1*412f47f9SXin Li// polynomial for approximating cos(x) 2*412f47f9SXin Li// 3*412f47f9SXin Li// Copyright (c) 2023, Arm Limited. 4*412f47f9SXin Li// SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 5*412f47f9SXin Li 6*412f47f9SXin Li// This script only finds the coeffs for cos - see math/tools/sin.sollya for sin coeffs. 7*412f47f9SXin Li 8*412f47f9SXin Lideg = 8; // polynomial degree 9*412f47f9SXin Lia = -pi/4; // interval 10*412f47f9SXin Lib = pi/4; 11*412f47f9SXin Li 12*412f47f9SXin Li// find even polynomial with minimal abs error compared to cos(x) 13*412f47f9SXin Li 14*412f47f9SXin Lif = cos(x); 15*412f47f9SXin Li 16*412f47f9SXin Li// return p that minimizes |f(x) - poly(x) - x^d*p(x)| 17*412f47f9SXin Liapprox = proc(poly,d) { 18*412f47f9SXin Li return remez(f(x)-poly(x), deg-d, [a;b], x^d, 1e-10); 19*412f47f9SXin Li}; 20*412f47f9SXin Li 21*412f47f9SXin Li// first coeff is fixed, iteratively find optimal double prec coeffs 22*412f47f9SXin Lipoly = 1; 23*412f47f9SXin Lifor i from 1 to deg/2 do { 24*412f47f9SXin Li p = roundcoefficients(approx(poly,2*i), [|single ...|]); 25*412f47f9SXin Li poly = poly + x^(2*i)*coeff(p,0); 26*412f47f9SXin Li}; 27*412f47f9SXin Li 28*412f47f9SXin Lidisplay = hexadecimal; 29*412f47f9SXin Li//print("rel error:", accurateinfnorm(1-poly(x)/f(x), [a;b], 30)); 30*412f47f9SXin Li//print("abs error:", accurateinfnorm(f(x)-poly(x), [a;b], 30)); 31*412f47f9SXin Liprint("in [",a,b,"]"); 32*412f47f9SXin Liprint("coeffs:"); 33*412f47f9SXin Lifor i from 0 to deg do coeff(poly,i); 34