Specialize sign-related functions

[kimikage]

This is part of the issue #185.
Edit:
This prohibits copysign/flipsign for Normed. They should be confusing when the signed Normed is supported in the future. Furthermore, if signed Normed is available, we should not do unsafe sign operations for unsigned Normed.

[kimikage]

Benchmark

julia> versioninfo()
Julia Version 1.4.2
Commit 44fa15b150* (2020-05-23 18:35 UTC)
Platform Info:
  OS: Windows (x86_64-w64-mingw32)
  CPU: Intel(R) Core(TM) i7-8565U CPU @ 1.80GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-8.0.1 (ORCJIT, skylake)

before

julia> @btime copysign.(x, y) setup=(x=collect(rand(Q0f7,100,100)); y=collect(rand(Q0f7,100,100)));
  31.100 μs (1 allocation: 9.94 KiB)

julia> @btime flipsign.(x, y) setup=(x=collect(rand(Q0f7,100,100)); y=collect(rand(Q0f7,100,100)));
  30.900 μs (1 allocation: 9.94 KiB)
  
julia> @btime signbit.(x) setup=(x=collect(rand(Q0f7,100,100)));
  5.750 μs (3 allocations: 5.56 KiB)

julia> @btime signbit.(x) setup=(x=collect(rand(N0f8,100,100)));
  2.744 μs (3 allocations: 5.56 KiB)
  
julia> @btime abs.(x) setup=(x=collect(rand(N0f8,100,100)));
  2.962 μs (1 allocation: 9.94 KiB)

after

julia> @btime copysign.(x, y) setup=(x=collect(rand(Q0f7,100,100)); y=collect(rand(Q0f7,100,100)));
  7.500 μs (1 allocation: 9.94 KiB)
  
julia> @btime flipsign.(x, y) setup=(x=collect(rand(Q0f7,100,100)); y=collect(rand(Q0f7,100,100)));
  5.350 μs (1 allocation: 9.94 KiB)
  
julia> @btime signbit.(x) setup=(x=collect(rand(Q0f7,100,100)));
  5.316 μs (3 allocations: 5.56 KiB)

julia> @btime signbit.(x) setup=(x=collect(rand(N0f8,100,100)));
  1.700 μs (3 allocations: 5.56 KiB)

julia> @btime abs.(x) setup=(x=collect(rand(N0f8,100,100)));
  2.962 μs (1 allocation: 9.94 KiB)

[codecov]

Codecov Report

Merging #187 into master will increase coverage by 0.14%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##           master     #187      +/-   ##
==========================================
+ Coverage   89.15%   89.30%   +0.14%     
==========================================
  Files           6        6              
  Lines         452      458       +6     
==========================================
+ Hits          403      409       +6     
  Misses         49       49              

Impacted Files	Coverage Δ
src/fixed.jl	90.17% <ø> (-0.09%)	⬇️
src/normed.jl	88.88% <ø> (-0.12%)	⬇️
src/FixedPointNumbers.jl	87.71% <100.00%> (+1.05%)	⬆️

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[kimikage]

rebased

[kimikage]

I'll merge this, but wait a little longer for tagging.