347 lines
14 KiB
Text
347 lines
14 KiB
Text
/-
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Copyright (c) 2018 Microsoft Corporation. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Leonardo de Moura
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-/
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prelude
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import Init.Data.Fin.Basic
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import Init.System.Platform
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open Nat
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@[extern "lean_uint8_of_nat"]
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def UInt8.ofNat (n : @& Nat) : UInt8 := ⟨Fin.ofNat n⟩
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abbrev Nat.toUInt8 := UInt8.ofNat
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@[extern "lean_uint8_to_nat"]
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def UInt8.toNat (n : UInt8) : Nat := n.val.val
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@[extern c inline "#1 + #2"]
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def UInt8.add (a b : UInt8) : UInt8 := ⟨a.val + b.val⟩
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@[extern c inline "#1 - #2"]
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def UInt8.sub (a b : UInt8) : UInt8 := ⟨a.val - b.val⟩
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@[extern c inline "#1 * #2"]
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def UInt8.mul (a b : UInt8) : UInt8 := ⟨a.val * b.val⟩
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@[extern c inline "#2 == 0 ? 0 : #1 / #2"]
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def UInt8.div (a b : UInt8) : UInt8 := ⟨a.val / b.val⟩
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@[extern c inline "#2 == 0 ? #1 : #1 % #2"]
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def UInt8.mod (a b : UInt8) : UInt8 := ⟨a.val % b.val⟩
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@[extern "lean_uint8_modn"]
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def UInt8.modn (a : UInt8) (n : @& Nat) : UInt8 := ⟨a.val % n⟩
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@[extern c inline "#1 & #2"]
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def UInt8.land (a b : UInt8) : UInt8 := ⟨Fin.land a.val b.val⟩
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@[extern c inline "#1 | #2"]
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def UInt8.lor (a b : UInt8) : UInt8 := ⟨Fin.lor a.val b.val⟩
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@[extern c inline "#1 ^ #2"]
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def UInt8.xor (a b : UInt8) : UInt8 := ⟨Fin.xor a.val b.val⟩
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@[extern c inline "#1 << #2 % 8"]
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def UInt8.shiftLeft (a b : UInt8) : UInt8 := ⟨a.val <<< (modn b 8).val⟩
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@[extern c inline "#1 >> #2 % 8"]
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def UInt8.shiftRight (a b : UInt8) : UInt8 := ⟨a.val >>> (modn b 8).val⟩
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def UInt8.lt (a b : UInt8) : Prop := a.val < b.val
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def UInt8.le (a b : UInt8) : Prop := a.val ≤ b.val
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instance : OfNat UInt8 n := ⟨UInt8.ofNat n⟩
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instance : Add UInt8 := ⟨UInt8.add⟩
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instance : Sub UInt8 := ⟨UInt8.sub⟩
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instance : Mul UInt8 := ⟨UInt8.mul⟩
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instance : Mod UInt8 := ⟨UInt8.mod⟩
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instance : HMod UInt8 Nat UInt8 := ⟨UInt8.modn⟩
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instance : Div UInt8 := ⟨UInt8.div⟩
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instance : LT UInt8 := ⟨UInt8.lt⟩
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instance : LE UInt8 := ⟨UInt8.le⟩
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@[extern c inline "~ #1"]
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def UInt8.complement (a:UInt8) : UInt8 := 0-(a+1)
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instance : Complement UInt8 := ⟨UInt8.complement⟩
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instance : AndOp UInt8 := ⟨UInt8.land⟩
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instance : OrOp UInt8 := ⟨UInt8.lor⟩
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instance : Xor UInt8 := ⟨UInt8.xor⟩
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instance : ShiftLeft UInt8 := ⟨UInt8.shiftLeft⟩
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instance : ShiftRight UInt8 := ⟨UInt8.shiftRight⟩
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set_option bootstrap.genMatcherCode false in
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@[extern c inline "#1 < #2"]
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def UInt8.decLt (a b : UInt8) : Decidable (a < b) :=
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match a, b with
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| ⟨n⟩, ⟨m⟩ => inferInstanceAs (Decidable (n < m))
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set_option bootstrap.genMatcherCode false in
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@[extern c inline "#1 <= #2"]
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def UInt8.decLe (a b : UInt8) : Decidable (a ≤ b) :=
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match a, b with
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| ⟨n⟩, ⟨m⟩ => inferInstanceAs (Decidable (n <= m))
