1bbbf1280Sopenharmony_ci// polynomial for approximating e^x 2bbbf1280Sopenharmony_ci// 3bbbf1280Sopenharmony_ci// Copyright (c) 2019, Arm Limited. 4bbbf1280Sopenharmony_ci// SPDX-License-Identifier: MIT 5bbbf1280Sopenharmony_ci 6bbbf1280Sopenharmony_cideg = 5; // poly degree 7bbbf1280Sopenharmony_ciN = 128; // table entries 8bbbf1280Sopenharmony_cib = log(2)/(2*N); // interval 9bbbf1280Sopenharmony_cib = b + b*0x1p-16; // increase interval for non-nearest rounding (TOINT_NARROW) 10bbbf1280Sopenharmony_cia = -b; 11bbbf1280Sopenharmony_ci 12bbbf1280Sopenharmony_ci// find polynomial with minimal abs error 13bbbf1280Sopenharmony_ci 14bbbf1280Sopenharmony_ci// return p that minimizes |exp(x) - poly(x) - x^d*p(x)| 15bbbf1280Sopenharmony_ciapprox = proc(poly,d) { 16bbbf1280Sopenharmony_ci return remez(exp(x)-poly(x), deg-d, [a;b], x^d, 1e-10); 17bbbf1280Sopenharmony_ci}; 18bbbf1280Sopenharmony_ci 19bbbf1280Sopenharmony_ci// first 2 coeffs are fixed, iteratively find optimal double prec coeffs 20bbbf1280Sopenharmony_cipoly = 1 + 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("rel error:", accurateinfnorm(1-poly(x)/exp(x), [a;b], 30)); 28bbbf1280Sopenharmony_ciprint("abs error:", accurateinfnorm(exp(x)-poly(x), [a;b], 30)); 29bbbf1280Sopenharmony_ciprint("in [",a,b,"]"); 30bbbf1280Sopenharmony_ci// double interval error for non-nearest rounding 31bbbf1280Sopenharmony_ciprint("rel2 error:", accurateinfnorm(1-poly(x)/exp(x), [2*a;2*b], 30)); 32bbbf1280Sopenharmony_ciprint("abs2 error:", accurateinfnorm(exp(x)-poly(x), [2*a;2*b], 30)); 33bbbf1280Sopenharmony_ciprint("in [",2*a,2*b,"]"); 34bbbf1280Sopenharmony_ciprint("coeffs:"); 35bbbf1280Sopenharmony_cifor i from 0 to deg do coeff(poly,i); 36