3.5.10 Operations of Fixed Point Types
The following attributes
are defined for every fixed point subtype S:
S'Small denotes the small
type of S. The value of this attribute is of the type universal_real
Small may be specified for nonderived
ordinary fixed point types via an attribute_definition_clause
); the expression of such a clause
shall be static and positive
Aspect Description for Small: Scale
factor for a fixed point type.
S'Delta denotes the delta
of the fixed point subtype S. The value of this attribute is of the type
with the sub
type as opposed to the type, because of the possibility
of an (obsolescent) delta_constraint
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 one-character 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
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
The following additional
attributes are defined for every decimal fixed point subtype S:
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
value is determined as follows:
Implementation Note: Although a decimal
subtype can be both range-constrained and digits-constrained, 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.
The digits of a base subtype is the largest
integer D such that the range –(10**D–1)*delta
.. +(10**D–1)*delta is included in the base range
of the type.
S'Scale denotes the scale
of the subtype S, defined as the value N such that S'Delta = 10.0**(–N).
[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
Ramification: S'Scale is negative if
S'Delta is greater than one. By contrast, S'Aft is always positive.
S'Round denotes a function with
the following specification:
function S'Round(X : universal_real)
The function returns the value obtained
by rounding X (away from 0, if X is midway between two values of the
type of S).
NOTE 1 All subtypes of a fixed point
type will have the same value for the Delta attribute, in the absence
NOTE 2 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.
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
NOTE 4 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
Wording Changes from Ada 95
Clarified that small
may be specified only
for ordinary fixed point types.
Wording Changes from Ada 2012
Correction: Clarified that small
may be specified only with positive values.
Ada 2005 and 2012 Editions sponsored in part by Ada-Europe