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A "Node" is 4 ints (128 bits).
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"Memory" is an array of nodes. Example:
| NODE 0 | NODE 1 | NODE 2 | ... | Int | Int | Int | Int | Int | Int | Int | Int | Int | Int | Int | Int | ...
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The input is an initial Memory encoding a λ-term.
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You call a
rewrite
function on arbitrary positions of Memory until it doesn't change anymore. -
The output, i.e., the final Memory state, encodes the normal form of the λ-term.
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The function
void rewrite(int *a, int *b, int *c)
takes 3 sequential nodes and rewrites them locally. -
Rewrites can be done in parallel. For example:
// The 4 calls below could be made in parallel. // (pointers omitted, should be `Memory + 0 * node_size`, etc) rewrite(0, 1, 2), rewrite(3, 4, 5), rewrite(6, 7, 8), rewrite(9, 10,11);
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You can call
rewrite
in whatever order you want. -
Don't isolate communication: you need to alternate the alignments of the rewrites!
CORRECT (parallel, alternating alignments): rewrite(0, 1, 2), rewrite(3, 4, 5), rewrite(6, 7, 8), rewrite( 9, 10, 11), ... rewrite(1, 2, 3), rewrite(4, 5, 6), rewrite(7, 8, 9), rewrite(10, 11, 10), ... rewrite(2, 3, 4), rewrite(5, 6, 7), rewrite(8, 9, 10), rewrite(11, 10, 12), ... rewrite(0, 1, 2), rewrite(3, 4, 5), rewrite(6, 7, 8), rewrite( 9, 10, 11), ... rewrite(1, 2, 3), rewrite(4, 5, 6), rewrite(7, 8, 9), rewrite(10, 11, 10), ... rewrite(2, 3, 4), rewrite(5, 6, 7), rewrite(8, 9, 10), rewrite(11, 10, 12), ... rewrite(0, 1, 2), rewrite(3, 4, 5), rewrite(6, 7, 8), rewrite( 9, 10, 11), ... rewrite(1, 2, 3), rewrite(4, 5, 6), rewrite(7, 8, 9), rewrite(10, 11, 10), ... rewrite(2, 3, 4), rewrite(5, 6, 7), rewrite(8, 9, 10), rewrite(11, 10, 12), ... ... CORRECT (sequential, random positions): rewrite(0, 1, 2); rewrite(3, 4, 5); rewrite(0, 1, 2); rewrite(7, 8, 9); rewrite(4, 5, 6); ... WRONG (parallel, non-alternating alignments, communication inhibited!): rewrite(0, 1, 2), rewrite(3, 4, 5), rewrite(6, 7, 8), rewrite( 9, 10, 11), ... rewrite(0, 1, 2), rewrite(3, 4, 5), rewrite(6, 7, 8), rewrite( 9, 10, 11), ... rewrite(0, 1, 2), rewrite(3, 4, 5), rewrite(6, 7, 8), rewrite( 9, 10, 11), ... rewrite(0, 1, 2), rewrite(3, 4, 5), rewrite(6, 7, 8), rewrite( 9, 10, 11), ... rewrite(0, 1, 2), rewrite(3, 4, 5), rewrite(6, 7, 8), rewrite( 9, 10, 11), ... ...
