ExactConvolution

This package is intended for computing exact convolutions of integers vectors.

It is essentialy a wrapper over GMP's BigInt multiplications, and as such it is very efficient. Convolutions of two Int64 arrays of length 10^5 can take about 60ms, or 120ms if negative values are presented.

For integers that floating point computations might be sufficient exact for, please use DSP.jl, which for some cases can be 10x faster.

Installation

pkg> add ExactConvolution

Or, equivalently, via Pkg API:

julia> import Pkg; Pkg.add("ExactConvolution")

Usage

julia> using ExactConvolution

julia> exact_conv(Int16, [1,2], [4,5,6])
4-element Vector{Int16}:
  4
 13
 16
 12

julia> exact_conv(BigInt, [big"2"^80, big"5"^42], [4,5,6])
4-element Vector{BigInt}:
       4835703278458516698824704
  909500746402026311060912593380
 1136875630771077985168847065181
 1364242052659392356872558593750

julia> exact_conv(Int128, [big"2"^80, big"5"^42], [4,5,6])
4-element Vector{Int128}:
       4835703278458516698824704
  909500746402026311060912593380
 1136875630771077985168847065181
 1364242052659392356872558593750

julia> exact_conv(Int8, [1,-2], [4,5,6])
4-element Vector{Int8}:
   4
  -3
  -4
 -12

julia> using BenchmarkTools

julia> rand_array(bits) = rand(0:2^bits, 10^5);

julia> arr1,arr2 = rand_array(20),rand_array(20);

julia> @btime exact_conv(Int64, arr1, arr2);
  64.988 ms (600085 allocations: 27.98 MiB)

julia> using DSP

julia> @btime conv(arr1, arr2);
  5.548 ms (94 allocations: 10.69 MiB)