Showing papers on "Division (mathematics) published in 1993"

Computer Arithmetic Algorithms

Abstract: This text explains the fundamental principles of algorithms available for performing arithmetic operations on digital computers. These include basic arithmetic operations like addition, subtraction, multiplication, and division in fixed-point and floating-point number systems as well as more complex operations such as square root extraction and evaluation of exponential, logarithmic, and trigonometric functions. The algorithms described are independent of the particular technology employed for their implementation.

Adaptive refinement-coarsening scheme for three-dimensional unstructured meshes

Abstract: The paper describes the development and application of an adaptive algorithm for tetrahedral grids. An initial unstructured grid is adapted by employing local division, as well as deletion of the tetrahedral cells. The process is dynamic, and the adapted grid changes follow evolution of the solution. Adaptation of the cells consists of normal division of a tetrahedron into eight subcells, as well as directional division into two or four subcells. A major issue of such adaptive grid algorithms is elimination of hanging nodes that appear on the edges in the interface between the embedded and unembedded zones. A novel technique has been developed for treatment of such interface cells that can be applied to eliminate any possible hanging node configuration in a simple way. A special data structure based on octrees has been developed, which is flexible to handle all different types of cell division/deletion. Application cases include a moving source, as well as transonic flow around the ONERA M6 wing.

Finite Lorentz transformations, automorphisms, and division algebras

Abstract: An explicit algebraic description of finite Lorentz transformations of vectors in ten‐dimensional Minkowski space is given by means of a parametrization in terms of the octonions. The possible utility of these results for superstring theory is mentioned. Along the way automorphisms of the two highest dimensional normed division algebras, namely, the quaternions and the octonions, are described in terms of conjugation maps. Similar techniques are used to define SO(3) and SO(7) via conjugation, SO(4) via symmetric multiplication, and SO(8) via both symmetric multiplication and one‐sided multiplication. The noncommutativity and nonassociativity of these division algebras plays a crucial role in our constructions.

Image reading apparatus providing high quality images through synthesis of segmented image data

Abstract: An image reading apparatus for obtaining a digital image having gradation of binary-level or multi level in a computer, a word processor, a digital copying machine, or like apparatus. The image reading apparatus includes an imaging device, an optical unit located for exposing the imaging device and capable of moving in two directions perpendicular to each other, a reading operation control unit for controlling a first reading operation in which whole information of the original image is read, and a second reading operation in which division image information in division areas of the original image is read, a resolution setting unit for setting a resolution in the second reading operation, and a data processing unit for connecting a plurality of division image information sets which are read in a plural number of times of the second reading operations, as a front view image information on the original image.

New algorithms and VLSI architectures for SRT division and square root

Abstract: Radix two algorithms for SRT division and square-rooting are developed. For these schemes, the result digits and the residuals are computed concurrently and the computations in adjacent rows are overlapped. Consequently, their performance should exceed that of the radix 2 SRT methods. VLSI array architectures for implementing the new division and square-rooting methods are also presented. >

SIGMA: a VLSI systolic array implementation of a Galois field GF(2/sup m/) based multiplication and division algorithm

Abstract: Finite or Galois fields are used in numerous applications like error correcting codes, digital signal processing and cryptography. The design of efficient methods for Galois field arithmetic such as multiplication and division is critical for these applications. A new algorithm based on a pattern matching technique for computing multiplication and division in GF(2/sup m/) is presented. An efficient systolic architecture is described for implementing the algorithm which can produce a new result every clock cycle and the multiplication and division operations can be interleaved. The architecture has been implemented using 2- mu m CMOS technology. The chip yields a computational rate of 33.3 million multiplications/divisions per second. >

Holographic code division multiple access

Abstract: A technique for all-optical Code Division Multiple Access (CDMA) system based on optical holography is disclosed. In this technique the energy of an incoming information light signal is spread over a spatial domain by a two-dimensional spatial encoder which includes a mask having regions of first and second transmission characteristics corresponding to the unique code assigned to a particular source. Subsequent decoding, which is accomplished by an optical matched filter through the use of a hologram, spatially despreads the energy of the information light signal and produces a focused light beam which serves as input to a code division detector.

Introduction to division algebras, sphere algebras and twistors

Abstract: A very basic introduction is given to the roles of division algebras and the related sphere algebras concerning the structure of space-time in the dimensionalities D=3,4,6 and 10, with special emphasis on twistors transformations for light-likeness conditions and Hopf maps, together with some outlook for particle and string theory.

