Surprisingly useful little identity: if a, b, c >= 0, then saturate(a + b - c) = saturate(saturate(a + saturate(b - c)) - saturate(c - b)) where saturate(x) = min(max(x, 0), k) for some real k >= 0
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And, more generally, when (x&~mask)==0 and (y&~mask)==0, pdep(pext(x, mask) - pext(y, mask), mask) = (x - y) & mask (the increment-by-1 formula is the special case y=-1 & mask=mask)
That's a pretty cool identity! I don't know why but I would write it like this without the quantifier: pdep(pext(x, mask) - pext(y, mask), mask) = ((x&mask) - (y&mask)) & mask
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I like it with that qualifier just because it emphasizes that the set is closed under the (such-defined) addiiton/subtraction.
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