Abstract: An arithmetic processing device includes a processor that calculates a constant multiplication value by multiplying a constant value obtained by dividing a first value by a natural logarithm of 2 and a data value, separates the constant multiplication value into an integer portion and a fractional portion, calculates a fractional power value corresponding to a value of the fractional portion, calculates an integer power value corresponding to a value obtained by multiplying a value of the integer portion by a second value, calculates a power addition value by adding the fractional power value and the integer power value, calculate a power subtraction value by subtracting the integer power value from the fractional power value, and calculate a division value by dividing the power subtraction value by the power addition value as a result of an execution of an arithmetic operation of a hyperbolic tangent function with the data value.

Abstract: The invention relates to a method for decoding a received RDS signal (R), comprising the following steps: determining an extreme value from among the absolute values of the RDS signal (R) integrals obtained in an elementary range interval (Te), and sliding from a starting point in at least one slide range (Tg); and extracting a binary pattern “0” if the extreme value is a minimum value, and a binary pattern “1” if the extreme value is a maximum value.

Abstract: A method and apparatus for additive range reduction are disclosed. A constant may be pre-stored in a look-up table (LUT), and at least one section of the constant may be retrieved from the LUT for generating a product of an input argument and the constant such that a precision of the product may be controlled in any granularity. For a trigonometric function, 2/? is stored in the LUT, and at least one section of 2/? may be retrieved from the LUT. The argument is multiplied with the retrieved sections of 2/?. The retrieved sections are determined to correctly generate the two least significant bits (LSBs) of an integer portion and a scalable number of most significant bits of the multiplication result. An output of the trigonometric function is generated for the argument with a fractional portion of the multiplication result based on two LSBs of the integer portion of the multiplication result.

Abstract: A math circuit for computing an estimate of a transcendental function is described. A lookup table storage circuit has stored therein several groups of binary values, where each group of values represents a respective coefficient of a first polynomial that estimates the function to a high precision. A computing circuit uses a portion of a binary value, that is also taken from one of the groups of values, to evaluate a second polynomial that estimates the function to a low precision. Other embodiments are also described and claimed.

Abstract: Processors and methods for solving mathematical equations are disclosed herein. An embodiment of the processor includes a hardware device that calculates coefficients based on a mathematical operation that is to be performed. An indexing device transmits the coefficients to and from a look up table. A hardware multiplier multiplies certain coefficients by the derivative of a function related to the mathematical operation. A hardware adder adds a first coefficient to the product of a second coefficient and the first order derivative of the function.

Abstract: Circuitry for computing a tangent function of an input value includes first look-up table circuitry that stores pre-calculated tangent values of a limited number of sample values, circuitry for inputting bits of the input value of most significance as inputs to the first look-up table circuitry to look up one of the pre-calculated tangent values as a first intermediate tangent value, circuitry for calculating a second intermediate tangent value from one or more ranges of remaining bits of the input value, and circuitry for combining the first intermediate tangent value and the second intermediate tangent value to yield the tangent function of the input value.

Abstract: Circuitry for computing a trigonometric function of an input includes circuitry for relating the input to another value to generate an intermediate value, circuitry for selecting one of the input and the intermediate value as a trigonometric input value, circuitry for determining respective initial values of a plurality of trigonometric functions for the trigonometric input value, and circuitry for deriving, based at least in part on a trigonometric identity, a final value of the first trigonometric function from the respective initial values of the plurality of trigonometric functions. The trigonometric function may be any of sine, cosine and tangent and their inverse functions. The trigonometric identities used allow a computation of a trigonometric function to be broken into pieces that either are easier to perform or can be performed more accurately.

Abstract: An apparatus and method for angle rotation is disclosed to rotate a complex input by the angle ? to produce a rotated complex output signal. A memory storage device generates control information based on a coarse angle ?M. A coarse rotation butterfly circuit uses the control information to rotate the complex input signal by the coarse angle ?M to produce an intermediate complex number. The control information controls one or more multiplexers and/or adders in the coarse rotation butterfly circuit to rotate the complex input signal. The fine rotation butterfly circuit uses the control information to rotate the intermediate complex number by a fine angle ?L to produce the complex output signal. The control information controls one or more multiplexers and/or adders in the fine rotation butterfly circuit to rotate the intermediate complex number.

