lemire / backward_multiplication

Multiplying... backward?

Backward Multiplication

This C/C++ code illustrates how we might do a multiword multiplication backward, starting from the most significant words.

Blog post: Multiplying backward for profit.

To do the full computation the usual way, use the following function:

#include "backwardmultiply.h"
using backwardmultiply;

// Multiply the integer represented by 'w' with the integer represented
// by the multiword integer b[0], b[1],..., b[n-1]
// Result gets written to output, up to n+1 words can be written: caller is
// responsible to ensure that the memory was allocated.
void multiplication(uint64_t w, const uint64_t *b, size_t n, uint64_t *output);

If you just want a few of the most significant words, use the following function:

// Multiply the integer represented by 'w' with the integer represented
// by the multiword integer b[0], b[1],..., b[n-1]
// Result gets written to output, up to n+1 words can be written: caller is
// responsible to ensure that the memory was allocated. The parameter "minexactwords"
// represents the minimal number of exact words (starting from the most
// significant words) that you need. Returns the number of exact words computed
// (starting from the most significant words).
size_t multiplication_backward_limit(uint64_t w, const uint64_t *b, size_t n,
                                     uint64_t *output, size_t minexactwords)

Requirements

• Modern C++ compiler

Usage

There is a single header. You can run tests with make && make test.