Abstract: An embodiment of a system and method for performing a numerical operation on input data in a hybrid floating-point format includes representing input data as a sign bit, exponent bits, and mantissa bits. The exponent bits are represented as an unsigned integer including an exponent bias, and a signed numerical value of zero is represented as a first reserved combination of the mantissa bits and the exponent bits. Each of all other combinations of the mantissa bits and the exponent bits represents a real finite non-zero number. The mantissa bits are operated on with a “one” bit before a radix point for the all other combinations of the mantissa bits and the exponent bits.

Abstract: A computation processor outputs whether a carry-out is generated, by incrementing a result of computation by 1, during rounding of the result of the computation. The computation processor includes a computing unit that performs the computation; a shift amount calculating unit that calculates a shift amount of the result of the computation; a normalizing unit that performs normalization of the result of the computation, by using the shift amount; a predicting unit that, when the result of the computation is shifted by an amount equal to or more than a predetermined shift amount by using the shift amount, predicts whether each of bits in a predetermined region of a shift result is 1, in parallel with the normalization; and a detecting unit that detects a generation of the carry-out, by receiving a normalized result from the normalizing unit and a predicted result from the predicting unit.

Abstract: A round-for-reround mode (preferably in a BID encoded Decimal format) of a floating point instruction prepares a result for later rounding to a variable number of digits by detecting that the least significant digit may be a 0, and if so changing it to 1 when the trailing digits are not all 0. A subsequent reround instruction is then able to round the result to any number of digits at least 2 fewer than the number of digits of the result. An optional embodiment saves a tag indicating the fact that the low order digit of the result is 0 or 5 if the trailing bits are non-zero in a tag field rather than modify the result. Another optional embodiment also saves a half-way-and-above indicator when the trailing digits represent a decimal with a most significant digit having a value of 5. An optional subsequent reround instruction is able to round the result to any number of digits fewer or equal to the number of digits of the result using the saved tags.

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: A first floating-point operation unit receives first and second variables and performs a first operation generating a first output. A first rounding unit receives and rounds the first output to generate a second output if a control bit is in a first state. A second floating-point operation unit receives a third variable and either the first output or the second output and performs a second operation on the third variable and either the first output or the second output, to generate a third output. The second floating-point operation unit receives and operates on the first output if the control bit is in the first state, or the second output if the control bit is in the second state. A second rounding unit receives and rounds the third output.

Abstract: In one embodiment, the present invention includes a method for receiving a rounding instruction and an immediate value in a processor, determining if a rounding mode override indicator of the immediate value is active, and if so executing a rounding operation on a source operand in a floating point unit of the processor responsive to the rounding instruction and according to a rounding mode set forth in the immediate operand. Other embodiments are described and claimed.

Abstract: A round-far-reround mode (preferably in a BID encoded Decimal format) of a floating point instruction prepares a result for later rounding to a variable number of digits by detecting that the least significant digit may be a 0, and if so changing it to 1 when the trailing digits are not all 0. A subsequent reround instruction is then able to round the result to any number of digits at least 2 fewer than the number of digits of the result. An optional embodiment saves a tag indicating the fact that the low order digit of the result is 0 or 5 if the trailing bits are non-zero in a tag field rather than modify the result. Another optional embodiment also saves a half-way-and-above indicator when the trailing digits represent a decimal with a most significant digit having a value of 5. An optional subsequent rewound instruction is able to round the result to any number of digits fewer or equal, to the number of digits of the result using the saved tags.

Abstract: An apparatus and method for computing a rounded floating point number. A floating point unit (FPU) receives an instruction to round a floating point number to a nearest integral value and retrieves a binary source operand having an exponent of a fixed first number of bits and a mantissa of a fixed second number of bits. If the unbiased exponent value is greater than or equal to zero and less than the fixed second number, the FPU generates a mask having N consecutive ‘1’ bits beginning with the least significant bit and whose remaining bits have a value of ‘0’, where N is equal to the fixed second number minus the unbiased exponent value. The FPU computes a bitwise OR of the source operand with the mask, increments the result if the instruction is to round up, and computes a bitwise AND of the result with the inverse of the mask.

