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Anobvio r simila nguage, which refers to a very simple archi- 4]. The proposed VLSI algorithm, ber of sorting units fixed to 99, has ock cycles, . Table 1 shows that the proposed algorithm, with 99 r time comp ithms with up eral, the nu us way of sorting N integers is to store the number in a computer memory and use a ng algorithm. Of course this ap- convenient, in terms of circuit area s, namely the Quicksort and Heapsort, for es of input size. Table 1 compares, the complexity in dif- sorting units, has bet- exity than O(N InN) to 1 - 10* input num- mber of sorting units A sorting device performs the sorting of thei put data; its bloc data enters from the input inp_dm al exits - sorted according to the key field - m. The signals depicted on tl e data source an on the right side t devices, the signals on th ternal memory and tho he top deal with the cascading mechanism. 1 logic manages the function mal al function and the mark da mish a reference for the the output out_d mally, a con of the other inte latch has a delay blocks are used Te-C irculation fu tO to fu NC =} 5 fed) Ko} (a>) Mn ct =) k diagram is depicted in Fig. 10. nd external circuits. T N- nd to he tion.

Table 1 Anobvio r simila nguage, which refers to a very simple archi- 4]. The proposed VLSI algorithm, ber of sorting units fixed to 99, has ock cycles, . Table 1 shows that the proposed algorithm, with 99 r time comp ithms with up eral, the nu us way of sorting N integers is to store the number in a computer memory and use a ng algorithm. Of course this ap- convenient, in terms of circuit area s, namely the Quicksort and Heapsort, for es of input size. Table 1 compares, the complexity in dif- sorting units, has bet- exity than O(N InN) to 1 - 10* input num- mber of sorting units A sorting device performs the sorting of thei put data; its bloc data enters from the input inp_dm al exits - sorted according to the key field - m. The signals depicted on tl e data source an on the right side t devices, the signals on th ternal memory and tho he top deal with the cascading mechanism. 1 logic manages the function mal al function and the mark da mish a reference for the the output out_d mally, a con of the other inte latch has a delay blocks are used Te-C irculation fu tO to fu NC =} 5 fed) Ko} (a>) Mn ct =) k diagram is depicted in Fig. 10. nd external circuits. T N- nd to he tion.

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VHDL Design of a Scalable VLSI Sorting Device Based on Pipelined Computation Proposition 1. A cascade of (N — 1) sorting units realizes a complete ordering of a N-long data sequence. 2.3. Complexity Analysis
VHDL Design of a Scalable VLSI Sorting Device Based on Pipelined Computation Proposition 1. A cascade of (N — 1) sorting units realizes a complete ordering of a N-long data sequence. 2.3. Complexity Analysis
Fg. 4. Sorting aan of 3 keys with 2 SU. The delimiter symbol # represents a number greater than all the keys in the Sequence, The rectangles marked in bold denote the T1 and T2 registers. In each rectangle, T1 and T2 are in the lower and unner position resnectivelv
Fg. 4. Sorting aan of 3 keys with 2 SU. The delimiter symbol # represents a number greater than all the keys in the Sequence, The rectangles marked in bold denote the T1 and T2 registers. In each rectangle, T1 and T2 are in the lower and unner position resnectivelv
Fig. 6. Architecture of the sorting device with external memory. The S bit aims at solvi ng the following question: ifa block inside a sequence needs re- circulation, how many turns must itdo? From a theo retical point of view, in [ “5+ ] turns the goal is reached. However, the integra priori the length of th al irculation or not. Moreover, if it also ted circuit doesn if it has to perform cascade. To solve thi there may be other sorting circui known to the circuit, e sequence of data t Cc th uences, a division between (N — 1) and U is needed and this leads t Dp d roblems: the division is a computational bur- ts connected in s problem, we must recall e sorti eneral e layo CHotsH sen app cells or ostly on the ng unit ut of th he speed limits of this a speed of the and on the length of the FIFO. y speaking, the cl e VLSI, on roach for the desi considered later on. OC the technology n the number of metal layers and on the comparator i k speed depen rchitecture depend nside dson used, cho- gn, namely stan full custom; this topic will be further dard
