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3.5.10 Operations of Fixed Point Types
Static Semantics
1
The following attributes
are defined for every fixed point subtype S:
2/1
 S'Small

{8652/0005}
S'Small denotes the small of the type of S. The value of this
attribute is of the type universal_real. {specifiable
(of Small for fixed point types) [partial]} {Small
clause} Small may be specified for nonderived
ordinary fixed point types via an attribute_definition_clause
(see 13.3); the expression of such a clause
shall be static.
3
 S'Delta

S'Delta denotes the delta
of the fixed point subtype S. The value of this attribute is of the type
universal_real.
3.a
Reason: The delta
is associated with the subtype as opposed to the type, because
of the possibility of an (obsolescent) delta_constraint.
4
 S'Fore

S'Fore yields the minimum number
of characters needed before the decimal point for the decimal representation
of any value of the subtype S, assuming that the representation does
not include an exponent, but includes a onecharacter prefix that is
either a minus sign or a space. (This minimum number does not include
superfluous zeros or underlines, and is at least 2.) The value of this
attribute is of the type universal_integer.
5
 S'Aft

S'Aft yields the number of decimal
digits needed after the decimal point to accommodate the delta
of the subtype S, unless the delta of the subtype S is greater
than 0.1, in which case the attribute yields the value one. [(S'Aft is
the smallest positive integer N for which (10**N)*S'Delta is greater
than or equal to one.)] The value of this attribute is of the type universal_integer.
6
The following additional
attributes are defined for every decimal fixed point subtype S:
7
 S'Digits

S'Digits denotes the digits
of the decimal fixed point subtype S, which corresponds to the number
of decimal digits that are representable in objects of the subtype. The
value of this attribute is of the type universal_integer. Its
value is determined as follows: {digits (of a decimal
fixed point subtype)}
8
 For a first subtype or a subtype defined by a subtype_indication
with a digits_constraint, the digits
is the value of the expression given after the reserved word digits;
9
 For a subtype defined by a subtype_indication
without a digits_constraint, the
digits of the subtype is the same as that of the subtype denoted by the
subtype_mark in the subtype_indication.
9.a
Implementation Note: Although
a decimal subtype can be both rangeconstrained and digitsconstrained,
the digits constraint is intended to control the Size attribute of the
subtype. For decimal types, Size can be important because input/output
of decimal types is so common.
10
 The digits of a base subtype is the largest integer D
such that the range (10**D1)*delta .. +(10**D1)*delta
is included in the base range of the type.
11
 S'Scale

S'Scale denotes the scale
of the subtype S, defined as the value N such that S'Delta = 10.0**(N).
{scale (of a decimal fixed point subtype)}
[The scale indicates the position of the point relative
to the rightmost significant digits of values of subtype S.] The value
of this attribute is of the type universal_integer.
11.a
Ramification: S'Scale is
negative if S'Delta is greater than one. By contrast, S'Aft is always
positive.
12
 S'Round

S'Round denotes a function with
the following specification:
13
function S'Round(X : universal_real)
return S'Base
14
 The function returns the value obtained by rounding
X (away from 0, if X is midway between two values of the type of S).
15
37 All subtypes of a fixed
point type will have the same value for the Delta attribute, in the absence
of delta_constraints (see J.3).
16
38 S'Scale is not always
the same as S'Aft for a decimal subtype; for example, if S'Delta = 1.0
then S'Aft is 1 while S'Scale is 0.
17
39 {predefined
operations (of a fixed point type) [partial]} The
predefined operations of a fixed point type include the assignment operation,
qualification, the membership tests, and explicit conversion to and from
other numeric types. They also include the relational operators and the
following predefined arithmetic operators: the binary and unary adding
operators  and +, multiplying operators, and the unary operator abs.
18
40 As for all types, objects
of a fixed point type have Size and Address attributes (see 13.3).
Other attributes of fixed point types are defined in A.5.4.
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