Thread: False Boolean Value?

When the following code is executed, the loop does not run when f == 2.0
Why wouldn't it?

Code:

int main()
{
        printf("\n\n\n"); //spacer

        float f = .1;
        while (f <= 2.0)
        {
                printf("&#37;.1f*Pi:  sin() = %f  cos() = %f  tan() = %f\n",
                                                        f,
                                                        sin(PI*f),
                                                        cos(PI*f),
                                                        tan(PI*f));
                f += .1;
                printf("\nf now equals %f",f);
        }
        printf("\n\n\n"); //spacer


        return 0;
}

last line of output from program:

Code:

1.9*Pi:  sin() = -0.309016  cos() = 0.951057  tan() = -0.324919

f now equals 2.000000

I also tried to see if this statement returned a true value:

Code:

(2.0 == 2.00)

..and it did, so I have no idea why my loop only runs until f == 1.9

I know I could eliminate the problem by changing my loop to:

Code:

while (f < 2.1)

But i'm curious as to why it isn't working as is.

Thank you for any help.

Sigh...

The value 0.1 cannot be exactly represented in a binary format. There is no way to repeatedly add the value 0.1 to itself to achieve the value 2.0. Read any basic introduction to floating point arithmetic.

www.cygnus-software.com/papers/comparingfloats/comparingfloats.htm

Found the section on epsilon comparisons especially helpful. Thanks.

Originally Posted by kwikness

I was under the impression that floats stored 6 significant digits, so I thought that this was the entire value of f.

No, that's just what got printed. The actual value may have been something like 2.00000000001.

A float doesn't store a certain number of digits. The decimal point can "float" back and forth, thus the name. Since it is intrinsically a binary, not decimal, object, it is impossible to characterize the number of decimal digits it can represent -- unless you want to refer to a fractional number of digits.

For instance if you had 16 bits available to represent a fractional value, that's equivalent to 16 * log(2) / log(10) = 4.816... decimal digits.

I was wrong then if it the float doesnt have const no of decimal places after the point.

ssharish