Abstract: Upon execution of four sets of m/2 bit×n/2 bit multiplication, four multiplicand selectors select m/2-bit multiplicands respectively and four multiplicator selectors select corresponding n/2-bit multiplicators respectively, then the selected m/2-bit multiplicands and n/2-bit multiplicators are input into four multipliers, and then four sets of m/2 bit×n/2 bit multiplication are executed in parallel.

Abstract: A multiply unit uses four multipliers independently to perform for four parallel multiplications of single-width operands or uses the four multiplier cooperatively with an adder to perform a multiplication of double-width operands. In alternative embodiments, the adder operates in the same clock cycle as the multipliers or in a following clock cycle. Operand selection logic selects pairs of either single-width multiplicands or single-width partial multiplicands depending on for single or double-width multiplies.

Abstract: A multiplication device for performing a multiplication operation on a multiplicand X and two fixed coefficients C1 and C2 where C1>C2. The multiplication device comprises a multiplier for multiplying multiplicand X and the average CA of the two fixed coefficients C1 and C2; a shift register for obtaining a sum of the multiplicand X data after being shifted up according to a position of a “1” bit in bit data where the bit data is the remainder coefficient obtained by subtracting average CA from fixed coefficient C1; and a selector for selecting a product obtained for one of the fixed coefficients C1 and C2. When the fixed coefficient C1 is selected, the selector outputs the sum of the product returned by the multiplier and the accumulated value obtained by the shift register; when fixed coefficient C2 is selected, the selector outputs the difference of the product returned by the multiplier minus the accumulated value obtained by the shift register.

Abstract: The high speed multiplier takes advantage of results from previous calculations by recognizing that in many cases the multiplicand between a first and second multiplication differs only slightly. Thus, the present system divides the multiplicand into a cache lookup bit (CLB) and a table lookup bit (TLB). The results of a first multiplication are stored in a cache. The CLB of a of the multiplicand in the second multiplication is then compared to the CLB of the multiplicand in the second multiplication. If the CLB matches, the product of the first multiplication is retrieved. The product of the TLB of the multiplicand and the multiplier is then retrieved from a lookup table and either added or subtracted from the retrieved product.

Abstract: Upon execution of four sets of m/2 bit×n/2 bit multiplication, four multiplicand selectors select m/2-bit multiplicands respectively and four multiplicator selectors select corresponding n/2-bit multiplicators respectively, then the selected m/2-bit multiplicands and n/2-bit multiplicators are input into four multipliers, and then four sets of m/2 bit×n/2 bit multiplication are executed in parallel.

Abstract: An adder tree is partitioned into two parts. One multiplexer provides a first bit group to the first part of the tree. A second multiplexer provides a second bit group to the second part of the tree. The two multiplexers provide the same bits groups to the respective parts in response to a first instruction, and provide different bit groups in response to a second instruction. Therefore, the first instruction allows for the single multiplication of the number represented by the first bit group by another number provided to collectively represented to both parts of the tree. The second instruction causes the multiplication of the first bit group by the third bit group in the first part of the adder tree, and causes another multiplication of the second bit group by the fourth bit group in the second part of the adder tree.

Abstract: In a binary fixed-point number system in which the most significant bit is a sign bit and the decimal point is between the most significant bit and a bit which is lower by one bit than the most significant bit, the circuit scale for digit place aligning means is reduced and a double-precision multiplication with an excellent efficiency is realized. Products of the high-order word/low-order word of a double-precision multiplicand and the high-order word/low-order word of a double-precision multiplier are obtained by using a single-precision multiplying device. A digit place alignment addition operation is performed on the obtained products to produce a double-precision multiplication result.

Abstract: Two related extended precision operand formats provide for efficient multiply/accumulate operations in a SIMD data processing system. Each format utilizes a group of “b” bit elements in a vector register. Each of the elements provides “m” bits of precision, with b>m. The remaining b−m bits in each element accumulate overflows and carries across multiple additions and subtractions. Existing SIMD multiply-sum instructions can be used to efficiently take input operands from the first format and produce output results in the second extended precision format when b2=2b1 and m2=2m1.

Abstract: Beginning with a successive commanded end-effector destination shift, the method of the invention, which includes a calculation corresponding to a special algorithm of inverse kinematics using the Jacobi Matrix in the control of a manipulator, effects an optimization of weighted criteria (energy criteria, acceleration criteria and reference-position criteria) in a real-time cycle while reliably maintaining all path limitations and resulting in an optimized acceleration behavior. The method of the invention can be used in interactive path guidance of a manipulator and/or as a modular component of a superordinate task, such as for force-control objectives.

