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1// polynomial for approximating 2^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 7// exp2f parameters8deg = 3; // poly degree9N = 32; // table entries10b = 1/(2*N); // interval11a = -b;12 13//// exp2 parameters14//deg = 5; // poly degree15//N = 128; // table entries16//b = 1/(2*N); // interval17//a = -b;18 19// find polynomial with minimal relative error20 21f = 2^x;22 23// return p that minimizes |f(x) - poly(x) - x^d*p(x)|/|f(x)|24approx = proc(poly,d) {25 return remez(1 - poly(x)/f(x), deg-d, [a;b], x^d/f(x), 1e-10);26};27// return p that minimizes |f(x) - poly(x) - x^d*p(x)|28approx_abs = proc(poly,d) {29 return remez(f(x) - poly(x), deg-d, [a;b], x^d, 1e-10);30};31 32// first coeff is fixed, iteratively find optimal double prec coeffs33poly = 1;34for i from 1 to deg do {35 p = roundcoefficients(approx(poly,i), [|D ...|]);36// p = roundcoefficients(approx_abs(poly,i), [|D ...|]);37 poly = poly + x^i*coeff(p,0);38};39 40display = hexadecimal;41print("rel error:", accurateinfnorm(1-poly(x)/2^x, [a;b], 30));42print("abs error:", accurateinfnorm(2^x-poly(x), [a;b], 30));43print("in [",a,b,"]");44// double interval error for non-nearest rounding:45print("rel2 error:", accurateinfnorm(1-poly(x)/2^x, [2*a;2*b], 30));46print("abs2 error:", accurateinfnorm(2^x-poly(x), [2*a;2*b], 30));47print("in [",2*a,2*b,"]");48print("coeffs:");49for i from 0 to deg do coeff(poly,i);50