Floating-Point: multi-rounding model

1b24d75d · MARCHE Claude · 3fb5845a · 1b24d75d · 1b24d75d · 1b24d75d
Commit 1b24d75d authored Jun 18, 2012 by MARCHE Claude
--- a/Makefile.in
+++ b/Makefile.in
@@ -887,7 +887,7 @@ COQLIBS_NUMBER_FILES = Divisibility Gcd Parity Prime
 COQLIBS_NUMBER = $(addprefix lib/coq/number/, $(COQLIBS_NUMBER_FILES))

 ifeq (@enable_coq_fp_libs@,yes)
-COQLIBS_FP_FILES = Rounding Single Double
+COQLIBS_FP_FILES = Rounding SingleFormat Single DoubleFormat Double
 COQLIBS_FP_ALL_FILES = GenFloat $(COQLIBS_FP_FILES)
 COQLIBS_FP = $(addprefix lib/coq/floating_point/, $(COQLIBS_FP_ALL_FILES))
 endif

--- a/drivers/gappa.drv
+++ b/drivers/gappa.drv
@@ -167,6 +167,16 @@ theory real.FromInt

 end

+theory floating_point.Rounding
+
+  syntax function NearestTiesToEven "ne"
+  syntax function ToZero "zr"
+  syntax function Up "up"
+  syntax function Down "dn"
+  syntax function NearestTiesToAway "na"
+
+end
+
 theory floating_point.Single

  syntax function round "float<ieee_32,%1>(%2)"
@@ -181,15 +191,22 @@ theory floating_point.Double

 end

-theory floating_point.Rounding
+(*
+theory floating_point.SingleMultiRounding

-  syntax function NearestTiesToEven "ne"
-  syntax function ToZero "zr"
-  syntax function Up "up"
-  syntax function Down "dn"
-  syntax function NearestTiesToAway "na"
+  syntax function round "float<ieee_32,%1>(%2)"
+  meta "instantiate : auto" prop Bounded_value

 end
+*)
+
+theory floating_point.DoubleMultiRounding
+
+  syntax function round "float<ieee_64,%1>(%2)"
+  meta "instantiate : auto" prop Bounded_value
+
+end
+

 (*
 Local Variables:

--- a/examples/bts/12475/why3session.xml
+++ b/examples/bts/12475/why3session.xml
 <?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE why3session SYSTEM "/home/cmarche/recherche/why3/share/why3session.dtd">
+<!DOCTYPE why3session SYSTEM "/home/marche/why3/share/why3session.dtd">
 <why3session
 name="bts/12475/why3session.xml">
 <prover
@@ -34,7 +34,7 @@
    name="toto"
    locfile="bts/12475/../12475.why"
    loclnum="6" loccnumb="7" loccnume="11"
-    sum="1528698e7ee515779e096133af624d2f"
+    sum="07763c823feaf262c263cca6378f25f1"
    proved="true"
    expanded="true"
    shape="ainfix &lt;V0ainfix +aroundaUpV0c1.F">
@@ -44,7 +44,7 @@
     memlimit="0"
     obsolete="false"
     archived="false">
-     <result status="valid" time="0.02"/>
+     <result status="valid" time="0.01"/>
    </proof>
    <proof
     prover="1"
@@ -52,7 +52,7 @@
     memlimit="0"
     obsolete="false"
     archived="false">
-     <result status="valid" time="0.03"/>
+     <result status="valid" time="0.00"/>
    </proof>
    <proof
     prover="0"
@@ -68,7 +68,7 @@
     memlimit="0"
     obsolete="false"
     archived="false">
-     <result status="unknown" time="0.01"/>
+     <result status="unknown" time="0.00"/>
    </proof>
   </goal>
  </theory>

