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The Java language provides two primitive floating-point types, float and double, which are associated with the single-precision 32-bit and double-precision 64-bit format values and operations specified by IEEE 754 [IEEE 754]. Each of the floating-point types has a fixed, limited number of mantissa bits. Consequently, it is impossible to precisely represent any irrational number (for example, pi). Further, because these types use a binary mantissa, they cannot precisely represent many finite decimal numbers, such as 0.1, because these numbers have repeating binary representations.

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When precise computation is unnecessary, floating-point representations may be used. In these cases, you must carefully and methodically estimate the maximum cumulative error of the computations to ensure that the resulting error is within acceptable tolerances. Consider using numerical analysis to properly understand the problem. See Goldberg's work for an introduction to this topic [Goldberg 1991].

Noncompliant Code Example

This noncompliant code example performs some basic currency calculations.:

double dollar = 1.00;
double dime = 0.10;
int number = 7;
System.out.println(
  "A dollar less " + number + " dimes is $" +
                   (dollar - number * dime)  
);

Because the value 0.10 lacks an exact representation in either Java floating-point type (or any floating-point format that uses a binary mantissa), on most platforms, this program prints the following:

A dollar less 7 dimes is $0.29999999999999993

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This compliant solution uses an integer type (such as long int) and works with cents rather than dollars.:

longint dollar = 100;
longint dime = 10;
int number = 7;
System.out.println(
  ("A dollar less " + number + " dimes is $0." +
		    (dollar - number * dime) + " cents" 
);

This code correctly outputs the following:

A dollar less 7 dimes is $0.30 cents

Compliant Solution

This compliant solution uses the BigDecimal type, which provides exact representation of decimal values. Note that on most platforms, computations performed using BigDecimal are less efficient than those performed using primitive types. The importance of this reduced efficiency is application specific. 

import java.math.BigDecimal;

BigDecimal dollar = new BigDecimal("1.0");
BigDecimal dime = new BigDecimal("0.1");
int number = 7;
System.out.println ("A dollar less " + number + " dimes is $" +
	(dollar.subtract(new BigDecimal(number).multiply(dime) )) );

This code outputs the following:

A dollar less 7 dimes is $0.3

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Using floating-point representations when precise computation is required can result in a loss of precision and incorrect values.

Automated Detection

Automated detection of floating-point arithmetic is straight forwardstraightforward. However, determining which code suffers from insufficient precision is not feasible in the general case. Heuristic checks, such as flagging floating-point literals that cannot be represented precisely, could be useful.

Related Guidelines

Android Implementation Details

The use of floating-point on Android is not recommended for performance reasons.

Bibliography

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Image Added Image Added Image Added denormalized numbers