131914882SAlex Richardson// polynomial for approximating sin(x) 231914882SAlex Richardson// 331914882SAlex Richardson// Copyright (c) 2019, Arm Limited. 4*072a4ba8SAndrew Turner// SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 531914882SAlex Richardson 631914882SAlex Richardsondeg = 7; // polynomial degree 731914882SAlex Richardsona = -pi/4; // interval 831914882SAlex Richardsonb = pi/4; 931914882SAlex Richardson 1031914882SAlex Richardson// find even polynomial with minimal abs error compared to sin(x)/x 1131914882SAlex Richardson 1231914882SAlex Richardson// account for /x 1331914882SAlex Richardsondeg = deg-1; 1431914882SAlex Richardson 1531914882SAlex Richardson// f = sin(x)/x; 1631914882SAlex Richardsonf = 1; 1731914882SAlex Richardsonc = 1; 1831914882SAlex Richardsonfor i from 1 to 60 do { c = 2*i*(2*i + 1)*c; f = f + (-1)^i*x^(2*i)/c; }; 1931914882SAlex Richardson 2031914882SAlex Richardson// return p that minimizes |f(x) - poly(x) - x^d*p(x)| 2131914882SAlex Richardsonapprox = proc(poly,d) { 2231914882SAlex Richardson return remez(f(x)-poly(x), deg-d, [a;b], x^d, 1e-10); 2331914882SAlex Richardson}; 2431914882SAlex Richardson 2531914882SAlex Richardson// first coeff is fixed, iteratively find optimal double prec coeffs 2631914882SAlex Richardsonpoly = 1; 2731914882SAlex Richardsonfor i from 1 to deg/2 do { 2831914882SAlex Richardson p = roundcoefficients(approx(poly,2*i), [|D ...|]); 2931914882SAlex Richardson poly = poly + x^(2*i)*coeff(p,0); 3031914882SAlex Richardson}; 3131914882SAlex Richardson 3231914882SAlex Richardsondisplay = hexadecimal; 3331914882SAlex Richardsonprint("rel error:", accurateinfnorm(1-poly(x)/f(x), [a;b], 30)); 3431914882SAlex Richardsonprint("abs error:", accurateinfnorm(sin(x)-x*poly(x), [a;b], 30)); 3531914882SAlex Richardsonprint("in [",a,b,"]"); 3631914882SAlex Richardsonprint("coeffs:"); 3731914882SAlex Richardsonfor i from 0 to deg do coeff(poly,i); 38