wehub-resource-sync
99 lines
2.8 KiB
C++
99 lines
2.8 KiB
C++
/* ******************************************************************************
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*
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*
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* This program and the accompanying materials are made available under the
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* terms of the Apache License, Version 2.0 which is available at
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* https://www.apache.org/licenses/LICENSE-2.0.
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*
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* See the NOTICE file distributed with this work for additional
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* information regarding copyright ownership.
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
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* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
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* License for the specific language governing permissions and limitations
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* under the License.
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*
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* SPDX-License-Identifier: Apache-2.0
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******************************************************************************/
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//
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// Created by Yurii Shyrma on 12.12.2017.
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//
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#ifndef LIBND4J_ZETA_H
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#define LIBND4J_ZETA_H
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#include <ops/declarable/helpers/helpers.h>
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#include "array/NDArray.h"
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namespace sd {
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namespace ops {
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namespace helpers {
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// calculate the Hurwitz zeta function for arrays
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SD_LIB_HIDDEN void zeta(LaunchContext* context, NDArray& x, NDArray& q, NDArray& output);
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// calculate the Hurwitz zeta function for scalars
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// fast implementation, it is based on Euler-Maclaurin summation formula
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template <typename T>
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SD_LIB_HIDDEN SD_HOST_DEVICE T zetaScalar(const T x, const T q) {
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const T machep = T(1.11022302462515654042e-16);
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// FIXME: @raver119
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// expansion coefficients for Euler-Maclaurin summation formula (2k)! / B2k, where B2k are Bernoulli numbers
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const T coeffZeta[] = {T(12.0),
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T(-720.0),
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T(30240.0),
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T(-1209600.0),
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T(47900160.0),
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T(-1.8924375803183791606e9),
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T(7.47242496e10),
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T(-2.950130727918164224e12),
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T(1.1646782814350067249e14),
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T(-4.5979787224074726105e15),
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T(1.8152105401943546773e17),
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T(-7.1661652561756670113e18)};
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T a, b = T(0.0), k, s, t, w;
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s = math::sd_pow<T, T, T>(q, -x);
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a = q;
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int i = 0;
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while (i < 9 || a <= T(9.0)) {
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i += 1;
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a += T(1.0);
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b = math::sd_pow<T, T, T>(a, -x);
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s += b;
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if (math::sd_abs<T,T>(b / s) < machep) return s;
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}
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w = a;
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s += b * (w / (x - T(1.0)) - T(0.5));
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a = T(1.0);
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k = T(0.0);
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for (i = 0; i < 12; ++i) {
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a *= x + k;
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b /= w;
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t = a * b / coeffZeta[i];
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s += t;
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t = math::sd_abs<T,T>(t / s);
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if (t < machep) return s;
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k += T(1.0);
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a *= x + k;
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b /= w;
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k += T(1.0);
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}
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return s;
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}
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} // namespace helpers
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} // namespace ops
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} // namespace sd
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#endif // LIBND4J_ZETA_H
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