Abstract: Systems and methods for multi-precision computation are disclosed. One embodiment of the present invention includes a plurality of multiply-add units (MADDs) configured to perform one or more single precision operations and an arrangement generator to generate one or more mantissa arrangements using a plurality of double precision numbers. Each MADD is configured to receive and load said mantissa arrangements from the arrangement generator. The MADDs compute a result of a multi-precision computation using the mantissa arrangements. In an embodiment, the MADDs are configured to simultaneously perform operations that include, single precision operations, double-precision additions and double-precision multiply and additions.

Abstract: Systems and methods for multi-precision computation are disclosed. One embodiment of the present invention includes a plurality of multiply-add units (MADDs) configured to perform one or more single precision operations and an arrangement generator to generate one or more mantissa arrangements using a plurality of double precision numbers. Each MADD is configured to receive and load said mantissa arrangements from the arrangement generator. The MADDs compute a result of a multi-precision computation using the mantissa arrangements. In an embodiment, the MADDs are configured to simultaneously perform operations that include, single precision operations, double-precision additions and double-precision multiply and additions.

Abstract: Systems and methods for improved vector data processing based on separately processing elements of a vector in multiple simultaneously executing vector element processing units are disclosed. One embodiment of the present invention is a vector processing system including a plurality of vector element processing units and a routing infrastructure. The routing infrastructure is configured to route each element of a received vector to a respective one of the vector element processing units. The received vector may be from a memory which is coupled to the vector element processing units by the routing infrastructure. Each vector element processing unit is configured to simultaneously process two or more elements, wherein each of the two or more elements is from a separate vector. Embodiments of the present invention also provide for forwarding of data and results of computation between vector element processing units.

Abstract: A technique for approximating output values of a function based on LaGrange polynomials is provided. Factorization of a LaGrange polynomial results in a simplified representation of the LaGrange polynomial. With this simplified representation, an output value of a function may be determined based on an input value comprising a fixed point input mantissa and an input exponent. Based on a first portion of the fixed point input mantissa, a point value and at least one slope value are provided. At least one slope value is based on a LaGrange polynomial approximation of the function. Thereafter, the point value and the at least one slope value are combined with a second portion of the fixed point input mantissa to provide an output mantissa. Based on this technique, a single set of relatively simple hardware elements may be used to implement a variety of functions with high precision.

Abstract: A technique for approximating output values of a function based on LaGrange polynomials is provided. Factorization of a LaGrange polynomial results in a simplified representation of the LaGrange polynomial. With this simplified representation, an output value of a function may be determined based on an input value that includes an input mantissa and an input exponent. Based on a first portion of the input mantissa, a point value and at least one slope value are provided. Each of the at least one slope value is based on a LaGrange polynomial approximation of the function. Thereafter, the point value and the at least one slope value are combined with a second portion of the input mantissa to provide an output mantissa. Based on this technique, a single set of relatively simple hardware elements may be used to implement a variety of functions with high precision.

Abstract: A technique for approximating output values of a function based on LaGrange polynomials is provided. Factorization of a LaGrange polynomial results in a simplified representation of the LaGrange polynomial. With this simplified representation, an output value of a function may be determined based on an input value comprising an input mantissa and an input exponent. Based on a first portion of the input mantissa, a point value and at least one slope value are provided. Each of the at least one slope value is based on a LaGrange polynomial approximation of the function. Thereafter, the point value and the at least one slope value are combined with a second portion of the input mantissa to provide an output mantissa. Based on this technique, a single set of relatively simple hardware elements may be used to implement a variety of functions with high precision.

Abstract: A method and system for rendering a feature, such as a line, for display on an array of pixels. With this method, the line is identified on the pixel array, the line is expanded into a polygon, and color values are determined for the pixels within the polygon. Also, an antialiasing region is identified in the polygon, and blend values are computed for the pixels in this antialiasing region. Then, the color values determined for the pixels in the antialiasing region are modified as a function of these computed blend values. The pixels in the antialiasing region may then be shown at their modified color values, while the pixels that are in the polygon but not in the antialising region may be shown at their original determined color value. Preferably, the blend values for the pixels in the antialiasing region are calculated as a function of the locations of the pixels in that region.

Abstract: A resource access security system for use in a data processing system for controlling access to resources correspondingly assigned to addresses in an address space of the data processing system by the use of descriptors. The descriptors correspondingly identify the resources and access to the resources is controlled by requiring the input of a descriptor of the resource to which access is sought. The resource access security system controls access to the resources by translating each descriptor being taught to gain access to a resource by use of a plurality of tables having stored therein user/job information, domain information and page information and a descriptor translator which controls the descriptor translation process. The descriptors are virtual addresses of addresses assigned to the resources of the data processing system.