1// polynomial for approximating cos(x) 2// 3// Copyright (c) 2023, Arm Limited. 4// SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 5 6// This script only finds the coeffs for cos - see math/aarch64/v_sin.c for sin coeffs 7 8deg = 14; // polynomial degree 9a = -pi/4; // interval 10b = pi/4; 11 12// find even polynomial with minimal abs error compared to cos(x) 13 14f = cos(x); 15 16// return p that minimizes |f(x) - poly(x) - x^d*p(x)| 17approx = proc(poly,d) { 18 return remez(f(x)-poly(x), deg-d, [a;b], x^d, 1e-10); 19}; 20 21// first coeff is fixed, iteratively find optimal double prec coeffs 22poly = 1; 23for i from 1 to deg/2 do { 24 p = roundcoefficients(approx(poly,2*i), [|double ...|]); 25 poly = poly + x^(2*i)*coeff(p,0); 26}; 27 28display = hexadecimal; 29//print("rel error:", accurateinfnorm(1-poly(x)/f(x), [a;b], 30)); 30//print("abs error:", accurateinfnorm(f(x)-poly(x), [a;b], 30)); 31print("in [",a,b,"]"); 32print("coeffs:"); 33for i from 0 to deg do coeff(poly,i); 34