Data processing method using record division storing scheme and apparatus therefor

Abstract: A record having a fixed length data portion and a variable length data portion is stored in memory units, each capable of being inputted/outputted independently, in unit of sub-record while the fixed length data portion is divided into a plurality of fixed length sub-records each having the same length and the variable length data portion is made one variable length sub-record. When data operation of the record such as retrieval, update and deletion is required, sub-records necessary for the data operation are limited and the data operation is made in a unit of one or more sub-records, so that data processing of unnecessary sub-records is not made.

Iterative division apparatus, system and method employing left most one's detection and left most one's detection with exclusive OR

Abstract: This invention is an iterative technique for division. The divisor has N bits and the numerator has more than N bits, generally 2N bits. Each iteration includes initial detection of the position of a left most one bit (1011, 1035) of N most significant bits of the numerator. If this L is not zero, then the numerator in left shifted by L places (1016, 1039), the next L quotient bits are set to zero and the number of completed iterations of the division is incremented by L. An alternative embodiment detects bit position of the left most one of an exclusive OR of the N most significant bits of the numerator and the divisor. If this is nonzero, then the numerator shifts this number of places and the corresponding quotient bits are set to "0". Next the division technique calculates the difference between the N most significant bits of the numerator and the divisor. If the difference is greater than or equal to zero, then the next quotient bit is "1". If the difference is less than zero, then the next quotient bit is "0". The difference is substituted for the N most significant bits of the numerator, if this difference was greater than or equal to zero. Then the numerator is left shifted one place. These iterations repeat until the number of iterations exceeds N. Then the quotient is completely formed and the data of the last numerator is the remainder of the division. This technique eliminates useless data manipulation for the cases where this technique determines the quotient bits are "0". Using pre- and post-processing this technique can be used with signed numbers. In the preferred embodiment of this invention, the division logic is embodied in at least one digital image/graphics processor as a part of a multiprocessor formed in a single integrated circuit used in image processing.

Apparatus and method for determining the profile of the tread of a tire

Abstract: The invention provides an apparatus, and a method, for detecting the tread profile of a tire mounted about an X-axis comprising a non-contact Y detection means movable in parallel to the X-axis for measuring the distance at a right angle between such means and the peripheral surface of the tread profile in the direction of the Y-axis, X detection means for detecting the position of the Y detection means along the direction of the X-axis, data memory means for storing X and Y data pairs obtained by both such detection means, and radius calculating means for calculating the radius of the article from the X and Y data stored in the data memory means. The radius calculating means includes division means for dividing the X and Y data for a plurality of portions of the tread profile based on predetermined reference values for the tread profile of the tire being measured and arithmetic means for determining the radii of the respective portions each from the corresponding data divided by the division means, the arithmetic means determining the circle equation of: x 2 +y 2 +ax+by+c=0, from the X and Y data to calculate the radius of the tread profile, the coefficients a, b and c of the circle equation being determined by least square approximation.

The design of a 64-bit integer multiplier/divider unit

Abstract: The highlights of the design of an integer multiplier/divider unit for a 64-b processor are presented. The final design is the result of a compromise between performance, complexity, and transistor count. It is optimized for two specific operations with the same hardware being shared by the remaining operations. Thus, for example, the multiplier can be configured for the execution of several different multiply operations and its hardware is also heavily utilized in division. The divider design is optimized for repetitive division by small numbers, since this is a characteristic of several important applications planned for the processor. For such small divisors, the reciprocal is calculated and stored in a content-addressable memory. The stored reciprocals can then be used to generate quotients through fast multiplication. Simulations of the planned applications show a 20% to 30% performance increase over alternative designs. >

Method of and system for producing solid models

Abstract: A method of and an apparatus for producing solid models, in which input data consisting of the coordinates of terminal points and a formula of a curved line of each arc of a given wire frame model is read. The coordinates of a node and a set of arcs connected thereto are determined based on the input coordinates of the terminal points. A set of arcs looping around an indivisible surface of the wire frame model are specified as the outermost line surrounding the whole wire frame model. A region of the wire frame model surrounded by the outermost line or division lines is divided into two new partial wire frame models by a new division line starting from a node located on the outermost line or the division lines, traversing the region without making a loop, passing along each of the arcs included in the region only once, and reaching another node located on the outermost line or the division lines. The division is repeated until there remains no arc which has not yet been passed through in any of the partial wire frame models. A a set of arcs looping around each of the further-indivisible partial wire frame models is defined as surface loop.

Wavelength division multiplexer suitable for integrated optical systems

Abstract: In a wavelength division multiplexer suitable for integrated optical systems, to multiplex a succession of waves ranked according to their wavelength two diffraction gratings are formed at the edges of a common guide area. One focuses odd ranked waves onto a first entry of an output guide. The other focuses even ranked waves onto a second entry of the same output guide.

