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EXAMPLE 1.15 Integer Operators
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This program illustrates the use of the six arithmetic operators:
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#include <iostream.h> // Tests arithmetic operators: main0 { int m = 38, n = 5; tout << m << ' + fl << n << 1 = ' << (m + n) << endl; tout << m << ' - u << n CC fl = n CC (m - n) << endl; tout << cc n << ' = 'I << (-n) << endl; tout << m << ' * ' << n << ' = ' << (m * n) << endl; tout << m << ' / ' << n << ' = ' << (m / n) << endl; tout << m << ' % ' << n << ' = ' << (m % n) << endl; return 0; 1
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* i %
Note that 3 8 / 5 = 7 a n d 3 8 % 5 = 3. These two operations together provide complete information about the ordinary division of 38 by 5: 38 + 5 = 7.6. The resulting integer part is 35+5 = 7, and the fractional part is 3+5 = 0.6. The integer quotient 7 and the integer remainder 3 can be recombined with the dividend 38 and the divisor 5 in the following relation: 7 x 5 + 3 = 3 8 .
The integer quotient and remainder operators are more complicated if the integers are not positive. Of course, the divisor should never be zero. But if either m or n is negative, then m/n and m%n may give different results on different machines. The only requirement is that
q*n + r == m
where q = m/n and r = m%n. For example, -14 divided by 5 is -2.8. For the integer quotient, this could be rounded to -3 or to -2. If your computer rounds the quotient g to -3, then the integer remainder r will be 1. But if your computer rounds g to -2, then r will be -4.
INTRODUCTION TO PROGRAMMING IN C++
[CHAP. 1
EXAMPLE 1.16 Division with Negative Integers
This program is used to determine how the computer handles the division of negative integers:
#include ciostream.h> // Tests quotient and main0 int m = -14, tout << "rn = tout << '92 = tout CC "q = tout CC 'r = tout << q*n << r << return 0; remainder operators:
n = 5, q = m/n, r = m%n; ' C-C m CC endl; u -CC n C-C endl; " << q CC endl; ' << r C-C endl; + r = 1 << 1 ( << q << ")*('I << n CC ") + " = ' << q*n + r CC ' = ' -CC m CC endl;
m = -14 n a5 q s -2 IT = -4 cpn + r .= (-2] (5) + -4 t= -24 == 44
. : . . : . :
This shows the same results both from a UNIX workstation using a Motorola 68040 processor and from a DOS PC using an Intel Pentium processor.
1.14 OPERATOR PRECEDENCE AND ASSOCIATIVITY
C++ has a rich repertoire of operators. (Appendix C lists all 55 of them.) Since an expression may include several operators, it is important to know in what order the evaluations of the operators occurs. We are already familiar with the precedence of ordinary arithmetic operators: the *,
/, and % operators have higher precedence than the + and - operators; i.e., they are evaluated first. For example,
42 - 3*5
is evaluated as
42 (3*5) = 42 - 15 = 27
Moreover, all the arithmetic operators have higher precedence than the assignment and output operators. For example, the statement
n = 42 - 3*5;
will assign the value 27 to n. First the operator * is invoked to evaluate 3 * 5, then the operator - is invoked to evaluate 4 2 - 15, and then the operator = is invoked to assign 2 7 to n.
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