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1// polynomial used for __v_log(x)2//3// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.4// See https://llvm.org/LICENSE.txt for license information.5// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception6 7deg = 6; // poly degree8a = -0x1.fc1p-9;9b = 0x1.009p-8;10 11// find log(1+x)/x polynomial with minimal relative error12// (minimal relative error polynomial for log(1+x) is the same * x)13deg = deg-1; // because of /x14 15// f = log(1+x)/x; using taylor series16f = 0;17for i from 0 to 60 do { f = f + (-x)^i/(i+1); };18 19// return p that minimizes |f(x) - poly(x) - x^d*p(x)|/|f(x)|20approx = proc(poly,d) {21 return remez(1 - poly(x)/f(x), deg-d, [a;b], x^d/f(x), 1e-10);22};23 24// first coeff is fixed, iteratively find optimal double prec coeffs25poly = 1;26for i from 1 to deg do {27 p = roundcoefficients(approx(poly,i), [|D ...|]);28 poly = poly + x^i*coeff(p,0);29};30 31display = hexadecimal;32print("rel error:", accurateinfnorm(1-poly(x)/f(x), [a;b], 30));33print("in [",a,b,"]");34print("coeffs:");35for i from 0 to deg do coeff(poly,i);36