Programmers Stack Exchange is a question and answer site for professional programmers interested in conceptual questions about software development. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Back in my C programming days I thought there was a constant or function (I can't remember what it was called, let's call it SMALL) whose value was the smallest possible positive value. (Imagine the LSB=1 and all other bits = 0.) It was used to avoid a divide by zero error.

For example, let's say you want to compute z = x/y. Then you could calculate
z = x / (y + SMALL);

Is there a built-in function in MS EXCEL that implements SMALL? For that matter, does it exist in C/C++ or am I going crazy?

share|improve this question
I've never heard of this, and it sounds like a terrible way to avoid a divide by zero error. The small price of an if statement is nothing compared to knowingly making all your calculations less accurate. – Ryathal Feb 23 '12 at 16:48
"It was used to avoid a divide by zero error." That has EPIC FAIL written all over it. – S.Lott Feb 23 '12 at 16:52
What if y == -SMALL? As others have said, using this to avoid division by zero is a horrifically bad idea, and is a good sign that you need to rethink what you're doing. – Jack Maney Feb 23 '12 at 18:09
In my case x and y are both nonnegative. z is a percentage and is rounded. – Stainsor Feb 24 '12 at 14:28
up vote 3 down vote accepted

Take a look at the FLT_EPSILON can be used to compare a float variable to 0 (zero), or nearly zero in that case.

There's an other article here:

EDIT: what you need is this q&a: it describes the epsilon value in excel.

share|improve this answer
Yes, that q&a answers it. I guess "=2^-1022" is the simplest way. – Stainsor Feb 24 '12 at 15:31

I think you're probably remembering FLT_EPSILON, DBL_EPSILON, and so on.

They aren't quite what you're describing though: they're not the smallest number greater than 0. Rather, they're the smallest number greater than 1. For better or worse, however, DBL_EPSILON-1 won't be even close to the smallest number greater than 0. Epsilon is really intended to be scaled by multiplication, not addition or subtraction.

This is not normally used to avoid problems with division by zero, but to give some idea of the smallest possible difference between two numbers, and whether two numbers are "substantially different", or any inequality between them is really due to rounding errors (and such).

I'd also note that replacing x/y with x/(y+EPSILON) could quite easily cause a division by zero rather than preventing it (i.e., if y == -EPSILON).

share|improve this answer
Excellent answer. I think I was remembering EPSILON, but no one really ever told me how to use it. So Thanks! – Stainsor Feb 24 '12 at 15:29

The proper C++ way is in the <limits> header:

in particular std::numeric_limits<T>::epsilon() is defined (specialized) for all the built-in types as in cppreference

share|improve this answer
great example at that link showing the scaling method Jerry referred to – Stainsor Feb 24 '12 at 15:32

As @Rythal said its a terrible way of avoiding divide by zero, however, if you wish to persist, the minimum (and maximum) values for float and double are defined in float.h. This is explored here.

share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.