eval-k

▸ function evalK (p: number[], x: number): number

Defined in evaluate/double/eval-k.ts:30

Returns the result of evaluating the given polynomial at x such that at least the sign bit is correct up to 3-times compensated evaluation (K = 4), i.e. as if evaluating in double-double-double-double precision.

• uses a staggered algorithm, first trying in double precision, then in double-double and finally in double-double-double-double

• 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: number