In Java, what does NaN mean?

Question

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.

NaN means “Not a Number” and is basically a representation of a special floating point value in the IEE 754 floating point standard. NaN generally means that the value is something that cannot be expressed with a valid floating point number.

A conversion will result in this value, when the value being converted is something else, for example when converting a string that does not represent a number.

NaN means "Not a Number" and is the result of undefined operations on floating point numbers like for example dividing zero by zero. (Note that while dividing a non-zero number by zero is also usually undefined in mathematics, it does not result in NaN but in positive or negative infinity).

Minimal runnable example

The first thing that you have to know, is that the concept of NaN is implemented directly on the CPU hardware.

All major modern CPUs seem to follow IEEE 754 which specifies floating point formats, and NaNs, which are just special float values, are part of that standard.

Therefore, the concept will be the very similar across any language, including Java which just emits floating point code directly to the CPU.

Before proceeding, you might want to first read up the following answers I've written:

• a quick refresher of the IEEE 754 floating point format: What is a subnormal floating point number?
• some lower level NaN basics covered using C / C++: What is difference between quiet NaN and signaling NaN?

Now for some Java action. Most of the functions of interest that are not in the core language live inside java.lang.Float.

Nan.java

import java.lang.Float;
import java.lang.Math;

public class Nan {
    public static void main(String[] args) {
        // Generate some NaNs.
        float nan            = Float.NaN;
        float zero_div_zero  = 0.0f / 0.0f;
        float sqrt_negative  = (float)Math.sqrt(-1.0);
        float log_negative   = (float)Math.log(-1.0);
        float inf_minus_inf  = Float.POSITIVE_INFINITY - Float.POSITIVE_INFINITY;
        float inf_times_zero = Float.POSITIVE_INFINITY * 0.0f;
        float quiet_nan1     = Float.intBitsToFloat(0x7fc00001);
        float quiet_nan2     = Float.intBitsToFloat(0x7fc00002);
        float signaling_nan1 = Float.intBitsToFloat(0x7fa00001);
        float signaling_nan2 = Float.intBitsToFloat(0x7fa00002);
        float nan_minus      = -nan;

        // Generate some infinities.
        float positive_inf   = Float.POSITIVE_INFINITY;
        float negative_inf   = Float.NEGATIVE_INFINITY;
        float one_div_zero   = 1.0f / 0.0f;
        float log_zero       = (float)Math.log(0.0);

        // Double check that they are actually NaNs.
        assert  Float.isNaN(nan);
        assert  Float.isNaN(zero_div_zero);
        assert  Float.isNaN(sqrt_negative);
        assert  Float.isNaN(inf_minus_inf);
        assert  Float.isNaN(inf_times_zero);
        assert  Float.isNaN(quiet_nan1);
        assert  Float.isNaN(quiet_nan2);
        assert  Float.isNaN(signaling_nan1);
        assert  Float.isNaN(signaling_nan2);
        assert  Float.isNaN(nan_minus);
        assert  Float.isNaN(log_negative);

        // Double check that they are infinities.
        assert  Float.isInfinite(positive_inf);
        assert  Float.isInfinite(negative_inf);
        assert !Float.isNaN(positive_inf);
        assert !Float.isNaN(negative_inf);
        assert one_div_zero == positive_inf;
        assert log_zero == negative_inf;
            // Double check infinities.

        // See what they look like.
        System.out.printf("nan            0x%08x %f\n", Float.floatToRawIntBits(nan           ), nan           );
        System.out.printf("zero_div_zero  0x%08x %f\n", Float.floatToRawIntBits(zero_div_zero ), zero_div_zero );
        System.out.printf("sqrt_negative  0x%08x %f\n", Float.floatToRawIntBits(sqrt_negative ), sqrt_negative );
        System.out.printf("log_negative   0x%08x %f\n", Float.floatToRawIntBits(log_negative  ), log_negative  );
        System.out.printf("inf_minus_inf  0x%08x %f\n", Float.floatToRawIntBits(inf_minus_inf ), inf_minus_inf );
        System.out.printf("inf_times_zero 0x%08x %f\n", Float.floatToRawIntBits(inf_times_zero), inf_times_zero);
        System.out.printf("quiet_nan1     0x%08x %f\n", Float.floatToRawIntBits(quiet_nan1    ), quiet_nan1    );
        System.out.printf("quiet_nan2     0x%08x %f\n", Float.floatToRawIntBits(quiet_nan2    ), quiet_nan2    );
        System.out.printf("signaling_nan1 0x%08x %f\n", Float.floatToRawIntBits(signaling_nan1), signaling_nan1);
        System.out.printf("signaling_nan2 0x%08x %f\n", Float.floatToRawIntBits(signaling_nan2), signaling_nan2);
        System.out.printf("nan_minus      0x%08x %f\n", Float.floatToRawIntBits(nan_minus     ), nan_minus     );
        System.out.printf("positive_inf   0x%08x %f\n", Float.floatToRawIntBits(positive_inf  ), positive_inf  );
        System.out.printf("negative_inf   0x%08x %f\n", Float.floatToRawIntBits(negative_inf  ), negative_inf  );
        System.out.printf("one_div_zero   0x%08x %f\n", Float.floatToRawIntBits(one_div_zero  ), one_div_zero  );
        System.out.printf("log_zero       0x%08x %f\n", Float.floatToRawIntBits(log_zero      ), log_zero      );

