Cellular multiplier comprising a tree of the overturned stairs type, and ...

1. An overturned stairs type cellular structure adder tree for processing a given integer number of N greater than 23 operands and including a plurality of interconnected carry-save adders, said carry-save adders being connected together in a plurality of Q degrees of given horizontal rank q, with 1.ltoreq.q.ltoreq.Q and given depth, each of said carry-save adders having a sum output, a carry output and three inputs, said carry-save adders receiving one of said N operands as an input for each of said three inputs not receiving an input from another carry-save adder of said adder tree, wherein said cellular structure adder tree of order p and depth n', where p designates a parameter order of summing processing time of the form N.sup.1/(p+1) of said multiple operands and n' designates the maximum number of carry-save adders passed through by each operand for complete processing, at least comprises:

a multiplier root R constituted by a carry-save adder, and

a first multiplier body CO(p,n), of order p, depth n, with n=n'-1, and rank q=1, connected to said multiplier root R, said first multiplier body including:

a five-input connector operator C(n,q) of rank q=1 and including first and second carry-save adders connected in cascade, the carry output of said first carry-save adder being connected to one of the inputs of said second carry-save adder, said five-input connector operator C(n,q) further including three outputs constituted by the sum output of the first carry-save adder, and the sum and the carry outputs of the second carry-save adder, and being connected to said multiplier root R, and

a tree of order p-1, depth n-2 and rank q=1 comprising a plurality of interconnected carry-save adders including a final carry-save adder constituting a tree root r, the sum and the carry outputs of said tree root being connected to respective inputs of the first carry-save adder of said five-input connector operator of rank q=1,

at least four successive sub-multiplier bodies of order p and of decremented depth determined by successively decrementing the depth n=n'-1 by one and incremented rank determined by successively incrementing the rank q by one, with 2.ltoreq.q.ltoreq.Q-1, each of said sub-multiplier bodies comprising:

a single five-input connector operator of corresponding incremented rank and corresponding decremented depth and including first and second carry-save adders connected in cascade and connected to the five-input connector operator of the sub-multiplier body of immediately preceding rank,

a tree of order p-1 and successively decremented in depth by 1 with respect to said tree of the sub-multiplier body of immediately preceding rank, said tree being connected to said single five-input connector operator of corresponding rank;

the successive sub-multiplier body of rank q=Q-1 thus consisting of a single five-input connector operator of corresponding rank,

the five-input connector operator of said sub-multiplier bodies of rank 2 being connected to the five-input connector operator of the first multiplier body,

said adder tree further including, forming said degree of rank Q, a carry-save adder of rank q=Q and depth n=1 having carry and sum outputs connected to the first carry-save adder of the five-input connector operator of the submultiplier of the immediately preceding rank Q-1.

2. A multiplier according to claim 1, wherein said adders are disposed in a plane and vertical topology.

3. A multiplier according to claim 1, having a depth n'=7, an order p=1, and N=24 operands.

4. The adder tree of claim 1, in which said first multiplier body and successive sub-multiplier bodies of rank q and depth n constitute successive degrees of corresponding rank q with 1.ltoreq.q.ltoreq.Q-2, each of said degrees consisting at least of one five-input connector operator of same rank q and a tree of same rank q and given depth, thereby forming an overturned stairs structure cellular adder tree.

5. A multiplier according to claim 4, said carry-save adders being stacked-connected in degrees of decremented depth n with incremented horizontal rank q, each degree of rank q, for q>Q-2, comprising:

a branch of same rank q having a plurality of n-2 successive carry-save adders; and

a five-input connector operator of same rank q including first and second adders connected in cascade, inputs of said connector operator of same rank q being connected firstly to said branch to form said degree of rank q, where n represents the number of carry-save adders in said degree and secondly to the connector operator of higher rank q+1 to form a cellular multiplier body having a tree structure with corresponding arborescence for the subassembly constituted by the Q-q degrees of higher rank;

said multiplier further including

a degree of rank Q-1 having a five-input connector operator interconnected to degree of rank Q-2,

a degree of rank Q having an adder interconnected to said degree of rank Q-1, and

an output carry-save adder interconnected with said connector operator of rank 1.

6. A multiplier according to claim 5, wherein each branch Bq of rank q including n-2 successive adders has n operand inputs.

7. A multiplier according to claim 6, wherein the sum and carry outputs from an adder in each branch are connected to the corresponding inputs of the immediately subsequent adder in the same branch.

8. A multiplier according to claim 6, wherein for each connector operator of rank q where 1<q<Q-2:

the three inputs of the first adder are respectively connected to the sum output and to the carry output of the last adder in the corresponding branch of rank q, and to the sum output of the first adder of the connector operator of higher rank q+1;

the carry output and the sum output of the first adder of rank q are respectively connected to an input of the second adder and to an input of the first adder of the connector operator of lower rank q-1; and

two inputs of the second adder of rank q are respectively connected to the sum output and to the carry output of the second adder of the connector operator of higher rank q+1.