34results about "Logarithmic/exponential functions" patented technology

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.

An apparatus for calculating an exponential calculating result for a base 2 floating-point number comprises a transforming device, K exponential tables and a multiplier. The transforming device receives the floating-point number, transforms the floating-point number to an integer part and a fractional part and outputs the integer part and the fractional part. The fractional part is an N-bit number and divided into K parts which have N1, N2, . . . , NK bits respectively, wherein N=N1+N2+ . . . +NK. Each of the exponential tables receives one of the K parts divided from the fractional part and outputs a result. The multiplier receives all results from the exponential tables and outputs a mantissa. The integer part outputted form the transforming device is an exponent. The mantissa, the exponent and a sign whose value is 0 is used to represent an exponential calculating result which is represented in the following format: (−1)Sy·2Ey·my, where Sy is the sign whose value is 0, Ey is the integer part, my is the mantissa and 1≦my<2.

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.

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.

A datapath circuit may include a digital multiply and accumulate circuit (MAC) and a digital hardware calculator for parallel computation. The digital hardware calculator and the MAC may be coupled to an input memory element for receipt of input operands. The MAC may include a digital multiplier structure with partial product generators coupled to an adder to multiply a first and second input operands and generate a multiplication result. The digital hardware calculator may include a first look-up table coupled between a calculator input and a calculator output register. The first look-up table may include table entry values mapped to corresponding math function results in accordance with a first predetermined mathematical function. The digital hardware calculator may be configured to calculate, based on the first look-up table, a computationally hard mathematical function such as a logarithm function, an exponential function, a division function and a square root function.

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(π*Min(FracX, 1.0−FracX) / Min(FracX, 1.0−FracX). A pipline portion approximates Sin(π*FracX) using tables and interpolation and a subsequent stage multiplies this approximation by FracX. For input arguments of x close 1.0. LOG2(x−1) / (x−1) is computed using a first pipeline portion using tables and interpolation and subsequently multiplied by (x−1). A DIV operation may also be performed with input arguments scaled up to avoid underflow as needed.

Efficiency of computation of logarithmic and exponential functions may be improved using multiplication by pre-computed coefficients to obtain intermediate products.

A calculator calculates an approximate value of a function Y=log (1+e−x) using input data x. In the calculator, a decoder outputs m-bit data that represents a value corresponding to the slope of a straight line, and further outputs intercept data of the straight line. The straight line interpolates the function Y=log (1+e−x) for an interval that includes the input data x as an X-value, and has a slope of −2n. The intercept data represents Y-intercept of the straight line. A shifter shifts the input data x by |n| bits based on the m-bit data, and provides the resultant value as first term data. An adder generates the sum of the first term data and the intercept data, and outputs the generated sum as an approximate value of the function log Y=(1+e−x)

Methods and apparatus is provided for computing mathematical functions comprising a single pipeline for performing a polynomial approximation (e.g. a quadratic polynomial 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.

The present invention provides a logarithm calculation method, wherein the logarithm calculation method includes the steps of: (a) selecting a first parameter, a second parameter, a third parameter and a fourth parameter corresponding to an i-th iteration operation; (b) determining whether an input value is greater than the third parameter or smaller than the fourth parameter (c) if the input value is greater than the third parameter, updating the input value by multiplying the first parameter, and updating an output value by subtracting a logarithmic value of the first parameter; if the input value is less than the fourth parameter, updating the input value by multiplying the second parameter, and updating the output value by subtracting a logarithmic value of the second parameter (d) adding one to ‘i’ and return to step (a); (e) when ‘i’ is equal to a predetermined value, outputting the current output value.

Efficiency of computation of logarithmic and exponential functions may be improved using multiplication by pre-computed coefficients to obtain intermediate products.

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(π*Min(FracX, 1.0−FracX) / Min(FracX, 1.0−FracX). A pipeline portion approximates Sin(π*FracX) using tables and interpolation and a subsequent stage multiplies this approximation by FracX. For input arguments of x close 1.0. LOG 2(x−1) / (x−1) is computed using a first pipeline portion using tables and interpolation and subsequently multiplied by (x−1). A DIV operation may also be performed with input arguments scaled up to avoid underflow as needed.

The invention relates to a logarithm calculation method and a logarithm calculation circuit. The logarithm calculation method disclosed by the invention comprises the following steps: (a) selecting a first parameter, a second parameter, a third parameter and a fourth parameter corresponding to the i iterative operation; (b) judging whether an input value is larger than the third parameter or smaller than the fourth parameter; (c) if the input value is greater than the third parameter, updating the input value by multiplying the input value by the first parameter, and updating an output value by subtracting the logarithm value of the first parameter, or if the input value is smaller than the fourth parameter, updating the input value by multiplying the input value by the second parameter, and updating the output value by subtracting the logarithm value of the second parameter, or if the input value is between the third parameter and the fourth parameter, not changing the input value and the output value; (d) adding 1 to i, and returning to the step (a) until i is equal to a preset value; and (e) when i is equal to the preset value, taking a current output value as a calculation result.