58 lines
1.8 KiB
Text
58 lines
1.8 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.Meta
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import Init.Data.Float
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import Init.Data.Nat.Log2
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/-- For decimal and scientific numbers (e.g., `1.23`, `3.12e10`).
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Examples:
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- `1.23` is syntax for `OfScientific.ofScientific (nat_lit 123) true (nat_lit 2)`
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- `121e100` is syntax for `OfScientific.ofScientific (nat_lit 121) false (nat_lit 100)`
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Note the use of `nat_lit`; there is no wrapping `OfNat.ofNat` in the resulting term.
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-/
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class OfScientific (α : Type u) where
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ofScientific (mantissa : Nat) (exponentSign : Bool) (decimalExponent : Nat) : α
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/-- Computes `m * 2^e`. -/
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def Float.ofBinaryScientific (m : Nat) (e : Int) : Float :=
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let s := m.log2 - 63
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let m := (m >>> s).toUInt64
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let e := e + s
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m.toFloat.scaleB e
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protected opaque Float.ofScientific (m : Nat) (s : Bool) (e : Nat) : Float :=
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if s then
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let s := 64 - m.log2 -- ensure we have 64 bits of mantissa left after division
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let m := (m <<< (3 * e + s)) / 5^e
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Float.ofBinaryScientific m (-4 * e - s)
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else
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Float.ofBinaryScientific (m * 5^e) e
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/--
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The `OfScientific Float` must have priority higher than `mid` since
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the default instance `Neg Int` has `mid` priority.
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```
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#check -42.0 -- must be Float
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```
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-/
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@[default_instance mid+1]
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instance : OfScientific Float where
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ofScientific := Float.ofScientific
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@[export lean_float_of_nat]
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def Float.ofNat (n : Nat) : Float :=
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OfScientific.ofScientific n false 0
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def Float.ofInt : Int → Float
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| Int.ofNat n => Float.ofNat n
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| Int.negSucc n => Float.neg (Float.ofNat (Nat.succ n))
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instance : OfNat Float n := ⟨Float.ofNat n⟩
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abbrev Nat.toFloat (n : Nat) : Float :=
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Float.ofNat n
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