Abstract: Methods and apparatus to determine a remainder value are disclosed. A disclosed example method involves, during a compilation phase, causing a processor to multiply a dividend value by a first value to generate a second value associated with a product. The first value is associated with a scaled approximate reciprocal of a divisor value, and the scaled approximate reciprocal of the divisor value is determined using a compound exponent value. During a runtime phase, the processor is caused to multiply a third value from the second value. The third value is generated using at least a subset bitfield of the second value. During the runtime phase, the processor is caused to determine a remainder value based on the third value. The processor is caused to store the remainder value in a memory.

Abstract: Methods and apparatus to provide rounding of a binary integer are described. In one embodiment, a value that indicates whether a divisor divides a binary integer is extracted from a product of the binary integer and a scaled approximate reciprocal of the divisor.

Abstract: Methods, apparatus, and articles of manufacture for performing calculations using reduced-width data are disclosed. In particular, an example method determines reduced-width data values associated with generating and evaluating functions. Some of the reduced-width data values are stored within instructions in an instruction memory during a compile phase and retrieved from instruction memory during a runtime phase.

Abstract: The present invention discloses a method for prevention of distorted sub-picture display on a flat panel display. The display image of the flat panel display comprises a main picture and a sub-picture. While a drop line is performed on the main picture, image data output of the sub-picture is stopped. As the drop line is finished, image data output of the sub-picture is resumed. The method of stopping the output of image data of the sub-picture is adopted as a way to stop outputting a timing control signal used for controlling the image data output of the sub-picture, wherein the timing control signal is a horizontal synchronization signal or a clock signal. The timing control signal does not change logic state level while the drop line occurs. The image data of the sub-picture will not be discarded or masked while the drop line occurs. This prevents a distorted sub-picture on the flat panel display.

Abstract: An apparatus, method, and system for performing an enhanced fused multiply-add operation is disclosed. In one embodiment, an apparatus includes an exponent unit. The exponent unit includes a first adder to generate S1, where S1 is the sum of an integer k, the exponent of a floating point value A, and the exponent of a floating point value B. The exponent unit also includes a comparator to generate E1, where E1 is the greater of S1 and the exponent of a floating point value C. The apparatus also includes a partial multiplier, a shifter, and a second adder. The partial multiplier generates the partial products of the mantissas of A and B. The shifter aligns the partial products and the mantissa of C, based on E1. The second adder adds the aligned partial products and the mantissa of C. The apparatus is able to generate not only (A*B+C), but is enhanced to also be able to generate (2k*A*B+C) and the closest integer to (2k*A*B) in two's complement or floating point format.

Abstract: Methods, apparatus, and articles of manufacture for determining quotient values are disclosed. An example method identifies a reciprocal value of a divisor value. A bias value is then identified and a biased quotient value is determined based on a dividend value, the reciprocal value, and at least a portion of the bias value. A quotient value is then determined based on the biased quotient value.

Abstract: In one embodiment, the present invention includes a method for reducing an input argument x of a function to a range reduced value r according to a first reduction sequence, approximating a polynomial for a corresponding function of r having a dominant portion f(A)+?r, and obtaining a result for the function using the polynomial.

Abstract: Methods, apparatus, and articles of manufacture for performing mathematical operations using scaled integers are disclosed. In particular, an example method identifies a scaled-integer value and determines a multiplier value and a scale value based on the scaled-integer value. The multiplier value is determined by extracting information from a first portion of a bitfield based on the scaled-integer value. The scale value is determined by extracting information from a second portion of the bitfield based on the scaled-integer value. The first and second portions of the bitfield are configurable to include signed integer values. The example method then performs an arithmetic operation based on the multiplier value and the scale value.

Abstract: Methods, apparatus, and articles of manufacture for performing calculations using reduced-width data are disclosed. In particular, an example method determines reduced-width data values associated with generating and evaluating functions. Some of the reduced-width data values are stored within instructions in an instruction memory during a compile phase and retrieved from instruction memory during a runtime phase.

Abstract: Methods and apparatus for determining approximating polynomials using instruction-embedded coefficients are disclosed. In particular, the methods and apparatus use a plurality of coefficient values stored in a plurality of instructions. The coefficient values are associated with a runtime approximating polynomial of a K-th root family function. The coefficient values and the instructions stored in an instruction memory enable the processor system to determine a K-th root family function approximation value based on the runtime approximating polynomial.

Abstract: Methods and apparatus for determining a remainder value are disclosed. The methods and apparatus extracts a residuary subset bitfield value from a binary value that is calculated using a scaled approximate reciprocal value that is associated with a compound exponent scaling value. The residuary subset bitfield value is part of a range of contiguous bits that is associated with upper and lower boundary bit-position values that are part of the compound exponent scaling value. The methods and apparatus determine the remainder value based on the residuary subset bitfield value.

Abstract: A method of cleaning a probe card with probe pins contaminated by testing residue. A cleaning wafer is provided and the uneven surface and the grooves thereon are used to polish surfaces of the probe pins. Two kinds of cleaning operations, which utilize smaller and larger accelerations driving the cleaning wafer, are performed. The cleaning operations utilizing the smaller acceleration are used to polish the surfaces of the probe pins and the cleaning operations utilizing the larger acceleration are used to smooth the uneven surfaces of the probe pins after the former polishing operations. In addition, the cleaning wafer is rotated by various rotation angles to obtain superior cleaning.

Abstract: A method of cleaning a probe card with probe pins contaminated by testing residue. A cleaning wafer is provided and the uneven surface and the grooves thereon are used to polish surfaces of the probe pins. Two kinds of cleaning operations, which utilize smaller and larger accelerations driving the cleaning wafer, are performed. The cleaning operations utilizing the smaller acceleration are used to polish the surfaces of the probe pins and the cleaning operations utilizing the larger acceleration are used to smooth the uneven surfaces of the probe pins after the former polishing operations. In addition, the cleaning wafer is rotated by various rotation angles to obtain superior cleaning.

Abstract: A size reduction apparatus and process for reducing the size of a heterogeneous or homogeneous article or articles using variable and interchangeable interior parts for varying article output size and an air handling system for introducing air and/or fluid into the process of size-reduction. The components of a heterogeneous article are separated and used to aid in the size-reduction process.

Abstract: An improved hand held dental instrument adapted for cleaning teeth is provided which, in its preferred form, comprises an elongated shaft and an angularly projected head, the head being provided with a longitudinal groove in the head's upper planar surface and being tapered so as to form a thin, flat tip suitable for deformation in a direction and manner to easily reach teeth crevices without sacrificing longitudinal rigidity of the head. The opposite end of this integrally formed device's shaft is provided with a second tapered tip, which may be similarly grooved, and is adapted for cleaning of tooth surfaces.