floating point operations

Question

i have read that some machine can't express exaclty floating point number for example 1.1 let's take code

float x=0.1;
do{

x+=0.1;
printf("%f\n",x);
} while(x!=1.1);

this code never finished how can i make that code finish? maybe convert it to double or?

You are not supposed to use equality comparisons on floating point numbers. — phkahler, Jul 30 '10 at 14:06
This is my favorite explanation of why floating point numbers, of any precision or type, cannot exactly represent all real numbers: http://stackoverflow.com/questions/1089018/why-cant-decimal-numbers-be-represented-exactly-in-binary/1089026#1089026 — mtrw, Jul 30 '10 at 16:55

score 3 · Answer 1 · answered Jul 30 '10 at 13:24

3

For numerical problems, it is common to specify an epsilon of accuracy:

bool within_epsilon(float x, float y, float e) {
    if (abs(x - y) > e) {
        return false
    } else {
        return true
    }
}

The epsilon you choose will change your accuracy, and the epsilon you can choose is dependent on your floating point implementation: Machine epsilon.

answered Jul 30 '10 at 13:24

tkerwin

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+1 for referring to epsilon, since this will enable people to google for this information in an easier way – davbryn Jul 30 '10 at 13:30

relet · Answer 2 · 2010-07-30T13:26:54.403

2

For example, compare within an acceptable margin. I.e.

while (abs(x-1.1)>0.001);

Doubles will have the same issue, just with more precision. Some languages also offer you rational types, where you can specify a number as the fraction 1/10, or fixed point data types.

edited Jul 30 '10 at 13:26

answered Jul 30 '10 at 13:16

relet

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score 0 · Accepted Answer · answered Jul 30 '10 at 13:19

0

In this case, checking "<" will do the trick:

float x=0.1;
do{

x+=0.1;
printf("%f\n",x);
} while(x<1.05);

In general, you should test against an "epsilon". Look here for further information.

answered Jul 30 '10 at 13:19

Doc Brown

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score 0 · Answer 4 · answered Jul 30 '10 at 13:22

0

Work in fixed point, for that kind of task.

The decimal type for example might help. It's not the solution for all problems though.

answered Jul 30 '10 at 13:22

Mau

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score -1 · Answer 5 · answered Jul 30 '10 at 13:22

If you want to do code precisely like you are saying then you want to use a type like decimal (where available) which is a base 10 floating point implementation rather than a base 2.

Further reading: http://en.wikipedia.org/wiki/Floating_point#Accuracy_problems and http://en.wikipedia.org/wiki/Decimal_floating_point

floating point operations

5 Answers5