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4.5 Operators and Expression Evaluation
1
[
{precedence of operators}
{operator precedence}
The language defines the following six categories
of operators (given in order of increasing precedence). The corresponding
operator_symbols, and only those,
can be used as
designators in declarations
of functions for user-defined operators. See
6.6,
``
Overloading of Operators''.]
Syntax
2
logical_operator
::= and |
or |
xor
3
relational_operator
::= = | /= | < | <= | > | >=
4
binary_adding_operator
::= + | - | &
5
unary_adding_operator
::= + | -
6
multiplying_operator
::= * | / |
mod |
rem
7
highest_precedence_operator
::= ** |
abs |
not
7.a
Discussion: Some of the
above syntactic categories are not used in other syntax rules. They are
just used for classification. The others are used for both classification
and parsing.
Static Semantics
8
For a sequence of operators of the same precedence
level, the operators are associated with their operands in textual order
from left to right. Parentheses can be used to impose specific associations.
8.a
Discussion: The left-associativity
is not directly inherent in the grammar of 4.4,
though in 1.1.4 the definition of the metasymbols
{} implies left associativity. So this could be seen as redundant,
depending on how literally one interprets the definition of the {}
metasymbols.
8.b
See the Implementation Permissions
below regarding flexibility in reassociating operators of the same precedence.
9
{predefined operator}
{operator (predefined)}
For each form of type definition, certain of the
above operators are
predefined; that is, they are implicitly declared
immediately after the type definition.
{binary operator}
{operator (binary)}
{unary operator} {operator
(unary)} For each such implicit operator
declaration, the parameters are called Left and Right for
binary
operators; the single parameter is called Right for
unary operators.
[An expression of the form X op Y, where op is a binary operator, is
equivalent to a
function_call of
the form "op"(X, Y). An expression of the form op Y, where
op is a unary operator, is equivalent to a
function_call
of the form "op"(Y). The predefined operators and their effects
are described in subclauses
4.5.1 through
4.5.6.]
Dynamic Semantics
10
[
{Constraint_Error (raised
by failure of run-time check)} The predefined
operations on integer types either yield the mathematically correct result
or raise the exception Constraint_Error. For implementations that support
the Numerics Annex, the predefined operations on real types yield results
whose accuracy is defined in
Annex G, or raise
the exception Constraint_Error. ]
10.a
To be honest: Predefined
operations on real types can ``silently'' give wrong results when the
Machine_Overflows attribute is false, and the computation overflows.
Implementation Requirements
11
{Constraint_Error (raised
by failure of run-time check)} The implementation
of a predefined operator that delivers a result of an integer or fixed
point type may raise Constraint_Error only if the result is outside the
base range of the result type.
12
{Constraint_Error (raised
by failure of run-time check)} The implementation
of a predefined operator that delivers a result of a floating point type
may raise Constraint_Error only if the result is outside the safe range
of the result type.
12.a
To be honest: An exception
is made for exponentiation by a negative exponent in 4.5.6.
Implementation Permissions
13
For a sequence of predefined operators of the
same precedence level (and in the absence of parentheses imposing a specific
association), an implementation may impose any association of the operators
with operands so long as the result produced is an allowed result for
the left-to-right association, but ignoring the potential for failure
of language-defined checks in either the left-to-right or chosen order
of association.
13.a
Discussion: Note that
the permission to reassociate the operands in any way subject to producing
a result allowed for the left-to-right association is not much help for
most floating point operators, since reassociation may introduce significantly
different round-off errors, delivering a result that is outside the model
interval for the left-to-right association. Similar problems arise for
division with integer or fixed point operands.
13.b
Note that this permission does
not apply to user-defined operators.
14
11 The two operands of
an expression of the form X op Y, where op is a binary operator, are
evaluated in an arbitrary order, as for any function_call
(see 6.4).
Examples
15
Examples of
precedence:
16
not Sunny or Warm -- same as (not Sunny) or Warm
X > 4.0 and Y > 0.0 -- same as (X > 4.0) and (Y > 0.0)
17
-4.0*A**2 -- same as -(4.0 * (A**2))
abs(1 + A) + B -- same as (abs (1 + A)) + B
Y**(-3) -- parentheses are necessary
A / B * C -- same as (A/B)*C
A + (B + C) -- evaluate B + C before adding it to A
Wording Changes from Ada 83
17.a
We don't give a detailed definition
of precedence, since it is all implicit in the syntax rules anyway.
17.b
The permission to reassociate
is moved here from RM83-11.6(5), so it is closer to the rules defining
operator association.
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