Abstract: One embodiment of the present invention provides a system that performs a carry-save square root operation that calculates an approximation of a square root, Q, of a radicand, R. The system calculates Q by iteratively selecting an operation to perform based on higher-order bits of a remainder, r, and then performs the operation. This operation can include subtracting two times a square root calculated thus far, q, and a coefficient, c, from r, and adding c to q. During this operation, the system maintains r in carry-save form, which eliminates the need for carry propagation while updating r, thereby speeding up the square root operation. Furthermore, the selection logic, which decides what operation to perform next, is simpler than previous square-root implementations, thereby providing a further speedup.

Abstract: A square root extraction circuit and a floating-point square root extraction device which simplify a circuit structure and improve an operation speed are provided. Portions for generating square root partial data (q3 to q8) include carry output prediction circuits (3 to 8), respectively. The carry output prediction circuit (i) (i equals any one of 3 to 8) receives condition flags (AHin, ALin), the most significant addition result (SUM), and square root partial data (q(i−1)) from the preceding square root partial data generating portion, and also receives a carry input (Cin) to output condition flags (AHout, ALout) for the next square root partial data generating portion, and square root partial data (q(i)). The condition flags (AHout, ALout) serve as the condition flags (AHin, ALin) for the carry output prediction circuit (i+1), respectively.

Abstract: Computer method and apparatus for performing a square root or division operation generating a root or quotient. A partial remainder is stored in radix-2 or radix-4 signed digit format. A decoder is provided for computing a root or quotient digit, and a correction term dependent on a number of the most significant digits of the partial remainder. An adder is provided for computing the sum of the signed digit partial remainder and the correction term in binary format, and providing the result in signed digit format. The adder computes a carry out independent of a carry in bit and a sum dependent on a Carry_in bit providing a fast adder independent of carry propagate delays. The scaler performs a multiplication by two of the result output from the adder in signed digit format to provide a signed digit next partial remainder.

Abstract: A floating point inverse square root circuit is disclosed. The circuit is configured to receive a floating point value comprised of a sign bit, an exponent field, and a mantissa field. The inverse square root circuit includes a lookup table configured to receive at least a portion of the floating point value and further configured to generate an initial approximation (x0) of the inverse square root of the floating point value from the received portion of the floating point value. The inverse square root circuit further includes a first estimation circuit that receives the initial approximation from the lookup table and at least a portion of a value L derived from the floating point value mantissa field (M) and further configured to produce a first approximation (x1) of the floating point value's inverse square root based upon L and x0 where x1 is a more accurate estimate of the inverse square root than x0.

Abstract: The invention provides improved methods and systems for generation of square roots of vector and administrative operands. The methods utilize bit-manipulation operations to halve intermediate values, generated by a processor reciprocal square root operation, during a multistep process square root determination. Such methods can also multiply an original operand (whose square root is being determined) with such an intermediate value, e.g., or a halved or other value thereon. The invention also provides methods and apparatus for determination of square roots square roots of large groups of numbers by interleaving vector and administrative instructions to take advantage of necessary delays in the vector processing pipeline architecture to speed overall processing.

Abstract: A method optimizes function evaluations performed by of a VLIW processor through enhanced parallelism by evaluating the function by table approximation using decomposition into a Taylor series.

Abstract: A system for providing a floating point square root comprises an analyzer circuit configured to determine a first status of a first floating point operand based upon data within the first floating point operand. In addition, the system comprises a results circuit coupled to the analyzer circuit. The results circuit is configured to assert a resulting floating point operand containing the square root of the first floating point operand and a resulting status embedded within the resulting floating point operand.

Abstract: An optimized, superscalar microprocessor architecture for supporting graphics operations in addition to the standard microprocessor integer and floating point operations. A number of specialized graphics instructions and accompanying hardware for executing them are disclosed to optimize the execution of graphics instruction with minimal additional hardware for a general purpose CPU.

Abstract: A method of computing a square root or a reciprocal square root of a number in a computing device uses a piece-wise quadratic approximation of the number. The square root computation uses the piece-wise quadratic approximation in the form: squareroot(X)={overscore (A)}ix2+{overscore (B)}ix+{overscore (C)}i, in each interval i. The reciprocal square root computation uses the piece-wise quadratic approximation in the form: 1/squareroot(X)=Aix2+Bix+Ci, in each interval i. The coefficients {overscore (A)}i, {overscore (B)}i, and {overscore (C)}i, and Ai, Bi, and Ci are derived for the square root operation and for the reciprocal square root operation to reduce the least mean square error using a least squares approximation of a plurality of equally-spaced points within an interval. In one embodiment, 256 equally-spaced intervals are defined to represent the 23 bits of the mantissa.

Abstract: A parallel fixed-point square root and reciprocal square root computation uses the same coefficient tables as the floating point square root and reciprocal square root computation by converting the fixed-point numbers into a floating-point structure with a leading implicit 1. The value of a number X is stored as two fixed-point numbers. In one embodiment, the fixed-point numbers are converted to the special floating-point structure using a leading zero detector and a shifter. Following the square root computation or the reciprocal square root computation, the floating point result is shifted back into the two-entry fixed-point format. The shift count is determined by the number of leaded zeros detected during the conversion from fixed-point to floating-point format.

