| // polynomial for approximating cos(x) |
| // |
| // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. |
| // See https://llvm.org/LICENSE.txt for license information. |
| // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception |
| |
| deg = 8; // polynomial degree |
| a = -pi/4; // interval |
| b = pi/4; |
| |
| // find even polynomial with minimal abs error compared to cos(x) |
| |
| f = cos(x); |
| |
| // return p that minimizes |f(x) - poly(x) - x^d*p(x)| |
| approx = proc(poly,d) { |
| return remez(f(x)-poly(x), deg-d, [a;b], x^d, 1e-10); |
| }; |
| |
| // first coeff is fixed, iteratively find optimal double prec coeffs |
| poly = 1; |
| for i from 1 to deg/2 do { |
| p = roundcoefficients(approx(poly,2*i), [|D ...|]); |
| poly = poly + x^(2*i)*coeff(p,0); |
| }; |
| |
| display = hexadecimal; |
| print("rel error:", accurateinfnorm(1-poly(x)/f(x), [a;b], 30)); |
| print("abs error:", accurateinfnorm(f(x)-poly(x), [a;b], 30)); |
| print("in [",a,b,"]"); |
| print("coeffs:"); |
| for i from 0 to deg do coeff(poly,i); |
