/**
* @license Apache-2.0
*
* Copyright (c) 2020 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
*    http://www.apache.org/licenses/LICENSE-2.0
*
* 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.
*/

#include "stdlib/blas/ext/base/dcusumpw.h"
#include "stdlib/strided/base/stride2offset.h"
#include "stdlib/blas/base/shared.h"

/**
* Computes the cumulative sum of double-precision floating-point strided array elements using pairwise summation.
*
* @param N        number of indexed elements
* @param sum      initial sum
* @param X        input array
* @param strideX  X stride length
* @param Y        output array
* @param strideY  Y stride length
*/
void API_SUFFIX(stdlib_strided_dcusumpw)( const CBLAS_INT N, const double sum, const double *X, const CBLAS_INT strideX, double *Y, const CBLAS_INT strideY ) {
	const CBLAS_INT ox = stdlib_strided_stride2offset( N, strideX );
	const CBLAS_INT oy = stdlib_strided_stride2offset( N, strideY );
	API_SUFFIX(stdlib_strided_dcusumpw_ndarray)( N, sum, X, strideX, ox, Y, strideY, oy );
}

/**
* Computes the cumulative sum of double-precision floating-point strided array elements using pairwise summation and indexing semantics.
*
* ## Method
*
* -   This implementation uses pairwise summation, which accrues rounding error `O(log2 N)` instead of `O(N)`. The recursion depth is also `O(log2 N)`.
*
* ## References
*
* -   Higham, Nicholas J. 1993. "The Accuracy of Floating Point Summation." _SIAM Journal on Scientific Computing_ 14 (4): 783–99. doi:[10.1137/0914050](https://doi.org/10.1137/0914050).
*
* @param N        number of indexed elements
* @param sum      initial sum
* @param X        input array
* @param strideX  X index increment
* @param offsetX  X starting index
* @param Y        output array
* @param strideY  Y index increment
* @param offsetY  Y starting index
*/
void API_SUFFIX(stdlib_strided_dcusumpw_ndarray)( const CBLAS_INT N, const double sum, const double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, double *Y, const CBLAS_INT strideY, const CBLAS_INT offsetY ) {
	CBLAS_INT ix;
	CBLAS_INT iy;
	CBLAS_INT i;
	CBLAS_INT n;
	double s;

	if ( N <= 0 ) {
		return;
	}
	ix = offsetX;
	iy = offsetY;
	// Blocksize for pairwise summation...
	if ( N <= 128 ) {
		s = 0.0;
		for ( i = 0; i < N; i++ ) {
			s += X[ ix ];
			Y[ iy ] = sum + s;
			ix += strideX;
			iy += strideY;
		}
		return;
	}
	n = N / 2;
	API_SUFFIX(stdlib_strided_dcusumpw_ndarray)( n, sum, X, strideX, ix, Y, strideY, iy );
	iy += (n-1) * strideY;
	API_SUFFIX(stdlib_strided_dcusumpw_ndarray)( N-n, Y[ iy ], X, strideX, ix+(n*strideX), Y, strideY, iy+strideY );
	return;
}