Abstract: Methods, apparatus, instructions and logic are disclosed providing double rounded combined floating-point multiply and add functionality as scalar or vector SIMD instructions or as fused micro-operations. Embodiments include detecting floating-point (FP) multiplication operations and subsequent FP operations specifying as source operands results of the FP multiplications. The FP multiplications and the subsequent FP operations are encoded as combined FP operations including rounding of the results of FP multiplication followed by the subsequent FP operations. The encoding of said combined FP operations may be stored and executed as part of an executable thread portion using fused-multiply-add hardware that includes overflow detection for the product of FP multipliers, first and second FP adders to add third operand addend mantissas and the products of the FP multipliers with different rounding inputs based on overflow, or no overflow, in the products of the FP multiplier.

Abstract: According to one general aspect, an apparatus may include a memory, a normalization engine, a lookup table, and an adder. The memory may be configured to store a floating-point number formatted in a floating-point format. The normalization engine may be configured to normalize at least a portion of the floating-point number to create a normalized number. The lookup table may be configured to generate an injection constant based upon a predefined set of rounding values specifically for converting a floating-point number to an integer number. The adder may be configured to create an integer result by adding the normalized number and the injection constant.

Abstract: A decimal floating point finite number in a decimal floating point format is composed from the number in a different format. A decimal floating point format includes fields to hold information relating to the sign, exponent and significand of the decimal floating point finite number. Other decimal floating point data, including infinities and NaNs (not a number), are also composed. Decimal floating point data are also decomposed from the decimal floating point format to a different format.

Abstract: A circuit for calculating the fused sum of an addend and product of two multiplication operands, the addend and multiplication operands being binary floating-point numbers represented in a standardized format as a mantissa and an exponent is provided. The multiplication operands are in a lower precision format than the addend, with q>2p, where p and q are the mantissa size of the multiplication operand and addend precision formats. The circuit includes a p-bit multiplier receiving the mantissas of the multiplication operands; a shift circuit aligning the mantissa of the addend with the product output by the multiplier based on the exponent values of the addend and multiplication operands; and an adder processing q-bit mantissas, receiving the aligned mantissa of the addend and the product, the input lines of the adder corresponding to the product being completed to the right by lines at 0 to form a q-bit mantissa.

Abstract: Machine instructions, referred to herein as a long Convert from Zoned instruction (CDZT) and extended Convert from Zoned instruction (CXZT), are provided that read EBCDIC or ASCII data from memory, convert it to the appropriate decimal floating point format, and write it to a target floating point register or floating point register pair. Further, machine instructions, referred to herein as a long Convert to Zoned instruction (CZDT) and extended Convert to Zoned instruction (CZXT), are provided that convert a decimal floating point (DFP) operand in a source floating point register or floating point register pair to EBCDIC or ASCII data and store it to a target memory location.

Abstract: Machine instructions, referred to herein as a long Convert from Zoned instruction (CDZT) and extended Convert from Zoned instruction (CXZT), are provided that read EBCDIC or ASCII data from memory, convert it to the appropriate decimal floating point format, and write it to a target floating point register or floating point register pair. Further, machine instructions, referred to herein as a long Convert to Zoned instruction (CZDT) and extended Convert to Zoned instruction (CZXT), are provided that convert a decimal floating point (DFP) operand in a source floating point register or floating point register pair to EBCDIC or ASCII data and store it to a target memory location.

Abstract: Machine instructions, referred to herein as a long Convert from Zoned instruction (CDZT) and extended Convert from Zoned instruction (CXZT), are provided that read EBCDIC or ASCII data from memory, convert it to the appropriate decimal floating point format, and write it to a target floating point register or floating point register pair. Further, machine instructions, referred to herein as a long Convert to Zoned instruction (CZDT) and extended Convert to Zoned instruction (CZXT), are provided that convert a decimal floating point (DFP) operand in a source floating point register or floating point register pair to EBCDIC or ASCII data and store it to a target memory location.