Abstract: An apparatus and method for calculating a square root of an operand in a microprocessor are provided. The microprocessor has a plurality of square root instructions, each of which specifies a square root calculation precision. The apparatus includes translation logic and execution logic. The translation logic decodes the square root macro instruction into a plurality of prescribed-precision machine instructions according to the square root calculation precision specified by the plurality of square root instructions. The execution logic, coupled to the translation logic, receives the plurality of prescribed-precision machine instructions and calculates the square root of the operand according to the specified square root calculation precision. At least one of the plurality of square root instructions specifies the square root calculation precision such that less significant bits are calculated in the square root than are provided in the operand.

Abstract: A numerical processing method on a computer system in which an instruction having at least one operand and a type control is retrieved, and the operand is converted to a precision specified by the type control. The instruction is executed in the precision specified by the type control to obtain a result, and when the destination precision differs from the precision specified by the type control, the result is converted to the destination precision using a second instruction.

Abstract: A system and method of using a computer processor (34) to generate a solution to a linear system of equations is provided. The computer processor (34) executes a Jacobi iterative technique to produce outputs representing the solution. Multiplication operations required by the iterative technique are performed using logarithmic arithmetic. With logarithmic arithmetic, a multiplication operation is accomplished using addition. For a given n.times.n matrix A, the computer processor (34) can compute an inverse matrix A.sup.-1 by repeatedly executing the iterative technique to solve n linear systems.

Abstract: A data processing apparatus (71) includes a data processor bus (103), the rotation register (208) and a register selection circuit. The rotation register (208) is embodied by a plurality of data registers (200) each having a plurality of equal bit groups. The number of bits within each bit group of each data register preferably equals the number N of data registers. The register selection circuit permits normal register reads and writes via the data processor bus. The register selection circuit permits special rotational data accesses. In a rotation read mode the register selection circuit selects noncontiguous bits from a predetermined position within each sections for each of the data registers for read access. In a rotation write mode the register selection circuit selects noncontiguous bits from a predetermined position within each sections for each of the data registers for write access. The data registers (200) are connected together in a loop (208).

Abstract: This invention is a technique for summing plural sections of a single data word. The technique uses a repeated process forming larger and larger partial sums. Initially the single data word is rotated one section. The original single data word and the rotated single data word are masked with a mask having "1's" and "0's" in alternate sections. The mask blocks alternate sections so that adjacent sections of the original data word may be summed on a whole data word basis without any overflow disrupting the partial products. The two masked data words are then summed. This sum results in half as many partial sums as before. Each of these larger partial sums now occupies two original sections of the data word. The process can be repeated for these large partial sums. In the preferred embodiment this technique is used with an arithmetic logic unit (230) capable of forming mixed arithmetic and Boolean combinations of three inputs having a barrel rotator (235) driving one input.

Abstract: Described is a floating point processor comprising a multiply section and an add section, for performing a multiplication-add operation comprised of a multiplication operation prior to an addition operation which is using the result of the multiplication operation. The floating point processor comprises a multiply add controller (MAC1) which receives signals representing the exponents of the operands for the multiplication-add operation and signals representing the leading zero digits of an un-normalized result of the multiplication operation. The floating point processor further comprises a pair of shift units, (AL1, BN1), one receiving the un-normalized result of the multiplication operation and the other the operand to be added thereto. The multiply add controller (MAC1) determines shift values (Block.sub.-- Norm.sub.-- Value, AL1.sub.-- Align.sub.

Abstract: Quotient digit selection logic is modified so as to prevent a partial remainder equal to the negative divisor from occurring. An enhanced quotient digit selection function prevents the working partial remainder from becoming negative if the result is exact, choosing a quotient digit of zero instead of a quotient digit of one when the actual partial remainder is zero. Using a five bit estimated partial remainder where the upper four bits are zero, a possible carry propagation into fourth most significant bit is detected. This can be accomplished by looking at the fifth most significant sum and carry bits of the redundant partial remainder. If they are both zero, then a carry propagation out of that bit position into the least significant position of the estimated partial remainder is not possible, and a quotient digit of zero is chosen. This provides a one cycle savings since negative partial remainders no longer need to be restored before calculating the sticky bit.

Abstract: A floating-point arithmetic processing apparatus has a circuit for generating a limit value for normalization shift by subtracting an exponent of the minimum value of a normalized number from a value of an exponent of an intermediate result, and a circuit for generating, as a normalization shift number, smaller one of a shift number necessary for making the mantissa of the intermediate result a normalized number and the limit value for normalization shift. The floating-point arithmetic processing apparatus further has a circuit having a circuit for detecting a condition for overflow before the rounding process and a circuit for generating a value in the case of overflow, so that a predetermined value is delivered as a final result only when the overflow condition is detected before the rounding process but in the other case, a result obtained by performing the normalization process and the rounding process is delivered.