5.7. Overflow Modes

Annotations such as preconditions, postconditions, assertions, loop invariants, are analyzed by GNATprove with the exact same meaning that they have during execution. In particular, evaluating the expressions in an annotation may raise a run-time error, in which case GNATprove will attempt to prove that this error cannot occur, and report a warning otherwise.

Integer overflows are a kind of run-time error that occurs when the result of an arithmetic computation does not fit in the bounds of the machine type used to hold the result. In some cases, it is convenient to express properties in annotations as they would be expressed in mathematics, where quantities are unbounded. This is best achieved using the Big Numbers Library, which defines types for unbounded integers and rational numbers, operations on these and conversions from/to machine integers and reals.

Alternatively, GNATprove supports different overflow modes, so that the usual signed arithmetic operations are interpreted differently from their standard interpretation. For example:

 function Add (X, Y : Integer) return Integer with
   Pre  => X + Y in Integer,
   Post => Add'Result = X + Y;

The precondition of Add states that the result of adding its two parameters should fit in type Integer. In the default mode, evaluating this expression will fail an overflow check, because the result of X + Y is stored in a temporary of type Integer. If the compilation switch -gnato13 is used, then annotations are compiled specially, so that arithmetic operations use unbounded intermediate results. In this mode, GNATprove does not generate a check for the addition of X and Y in the precondition of Add, as there is no possible overflow here.

There are three overflow modes:

  • Use base type for intermediate operations (STRICT): in this mode, all intermediate results for predefined arithmetic operators are computed using the base type, and the result must be in range of the base type.

  • Most intermediate overflows avoided (MINIMIZED): in this mode, the compiler attempts to avoid intermediate overflows by using a larger integer type, typically Long_Long_Integer, as the type in which arithmetic is performed for predefined arithmetic operators.

  • All intermediate overflows avoided (ELIMINATED): in this mode, the compiler avoids all intermediate overflows by using arbitrary precision arithmetic as required.

The desired mode for handling intermediate overflow can be specified using either the Overflow_Mode pragma or an equivalent compiler switch. The pragma has the form:

pragma Overflow_Mode ([General =>] MODE [, [Assertions =>] MODE]);

where MODE is one of

  • STRICT: intermediate overflows checked (using base type)

  • MINIMIZED: minimize intermediate overflows

  • ELIMINATED: eliminate intermediate overflows

For example:

pragma Overflow_Mode (General => Strict, Assertions => Eliminated);

specifies that general expressions outside assertions be evaluated in the usual strict mode, and expressions within assertions be evaluated in “eliminate intermediate overflows” mode. Currently, GNATprove only supports pragma Overflow_Mode being specified as a configuration pragma, either in a configuration pragma file or directly in a unit.

Additionally, a compiler switch -gnato?? can be used to control the checking mode default. Here ? is one of the digits 1 through 3:

  1. use base type for intermediate operations (STRICT)

  2. minimize intermediate overflows (MINIMIZED)

  3. eliminate intermediate overflows (ELIMINATED)

The switch -gnato13, like the Overflow_Mode pragma above, specifies that general expressions outside assertions be evaluated in the usual strict mode, and expressions within assertions be evaluated in “eliminate intermediate overflows” mode.

Note that these modes apply only to the evaluation of predefined arithmetic, membership, and comparison operators for signed integer arithmetic.

For further details of the meaning of these modes, and for further information about the treatment of overflows for fixed-point and floating-point arithmetic please refer to the “Overflow Check Handling in GNAT” appendix in the GNAT User’s Guide.