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instance (a b : UInt8) : Decidable (a < b) := UInt8.decLt a b
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instance (a b : UInt8) : Decidable (a ≤ b) := UInt8.decLe a b
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@[extern "lean_uint16_of_nat"]
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def UInt16.ofNat (n : @& Nat) : UInt16 := ⟨Fin.ofNat n⟩
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abbrev Nat.toUInt16 := UInt16.ofNat
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@[extern "lean_uint16_to_nat"]
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def UInt16.toNat (n : UInt16) : Nat := n.val.val
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@[extern c inline "#1 + #2"]
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def UInt16.add (a b : UInt16) : UInt16 := ⟨a.val + b.val⟩
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@[extern c inline "#1 - #2"]
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def UInt16.sub (a b : UInt16) : UInt16 := ⟨a.val - b.val⟩
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@[extern c inline "#1 * #2"]
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def UInt16.mul (a b : UInt16) : UInt16 := ⟨a.val * b.val⟩
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@[extern c inline "#2 == 0 ? 0 : #1 / #2"]
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def UInt16.div (a b : UInt16) : UInt16 := ⟨a.val / b.val⟩
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@[extern c inline "#2 == 0 ? #1 : #1 % #2"]
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def UInt16.mod (a b : UInt16) : UInt16 := ⟨a.val % b.val⟩
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@[extern "lean_uint16_modn"]
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def UInt16.modn (a : UInt16) (n : @& Nat) : UInt16 := ⟨a.val % n⟩
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@[extern c inline "#1 & #2"]
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def UInt16.land (a b : UInt16) : UInt16 := ⟨Fin.land a.val b.val⟩
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@[extern c inline "#1 | #2"]
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def UInt16.lor (a b : UInt16) : UInt16 := ⟨Fin.lor a.val b.val⟩
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@[extern c inline "#1 ^ #2"]
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def UInt16.xor (a b : UInt16) : UInt16 := ⟨Fin.xor a.val b.val⟩
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@[extern c inline "#1 << #2 % 16"]
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def UInt16.shiftLeft (a b : UInt16) : UInt16 := ⟨a.val <<< (modn b 16).val⟩
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@[extern c inline "#1 >> #2 % 16"]
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def UInt16.shiftRight (a b : UInt16) : UInt16 := ⟨a.val >>> (modn b 16).val⟩
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def UInt16.lt (a b : UInt16) : Prop := a.val < b.val
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def UInt16.le (a b : UInt16) : Prop := a.val ≤ b.val
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instance : OfNat UInt16 n := ⟨UInt16.ofNat n⟩
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instance : Add UInt16 := ⟨UInt16.add⟩
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instance : Sub UInt16 := ⟨UInt16.sub⟩
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instance : Mul UInt16 := ⟨UInt16.mul⟩
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instance : Mod UInt16 := ⟨UInt16.mod⟩
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instance : HMod UInt16 Nat UInt16 := ⟨UInt16.modn⟩
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instance : Div UInt16 := ⟨UInt16.div⟩
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instance : LT UInt16 := ⟨UInt16.lt⟩
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instance : LE UInt16 := ⟨UInt16.le⟩
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@[extern c inline "~ #1"]
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def UInt16.complement (a:UInt16) : UInt16 := 0-(a+1)
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instance : Complement UInt16 := ⟨UInt16.complement⟩
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instance : AndOp UInt16 := ⟨UInt16.land⟩
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instance : OrOp UInt16 := ⟨UInt16.lor⟩
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instance : Xor UInt16 := ⟨UInt16.xor⟩
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instance : ShiftLeft UInt16 := ⟨UInt16.shiftLeft⟩
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instance : ShiftRight UInt16 := ⟨UInt16.shiftRight⟩
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set_option bootstrap.genMatcherCode false in
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@[extern c inline "#1 < #2"]
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def UInt16.decLt (a b : UInt16) : Decidable (a < b) :=
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match a, b with
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set_option bootstrap.genMatcherCode false in
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@[extern c inline "#1 <= #2"]
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def UInt16.decLe (a b : UInt16) : Decidable (a ≤ b) :=
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match a, b with
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instance (a b : UInt16) : Decidable (a < b) := UInt16.decLt a b
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instance (a b : UInt16) : Decidable (a ≤ b) := UInt16.decLe a b
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@[extern "lean_uint32_of_nat"]
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def UInt32.ofNat (n : @& Nat) : UInt32 := ⟨Fin.ofNat n⟩
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@[extern "lean_uint32_of_nat"]
