Abstract: Techniques for operating on and calculating binary floating-point numbers using an enhanced floating-point number format are presented. The enhanced format can comprise a single sign bit, six bits for the exponent, and nine bits for the fraction. Using six bits for the exponent can provide an enhanced exponent range that facilitates desirably fast convergence of computing-intensive algorithms and low error rates for computing-intensive applications. The enhanced format can employ a specified definition for the lowest binade that enables the lowest binade to be used for zero and normal numbers; and a specified definition for the highest binade that enables it to be structured to have one data point used for a merged Not-a-Number (NaN)/infinity symbol and remaining data points used for finite numbers. The signs of zero and merged NaN/infinity can be “don't care” terms. The enhanced format employs only one rounding mode, which is for rounding toward nearest up.

Abstract: Methods and systems for division operation are described. A processor can initialize an estimated quotient between the dividend and the divisor separately from a floating-point unit (FPU) pipeline. The processor can implement the FPU pipeline to execute a refinement process that can include at least a first iteration of operations and a second iteration of operations. The refinement process can include, in the first iteration of operations, generating a first unnormalized floating-point value using the initialized estimated quotient. The refinement process can include, in the second iteration of operations, generating a second unnormalized floating-point value using the first unnormalized floating-point value. The processor can determine a final quotient based on the second unnormalized floating-point value.

Abstract: A processor includes a core and a plurality of registers including a first register, a second register, and a third register. The core is configured to perform a division operation that includes execution of a sign extraction instruction in which a sign of at least one of a numerator value and a denominator value is stored, a conditional subtraction instruction which divides the numerator value by the denominator value to generate a quotient value and a remainder value, and a sign assignment instruction which adjusts the sign of at least one of the quotient and remainder values. The conditional subtraction instruction is configured to cause the core to perform multiple iterations of a conditional subtraction in one execution of the conditional subtraction instruction and in one clock cycle. Others methods and apparatus are described as well.

Abstract: An integer division circuit includes a first bit-shifting circuit configured to shift the bits of a dividend to produce a normalized dividend. The circuit also includes a second bit-shifting circuit configured to shift the bits of a divisor to produce a normalized divisor. A divider tree circuit is configured to divide the normalized dividend by the normalized divisor to produce a normalized quotient. The circuit further includes a third bit-shifting circuit configured to shift the bits of the normalized quotient to produce a quotient.

Abstract: A data processing device has an instruction decoder, a control logic unit, and ALU. The instruction decoder decodes instruction codes of an arithmetic instruction. The control logic unit detects the effective data width of operation data to be processed according to the decode result from the instruction decoder and determines the number of cycles for the instruction execution corresponding to the effective, data width. The ALU executes the instruction with the number of cycles of the instruction execution determined by the control logic unit.

Abstract: A data processing apparatus is provided, for performing a determination of whether a value falls within a boundary defined by a lower limit between 0 and 2m and an upper limit between 0 and 2m. The apparatus includes storage circuitry that stores each of the lower limit and the upper limit in a compressed form as a mantissa of q<m bits and a shared exponent e. A most significant m-q-e bits of said lower limit and said upper limit are equal to a most significant m-q-e bits of said value. Adjustment circuitry performs adjustments to the lower limit and the upper limit in compressed form and boundary comparison circuitry performs the determination on the value using the lower limit and the upper limit in the compressed form.

Abstract: Systems, apparatuses, and methods for implementing a fractional pointer lookup table are disclosed. A system includes a fractional pointer lookup table and control logic coupled to the table. The control logic performs an access to the table with a numerator and a denominator, wherein the numerator and the denominator are integers. The control logic receives a result of the lookup, wherein the result is either a rounded-up value of a quotient of the numerator and denominator or a rounded-down value of the quotient. In one embodiment, the control logic provides a fractional pointer to the table with each access and receives a fractional pointer limit from the table. The control logic initializes the fractional pointer to zero, increments the fractional pointer after each access to the table, and resets the fractional pointer to zero when the fractional pointer reaches the fractional pointer limit.

