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 = 6; // poly degree 7bbbf1280Sopenharmony_ci// interval ~= 1/(2*N), where N is the table entries 8bbbf1280Sopenharmony_cia = -0x1.fp-9; 9bbbf1280Sopenharmony_cib = 0x1.fp-9; 10bbbf1280Sopenharmony_ci 11bbbf1280Sopenharmony_ci// find log(1+x) polynomial with minimal absolute error 12bbbf1280Sopenharmony_cif = log(1+x); 13bbbf1280Sopenharmony_ci 14bbbf1280Sopenharmony_ci// return p that minimizes |f(x) - poly(x) - x^d*p(x)| 15bbbf1280Sopenharmony_ciapprox = proc(poly,d) { 16bbbf1280Sopenharmony_ci return remez(f(x) - poly(x), deg-d, [a;b], x^d, 1e-10); 17bbbf1280Sopenharmony_ci}; 18bbbf1280Sopenharmony_ci 19bbbf1280Sopenharmony_ci// first coeff is fixed, iteratively find optimal double prec coeffs 20bbbf1280Sopenharmony_cipoly = x; 21bbbf1280Sopenharmony_cifor i from 2 to deg do { 22bbbf1280Sopenharmony_ci p = roundcoefficients(approx(poly,i), [|D ...|]); 23bbbf1280Sopenharmony_ci poly = poly + x^i*coeff(p,0); 24bbbf1280Sopenharmony_ci}; 25bbbf1280Sopenharmony_ci 26bbbf1280Sopenharmony_cidisplay = hexadecimal; 27bbbf1280Sopenharmony_ciprint("abs error:", accurateinfnorm(f(x)-poly(x), [a;b], 30)); 28bbbf1280Sopenharmony_ci// relative error computation fails if f(0)==0 29bbbf1280Sopenharmony_ci// g = f(x)/x = log(1+x)/x; using taylor series 30bbbf1280Sopenharmony_cig = 0; 31bbbf1280Sopenharmony_cifor i from 0 to 60 do { g = g + (-x)^i/(i+1); }; 32bbbf1280Sopenharmony_ciprint("rel error:", accurateinfnorm(1-poly(x)/x/g(x), [a;b], 30)); 33bbbf1280Sopenharmony_ciprint("in [",a,b,"]"); 34bbbf1280Sopenharmony_ciprint("coeffs:"); 35bbbf1280Sopenharmony_cifor i from 0 to deg do coeff(poly,i); 36