# Slow code to compute b=A\*x

**URL:** <https://discourse.julialang.org/t/slow-code-to-compute-b-a-x/116562>\
**Category:** Performance\
**Tags:** question\
**Created:** [July 3, 2024, 5:33am UTC](https://discourse.julialang.org/t/slow-code-to-compute-b-a-x/116562 "2024-07-03T05:33:10Z")\
**Posts on this page:** 8\
**Page:** 1

<div class="post-metadata">

**Author:** ![ww1g11](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ww1g11/32/14205_2.png) [@ww1g11](https://discourse.julialang.org/u/ww1g11)\
**Post date:** [July 3, 2024, 5:33am UTC](https://discourse.julialang.org/t/slow-code-to-compute-b-a-x/116562/1 "2024-07-03T05:33:10Z")

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Hi all,

I wrote a very simple code to compute b=A\*x and found that it is slow, please see the following codes to compare sum1, sum2 and sum3:

```julia
using TimerOutputs
const timer = TimerOutput()

function test(N=20000)
    A = rand(N, N)
    b = zeros(N)
    x = rand(N)

    @timeit timer "sum1" begin
        for i in 1:N
            f = 0.0
            for j in 1:N
                f += A[i, j] * x[j]
            end
            b[i] = f
        end
    end

    @timeit timer "sum2" begin
        for i in 1:N
            f = 0.0
            for j in 1:N
                f = A[i, j] * x[j]
            end
            b[i] = f
        end
    end

    @timeit timer "sum3" begin
        for i in 1:N
            f = 0.0
            for j in 1:N
                f += A[i, j] * x[j]
            end
            #b[i] = f
        end
    end

end

test()
println(timer)

```

The output is

```bash
 ────────────────────────────────────────────────────────────────────
                            Time Allocations
                   ─────────────────────── ────────────────────────
 Tot / % measured: 3.96s / 79.5% 3.00GiB / 0.0%

 Section ncalls time %tot avg alloc %tot avg
 ────────────────────────────────────────────────────────────────────
 sum1 1 2.90s 92.3% 2.90s 0.00B - % 0.00B
 sum3 1 122ms 3.9% 122ms 0.00B - % 0.00B
 sum2 1 121ms 3.8% 121ms 0.00B - % 0.00B
 ────────────────────────────────────────────────────────────────────

```

I just wonder why sum1 is much slower than sum2 or sum3.

The versioninfo() in the test computer gives

```bash
julia> versioninfo()
Julia Version 1.10.2
Commit bd47eca2c8 (2024-03-01 10:14 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Windows (x86_64-w64-mingw32)
  CPU: 24 × 13th Gen Intel(R) Core(TM) i7-13700F
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, goldmont)
Threads: 1 default, 0 interactive, 1 GC (on 24 virtual cores)
Environment:
  JULIA_PKG_SERVER = https://mirrors.ustc.edu.cn/julia
  JULIA_SSL_CA_ROOTS_PATH =

```

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<div class="post-metadata">

**Author:** ![jling](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jling/32/212909_2.png) [@jling](https://discourse.julialang.org/u/jling)\
**Post date:** [July 3, 2024, 5:34am UTC](https://discourse.julialang.org/t/slow-code-to-compute-b-a-x/116562/2 "2024-07-03T05:34:06Z")

</div>

JIT compilation?

---

<div class="post-metadata">

**Author:** ![ww1g11](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ww1g11/32/14205_2.png) [@ww1g11](https://discourse.julialang.org/u/ww1g11)\
**Post date:** [July 3, 2024, 5:39am UTC](https://discourse.julialang.org/t/slow-code-to-compute-b-a-x/116562/3 "2024-07-03T05:39:51Z")

</div>

it seems not,

I added the following code and test again,

```julia
reset_timer!(timer)
test()
println(timer)

```

but the output is similar.

---

<div class="post-metadata">

**Author:** ![sgaure](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/sgaure/32/14779_2.png) [@sgaure](https://discourse.julialang.org/u/sgaure)\
**Post date:** [July 3, 2024, 5:49am UTC](https://discourse.julialang.org/t/slow-code-to-compute-b-a-x/116562/4 "2024-07-03T05:49:58Z")

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In `sum2` you only use the last `f` from the inner loop, so the compiler probably optimizes it away and replaces it with a single assignment. In `sum3` you are not using the result of the inner loop, so it’s probably optimized out.

`sum1` is probably slow because you do it the wrong way. The first index should be looped over in the inner loop.

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<div class="post-metadata">

**Author:** ![ww1g11](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ww1g11/32/14205_2.png) [@ww1g11](https://discourse.julialang.org/u/ww1g11)\
**Post date:** [July 3, 2024, 6:13am UTC](https://discourse.julialang.org/t/slow-code-to-compute-b-a-x/116562/5 "2024-07-03T06:13:48Z")

</div>

I know first index should be placed in the inner loop for a column-major matrix, but why sum1 is much slower than sum2 or sum3, because in principle, they do not fit the memory layout either.

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<div class="post-metadata">

**Author:** ![sgaure](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/sgaure/32/14779_2.png) [@sgaure](https://discourse.julialang.org/u/sgaure)\
**Post date:** [July 3, 2024, 6:18am UTC](https://discourse.julialang.org/t/slow-code-to-compute-b-a-x/116562/6 "2024-07-03T06:18:11Z")

</div>

`sum2` and `sum3` effectively do not have an inner loop. The compiler will optimize it away since the results of the inner loop are not used.

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<div class="post-metadata">

**Author:** ![ww1g11](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ww1g11/32/14205_2.png) [@ww1g11](https://discourse.julialang.org/u/ww1g11)\
**Post date:** [July 3, 2024, 6:39am UTC](https://discourse.julialang.org/t/slow-code-to-compute-b-a-x/116562/7 "2024-07-03T06:39:41Z")

</div>

Thanks, I guess this is the reason.

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<div class="post-metadata">

**Author:** ![sgaure](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/sgaure/32/14779_2.png) [@sgaure](https://discourse.julialang.org/u/sgaure)\
**Post date:** [July 3, 2024, 7:55am UTC](https://discourse.julialang.org/t/slow-code-to-compute-b-a-x/116562/8 "2024-07-03T07:55:35Z")

</div>

You can compare it to `LinearAlgebra.mul!(b, A, x)`. This calls into the BLAS, and is probably very hard to beat.