Counting FLOPs

Have you ever wondered how many floating point operations (FLOPs) a certain block of code, e.g. a Julia function, has actually triggered in a CPU core? With LIKWID.jl you can readily answer this question!

Let's consider a simple example: daxpy. The abbreviation daxpy stands for double-precision (Float64) a times x plus y, i.e. the computation

\[z = a \cdot x + y\]

Of course, we can readily write this as a Julia function.

daxpy!(z, a, x, y) = z .= a .* x .+ y

daxpy! (generic function with 1 method)

Preparing some random input we can perform the daxpy! operation as per usual (we're suppressing the unimportant output below).

const N = 10_000
const a = 3.141
const x = rand(N)
const y = rand(N)
const z = zeros(N)

daxpy!(z, a, x, y);

Let's now use LIKWID to count the actually performed FLOPs for this computation! Concretely, we measure the FLOPS_DP performance group, in which "DP" stands for "double precision".

using LIKWID
metrics, events = @perfmon "FLOPS_DP" daxpy!(z, a, x, y);

Group: FLOPS_DP
┌──────────────────────────────────────────┬──────────┐
│                                    Event │ Thread 1 │
├──────────────────────────────────────────┼──────────┤
│                        INSTR_RETIRED_ANY │  11759.0 │
│                    CPU_CLK_UNHALTED_CORE │ 133737.0 │
│                     CPU_CLK_UNHALTED_REF │  88320.0 │
│ FP_ARITH_INST_RETIRED_128B_PACKED_DOUBLE │      0.0 │
│      FP_ARITH_INST_RETIRED_SCALAR_DOUBLE │      0.0 │
│ FP_ARITH_INST_RETIRED_256B_PACKED_DOUBLE │   5000.0 │
│ FP_ARITH_INST_RETIRED_512B_PACKED_DOUBLE │      0.0 │
└──────────────────────────────────────────┴──────────┘
┌──────────────────────┬────────────┐
│               Metric │   Thread 1 │
├──────────────────────┼────────────┤
│  Runtime (RDTSC) [s] │ 7.18004e-5 │
│ Runtime unhalted [s] │ 5.58628e-5 │
│          Clock [MHz] │    3625.11 │
│                  CPI │    11.3732 │
│         DP [MFLOP/s] │     278.55 │
│     AVX DP [MFLOP/s] │     278.55 │
│  AVX512 DP [MFLOP/s] │        0.0 │
│     Packed [MUOPS/s] │    69.6375 │
│     Scalar [MUOPS/s] │        0.0 │
│  Vectorization ratio │      100.0 │
└──────────────────────┴────────────┘

That was easy. Let's see what we got. Among all those results, for computing the total number of FLOPs we care about the metrics "DP [MFLOP/s]", which gives the MFLOPs per second, and "Runtime (RDTSC) [s]", which indicates the total runtime. By multiplying the two we get the desired total number of FLOPs.

flops_per_second = first(metrics["FLOPS_DP"])["DP [MFLOP/s]"] * 1e6
runtime = first(metrics["FLOPS_DP"])["Runtime (RDTSC) [s]"]
NFLOPs_actual = round(Int, flops_per_second * runtime)

20000

Let's check whether this number makes sense. Our vectors are of length N and for each element we perform two FLOPs in the daxpy operation: one multiplication and one addition. Hence, our expectation is

NFLOPs_expected(N) = 2 * N
NFLOPs_expected(N)

20000

Note that this perfectly matches our measurement result above!

NFLOPs_actual == NFLOPs_expected(N)

true

To rule out that this is just a big coincidence, let's try to modify N and check again. For convenience, let's wrap the above procedure into a function.

function count_FLOPs(N)
    a = 3.141
    x = rand(N)
    y = rand(N)
    z = zeros(N)
    metrics, _ = perfmon(() -> daxpy!(z, a, x, y), "FLOPS_DP"; print=false)
    flops_per_second = first(metrics["FLOPS_DP"])["DP [MFLOP/s]"] * 1e6
    runtime = first(metrics["FLOPS_DP"])["Runtime (RDTSC) [s]"]
    return round(Int, flops_per_second * runtime)
end

count_FLOPs (generic function with 1 method)

See how it still matches our expectation when varying the input!

count_FLOPs(2 * N) == NFLOPs_expected(2 * N)

true

Feel free to play around further and apply this knowledge to other operations! As an inspiration: How many FLOPs does an exp.(x) or sin.(x) trigger? Does the answer depend on the length of x?

Bonus: Reactive FLOPs Counting

It is a lot of fun to combine the low-level performance monitoring tools of LIKWID.jl with the beautiful high-level interface provided by Pluto.jl. In the following example, we can arbitrarily modify the function computation and - through Pluto's reactivity - the counted number of FLOPs will automatically update.

This page was generated using Literate.jl.