Value of float changes on assignment in Java

Question

When I assign 2.3211232f as value to a float variable in Java it is assigned as 2.3211231 to that variable. Why does this happen ?

Answer 1

In Java, floating-point values are denominated in units of powers of two. For numbers between 2 and 4, the unit used for float is 2⁻²². This is because float has 24-bit significands, so, when the high bit represents 2¹, as it must for numbers between 2 and 4, the low bit represents 2¹⁻²³ = 2⁻²².

2⁻²² is 0.0000002384185791015625, so the representable numbers between 2 and 4 are spaced in steps of that size. The representable numbers near 2.3211232 are:

• 2.3211228847503662109375
• 2.3211231231689453125000
• 2.3211233615875244140625

Of those, 2.3211231231689453125000 is the closest to 2.3211232, so, when the source text 2.3211232f is converted to float, the result is 2.3211231231689453125000.

Java’s default formatting displays this as “2.3211231”, because it uses just enough decimal digits to uniquely identify the value. It does not show all the digits of the exact value, so it misrepresents the value. Never take the result of default formatting as the actual value.

Answer 2

A Java float is a 32-bit floating-point value. Wikipedia says:

This gives from 6 to 9 significant decimal digits precision.

Your number has 8 digits, and it seems that it exceeding what a float can handle.

If you want to see the precision at the value you have, call the Math.ulp(float f) method.

If you want to see what next value down/up a float can handle, use the Math.nextDown(float f) and Math.nextUp(float f) methods.

float f = 2.3211232f;
System.out.println("f    = " + f);
System.out.println("down = " + Math.nextDown(f));
System.out.println("up   = " + Math.nextUp(f));
System.out.println("ulp  = " + Math.ulp(f));

Output

f    = 2.3211231
down = 2.321123
up   = 2.3211234
ulp  = 2.3841858E-7

As you can see, your value 2.3211232 cannot be stored in a float, because the next value up from 2.3211231 is 2.3211234.

As the ULP (Unit in the Last Place) shows, the precision at the last (7th) digit is 2.4, so there is between 2 and 3 steps in the 7th digit between adjacent values.