System and method of computing functions approximation

1 . A method of generating, by one or more processors, instructions for manufacturing an electrical approximation circuit that approximates a target function over a predetermined interval with uniform error distribution, the method comprising:

generating an initial approximation function, approximating the target function over the predetermined interval;

constructing an objective function based on the initial approximation function, wherein the objective function is configured to control error distribution at the predetermined interval's boundaries;

performing an iterative optimization process on the objective function to find a set of outcome coefficient values that define an outcome approximation function, wherein the outcome approximation function (a) approximates the target function, satisfying an accuracy requirement and (b) produces substantially uniform error distribution across the predetermined interval, thereby addressing oscillatory behavior at the interval's boundaries;

generating, based on the outcome approximation function, schematic data translatable into a physical layout design for an integrated circuit; and

outputting instructions for manufacturing the integrated circuit based on the physical layout design,

wherein the integrated circuit is adapted to:

receive a signal representing an input value within the predetermined interval; and

produce an output signal representing an estimation of the target function at the input value according to the outcome approximation function.

2 . A system for designing an integrated circuit, adapted to calculate an approximation of a target function over a predetermined interval, the system comprising: a non-transitory memory device, wherein modules of instruction code are stored, and at least one processor associated with the memory device, and configured to execute the modules of instruction code, whereupon execution of said modules of instruction code, the at least one processor is configured to:

employ an approximation algorithm, to calculate a first approximation function, approximating the target function, wherein the first approximation function is defined by an initial set of coefficient values;

construct an objective function based on the first approximation function;

based on the objective function, calculating a first set of outcome coefficient values, which define an outcome approximation function; and

based on the outcome approximation function, generate and output an approximation circuit schematic, which represents an electrical approximation circuit, wherein the electrical approximation circuit is adapted to (i) receive an input value within the predetermined interval, and (ii) produce an estimation of the mathematical function at the input value, according to the outcome approximation function.

3 . The system of claim 2 , wherein the approximation circuit schematic is adapted to be translated into a physical layout design, utilizable for fabricating an Integrated Circuit that comprises the electrical approximation circuit.

4 . The system of claim 2 , wherein the at least one processor is further configured to:

calculate an initial error function, describing a difference between the target function and the first approximation function along the interval;

identify a set of peak points of the initial error function;

receive a requirement of target accuracy for approximating the target function at the set of peak points; and

minimize the objective function, to find the first set of outcome coefficient values, such that the outcome approximation function satisfies the target accuracy requirement.

5 . The system of claim 4 , wherein the at least one processor is further configured to:

obtain a set of coefficient constraints, defining desired properties of coefficients of the outcome approximation function;

construct the objective function further based on the set of coefficient constraints; and

minimize the objective function, to find the first set of outcome coefficient values, wherein the first set of outcome coefficient values comply with the coefficient constraints.

6 . The system of claim 5 , wherein said coefficient constraints are selected from a list consisting of: a representation of one or more coefficients, a precision of representation of one or more coefficients, and a rounding of one or more coefficients.

7 . The system of claim 5 , wherein the at least one processor is further configured to:

obtain a set of polynomial power constraints, defining properties of powers of the outcome approximation function;

construct the objective function further based on the set of polynomial power constraints; and

minimize the objective function such that powers of the outcome approximation function comply further with the set of polynomial power constraints.

8 . The system of claim 7 , wherein the at least one processor is further configured to:

obtain one or more computational constraints, defining limitations for computational resource consumption of the electrical approximation circuit;

assess compliance of the electrical approximation circuit with the computational constraints; and

when such compliance is not achieved, iteratively modify the polynomial power constraints and/or the coefficient constraints until the computational constraints are met.

9 . The system of claim 8 , wherein the computational constraints are selected from a list consisting of a limitation of silicon area in the electrical approximation circuit, power consumption of the electrical approximation circuit, latency of the electrical approximation circuit, and computing cycles required by the electrical approximation circuit.

