1// polynomial for approximating v_log10f(1+x) 2// 3// Copyright (c) 2019-2023, Arm Limited. 4// SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 5 6deg = 9; // poly degree 7// |log10(1+x)| > 0x1p-4 outside the interval 8a = -1/3; 9b = 1/3; 10 11display = hexadecimal; 12print("log10(2) = ", single(log10(2))); 13 14ln10 = evaluate(log(10),0); 15invln10 = single(1/ln10); 16 17// find log10(1+x)/x polynomial with minimal relative error 18// (minimal relative error polynomial for log10(1+x) is the same * x) 19deg = deg-1; // because of /x 20 21// f = log(1+x)/x; using taylor series 22f = 0; 23for i from 0 to 60 do { f = f + (-x)^i/(i+1); }; 24f = f/ln10; 25 26// return p that minimizes |f(x) - poly(x) - x^d*p(x)|/|f(x)| 27approx = proc(poly,d) { 28 return remez(1 - poly(x)/f(x), deg-d, [a;b], x^d/f(x), 1e-10); 29}; 30 31// first coeff is fixed, iteratively find optimal double prec coeffs 32poly = invln10; 33for i from 1 to deg do { 34 p = roundcoefficients(approx(poly,i), [|SG ...|]); 35 poly = poly + x^i*coeff(p,0); 36}; 37display = hexadecimal; 38print("invln10:", invln10); 39print("rel error:", accurateinfnorm(1-poly(x)/f(x), [a;b], 30)); 40print("in [",a,b,"]"); 41print("coeffs:"); 42for i from 0 to deg do single(coeff(poly,i)); 43 44display = decimal; 45print("in [",a,b,"]"); 46