Abstract: A processor or other device, such as a programmable and/or massively parallel processor or other device, includes processing elements designed to perform arithmetic operations (possibly but not necessarily including, for example, one or more of addition, multiplication, subtraction, and division) on numerical values of low precision but high dynamic range (“LPHDR arithmetic”). Such a processor or other device may, for example, be implemented on a single chip. Whether or not implemented on a single chip, the number of LPHDR arithmetic elements in the processor or other device in certain embodiments of the present invention significantly exceeds (e.g., by at least 20 more than three times) the number of arithmetic elements, if any, in the processor or other device which are designed to perform high dynamic range arithmetic of traditional precision (such as 32 bit or 64 bit floating point arithmetic).

Abstract: A method for open-loop or closed-loop control of the temperature of a chuck for a wafer includes detecting the position of a test device for testing a wafer and determining the spatial distances between the test device and a plurality of temperature measurement devices for measuring the temperature of the chuck or of a wafer supported or clamped by the chuck. The method proceeds by selecting at least one temperature measurement device from the plurality of temperature measurement devices as a reference temperature measurement device; and controlling the temperature of the chuck by open-loop or closed-loop control on the basis of the temperature(s) of the chuck or wafer as measured by the selected one or more reference temperature measurement devices.

Abstract: The present invention extends to methods, systems, and computing system program products for elimination of rounding error accumulation in iterative calculations for Big Data or streamed data. Embodiments of the invention include iteratively calculating a function for a primary computation window of a pre-defined size while incrementally calculating the function for one or more backup computation windows started at different time points and whenever one of the backup computation windows reaches a size of the pre-defined size, swapping the primary computation window and the backup computation window. The result(s) of the function is/are generated by either the iterative calculation performed for the primary computation window or the incremental calculation performed for a backup computation window which reaches the pre-defined size.

Abstract: Systems and methods for reducing data movement in a computer system. The systems and methods use information or knowledge about the structure of an algorithm, operations to be executed at a receiving processing unit, variables or subsets or groups of variables in a distributed algorithm, or other forms of contextual information, for reducing the number of bits transmitted from at least one transmitting processing unit to at least one receiving processing unit or storage device.

Abstract: Circuits and associated methods for processing two floating-point numbers (A, B) to generate a sum (A+B) of the two numbers and a difference (A-B) of the two numbers include calculating (806) a sum (|A|+|B|) of the absolute values of the two floating-point numbers, using a same-sign floating-point adder (1020), to produce a first result. The method further comprises calculating (808) a difference (|A|?|B|) of the absolute values to produce a second result. The sum (A+B) and the difference (A-B) are generated (810, 812) based on the first result (|A|+|B|), the second result (|A|?|B|), and the sign of each floating-point number.

Abstract: Full adder, a chip and a computing device are disclosed. A full adder includes: a plurality of primary logic cells and at least one secondary logic cell, wherein an output terminal of each primary logic cell is at least connected to an input terminal of a first secondary logic cell in the at least one secondary logic cell. The plurality of primary logic cells includes: a first primary logic cell, a second primary logic cell and a third primary logic cell respectively configured to generate a first intermediate signal, a second intermediate signal and a carry-related signal based on a first input signal, a second input signal and a carry input signal input to the full adder. Furthermore, the first secondary logic cell is configured to generate a sum output signal of the full adder based on the first intermediate signal, the second intermediate signal and the carry-related signal.

Abstract: An arithmetic circuit includes an input buffer latching each of a plurality of input signals, sequentially input, and sequentially outputting a plurality of first addition signals and a plurality of second addition signals based on the plurality of input signals; a first ripple carry adder (RCA) performing a first part of an accumulation operation on the first addition signals to generate a carry; a flip-flop; a second RCA performing a second part of the accumulation operation on the second addition signals and an output of the flop-flop; the first RCA latching the carry in the flip-flop after the accumulation operation is performed; and an output buffer latching an output signal of the first RCA and an output signal of the second RCA, and outputting a sum signal representing a sum of the plurality of input signals.