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def UInt32.ofNat' (n : Nat) (h : n < UInt32.size) : UInt32 := ⟨⟨n, h⟩⟩
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abbrev Nat.toUInt32 := UInt32.ofNat
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@[extern c inline "#1 + #2"]
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def UInt32.add (a b : UInt32) : UInt32 := ⟨a.val + b.val⟩
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@[extern c inline "#1 - #2"]
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def UInt32.sub (a b : UInt32) : UInt32 := ⟨a.val - b.val⟩
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@[extern c inline "#1 * #2"]
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def UInt32.mul (a b : UInt32) : UInt32 := ⟨a.val * b.val⟩
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@[extern c inline "#2 == 0 ? 0 : #1 / #2"]
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def UInt32.div (a b : UInt32) : UInt32 := ⟨a.val / b.val⟩
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@[extern c inline "#2 == 0 ? #1 : #1 % #2"]
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def UInt32.mod (a b : UInt32) : UInt32 := ⟨a.val % b.val⟩
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@[extern "lean_uint32_modn"]
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def UInt32.modn (a : UInt32) (n : @& Nat) : UInt32 := ⟨a.val % n⟩
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@[extern c inline "#1 & #2"]
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def UInt32.land (a b : UInt32) : UInt32 := ⟨Fin.land a.val b.val⟩
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@[extern c inline "#1 | #2"]
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def UInt32.lor (a b : UInt32) : UInt32 := ⟨Fin.lor a.val b.val⟩
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@[extern c inline "#1 ^ #2"]
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def UInt32.xor (a b : UInt32) : UInt32 := ⟨Fin.xor a.val b.val⟩
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@[extern c inline "#1 << #2 % 32"]
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def UInt32.shiftLeft (a b : UInt32) : UInt32 := ⟨a.val <<< (modn b 32).val⟩
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@[extern c inline "#1 >> #2 % 32"]
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def UInt32.shiftRight (a b : UInt32) : UInt32 := ⟨a.val >>> (modn b 32).val⟩
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@[extern c inline "((uint8_t)#1)"]
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def UInt32.toUInt8 (a : UInt32) : UInt8 := a.toNat.toUInt8
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@[extern c inline "((uint16_t)#1)"]
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def UInt32.toUInt16 (a : UInt32) : UInt16 := a.toNat.toUInt16
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@[extern c inline "((uint32_t)#1)"]
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def UInt8.toUInt32 (a : UInt8) : UInt32 := a.toNat.toUInt32
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instance : OfNat UInt32 n := ⟨UInt32.ofNat n⟩
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instance : Add UInt32 := ⟨UInt32.add⟩
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instance : Sub UInt32 := ⟨UInt32.sub⟩
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instance : Mul UInt32 := ⟨UInt32.mul⟩
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instance : Mod UInt32 := ⟨UInt32.mod⟩
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instance : HMod UInt32 Nat UInt32 := ⟨UInt32.modn⟩
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instance : Div UInt32 := ⟨UInt32.div⟩
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@[extern c inline "~ #1"]
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def UInt32.complement (a:UInt32) : UInt32 := 0-(a+1)
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instance : Complement UInt32 := ⟨UInt32.complement⟩
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instance : AndOp UInt32 := ⟨UInt32.land⟩
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instance : OrOp UInt32 := ⟨UInt32.lor⟩
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instance : Xor UInt32 := ⟨UInt32.xor⟩
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instance : ShiftLeft UInt32 := ⟨UInt32.shiftLeft⟩
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instance : ShiftRight UInt32 := ⟨UInt32.shiftRight⟩
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@[extern "lean_uint64_of_nat"]
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def UInt64.ofNat (n : @& Nat) : UInt64 := ⟨Fin.ofNat n⟩
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abbrev Nat.toUInt64 := UInt64.ofNat
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@[extern "lean_uint64_to_nat"]
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def UInt64.toNat (n : UInt64) : Nat := n.val.val
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@[extern c inline "#1 + #2"]
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def UInt64.add (a b : UInt64) : UInt64 := ⟨a.val + b.val⟩
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@[extern c inline "#1 - #2"]
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def UInt64.sub (a b : UInt64) : UInt64 := ⟨a.val - b.val⟩
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@[extern c inline "#1 * #2"]
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def UInt64.mul (a b : UInt64) : UInt64 := ⟨a.val * b.val⟩
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@[extern c inline "#2 == 0 ? 0 : #1 / #2"]
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def UInt64.div (a b : UInt64) : UInt64 := ⟨a.val / b.val⟩
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@[extern c inline "#2 == 0 ? #1 : #1 % #2"]
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def UInt64.mod (a b : UInt64) : UInt64 := ⟨a.val % b.val⟩