Abstract: Provided two CORDIC processors, each including: two input ports representing real and imaginary input ports; and two output ports representing real and imaginary output ports; wherein real and imaginary parts of a first input signal are applied to the imaginary input ports of the first and second CORDIC processors; real and imaginary parts of a second input signal are applied to the real input ports of the first and second CORDIC processors; the first and second CORDIC processors rotate the respective input signals applied thereto by 45 degrees in the clockwise direction; respective data from the real output ports of said first and second CORDIC processors constitute real and imaginary parts of a first output signal; and respective data from the imaginary output ports of said first and second CORDIC processors constitute real part and imaginary part of a second output signal.

Abstract: An apparatus for estimating a transfer function of at target object having divided systems is disclosed. The apparatus acquires an estimation equation to estimate the transfer function of the target object, and determines, for each arithmetic operation in the estimation equation, whether the arithmetic operation is an addition or a multiplication. For the multiplication, the apparatus performs the multiplication of frequency response characteristics in the frequency domain. For addition, the apparatus converts the frequency response characteristics into time response characteristics, performs the addition of the time response characteristics in the time domain, and reconverts a result of the addition into the frequency domain.

Abstract: Circuitry for computing a trigonometric function of an input includes circuitry for relating the input to another value to generate an intermediate value, circuitry for selecting one of the input and the intermediate value as a trigonometric input value, circuitry for determining respective initial values of a plurality of trigonometric functions for the trigonometric input value, and circuitry for deriving, based at least in part on a trigonometric identity, a final value of the first trigonometric function from the respective initial values of the plurality of trigonometric functions. The trigonometric function may be any of sine, cosine and tangent and their inverse functions. The trigonometric identities used allow a computation of a trigonometric function to be broken into pieces that either are easier to perform or can be performed more accurately.

Abstract: An arctangent calculation apparatus includes a phase angle memory unit in which a phase angle is stored in advance, the phase angle corresponding to a two-dimensional vector value corresponding to in a range of 0° to substantially 22.5°; a vector rotation unit that performs a vector rotation operation on a two-dimensional vector value corresponding to in a range of 0° to 360° and converts the two-dimensional vector value corresponding to in a range of 0° to 360° into a two-dimensional vector value corresponding to in a range of 0° to substantially 2.5°; an arctangent calculation unit that outputs, from the phase angle memory unit, a phase angle that corresponds to the two-dimensional vector value corresponding to in a range of 0° to substantially 22.5°; and a phase angle conversion unit that converts the phase angle into a phase angle in a range of 0° to 360°.

Abstract: Disclosed is a processor that is able to efficiently execute DFT operations without having part of a basic operational circuit idle even during non-DFT-operation processing. The processor (1) has an operational means (operation unit) (2) and a control means (control unit) (3). The operation means (2) has a plurality of shift addition-and-subtraction means connected such that CORDIC (COordinate Rotation DIgital Computer) operations can be executed. The shift adding-and-subtracting means also execute shift addition-and-subtraction processing of butterfly operations that process shift addition-and-subtraction for one stage or more. The control means (3) instructs the operation means (2) to execute either CORDIC operations or butterfly operations, based on a plurality of data received from the outside.

Abstract: An amplitude calculation apparatus or an amplitude calculation program of an output signal of an encoder dividing a resurge waveform into a predetermined number of angle areas, presetting and storing coefficient ? of the A-phase and the coefficient ? of the B-phase corresponding to the divided angle areas, the coefficients being set so that ?A+?B approximates the radius of the theoretical resurge waveform, calculating the radius of the resurge waveform as ?A+?B, and making the calculated radius the amplitude of the output signal of the encoder or converting a phase angle ? of a quadrant n to a phase angle ?? of the quadrant 1, and calculating the radius of the resurge waveform as ?|A|+?|B|, whereby the circuit size of the apparatus for calculating the resurge radius from the output of the encoder is reduced and the processing time by software for calculating the resurge radius is shortened.