Abstract: Low precision computers can be efficient at finding possible answers to search problems. However, sometimes the task demands finding better answers than a single low precision search. A computer system augments low precision computing with a small amount of high precision computing, to improve search quality with little additional computing.

Abstract: Low precision computers can be efficient at finding possible answers to search problems. However, sometimes the task demands finding better answers than a single low precision search. A computer system augments low precision computing with a small amount of high precision computing, to improve search quality with little additional computing.

Abstract: Low precision computers can be efficient at finding possible answers to search problems. However, sometimes the task demands finding better answers than a single low precision search. A computer system augments low precision computing with a small amount of high precision computing, to improve search quality with little additional computing.

Abstract: Adder circuits and associated methods for processing a set of at least three floating-point numbers to be added together include identifying, from among the at least three numbers, at least two numbers that have the same sign—that is, at least two numbers that are both positive or both negative. The identified at least two numbers are added together (608) using one or more same-sign floating-point adders (120, 220a, 320, 420). A same-sign floating-point adder comprises circuitry configured to add together floating-point numbers having the same sign and does not include circuitry configured to add together numbers having different signs.

Abstract: The present invention extends to methods, systems, and computing system program products for elimination of rounding error accumulation in iterative calculations for Big Data or streamed data. Embodiments of the invention include iteratively calculating a function for a primary computation window of a pre-defined size while incrementally calculating the function for one or more backup computation windows started at different time points and whenever one of the backup computation windows reaches a size of the pre-define size, swapping the primary computation window and the backup computation window. The result(s) of the function is/are always generated by the iterative calculation performed for the primary computation window. Elimination of rounding error accumulation enables a computing system to steadily and smoothly run iterative calculations for unlimited number of iterations without rounding error accumulation.

Abstract: A floating-point adding circuitry is provided to add first and second floating-point operands each comprising a significand and an exponent. Alignment shift circuitry shifts a smaller-operand significand to align with a larger-operand significand, based on an exponent difference. Incrementing circuitry generates alternative versions of the larger-operand significand, each version based on a different rounding increment applied to the larger-operand significand. A number of candidate sum values are generated by adding circuits, each candidate sum value representing a sum of the shifted smaller-operand significand and a respective one of the alternative versions of the larger-operand significand. One of the candidate sum values is selected as a rounded result of adding the first and second floating-point operands. This allows floating-point addition to be performed faster as the latency of the rounding increment can be hidden in the shadow of the latency of the alignment shift.

Abstract: A multiplier circuit is described in which sub-products calculated in a first stage of a carry-save adder (CSA) network are output early, processed by applying a processing function, and re-injected into a subsequent stage of the CSA network to add the processed sub-products. This allows a CSA network provided for multiplication operations to be reused for operations which require sub-products to be processed and added, such as floating-point dot product operations performed on floating-point values represented in bfloatl6 format.

Abstract: A mechanism is described for facilitating efficient training of neural networks at computing devices. A method of embodiments, as described herein, includes detecting one or more inputs for training of a neural network, and introducing randomness in floating point (FP) numbers to prevent overtraining of the neural network, where introducing randomness includes replacing less-significant low-order bits of operand and result values with new low-order bits during the training of the neural network.

Abstract: Systems and methods for reducing data movement in a computer system. The systems and methods use information or knowledge about the structure of an algorithm, operations to be executed at a receiving processing unit, variables or subsets or groups of variables in a distributed algorithm, or other forms of contextual information, for reducing the number of bits transmitted from at least one transmitting processing unit to at least one receiving processing unit or storage device.

Abstract: An apparatus integrates arithmetic with logic operations. The apparatus includes a calculation device that calculates source data to generate and output first destination data. The apparatus further includes a normalization unit, coupled to the calculation device, that normalizes the first destination data to generate second destination data of a first type when receiving a signal indicating an output of first-type data, and normalizing the first destination data to generate the second destination data of a second type when receiving the signal indicating an output of second-type data.

