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Floating point arithmetic presents the additional problem of accuracy: only a fixed number of digits are available to represent values within the computer Floating point roundoff occurs when a value is modified to fit within the float, double, or long double type intended to represent it The resulting accuracy of addition, multiplication, and subtraction of floating point numbers is affected by the fixed precision of the underlying data type (For a detailed discussion of roundoff error in numerical computation, see [SHAMPINE97]) Exercise 41 What is the primary difference between the following two division expressions
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double dval1 = 100, dval2 = 30; int ival1 = 10, ival2 = 3; dval1 / dval2; ival1 / ival2;
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Exercise 42 Given an integral object, what operator might we use to determine whether it is even or odd Write the expression Exercise 43 Locate and examine the Standard C++ header file limits and the Standard C header files climits and cfloat on your system
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Equality, Relational, and Logical Operators
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Table Equality, Relational, and Logical Operators Operator ! < <= > >= == != && Function logical NOT less than less than or equal greater than greater than or equal equality inequality logical AND logical OR Use !expr expr < expr expr <= expr expr > expr expr >= expr expr == expr expr != expr expr && expr expr expr
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The equality, relational, and logical operators evaluate to either of the bool constants true or false If such an operator is used within a context requiring an integer value, the result is promoted to a value of either 1 (true) or 0 (false) For example, in the following code fragment, we wish to count all the elements of a vector less than a user-specified value To accomplish this, we add the result of the less-than operator to a count of the elements (The += operator is a shorthand notation; it means that we are adding the right-hand expression to the current value of the left-hand operand We discuss the compound assignment operators in Section 44)
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int elem_cnt = 0; vector<int>::iterator iter = ivecbegin(); while ( iter != ivecend() ) {
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// same as: elem_cnt = elem_cnt + (*iter < some_value) // true/false value of *iter < some_value // is promoted to either 1 or 0 elem_cnt += *iter < some_value; ++iter; }
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The logical AND (&&) operator evaluates to true only if both its operands evaluate to true The logical OR (||) operator evaluates to true if either of its operands evaluates to true The operands are guaranteed to be evaluated from left to right Evaluation stops as soon as the truth or falsity of the expression is determined Given the forms
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expr1 && expr2 expr1 || expr2
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expr2 is guaranteed not to be evaluated if either of the following is true:
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In a logical AND expression, expr1 evaluates to false In a logical OR expression, expr1 evaluates to true
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A valuable use of the logical AND operator is to have expr1 evaluate to false in the presence of some boundary condition that would make the evaluation of expr2 dangerous For example:
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while ( ptr != 0 && ptr->value < upperBound && ptr->value >= 0 && notFound( ia[ ptr->value ] )) { }
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A pointer with a value of 0 is not addressing an object Applying the member access operator to a 0-valued pointer is always troublesome The first logical AND operator guards against that happening Equally troublesome is an out-of-bounds array index The second and third operands guard against that possibility The last operand is safe to evaluate only when the first three operands evaluate as true The logical NOT operator (!) evaluates to true if its operand has a value of false or zero; otherwise, it evaluates to false For example:
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bool found = false; // while the item has not been found // and ptr still addresses an object while ( ! found && ptr ) { found = lookup( *ptr ); ++ptr; }
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