Most of the preparation here is involved in convolving the environment map. The following pseudocode outlines this process:

nSamples = 1000
foreach texel t in output map
  n = direction towards t
  rad = 0
  for i = 1 to nSamples
     li = uniform random direction in the 
          hemisphere around n in world coords
     L = read from environment map at li
     nDotL = dot( n, li )
     rad += L * nDotL
  set texel t to (2 / nSamples) * rad