Abstract: An apparatus and method for performing dual concurrent multiplications of packed data elements.

Abstract: An arithmetic processing apparatus includes: a memory that stores, when a training of a given machine learning model is repeatedly performed in a plurality of iterations, an error of a decimal point position of each of a plurality of fixed-point number data obtained one in each of the plurality of iterations, the error being obtained based on statistical information related to a distribution of leftmost set bit positions for positive number and leftmost unset bit positions for negative number or a distribution of rightmost set bit positions of the plurality of fixed-point number data; and a processor coupled to the memory, the processor being configured to: determine, based on a tendency of the error in each of the plurality of iterations, an offset amount for correcting a decimal point position of fixed-point number data used in the training.

Abstract: Compressed domain processors configured to perform operations on data compressed in a format that preserves order. The Compressed domain processors may include operations such as addition, subtraction, multiplication, division, sorting, and searching. In some cases, compression engines for compressing the data into the desired formats are provided.

Abstract: Disclosed embodiments relate to instructions for dual-destination type conversion, accumulation, and atomic memory operations. In one example, a system includes a memory, a processor including: a fetch circuit to fetch the instruction from a code storage, the instruction including an opcode, a first destination identifier, and a source identifier to specify a source vector register, the source vector register including a plurality of single precision floating point data elements, a decode circuit to decode the fetched instruction, and an execution circuit to execute the decoded instruction to: convert the elements of the source vector register into double precision floating point values, store a first half of the double precision floating point values to a first location identified by the first destination identifier, and store a second half of the double precision floating point values to a second location.

Abstract: The application provides a vector quantization digital-to-analog conversion circuit, applied to an oversampling converter, characterized that the vector quantization digital-to-analog conversion circuit includes a vector quantization circuit, configured to generate a vector quantization signal, a data weighted averaging circuit, coupled to the vector quantization circuit, including a plurality of data weighted averaging sub-circuits, configured to receive the vector quantization signal to generate a plurality of data weighted averaging signals; and a digital-to-analog conversion circuit, coupled to the data weighted averaging circuit, including a plurality of digital-to-analog conversion sub-circuits, configured to receive the data weighted averaging signal to generate the analog signal.

Abstract: An apparatus to facilitate compute optimization is disclosed. The apparatus includes sorting logic to sort processing threads into thread groups based on bit depth of floating point thread operations.

Abstract: A processor includes circuitry to decode at least one instruction and an execution unit. The decoded instruction may compute a floating point result. The execution unit includes circuitry to execute the instruction to determine the floating point result, compute the amount of precision lost in a mantissa of the floating point result, compare the amount of precision lost to a numeric accumulation error precision threshold, determine whether a numeric accumulation error occurred based on the comparison, and write a value to a flag. The amount of precision lost corresponds to a plurality of bits lost in the mantissa of the floating point result. The value to be written to the flag may be based on the determination that the numeric accumulation error occurred. The flag may be for notification that the numeric accumulation error occurred.

Abstract: A hardware integer saturation detector that detects both whether packing a 32-bit integer value causes saturation and whether packing each of first and second 16-bit integer values causes saturation, where the first 16-bit integer value is the upper 16 bits of the 32-bit integer value and the second 16-bit integer value is the lower 16 bits of the 32-bit integer value. The detector includes hardware signal logic, configured to generate four signals with information about the integer values. The hardware integer detector also includes saturation logic, configured to gate the four signals to generate a saturation signal. Each bit of the saturation signal indicates whether packing the 32-bit integer value or whether packing one of the first and second 16-bit integer values will cause saturation respectively.

Abstract: A low-error reduced-width multiplier is provided by the present invention. The multiplier can dynamically compensate the truncation error. The compensation value is derived by the dependencies among the multiplier partial products, and thus, can be analyzed according to the multiplication type and the multiplier input statistics.

Abstract: The forcing of the result or output of a rounder portion of a floating point processor occurs only in a fraction non-increment data path within the rounder and not in the fraction increment data path within the rounder. The fraction forcing is active on a corner case such as a disabled overflow exception. A disabled overflow exception may be detected by inspecting the normalized exponent. If a disabled overflow exception is detected, the round mode is selected to execute only in the non-increment data path thereby preventing the fraction increment data path from being selected.

