From 7b4e6a522bcf1f247ef9b3517af328b5da670a98 Mon Sep 17 00:00:00 2001 From: Cyril SIX Date: Fri, 4 Oct 2019 17:57:25 +0200 Subject: Ibuiltin proof --- lib/Floats.v | 63 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++- 1 file changed, 62 insertions(+), 1 deletion(-) (limited to 'lib/Floats.v') diff --git a/lib/Floats.v b/lib/Floats.v index 13350dd0..272efa52 100644 --- a/lib/Floats.v +++ b/lib/Floats.v @@ -16,7 +16,7 @@ (** Formalization of floating-point numbers, using the Flocq library. *) -Require Import Coqlib Zbits Integers. +Require Import Coqlib Zbits Integers Axioms. (*From Flocq*) Require Import Binary Bits Core. Require Import IEEE754_extra. @@ -27,8 +27,69 @@ Close Scope R_scope. Open Scope Z_scope. Definition float := binary64. (**r the type of IEE754 double-precision FP numbers *) + +Definition float_eq: forall (i1 i2: float), {i1=i2} + {i1<>i2}. +Proof. + intros. destruct i1. +(* B754_zero *) + - destruct i2; try (right; discriminate). + destruct (eqb s s0) eqn:BEQ. + + apply eqb_prop in BEQ. subst. left. reflexivity. + + apply eqb_false_iff in BEQ. right. intro. inv H. contradiction. +(* B754_infinity *) + - destruct i2; try (right; discriminate). + destruct (eqb s s0) eqn:BEQ. + + apply eqb_prop in BEQ. subst. left. reflexivity. + + apply eqb_false_iff in BEQ. right. intro. inv H. contradiction. +(* B754_nan *) + - destruct i2; try (right; discriminate). + destruct (eqb s s0) eqn:BEQ. + + generalize (Pos.eq_dec pl pl0). intro. inv H. + ++ left. apply eqb_prop in BEQ. subst. + assert (e = e0) by (apply proof_irr). congruence. + ++ right. intro. inv H. contradiction. + + apply eqb_false_iff in BEQ. right. intro. inv H. contradiction. +(* B754_finite *) + - destruct i2; try (right; discriminate). + destruct (eqb s s0) eqn:BEQ; [apply eqb_prop in BEQ | apply eqb_false_iff in BEQ]. + generalize (Pos.eq_dec m m0). intro. inv H. + generalize (Z.eq_dec e e1). intro. inv H. + 1: { left. assert (e0 = e2) by (apply proof_irr). congruence. } + all: right; intro; inv H; contradiction. +Qed. + Definition float32 := binary32. (**r the type of IEE754 single-precision FP numbers *) +Definition float32_eq: forall (i1 i2: float32), {i1=i2} + {i1<>i2}. +Proof. + intros. destruct i1. +(* B754_zero *) + - destruct i2; try (right; discriminate). + destruct (eqb s s0) eqn:BEQ. + + apply eqb_prop in BEQ. subst. left. reflexivity. + + apply eqb_false_iff in BEQ. right. intro. inv H. contradiction. +(* B754_infinity *) + - destruct i2; try (right; discriminate). + destruct (eqb s s0) eqn:BEQ. + + apply eqb_prop in BEQ. subst. left. reflexivity. + + apply eqb_false_iff in BEQ. right. intro. inv H. contradiction. +(* B754_nan *) + - destruct i2; try (right; discriminate). + destruct (eqb s s0) eqn:BEQ. + + generalize (Pos.eq_dec pl pl0). intro. inv H. + ++ left. apply eqb_prop in BEQ. subst. + assert (e = e0) by (apply proof_irr). congruence. + ++ right. intro. inv H. contradiction. + + apply eqb_false_iff in BEQ. right. intro. inv H. contradiction. +(* B754_finite *) + - destruct i2; try (right; discriminate). + destruct (eqb s s0) eqn:BEQ; [apply eqb_prop in BEQ | apply eqb_false_iff in BEQ]. + generalize (Pos.eq_dec m m0). intro. inv H. + generalize (Z.eq_dec e e1). intro. inv H. + 1: { left. assert (e0 = e2) by (apply proof_irr). congruence. } + all: right; intro; inv H; contradiction. +Qed. + (** Boolean-valued comparisons *) Definition cmp_of_comparison (c: comparison) (x: option Datatypes.comparison) : bool := -- cgit