1*412f47f9SXin Li// polynomial for approximating e^x 2*412f47f9SXin Li// 3*412f47f9SXin Li// Copyright (c) 2019, Arm Limited. 4*412f47f9SXin Li// SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 5*412f47f9SXin Li 6*412f47f9SXin Lideg = 4; // poly degree 7*412f47f9SXin LiN = 128; // table entries 8*412f47f9SXin Lib = log(2)/(2*N); // interval 9*412f47f9SXin Lia = -b; 10*412f47f9SXin Li 11*412f47f9SXin Li// find polynomial with minimal abs error 12*412f47f9SXin Li 13*412f47f9SXin Li// return p that minimizes |exp(x) - poly(x) - x^d*p(x)| 14*412f47f9SXin Liapprox = proc(poly,d) { 15*412f47f9SXin Li return remez(exp(x)-poly(x), deg-d, [a;b], x^d, 1e-10); 16*412f47f9SXin Li}; 17*412f47f9SXin Li 18*412f47f9SXin Li// first 2 coeffs are fixed, iteratively find optimal double prec coeffs 19*412f47f9SXin Lipoly = 1 + x; 20*412f47f9SXin Lifor i from 2 to deg do { 21*412f47f9SXin Li p = roundcoefficients(approx(poly,i), [|D ...|]); 22*412f47f9SXin Li poly = poly + x^i*coeff(p,0); 23*412f47f9SXin Li}; 24*412f47f9SXin Li 25*412f47f9SXin Lidisplay = hexadecimal; 26*412f47f9SXin Liprint("rel error:", accurateinfnorm(1-poly(x)/exp(x), [a;b], 30)); 27*412f47f9SXin Liprint("abs error:", accurateinfnorm(exp(x)-poly(x), [a;b], 30)); 28*412f47f9SXin Liprint("in [",a,b,"]"); 29*412f47f9SXin Liprint("coeffs:"); 30*412f47f9SXin Lifor i from 0 to deg do coeff(poly,i); 31