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li_recognizer.c

/*
 *  li_recognizer.c
 *
 *    Copyright 2000 Compaq Computer Corporation.
 *    Copying or modifying this code for any purpose is permitted,
 *    provided that this copyright notice is preserved in its entirety
 *    in all copies or modifications.
 *    COMPAQ COMPUTER CORPORATION MAKES NO WARRANTIES, EXPRESSED OR
 *    IMPLIED, AS TO THE USEFULNESS OR CORRECTNESS OF THIS CODE OR
 *
 *
 *  Adapted from cmu_recognizer.c by Jay Kistler.
 *  
 *  Where is the CMU copyright???? Gotta track it down - Jim Gettys
 *
 *  Credit to Dean Rubine, Jim Kempf, and Ari Rapkin.
 */


#include <sys/types.h>
#include <stdio.h>
#include <string.h>
#ifndef ELX
#include <stdlib.h>
#endif
#include <math.h>
#include <locale.h>
#include <hre_internal.h>
#include <setjmp.h>
#include "util.h"
#include "matrix.h"
#include "sc.h"
#include "li_recognizer.h"
#include "li_recognizer_internal.h"


int lidebug = 0;

/*LI Magic Number.*/

#define LI_MAGIC 0xACCBADDD

#define CHECK_LI_MAGIC(_a) \
  ((_a) != NULL && ((li_recognizer*)(_a))->li_magic == LI_MAGIC)


static void lialg_initialize(rClassifier *);
static int lialg_read_classifier_digest(rClassifier *);
static int lialg_canonicalize_examples(rClassifier *);
static char *lialg_recognize_stroke(rClassifier *, point_list *);


char* li_err_msg = NULL;
char _zdebug_flag[128];

#ifndef __ECOS
// This is standard - defined in <stdlib.h>
#define bcopy(s1,s2,n) memcpy(s2,s1,n)
#endif

#if 0 /* was #ifdef mips*/
char *strdup(char* from) {
   char* to;
   int len = strlen(from) + 1;

   /*   to = (char *) safe_malloc( len * sizeof(char) );*/
   to = allocate(len, char);
   memcpy(to, from, len);
   return to;
}
#endif


/*Freeing classifier*/

static void
free_rClassifier(rClassifier* rc);

/*
 * Point List Support
*/

static point_list*
add_example(point_list* l,int npts,pen_point* pts)
{
    pen_point* lpts = make_pen_point_array(npts);
    /*    point_list* p = (point_list*)safe_malloc(sizeof(point_list));*/
    point_list *p = allocate(1, point_list);

    p->npts = npts;
    p->pts = lpts;
    p->next = l;       /*Order doesn't matter, so we stick on end.*/

    /*Copy points.*/

    bcopy(pts,lpts,npts * sizeof(pen_point));

    return(p);
}
    

static void
delete_examples(point_list* l)
{
    point_list* p;

    for( ; l != NULL; l = p ) {
      p = l->next;
      free(l->pts);
      free(l);
    }
}

/*
 * Local functions
 */

/*
 * recognize_internal-Form Vector, use Classifier to classify, return char.
 */

static char*
  recognize_internal(rClassifier* rec,pen_stroke* str,int* rconf)
{
    char *res = NULL;
    point_list *stroke = NULL;

    stroke = add_example(NULL, str->ps_npts, str->ps_pts);
    if (stroke == NULL) return(NULL);

    res = lialg_recognize_stroke(rec, stroke);

    delete_examples(stroke);
    return(res);
}

/*
 * file_path-Construct pathname, check for proper extension.
 */

static int
  file_path(char* dir,char* filename,char* pathname)
{
    char* dot;
    
    /*Check for proper extension on file name.*/
    
    dot = strrchr(filename,'.');
    
    if( dot == NULL ) {
      return(-1);
    }

    /*Determine whether a gesture or character classifier.*/

    if( strcmp(dot,LI_CLASSIFIER_EXTENSION) != 0 ) {
      return(-1);
    }

    /*Concatenate directory and filename into pathname.*/
    
    strcpy(pathname,dir);
    strcat(pathname,"/");
    strcat(pathname,filename);
    
    return(0);
}

/*read_classifier_points-Read points so classifier can be extended.*/

static int 
read_classifier_points(FILE* fd,int nclss,point_list** ex,char** cnames)
{
    int i,j,k;
    char buf[BUFSIZ];
    int nex = 0;
    char* names[MAXSCLASSES];
    point_list* examples[MAXSCLASSES];
    pen_point* pts;
    int npts;

    /*Initialize*/

    for( i = 0; i < MAXSCLASSES; i++ ) {
      names[i] = NULL;
      examples[i] = NULL;
    }

    /*Go thru classes.*/

/* ari */
/* fprintf(stderr, "Classes: [ "); */

    for( k = 0; k < nclss; k++ ) {

      /*Read class name and number of examples.*/
      
      if( fscanf(fd,"%d %s",&nex,buf) != 2 ) {
            printf("%s *FAILED* - line: %d\n", __FUNCTION__, __LINE__);
          goto unallocate;
      }
      
      /*Save class name*/
      
      names[k] = strdup(buf);
/* ari */
/* fprintf(stderr, "%s ", buf); */

      /*Read examples.*/
      
      for( i = 0; i < nex; i++ ) {
          
          /*Read number of points.*/
          
          if( fscanf(fd,"%d",&npts) != 1 ) {
                printf("%s *FAILED* - line: %d\n", __FUNCTION__, __LINE__);
            goto unallocate; /*Boy would I like exceptions!*/
          }
          
          /*Allocate array for points.*/
          
          if( (pts = make_pen_point_array(npts)) == NULL ) {
                printf("%s *FAILED* - line: %d\n", __FUNCTION__, __LINE__);
            goto unallocate;
          }
          
