1bbbf1280Sopenharmony_ci// polynomial for approximating log(1+x) 2bbbf1280Sopenharmony_ci// 3bbbf1280Sopenharmony_ci// Copyright (c) 2019, Arm Limited. 4bbbf1280Sopenharmony_ci// SPDX-License-Identifier: MIT 5bbbf1280Sopenharmony_ci 6bbbf1280Sopenharmony_cideg = 12; // poly degree 7bbbf1280Sopenharmony_ci// |log(1+x)| > 0x1p-4 outside the interval 8bbbf1280Sopenharmony_cia = -0x1p-4; 9bbbf1280Sopenharmony_cib = 0x1.09p-4; 10bbbf1280Sopenharmony_ci 11bbbf1280Sopenharmony_ci// find log(1+x)/x polynomial with minimal relative error 12bbbf1280Sopenharmony_ci// (minimal relative error polynomial for log(1+x) is the same * x) 13bbbf1280Sopenharmony_cideg = deg-1; // because of /x 14bbbf1280Sopenharmony_ci 15bbbf1280Sopenharmony_ci// f = log(1+x)/x; using taylor series 16bbbf1280Sopenharmony_cif = 0; 17bbbf1280Sopenharmony_cifor i from 0 to 60 do { f = f + (-x)^i/(i+1); }; 18bbbf1280Sopenharmony_ci 19bbbf1280Sopenharmony_ci// return p that minimizes |f(x) - poly(x) - x^d*p(x)|/|f(x)| 20bbbf1280Sopenharmony_ciapprox = proc(poly,d) { 21bbbf1280Sopenharmony_ci return remez(1 - poly(x)/f(x), deg-d, [a;b], x^d/f(x), 1e-10); 22bbbf1280Sopenharmony_ci}; 23bbbf1280Sopenharmony_ci 24bbbf1280Sopenharmony_ci// first coeff is fixed, iteratively find optimal double prec coeffs 25bbbf1280Sopenharmony_cipoly = 1; 26bbbf1280Sopenharmony_cifor i from 1 to deg do { 27bbbf1280Sopenharmony_ci p = roundcoefficients(approx(poly,i), [|D ...|]); 28bbbf1280Sopenharmony_ci poly = poly + x^i*coeff(p,0); 29bbbf1280Sopenharmony_ci}; 30bbbf1280Sopenharmony_ci 31bbbf1280Sopenharmony_cidisplay = hexadecimal; 32bbbf1280Sopenharmony_ciprint("rel error:", accurateinfnorm(1-poly(x)/f(x), [a;b], 30)); 33bbbf1280Sopenharmony_ciprint("in [",a,b,"]"); 34bbbf1280Sopenharmony_ciprint("coeffs:"); 35bbbf1280Sopenharmony_cifor i from 0 to deg do coeff(poly,i); 36