//
//    FILE: Statistic.cpp
//  AUTHOR: Rob dot Tillaart at gmail dot com
//          modified at 0.3 by Gil Ross at physics dot org
// VERSION: 0.4.1
// PURPOSE: Recursive statistical library for Arduino
//
// NOTE: 2011-01-07 Gill Ross
// Rob Tillaart's Statistic library uses one-pass of the data (allowing
// each value to be discarded), but expands the Sum of Squares Differences to
// difference the Sum of Squares and the Average Squared. This is susceptible
// to bit length precision errors with the float type (only 5 or 6 digits
// absolute precision) so for long runs and high ratios of
// the average value to standard deviation the estimate of the
// standard error (deviation) becomes the difference of two large
// numbers and will tend to zero.
//
// For small numbers of iterations and small Average/SE th original code is
// likely to work fine.
// It should also be recognised that for very large samples, questions
// of stability of the sample assume greater importance than the
// correctness of the asymptotic estimators.
//
// This recursive algorithm, which takes slightly more computation per
// iteration is numerically stable.
// It updates the number, mean, max, min and SumOfSquaresDiff each step to
// deliver max min average, population standard error (standard deviation) and
// unbiassed SE.
// -------------
//
// HISTORY:
// 0.1     2010-10-29 initial version
// 0.2     2010-10-29 stripped to minimal functionality
// 0.2.01  2010-10-30
//         added minimim, maximum, unbiased stdev,
//         changed counter to long -> int overflows @32K samples
// 0.3     2011-01-07
//         branched from 0.2.01 version of Rob Tillaart's code
// 0.3.1   2012-11-10 minor edits
// 0.3.2   2012-11-10 minor edits
//         changed count -> unsigned long allows for 2^32 samples
//         added variance()
// 0.3.3   2015-03-07
//         float -> double to support ARM (compiles)
//          moved count() sum() min() max() to .h; for optimizing compiler
// 0.3.4   2017-07-31
//         Refactored const in many places
//         [reverted] double to float on request as float is 99.99% of the cases
//         good enough and float(32 bit) is supported in HW for some processors.
// 0.3.5   2017-09-27
//         Added #include <Arduino.h> to fix uint32_t bug
// 0.4.0   2020-05-13
//         refactor
//         Added flag to switch on the use of stdDev runtime. [idea marc.recksiedl]
// 0.4.1   2020-06-19 fix library.json
//

#include "Statistic.h"

Statistic::Statistic(bool useStdDev)
{
    clear(useStdDev);
}

void Statistic::clear(bool useStdDev)	// useStdDev default true.
{
    _cnt = 0;
    _sum = 0;
    _min = 0;
    _max = 0;
    _useStdDev = useStdDev;
    _ssqdif = 0.0;
    // note not _ssq but sum of square differences
    // which is SUM(from i = 1 to N) of f(i)-_ave_N)**2
}

// adds a new value to the data-set
void Statistic::add(const float value)
{
    if (_cnt == 0)
    {
        _min = value;
        _max = value;
    } else {
        if (value < _min) _min = value;
        else if (value > _max) _max = value;
    }
    _sum += value;
    _cnt++;

    if (_useStdDev && (_cnt > 1))
    {
        float _store = (_sum / _cnt - value);
        _ssqdif = _ssqdif + _cnt * _store * _store / (_cnt - 1);

        // ~10% faster but limits the amount of samples to 65K as _cnt*_cnt overflows
        // float _store = _sum - _cnt * value;
        // _ssqdif = _ssqdif + _store * _store / (_cnt*_cnt - _cnt);
		//
		// solution:  TODO verify
		// _ssqdif = _ssqdif + (_store * _store / _cnt) / (_cnt - 1);
    }
}

// returns the average of the data-set added sofar
float Statistic::average() const
{
    if (_cnt == 0) return NAN; // prevent DIV0 error
    return _sum / _cnt;
}

// Population standard deviation = s = sqrt [ S ( Xi - µ )2 / N ]
// http://www.suite101.com/content/how-is-standard-deviation-used-a99084
float Statistic::variance() const
{
    if (!_useStdDev) return NAN;
    if (_cnt == 0) return NAN; // prevent DIV0 error
    return _ssqdif / _cnt;
}

float Statistic::pop_stdev() const
{
    if (!_useStdDev) return NAN;
    if (_cnt == 0) return NAN; // prevent DIV0 error
    return sqrt( _ssqdif / _cnt);
}

float Statistic::unbiased_stdev() const
{
    if (!_useStdDev) return NAN;
    if (_cnt < 2) return NAN; // prevent DIV0 error
    return sqrt( _ssqdif / (_cnt - 1));
}

// -- END OF FILE --