          /*Read in points.*/
          
          for( j = 0; j < npts; j++ ) {
            int x,y;
                int jj;
            if( fscanf(fd,"%d %d",&x,&y) != 2 ) {
                delete_pen_point_array(pts);
                    printf("%s *FAILED* - line: %d\n", __FUNCTION__, __LINE__);
                    printf("class = %d/%d/%s, ex = %d/%d, pt: %d/%d\n", 
                                k, nclss, names[k], i, nex, j, npts);
                    for (jj = 0;  jj < j;  jj++) {
                        printf("pts[%d] = %d/%d\n", jj, pts[jj].x, pts[jj].y);
                    }
                goto unallocate;
            }
            pts[j].x = x;
            pts[j].y = y;
          }
          
          /*Add example*/
          
          if( (examples[k] = add_example(examples[k],npts,pts)) == NULL ) {
            delete_pen_point_array(pts);
                printf("%s *FAILED* - line: %d\n", __FUNCTION__, __LINE__);
            goto unallocate;
          }
          
          delete_pen_point_array(pts);
          
        }
      }

/* ari -- end of list of classes */
/* fprintf(stderr, "]\n"); */

    /*Transfer to recognizer.*/

    bcopy(examples,ex,sizeof(examples));
    bcopy(names,cnames,sizeof(names));

    return(0);

    /*Error. Deallocate memory and return.*/

  unallocate:

    for( ; k >= 0; k-- ) {
      delete_examples(examples[k]);
      free(names[k]);
    }

    error("Error in reading example points from classifier file");
    return(-1);
}

/*read_classifier-Read a classifier file.*/

static int read_classifier(FILE* fd,rClassifier* rc)
{
    sClassifier sc;
    
    li_err_msg = NULL;

    /*Read in classifier file.*/
    
    if( (sc = sRead(fd)) == NULL ) {
      return(-1);
    }
    
    /*Read in the example points, so classifier can be extended.*/

    if( read_classifier_points(fd,sc->nclasses,rc->ex,rc->cnames) != 0 ) {
      sFreeClassifier(sc);
      return(-1);
    }

    /*Transfer sClassifier to the rClassifier*/

    rc->sc = sc;
    
    return(0);
}

/*
 * Extension Functions
*/

/* getClasses and clearState are by Ari */

static int
recognizer_getClasses (recognizer r, char ***list, int *nc)
{
    int i, nclasses;
    li_recognizer* rec;
    sClassifier sc;
    char **ret;

    rec = (li_recognizer*)r->recognizer_specific;

    /*Check for LI recognizer.*/

    if( !CHECK_LI_MAGIC(rec) ) {
      li_err_msg = "Not a LI recognizer";
      return(-1);
    }
    
    sc = rec->li_rc.sc;
    *nc = nclasses = sc->nclasses;
    /*    ret = (char **) safe_malloc (nclasses * sizeof(char*));*/
    ret = allocate(nclasses, char*);

    for (i = 0; i < nclasses; i++) {
      ret[i] = rec->li_rc.cnames[i];   /* only the 1st char of the cname */
    }
    *list = ret;
    return 0;
}

static int
recognizer_clearState (recognizer r)
{
  /*This operation isn't supported by the LI recognizer.*/

  li_err_msg = "Clearing state is not supported by the LI recognizer";

  return(-1);
}

static bool isa_li(recognizer r)
{ return(CHECK_LI_MAGIC(r)); }

static int
recognizer_train(recognizer r,rc* rec_xt,u_int nstrokes,
                pen_stroke* strokes,rec_element* re,
                bool replace_p)
{
  /*This operation isn't supported by the LI recognizer.*/

  li_err_msg = "Training is not supported by the LI recognizer";

  return(-1);
}

int
li_recognizer_get_example (recognizer     r,
                     int            class, 
                     int            instance,
                     char           **name, 
                     pen_point      **points,
                     int            *npts)
{
    li_recognizer   *rec = (li_recognizer*)r->recognizer_specific;
    sClassifier       sc = rec->li_rc.sc;
    point_list        *pl;
    
    if( !CHECK_LI_MAGIC(rec) ) {
      li_err_msg = "Not a LI recognizer";
      return(-1);
    }
    if (class > sc->nclasses)
      return -1;
    pl = rec->li_rc.canonex[class];
    while (instance && pl)
    {
      pl = pl->next;
      instance--;
    }
    if (!pl)
      return -1;
    *name = rec->li_rc.cnames[class];
    *points = pl->pts;
    *npts = pl->npts;
    return 0;
}

/*
 * API Functions
 */


/*li_recognizer_load-Load a classifier file.*/

static int li_recognizer_load(recognizer r,char* dir,char* filename)
{ 
    FILE *fd;
    char* pathname;
    li_recognizer* rec;
    rClassifier* rc;
    
    rec = (li_recognizer*)r->recognizer_specific;

    /*Make sure recognizer's OK*/

    if( !CHECK_LI_MAGIC(rec) ) {
      li_err_msg = "Not a LI recognizer";
      return(-1);
    }

    rc = &(rec->li_rc);

    /*Check parameters.*/

    if( filename == NULL ) {
      li_err_msg = "Invalid parameters";
      return(-1);
    }

    /*We let the directory be null.*/

    if( dir == NULL || (int)strlen(dir) <= 0 ) {
      dir = ".";
    }

    /*Make full pathname and check filename*/

    /* pathname = (char*)safe_malloc(strlen(dir) + strlen(filename) + 2)); */

    pathname = allocate(strlen(dir) + strlen(filename) + 2, char);
    if( file_path(dir,filename,pathname) == -1 ) {
      free(pathname);
      li_err_msg = "Not a LI recognizer classifier file";
      return(-1);
    }

    /* Try to short-circuit the full classifier-file processing. */
    rc->file_name = pathname;
    if (lialg_read_classifier_digest(rc) == 0)
      return(0);
    rc->file_name = NULL;

    /*Open the file*/

    if( (fd = fopen(pathname,"r")) == NULL ) {
      free(pathname);
      li_err_msg = "Can't open classifier file";
/* ari */
      /* fprintf(stderr, "Trying to open %s.\n", pathname); */
      return(-1);

