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