Patent ID: 8332446
Filing Date: 2012-12-11
Classification: G06F

Abstract:
1. A machine executed method for translating polynomials, of one unknown, into alternative polynomial representations to eliminate cancellation errors when evaluating the alternative polynomial representations, comprising: within a constructor environment, preparing a target form for a target environment with a predetermined floating point number system, or target number system, wherein a number of mantissa bits of the target number system defines a target precision, wherein said target form defines a substitute polynomial throughout a predetermined input domain, defined within said target number system, wherein preparing the target form comprises: (A) supplying a sequence of raw factors, wherein the combined product of raw factors represents a polynomial, including a raw lead factor of at least said target precision, and raw root factors, wherein all represented roots are at least twice said target precision based on relative precision with respect to the origin, (B) constructing a target form, and storing said target form in a memory storage system, based at least in part on an interface for accepting and processing a sequence of minimal factors, and by converting the incoming sequence of said minimal factors into said target form for use within said target environment, (C) converting a predetermined raw factor into a corresponding minimal factor, wherein rounding of values within said raw factors into said minimal factors, is the two step process of rounding each axis of each root into a high order, followed by rounding the difference of the axis value and said high order into a low order value, wherein the rounding is based on said target precision, and upon completion, returning said minimal factor, (D) creating said target form from the polynomial, at least in part by: