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

f = asin(x);
dtype = single;

a = 0x1p-24;
b = 0.25;

deg = 4;

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

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

approx = proc(poly, d) {
  return remez(1 - poly(x) / forward(f, x), deg - d, [a;b], x^d/forward(f, x), 1e-16);
};

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

display = hexadecimal!;
print("rel error:", accurateinfnorm(1-backward(poly, x)/f(x), [a;b], 30));
print("in [", a, b, "]");
for i from 0 to deg do print(coeff(poly, i));