Created
February 24, 2014 16:41
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「なんで末尾呼び出しだと使うメモリの量が減るのか可視化してみた」by @naohaq さん
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-- http://na.yuki.st/src/tailcall.txt より。 | |
-- 末尾呼出でない定義 | |
fact 0 = 1 | |
fact n = n * fact (n - 1) | |
-- 末尾呼出な定義 | |
fact' a 0 = a | |
fact' a n = fact' (a * n) (n - 1) | |
-- ******************************************-- | |
-- 末尾呼出でない定義 | |
fact 0 = 1 | |
fact n = n * fact (n - 1) | |
-- 計算してみる | |
fact 20 = 20 * fact (20 - 1) | |
= 20 * fact 19 | |
= 20 * (19 * fact (19 - 1)) | |
= 20 * (19 * fact 18) | |
= 20 * (19 * (18 * fact (18 -1))) | |
= 20 * (19 * (18 * fact 17)) | |
= 20 * (19 * (18 * (17 * fact (17 - 1)))) | |
= 20 * (19 * (18 * (17 * fact 16))) | |
= 20 * (19 * (18 * (17 * (16 * fact 15)))) | |
= 20 * (19 * (18 * (17 * (16 * (15 * fact 14))))) | |
= 20 * (19 * (18 * (17 * (16 * (15 * (14 * fact 13)))))) | |
= 20 * (19 * (18 * (17 * (16 * (15 * (14 * (13 * fact 12))))))) | |
= 20 * (19 * (18 * (17 * (16 * (15 * (14 * (13 * (12 * fact 11)))))))) | |
= 20 * (19 * (18 * (17 * (16 * (15 * (14 * (13 * (12 * (11 * fact 10))))))))) | |
= 20 * (19 * (18 * (17 * (16 * (15 * (14 * (13 * (12 * (11 * (10 * fact 9)))))))))) | |
= 20 * (19 * (18 * (17 * (16 * (15 * (14 * (13 * (12 * (11 * (10 * (9 * fact 8))))))))))) | |
= 20 * (19 * (18 * (17 * (16 * (15 * (14 * (13 * (12 * (11 * (10 * (9 * (8 * fact 7)))))))))))) | |
= 20 * (19 * (18 * (17 * (16 * (15 * (14 * (13 * (12 * (11 * (10 * (9 * (8 * (7 * fact 6))))))))))))) | |
= 20 * (19 * (18 * (17 * (16 * (15 * (14 * (13 * (12 * (11 * (10 * (9 * (8 * (7 * (6 * fact 5)))))))))))))) | |
= 20 * (19 * (18 * (17 * (16 * (15 * (14 * (13 * (12 * (11 * (10 * (9 * (8 * (7 * (6 * (5 * fact 4))))))))))))))) | |
= 20 * (19 * (18 * (17 * (16 * (15 * (14 * (13 * (12 * (11 * (10 * (9 * (8 * (7 * (6 * (5 * (4 * fact 3)))))))))))))))) | |
= 20 * (19 * (18 * (17 * (16 * (15 * (14 * (13 * (12 * (11 * (10 * (9 * (8 * (7 * (6 * (5 * (4 * (3 * fact 2))))))))))))))))) | |
= 20 * (19 * (18 * (17 * (16 * (15 * (14 * (13 * (12 * (11 * (10 * (9 * (8 * (7 * (6 * (5 * (4 * (3 * (2 * fact 1)))))))))))))))))) | |
= 20 * (19 * (18 * (17 * (16 * (15 * (14 * (13 * (12 * (11 * (10 * (9 * (8 * (7 * (6 * (5 * (4 * (3 * (2 * (1 * fact 0))))))))))))))))))) | |
= 20 * (19 * (18 * (17 * (16 * (15 * (14 * (13 * (12 * (11 * (10 * (9 * (8 * (7 * (6 * (5 * (4 * (3 * (2 * (1 * 1))))))))))))))))))) | |
= 20 * (19 * (18 * (17 * (16 * (15 * (14 * (13 * (12 * (11 * (10 * (9 * (8 * (7 * (6 * (5 * (4 * (3 * (2 * 1)))))))))))))))))) | |
= 20 * (19 * (18 * (17 * (16 * (15 * (14 * (13 * (12 * (11 * (10 * (9 * (8 * (7 * (6 * (5 * (4 * (3 * 2))))))))))))))))) | |
= 20 * (19 * (18 * (17 * (16 * (15 * (14 * (13 * (12 * (11 * (10 * (9 * (8 * (7 * (6 * (5 * (4 * 6)))))))))))))))) | |
