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G.2.2 ModelOriented Attributes of Floating Point Types
1
In implementations that support the Numerics Annex,
the modeloriented 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
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 A.5.3).
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.
3.a
Ramification: S'Model_Epsilon,
which is defined in terms of S'Model_Mantissa (see A.5.3),
yields the absolute value of the difference between one and the next
model number of the type T above one. It is equal to or larger
than the absolute value of the difference between one and the next machine
number of the type T above one.
4
 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.
4.a
Ramification: S'Model_Small,
which is defined in terms of S'Model_Emin (see A.5.3),
yields the smallest positive (nonzero) model number of the type T.
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
 {Constraint_Error (raised by failure of runtime
check)} 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. {Overflow_Check [partial]}
{check, languagedefined (Overflow_Check)}
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:
9
 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 strictmode requirements of
G.2.1 in terms of the model numbers and safe
range induced by these attributes.
10
 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 strictmode 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
 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 strictmode 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.
11.a
Ramification: {IEEE
floating point arithmetic} {IEC 559:1989}
The following table shows appropriate attribute values
for IEEE basic single and double precision types (ANSI/IEEE Std 7541985,
IEC 559:1989). Here, we use the names IEEE_Float_32 and IEEE_Float_64,
the names that would typically be declared in package Interfaces, in
an implementation that supports IEEE arithmetic. In such an implementation,
the attributes would typically be the same for Standard.Float and Long_Float,
respectively.
11.b
Attribute IEEE_Float_32 IEEE_Float_64
11.c
'Machine_Radix 2 2
'Machine_Mantissa 24 53
'Machine_Emin 125 1021
'Machine_Emax 128 1024
'Denorm True True
'Machine_Rounds True True
'Machine_Overflows True/False True/False
'Signed_Zeros should be True should be True
11.d
'Model_Mantissa (same as 'Machine_Mantissa) (same as 'Machine_Mantissa)
'Model_Emin (same as 'Machine_Emin) (same as 'Machine_Emin)
'Model_Epsilon 2.0**(23) 2.0**(52)
'Model_Small 2.0**(126) 2.0**(1022)
'Safe_First 2.0**128*(1.02.0**(24)) 2.0**1024*(1.02.0**(53))
'Safe_Last 2.0**128*(1.02.0**(24)) 2.0**1024*(1.02.0**(53))
11.e
'Digits 6 15
'Base'Digits (same as 'Digits) (same as 'Digits)
11.f
'First (same as 'Safe_First) (same as 'Safe_First)
'Last (same as 'Safe_Last) (same as 'Safe_Last)
'Size 32 64
11.g
Note: 'Machine_Overflows can be
True or False, depending on whether the Ada implementation raises Constraint_Error
or delivers a signed infinity in overflow and zerodivide situations (and
at poles of the elementary functions).
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