1// polynomial for approximating log10f(1+x) 2// 3// Copyright (c) 2019-2023, Arm Limited. 4// SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 5 6// Computation of log10f(1+x) will be carried out in double precision 7 8deg = 4; // poly degree 9// [OFF; 2*OFF] is divided in 2^4 intervals with OFF~0.7 10a = -0.04375; 11b = 0.04375; 12 13// find log(1+x)/x polynomial with minimal relative error 14// (minimal relative error polynomial for log(1+x) is the same * x) 15deg = deg-1; // because of /x 16 17// f = log(1+x)/x; using taylor series 18f = 0; 19for i from 0 to 60 do { f = f + (-x)^i/(i+1); }; 20 21// return p that minimizes |f(x) - poly(x) - x^d*p(x)|/|f(x)| 22approx = proc(poly,d) { 23 return remez(1 - poly(x)/f(x), deg-d, [a;b], x^d/f(x), 1e-10); 24}; 25 26// first coeff is fixed, iteratively find optimal double prec coeffs 27poly = 1; 28for i from 1 to deg do { 29 p = roundcoefficients(approx(poly,i), [|D ...|]); 30 poly = poly + x^i*coeff(p,0); 31}; 32 33display = hexadecimal; 34print("rel error:", accurateinfnorm(1-poly(x)/f(x), [a;b], 30)); 35print("in [",a,b,"]"); 36print("coeffs:"); 37for i from 0 to deg do double(coeff(poly,i)); 38