Carry propagation in multiplication by constants

Multiplication by Rational Constants

Multiplications by simple rational constants often appear in fixed-point or floating-point application code, for instance in the form of division by an integer constant. The hardware implementation of such operations is of practical interest to FPGA-accelerated computing. It is well known that the binary representation of rational constants is eventually periodic. This article shows how this fe...

Multiplication by rational constants LIP research report

Multiplications by simple rational constants often appear in fixed-point or floating-point application code, for instance in the form of division by an integer constant. The hardware implementation of such operations is of practical interest to FPGA-accelerated computing. It is well known that the binary representation of rational constants is eventually periodic. This article shows how this fe...

Fast Multiplication Without Carry-Propagate Addition

Decimal Multiplication Via Carry-Save Addition

Decimal multiplication is important in many commercial applications including financial analysis, banking, tax calculation, currency conversion, insurance, and accounting. This paper presents two novel designs for fixed-point decimal multiplication that utilize decimal carry-save addition to reduce the critical path delay. First, a multiplier that stores a reduced number of multiplicand multipl...

Efficient Algorithms for Integer Division by Constants Using Multiplication

We present a complete analysis of the integer division of a single unsigned dividend word by a single unsigned divisor word based on double-word multiplication of the dividend by an inverse of the divisor. The well-known advantage of this method yields run-time efficiency, if the inverse of the divisor can be calculated at compile time, since multiplication is much faster than division in arith...