asked on

floating point addition and multiplication not necessarily associative.

(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.

ozo

(FLT_EPSILON + FLT_EPSILON) + 2
FLT_EPSILON + (FLT_EPSILON + 2)

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

panaz

ASKER

FLT_EPSILON : is this a standard global constant in C/ C++?

ozo

(FLT_EPSILON + 2.5) + -2.5
FLT_EPSILON + (2.5 + -2.5)

ozo

FLT_EPSILON is in
#include <float.h>

panaz

ASKER

thanks

panaz

ASKER

#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

panaz

ASKER

a and b have the same values here. looks like it dont work?

ozo

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;

panaz

ASKER

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

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ozo

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panaz

ASKER

okay

panaz

ASKER

#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