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

f = asin(x);
dtype = double;

prec=256;

a = 0x1p-106;
b = 0.25;

deg = 11;

backward = proc(poly, d) {
  return d + d ^ 3 * poly(d * d);
};

forward = proc(f, d) {
  return (f(sqrt(d))-sqrt(d))/(d*sqrt(d));
};

poly = fpminimax(forward(f, x), [|0,...,deg|], [|dtype ...|], [a;b], relative, floating);

display = hexadecimal!;
print("rel error:", dirtyinfnorm(1-backward(poly, x)/f(x), [a;b]));
print("in [", a, b, "]");
for i from 0 to deg do print(coeff(poly, i));