What does 1.#INF00, -1.#IND00 and -1.#IND means?

Question

I'm messing around with some C code using floats and I'm getting 1.#INF00, -1.#IND00 and -1.#IND when I try to print floats in the screen. What does those values mean? I believe that 1.#INF00 means positive infinity, but what about -1.#IND00 and -1.#IND? I also saw sometimes this value: 1.$NaN which is Not a Number but what causes those strange values and how can those help me with debugging?

I'm using MingW which I believe uses IEEE 754 representation for float points.

Can someone list all those invalid values and what they mean?

Answer 1

From IEEE floating-point exceptions in C++ :

This page will answer the following questions.

• My program just printed out 1.#IND or 1.#INF (on Windows) or nan or inf (on Linux). What happened?
• How can I tell if a number is really a number and not a NaN or an infinity?
• How can I find out more details at runtime about kinds of NaNs and infinities?
• Do you have any sample code to show how this works?
• Where can I learn more?

These questions have to do with floating point exceptions. If you get some strange non-numeric output where you're expecting a number, you've either exceeded the finite limits of floating point arithmetic or you've asked for some result that is undefined. To keep things simple, I'll stick to working with the double floating point type. Similar remarks hold for float types.

Debugging 1.#IND, 1.#INF, nan, and inf

If your operation would generate a larger positive number than could be stored in a double, the operation will return 1.#INF on Windows or inf on Linux. Similarly your code will return 11.#INF or -inf if the result would be a negative number too large to store in a double. Dividing a positive number by zero produces a positive infinity and dividing a negative number by zero produces a negative infinity. Example code at the end of this page will demonstrate some operations that produce infinities.

Some operations don't make mathematical sense, such as taking the square root of a negative number. (Yes, this operation makes sense in the context of complex numbers, but a double represents a real number and so there is no double to represent the result.) The same is true for logarithms of negative numbers. Both sqrt(-1.0) and log(-1.0) would return a NaN, the generic term for a "number" that is "not a number". Windows displays a NaN as -1.#IND ("IND" for "indeterminate") while Linux displays nan. Other operations that would return a NaN include 0/0, 0*∞, and ∞/∞. See the sample code below for examples.

In short, if you get 1.#INF or inf, look for overflow or division by zero. If you get 1.#IND or nan, look for illegal operations. Maybe you simply have a bug. If it's more subtle and you have something that is difficult to compute, see Avoiding Overflow, Underflow, and Loss of Precision. That article gives tricks for computing results that have intermediate steps overflow if computed directly.