Make sintau/costau consistent with sinpi/cospi

[giordano]

julia> sin(NaN)
NaN

julia> sin(Inf)
ERROR: DomainError:
Stacktrace:
 [1] nan_dom_err at ./math.jl:299 [inlined]
 [2] sin(::Float64) at ./math.jl:416

julia> sintau(NaN)
NaN

julia> sintau(Inf)
ERROR: DomainError:
Stacktrace:
 [1] sintau(::Float64) at /home/mose/.julia/v0.7/Tau/src/trig.jl:5

Note that this PR makes the test fail on Julia 0.4 (see #13) because in Julia 0.4:

julia> sin(complex(Inf, Inf))
Inf + NaN*im

while in Julia 0.5 and later

julia> sin(complex(Inf, Inf))
NaN + Inf*im

I also changed the first test to

@test tau ≠ 2 * pi

because it's exactly the fact that tau isn't the same as 2 * pi that makes this package particularly useful.

[codecov-io]

Codecov Report

Merging #19 into master will increase coverage by 5.55%.
The diff coverage is 100%.

@@           Coverage Diff            @@
##           master    #19      +/-   ##
========================================
+ Coverage   94.44%   100%   +5.55%     
========================================
  Files           2      2              
  Lines          54     61       +7     
========================================
+ Hits           51     61      +10     
+ Misses          3      0       -3

Impacted Files	Coverage Δ
src/trig.jl	100% <100%> (+5.66%)	⬆️

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[waldyrious]

Thanks for doing this! I should be able to do a proper review in the weekend.

[giordano]

I added more extensive tests. I always compare the results with sinpi/cospi, rather that with sin/cos, because the formers are more accurate.

For the record, the new methods of sintau/costau with complex arguments are often faster than before. Before the PR:

julia> z = complex(0.0, 0.0)
0.0 + 0.0im

julia> @benchmark sintau($z)
BenchmarkTools.Trial: 
  memory estimate:  0 bytes
  allocs estimate:  0
  --------------
  minimum time:     34.275 ns (0.00% GC)
  median time:      36.908 ns (0.00% GC)
  mean time:        37.036 ns (0.00% GC)
  maximum time:     87.059 ns (0.00% GC)
  --------------
  samples:          10000
  evals/sample:     993

julia> z = complex(-1.0, 1.0)
-1.0 + 1.0im

julia> @benchmark sintau($z)
BenchmarkTools.Trial: 
  memory estimate:  0 bytes
  allocs estimate:  0
  --------------
  minimum time:     87.628 ns (0.00% GC)
  median time:      87.806 ns (0.00% GC)
  mean time:        89.831 ns (0.00% GC)
  maximum time:     208.251 ns (0.00% GC)
  --------------
  samples:          10000
  evals/sample:     963

julia> z = complex(3.5, -2.7)
3.5 - 2.7im

julia> @benchmark sintau($z)
BenchmarkTools.Trial: 
  memory estimate:  0 bytes
  allocs estimate:  0
  --------------
  minimum time:     121.915 ns (0.00% GC)
  median time:      122.128 ns (0.00% GC)
  mean time:        123.617 ns (0.00% GC)
  maximum time:     346.113 ns (0.00% GC)
  --------------
  samples:          10000
  evals/sample:     909

After the PR:

julia> z = complex(0.0, 0.0)
0.0 + 0.0im

julia> @benchmark sintau($z)
BenchmarkTools.Trial: 
  memory estimate:  0 bytes
  allocs estimate:  0
  --------------
  minimum time:     10.041 ns (0.00% GC)
  median time:      10.047 ns (0.00% GC)
  mean time:        10.090 ns (0.00% GC)
  maximum time:     29.297 ns (0.00% GC)
  --------------
  samples:          10000
  evals/sample:     999

julia> z = complex(-1.0, 1.0)
-1.0 + 1.0im

julia> @benchmark sintau($z)
BenchmarkTools.Trial: 
  memory estimate:  0 bytes
  allocs estimate:  0
  --------------
  minimum time:     35.591 ns (0.00% GC)
  median time:      35.624 ns (0.00% GC)
  mean time:        35.943 ns (0.00% GC)
  maximum time:     71.093 ns (0.00% GC)
  --------------
  samples:          10000
  evals/sample:     993

julia> z = complex(3.5, -2.7)
3.5 - 2.7im

julia> @benchmark sintau($z)
BenchmarkTools.Trial: 
  memory estimate:  0 bytes
  allocs estimate:  0
  --------------
  minimum time:     118.415 ns (0.00% GC)
  median time:      118.493 ns (0.00% GC)
  mean time:        120.525 ns (0.00% GC)
  maximum time:     226.772 ns (0.00% GC)
  --------------
  samples:          10000
  evals/sample:     911

I believe that there is much room for improvement in the sintau/costau methods with real arguments. They are based on old implementations of the sinpi/cospi functions, the new ones are way faster. However, adapting them to sintau/costau goes beyond my abilities.

[waldyrious]

LGTM. Nice that the test coverage has reached 100% :)

I would like to discuss the @test tau ≠ 2 * pi change, but that is a separate issue.