Abstract: A method for binary division includes the steps of having a current remainder provided as a sum bit-vector and a carry bit-vector, performing a carry save add operation between the sum bit-vector and the carry bit-vector and a two's complement representation of a denominator to produce a temporary sum and a temporary carry, predicting a sign bit of a full total of the temporary sum and the temporary carry and updating the remainder with the temporary sum and the temporary carry and incrementing a quotient if the sign bit is 0.

Abstract: In a parallel computer system having multiple information processing apparatuses, a first information processing apparatus includes circuitry configured to wait for calculation target data from each of one or more other information processing apparatuses being included in the plurality of information processing apparatus; carry out an average calculation that calculates an average value of a plurality of calculation target data including the waited calculation target data; and transmit the calculated average value to a second information processing apparatus being one of the plurality of information processing apparatuses and being different from the other information processing apparatuses. This configuration makes it possible to achieve highly-precise collective average calculation without requiring bit expansion.

Abstract: One embodiment provides for a compute apparatus to perform machine learning operations, the compute apparatus comprising a fetch unit to fetch a single instruction having multiple input operands, wherein the multiple input operands have an unequal bit-length, a first input operand having a first bit-length and a second input operand having a second bit-length; a decode unit to decode the single instruction into a decoded instruction; an operand length unit to determine a smaller bit-length of the first bit-length and the second bit-length; and a compute unit to perform a matrix operation on the multiple input operands to generate an output value having a bit length of the smaller bit length.

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: 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 modulo N calculating method for an M1*M2-bit binary integer, wherein N, M1 and M2 are integers, includes the steps of dividing the M1*M2-bit binary integer into M1 bits and performing AND operation on each M1 bits and a specific binary integer; and changing a value of an output register depending on the AND operation result and storing the value thereto. A modulo N calculating apparatus includes an input unit for receiving an M1*M2-bit binary integer, wherein N, M1 and M2 are integers; and an AND operation unit for performing AND operation on the M1*M2-bit binary integer and a specific binary integer. Furthermore, when the M1 and the N may be 4 and 3, respectively, the specific binary value may be 1010 or 0101.

Abstract: The present invention relates to a divider for dividing a dividend by a divisor. The divider includes a subtractor for subtracting the divisor from the dividend to produce a result, storage space with a preliminary answer, and a processor for revising the dividend and preliminary answer based on the result. Each interation the divider is adapted to reiterate the subtraction and revision multiple times, based on a revised dividend and revised preliminary answer.

Abstract: A device for determining an inverse of an initial value related to a modulus, comprising a unit configured to process an iterative algorithm in a plurality of iterations, wherein an iteration includes two modular reductions and has, as an iteration loop result, values obtained by an iteration loop of an extended Euclidean algorithm.

Abstract: Non-restoring radix-2 division and square rooting procedures are provided. The proposed procedures utilize a quotient/root digit set {?1, 0, +1} and a quotient/root prediction table (QRT/RPT). The i'th quotient/root digit is determined with reference to a partial remainder from (i?2)'th iterative operation and by the quotient/root prediction table. The present procedures generate the (i?1)'th correction term, which is to be applied in calculating the i'th partial remainder, simultaneously with the (i?2)'th correction term, and need not to perform an iterative operation to obtain the i'th partial remainder.

Abstract: A computational method for implementation in an electronic digital processing system performs integer division upon very large (multi-word) operands. An approximated reciprocal of the divisor is obtained by extracting the two most significant words of the divisor, adding one to the extracted value and dividing from a power of two out to two significant words. Multiplying this reciprocal value by a remainder (initialized as the dividend) obtains a quotient value, which is then decremented by a random value. The randomized quotient is multiplied by the actual divisor, and decremented from the remainder. The quotient value is accumulated to obtain updated quotient values. This process is repeated over a fixed number of rounds related to the relative sizes in words of the dividend and divisor. Each round corrects approximation and randomization errors from a preceding round.

