Fix fastmath methods of sin, cos, tan, atan2

[giordano]

These functions now have a fast pure Julia implementation, let the fastmath
versions fall back on the default methods.

I'm not very familiar with @fastmath stuff, so please double (or even triple) check I'm not missing something :-) At least, fastmath tests are passing locally.

[giordano]

Bump

[StefanKarpinski]

@simonbyrne, it would be great if you could review this when you get a chance.

[giordano]

Patch rebased on current master

[giordano]

Bump

[KristofferC]

Can you show some benchmarks of before and after this PR for the relevant functions when using fastmath?

[giordano]

You can simply compare sin and @fastmath sin, currently the former is faster than the latter:

julia> using BenchmarkTools

julia> function f()
       a = 0.0
       for x in -100:0.01:100
           a = @fastmath sin(x)
       end
       return a
       end
f (generic function with 1 method)

julia> function g()
       a = 0.0
       for x in -100:0.01:100
           a = sin(x)
       end
       return a
       end
g (generic function with 1 method)

julia> @benchmark f()
BenchmarkTools.Trial: 
  memory estimate:  0 bytes
  allocs estimate:  0
  --------------
  minimum time:     382.706 μs (0.00% GC)
  median time:      383.062 μs (0.00% GC)
  mean time:        389.019 μs (0.00% GC)
  maximum time:     655.759 μs (0.00% GC)
  --------------
  samples:          10000
  evals/sample:     1

julia> @benchmark g()
BenchmarkTools.Trial: 
  memory estimate:  0 bytes
  allocs estimate:  0
  --------------
  minimum time:     356.151 μs (0.00% GC)
  median time:      356.489 μs (0.00% GC)
  mean time:        356.659 μs (0.00% GC)
  maximum time:     486.692 μs (0.00% GC)
  --------------
  samples:          10000
  evals/sample:     1

With this PR the performance of f and g is just the same

[giordano]

Bump. I think it might be good to have this reviewd and merged before 0.7

[simonbyrne]

LGTM. Just needs a rebase.

[giordano]

Rebased on master

[vchuravy]

Circleci is: Got exception LoadError("/tmp/julia/share/julia/stdlib/v0.7/OldPkg/test/pkg.jl", 56, KeyError("SparseArrays")) outside of a @test LoadError: KeyError: key "SparseArrays" not found Stacktrace: