1*f3087befSAndrew Turner// polynomial for approximating atan(x) and atan2(y, x) 2*f3087befSAndrew Turner// 3*f3087befSAndrew Turner// Copyright (c) 2022-2024, Arm Limited. 4*f3087befSAndrew Turner// SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 5*f3087befSAndrew Turner 6*f3087befSAndrew Turner// atan is odd, so approximate with an odd polynomial: 7*f3087befSAndrew Turner// x + ax^3 + bx^5 + cx^7 + ... 8*f3087befSAndrew Turner// We generate a, b, c, ... such that we can approximate atan(x) by: 9*f3087befSAndrew Turner// x + x^3 * (a + bx^2 + cx^4 + ...) 10*f3087befSAndrew Turner 11*f3087befSAndrew Turner// Assemble monomials 12*f3087befSAndrew Turnerdeg = 20; 13*f3087befSAndrew Turnermons = [|1,...,deg|]; 14*f3087befSAndrew Turnerfor i from 0 to deg-1 do mons[i] = mons[i] * 2 + 1; 15*f3087befSAndrew Turner 16*f3087befSAndrew Turnera = 0x1.0p-1022; 17*f3087befSAndrew Turnerb = 1; 18*f3087befSAndrew Turner 19*f3087befSAndrew Turnerpoly = fpminimax(atan(x)-x, mons, [|double ...|], [a;b]); 20*f3087befSAndrew Turner 21*f3087befSAndrew Turnerdisplay = hexadecimal; 22*f3087befSAndrew Turnerprint("coeffs:"); 23*f3087befSAndrew Turnerfor i from 0 to deg-1 do coeff(poly,mons[i]); 24