1// polynomial for approximating e^x 2// 3// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. 4// See https://llvm.org/LICENSE.txt for license information. 5// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception 6 7deg = 4; // poly degree 8N = 128; // table entries 9b = log(2)/(2*N); // interval 10a = -b; 11 12// find polynomial with minimal abs error 13 14// return p that minimizes |exp(x) - poly(x) - x^d*p(x)| 15approx = proc(poly,d) { 16 return remez(exp(x)-poly(x), deg-d, [a;b], x^d, 1e-10); 17}; 18 19// first 2 coeffs are fixed, iteratively find optimal double prec coeffs 20poly = 1 + x; 21for i from 2 to deg do { 22 p = roundcoefficients(approx(poly,i), [|D ...|]); 23 poly = poly + x^i*coeff(p,0); 24}; 25 26display = hexadecimal; 27print("rel error:", accurateinfnorm(1-poly(x)/exp(x), [a;b], 30)); 28print("abs error:", accurateinfnorm(exp(x)-poly(x), [a;b], 30)); 29print("in [",a,b,"]"); 30print("coeffs:"); 31for i from 0 to deg do coeff(poly,i); 32