Abstract: Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for a circuit configured to perform computations using multiple inputs. The circuit includes multiple adder circuits and a selection circuit that includes multiple input selector. Each adder circuit performs an addition operation using sets of inputs derived from the multiple inputs. The input selectors are configured to select one or more inputs from a set of inputs derived from the multiple inputs based on a sign bit for an input in the set and pass the selected inputs to an adder circuit that generates a sum using the selected inputs. The circuit determines a routing of the sum to another adder circuit based in part on a sign bit for the input in the set of inputs.

Abstract: Processing circuitry is provided for comparing a number of adjacent widths having a common value and extending from a starting position within an input number with a runlength specified by a variable number. The circuitry includes a mask generator for generating a mask value in dependence upon the variable number, combination circuitry for performing a logical combination operation upon respective bits within the input number starting from the starting position and corresponding bits within the mask value so as to generate an intermediate value. Result circuitry then generates a result indicative of whether or not the number of adjacent bits is less than or equal to the run length in dependence upon a determination if any bits within the intermediate value have a predetermined value.

Abstract: A method of exhaustively verifying a property of a hardware design to implement a floating point power function. The method includes, formally verifying that the hardware design is recurrent over sets of ? input exponents, wherein ? is an integer that is a multiple of the reciprocal of the exponent of the power function; and for each recurrent input range of the hardware design, exhaustively simulating the hardware design over a simulation range to verify the property is true over the simulation range, wherein the simulation range comprises only ? input exponents.

Abstract: Methods, systems, and computer readable media for non-parametric dependence detection using bitwise operations in a computing system are disclosed. One method for non-parametric dependence detection using bitwise operations in a computing system includes receiving a set of p variables, wherein p represents an integer greater than or equal to two. The method also includes generating a set of binary interaction designs (BIDs) using a depth value d and bitwise operations, wherein each of the set of BIDs indicates a dependence structure based on arrangement of partitions in the respective BID. The method further includes determining, using the BIDs generated using bitwise operations in a computing system, non-parametric dependence between the set of p variables. The method also includes performing data analysis involving the set of p variables using the non-parametric dependence between the set of p variables. The method further includes generating output related to the data analysis.

Abstract: An apparatus and method are provided for subtracting a first significand value of a first floating-point operand and a second significand value of a second floating-point operand. Significand shift control circuitry asserts a shift signal when a difference is detected between at least one corresponding low order bit in the exponent values of the two floating-point operands. First processing circuitry is arranged to produce a first difference value by performing a first subtraction operation to subtract the second significand value from the first significand value when the shift signal is unasserted, and to subtract a right-shifted version of the second significand value from the first significand value when the shift signal is asserted.

Abstract: A method of exhaustively verifying a property of a hardware design to implement a floating point power function. The method includes, formally verifying that the hardware design is recurrent over sets of ? input exponents, wherein ? is an integer that is a multiple of the reciprocal of the exponent of the power function; and for each recurrent input range of the hardware design, exhaustively simulating the hardware design over a simulation range to verify the property is true over the simulation range, wherein the simulation range comprises only ? input exponents.

Abstract: In an approach for protecting recoding logic in a computing environment, a processor obtains an operand of an instruction in a first data format. A processor converts the operand from the first data format to a second data format. A processor generates a predicted residue of the operand in the second data format, wherein generating the predicted residue of the operand in the second data format comprises: generating a residue of the operand from the first data format.

Abstract: The present embodiments relate to integrated circuits with circuitry that efficiently performs mixed-precision floating-point arithmetic operations. Such circuitry may be implemented in specialized processing blocks. The specialized processing blocks may include configurable interconnect circuitry to support a variety of different use modes. For example, the specialized processing blocks may implement fixed-point addition, floating-point addition, fixed-point multiplication, floating-point multiplication, sum of two multiplications in a first floating-point precision, with or without casting to a second floating-point precision and the latter followed by a subsequent addition in the second floating-point precision, if desired, just to name a few.

