Model-Oriented Attributes of Floating Point Types
Author: JTC1/SC22/WG9/ARG, by Randall Brukardt, ARG Editor

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# 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 A.5.3.

#### Static Semantics

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For every subtype S of a floating point type T:
3/2
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
3.1/2
Ceiling(d · log(10) / log(T'Machine_Radix)) + g
3.2/2
where d is the requested decimal precision of T, and g is 0 if T'Machine_Radix is a positive power of 10 and 1 otherwise. In addition, T'Model_Mantissa shall be less than or equal to the value of T'Machine_Mantissa. This attribute yields a value of the type universal_integer.
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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.
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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.
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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.
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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.
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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:
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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.
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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.
11/3
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 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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