Abstract: A processor, an instruction set architecture, an instruction, a computer readable medium and a method for implementing optimal per-instruction encoding of rounding control to emulate directed rounding are disclosed. In one embodiment, an apparatus designed to perform directed rounding includes an instruction decoder configured to decode an instruction, which includes a rounding control information to calculate a result boundary. The apparatus also includes a directed rounding emulator configured to adjust the result boundary to form an adjusted result boundary as a function of the rounding control bit. The adjusted result boundary establishes an endpoint for an interval that includes a result. In one embodiment, the directed round emulator is further configured to emulate a round-to-negative infinity rounding mode and a round-to-positive infinity rounding mode based on at least the single rounding control bit.

Abstract: An electronic computing circuit for implementing a method for reducing the bit width of two operands from a bit length N to a reduced bit length M, thus, M<N. To enable a wider re-usage of existing designs or building blocks being all specialized to the usual bit length of a power of 2 (8, 16, 32, 64 etc.), the chip structure of which is already highly optimized in regard of speed and space savings, a circuit is implemented as an addend width reduction circuit to perform the steps of: receiving said two N-bit operands as an input, adding the (N?M+1) most significant bits of said two N-bit operands separately in an auxiliary adder logic, calculating at least the two most significant bits of reduced-bit-length output operands in a decision logic processing the add result of said auxiliary adder logic, such that a predetermined post-processing can be correctly performed with said output operands.

Abstract: A method and system to perform shifting and rounding operations within a microprocessor, such as, for example, a digital signal processor, during execution of a single instruction are described. An instruction to shift and round data within a source register unit of a register file structure is received within a processing unit. The instruction includes a shifting bit value indicating the bit amount for a right shift operation and is subsequently executed to shift data within the source register unit to the right by an encoded bit value, calculated by subtracting a single bit from the shifting bit value contained within the instruction. A predetermined bit extension is further inserted within the vacated bit positions adjacent to the shifted data. Subsequently, an addition operation is performed on the shifted data and a unitary integer value is added to the shifted data to obtain resulting data.

Abstract: The apparatus and method herein splits the function of a digital subscriber line (DSL) modem data pump between a digital signal processor (DSP 106) and a general purpose host central processing unit (CPU 102). The DSP (106) handles all front end data pump processing such as interface to an analog front end (108 and 110), FFT processing, FEQ processing, QAM decoding, and bit formatting. The host CPU (102) handles all back end data pump processing such as DMT tone deordering, data deinterleaving, error detection and correcting, bit descrambling, CRC processing, and the like. In order to enable the DSP (106) and the CPU (102) to communicate with each other effectively, buffers (132) under the control of specialized buffer management methodology (FIG. 4) are used.

Abstract: Methods and apparatus for reducing precision of an input signal, by comparing a portion of the input signal to a preselected threshold value, and determining a selectable bias responsive to the comparison. By combining a portion of the input signal with the selectable bias, a reduced precision signal, having minimized or eliminated rounding error, is generated. The selectable bias corresponds to a predetermined characteristic of one of bias, an error signal, the input datum, the reduced precision datum, and a combination thereof.

Abstract: Systems, methods, processors, media, and other embodiments associated with integer rounding a floating point number in one micro-operation (uop) are described. One system embodiment includes a memory to store an integer rounding floating point instruction and a processor to perform the integer rounding floating point instruction. The processor may include a floating point unit that includes circuits and/or logics that integer round the floating point number.

Abstract: A method in a signal processor for quantizing a digital signal is provided. A fixed-point approximation of a value X÷Q is generated, wherein X is a fixed-point value based on one or more samples in the digital signal, and wherein Q is a fixed-point quantization parameter. A correction is generated, and the approximation is modified with the correction.

Abstract: An arrangement is provided for using 2's complement arithmetic without the high switching activity of the prior art. In particular, the invention operates to exploit the sign-extension property of a 2's complement number. A reduced representation for 2's complement numbers is provided to avoid sign-extension and the switching of sign-extension bits. The maximum magnitude of a 2's complement number is detected and its reduced representation is dynamically generated to represent the signal. A constant error introduced by the reduced representation is also dynamically compensated.

Abstract: An error compensation bias circuit and method for a canonic signed digit (CSD) fixed-width multiplier that receives a W-bit input and produces a W-bit product. Truncated bits of the multiplier are divided into two groups (a major group and a minor group) depending upon their effects on quantization error. An error compensation bias is expressed in terms of the truncated bits in the major group. The effects of the remaining truncated bits in the minor group are taken into account by a probabilistic estimation. The error compensation bias circuit typically requires only a few logic gates to implement.

