Thorsten Ottosen wrote:
Johan Råde skrev:
Robert Kawulak wrote:
From: Johan Rade The statement is "x <= y before truncation implies x <= y after truncation".
Or more specifically: "x < y before truncation implies x <= y after truncation" Is this right?
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Thought about it again. None if these statements are true, unfortunately, if you consider the case when one number is truncated to 64 bits and the other is kept at 80 bits. Then you can even have x < y before and x > y after.
Hm. This sucks.
Do we know if that 80-bit floating point values are guaranteed to be a superset of 64-bit and 32-bit floats (or if 64-bit is a superset of 32-bit floats).
I suspect the answer might be yes. If so, I don't think
x < y before ==> x > y after
can be true. If x is rounded upwards, y would be an upper bound.
Imagine the following case, 1) x and y are stored in 80-bit registers 2) x < y 3) both x and y are just below 1.0, so close that they would be rounded to 1.0 if truncated to 64 bits If now x is truncated to 64 bits, and then moved back to an 80-bit register, while y is unchanged, then x > y. --Johan Råde