Performance with Julia. Looping through boolean data

Question

N = 100000
a = randbool(N)
b = randbool(N)

Here is my current code (the slow part of my code)

onefalse = a $ b
twofalses = !a & !b
sum(onefalse)
sum(twofalses)

Is there any way to improve this code? I am feeling like I am looping twice through a and through b. I tried with a for loop and if statements but it was way slower.

for i = 1:N
        if a[i]
            if b[i]

            else
                onefalse+=1
            end
        else
            if b[i]
                onefalse+=1
            else
                twofalses+=1
            end
        end
       end

Answer 1

First of all, a valid question is why is the for loop version slow. Its partly because randbool gives a BitArray, not a normal array. I decided to compare with Array{Bool} out of curiosity. I was able to speed it up a bit - I think you are probably at the limits of what is possible though. In particular, indexing into an Array{Bool} seems to be faster than BitArray, but operations on BitArrays like those done here are hard to beat.

function countfalse1(N, a, b)
    return sum(a $ b), sum(!a & !b)
end

function countfalse2(N, a, b)
    return N-sum(a), N-sum(a|b)
end

function countfalse3(N, a, b)
    onef, twof = 0, 0
    @inbounds for i = 1:N
        if a[i]
            if !b[i]
                onef += 1
            end
        else
            if b[i]
                onef += 1
            else
                twof += 1
            end
        end
   end
   return onef, twof
end

srand(1000)
N = 10000000
a = randbool(N)
b = randbool(N)
c = Bool[a[i] for i in 1:N]
d = Bool[b[i] for i in 1:N]

println("BitArray")
@show countfalse1(N, a, b)
@time countfalse1(N, a, b)
@time countfalse1(N, a, b)
@time countfalse1(N, a, b)

@show countfalse2(N, a, b)
@time countfalse2(N, a, b)
@time countfalse2(N, a, b)
@time countfalse2(N, a, b)

@show countfalse3(N, a, b)
@time countfalse3(N, a, b)
@time countfalse3(N, a, b)
@time countfalse3(N, a, b)

println("\nArray{Bool}")
@show countfalse1(N, c, d)
@time countfalse1(N, c, d)
@time countfalse1(N, c, d)
@time countfalse1(N, c, d)

@show countfalse2(N, c, d)
@time countfalse2(N, c, d)
@time countfalse2(N, c, d)
@time countfalse2(N, c, d)

@show countfalse3(N, c, d)
@time countfalse3(N, c, d)
@time countfalse3(N, c, d)
@time countfalse3(N, c, d)

gives

BitArray
countfalse1(N,a,b) => (5001756,2500026)
elapsed time: 0.004565573 seconds (5014328 bytes allocated)
elapsed time: 0.003607561 seconds (5000528 bytes allocated)
elapsed time: 0.013880181 seconds (5000528 bytes allocated, 83.83% gc time)
countfalse2(N,a,b) => (5003620,2500026)
elapsed time: 0.000784883 seconds (1250240 bytes allocated)
elapsed time: 0.000752576 seconds (1250240 bytes allocated)
elapsed time: 0.000758695 seconds (1250240 bytes allocated)
countfalse3(N,a,b) => (5001812,2500026)
elapsed time: 0.120491323 seconds (144 bytes allocated)
elapsed time: 0.118401949 seconds (144 bytes allocated)
elapsed time: 0.11807728 seconds (144 bytes allocated)

Array{Bool}
countfalse1(N,c,d) => (5001756,2500026)
elapsed time: 0.098838752 seconds (40000640 bytes allocated)
elapsed time: 0.112468122 seconds (40000640 bytes allocated, 10.64% gc time)
elapsed time: 0.11305269 seconds (40000640 bytes allocated, 10.22% gc time)
countfalse2(N,c,d) => (5003620,2500026)
elapsed time: 0.066169587 seconds (10000328 bytes allocated)
elapsed time: 0.084794646 seconds (10000328 bytes allocated, 17.78% gc time)
elapsed time: 0.067458965 seconds (10000328 bytes allocated)
countfalse3(N,c,d) => (5001812,2500026)
elapsed time: 0.066095076 seconds (144 bytes allocated)
elapsed time: 0.067585543 seconds (144 bytes allocated)
elapsed time: 0.06718118 seconds (144 bytes allocated)