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* [gcc r12-6288] [Ada] Proof of runtime units for binary modular exponentiation
@ 2022-01-06 17:12 Pierre-Marie de Rodat
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From: Pierre-Marie de Rodat @ 2022-01-06 17:12 UTC (permalink / raw)
To: gcc-cvs
https://gcc.gnu.org/g:ed722edd2f4accad60744b95426dba3fc9ca084c
commit r12-6288-ged722edd2f4accad60744b95426dba3fc9ca084c
Author: Yannick Moy <moy@adacore.com>
Date: Thu Dec 2 10:55:04 2021 +0100
[Ada] Proof of runtime units for binary modular exponentiation
gcc/ada/
* libgnat/s-explllu.ads: Mark in SPARK.
* libgnat/s-expllu.ads: Mark in SPARK.
* libgnat/s-exponu.adb: Add loop invariants and needed
assertions.
* libgnat/s-exponu.ads: Add functional contract.
* libgnat/s-expuns.ads: Mark in SPARK.
Diff:
---
gcc/ada/libgnat/s-explllu.ads | 15 ++++++++++++++-
gcc/ada/libgnat/s-expllu.ads | 15 ++++++++++++++-
gcc/ada/libgnat/s-exponu.adb | 23 ++++++++++++++++++++++-
gcc/ada/libgnat/s-exponu.ads | 16 +++++++++++++++-
gcc/ada/libgnat/s-expuns.ads | 15 ++++++++++++++-
5 files changed, 79 insertions(+), 5 deletions(-)
diff --git a/gcc/ada/libgnat/s-explllu.ads b/gcc/ada/libgnat/s-explllu.ads
index 5a54ada1a4e..eb883a43f57 100644
--- a/gcc/ada/libgnat/s-explllu.ads
+++ b/gcc/ada/libgnat/s-explllu.ads
@@ -34,10 +34,23 @@
-- The result is always full width, the caller must do a masking operation if
-- the modulus is less than 2 ** Long_Long_Long_Unsigned'Size.
+-- Preconditions in this unit are meant for analysis only, not for run-time
+-- checking, so that the expected exceptions are raised. This is enforced
+-- by setting the corresponding assertion policy to Ignore. Postconditions
+-- and contract cases should not be executed at runtime as well, in order
+-- not to slow down the execution of these functions.
+
+pragma Assertion_Policy (Pre => Ignore,
+ Post => Ignore,
+ Contract_Cases => Ignore,
+ Ghost => Ignore);
+
with System.Exponu;
with System.Unsigned_Types;
-package System.Exp_LLLU is
+package System.Exp_LLLU
+ with SPARK_Mode
+is
subtype Long_Long_Long_Unsigned is Unsigned_Types.Long_Long_Long_Unsigned;
diff --git a/gcc/ada/libgnat/s-expllu.ads b/gcc/ada/libgnat/s-expllu.ads
index 9f7b404aeb4..e028f670f94 100644
--- a/gcc/ada/libgnat/s-expllu.ads
+++ b/gcc/ada/libgnat/s-expllu.ads
@@ -34,10 +34,23 @@
-- The result is always full width, the caller must do a masking operation if
-- the modulus is less than 2 ** Long_Long_Unsigned'Size.
+-- Preconditions in this unit are meant for analysis only, not for run-time
+-- checking, so that the expected exceptions are raised. This is enforced
+-- by setting the corresponding assertion policy to Ignore. Postconditions
+-- and contract cases should not be executed at runtime as well, in order
+-- not to slow down the execution of these functions.
