Float64sr via Double64

[milankl]

fixes #59

julia> using StochasticRounding

julia> A = Float64sr.(rand(4,4))
4×4 Matrix{Float64sr}:
 Float64sr(0.38418416963682733)  …  Float64sr(0.5286745680704084)
 Float64sr(0.6002555882832199)      Float64sr(0.5193716738812405)
 Float64sr(0.7037500894099693)      Float64sr(0.4781770819341078)
 Float64sr(0.8019156074397128)      Float64sr(0.522393411487242)

julia> b = Float64sr.(rand(4))
4-element Vector{Float64sr}:
 Float64sr(0.7554796403393423)
 Float64sr(0.4199864825038644)
 Float64sr(0.30487539136735975)
 Float64sr(0.7228777754787546)

julia> A\b
4-element Vector{Float64sr}:
 Float64sr(-0.5018580578417031)
 Float64sr(-1.1517596349045047)
 Float64sr(0.21765870439733434)
 Float64sr(2.8794910547991557)

julia> A\b   # do it again, slightly different answer
4-element Vector{Float64sr}:
 Float64sr(-0.5018580578417027)
 Float64sr(-1.1517596349045056)
 Float64sr(0.21765870439733445)
 Float64sr(2.879491054799156)

@avleenk2312 could you try out this branch (and maybe even write some tests for it? 😄) before I merge it?

[avleenk2312]

Sure, I will try it out. ◡̎

[milankl]

A single error is occurring, unrelated to this pull request

Test Summary:   |  Pass  Fail  Total   Time
Test for U(0,1) | 29999     1  30000  15.4s

which seems to be because a Float16sr isn't rounded to either of two but of three (for whatever buggy reason) numbers

 Test for U(0,1): Test Failed at /home/runner/work/StochasticRounding.jl/StochasticRounding.jl/test/float16sr.jl:114
  Expression: Ndown + Nup == N
   Evaluated: 99999 == 100000

[milankl]

This ☝🏼 error is now issued in #62, so @avleenk2312 please ignore it here. Have you had a chance to test Float64sr?

[avleenk2312]

Thanks for pointing out this error. We just completed our code that uses Float32sr tonight. I have started looking into Float64sr now. I will get back to you.

[milankl]

@avleenk2312 As #62 was resolved with #67 these tests here now pass. However, we're not actually testing Float64sr in /test yet.

[milankl]

Have added a small test set similar to other formats, locally tests pass. So the implementation looks good!

[milankl]

Screw this, there's another one of those from #62

 [ Info: Test failed for 5.5849552e-5, 0000001110101001
Test for subnormals: Test Failed at /home/runner/work/StochasticRounding.jl/StochasticRounding.jl/test/float16sr.jl:179
  Expression: Ndown + Nup == N
   Evaluated: 99990 == 100000

[ Info: Test failed for -5.5849552e-5, 1000001110101001
Test Summary:       |  Pass  Fail  Total   Time
Test for subnormals | 59998     2  60000  25.1s
ERROR: LoadError: Some tests did not pass: 59998 passed, 2 failed, 0 errored, 0 broken.
in expression starting at /home/runner/work/StochasticRounding.jl/StochasticRounding.jl/test/float16sr.jl:162