Switch for self-healing ring

Abstract: First stage and third stage four-input four-output space division switches are arranged before and after a second stage time division switch, and two outputs of the first stage space division switch and two inputs of the third stage space division switch are connected by bypassing the time division switch. The time division switch has n control memories. A first control memory stores connection information in a normal state of each path set in the transmission line, a second control memory stores connection information of a first alternative path when failures occur in a path, and an n-th control memory (n is any integer equal or greater than 3) stores connection information of an (n-1)th alternative path, and a control memory corresponding the a failure pattern is selected from the n control memories for each path.

An optical information reproducing apparatus

Abstract: An optical information-reproducing apparatus comprising a light emitting means (11), and an optical system (13) that focuses light emitted from the light emitting means on a recording medium (14) and that detects the reflected light from the recording medium to supply to a diffracting element (12), and a photodetector (15) that includes a plurality of photodetecting portions (15a,b,c,d) divided by division lines and that converts the diffracted light from the diffracting element focussed on the division lines into an electrical signal by the photodetecting portions on both sides of the division lines, wherein the photodetector is so constructed that division lines on which diffracted light from the diffracting element is focused are inclined with respect to the direction of the diffraction of the reflected light in the diffracting element such that the amount of focusing spot light received by the photodetecting portions on both sides of the division lines become substantially equal.

One Hundred Hungry Ants

Abstract: Use practical and informal methods to multiply and divide 2 digit numbers, round remainders up or down depending on context. Develop and use written methods to record, support and explain multiplication and division of 2 digit numbers by a 1 digit number, including division with remainders. Find unit fractions of numbers and quantities. Outcome: teach x/÷ through arrays and number lines. Relate to repeated addition. Teach fractions through dividing 100 by 2, 4, 5, 10. Calculating Knowing and using number facts Using and applying Reognise and continue number sequences formed by counting on or back in steps of constant size. Recognise the equivalence between decimal and fraction forms of one half, quarters, tenths and hundredths.

Division by iteration employing subtraction and conditional source selection of a prior difference or a left shifted remainder

Abstract: A data processing apparatus iteratively forms quotient, includes data registers ( 200 ) for storing various initial and intermediate quantities, a multiplexer ( 215 ) for selecting data from one of two data registers, a barrel rotator ( 235 ) and an arithmetic logic unit ( 230 ). A first register ( 200 a ) stores the numerator, which is left shifted each iteration. A second register ( 200 c ) stores the difference formed by the prior trial subtractions. A status register ( 210 ) set by the prior arithmetic logic unit ( 230 ) result controls the selection made by the multiplexer ( 215 ). A barrel rotator ( 235 ) rotates the data selected by multiplexer ( 215 ). The arithmetic logic unit ( 230 ) subtracts the divisor from the rotated quantity this result controls the iterative division process. If the difference is less than zero, then the rotated data is selected and the quotient bit is “0”. Otherwise, the prior difference is selected and the quotient bit is “1”. In the preferred embodiment, the numerator is split between two registers. The trial difference involves only the most significant bits of the numerator. In the preferred embodiment, the inverse of the divisor is stored and the difference is formed by adding the inverse of the divisor. The division processing repeats until the quotient is completely formed and loop logic controls the number of iterations. Also, the data processing apparatus is embodied as at least one digital image/graphics processor ( 71, 72, 73, 74 ) as a part of a multiprocessor ( 100 ) formed in a single integrated circuit.

Filter unit and high-pressure sizing apparatus

Abstract: A filter unit comprises a metallic supporting plate possessed of stepped through holes opening with a larger diameter in one main surface and with a smaller diameter in the other main surface (wherein the diameter ratio of larger-diameter openings to smaller-diameter openings is desired to be in the range of 1:0.01 to 1:0.5) or a pressureproof supporting plate having in one surface thereof inclined liquid flow grooves arranged in a radial pattern and concentric circular liquid flow grooves adapted to intersect the radially arranged liquid flow grooves and a membrane filter disposed on the surface of the supporting plate containing larger-diameter openings or liquid flow grooves. This filter unit is ideally used for finely dividing and uniformly sizing suspended lipid particles assuming a definite average particle size and a specific particle size distribution. The high-pressure sizing apparatus and the method for production of suspended lipid particles utilize the filter unit constructed as described above and rely essentially for their operation on effecting fine division of lipid particles in the suspension by supplying the suspension of lipid particles from the membrane filter side under pressure and causing the suspension to pass through the membrane filter. Thus, they constitute themselves effective measures for pharmacological products and cosmetic products which are in need of lipid particles assuming a definite average particle size and a specific particle size distribution.

