131914882SAlex Richardson// polynomial for approximating cos(x) 231914882SAlex Richardson// 331914882SAlex Richardson// Copyright (c) 2019, Arm Limited. 4*072a4ba8SAndrew Turner// SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 531914882SAlex Richardson 631914882SAlex Richardsondeg = 8; // polynomial degree 731914882SAlex Richardsona = -pi/4; // interval 831914882SAlex Richardsonb = pi/4; 931914882SAlex Richardson 1031914882SAlex Richardson// find even polynomial with minimal abs error compared to cos(x) 1131914882SAlex Richardson 1231914882SAlex Richardsonf = cos(x); 1331914882SAlex Richardson 1431914882SAlex Richardson// return p that minimizes |f(x) - poly(x) - x^d*p(x)| 1531914882SAlex Richardsonapprox = proc(poly,d) { 1631914882SAlex Richardson return remez(f(x)-poly(x), deg-d, [a;b], x^d, 1e-10); 1731914882SAlex Richardson}; 1831914882SAlex Richardson 1931914882SAlex Richardson// first coeff is fixed, iteratively find optimal double prec coeffs 2031914882SAlex Richardsonpoly = 1; 2131914882SAlex Richardsonfor i from 1 to deg/2 do { 2231914882SAlex Richardson p = roundcoefficients(approx(poly,2*i), [|D ...|]); 2331914882SAlex Richardson poly = poly + x^(2*i)*coeff(p,0); 2431914882SAlex Richardson}; 2531914882SAlex Richardson 2631914882SAlex Richardsondisplay = hexadecimal; 2731914882SAlex Richardsonprint("rel error:", accurateinfnorm(1-poly(x)/f(x), [a;b], 30)); 2831914882SAlex Richardsonprint("abs error:", accurateinfnorm(f(x)-poly(x), [a;b], 30)); 2931914882SAlex Richardsonprint("in [",a,b,"]"); 3031914882SAlex Richardsonprint("coeffs:"); 3131914882SAlex Richardsonfor i from 0 to deg do coeff(poly,i); 32