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: An arithmetic circuit for rounding pre-rounded data includes a first register to store first-format pre-rounded data that includes a mantissa of a fixed-precision floating-point number using a base-N numbering system, and includes an exponent for the mantissa, a second register to store rounding precision data indicative of precision for rounding the pre-rounded data, a leading zero counting unit to count consecutive zeros starting from a most significant bit of the mantissa stored in the first register, an exponent generating unit to generate a post-round exponent indicative of an exponent for a rounded significant by subtracting the number of zeros counted by the leading zero counting unit and the rounding precision data from a sum of one and the exponent stored in the first register, and an output register to store the post-round exponent and a rounding-add value that is to be added to a digit at which rounding is performed.

Abstract: A programmable integrated circuit device is programmed to normalize multiplication operations by examining the input or output values to determined the likelihood of overflow or underflow and then to adjust the input or output values accordingly. The examination of the inputs can include an examination of the number of adder stages feeding into the inputs, as well as a count of leading bits ahead of the first significant bit. Adjustment of an input can include shifting the mantissa by the leading bit count and adjusting the exponent accordingly, while adjustment of the output can include shifting the mantissa by the sum of the leading bit counts of the inputs and adjusting the exponent accordingly. Or the output can be examined to find its leading bit count and the output then can be adjusted by shifting the mantissa by the leading bit count and adjusting the exponent accordingly.

Abstract: An integrated multiplier circuit that operates on a variety of data formats including integer fixed point, signed or unsigned, real or complex, 8 bit, 16 bit or 32 bit as well as floating point data that may be single precision real, single precision complex or double precision. The circuit uses a single set of multiplier arrays to perform 16×16, 32×32 and 64×64 multiplies, 32×32 and 64×64 complex multiplies, 32×32 and 64×64 complex multiplies with one operand conjugated.

Abstract: A method for controlling rounding modes in a single instruction multiple data (SIMD) floating-point unit is disclosed. The SIMD floating-point unit includes a floating-point status-and-control register (FPSCR) having a first rounding mode bit field and a second rounding mode bit field. The SIMD floating-point unit also includes means for generating a first slice and a second slice. During a floating-point operation, the SIMD floating-point unit concurrently performs a first rounding operation on the first slice and a second rounding operation on the second slice according to a bit in the first rounding mode bit field and a bit in the second rounding mode bit field within the FPSCR, respectively.

Abstract: A computer processor including a single fused-unfused floating point multiply-add (FMA) module computes the result of the operation A*B+C for floating point numbers for fused multiply-add rounding operations and unfused multiply-add rounding operations. In one embodiment, a fused multiply-add rounding implementation is augmented with additional hardware which calculates an unfused multiply-add rounding result without adding additional pipeline stages. In one embodiment, a computation by the fused-unfused floating point multiply-add (FMA) module is initiated using a single opcode which determines whether a fused multiply-add rounding result or unfused multiply-add rounding result is generated.

Abstract: A method for performing a decimal floating-point division, including: receiving, by a decimal floating-point divider, a decimal floating-point dividend and a decimal floating-point divisor; obtaining, by the decimal floating-point divider, a preliminary quotient having a first precision level, where the preliminary quotient is calculated from the decimal floating-point dividend and the decimal-floating point divisor; receiving, by the decimal floating-point divider, a rounding mode; selecting a rounding action based on the preliminary quotient and the rounding mode; and obtaining a rounded quotient having a second precision level by rounding the preliminary quotient according to the rounding action, where the first precision level is at least one digit greater than the second precision level.

Abstract: A decimal floating-point Fused-Multiply-Add (FMA) unit that performs the operation of ±(A×B)±C on decimal floating-point operands. The decimal floating-point FMA unit executes the multiplication and addition operations compliant with the IEEE 754-2008 standard. Specifically, the decimal floating-point FMA includes a parallel multiplier and injects the addend after required alignment as an additional partial product in the reduction tree used in the parallel multiplier. The decimal floating-point FMA unit may be configured to perform addition-subtraction operations or multiplication operations as standalone operations.

