Looping over a range of floats in C

Question

I am trying to write a program in C to accomplish the following task.

Input: Three double-precision numbers, a, b, and c.

Output: All the numbers from b to a, that can be reached by decrements of c.

Here is a simple program (filename: range.c).

#include <stdlib.h>
#include <stdio.h>

int main()
{
    double high, low, step, var;
    printf("Enter the <lower limit> <upperlimit> <step>\n>>");
    scanf("%lf %lf %lf", &low, &high, &step);
    printf("Number in the requested range\n");
    for (var = high; var >= low; var -= step)
        printf("%g\n", var);
    return 0;
}

However, the for loop behaves rather bizarrely for some inputs. For instance, the following.

10-236-49-81:stackoverflow pavithran$ ./range.o 
Enter the <lower limit> <upperlimit> <step>
>>0.1 0.9 0.2
Number in the requested range
0.9
0.7
0.5
0.3
10-236-49-81:stackoverflow pavithran$

I cannot figure out why the loop quits at var = 0.1. While for another input, it behaves as expected.

10-236-49-81:stackoverflow pavithran$ ./range.o 
Enter the <lower limit> <upperlimit> <step>
>>0.1 0.5 0.1
Number in the requested range
0.5
0.4
0.3
0.2
0.1
10-236-49-81:stackoverflow pavithran$

Had the weird behaviour in the first situation got something to do with numeric precision?

How can I ensure that the range will always contain floor((high - low)/step) + 1 numbers?

I have tried an alternate method of looping over floats, where I scale the loop variables to integers, and print the result of the loop variable divided by the scaling used. But there's perhaps a better way...

Possible duplicate of [Is floating point math broken?](http://stackoverflow.com/questions/588004/is-floating-point-math-broken) — LPs, Oct 19 '16 at 15:02
I think the problem needs clarification. Are the decrements supposed to be in double arithmetic or in real number arithmetic? — Patricia Shanahan, Oct 19 '16 at 22:49

Bathsheba · Accepted Answer · 2016-10-19T15:08:08.783

Using a double as a counter in a for loop requires very careful consideration. In many instances it's best avoided.

I'm sure you know that not all numbers that are exact in decimal are also exact in binary floating point. In fact, for IEEE754 floating point, only dyadic rationals are. So 0.5 is, but 0.4, 0.3, 0.2, and 0.1 are not.

The closest IEEE754 floating point double to 0.2 is actually the slightly larger 0.200000000000000011102230246251565404236316680908203125.

In your case a repeated subtraction of this from 0.9 eventually causes a number whose first significant figure is a to become a number whose first significant figure is a - 3: your bug then manifests itself.

The simple remedy is to work in integers, decement by 1 each time, and scale your output using step.

Looping over a range of floats in C

1 Answers1