Example: 3 bit floating point arithmetic.
a = 11
b = 1.01
a+b = 100.01 exact, 100 rounded.
Fast-Two-Sum (11, 1.01) |
|
x = a + b | x = 11 + 1.01 = 100 rounded |
bv = x - a | bv = 100 - 11 = 1 |
y = b + bv | y = 1.01 - 1 = 0.01 |
(x,y) | (100, 0.01) = 100.01 |