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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2023 Klaus Spanderen
This file is part of QuantLib, a free-software/open-source library
for financial quantitative analysts and developers - http://quantlib.org/
QuantLib is free software: you can redistribute it and/or modify it
under the terms of the QuantLib license. You should have received a
copy of the license along with this program; if not, please email
<quantlib-dev@lists.sf.net>. The license is also available online at
<https://www.quantlib.org/license.shtml>.
This program is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the license for more details.
*/
#include <ql/math/expm1.hpp>
#include <ql/math/functional.hpp>
#include <cmath>
namespace QuantLib {
std::complex<Real> expm1(const std::complex<Real>& z) {
if (std::abs(z) < 1.0) {
const Real a = z.real(), b = z.imag();
const Real exp_1 = std::expm1(a);
const Real cos_1 = -2*squared(std::sin(0.5*b));
return std::complex<Real>(
exp_1*cos_1 + exp_1 + cos_1,
std::sin(b)*std::exp(a)
);
}
else {
return std::exp(z)-1.0;
}
}
std::complex<Real> log1p(const std::complex<Real>& z) {
const Real a = z.real(), b = z.imag();
if (std::abs(a) < 0.5 && std::abs(b) < 0.5) {
return std::complex<Real>(
0.5*std::log1p(a*a + 2*a + b*b),
std::arg(1.0 + z)
);
}
else {
return std::log(1.0+z);
}
}
}
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