1*f3087befSAndrew Turner// polynomial for approximating log(1+x) in double precision 2*f3087befSAndrew Turner// 3*f3087befSAndrew Turner// Copyright (c) 2022-2024, Arm Limited. 4*f3087befSAndrew Turner// SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 5*f3087befSAndrew Turner 6*f3087befSAndrew Turnerdeg = 20; 7*f3087befSAndrew Turner 8*f3087befSAndrew Turnera = sqrt(2)/2-1; 9*f3087befSAndrew Turnerb = sqrt(2)-1; 10*f3087befSAndrew Turner 11*f3087befSAndrew Turnerf = proc(y) { 12*f3087befSAndrew Turner return log(1+y); 13*f3087befSAndrew Turner}; 14*f3087befSAndrew Turner 15*f3087befSAndrew Turnerapprox = proc(poly, d) { 16*f3087befSAndrew Turner return remez(1 - poly(x)/f(x), deg-d, [a;b], x^d/f(x), 1e-10); 17*f3087befSAndrew Turner}; 18*f3087befSAndrew Turner 19*f3087befSAndrew Turnerpoly = x; 20*f3087befSAndrew Turnerfor i from 2 to deg do { 21*f3087befSAndrew Turner p = roundcoefficients(approx(poly,i), [|D ...|]); 22*f3087befSAndrew Turner poly = poly + x^i*coeff(p,0); 23*f3087befSAndrew Turner}; 24*f3087befSAndrew Turner 25*f3087befSAndrew Turner 26*f3087befSAndrew Turnerprint("coeffs:"); 27*f3087befSAndrew Turnerdisplay = hexadecimal; 28*f3087befSAndrew Turnerfor i from 2 to deg do coeff(poly,i); 29*f3087befSAndrew Turnerprint("rel error:", accurateinfnorm(1-poly(x)/f(x), [a;b], 30)); 30*f3087befSAndrew Turnerprint("in [",a,b,"]"); 31