    }

    /*If rClassifier is OK, then delete it first.*/

    if( rc->file_name != NULL ) {
      free_rClassifier(rc);
    }

    /*Read classifier.*/
    
    if( read_classifier(fd,rc) < 0 ) {
      free(pathname);
      return(-1);
    }

    /*Close file.*/

    fclose(fd);

    /*Add classifier name.*/

    rc->file_name = pathname;

    /* Canonicalize examples. */
    if (lialg_canonicalize_examples(rc) != 0) {
      free(pathname);
      rc->file_name = NULL;
      return(-1);
    }

    return(0);
}

/*li_recognizer_save-Save a classifier file.*/

static int li_recognizer_save(recognizer r,char* dir,char* filename)
{ 
  /*This operation isn't supported by the LI recognizer.*/

  li_err_msg = "Saving is not supported by the LI recognizer";

  return(-1);
}

static wordset
li_recognizer_load_dictionary(recognizer rec,char* directory,char* name)
{
  /*This operation isn't supported by the LI recognizer.*/

  li_err_msg = "Dictionaries are not supported by the LI recognizer";

  return(NULL);

}

static int
li_recognizer_save_dictionary(recognizer rec,
                         char* directory,
                         char* name,
                         wordset dict)
{
  /*This operation isn't supported by the LI recognizer.*/

  li_err_msg = "Dictionaries are not supported by the LI recognizer";

  return(-1);

}

static int
li_recognizer_free_dictionary(recognizer rec,wordset dict)
{
  /*This operation isn't supported by the LI recognizer.*/

  li_err_msg = "Dictionaries are not supported by the LI recognizer";

  return(-1);

}

static int
li_recognizer_add_to_dictionary(recognizer rec,letterset* word,wordset dict)
{
  /*This operation isn't supported by the LI recognizer.*/

  li_err_msg = "Dictionaries are not supported by the LI recognizer";

  return(-1);

}

static int
li_recognizer_delete_from_dictionary(recognizer rec,
                              letterset* word,
                              wordset dict)
{
  /*This operation isn't supported by the LI recognizer.*/

  li_err_msg = "Dictionaries are not supported by the LI recognizer";

  return(-1);

}

static char*
li_recognizer_error(recognizer rec)
{
    char* ret = li_err_msg;

    /*Check for LI recognizer.*/

    if( !CHECK_LI_MAGIC(rec->recognizer_specific) ) {
      li_err_msg = "Not a LI recognizer";
      return(NULL);
    }

    li_err_msg = NULL;

    return(ret);
}

static int 
li_recognizer_clear(recognizer r,bool delete_points_p)
{
    li_recognizer* rec; 

    rec = (li_recognizer*)r->recognizer_specific;

    /*Check for LI recognizer.*/

    if( !CHECK_LI_MAGIC(rec) ) {
      li_err_msg = "Not a LI recognizer";
      return(0);
    }
  
    return(0);
}

static int 
li_recognizer_set_context(recognizer r,rc* rec_xt)
{
  /*This operation isn't supported by the LI recognizer.*/

  li_err_msg = "Contexts are not supported by the LI recognizer";

  return(-1);
}

static rc*
li_recognizer_get_context(recognizer r)
{
  /*This operation isn't supported by the LI recognizer.*/

  li_err_msg = "Contexts are not supported by the LI recognizer";

  return(NULL);
}

static int 
li_recognizer_get_buffer(recognizer r, u_int* nstrokes,pen_stroke** strokes)
{
  /*This operation isn't supported by the LI recognizer.*/

  li_err_msg = "Buffer get/set are not supported by the LI recognizer";

  return(-1);
}

static int 
li_recognizer_set_buffer(recognizer r,u_int nstrokes,pen_stroke* strokes)
{
  /*This operation isn't supported by the LI recognizer.*/

  li_err_msg = "Buffer get/set are not supported by the LI recognizer";

  return(-1);
}

static int
li_recognizer_translate(recognizer r,
                   u_int ncs,
                   pen_stroke* tps,
                   bool correlate_p,
                   int* nret,
                   rec_alternative** ret)
{
    char* clss = NULL;
    li_recognizer* rec; 
    int conf;
    rClassifier* rc;
      
    rec = (li_recognizer*)r->recognizer_specific;

    *nret = 0;
    *ret = NULL;

    /*Check for LI recognizer.*/

    if( !CHECK_LI_MAGIC(rec) ) {
      li_err_msg = "Not a LI recognizer";
      return(-1);
    }

   rc = &(rec->li_rc);

    /*Check for valid parameters.*/
    if (ncs < 1) {
      li_err_msg = "Invalid parameters: ncs";
      return(-1);
    }
    if( tps == NULL) {
      li_err_msg = "Invalid parameters: tps";
      return(-1);
    }
    if( nret == NULL) {
      li_err_msg = "Invalid parameters: nret";
      return(-1);
    }
    if( ret == NULL) {
      li_err_msg = "Invalid parameters: ret";
      return(-1);
    }

/*    if( ncs < 1 || tps == NULL || nret == NULL || ret == NULL) {
      li_err_msg = "Invalid parameters";
      return(-1);
    }
*/

    /*Check for null classifier. It must have at least one.*/
/*
    if( rec->li_rc.sc == NULL ) {
      li_err_msg = "No classifier";
      return(-1);
    }
*/

    /*
     * Go through the stroke array and recognize. Since this is a single
     *   stroke recognizer, each stroke is treated as a separate
     *   character or gesture. We allow only characters or gestures
     *   to be recognized at one time, since otherwise, handling
     *   the display of segmentation would be difficult. 
    */
    clss = recognize_internal(rc,tps,&conf);
    if (clss == NULL) {
/*
      li_err_msg = "unrecognized character";
      return(-1);
*/
      *nret = 1;
      return(0);
    }

