Re: Ideas for faster math in lua

[David Manura <dm.lua@...>]

Niklas Frykholm writes:
> I would like to be able to process lots of small mathematical objects 
> (vector3 and quaternions) in a resource constrained environment 
> (computer game), without having to pay the cost of new-ing and garbage 
> collecting them. ... So here are some ideas...

If you're willing to sacrifice the first-classness of these objects, some macro
processing can translate them into local variables on the stack[1].

local lua = [[
  -- typical implementation (without filtering)
  local function cross_vector2(u, v, result)
    local u1, u2, u3 = u[1], u[2], u[3]
    local v1, v2, v3 = v[1], v[2], v[3]
    result[1], result[2], result[3] = u2*v3-u3*v2, u3*v1-u1*v3, u1*v2-u2*v1
    return result
  end

  -- test and benchmark
  local function benchmark(func)
    local t1 = os.clock()
    func()
    local t2 = os.clock()
    print("time:", t2-t1)
  end
  benchmark(function()
    local vector u = 1, 0, 0
    local vector v = 0, 1, 0
    for n = 1,5000000 do
      cross_vector(u,v,u)
      --print("DEBUG: u=" .. stringify_vector(u))
    end
  end)
  benchmark(function()
    local u = {1, 0, 0}
    local v = {0, 1, 0}
    for n = 1,5000000 do
      cross_vector2(u,v,u)
      -- print("DEBUG: u=" .. table.concat(u, ', '))
    end
  end)
]]

-- source filtering implementation
lua = string.gsub(lua, 
  "local%s+vector%s+(%w+)%s*=%s*(%w+)%s*,%s*(%w+)%s*,%s*(%w+)",
  "local %1_1, %1_2, %1_3 = %2, %3, %4")
lua = string.gsub(lua,
  "cross_vector%s*%(%s*(%w+)%s*,%s*(%w+)%s*,%s*(%w+)%s*%)",
  "%3_1, %3_2, %3_3 = " ..
  "%1_2*%2_3-%1_3*%2_2, %1_3*%2_1-%1_1*%2_3, %1_1*%2_2-%1_2*%2_1")
lua = string.gsub(lua,
  "stringify_vector%((%w+)%)", "(%1_1 .. ',' .. %1_2 .. ',' .. %1_3)")

-- source filter
print("DEBUG[\n" .. lua .. "]")
assert(loadstring(lua))()

Results on one system with Lua 5.1:

  time: 0.937 
  time: 4.078 

or with LuaJIT 1.1:

  time: 0.141
  time: 0.593

[1] http://lua-users.org/wiki/SourcePreprocessing