Abstract: A device for calculating a result or an integer multiple of the result of a division of a numerator by a denominator includes a unit for providing a factor which is selected such that a product of the factor and the denominator is greater than the result. The device further includes a unit for modularly reducing a first product of the numerator and the factor using a modulus equaling a sum of a second product of the denominator and the factor and of an integer to obtain an auxiliary quantity having the result. A unit is used to extract the result or the integer multiple of the result from the auxiliary quantity. A division is thus reduced to a modular reduction and an extraction which is uncomplicated as far as calculation is concerned so that, in particular in long-number division tasks, the speed on the one hand and the safety on the other hand are increased.

Abstract: A method of dividing, in a micro computer unit (MCU), a first binary number (N), having a first number of significant bits, by a second binary number (D), having a second number of significant bits, produces an integer result (Y). The method includes: determining the difference (K) between the first and second numbers of significant bits; aligning the most significant bits (MSBs) of N and D by shifting the bits of D, by K bit positions, such that its MSB occupies the same relative bit position as the MSB of N; repeating K times: multiplying Y by 2; dividing D by 2; and, if N is greater than or equal to D: increasing Y by 1; setting N equal to N?D.

Abstract: A circuit which first shifts both a dividend and a divisor by an extra bit such that a 1-bit shift can be avoided after subtraction of the shifted values of dividend and the divisor, while performing a conditional subtraction instruction. The shifted divisor can conveniently replace the dividend as required for the instruction. The approach can be used to implement, among others, 2N-bit/N-bit (denoted 2N/N) division using an N-bit ALU, N/N division using N-bit ALU. The division can be implemented for all possible values of N without requiring substantially more complexity in the implementation.

Abstract: The specification discloses a structure of and a method of operating a subtractive division (SD) cell where a portion of the partial remainder or estimated partial remainder directly indicates the next quotient digit. More particularly, by sufficiently constraining the prescaled range for each possible divisor, only a few bits of the partial remainder (the exact number dependent upon the radix), along with their related carries (if any), directly indicate the value of the next quotient digit. Because fewer bits of the partial remainder are needed to make this determination than needed in related art devices, and further because no look-up table or hard-coded decision tree is required, calculation time within each SD cell is shorter than related art devices. Having a shorter calculation time within each SD cell allows for either completion of a greater number of SD cells within each clock cycle, or completion of the calculation to full precision in less time.

Abstract: Disclosed is a method and apparatus for synchronizing data. In one embodiment, the apparatus includes a first communication link for transmitting first data and a second communication link for transmitting second data. A circuit coupled to the first and second communication links. The circuit is configured to receive the first and second data. The circuit is configured to synchronously output the first and second data when the first and second data are received by the circuit out of synchronization.

Abstract: A calculation circuit for the division of a fixed-point input signal comprising a sequence of digital data values having a width of n bits by an adjustable division factor 2a for the purpose of generating a divided fixed-point output signal, having a signal input (2) for applying the data value sequence of the fixed-point input signal, a first addition circuit (6), which adds the digital data value present at the signal input (2) to a data value buffer-stored in a register (33) to form a digital first summation data value having a width of max (n, a+1)+1 bits, a shift circuit (11) which shifts the first summation data value present by a data bits toward the right, with the result that the max (n, a+1)?a+1 more significant data bits of the first summation data value are output at an output of the shift circuit (11), a logic circuit (16), which, as a function of the sign of the first summation data value, logically ANDs the a less significant data bits of the first summation data value with a logic combination

Abstract: An integer Z101 is divided by an integer I102 to obtain a remainder R109. The integer I102 includes a polynomial of power of a basic operational unit of a computer. In this way, the integer I for divisor is limited based on the basic operational unit of the computer, thus a shift operation, which is required for a conventional operation method, can be eliminated. The remainder can be calculated by only addition and subtraction. Accordingly, a code size becomes compact and the remainder of the integer can be calculated at a high speed.

