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Unformatted text preview: The worst case accumulation is: 8 16 1 16 1 16 2 256 16 * 16 4 * 4 = = = ≤ = ∑ ∑ = = i i i i Y X Z The extended precision accumulator wordwidth has 4additional bits of precision (headroom) to permit 16 full precision products to the accumulated without overflowThe data format for the accumulator output word is shown below. Retaining the 16most significant bits results in a output data word having the format shown below. The weight of the LSB of the SAXPY result is now ∆ =27 . The error statistics, in bits, is therefore (assuming rounding) E ( e )=0; σ 2 = ∆ /12 log 2 ( σ = ∆ /sqrt(12)) = log 2 (27 /sqrt(12)) = 7 – 1.79 ~ 9 or, approximately 9 bits of fractional precision is left in the accumulator’s output. Why did Motorola call its 24DSP fixedpoint product the DSP56xxx? S F=83=5 I=2 S F=165=11 I=2+2=4 S I=4+4=8 F=209=11 S I=8 F=169=7...
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 Summer '09
 yang
 Yi, extended precision accumulator

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