forestbelton/fp — Issue #2: Research and compare reciprocal approximations
Author: forestbelton
Created: 2012-02-24 16:47:16+00:00
State: open

The current idea of the implementation of division involves computing the reciprocal of the divisor and multiplying that by the dividend. We can use the Newton-Raphson method for improving our reciprocal approximation, but an initial guess is still required. Ideally, this guess should be as close to the proper value as possible, while minimizing the amount of computation involved. Even though Newton-Raphson converges quadratically, it's still preferable to reduce the number of iterations required to a bare minimum since division is such a fundamental operation.

Approaches I've already investigated
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* Nonlinear regression
* Taylor series approximation
* Fourier series approximation, by translating 1/x and pretending it's periodic (Silly, I know)
* Cubic spline interpolation