------------------------------------------------------------------------
-- 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
import Data.Maybe.Base as Maybe
import Data.Maybe.Properties as Maybe
import Data.Nat.Properties as ℕ
import Data.Word64.Base as Word64
import Data.Word64.Properties as Word64
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
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  _≈?_
_≈?_ : 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  _≟_
_≟_ : 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."
#-}