Abstract: A method and apparatus for additive range reduction are disclosed. A constant may be pre-stored in a look-up table (LUT), and at least one section of the constant may be retrieved from the LUT for generating a product of an input argument and the constant such that a precision of the product may be controlled in any granularity. For a trigonometric function, 2/? is stored in the LUT, and at least one section of 2/? may be retrieved from the LUT. The argument is multiplied with the retrieved sections of 2/?. The retrieved sections are determined to correctly generate the two least significant bits (LSBs) of an integer portion and a scalable number of most significant bits of the multiplication result. An output of the trigonometric function is generated for the argument with a fractional portion of the multiplication result based on two LSBs of the integer portion of the multiplication result.

Abstract: The invention concerns a method and apparatus (28) for determining an angle (9) by means of a resolver (3). In the method, an excitation signal (29) of constant frequency is supplied to the resolver (3), the resolver response signals (13, 14) are measured, successive (16) measurements of each response signal are stored into a sample buffer (5), FIR filtering (10) is computed for the response signal values (16) present in the sample buffer (5) at the instant of computation, the computation points (23, 24) and the set of computation result values (18) corresponding to these points are stored in memory, at least two sets of values (18, 19) of computation results are compared to each other and of these the value set Amax (19) which contains the highest computation result as an unsigned value is selected, and FIR filtering (10) is repeatedly computed at the computation points (25, 26) corresponding to value set Amax (19).

Abstract: A double-step CORDIC algorithm is implemented for conventional signed arithmetic using multiple iteration stages in which at least one stage implements decision postponing, in which the decision for each stage is delayed until the next stage. In one implementation, the decision for the previous stage is implemented in parallel with the execution of CORDIC equation functions for the current stage. Implementing the double-step CORDIC with decision postponing algorithm can increase the speed of the CORDIC function compared to prior-art CORDIC implementations.

Abstract: A method, computer-readable medium, and an apparatus for generating a transcendental value. The method includes receiving an input containing an input value and an opcode and determining whether the opcode corresponds to a trigonometric operation or a power-of-two operation. The method also includes calculating a fractional value and an integer value from the input value, generating the transcendental value based on the fractional value by adding at least a portion of the fractional value with at least one of a shifted fractional value produced by shifting the portion of the fractional value and a constant value, and providing the transcendental value in response to the request. In this fashion, the same circuit area may be used to carry out both trigonometric and power-of-two calculations, leading to greater circuit area savings and performance advantages while not sacrificing significant accuracy.

Abstract: Systems, methods, and apparatus described include waveform alignment operations in which a single set of evaluated cosines and sines is used to calculate cross-correlations of two periodic waveforms at two different phase shifts.

Abstract: An apparatus and method for angle is disclosed to rotate a complex input by the angle ? to produce a rotated complex output signal. A memory storage device generates control information based on a coarse angle ?M. A coarse rotation butterfly circuit uses the control information to rotate the complex input signal by the coarse angle ?M to produce an intermediate complex number. The control information controls one or more multiplexers and/or adders in the coarse rotation butterfly circuit to information to rotate the complex input signal. The fine rotation butterfly circuit uses the control information to rotate the intermediate complex number by a fine angle ?L to produce the complex output signal. The control information controls one or more multiplexers and/or adders in the fine rotation butterfly circuit to rotate the intermediate complex number.

Abstract: Circuitry for computing a tangent function of an input value includes first look-up table circuitry that stores pre-calculated tangent values of a limited number of sample values, circuitry for inputting bits of the input value of most significance as inputs to the first look-up table circuitry to look up one of the pre-calculated tangent values as a first intermediate tangent value, circuitry for calculating a second intermediate tangent value from one or more ranges of remaining bits of the input value, and circuitry for combining the first intermediate tangent value and the second intermediate tangent value to yield the tangent function of the input value.

