1// polynomial for approximating sin(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 = 7; // polynomial degree 8a = -pi/4; // interval 9b = pi/4; 10 11// find even polynomial with minimal abs error compared to sin(x)/x 12 13// account for /x 14deg = deg-1; 15 16// f = sin(x)/x; 17f = 1; 18c = 1; 19for i from 1 to 60 do { c = 2*i*(2*i + 1)*c; f = f + (-1)^i*x^(2*i)/c; }; 20 21// return p that minimizes |f(x) - poly(x) - x^d*p(x)| 22approx = proc(poly,d) { 23 return remez(f(x)-poly(x), deg-d, [a;b], x^d, 1e-10); 24}; 25 26// first coeff is fixed, iteratively find optimal double prec coeffs 27poly = 1; 28for i from 1 to deg/2 do { 29 p = roundcoefficients(approx(poly,2*i), [|D ...|]); 30 poly = poly + x^(2*i)*coeff(p,0); 31}; 32 33display = hexadecimal; 34print("rel error:", accurateinfnorm(1-poly(x)/f(x), [a;b], 30)); 35print("abs error:", accurateinfnorm(sin(x)-x*poly(x), [a;b], 30)); 36print("in [",a,b,"]"); 37print("coeffs:"); 38for i from 0 to deg do coeff(poly,i); 39