Abstract: A functional unit in a digital system is provided with a rounding Multiplication instruction, wherein a most significant product of first pair of elements is combined with a least significant product of a second pair of elements, the combined product is rounded, and the final result is stored in a destination. Rounding is performed by adding a rounding value to form an intermediate result, and then shifting the intermediate result right. A combined result is rounded to a fixed length shorter than the combined product.

Abstract: Methods and apparatus for reducing precision of an input signal, by comparing a portion of the input signal to a preselected threshold value, and determining a selectable bias responsive to the comparison. By combining a portion of the input signal with the selectable bias, a reduced precision signal, having minimized or eliminated rounding error, is generated. The selectable bias corresponds to a predetermined characteristic of one of bias, an error signal, the input datum, the reduced precision datum, and a combination thereof.

Abstract: Precision of multi-stage digital signal processing is increased by preserving least significant bits of one or more output samples of a particular processing stage, having finite word widths, while avoiding the loss of most significant bits. The technique is applicable to one or more stages of multi-stage digital signal processing, thereby increasing precision therein and the signal-to-noise ratio. A plurality of output samples are calculated using a plurality of input samples, and the dynamic range of one or more of the output samples is decreased if the output sample can be represented in a smaller dynamic range without losing a significant bit. The input samples of a particular stage, obtained from the output samples of a previous stage, may further be normalized so that the input samples are represented in the same dynamic range before being processed.

Abstract: This invention discloses a reduced-width, low-error multiplier that can be used in Digital Signal Processing (DSP). Specifically, this invention relates to a reduced-width, low-error multiplier capable of processing digital signals of communication systems such as a timing recovery circuit, a carrier recovery circuit, and a FIR filter, etc. This invention derives a binary compensation vector to compensate for the error caused by the reduction of area without any hardware overhead, and implements the compensation structure of an Array and a Booth multiplier to reduce hardware complexity.

Abstract: The present invention provides a system and method to efficiently round real numbers. The system includes a rounding apparatus to accept an input value that is a real number represented in floating-point format, and to perform a rounding operation on the input value to generate an output value that is an integer represented in floating-point format. The system also includes a memory to store a computer program that utilizes the rounding apparatus. The system further includes a central processing unit (CPU) to execute the computer program. The CPU is cooperatively connected to the rounding apparatus and the memory.

Abstract: Methods and apparatus for reducing precision of an input signal, by comparing a portion of the input signal to a preselected threshold value, and determining a selectable bias responsive to the comparison. By combining a portion of the input signal with the selectable bias, a reduced precision signal, having minimized or eliminated rounding error, is generated. The selectable bias corresponds to a predetermined characteristic of one of bias, an error signal, the input datum, the reduced precision datum, and a combination thereof.

Abstract: A circuit for reducing the number of bits in a K bit value from K to N bits. The circuit generally comprises a first summing circuit, a control circuit, an error feedback circuit, a second summing circuit, and a processor. The first summing circuit may add an error offset value and the N+m MSB's of the K bit value to produce a result data value. The control circuit may generate a dither offset value. The error feedback circuit may receive m LSBs of the result data value and generate an error value in dependence on the m LSBs. The second summing circuit may add the dither offset value and the error value to provide the error offset value. The processor may selectively control generation of the dither offset value and the error value.

Abstract: An object of the present invention is to provide a multiply-accumulate unit with a rounding function which is capable of effecting 16-bit multiply-accumulate operations taking into account the position of an addend in a register. The multiply-accumulate unit with the rounding function has a selection inputting and expanding means 42 for expanding an addend from 31st-16th bits of 40-bit register 1 into 40-bit data and transmitting the 40-bit data to MAC (multiply-accumulate) unit 41 if control signal Position from an external source is “1”, and expanding an addend from 15th-0th bits of 40-bit register 1 into 40-bit data and transmitting the 40-bit data to MAC unit 41 if control signal Position is “0”. MAC unit 41 performs a multiply-accumulate operation on the 40-bit data, 16-bit data multiplicand B, and multiplier C.

Abstract: A data calculating device preferably used to improve the calculation precision when fixed-point calculation is performed by block-floating-point system. Each piece of data of a data group is calculated, the minimum scale factor representative of the calculated data is detected as a group scale factor (GSF), and calculated data is subjected to scaling based on the detected GSFs. These processing are applied to each data group of a data block. The minimum GSF out of the detected GSFs is detected as a block scale factor (BSF). When calculation of the calculated data is performed again, the calculated data of the data group is subjected to scaling according to the GSFs and BSF before the calculation performed again.