Abstract: A method, computer-readable medium, and apparatus for generating a trigonometric value. The method includes receiving a request to calculate a trigonometric value for an angle value and calculating a fractional value from the angle value. The fractional value corresponds to one of a first quadrant value, a second quadrant value, a third quadrant value, and a fourth quadrant value. The method also includes using the fractional value to determine whether to perform at least one of inverting the fractional value and negating the trigonometric value. The method further includes generating the trigonometric value from the fractional value by adding at least a portion of the fractional value with at least one of a shifted fractional value produced by shifting the portion of the fractional value and a constant value and providing the trigonometric value in response to the request.

Abstract: Circuitry for computing a trigonometric function of an input includes circuitry for relating the input to another value to generate an intermediate value, circuitry for selecting one of the input and the intermediate value as a trigonometric input value, circuitry for determining respective initial values of a plurality of trigonometric functions for the trigonometric input value, and circuitry for deriving, based at least in part on a trigonometric identity, a final value of the first trigonometric function from the respective initial values of the plurality of trigonometric functions. The trigonometric function may be any of sine, cosine and tangent and their inverse functions. The trigonometric identities used allow a computation of a trigonometric function to be broken into pieces that either are easier to perform or can be performed more accurately.

Abstract: The present invention relates to digital signal processors with an integrated module configured to compute a Coordinate Rotation Digital Computer (CORDIC) in a pipeline. The pipelined module can advantageously complete computation of one CORDIC computation for each clock pulse applied to the CORDIC module, thereby providing a CORDIC computation for each clock pulse. One embodiment advantageously computes a first portion of a computation with a lookup table and a second portion in accordance with a CORDIC algorithm. Advantageously, data in a CORDIC pipeline is automatically advanced in response to read instructions and can be automatically advanced from the beginning of the pipeline to the end of the pipeline to reinitialize the pipeline. This allows information to be retrieved from the CORDIC pipeline with relatively little overhead. The automatic starting and stopping of the CORDIC pipeline advantageously allows the retrieval of computations from efficient pipeline architectures on an as-needed basis.

Abstract: An arctangent calculation apparatus includes a phase angle memory unit in which a phase angle is stored in advance, the phase angle corresponding to a two-dimensional vector value corresponding to in a range of 0° to substantially 22.5°; a vector rotation unit that performs a vector rotation operation on a two-dimensional vector value corresponding to in a range of 0° to 360° and converts the two-dimensional vector value corresponding to in a range of 0° to 360° into a two-dimensional vector value corresponding to in a range of 0° to substantially 22.5°; an arctangent calculation unit that outputs, from the phase angle memory unit, a phase angle that corresponds to the two-dimensional vector value corresponding to in a range of 0° to substantially 22.5°; and a phase angle conversion unit that converts the phase angle into a phase angle in a range of 0° to 360°.

Abstract: A phase calculation apparatus using a binary search is provided. The phase calculation apparatus includes a quarter surface preprocessor determining the bigger one between an absolute value of I component data and an absolute value of Q component data as horizontal component data and the smaller one as perpendicular component data, and detecting information on a phase region indicating an mth (m=1 to 8) phase region (the mth phase region is between (m?1) ?/4 and m ?/4 in which the I/Q component data are located; a phase representative value detector detecting phase representative values x corresponding to the horizontal component data and the perpendicular component data; and a quarter surface postprocessor calculating phase values of the I/Q component data based on the detected information about the phase region and the detected phase representative values x. The phase can be calculated using a limited memory, low complexity of calculation and regardless of the number of bits of I/Q component data.

Abstract: An object ranging system operates by transmitting pulses derived from a frequency-swept signal and determining the beat frequency of a combination of the frequency-swept signal and its reflection from an object. To determine the range of close objects the beat frequency is determined in the time domain by integrating samples of the beat frequency signal to obtain a value representing the integral of a half cycle of the sine wave, establishing integration thresholds representing when, according to the integration value, the sine wave would have reached predetermined stages in its cycle, and measuring the time taken for the integral of the sine wave to change from one threshold to another, this time thereby indicating the period of the beat frequency.

