/**
* @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/stats/base/smeanpn.h"
#include "stdlib/blas/ext/base/ssumpw.h"
#include "stdlib/blas/ext/base/sapxsumpw.h"
#include <stdint.h>

/**
* Computes the arithmetic mean of a single-precision floating-point strided array using a two-pass error correction algorithm.
*
* ## Method
*
* -   This implementation uses a two-pass approach, as suggested by Neely (1966).
*
* ## References
*
* -   Neely, Peter M. 1966. "Comparison of Several Algorithms for Computation of Means, Standard Deviations and Correlation Coefficients." _Communications of the ACM_ 9 (7). Association for Computing Machinery: 496–99. doi:[10.1145/365719.365958](https://doi.org/10.1145/365719.365958).
* -   Schubert, Erich, and Michael Gertz. 2018. "Numerically Stable Parallel Computation of (Co-)Variance." In _Proceedings of the 30th International Conference on Scientific and Statistical Database Management_. New York, NY, USA: Association for Computing Machinery. doi:[10.1145/3221269.3223036](https://doi.org/10.1145/3221269.3223036).
*
* @param N       number of indexed elements
* @param X       input array
* @param stride  stride length
* @return        output value
*/
float stdlib_strided_smeanpn( const int64_t N, const float *X, const int64_t stride ) {
	double dN;
	float mu;
	float c;

	if ( N <= 0 ) {
		return 0.0 / 0.0; // NaN
	}
	if ( N == 1 || stride == 0 ) {
		return X[ 0 ];
	}
	dN = (double)N;

	// Compute an estimate for the mean:
	mu = (double)stdlib_strided_ssumpw( N, X, stride ) / dN;

	// Compute an error term:
	c = (double)stdlib_strided_sapxsumpw( N, -mu, X, stride ) / dN;

	return mu + c;
}