+
+pragma Assertion_Policy (Pre => Ignore,
+ Post => Ignore,
+ Contract_Cases => Ignore,
+ Ghost => Ignore);
+
with System.Exponu;
with System.Unsigned_Types;
-package System.Exp_LLU is
+package System.Exp_LLU
+ with SPARK_Mode
+is
subtype Long_Long_Unsigned is Unsigned_Types.Long_Long_Unsigned;
diff --git a/gcc/ada/libgnat/s-exponu.adb b/gcc/ada/libgnat/s-exponu.adb
index 95256386960..06ed5099c25 100644
--- a/gcc/ada/libgnat/s-exponu.adb
+++ b/gcc/ada/libgnat/s-exponu.adb
@@ -29,7 +29,19 @@
-- --
------------------------------------------------------------------------------
-function System.Exponu (Left : Int; Right : Natural) return Int is
+function System.Exponu (Left : Int; Right : Natural) return Int
+ with SPARK_Mode
+is
+ -- Preconditions, postconditions, 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 (Pre => Ignore,
+ Post => Ignore,
+ Ghost => Ignore,
+ Loop_Invariant => Ignore,
+ Assert => Ignore);
-- Note that negative exponents get a constraint error because the
-- subtype of the Right argument (the exponent) is Natural.
@@ -49,7 +61,16 @@ begin
if Exp /= 0 then
loop
+ pragma Loop_Invariant (Exp > 0);
+ pragma Loop_Invariant (Result * Factor ** Exp = Left ** Right);
+ pragma Loop_Variant (Decreases => Exp);
+
if Exp rem 2 /= 0 then
+ pragma Assert
+ (Result * (Factor * Factor ** (Exp - 1)) = Left ** Right);
+ pragma Assert
+ ((Result * Factor) * Factor ** (Exp - 1) = Left ** Right);
+
Result := Result * Factor;
end if;
diff --git a/gcc/ada/libgnat/s-exponu.ads b/gcc/ada/libgnat/s-exponu.ads
index 7faa1229efd..b18a3a4119c 100644
--- a/gcc/ada/libgnat/s-exponu.ads
+++ b/gcc/ada/libgnat/s-exponu.ads
@@ -31,8 +31,22 @@
-- Modular integer exponentiation
+-- Preconditions in this unit are meant for analysis only, not for run-time
+-- checking, so that the expected exceptions are raised. This is enforced
+-- by setting the corresponding assertion policy to Ignore. Postconditions
+-- and contract cases should not be executed at runtime as well, in order
+-- not to slow down the execution of these functions.
+
+pragma Assertion_Policy (Pre => Ignore,
+ Post => Ignore,
+ Contract_Cases => Ignore,
+ Ghost => Ignore);
+
generic
type Int is mod <>;
-function System.Exponu (Left : Int; Right : Natural) return Int;
+function System.Exponu (Left : Int; Right : Natural) return Int
+with
+ SPARK_Mode,
+ Post => System.Exponu'Result = Left ** Right;
diff --git a/gcc/ada/libgnat/s-expuns.ads b/gcc/ada/libgnat/s-expuns.ads
index b49e7c0ca05..751f3fa275a 100644
--- a/gcc/ada/libgnat/s-expuns.ads
+++ b/gcc/ada/libgnat/s-expuns.ads
@@ -34,10 +34,23 @@
-- The result is always full width, the caller must do a masking operation if
-- the modulus is less than 2 ** Unsigned'Size.
+-- Preconditions in this unit are meant for analysis only, not for run-time
+-- checking, so that the expected exceptions are raised. This is enforced
+-- by setting the corresponding assertion policy to Ignore. Postconditions
+-- and contract cases should not be executed at runtime as well, in order
+-- not to slow down the execution of these functions.
+
+pragma Assertion_Policy (Pre => Ignore,
+ Post => Ignore,
+ Contract_Cases => Ignore,
+ Ghost => Ignore);
+
with System.Exponu;
with System.Unsigned_Types;
-package System.Exp_Uns is
+package System.Exp_Uns
+ with SPARK_Mode
+is
subtype Unsigned is Unsigned_Types.Unsigned;
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2022-01-06 17:12 [gcc r12-6288] [Ada] Proof of runtime units for binary modular exponentiation Pierre-Marie de Rodat
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