    /*Return values.*/
    *nret = 1;
    return(*clss);
}


static rec_fn*
li_recognizer_get_extension_functions(recognizer rec)
{
    rec_fn* ret;

    /*Check for LI recognizer.*/

    if( !CHECK_LI_MAGIC(rec->recognizer_specific) ) {
      li_err_msg = "Not a LI recognizer";
      return(NULL);
    }

    ret = make_rec_fn_array(LI_NUM_EX_FNS);

/* ari -- clearState & getClasses are mine */
    ret[LI_GET_CLASSES] = (rec_fn)recognizer_getClasses;
    ret[LI_CLEAR] = (rec_fn)recognizer_clearState;
    ret[LI_ISA_LI] = (rec_fn)isa_li;
    ret[LI_TRAIN] = (rec_fn)recognizer_train;

    return(ret);
}

static char**
li_recognizer_get_gesture_names(recognizer r)
{
  /*This operation isn't supported by the LI recognizer.*/

  li_err_msg = "Gestures are not supported by the LI recognizer";

  return(NULL);
}

static xgesture
li_recognizer_set_gesture_action(recognizer r,
                          char* name,
                          xgesture fn,
                          void* wsinfo)
{
  /*This operation isn't supported by the LI recognizer.*/

  li_err_msg = "Gestures are not supported by the LI recognizer";

  return(NULL);
}

/*
 * Exported Functions
*/

/*RECOGNIZER_INITIALIZE-Initialize the recognizer.*/

/* note from ari:  this expands via pre-processor to
 *
 * recognizer __recognizer_internal_initialize(rec_info* ri)
*/

RECOGNIZER_INITIALIZE(ri)
{
    recognizer r;
    li_recognizer* rec;
    int i;

    /*Check that locale matches.*/

    if( strcmp(ri->ri_locale,LI_SUPPORTED_LOCALE) != 0 ) {
      li_err_msg = "Not a supported locale";
fprintf(stderr, "Locale error.\n");
#if 0
      return(NULL);
#endif
    }

    /*
     * Check that character sets match. Note that this is only approximate,
     * since the classifier file will have more information.
    */

    if( ri->ri_subset != NULL ) {
      for(i = 0; ri->ri_subset[i] != NULL; i++ ) {

      if( strcmp(ri->ri_subset[i],UPPERCASE) != 0 &&
          strcmp(ri->ri_subset[i],LOWERCASE) != 0  &&
          strcmp(ri->ri_subset[i],DIGITS) != 0 &&
          strcmp(ri->ri_subset[i],GESTURE) != 0 ) {
        li_err_msg = "Not a supported character set";
fprintf(stderr, "charset error.\n");

        return(NULL);
      }
      }
    }
           
/* ari */
    r = make_recognizer(ri);
    /*fprintf(stderr, "past make_recognizer.\n");*/

    if( r == NULL ) {
      li_err_msg = "Can't allocate storage";

      return(NULL);
    }

    /*Make a LI recognizer structure.*/


    /* rec = (li_recognizer*)safe_malloc(sizeof(li_recognizer))) == NULL ); */

    rec = allocate(1, li_recognizer);

    r->recognizer_specific = rec;

    rec->li_rc.file_name = NULL;
    rec->li_rc.sc = NULL;

    /*Initialize the recognizer struct.*/

    r->recognizer_load_state = li_recognizer_load;
    r->recognizer_save_state = li_recognizer_save;
    r->recognizer_load_dictionary = li_recognizer_load_dictionary;
    r->recognizer_save_dictionary = li_recognizer_save_dictionary;
    r->recognizer_free_dictionary = li_recognizer_free_dictionary;
    r->recognizer_add_to_dictionary = li_recognizer_add_to_dictionary;
    r->recognizer_delete_from_dictionary = li_recognizer_delete_from_dictionary;
    r->recognizer_error = li_recognizer_error;
    r->recognizer_translate = li_recognizer_translate;
    r->recognizer_get_context = li_recognizer_get_context;
    r->recognizer_set_context = li_recognizer_set_context;
    r->recognizer_get_buffer = li_recognizer_get_buffer;
    r->recognizer_set_buffer = li_recognizer_set_buffer;
    r->recognizer_clear = li_recognizer_clear;
    r->recognizer_get_extension_functions = 
      li_recognizer_get_extension_functions;
    r->recognizer_get_gesture_names = li_recognizer_get_gesture_names;
    r->recognizer_set_gesture_action = 
      li_recognizer_set_gesture_action;

    /*Initialize LI Magic Number.*/

    rec->li_magic = LI_MAGIC;

    /*Initialize rClassifier.*/

    rec->li_rc.file_name = NULL;

    for( i = 0; i < MAXSCLASSES; i++ ) {
      rec->li_rc.ex[i] = NULL;
      rec->li_rc.cnames[i] = NULL;
    }

    lialg_initialize(&rec->li_rc);

    /*Get rid of error message. Not needed here.*/
    li_err_msg = NULL;

    return(r);
}

/*free_rClassifier-Free the rClassifier.*/

static void
free_rClassifier(rClassifier* rc)
{
    int i;

    if( rc->file_name != NULL) {
      free(rc->file_name);
    }

    for( i = 0; rc->ex[i] != NULL; i++) {
      delete_examples(rc->ex[i]);
      free(rc->cnames[i]);
    }

    if(rc->sc != NULL ) {
      sFreeClassifier(rc->sc);
    }
}

/*RECOGNIZER_FINALIZE-Deallocate the recognizer, finalize.*/

RECOGNIZER_FINALIZE(r)
{
    li_recognizer* rec = (li_recognizer*)r->recognizer_specific;

    /*Make sure this is a li_recognizer first*/

    if( !CHECK_LI_MAGIC(rec) ) {
      li_err_msg = "Not a LI recognizer";
      return(-1);
    }

    /*Deallocate rClassifier resources.*/

    free_rClassifier(&(rec->li_rc));

