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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 4-additional 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 16-most significant bits results in a output data word having the format shown below. The weight of the LSB of the SAXPY result is now ∆ =2-7 . The error statistics, in bits, is therefore (assuming rounding) E ( e )=0; σ 2 = ∆ /12 log 2 ( σ = ∆ /sqrt(12)) = log 2 (2-7 /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 24-DSP fixed-point product the DSP56xxx? S F=8-3=5 I=2 S F=16-5=11 I=2+2=4 S I=4+4=8 F=20-9=11 S I=8 F=16-9=7...
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- Summer '09
- Yi, extended precision accumulator