Exhausting floating point precision in a (seemingly) infinite loop
floating-accuracy, floating-point, floating-point-precision, python
Solution
- 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.
Problem
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, terminates pretty quickly if x is a floating point number. But if i change x to 300000000 instead, it gets into an infinite loop (runs longer than a minute in my test). I think this is to do with the fact that it's exhausting the precision of a floating point number that can be represented in memory. Can someone provide a more detailed explanation why this is?