117 lines
4.2 KiB
Text
117 lines
4.2 KiB
Text
/-
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Copyright (c) 2020 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.Core
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import Init.Data.Int.Basic
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import Init.Data.ToString.Basic
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structure FloatSpec where
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float : Type
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val : float
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lt : float → float → Prop
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le : float → float → Prop
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decLt : DecidableRel lt
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decLe : DecidableRel le
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-- Just show FloatSpec is inhabited.
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constant floatSpec : FloatSpec := {
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float := Unit,
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val := (),
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lt := fun _ _ => True,
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le := fun _ _ => True,
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decLt := fun _ _ => inferInstanceAs (Decidable True),
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decLe := fun _ _ => inferInstanceAs (Decidable True)
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}
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structure Float where
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val : floatSpec.float
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instance : Inhabited Float := ⟨{ val := floatSpec.val }⟩
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@[extern "lean_float_add"] constant Float.add : Float → Float → Float
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@[extern "lean_float_sub"] constant Float.sub : Float → Float → Float
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@[extern "lean_float_mul"] constant Float.mul : Float → Float → Float
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@[extern "lean_float_div"] constant Float.div : Float → Float → Float
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@[extern "lean_float_negate"] constant Float.neg : Float → Float
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set_option bootstrap.genMatcherCode false
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def Float.lt : Float → Float → Prop := fun a b =>
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match a, b with
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| ⟨a⟩, ⟨b⟩ => floatSpec.lt a b
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def Float.le : Float → Float → Prop := fun a b =>
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floatSpec.le a.val b.val
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instance : Add Float := ⟨Float.add⟩
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instance : Sub Float := ⟨Float.sub⟩
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instance : Mul Float := ⟨Float.mul⟩
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instance : Div Float := ⟨Float.div⟩
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instance : Neg Float := ⟨Float.neg⟩
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instance : LT Float := ⟨Float.lt⟩
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instance : LE Float := ⟨Float.le⟩
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@[extern "lean_float_beq"] constant Float.beq (a b : Float) : Bool
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instance : BEq Float := ⟨Float.beq⟩
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@[extern "lean_float_decLt"] constant Float.decLt (a b : Float) : Decidable (a < b) :=
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match a, b with
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| ⟨a⟩, ⟨b⟩ => floatSpec.decLt a b
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@[extern "lean_float_decLe"] constant Float.decLe (a b : Float) : Decidable (a ≤ b) :=
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match a, b with
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| ⟨a⟩, ⟨b⟩ => floatSpec.decLe a b
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instance floatDecLt (a b : Float) : Decidable (a < b) := Float.decLt a b
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instance floatDecLe (a b : Float) : Decidable (a ≤ b) := Float.decLe a b
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@[extern "lean_float_to_string"] constant Float.toString : Float → String
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@[extern "lean_float_to_uint8"] constant Float.toUInt8 : Float → UInt8
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@[extern "lean_float_to_uint16"] constant Float.toUInt16 : Float → UInt16
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@[extern "lean_float_to_uint32"] constant Float.toUInt32 : Float → UInt32
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@[extern "lean_float_to_uint64"] constant Float.toUInt64 : Float → UInt64
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@[extern "lean_float_to_usize"] constant Float.toUSize : Float → USize
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instance : ToString Float where
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toString := Float.toString
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instance : Repr Float where
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reprPrec n _ := Float.toString n
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instance : ReprAtom Float := ⟨⟩
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@[extern "lean_uint64_to_float"] constant UInt64.toFloat (n : UInt64) : Float
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@[extern "sin"] constant Float.sin : Float → Float
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@[extern "cos"] constant Float.cos : Float → Float
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@[extern "tan"] constant Float.tan : Float → Float
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@[extern "asin"] constant Float.asin : Float → Float
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@[extern "acos"] constant Float.acos : Float → Float
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@[extern "atan"] constant Float.atan : Float → Float
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@[extern "atan2"] constant Float.atan2 : Float → Float → Float
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@[extern "sinh"] constant Float.sinh : Float → Float
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@[extern "cosh"] constant Float.cosh : Float → Float
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@[extern "tanh"] constant Float.tanh : Float → Float
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@[extern "asinh"] constant Float.asinh : Float → Float
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@[extern "acosh"] constant Float.acosh : Float → Float
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@[extern "atanh"] constant Float.atanh : Float → Float
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@[extern "exp"] constant Float.exp : Float → Float
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@[extern "exp2"] constant Float.exp2 : Float → Float
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@[extern "log"] constant Float.log : Float → Float
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@[extern "log2"] constant Float.log2 : Float → Float
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@[extern "log10"] constant Float.log10 : Float → Float
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@[extern "pow"] constant Float.pow : Float → Float → Float
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@[extern "sqrt"] constant Float.sqrt : Float → Float
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@[extern "cbrt"] constant Float.cbrt : Float → Float
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instance : Pow Float Float := ⟨Float.pow⟩
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/--
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Efficiently computes `x * 2^i`.
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-/
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@[extern "lean_float_scaleb"]
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constant Float.scaleB (x : Float) (i : @& Int) : Float
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