Abstract: Systems and methods are provided for diffusing clipping error in a computing system. When a data set contains values which are to be restricted to a range, and the data set includes one or more values which are beyond the range, the invention provides methodology that is an improvement over clipping extraneous values to the range or squeezing the values to the range. Advantageously, systems and methods are provided for distributing or diffusing error to neighboring samples of the data set, thereby spreading localized error, and minimizing the effects associated with remapping the data set to the restrictive range.

Abstract: An operation method has processing for applying a same type of operation in parallel to N M-bit operands to obtain N M-bit operation results executed on a computer. Here, N is an integer equal to or greater than 2 and M is an integer equal to or greater than 1. The operation method includes: an operation step of applying the type of operation to an N*M-bit provisional operand that is formed by concatenating the N M-bit operands, to obtain one N*M-bit provisional operation result, and generating correction information based on an effect had, by applying the operation, on each M bits of the provisional operation result from a bit that neighbors the M bits; and a correction step of correcting the provisional operation result in M-bit units with use of the correction information, to obtain the N M-bit operation results.

Abstract: A method in a signal processor for quantizing a digital signal is provided. A fixed-point approximation of a value X÷Q is generated, wherein X is a fixed-point value based on one or more samples in the digital signal, and wherein Q is a fixed-point quantization parameter. A correction is generated, and the approximation is modified with the correction.

Abstract: An arithmetic unit, for example a multiply and accumulate (MAC) unit 42, for a processing engine includes a partial product reduction tree 480. The partial product reduction tree will generate carry results and provides a final output to a final adder 470 connected to the partial production reduction tree. Unbiased rounding logic 476 is provided. A carry propagation tree is responsive to the carry results for anticipating a zero on each of N least significant bits of the final adder. When zero is anticipated on each of N least significant bits of the final adder, the carry propagation tree is operable to generate an output signal 477 which is used by the unbiased rounding stage to force the (N+1)th least significant bit of the final adder to zero.

Abstract: A quantization circuit includes a set of prime number dividers that can be implemented as look-up tables and a shifter. A shifter implements divisions by prime number (two) and by powers of two. Multiplexing circuitry interconnects the prime number dividers to permit performance of a series of prime number divisions in a single clock cycle. The quantization circuit can thus implement one-cycle divisions by divisors that are products of the prime numbers and powers of two in the series that the multiplexing circuitry selects. For divisors that are longer series of the prime numbers implemented in the quantization circuit, the quantization circuit can implement multi-cycle divisions by feeding an output signal back through further series of the prime number dividers.

Abstract: Precision of multi-stage digital signal processing is increased by preserving least significant bits of one or more output samples of a particular processing stage, having finite word widths, while avoiding the loss of most significant bits. The technique is applicable to one or more stages of multi-stage digital signal processing, thereby increasing precision therein and the signal-to-noise ratio. A plurality of output samples are calculated using a plurality of input samples, and the dynamic range of one or more of the output samples is decreased if the output sample can be represented in a smaller dynamic range without losing a significant bit. The input samples of a particular stage, obtained from the output samples of a previous stage, may further be normalized so that the input samples are represented in the same dynamic range before being processed.

Abstract: A system and method for overflow and saturation processing during accumulator operations that reduces the error in a saturation operation. Upon overflow, additional guard bits used in conjunction with an accumulator allow a user to continue processing without any error in the values used in computations following the overflow. A saturation condition can be detected following the overflow the appropriate maximum value stored in the accumulator upon detecting saturation.

Abstract: A quantization circuit includes a set of prime number dividers that can be implemented as look-up tables and a shifter. A shifter implements divisions by prime number (two) and by powers of two. Multiplexing circuitry interconnects the prime number dividers to permit performance of a series of prime number divisions in a single clock cycle. The quantization circuit can thus implement one-cycle divisions by divisors that are products of the prime numbers and powers of two in the series that the multiplexing circuitry selects. For divisors that are longer series of the prime numbers implemented in the quantization circuit, the quantization circuit can implement multi-cycle divisions by feeding an output signal back through further series of the prime number dividers.

