On Dec 11, 2008, at 11:45 AM, Thorsten Ottosen wrote:
We need to make either x or y one of the bounds of our interval. Let us assume it is y.
Furthermore, we know y has been specified such that it is representable exactly in float or double. Since the 80-bit floating point values are a superset, we know y can also be represented exactly in this format, and we know that truncation on y will have no effect.
Basically, y will have the same value no matter if it is stored in a register or at some memory location.
The question is know, can
x < y
pass, and then x is assigned to the a bounded_float (where it will be stored in x'), only to discover that
x' < y
? We know y will always have the same value, so only x may switch location.
Case 1: x is in memory, x' is in register. Then x == x' by the superset property.
Case 2: x is in register, x' is register. Then x == x'.
Case 3: x is in register, x' is in memory. Then we might have x' == y, but not x' > y, since that would violate the fact that y is exactly representable in both formats.
Well said. It seems that a truncated bound is key. Surely it will be if it's stored as a runtime field, I am not so sure when it's one of those nice optimized-away functors. So the next questions are 1. how to implement 0. how to test I will inquire of a local float enthusiast, one of my profs at NYU. Gordon