The name "M4RI" stands for , an algorithm derived from the "Method of the Four Russians" multiplication (M4RM). Key Papers Related to M4RI
"Matrix Inversion (or LUP-Factorization) via the Method of Four Russians": Gregory Bard's paper introduces the inversion algorithm, demonstrating logarithmic speedups over standard Gaussian elimination. M4ri (100).JPG
"Algorithm 898: Efficient Multiplication of Dense Matrices over GF(2)": This paper, published in ACM Transactions on Mathematical Software , describes the M4RM algorithm and its performance on modern CPUs. The name "M4RI" stands for , an algorithm
Bit-packing allows 64-bit machine words to process 64 elements in parallel because addition in is a logical XOR and multiplication is a logical AND . Bit-packing allows 64-bit machine words to process 64
The reference most likely refers to the academic work and implementation of the M4RI library , which focuses on fast arithmetic for dense matrices over the finite field
[0811.1714] Efficient Multiplication of Dense Matrices over GF(2)
"Efficient Dense Gaussian Elimination over the Finite Field with Two Elements": This work details a block-iterative algorithm for PLE decomposition, which has been adopted into the SageMath software . Technical Details of the Algorithm M4RI's efficiency comes from two primary techniques: Gray code tables are used with a length of to enumerate vectors in a subspace spanned by rows. This reduces the number of vector additions.