Multiple precision matrices

Torbjörn Granlund tg at
Wed May 25 13:08:11 UTC 2016

Kartik Gupta <kartik.kailash.gupta at> writes:

  Does GMP provide the functionality of doing fast multiple precision matrix
  operations like addition, multiplication, etc?
  Or is there any other library available which builds upon GMP or otherwise
  provides these functionalities?
  I am building a system where I will be using matrices of multiple precision
  integers and performing some computations on them.
We might want to support that at some point, as the benefits of doing it
at a low level are great.  If one uses that plain O(mnk) algorithm (for
multiplying an m,n and an n,k matrix) one currently will perform 3mnk
FFT transforms.  If we implement this with access to the FFT types, one
could reduce this to mn + nk + mk FFT transforms.

(Depending on which ring we use for the polynomial coefficients in FFT,
this may not only save most of the work in practice, but also reduce the
time complexity.  This is not true for the current GMP FFT, but is true
for the small primes FFT which we have in the works.)

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