1// polynomial for approximating cos(x) 2// 3// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. 4// See https://llvm.org/LICENSE.txt for license information. 5// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception 6 7deg = 8; // polynomial degree 8a = -pi/4; // interval 9b = pi/4; 10 11// find even polynomial with minimal abs error compared to cos(x) 12 13f = cos(x); 14 15// return p that minimizes |f(x) - poly(x) - x^d*p(x)| 16approx = proc(poly,d) { 17 return remez(f(x)-poly(x), deg-d, [a;b], x^d, 1e-10); 18}; 19 20// first coeff is fixed, iteratively find optimal double prec coeffs 21poly = 1; 22for i from 1 to deg/2 do { 23 p = roundcoefficients(approx(poly,2*i), [|D ...|]); 24 poly = poly + x^(2*i)*coeff(p,0); 25}; 26 27display = hexadecimal; 28print("rel error:", accurateinfnorm(1-poly(x)/f(x), [a;b], 30)); 29print("abs error:", accurateinfnorm(f(x)-poly(x), [a;b], 30)); 30print("in [",a,b,"]"); 31print("coeffs:"); 32for i from 0 to deg do coeff(poly,i); 33