Example 51

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Operand Evaluation Order

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public class OperandEvaluationOrder { public static void main(String[] args) { // Evaluate: 4 + 5 * 6 int i = operandEval(1, 4) + operandEval(2, 5) * operandEval(3, 6); Systemoutprintln(); Systemoutprintln("Value of i: " + i); } static int operandEval(int opNum, int operand) { Systemoutprint(opNum); return operand; } }

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// (1)

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// (2)

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Output from the program:

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123 Value of i: 34

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Range of Numeric Values

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As we have seen, all numeric types have a range of valid values (Section 22, p 28) This range is given by the constants named MAX_VALUE and MIN_VALUE, which are defined in each numeric wrapper class The arithmetic operators are overloaded, meaning that the operation of an operator varies depending on the type of its operands Floating-point arithmetic is performed if any operand of an operator is of floating-point type, otherwise, integer arithmetic is performed Values that are out-of-range or are the results of invalid expressions are handled differently depending on whether integer or floating-point arithmetic is performed

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Integer Arithmetic

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Integer arithmetic always returns a value that is in range, except in the case of integer division by zero and remainder by zero, which causes an ArithmeticException (see the division operator / and the remainder operator % below) A valid value does not necessarily mean that the result is correct, as demonstrated by the following examples:

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int tooBig = IntegerMAX_VALUE + 1; int tooSmall = IntegerMIN_VALUE - 1; // -2147483648 which is IntegerMIN_VALUE // 2147483647 which is IntegerMAX_VALUE

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The results above should be values that are out-of-range However, integer arithmetic wraps if the result is out-of-range, ie, the result is reduced modulo in the range of the result type In order to avoid wrapping of out-of-range values, pro-

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CHAPTER 5: OPERATORS AND EXPRESSIONS

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grams should either use explicit checks or a wider type If the type long is used in the examples above, the results would be correct in the long range:

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long notTooBig = IntegerMAX_VALUE + 1L; long notTooSmall = IntegerMIN_VALUE - 1L; // 2147483648L in range // -2147483649L in range

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Floating-Point Arithmetic

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Certain floating-point operations result in values that are out-of-range Typically, adding or multiplying two very large floating-point numbers can result in an out-of-range value which is represented by Infinity (see Figure 52) Attempting floating-point division by zero also returns infinity The examples below show how this value is printed as signed infinity

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Systemoutprintln( 40 / 00); Systemoutprintln(-40 / 00); // Prints: Infinity // Prints: -Infinity

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Both positive and negative infinity represent overflow to infinity, that is, the value is too large to be represented as a double or float (see Figure 52) Signed infinity is represented by named constants POSITIVE_INFINITY and NEGATIVE_INFINITY in the wrapper classes javalangFloat and javalangDouble A value can be compared with these constants to detect overflow

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Overflow and Underflow in Floating-point Arithmetic

DoubleMIN_VALUE positive zero negative zero [ -DoubleMAX_VALUE DoubleNEGATIVE_INFINITY ] -Infinity (Not drawn to scale) -DoubleMIN_VALUE ]

DoublePOSITIVE_INFINITY DoubleMAX_VALUE

Infinity

Overflow 00 -00 Underflow

Out-of-range

Floating-point arithmetic can also result in underflow to zero, ie, the value is too small to be represented as a double or float (see Figure 52) Underflow occurs in the following situations:

56: ARITHMETIC OPERATORS: *, /, %, +, -

the result is between DoubleMIN_VALUE (or FloatMIN_VALUE) and zero; eg, the result of (51E-324 - 49E-324) Underflow then returns positive zero 00 (or 00F) the result is between -DoubleMIN_VALUE (or -FloatMIN_VALUE) and zero; eg, the result of (-DoubleMIN_VALUE * 1E-1) Underflow then returns negative zero -00 (or -00F) Negative zero compares equal to positive zero, ie, (-00 == 00) is true Certain operations have no mathematical result, and are represented by NaN (Not a Number) For example, calculating the square root of -1 Another example is (floating-point) dividing zero by zero:

Systemoutprintln(00 / 00); // Prints: NaN

NaN is represented by the constant named NaN in the wrapper classes javalangFloat and javalangDouble Any operation involving NaN produces NaN Any comparison (except inequality !=) involving NaN and any other value (including NaN) returns false An inequality comparison of NaN with another value (including NaN) always returns true However, the recommended way of checking a value for NaN is to use the static method isNaN() defined in both wrapper classes, javalangFloat and javalangDouble