Abstract: Methods and arrangements to correct for double rounding errors when rounding floating point numbers to nearest away are described. Embodiments include transformations, code, state machines or other logic to perform a floating point operation on one or more floating point numbers of precision P1 in base b, producing positive result res0 of precision greater than precision P1; rounding positive result res0 to precision P1 to the nearest away, producing positive result res1; and rounding the result res1 to precision P2 to the nearest away, where P2 is narrower than P1, producing result res2. The embodiments may also include correcting res2 for double rounding errors. The correcting may include determining that res1 is midway between two consecutive floating point numbers of precision P2, the larger being res2, determining that rounding res0 to produce res1 involved rounding up, and decrementing the significand of res2 to obtain the corrected result.

Abstract: Techniques are disclosed for calculating large precision common logarithms. A common logarithm may be calculated using addition and/or subtraction of known logarithm values. Embodiments of the invention permit calculation of common logarithms of real numbers stored within character arrays, where each element of the array corresponds to a digit in the real number.

Abstract: Methods and arrangements to correct for double rounding errors when rounding floating point numbers to nearest even are described. Embodiments include transformations, code, state machines or other logic to perform a floating point operation on one or more floating point numbers of precision P1 in base b, producing positive result res0 of precision greater than precision P1; rounding positive result res0 to precision P1 to the nearest even, producing positive result res1; and rounding the result res1 to precision P2 to the nearest even, where P2 is narrower than P1, producing result res2. The embodiments may also include correcting res2 for double rounding errors. The correcting may include determining that res1 is midway between two consecutive floating point numbers of precision P1, the larger (smaller) being res2, determining that rounding res0 to produce res1 involved rounding up (down), and decrementing (incrementing) the significand of res2 to obtain the corrected result res2?.

Abstract: Apparatus and methods are disclosed for a floating point adder having half-adder capability that does not have the overhead of determining half-adder conditions prior to starting the SED, LED, and EXP datapaths.

Abstract: A normalization factor for a current frame of a signal may be determined. The normalization factor may depend on an amplitude of the current frame of the signal. The normalization factor may also depend on values of states after one or more operations were performed on a previous frame of a normalized signal. The current frame of the signal may be normalized based on the normalization factor that is determined. The states' normalization factor may be adjusted based on the normalization factor that is determined.

Abstract: A system and method for efficient floating-point rounding in computer systems. A computer system may include at least one floating-point unit for floating-point arithmetic operations such as addition, subtraction, multiplication, division and square root. For the division operation, the constraints for the remainder may be relaxed in order to reduce the area for look-up tables. An extra internal precision bit may not be used. Only one quotient may be calculated, rather than two, further reducing needed hardware to perform the rounding. Comparison logic may be required that may add a couple of cycles to the rounding computation beyond the calculation of the remainder. However, the extra latency is much smaller than a second floating-point multiply accumulate latency.

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: A specialized processing block for a configurable integrated circuit device includes circuitry for performing multiplications and sums thereof, as well as circuitry for rounding the result. The rounding circuitry reuses an adder that is also available, in other configurations, for accumulation of the result. Rounding is performed by adding a constant to the result and then truncating at the bit position at which rounding is desired. The constant may be entered by a user, or may be derived based on a desired rounding method from mask data entered by the user to identify the rounding bit position.

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: A fused multiply add floating point unit 1 includes multiplying circuitry 4 and adding circuitry 8. The multiply circuitry 4 multiplies operands B and C having N-bit significands to generate an unrounded product B*C. The unrounded product B*C has an M-bit significand, where M>N. The adding circuitry 8 receives an operand A that is input at a later processing cycle than a processing cycle at which the multiplying circuitry 4 receives operands B and C. The adding circuitry 8 commences processing of the operand A after the unrounded product B*C is generated by the multiplying circuitry 4. The adding circuitry 8 adds the operand A to the unrounded product B*C and outputs a rounded result A+B*C.

Abstract: An apparatus and method for computing a rounded floating point number. A floating point unit (FPU) receives an instruction to round a floating point number to a nearest integral value and retrieves a binary source operand having an exponent of a fixed first number of bits and a mantissa of a fixed second number of bits. If the unbiased exponent value is greater than or equal to zero and less than the fixed second number, the FPU generates a mask having N consecutive ‘1’ bits beginning with the least significant bit and whose remaining bits have a value of ‘0’, where N is equal to the fixed second number minus the unbiased exponent value. The FPU computes a bitwise OR of the source operand with the mask, increments the result if the instruction is to round up, and computes a bitwise AND of the result with the inverse of the mask.