Abstract: An integrated circuit may include a floating-point adder that supports variable precisions. The floating-point adder may receive first and second inputs to be added, where the first and second inputs each have a mantissa and an exponent. The mantissa and exponent values may be split into a near path and a far path using a dual path floating-point adder architecture depending on the difference of the exponents and on whether an addition or subtraction is being performed. The mantissa values may be left justified, while the sticky bits are right justified. The hardware for the largest mantissa can be used to support the calculations for the smaller mantissas using no additional arithmetic structures, with only some multiplexing and decoding logic.

Abstract: An arithmetic operation is performed using a first instruction execution unit to generate an intermediate result vector and a plurality of calculation control indicators that indicate how subsequent calculations to generate a final result from the intermediate result vector should proceed. The intermediate result vector and the plurality of calculation control indicators are stored in memory external to the instruction execution unit, and later read by a second instruction execution unit to complete the arithmetic operation.

Abstract: A method for enhancing an accuracy of a sum of a plurality of floating-point numbers. The method receives a floating-point number and generates a plurality of provisional numbers with a value of zero. The method further generates a surjective map from the values of an exponent and a sign of a mantissa to the provisional numbers in the plurality of provisional numbers. The method further maps a value of the exponent and the sign of the mantissa to a first provisional number with the surjective map. The method further generates a test number from the first provisional number and if the test number exceeds a limit, modifies a second provisional number by using at least part of the test number. The method further equates the first provisional number to the test number if the test number does not exceed the limit. The method further sums the plurality of provisional numbers.

Abstract: A microprocessor comprises an instruction execution unit operable to generate an intermediate result vector and a plurality of calculation control indicators and storage external to the instruction execution unit which stores the intermediate result vector and the plurality of calculation control indicators. The intermediate result vector is generated from an application of at least a first arithmetic operation of a compound arithmetic operation. The calculation control indicators indicate how subsequent calculations to generate a final result from the intermediate result vector should proceed. The subsequent calculations may involve one or more remaining arithmetic operations of the compound arithmetic operation.

Abstract: A method for enhancing an accuracy of a sum of a plurality of floating-point numbers. The method receives a floating-point number and generates a plurality of provisional numbers with a value of zero. The method further generates a surjective map from the values of an exponent and a sign of a mantissa to the provisional numbers in the plurality of provisional numbers. The method further maps a value of the exponent and the sign of the mantissa to a first provisional number with the surjective map. The method further generates a test number from the first provisional number and if the test number exceeds a limit, modifies a second provisional number by using at least part of the test number. The method further equates the first provisional number to the test number if the test number does not exceed the limit. The method further sums the plurality of provisional numbers.

Abstract: An apparatus and method for generating a sum of floating-point input values are provided. To sum the values multiple partial sum floating-point values are maintained and the partial sum to which an input value may be added is selected by a least significant portion of the exponent of the input value. If the exponent of the input value is equal to the exponent of the value stored in the selected partial sum a mantissa sum of the input value and stored partial sum value replaces the mantissa value of the selected partial sum value. If the exponent of the input value is larger than the exponent of the value stored in the selected partial sum the selected partial sum value is replaced with the input value. An associative and deterministic summation is thus provided.

Abstract: Embodiments of a processor are disclosed for performing arithmetic operations on a machine independent number format. The processor may include a floating point unit, and a number unit. The number format may include a sign/exponent block, a length block, and multiple mantissa digits. The number unit may be configured to perform an operation on two operands by converting the digit format of each mantissa digit of each operand, to perform the operation using the converted mantissa digits, and then to convert each mantissa digit of the result of the operation back into the original digit format.

Abstract: Various techniques for processing and pre-decoding branches within an IT instruction block. Instructions are fetched and cached in an instruction cache, and pre-decode bits are generated to indicate the presence of an IT instruction and the likely boundaries of the IT instruction block. If an unconditional branch is detected within the likely boundaries of an IT instruction block, the unconditional branch is treated as if it were a conditional branch. The unconditional branch is sent to the branch direction predictor and the predictor generates a branch direction prediction for the unconditional branch.

