comp-horner-is-faithful

▸ function compHornerIsFaithful (p: number[], x: number): object

Defined in evaluate/double/comp-horner-is-faithful.ts:38

Returns the result of evaluating a univariate polynomial using once compensated Horner's method, including a dynamic check for faithfull rounding and a certified running error bound.

• once compensated means the error in the evaluation is reduced by roughly 1 / Number.EPSILON which is again roughly 2^53 - it is the same as using double-double precision in a normal Horner evaluation

• see Algorithms for Accurate, Validated and Fast Polynomial Evaluation, Stef Graillat, Philippe Langlois and Nicolas Louvet

• see also Philippe Langlois, Nicolas Louvet. Faithful Polynomial Evaluation with Compensated Horner Algorithm. ARITH18: 18th IEEE International Symposium on Computer Arithmetic, Jun 2007, Montpellier, France. pp.141–149. ffhal-00107222f

• see also Horner's Method

Parameters:

Name	Type	Description
p	number[]	a polynomial with coefficients given densely as an array of double floating point numbers from highest to lowest power, e.g. [5,-3,0] represents the polynomial 5x^2 - 3x
x	number	the value at which to evaluate the polynomial

Returns: object

Name	Type
isFaithful	boolean
errBound	number
r̄	number