Abstract: A processor includes a core and a plurality of registers including a first register, a second register, and a third register. The core is configured to perform a division operation that includes execution of a sign extraction instruction in which a sign of at least one of a numerator value and a denominator value is stored, a conditional subtraction instruction which divides the numerator value by the denominator value to generate a quotient value and a remainder value, and a sign assignment instruction which adjusts the sign of at least one of the quotient and remainder values. The conditional subtraction instruction is configured to cause the core to perform multiple iterations of a conditional subtraction in one execution of the conditional subtraction instruction and in one clock cycle. Others methods and apparatus are described as well.

Abstract: A data processing apparatus comprises signal receiving circuitry to receive a signal corresponding to a divide instruction that identifies a dividend x and a divisor d. Processing circuitry performs, in response to said divide instruction, a radix-N division algorithm to generate a result value q=x/d, where N is an integer power of 2 and greater than 1. Said division algorithm comprises a plurality of iterations, each of said plurality of iterations being performed by quotient digit calculation circuitry to determine a quotient value of that iteration q[i+1] based on a remainder value of a previous iteration rem[i]; and remainder calculation circuitry to determine a remainder value of that iteration rem[i+1] based on said quotient value of that iteration q[i+1] and said remainder value of said previous iteration rem[i]. Result calculation circuitry derives said result value q based on each quotient value selected by said digit selection circuitry for each of said plurality of iterations.

Abstract: Apparatuses and methods of manufacturing same, systems, and methods for performing recursive operations using a partial remainder-divisor (PD) table are described. In one aspect, it is determined whether a current cell in the PD table indicated by a current partial remainder/radicand row value and a current divisor/root column value is outside a primary region of the PD table. If the current cell is outside the primary region of the PD table, at least one of the current partial remainder/radicand row value and the current divisor/root column value are adjusted so that the indicated current cell falls within the primary region of the PD table.

Abstract: A method for fast parallel adder processing. The method includes receiving parallel inputs from a communications path, wherein each input comprises one bit, adding the inputs using a parallel structure, wherein the parallel structure is optimized to accelerate the addition by utilizing a characteristic that the inputs are one bit each, and transmitting the resulting outputs to a subsequent stage.

Abstract: A method is provided to narrow down the exponent range throughout most part of the division and square root calculations, to make both software assistance and precision extension unnecessary. The method adjusts the exponent at the end of the calculation to reach IEEE-754 results.

Abstract: The disclosed embodiments disclose techniques for using a split division circuit that includes a first divider that is optimized for a first range of divisor values and a second divider that is optimized for a second range of divisor values; the first range is distinct from the second range. During operation, the circuit receives a divisor for the division operation. The circuit: determines whether the divisor is in the first range or the second range to determine whether the first divider or the second divider should perform the division operation; performs the division operation in the selected host divider; and then outputs the result that was generated by the selected host divider.

Abstract: Divisions by numbers that are not divisible by two (2) can be performed in a computing system based on a summation that estimates and/or approximates the reciprocal of the dividing number or denominator value. By way of example, dividing by three (3) can be calculated based on a summation that approximates or estimates one third (?) represented as the sum of a selected group of the inverses of the powers of two (2) in a pattern, namely the sum of: ¼, 1/16, 1/64, 1/256, . . . ). Applications of the division techniques are virtually unlimited and include memory mapping of global memory addresses to memory channel addresses by dividing a global memory address into the number of memory channels, allowing memory mapping to be performed in an efficient manner even for large memory spaces using a number of memory channels that are not divisible by two, including prime numbers.

Abstract: Techniques are disclosed relating to integrated circuits that include hardware support for divide and/or square root operations. In one embodiment, an integrated circuit is disclosed that includes a division unit that, in turn, includes a normalization circuit and a plurality of divide engines. The normalization circuit is configured to normalize a set of operands. Each divide engine is configured to operate on a respective normalized set of operands received from the normalization circuit. In some embodiments, the integrated circuit includes a scheduler unit configured to select instructions for issuance to a plurality of execution units including the division unit. The scheduler unit is further configured to maintain a counter indicative of a number of instructions currently being operated on by the division unit, and to determine, based on the counter whether to schedule subsequent instructions for issuance to the division unit.

Abstract: A processor for dividing by calculating repeatedly an n-bit width partial quotient includes, a dividend zero count value counter that counts a dividend zero count value, a divisor zero count value counter that counts a divisor zero count value, a correction value calculator that calculates a correction value to a loop count value, a correction loop count value calculator that calculates a correction loop count value, a dividend shift unit that shifts leftward an absolute value of the dividend by the dividend zero count value and shifts rightward the leftward-shifted absolute value of the dividend by the correction value, a divisor shift unit that shifts leftward an absolute value of the divisor by the divisor zero count value, and a division loop operation unit that divides based on an output value from the dividend shift unit, an output value from the divisor shift unit, and the correction loop count value.

Abstract: Mechanisms for utilizing a reduced lookup table circuit to perform an operation in a data processing device are provided. A first input value is input for selecting a subset of values from the reduced lookup table circuit. The reduced lookup table circuit stores only boundary cell values from a fully filled lookup table corresponding to the reduced lookup table circuit. The subset of values comprises only a subset of boundary cell values corresponding to the first input value. A second value is input and a comparison, by the reduced lookup table circuit, of the second value to each of the boundary cell values in the subset of boundary cell values is performed. The reduced lookup table circuit outputs an output value based on results of the comparison of the second value to each of the boundary cell values in the subset of boundary cell values.

Abstract: The high-radix multiplier-divider provides a system and method utilizing an SRT digit recurrence algorithm that provides for simultaneous multiplication and division using a single recurrence relation. When A, B, D and Q are fractions (e.g., Q=0·q?1 q?2 . . . q?n), then the algorithm provides for computing S = AB D to yield a w-bit quotient Q and w-bit remainder R by: (1) determining the next quotient digit q?j using a quotient digit selection function; (2) generating the product q?jD; and (3) performing the triple addition of rRj-1, (?q?jD) and b - ( j - 1 ) ? ( A r ) where R0=b?1Ar?1. The recurrence relation may be implemented with carry-save adders for computation using bitwise logical operators (AND, OR, XOR).

Abstract: A pipelined circuit for performing a divide operation on small operand sizes. The circuit includes a plurality of stages connected together in a series to perform a subtractive divide algorithm based on iterative subtractions and shifts. Each stage computes two quotient bits and outputs a partial remainder value to the next stage in the series. The first and last stages utilize a radix-4 serial architecture with edge modifications to increase efficiency. The intermediate stages utilize a radix-4 parallel architecture. The divide architecture is pipelined such that input operands can be applied to the divider on each clock cycle.

Abstract: The invention relates to a program storage device readable by a machine, tangibly embodying a program of instructions executable by a specific semiconductor-based computational device situated in the machine to perform the steps of a partial SRT (PSRT) division of a dividend X by a divisor D to obtain a quotient Q. The steps include: causing a computer to obtain the dividend X and the divisor D; representing the dividend X and the divisor D as a digital representation having a plurality of bits; and performing iteratively a series of steps until a desired accuracy of the quotient Q is achieved. The invention also relates to an article of manufacture including a computer usable medium having computer readable program code embodied therein for causing a partial SRT (PSRT) division of a dividend X by a divisor D to generate a quotient Q.

Abstract: A method, system and computer program product for verifying a result of a floating point division operation are provided. The method includes: receiving a result of a floating point division operation for a dividend and a divisor; performing a comparison of a magnitude of a least significant bit (LSB) of the dividend and a magnitude of a most significant bit (MSB) of a remainder; and determining whether the result is correct based on the comparison.