Abstract: A specialized processing block on an integrated circuit is provided that performs pipelined floating-point accumulation operations. The specialized processing block may be configured to perform one accumulation operation and produce the result of the accumulation at every other clock cycle. Alternatively, the specialized processing block may be configured to perform two independent accumulation operations and produce the result of each of the accumulation operations alternating at consecutive clock cycles. The specialized processing block may include a dedicated three-input floating-point adder circuit. The specialized processing block may also fuse two independent two-input floating-point adder circuits to be configurable as two independent two-input floating-point adders or one three-input floating-point adder.

Abstract: A data processing apparatus and method of data processing are provided. The data processing apparatus comprises execution circuitry configured to execute a sequence of program instructions. Checkpoint circuitry is configured to identify an instance of a predetermined type of instruction in the sequence of program instructions and to store checkpoint information associated with that instance. The checkpoint information identifies a state of the data processing apparatus prior to execution of that instance of the predetermined type of instruction, wherein the predetermined type of instruction has an expected long completion latency.

Abstract: An accumulation apparatus, which adds a number of data values, has an adder and an asynchronous ripple counter. The adder adds each current data value to an adder sum of the preceding data values. The asynchronous ripple counter, which is coupled to the adder, generates a ripple count by counting occurrences of overflow of the adder. The accumulation apparatus outputs an accumulated data value having the adder sum as least significant part and the ripple count as most significant part.

Abstract: A hardware circuit component configured to support vector operations in a scalar data path. The hardware circuit component configured to operate in a vector mode configuration and in a scalar mode configuration. The hardware circuit component configured to split the scalar mode configuration into a left half and a right half of the vector mode configuration. The hardware circuit component configured to perform one or more bit shifts over one or more stages of interconnected multiplexers in the vector mode configuration. The hardware circuit component configured to include duplicated coarse shift multiplexers at bit positions that receive data from both the left half and the right half of the vector mode configuration, resulting in one or more coarse shift multiplexers sharing the bit position.

Abstract: A configurable specialized processing block includes a first floating-point arithmetic operator stage, a second floating-point arithmetic operator stage, and configurable interconnect within the configurable specialized processing block for routing signals into and out of each of the first and second floating-point arithmetic operator stages.

Abstract: A fused floating-point add-subtract unit includes far path logic, close path logic, and selection logic. The far path logic is configured to perform addition and subtraction operations on first and second significands of first and second operands, respectively, to produce a far path sum and a far path difference. The close path logic is configured to perform addition and subtraction operations on the first and second significands of the first and second operands, substantially concurrently with the addition and subtraction operations of the far path logic, to produce a close path sum and a close path difference. The selection logic selectively provides one of the far path sum and the close path sum as a significand of a sum output and one of the far path difference and the close path difference as a significand of a difference output.

Abstract: According to one general aspect, an apparatus may include a floating-point addition unit that includes a far path circuit, a close path circuit, and a final result selector circuit. The far path circuit may be configured to compute a far path result based upon either the addition or the subtraction of the two floating point numbers regardless of whether the operands or the result include normal or denormal numbers. The close path circuit may be configured to compute a close path result based upon the subtraction of the two floating point operands regardless of whether the operands or the result include normal or denormal numbers. The final result selector circuit may be configured to select between the far path result and the close path result based, at least in part, upon an amount of difference in the exponent portions of the two floating point operands.

Abstract: Floating point adder circuitry 16, 18, 20 is provided with far-path circuitry 18 and near-path circuitry 20. The far-path circuitry utilises a count of trailing zeros TZ and a difference in the input operand exponents to form respective suffix values which are concatenated with the mantissas of the input addends and serve when summed to generate a carry out taking the place of a conventionally calculated sticky bit. Within the near-path, minimum value circuitry 46 is used to calculate the lower of a leading zeros count of the intermediate mantissa produced in a subtraction and the larger of the input operand exponent values such that a left shift applied to the intermediate mantissa value is not able to produce a invalid floating point result due to applying a left shift to remove leading zeros that is too larger and accordingly corresponds to an exponent which cannot be validly represented.