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@[extern "lean_uint64_modn"]
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def UInt64.modn (a : UInt64) (n : @& Nat) : UInt64 := ⟨a.val % n⟩
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@[extern c inline "#1 & #2"]
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def UInt64.land (a b : UInt64) : UInt64 := ⟨Fin.land a.val b.val⟩
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@[extern c inline "#1 | #2"]
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def UInt64.lor (a b : UInt64) : UInt64 := ⟨Fin.lor a.val b.val⟩
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@[extern c inline "#1 ^ #2"]
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def UInt64.xor (a b : UInt64) : UInt64 := ⟨Fin.xor a.val b.val⟩
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@[extern c inline "#1 << #2 % 64"]
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def UInt64.shiftLeft (a b : UInt64) : UInt64 := ⟨a.val <<< (modn b 64).val⟩
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@[extern c inline "#1 >> #2 % 64"]
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def UInt64.shiftRight (a b : UInt64) : UInt64 := ⟨a.val >>> (modn b 64).val⟩
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def UInt64.lt (a b : UInt64) : Prop := a.val < b.val
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def UInt64.le (a b : UInt64) : Prop := a.val ≤ b.val
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@[extern c inline "((uint8_t)#1)"]
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def UInt64.toUInt8 (a : UInt64) : UInt8 := a.toNat.toUInt8
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@[extern c inline "((uint16_t)#1)"]
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def UInt64.toUInt16 (a : UInt64) : UInt16 := a.toNat.toUInt16
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@[extern c inline "((uint32_t)#1)"]
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def UInt64.toUInt32 (a : UInt64) : UInt32 := a.toNat.toUInt32
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@[extern c inline "((uint64_t)#1)"]
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def UInt32.toUInt64 (a : UInt32) : UInt64 := a.toNat.toUInt64
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instance : OfNat UInt64 n := ⟨UInt64.ofNat n⟩
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instance : Add UInt64 := ⟨UInt64.add⟩
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instance : Sub UInt64 := ⟨UInt64.sub⟩
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instance : Mul UInt64 := ⟨UInt64.mul⟩
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instance : Mod UInt64 := ⟨UInt64.mod⟩
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instance : HMod UInt64 Nat UInt64 := ⟨UInt64.modn⟩
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instance : Div UInt64 := ⟨UInt64.div⟩
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instance : LT UInt64 := ⟨UInt64.lt⟩
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instance : LE UInt64 := ⟨UInt64.le⟩
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@[extern c inline "~ #1"]
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def UInt64.complement (a:UInt64) : UInt64 := 0-(a+1)
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instance : Complement UInt64 := ⟨UInt64.complement⟩
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instance : AndOp UInt64 := ⟨UInt64.land⟩
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instance : OrOp UInt64 := ⟨UInt64.lor⟩
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instance : Xor UInt64 := ⟨UInt64.xor⟩
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instance : ShiftLeft UInt64 := ⟨UInt64.shiftLeft⟩
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instance : ShiftRight UInt64 := ⟨UInt64.shiftRight⟩
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@[extern c inline "(uint64_t)#1"]
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def Bool.toUInt64 (b : Bool) : UInt64 := if b then 1 else 0
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set_option bootstrap.genMatcherCode false in
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@[extern c inline "#1 < #2"]
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def UInt64.decLt (a b : UInt64) : Decidable (a < b) :=
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match a, b with
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set_option bootstrap.genMatcherCode false in
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@[extern c inline "#1 <= #2"]
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def UInt64.decLe (a b : UInt64) : Decidable (a ≤ b) :=
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match a, b with
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| ⟨n⟩, ⟨m⟩ => inferInstanceAs (Decidable (n <= m))
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instance (a b : UInt64) : Decidable (a < b) := UInt64.decLt a b
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instance (a b : UInt64) : Decidable (a ≤ b) := UInt64.decLe a b
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theorem usizeSzGt0 : USize.size > 0 :=
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Nat.posPowOfPos System.Platform.numBits (Nat.zeroLtSucc _)
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@[extern "lean_usize_of_nat"]
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def USize.ofNat (n : @& Nat) : USize := ⟨Fin.ofNat' n usizeSzGt0⟩
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abbrev Nat.toUSize := USize.ofNat
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@[extern "lean_usize_to_nat"]
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def USize.toNat (n : USize) : Nat := n.val.val
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@[extern c inline "#1 + #2"]
