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1// polynomial for approximating e^x2//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-exception6 7deg = 4; // poly degree8N = 128; // table entries9b = log(2)/(2*N); // interval10a = -b;11 12// find polynomial with minimal abs error13 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 coeffs20poly = 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