/*
* ******************************************************************************
* *
* *
* * This program and the accompanying materials are made available under the
* * terms of the Apache License, Version 2.0 which is available at
* * https://www.apache.org/licenses/LICENSE-2.0.
* *
* * See the NOTICE file distributed with this work for additional
* * information regarding copyright ownership.
* * Unless required by applicable law or agreed to in writing, software
* * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
* * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
* * License for the specific language governing permissions and limitations
* * under the License.
* *
* * SPDX-License-Identifier: Apache-2.0
* *****************************************************************************
*/
//
// @author Yurii Shyrma (iuriish@yahoo.com)
//
#include<cmath>
#include <array/DataTypeUtils.h>
#include<ops/declarable/helpers/betaInc.h>
#include <helpers/PointersManager.h>
namespace sd {
namespace ops {
namespace helpers {
///////////////////////////////////////////////////////////////////
// modified Lentz’s algorithm for continued fractions,
// reference: Lentz, W.J. 1976, “Generating Bessel Functions in Mie Scattering Calculations Using Continued Fractions,”
template <typename T>
__device__ T continuedFractionCuda(const T a, const T b, const T x) {
extern __shared__ unsigned char shmem[];
T* coeffs = reinterpret_cast<T*>(shmem);
const T min = DataTypeUtils::min<T>() / DataTypeUtils::eps<T>();
const T aPlusb = a + b;
T val, aPlus2i;
T t2 = coeffs[1];
T t1 = coeffs[0];
if(math::nd4j_abs<T>(t1) < min)
t1 = min;
t1 = static_cast<T>(1) / t1;
T result = t1;
for(uint i = 1; i <= maxIter; ++i) {
const uint i2 = 2*i;
aPlus2i = a + static_cast<T>(i2);
// t1
t1 = static_cast<T>(1) + coeffs[i2] * t1;
if(math::nd4j_abs<T>(t1) < min)
t1 = min;
t1 = static_cast<T>(1) / t1;
// t2
t2 = static_cast<T>(1) + coeffs[i2] / t2;
if(math::nd4j_abs<T>(t2) < min)
t2 = min;
// result
result *= t2 * t1;
// t1
t1 = static_cast<T>(1) + coeffs[i2 + 1] * t1;
if(math::nd4j_abs<T>(t1) < min)
t1 = min;
t1 = static_cast<T>(1) / t1;
// t2
t2 = static_cast<T>(1) + coeffs[i2 + 1] / t2;
if(math::nd4j_abs<T>(t2) < min)
t2 = min;
// result
val = t2 * t1;
result *= val;
// condition to stop loop
if(math::nd4j_abs<T>(val - static_cast<T>(1)) <= DataTypeUtils::eps<T>())
return result;
}
return DataTypeUtils::infOrMax<T>(); // no convergence, more iterations is required, return infinity
}
///////////////////////////////////////////////////////////////////
template<typename T>
__global__ void betaIncForArrayCuda(const void* va, const Nd4jLong* aShapeInfo,
const void* vb, const Nd4jLong* bShapeInfo,
const void* vx, const Nd4jLong* xShapeInfo,
void* vz, const Nd4jLong* zShapeInfo) {
extern __shared__ unsigned char shmem[];
T* sharedMem = reinterpret_cast<T*>(shmem);
const Nd4jLong j = blockIdx.x; // one block per each element
T& z = *(reinterpret_cast<T*>(vz) + shape::getIndexOffset(j, zShapeInfo));
__shared__ T a, b, x;
__shared__ bool symmCond;
if (threadIdx.x == 0) {
a = *(reinterpret_cast<const T*>(va) + shape::getIndexOffset(j, aShapeInfo));
b = *(reinterpret_cast<const T*>(vb) + shape::getIndexOffset(j, bShapeInfo));
x = *(reinterpret_cast<const T*>(vx) + shape::getIndexOffset(j, xShapeInfo));
symmCond = x > (a + static_cast<T>(1)) / (a + b + static_cast<T>(2));
if(symmCond) { // swap a and b, x = 1 - x
T temp = a;
a = b;
b = temp;
x = static_cast<T>(1) - x;
}
}
__syncthreads();
// t^{n-1} * (1 - t)^{n-1} is symmetric function with respect to x = 0.5
if(a == b && x == static_cast<T>(0.5)) {
z = static_cast<T>(0.5);
return;
}
if (x == static_cast<T>(0) || x == static_cast<T>(1)) {
z = symmCond ? static_cast<T>(1) - x : x;
return;
}
// calculate two coefficients per thread
if(threadIdx.x != 0) {
const int i = threadIdx.x;
const T aPlus2i = a + 2*i;
sharedMem[2*i] = i * (b - i) * x / ((aPlus2i - static_cast<T>(1)) * aPlus2i);
sharedMem[2*i + 1] = -(a + i) * (a + b + i) * x / ((aPlus2i + static_cast<T>(1)) * aPlus2i);
}
__syncthreads();
if(threadIdx.x == 0) {
const T gammaPart = lgamma(a) + lgamma(b) - lgamma(a + b);
const T front = math::nd4j_exp<T,T>(math::nd4j_log<T, T>(x) * a + math::nd4j_log<T, T>(1.f - x) * b - gammaPart);
sharedMem[0] = static_cast<T>(1) - (a + b) * x / (a + static_cast<T>(1));
sharedMem[1] = static_cast<T>(1);
z = front * continuedFractionCuda(a, b, x) / a;
if(symmCond) // symmetry relation
z = static_cast<T>(1) - z;
}
}
///////////////////////////////////////////////////////////////////
template<typename T>
static void betaIncForArrayCudaLauncher(const int blocksPerGrid, const int threadsPerBlock, const int sharedMem, const cudaStream_t *stream,
const void* va, const Nd4jLong* aShapeInfo,
const void* vb, const Nd4jLong* bShapeInfo,
const void* vx, const Nd4jLong* xShapeInfo,
void* vz, const Nd4jLong* zShapeInfo) {
betaIncForArrayCuda<T><<<blocksPerGrid, threadsPerBlock, sharedMem, *stream>>>(va, aShapeInfo, vb, bShapeInfo, vx, xShapeInfo, vz, zShapeInfo);
}
///////////////////////////////////////////////////////////////////
// overload betaInc for arrays, shapes of a, b and x must be the same !!!
void betaInc(sd::LaunchContext* context, const NDArray& a, const NDArray& b, const NDArray& x, NDArray& output) {
const int threadsPerBlock = maxIter;
const int blocksPerGrid = output.lengthOf();
const int sharedMem = 2 * output.sizeOfT() * threadsPerBlock + 128;
const auto xType = x.dataType();
PointersManager manager(context, "betaInc");
NDArray::prepareSpecialUse({&output}, {&a, &b, &x});
BUILD_SINGLE_SELECTOR(xType, betaIncForArrayCudaLauncher, (blocksPerGrid, threadsPerBlock, sharedMem, context->getCudaStream(), a.specialBuffer(), a.specialShapeInfo(), b.specialBuffer(), b.specialShapeInfo(), x.specialBuffer(), x.specialShapeInfo(), output.specialBuffer(), output.specialShapeInfo()), FLOAT_TYPES);
NDArray::registerSpecialUse({&output}, {&a, &b, &x});
manager.synchronize();
}
}
}
}