Abstract: Novel methods for converting coordinates for a position from a first coordinate system into coordinates in a second coordinate system are provided. Linear approximations of trigonometric functions are used to calculate values for the trigonometric functions when a position to be converted is within an acceptable bound of a previous position and more precise values of the trigonometric functions are used to perform the conversion when the position to be converted is not within an acceptable bound of a previous position. The present invention can be advantageously utilized to reduce the computation load in a distributed simulation environment, such as a federation of distributed interactive simulations.

Abstract: The invention discloses a method for classifying a transponder (1) and/or signals originating from a transponder (1) and a reader (20) for the inventive method. According to the invention, a reader (20) receives a signal (27, 28) from the transponder (1) and determines the the velocity (v), with which the transponder (1) is moving. Finally, the transponder (1) and/or signals (28) originating from the transponder (1) are classified as valid or invalid in response to the determined velocity (v).

Abstract: A system and method for Fourier encoding a nuclear magnetic resonance (NMR) signal is disclosed. A static magnetic field B0 is provided along a first direction. An NMR signal from the sample is Fourier encoded by applying a rotating-frame gradient field BG superimposed on the B0, where the BG comprises a vector component rotating in a plane perpendicular to the first direction at an angular frequency ? in a laboratory frame. The Fourier-encoded NMR signal is detected.

Abstract: A method for detecting steady-state convergence of noisy or noise free signal comprising the steps of calculating derivative of signal input, calculating the tan inverse of the ratio of positive and negative derivatives and validation of establishment of steady state from the arctan value thereof.

Abstract: A computer-implemented method for performing a calculation using a coordinate rotation digital computer (CORDIC) algorithm. A step of the coordinate rotation digital computer algorithm is performed. As a result of performing the step, a value of the coordinate rotation digital computer algorithm is reduced. The value is shifted using a physical adder. A set of bits of the physical adder is disabled, wherein the set of bits corresponds to at least one high order zero of the value.

Abstract: Computing an angle between a real part and an imaginary part of a complex number includes receiving complex number data; generating a first value, a second value and a determination result according to the complex number data; choosing a dividend and a divisor of a division operation from the first value and the second value for generating a division result according to magnitudes of the first value and the second value; performing table look-up for the division result to generate a table look-up result according to a preserved table; and adjusting the table look-up result for generating an angle corresponding to the complex number data according to the determination result.

Abstract: A method, computer-readable medium, and an apparatus for generating a transcendental value. The method includes receiving an input containing an input value and an opcode and determining whether the opcode corresponds to a trigonometric operation or a power-of-two operation. The method also includes calculating a fractional value and an integer value from the input value, generating the transcendental value based on the fractional value by adding at least a portion of the fractional value with at least one of a shifted fractional value produced by shifting the portion of the fractional value and a constant value, and providing the transcendental value in response to the request. In this fashion, the same circuit area may be used to carry out both trigonometric and power-of-two calculations, leading to greater circuit area savings and performance advantages while not sacrificing significant accuracy.

Abstract: A direct digital synthesizer employs a trigonometric function generator utilizing decomposition of a larger angle into smaller sub-angles, interpolation of a desired sub-angle between two known angles and calculating the trigonometric function using complex arithmetic. The direct digital synthesizer has a phase accumulator to generate an angular increment signal of the output signal. A trigonometric function generator in communication with the phase accumulator receives the angle signal and from the angle signal creates the trigonometric function signal. An angle decomposing circuit is connected to receive the angle signal to separate the angle signal into sub-angles of the angular increment, a sum of the sub-angles equaling the angular increment. An interpolation circuit receives the smallest of the sub-angles to generate the trigonometric function for the smallest of the sub-angles by interpolating between the trigonometric function of two known angles.

Abstract: A DTD-compliant XML document editor is disclosed. The XML document editor generates hints for required elements and required element slots automatically in the process of document creation and edition so as to guide the user to produce a valid document, while syntactic violations are avoided at the same time. The editor also suggests optional elements that may be added into the document to be edited. The user requires no knowledge about XML and DTD to edit DTD-compliant XML documents. The editing process is user-interface-neutral, being able to support user interfaces based on tree views, presentation views and forms. By combining the DTD-compliant editing process with the simplicity of forms, a simple XML document editor with forms as its user interface is developed.

