9f06aff834
This PR adds optimized division functions for `Int` and `Nat` when the arguments are known to be divisible (such as when normalizing rationals). These are backed by the gmp functions `mpz_divexact` and `mpz_divexact_ui`. See also leanprover-community/batteries#1202.
25 lines
1.2 KiB
Text
25 lines
1.2 KiB
Text
#guard Nat.divExact 4 2 (by decide) == 2
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#guard Nat.divExact 0 0 (by decide) == 0
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#guard Nat.divExact 0 2 (by decide) == 0
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#guard Nat.divExact 0 (2 ^ 100) (by decide) == 0
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#guard Nat.divExact (2 ^ 100) (2 ^ 100) (by decide) == 1
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#guard Nat.divExact (2 ^ 100) 4 (by decide) == 2 ^ 98
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#guard Nat.divExact (3 ^ 200) (3 ^ 100) (by decide) == 3 ^ 100
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#guard Nat.divExact (2 ^ 100) (2 ^ 60) (by decide) == 2 ^ 40
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#guard Int.divExact 4 2 (by decide) == 2
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#guard Int.divExact 0 0 (by decide) == 0
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#guard Int.divExact 0 2 (by decide) == 0
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#guard Int.divExact 0 (2 ^ 100 : Nat) (by decide) == 0
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#guard Int.divExact (2 ^ 100 : Nat) (2 ^ 100 : Nat) (by decide) == 1
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#guard Int.divExact (2 ^ 100 : Nat) 4 (by decide) == 2 ^ 98
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#guard Int.divExact (3 ^ 200 : Nat) (3 ^ 100 : Nat) (by decide) == 3 ^ 100
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#guard Int.divExact 4 (-2) (by decide) == -2
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#guard Int.divExact (-8) (-2) (by decide) == 4
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#guard Int.divExact 0 (-2) (by decide) == 0
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#guard Int.divExact 0 (-(2 ^ 100 : Nat)) (by decide) == 0
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#guard Int.divExact (2 ^ 100 : Nat) (-(2 ^ 100 : Nat)) (by decide) == -1
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#guard Int.divExact (-(3 ^ 200 : Nat)) (-(3 ^ 100 : Nat)) (by decide) == 3 ^ 100
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#guard Int.divExact (-(3 ^ 100 : Nat)) 3 (by decide) == -3 ^ 99
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#guard Int.divExact (-(2 ^ 31 : Nat)) (2 ^ 31 : Nat) (by decide) == -1
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