Exhausting Floating Point Precision In A (seemingly) Infinite Loop

I've got the following Python script: x = 300000000.0 while (x < x + x): x = x + x print 'exec: ' + str(x) print 'terminated' + str(x) This seemingly infinite loop, ter

Solution 1:

• When you initialize x to 300000000, integer math is used throughout the program.
• When you initialize x to 300000000.0, floating-point math is used instead.

In Python, integers can grow arbitrarily large. (More accurately, they're limited by the available memory.) This means that the integer version of your program takes a very long time to terminate.

The largest float is about 1.8e308. It takes about 1000 iterations of the floating-point version of the loop to exceed that value, at which point x gets set to positive infinity, and the program terminates.

Solution 2:

This is because a floating-point overflow occurs. In that case, as per IEEE754, x will adopt the value positive infinity, which is by definition not less than anything else:

>>>x = float("inf")>>>x
inf
>>>x + x
inf
>>>x < x + x
False

Solution 3:

x doubles after each step. A finite number x is never equal to 2 * x. But once you exceed the maximum exponent of your floating point type, the doubling turns x to +infinity. And +infinity = 2*+infinity. So the loop terminates at that point.