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1// polynomial for approximating log(1+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 degree8// interval ~= 1/(2*N), where N is the table entries9a = -0x1.fp-9;10b = 0x1.fp-9;11 12// find log(1+x) polynomial with minimal absolute error13f = log(1+x);14 15// return p that minimizes |f(x) - poly(x) - x^d*p(x)|16approx = proc(poly,d) {17 return remez(f(x) - poly(x), deg-d, [a;b], x^d, 1e-10);18};19 20// first coeff is fixed, iteratively find optimal double prec coeffs21poly = x;22for i from 2 to deg do {23 p = roundcoefficients(approx(poly,i), [|D ...|]);24 poly = poly + x^i*coeff(p,0);25};26 27display = hexadecimal;28print("abs error:", accurateinfnorm(f(x)-poly(x), [a;b], 30));29// relative error computation fails if f(0)==030// g = f(x)/x = log(1+x)/x; using taylor series31g = 0;32for i from 0 to 60 do { g = g + (-x)^i/(i+1); };33print("rel error:", accurateinfnorm(1-poly(x)/x/g(x), [a;b], 30));34print("in [",a,b,"]");35print("coeffs:");36for i from 0 to deg do coeff(poly,i);37