?
Solved

floating point addition and multiplication not necessarily associative.

Posted on 2008-09-30
12
Medium Priority
?
684 Views
Last Modified: 2012-05-05
(a) Give an example to show that floating point addition is not necessarily associative.
(b) Give an example to show that floating point multiplication is not necessarily associative.
0
Comment
Question by:panaz
  • 7
  • 5
12 Comments
 
LVL 85

Expert Comment

by:ozo
ID: 22610072
(FLT_EPSILON + FLT_EPSILON) + 2
FLT_EPSILON + (FLT_EPSILON + 2)


FLT_MAX * (FLT_MAX * FLT_MIN)
(FLT_MAX * FLT_MAX) * FLT_MIN
0
 

Author Comment

by:panaz
ID: 22610091
FLT_EPSILON : is this a standard global constant in C/ C++?
0
 
LVL 85

Expert Comment

by:ozo
ID: 22610099
(FLT_EPSILON + 2.5) + -2.5  
FLT_EPSILON + (2.5 + -2.5)
0
[Webinar On Demand] Database Backup and Recovery

Does your company store data on premises, off site, in the cloud, or a combination of these? If you answered “yes”, you need a data backup recovery plan that fits each and every platform. Watch now as as Percona teaches us how to build agile data backup recovery plan.

 
LVL 85

Expert Comment

by:ozo
ID: 22610189
FLT_EPSILON is in
#include <float.h>
0
 

Author Comment

by:panaz
ID: 22610195
thanks
0
 

Author Comment

by:panaz
ID: 22610277
#include<float.h>
#include<iostream>

using namespace std;
int main()
{
float a,b,c,d;

a = (FLT_EPSILON + 2.5) + -2.5 ;
b = FLT_EPSILON + (2.5 + -2.5);

cout<<"a :"<<a<<endl;

cout<<"b :"<<b<<endl;



return 0;
}


csci>a.out
a :1.19209e-07
b :1.19209e-07


0
 

Author Comment

by:panaz
ID: 22610281
a and b have the same values here. looks like it dont work?
0
 
LVL 85

Expert Comment

by:ozo
ID: 22610440
You are probably doing double precision arithmetic
try

a =  (FLT_EPSILON + 2.5);
cout<<"a :"<<a<<endl;
b = a + -2.5;
cout<<"b :"<<b<<endl;
c = 2.5;
d = -2.5;
a = (FLT_EPSILON + c) + d;
cout<<"a :"<<a<<endl;
b = (float)(FLT_EPSILON + 2.5) + -2.5;
cout<<"b :"<<b<<endl;
b =(FLT_EPSILON + 2.5f) + -2.5f;
cout<<"b :"<<b<<endl;
0
 

Author Comment

by:panaz
ID: 22610472
I guess its still the same values:

int main()
{
double a,b,c,d;

a =  (FLT_EPSILON + 2.5);
cout<<"a :"<<a<<endl;
b = a + -2.5;
cout<<"b :"<<b<<endl;
c = 2.5;
d = -2.5;
a = (FLT_EPSILON + c) + d;
cout<<"a :"<<a<<endl;

b = (float)(FLT_EPSILON + 2.5) + -2.5;
cout<<"b :"<<b<<endl;

b =(FLT_EPSILON + 2.5f) + -2.5f;
cout<<"b :"<<b<<endl;

return 0;

}

 [ Wrote 28 lines ]

csci>g++ test.cpp
csci>a.out
a :2.5
b :1.19209e-07
a :1.19209e-07
b :0
b :0
0
 
LVL 85

Accepted Solution

by:
ozo earned 1000 total points
ID: 22610562
You changed
float a,b,c,d;
to
double a,b,c,d;
For doubles, use DBL_EPSILON instead of FLT_EPSILON
0
 

Author Comment

by:panaz
ID: 22610575
okay
0
 

Author Comment

by:panaz
ID: 22610628
#include<float.h>
#include<iostream>
#include<limits>

using namespace std;

int main()
{
float a,b,c,d;

a =  (FLT_EPSILON + 2.5);
cout<<"a :"<<a<<endl;
b = a + -2.5;
cout<<"b :"<<b<<endl;

c = 2.5;
d = -2.5;
a = (FLT_EPSILON + c) + d;
cout<<"a :"<<a<<endl;

b = (float)(FLT_EPSILON + 2.5) + -2.5;
cout<<"b :"<<b<<endl;

b =(FLT_EPSILON + 2.5f) + -2.5f;
cout<<"b :"<<b<<endl;


return 0;

}


csci>g++ test.cpp
csci>a.out
a :2.5
b :0
a :0
b :0
b :0
0

Featured Post

Free Tool: Path Explorer

An intuitive utility to help find the CSS path to UI elements on a webpage. These paths are used frequently in a variety of front-end development and QA automation tasks.

One of a set of tools we're offering as a way of saying thank you for being a part of the community.

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

This article explores the difference between two entities: List and Category.   In part one,  we'll look at the basic concepts, and set some groundwork.  In part two, we'll get to some conclusions. I know that these two things are different, but…
Introduction This article explores the design of a cache system that can improve the performance of a web site or web application.  The assumption is that the web site has many more “read” operations than “write” operations (this is commonly the ca…
The Relationships Diagram is a good way to get an overall view of what a database is keeping track of. It is also where relationships are defined. A relationship specifies how two tables connect to each other. As you build tables in Microsoft Ac…
How can you see what you are working on when you want to see it while you to save a copy? Add a "Save As" icon to the Quick Access Toolbar, or QAT. That way, when you save a copy of a query, form, report, or other object you are modifying, you…
Suggested Courses
Course of the Month8 days, 15 hours left to enroll

621 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question