Loopy Puzzlers - Java Puzzlers: Traps, Pitfalls, and Corner Cases - page 75

example:
double i = 1.0 / 0.0;
Better yet, you can take advantage of a constant that is provided for you by the standard libraries:
double i = Double.POSITIVE_INFINITY;
In fact, you don't have to initialize i to infinity to make the loop spin forever. Any sufficiently large
floating-point value will do; for example:
double i = 1.0e40;
This works because the larger a floating-point value, the larger the distance between the value and
its successor. This distribution of floating-point values is a consequence of their representation with
a fixed number of significant bits. Adding 1 to a floating-point value that is sufficiently large will
not change the value, because it doesn't "bridge the gap" to its successor.
Floating-point operations return the floating-point value that is closest to their exact mathematical
result. Once the distance between adjacent floating-point values is greater than 2, adding 1 to a
floating-point value will have no effect, because the half-way point between values won't be
reached. For the float type, the least magnitude beyond which adding 1 will have no effect is 2 25 ,
or 33,554,432; for the double type, it is 2 54 , or approximately 1.8 x 10 16 .
The distance between adjacent floating-point values is called an ulp , which is an acronym for unit
in the last place. In release 5.0, the Math.ulp method was introduced to calculate the ulp of a float
or double value.
In summary, it is possible to represent infinity as a double or a float . Most people find this
somewhat surprising the first time they hear of it, perhaps because you can't represent infinity by
using any of the integral types. Second, adding a small floating-point value to a large one will not
change the large value . This too may be counterintuitive, as it isn't true for the real numbers. It is
worth remembering that binary floating-point arithmetic is only an approximation to real
arithmetic .