Abstract: A multiplier circuit multiplies together both natural and two's complement binary numbers, which it receives in the form of electric signals having predetermined logic values, that are applied to input terminals of logic gating circuits. The logic gating circuits provide partial products of the bits of the two binary factors, and a combinatorial network provides the final sum of the partial products. The partial multiplications that include at least one of the more significant bits of the operands are performed by logic gating circuits which can be enabled to also carry out a two's complement partial multiplication. The multiplier circuit further includes additional logic gating circuits which supply the combinatorial network with additive constants with predetermined logic values unrelated to the factors.

Abstract: There is disclosed a multiplier having a digit rounding function which operates by selecting an added value for rounding a digit in the process of adding partial products, thereby reducing a circuit magnitude and realizing a high-speed operation. A multiplier 13 is provided with selection circuits 18, 19 and 1A which can switch values of the partial products obtained in a secondary Booth algorithm in response to a signal for controlling the presence of the digit rounding function.

Abstract: A new logic with shift switches incorporating novel parallel compressors and counters called C4 and (7,3) families. This shift switch logic deals with modulo arithmetic operations. It employs a type of special digital signals, called state signals (as a major addition to the binary signals), and a set of electronic components, called shift switches, to manipulate such signals and conduct the logic operations. A useful modulo arithmetic produces two values: a remainder and a quotient, given two small (non-negative) integers. One integer is a variable numerator represented by a set of input digital signals (including regular and/or state signals), while the other is a dominator (base or radix) provided by the shift switch circuit as a parameter. Using C4 and (7,3) devices, two novel, parallel-structured, full array, 64.times.64 floating point multiplier schemes are disclosed.

Abstract: A processor capable of efficiently performing iterative calculations is disclosed. The processor comprises a multiplier that is configured to perform iterative multiplication operations to evaluate constant powers of an operand such as the reciprocal and reciprocal square root. Intermediate products that are formed are compressed and decompressed to reduce interim storage requirements. The intermediate products may be rounded and normalized in two paths, one assuming an overflow will occur, and then compressed and stored for use in the next iteration.

Abstract: A modular computational structure includes a pipeline having first and second adder stages. Each adder stage includes a pair of adders which operate in parallel, and outputs ports of the first adder stage are coupled to input ports of the second adder stage. Rounding logic and an accumulator are included in the second stage. By varying the inputs to the first and second stages a variety of complex arithmetic functions suitable for video encoding can be implemented. Examples of the operations include completion of multiply and multiply-and-accumulate operations, averages of two values, averages of four values, and merged difference and absolute value calculation.

Abstract: A computer-based method and system is disclosed that automates the design and layout of digital multiplier circuits. The preferred method utilizes an automatic design generator having a user interface which receives design requirements for a digital multiplier circuit design. A digital multiplier design generator receives the design requirements for the digital multiplier and retrieves relevant component implementations from a component library. Stored digital multiplier benchmarks are then retrieved from a benchmark memory and applied to corresponding digital multipliers to determine which of the various implementations optimally satisfies the user design requirements. Once the optimal digital multiplier implementation is selected, the digital multiplier design generator produces a logic design including a netlist and a physical design including design directives which are then used to place and route the digital multiplier as a finished layout.

Abstract: An apparatus sums a plurality of columns of binary bits to produce a plurality of partial sum and carry bits. The bits of a particular column being of the same order of magnitude, and the bits of different columns differing in orders of magnitude. The apparatus includes one or more full adder. Each full adder receives three bits as an input to produce a first sum bit and a first carry bit as output. The apparatus also includes one or more half adders. Each half adder receives two bits as input to produce a second sum bit and a second carry bit as output. The full adders and half adder are interconnected as a plurality of interconnecting column adders. Each column adder sums bits of the input of at least one column and generates a partial sum and carry bit. Each column adder has a plurality of stages. A plurality of conductors interconnect the stages of each column adder with other stages in the same column adder and with stages in other adjacent column adders.

Abstract: A multiplier architecture in accordance with the present invention provides increased operating speed, and yet maintains regularity in its structure in order to achieve a small floor plan when reduced to silicon. A Hekstra-type multiplier is modified by replacing full adders circuits with compressor circuits in a manner that preserves the balance of the signal propagation delays. The result is an architecture having a regular layout that greatly facilitates its implementation in silicon.

