Improve evaluation of LaurentPolynomial

[martinholters]

Use ntuple instead of NTuple for constructing the coefficient tuples passed to evalpoly. This compiles much faster on Julia 1.0 (especially for high-degree polynomials) and is also faster to evaluate even on current Julia.

Julia 1.0.5:

julia> @time LaurentPolynomial(ones(5))(1)
  0.253496 seconds (990.00 k allocations: 47.603 MiB, 4.10% gc time) # master
  0.861258 seconds (2.45 M allocations: 119.648 MiB, 4.13% gc time) # PR
5.0

julia> @btime LaurentPolynomial(ones(5))(1)
  608.573 ns (12 allocations: 656 bytes) # master
  114.681 ns (8 allocations: 416 bytes) # PR
5.0

julia> @time LaurentPolynomial(ones(150))(1)
 22.524473 seconds (77.11 M allocations: 3.157 GiB, 8.39% gc time) # master
  0.087917 seconds (187.70 k allocations: 9.934 MiB, 3.63% gc time) # PR
150.0

julia> @btime LaurentPolynomial(ones(150))(1)
  375.336 μs (11011 allocations: 265.31 KiB) # master
  6.042 μs (161 allocations: 7.72 KiB) # PR
150.0

Julia 1.6.0-DEV.1408:

julia> @time LaurentPolynomial(ones(5))(1)
  0.076117 seconds (137.39 k allocations: 7.787 MiB, 99.90% compilation time) # master
  0.023298 seconds (26.14 k allocations: 1.687 MiB, 99.86% compilation time) # PR
5.0

julia> @btime LaurentPolynomial(ones(5))(1)
  595.810 ns (10 allocations: 608 bytes) # master
  118.526 ns (6 allocations: 352 bytes) # PR
5.0

julia> @time LaurentPolynomial(ones(150))(1)
  0.089302 seconds (211.92 k allocations: 12.811 MiB, 99.88% compilation time) # master
  0.056672 seconds (170.88 k allocations: 10.229 MiB, 99.90% compilation time) # PR
150.0

julia> @btime LaurentPolynomial(ones(150))(1)
  8.637 μs (161 allocations: 9.00 KiB) # master
  5.936 μs (157 allocations: 7.59 KiB) # PR
150.0

The compile time on 1.0.5 grows super-linear, making it impossible to evaluate even higher-order polynomials without this PR.

[codecov]

Codecov Report

Merging #292 into master will not change coverage.
The diff coverage is 75.00%.

@@           Coverage Diff           @@
##           master     #292   +/-   ##
=======================================
  Coverage   88.66%   88.66%           
=======================================
  Files          16       16           
  Lines        1827     1827           
=======================================
  Hits         1620     1620           
  Misses        207      207           

Impacted Files	Coverage Δ
src/polynomials/LaurentPolynomial.jl	83.94% <75.00%> (ø)

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[jverzani]

Thanks! I hadn't realized this would be an issue.

[martinholters]

Could you tag the new version?

[jverzani]

Yes, just did. I didn't include the qr fix. Thanks for your help with this!