--- a/examples/check-builtin/floats/why3session.xml
+++ b/examples/check-builtin/floats/why3session.xml
 <?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE why3session SYSTEM "/home/cmarche/recherche/why3/share/why3session.dtd">
+<!DOCTYPE why3session SYSTEM "/home/marche/why3/share/why3session.dtd">
 <why3session
 name="check-builtin/floats/why3session.xml">
 <prover
@@ -32,7 +32,7 @@
    name="Round_single_01"
    locfile="check-builtin/floats/../floats.why"
    loclnum="11" loccnumb="7" loccnume="22"
-    sum="3242b4e9102c2fc37a9a7dd6cfd10efa"
+    sum="397906d94bbb0b5341288dfce84f89dc"
    proved="true"
    expanded="true"
    shape="ainfix =aroundaNearestTiesToEvenc0.1c0x1.99999ap-4">
@@ -49,7 +49,7 @@
    name="Round_double_01"
    locfile="check-builtin/floats/../floats.why"
    loclnum="14" loccnumb="7" loccnume="22"
-    sum="95147a77cfc066399edef8befff58feb"
+    sum="35b08355e175d22b4d9ab4c1c827526f"
    proved="true"
    expanded="true"
    shape="ainfix =aroundaNearestTiesToEvenc0.1c0x1.999999999999ap-4">
@@ -66,7 +66,7 @@
    name="Test00"
    locfile="check-builtin/floats/../floats.why"
    loclnum="17" loccnumb="8" loccnume="14"
-    sum="f04ce085ad30e1fb1b6594cd78d977bd"
+    sum="e45b8dc86a2bf34e6b3beb8b8a8a720e"
    proved="true"
    expanded="true"
    shape="ainfix &lt;=aprefix -c3.0V0Iainfix &lt;=aabsV0c2.0F">
@@ -76,7 +76,7 @@
     memlimit="0"
     obsolete="false"
     archived="false">
-     <result status="valid" time="0.06"/>
+     <result status="valid" time="0.02"/>
    </proof>
    <proof
     prover="1"
@@ -84,7 +84,7 @@
     memlimit="0"
     obsolete="false"
     archived="false">
-     <result status="valid" time="0.04"/>
+     <result status="valid" time="0.01"/>
    </proof>
    <proof
     prover="0"
@@ -92,7 +92,7 @@
     memlimit="0"
     obsolete="false"
     archived="false">
-     <result status="valid" time="0.00"/>
+     <result status="valid" time="0.01"/>
    </proof>
    <proof
     prover="2"
@@ -107,7 +107,7 @@
    name="Test01"
    locfile="check-builtin/floats/../floats.why"
    loclnum="19" loccnumb="8" loccnume="14"
-    sum="512a97ac8833620d3c1fe4338f5109c6"
+    sum="ebff461c0eb487a4284b1d316905f8a2"
    proved="true"
    expanded="true"
    shape="ainfix &lt;=aabsainfix -ainfix *avalueV0avalueV0aroundaNearestTiesToEvenainfix *avalueV0avalueV0c0x1.p-52Iainfix &lt;=avalueV0c2.0Aainfix &lt;=aprefix -c2.0avalueV0F">
@@ -117,14 +117,14 @@
     memlimit="0"
     obsolete="false"
     archived="false">
-     <result status="valid" time="0.01"/>
+     <result status="valid" time="0.00"/>
    </proof>
   </goal>
   <goal
    name="Test02"
    locfile="check-builtin/floats/../floats.why"
    loclnum="25" loccnumb="8" loccnume="14"
-    sum="303330d34dd6e52d73fcdcc7f34319f3"
+    sum="10d968c72c3f3e64f89fa7904576ed89"
    proved="true"
    expanded="true"
    shape="ainfix &lt;=aabsainfix -ainfix *avalueV1avalueV1aroundaNearestTiesToEvenainfix *avalueV0avalueV0c0x1.p-52Iainfix =V1V0Iainfix &lt;=aabsavalueV0c2.0F">
@@ -134,14 +134,14 @@
     memlimit="0"
     obsolete="false"
     archived="false">
-     <result status="valid" time="0.01"/>
+     <result status="valid" time="0.00"/>
    </proof>
   </goal>
   <goal
    name="Test03"
    locfile="check-builtin/floats/../floats.why"
    loclnum="32" loccnumb="8" loccnume="14"
-    sum="2d6c2d43256f71efff7bd2e63cb3541e"
+    sum="07cb638f137dc0341ef32cb3e91c11fc"
    proved="true"
    expanded="true"
    shape="ainfix &lt;=asqrtainfix *ainfix -avalueV2ainfix *avalueV0avalueV0ainfix -avalueV1ainfix *avalueV0avalueV0c0x1.p-52Iainfix =V2V1Iainfix =avalueV1aroundaNearestTiesToEvenainfix *avalueV0avalueV0Iainfix &lt;=aabsavalueV0c2.0F">
@@ -151,7 +151,7 @@
     memlimit="0"
     obsolete="false"
     archived="false">
-     <result status="valid" time="0.01"/>
+     <result status="valid" time="0.00"/>
    </proof>
   </goal>
  </theory>

