# mandelbrot Julia #6 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
=#

const masks = (0b01111111, 0b10111111, 0b11011111, 0b11101111, 0b11110111,
0b11111011, 0b11111101, 0b11111110)

# Calculate the byte to print for a given vector of 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)
r = cr
t = i = ntuple(_-> ci, 8)

# 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
r, i, t = calc_sum(r, i, cr, ci)
end
all(>(4.0), t) && return 0x00
end
else
for _=1:50
r, i, t = calc_sum(r, i, cr, ci)
end
end

byte = 0xff
for i=1:8
t[i] <= 4.0 || (byte &= masks[i])
end
byte
end

# Single iteration of mandelbrot calculation for vector r of real
# components and vector i or imaginary components.
@inline function calc_sum(r, i, cr, ci)
r2 = r .* r
i2 = i .* i
ri = r .* i

t = r2 .+ i2
r = r2 .- i2 .+ cr
i = ri .+ ri .+ ci
r, i, t
end

# Write n by n portable bitmap image of mandelbrot set to io
function mandelbrot(io, n)
inv_ = 2.0 / n
xvals = Float64[i * inv_ - 1.5 for i=0:n-1]
yvals = Float64[i * inv_ - 1.0 for i=0:n-1]

rows = Vector{UInt8}(undef, n * n ÷ 8)
ci = @inbounds yvals[y]
start = (y - 1) * n ÷ 8
# The first iteration within a row will generally return 0x00
prune = true
@inbounds for x=1:8:n
cr = ntuple(i-> xvals[x+i-1], 8)
res = mand8(cr, ci, prune)

rows[start + x÷8 + 1] = res
prune = res == 0x00
end
end

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

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

## notes, command-line, and program output

```NOTES:
julia version build 19.0.1+10-21

Wed, 25 Jan 2023 02:37:15 GMT

MAKE: