About those eight seconds

Sunday, August 04, 2013

In my previous post, I mentioned a program that took a year to run twenty-some years ago on a then state-of-the-art workstation could now be done in 17 minutes on a two year old laptop.

What I didn't mention is that the program twenty-some years ago was written in C and the program I ran today was written in Lua.

Yes, computers are so fast these days that a scripting language can out-perform computers from two decades ago.

“Okay,” you say. “But I won't want to wait 17 minutes for my data.”

Okay, fine. I see two options, and let's try the first option and one that most people would do—drop down to C. And yes, that does give us an improvement, an impressive improvement—only 2.5 seconds per frame, and across four cores that means you'll have the results in a little over five minutes. Not that bad.

The other option, and hear me out—is to take our Lua code and run it via LuaJIT, a (pretty much) drop in replacement for Lua that compiles down to native code. Even if it's a bit slower than C, it should still be faster than Lua with no code changes.

So how does LuaJIT fare?

Personally, I was expecting the C version (which I actually wrote first) to be faster, if only buy a little bit, but …

So, here's the C version (which generates a single image):

[spc]saltmine:~/source/play>time ./a.out >/dev/null

real    0m2.483s
user    0m2.470s
sys     0m0.000s

And now the LuaJIT version:

[spc]saltmine:~/source/play>time luajit amap.lua >/dev/null

real    0m0.849s
user    0m0.840s
sys     0m0.000s

[Yeah, that's what I did when I saw these results]

And no, that's not a mistake (belive me, I checked and rechecked)—here:

[spc]saltmine:~/source/play>time lua amap.lua >/dev/null

real    0m8.091s
user    0m8.060s
sys     0m0.000s
[spc]saltmine:~/source/play>time luajit amap.lua >/dev/null

real    0m0.856s
user    0m0.850s
sys     0m0.000s

So … um … I can have that data to you in two minutes? Is that fast enough?

On reflection, it makes sense that LuaJIT will outperform C in this case. It's heavily CPU bound and the fact that the main function:

function mainloop(A,B,C,D)
  local pix = {}
  local xn  = 0.5
  local yn  = 0.5
  
  for count = 1 , MAX do
    local xn1 = ((A * yn) + B) * xn * (1.0 - xn)
    local yn1 = ((C * xn) + D) * yn * (1.0 - yn)
    
    xn = xn1
    yn = yn1
    
    if xn <  0 then return MAX-1 end
    if xn >= 1 then return MAX-1 end
    if yn <  0 then return MAX-1 end
    if yn >= 1 then return MAX-1 end
    
    local ix = math.floor(xn * DIM)
    local iy = math.floor(yn * DIM)
    local f  = iy * DIM + ix -- Lua doesn't really do N-dimensional arrays
    
    if pix[f] then return count-1 end
    pix[f] = true
  end
end

can be recompiled per call to take advantage of the paramters. For instance, when A and B are both 0, the first expression then becomes:

local xn1 = xn * (1.0 - xn)

and given that I'm doing 32,768 interations of this (oh, did I fail to mention that? Yes, I'm doing 27,768 more interations than the code did twenty-some years ago) this does save quite a bit of time.

Update on August 5^th, 2013

Oops, I made a slight mistake …

Update on Tuesday, August 6^th, 2013

Mistakes were made alright.

The Boston Diaries

Sunday, August 04, 2013