Calculating circuit and method for computing an N-th rooth and a reciprocal of a number

A calculating circuit for generating an output signal representing an output number approximating an N-th root of an input number represented by an input signal, the calculating circuit comprising:

• a subtractor circuit responsive to said input signal and configured for generating an error signal representing a difference between said input signal and a feedback signal representing the output signal raised to the power N;
• an integrator circuit responsive to said error signal and configured for computing said output signal;
• and
• a multiplier circuit responsive to said output signal and configured for generating the feedback signal.

A calculating circuit for generating an output signal representing an output number approximating a reciprocal of an input number represented by an input signal, the calculating circuit comprising:

• a subtractor circuit responsive to said input signal for generating an error signal representing a difference between a reference signal and a feedback signal representing a product of an output signal and said input signal;
• an integrator circuit responsive to said error signal for generating said output signal;
• and
• a multiplier circuit responsive to said output signal and to said input signal for generating said feedback signal.

A method for generating an output signal Zout(j) representing an output number approximating an N-th root or a reciprocal of an input number represented by an input signal Zin, the method comprising the iterative steps:

• (a) generating an error signal E(j) representing a difference between a first signal and a feedback signal at a j-th iteration,
• (b) integrating said error signal E(j) for obtaining said output signal Zout(j);
• (c) generating the feedback signal Zfb(j);
• (d) repeating steps (i) to (iii) as required to obtain said N-th root or said reciprocal with a required accuracy.

A method for generating an output signal Zout(j) representing an output number approximating an N-th root of an input number represented by an input signal Zin, the method comprising the iterative steps:

• (a) generating an error signal E(j) at a j-th iteration representing a difference between said input signal Zin and a feedback signal Zfb(j) representing said output signal raised to the power N,
• (b) integrating said error signal E(j) for obtaining said output signal Zout(j);
• (c) generating said feedback signal;
• (d) repeating steps (i) to (iii) as required to obtain said N-th root with a required accuracy.

A method for generating an output signal Zout(j) representing an output number approximating a reciprocal of an input number represented by an input signal Zin, the method comprising the iterative steps:

• (a) generating an error signal E(j) representing a difference between a reference signal and a feedback signal Zfb(j) at a j-th iteration,
• (b) integrating said error signal E(j) for obtaining said output signal Zout(j);
• (c) generating said feedback signal representing a product of said output signal Zout(j) and said input signal Zin;
• (d) repeating steps (i) to (iii) as required to obtain said reciprocal of the input number with a required accuracy.