// polynomial for approximating asinh(x)
//
// Copyright (c) 2022-2023, Arm Limited.
// SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception

deg = 9;

a = 0x1.0p-12;
b = 1.0;

f = proc(y) {
  return asinh(x);
};

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), [|SG ...|]);
  poly = poly + x^i*coeff(p,0);
};

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