twz-point.c

//  twz-point.c
//  Author: Peter Meyer
//  Calculate the value of the timewave at a point.
//  Last mod.: 1998-01-05

// Ported to Linux
// John A Phelps
// 04 OCT 2009


/*

This is free and unencumbered software released into the public domain.

Anyone is free to copy, modify, publish, use, compile, sell, or
distribute this software, either in source code form or as a compiled
binary, for any purpose, commercial or non-commercial, and by any
means.

In jurisdictions that recognize copyright laws, the author or authors
of this software dedicate any and all copyright interest in the
software to the public domain. We make this dedication for the benefit
of the public at large and to the detriment of our heirs and
successors. We intend this dedication to be an overt act of
relinquishment in perpetuity of all present and future rights to this
software under copyright law.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR
OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
OTHER DEALINGS IN THE SOFTWARE.

For more information, please refer to <http://unlicense.org/>

09 Dec 2012
*/

#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <string.h>


#define FALSE 0
#define TRUE  1
#define NUM_POWERS 64
#define PREC 16 // long double (80 bit) numbers have about 16 significant digits  INTEL / AMD / x86_64
//#define PREC 32 // long double (128 bit) numbers have about 32 significant digits (QUAD PRECISION)
#define NUM_SETS 4
#define NUM_DATA_POINTS 384 
#define CALC_PREC       1000000  //  precision in calculation of wave values

long double powers[NUM_POWERS];
//  Powers of (normally) 64.
//  Due to the limitations of double precision
//  floating point arithmetic these values are
//  exact only up to powers[8] for powers of 64.

int64_t wave_factor = 64;   //  default wave factor 
int64_t number_set, stringchar;

char *usage = "\nUse: twz-point dtz1 dtz2 dtz3 ... [wf=nn]."
  "\nwf = wave factor (default 64, range 2-10000)\n";
  
char temp[32];

char *set_name[NUM_SETS] = { "Kelley", "Watkins", "Sheliak", "Huang Ti" };  

//  The number sets.
int64_t w[NUM_SETS][NUM_DATA_POINTS] = 
{
  {
#include "DATA/DATA.TW1" //  half-twist
  },
  { 
#include "DATA/DATA.TW2" //  no half-twist
  },
  { 
#include "DATA/DATA.TW3" //  Sheliak 
  }, 
  { 
#include "DATA/DATA.TW4" //  HuangTi (no half-twist)
  } 
};

void set_powers(void);
long double f(long double x, int64_t number_set);
long double v(long double y, int64_t number_set);
long double mult_power(long double x, int64_t i);
long double div_power(long double x, int64_t i);

/*-----------------------------*/
int main(int argc, char *argv[])
{
long double dtzp;
int64_t i, j, ch;

if ( argc == 1 )
    {
    printf("%s",usage);
    exit(1);
    } 

for ( i=1; i<argc; i++ )
    {
    for( stringchar = 0; argv[i][stringchar]; stringchar++) { argv[i][stringchar] = tolower( argv[i][stringchar] ); }
    if ( !memcmp(argv[i],"wf=",3) )
        {
        wave_factor = atoi(&argv[i][3]);
        if ( wave_factor < 2 || wave_factor > 10000 )
        {
        printf("%s",usage);
        exit(2);
        }
    }
else
    {
    ch = argv[i][0];
    // if ( ! ( ( ch == '.' )
    // || ( (unsigned int)(ch-'0') <= 9 ) ) )
    //    {
    //    printf("%s",usage);
    //    exit(3);
    //    }
    }
}

set_powers();
printf("\nWave factor = %ld\n",wave_factor);

for ( i=1; i<argc; i++ )
    {
    if ( memcmp(argv[i],"wf=",3) )
        {
        dtzp = atof(argv[i]);
        sprintf(temp,"%.*Lf",PREC,dtzp);
        j = strlen(temp) - 1;
        while ( ( temp[j] == '0' ) && j > 0 )
            temp[j--] = 0;
        strcat(temp,"0 day");
        if ( dtzp != 1.0 )
            strcat(temp,"s");
	
	if( dtzp >= 0)
	    printf("\nThe value of the timewave %.*Lf days BEFORE the zero point is\n",PREC, dtzp); 
	else
	    printf("\nThe value of the timewave %.*Lf days AFTER the zero point is\n",PREC, dtzp * -1); 
	
        for ( number_set=0; number_set<NUM_SETS; number_set++ )
            {
            printf("%.*Lf (%s)\n",PREC,f(dtzp,number_set),set_name[number_set]);
            }
    
        }
    }
}

//  wave_factor is a global variable
/*-----------------*/
void set_powers(void)
{
uint64_t j;

/*  put powers[j] = wave_factor^j  */

powers[0] = (long double)1;
for ( j=1; j<NUM_POWERS; j++ )
    powers[j] = wave_factor*powers[j-1];
}

/*  x is number of days to zero date  */
/*--------------*/
long double f(long double x,
         int64_t number_set)
{
register i;
long double sum = 0.0, last_sum = 0.0;

if ( x )
    {
    for ( i=0; x>=powers[i]; i++ )
    sum += mult_power(v(div_power(x,i),number_set),i);

    i = 0;
    do
        {
        if ( ++i > CALC_PREC+2 )
            break;
        last_sum = sum;
        sum += div_power(v(mult_power(x,i),number_set),i);
        } while ( ( sum == 0.0 ) || ( sum > last_sum ) );
    }

/*  dividing by 64^3 gives values consistent with the Apple // version
 *  and provides more convenient y-axis labels
 */
sum = div_power(sum,3);

return ( sum );
}

/*--------------*/
long double v(long double y,
         int64_t number_set)
{ 
int64_t i = (int64_t)(fmod(y,(long double)NUM_DATA_POINTS));
int64_t j = (i+1)%NUM_DATA_POINTS;
long double z = y - floor(y);

return ( z==0.0 ? (long double)w[number_set][i] : 
    ( w[number_set][j] - w[number_set][i] )*z + w[number_set][i] );
}

/*  in order to speed up the calculation, if wave factor = 64
 *  then instead of using multiplication or division operation
 *  we act directly on the floating point representation;
 *  multiplying by 64^i is accomplished by adding i*0x60
 *  to the exponent (the last 2 bytes of the 8-byte representation);
 *  dividing by 64^i is accomplished by subtracting i*0x60
 *  from the exponent
 */

/*-----------------------*/
long double mult_power(long double x,
                  int64_t i)
{
/* Removing this code: Swithing to 64-bit datatypes
int64_t *exponent = (int64_t *)&x + 3;
if ( wave_factor == 64 )
    *exponent += i*0x60; //  measurably faster
else
*/
    x *= powers[i];

return ( x );
}

/*----------------------*/
long double div_power(long double x,
                 int64_t i)
{
/* Removing trick: moving to 64-bit datatypes
int64_t *exponent = (int64_t *)&x + 3;
if ( ( wave_factor == 64 ) && ( *exponent > i*0x60 ) )
    *exponent -= i*0x60;
else
*/
    x /= powers[i];

return ( x );
}