G.2.2 Model-Oriented Attributes of Floating Point Types

1. 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 See section A.5.3 Attributes of Floating Point Types.
   Static Semantics
   
2. For every subtype S of a floating point type T:
3. S'Model_Mantissa

   Yields the number of digits in the mantissa of the
   canonical form of the model numbers of T, See section A.5.3 Attributes of Floating Point Types.
   The value of this attribute shall be greater than or
   equal to Ceiling(d*log (10)/log (T'Machine_Radix))+1,
   where d is the requested decimal precision of T. In
   addition, it shall be less than or equal to the value of
   T'Machine_Mantissa. This attribute yields a value of the
   type universal_integer.
   

4. S'Model_Emin

   Yields the minimum exponent of the canonical form of the model
   numbers of T, See section A.5.3 Attributes of Floating Point Types. 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.
   

5. 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.
   

6. 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.
   

7. S'Model

   Denotes a function (of a parameter X) whose specification is
   given in See section A.5.3 Attributes of Floating Point Types. 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.
   

8. 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:
   1. 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 See section G.2.1 Model of Floating Point Arithmetic, in terms of the model numbers and safe range induced by these attributes.
   2. 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 See section G.2.1 Model of Floating Point Arithmetic, in terms of the model numbers and safe range induced by these attributes and the previously determined value of S'Model_Mantissa.
   3. 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 See section G.2.1 Model of Floating Point Arithmetic, 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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