Abstract: Machine instructions, referred to herein as a long Convert from Zoned instruction (CDZT) and extended Convert from Zoned instruction (CXZT), are provided that read EBCDIC or ASCII data from memory, convert it to the appropriate decimal floating point format, and write it to a target floating point register or floating point register pair. Further, machine instructions, referred to herein as a long Convert to Zoned instruction (CZDT) and extended Convert to Zoned instruction (CZXT), are provided that convert a decimal floating point (DFP) operand in a source floating point register or floating point register pair to EBCDIC or ASCII data and store it to a target memory location.

Abstract: A system to improve numerical conversion may include a data processor and a controller configured to convert a floating-point number from the data processor to more than one different floating-point type number. The conversion may enable the selection of the more than one different floating-point type number that satisfies the requirements of an executing application and/or is closest to the original number.

Abstract: A decimal floating point finite number in a decimal floating point format is composed from the number in a different format. A decimal floating point format includes fields to hold information relating to the sign, exponent and significand of the decimal floating point finite number. Other decimal floating point data, including infinities and NaNs (not a number), are also composed. Decimal floating point data are also decomposed from the decimal floating point format to a different format. For composition and decomposition, one or more instructions may be employed, including a shift significand instruction.

Abstract: A system and method for detecting decimal floating point data processing exceptions. A processor accepts at least one decimal floating point operand and performs a decimal floating point operation on the at least one decimal floating point operand to produce a decimal floating point result. A determination is made as to whether the decimal floating point result fails to maintain a preferred quantum. The preferred quantum indicates a value represented by a least significant digit of a significand of the decimal floating point result. An output is provided, in response to the determining that the decimal floating point result fails to maintain the preferred quantum, indicating an occurrence of a quantum exception. A maskable exception can be generated that is immediately trapped or later detected to control conditional processing.

Abstract: A digital signal processor is provided having an instruction set with a logarithm function that uses a reduced look-up table.

Abstract: A data processing apparatus includes processing circuitry for performing a convert-to-integer operation for converting a floating-point value to a rounded two's complement integer value. The convert-to-integer operation uses round-to-nearest, ties away from zero, rounding (RNA rounding). The operation is performed by generating an intermediate value based on the floating-point value, adding a rounding value to the intermediate value to generate a sum value, and outputting the integer-valued bits of the sum value as the rounded two's complement integer value. If the floating-point value is negative, then the intermediate value is generated by inverting the bits without adding a bit value of 1 to a least significant bit of the inverted value.

Abstract: One aspect of the present invention will provide a circular floating-point number generator (400) for generating, from an input fixed-point number, a circular floating-point number including sign-bit field (S), exponent field (E), and circular-mantissa field (M). The generator assigns the input bits in the fixed-point number to a plurality of slots, generates the sign-bit field (S), generate the exponent field (E) based on a bit position of a leading significant bit, and generate the mantissa field (M) by extracting a first bit group and a second bit group and by providing a start bit of the first bit group after a last bit of the second bit group.

Abstract: Method, apparatus, and program means for performing a conversion. In one embodiment, a disclosed apparatus includes a destination storage location corresponding to a first architectural register. A functional unit operates responsive to a control signal, to convert a first packed first format value selected from a set of packed first format values into a plurality of second format values. Each of the first format values has a plurality of sub elements having a first number of bits The second format values have a greater number of bits. The functional unit stores the plurality of second format values into an architectural register.

Abstract: Method, apparatus, and program means for performing a conversion. In one embodiment, a disclosed apparatus includes a destination storage location corresponding to a first architectural register. A functional unit operates responsive to a control signal, to convert a first packed first format value selected from a set of packed first format values into a plurality of second format values. Each of the first format values has a plurality of sub elements having a first number of bits The second format values have a greater number of bits. The functional unit stores the plurality of second format values into an architectural register.

Abstract: Method, apparatus, and program means for performing a conversion. In one embodiment, a disclosed apparatus includes a destination storage location corresponding to a first architectural register. A functional unit operates responsive to a control signal, to convert a first packed first format value selected from a set of packed first format values into a plurality of second format values. Each of the first format values has a plurality of sub elements having a first number of bits The second format values have a greater number of bits. The functional unit stores the plurality of second format values into an architectural register.