Abstract: A vector processor provides a data path divided into smaller slices of data, with each slice processed in parallel with the other slices. Furthermore, an execution unit provides smaller arithmetic and functional units chained together to execute more complex microprocessor instructions requiring multiple cycles by sharing single-cycle operations, thereby reducing both costs and size of the microprocessor. One embodiment handles 288-bit data widths using 36-bit data path slices. Another embodiment executes integer multiply and multiply-and-accumulate and floating point add/subtract and multiply operations using single-cycle arithmetic logic units. Other embodiments support 8-bit, 9-bit, 16-bit, and 32-bit integer data types and 32-bit floating data types.

Abstract: A method and apparatus are used for determining a metric in a decoding algorithm, such as a Viterbi algorithm, using an n-bit processing module, on the basis of plural m-bit soft input words, wherein n≧2×m. The technique comprises: receiving plural m-bit soft input words; assembling at least two of the plural m-bit soft input words into a single n-bit composite soft input word; computing the respective distances between the at least two soft input words in the composite soft input word and expected codeword values to produce a composite distance word; summing the respective distances together to produce the metric; and extracting the metric. The n-bit processing module may comprise a 16-bit processing module employing 16-bit words, and the m-bit soft input words may each comprise a 4-bit word. Processing the plural soft input words en bloc increases the speed and information transfer rate of the decoder, and reduces the memory requirements of the decoder.

Abstract: A bit position, M, that determines the accuracy and efficiency of the approximation is selected from an N bit binary number. The multiplicand is generated by removing the Mth bit from the binary number, shifting the bits of lower order than the Mth bit up on position, then filling the lowest order bit with a zero. The multiplier is generated by removing the Mth bit, and all lower order bits from the binary number. Booth's algorithm is then used to multiply the multiplicand and the multiplier except that the Mth bit is used instead of an assumed zero during the first step of the multiplication. In hardware, a partial Booth-encoded multiplier is used to produce and approximate square of a binary number. For an N bit number, and a selected bit in the Mth position, the partial Booth-encoded multiplier has N columns, and N−M rows and N−M booth encoders.

Abstract: Methods and apparatus for reducing precision of an input signal, by comparing a portion of the input signal to a preselected threshold value, and determining a selectable bias responsive to the comparison. By combining a portion of the input signal with the selectable bias, a reduced precision signal, having minimized or eliminated rounding error, is generated. The selectable bias corresponds to a predetermined characteristic of one of bias, an error signal, the input datum, the reduced precision datum, and a combination thereof.

Abstract: There is disclosed a multiplier having a digit rounding function which operates by selecting an added value for rounding a digit in the process of adding partial products, thereby reducing a circuit magnitude and realizing a high-speed operation. A multiplier 13 is provided with selection circuits 18, 19 and 1A which can switch values of the partial products obtained in a secondary Booth algorithm in response to a signal for controlling the presence of the digit rounding function.

Abstract: A processor capable of efficiently performing iterative calculations is disclosed. The processor comprises a multiplier that is configured to perform iterative multiplication operations to evaluate constant powers of an operand such as the reciprocal and reciprocal square root. Intermediate products that are formed are compressed and decompressed to reduce interim storage requirements. The intermediate products may be rounded and normalized in two paths, one assuming an overflow will occur, and then compressed and stored for use in the next iteration.

Abstract: A data processing apparatus (200) which improves the accuracy of resultant data. The data processing apparatus includes an input (220, 222) configured to receive input data. The input data includes data corresponding to an input coefficient to be multiplied by the square root of two (.sqroot.2) and input addend. The data processing apparatus further includes a first memory (202) for storing a coefficient of the square root of two, a second memory (204) for storing an addend, a summer (206, 208) which independently sums the input coefficient and the coefficient to produce a combined coefficient and sums the input addend and the addend to produce an addend sum, a multiplier (210) which multiplies the combined coefficient and an approximation of the square root of two to produce an intermediate result, and a summer (214) which sums the intermediate result and the addend sum to produce the resultant data.

Abstract: A processor contains a storage area for a dynamic rounding mode control value, and a circuit coupled to the storage area configured to execute an instruction using a rounding mode. When the instruction is a first predetermined instruction, a first predetermined rounding mode is used during execution of the instruction. When the instruction is not the first predetermined instruction and the rounding mode specified by the instruction is not a dynamic override, the circuit executes the instruction using a rounding mode specified by the instruction. When the instruction is not the first predetermined instruction and the rounding mode specified by the instruction is the dynamic override, the circuit executes the instruction using a rounding mode specified by the dynamic rounding mode control value.