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--- This file implements the mid-square hashing function in Juvix. See: | ||
--- https://research.cs.vt.edu/AVresearch/hashing/midsquare.php | ||
--- | ||
--- The implementation is for hashing natural numbers with maximum 16 bits into 6 | ||
--- bits. In order to facilitate the translation to the current version of the | ||
--- GEB backend, no recursion is used (it is manually unrolled). | ||
--- | ||
module MidSquareHash; | ||
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open import Stdlib.Prelude; | ||
open import Stdlib.Data.Nat.Ord; | ||
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--- `powN` is 2 ^ N | ||
pow0 : Nat := 1; | ||
pow1 : Nat := 2 * pow0; | ||
pow2 : Nat := 2 * pow1; | ||
pow3 : Nat := 2 * pow2; | ||
pow4 : Nat := 2 * pow3; | ||
pow5 : Nat := 2 * pow4; | ||
pow6 : Nat := 2 * pow5; | ||
pow7 : Nat := 2 * pow6; | ||
pow8 : Nat := 2 * pow7; | ||
pow9 : Nat := 2 * pow8; | ||
pow10 : Nat := 2 * pow9; | ||
pow11 : Nat := 2 * pow10; | ||
pow12 : Nat := 2 * pow11; | ||
pow13 : Nat := 2 * pow12; | ||
pow14 : Nat := 2 * pow13; | ||
pow15 : Nat := 2 * pow14; | ||
pow16 : Nat := 2 * pow15; | ||
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--- `hashN` hashes a number with max N bits (i.e. smaller than 2^N) into 6 bits | ||
--- (i.e. smaller than 64) using the mid-square algorithm. | ||
hash0 : Nat -> Nat; | ||
hash0 x := 0; | ||
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hash1 : Nat -> Nat; | ||
hash1 x := x * x; | ||
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hash2 : Nat -> Nat; | ||
hash2 x := x * x; | ||
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hash3 : Nat -> Nat; | ||
hash3 x := x * x; | ||
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hash4 : Nat -> Nat; | ||
hash4 x := if (x < pow3) (hash3 x) (mod (div (x * x) pow1) pow6); | ||
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hash5 : Nat -> Nat; | ||
hash5 x := if (x < pow4) (hash4 x) (mod (div (x * x) pow2) pow6); | ||
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hash6 : Nat -> Nat; | ||
hash6 x := if (x < pow5) (hash5 x) (mod (div (x * x) pow3) pow6); | ||
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hash7 : Nat -> Nat; | ||
hash7 x := if (x < pow6) (hash6 x) (mod (div (x * x) pow4) pow6); | ||
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hash8 : Nat -> Nat; | ||
hash8 x := if (x < pow7) (hash7 x) (mod (div (x * x) pow5) pow6); | ||
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hash9 : Nat -> Nat; | ||
hash9 x := if (x < pow8) (hash8 x) (mod (div (x * x) pow6) pow6); | ||
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hash10 : Nat -> Nat; | ||
hash10 x := if (x < pow9) (hash9 x) (mod (div (x * x) pow7) pow6); | ||
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hash11 : Nat -> Nat; | ||
hash11 x := if (x < pow10) (hash10 x) (mod (div (x * x) pow8) pow6); | ||
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hash12 : Nat -> Nat; | ||
hash12 x := if (x < pow11) (hash11 x) (mod (div (x * x) pow9) pow6); | ||
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hash13 : Nat -> Nat; | ||
hash13 x := if (x < pow12) (hash12 x) (mod (div (x * x) pow10) pow6); | ||
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hash14 : Nat -> Nat; | ||
hash14 x := if (x < pow13) (hash13 x) (mod (div (x * x) pow11) pow6); | ||
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hash15 : Nat -> Nat; | ||
hash15 x := if (x < pow14) (hash14 x) (mod (div (x * x) pow12) pow6); | ||
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hash16 : Nat -> Nat; | ||
hash16 x := if (x < pow15) (hash15 x) (mod (div (x * x) pow13) pow6); | ||
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hash : Nat -> Nat := hash16; | ||
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main : Nat; | ||
main := hash 1367; | ||
-- result: 3 | ||
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end; |
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