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order of precedence


    This subchapter looks at order of precedence.

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order of precedence

    This subchapter looks at order of precedence.

    Every programming language needs to have some system for determining the order of evaluation of expressions.

    x := 5 + 6 * 7;
    x = 5 + 6 * 7

    Is x 47 or 77?

    (5 + 6) = 11; followed by 11 * 7 = 77

    (6 * 7) = 42; 5 + 42 = 47

    The normal rules of elementary algebra call for multiplication (and division) to have a higher priority than addition (or subtraction), which would make x = 42.

elementary algebra

    A strict left to right evaluation would make the answer x = 77.

    A strict right to left evaluation would make the answer x = 42.

    The use of a reverse Polish notation (RPN, such as is used in Forth) avoids the question.

    The two most common approaches used in computer programming languages are either (1) some order of precendence) or (2) directional evaluation (left-to-right or right-to-left).

    The use of parenthesis can be used to change the normal order of evaluation.

    Parenthesis can also be used to make complicated expressions more clear to a human reader. This makes the program easier to udnerstand and easier to maintain over years or decades of use.

    The order of precedence in the following charts are from highest to lowest (top to bottom). Items on the same level are of equal order of precendence.


Primary-expression operators
15( )    [ ]    .    ->
Unary operators
14*    &    -    !    ~    ++    --    sizeof (type)
13*    /    %
12+    -
11>>    <<
10<    >    <=    >=
9==    !=
Assignment operators
2=    +=     -=    *=    /=    %=
>>    =<    <=    &=    ^=    |=
Sequence operator
1, (comma)


unary +    unary -    not
*    /    div    mod    and
+    -    or
=    <>    <    <=    >    >=    in


1all subexpressions in parenthesis
from innermost to outermost
2all exponentiations
from right to left
3all multiplications and divisions
from left to right
4all additions and subtractions
from left to right


2↑ (exponentiation)
3×    /    ÷
(multiplication and division)
4+    -
(addition and subtraction)
5<    ≤    =    ≠    ≥    >
(relational operators)
6¬ (not)
7∧ (and)
8∨ (or)
9⊃ (implies)
10≡ (is equivalent to)

    Note that the actual ALGOL symbol for is not greater than has the less than symbol over the equals symbol rather than ≤ and the ALGOL symbol for not less than has the greater than symbol over the equals symbol rather than ≥.


    The following material is from the unclassified Computer Programming Manual for the JOVIAL (J73) Language, RADC-TR-81-143, Final Technical Report of June 1981.

    1.1.3 Calculations

    In the simplest case, calculations is performed by an assignment
    statement.  An example is:

    AVERAGE = (X1 + X2)/2;

    The right-hand-side of this assigment is a formula; it forms the
    sum of X1 and X2 and divides it by 2.  The details of the
    operation depend on how X1 and X2 are declared.  If X1 and X2 are
    declared float, the calculation is very likely to produce the
    expected result.  In contrast, if the X1 and X2 are declared
    fixed, the scaling must be worked out by the programmer to make
    sure the calculation will succeed.  And if X1 and X2 are declared
    character-string, the compiler will reject it because JOVIAL does
    not automatically convert values into the types required by

    In the example just given, the parenthesis show that the addition
    is performed before the division.  When parenthesis are not
    given, JOVIAL recognizes the usual order of evaluation.  Here is
    an example:

         POLY = BETA*X1**2 - GAMMA*X2 + DELTA;

    JOVIAL applies its "rules of precedence" to the formula in this
    assignment and thus interprets it as:

         POLY = (((BETA*(X1**2)) - (GAMMA*X2)) + DELTA);

    The complete precedence rules are given in Chapter 11.

    Chapter 1 Introduction, page 6

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    View music player in action:

    Create your own copy from the original source code/ (presented for learning programming).

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    Created: October 31, 2010

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