Air conditioning system

Abstract: PURPOSE:To control an air conditioner by the outputs of a plurality of sensors without increasing the number of wirings. CONSTITUTION:A main controller 1 is connected to a plurality of peripheral units 2-4 by a branch method through a transmission line Ls which consists of a pair of lines. The output of sensor unit 5 provided with a sensor is inputted to the peripheral unit 2 to transmit to the main controller 1 monitoring data which correspond to the value of detection of the sensor. And the main controller 1 supplies the peripheral unit 3 with the control data which are the control values of an air conditioner based on monitoring data. The peripheral unit 3 regulates the output of the air conditioner 6 which is connected as a load based on control data. Between the main controller 1 and peripheral units 2-4, the data is transmitted by a time division multiple system. Since, if an increase in the number of sensors results in an increased installation of peripheral unit 2, it only requires to connect to the transmission line the peripheral unit 2 to which the sensor is connected, there is no increase in the number of wirings.

A new digit-serial divider architecture

Abstract: A new simple algorithm for performing digit-serial division is described The non-restoring binary division algorithm has been modified to obtain an equivalent algorithm suitable for general radix Also, a digit-serial pipelined divider architecture is presented to carry out division digit serially so that many samples can be processed simultaneously Our architecture is different from existing digit-serial dividers in that it is based on a radix-2 n division algorithm It is simple and general for any value of n or any number of digits Furthermore, it can be made fully pipelined and can deal with positive as well as negative operands

Parallel high-radix nonrestoring division

Abstract: An algorithm for high-radix nonrestoring division is proposed which combines a cost-efficient quotient estimation technique with collapsing of the division into one operation each iteration. The quotient estimation technique is a direct combinatorial algorithm which allows a more generalized partial remainder than similar studies. In addition, the successor partial remainder is calculated directly from the previous partial remainder. The intermediate steps of calculating the next quotient estimate, multiplying it by the divisor, and then subtracting the result from the previous remainder are telescoped into one step. This is possible due to the use of simple direct combinatorial equations for the quotient estimate. Thus, one operation is used to generate the next remainder from the previous remainder. This operation is similar to a multiplication with a reduced carry propagate adder. This algorithm reduces the latency of each iteration to less than the delay of one multiplication. Thus, high-radix nonrestoring division is possible with a low latency and no need for an off-chip ROM to hold a quotient estimate. >

Ink jet recording method and recorder

Abstract: PURPOSE:To obtain ink jet recording method and recorder realizing the improvement of a bad effect on an image, unevenness of color, and the like caused by a positional shift of dots. CONSTITUTION:In an ink jet recorder, a multihead 702 including four color heads 701 is provided on a carriage, and a printing image is being completed on printing paper 707 by conducting a plurality of times of reciprocative recording operations on the same image area while paper is relatively and successively fed by a paper feed roller 703 and an auxiliary roller 704. Divided thinned-out pixel arrangement patterns used for every recording operation are compensated with each other. A division printing means is provided for making the divided thinned-out pixel arrangement pattern by arranging basic pixel groups, each of which is a rectangle (m) pixels long by (n) pixels wide meeting m

Adaptive beamforming using RNS arithmetic

Abstract: The adaptive beamforming problem is solved using an algorithm-architecture-arithmetic combination that can be used for a small platform such as are found on aircraft or sonobuoys. The arithmetic used is the RNS system implemented on an array of processors that can be reassigned as the algorithm proceeds. The underlying algorithm is a modified Gaussian elimination. The (non-RNS) division operations are eliminated in favor of some scaling and the adaptive use of the processor array to accommodate the growth in dynamic range. >

Method and apparatus for printing continuous pattern

Abstract: Disclosed is a method and apparatus for printing a pattern which is obtained by making a second basic figure from the first basic figure; making output data based on the second basic figure, the output data representing an output figure which is obtained by joining a plurality of the second basic figures consecutively side by side in both the first and second directions so that the second basic figures are arranged in a plurality of parallel rows extending in the second direction, while shifting in the second direction the second basic figures located in each one of the rows from the second basic figures located in another row adjacent to the one row by a predetermined shifting distance including zero; and printing on a given web the output figure by using the output data; wherein the step of making the second basic figure comprises a first substep of dividing the first basic figure into first and second areas of equal sizes in the first direction; a second substep of dividing in the second direction each of the first and second areas into two small regions with a division ratio determined by a ratio of the shifting distance to a length of the first basic figure in the second direction such that the two small regions diagonally positioned have equal sizes; and a third substep of replacing the two small regions diagonally positioned by each other thereby to form the second basic figure.