Straightforward construction of depth-size optimal, parallel prefix circuits with fan-out 2

Abstract

Prefix computation is used in various areas and is considered as a primitive operation. Parallel prefix circuits are parallel prefix algorithms on the combinational circuit model. The depth of a prefix circuit is a measure of its processing time; smaller depth implies faster computation. The size of a prefix circuit is the number of operation nodes in it. Smaller size implies less power consumption, less VLSI area, and less cost. A prefix circuit with n inputs is depth-size optimal if its depth plus size equals 2n -2. A circuit with a smaller fan-out is in general faster and occupies less VLSI area. To be of practical use, the depth and fan-out of a prefix circuit should be small. In this paper, a family of depth-size optimal, parallel prefix circuits with fan-out 2 is presented. This family of prefix circuits is easier to construct and more amenable to automatic synthesis than two other families of the same type, although the three families have the same minimum depth among all depth-size optimal prefix circuits with fan-out 2. The balanced structure of the new family is also a merit.

Functional and dynamic programming in the design of parallel prefix networks

“…We need to keep the waist and depth equal, by making sure that the last element of the top sequence is 1 (and not zero). A recent paper, also by Lin, studies this problem, comparing the Lin and Liu construction to two others (Lin & Hung 2009). Note how each odd numbered wire has exactly one fanout on it, to the adjacent wire.…”

“…The improvements for depths 10 and 11 are substantial. the recent paper by Lin et al (2009), which contains a good list of relevant references). Right at the limit, there seems to be only one choice of partition, but for narrower networks, it would be good to be able to consider a variety of choices and to choose using the measure function, completely Table 3.…”

“…Right at the limit, there seems to be only one choice of partition, but for narrower networks, it would be good to be able to consider a variety of choices and to choose using the measure function, completely Table 3. Lin & Hung 2009), or tackle the simpler case in which the maximum fanout is the same as the depth, as in Zhu et al (2006). Size/fanout for generated networks and classic LF, with slack 1, that is depth one greater than minimum.…”

“…The reader might like to consider other possible solutions. A recent paper, also by Lin, studies this problem, comparing the Lin and Liu construction to two others (Lin & Hung 2009). We will move on to the much harder question of how to deal with fanout greater than two, both in the production of DSO networks and of larger but shallower networks.…”

“…Depth Size Optimal networks have been much studied (see e.g. the recent paper by Lin et al (2009), which contains a good list of relevant references). Our previous work on DSO network construction (Sheeran & Parberry 2006) was the first to produce DSO networks while retaining control of fanout.…”