What happens when we assign a float value to a double variable?

Question

class Test {
    public static void main (String[] args){
        double pi = 3.1415f;
        System.out.println(pi);
    }
}

When compiling and executing the above code, I got the return: 3.1414999961853027
This is not a question to solve a problem.
I just wish I could understand what’s going on here...

Answer 1

No magic is happening here. It is only the way the information is being displayed that ends up confusing the user (developer). That’s the way the float is implemented when you write 3.1415f this is not the real value that will be applied to the variable, this is not exactly the value found in memory as the implementation of float. You can perform some tests:

float a = 3.1415f;
float b = 3.1414999961853027f;

System.out.println("a = " + a); // a = 3.1415
System.out.println("b = " + b); // b = 3.1415
System.out.println(a == b); // true

The value displayed for both cases receives a "rounding", but the actual value found in the variable is not 3.1415f. This "problem" is not very common to find when working only with floats, but when there is the value coercion of a float for a double people notice this difference because the double ends up displaying all the information, thus appearing that the values are different (when in fact they are not).

double c = a;
System.out.println("c = " + c); // c = 3.1414999961853027

You can see here a few more tests proving that both values are exactly the same.

NOTE: This is not something characteristic only of Java, Several languages implement this standard and developers often struggle with it when they need a lot of precision. C# implements the same standards for float and the double, when something needs a lot of precision like monetary values they have an implementation decimal to meet these demands. Other languages such as JavaScript have only one implementation to represent numbers, and end suffering from it, from problems with precision to the representation of large numbers, requiring libraries to solve the problem.

Answer 2

Turns out the variables have different sizes:

Float Represents numbers in standard floating point notation in simple precision of 32 bits in accordance with IEEE 754-1985. The lowest repressable positive value for this type is 1.40239846e-46 and the highest is 3.40282347e+38

Double Represents numbers in standard floating point notation in double precision of 64 bits in accordance with IEEE 754-1985. The lowest representative positive value is 4.94065645841246544e-324 and the highest is 1.7976931348623157e+308

When you make the assignment of a value double in float it truncates the value to the supported size, half the size, decreasing the accuracy of the value. Only this.

See more information on: http://www.dm.ufscar.br/~Waldeck/curso/java/part22.html