Abstract: A data processing apparatus is arranged to perform a fused multiply add operation. The apparatus 100 has multiplying circuitry 110 configured to multiply operands B and C to generate a product B*C having a high order portion 160 and a low order portion 170. The apparatus has adding circuitry 130 configured to: (i) add an operand A to one of the high order portion 160 and the low order portion 170 to generate an intermediate sum value; and (ii) add the intermediate sum value to a remaining one of the high order portion 160 and the low order portion 170 to generate a result A+B*C.

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

Abstract: Methods and apparatus, including computer systems and program products, for normalizing computer-represented collections of objects. A first minimum value can be normalized based on a second minimum value of a universal set object that corresponds to the first set object. The second minimum value is both a minimum value supported by a data type (e.g., 1-byte integer) and a minimum value defined to be in the universal set object (e.g., 0 for a universal set of all natural numbers). Similarly, a first maximum value can be normalized based on a second maximum value of the universal set object where the second maximum value is both a maximum value supported by a data type and in the universal set object. Intervals can be normalized, which can involve replacing half-open intervals with equivalent half-closed intervals. Also, a consecutively ordered, uninterrupted, sequence of values of a set object can be normalized.

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

Abstract: A system for performing floating point arithmetic operations including an input register adapted for receiving an operand. The system also includes a mechanism for performing a shift or masking operation in response to determining that the operand is in an un-normalized format. The system also includes instructions for performing single precision incrementing of the operand in response to determining that the operand is single precision, that the operand requires the incrementing based on the results of a previous operation and that the previous operation did not perform the incrementing. The operand was created in the previous operation. The system further includes instructions for performing double precision incrementing of the operand in response to determining that the operand is double precision, that the operand requires the incrementing based on the results of the previous operation and that the previous operation did not perform the incrementing.

Abstract: A floating-point processor with selectable subprecision includes a register configured to store a plurality of bits in a floating-point format, a controller, and a floating-point mathematical operator. The controller is configured to select a subprecision for a floating-point operation, in response to user input. The controller is configured to determine a subset of the bits, in accordance with the selected subprecision. The floating-point operator is configured to perform the floating-point operation using only the subset of the bits. Excess bits that are not used in the floating-point operation may be forced into a low-leakage state. The output value resulting from the floating-point operation is either truncated or rounded to the selected subprecision.

Abstract: A floating point unit, a central processing unit, and a method are provided for adjusting the exponent of a floating point number. During an addition or subtraction of two floating point numbers, the significand of the floating point result is rounded, and the exponent of the result may be adjusted due to normalization or renormalization. The exponent adjustment due to renormalization or the exponent adjustment due to normalization and renormalization is combined with the significand rounding operation.

Abstract: An arithmetic operation unit, which generates information representing whether or not an arithmetic operation result has been shifted when the arithmetic operation result is normalized, has an arithmetic logical unit outputting the arithmetic operation result, a normalizer having a plurality of shifter normalizing the arithmetic operation result, a shift amount calculator calculating a plurality of shift amounts for the plural shifter, and a predictor generating interim information that is a result of prediction of whether or not the arithmetic operation result is to be shifted when the arithmetic operation result is normalized, by using the plural shift amounts, and a generator generating the information by using the interim information. The cycle time required to generate a sticky bit is shortened to efficiently generate the sticky bit, and the hardware resources for generating the sticky bit is reduced.

Abstract: An apparatus, method and computer program product for processing a binary floating-point number having a sign bit and a mantissa having a fraction portion. It includes identifying the fraction portion of the binary floating-point number; and replacing each bit of the fraction portion with the sign bit, thereby producing a floor of the binary floating-point number.

