1// polynomial for approximating e^x
2//
3// Copyright (c) 2019, Arm Limited.
4// SPDX-License-Identifier: MIT
5
6deg = 4; // poly degree
7N = 128; // table entries
8b = log(2)/(2*N);  // interval
9a = -b;
10
11// find polynomial with minimal abs error
12
13// return p that minimizes |exp(x) - poly(x) - x^d*p(x)|
14approx = proc(poly,d) {
15  return remez(exp(x)-poly(x), deg-d, [a;b], x^d, 1e-10);
16};
17
18// first 2 coeffs are fixed, iteratively find optimal double prec coeffs
19poly = 1 + x;
20for i from 2 to deg do {
21  p = roundcoefficients(approx(poly,i), [|D ...|]);
22  poly = poly + x^i*coeff(p,0);
23};
24
25display = hexadecimal;
26print("rel error:", accurateinfnorm(1-poly(x)/exp(x), [a;b], 30));
27print("abs error:", accurateinfnorm(exp(x)-poly(x), [a;b], 30));
28print("in [",a,b,"]");
29print("coeffs:");
30for i from 0 to deg do coeff(poly,i);
31