Abstract: An integrated circuit is provided that performs floating-point addition or subtraction operations involving at least three floating-point numbers. The floating-point numbers are pre-processed by dynamically extending the number of mantissa bits, determining the floating-point number with the biggest exponent, and shifting the mantissa of the other floating-point numbers to the right. Each extended mantissa has at least twice the number of bits of the mantissa entering the floating-point operation. The exact bit extension is dependent on the number of floating-point numbers to be added. The mantissas of all floating-point numbers with an exponent smaller than the biggest exponent are shifted to the right. The number of right shift bits is dependent on the difference between the biggest exponent and the respective floating-point exponent.

Abstract: An apparatus and method are provided for performing an addition operation on operands A and B in order to produce a result R, the operands A and B and the result R being floating point values each having a significand and an exponent. The apparatus comprises prediction circuitry for generating a shift indication based on a prediction of the number of leading zeros that would be present in an output produced by subjecting the operands A and B to an unlike signed addition. Further, result pre-normalization circuitry performs a shift operation on the significands of both operand A and operand B prior to addition of the significands, this serving to discard a number of most significant bits of the significands of both operands as determined by the shift indication in order to produce modified significands for operands A and B.

Abstract: Systems and methods are provided for channel estimation using linear phase estimation. These systems and methods enable improved channel estimation by estimating a linear channel phase between received pilot subcarrier signals. The estimated linear phase can then be removed from the received pilot subcarrier signals. After the estimated linear phase is removed from the received pilot subcarrier signals, a channel response can be estimated. A final estimated channel response can be generated by multiplying the results of the linear channel estimation by the estimated linear phase.

Abstract: A logic circuit computes various modal interval arithmetic values using a plurality of arithmetic function units. A multiplexer gates the desired arithmetic values to a storage register.

Abstract: An arithmetic circuit for quantizing pre-quantized data includes a first input register to store first-format pre-quantized data that includes a mantissa and an exponent, a second input register to store a quantization target exponent, an exponent-correction-value indicating unit to indicate an exponent correction value, an exponent generating unit to generate a quantized exponent obtained by subtracting the exponent correction value from the quantization target exponent, a shift amount generating unit to generate a shift amount obtained by subtracting the exponent of the pre-quantized data and the exponent correction value from the quantization target exponent, a shift unit to generate a quantized mantissa obtained by shifting the mantissa of the pre-quantized data by the shift amount generated by the shift amount generating unit, and an output register to store quantized data that includes the quantized exponent generated by the exponent generating unit and the quantized mantissa generated by the shift unit

Abstract: A system and method are provided for dynamically reducing power consumption of floating-point logic. A disable control signal that is based on a characteristic of a floating-point format input operand is received and a portion of a logic circuit is disabled based on the disable control signal. The logic circuit processes the floating-point format input operand to generate an output.

Abstract: A method of subtracting floating-point numbers includes determining whether a first sign associated with a first floating-point number is unequal to a second sign associated with a second floating-point number, determining whether a first exponent associated with the first floating-point number is less than a second exponent associated with the second floating-point number, negating a first mantissa associated with the first floating-point number when the first sign is unequal to the second sign and determining that the first exponent is less than the second exponent, and adding the first mantissa to a second mantissa associated with the second floating-point number when the first sign is unequal to the second sign and determining that the first exponent is less than the second exponent. Embodiments of a corresponding computer-readable medium and device are also provided.

Abstract: A data processing system, method and computer program product to receive general-purpose code for iterative summation of an aggregate number of addends, wherein each addend has a precision. The data processing system operates an arithmetic hardware unit to set a first set of input registers to be a target of memory mapped registers and uses a broad-based adder to generate an adder result, wherein the broad-based adder has a broad-based adder size of inputs, and the broad-based adder size is less than the aggregate number of addends and greater than two, wherein each input register of the first set of input registers is connected to each input. Further, the data processing system may write the adder result to a storage array in memory, wherein the adder result is the sum of the inputs, and the adder result is placed in the storage array as indexed by a storage array index.

Abstract: An arithmetic circuit calculates a correction value for a value that is obtained by an add-subtract operation of two values and that is expressed in a predetermined fixed precision.