1// polynomial for approximating asinh(x) 2// 3// Copyright (c) 2022-2023, Arm Limited. 4// SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 5 6// Polynomial is used in [2^-26, 1]. However it is least accurate close to 1, so 7// we use 2^-6 as the lower bound for coeff generation, which yields sufficiently 8// accurate results in [2^-26, 2^-6]. 9a = 0x1p-6; 10b = 1.0; 11 12f = (asinh(sqrt(x)) - sqrt(x))/x^(3/2); 13 14approx = proc(poly, d) { 15 return remez(1 - poly(x)/f(x), deg-d, [a;b], x^d/f(x), 1e-10); 16}; 17 18poly = 0; 19for i from 0 to deg do { 20 i; 21 p = roundcoefficients(approx(poly,i), [|D ...|]); 22 poly = poly + x^i*coeff(p,0); 23}; 24 25 26display = hexadecimal; 27print("coeffs:"); 28for i from 0 to deg do coeff(poly,i); 29