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// polynomial for approximating e^x
//
// Copyright (c) 2019, Arm Limited.
// SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
deg = 4; // poly degree
N = 128; // table entries
b = log(2)/(2*N); // interval
a = -b;
// find polynomial with minimal abs error
// return p that minimizes |exp(x) - poly(x) - x^d*p(x)|
approx = proc(poly,d) {
return remez(exp(x)-poly(x), deg-d, [a;b], x^d, 1e-10);
};
// first 2 coeffs are fixed, iteratively find optimal double prec coeffs
poly = 1 + x;
for i from 2 to deg do {
p = roundcoefficients(approx(poly,i), [|D ...|]);
poly = poly + x^i*coeff(p,0);
};
display = hexadecimal;
print("rel error:", accurateinfnorm(1-poly(x)/exp(x), [a;b], 30));
print("abs error:", accurateinfnorm(exp(x)-poly(x), [a;b], 30));
print("in [",a,b,"]");
print("coeffs:");
for i from 0 to deg do coeff(poly,i);
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