Abstract: An apparatus and method for angle is disclosed to rotate a complex input by the angle ? to produce a rotated complex output signal. A memory storage device generates control information based on a coarse angle ?M. A coarse rotation butterfly circuit uses the control information to rotate the complex input signal by the coarse angle ?M to produce an intermediate complex number. The control information controls one or more multiplexers and/or adders in the coarse rotation butterfly circuit to information to rotate the complex input signal. The fine rotation butterfly circuit uses the control information to rotate the intermediate complex number by a fine angle ?L to produce the complex output signal. The control information controls one or more multiplexers and/or adders in the fine rotation butterfly circuit to rotate the intermediate complex number.

Abstract: Described is fast motion estimation based upon epipolar geometry, which can be used in compressing multi-view video. An epipolar line is computed based on a point (e.g., a centroid point) in a macroblock to be predicted, and a temporary starting point in an image is determined, such as a median predicted search center. A search starting point is further determined based on the temporary starting point and the epipolar line, e.g., a point on the epipolar line corresponding to an intersecting line that is projected orthogonally from the temporary point to the epipolar line. A motion estimation mechanism searches the search space to produce a motion vector. The search may be conducted starting at the search starting point in a reduced search area located around the epipolar line, e.g., a local diamond search and/or rotated unsymmetrical rood-pattern search.

Abstract: A CORDIC method and a CORDIC architecture applied in vector rotation are disclosed. An elementary angles set is extended by representing the elementary angles as the arctangent of the sum of two single signed-power-of-two terms to an extended elementary angles set. A combination of elementary angles is found from the extended elementary angles set such that the residue angle error can be minimized. A quantized scaling factor is used to scale the combination of elementary angles after being micro-rotated.

Abstract: A method for generating a trigonometric function is provided that includes an input angle being received and automatically separated into a first component angle and a second component angle. A sine value for the input angle is automatically determined based upon the first and second component angles. A cosine value for the input angle is automatically determined based upon the first and second component angles. The trigonometric function is automatically generated based upon the sine and cosine values for the input angle.

Abstract: The invention provides a method and system for computing transcendental functions quickly: (1) the multiply ALU is enhanced to add a term to the product, (2) rounding operations for intermediate multiplies are skipped, and (3) the Taylor series is separated into two partial series which are performed in parallel. Transcendental functions with ten terms (e.g., SIN or COS), are thus performed in about ten clock times.

Abstract: A fast CORDIC algorithm and the resulting VLSI architecture for the evaluation of trigonometric functions are disclosed. The new method employs signed digits to represent intermediate operands and requires a constant scaling or normalization factor which can be pre-computed and made available in read-only hardware for any desired target precision (i.e., word length). The speedup is achieved by performing CORDIC iterations in parallel in two separate modules. Each module executes a “double step” or two basic CORDIC rotations at every iteration cycle. Two angles arctan 2−2i and arctan 2−(2i+1) are used in each step i of the method. As a result, approximately {fraction (n/2)} steps (exactly ⌈ n + 3 2 ⌉ steps) are required to evaluate sine/cosine of n bit input argument up to n bits of accuracy.

Abstract: A sign determination circuit is input with in-phase signal I, and outputs in-phase sign determination signal SPI to indicate the sign, positive or negative, of in-phase signal I. Another sign determination circuit is input with orthogonal signal Q, and outputs orthogonal sign determination signal SPQ to indicate the sign, positive or negative, of orthogonal signal Q. A decoder is input with in-phase sign determination signal SPI and orthogonal sign determination signal SPQ, judging which quadrant the vector represented by in-phase signal I and orthogonal signal Q belongs to, thereby determining I&thgr;4, I&thgr;3 to indicate the 180° bit and 90°-bit, respectively, of angle information I&thgr;. Also, I&thgr;2, I&thgr;1 to indicate the 45°-bit and 22.5°-bit, respectively, of angle information I&thgr; is given by the other decoders.

