1*f3087befSAndrew Turner// polynomial for approximating cos(x) 2*f3087befSAndrew Turner// 3*f3087befSAndrew Turner// Copyright (c) 2023-2024, Arm Limited. 4*f3087befSAndrew Turner// SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 5*f3087befSAndrew Turner 6*f3087befSAndrew Turner// This script only finds the coeffs for cos - see math/tools/sin.sollya for sin coeffs. 7*f3087befSAndrew Turner 8*f3087befSAndrew Turnerdeg = 8; // polynomial degree 9*f3087befSAndrew Turnera = -pi/4; // interval 10*f3087befSAndrew Turnerb = pi/4; 11*f3087befSAndrew Turner 12*f3087befSAndrew Turner// find even polynomial with minimal abs error compared to cos(x) 13*f3087befSAndrew Turner 14*f3087befSAndrew Turnerf = cos(x); 15*f3087befSAndrew Turner 16*f3087befSAndrew Turner// return p that minimizes |f(x) - poly(x) - x^d*p(x)| 17*f3087befSAndrew Turnerapprox = proc(poly,d) { 18*f3087befSAndrew Turner return remez(f(x)-poly(x), deg-d, [a;b], x^d, 1e-10); 19*f3087befSAndrew Turner}; 20*f3087befSAndrew Turner 21*f3087befSAndrew Turner// first coeff is fixed, iteratively find optimal double prec coeffs 22*f3087befSAndrew Turnerpoly = 1; 23*f3087befSAndrew Turnerfor i from 1 to deg/2 do { 24*f3087befSAndrew Turner p = roundcoefficients(approx(poly,2*i), [|single ...|]); 25*f3087befSAndrew Turner poly = poly + x^(2*i)*coeff(p,0); 26*f3087befSAndrew Turner}; 27*f3087befSAndrew Turner 28*f3087befSAndrew Turnerdisplay = hexadecimal; 29*f3087befSAndrew Turner//print("rel error:", accurateinfnorm(1-poly(x)/f(x), [a;b], 30)); 30*f3087befSAndrew Turner//print("abs error:", accurateinfnorm(f(x)-poly(x), [a;b], 30)); 31*f3087befSAndrew Turnerprint("in [",a,b,"]"); 32*f3087befSAndrew Turnerprint("coeffs:"); 33*f3087befSAndrew Turnerfor i from 0 to deg do coeff(poly,i); 34