Utilize precompilable bigints in their fullest of glory

[ChrisRackauckas]

JuliaLang/julia#28296 (comment)

[StefanKarpinski]

I don’t think you need the BigInt constructor calls since these values are too big for native integer types.

[ChrisRackauckas]

Not all of them. There are some expressions in there that will overflow if you don't make them bigfloats since the numbers are smaller than bigfloat but the rational numbers you get would require bigfloat. I think lines like this are it:

https://github.com/JuliaDiffEq/DiffEqDevTools.jl/pull/14/files#diff-c23f684630d78ba4c89b132bc1ec4157R4870

[StefanKarpinski]

I mean that BigInt(123... lots of digits ... 789) is redundant since with that many digits the integer is already parsed as a BigInt.

[ChrisRackauckas]

Yes, in those cases. But not every case is like that. In some cases you get Rational{Int128} + Rational{Int64} and the result overflows, and I think the line I linked is one of them. Way back when I wrote this I kept upconverting everything I could to parse(BigInt,"") until that issue was gone. Now I just throw a find/replace on all of the parse statements, but to avoid this issue I put BigInt($1). So it's not needed in all cases but it is in some, and where it isn't needed it's harmless so I'll go make it cleaner later haha.

[codecov]

Codecov Report

Merging #14 into master will not change coverage.
The diff coverage is n/a.

@@           Coverage Diff           @@
##           master      #14   +/-   ##
=======================================
  Coverage   99.39%   99.39%           
=======================================
  Files           6        6           
  Lines        6800     6800           
=======================================
  Hits         6759     6759           
  Misses         41       41

Impacted Files	Coverage Δ
src/ode_tableaus.jl	100% <ø> (ø)	⬆️
src/convergence.jl	84.61% <0%> (ø)	⬆️
src/benchmark.jl	72.54% <0%> (ø)	⬆️

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