Abstract: A data processing system 2 includes an instruction decoder 22 responsive to polynomial divide instructions DIVL.PN to generate control signals that control processing circuitry 26 to perform a polynomial division operation. The denominator polynomial is represented by a denominator value stored within a register with an assumption that the highest degree term of the polynomial always has a coefficient of “1” such that this coefficient need not be stored within the register storing the denominator value and accordingly the denominator polynomial may have a degree one higher than would be possible with the bit space within the register storing the denominator value alone. The polynomial divide instruction returns a quotient value and a remainder value respectively representing the quotient polynomial and the remainder polynomial.

Abstract: Systems and methods for efficiently handling problematic corner cases in floating point operations without raising flags or exceptions. One or more floating point numbers that will generate a problematic corner case in floating point computations, such as division or square root computation, are detected. Fix-up operations are applied to modify the computation such that the problematic corner case is avoided. The modified computation then is performed, while suppressing error flags are suppressed during intermediate stages.

Abstract: A decimal floating-point (DFP) adder includes a decimal leading-zero anticipator (LZA). The DFP adder receives DFP operands. Each operand includes a significand, an exponent, a sign bit and a leading zero count for the significand. The DFP adder adds or subtracts the DFP operands to obtain a DFP result. The LZA determines the leading zero count associated with the significand of the DFP result. The LZA operates at least partially in parallel with circuitry (in the DFP adder) that computes the DFP result. The LZA does not wait for that circuitry to finish computation of the DFP result. Instead it “anticipates” the number of leading zeros that the result's significand will contain.

Abstract: A device for calculating the quotient q and remainder r of the division (y·k1+x)/k2, wherein k1 and k2 are integers and constant, and wherein x and y are integers. The device comprises a first digital circuit for receiving as input values of y and identifying corresponding values of the quotient qy and the remainder ry of the function y·k1/k2, a second digital circuit for calculating the remainder r of the division, by a) calculating a combined value (x+ry) of the remainder ry and the value of x, b) verifying if the combined value (x+ry) is less than k2, c) correcting the combined value (x+ry) if the verification indicates that the combined value (x+ry) is not less than k2, and d) assigning the corrected combined value (x+ry) to the remainder r, a third digital circuit for calculating the quotient q of the division, by a) correcting the quotient qy if the verification (2206) indicates that the combined value (x+ry) is not less than k2, and b) assigning the corrected quotient qy to the quotient q.

Abstract: A dividing unit sets an actual packet length transferred from a packet receiving section to a variable U, and then sets 2? to a variable V. If a positive number determining section determines that a subtraction result of subtracting a remainder N0 from a quotient M0, both found by dividing U by V, is a positive number, the dividing unit overwrites the subtraction result to U. The dividing unit repeats such operations of dividing the subtraction result by V, until the positive number determining section determines that the subtraction result of subtracting the remainder from the quotient, both found by dividing U by V, is a non-positive number. When the subtraction result becomes a non-positive number and the quotient and the remainder match, a packet length determining section determines that received data has a normal size, and notifies it to a discard determining section.

Abstract: A decimal floating-point (DFP) adder includes a decimal leading-zero anticipator (LZA). The DFP adder receives DFP operands. Each operand includes a significand, an exponent, a sign bit and a leading zero count for the significand. The DFP adder adds or subtracts the DFP operands to obtain a DFP result. The LZA determines the leading zero count associated with the significand of the DFP result. The LZA operates at least partially in parallel with circuitry (in the DFP adder) that computes the DFP result. The LZA does not wait for that circuitry to finish computation of the DFP result. Instead it “anticipates” the number of leading zeros that the result's significand will contain.

Abstract: Techniques are disclosed relating to integrated circuits that include hardware support for divide and/or square root operations. In one embodiment, an integrated circuit is disclosed that includes a division unit that, in turn, includes a normalization circuit and a plurality of divide engines. The normalization circuit is configured to normalize a set of operands. Each divide engine is configured to operate on a respective normalized set of operands received from the normalization circuit. In some embodiments, the integrated circuit includes a scheduler unit configured to select instructions for issuance to a plurality of execution units including the division unit. The scheduler unit is further configured to maintain a counter indicative of a number of instructions currently being operated on by the division unit, and to determine, based on the counter whether to schedule subsequent instructions for issuance to the division unit.

