Merge PR #9867: Add primitive floats (binary64 floating-point numbers)

Ack-by: SkySkimmer
Reviewed-by: Zimmi48
Ack-by: ejgallego
Reviewed-by: maximedenes
Ack-by: proux01
Ack-by: silene
Ack-by: vbgl

4 files changed, 177 insertions, 0 deletions

diff --git a/test-suite/output/FloatExtraction.out b/test-suite/output/FloatExtraction.out
new file mode 100644
index 0000000000..cfd6633752
--- /dev/null
+++ b/test-suite/output/FloatExtraction.out
@@ -0,0 +1,67 @@
+
+(** val infinity : Float64.t **)
+
+let infinity =
+  (Float64.of_float (infinity))
+
+(** val neg_infinity : Float64.t **)
+
+let neg_infinity =
+  (Float64.of_float (neg_infinity))
+
+(** val nan : Float64.t **)
+
+let nan =
+  (Float64.of_float (nan))
+
+(** val one : Float64.t **)
+
+let one =
+  (Float64.of_float (0x1p+0))
+
+(** val zero : Float64.t **)
+
+let zero =
+  (Float64.of_float (0x0p+0))
+
+(** val two : Float64.t **)
+
+let two =
+  (Float64.of_float (0x1p+1))
+
+(** val list_floats : Float64.t list **)
+
+let list_floats =
+  nan :: (infinity :: (neg_infinity :: (zero :: (one :: (two :: ((Float64.of_float (0x1p-1)) :: ((Float64.of_float (0x1.47ae147ae147bp-7)) :: ((Float64.of_float (-0x1p-1)) :: ((Float64.of_float (-0x1.47ae147ae147bp-7)) :: ((Float64.of_float (0x1.e42d130773b76p+1023)) :: ((Float64.of_float (-0x0.c396c98f8d899p-1022)) :: [])))))))))))
+
+
+(** val sqrt : Float64.t -> Float64.t **)
+
+let sqrt = Float64.sqrt
+
+(** val opp : Float64.t -> Float64.t **)
+
+let opp = Float64.opp
+
+(** val mul : Float64.t -> Float64.t -> Float64.t **)
+
+let mul = Float64.mul
+
+(** val sub : Float64.t -> Float64.t -> Float64.t **)
+
+let sub = Float64.sub
+
+(** val div : Float64.t -> Float64.t -> Float64.t **)
+
+let div = Float64.div
+
+(** val discr : Float64.t -> Float64.t -> Float64.t -> Float64.t **)
+
+let discr a b c =
+  sub (mul b b) (mul (mul (Float64.of_float (0x1p+2)) a) c)
+
+(** val x1 : Float64.t -> Float64.t -> Float64.t -> Float64.t **)
+
+let x1 a b c =
+  div (sub (opp b) (sqrt (discr a b c))) (mul (Float64.of_float (0x1p+1)) a)
+
diff --git a/test-suite/output/FloatExtraction.v b/test-suite/output/FloatExtraction.v
new file mode 100644
index 0000000000..f296e8e871
--- /dev/null
+++ b/test-suite/output/FloatExtraction.v
@@ -0,0 +1,33 @@
+(************************************************************************)
+(*         *   The Coq Proof Assistant / The Coq Development Team       *)
+(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
+(* <O___,, *       (see CREDITS file for the list of authors)           *)
+(*   \VV/  **************************************************************)
+(*    //   *    This file is distributed under the terms of the         *)
+(*         *     GNU Lesser General Public License Version 2.1          *)
+(*         *     (see LICENSE file for the text of the license)         *)
+(************************************************************************)
+
+Require Import Floats ExtrOCamlFloats.
+
+Require Import List. Import ListNotations.
+
+(* from Require Import ExtrOcamlBasic. *)
+Extract Inductive list => list [ "[]" "( :: )" ].
+
+Local Open Scope float_scope.
+
+(* Avoid exponents with less than three digits as they are usually
+   displayed with two digits (1e7 is displayed 1e+07) except on
+   Windows where three digits are used (1e+007). *)
+Definition list_floats :=
+  [nan; infinity; neg_infinity; zero; one; two;
+   0.5; 0.01; -0.5; -0.01; 1.7e+308; -1.7e-308].
+
+Recursive Extraction list_floats.
+
+Definition discr a b c := b * b - 4.0 * a * c.
+
+Definition x1 a b c := (- b - sqrt (discr a b c)) / (2.0 * a).
+
+Recursive Extraction x1.
diff --git a/test-suite/output/FloatSyntax.out b/test-suite/output/FloatSyntax.out
new file mode 100644
index 0000000000..668a55977d
--- /dev/null
+++ b/test-suite/output/FloatSyntax.out
@@ -0,0 +1,40 @@
+2%float
+     : float
+2.5%float
+     : float
+(-2.5)%float
+     : float
+2.4999999999999999e+123%float
+     : float
+(-2.5000000000000001e-123)%float
+     : float
+(2 + 2)%float
+     : float
+(2.5 + 2.5)%float
+     : float
+2
+     : float
+2.5
+     : float
+-2.5
+     : float
+2.4999999999999999e+123
+     : float
+-2.5000000000000001e-123
+     : float
+2 + 2
+     : float
+2.5 + 2.5
+     : float
+2
+     : nat
+2%float
+     : float
+t = 2%flt
+     : float
+t = 2%flt
+     : float
+2
+     : nat
+2
+     : float
diff --git a/test-suite/output/FloatSyntax.v b/test-suite/output/FloatSyntax.v
new file mode 100644
index 0000000000..85f611352c
--- /dev/null
+++ b/test-suite/output/FloatSyntax.v
@@ -0,0 +1,37 @@
+Require Import Floats.
+
+Check 2%float.
+Check 2.5%float.
+Check (-2.5)%float.
+(* Avoid exponents with less than three digits as they are usually
+   displayed with two digits (1e7 is displayed 1e+07) except on
+   Windows where three digits are used (1e+007). *)
+Check 2.5e123%float.
+Check (-2.5e-123)%float.
+Check (2 + 2)%float.
+Check (2.5 + 2.5)%float.
+
+Open Scope float_scope.
+
+Check 2.
+Check 2.5.
+Check (-2.5).
+Check 2.5e123.
+Check (-2.5e-123).
+Check (2 + 2).
+Check (2.5 + 2.5).
+
+Open Scope nat_scope.
+
+Check 2.
+Check 2%float.
+
+Delimit Scope float_scope with flt.
+Definition t := 2%float.
+Print t.
+Delimit Scope nat_scope with float.
+Print t.
+Check 2.
+Close Scope nat_scope.
+Check 2.
+Close Scope float_scope.