Avoid allocations by inlining functions accepting accumulators

[chriselrod]

By preventing the mutable structs from escaping (by inlining all the functions they are passed to as arguments) we avoid allocations and get better performance.

Before PR:

julia> using AccurateArithmetic, BenchmarkTools

julia> x = rand(1024);

julia> y = rand(1024);

julia> @benchmark sum_kbn($x)
BenchmarkTools.Trial: 
  memory estimate:  592 bytes
  allocs estimate:  5
  --------------
  minimum time:     238.235 ns (0.00% GC)
  median time:      243.833 ns (0.00% GC)
  mean time:        324.037 ns (22.48% GC)
  maximum time:     14.107 μs (96.99% GC)
  --------------
  samples:          10000
  evals/sample:     442

julia> @benchmark sum_oro($x)
BenchmarkTools.Trial: 
  memory estimate:  16 bytes
  allocs estimate:  1
  --------------
  minimum time:     150.962 ns (0.00% GC)
  median time:      152.232 ns (0.00% GC)
  mean time:        156.910 ns (1.02% GC)
  maximum time:     8.306 μs (97.48% GC)
  --------------
  samples:          10000
  evals/sample:     818

julia> @benchmark dot_oro($x,$y)
BenchmarkTools.Trial: 
  memory estimate:  1.16 KiB
  allocs estimate:  9
  --------------
  minimum time:     379.704 ns (0.00% GC)
  median time:      402.424 ns (0.00% GC)
  mean time:        561.343 ns (26.13% GC)
  maximum time:     30.973 μs (97.65% GC)
  --------------
  samples:          10000
  evals/sample:     203

after PR:

julia> using AccurateArithmetic, BenchmarkTools
[ Info: Precompiling AccurateArithmetic [22286c92-06ac-501d-9306-4abd417d9753]

julia> x = rand(1024);

julia> y = rand(1024);

julia> @benchmark sum_kbn($x)
BenchmarkTools.Trial: 
  memory estimate:  0 bytes
  allocs estimate:  0
  --------------
  minimum time:     186.095 ns (0.00% GC)
  median time:      186.521 ns (0.00% GC)
  mean time:        189.388 ns (0.00% GC)
  maximum time:     424.038 ns (0.00% GC)
  --------------
  samples:          10000
  evals/sample:     666

julia> @benchmark sum_oro($x)
BenchmarkTools.Trial: 
  memory estimate:  0 bytes
  allocs estimate:  0
  --------------
  minimum time:     140.254 ns (0.00% GC)
  median time:      140.663 ns (0.00% GC)
  mean time:        142.889 ns (0.00% GC)
  maximum time:     349.425 ns (0.00% GC)
  --------------
  samples:          10000
  evals/sample:     855

julia> @benchmark dot_oro($x,$y)
BenchmarkTools.Trial: 
  memory estimate:  0 bytes
  allocs estimate:  0
  --------------
  minimum time:     219.204 ns (0.00% GC)
  median time:      220.613 ns (0.00% GC)
  mean time:        223.682 ns (0.00% GC)
  maximum time:     479.681 ns (0.00% GC)
  --------------
  samples:          10000
  evals/sample:     501

The above tests were run on:

julia> versioninfo()
Julia Version 1.4.0-DEV.0
Commit 2ef0ed159d* (2019-08-17 17:21 UTC)
Platform Info:
  OS: Linux (x86_64-generic-linux)
  CPU: Intel(R) Core(TM) i9-7900X CPU @ 3.30GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-8.0.0 (ORCJIT, skylake)

[ffevotte]

Thanks a lot!