
MSDF: Online Arithmetic
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and propagated to the left by one position due to the term 2w[j]. For residuals
formed using a [4:2] adder, the error in cycle p + 1 (after left shift) affects bits
in positions p - 2, p - 1, p (Figure 9.17(b)). After cycles p + 1, ..., p + h are
performed, the truncation error has affected all bit positions up to and including
bit position p - 2h + 8 (in the last ~ cycles the input digits are 0 and the error
propagation is caused by the left shift of the residual). To have a valid selection
using an estimate of t fractional bits,
p - 2h + 8 > t 9.87
Since p + h = n + 8, we obtain ...