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Example computation:
INPUT: ((λ f x . f (f x)) (λ f x . f (f x)) (λ x . x)) (Memory ordered top-bottom, then left-right, i.e, (0,0) (0,1) (0,2) (0,3) (1,0) (1,1) (1,2)..) 03> |03> |03> |04> |03> |03> |03> |03> |05> |03> |03> |03> |03> | | | | | | | | | | | | | | | 02> |04> |04< |06< |08< |07< |09< |05< |0d< |0f< |0e< |10< |03< | | | | | | | | | | | | | | | 03> |05> |06> |08> |0a> |0a< |0b< |0d> |0f> |11> |11< |12< |14> | | | | | | | | | | | | | | | 01<__|02<__|07>__|09>__|0b>__|0c>__|0c<__|0e>__|10>__|12>__|13>__|13<__|14<__|__|__|__|__|__|__|__|__|__|__|__|__|__|__| COMPUTATION 03> |03> |03> |04> |03> |03> |03> |03> |05> |03> |03> |03> |03> | | | | | | | | | | | | | | | 02> |04> |04< |06< |08< |07< |09< |05< |0d< |0f< |0e< |10< |03< | | | | | | | | | | | | | | | 03> |05> |06> |08> |0a> |0a< |0b< |0d> |0f> |11> |11< |12< |14> | | | | | | | | | | | | | | | 01<__|02<__|07>__|09>__|0b>__|0c>__|0c<__|0e>__|10>__|12>__|13>__|13<__|14<__|__|__|__|__|__|__|__|__|__|__|__|__|__|__| 03> |03> |03> |04> |03> |03> |03> |03> |05> |03> |03> |03> |03> | | | | | | | | | | | | | | | 02> |04> |04< |06< |08< |07< |09< |05< |0d< |0f< |0e< |10< |03< | | | | | | | | | | | | | | | 03> |05> |06> |08> |0a> |0a< |0b< |0d> |0f> |11> |11< |12< |14> | | | | | | | | | | | | | | | 01<__|02<__|07>__|09>__|0b>__|0c>__|0c<__|0e>__|10>__|12>__|13>__|13<__|14<__|__|__|__|__|__|__|__|__|__|__|__|__|__|__| 03> |%%| |%%| |04> |03> |03> |03> |03> |05> |03> |03> |03> |03> | | | | | | | | | | | | | | | 02> |06> |07> |06< |08< |07< |09< |05< |0d< |0f< |0e< |10< |03< | | | | | | | | | | | | | | | 03> |05> |02< |08> |0a> |0a< |0b< |0d> |0f> |11> |11< |12< |14> | | | | | | | | | | | | | | | 01<__|__|__|__|__|09>__|0b>__|0c>__|0c<__|0e>__|10>__|12>__|13>__|13<__|14<__|__|__|__|__|__|__|__|__|__|__|__|__|__|__| 03> |%%| |%%| |04> |03> |03> |03> |03> |05> |03> |03> |03> |03> | | | | | | | | | | | | | | | 02> |06> |07> |06< |08< |07< |09< |05< |0d< |0f< |0e< |10< |03< | | | | | | | | | | | | | | | 03> |05> |02< |08> |0a> |0a< |0b< |0d> |0f> |11> |11< |12< |14> | | | | | | | | | | | | | | | 01<__|__|__|__|__|09>__|0b>__|0c>__|0c<__|0e>__|10>__|12>__|13>__|13<__|14<__|__|__|__|__|__|__|__|__|__|__|__|__|__|__| 03> |%%| |04> |%%| |03> |03> |03> |03> |05> |03> |03> |03> |03> | | | | | | | | | | | | | | | 02> |06> |06< |07> |08< |07< |09< |05< |0d< |0f< |0e< |10< |03< | | | | | | | | | | | | | | | 03> |05> |08> |02< |0a> |0a< |0b< |0d> |0f> |11> |11< |12< |14> | | | | | | | | | | | | | | | 01<__|__|__|09>__|__|__|0b>__|0c>__|0c<__|0e>__|10>__|12>__|13>__|13<__|14<__|__|__|__|__|__|__|__|__|__|__|__|__|__|__| 03> |04> | | |%%| |03> |03> |03> |03> |05> |03> |03> |03> |03> | | | | | | | | | | | | | | | 02> |05> | | |07> |08< |07< |09< |05< |0d< |0f< |0e< |10< |03< | | | | | | | | | | | | | | | 03> |08> | | |02< |0a> |0a< |0b< |0d> |0f> |11> |11< |12< |14> | | | | | | | | | | | | | | | 01<__|09>__|__|__|__|__|0b>__|0c>__|0c<__|0e>__|10>__|12>__|13>__|13<__|14<__|__|__|__|__|__|__|__|__|__|__|__|__|__|__| 03> |04> | | 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Is this efficient?
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If not, can this become something efficient?
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Perhaps improving movement rules?
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I'm a CUDA noob. How can I make the best use of the GPU?