### Table 2. Bit-pair recoded modulo (2n + 1) par- tial products.

1999

"... In PAGE 8: ... The terms have been exhaustively verified in a circuit implementation. The n=2 + 1 partial products are given in Table2 and summed up as follows: X Y mod (2n + 1) (35) = ? n=2 X i=0 (PPi + 1) + 1 + T mod (2n + 1) 3.3.... ..."

Cited by 1

### Table 2. Bit-pair recoded modulo (2n + 1) par- tial products.

"... In PAGE 8: ... The terms have been exhaustively verified in a circuit implementation. The n=2 + 1 partial products are given in Table2 and summed up as follows: X Y mod (2n + 1) (35) = ? n=2 X i=0 (PPi + 1) + 1 + T mod (2n + 1) 3.3.... ..."

### Table 3. Modulo operation

"... In PAGE 4: ... Experiment We consider modulo addition based on WLDDs: ( n?1 X i=0 2ixi + n?1 X i=0 2iyi)%2n (3) We represent the formula by a K*BMD with only pD de- composition using an interleaved variable ordering. The results of our approach in comparison to the con- ventional approach based on Shannon expansion for vary- ing bit-length are given in Table3 . Even though the size of the output function grows only linear with the bit-length, the straightforward approach fails for more than 16 bits, while our algorithm can handle the function with 512 bits (and 1024 variables) in less than 300 CPU seconds.... ..."

### Table 1. Bit-pair recoded modulo (2n ? 1) par- tial products.

1999

"... In PAGE 6: ... Equation (1) can be rewritten for the multiplier X as X = n=2 X i=0 22i(x2i?1 + x2i ? 2x2i+1 | {z } f?2;?1;0;+1;+2g ) (26) where xn+1; xn; x?1 = 0. The resulting n=2 + 1 bit pairs (x2i+1; x2i) are used to specify n=2 + 1 partial products according to Table1 (note that the third bit x2i?1 must also be considered), which are summed up as follows: X Y mod (2n ? 1) = n=2 X i=0 PPi mod (2n ? 1) (27) The carry-save adder is thereby cut in half (i.e.... ..."

Cited by 1

### Table 1. Bit-pair recoded modulo (2n ? 1) par- tial products.

"... In PAGE 6: ... Equation (1) can be rewritten for the multiplier X as X = n=2 X i=0 22i(x2i?1 + x2i ? 2x2i+1 | {z } f?2;?1;0;+1;+2g ) (26) where xn+1; xn; x?1 = 0. The resulting n=2 + 1 bit pairs (x2i+1; x2i) are used to specify n=2 + 1 partial products according to Table1 (note that the third bit x2i?1 must also be considered), which are summed up as follows: X Y mod (2n ? 1) = n=2 X i=0 PPi mod (2n ? 1) (27) The carry-save adder is thereby cut in half (i.e.... ..."

### Table 1: Minimizing parameters The corresponding minimal sums of squares divided by the number of data n are given in Table 2.

1991

"... In PAGE 15: ... Starting from an initial estimate for the parameters, the algorithm converges to a local minimum. A systematic search with a variety of initial estimates and the use of graphics indicates that in all examples the numbers listed in Table 2 with corresponding parameters in Table1 are the unique global minima of SSQ. In one case, for (OSCIL) and the hardwall data, a second local minimum 103 SSQ=n = 4:5075 is located at m = ?1708:4; d = 9:3346; k = ?15384: Considering (IMPED), a simple algebraic argument shows that the gradient of SSQ with respect to the two real parameters (Re ; Im ) 2 R2 vanishes if and only if Re R = P Re Rj=n and ImR = P ImRj=n: Thus, to get the optimal least-squares t for (IMPED), we compute the mean values of Re Rj and ImRj and then according... In PAGE 16: ...593 Table 2: Residual sum of squares The experimental data (measured re ection coe cients - real and imaginary parts - as a function of frequency) are represented by solid lines in Figures 2 - 5 for hardwall, free radiation, wedge and foam terminations, respectively. The re ection co- e cients corresponding to the models with boundary conditions (OSCIL), (ELAST), (IMPED) evaluated at the optimal parameters given in Table1 are plotted in each gure by dashed, dotted, dashed-dotted lines, respectively.... ..."

### Table 3: Function Pro le The operational pro le for Ex2 is essentially the same as the functional pro le because we are dealing with a node within a switch. At this low-level, a function is an operation (modulo exceptional situations). To emphasise that context is important, and that each 6

1997

Cited by 1

### Table 2. Bit-pair recoded modulo #282n + 1#29 par-

"... In PAGE 8: ... The terms have been exhaustively verified in a circuit implementation. The n=2 + 1 partial products are given in Table2 and summed up as follows: X #01 Y mod #282n + 1#29 (35) = , n= 2 X i=0 #28PP i + 1#29+1 + T #01 mod #282n + 1#29 3.3.... ..."

### Table 1: Prime modulo set fragmentation.

2004

"... In PAGE 3: ...on-trivial 6.3%. Since we target the L2 cache, however, this fragmentation becomes negligible. Table1 shows that the percentage of the sets that are wasted in an L2 cache is small for com- monly used numbers of the sets in the L2 cache. The frag- mentation falls below 1% when there are 512 physical sets or more.... In PAGE 7: ...ure. The architecture is modeled cycle by cycle. Prime Numbers. The prime modulo function uses the prime number shown in Table1 . The prime displacement function uses a number 9 when it is used as a single hash- ing function.... ..."

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### Table 1. Bit-pair recoded modulo #282n , 1#29 par-

"... In PAGE 6: ... Equation (1) can be rewritten for the multiplier X as X = n=2 X i=0 22i #28x 2i,1 + x 2i , 2x 2i+1 | #7Bz #7D f,2;,1;0;+1;+2g #29 (26) where x n+1;x n ;x ,1 = 0. The resulting n=2 + 1 bit pairs #28x 2i+1;x 2i #29 are used to specify n=2 + 1 partial products according to Table1 (note that the third bit x 2i,1 must also be considered), which are summed up as follows: X #01 Y mod #282n , 1#29= n=2 X i= 0 PP i mod #282n , 1#29 (27) The carry-save adder is thereby cut in half (i.e.... ..."