Abstract: Weight normalization in hardware or software without a division operator is described, using only right bit shift, addition and subtraction operations. A right bit shift is performed on an expected sum to effectively divide the expected sum by two to provide a first updated value for the expected sum. An iteration is performed which includes: incrementing with a first adder a first variable by the first updated value of the expected sum to provide an updated value for the first variable; subtracting with a first subtractor a second weight from a first weight to provide a first updated value for the first weight; and performing a left bit shift on the second weight to effectively multiply the second weight by two to provide a first updated value for the second weight.

Abstract: Mechanisms for utilizing a reduced lookup table circuit to perform an operation in a data processing device are provided. A first input value is input for selecting a subset of values from the reduced lookup table circuit. The reduced lookup table circuit stores only boundary cell values from a fully filled lookup table corresponding to the reduced lookup table circuit. The subset of values comprises only a subset of boundary cell values corresponding to the first input value. A second value is input and a comparison, by the reduced lookup table circuit, of the second value to each of the boundary cell values in the subset of boundary cell values is performed. The reduced lookup table circuit outputs an output value based on results of the comparison of the second value to each of the boundary cell values in the subset of boundary cell values.

Abstract: A floating-point circuit may include a floating-point operand normalization circuit configured to receive input floating-point operands of a given floating-point divide operation, the operands comprising a dividend and a divisor, as well as a divide engine coupled to the normalization circuit. In response to determining that one or more of the input floating-point operands is a denormal number, the operand normalization circuit may be further configured to normalize the one or more of the input floating-point operands and output a normalized dividend and normalized divisor to the divide engine, and dependent upon respective numbers of leading zeros of the dividend and divisor prior to normalization, generate a value indicative of a maximum possible number of digits of a quotient (NDQ). The divide engine may be configured to iteratively generate NDQ digits of a floating-point quotient from the normalized dividend and the normalized divisor provided by the floating-point operand normalization circuit.

Abstract: A mechanism for executing fixed point divide operations using a floating point multiply-add pipeline are provided. With the mechanism, the floating point execution unit in a processor is modified to include elements that may be used to perform fixed point divide operations. These additional elements include a leading zero counter, a leading one counter, an estimate table unit, and a state machine. The fixed point divide operands are converted to a floating point format and an estimate of the reciprocal of the divisor is generated using estimate tables. These values are used in multiple passes through the floating point unit for calculating estimates of the quotient and corresponding error values. The estimates of the quotient are based on previous estimates of the quotient in a prior pass through the floating point unit and a corresponding error value. The final quotient estimate is truncated.

Abstract: A method, computer program product and a system for controlling a fixed point division operation are provided. The method includes: receiving an instruction to perform a division operation for a dividend and a divisor, the operation comprising a maximum number of iterations to produce a quotient having a maximum precision; calculating a magnitude of at least one of the dividend and the divisor; determining a quotient precision based on the magnitude; and computing a required number of iterations needed to produce the quotient precision and performing the number of iterations.

Abstract: A computer-implemented method for executing a floating-point calculation where an exact value of an associated result cannot be expressed as a floating-point value is disclosed. The method involves: generating an estimate of the associated result and storing the estimate in memory; calculating an amount of error for the estimate; determining whether the amount of error is less than or equal to a threshold of error for the associated result; and if the amount of error is less than or equal to the threshold of error, then concluding that the estimate of the associated result is a correctly rounded result of the floating-point calculation; or if the amount of error is greater than the threshold of error, then testing whether the floating-point calculation constitutes an exception case.

Abstract: The invention relates to a cryptographic method involving an integer division of type q=a div b and r=a mod b, wherein a is a number of m bits, b is a number of n bits, with n being less than or equal to m, and bn?1 being non-null and the most significant bit of b. In addition, each iteration of a loop subscripted by i, which varies between 1 and m?n+1, involves a partial division of a word A of n bits of number a by number b in order to obtain one bit of quotient q. According to the invention, the same operations are performed with each iteration, regardless of the value of the quotient bit obtained. In different embodiments of the invention, one of the following is also performed with each iteration: the addition and subtraction of number b to/from word A; the addition of number b or a complementary number /b of b to word A; or a complement operation at 2n of an updated datum (b or /b) or a dummy datum (c or /c) followed by the addition of the datum updated with word A.