    /*Deallocate the li_recognizer struct.*/

    free(rec);

    /*Deallocate the recognizer*/

    delete_recognizer(r);

    return(0);
}


/* **************************************************

  Implementation of the Li/Yeung recognition algorithm

************************************************** */

/*#include <assert.h>*/
#ifdef __ECOS
#define MAXINT 0x7FFFFFFF
#else
#include <values.h>
#endif
#include <sys/time.h>

#ifdef      __ultrix
/* Ultrix doesn't have these declarations in math.h! */
extern double rint(double);
extern float expf(float);
#endif

#ifdef      ELX
extern double rint (double);
extern float expf (float);    /* N.B.  exp() appears to be broken on ELX! */
#endif

#define     WORST_SCORE MAXINT

/* Dynamic programming parameters */
#define     DP_BAND           3
#define     MIN_SIM           0
#define     MAX_DIST    MAXINT
#define     SIM_THLD    60    /* x 100 */
#define     DIST_THLD   3200  /* x 100 */

/* Low-pass filter parameters -- empirically derived */
#define     LP_FILTER_WIDTH   6
#define     LP_FILTER_ITERS   8
#define     LP_FILTER_THLD    250   /* x 100 */
#define     LP_FILTER_MIN     5

/* Pseudo-extrema parameters -- empirically derived */
#define     PE_AL_THLD  1500  /* x 100 */
#define     PE_ATCR_THLD      135   /* x 100 */

/* Contour-angle derivation parameters */
#define     T_ONE       1
#define     T_TWO       20

/* Pre-processing and canonicalization parameters */
#define     CANONICAL_X 108
#define     CANONICAL_Y 128
#define     DIST_SQ_THRESHOLD   (3*3)     /* copied from fv.h */
#define     NCANONICAL  50

/* Tap-handling parameters */
#define     TAP_CHAR    "."
#define     TAP_TIME_THLD     150       /* msec */
#define     TAP_DIST_THLD     75        /* dx * dx + dy * dy */
#define     TAP_PATHLEN 1000      /* x 100 */


/* Overload the time field of the pen_point struct with the chain-code. */
#define     chaincode   time

/* region types */
#define     RGN_CONVEX  0
#define     RGN_CONCAVE 1
#define     RGN_PLAIN   2
#define     RGN_PSEUDO  3


typedef struct RegionList {
    int start;
    int end;
    int type;
    struct RegionList *next;
} region_list;


/* direction-code table; indexed by dx, dy */
static int lialg_dctbl[3][3] = {{1, 0, 7}, {2, 0x7FFFFFFF, 6}, {3, 4, 5}};

/* low-pass filter weights */
static int lialg_lpfwts[2 * LP_FILTER_WIDTH + 1];
static int lialg_lpfconst = -1;


static int lialg_preprocess_stroke(point_list *);
static point_list *lialg_compute_dominant_points(point_list *);
static point_list *lialg_interpolate_points(point_list *);
static void lialg_bresline(pen_point *, pen_point *, point_list *, int *);
static void lialg_compute_chain_code(point_list *);
static void lialg_compute_unit_chain_code(point_list *);
static region_list *lialg_compute_regions(point_list *);
static point_list *lialg_compute_dompts(point_list *, region_list *);
static int *lialg_compute_contour_angle_set(point_list *, region_list *);
static void lialg_score_stroke(point_list *, point_list *, int *, int *);
static int lialg_compute_similarity(point_list *, point_list *);
static int lialg_compute_distance(point_list *, point_list *);

static int lialg_read_classifier_digest(rClassifier *);

static int lialg_canonicalize_examples(rClassifier *);
static int lialg_canonicalize_example_stroke(point_list *);
static int lialg_compute_equipoints(point_list *);

static int lialg_compute_pathlen(point_list *);
static int lialg_compute_pathlen_subset(point_list *, int, int);
static int lialg_filter_points(point_list *);
static int lialg_translate_points(point_list *, int, int, int, int);
static void lialg_get_bounding_box(point_list *, int *, int *, int *, int *);
static void lialg_compute_lpf_parameters();
static int isqrt(int);
static int likeatan(int, int);
static int quadr(int);


/*************************************************************

  Core routines for the Li/Yeung recognition algorithm

 *************************************************************/

static void lialg_initialize(rClassifier *rec) {
    int i;

    /* Initialize the dompts arrays. */
    for (i = 0; i < MAXSCLASSES; i++) {
      rec->dompts[i] = NULL;
    }
}


/*
 *  Main recognition routine -- called by HRE API.
 */
static char *lialg_recognize_stroke(rClassifier *rec, point_list *stroke) {
    int i;
    char *name = NULL;
    point_list *input_dompts = NULL;
    char *best_name = NULL;
    int best_score = WORST_SCORE;
    char *curr_name;
    point_list *curr_dompts = NULL;
    /*struct timeval stv, etv;
    int     elapsed;*/

    /*    (void)gettimeofday(&stv, NULL);*/

    if (stroke->npts < 1) goto done;

    /* Check for tap. */
    {
/*
      pen_point *startpt = &stroke->pts[0];
      pen_point *endpt = &stroke->pts[stroke->npts - 1];
      int dt = endpt->time - startpt->time;
      int dx = endpt->x - startpt->x;
      int dy = endpt->y - startpt->y;
      int magsq = dx * dx + dy * dy;
*/

      /* First thing is to filter out ``close points.'' */
      if (lialg_filter_points(stroke) != 0) return(NULL);

      /* Unfortunately, we don't have the actual time that each point */
      /* was recorded (i.e., dt is invalid).  Hence, we have to use a */
      /* heuristic based on total distance and the number of points. */
      if (stroke->npts == 1 || lialg_compute_pathlen(stroke) < TAP_PATHLEN)
          return(TAP_CHAR);
    }

    /* Pre-process input stroke. */
    if (lialg_preprocess_stroke(stroke) != 0) goto done;

