In Java, What Does Nan Mean

In Java, what does NaN mean?

Taken from this page:

"NaN" stands for "not a number". "Nan"
is produced if a floating point
operation has some input parameters
that cause the operation to produce
some undefined result. For example,
0.0 divided by 0.0 is arithmetically undefined. Taking the square root of a
negative number is also undefined.

Why does Double.NaN==Double.NaN return false?

NaN means "Not a Number".

Java Language Specification (JLS) Third Edition says:

An operation that overflows produces a signed infinity, an operation that underflows produces a denormalized value or a signed zero, and an operation that has no mathematically definite result produces NaN. All numeric operations with NaN as an operand produce NaN as a result. As has already been described, NaN is unordered, so a numeric comparison operation involving one or two NaNs returns false and any != comparison involving NaN returns true, including x!=x when x is NaN.

what is NaN? and how is been created?

NaN stands for Not-a-Number. It can arise in a variety of ways, for example as a result of 0./0., sqrt(-1), or as the result of a calculation involving other NaNs.

The easiest way to check whether v is a NaN is by using Double.isNaN(v):

public static double sum(double arr[]) {
  double sum = 0.0;
  for (double val : arr) {
    if (!Double.isNaN(val)) {
      sum += val;
    }
  }
  return sum;
}

edit: @Stephen C makes a good point in the comments: before deciding to ignore that NaN, it would be prudent to understand where it came from. It could be that it is the result of a bug elsewhere in your code, and by blindly ignoring the NaN you could simply be masking the bug instead of fixing it.

What is NaN (Not a Number) in the words of a beginner?

You've asked a series of great questions here. Here's my attempt to address each of them.

What is a NaN value or NaN exactly (in the words of a non-math professor)?

Let's suppose you're working with real numbers - numbers like 1, π, e, -137, 6.626, etc. In the land of real numbers, there are some operations that usually can be performed, but sometimes don't have a defined result. For example, let's look at logarithms. You can take the logarithm of lots of real numbers: ln e = 1, for example, and ln 10 is about 2.3. However, mathematically, the log of a negative number isn't defined. That is, we can't take ln (-4) and get back a real number.

So now, let's jump to programming land. Imagine that you're writing a program that or computes the logarithm of a number, and somehow the user wants you to divide by take the logarithm of a negative number. What should happen?

There's lots of reasonable answers to this question. You could have the operation throw an exception, which is done in some languages like Python.

However, at the level of the hardware the decision that was made (by the folks who designed the IEEE-754 standard) was to give the programmer a second option. Rather than have the program crash, you can instead have the operation produce a value that means "you wanted me to do something impossible, so I'm reporting an error." The way this is done is by having the operation produce the special value NaN ("Not a Number"), indicating that, somewhere in your calculation, you tried to perform an operation that's mathematically not defined.

There are some advantages to this approach. In many scientific computing settings, the code performs a series of long calculations, periodically generating intermediate results that might be of interest. By having operations that aren't defined produce NaN as a result, the programmer can write code that just does the math as they want it to be done, then introduce specific spots in the code where they'll test whether the operation succeeded or not. From there, they can decide what to do. Contrast this with tripping an exception or crashing the program outright - that would mean the programmer either needs to guard every series of floating point operations that could fail or has to manually test things herself. It’s a judgment call about which option is better, which is why you can enable or disable the floating point NaN behavior.

What are operations which causing a NaN value as result?

There are many ways to get a NaN result from an operation. Here's a sampler, though this isn't an exhaustive list:

Taking the log of a negative number.
Taking the square root of a negative number.
Subtracting infinity from infinity.
Performing any arithmetic operation on NaN.

There are, however, some operations that don't produce NaN even though they're mathematically undefined. For example, dividing a positive number by zero gives positive infinity as a result, even though this isn't mathematically defined. The reason for this is that if you take the limit of x / y for positive x as y approaches zero from the positive direction, the value grows without bound.

Why is the result of 0.0 / 0.0 declared as undefined? Shouldn´t it be 0?

This is more of a math question than anything else. This has to do with how limits work. Let's think about how to define 0 / 0. One option would be to say the following: if we look at the expression 0 / x and take the limit as x approaches zero, then we'd see 0 at each point, so the limit should be zero. On the other hand, if we look at the expression x / x and take the limit as x approaches 0, we'd see 1 at each point, so the limit should be one. This is problematic, since we'd like the value of 0 / 0 to be consistent with what you'd find as you evaluated either of these expressions, but we can't pick a fixed value that makes sense. As a result, the value of 0 / 0 gets evaluated as NaN, indicating that there's no clear value to assign here.