Abstract: An improved method and apparatus for performing floating-point division is disclosed. In a particular embodiment, fractional operands are pre-scaled and an estimate of a reciprocal of the pre-scaled fractional divisor is obtained from a lookup table using a portion of the bits of the pre-scaled fractional divisor. This value is used to scale the fractional operands and a multiply-add operation is used based on principles of series expansion to compute a final result with an acceptable degree of accuracy.

Abstract: Methods and a system are disclosed for one or more appliances including a controller for managing power consumption within a household. The controller is configured to receive and process a signal indicative of one or more energy parameters of an associated energy utility, including at least a peak demand period or an off-peak demand period. A generated serial number is obtained from an original serial number of the appliance or controller, which is configured for a signal to communicate to the appliance within a population and command the appliance to operate in an energy savings mode and a normal mode at various time periods. The generated serial number (GSN) is used to segregate a total population into segments to provide granularity in assigning DR activations and deactivations based upon the GSN.

Abstract: When division X/Y of floating point numbers is performed, bit string data of a mantissa x including a fraction xf of X or a mantissa y including a fraction yf of Y is shifted in accordance with magnitude relation between them to perform a fraction computation. Thereby, a fraction division result in which the position of the most significant bit is fixed at a prescribed digit is generated. When a square root operation ?Y is performed, a fraction square root operation result in which the position of the most significant bit is fixed at a prescribed digit is generated by an exception handling if all of the three conditions that all the bits in the fraction of Y are one, a difference between the exponent ye of Y and a bias value b is an odd number, and a rounding mode is a positive infinity direction are satisfied.

Abstract: A method is provided of characterising a data stream of binary symbols, the method comprising sampling the stream at a predetermined rate sufficient to capture at least two samples per binary symbol, identifying the shortest continuous run of samples having the same logic level and assigning a symbol rate to the stream on the basis that the identified run is one symbol in length.

Abstract: A method and apparatus provides for performing floating-point division using input check/output correction floating-point division logic and a floating-point division fix-up instruction (e.g., an instruction, command, signal or other indicator). In one example, the apparatus includes a processor having a floating-point arithmetic logic unit (ALU) that includes the input check/output correction floating-point division logic. The input check/output correction floating-point division logic is responsive to the floating-point division fix-up instruction executable by the floating-point ALU that causes the input check/output correction floating-point division logic to examine a first input representing a numerator and a second input representing a denominator to determine whether a special case of floating-point division occurs.

Abstract: A floating point divider includes a mantissa repetitive processing unit and an operation execution control unit. The mantissa repetitive processing unit calculates a quotient and a partial remainder by a digit-recurrence process for a mantissa of a dividend of an input operand. The operation execution control unit determines a bit value at a specified position uniquely specified based on a radix of an operation execution process with respect to the partial remainder. The mantissa repetitive processing unit reduces the number of digit-recurrence processes by calculating a quotient and a remainder based on a determining result of the operation execution control unit. The number of bits of the quotient is double of that of a quotient calculated once every the digit-recurrence process. The number of left-shift processes processed on the remainder is double of that of a remainder calculated once every the digit-recurrence process.

Abstract: A division and square root arithmetic unit carries out a division operation of a higher radix and a square root extraction operation of a lower radix. A certain bit number (determined on the basis of a radix of an operation) of data selected from upper bits of the output of a carry save adder and the output of the adder are input to convert the data into twos complement representation data, and the twos complement representation data is shifted a certain bit number (determined on the basis of the radix of the operation) to use the shifted data for a partial remainder of the next digit. Hence, a large number of parts such as registers of a divisor and a partially extracted square root can be commonly used in a divider and a square root extractor to realize an effective and high performance arithmetic unit.