Abstract: A method and apparatus for performing N bit by 2*N (or 2*N-1) bit signed multiplication using two N bit multiply instructions. According to one aspect of the invention, a method for performing signed multiplication of A times B (where B has N bits and A has N*2 bits) is described. In this method, A.sub.high and A.sub.low respectively represent the most and least significant halves of A. According to this method, A.sub.low is logically shifted right by one bit to generate A.sub.low >>1. Then, A.sub.low >>1 is multiplied by B using signed multiplication to generate a first partial result. In addition, a second partial result is generated by performing signed multiplication of A.sub.high times B. One or both of the first and second partial results is shifted to align the first and second partial results for addition, and then the addition is performed to generate a final result representing A multiplied by B.

Abstract: In a circuit arrangement wherein all logic elements can be represented in the form of a threshold value equation, for this purpose, transistors connected in parallel of a transistor unit are dimensioned in such a way that the cross-currents flowing through the transistors respectively represent a weighted summand of a first term of the threshold value equation. A second term of the threshold value equation is formed by a reference current representing the second term value. An evaluation unit compares an overall current, which results from the sum of cross-currents, with the reference current. The evaluation result is present at an output of the evaluation unit in the form of a stable output signal.

Abstract: A number of adder structures (also referred to herein as "tiles" and "Quickadders.TM.") are provided which may be constructed with positively and/or negatively weighted and signed inputs and outputs and which may be placed so as to span one or more bitslices of a multiplier array. In a second aspect of the present invention, groups of replicable circuitry columns are provided for forming multiplier arrays for multiplying binary numbers X and Y to obtain a binary product Z. These groups of columns of circuitry include left column groups to handle X-inputs to the array, internal column groups, and right column groups to handle outputs to a CLA adder/subtractor (or equivalent) for processing the MSBs of the product. The LSBs of the product are produced directly by the array. The groups may be thought of as replacing 2, 3 or 4 conventional columns of full-adder circuitry of a basic array such as that shown in FIGS. 1 and 2.

Abstract: A multiplication circuit for binary coded numbers uses rows of adders and multipliers for parallel computation. Sign bit supplementation is used in which sign bits are supplemented by binary digits in the rows of adders. In particular, the required addition of the sign bit first occurs in the first multiplier row where elements representing simple loads are used in place of adders with inputs that represent multiple input loads. Wiring simplification also is applied in the higher order adders of subsequent adder rows. Circuit simplification is achieved by replacing half adders with inverters.

Abstract: A fast carry-sum form Booth encoder is used in a multiplicative divider to iteratively multiply one number by a series of numbers to produce the result of a divide or square root operation. The fast Booth encoder inputs a binary sum and a binary carry row representing the first number. The encoder adds the two numbers and at the same time Booth-encodes the result and outputs this result to a partial product generator to be combined with one of the series of numbers. Included in the fast Booth encoder are a multiplicity of interconnected logic cells. Each logic cell receives a number of distinct sequential bits from each of the binary sum and carry rows. The sequential bits from one binary number correspond to sequential bits in the other binary number. Each cell then produces an associated cell output. Each logic cell includes a carry bit generator for producing a number of carry bits to transmit to a next interconnected logic cell.

Abstract: A multiplier circuit which multiplies together both natural and two's complement binary numbers, which it receives in the form of electric signals having predetermined logic values, that are applied to input terminals of logic gating circuits. The logic gating circuits provide partial products of the bits of the two binary numbers, and a combinatorial network provides the final sum of the partial products. The partial products that include at least one of the more significant bits of either of the operands are performed by logic gating circuits which can be enabled to complement the partial product. The multiplier circuit further includes additional logic gating circuits which supply the combinatorial network with additive constants with predetermined logic values.

Abstract: The present invention provides a data processing circuit and method for performing arithmetic processing on data signals input to the circuit, comprising: a plurality of input terminals for receiving a plurality of data signals to be processed; a plurality of interconnected arithmetic processing units, one corresponding to each input terminal, for processing the data signals received at the corresponding input terminal; and a selector for routing the data signals at said input terminals to the corresponding arithmetic processing units in a first mode of operation, or for routing a selected one of said data signals to said plurality of arithmetic processing units in a second mode of operation; whereby, in said first mode of operation, data signals arriving at said input terminals are processed in parallel by said corresponding arithmetic processing units, and, in said second mode of operation, at any point in time, one of said data signals is processed by said plurality of arithmetic processing units.