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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-exception6 7deg = 8; // polynomial degree8a = -pi/4; // interval9b = 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 coeffs21poly = 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