        // NaN comparisons always fail.
        // Therefore, all tests that we will do afterwards will be just isNaN.
        assert !(1.0f < nan);
        assert !(1.0f == nan);
        assert !(1.0f > nan);
        assert !(nan == nan);

        // NaN propagate through most operations.
        assert Float.isNaN(nan + 1.0f);
        assert Float.isNaN(1.0f + nan);
        assert Float.isNaN(nan + nan);
        assert Float.isNaN(nan / 1.0f);
        assert Float.isNaN(1.0f / nan);
        assert Float.isNaN((float)Math.sqrt((double)nan));
    }
}

GitHub upstream.

Run with:

javac Nan.java && java -ea Nan

Output:

nan            0x7fc00000 NaN
zero_div_zero  0x7fc00000 NaN
sqrt_negative  0xffc00000 NaN
log_negative   0xffc00000 NaN
inf_minus_inf  0x7fc00000 NaN
inf_times_zero 0x7fc00000 NaN
quiet_nan1     0x7fc00001 NaN
quiet_nan2     0x7fc00002 NaN
signaling_nan1 0x7fa00001 NaN
signaling_nan2 0x7fa00002 NaN
nan_minus      0xffc00000 NaN
positive_inf   0x7f800000 Infinity
negative_inf   0xff800000 -Infinity
one_div_zero   0x7f800000 Infinity
log_zero       0xff800000 -Infinity

So from this we learn a few things:

• weird floating operations that don't have any sensible result give NaN:

  • 0.0f / 0.0f
  • sqrt(-1.0f)
  • log(-1.0f)

  generate a NaN.

  In C, it is actually possible to request signals to be raised on such operations with feenableexcept to detect them, but I don't think it is exposed in Java: Why does integer division by zero 1/0 give error but floating point 1/0.0 returns "Inf"?

• weird operations that are on the limit of either plus or minus infinity however do give +- infinity instead of NaN

  • 1.0f / 0.0f
  • log(0.0f)

  0.0 almost falls in this category, but likely the problem is that it could either go to plus or minus infinity, so it was left as NaN.

• if NaN is the input of a floating operation, the output also tends to be NaN

• there are several possible values for NaN 0x7fc00000, 0x7fc00001, 0x7fc00002, although x86_64 seems to generate only 0x7fc00000.

• NaN and infinity have similar binary representation.

  Let's break down a few of them:

  nan          = 0x7fc00000 = 0 11111111 10000000000000000000000
  positive_inf = 0x7f800000 = 0 11111111 00000000000000000000000
  negative_inf = 0xff800000 = 1 11111111 00000000000000000000000
                              | |        |
                              | |        mantissa
                              | exponent
                              |
                              sign
  

  From this we confirm what IEEE754 specifies:

  • both NaN and infinities have exponent == 255 (all ones)
  • infinities have mantissa == 0. There are therefore only two possible infinities: + and -, differentiated by the sign bit
  • NaN has mantissa != 0. There are therefore several possibilities, except for mantissa == 0 which is infinity

• NaNs can be either positive or negative (top bit), although it this has no effect on normal operations

Tested in Ubuntu 18.10 amd64, OpenJDK 1.8.0_191.

NaN means "Not a number." It's a special floating point value that means that the result of an operation was not defined or not representable as a real number.

See here for more explanation of this value.

NaN stands for Not a Number. It is used to signify any value that is mathematically undefined. Like dividing 0.0 by 0.0. You can look here for more information: https://web.archive.org/web/20120819091816/http://www.concentric.net/~ttwang/tech/javafloat.htm

Post your program here if you need more help.

NaN = Not a Number.