Abstract: Method, apparatus, and program means for performing a conversion. In one embodiment, a disclosed apparatus includes a destination storage location corresponding to a first architectural register. A functional unit operates responsive to a control signal, to convert a first packed first format value selected from a set of packed first format values into a plurality of second format values. Each of the first format values has a plurality of sub elements having a first number of bits The second format values have a greater number of bits. The functional unit stores the plurality of second format values into an architectural register.

Abstract: The standing wave simple math processor is a new system for doing simple math (addition). By utilizing standing waves and conventional connections, a charge of direct current is transferred from 2 adjacent standing waves to 1 final standing wave representing the output. In essence the two input waves function as operands in a math problem. The operator, in this sense, is an interconnection of DC current between the 3 standing waves, as well as a set of redistribution rules. The final solution is retrieved upon completion of the redistribution rules.

Abstract: Apparatus for processing data includes processing circuitry 16, 18, 20, 22, 24, 26 and decoder circuitry 14 for decoding program instructions. The program instructions decoded include a floating point pre-conversion instruction which performs round-to-nearest ties to even rounding upon the mantissa field of an input floating number to generate an output floating point number with the same mantissa length but with the mantissa rounded to a position corresponding to a shorter mantissa field. The output mantissa field includes a suffix of zero values concatenated the rounded value. The decoder for circuitry 14 is also responsive to an integer pre-conversion instruction to quantise and input integer value using round-to-nearest ties to even rounding to form an output integer operand with a number of significant bits matched to the mantissa size of a floating point number to which the integer is later to be converted using an integer-to-floating point conversion instruction.

Abstract: A method for determining a logarithmic functional unit comprises providing a segment number; using the segment number to determine a piecewise linear approximation on a plurality of corresponding intervals for approximating a function for converting a fraction; providing a bit precision; converting endpoints separating the plurality of intervals to corresponding binary endpoints separating an additional plurality of intervals in the bit precision; determining an adjusted piecewise linear approximation that has an approximation error less than a threshold and is on the additional plurality of intervals; encoding coefficients of the adjusted piecewise linear approximation; determining a less precise approximation from the adjusted piecewise linear approximation as a candidate linear approximation, wherein the less precise approximation uses an argument value having a least bit-width while still being able to have an approximation error less than the threshold; and implementing the less precise approximation to

Abstract: Methods and systems for residue number system based ALUs, processors, and other hardware provide the full range of arithmetic operations while taking advantage of the benefits of the residue numbers in certain operations.

Abstract: A method and system are disclosed for solving a convex integer quadratic programming problem using a binary optimizer, the method comprising use of a processor for receiving a convex integer quadratic programming problem; converting the convex integer quadratic programming problem into a plurality of constrained and unconstrained binary quadratic programming problems and providing the plurality of unconstrained binary quadratic programming problems to the binary optimizer to thereby solve the convex integer quadratic programming problem.

Abstract: A control device includes: a first conversion unit that converts floating point data generated by an operation of a floating point operation command into a numeric string in first format; and a second conversion unit that converts the numeric string in first format into a numeric string in second format. A character string data generation unit generates a character string data including the numeric strings in first format and in second format and outputs the character string data to an external device or an external storage medium.

Abstract: Disclosure for representing one or more numbers as a geometric counting mechanism that comprises an arrangement of geometric shapes and decoding the geometric counting mechanism into the represented number or numbers is provided. Decoding a geometric counting mechanism includes at least identifying a container geometry, determining a primary multiplier, a secondary multiplier, and an additive component value based on the geometric shapes identified in the geometric counting mechanism and their locations in the arrangement. The geometric counting mechanism can be decoded in a clockwise and/or counterclockwise manner, therefore one geometric counting mechanism can represent more than one number.

Abstract: Method, apparatus, and program means for performing a conversion. In one embodiment, a disclosed apparatus includes a destination storage location corresponding to a first architectural register. A functional unit operates responsive to a control signal, to convert a first packed first format value selected from a set of packed first format values into a plurality of second format values. Each of the first format values has a plurality of sub elements having a first number of bits. The second format values have a greater number of bits. The functional unit stores the plurality of second format values into an architectural register.

