# A limit to free operations of my own type

**URL:** <https://discourse.julialang.org/t/a-limit-to-free-operations-of-my-own-type/87690>\
**Category:** Performance\
**Created:** [September 23, 2022, 8:33am UTC](https://discourse.julialang.org/t/a-limit-to-free-operations-of-my-own-type/87690 "2022-09-23T08:33:38Z")\
**Posts on this page:** 1\
**Page:** 1

<div class="post-metadata">

**Author:** ![mongi](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mongi/32/43334_2.png) [@mongi](https://discourse.julialang.org/u/mongi)\
**Post date:** [September 23, 2022, 8:33am UTC](https://discourse.julialang.org/t/a-limit-to-free-operations-of-my-own-type/87690/1 "2022-09-23T08:33:38Z")

</div>

Hi,  
I have my own type (fields Vector and Int) and implemented (+,-,\*,/) for it “mulT(args…), addT, subT, divT”, and it works without allocations until length(args)\>7 for multiplication and 9 for addition. For each operation there is a cache in the args that receives the result (to avoid allocations and that s why i used mulT instead of \*).  
here is a copy of my MWE code. you can copy and test it yourselves.  
It does not allocate. add one argument and it will allocate.  
thank you for your time.  
I asked this question here [A limit to free operations - #6 by mongi](https://discourse.julialang.org/t/a-limit-to-free-operations/87568/6) but i think the question was misunderstood and did not get an answer.

```julia
using BenchmarkTools
import Base: eachindex, getindex, setindex!

struct MyType{T<:Number} 
    coeffs :: Array{T,1}
    size :: Int
end

function mulTT(a::MyType{T}, b::T,cache1::MyType{T},cache2::MyType{T}) where {T<:Number}
  fill!(cache2.coeffs, b)
  @ __dot__ cache1.coeffs = a.coeffs * cache2.coeffs ##fixed broadcast dimension mismatch
  return cache1
end
mulTT(a::T,b::MyType{T}, cache1::MyType{T},cache2::MyType{T}) where {T<:Number} = mulTT(b , a,cache1,cache2)
function mulTT(a::MyType{T}, b::MyType{T},cache1::MyType{T},cache2::MyType{T}) where {T<:Number}
 for k in eachindex(a)
      @inbounds cache2[k] = a[0] * b[k]
      @inbounds for i = 1:k
        cache2[k] += a[i] * b[k-i]
      end
  end
  @ __dot__ cache1.coeffs = cache2.coeffs
  return cache1
end
function mulTT(a::T, b::T,cache1::MyType{T},cache2::MyType{T}) where {T<:Number}
  cache1[0]=a*b  
  return cache1
end
function mulTT(a::P, b::R, c::Q, xs...)where {P,Q,R <:Union{MyType,Number}}
    if length(xs)>1
      mulTfoldl( mulTT( mulTT(a,b,xs[end-1],xs[end]) , c,xs[end-1] ,xs[end] ), xs...)
    end
end
getindex(a::MyType, n::Int) = a.coeffs[n+1]
setindex!(a::MyType{T}, x::T, n::Int) where {T<:Number} = a.coeffs[n+1] = x
@inline firstindex(a::MyType) = 0
@inline lastindex(a::MyType) = a.size
@inline eachindex(a::MyType) = firstindex(a):lastindex(a)
function mulTfoldl(res::P, bs...) where {P<:MyType}
    l = length(bs)
    i = 2; l == i && return res 
    i = 3; l == i && return mulTT(res, bs[1],bs[end-1],bs[end])
    i = 4; l == i && return mulTT(mulTT(res, bs[1],bs[end-1],bs[end]),bs[2],bs[end-1],bs[end])
    i = 5; l == i && return mulTT(mulTT(mulTT(res, bs[1],bs[end-1],bs[end]),bs[2],bs[end-1],bs[end]),bs[3],bs[end-1],bs[end])
    i = 6; l == i && return mulTT(mulTT(mulTT(mulTT(res, bs[1],bs[end-1],bs[end]),bs[2],bs[end-1],bs[end]),bs[3],bs[end-1],bs[end]),bs[4],bs[end-1],bs[end])
end

av = vec(3(rand(1,3) .- 1.5)) 
bv = vec(3(rand(1,3) .- 1.5))
cv = vec(3(rand(1,3) .- 1.5))
dv = vec(3(rand(1,3) .- 1.5))

a0 = MyType(av,2)
b0 = MyType(bv,2)
c0 = MyType(cv,2)
d0 = MyType(dv,2)
e=3rand() - 1.5
f=3rand() - 1.5
cache=[MyType([0.0,0.0,0.0],2),MyType([0.0,0.0,0.0],2)]
function boundaryTest(a0::MyType{Float64},b0::MyType{Float64},c0::MyType{Float64},d0::MyType{Float64},cache::Vector{MyType{Float64}},e::Float64,f::Float64)
     mulTT(e, f, a0, b0, e, c0, cache[1], cache[2])
   #mulTT(e, f, a0, b0, e, c0, d0, cache[1], cache[2])# increasing the args here will allocate
end
@btime boundaryTest(a0,b0,c0,d0,cache,e,f)

```