Speeding up computation of sinh(x) and cosh(x)

[ericagol]

• [ ] Try the following: expmx=exp(-x);y=expmx*expm1(2x)/2; z=(expmx+inv(expmx))/2 where y=sinh(x) and z=cosh(x). This gives about a 25% savings in computing these in v1.5.2.

[giordano]

Note that in Julia v1.6 sinh and cosh are much faster: https://github.com/JuliaLang/julia/pull/37426

Julia v1.5:

julia> using BenchmarkTools

julia> @btime y .= sinh.(x) setup = (x = randn(1000); y = similar(x));
  22.414 μs (0 allocations: 0 bytes)

julia> @btime y .= cosh.(x) setup = (x = randn(1000); y = similar(x));
  15.094 μs (0 allocations: 0 bytes)

Julia v1.6:

julia> using BenchmarkTools

julia> @btime y .= sinh.(x) setup = (x = randn(1000); y = similar(x));
  8.082 μs (0 allocations: 0 bytes)

julia> @btime y .= cosh.(x) setup = (x = randn(1000); y = similar(x));
  6.833 μs (0 allocations: 0 bytes)

[ericagol]

Thanks, @giordano ! It looks like these are ~twice as fast as the expressions I've written above; nice! Do you know if there is a function like sincos(x), but hyperbolic which computes sinh(x) and cosh(x) simultaneously (with time savings)?

[giordano]

Hehe, I also looked for it. There doesn't seem to be a sincosh, but that'd probably a good addition. Mind opening an issue?

[ericagol]

Leaving this for now.