1*f3087befSAndrew Turner// polynomial for approximating sinpi(x) 2*f3087befSAndrew Turner// 3*f3087befSAndrew Turner// Copyright (c) 2023-2024, Arm Limited. 4*f3087befSAndrew Turner// SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 5*f3087befSAndrew Turner 6*f3087befSAndrew Turnerdeg = 19; // polynomial degree 7*f3087befSAndrew Turnera = -1/2; // interval 8*f3087befSAndrew Turnerb = 1/2; 9*f3087befSAndrew Turner 10*f3087befSAndrew Turner// find even polynomial with minimal abs error compared to sinpi(x) 11*f3087befSAndrew Turner 12*f3087befSAndrew Turner// f = sin(pi* x); 13*f3087befSAndrew Turnerf = pi*x; 14*f3087befSAndrew Turnerc = 1; 15*f3087befSAndrew Turnerfor i from 1 to 80 do { c = 2*i*(2*i + 1)*c; f = f + (-1)^i*(pi*x)^(2*i+1)/c; }; 16*f3087befSAndrew Turner 17*f3087befSAndrew Turner// return p that minimizes |f(x) - poly(x) - x^d*p(x)| 18*f3087befSAndrew Turnerapprox = proc(poly,d) { 19*f3087befSAndrew Turner return remez(f(x)-poly(x), deg-d, [a;b], x^d, 1e-10); 20*f3087befSAndrew Turner}; 21*f3087befSAndrew Turner 22*f3087befSAndrew Turner// first coeff is predefine, iteratively find optimal double prec coeffs 23*f3087befSAndrew Turnerpoly = pi*x; 24*f3087befSAndrew Turnerfor i from 0 to (deg-1)/2 do { 25*f3087befSAndrew Turner p = roundcoefficients(approx(poly,2*i+1), [|D ...|]); 26*f3087befSAndrew Turner poly = poly + x^(2*i+1)*coeff(p,0); 27*f3087befSAndrew Turner}; 28*f3087befSAndrew Turner 29*f3087befSAndrew Turnerdisplay = hexadecimal; 30*f3087befSAndrew Turnerprint("abs error:", accurateinfnorm(sin(pi*x)-poly(x), [a;b], 30)); 31*f3087befSAndrew Turnerprint("in [",a,b,"]"); 32*f3087befSAndrew Turnerprint("coeffs:"); 33*f3087befSAndrew Turnerfor i from 0 to deg do coeff(poly,i); 34