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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 Computers can represent only a finite number of digits. It is therefore impossible to precisely represent repeating binary sequences of floating point numbers. This includes many finite decimal numbers, such as 1/10 which 0.1, because these numbers have repeating binary representations.

When precise computation is necessary, and especially such as when doing performing currency calculations, consider alternative representations that may be able to completely represent values rather than the floating point representations float and doublefloating-point types must not be used. Instead, use an alternative representation that can completely represent the necessary values.

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 = 1.000;
double dime = 0.110;
int number = 7;
System.out.println(
  ("A dollar less " + number + " dimes is $" +
		    (dollar - number * dime)  
);

Unfortunately, because of the imprecision of floating point arithmeticBecause the value 0.10 lacks an exact representation in 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

Compliant Solution

This compliant solution uses an integer type (such as long int) and works in 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 prints out:correctly outputs the following:

A dollar less 7 dimes is $0.30

...

Compliant Solution

An alternative approach is to use This compliant solution uses the BigDecimal type, though it is less efficient.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. 

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 prints out:outputs the following:

A dollar less 7 dimes is $0.3

Risk Assessment

Using a representation other than floating point may allow for more precision and accuracy for critical arithmetic.-point representations when precise computation is required can result in a loss of precision and incorrect values.

Automated Detection

TODO

Related Vulnerabilities

Search for vulnerabilities resulting from the violation of this rule on the CERT website.

Other Languages

Automated detection of floating-point arithmetic is straightforward. 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

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Android Implementation Details

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

Bibliography

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References

\[[JLS 05|AA. Java References#JLS 05]\] [Section 4.2.3, Floating-Point Types, Formats, and Values|http://java.sun.com/docs/books/jls/third_edition/html/typesValues.html#4.2.3]
\[[Bloch 08|AA. Java References#Bloch 08]\] Item 48: Avoid {{float}} and {{double}} if exact answers are required
\[[Bloch 05|AA. Java References#Bloch 05]\] Puzzle 2: Time for a Change
\[[Goldberg 91|AA. Java References#Goldberg 91]\]

06. Floating Point (FLP)      06. Floating Point (FLP)      FLP01-J. Take care in rearranging floating point expressions