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