Abstract: Described herein are systems and methods for conversion of numeric values between different number base formats, for use with software applications. In accordance with an embodiment, an integral part of a passed floating-point numeric value in a source number base (e.g., binary) format is isolated and converted to an integer. A fractional part of the numeric value is also isolated and converted to an integer, while limiting the isolation and conversion of the fractional part to a required precision or number of digits, depending on the particular requirements of a software application. The fractional part can be rounded, including determining an exact roundoff as appropriate, and if necessary propagating the rounding to the integral part. Digits from the resulting integers representing the integral and fractional parts can then be collected and used to prepare a representation of the original numeric value in a target number base (e.g., decimal) format.

Abstract: A technique is provided for performing a mixed precision estimate. A processing circuit receives an input of a first precision having a wide precision value. The processing circuit computes an output in an output exponent range corresponding to a narrow precision value based on the input having the wide precision value.

Abstract: Determination of digital compensation to compensate for non-linearity of stochastic system configured to sample a phase difference, based on statistical analysis of calibration data generated by the stochastic system in response to a linear phase ramp. The stochastic system may include a set of stochastic sampler circuits to sample a phase difference at periodic events, and calibration data may include a digital value of set of stochastic samples for each of multiple events. The calibration data may include sequences of the digital values in which the digital values increment over a range of the stochastic system (i.e., between saturation states of the stochastic system). Statistical analysis may include histogram analysis to estimate the probability distribution of the calibration data. The stochastic system may be configured as part of a time-to-digital converter, which may be configured within a feedback loop of a digitally controllable phase lock loop.

Abstract: The disclosed embodiments facilitate converting binary values into the BCC format. One technique facilitates the direct conversion of binary numbers into BCC. A second variation first converts a binary number into an intermediate BCD value, and then converts that BCD value into a BCC value. Look-ahead comparators can further improve conversion performance by decreasing the latency of the conversion operation. By speeding up the conversion of binary values to decimal-format values, the disclosed techniques facilitate leveraging dedicated binary-format hardware for decimal-format operations, and thus improve the performance of decimal-format operations.

Abstract: Apparatus for processing data includes processing circuitry 16, 18, 20, 22, 24, 26 and decoder circuitry 14 for decoding program instructions. The program instructions decoded include a floating point pre-conversion instruction which performs round-to-nearest ties to even rounding upon the mantissa field of an input floating number to generate an output floating point number with the same mantissa length but with the mantissa rounded to a position corresponding to a shorter mantissa field. The output mantissa field includes a suffix of zero values concatenated the rounded value. The decoder for circuitry 14 is also responsive to an integer pre-conversion instruction to quantize and input integer value using round-to-nearest ties to even rounding to form an output integer operand with a number of significant bits matched to the mantissa size of a floating point number to which the integer is later to be converted using an integer-to-floating point conversion instruction.

Abstract: Techniques are disclosed relating to type conversion using a floating-point unit. In one embodiment, to convert a floating-point value to a normalized integer format, a floating-point unit is configured to perform an operation to generate a result having a significant portion and an exponent portion, where the operation includes multiplying the floating-point value by a constant. In one embodiment, the apparatus is further configured to add a value to the exponent portion of the result, and set a rounding mode to round to nearest. The constant may be a greatest value less than one that can be represented using the particular number of unsigned bits. The value added to the initial exponent may be equal to the number of unsigned bits of the normalized integer format. The apparatus may perform this conversion in response to a pack instruction.

Abstract: Polynomial circuitry for calculating a polynomial having terms including powers of an input variable, where the input variable has a mantissa and an exponent, and the circuitry has a number of bits of precision, includes multiplier circuitry that calculates a common power of the input variable factored out of terms of the polynomial having powers of the variable greater than 1. The polynomial circuitry further includes, for each respective remaining term of the polynomial that contributes to the number of bits of precision: (1) a coefficient memory loaded with a plurality of instances of a coefficient for the respective term, each instance being shifted by a different number of bits, (2) address circuitry for selecting one of the instances of the coefficient based on the exponent, and (3) circuitry for combining the selected instance of the coefficient with a corresponding power of the input variable to compute the respective term.