Fig. 6. Architecture of the sorting device with external memory. The S bit aims at solvi ng the following question: ifa block inside a sequence needs re- circulation, how many turns must itdo? From a theo retical point of view, in [ “5+ ] turns the goal is reached. However, the integra priori the length of th al irculation or not. Moreover, if it also ted circuit doesn if it has to perform cascade. To solve thi there may be other sorting circui known to the circuit, e sequence of data t Cc th uences, a division between (N — 1) and U is needed and this leads t Dp d roblems: the division is a computational bur- ts connected in s problem, we must recall e sorti eneral e layo CHotsH sen app cells or ostly on the ng unit ut of th he speed limits of this a speed of the and on the length of the FIFO. y speaking, the cl e VLSI, on roach for the desi considered later on. OC the technology n the number of metal layers and on the comparator i k speed depen rchitecture depend nside dson used, cho- gn, namely stan full custom; this topic will be further dard
Fig. 8. Sorting example of five of the keys with 2 SU. Regarding the computational complexity of the algorithm in the case N > U + 1, we have to consider two cases separately, namely when N
Fig. 8. Sorting example of five of the keys with 2 SU. Regarding the computational complexity of the algorithm in the case N > U + 1, we have to consider two cases separately, namely when N
Fig. 7. Sorting example of three keys with 1 SU and 1-element FIFO. The delimiter symbol # represents a number greater than all the keys in the sequence. VHDL Design of a Scalable VLSI Sorting Device Based on Pipelined Computation
Fig. 7. Sorting example of three keys with 1 SU and 1-element FIFO. The delimiter symbol # represents a number greater than all the keys in the sequence. VHDL Design of a Scalable VLSI Sorting Device Based on Pipelined Computation
Fig. 9. Sorting time (in terms of number of cycles) vs. input size for the currently described algorithm. Different curves have been obtained by varying the number of sorting units U.
Fig. 9. Sorting time (in terms of number of cycles) vs. input size for the currently described algorithm. Different curves have been obtained by varying the number of sorting units U.
VHDL Design of a Scalable VLSI Sorting Device Based on Pipelined Computation
VHDL Design of a Scalable VLSI Sorting Device Based on Pipelined Computation
Fig. 12. Cascade of two sorting blocks. VHDL Design of a Scalable VLSI Sorting Device Based on Pipelined Computation igh degree of kn "Oa Bp Bea$5 iency can be ob sibility is the behavi using a set LO USE au ology since transi esigned on silicon. is possible only for n this case the work is done m esigner who, among other tained; simp echips. things, must h irings are di igh degrees of ution, however, anually by the ave a tech- rectly f effi- the VLSI The other pos- the structural syn tomatic tools, th oural description into a structural one of standard cells. The latter so was adopted in thi at can convert ution s work. The system used for thesis was ALLIANCE 3). bit sorted flow. In this way, the data upsizing can be increased in steps of 16 bits. The key field, which is the basis of the sorting process, is left unchanged to the original 16 bits. Unfortu- nately, the key upsizing is not so easy as the data upsizing, because it would require either some additional external logic or a chip redesign.
Fig. 12. Cascade of two sorting blocks. VHDL Design of a Scalable VLSI Sorting Device Based on Pipelined Computation igh degree of kn "Oa Bp Bea$5 iency can be ob sibility is the behavi using a set LO USE au ology since transi esigned on silicon. is possible only for n this case the work is done m esigner who, among other tained; simp echips. things, must h irings are di igh degrees of ution, however, anually by the ave a tech- rectly f effi- the VLSI The other pos- the structural syn tomatic tools, th oural description into a structural one of standard cells. The latter so was adopted in thi at can convert ution s work. The system used for thesis was ALLIANCE 3). bit sorted flow. In this way, the data upsizing can be increased in steps of 16 bits. The key field, which is the basis of the sorting process, is left unchanged to the original 16 bits. Unfortu- nately, the key upsizing is not so easy as the data upsizing, because it would require either some additional external logic or a chip redesign.
This section deals with the generation of the Caltech Intermediate File (CIF). The goal is to deliver the sorting unit as a new macrocell, This section deals with the generation of the Caltech Intermediate File (CIF). The goal is to deliver the sorting unit as a new macrocell,
This section deals with the generation of the Caltech Intermediate File (CIF). The goal is to deliver the sorting unit as a new macrocell, This section deals with the generation of the Caltech Intermediate File (CIF). The goal is to deliver the sorting unit as a new macrocell,
Table 2. Main characteristics of the structural design.
Table 2. Main characteristics of the structural design.
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