/**
* @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/dapxsumkbn2.h"
#include "stdlib/blas/base/shared.h"
#include "stdlib/strided/base/stride2offset.h"
#include "stdlib/math/base/special/abs.h"

/**
* Adds a scalar constant to each double-precision floating-point strided array element and computes the sum using a second-order iterative Kahan–Babuška algorithm.
*
* ## Method
*
* -   This implementation uses a second-order iterative Kahan–Babuška algorithm, as described by Klein (2005).
*
* ## References
*
* -   Klein, Andreas. 2005. "A Generalized Kahan-Babuška-Summation-Algorithm." _Computing_ 76 (3): 279–93. doi:[10.1007/s00607-005-0139-x](https://doi.org/10.1007/s00607-005-0139-x).
*
* @param N        number of indexed elements
* @param alpha    scalar constant
* @param X        input array
* @param strideX  stride length
* @return         output value
*/
double API_SUFFIX(stdlib_strided_dapxsumkbn2)( const CBLAS_INT N, const double alpha, const double *X, const CBLAS_INT strideX ) {
	CBLAS_INT ox = stdlib_strided_stride2offset( N, strideX );
	return API_SUFFIX(stdlib_strided_dapxsumkbn2_ndarray)( N, alpha, X, strideX, ox );
}

/**
* Adds a scalar constant to each double-precision floating-point strided array element and computes the sum using a second-order iterative Kahan–Babuška algorithm and alternative indexing semantics.
*
* ## Method
*
* -   This implementation uses a second-order iterative Kahan–Babuška algorithm, as described by Klein (2005).
*
* ## References
*
* -   Klein, Andreas. 2005. "A Generalized Kahan-Babuška-Summation-Algorithm." _Computing_ 76 (3): 279–93. doi:[10.1007/s00607-005-0139-x](https://doi.org/10.1007/s00607-005-0139-x).*
*
* @param N        number of indexed elements
* @param alpha    scalar constant
* @param X        input array
* @param strideX  index increment
* @param offsetX  starting index
* @return         output value
*/
double stdlib_strided_dapxsumkbn2_ndarray( const CBLAS_INT N, const double alpha, const double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX  ) {
	double sum;
	double ccs;
	CBLAS_INT ix;
	CBLAS_INT i;
	double cs;
	double cc;
	double v;
	double t;
	double c;

	if ( N <= 0 ) {
		return 0.0;
	}
	if ( N == 1 || strideX == 0 ) {
		return alpha + X[ 0 ];
	}
	ix = offsetX;
	sum = 0.0;
	ccs = 0.0; // second order correction term for lost low order bits
	cs = 0.0; // first order correction term for lost low order bits
	for ( i = 0; i < N; i++ ) {
		v = alpha + X[ ix ];
		t = sum + v;
		if ( stdlib_base_abs( sum ) >= stdlib_base_abs( v ) ) {
			c = (sum-t) + v;
		} else {
			c = (v-t) + sum;
		}
		sum = t;
		t = cs + c;
		if ( stdlib_base_abs( cs ) >= stdlib_base_abs( c ) ) {
			cc = (cs-t) + c;
		} else {
			cc = (c-t) + cs;
		}
		cs = t;
		ccs += cc;
		ix += strideX;
	}
	return sum + cs + ccs;
}