1*412f47f9SXin Li// polynomial for approximating asinf(x) 2*412f47f9SXin Li// 3*412f47f9SXin Li// Copyright (c) 2023, Arm Limited. 4*412f47f9SXin Li// SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 5*412f47f9SXin Li 6*412f47f9SXin Lif = asin(x); 7*412f47f9SXin Lidtype = single; 8*412f47f9SXin Li 9*412f47f9SXin Lia = 0x1p-24; 10*412f47f9SXin Lib = 0.25; 11*412f47f9SXin Li 12*412f47f9SXin Lideg = 4; 13*412f47f9SXin Li 14*412f47f9SXin Libackward = proc(poly, d) { 15*412f47f9SXin Li return d + d ^ 3 * poly(d * d); 16*412f47f9SXin Li}; 17*412f47f9SXin Li 18*412f47f9SXin Liforward = proc(f, d) { 19*412f47f9SXin Li return (f(sqrt(d))-sqrt(d))/(d*sqrt(d)); 20*412f47f9SXin Li}; 21*412f47f9SXin Li 22*412f47f9SXin Liapprox = proc(poly, d) { 23*412f47f9SXin Li return remez(1 - poly(x) / forward(f, x), deg - d, [a;b], x^d/forward(f, x), 1e-16); 24*412f47f9SXin Li}; 25*412f47f9SXin Li 26*412f47f9SXin Lipoly = 0; 27*412f47f9SXin Lifor i from 0 to deg do { 28*412f47f9SXin Li i; 29*412f47f9SXin Li p = roundcoefficients(approx(poly,i), [|dtype ...|]); 30*412f47f9SXin Li poly = poly + x^i*coeff(p,0); 31*412f47f9SXin Li}; 32*412f47f9SXin Li 33*412f47f9SXin Lidisplay = hexadecimal!; 34*412f47f9SXin Liprint("rel error:", accurateinfnorm(1-backward(poly, x)/f(x), [a;b], 30)); 35*412f47f9SXin Liprint("in [", a, b, "]"); 36*412f47f9SXin Lifor i from 0 to deg do print(coeff(poly, i)); 37