/**
* @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/snanmeanpn.h"
#include <stdint.h>

/**
* Computes the arithmetic mean of a single-precision floating-point strided array, ignoring `NaN` values and 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_snanmeanpn( const int64_t N, const float *X, const int64_t stride ) {
	int64_t ix;
	int64_t i;
	int64_t n;
	int64_t o;
	double dn;
	float s;
	float t;
	float v;

	if ( N <= 0 ) {
		return 0.0f / 0.0f; // NaN
	}
	if ( N == 1 || stride == 0 ) {
		return X[ 0 ];
	}
	if ( stride < 0 ) {
		ix = (1-N) * stride;
	} else {
		ix = 0;
	}
	o = ix;

	// Compute an estimate for the mean...
	s = 0.0f;
	n = 0;
	for ( i = 0; i < N; i++ ) {
		v = X[ ix ];
		if ( v == v ) {
			s += v;
			n += 1;
		}
		ix += stride;
	}
	if ( n == 0 ) {
		return 0.0f / 0.0f; // NaN
	}
	dn = (double)n;
	s = (double)s / dn;

	// Compute an error term...
	t = 0.0f;
	ix = o;
	for ( i = 0; i < N; i++ ) {
		v = X[ ix ];
		if ( v == v ) {
			t += v - s;
		}
		ix += stride;
	}
	return s + (float)((double)t/dn);
}