//====================================================== file = ztail.c =====
//=  Program to compute positive (one-sided) tail values using Z score      =
//=    - Hardcoded for 95%, 98%, and 99% values                             =
//===========================================================================
//=  Notes:                                                                 =
//=    1) Input from input file "in.dat" to stdin (see example below)       =
//=        * Comments are bounded by "&" characters at the beginning and    =
//=          end of the comment block                                       =
//=    2) Output is to stdout                                               =
//=    3) Minimum number of values should be 30 for a valid result          =
//=    4) Assumes population values, so variance is computed with N         =
//=-------------------------------------------------------------------------=
//= Example "in.dat" file:                                                  =
//=   Input is values 1, 2, 3, ... 30 (one value per line)                  =
//=-------------------------------------------------------------------------=
//= Example output (for above "in.dat"):                                    =
//=   ------------------------------------------------- ztail.c -----       =
//=     Total of 30 value                                                   =
//=       Mean                   = 15.500000                                =
//=       Variance               = 74.916667                                =
//=       95% tail value         = 29.737336                                =
//=       98% tail value         = 33.275680                                =
//=       99% tail value         = 35.635153                                =
//=   ---------------------------------------------------------------       =
//=-------------------------------------------------------------------------=
//=  Build: bcc32 ztail.c                                                   =
//=-------------------------------------------------------------------------=
//=  Execute: ztail < in.dat                                                =
//=-------------------------------------------------------------------------=
//=  Author: Ken Christensen                                                =
//=          University of South Florida                                    =
//=          WWW: http://www.csee.usf.edu/~christen                         =
//=          Email: christen@csee.usf.edu                                   =
//=-------------------------------------------------------------------------=
//=  History: KJC (06/04/18) - Genesis  (from ztest.c)                      =
//===========================================================================
//----- Include files -------------------------------------------------------
#include <stdio.h>                 // Needed for printf()
#include <math.h>                  // Needed for pow() and sqrt()
#include <stdlib.h>                // Needed for exit() and feof()
#include <string.h>                // Needed for strcmp()

//----- Defines -------------------------------------------------------------
#define MAX_VALUES   2000000       // Maximum number of values
#define MIN_VALUES        30       // Minimum number of value (this is 30)
#define Z_SCORE95         1.6449   // Z-score for 95% positive tail value
#define Z_SCORE98         2.0537   // Z-score for 98% postive tail value
#define Z_SCORE99         2.3263   // Z-score for 99% positive tail value

//----- Globals -------------------------------------------------------------
double     X[MAX_VALUES];          // Array of values read from "in.dat"
int        N;                      // Number of values

//----- Function prototypes -------------------------------------------------
void   load_X_array(void);         // Load X array
double compute_mean(void);         // Compute mean
double compute_var(double mean);   // Compute variance

//===========================================================================
//=  Main program                                                           =
//===========================================================================
void main(void)
{
  double   mean;                   // Mean of values
  double   variance;               // Variance of values
  double   tail_value95;           // Computed 95% positive tail value
  double   tail_value98;           // Computed 98% positive tail value
  double   tail_value99;           // Computed 99% positive tail value

  // Load the values into X and determine global variable N
  printf("------------------------------------------------- ztail.c -----\n");
  load_X_array();

  // Make sure than N is at least MIN_VALUES
  if (N < MIN_VALUES)
  {
    printf("*** ERROR - not enough value (minimum is %d) \n", MIN_VALUES);
    exit(1);
  }

  // Compute mean, variance, and tail values for X
  mean = compute_mean();
  variance = compute_var(mean);
  tail_value95 = mean + (Z_SCORE95 * sqrt(variance));
  tail_value98 = mean + (Z_SCORE98 * sqrt(variance));
  tail_value99 = mean + (Z_SCORE99 * sqrt(variance));

  // Output results
  printf("  Total of %d values              \n", N);
  printf("    Mean                    = %f  \n", mean);
  printf("    Variance                = %f  \n", variance);
  printf("    95%% positive tail value = %f \n", tail_value95);
  printf("    98%% positive tail value = %f \n", tail_value98);
  printf("    99%% positive tail value = %f \n", tail_value99);
  printf("---------------------------------------------------------------\n");
}

//===========================================================================
//=  Function to load X array from stdin and determine N                    =
//===========================================================================
void load_X_array(void)
{
  char      temp_string[1024];     // Temporary string variable

  // Read all values into X
  N = 0;
  while(1)
  {
    scanf("%s", temp_string);
    if (feof(stdin)) goto end;

    // This handles a comment bounded by "&" symbols
    while (strcmp(temp_string, "&") == 0)
    {
      do
      {
        scanf("%s", temp_string);
        if (feof(stdin)) goto end;
      } while (strcmp(temp_string, "&") != 0);
      scanf("%s", temp_string);
      if (feof(stdin)) goto end;
    }

    // Enter value in array and increment array index
    X[N] = atof(temp_string);
    N++;

    // Check if MAX_VALUES data values exceeded
    if (N > MAX_VALUES)
    {
      printf("*** ERROR - greater than %ld values \n", MAX_VALUES);
      exit(1);
    }
  }

  // End-of-file escape
  end:

  return;
}

//===========================================================================
//=  Function to compute mean for a series X of N values                    =
//===========================================================================
double compute_mean(void)
{
  double   mean;                 // Computed mean value
  int      i;                    // Loop counter

  // Loop to compute mean
  mean = 0.0;
  for (i=0; i<N; i++)
    mean = mean + (X[i] / N);

  return(mean);
}

//===========================================================================
//=  Function to compute variance for a series X of N values                =
//===========================================================================
double compute_var(double mean)
{
  double   var;                  // Computed variance value
  int      i;                    // Loop counter

  // Loop to compute variance
  var = 0.0;
  for (i=0; i<N; i++)
    var = var + (pow((X[i] - mean), 2.0) / N);

  return(var);
}