compare.jl

import Base.Math: rem_pio2_kernel, sin_kernel, cos_kernel

function nansin(x::T) where T<:Union{Float64}
    absx = abs(x)
    if absx < T(pi)/4 #|x| ~<= pi/4, no need for reduction
        if absx < sqrt(eps(T))
            return x
        end
        return sin_kernel(x)
    elseif isnan(x)
        return T(NaN)
    elseif isinf(x)
        return T(NaN)
    end
    n, y = rem_pio2_kernel(x)
    n = n&3
    if n == 0
        return sin_kernel(y)
    elseif n == 1
        return cos_kernel(y)
    elseif n == 2
        return -sin_kernel(y)
    else
        return -cos_kernel(y)
    end
end

using StaticArrays, BenchmarkTools


x = 2.3
# minimum times are exactly the same
@benchmark sin($(Ref(x))[])
@benchmark nansin($(Ref(x))[])


 const v = @SVector(rand(20))

function test1(x)
    sinx = nansin(x)
    return v .+ sinx
end

function test2(x)
    sinx = sin(x)
    return v .+ sinx
end

# minimum times are exactly the same
@benchmark test1((Ref(2.2))[]);
@benchmark test2((Ref(2.2))[]);