// polynomial for approximating log(1+x) in double precision
//
// Copyright (c) 2022-2023, Arm Limited.
// SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception

deg = 20;

a = sqrt(2)/2-1;
b = sqrt(2)-1;

f = proc(y) {
  return log(1+y);
};

approx = proc(poly, d) {
  return remez(1 - poly(x)/f(x), deg-d, [a;b], x^d/f(x), 1e-10);
};

poly = x;
for i from 2 to deg do {
  p = roundcoefficients(approx(poly,i), [|D ...|]);
  poly = poly + x^i*coeff(p,0);
};


print("coeffs:");
display = hexadecimal;
for i from 2 to deg do coeff(poly,i);
print("rel error:", accurateinfnorm(1-poly(x)/f(x), [a;b], 30));
print("in [",a,b,"]");