    /* Compute its dominant points. */
    input_dompts = lialg_compute_dominant_points(stroke);
    if (input_dompts == NULL) goto done;

    /* Score input stroke against every class in classifier. */
    for (i = 0, curr_name = rec->cnames[i], curr_dompts = rec->dompts[i];
        i < MAXSCLASSES && curr_name != NULL && curr_dompts != NULL;
        i++, curr_name = rec->cnames[i], curr_dompts = rec->dompts[i]) {
      int sim;
      int dist;
      int curr_score;

      lialg_score_stroke(input_dompts, curr_dompts, &sim, &dist);
      curr_score = dist;

      if (lidebug && curr_score < DIST_THLD)
          fprintf(stderr, "(%s, %d, %d) ", curr_name, sim, dist);

      /* Is it the best so far? */
      if (curr_score < best_score && curr_score <= DIST_THLD) {
          best_score = curr_score;
          best_name = curr_name;
      }
    }

    if (lidebug)
      fprintf(stderr, "\n");

    /* No errors. */
    name = best_name;

done:
    delete_examples(input_dompts);
    /*    (void)gettimeofday(&etv, NULL);
        elapsed = (1000 * (etv.tv_sec - stv.tv_sec)) + ((etv.tv_usec - stv.tv_usec + 500) / 1000);
        fprintf(stderr, "elapsed = %d\n", elapsed);
     */
    return(name);
}


static int lialg_preprocess_stroke(point_list *points) {
    int minx, miny, maxx, maxy, xrange, yrange, scale, xoff, yoff;

    /* Filter out points that are too close. */
    /* We did this earlier, when we checked for a tap. */
/*
    if (lialg_filter_points(points) != 0) return(-1);
*/

/*    assert(points->npts > 0);*/

    /* Scale up to avoid conversion errors. */
    lialg_get_bounding_box(points, &minx, &miny, &maxx, &maxy);
    xrange = maxx - minx;
    yrange = maxy - miny;
    scale = ( ((100 * xrange + CANONICAL_X / 2) / CANONICAL_X) > 
            ((100 * yrange + CANONICAL_Y / 2) / CANONICAL_Y))
      ? (100 * CANONICAL_X + xrange / 2) / xrange
      : (100 * CANONICAL_Y + yrange / 2) / yrange;
    if (lialg_translate_points(points, minx, miny, scale, scale) != 0)
      return(-1);

    /* Center the stroke. */
    lialg_get_bounding_box(points, &minx, &miny, &maxx, &maxy);
    xrange = maxx - minx;
    yrange = maxy - miny;
    xoff = -((CANONICAL_X - xrange + 1) / 2);
    yoff = -((CANONICAL_Y - yrange + 1) / 2);
    if (lialg_translate_points(points, xoff, yoff, 100, 100) != 0) return(-1);

    /* Store the x and y ranges in the point list. */
    xrange = maxx - minx;
    yrange = maxy - miny;
    points->xrange = xrange;
    points->yrange = yrange;

    if (lidebug) {
      int i;
      fprintf(stderr, "After pre-processing:   %d %d %d %d\n",
            minx, miny, maxx, maxy);
      for (i = 0; i < points->npts; i++)
          fprintf(stderr, "      (%d %d)\n",
                points->pts[i].x, points->pts[i].y);
      fflush(stderr);
    }

    return(0);
}


static point_list *lialg_compute_dominant_points(point_list *points) {
    point_list *ipts = NULL;
    region_list *regions = NULL;
    point_list *dpts = NULL;

    /* Interpolate points. */
    ipts = lialg_interpolate_points(points);
    if (ipts == NULL) return(NULL);
    if (lidebug) {
      int j;
      fprintf(stderr, "After interpolation:  %d ipts\n", ipts->npts);
      for (j = 0; j < ipts->npts; j++) {
          fprintf(stderr, "  (%d, %d), %ld\n",
                ipts->pts[j].x, ipts->pts[j].y, ipts->pts[j].chaincode);
      }
      fflush(stderr);
    }

    /* Compute regions. */
    regions = lialg_compute_regions(ipts);
/*    assert(regions != NULL);*/

    /* Compute dominant points. */
    dpts = lialg_compute_dompts(ipts, regions);
    if (lidebug) {
      int j;
      fprintf(stderr, "Dominant points:  ");
      for (j = 0; j < dpts->npts; j++) {
          fprintf(stderr, "%d %d (%ld)  ",
                dpts->pts[j].x, dpts->pts[j].y, dpts->pts[j].chaincode);
      }
      fprintf(stderr, "\n");
      fflush(stderr);
    }

    /* Delete region data structure. */
    {
      region_list *curr, *next;
      for (curr = regions; curr != NULL; ) {
          next = curr->next;
          free(curr);
          curr = next;
      }
    }
    delete_examples(ipts);
    return(dpts);
}


/* Input points are assumed to be integer-valued! */
static point_list *lialg_interpolate_points(point_list *points) {
    int i, j;
    int maxpts;
    point_list *newpts;

    /* Compute an upper-bound on the number of interpolated points. */
    maxpts = 0;
    for (i = 0; i < (points->npts - 1); i++) {
      pen_point *pta = &(points->pts[i]);
      pen_point *ptb = &(points->pts[i+1]);
      maxpts += abs(pta->x - ptb->x) + abs(pta->y - ptb->y);
    }

    /* Allocate an array of the requisite size. */
    maxpts += points->npts;
    /* newpts = (point_list *)safe_malloc(sizeof(point_list)); */
    newpts = allocate(1, point_list);
    newpts->pts = make_pen_point_array(maxpts);
    if (newpts->pts == NULL) {
      free(newpts);
      return(NULL);
    }
    newpts->npts = maxpts;
    newpts->next = NULL;

