NTL: Wish List

Things that I would like to see in NTL

• Add more thread boosting to various parts of the library
• Add SIMD support for other architectures besides x86
• Add conversions from long long and unsigned long long to ZZ (and perhaps other types), at least for C++11. Note that on most Unix-based platforms, these are the same size as long, but some platforms define types such as int64_t in terms of the long long variants, so even on Unix-based platforms this would be useful
• Reduce linear algebra operations over ZZ_p (like matrix inversion, system solving, etc) to matrix multiplication (which is much faster)
  • This should be a fairly straightforward and self contained project
• Fast algorithms for general (or more specifice) multi-point evaluation and interpolation over ZZ_p (and other coefficient domains)
  • This should be a fairly straightforward and self contained project
• Bivariate polynomial arithmetic:
  • Multiplication can be implemented by reduction to univariate multiplication vie Kronecker substitution (the logic for this is already written for polynomial multiplication over extension fields, and can be easily repurposed)
  • GCD can be reduced can also be implemented by reduction to univariate polynomials (via multi-point evaluation and interpolation)
  • There are a number of programming interface issues that would have to be worked out to maintain consistency with the rest of NTL
• Matrix arithmetic over polynomials:
  • Many operaations can be reduced to operations over the coefficient domain (via multi-point evaluation and interpolation)
  • There are a number of programming interface issues that would have to be worked out to maintain consistency with the rest of NTL

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