--- a/examples/my_cosine/my_cosine_CosineSingle_MethodError_1.v
+++ b/examples/my_cosine/my_cosine_CosineSingle_MethodError_1.v
@@ -13,8 +13,9 @@ Require int.Int.
 Require real.Square.
 Require floating_point.Rounding.
 Require floating_point.Single.
-Axiom Pi_interval : ((314159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196 / 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)%R <  PI)%R /\
-  (PI <  (314159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038197 / 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)%R)%R.
+
+Axiom Pi_interval : ((314159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196 / 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)%R < PI)%R /\
+  (PI < (314159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038197 / 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)%R)%R.

 Axiom Cos_plus_pi : forall (x:R),
  ((Rtrigo_def.cos (x + PI)%R) = (-(Rtrigo_def.cos x))%R).
@@ -41,19 +42,18 @@ Axiom Sin_sum : forall (x:R) (y:R),

 Parameter atan: R -> R.

-
 Axiom Tan_atan : forall (x:R), ((Rtrigo.tan (atan x)) = x).

-(* YOU MAY EDIT THE CONTEXT BELOW *)
+Parameter single : Type.
+
 Require Import Interval_tactic.
-(* DO NOT EDIT BELOW *)

+(* Why3 goal *)
 Theorem MethodError : forall (x:R), ((Rabs x) <= (1 / 32)%R)%R ->
  ((Rabs ((1%R - ((05 / 10)%R * (x * x)%R)%R)%R - (Rtrigo_def.cos x))%R) <= (1 / 16777216)%R)%R.
 (* YOU MAY EDIT THE PROOF BELOW *)
 intros x H.
 interval with (i_bisect_diff x).
 Qed.
-(* DO NOT EDIT BELOW *)


--- a/examples/my_cosine/why3session.xml
+++ b/examples/my_cosine/why3session.xml
@@ -28,7 +28,7 @@
    name="MethodError"
    locfile="examples/my_cosine/../my_cosine.why"
    loclnum="13" loccnumb="6" loccnume="17"
-    sum="2467a67484295345557f0076ed412561"
+    sum="5654505132d0df95fb8d98d86e9154f0"
    proved="true"
    expanded="true"
    shape="ainfix &lt;=aabsainfix -ainfix -c1.0ainfix *c0.5ainfix *V0V0acosV0c0x1.p-24Iainfix &lt;=aabsV0c0x1.p-5F">
@@ -39,14 +39,14 @@
     edited="my_cosine_CosineSingle_MethodError_1.v"
     obsolete="false"
     archived="false">
-     <result status="valid" time="3.77"/>
+     <result status="valid" time="3.68"/>
    </proof>
   </goal>
   <goal
    name="TotalErrorFullyExpanded"
    locfile="examples/my_cosine/../my_cosine.why"
    loclnum="20" loccnumb="6" loccnume="29"
-    sum="16c317808f261ff9cc5b16296167cd8b"
+    sum="b272d2bbaa334f583a44d792f1e66da2"
    proved="true"
    expanded="true"
    shape="ainfix &lt;=aabsainfix -V3acosavalueV0c0x1.p-23Iainfix =V3aroundaNearestTiesToEvenainfix -c1.0V2Iainfix =V2aroundaNearestTiesToEvenainfix *c0.5V1Iainfix =V1aroundaNearestTiesToEvenainfix *avalueV0avalueV0FIainfix &lt;=aabsainfix -ainfix -c1.0ainfix *c0.5ainfix *avalueV0avalueV0acosavalueV0c0x1.p-24Iainfix &lt;=aabsavalueV0c0x1.p-5F">
@@ -56,14 +56,14 @@
     memlimit="0"
     obsolete="false"
     archived="false">
-     <result status="valid" time="0.01"/>
+     <result status="valid" time="0.00"/>
    </proof>
   </goal>
   <goal
    name="TotalErrorExpanded"
    locfile="examples/my_cosine/../my_cosine.why"
    loclnum="31" loccnumb="6" loccnume="24"
-    sum="fe418525d8a2ed9a3cc54a44066dff60"
+    sum="e8eb30517031d5f9aa29e249a13fcaaf"
    proved="true"
    expanded="true"
    shape="LaroundaNearestTiesToEvenainfix *avalueV0avalueV0LaroundaNearestTiesToEvenainfix *c0.5V1LaroundaNearestTiesToEvenainfix -c1.0V2ainfix &lt;=aabsainfix -V3acosavalueV0c0x1.p-23Iainfix &lt;=aabsavalueV0c0x1.p-5F">
@@ -73,14 +73,14 @@
     memlimit="0"
     obsolete="false"
     archived="false">
-     <result status="valid" time="1.22"/>
+     <result status="valid" time="0.82"/>
    </proof>
   </goal>
   <goal
    name="TotalError"
    locfile="examples/my_cosine/../my_cosine.why"
    loclnum="51" loccnumb="6" loccnume="16"
-    sum="967dbbbd6b72c88306fbf58d0d697b15"
+    sum="0457c10047c2e650ca89f0b4f6c924e4"
    proved="true"
    expanded="true"
    shape="Lacos_singleV0ainfix &lt;=aabsainfix -avalueV1acosavalueV0c0x1.p-23Iainfix &lt;=aabsavalueV0c0x1.p-5F">
@@ -90,7 +90,7 @@
     memlimit="0"
     obsolete="false"
     archived="false">
-     <result status="valid" time="4.56"/>
+     <result status="valid" time="3.13"/>
    </proof>
   </goal>
  </theory>

