ExactConvolution

Implement efficient exact integer convolution using BigInt's multiplication.

exact_conv([T,] a, b)

Convolve arrays of integers a and b, and return the resulting array.

\[exact\_conv(a,b)[k] = \sum_{i+j=k} a[i] \cdot b[j]\]

Notes:

• The implementation uses GMP's BigInt multiplication as the underling DSP engine (FFT for big enough inputs).
• T must be sufficient to support the result.
• Using negative values in a and b is supported but discouraged for runtime reasons.

Examples

julia> exact_conv(Int32, [1,2], [4,5,6])
4-element Vector{Int32}:
  4
 13
 16
 12