1// polynomial for approximating cos(x) 2// 3// Copyright (c) 2019, Arm Limited. 4// SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 5 6deg = 8; // polynomial degree 7a = -pi/4; // interval 8b = pi/4; 9 10// find even polynomial with minimal abs error compared to cos(x) 11 12f = cos(x); 13 14// return p that minimizes |f(x) - poly(x) - x^d*p(x)| 15approx = proc(poly,d) { 16 return remez(f(x)-poly(x), deg-d, [a;b], x^d, 1e-10); 17}; 18 19// first coeff is fixed, iteratively find optimal double prec coeffs 20poly = 1; 21for i from 1 to deg/2 do { 22 p = roundcoefficients(approx(poly,2*i), [|D ...|]); 23 poly = poly + x^(2*i)*coeff(p,0); 24}; 25 26display = hexadecimal; 27print("rel error:", accurateinfnorm(1-poly(x)/f(x), [a;b], 30)); 28print("abs error:", accurateinfnorm(f(x)-poly(x), [a;b], 30)); 29print("in [",a,b,"]"); 30print("coeffs:"); 31for i from 0 to deg do coeff(poly,i); 32