--- a/examples/programs/my_cosine/my_cosine_M_WP_parameter_my_cosine_1.v
+++ b/examples/programs/my_cosine/my_cosine_M_WP_parameter_my_cosine_1.v
@@ -6,33 +6,35 @@ Require Import Rbasic_fun.
 Require Import R_sqrt.
 Require Import Rtrigo.
 Require Import AltSeries. (* for def of pi *)
-Require int.Int.
 Require real.Real.
+Require real.RealInfix.
 Require real.Abs.
 Require real.FromInt.
+Require int.Int.
 Require real.Square.
 Require floating_point.Rounding.
 Require floating_point.Single.
+
+(* Why3 assumption *)
 Definition unit  := unit.

 Parameter qtmark : Type.

 Parameter at1: forall (a:Type), a -> qtmark -> a.
-
 Implicit Arguments at1.

 Parameter old: forall (a:Type), a -> a.
-
 Implicit Arguments old.

+(* Why3 assumption *)
 Definition implb(x:bool) (y:bool): bool := match (x,
  y) with
  | (true, false) => false
  | (_, _) => true
  end.

-Axiom Pi_interval : ((314159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196 / 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)%R <  PI)%R /\
-  (PI <  (314159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038197 / 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)%R)%R.
+Axiom Pi_interval : ((314159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196 / 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)%R < PI)%R /\
+  (PI < (314159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038197 / 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)%R)%R.

 Axiom Cos_plus_pi : forall (x:R),
  ((Rtrigo_def.cos (x + PI)%R) = (-(Rtrigo_def.cos x))%R).
@@ -59,15 +61,12 @@ Axiom Sin_sum : forall (x:R) (y:R),

 Parameter atan: R -> R.

-
 Axiom Tan_atan : forall (x:R), ((Rtrigo.tan (atan x)) = x).

-(* YOU MAY EDIT THE CONTEXT BELOW *)
-
 Require Import Interval_tactic.

