1bbbf1280Sopenharmony_ci// polynomial for approximating sin(x) 2bbbf1280Sopenharmony_ci// 3bbbf1280Sopenharmony_ci// Copyright (c) 2019, Arm Limited. 4bbbf1280Sopenharmony_ci// SPDX-License-Identifier: MIT 5bbbf1280Sopenharmony_ci 6bbbf1280Sopenharmony_cideg = 15; // polynomial degree 7bbbf1280Sopenharmony_cia = -pi/2; // interval 8bbbf1280Sopenharmony_cib = pi/2; 9bbbf1280Sopenharmony_ci 10bbbf1280Sopenharmony_ci// find even polynomial with minimal abs error compared to sin(x)/x 11bbbf1280Sopenharmony_ci 12bbbf1280Sopenharmony_ci// account for /x 13bbbf1280Sopenharmony_cideg = deg-1; 14bbbf1280Sopenharmony_ci 15bbbf1280Sopenharmony_ci// f = sin(x)/x; 16bbbf1280Sopenharmony_cif = 1; 17bbbf1280Sopenharmony_cic = 1; 18bbbf1280Sopenharmony_cifor i from 1 to 60 do { c = 2*i*(2*i + 1)*c; f = f + (-1)^i*x^(2*i)/c; }; 19bbbf1280Sopenharmony_ci 20bbbf1280Sopenharmony_ci// return p that minimizes |f(x) - poly(x) - x^d*p(x)| 21bbbf1280Sopenharmony_ciapprox = proc(poly,d) { 22bbbf1280Sopenharmony_ci return remez(f(x)-poly(x), deg-d, [a;b], x^d, 1e-10); 23bbbf1280Sopenharmony_ci}; 24bbbf1280Sopenharmony_ci 25bbbf1280Sopenharmony_ci// first coeff is fixed, iteratively find optimal double prec coeffs 26bbbf1280Sopenharmony_cipoly = 1; 27bbbf1280Sopenharmony_cifor i from 1 to deg/2 do { 28bbbf1280Sopenharmony_ci p = roundcoefficients(approx(poly,2*i), [|D ...|]); 29bbbf1280Sopenharmony_ci poly = poly + x^(2*i)*coeff(p,0); 30bbbf1280Sopenharmony_ci}; 31bbbf1280Sopenharmony_ci 32bbbf1280Sopenharmony_cidisplay = hexadecimal; 33bbbf1280Sopenharmony_ciprint("abs error:", accurateinfnorm(sin(x)-x*poly(x), [a;b], 30)); 34bbbf1280Sopenharmony_ciprint("in [",a,b,"]"); 35bbbf1280Sopenharmony_ciprint("coeffs:"); 36bbbf1280Sopenharmony_cifor i from 0 to deg do coeff(poly,i); 37