1*412f47f9SXin Li// polynomial for approximating sinpi(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 Lideg = 19; // polynomial degree 7*412f47f9SXin Lia = -1/2; // interval 8*412f47f9SXin Lib = 1/2; 9*412f47f9SXin Li 10*412f47f9SXin Li// find even polynomial with minimal abs error compared to sinpi(x) 11*412f47f9SXin Li 12*412f47f9SXin Li// f = sin(pi* x); 13*412f47f9SXin Lif = pi*x; 14*412f47f9SXin Lic = 1; 15*412f47f9SXin Lifor i from 1 to 80 do { c = 2*i*(2*i + 1)*c; f = f + (-1)^i*(pi*x)^(2*i+1)/c; }; 16*412f47f9SXin Li 17*412f47f9SXin Li// return p that minimizes |f(x) - poly(x) - x^d*p(x)| 18*412f47f9SXin Liapprox = proc(poly,d) { 19*412f47f9SXin Li return remez(f(x)-poly(x), deg-d, [a;b], x^d, 1e-10); 20*412f47f9SXin Li}; 21*412f47f9SXin Li 22*412f47f9SXin Li// first coeff is predefine, iteratively find optimal double prec coeffs 23*412f47f9SXin Lipoly = pi*x; 24*412f47f9SXin Lifor i from 0 to (deg-1)/2 do { 25*412f47f9SXin Li p = roundcoefficients(approx(poly,2*i+1), [|D ...|]); 26*412f47f9SXin Li poly = poly + x^(2*i+1)*coeff(p,0); 27*412f47f9SXin Li}; 28*412f47f9SXin Li 29*412f47f9SXin Lidisplay = hexadecimal; 30*412f47f9SXin Liprint("abs error:", accurateinfnorm(sin(pi*x)-poly(x), [a;b], 30)); 31*412f47f9SXin Liprint("in [",a,b,"]"); 32*412f47f9SXin Liprint("coeffs:"); 33*412f47f9SXin Lifor i from 0 to deg do coeff(poly,i); 34