standard CPUs without requiring specialized GPU hardware or complex parallelization code. This makes high-performance computing more accessible to developers working with limited hardware resources. The language provides a mathematical approach to parallel computing that can be implemented on basic hardware, potentially reducing costs and complexity compared to GPU-based solutions. Additionally, its foundation in finite field theory makes it particularly suitable for certain types of mathematical computations and cryptographic applications. The system is also designed to be extensible, allowing developers to create custom mathematical systems tailored to their specific computational needs.

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