Probabilistic Error Modeling for Two-part Segmented Approximate Adders
Citations
11 citations
Cites methods from "Probabilistic Error Modeling for Tw..."
...on the proposed approach, we first provide an analytical proof to support the structure of the LOA imprecise adder as one of the most efficient and most cited existing adders [29], [30], [31], [32], [33], [34], [35], [36]....
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...Exploiting a systematicmathematical-logical approach to support hardware structure of the small constant mean error LOA adder as one of the most efficient existing imprecise adders [29], [30], [31], [32], [33], [34], [35], [36], [37]....
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8 citations
Cites methods from "Probabilistic Error Modeling for Tw..."
...Error metrics such as mean error distance (MED) and mean square error (MSE) are commonly used for the evaluation of approximate circuits [16]....
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2 citations
Cites background from "Probabilistic Error Modeling for Tw..."
...Further, the probabilistic error analysis of these segment-based adders is presented in [20, 21]....
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1 citations
Cites methods from "Probabilistic Error Modeling for Tw..."
...Its error metrics are derived in our earlier work [16]....
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1 citations
References
921 citations
637 citations
"Probabilistic Error Modeling for Tw..." refers background or methods in this paper
...MSEama5 = Pk−12 2(k−1) + k−2∑ i=0 Pi2 2i + k−2∑ i=0 k−2∑ j=0,j 6=i Pij2 i+j − 2kPk−1 k−2∑ i=0 Pi2 i (16) MSEloa = k−2∑ i=0 P 2i 2 2i + k−2∑ i=0 k−2∑ j=0,j 6=i P 2ij2 i+j + P 2k−12 2(k−1) − 2kP 2k−1 k−2∑ i=0 P 2i 2 i. (17) Thus, we see that MSE of truncation, AMA5 and LOA depends only on Pi and the joint probability Pij ....
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...From the description in the previous section, for Truncation, LOA and AMA5 adders, ck−1, SL = {0, 0}, Truncation {ak−1&bk−1, ak−1:0||bk−1:0},LOA {ak−1, bk−1:0}, AMA5 (1) For the ETA, ck−1 = 0....
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...In the approximate mirror adder 5 (AMA5) proposed in [4], the lower part of the result is set as SL = AL and the carry is set as ck−1 = bk−1....
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...Approximate logic is used to compute the lower part of the sum containing the remaining least significant bits (LSBs) [4], [5], [6], [7]....
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...Although [4] contains a detailed derivation of the mean error for uniformly distributed inputs, there are no expressions for either MSE or MED....
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458 citations
"Probabilistic Error Modeling for Tw..." refers background or methods in this paper
...Among the considered two-part segmented adders, LOA and ETA have the least MED, which is approximately one-fifth that of truncation adder....
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...MED of LOA is given by MEDloa = (1− P 2k−1) k−2∑ i=0 P 2i 2 i + P 2k−1 ( 2k−1 − k−2∑ i=0 P 2i 2 i ) = (1− 2P 2k−1) k−2∑ i=0 P 2i 2 i + P 2k−12 k−1....
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...MSEama5 = Pk−12 2(k−1) + k−2∑ i=0 Pi2 2i + k−2∑ i=0 k−2∑ j=0,j 6=i Pij2 i+j − 2kPk−1 k−2∑ i=0 Pi2 i (16) MSEloa = k−2∑ i=0 P 2i 2 2i + k−2∑ i=0 k−2∑ j=0,j 6=i P 2ij2 i+j + P 2k−12 2(k−1) − 2kP 2k−1 k−2∑ i=0 P 2i 2 i. (17) Thus, we see that MSE of truncation, AMA5 and LOA depends only on Pi and the joint probability Pij ....
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...(13) Using (6), the error distance of LOA is given by edloa = k−2∑ i=0 (ai&bi)2 i, ak−1&bk−1 = 0 2k−1 − k−2∑ i=0 (ai&bi)2 i, ak−1&bk−1 = 1....
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...For the LOA, the authors have included an expression for MSE in [5] assuming uniformly distributed inputs, but it is not clear how it was derived....
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453 citations
"Probabilistic Error Modeling for Tw..." refers background in this paper
...The two metrics that are used most often to evaluate these adders are MED and MSE [16], [17], [9]....
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...We derive expressions for mean error, MED and MSE....
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...We assume both the inputs A and B to be independent and identically distributed (i.i.d.) and derive expressions for mean error, MED and MSE....
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...Metrics The two metrics that are used most often to evaluate these adders are MED and MSE [16], [17], [9]....
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385 citations
"Probabilistic Error Modeling for Tw..." refers background in this paper
...There are other approximate adders [8], [9], [10], [11] which do not split the output into approximate lower part and accurate upper part....
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...Metrics The two metrics that are used most often to evaluate these adders are MED and MSE [16], [17], [9]....
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