Methods for implementing or synthesizing functions in hardware and fixed-function hardware include generating a look-up table, LUT, representing the function and then applying a transform to the LUT to transform the LUT into a plurality of derived LUTs. The transform may be applied recursively. A hardware design implementing each of the derived LUTs in fixed-function hardware logic, along with a logic unit that performs the inverse transform, is then created.

An aspect includes an apparatus for evaluating a mathematical function at an input value. The apparatus includes a selector for selecting a mathematical function, an input for a value at which to evaluate the function, an identifier for identifying an interval containing the input value. The interval is described by at least one polynomial function. At least one control point representing the polynomial function is retrieved from at least one look up table, and the polynomial function can be derived from the control points. The function is evaluated at the input value and an output of the evaluation is used as a value of the function at that input value.

An aspect includes an apparatus for evaluating a mathematical function at an input value. The apparatus includes a selector for selecting a mathematical function, an input for a value at which to evaluate the function, an identifier for identifying an interval containing the input value. The interval is described by at least one polynomial function. At least one control point representing the polynomial function is retrieved from at least one look up table, and the polynomial function can be derived from the control points. The function is evaluated at the input value and an output of the evaluation is used as a value of the function at that input value.

Control circuitry coupled to a multiply unit which includes a plurality of stage, each of which may be configured to perform a corresponding arithmetic function, may be configured to retrieve a given entry from a lookup table dependent upon a first portion of a binary representation of an input operand. An error value of an error function evaluated dependent upon a lookup value in a given entry of the plurality of entries is included in a predetermined error range. The control circuitry may be further configured to determine an initial approximation of a result of an iterative arithmetic operation using the first entry and initiate the iterative arithmetic operation using the initial approximation and the input operand.

A non-linear activation function may be approximated by linear functions. The input range of the activation function may be divided into input segments. One or more input segments may be selected based on statistical analysis of input data elements in the input range. A parameter of a first linear function that approximates the activation function for at least part of a selected input segment may be stored in a first portion of a first look-up table (LUT). The first portion of the first LUT is dedicated to a first group of post processing engines (PPEs). A parameter of a second linear function that approximates the activation function for at least part of an unselected input segment may be stored in a shared pool of LUT entries, which includes a second portion of the first LUT and a portion of a second LUT and is shared by multiple groups of PPEs.

Instead of logic-based computation (LBC), the preferred processor disclosed in the present invention uses memory-based computation (MBC). It comprises an array of computing elements, with each computing element comprising a memory array on a memory level for storing a look-up table (LUT) and an arithmetic logic circuit (ALC) on a logic level for performing arithmetic operations on selected LUT data. The memory level and the logic level are different physical levels.

Control circuitry coupled to a multiply unit which includes a plurality of stage, each of which may be configured to perform a corresponding arithmetic function, may be configured to retrieve a given entry from a lookup table dependent upon a first portion of a binary representation of an input operand. An error value of an error function evaluated dependent upon a lookup value in a given entry of the plurality of entries is included in a predetermined error range. The control circuitry may be further configured to determine an initial approximation of a result of an iterative arithmetic operation using the first entry and initiate the iterative arithmetic operation using the initial approximation and the input operand.

Mathematical functions are computed in a single pipeline performing a polynomial approximation (e.g. a quadratic approximation, or the like) using data tables for RCP, SQRT, EXP or LOG using a single pipeline according and opcodes. SIN and COS are also computed using the pipeline according to the approximation ((1)^IntX)*Sin(*Min(FracX, 1.0FracX)/Min(FracX, 1.0FracX). A pipeline portion approximates Sin(*FracX) using tables and interpolation and a subsequent stage multiplies this approximation by FracX. For input arguments of x close 1.0. LOG 2(x1)/(x1) is computed using a first pipeline portion using tables and interpolation and subsequently multiplied by (x1). A DIV operation may also be performed with input arguments scaled up to avoid underflow as needed. Inverse trigonometric functions may be calculated using a pre-processing stage and post processing stage in order to obtain multiple inverse trigonometric functions from a single pipeline.

Mathematical functions are computed in a single pipeline performing a polynomial approximation (e.g. a quadratic approximation, or the like); and one or more data tables corresponding to at least one of the RCP, SQRT, EXP or LOG functions operable to be coupled to the single pipeline according to one or more opcodes; wherein the single pipeline is operable for computing at least one of RCP, SQRT, EXP or LOG functions according to the one or more opcodes. SIN and COS are also computed using the pipeline according to the approximation ((1)^IntX)*Sin(*Min(FracX, 1.0FracX)/Min(FracX, 1.0FracX). A pipeline portion approximates Sin(*FracX) using tables and interpolation and a subsequent stage multiplies this approximation by FracX. For input arguments of x close 1.0. LOG 2(x1)/(x1) is computed using a first pipeline portion using tables and interpolation and subsequently multiplied by (x1). A DIV operation may also be performed with input arguments scaled up to avoid underflow as needed.