Abstract: An apparatus including a first circuit and a second circuit. The first circuit may be configured to receive a first 2N-bit complex number and a second 2N-bit complex number, each having a first format, and to reformat the first and the second 2N-bit complex numbers to a second format such that a lower portion of each real and imaginary part of each 2N-bit complex number is positive. The second circuit may be configured to multiply the first and the second 2N-bit complex numbers using at least one N-bit signed complex multiplier, where N is an integer.

Abstract: A digital processing system comprises an input configured for receiving data in block exponent integer format, wherein each block comprises a plurality of data values sharing a single exponent. The plurality of data values has a common data bit width, and the exponent has an exponent bit width. An arithmetic processor performs arithmetic operations on the input data to produce output data in block exponent integer format. The arithmetic processor comprises a format optimizer for reducing at least one of the data bit width and the exponent bit width prior to performing arithmetic operations. The bit width is reduced to improve system power efficiency while meeting a predetermined target system performance.

Abstract: A method for double precision approximation of a single precision operation is disclosed. The method may include steps (A) to (B). Step (A) may store an input value in a processor. The processor generally implements a plurality of first operations in hardware. Each first operation may receive a first variable as an argument. The first variable may be implemented in a fixed point format at a single precision. The input value may be implemented in the fixed point format at a double precision. Step (B) may generate an output value by emulating a selected one of the first operations using the input value as the argument. The emulation may utilize the selected first operation in hardware. The output value may be implemented in the fixed point format at the double precision. The emulation is generally performed by a plurality of instructions executed by the processor.

Abstract: A system, method and apparatus are disclosed, in which a processing unit is configured to perform secondary processing on graphics pipeline data outside the graphics pipeline, with the output from the secondary processing being integrated into the graphics pipeline so that it is made available to the graphics pipeline. A determination is made whether to use secondary processing, and in a case that secondary processing is to be used, a command stream, which can comprise one or more commands, is provided to the secondary processing unit, so that the unit can locate and operate on buffered graphics pipeline data. Secondary processing is managed and monitored so as to synchronize data access by the secondary processing unit with the graphics pipeline processing modules.

Abstract: A method of coordinating communications between a plurality of Unmanned Air Vehicles (UAVs) operating in connection with differing communication languages. A common language is provided which includes common language commands and common language data objects. Common language commands are communicated from a user to a plurality of UAVs through a UAV Interoperability Agent (UIA), which converts the common language commands to UAV-specific commands which can be understood by the specific UAV. Additionally, UAVs send data in a native platform format to the UIA, which converts the native platform data to common language format for collection and interpretation by the user.

Abstract: According to one embodiment, a NAF conversion apparatus which converts a binary representation of an integer into a w-NAF redundant binary representation includes an acceptance device, a storage device, a shift register, and an update device. The acceptance device accepts the binary representation of the integer for every bit from lower bits. The storage device stores a state value expressed by 1 bit. The shift register stores a state value expressed by (w?1) bits. The update device determines a state of the storage device and a state of the (w?1)-bit shift register at next time, and determines a w-bit parallel output at current time by referring to a 1-bit value accepted by the acceptance device, the state value in the storage device, and the state value in the (w?1)-bit shift register.

Abstract: An arithmetic operation circuit includes: an extractor circuit that extracts one or a plurality of bits consecutive from a most significant bit or from a least significant bit of a binary number; a sum register that stores an X-adic sum, where X is an integer more than two; and an update circuit that updates the stored X-adic sum with a value obtained by adding a first X-adic number to be cyclically multiplied by a certain coefficient to the X-adic sum in accordance with the extracted one or plurality of bits.

