f5fd962a25
Summary: - Adds configuration option `exponentiation.threshold` - An expression `b^n` where `b` and `n` are literals is not reduced by `whnf`, `simp`, and `isDefEq` if `n > exponentiation.threshold`. Motivation: prevents system from becoming irresponsive and/or crashing without memory. TODO: improve support in the kernel. It is using a hard-coded limit for now.
68 lines
2.3 KiB
Text
68 lines
2.3 KiB
Text
import Lean
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/-! Basic tests, including edge cases. -/
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example : Nat.gcd 0 0 = 0 := rfl
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example : Nat.gcd 0 1 = 1 := rfl
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example : Nat.gcd 0 17 = 17 := rfl
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example : Nat.gcd 1 0 = 1 := rfl
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example : Nat.gcd 17 0 = 17 := rfl
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example : Nat.gcd 1 1 = 1 := rfl
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example : Nat.gcd 1 17 = 1 := rfl
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example : Nat.gcd 17 1 = 1 := rfl
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example : Nat.gcd 2 2 = 2 := rfl
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example : Nat.gcd 2 3 = 1 := rfl
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example : Nat.gcd 2 4 = 2 := rfl
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example : Nat.gcd 9 6 = 3 := rfl
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/-!
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We check that `Nat.gcd` is evaluated using bignum functions in the kernel.
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Because of variations in run time on different operating systems during CI,
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for the larger calculations we don't attempt to do any timing.
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All of the "large" calculations below used to fail with
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```
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maximum recursion depth has been reached (use `set_option maxRecDepth <num>` to increase limit)
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```
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prior to lean4#2533.
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-/
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open Lean Elab Command in
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elab "#fast" c:command : command => do
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let start ← IO.monoMsNow
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elabCommand c
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let elapsed := (← IO.monoMsNow) - start
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if elapsed > 1000 then throwError m!"Too slow! {elapsed}ms"
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-- Used to take ~1500ms, now takes ~3ms.
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#fast example : Nat.gcd 45 (Nat.gcd 15 85) = 5 := rfl
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example : Nat.gcd (115249 * 180811) (115249*181081) = 115249 := rfl
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/-- Mersenne primes. -/
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def m (p : Nat) := 2^p - 1
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/-- Largish primes, targeting <100ms GCD calculations. -/
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def p_29 := 110503
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def p_30 := 132049
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def p_31 := 216091
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def p_32 := 756839
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def p_33 := 859433
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set_option exponentiation.threshold 10000000
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/- GCD with large prime factors on one side, and small primes on the other. -/
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example : Nat.gcd (p_29 * p_30 * p_31 * p_32 * p_33) 2^(2^20) = 1 := rfl
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/- GCD with two prime factors on both sides, including one in common. -/
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example : Nat.gcd (m p_31 * m p_33) (m p_32 * m p_33) - m p_33 = 0 := rfl
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/- GCD with many small prime factors. -/
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example :
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Nat.gcd (2^1 * 3^1 * 5^2 * 7^3 * 11^5 * 13^8) (2^8 * 3^5 * 5^3 * 7^2 * 11^1 * 13^1) =
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2 * 3 * 5^2 * 7^2 * 11 * 13 := rfl
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-- #eval Lean.maxSmallNat -- 9223372036854775807
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def maxSmallNat := 9223372036854775807
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example : maxSmallNat = 7^2 * 73 * 127 * 337 * 92737 * 649657 := rfl
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-- Calculate GCDs of numbers on either side of `maxSmallNat`.
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example : Nat.gcd (maxSmallNat - 92737) (maxSmallNat + 92737) = 185474 := rfl
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example : Nat.gcd (maxSmallNat / 649657) (maxSmallNat * 649657) = 14197294936951 := rfl
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