Handle units consistently in handle_infinites

[lxvm]

Fixes #95
This pr changes handle_infinities to always pass limits with units to do_quadgk so that the same segbuf can be used with finite and infinite limits.
It also adds some tests to check this works for inplace and batched integrands.

Unfortunately, the endpoints of the segments in a segbuf don't correspond to the intervals used in the original domain when using the infinity transformation. However, changing that would be a lot more involved than what is needed for this pr.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (135432c) 98.21% compared to head (f328bd7) 98.27%.

Additional details and impacted files

@@            Coverage Diff             @@
##           master      #96      +/-   ##
==========================================
+ Coverage   98.21%   98.27%   +0.06%     
==========================================
  Files           6        6              
  Lines         615      637      +22     
==========================================
+ Hits          604      626      +22     
  Misses         11       11              

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[stevengj]

This pays the cost of a division for every integrand evaluation?

[stevengj]

Oh, that is just for the segments.

[lxvm]

@stevengj this pr is now updated to pass unitless limits to do_quadgk and the new tests are more careful about verifying this behavior.
Here are also timings on Julia 1.10 that show a median slowdown under 2.5% in general:

branch	integrand	median time
pr	x	35.839 ns
master	x	35.007 ns
pr	sin(100x)	11.965 μs
master	sin(100x)	11.762 μs

benchmark for this pr

julia> using BenchmarkTools

julia> using QuadGK

julia> @benchmark quadgk(x -> x, 0, 1) # zero-cost integrand, no subdivisions
BenchmarkTools.Trial: 10000 samples with 993 evaluations.
 Range (min … max):  35.383 ns … 107.806 ns  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     35.839 ns               ┊ GC (median):    0.00%
 Time  (mean ± σ):   36.505 ns ±   4.703 ns  ┊ GC (mean ± σ):  0.00% ± 0.00%

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  ██▃▃▂▂▂▂▂▂▁▂▂▂▁▂▁▂▁▁▁▁▁▁▂▁▁▂▁▁▂▂▁▁▂▂▂▂▁▁▂▂▂▂▂▂▂▂▂▂▂▁▂▂▂▁▁▁▂▂ ▂
  35.4 ns         Histogram: frequency by time         63.2 ns <

 Memory estimate: 0 bytes, allocs estimate: 0.

julia> @benchmark quadgk(x -> sin(100x), 0, 1) # low-cost integrand with subdivisions
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
 Range (min … max):  11.611 μs … 55.500 μs  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     11.965 μs              ┊ GC (median):    0.00%
 Time  (mean ± σ):   12.100 μs ±  1.526 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

                        ▃█▇█▅▄▂▁                               
  ▂▂▂▂▂▂▂▁▂▁▁▂▁▁▁▂▁▂▂▃▅█████████▇▆▆▅▄▄▃▃▃▃▃▃▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂ ▃
  11.6 μs         Histogram: frequency by time        12.4 μs <

 Memory estimate: 1.69 KiB, allocs estimate: 3.

benchmark on master

julia> using BenchmarkTools

julia> using QuadGK

julia> @benchmark quadgk(x -> x, 0, 1) # zero-cost integrand, no subdivisions
BenchmarkTools.Trial: 10000 samples with 992 evaluations.
 Range (min … max):  33.998 ns … 402.374 ns  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     35.007 ns               ┊ GC (median):    0.00%
 Time  (mean ± σ):   36.006 ns ±   7.741 ns  ┊ GC (mean ± σ):  0.00% ± 0.00%

  ▃█                                                            
  ██▃▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ ▁
  34 ns           Histogram: frequency by time         70.1 ns <

 Memory estimate: 0 bytes, allocs estimate: 0.

julia> @benchmark quadgk(x -> sin(100x), 0, 1) # low-cost integrand with subdivisions
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
 Range (min … max):  11.362 μs … 57.351 μs  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     11.762 μs              ┊ GC (median):    0.00%
 Time  (mean ± σ):   12.303 μs ±  1.512 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

     █▄                                                        
  ▇▅▂██▃▂▂▂▂▁▁▁▂▃▄▃▃▇▆▃▃▂▂▂▂▂▂▂▂▂▂▂▂▂▂▁▂▁▂▁▂▂▂▂▂▂▂▂▁▂▂▁▁▂▁▁▁▂ ▃
  11.4 μs         Histogram: frequency by time          17 μs <

 Memory estimate: 1.69 KiB, allocs estimate: 3.

I think this is ready and could be a patch release

[stevengj]

It's not great that we pay the price of having an additional point array here …