If-else block and unexpected results with float datatype. [Edited with one more question]

Question

Hello, I compiled the following program with gcc 4.4.1 and I get unexpected output (Well, unexpected for me)

#include<stdio.h>

int main()
{
        float x=0.3, y=0.7;

        if(x==0.3)
        {
                if(y==0.7)
                        printf("Y\n\n");
                else
                        printf("X\n\n");
        }
        else
                printf("NONE\n\n");
}


Output: NONE

---

#include<stdio.h>

int main()
{
        float x=0.3, y=0.7;

        if(x<0.3)
        {
                if(y==0.7)
                        printf("Y\n\n");
                else
                        printf("X\n\n");
        }
        else
                printf("NONE\n\n");
}

Output: NONE

---

#include<stdio.h>

int main()
{
        float x=0.3, y=0.7;

        if(x>0.3)
        {
                if(y>0.7)
                        printf("Y\n\n");
                else
                        printf("X\n\n");
        }
        else
                printf("NONE\n\n");
}

    Output:X

So, it's clearly visible that the stored value in "x" is greater than 0.3 and the stored value in "y" is less than 0.7

Why is this happening? Is this a property of float datatype or the if-else statements interpret float in a different way?

Thanks.

---

Edit: Alright, I pondered it over and I'm getting a little confused now. Kindly tell if my understanding of this problem is correct or not.

float x=0.3;

This stores x=0.30000001192092895508 in the memory. Clearly, this is greater than 0.3 (Is this correct?)

Now, double x=0.3 results in x=0.29999999999999998890 and this is smaller than 0.3 (Is this correct too?)

Main question: So if I use store 0.3 in float x, then the following statement if(x>0.3) results in x=0.30000001192092895508 being implicitly casted as a double and 0.3 is also a double instead of a float. Hence 0.3=0.29999999999999998890 and the internal operation is if((double) 0.30000001192092895508 > (double) 0.29999999999999998890). Is this correct?

Answer 1

Computers can't store floating point numbers exactly. Just like 1/7 can't be represented in a finite number of decimal digits, lots of numbers can't be represented exactly in binary. 3/10 is such a number. When you write 0.3 your program actually stores 0.30000001192092895508 as that's the best it can do with the 32 bits available to it in a float variable.

And it so happens that this value also differs from the double value of 0.3 since the computer can store more digits in a 64-bit double. When you write if (x == 0.3) your value is actually promoted to a double since floating-point constants are doubles unless explicitly specified otherwise. It's equivalent to writing if ((double) x == 0.3).

jkugelman$ cat float.c
#include <stdio.h>

int main() {
    printf("%.20f\n", (float)  0.3);  // Can also be written "0.3f".
    printf("%.20f\n", (double) 0.3);  // Cast is redundant, actually.
    return 0;
}

jkugelman$ gcc -Wall -o float float.c

jkugelman$ ./float
0.30000001192092895508
0.29999999999999998890

Notice how the 0.2999... value has more 9's in it than the 0.3000... one. The double-precision value is closer to 0.3 thanks to the extra bits.

Answer 2

You're using float for storage, but you comparisons are being performed against the literals which are of type double.

The values of x and y aren't exactly 0.3 and 0.7, as those numbers aren't representable in binary floating point. It happens that the closest float to 0.3 is greater than the closest double to 0.3, and the closest float to 0.7 is less than the closest double to 0.7... hence your comparison results.

Assuming the representations are the same as in C# (where I happen to have some tools to help) the values involved are:

0.3 as float = 0.300000011920928955078125
0.3 as double = 0.299999999999999988897769753748434595763683319091796875
0.7 as float = 0.699999988079071044921875
0.7 as double = 0.6999999999999999555910790149937383830547332763671875

So that explains why it's happening... but it doesn't explain how to work around the issue for whatever your code is actually trying to do, of course. If you can give more context to the bigger problem, we may be able to help more.