-(* DO NOT EDIT BELOW *)

+(* Why3 goal *)
 Theorem WP_parameter_my_cosine : forall (x:floating_point.Single.single),
  ((Rabs (floating_point.Single.value x)) <= (1 / 32)%R)%R ->
  ((Rabs ((1%R - (((floating_point.Single.value x) * (floating_point.Single.value x))%R * (05 / 10)%R)%R)%R - (Rtrigo_def.cos (floating_point.Single.value x)))%R) <= (1 / 16777216)%R)%R.
@@ -75,6 +74,5 @@ Theorem WP_parameter_my_cosine : forall (x:floating_point.Single.single),
 intros x H.
 interval with (i_bisect_diff (Single.value x)).
 Qed.
-(* DO NOT EDIT BELOW *)


--- a/examples/programs/my_cosine/why3session.xml
+++ b/examples/programs/my_cosine/why3session.xml
 <?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE why3session SYSTEM "/usr/local/share/why3/why3session.dtd">
+<!DOCTYPE why3session SYSTEM "/home/marche/why3/share/why3session.dtd">
 <why3session
 name="examples/programs/my_cosine/why3session.xml">
 <prover
@@ -25,7 +25,7 @@
    locfile="examples/programs/my_cosine/../my_cosine.mlw"
    loclnum="30" loccnumb="4" loccnume="13"
    expl="parameter my_cosine"
-    sum="8c5ef4e174040dfc2edbec12b7ad11c9"
+    sum="43a387020a8494975293041bea91d995"
    proved="true"
    expanded="true"
    shape="ainfix &lt;=.aabsainfix -.avalueV5acosavalueV0c0x1.p-23Iainfix =avalueV5aroundaNearestTiesToEvenainfix -.avalueV1avalueV4FAainfix &lt;=aabsaroundaNearestTiesToEvenainfix -.avalueV1avalueV4amax_singleIainfix =avalueV4aroundaNearestTiesToEvenainfix *.avalueV2avalueV3FAainfix &lt;=aabsaroundaNearestTiesToEvenainfix *.avalueV2avalueV3amax_singleIainfix =avalueV3c0.5FIainfix =avalueV2aroundaNearestTiesToEvenainfix *.avalueV0avalueV0FAainfix &lt;=aabsaroundaNearestTiesToEvenainfix *.avalueV0avalueV0amax_singleIainfix =avalueV1c1.0FAainfix &lt;=.aabsainfix -.ainfix -.c1.0ainfix *.ainfix *.avalueV0avalueV0c0.5acosavalueV0c0x1.p-24Iainfix &lt;=.aabsavalueV0c0x1.p-5F">
@@ -40,7 +40,7 @@
      locfile="examples/programs/my_cosine/../my_cosine.mlw"
      loclnum="30" loccnumb="4" loccnume="13"
      expl="assertion"
-      sum="f19d8615cb5c434b8497ae0d46cb1e88"
+      sum="1847af31ffb0fc79bb3f99eb48677194"
      proved="true"
      expanded="true"
      shape="ainfix &lt;=.aabsainfix -.ainfix -.c1.0ainfix *.ainfix *.avalueV0avalueV0c0.5acosavalueV0c0x1.p-24Iainfix &lt;=.aabsavalueV0c0x1.p-5F">
@@ -48,12 +48,12 @@
       name="expl:parameter my_cosine"/>
      <proof
       prover="0"
-       timelimit="12"
-       memlimit="0"
+       timelimit="5"
+       memlimit="1000"
       edited="my_cosine_M_WP_parameter_my_cosine_1.v"
       obsolete="false"
       archived="false">
-       <result status="valid" time="3.69"/>
+       <result status="valid" time="3.58"/>
      </proof>
     </goal>
     <goal
@@ -61,7 +61,7 @@
      locfile="examples/programs/my_cosine/../my_cosine.mlw"
      loclnum="30" loccnumb="4" loccnume="13"
      expl="precondition"