    /* Interpolate each of the segments. */
    j = 0;
    for (i = 0; i < (points->npts - 1); i++) {
      pen_point *startpt = &(points->pts[i]);
      pen_point *endpt = &(points->pts[i+1]);

      lialg_bresline(startpt, endpt, newpts, &j);

      j--;  /* end point gets recorded as start point of next segment! */
    }

    /* Add-in last point. */
    newpts->pts[j++] = points->pts[points->npts - 1];
    newpts->npts = j;

    /* Compute the chain code for P (the list of points). */
    lialg_compute_unit_chain_code(newpts);

    return(newpts);
}


/* This implementation is due to Kenny Hoff. */
static void lialg_bresline(pen_point *startpt, pen_point *endpt,
                      point_list *newpts, int *j) {
    int Ax, Ay, Bx, By, dX, dY, Xincr, Yincr;

    Ax = startpt->x;
    Ay = startpt->y;
    Bx = endpt->x;
    By = endpt->y;

    /* INITIALIZE THE COMPONENTS OF THE ALGORITHM THAT ARE NOT AFFECTED */
    /* BY THE SLOPE OR DIRECTION OF THE   LINE */
    dX = abs(Bx-Ax);    /* store the change in X and Y of the line endpoints */
    dY = abs(By-Ay);

    /* DETERMINE "DIRECTIONS" TO INCREMENT X AND Y (REGARDLESS OF DECISION) */
    if (Ax > Bx) { Xincr=-1; } else { Xincr=1; }    /* which direction in X? */
    if (Ay > By) { Yincr=-1; } else { Yincr=1; }    /* which direction in Y? */

    /* DETERMINE INDEPENDENT VARIABLE (ONE THAT ALWAYS INCREMENTS BY 1 (OR -1) ) */
    /* AND INITIATE APPROPRIATE LINE DRAWING ROUTINE (BASED ON FIRST OCTANT */
    /* ALWAYS). THE X AND Y'S MAY BE FLIPPED IF Y IS THE INDEPENDENT VARIABLE. */
    if (dX >= dY) {         /* if X is the independent variable */
      int dPr     = dY<<1;        /* amount to increment decision if right is chosen (always) */
      int dPru = dPr - (dX<<1);   /* amount to increment decision if up is chosen */
      int P =     dPr - dX;       /* decision variable start value */

      /* process each point in the line one at a time (just use dX) */
      for (; dX>=0; dX--) {
          newpts->pts[*j].x = Ax;
          newpts->pts[*j].y = Ay;
          (*j)++;

          if (P > 0) {  /* is the pixel   going right AND   up? */
            Ax+=Xincr;  /* increment independent variable */
            Ay+=Yincr;  /* increment dependent variable */
            P+=dPru;    /* increment decision (for up) */
          }
          else {        /* is the pixel just going right? */
            Ax+=Xincr;  /* increment independent variable */
            P+=dPr;           /* increment decision (for right) */
          }
      }
    }
    else {            /* if Y is the independent variable */
      int dPr     = dX<<1;        /* amount to increment decision if right is chosen (always) */
      int dPru = dPr - (dY<<1);   /* amount to increment decision if up is chosen */
      int P  = dPr - dY;          /* decision variable start value */

      /* process each point in the line one at a time (just use dY) */
      for (; dY>=0; dY--) {
          newpts->pts[*j].x = Ax;
          newpts->pts[*j].y = Ay;
          (*j)++;

          if (P > 0) {  /* is the pixel going up AND right? */
            Ax+=Xincr;  /* increment dependent variable */
            Ay+=Yincr;  /* increment independent variable */
            P+=dPru;    /* increment decision (for up) */
          }
          else {        /* is the pixel just going up? */
            Ay+=Yincr;  /* increment independent variable */
            P+=dPr;           /* increment decision (for right) */
          }
      }
    }
}


static void lialg_compute_chain_code(point_list *pts) {
    int i;

    for (i = 0; i < (pts->npts - 1); i++) {
      pen_point *startpt = &(pts->pts[i]);
      pen_point *endpt = &(pts->pts[i+1]);
      int dx = endpt->x - startpt->x;
      int dy = endpt->y - startpt->y;
/*
      int tmp     = rint(4.0 * atan2((double)dx, (double)dy) / M_PI);
      int dircode = (10 + tmp) % 8;
*/
      int tmp = quadr(likeatan(dy, dx));
      int dircode = (12 - tmp) % 8;

      startpt->chaincode = dircode;
    }
}


static void lialg_compute_unit_chain_code(point_list *pts) {
    int i;

    for (i = 0; i < (pts->npts - 1); i++) {
      pen_point *startpt = &(pts->pts[i]);
      pen_point *endpt = &(pts->pts[i+1]);
      int dx = endpt->x - startpt->x;
      int dy = endpt->y - startpt->y;
      int dircode = lialg_dctbl[dx+1][dy+1];

/*    assert(dircode < 8);*/
      startpt->chaincode = dircode;
    }
}


static region_list *lialg_compute_regions(point_list *pts) {
    region_list *regions = NULL;
    region_list *curr_reg = NULL;
    int *R[2 + LP_FILTER_ITERS];
    int *junk;
    int *curr, *next;
    int i, j;

    /* Initialize low-pass filter parameters if necessary. */
    if (lialg_lpfconst == -1)
      lialg_compute_lpf_parameters();

    /* Allocate a 2 x pts->npts array for use in computing the (filtered) Angle set, A_n. */
    /*    junk = (int *)safe_malloc((2 + LP_FILTER_ITERS) * pts->npts * sizeof(int)); */
    junk = allocate((2 + LP_FILTER_ITERS) * pts->npts, int);
    for (i = 0; i < (2 + LP_FILTER_ITERS); i++)
      R[i] = junk + (i * pts->npts);
    curr = R[0];

    /* Compute the Angle set, A, in the first element of array R. */
    /* Values in R are in degrees, x 100. */
    curr[0] = 18000;                      /* a_0 */
    for (i = 1; i < (pts->npts - 1); i++) {
      int d_i = pts->pts[i].chaincode;
      int d_iminusone = pts->pts[i-1].chaincode;
      int a_i;

      if (d_iminusone < d_i)
          d_iminusone += 8;

      a_i = (d_iminusone - d_i) % 8;

