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