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 = 4; // poly degree
7bbbf1280Sopenharmony_ciN = 128; // table entries
8bbbf1280Sopenharmony_cib = log(2)/(2*N);  // interval
9bbbf1280Sopenharmony_cia = -b;
10bbbf1280Sopenharmony_ci
11bbbf1280Sopenharmony_ci// find polynomial with minimal abs error
12bbbf1280Sopenharmony_ci
13bbbf1280Sopenharmony_ci// return p that minimizes |exp(x) - poly(x) - x^d*p(x)|
14bbbf1280Sopenharmony_ciapprox = proc(poly,d) {
15bbbf1280Sopenharmony_ci  return remez(exp(x)-poly(x), deg-d, [a;b], x^d, 1e-10);
16bbbf1280Sopenharmony_ci};
17bbbf1280Sopenharmony_ci
18bbbf1280Sopenharmony_ci// first 2 coeffs are fixed, iteratively find optimal double prec coeffs
19bbbf1280Sopenharmony_cipoly = 1 + x;
20bbbf1280Sopenharmony_cifor i from 2 to deg do {
21bbbf1280Sopenharmony_ci  p = roundcoefficients(approx(poly,i), [|D ...|]);
22bbbf1280Sopenharmony_ci  poly = poly + x^i*coeff(p,0);
23bbbf1280Sopenharmony_ci};
24bbbf1280Sopenharmony_ci
25bbbf1280Sopenharmony_cidisplay = hexadecimal;
26bbbf1280Sopenharmony_ciprint("rel error:", accurateinfnorm(1-poly(x)/exp(x), [a;b], 30));
27bbbf1280Sopenharmony_ciprint("abs error:", accurateinfnorm(exp(x)-poly(x), [a;b], 30));
28bbbf1280Sopenharmony_ciprint("in [",a,b,"]");
29bbbf1280Sopenharmony_ciprint("coeffs:");
30bbbf1280Sopenharmony_cifor i from 0 to deg do coeff(poly,i);
31