Abstract: A method and apparatus for perfectly lossless and minimal-loss interconversion of digital color data between spectral color spaces (RGB) and perceptually based luma-chroma color spaces (Y?CBCR) is disclosed. In particular, the present invention provides a process for converting digital pixels from R?G?B? space to Y?CBCR space and back, or from Y?CBCR space to R?G?B? space and back, with zero error, or, in constant-precision implementations, with guaranteed minimal error. This invention permits digital video editing and image editing systems to repeatedly interconvert between color spaces without accumulating errors. In image codecs, this invention can improve the quality of lossy image compressors independently of their core algorithms, and enables lossless image compressors to operate in a different color space than the source data without thereby becoming lossy.

Abstract: A microprocessor having a Precision Control (PC) field, an instruction dispatcher, and a Floating Point unit (FPU). The FPU receives an FP Add instruction from the instruction dispatcher, and generates a sum from its addends. The FPU determines whether any conditions exist in the addends with respect to their contribution to a rounding determination and relative to the PC field. If none of the conditions exists, the FPU makes the rounding determination based on the smaller addend and the PC field, and selectively rounds the sum based on the rounding determination. If any conditions exist, the FPU saves the sum and rounding information derived from the addends, and signals the instruction dispatcher to re-dispatch the instruction. On re-dispatch, the FPU makes the rounding determination based on the saved rounding information and the PC field, and selectively rounds the sum based on the rounding determination.

Abstract: Methods and arrangements to correct for double rounding errors when rounding floating point numbers to nearest away are described. Embodiments include transformations, code, state machines or other logic to perform a floating point operation on one or more floating point numbers of precision P1 in base b, producing positive result res0 of precision greater than precision P1; rounding positive result res0 to precision P1 to the nearest away, producing positive result res1; and rounding the result res1 to precision P2 to the nearest away, where P2 is narrower than P1, producing result res2. The embodiments may also include correcting res2 for double rounding errors. The correcting may include determining that res1 is midway between two consecutive floating point numbers of precision P2, the larger being res2, determining that rounding res0 to produce res1 involved rounding up, and decrementing the significand of res2 to obtain the corrected result.

Abstract: Methods and arrangements to correct for double rounding errors when rounding floating point numbers to nearest even are described. Embodiments include transformations, code, state machines or other logic to perform a floating point operation on one or more floating point numbers of precision P1 in base b, producing positive result res0 of precision greater than precision P1; rounding positive result res0 to precision P1 to the nearest even, producing positive result res1; and rounding the result res1 to precision P2 to the nearest even, where P2 is narrower than P1, producing result res2. The embodiments may also include correcting res2 for double rounding errors. The correcting may include determining that res1 is midway between two consecutive floating point numbers of precision P1, the larger (smaller) being res2, determining that rounding res0 to produce res1 involved rounding up (down), and decrementing (incrementing) the significand of res2 to obtain the corrected result res2?.

Abstract: A system and method for efficient floating-point rounding in computer systems. A computer system may include at least one floating-point unit for floating-point arithmetic operations such as addition, subtraction, multiplication, division and square root. For the division operation, the constraints for the remainder may be relaxed in order to reduce the area for look-up tables. An extra internal precision bit may not be used. Only one quotient may be calculated, rather than two, further reducing needed hardware to perform the rounding. Comparison logic may be required that may add a couple of cycles to the rounding computation beyond the calculation of the remainder. However, the extra latency is much smaller than a second FMAC latency.

Abstract: A method and apparatus for adding and multiplying floating-point operands such that a fixed-size mantissa result is produced. In accordance with the present addition method, the mantissa of a first floating-point operand is shifted in accordance with relative operand exponent information. Next, the first operand mantissa is added to the second operand mantissa. The addition step includes replacing a least significant non-overlapped portion of the first operand mantissa with a randomly-generated carry-in bit. In accordance with the multiplication method, a partial product array is generated from a pair of floating-point operand mantissas. Next, prior to compressing the partial product array into a compressed mantissa result, a lower-order bit portion of the partial product array is replaced with a randomly generated carry-in value.

