The Computer Language
22.05 Benchmarks Game

mandelbrot Julia #8 program

source code

#=
The Computer Language Benchmarks Game
 https://salsa.debian.org/benchmarksgame-team/benchmarksgame/

 direct transliteration of the swift#3 program by Ralph Ganszky and Daniel Muellenborn

 modified for Julia 1.0 by Simon Danisch
 tweaked for performance by maltezfaria and Adam Beckmeyer
=#

using Base.Cartesian

# Calculate the byte to print for a given vector of 8 real numbers cr
# and a given imaginary component ci. This function should give the
# same result whether prune is true or false but may be faster or
# slower depending on the input.
function mand8(cr, ci, prune)
    zr = zi = tr = ti = @ntuple 8 _-> 0.0

    # In cases where the last call to mand8 resulted in 0x00, the next
    # call is much more likely to result in 0x00, so it's worth it to
    # check several times if the calculation can be aborted
    # early. Otherwise, the relatively costly check can be eliminated.
    if prune
        for _=1:10
            for _=1:5
                zr, zi, tr, ti = calc_sum(cr, ci, zr, zi , tr, ti)
            end
            # If all values are already > 4.0, we already know no
            # values will be <= 4.0 at end of iterations.
            test = true
            for k=1:8
                test &= @inbounds tr[k] + ti[k] > 4.0
            end
            test && return 0x00
        end
    else
        for _=1:50
            zr, zi, tr, ti = calc_sum(cr, ci, zr, zi , tr, ti)
        end
    end

    # For each value <= 4.0, the k-th bit (counting from left) is set to 1
    byte = 0x00
    for k=1:8
        byte |= @inbounds UInt8(tr[k] + ti[k] <= 4.0) << (8 - k)
    end
    return byte 
end

# Single iteration of mandelbrot calculation for vector r of real
# components and vector i or imaginary components.
@inline function calc_sum(cr, ci, zr, zi, tr, ti)
    # Broadcasting here results in less efficient codegen than using @ntuple
    zi = @ntuple 8 k-> muladd(zr[k] + zr[k], zi[k], ci)
    zr = @ntuple 8 k-> tr[k] - ti[k] + cr[k]
    tr = @ntuple 8 k-> zr[k] * zr[k]
    ti = @ntuple 8 k-> zi[k] * zi[k]
    return zr, zi, tr, ti
end

# Write n by n portable bitmap image of mandelbrot set to io
function mandelbrot(io, n)
    n % 8 == 0 || error("n must be multiple of 8")

    # Precalculate real coordinates to check
    xvals = Float64[2i/n - 1.5 for i=0:n-1]
    # Precalculate imaginary coordinates to check
    yvals = Float64[2i/n - 1.0 for i=0:n-1]

    # Create a vector of bytes to output
    out = Vector{UInt8}(undef, n * n ÷ 8)
    # For each row (each imaginary coordinate), spawn a thread to fill
    # out values. At small values of n, this is too fine-grained of
    # parallelism to really be efficient, but it works well for large n.
    @sync for y=1:n
        # Threads.@spawn allows dynamic scheduling instead of static scheduling
        # of Threads.@threads macro.
        # See <https://github.com/JuliaLang/julia/issues/21017>.
        Threads.@spawn @inbounds begin
            ci = yvals[y]
            startofrow = (y - 1) * n ÷ 8
            # The first iteration within a row will generally return 0x00
            prune = true
            for x=1:8:n
                # Calculate whether the (x:x+7)-th real coordinates with
                # the y-th imaginary coordinate belong to the
                # mandelbrot set.
                byte = mand8(@ntuple(8, k-> xvals[x+k-1]), ci, prune)
                out[startofrow +8 + 1] = byte
                prune = byte == 0x00
            end
        end
    end

    write(io, "P4\n$n $n\n")
    write(io, out)
end

isinteractive() || mandelbrot(stdout, parse(Int, ARGS[1]))
    

notes, command-line, and program output

NOTES:
64-bit Ubuntu quad core
julia version 1.7.2


Wed, 04 May 2022 21:43:08 GMT

MAKE:
printenv JULIA_NUM_THREADS
4

0.07s to complete and log all make actions

COMMAND LINE:
/opt/src/julia-1.7.2/bin/julia -O3 --cpu-target=ivybridge --math-mode=ieee  -- mandelbrot.julia-8.julia 16000

(BINARY) PROGRAM OUTPUT NOT SHOWN