Mantissa–Exponent Square-Difference (MESD) algorithm

The Mantissa–Exponent Square-Difference (MESD) algorithm is a computational method for multiplying two numbers without performing a direct mantissa multiplication. Instead, MESD reformulates multiplication into a sequence of squaring, addition/subtraction, and bit-shift operations within a mantissa–exponent framework. This separation allows exponent adjustments to be handled through inexpensive bit shifts, while mantissa operations are confined to efficient squaring routines—often faster than general multiplication. Originally developed to minimise the cost of computing a single multiplicative term in a 2×2 matrix product, MESD’s optimisations can be replicated across all terms in the multiplication, amplifying computational savings in full matrix operations. Benchmark results demonstrate that MESD can outperform standard multiplication in contexts such as DSP pipelines, embedded systems, and FPGA implementations, particularly when operand reuse or lookup tables are feasible. An extension, the Odd-Index Shift-Add Multiplication (OISAM) variant, applies the same principles to an alternate number encoding, showing MESD’s adaptability beyond IEEE 754 floating-point representation. The paper presents the mathematical foundations, algorithmic flow, complexity analysis, and practical applications, highlighting MESD’s role in reducing multiplication complexity in both hardware- and software-constrained environments.