Java Floating Point Error
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Java Floating Point Precision
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Floating Point Number Java Example
way to fix precision errors is in Java. As you can see in the following example, there are precision errors: class FloatTest { public static void main(String[] args) { Float number1 = 1.89f; for(int i = 11; i < 800; i*=2) { System.out.println("loop value: " + i); System.out.println(i*number1); System.out.println(""); } } } The result displayed is: loop value: 11 20.789999 loop value: 22 41.579998 loop value: 44 83.159996 loop value: 88 166.31999 loop
Double Precision Floating Point Java
value: 176 332.63998 loop value: 352 665.27997 loop value: 704 1330.5599 Also, if someone can explain why it only does it starting at 11 and doubling the value every time. I think all other values (or many of them at least) displayed the correct result. Problems like this have caused me headache in the past and I usually use number formatters or put them into a String. Edit: As people have mentioned, I could use a double, but after trying it, it seems that 1.89 as a double times 792 still outputs an error (the output is 1496.8799999999999). I guess I'll try the other solutions such as BigDecimal java floating-point precision share|improve this question edited May 31 '12 at 15:49 mskfisher 1,94022036 asked Jul 15 '11 at 22:06 Adam Smith 1,85153156 both double and float are based on the binary system - simply speaking they are just sum of b1* 1/2 + b2*1/4 + b3*1/8 ... bn/2^n, they will never hold even one tenth precisely as you can't write down one tenth (0.1) in binary with finite number of nonzero digits - sorry for mentioning such obvious things –Boris Treukhov Jul 15 '11 at 22:25 add a comment| 8 Answers 8 active oldest votes up vote 8 down vote accepted If you really
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Java Double Precision Problem
Hierarchy View Source Export to PDF Export to Word Pages … SEI CERT Oracle Coding Standard for java ieee 754 Java 2 Rules Rule 03. Numeric Types and Operations (NUM) Skip to end of banner JIRA links Go to start of banner NUM04-J. Do not use floating-point http://stackoverflow.com/questions/6713673/precision-error-with-floats-in-java numbers if precise computation is required Skip to end of metadata Created by Fred Long, last modified by Arthur Hicken on Nov 03, 2015 Go to start of metadata DeprecatedThis rule may be deprecated and replaced by a similar guideline.06/28/2014 -- Version 1.0 The Java language provides two primitive floating-point types, float and double, which are https://www.securecoding.cert.org/confluence/display/java/NUM04-J.+Do+not+use+floating-point+numbers+if+precise+computation+is+required 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.When precise computation is necessary, such as when performing currency calculations, floating-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 ExampleThis noncompliant code example performs some basic curre
Study: Percolation 3.OOP 3.1Using Data Types 3.2Creating Data Types 3.3Designing Data Types 3.4Case Study: N-Body 4.Data Structures 4.1Performance 4.2Sorting http://introcs.cs.princeton.edu/java/91float/ and Searching 4.3Stacks and Queues 4.4Symbol Tables 4.5Case Study: https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html Small World Computer Science 5.Theory of Computing 5.1Formal Languages 5.2Turing Machines 5.3Universality 5.4Computability 5.5Intractability 9.9Cryptography 6.A Computing Machine 6.1Representing Info. 6.2TOY Machine 6.3TOY Programming 6.4TOY Simulator 7.Building a Computer 7.1Boolean Logic 7.2Basic Circuit Model 7.3Combinational Circuits 7.4Sequential Circuits 7.5Digital floating point Devices Beyond 8.Systems 8.1Library Programming 8.2Compilers 8.3Operating Systems 8.4Networking 8.5Applications Systems 9.Scientific Computation 9.1Floating Point 9.2Symbolic Methods 9.3Numerical Integration 9.4Differential Equations 9.5Linear Algebra 9.6Optimization 9.7Data Analysis 9.8Simulation Related Booksites Web Resources FAQ Data Code Errata Appendices A. Operator Precedence B. Writing Clear Code C. Glossary D. java floating point Java Cheatsheet E. Matlab Lecture Slides Programming Assignments 9.1 Floating Point This section under major construction. One distinguishing feature that separates traditional computer science from scientific computing is its use of discrete mathematics (0s and 1s) instead of continuous mathematics and calculus. Transitioning from integers to real numbers is more than a cosmetic change. Digital computers cannot represent all real numbers exactly, so we face new challenges when designing computer algorithms for real numbers. Now, in addition to analyzing the running time and memory footprint, we must be concerned with the "correctness" of the resulting solutions. This challenging problem is further exacerbated since many important scientific algorithms make additional approximations to accommodate a discrete computer. Just as we discovered that some discrete algorithms are inherently too slow (polynomial vs. exponential), we will see that some floating point algorithms are too
by David Goldberg, published in the March, 1991 issue of Computing Surveys. Copyright 1991, Association for Computing Machinery, Inc., reprinted by permission. Abstract Floating-point arithmetic is considered an esoteric subject by many people. This is rather surprising because floating-point is ubiquitous in computer systems. Almost every language has a floating-point datatype; computers from PCs to supercomputers have floating-point accelerators; most compilers will be called upon to compile floating-point algorithms from time to time; and virtually every operating system must respond to floating-point exceptions such as overflow. This paper presents a tutorial on those aspects of floating-point that have a direct impact on designers of computer systems. It begins with background on floating-point representation and rounding error, continues with a discussion of the IEEE floating-point standard, and concludes with numerous examples of how computer builders can better support floating-point. Categories and Subject Descriptors: (Primary) C.0 [Computer Systems Organization]: General -- instruction set design; D.3.4 [Programming Languages]: Processors -- compilers, optimization; G.1.0 [Numerical Analysis]: General -- computer arithmetic, error analysis, numerical algorithms (Secondary) D.2.1 [Software Engineering]: Requirements/Specifications -- languages; D.3.4 Programming Languages]: Formal Definitions and Theory -- semantics; D.4.1 Operating Systems]: Process Management -- synchronization. General Terms: Algorithms, Design, Languages Additional Key Words and Phrases: Denormalized number, exception, floating-point, floating-point standard, gradual underflow, guard digit, NaN, overflow, relative error, rounding error, rounding mode, ulp, underflow. Introduction Builders of computer systems often need information about floating-point arithmetic. There are, however, remarkably few sources of detailed information about it. One of the few books on the subject, Floating-Point Computation by Pat Sterbenz, is long out of print. This paper is a tutorial on those aspects of floating-point arithmetic (floating-point hereafter) that have a direct connection to systems building. It consists of three loosely connected parts. The first section, Rounding Error, discusses the implications of using different rounding strategies for the basic operations of addition, subtraction, multiplication and division. It also contains background information on the two methods of measuring rounding error, ulps and relative error. The second part discusses the IEEE floating-point standard, which