[Ada] Fix proof of runtime unit System.Exp_Mod
Commit Message
Regain the proof of System.Exp_Mod after changes in provers and Why3.
Tested on x86_64-pc-linux-gnu, committed on trunk
gcc/ada/
* libgnat/s-expmod.adb (Lemma_Add_Mod): Add new lemma to factor
out a complex sub-proof.
(Exp_Modular): Add assertion to help proof.
@@ -106,6 +106,13 @@ is
-------------------
procedure Lemma_Add_Mod (X, Y : Big_Natural; B : Big_Positive) is
+
+ procedure Lemma_Euclidean_Mod (Q, F, R : Big_Natural) with
+ Pre => F /= 0,
+ Post => (Q * F + R) mod F = R mod F;
+
+ procedure Lemma_Euclidean_Mod (Q, F, R : Big_Natural) is null;
+
Left : constant Big_Natural := (X + Y) mod B;
Right : constant Big_Natural := ((X mod B) + (Y mod B)) mod B;
XQuot : constant Big_Natural := X / B;
@@ -119,6 +126,8 @@ is
(Left = ((XQuot + YQuot) * B + X mod B + Y mod B) mod B);
pragma Assert (X mod B + Y mod B = AQuot * B + Right);
pragma Assert (Left = ((XQuot + YQuot + AQuot) * B + Right) mod B);
+ Lemma_Euclidean_Mod (XQuot + YQuot + AQuot, B, Right);
+ pragma Assert (Left = (Right mod B));
pragma Assert (Left = Right);
end if;
end Lemma_Add_Mod;
@@ -259,6 +268,7 @@ is
pragma Assert (Equal_Modulo
((Big (Result) * Big (Factor)) * Big (Factor) ** (Exp - 1),
Big (Left) ** Right));
+ pragma Assert (Big (Factor) >= 0);
Lemma_Mult_Mod (Big (Result) * Big (Factor),
Big (Factor) ** (Exp - 1),
Big (Modulus));