-      sum="13fda2c30862d2282aa50e9f3aed5e61"
+      sum="ed7fd59f8e3662b57ab5ff723e124166"
      proved="true"
      expanded="true"
      shape="ainfix &lt;=aabsaroundaNearestTiesToEvenainfix *.avalueV0avalueV0amax_singleIainfix =avalueV1c1.0FIainfix &lt;=.aabsainfix -.ainfix -.c1.0ainfix *.ainfix *.avalueV0avalueV0c0.5acosavalueV0c0x1.p-24Iainfix &lt;=.aabsavalueV0c0x1.p-5F">
@@ -81,7 +81,7 @@
      locfile="examples/programs/my_cosine/../my_cosine.mlw"
      loclnum="30" loccnumb="4" loccnume="13"
      expl="precondition"
-      sum="83faf9aa4fd66bb3090a0e3a03bfb095"
+      sum="01c28821422107c03234edd2f723d53e"
      proved="true"
      expanded="true"
      shape="ainfix &lt;=aabsaroundaNearestTiesToEvenainfix *.avalueV2avalueV3amax_singleIainfix =avalueV3c0.5FIainfix =avalueV2aroundaNearestTiesToEvenainfix *.avalueV0avalueV0FIainfix &lt;=aabsaroundaNearestTiesToEvenainfix *.avalueV0avalueV0amax_singleIainfix =avalueV1c1.0FIainfix &lt;=.aabsainfix -.ainfix -.c1.0ainfix *.ainfix *.avalueV0avalueV0c0.5acosavalueV0c0x1.p-24Iainfix &lt;=.aabsavalueV0c0x1.p-5F">
@@ -101,7 +101,7 @@
      locfile="examples/programs/my_cosine/../my_cosine.mlw"
      loclnum="30" loccnumb="4" loccnume="13"
      expl="precondition"
-      sum="c2a58280312e1542c64994f3bab49f6b"
+      sum="d30950e1e41f800ca0172d07dda83ad4"
      proved="true"
      expanded="true"
      shape="ainfix &lt;=aabsaroundaNearestTiesToEvenainfix -.avalueV1avalueV4amax_singleIainfix =avalueV4aroundaNearestTiesToEvenainfix *.avalueV2avalueV3FIainfix &lt;=aabsaroundaNearestTiesToEvenainfix *.avalueV2avalueV3amax_singleIainfix =avalueV3c0.5FIainfix =avalueV2aroundaNearestTiesToEvenainfix *.avalueV0avalueV0FIainfix &lt;=aabsaroundaNearestTiesToEvenainfix *.avalueV0avalueV0amax_singleIainfix =avalueV1c1.0FIainfix &lt;=.aabsainfix -.ainfix -.c1.0ainfix *.ainfix *.avalueV0avalueV0c0.5acosavalueV0c0x1.p-24Iainfix &lt;=.aabsavalueV0c0x1.p-5F">
@@ -121,7 +121,7 @@
      locfile="examples/programs/my_cosine/../my_cosine.mlw"
      loclnum="30" loccnumb="4" loccnume="13"
      expl="normal postcondition"
-      sum="fb20bbbd761cb5dae33e358483e311a4"
+      sum="2eafda4f7656e405bda4587b4c59ab3c"
      proved="true"
      expanded="true"
      shape="ainfix &lt;=.aabsainfix -.avalueV5acosavalueV0c0x1.p-23Iainfix =avalueV5aroundaNearestTiesToEvenainfix -.avalueV1avalueV4FIainfix &lt;=aabsaroundaNearestTiesToEvenainfix -.avalueV1avalueV4amax_singleIainfix =avalueV4aroundaNearestTiesToEvenainfix *.avalueV2avalueV3FIainfix &lt;=aabsaroundaNearestTiesToEvenainfix *.avalueV2avalueV3amax_singleIainfix =avalueV3c0.5FIainfix =avalueV2aroundaNearestTiesToEvenainfix *.avalueV0avalueV0FIainfix &lt;=aabsaroundaNearestTiesToEvenainfix *.avalueV0avalueV0amax_singleIainfix =avalueV1c1.0FIainfix &lt;=.aabsainfix -.ainfix -.c1.0ainfix *.ainfix *.avalueV0avalueV0c0.5acosavalueV0c0x1.p-24Iainfix &lt;=.aabsavalueV0c0x1.p-5F">

