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4.5 Operators and Expression Evaluation

1
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
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highest_precedence_operator ::=   **  | abs | not

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.
9
For each form of type definition, certain of the above operators are predefined; that is, they are implicitly declared immediately after the type definition. 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
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. 

Implementation Requirements

11
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
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. 

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. 
NOTES
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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

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Examples of precedence:
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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)
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-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 

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