= 20 * (19 * (18 * (17 * (16 * (15 * (14 * (13 * (12 * (11 * (10 * (9 * (8 * (7 * (6 * (5 * 24))))))))))))))) | |
= 20 * (19 * (18 * (17 * (16 * (15 * (14 * (13 * (12 * (11 * (10 * (9 * (8 * (7 * (6 * 120)))))))))))))) | |
= 20 * (19 * (18 * (17 * (16 * (15 * (14 * (13 * (12 * (11 * (10 * (9 * (8 * (7 * 720))))))))))))) | |
= 20 * (19 * (18 * (17 * (16 * (15 * (14 * (13 * (12 * (11 * (10 * (9 * (8 * 5040)))))))))))) | |
= 20 * (19 * (18 * (17 * (16 * (15 * (14 * (13 * (12 * (11 * (10 * (9 * 40320))))))))))) | |
= 20 * (19 * (18 * (17 * (16 * (15 * (14 * (13 * (12 * (11 * (10 * 362880)))))))))) | |
= 20 * (19 * (18 * (17 * (16 * (15 * (14 * (13 * (12 * (11 * 3628800))))))))) | |
= 20 * (19 * (18 * (17 * (16 * (15 * (14 * (13 * (12 * 39916800)))))))) | |
= 20 * (19 * (18 * (17 * (16 * (15 * (14 * 6227020800)))))) | |
= 20 * (19 * (18 * (17 * (16 * (15 * 87178291200))))) | |
= 20 * (19 * (18 * (17 * (16 * 1307674368000)))) | |
= 20 * (19 * (18 * (17 * 20922789888000))) | |
= 20 * (19 * (18 * 355687428096000)) | |
= 20 * (19 * 6402373705728000) | |
= 20 * 121645100408832000 | |
= 2432902008176640000 | |
-- ******************* -- | |
-- 末尾呼出な定義 | |
fact' a 0 = a | |
fact' a n = fact' (a * n) (n - 1) | |
fact' 1 20 = fact' (1 * 20) (20 - 1) | |
= fact' 20 19 | |
= fact' (20 * 19) (19 - 1) | |
= fact' 380 18 | |
= fact' (380 * 18) (18 - 1) | |
= fact' 6840 17 | |
= fact' (6840 * 17) (17 - 1) | |
= fact' 116280 16 | |
= fact' (116280 * 16) (16 - 1) | |
= fact' 1860480 15 | |
= fact' (1860480 * 15) (15 - 1) | |
= fact' 27907200 14 | |
= fact' (27907200 * 14) (14 - 1) | |
= fact' 390700800 13 | |
= fact' (390700800 * 13) (13 - 1) | |
= fact' 5079110400 12 | |
= fact' (5079110400 * 12) (12 - 1) | |
= fact' 60949324800 11 | |
= fact' (60949324800 * 11) (11 - 1) | |
= fact' 670442572800 10 | |
= fact' (670442572800 * 10) (10 - 1) | |
= fact' 6704425728000 9 | |
= fact' (6704425728000 * 9) (9 - 1) | |
= fact' 60339831552000 8 | |
= fact' (60339831552000 * 8) (8 - 1) | |
= fact' 482718652416000 7 | |
= fact' (482718652416000 * 7) (7 - 1) | |
= fact' 3379030566912000 6 | |
= fact' (3379030566912000 * 6) (6 - 1) | |
= fact' 20274183401472000 5 | |
= fact' (20274183401472000 * 5) (5 - 1) | |
= fact' 101370917007360000 4 | |
= fact' (101370917007360000 * 4) (4 - 1) | |
= fact' 405483668029440000 3 | |
= fact' (405483668029440000 * 3) (3 - 1) | |
= fact' 1216451004088320000 2 | |
= fact' (1216451004088320000 * 2) (2 - 1) | |
= fact' 2432902008176640000 1 | |
= fact' (2432902008176640000 * 1) (1 - 1) | |
= fact' 2432902008176640000 0 | |
= 2432902008176640000 |
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末尾再帰→ある種の再帰呼び出しのことを指す
末尾再帰最適化→末尾再帰でコールスタックを積まないという最適化のことを指す