10 . The system of claim 5 , wherein the at least one processor is further configured to:

obtain a set of error constraints, defining a behaviour of a desired error function, which represents difference between the target function and the outcome approximation function along the interval;

construct the objective function further based on the set of error constraints; and

minimize the objective function such that the desired error function complies further with the set of error constraints.

11 . The system of claim 2 , wherein the at least one processor is further configured to:

calculate an approximation error of the outcome approximation function at the set of peak points;

employ the approximation algorithm, based on (i) coefficients of the first outcome approximation function, and (ii) the calculated approximation error, to produce a second version of the outcome approximation function; and

generate the approximation circuit schematic based on the second version of the outcome approximation function.

12 . A method of calculating, by at least one processor, an approximation of a target function over a predetermined interval, the method comprising:

employing an approximation algorithm, to calculate a first approximation function, approximating the target function, wherein the first approximation function comprises an initial set of coefficient values;

calculating an initial error function, describing a difference between the target function and the first approximation function along the interval;

identifying a set of peak points of the initial error function;

receiving a requirement of a target accuracy for approximating the target function at the set of peak points;

obtaining a set of coefficient constraints, defining desired properties of coefficients of an outcome approximation function;

constructing an objective function based on the first approximation function and the set of coefficient constraints;

minimizing the objective function, to find a first set of outcome coefficient values, that (a) define the outcome approximation function, and (b) comply with the coefficient constraints, wherein the outcome approximation function satisfies the target accuracy requirement; and

using the outcome approximation to execute an instruction of an instruction set in software or hardware.

13 . The method of claim 12 , further comprising:

generating, based on the outcome approximation function, an approximation schematic, representing an electrical approximation circuit, wherein the electrical approximation circuit is adapted to:

receive a signal representing an input value within the predetermined interval; and

produce an output signal, representing an estimation of the mathematical function at the input value according to the outcome approximation function.

14 . The method of claim 13 , wherein the approximation schematic is adapted to be translated into a physical layout design, utilizable for fabricating an Integrated Circuit that comprises the electrical approximation circuit.

15 . The method of claim 12 , wherein said coefficient constraints are selected from a list consisting of: a representation of one or more coefficients, a precision of representation of one or more coefficients, and a rounding of one or more coefficients.

16 . The method of claim 12 , further comprising:

obtaining a set of polynomial power constraints, defining properties of powers of the outcome approximation function;

constructing the objective function further based on the set of polynomial power constraints; and

minimizing the objective function such that powers of the outcome approximation function comply further with the set of polynomial power constraints.

17 . The method of claim 16 , wherein said polynomial power constraints are selected from a list consisting of: using only even power polynomials, using only odd power polynomials, and using only powers selected from a list of predetermined power values.

18 . The method of claim 12 , further comprising:

obtaining a set of error constraints, defining a behaviour of a desired error function, which defines a difference between the target function and the outcome approximation function along the interval;

constructing the objective function further based on the set of error constraints; and

minimizing the objective function such that the desired error function complies further with the set of error constraints.

19 . The method of claim 18 , wherein said error constraints are selected from a list consisting of: requirement for oscillation of the desired error function, requirement for the desired error function to have sign-alternating peaks, limitation of an absolute value of the desired error function by a predetermined error level, and determination of a maximal value of the desired error function at extremities of the interval.

20 . The method of claim 18 , wherein minimizing the objective function comprises an iterative process, where each iteration comprises:

perturbating a current set of coefficient values, of a current iteration, to find a new set of coefficient values that (a) define an interim approximation function, and (b) comply with the coefficient constraints;

estimating an accuracy value of the interim approximation function, over a predefined set of input points;

when the estimated accuracy satisfies the target accuracy requirement, returning the interim approximation function as a first version of the outcome approximation function; and

when the estimated accuracy does not satisfy the target accuracy requirement, repeating the iterative process, with the new set of coefficient values serving as the current set of coefficient values, for a subsequent iteration.