Abstract: The invention proposes a Floating Point Unit with fused multiply-add, with one addend Method for calculating a result of a division with an A-register and a B-register for two multiplicand operands and a C-register for an addend operand, wherein a divide processor using a subtractive method for calculation with a divisor register and a partial remainder register and a multiplier associated to an subtractor uses the C-register as input, wherein while loading the fraction of the dividend through the divisor register into the partial remainder register of the divide processor a calculated shifting is applied for alignment by using the multiplier associated to the subtractor.

Abstract: A floating-point circuit may include a floating-point operand normalization circuit configured to receive input floating-point operands of a given floating-point divide operation, the operands comprising a dividend and a divisor, as well as a divide engine coupled to the normalization circuit. In response to determining that one or more of the input floating-point operands is a denormal number, the operand normalization circuit may be further configured to normalize the one or more of the input floating-point operands and output a normalized dividend and normalized divisor to the divide engine, and dependent upon respective numbers of leading zeros of the dividend and divisor prior to normalization, generate a value indicative of a maximum possible number of digits of a quotient (NDQ). The divide engine may be configured to iteratively generate NDQ digits of a floating-point quotient from the normalized dividend and the normalized divisor provided by the floating-point operand normalization circuit.

Abstract: A method for determining the correct result and the correct guard and sticky bits to obtain a more accurate result in floating point divide operations is presented. An intermediate divide result or quotient is obtained from a multiply-add hardware pipeline of a floating point processor. Remainders are calculated using the floating point numbers divided, the unit of least precision, and the unit of least precision plus one to determine where the infinitely precise result is with respect to the digital representation of the estimated quotient. Evaluating these remainders and the initial floating point numbers and comparing their signs and magnitudes leads to a selection of one of three choices as the most accurate representation of the infinitely precise result as calculated in the inventive rounding method: the intermediate result minus the unit of least precision; the intermediate divide result; or the intermediate divide result plus the unit of least precision.

Abstract: For eigenvalue decomposition, a first set of at least one variable is derived based on a first matrix being decomposed and using Coordinate Rotational Digital Computer (CORDIC) computation. A second set of at least one variable is derived based on the first matrix and using a look-up table. A second matrix of eigenvectors of the first matrix is then derived based on the first and second variable sets. To derive the first variable set, CORDIC computation is performed on an element of the first matrix to determine the magnitude and phase of this element, and CORDIC computation is performed on the phase to determine the sine and cosine of this element. To derive the second variable set, intermediate quantities are derived based on the first matrix and used to access the look-up table.

Abstract: A system for providing a floating point remainder comprises an analyzer circuit configured to determine a first status of a first floating point operand and a second status of a second floating point operand based upon data within the first floating point operand and the second floating point operand, respectively. In addition, the system comprises a results circuit coupled to the analyzer circuit. The results circuit is configured to assert a resulting floating point operand containing the remainder of the first floating point operand and the second floating point operand and a resulting status embedded within the resulting floating point operand.

Abstract: A method, system and computer program product for verifying a result of a floating point division operation are provided. The method includes: receiving a result of a floating point division operation for a dividend and a divisor; performing a comparison of a magnitude of a least significant bit (LSB) of the dividend and a magnitude of a most significant bit (MSB) of a remainder; and determining whether the result is correct based on the comparison.

Abstract: A method, computer program product and a system for controlling a fixed point division operation are provided. The method includes: receiving an instruction to perform a division operation for a dividend and a divisor, the operation comprising a maximum number of iterations to produce a quotient having a maximum precision; calculating a magnitude of at least one of the dividend and the divisor; determining a quotient precision based on the magnitude; and computing a required number of iterations needed to produce the quotient precision and performing the number of iterations.

Abstract: A method and device divides a dividend by a divisor, the dividend and the divisor both being integers. The method and device determine a maximum possible number of quotient digits (NDQ) based on a number of significant digits of the divisor and the dividend, normalizes the dividend and divisor, and calculates NDQ number of quotient digits from the normalized divisor and dividend.