Abstract: A high radix divider capable of reducing the size of the circuit of a quotient/remainder judgement unit in a radix 2k restoring division divider for finding a quotient k number of bits at a time, comparing multiples B, 2B, and 3B of a divisor B with a remainder R in parallel in two-input comparators and a three-input comparator and performing radix 4 division by finding a quotient 2 bits at a time. At this time, using a three-input comparator 313 in the comparison of 3B=(B+2B)≦R to realize comparison without the addition (B+2B), also, finding a new remainder Re in a three-input adder/subtractor for the simultaneous complex addition/subtraction R−(x+y) by a single ripple carry.

Abstract: The specification discloses a structure of and a method of operating a subtractive division (SD) cell where a portion of the partial remainder or estimated partial remainder directly indicates the next quotient digit. More particularly, by sufficiently constraining the prescaled range for each possible divisor, only a few bits of the partial remainder (the exact number dependent upon the radix), along with their related carries (if any), directly indicate the value of the next quotient digit. Because fewer bits of the partial remainder are needed to make this determination than needed in related art devices, and further because no look-up table or hard-coded decision tree is required, calculation time within each SD cell is shorter than related art devices. Having a shorter calculation time within each SD cell allows for either completion of a greater number of SD cells within each clock cycle, or completion of the calculation to full precision in less time.

Abstract: A data processing device comprises an instruction decoding unit for decoding a code of either a division instruction or a remainder instruction applied thereto, the instruction code having a size field for storing data size information. When a control unit receives a decoded result from the instruction decoding unit, the decoded result indicating the data size information stored in the size field of the instruction code, it presets a number of times that one loop iteration comprised of steps required for executing either the division instruction or the remainder instruction is to be carried out, based on the data size information. An ALU disposed within an arithmetic unit performs the loop iteration for either the division instruction or the remainder instruction only the number of times preset by the control unit.

Abstract: A digital processor and method for performing mathematical division in which performance degradation is mitigated by avoiding left shift and append (14) on the output of an ALU using pre-shift and append (18, 22) of the feedback from the quotient and remainder storage element (R, Q).

Abstract: A data processing system for designing a customized master slice data includes the steps of consecutively locating a cell base block based on the design data, a plurality of dummy gate blocks, and a possible number of intermediate blocks in the area of the semiconductor chip; replacing dummy gate blocks by gate array blocks while shifting the gate array blocks by half length; and locating intermediate blocks in an area generated by shifting the gate array blocks. The space between the gate array block and the cell base block is filled with the intermediate blocks for preventing interference therebetween.

Abstract: In division process of restoring type or non-restoring type, a partial remainder is compared with a divisor in terms of absolute value. If the partial remainder is larger or both are equal, a quotient of its column is regarded as 1 and if small, the quotient of that column is regarded as 0 upon this division.

Abstract: An integer Z101 is divided by an integer I102 to obtain a remainder R109. The integer I102 includes a polynomial of power of a basic operational unit of a computer. In this way, the integer I for divisor is limited based on the basic operational unit of the computer, thus a shift operation, which is required for a conventional operation method, can be eliminated. The remainder can be calculated by only addition and subtraction. Accordingly, a code size becomes compact and the remainder of the integer can be calculated at a high speed.

Abstract: The invention provides computer apparatus for performing a division operation having a dividend mathematically divided by a divisor. The dividend and the divisor are split between a state machine and an array of carry save adders. The most significant bits of the dividend and the divisor are input to the state machine and the least significant bits of the dividend and the divisor are input to the carry save adder array. The state machine is fully encoded with partial remainder values and quotient digit values for all possible combinations of the most significant bits of the divisor and the dividend. The carry save adders add the respective least significant bits of the dividend and the divisor and output spillover signals to the state machine. The state machine provides partial remainders and quotient digits selected from the encoded partial remainder values and quotient digit values dependent on (i.e. as a function of) the most significant bits of the dividend, divisor and the spillover signals.