Abstract: The three-term input floating-point adder-subtractor includes a pre-processing circuit which divides three inputted terms into a mantissa having an exponent of maximum value, mantissa having an exponent of intermediate value and mantissa having an exponent of minimum magnitude and outputting a mantissa obtained by right-shifting the mantissa having the exponent of intermediate value and the mantissa having the minimum exponent with a width of 2n+3 bits and adjusting digits and the mantissa having the maximum exponent, a carry save adder (CSA) which reduces the mantissas from the pre-processing circuit from three terms to two terms, a carry look-ahead adder (CLA) which carries out addition on the mantissas of the two terms, a normalization circuit which makes a left shift so that the most significant bit becomes 1, a rounding circuit which uses an (n+3)th bit from the most significant bit as a new sticky bit, takes logical OR with the lower bits and performs rounding and an exponent operation unit which output

Abstract: a round-far-reround mode (preferably in a BID encoded Decimal format) of a floating point instruction prepares a result for later rounding to a variable number of digits by detecting that the least significant digit may be a 0, and if so changing it to 1 when the trailing digits are not all 0. A subsequent reround instruction is then able to round the result to any number of digits at least 2 fewer than the number of digits of the result. An optional embodiment saves a tag indicating the fact that the low order digit of the result is 0 or 5 if the trailing bits are non-zero in a tag field rather than modify the result. Another optional embodiment also saves a half-way-and-above indicator when the trailing digits represent a decimal with a most significant digit having a value of 5. An optional subsequent rewound instruction is able to round the result to any number of digits fewer or equal, to the number of digits of the result using the saved tags.

Abstract: Methods for determining the square root, reciprocal square root, or reciprocal of a number performed by a processor of a computer system. The methods produce high precision estimates without using iterative steps. In addition, the methods taught herein utilize compressed tables for the coefficient terms A, B, and C from the quadratic expression Ax2+Bx+C, thus minimizing hardware requirements.

Abstract: A rounding circuit is provided that includes an input for receiving a 2's complement number to be rounded. The 2's complement number has a format SXY, where S represents a sign bit, X represents one or more bits to round and keep, and Y represents one or more bits to be discarded. The rounding circuit also includes first logic for adding a rounding bias to the 2's complement number, and second logic for at least one of subtracting the sign bit S from the 2's complement number, or adding the inverted sign bit !S to the 2's complement number. Moreover, the rounding circuit includes third logic for truncating Y bits from a result produced by the first and second logic to produce a rounded 2's complement number having a format SX.

Abstract: A method and system is used to determine the correct rounding of a floating point function. The method involves performing the floating point function to a higher precision than required and examining the portion of extra precision in the result known as the discriminant. If a critical pattern is found in the discriminant, this indicates that standard rounding may give an incorrect result and further calculation is needed. The method can work for various rounding modes and types of floating point representations. The method can be implemented in a system as part of a processor instruction set or any combination of hardware, microcode, and software.

Abstract: Embodiments consistent with the principles of the present invention provide improved results, compared to IEEE Std. 754, for floating point operations used in interval arithmetic calculations. One embodiment consistent with the principles of the present invention provides a method of enhancing support of an interval computation when performing a floating point arithmetic operation, comprising the steps, performed by a processor, of receiving a first floating point operand, receiving a second floating point operand, executing the floating point arithmetic operation on the first floating point operand and the second floating point operand, determining whether a NaN substitution is necessary, producing a floating point result if the NaN substitution is determined to be unnecessary, and substituting an alternative value as the floating point result if the NaN substitution is determined to be necessary.

Abstract: A method and system perform a rounding step of a floating point computation on at least one floating point operand to preserve an inexact status. Inexact status information generated from the rounding step may be encoded within the result, instead of requiring a separate floating point status register for the inexact status information. In one embodiment, inexact status information is preserved by determining whether the at least one operand is inexact. Further, an intermediate result of the floating point computation is analyzed to determine whether it is inexact. Finally, the intermediate result is rounded based on whether the at least one operand is inexact and whether the intermediate result is inexact to preserve an inexact status of the at least one operand and the intermediate result.

Abstract: For use in a floating-point unit that supports floating-point formats having fractional parts of varying widths and employs a datapath wider than the fractional parts, a circuit and method for normalizing and rounding floating-point results and processor incorporating the circuit or the method. In one embodiment, the circuit includes: (1) left-shift circuitry for aligning a fractional part of the floating-point result with a most significant bit of the datapath and irrespective of a width of the fractional part to yield a shifted fractional part and (2) rounding circuitry, coupled to the shift circuitry, that rounds the shifted fractional part.