4.5.6 Highest Precedence Operators
Static Semantics
The
highest precedence unary operator
abs (absolute value) is predefined
for every specific numeric type
T, with the following specification:
function "abs"(Right : T) return T
The
highest precedence unary operator
not (logical negation) is predefined
for every boolean type
T, every modular type
T, and for
every one-dimensional array type
T whose components are of a boolean
type, with the following specification:
function "not"(Right : T) return T
The result of the operator not for a modular
type is defined as the difference between the high bound of the base
range of the type and the value of the operand. [For a binary modulus,
this corresponds to a bit-wise complement of the binary representation
of the value of the operand.]
The operator
not that applies to a one-dimensional
array of boolean components yields a one-dimensional boolean array with
the same bounds; each component of the result is obtained by logical
negation of the corresponding component of the operand (that is, the
component that has the same index value).
A
check is made that each component of the result belongs to the component
subtype; the exception Constraint_Error is raised if this check fails.
Discussion: The check against the component
subtype is per AI83-00535.
The
highest precedence
exponentiation operator ** is predefined for
every specific integer type
T with the following specification:
function "**"(Left : T; Right : Natural) return T
Exponentiation is also
predefined for every specific floating point type as well as root_real,
with the following specification (where T is root_real
or the floating point type):
function "**"(Left : T; Right : Integer'Base) return T
{
AI05-0088-1}
The right operand of an exponentiation is the
exponent.
The value of X**N with the value of the exponent N positive is the same
as the value of X*X*...X (with N–1 multiplications) except that
the multiplications are associated in an arbitrary order. With N equal
to zero, the result is one. With the value of N negative [(only defined
for a floating point operand)], the result is the reciprocal of the result
using the absolute value of N as the exponent.
Ramification: The language does not specify
the order of association of the multiplications inherent in an exponentiation.
For a floating point type, the accuracy of the result might depend on
the particular association order chosen.
Implementation Permissions
The implementation of exponentiation
for the case of a negative exponent is allowed to raise Constraint_Error
if the intermediate result of the repeated multiplications is outside
the safe range of the type, even though the final result (after taking
the reciprocal) would not be. (The best machine approximation to the
final result in this case would generally be 0.0.)
19
As
implied by the specification given above for exponentiation of an integer
type, a check is made that the exponent is not negative.
Constraint_Error
is raised if this check fails.
Inconsistencies With Ada 83
{
8652/0100}
{
AI95-00018-01}
The definition of "**" allows arbitrary
association of the multiplications which make up the result. Ada 83 required
left-to-right associations (confirmed by AI83-00137). Thus it is possible
that "**" would provide a slightly different (and more potentially
accurate) answer in Ada 95 than in the same Ada 83 program.
Wording Changes from Ada 83
We now show the specification for "**"
for integer types with a parameter subtype of Natural rather than Integer
for the exponent. This reflects the fact that Constraint_Error is raised
if a negative value is provided for the exponent.
Wording Changes from Ada 2005
{
AI05-0088-1}
Correction: The equivalence definition for "**" was
corrected so that it does not imply that the operands are evaluated multiple
times.
Ada 2005 and 2012 Editions sponsored in part by Ada-Europe
