------------------------------------------------------------------------
-- The Agda standard library
--
-- Properties of operations on floats
------------------------------------------------------------------------
{-# OPTIONS --cubical-compatible --safe #-}
module Data.Float.Properties where
open import Data.Bool.Base as Bool using (Bool)
open import Data.Float.Base using (Float; _≈_; toWord64)
import Data.Maybe.Base as Maybe using (Maybe; just; nothing; map)
import Data.Maybe.Properties as Maybe using (map-injective; ≡-dec)
import Data.Nat.Properties as ℕ using (_≟_)
import Data.Word64.Base as Word64 using (Word64; toℕ)
import Data.Word64.Properties as Word64 using (≈⇒≡)
open import Function.Base using (_∘_)
open import Relation.Nullary.Decidable as RN using (map′)
open import Relation.Binary.Core using (_⇒_)
open import Relation.Binary.Bundles using (Setoid; DecSetoid)
open import Relation.Binary.Structures
using (IsEquivalence; IsDecEquivalence)
open import Relation.Binary.Definitions
using (Reflexive; Symmetric; Transitive; Substitutive; Decidable; DecidableEquality)
import Relation.Binary.Construct.On as On using (decidable)
open import Relation.Binary.PropositionalEquality.Core
using (_≡_; refl; cong; sym; trans; subst)
open import Relation.Binary.PropositionalEquality.Properties
using (setoid; decSetoid)
------------------------------------------------------------------------
-- Primitive properties
open import Agda.Builtin.Float.Properties
renaming (primFloatToWord64Injective to toWord64-injective)
public
------------------------------------------------------------------------
-- Properties of _≈_
≈⇒≡ : _≈_ ⇒ _≡_
≈⇒≡ eq = toWord64-injective _ _ (Maybe.map-injective Word64.≈⇒≡ eq)
≈-reflexive : _≡_ ⇒ _≈_
≈-reflexive eq = cong (Maybe.map Word64.toℕ ∘ toWord64) eq
≈-refl : Reflexive _≈_
≈-refl = refl
≈-sym : Symmetric _≈_
≈-sym = sym
≈-trans : Transitive _≈_
≈-trans = trans
≈-subst : ∀ {ℓ} → Substitutive _≈_ ℓ
≈-subst P x≈y p = subst P (≈⇒≡ x≈y) p
infix 4 _≈?_
_≈?_ : Decidable _≈_
_≈?_ = On.decidable (Maybe.map Word64.toℕ ∘ toWord64) _≡_ (Maybe.≡-dec ℕ._≟_)
≈-isEquivalence : IsEquivalence _≈_
≈-isEquivalence = record
{ refl = λ {i} → ≈-refl {i}
; sym = λ {i j} → ≈-sym {i} {j}
; trans = λ {i j k} → ≈-trans {i} {j} {k}
}
≈-setoid : Setoid _ _
≈-setoid = record
{ isEquivalence = ≈-isEquivalence
}
≈-isDecEquivalence : IsDecEquivalence _≈_
≈-isDecEquivalence = record
{ isEquivalence = ≈-isEquivalence
; _≟_ = _≈?_
}
≈-decSetoid : DecSetoid _ _
≈-decSetoid = record
{ isDecEquivalence = ≈-isDecEquivalence
}
------------------------------------------------------------------------
-- Properties of _≡_
infix 4 _≟_
_≟_ : DecidableEquality Float
x ≟ y = map′ ≈⇒≡ ≈-reflexive (x ≈? y)
≡-setoid : Setoid _ _
≡-setoid = setoid Float
≡-decSetoid : DecSetoid _ _
≡-decSetoid = decSetoid _≟_
------------------------------------------------------------------------
-- DEPRECATIONS
toWord-injective = toWord64-injective
{-# WARNING_ON_USAGE toWord-injective
"Warning: toWord-injective was deprecated in v2.1.
Please use toWord64-injective instead."
#-}
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