Class Math
The class Math contains methods for performing basic numeric operations such as the elementary exponential, logarithm, square root, and trigonometric functions.
Unlike some of the numeric methods of class StrictMath , all implementations of the equivalent functions of class Math are not defined to return the bit-for-bit same results. This relaxation permits better-performing implementations where strict reproducibility is not required.
By default many of the Math methods simply call the equivalent method in StrictMath for their implementation. Code generators are encouraged to use platform-specific native libraries or microprocessor instructions, where available, to provide higher-performance implementations of Math methods. Such higher-performance implementations still must conform to the specification for Math .
The quality of implementation specifications concern two properties, accuracy of the returned result and monotonicity of the method. Accuracy of the floating-point Math methods is measured in terms of ulps, units in the last place. For a given floating-point format, an ulp of a specific real number value is the distance between the two floating-point values bracketing that numerical value. When discussing the accuracy of a method as a whole rather than at a specific argument, the number of ulps cited is for the worst-case error at any argument. If a method always has an error less than 0.5 ulps, the method always returns the floating-point number nearest the exact result; such a method is correctly rounded. A correctly rounded method is generally the best a floating-point approximation can be; however, it is impractical for many floating-point methods to be correctly rounded. Instead, for the Math class, a larger error bound of 1 or 2 ulps is allowed for certain methods. Informally, with a 1 ulp error bound, when the exact result is a representable number, the exact result should be returned as the computed result; otherwise, either of the two floating-point values which bracket the exact result may be returned. For exact results large in magnitude, one of the endpoints of the bracket may be infinite. Besides accuracy at individual arguments, maintaining proper relations between the method at different arguments is also important. Therefore, most methods with more than 0.5 ulp errors are required to be semi-monotonic: whenever the mathematical function is non-decreasing, so is the floating-point approximation, likewise, whenever the mathematical function is non-increasing, so is the floating-point approximation. Not all approximations that have 1 ulp accuracy will automatically meet the monotonicity requirements.
The platform uses signed two’s complement integer arithmetic with int and long primitive types. The developer should choose the primitive type to ensure that arithmetic operations consistently produce correct results, which in some cases means the operations will not overflow the range of values of the computation. The best practice is to choose the primitive type and algorithm to avoid overflow. In cases where the size is int or long and overflow errors need to be detected, the methods addExact , subtractExact , multiplyExact , toIntExact , incrementExact , decrementExact and negateExact throw an ArithmeticException when the results overflow. For the arithmetic operations divide and absolute value, overflow occurs only with a specific minimum or maximum value and should be checked against the minimum or maximum as appropriate.
IEEE 754 Recommended Operations
The 2019 revision of the IEEE 754 floating-point standard includes a section of recommended operations and the semantics of those operations if they are included in a programming environment. The recommended operations present in this class include sin , cos , tan , asin , acos , atan , exp , expm1 , log , log10 , log1p , sinh , cosh , tanh , hypot , and pow . (The sqrt operation is a required part of IEEE 754 from a different section of the standard.) The special case behavior of the recommended operations generally follows the guidance of the IEEE 754 standard. However, the pow method defines different behavior for some arguments, as noted in its specification. The IEEE 754 standard defines its operations to be correctly rounded, which is a more stringent quality of implementation condition than required for most of the methods in question that are also included in this class.
Class Math
The class Math contains methods for performing basic numeric operations such as the elementary exponential, logarithm, square root, and trigonometric functions.
Unlike some of the numeric methods of class StrictMath , all implementations of the equivalent functions of class Math are not defined to return the bit-for-bit same results. This relaxation permits better-performing implementations where strict reproducibility is not required.
By default many of the Math methods simply call the equivalent method in StrictMath for their implementation. Code generators are encouraged to use platform-specific native libraries or microprocessor instructions, where available, to provide higher-performance implementations of Math methods. Such higher-performance implementations still must conform to the specification for Math .