Why can´t the result of any mathematical operation be expressed by a floating point or integer number? How can it be that a value is unrepresentable?

This has to do with the internals of IEEE-754 floating point numbers. Intuitively, this boils down to the simple fact that

there are infinitely many real numbers, infinitely many of which have infinitely long non-repeating decimals, but
your computer has finite memory.

As a result, storing an arbitrary real number might entail storing an infinitely long sequence of digits, which we can't do with our finite-memory computers. We therefore have floating point numbers store approximations of real numbers that aren't staggeringly huge, and the inability to represent values results from the fact that we're just storing approximations.

For more on how the numbers are actually stored, and what this means in practice, check out the legendary guide "What Every Programmer Should Know About Floating-Point Arithmetic"

Why is the square root of a negative number not a real number?

Let's take √(-1), for example. Imagine this is a real number x; that is, imagine that x = √(-1). The idea of a square root is that it's a number that, if multiplied by itself, gives you back the number you took the square root of.

So... what number is x? We know that x ≠ 0, because 0² = 0 isn't -1. We also know that x can't be positive, because any positive number times itself is a positive number. And we also know that x can't be negative, because any negative number times itself is positive.

We now have a problem. Whatever this x thing is, it would need to be not positive, not zero, and not negative. That means that it's not a real number.

You can generalize the real numbers to the complex numbers by introducing a number i where i² = -1. Note that no real numbers do this, for the reason given above.

Why is NaN not equivalent to indefinite?

There's a difference between "indefinite" and "whatever it is, it's not a real number." For example, 0 / 0 may be said to be indeterminate, because depending on how you approach 0 / 0 you might get back 0, or 1, or perhaps something else. On the other hand, √(-1) is perfectly well-defined as a complex number (assuming we have √(-1) give back i rather than -i), so the issue isn't "this is indeterminate" as much as "it's got a value, but that value isn't a real number."

Hope this helps!

NaN error while summing in Java

First, you need to understand what NaN stands for. Nan stands for Not a Number.

How you get NaN?

“Nan” is produced if a floating point operation has some input
parameters that cause the operation to produce some undefined result.

What may cause NaN?

For example, 0.0 divided by 0.0 is arithmetically undefined. Finding
out the square root of a negative number too is undefined.

Also,

All numeric operations with NaN as an operand produce NaN as a result.
Reason behind this is that NaN is unordered, so a numeric comparison
operation involving one or two NaNs returns false.

Since we fully understand NaN, now let's work our way around the solution now.

In your case the NaN is produced by Math.log(i1/i0);
Logarithmic functions are not defined on (-oo,0]. Hence every negative number entered as parameter Math.log(i1/i0); will return a NaN as result in java.

What you can do?

-> Build a tiny test on i1/i0 before passing it as parameter in Math.log()

Suggestion:

for (int i=0;i<evolution.size()-1; i++)
    {
        double i1 =evolution.get(i+1) ;
        double i0 = evolution.get(i) ;
        if (i1/i0>0)
        {
            //you are good 
            sommeTendance+= Math.log(i1/i0);
            sommeVarianceQuotidienne += Math.pow(Math.log(i1/i0),2);
        }
        else
        {
            //you are not good, the number will yield an undefined result 
            //do something else... like displaying an error....?
            System.out.println("Math.log will yield into an undefined result. Please check your input");
        }
    }

Useful links:

https://www.avocado.com.au/resources/tech-tips/java-double-nan-weirdness/
https://www.geeksforgeeks.org/nan-not-number-java/

Hope this helps.

what does NaN mean for doubles?

From Wikipedia :

In computing, NaN (Not a Number) is a value of the numeric data type representing an undefined or unrepresentable value, especially in floating-point calculations. Systematic use of NaNs was introduced by the IEEE 754 floating-point standard in 1985, along with the representation of other non-finite quantities like infinities.

And from MSDN :

Represents a value that is not a number (NaN). This field is constant.
The value of this constant is the result of dividing zero by zero.
This constant is returned when the result of an operation is undefined.
Use IsNaN to determine whether a value is not a number. It is not possible to determine whether a value is not a number by comparing it to another value equal to NaN.

Where as Infinity (positive infinity and negative infinity) is the result of a floating point operation that causes an overflow (For example 3.0 / 0).

In Java, What Does Nan Mean