Abstract: A method and apparatus for performing digital division in an integrated circuit is described. The inventive digital division is implemented by a combination of subtraction, logical OR, and shifting operations. The logical OR operation requires only approximately one gate per bit. The binary subtraction is only L bits wide at a Zth computation stage where Z equals L.

Abstract: A method and apparatus including conditional add and conditional add/subtract instructions are provided for use in the instruction set of a medical device instruction processor. More specifically, the conditional add and add/subtract instructions are provided to add two operands if a predetermined condition is satisfied within the instruction processor hardware. Additionally, the conditional add/subtract instruction may be used to subtract one operand from another operand if the predetermined condition is not satisfied. These instructions are adapted for use in implementing an efficient, interruptible, firmware-controlled multiplication or division mechanism. The inventive system allows multiplication or division operations to be interrupted at various intermediate points during the multiplication or division operation to thereby reducing interrupt latency.

Abstract: Division system and method support a hardware division address centrifuge to provide a flexible addressing scheme, and thus facilitates the reorganization and redistribution of data between remote and local memory blocks in a distributed memory massively parallel processing system. A flexible addressing scheme supports data organizations which can vary widely, depending on the processing task. Different data organizations in memory are supported by a PE internal address having certain bits designated as the target PE number and the remaining bits designating the offset within that PE's local memory. The PE and offset bits are distributed throughout the PE internal address to achieve various data distributions throughout memory. When a transfer occurs, the PE number bits and offset bits are separated via the centrifuge under control of a software-supplied mask.

Abstract: Burst-mode data transfers between a SCSI host bus adapter and at least one SCSI bus device interface adapter are implemented by hardware. For a first embodiment of the invention, the device interface adapter is equipped with a first, second and third data registers, a comparator, a subtractor, and control logic in the form of an application specific integrated circuit. When a burst-mode transfer is requested, the first register is programmed with a value corresponding to the length of the transfer in bytes, and the second register is programmed with the maximum possible number of bytes in a burst. The comparator then compares the value in stored in the first register with the value stored in the second register and determines which is the smaller. The smaller of the two values is written to the third register. The subtractor then subtracts said third value from said first value to obtain a remainder value. The first value is then replaced with a new first value equal to said remainder value.

Abstract: A circuit and method are provided for dividing a signed numerator by a signed denominator and generating a signal when the division results in overflow condition. The circuit generates a partial remainder using a partial remainder generation circuit, and a partial quotient using a partial quotient generation circuit. The partial remainder is initialized to a first value dependent upon the n most significant bits of the numerator, and the partial quotient is initialized to a first value dependent upon the n least significant bits of the numerator. Second values of the partial remainder and the partial quotient are generated dependent upon the first values of the partial remainder and the partial quotient. An overflow signal is generated if the second value of the partial quotient is equal to zero. The quotient and the remainder are generated dependent upon the second values of the partial remainder and the partial quotient, and the overflow signal is generated dependent upon the quotient.

Abstract: An apparatus and method for performing integer division in a microprocessor are provided. The apparatus includes translation logic, floating point execution logic, and integer execution logic. The translation logic decodes an integer divide instruction into an integer divide micro instruction sequence and an overflow detection micro instruction sequence. The integer divide micro instruction sequence is routed to and executed by the floating point execution logic. The overflow detection micro instruction sequence is routed to and executed by the integer execution logic. The integer execution logic and the floating point execution logic execute the overflow detection micro instruction sequence and the integer divide micro instruction sequence concurrently.

Abstract: In division process of restoring type or non-restoring type, a partial remainder is compared with a divisor in terms of absolute value. If the partial remainder is larger or both are equal, a quotient of its column is regarded as 1 and if smaller, the quotient of that column is regarded as 0 upon this division.