The quality of implementation specifications concern two properties, accuracy of the returned result and monotonicity of the method. Accuracy of the floating-point Math methods is measured in terms of ulps, units in the last place. For a given floating-point format, an ulp of a specific real number value is the distance between the two floating-point values bracketing that numerical value. When discussing the accuracy of a method as a whole rather than at a specific argument, the number of ulps cited is for the worst-case error at any argument. If a method always has an error less than 0.5 ulps, the method always returns the floating-point number nearest the exact result; such a method is correctly rounded. A correctly rounded method is generally the best a floating-point approximation can be; however, it is impractical for many floating-point methods to be correctly rounded. Instead, for the Math class, a larger error bound of 1 or 2 ulps is allowed for certain methods. Informally, with a 1 ulp error bound, when the exact result is a representable number, the exact result should be returned as the computed result; otherwise, either of the two floating-point values which bracket the exact result may be returned. For exact results large in magnitude, one of the endpoints of the bracket may be infinite. Besides accuracy at individual arguments, maintaining proper relations between the method at different arguments is also important. Therefore, most methods with more than 0.5 ulp errors are required to be semi-monotonic: whenever the mathematical function is non-decreasing, so is the floating-point approximation, likewise, whenever the mathematical function is non-increasing, so is the floating-point approximation. Not all approximations that have 1 ulp accuracy will automatically meet the monotonicity requirements.
The platform uses signed two’s complement integer arithmetic with int and long primitive types. The developer should choose the primitive type to ensure that arithmetic operations consistently produce correct results, which in some cases means the operations will not overflow the range of values of the computation. The best practice is to choose the primitive type and algorithm to avoid overflow. In cases where the size is int or long and overflow errors need to be detected, the methods whose names end with Exact throw an ArithmeticException when the results overflow.
IEEE 754 Recommended Operations
The 2019 revision of the IEEE 754 floating-point standard includes a section of recommended operations and the semantics of those operations if they are included in a programming environment. The recommended operations present in this class include sin , cos , tan , asin , acos , atan , exp , expm1 , log , log10 , log1p , sinh , cosh , tanh , hypot , and pow . (The sqrt operation is a required part of IEEE 754 from a different section of the standard.) The special case behavior of the recommended operations generally follows the guidance of the IEEE 754 standard. However, the pow method defines different behavior for some arguments, as noted in its specification. The IEEE 754 standard defines its operations to be correctly rounded, which is a more stringent quality of implementation condition than required for most of the methods in question that are also included in this class.
Package java.math
Provides classes for performing arbitrary-precision integer arithmetic ( BigInteger ) and arbitrary-precision decimal arithmetic ( BigDecimal ). BigInteger is analogous to the primitive integer types except that it provides arbitrary precision, hence operations on BigInteger s do not overflow or lose precision. In addition to standard arithmetic operations, BigInteger provides modular arithmetic, GCD calculation, primality testing, prime generation, bit manipulation, and a few other miscellaneous operations. BigDecimal provides arbitrary-precision signed decimal numbers suitable for currency calculations and the like. BigDecimal gives the user complete control over rounding behavior, allowing the user to choose from a comprehensive set of eight rounding modes.
Immutable objects which encapsulate the context settings which describe certain rules for numerical operators, such as those implemented by the BigDecimal class.
Report a bug or suggest an enhancement
For further API reference and developer documentation see the Java SE Documentation, which contains more detailed, developer-targeted descriptions with conceptual overviews, definitions of terms, workarounds, and working code examples. Other versions.
Java is a trademark or registered trademark of Oracle and/or its affiliates in the US and other countries.
Copyright © 1993, 2023, Oracle and/or its affiliates, 500 Oracle Parkway, Redwood Shores, CA 94065 USA.
All rights reserved. Use is subject to license terms and the documentation redistribution policy.
Math library for java
Commons Math: The Apache Commons Mathematics Library
Commons Math is a library of lightweight, self-contained mathematics and statistics components addressing the most common problems not available in the Java programming language or Commons Lang.
- Real-world application use cases determine development priority.
- This package emphasizes small, easily integrated components rather than large libraries with complex dependencies and configurations.
- All algorithms are fully documented and follow generally accepted best practices.
- In situations where multiple standard algorithms exist, a Strategy pattern is used to support multiple implementations.
- Limited dependencies. No external dependencies beyond Commons components and the core Java platform (at least Java 1.3 up to version 1.2 of the library, at least Java 5 starting with version 2.0 of the library).
Download Math
Releases
Download the Latest Release of Commons Math.
Copyright © 2003-2022 The Apache Software Foundation. All Rights Reserved.
Apache Commons, Apache Commons Math, Apache, the Apache feather logo, and the Apache Commons project logos are trademarks of The Apache Software Foundation. All other marks mentioned may be trademarks or registered trademarks of their respective owners.