memory-required.md

CurrentModule = BLASBenchmarksCPU

Memory Required for Large Matrices

This table shows how much memory is required for four matrices of the given size and type. (We need four matrices: A, B, C1, and C2.)

Matrix Size	Float64 Memory	Float32 Memory	Int64 Memory	Int32 Memory
1k by 1k	0.03 GiB	0.01 GiB	0.03 GiB	0.01 GiB
2k by 2k	0.12 GiB	0.06 GiB	0.12 GiB	0.06 GiB
3k by 3k	0.27 GiB	0.13 GiB	0.27 GiB	0.13 GiB
4k by 4k	0.48 GiB	0.24 GiB	0.48 GiB	0.24 GiB
5k by 5k	0.75 GiB	0.37 GiB	0.75 GiB	0.37 GiB
6k by 6k	1.07 GiB	0.54 GiB	1.07 GiB	0.54 GiB
7k by 7k	1.46 GiB	0.73 GiB	1.46 GiB	0.73 GiB
8k by 8k	1.91 GiB	0.95 GiB	1.91 GiB	0.95 GiB
9k by 9k	2.41 GiB	1.21 GiB	2.41 GiB	1.21 GiB
10k by 10k	2.98 GiB	1.49 GiB	2.98 GiB	1.49 GiB
11k by 11k	3.61 GiB	1.8 GiB	3.61 GiB	1.8 GiB
12k by 12k	4.29 GiB	2.15 GiB	4.29 GiB	2.15 GiB
13k by 13k	5.04 GiB	2.52 GiB	5.04 GiB	2.52 GiB
14k by 14k	5.84 GiB	2.92 GiB	5.84 GiB	2.92 GiB
15k by 15k	6.71 GiB	3.35 GiB	6.71 GiB	3.35 GiB
16k by 16k	7.63 GiB	3.81 GiB	7.63 GiB	3.81 GiB
17k by 17k	8.61 GiB	4.31 GiB	8.61 GiB	4.31 GiB
18k by 18k	9.66 GiB	4.83 GiB	9.66 GiB	4.83 GiB
19k by 19k	10.76 GiB	5.38 GiB	10.76 GiB	5.38 GiB
20k by 20k	11.92 GiB	5.96 GiB	11.92 GiB	5.96 GiB
30k by 30k	26.82 GiB	13.41 GiB	26.82 GiB	13.41 GiB
40k by 40k	47.68 GiB	23.84 GiB	47.68 GiB	23.84 GiB
50k by 50k	74.51 GiB	37.25 GiB	74.51 GiB	37.25 GiB
60k by 60k	107.29 GiB	53.64 GiB	107.29 GiB	53.64 GiB
70k by 70k	146.03 GiB	73.02 GiB	146.03 GiB	73.02 GiB
80k by 80k	190.73 GiB	95.37 GiB	190.73 GiB	95.37 GiB
90k by 90k	241.4 GiB	120.7 GiB	241.4 GiB	120.7 GiB
100k by 100k	298.02 GiB	149.01 GiB	298.02 GiB	149.01 GiB

Generating These Tables

mem_req(s, ::Type{T}) where {T} = 4s^2*sizeof(T) / (1 << 30)

function print_table(types::Vector{DataType}, Ns = nothing)
    println("| Matrix Size | $(join(types, " Memory | ")) Memory |")
    println("| ----------- | $(repeat(" ------ |", length(types)))")
    if Ns isa Nothing
        _Ns = sort(unique(vcat(collect(1:1:20), collect(20:10:100))))
    else
        _Ns = Ns
    end
    for N in _Ns
        mem = mem_req.(N * 1_000, types)
        m = round.(mem; digits = 2)
        println("| $(N)k by $(N)k | $(join(m, " GiB | ")) GiB |")
    end
    return nothing
end

julia> print_table([Float64, Float32, Int64, Int32])