1*412f47f9SXin Li// polynomial for approximating sin(x) 2*412f47f9SXin Li// 3*412f47f9SXin Li// Copyright (c) 2019, Arm Limited. 4*412f47f9SXin Li// SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 5*412f47f9SXin Li 6*412f47f9SXin Lideg = 7; // polynomial degree 7*412f47f9SXin Lia = -pi/4; // interval 8*412f47f9SXin Lib = pi/4; 9*412f47f9SXin Li 10*412f47f9SXin Li// find even polynomial with minimal abs error compared to sin(x)/x 11*412f47f9SXin Li 12*412f47f9SXin Li// account for /x 13*412f47f9SXin Lideg = deg-1; 14*412f47f9SXin Li 15*412f47f9SXin Li// f = sin(x)/x; 16*412f47f9SXin Lif = 1; 17*412f47f9SXin Lic = 1; 18*412f47f9SXin Lifor i from 1 to 60 do { c = 2*i*(2*i + 1)*c; f = f + (-1)^i*x^(2*i)/c; }; 19*412f47f9SXin Li 20*412f47f9SXin Li// return p that minimizes |f(x) - poly(x) - x^d*p(x)| 21*412f47f9SXin Liapprox = proc(poly,d) { 22*412f47f9SXin Li return remez(f(x)-poly(x), deg-d, [a;b], x^d, 1e-10); 23*412f47f9SXin Li}; 24*412f47f9SXin Li 25*412f47f9SXin Li// first coeff is fixed, iteratively find optimal double prec coeffs 26*412f47f9SXin Lipoly = 1; 27*412f47f9SXin Lifor i from 1 to deg/2 do { 28*412f47f9SXin Li p = roundcoefficients(approx(poly,2*i), [|D ...|]); 29*412f47f9SXin Li poly = poly + x^(2*i)*coeff(p,0); 30*412f47f9SXin Li}; 31*412f47f9SXin Li 32*412f47f9SXin Lidisplay = hexadecimal; 33*412f47f9SXin Liprint("rel error:", accurateinfnorm(1-poly(x)/f(x), [a;b], 30)); 34*412f47f9SXin Liprint("abs error:", accurateinfnorm(sin(x)-x*poly(x), [a;b], 30)); 35*412f47f9SXin Liprint("in [",a,b,"]"); 36*412f47f9SXin Liprint("coeffs:"); 37*412f47f9SXin Lifor i from 0 to deg do coeff(poly,i); 38