1*412f47f9SXin Li// polynomial for approximating asinh(x) 2*412f47f9SXin Li// 3*412f47f9SXin Li// Copyright (c) 2022-2023, Arm Limited. 4*412f47f9SXin Li// SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 5*412f47f9SXin Li 6*412f47f9SXin Li// Polynomial is used in [2^-26, 1]. However it is least accurate close to 1, so 7*412f47f9SXin Li// we use 2^-6 as the lower bound for coeff generation, which yields sufficiently 8*412f47f9SXin Li// accurate results in [2^-26, 2^-6]. 9*412f47f9SXin Lia = 0x1p-6; 10*412f47f9SXin Lib = 1.0; 11*412f47f9SXin Li 12*412f47f9SXin Lif = (asinh(sqrt(x)) - sqrt(x))/x^(3/2); 13*412f47f9SXin Li 14*412f47f9SXin Liapprox = proc(poly, d) { 15*412f47f9SXin Li return remez(1 - poly(x)/f(x), deg-d, [a;b], x^d/f(x), 1e-10); 16*412f47f9SXin Li}; 17*412f47f9SXin Li 18*412f47f9SXin Lipoly = 0; 19*412f47f9SXin Lifor i from 0 to deg do { 20*412f47f9SXin Li i; 21*412f47f9SXin Li p = roundcoefficients(approx(poly,i), [|D ...|]); 22*412f47f9SXin Li poly = poly + x^i*coeff(p,0); 23*412f47f9SXin Li}; 24*412f47f9SXin Li 25*412f47f9SXin Li 26*412f47f9SXin Lidisplay = hexadecimal; 27*412f47f9SXin Liprint("coeffs:"); 28*412f47f9SXin Lifor i from 0 to deg do coeff(poly,i); 29