Abstract: The present invention discloses an apparatus and method for implementing an inverse arctangent function using piecewise linear theorem to simplify and used to transform a right-angled coordinate point X and Y to a phase angle &thgr; of an inverse arctangent function. The present invention uses T-line combination to approach an inverse arctangent function between 0 degree to 45 degree, and determines which piecewise linear region the right-angled coordinate point is located at. A coefficient table stored in a memory is used to compute {circumflex over (&thgr;)} which is the approximate value of the phase angle &thgr;. The phase angle {circumflex over (&thgr;)} between 45 degree to 360 degree can be mapped to the approximate phase angle {circumflex over (&thgr;)} between 0 degree to 45 degree using linear combination.

Abstract: A system and method for computing the cosine of an input value. The system comprises a logical processing unit and an addition unit. The logical processing unit comprises an input bus with a plurality of input lines for receiving an input angle value. The logical processing unit includes a first plurality of gates, preferably AND gates, coupled to the input bus. Each gate of the first plurality of gates couples to two or more of the input lines. The logical processing unit generates N output operands on N corresponding output buses. At least one of the output buses includes (a) at least one output line coupled to an output of one of the first plurality of gates, and (b) at least one output line coupled to one of the input lines of the input bus. The number N of output buses is greater than or equal to two. The addition unit couples to the N output buses of the logical processing unit, and is configured to perform an addition of the N binary operands provided on the N output buses.

Abstract: The invention provides a method and system for computing transcendental functions quickly: (1) the multiply ALU is enhanced hanced to add a term to the product, (2) rounding operations for intermediate multiplies are skipped, and (3) the Taylor series is separated into two partial series which are performed in parallel. Transcendental functions with ten terms (e.g., SIN or COS), are thus performed in about ten clock times.

Abstract: A differential detection receiver with a reduced power consumption is provided by simplifying constituent circuits of the differential detection receiver. An arctangent calculator is realized without using an multiplier or a conversion table. Without using a D/A converter, a level adjusting circuit for adjusting the absolute value of a vector (Ax, Ay) given as input signals Ax and Ay so as to make it one. The power consumption of a differential detection demodulator is reduced by eliminating power consuming circuits such as a multiplier and a large conversion table from the system. There are disclosed some embodiments.

Abstract: A 64-bit precision digital circuit for computing the exponential function and a related 64-bit precision digital circuit for computing sine and cosine, each circuit comprising a master circuit and a slave circuit. The master circuit computes the remainders {tilde over (x)}i for every “logical” iteration i using fast, low-precision circuit, thereby accumulating temporary errors. Only at the end of every 8 i's, which marks the end of a “physical” iteration, is a complete and fast correction to the accumulated errors performed. The slave circuit computes quantities called the yi's, which will eventually converge to the desired output.

Abstract: A method for forming a sum of the absolute value of the difference between each pair of numbers of respective first and second sets of numbers. The method includes forming the difference between a first number of the first set and a second number of the second set. Next this difference is either added to or subtracted from a running sum based upon the sign of this difference. This is repeated until all number pairs are either added to or subtracted from the running sum of absolute values of the differences. The initial subtraction is used to set a status bit in a flag register (211) based upon a less than zero output or the carry-out. The status bit controls whether the difference is added to or subtracted from the running sum. The conditional addition to or subtraction from the running sum may generate a carry-out representing the most significant bit of the running sum. This carry-out is stored and later added to the running sum to recover the most significant overflow bits.

Abstract: A device suitable for determining arc-tangent of an angle .theta. is provided. Circuitry generates a first square wave at a frequency .omega.t and a second square wave at the frequency .omega.t but shifted by a phase difference equal to the angle .theta.. A pulse width modulation signal generator processes the first and second square waves to generate a pulse width modulation signal having a frequency of .omega.t and having a pulse width that is a function of the phase difference .theta.. The pulse width modulation signal is converted to a DC voltage that is a linear representation of the phase difference .theta..