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-rw-r--r--gcc/ada/libgnat/s-widthi.adb131
1 files changed, 0 insertions, 131 deletions
diff --git a/gcc/ada/libgnat/s-widthi.adb b/gcc/ada/libgnat/s-widthi.adb
index 9595790..c66d662 100644
--- a/gcc/ada/libgnat/s-widthi.adb
+++ b/gcc/ada/libgnat/s-widthi.adb
@@ -29,109 +29,9 @@
-- --
------------------------------------------------------------------------------
-with Ada.Numerics.Big_Numbers.Big_Integers_Ghost;
-use Ada.Numerics.Big_Numbers.Big_Integers_Ghost;
-
function System.Width_I (Lo, Hi : Int) return Natural is
-
- -- Ghost code, loop invariants and assertions in this unit are meant for
- -- analysis only, not for run-time checking, as it would be too costly
- -- otherwise. This is enforced by setting the assertion policy to Ignore.
-
- pragma Assertion_Policy (Ghost => Ignore,
- Loop_Invariant => Ignore,
- Assert => Ignore);
-
- -----------------------
- -- Local Subprograms --
- -----------------------
-
- package Signed_Conversion is new Signed_Conversions (Int => Int);
-
- function Big (Arg : Int) return Big_Integer renames
- Signed_Conversion.To_Big_Integer;
-
- -- Maximum value of exponent for 10 that fits in Uns'Base
- function Max_Log10 return Natural is
- (case Int'Base'Size is
- when 8 => 2,
- when 16 => 4,
- when 32 => 9,
- when 64 => 19,
- when 128 => 38,
- when others => raise Program_Error)
- with Ghost;
-
- ------------------
- -- Local Lemmas --
- ------------------
-
- procedure Lemma_Lower_Mult (A, B, C : Big_Natural)
- with
- Ghost,
- Pre => A <= B,
- Post => A * C <= B * C;
-
- procedure Lemma_Div_Commutation (X, Y : Int)
- with
- Ghost,
- Pre => X >= 0 and Y > 0,
- Post => Big (X) / Big (Y) = Big (X / Y);
-
- procedure Lemma_Div_Twice (X : Big_Natural; Y, Z : Big_Positive)
- with
- Ghost,
- Post => X / Y / Z = X / (Y * Z);
-
- ----------------------
- -- Lemma_Lower_Mult --
- ----------------------
-
- procedure Lemma_Lower_Mult (A, B, C : Big_Natural) is null;
-
- ---------------------------
- -- Lemma_Div_Commutation --
- ---------------------------
-
- procedure Lemma_Div_Commutation (X, Y : Int) is null;
-
- ---------------------
- -- Lemma_Div_Twice --
- ---------------------
-
- procedure Lemma_Div_Twice (X : Big_Natural; Y, Z : Big_Positive) is
- XY : constant Big_Natural := X / Y;
- YZ : constant Big_Natural := Y * Z;
- XYZ : constant Big_Natural := X / Y / Z;
- R : constant Big_Natural := (XY rem Z) * Y + (X rem Y);
- begin
- pragma Assert (X = XY * Y + (X rem Y));
- pragma Assert (XY = XY / Z * Z + (XY rem Z));
- pragma Assert (X = XYZ * YZ + R);
- pragma Assert ((XY rem Z) * Y <= (Z - 1) * Y);
- pragma Assert (R <= YZ - 1);
- pragma Assert (X / YZ = (XYZ * YZ + R) / YZ);
- pragma Assert (X / YZ = XYZ + R / YZ);
- end Lemma_Div_Twice;
-
- -- Local variables
-
W : Natural;
T : Int;
-
- -- Local ghost variables
-
- Max_W : constant Natural := Max_Log10 with Ghost;
- Big_10 : constant Big_Integer := Big (10) with Ghost;
-
- Pow : Big_Integer := 1 with Ghost;
- T_Init : constant Int :=
- Int'Max (abs Int'Max (Lo, Int'First + 1),
- abs Int'Max (Hi, Int'First + 1))
- with Ghost;
-
--- Start of processing for System.Width_I
-
begin
if Lo > Hi then
return 0;
@@ -151,41 +51,10 @@ begin
-- Increase value if more digits required
while T >= 10 loop
- Lemma_Div_Commutation (T, 10);
- Lemma_Div_Twice (Big (T_Init), Big_10 ** (W - 2), Big_10);
-
T := T / 10;
W := W + 1;
- Pow := Pow * 10;
-
- pragma Loop_Invariant (T >= 0);
- pragma Loop_Invariant (W in 3 .. Max_W + 3);
- pragma Loop_Invariant (Pow = Big_10 ** (W - 2));
- pragma Loop_Invariant (Big (T) = Big (T_Init) / Pow);
- pragma Loop_Variant (Decreases => T);
end loop;
- declare
- F : constant Big_Positive := Big_10 ** (W - 2) with Ghost;
- Q : constant Big_Natural := Big (T_Init) / F with Ghost;
- R : constant Big_Natural := Big (T_Init) rem F with Ghost;
- begin
- pragma Assert (Q < Big_10);
- pragma Assert (Big (T_Init) = Q * F + R);
- Lemma_Lower_Mult (Q, Big (9), F);
- pragma Assert (Big (T_Init) <= Big (9) * F + F - 1);
- pragma Assert (Big (T_Init) < Big_10 * F);
- pragma Assert (Big_10 * F = Big_10 ** (W - 1));
- end;
-
- -- This is an expression of the functional postcondition for Width_I,
- -- which cannot be expressed readily as a postcondition as this would
- -- require making the instantiation Signed_Conversion and function Big
- -- available from the spec.
-
- pragma Assert (Big (Int'Max (Lo, Int'First + 1)) < Big_10 ** (W - 1));
- pragma Assert (Big (Int'Max (Hi, Int'First + 1)) < Big_10 ** (W - 1));
-
return W;
end if;