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[个人原创]Why some unwanted result comes out in floating-point operation?

ranchgirl

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发贴: 801
积分: 132

于 2005-07-31 10:34

See a question in Java基础, copy my own article here written quite while ago.

Q. When I do floating-point operation, why some unwanted result comes out?


// Example, why do the digits 000000000003 extra after 20.255 come out?
double x = 27.475;
double y = 7.22; 
System.out.println(x - y); // 20.255000000000003

A: That is a famous floating-point phenomenon. Your number is represented in decimal, and your computer represents them in binary, some discrepancy will happen with that conversion back-and-forth. It is normal since Machine Language / Assembly / Fortran time. If you go to an interview, someone ask you this question, you don't know the answer, and inexperienced programmer situation will be exposed to the interviewer immediately.

When you output, format it to what you desired.

How the precision changed? Explanation is no easy job. You need understand what is radix.

Radix for decimal is 10
Radix for binary is 2

29.3 in decimal is actually
2 * 10¹ + 9 * 10⁰ + 3 * 10^-1
In binary
11101.010011001.............
Do the same thing, but replace 10 to 2.

However, the number will never end. You will find out something is short in decimal may become infinite long in binary. And the opposite will not be infinite long, but possible longer then the computer system allowed. Computer cannot allow infinite long number, it must be truncated to fit the precision of the floating-point number in the system.

Therefore, the value of some floating-point number changes in the conversion from one radix to another radix back-and-forth.

If 29.125 in decimal is converted to binary, there are no problems. It will be 11101.001 in binary precisely, since 0.125 is 2^-3 or 1/8. Smile

gongshi edited on 2005-07-31 15:07

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Re:[个人原创]Why some unwanted result comes out in floating-point operation? [Re:gongshi]

ranchgirl

版主

发贴: 801
积分: 132

于 2005-07-31 15:14

My original article was in xhtml, when I converted it to jute format, made a few mistakes. Now, I think they are fixed.

This is mostly math in computing problem. Real numbers in math are continuous. However, real numbers in computer must be discrete.

Theoretically, this kind unwanted results are inavoidable, no matter how accurate your computer is or will be in the future.

You'd better understand it. Thanks!

gongshi edited on 2005-07-31 15:26

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