--- a/examples/tests-provers/gappa/why3session.xml
+++ b/examples/tests-provers/gappa/why3session.xml
 <?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE why3session SYSTEM "/home/cmarche/recherche/why3/share/why3session.dtd">
+<!DOCTYPE why3session SYSTEM "/home/marche/why3/share/why3session.dtd">
 <why3session
 name="tests-provers/gappa/why3session.xml">
 <prover
@@ -20,7 +20,7 @@
    name="Round_single_01"
    locfile="tests-provers/gappa/../gappa.why"
    loclnum="11" loccnumb="8" loccnume="23"
-    sum="3242b4e9102c2fc37a9a7dd6cfd10efa"
+    sum="397906d94bbb0b5341288dfce84f89dc"
    proved="true"
    expanded="false"
    shape="ainfix =aroundaNearestTiesToEvenc0.1c0x1.99999ap-4">
@@ -37,7 +37,7 @@
    name="Round_double_01"
    locfile="tests-provers/gappa/../gappa.why"
    loclnum="14" loccnumb="8" loccnume="23"
-    sum="d39bb272fc8d9297bec1df1e1fb1106a"
+    sum="1e27690968c7f98982dcf973be229e14"
    proved="true"
    expanded="false"
    shape="ainfix =aroundaNearestTiesToEvenc0.1c0x1.999999999999ap-4">
@@ -54,7 +54,7 @@
    name="Test00"
    locfile="tests-provers/gappa/../gappa.why"
    loclnum="17" loccnumb="9" loccnume="15"
-    sum="9ebac93d6a57654f3787929bdc703aaf"
+    sum="f9eacb01a4307782d62d79a7cf147491"
    proved="true"
    expanded="false"
    shape="ainfix &lt;=aprefix -c3.0V0Iainfix &lt;=aabsV0c2.0F">
@@ -64,14 +64,14 @@
     memlimit="1000"
     obsolete="false"
     archived="false">
-     <result status="valid" time="0.01"/>
+     <result status="valid" time="0.00"/>
    </proof>
   </goal>
   <goal
    name="Test01"
    locfile="tests-provers/gappa/../gappa.why"
    loclnum="19" loccnumb="9" loccnume="15"
-    sum="bf409087a884fe327065f5dbc2eb0d4d"
+    sum="fb50504a077e11b75a2da8e2febba4b7"
    proved="true"
    expanded="false"
    shape="ainfix &lt;=aabsainfix -ainfix *avalueV0avalueV0aroundaNearestTiesToEvenainfix *avalueV0avalueV0c0x1.p-52Iainfix &lt;=avalueV0c2.0Aainfix &lt;=aprefix -c2.0avalueV0F">
@@ -81,14 +81,14 @@
     memlimit="1000"
     obsolete="false"
     archived="false">
-     <result status="valid" time="0.01"/>
+     <result status="valid" time="0.00"/>
    </proof>
   </goal>
   <goal
    name="Test02"
    locfile="tests-provers/gappa/../gappa.why"
    loclnum="25" loccnumb="9" loccnume="15"
-    sum="8feed07428304f0920d7f41124c883b3"
+    sum="14d6ea8815c6984e17fbf9f76ac012eb"
    proved="true"
    expanded="false"
    shape="ainfix &lt;=aabsainfix -ainfix *avalueV1avalueV1aroundaNearestTiesToEvenainfix *avalueV0avalueV0c0x1.p-52Iainfix =V1V0Iainfix &lt;=aabsavalueV0c2.0F">
@@ -98,14 +98,14 @@
     memlimit="1000"
     obsolete="false"
     archived="false">
-     <result status="valid" time="0.01"/>
+     <result status="valid" time="0.00"/>
    </proof>
   </goal>
   <goal
    name="Test03"
    locfile="tests-provers/gappa/../gappa.why"
    loclnum="32" loccnumb="9" loccnume="15"
-    sum="0da33f7c98ccd09c0d1e66fd78e72212"
+    sum="49f4cde6219c2d0ed441a51b636026e1"
    proved="true"
    expanded="false"
    shape="ainfix &lt;=asqrtainfix *ainfix -avalueV2ainfix *avalueV0avalueV0ainfix -avalueV1ainfix *avalueV0avalueV0c0x1.p-52Iainfix =V2V1Iainfix =avalueV1aroundaNearestTiesToEvenainfix *avalueV0avalueV0Iainfix &lt;=aabsavalueV0c2.0F">
@@ -115,7 +115,7 @@
