asinh.sollya

// polynomial for approximating asinh(x)
//
// Copyright (c) 2022-2024, Arm Limited.
// SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception

// Polynomial is used in [2^-26, 1]. However it is least accurate close to 1, so
// we use 2^-6 as the lower bound for coeff generation, which yields sufficiently
// accurate results in [2^-26, 2^-6].
a = 0x1p-6;
b = 1.0;

f = (asinh(sqrt(x)) - sqrt(x))/x^(3/2);

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

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


display = hexadecimal;
print("coeffs:");
for i from 0 to deg do coeff(poly,i);