exception - Why does division by zero with floating point (or double precision) numbers not throw java.lang.ArithmeticException: / by zero in Java

Question

The following statement throws java.lang.ArithmeticException: / by zero as obvious.

System.out.println(0/0);

because the literal 0 is considered to be an int literal and divide by zero is not allowed in integer arithmetic.

The following case however doesn't throw any exception like java.lang.ArithmeticException: / by zero.

int a = 0;
double b = 6.199;
System.out.println((b/a));

It displays Infinity.

The following statement produces NaN (Not a Number) with no exception.

System.out.println(0D/0); //or 0.0/0, or 0.0/0.0 or 0/0.0 - floating point arithmetic.

In this case, both of the operands are considered to be double.

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Similarly, the following statements don't throw any exception.

double div1 = 0D/0; //or 0D/0D
double div2 = 0/0D; //or 0D/0D

System.out.printf("div1 = %s : div2 = %s%n", div1, div2);
System.out.printf("div1 == div2 : %b%n", div1 == div2);
System.out.printf("div1 == div1 : %b%n", div1 == div1);
System.out.printf("div2 == div2 : %b%n", div2 == div2);
System.out.printf("Double.NaN == Double.NaN : %b%n", Double.NaN == Double.NaN);
System.out.printf("Float.NaN == Float.NaN : %b%n", Float.NaN == Float.NaN);

They produce the following output.

div1 = NaN : div2 = NaN
div1 == div2 : false
div1 == div1 : false
div2 == div2 : false
Double.NaN == Double.NaN : false
Float.NaN == Float.NaN : false

They all return false. Why is this operation (division by zero) allowed with floating point or double precision numbers?

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By the way, I can understand that floating point numbers (double precision numbers) have their values that represent positive infinity, negative infinity, not a number (NaN)...

Answer 1

In short, that's the way it's specified in the IEEE-754 standard, which is what Java's Floating-Point Operations are based on.

Why doesn't division by zero (or overflow, or underflow) stop the program or trigger an error? Why does a standard on numbers include "not-a-number" (NaN)?

The 754 model encourages robust programs. It is intended not only for numerical analysts but also for spreadsheet users, database systems, or even coffee pots. The propagation rules for NaNs and infinities allow inconsequential exceptions to vanish. Similarly, gradual underflow maintains error properties over a precision's range.

When exceptional situations need attention, they can be examined immediately via traps or at a convenient time via status flags. Traps can be used to stop a program, but unrecoverable situations are extremely rare. Simply stopping a program is not an option for embedded systems or network agents. More often, traps log diagnostic information or substitute valid results.

Flags offer both predictable control flow and speed. Their use requires the programmer be aware of exceptional conditions, but flag stickiness allows programmers to delay handling exceptional conditions until necessary.