Higher precision divide and square root approximations

A method comprising:

• approximating a function using an approximation algorithm comprising at least two iterations of:
• (i) a multiplication in a multiplier, and (ii) a difference approximation between a constant and a result of the multiplication, wherein the difference approximation is less than a difference between the constant and the result by one unit in the least significant bit of the difference approximation;
• during a first of the iterations, generating the difference approximation;
• and
• during a second of the iterations, supplying a correction vector to the multiplier, the multiplier incorporating the correction vector in the multiplication, the correction vector correcting the difference approximation.

A carrier medium comprising one or more data structures representing a floating point unit, the floating point unit comprising:

• a multiplier configured to generate a first result;
• an approximation circuit coupled to receive the first result and configured to generate an approximation of a difference of the first result from a constant;
• and
• a control circuit coupled to the multiplier and the approximation circuit, wherein the control circuit is configured to approximate a function specified by a floating point instruction provided to the floating point unit for execution using an approximation algorithm, the approximation algorithm comprising at least two iterations through the multiplier and optionally the approximation circuit, wherein the control circuit is configured to correct the approximation from the approximation circuit from a first iteration of the approximation algorithm during a second iteration of the approximation algorithm by supplying a correction vector to the multiplier during the second iteration;
• wherein the multiplier is configured to incorporate the correction vector into the first result during the second iteration.