1bbbf1280Sopenharmony_ci// polynomial for approximating cos(x) 2bbbf1280Sopenharmony_ci// 3bbbf1280Sopenharmony_ci// Copyright (c) 2019, Arm Limited. 4bbbf1280Sopenharmony_ci// SPDX-License-Identifier: MIT 5bbbf1280Sopenharmony_ci 6bbbf1280Sopenharmony_cideg = 8; // polynomial degree 7bbbf1280Sopenharmony_cia = -pi/4; // interval 8bbbf1280Sopenharmony_cib = pi/4; 9bbbf1280Sopenharmony_ci 10bbbf1280Sopenharmony_ci// find even polynomial with minimal abs error compared to cos(x) 11bbbf1280Sopenharmony_ci 12bbbf1280Sopenharmony_cif = cos(x); 13bbbf1280Sopenharmony_ci 14bbbf1280Sopenharmony_ci// return p that minimizes |f(x) - poly(x) - x^d*p(x)| 15bbbf1280Sopenharmony_ciapprox = proc(poly,d) { 16bbbf1280Sopenharmony_ci return remez(f(x)-poly(x), deg-d, [a;b], x^d, 1e-10); 17bbbf1280Sopenharmony_ci}; 18bbbf1280Sopenharmony_ci 19bbbf1280Sopenharmony_ci// first coeff is fixed, iteratively find optimal double prec coeffs 20bbbf1280Sopenharmony_cipoly = 1; 21bbbf1280Sopenharmony_cifor i from 1 to deg/2 do { 22bbbf1280Sopenharmony_ci p = roundcoefficients(approx(poly,2*i), [|D ...|]); 23bbbf1280Sopenharmony_ci poly = poly + x^(2*i)*coeff(p,0); 24bbbf1280Sopenharmony_ci}; 25bbbf1280Sopenharmony_ci 26bbbf1280Sopenharmony_cidisplay = hexadecimal; 27bbbf1280Sopenharmony_ciprint("rel error:", accurateinfnorm(1-poly(x)/f(x), [a;b], 30)); 28bbbf1280Sopenharmony_ciprint("abs error:", accurateinfnorm(f(x)-poly(x), [a;b], 30)); 29bbbf1280Sopenharmony_ciprint("in [",a,b,"]"); 30bbbf1280Sopenharmony_ciprint("coeffs:"); 31bbbf1280Sopenharmony_cifor i from 0 to deg do coeff(poly,i); 32