Brainfuck arbitrary size array implementation

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rep=string.rep

function read(n)
    return  seek(n,k,1,0,1)..
            rep(">",k)..
            rep("<"..rep(">",2*k+2*n)..
            "[-"..rep("<",n+k).."+"..rep("<",n+k).."+"..rep(">",2*n+2*k).."]"..
            rep("<",2*k+2*n).."[-"..rep(">",2*k+2*n).."+"..rep("<",2*k+2*n)..
            "]",k)..
            retur(n,k,1,0,1)
end

function left(n,k,w)
    return  rep(">",n+k-1)..
            rep(">"..rep("[-"..rep("<",k).."+"..rep(">",k).."]",1-w),k)..
            rep(">[-"..rep("<",k).."+"..rep(">",k).."]",n)..
            rep("<",2*k+2*n-1)..
            rep("<[-"..rep(">",2*k+2*n).."+"..rep("<",2*k+2*n).."]",k)
end

function retur(n,k,i,w,f)
    local ret=  rep(">",2*k+2*n-i).."[-"..rep("<",2*k+2*n-i)..
                left(n,k,w)..rep(">",2*k+2*n-i)
                if i>1 then ret=ret..
                rep(">-<"..rep("<",2*k+2*n-i)..
                retur(n,k,i-1,w,0)..
                rep(">",2*k+2*n-i),(i>1) and 1 or 0) end
                ret=ret.."]"..rep("<",2*k+2*n-i) --simplirosa kai mia ].
                if i<n and f==1 then ret=ret..rep(retur(n,k,i+1,w,1),(i<n and 1 or 0)*f) end
                return ret
end

function seek(n,k,i,w,f)
    local ret=  rep(">",n+k-i).."[-"..rep(rep(">",n+k).."+"..rep("<",n+k),f)..
                rep("<",n+k-i)..right(n,k,w)..
                rep(">",n+k-i) --diakopi apotoma se sxesi me to xarti
                if i>1 then ret=ret..rep(">-<"..rep("<",n+k-i)..
                seek(n,k,i-1,w,0)..
                rep(">",n+k-i),(i>1) and 1 or 0) end
                --apotomi sinexia
                ret=ret.."]"..rep("<",n+k-i)
                if i<n and f==1 then ret=ret..rep(seek(n,k,i+1,w,1),(i<n and 1 or 0)*f) end
                return ret
end

function write(n,k,i,w,f)
    return  seek(n,k,1,1,1)..
            rep(">",3*k+2*n)..
            rep("<[-]",k)..rep("<",n)..
            rep("<[-"..rep(">",n+k).."+"..rep("<",n+k).."]",k)..
            rep("<",n+k)..
            retur(n,k,1,1,1)
end

function right(n,k,w)
    return  rep(">",3*k+2*n)..
            rep("<[-"..rep("<",2*k+2*n).."+"..rep(">",2*k+2*n).."]",k)..
            rep("<[-"..rep(">",k).."+"..rep("<",k).."]",n)..
            rep("<"..rep("[-"..rep(">",k).."+"..rep("<",k).."]",w),k)..
            rep("<[-"..rep(">",k).."+"..rep("<",k).."]",n)
end

function optimize(code)
    repeat
        local changes=0
        local tempchanges=0
        code,tempchanges=string.gsub(code,"<>","")
        changes=tempchanges+changes
        code,tempchanges=string.gsub(code,"><","")
        changes=tempchanges+changes
        code,tempchanges=string.gsub(code,"%-%+","")
        changes=tempchanges+changes
        code,tempchanges=string.gsub(code,"%+%-","")
        changes=tempchanges+changes
        --print(changes)
    until changes==0
    return code
end

print("Brainfuck Array Wizard by Tritonio")
print()
io.write("How many bytes per cell? ")
k=io.read()/1
io.write("How many cells? ")
cells=io.read()
n=math.ceil(math.log(cells)/math.log(256))
if n==0 then n=1 end
print()
print("This is the structure of the table: "..rep("0",k)..rep("I",n)..rep("D",k)..rep("0",n).."("..cells*k.." empty cells for array data)") --to n*k den einai sosto.
print("(0 stands for empty cell, I for index, D for data)")
print("(The most significant index is the first one)")
print()
print("The total size of the table is "..cells*k+k+n+k+n..".")
print("The overhead because of the indexes etc is "..math.floor(0.5+100000*(k+n+k+n)/(cells*k+k+n+k+n))/1000 .."% of the total size.")
print()
print("To write to the table fill in the I (index) and the D (data) positions in the header, move the Brainfuck pointer to the beginning of the structure and execute the following code:")
print(optimize(write(n,k)))
print("After the execution, the indexes and the data fields will be zeroed and the Brainfuck pointer will be left at the beginning of the structure.")
--print(write(n,k))
print()
print("To read from the table fill the I (index) fields, move the Brainfuck pointer to the beginning of the structure and execute the following code:")
print(optimize(read(n,k)))
--print(read(n,k))
print("After the execution, the indexes will be zeroed, the Brainfuck pointer will be left at the beginning of the structure and the data fields will contain the read data.")
io.read()