Abstract: One or more continuous mappings are defined at a digital media encoder to convert input digital media data in a first high dynamic range format to a second format with a smaller dynamic range than the first format. The encoder converts the input digital media data to the second format with the smaller dynamic range using the continuous mapping and one or more conversion parameters relating to the continuous mapping. The encoder encodes the converted digital media data in a bitstream along with the conversion parameter(s). The conversion parameter(s) enable a digital media decoder to convert the converted digital media data back to the first high dynamic range format from the second format with the smaller dynamic range. Techniques for converting different input formats with different dynamic ranges are described.

Abstract: In an embodiment, a method performs computer operations using a first fractional precision and a second fractional precision. A computer program has a source variable, a destination variable, and an operation. The source variable has a first dynamic fractional precision, the destination variable has a second dynamic fractional precision that differs from the first dynamic fractional precision, and the operation is related to the source variable and the destination variable. The source variable is aligned to a format of the destination variable, according to the first dynamic fractional precision and the second dynamic fractional precision. The operation is performed using the destination variable and the source variable. A value is assigned to the destination variable according to the operation. In this manner, a single codebase may be written that operates on various hardware that each have different bit precision capabilities, without requiring additional development and verification effort.

Abstract: An apparatus and method for converting data between a floating-point number and an integer is provided. The apparatus includes a data converter configured to determine a sign of input binary data and an output format to which to convert the input binary data and convert the input binary data into a one's complement number based on the sign and the output format of the input binary data, a bias value generator configured to determine whether the input binary data has been rounded up based on a rounding mode of the input binary data and generate a bias value accordingly; and an adder configured to convert the input binary data into a two's complement number by adding the one's complement number and the bias value.

Abstract: A decimal floating point finite number in a decimal floating point format is composed from the number in a different format. A decimal floating point format includes fields to hold information relating to the sign, exponent and significand of the decimal floating point finite number. Other decimal floating point data, including infinities and NaNs (not a number), are also composed. Decimal floating point data are also decomposed from the decimal floating point format to a different format.

Abstract: In one embodiment, a computer program product includes a computer readable storage medium having computer readable program code embodied therewith, the computer readable program code being configured to: map a template-level configuration-management data structure to a discovery-level configuration-management data structure by a first mapping using mapping information included in the template-level configuration-management data structure, map a customized-level configuration-management data structure to the discovery-level configuration-management data structure by a second mapping using mapping information included in the customized-level configuration-management data structure, and determine a third mapping between the template-level configuration-management data structure and the customized-level configuration-management data structure using the first mapping and the second mapping.

Abstract: Faster methods for topological categorization and field line calculations are developed by using decomposition regions together with the self-winding techniques first developed in a prior patent application. A point iteration technique provides direct calculation of low order digits of winding counts without use of complex intervals. Easy to calculate derivatives define decomposition interval boundaries which substitute for methods using the slower complex interval processing of the prior patent. Methods common to this and the prior patent are developed for visualizing conformal mappings of iterated functions.

Abstract: Embodiments of the invention include an apparatus for performing Galois multiplication using an enhanced Galois table. Galois multiplication may include converting a first and second multiplicand to exponential forms using a Galois table, adding the exponential forms of the first and second multiplicands, and converting the added exponential forms of the first and second multiplicands to a decimal equivalent binary form using the Galois table to decimal equivalent binary result of the Galois multiplication.

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: A data processing apparatus includes a computing unit that performs a matrix computation between data streams whose unit data is of a matrix format; a determining unit that for each matrix obtained by the matrix computation by the computing unit, determines based on the value of each element included in the matrix, an exponent value for expressing each element included in the matrix as a floating decimal point value; a converting unit that converts the value of each element into a significand value of the element, according to the exponent value determined by the determining unit; and an output unit that correlates and outputs the exponent value and each matrix after conversion in which the value of each element in the matrix has been converted by the converting unit.

Abstract: A perform floating-point operation instruction is executed specifying a Test (T) bit of general register 0, if the T bit is ‘1’ the execution sets a condition code value indicating whether a specified conversion function is installed, if the T bit is ‘0’ the execution stores a result of a specified floating-point conversion function in general register 0 and sets a condition code value.