1// polynomial used for __v_log2f(x) 2// 3// Copyright (c) 2022-2023, Arm Limited. 4// SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 5 6deg = 9; // poly degree 7a = -1/3; 8b = 1/3; 9 10ln2 = evaluate(log(2),0); 11invln2 = single(1/ln2); 12 13// find log2(1+x)/x polynomial with minimal relative error 14// (minimal relative error polynomial for log2(1+x) is the same * x) 15deg = deg-1; // because of /x 16 17// f = log2(1+x)/x; using taylor series 18f = 0; 19for i from 0 to 60 do { f = f + (-x)^i/(i+1); }; 20f = f * invln2; 21 22// return p that minimizes |f(x) - poly(x) - x^d*p(x)|/|f(x)| 23approx = proc(poly,d) { 24 return remez(1 - poly(x)/f(x), deg-d, [a;b], x^d/f(x), 1e-10); 25}; 26 27// first coeff is fixed, iteratively find optimal double prec coeffs 28poly = invln2; 29for i from 1 to deg do { 30 p = roundcoefficients(approx(poly,i), [|SG ...|]); 31 poly = poly + x^i*coeff(p,0); 32}; 33 34display = hexadecimal; 35print("rel error:", accurateinfnorm(1-poly(x)/f(x), [a;b], 30)); 36print("in [",a,b,"]"); 37print("coeffs:"); 38for i from 0 to deg do coeff(poly,i); 39