Whats wrong with this simple ‘double’ calculation? [duplicate]

by

The problem

In binary 2.64 is 10.10100011110101110000101000111101 recurring, in other words not exactly representable in binary, hence the small error. Java is being kind to you with d3 but as soon as actual calculations are involved it has to fall back on the real representation.

Binary Calculator

Further more:

2.64= 10.10100011110101110000101000111101
4.64=100.1010001111010111000010100011110

Now, even though the .64 is the same in both cases, it is held to different precisions because the 4=100 uses up more of the double significant figures than 2=10, so when you say 4.64-2.0 and 2.64 the .64 is represented with a different rounding error in both cases, this lost information cannot be recovered for the final answer.

N.B. I’m not using the double number of significant figures here, just whatever the binary calculator would produce, however the effect is the same whatever the number of significant figures

Never assume double values are exact (although their inaccuracies are microscopic and caused only because certain numbers can’t be exactly expressed in binary).

Floating point numbers aren’t exact, but only from a decimal point of view

While you should always expect that doubles will have small errors for the last few decimal places it would be wrong to think of binary representations as “bad” or worse that decimal.

We are all used to certain numbers (like 1/3 for example) not being exactly representable in decimal and we accept that such a number will end up as 0.333333333333 rather than the true value (which I cannot write down without infinite space); it is within that context that binary numbers cannot be exactly expressed. 1/10 is such a number that cannot be exactly expressed in binary; this suprises us only because we are used to decimal

More Related Contents:

  1. Java BigDecimal precision problems
  2. Comparing double values for equality in Java.
  3. java if else errors not working properly
  4. Declaring variables inside or outside of a loop
  5. Effective gif/image color quantization?
  6. How can I convert int[] to Integer[] in Java?
  7. Image encryption/decryption using AES256 symmetric block ciphers [closed]
  8. Intellij fat one jar artifact does not generate a working output
  9. How to asynchronously call a method in Java
  10. How to get the selected index of a RadioGroup in Android
  11. Java Generics WildCard Question: List
  12. What is the best way to avoid maven-jar?
  13. Use Ant for running program with command line arguments
  14. Tomcat 7 and JSTL
  15. Accurate Sleep for Java on Windows
  16. Can I combine a @Query definition with a Specification in a Spring Data JPA repository method?
  17. Field.get(obj) returns all nulls on injected CDI managed beans, while manually invoking getters return correct values
  18. Can you get basic GC stats in Java?
  19. How can a Swing WindowListener veto JFrame closing
  20. How to Convert List to List
  21. Editing PDF text using Java
  22. Translating strings character by character
  23. Display JCheckBox in JTable
  24. Where should i place my files in order to be able to access them when i run the jar?
  25. Packaging Java apps for the Windows/Linux desktop
  26. JSP: EL expression is not evaluated [duplicate]
  27. Convert static windows library to dll
  28. Why are Integers immutable in Java?
  29. PDFBox 2.0 RC3 — Find and replace text
  30. Where are the generated JSP class files located?

Leave a Comment