Floating Point, how much can I trust less than / greater than comparisons?

Question

Let\'s say I have two floating point numbers, and I want to compare them. If one is greater than the other, the program should take one fork. If the opposite is true, it should

Answer 1

The IEEE 754 (floating point) standard states that addition or subtraction can result in a positive or negative infinity, so b + FLOAT_EPSILON and b - FLOAT_EPSILON can result in positive or negative infinity if b is FLT_MAX or -FLT_MAX. The floating point standard also states that infinity compares as you would expect, with FLT_MAX < +infinity returning true and -FLT_MAX > -infinity.

For a closer look at the floating point format and precision issues from a practical standpoint, I recommend taking a look at Christer Ericson's book Real Time Collision Detection or Bruce Dawson's blog posts on the subject, the latest of which (with a nice table of contents!) is at http://randomascii.wordpress.com/2013/02/07/float-precision-revisited-nine-digit-float-portability/.