G.2.2 Model-Oriented Attributes of Floating Point Types

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In implementations that support the Numerics Annex, the model-oriented attributes of floating point types shall yield the values defined here, in both the strict and the relaxed modes. These definitions add conditions to those in A.5.3.

Static Semantics

For every subtype S of a floating point type T:

S'Model_Mantissa: Yields the number of digits in the mantissa of the canonical form of the model numbers of T (see A.5.3). The value of this attribute shall be greater than or equal to Ceiling(d · log(10) / log(TMachine_Radix)) + 1, where d is the requested decimal precision of T. In addition, it shall be less than or equal to the value of TMachine_Mantissa. This attribute yields a value of the type universal_integer.

S'Model_Emin: Yields the minimum exponent of the canonical form of the model numbers of T (see A.5.3). The value of this attribute shall be greater than or equal to the value of T'Machine_Emin. This attribute yields a value of the type universal_integer.

S'Safe_First: Yields the lower bound of the safe range of T. The value of this attribute shall be a model number of T and greater than or equal to the lower bound of the base range of T. In addition, if T is declared by a floating_point_definition or is derived from such a type, and the floating_point_definition includes a real_range_specification specifying a lower bound of lb, then the value of this attribute shall be less than or equal to lb; otherwise, it shall be less than or equal to -10.0 ^{4 · d}, where d is the requested decimal precision of T. This attribute yields a value of the type universal_real.

S'Safe_Last: Yields the upper bound of the safe range of T. The value of this attribute shall be a model number of T and less than or equal to the upper bound of the base range of T. In addition, if T is declared by a floating_point_definition or is derived from such a type, and the floating_point_definition includes a real_range_specification specifying an upper bound of ub, then the value of this attribute shall be greater than or equal to ub; otherwise, it shall be greater than or equal to 10.0 ^{4 · d}, where d is the requested decimal precision of T. This attribute yields a value of the type universal_real.

S'Model: Denotes a function (of a parameter X) whose specification is given in A.5.3. If X is a model number of T, the function yields X; otherwise, it yields the value obtained by rounding or truncating X to either one of the adjacent model numbers of T. Constraint_Error is raised if the resulting model number is outside the safe range of S. A zero result has the sign of X when S'Signed_Zeros is True.

Subject to the constraints given above, the values of S'Model_Mantissa and S'Safe_Last are to be maximized, and the values of S'Model_Emin and S'Safe_First minimized, by the implementation as follows:

First, S'Model_Mantissa is set to the largest value for which values of S'Model_Emin, S'Safe_First, and S'Safe_Last can be chosen so that the implementation satisfies the strict-mode requirements of G.2.1 in terms of the model numbers and safe range induced by these attributes.
Next, S'Model_Emin is set to the smallest value for which values of S'Safe_First and S'Safe_Last can be chosen so that the implementation satisfies the strict-mode requirements of G.2.1 in terms of the model numbers and safe range induced by these attributes and the previously determined value of S'Model_Mantissa.
Finally, S'Safe_First and S'Safe_last are set (in either order) to the smallest and largest values, respectively, for which the implementation satisfies the strict-mode requirements of G.2.1 in terms of the model numbers and safe range induced by these attributes and the previously determined values of S'Model_Mantissa and S'Model_Emin.

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