     memlimit="1000"
     obsolete="false"
     archived="false">
-     <result status="valid" time="0.01"/>
+     <result status="valid" time="0.00"/>
    </proof>
   </goal>
  </theory>
@@ -129,7 +129,7 @@
    name="Test1"
    locfile="tests-provers/gappa/../gappa.why"
    loclnum="53" loccnumb="8" loccnume="13"
-    sum="33c71394fca93d3d410fb722fcb970b5"
+    sum="76814dc6e642481127875db73c1d2aba"
    proved="true"
    expanded="false"
    shape="ainfix &lt;=aabsainfix -avalueaac0.1c0x1.p-53Iainfix =aaarIainfix =avalueararoundaNearestTiesToEvenc0.1">
@@ -146,7 +146,7 @@
    name="Test2"
    locfile="tests-provers/gappa/../gappa.why"
    loclnum="58" loccnumb="8" loccnume="13"
-    sum="65602af0f639b8cea8843b1fc07542b7"
+    sum="a4abf368f1add9e3c8814776fd5d6011"
    proved="true"
    expanded="false"
    shape="ainfix &lt;=aabsainfix -avalueafc0c0.1c0x1.p-53Iainfix =afc0arIainfix =avalueararoundaNearestTiesToEvenc0.1">
@@ -156,14 +156,14 @@
     memlimit="1000"
     obsolete="false"
     archived="false">
-     <result status="valid" time="0.01"/>
+     <result status="valid" time="0.00"/>
    </proof>
   </goal>
   <goal
    name="Test3"
    locfile="tests-provers/gappa/../gappa.why"
    loclnum="63" loccnumb="8" loccnume="13"
-    sum="1764bc962492b20b5ca636eea0acb2b5"
+    sum="78fbf11d146c5e828a60bad7789bc85a"
    proved="true"
    expanded="false"
    shape="ainfix &lt;=aabsainfix -avalueagc0c1c0.1c0x1.p-53Iainfix =agc0c1arIainfix =avalueararoundaNearestTiesToEvenc0.1">
@@ -173,7 +173,7 @@
     memlimit="1000"
     obsolete="false"
     archived="false">
-     <result status="valid" time="0.02"/>
+     <result status="valid" time="0.00"/>
    </proof>
   </goal>
  </theory>
@@ -187,7 +187,7 @@
    name="G1"
    locfile="tests-provers/gappa/../gappa.why"
    loclnum="89" loccnumb="7" loccnume="9"
-    sum="f0532ec1f07ee528e1c4ad329cbd2426"
+    sum="5830193d59ffa5b88f451863e4d6161c"
    proved="true"
    expanded="true"
    shape="ainfix &lt;=ainfix -avaluearesultainfix *avalueaq1avalueaq2c0x1.p-52">
@@ -204,7 +204,7 @@
    name="G2"
    locfile="tests-provers/gappa/../gappa.why"
    loclnum="91" loccnumb="7" loccnume="9"
-    sum="76fd08ebf94a56233e552dcc7ba63305"
+    sum="4ecf70457e24cf2f84fc2ba52e7b1184"
    proved="true"
    expanded="true"
    shape="ainfix &lt;=ainfix -avalueV0ainfix *avalueaq1avalueaq2c0x1.p-52Iainfix =V0aresultF">
@@ -221,7 +221,7 @@
    name="G3"
    locfile="tests-provers/gappa/../gappa.why"
    loclnum="94" loccnumb="7" loccnume="9"
-    sum="147725714d029b09fa91b96558079798"
+    sum="4ffa5eddd14694f5c2cf635063c5b843"
    proved="true"
    expanded="true"
    shape="ainfix &lt;=ainfix -avalueV0ainfix *avalueaq1avalueaq2c0x1.p-52Iainfix =V0aresultF">
@@ -231,7 +231,7 @@
     memlimit="1000"
     obsolete="false"
     archived="false">
-     <result status="valid" time="0.01"/>
+     <result status="valid" time="0.00"/>
    </proof>
   </goal>
  </theory>

--- a/lib/coq/floating_point/Double.v
+++ b/lib/coq/floating_point/Double.v
@@ -8,44 +8,43 @@ Require real.Real.
 Require real.Abs.
 Require real.FromInt.
 Require floating_point.Rounding.
+Require floating_point.DoubleFormat.

 Require Import floating_point.GenFloat.

-(* Why3 goal *)
-Definition double : Type.