Okay, I rewrote my Lisp version without any weirdness (like #. or
optimize or type declarations), and got the following:
(let* ((n 1000)
(mat (make-array (* n n) :element-type 'double-float)))
(defun naive ()
(macrolet ((mat (n)
`(aref mat ,n)))
(dotimes (i (* n n))
(setf (mat i) 1.0d0))
(dotimes (i 10)
(loop
for pos1 from 1 below (1- n)
do (loop
for pos2 from (+ pos1 n) below (+ pos1 (* n (1- n))) by n
do (setf (mat pos2)
(* 0.11111111111111d0
(+ (mat (- pos2 1001)) (mat (1- pos2)) (mat (+ pos2 999))
(mat (- pos2 1000)) (mat pos2) (mat (+ pos2 1000))
(mat (- pos2 999)) (mat (1+ pos2)) (mat (+ pos2
1001))))))))
(princ (mat (1+ n))))))
I went through and added a minimum of type declarations, making them
as accurate as possible[*]. Unfortunately, Python wasn't able to
figure out the type of N or MAT on its own. Adding in the OPTIMIZE
declarations, I have the following code:
(let* ((n 1000)
(mat (make-array (* n n) :element-type 'double-float)))
(declare (type (eql 1000) n)
(type (simple-array double-float (1000000)) mat)
(optimize (speed 3) (safety 0) (debug 0) (space 0) (compilation-speed 0)))
(defun fast ()
(macrolet ((mat (n)
`(aref mat ,n)))
(dotimes (i (* n n))
(setf (mat i) 1.0d0))
(dotimes (i 10)
(loop
for pos1 of-type (integer 1 1000) from 1 below (1- n)
do (loop
for pos2 of-type (integer 1000 1000000)
from (+ pos1 n) below (+ pos1 (* n (1- n))) by n
do (setf (mat pos2)
(* 0.11111111111111d0
(+ (mat (- pos2 1001)) (mat (1- pos2)) (mat (+ pos2 999))
(mat (- pos2 1000)) (mat pos2) (mat (+ pos2 1000))
(mat (- pos2 999)) (mat (1+ pos2)) (mat (+ pos2
1001))))))))
(princ (mat (1+ n))))))
I'm quite happy with it. It's readible, not littered with type
information, and runs 1.08x the speed of GCC's code (1.1 for Sun's C
compiler). Note that it does the exact same computations as the C
version. There are still some things in the disassembly that are
suboptimal, but in all it's as good as the C.
[*] Thanks to Gerd for pointing out in his code that MAT is a
SIMPLE-ARRAY. Duh. For some reason I didn't notice that was missing.
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