/* 
 * Copyright (C) 2008-2011 Teluu Inc. (http://www.teluu.com)
 * Copyright (C) 2003-2008 Benny Prijono <benny@prijono.org>
 *
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or
 * (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA 
 */

#ifndef __PJ_MATH_H__
#define __PJ_MATH_H__

/**
 * @file math.h
 * @brief Mathematics and Statistics.
 */

#include <pj/string.h>
#include <pj/compat/high_precision.h>

PJ_BEGIN_DECL

/**
 * @defgroup pj_math Mathematics and Statistics
 * @ingroup PJ_MISC
 * @{
 *
 * Provides common mathematics constants and operations, and also standard
 * statistics calculation (min, max, mean, standard deviation). Statistics
 * calculation is done in realtime (statistics state is updated on time each
 * new sample comes).
 */

/**
 * Mathematical constants
 */
/** pi */
#define PJ_PI               3.14159265358979323846      /* pi       */
/** 1/pi */
#define PJ_1_PI             0.318309886183790671538     /* 1/pi     */

/**
 * Mathematical macros
 */
/** Get the absolute value */
#define PJ_ABS(x)       ((x) >  0 ? (x) : -(x))

/** Get the maximum of two values */
#define PJ_MAX(x, y)    ((x) > (y)? (x) : (y))

/** Get the minimum of two values */
#define PJ_MIN(x, y)    ((x) < (y)? (x) : (y))

/**
 * This structure describes statistics state.
 */
typedef struct pj_math_stat
{
    int              n;         /**< number of samples  */
    int              max;       /**< maximum value      */
    int              min;       /**< minimum value      */
    int              last;      /**< last value         */
    int              mean;      /**< mean               */

    /* Private members */
#if PJ_HAS_FLOATING_POINT
    float            fmean_;    /**< mean(floating point) */
#else
    int              mean_res_; /**< mean residue       */
#endif
    pj_highprec_t    m2_;       /**< variance * n       */
} pj_math_stat;

/**
 * Calculate integer square root of an integer.
 *
 * @param i         Integer to be calculated.
 *
 * @return          Square root result.
 */
PJ_INLINE(unsigned) pj_isqrt(unsigned i)
{
    unsigned res = 1, prev;
    
    /* Rough guess, calculate half bit of input */
    prev = i >> 2;
    while (prev) {
        prev >>= 2;
        res <<= 1;
    }

    /* Babilonian method */
    do {
        prev = res;
        res = (prev + i/prev) >> 1;
    } while ((prev+res)>>1 != res);

    return res;
}

/**
 * Initialize statistics state.
 *
 * @param stat      Statistic state.
 */
PJ_INLINE(void) pj_math_stat_init(pj_math_stat *stat)
{
    pj_bzero(stat, sizeof(pj_math_stat));
}

/**
 * Update statistics state as a new sample comes.
 *
 * @param stat      Statistic state.
 * @param val       The new sample data.
 */
PJ_INLINE(void) pj_math_stat_update(pj_math_stat *stat, int val)
{
#if PJ_HAS_FLOATING_POINT
    float            delta;
#else
    int              delta;
#endif

    stat->last = val;
    
    if (stat->n++) {
        if (stat->min > val)
            stat->min = val;
        if (stat->max < val)
            stat->max = val;
    } else {
        stat->min = stat->max = val;
    }

#if PJ_HAS_FLOATING_POINT
    delta = val - stat->fmean_;
    stat->fmean_ += delta/stat->n;
    
    /* Return mean value with 'rounding' */
    stat->mean = (int) (stat->fmean_ + 0.5);

    stat->m2_ += (int)(delta * (val-stat->fmean_));
#else
    delta = val - stat->mean;
    stat->mean += delta/stat->n;
    stat->mean_res_ += delta % stat->n;
    if (stat->mean_res_ >= stat->n) {
        ++stat->mean;
        stat->mean_res_ -= stat->n;
    } else if (stat->mean_res_ <= -stat->n) {
        --stat->mean;
        stat->mean_res_ += stat->n;
    }

    stat->m2_ += delta * (val-stat->mean);
#endif
}

/**
 * Get the standard deviation of specified statistics state.
 *
 * @param stat      Statistic state.
 *
 * @return          The standard deviation.
 */
PJ_INLINE(unsigned) pj_math_stat_get_stddev(const pj_math_stat *stat)
{
    if (stat->n == 0) return 0;
    return (pj_isqrt((unsigned)(stat->m2_/stat->n)));
}

/**
 * Set the standard deviation of statistics state. This is useful when
 * the statistic state is operated in 'read-only' mode as a storage of 
 * statistical data.
 *
 * @param stat      Statistic state.
 *
 * @param dev       The standard deviation.
 */
PJ_INLINE(void) pj_math_stat_set_stddev(pj_math_stat *stat, unsigned dev)
{
    if (stat->n == 0) 
        stat->n = 1;
    stat->m2_ = dev*dev*stat->n;
}

/** @} */

PJ_END_DECL

#endif /* __PJ_MATH_H__ */