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def USize.add (a b : USize) : USize := ⟨a.val + b.val⟩
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@[extern c inline "#1 - #2"]
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def USize.sub (a b : USize) : USize := ⟨a.val - b.val⟩
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@[extern c inline "#1 * #2"]
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def USize.mul (a b : USize) : USize := ⟨a.val * b.val⟩
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@[extern c inline "#2 == 0 ? 0 : #1 / #2"]
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def USize.div (a b : USize) : USize := ⟨a.val / b.val⟩
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@[extern c inline "#2 == 0 ? #1 : #1 % #2"]
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def USize.mod (a b : USize) : USize := ⟨a.val % b.val⟩
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@[extern "lean_usize_modn"]
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def USize.modn (a : USize) (n : @& Nat) : USize := ⟨a.val % n⟩
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@[extern c inline "#1 & #2"]
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def USize.land (a b : USize) : USize := ⟨Fin.land a.val b.val⟩
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@[extern c inline "#1 | #2"]
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def USize.lor (a b : USize) : USize := ⟨Fin.lor a.val b.val⟩
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@[extern c inline "#1 ^ #2"]
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def USize.xor (a b : USize) : USize := ⟨Fin.xor a.val b.val⟩
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@[extern c inline "#1 << #2 % (sizeof(size_t) * 8)"]
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def USize.shiftLeft (a b : USize) : USize := ⟨a.val <<< (modn b System.Platform.numBits).val⟩
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@[extern c inline "#1 >> #2 % (sizeof(size_t) * 8)"]
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def USize.shiftRight (a b : USize) : USize := ⟨a.val >>> (modn b System.Platform.numBits).val⟩
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@[extern c inline "#1"]
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def UInt32.toUSize (a : UInt32) : USize := a.toNat.toUSize
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@[extern c inline "((size_t)#1)"]
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def UInt64.toUSize (a : UInt64) : USize := a.toNat.toUSize
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@[extern c inline "(uint32_t)#1"]
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def USize.toUInt32 (a : USize) : UInt32 := a.toNat.toUInt32
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def USize.lt (a b : USize) : Prop := a.val < b.val
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def USize.le (a b : USize) : Prop := a.val ≤ b.val
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instance : OfNat USize n := ⟨USize.ofNat n⟩
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instance : Add USize := ⟨USize.add⟩
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instance : Sub USize := ⟨USize.sub⟩
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instance : Mul USize := ⟨USize.mul⟩
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instance : Mod USize := ⟨USize.mod⟩
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instance : HMod USize Nat USize := ⟨USize.modn⟩
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instance : Div USize := ⟨USize.div⟩
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instance : LT USize := ⟨USize.lt⟩
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instance : LE USize := ⟨USize.le⟩
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@[extern c inline "~ #1"]
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def USize.complement (a:USize) : USize := 0-(a+1)
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instance : Complement USize := ⟨USize.complement⟩
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instance : AndOp USize := ⟨USize.land⟩
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instance : OrOp USize := ⟨USize.lor⟩
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instance : Xor USize := ⟨USize.xor⟩
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instance : ShiftLeft USize := ⟨USize.shiftLeft⟩
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instance : ShiftRight USize := ⟨USize.shiftRight⟩
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set_option bootstrap.genMatcherCode false in
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@[extern c inline "#1 < #2"]
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def USize.decLt (a b : USize) : Decidable (a < b) :=
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match a, b with
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| ⟨n⟩, ⟨m⟩ => inferInstanceAs (Decidable (n < m))
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set_option bootstrap.genMatcherCode false in
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@[extern c inline "#1 <= #2"]
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def USize.decLe (a b : USize) : Decidable (a ≤ b) :=
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match a, b with
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| ⟨n⟩, ⟨m⟩ => inferInstanceAs (Decidable (n <= m))
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instance (a b : USize) : Decidable (a < b) := USize.decLt a b
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instance (a b : USize) : Decidable (a ≤ b) := USize.decLe a b
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theorem USize.modn_lt {m : Nat} : ∀ (u : USize), m > 0 → USize.toNat (u % m) < m
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| ⟨u⟩, h => Fin.modn_lt u h
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