      /* convert to degrees, x 100 */
      curr[i] = ((12 - a_i) % 8) * 45 * 100;
    }
    curr[pts->npts - 1] = 18000;          /* a_L-1 */

    /* Perform a number of filtering iterations. */
    next = R[1];
    for (j = 0; j < LP_FILTER_ITERS; j++, curr = R[j], next = R[j+1]) {
      for (i = 0; i < pts->npts; i++) {
          int k;

          next[i] = 0;

          for (k = i - LP_FILTER_WIDTH; k <= i + LP_FILTER_WIDTH; k++) {
            int oldval = (k < 0 || k >= pts->npts) ? 18000 : curr[k];
            next[i]     += oldval * lialg_lpfwts[k - (i     - LP_FILTER_WIDTH)];    /* overflow? */
          }

          next[i] /= lialg_lpfconst;
      }
    }

    /* Do final thresholding around PI. */
    /* curr and next are set-up correctly at end of previous loop! */
    for (i = 0; i < pts->npts; i++) {
      next[i] = (abs(curr[i] - 18000) < LP_FILTER_THLD)
        ? 18000
        : curr[i];
    }
    curr = next;

    /* Debugging. */
    if (lidebug > 1) {
      for (i = 0; i < pts->npts; i++) {
          fprintf(stderr, "%3d:  (%3d, %3d)  %ld  ",
                i, pts->pts[i].x, pts->pts[i].y, pts->pts[i].chaincode);
          for (j = 0; j < 2 + LP_FILTER_ITERS; j++)
            fprintf(stderr, "%d  ", R[j][i]);
          fprintf(stderr, "\n");
      }
    }

    /* Do the region segmentation. */
    {
      int start, end;
      int currtype;

#define     RGN_TYPE(val)\
    (((val) == 18000)\
      ? RGN_PLAIN\
      : ((val) < 18000 ? RGN_CONCAVE : RGN_CONVEX))

      start = 0;
      currtype = RGN_TYPE(curr[0]);
      /*    regions = (region_list *)safe_malloc(sizeof(region_list));*/
      regions = allocate(1, region_list);
      curr_reg = regions;
      curr_reg->start = start;
      curr_reg->end = 0;
      curr_reg->type = currtype;
      curr_reg->next = NULL;
      for (i = 1; i < pts->npts; i++) {
          int nexttype = RGN_TYPE(curr[i]);

          if (nexttype != currtype) {
            region_list *next_reg = NULL;

            end = i - 1;
            curr_reg->end = end;
            if (lidebug > 1)
                fprintf(stderr, "  (%d, %d), %d\n", start, end, currtype);

            start = i;
            currtype = nexttype;
            /* next_reg = (region_list *)safe_malloc(sizeof(region_list));*/
            next_reg = allocate(1, region_list);
            next_reg->start = start;
            next_reg->end = 0;
            next_reg->type = nexttype;
            next_reg->next = NULL;

            curr_reg->next = next_reg;
            curr_reg = next_reg;
          }
      }
      end = i - 1;
      curr_reg->end = end;
      if (lidebug > 1)
          fprintf(stderr, "  (%d, %d), %d\n", start, end, currtype);

      /* Filter out convex/concave regions that are too short. */
      for (curr_reg = regions; curr_reg; curr_reg = curr_reg->next)
          if (curr_reg->type == RGN_PLAIN) {
            region_list *next_reg;

            for (next_reg = curr_reg->next;
                 next_reg != NULL &&
                   (next_reg->end - next_reg->start) < LP_FILTER_MIN;
                 next_reg = curr_reg->next) {
                /* next_reg must not be plain, and it must be followed by a plain */
                /* assert(next_reg->type != RGN_PLAIN); */
                /* assert(next_reg->next != NULL && (next_reg->next)->type == RGN_PLAIN); */

                curr_reg->next = (next_reg->next)->next;
                curr_reg->end = (next_reg->next)->end;

                free(next_reg->next);
                free(next_reg);
            }
          }

      /* Add-in pseudo-extremes. */
      {
          region_list *tmp, *prev_reg;

          tmp = regions;
          regions = NULL;
          prev_reg = NULL;
          for (curr_reg = tmp; curr_reg; curr_reg = curr_reg->next) {
            if (curr_reg->type == RGN_PLAIN) {
                int arclen = lialg_compute_pathlen_subset(pts,
                                                curr_reg->start,
                                                curr_reg->end);
                int dx = pts->pts[curr_reg->end].x -
                  pts->pts[curr_reg->start].x;
                int dy = pts->pts[curr_reg->end].y -
                  pts->pts[curr_reg->start].y;
                int chordlen = isqrt(10000 * (dx * dx + dy * dy));
                int atcr = (chordlen == 0) ? 0 : (100 * arclen + chordlen / 2) / chordlen;

                if (lidebug)
                  fprintf(stderr, "%d, %d, %d\n", arclen, chordlen, atcr);

                /* Split region if necessary. */
                if (arclen >= PE_AL_THLD && atcr >= PE_ATCR_THLD) {
                  int mid = curr_reg->start + (curr_reg->end - curr_reg->start) / 2;
                  int end = curr_reg->end;
                  region_list *saved_next = curr_reg->next;

                  curr_reg->end = mid - 1;
                  if (prev_reg == NULL)
                      regions = curr_reg;
                  else
                      prev_reg->next = curr_reg;
                  prev_reg = curr_reg;

                  /* curr_reg = (region_list *)safe_malloc(sizeof(region_list));*/
                  curr_reg = allocate(1, region_list);
                  curr_reg->start = mid;
                  curr_reg->end = mid;
                  curr_reg->type = RGN_PSEUDO;
                  curr_reg->next = NULL;
                  prev_reg->next = curr_reg;
                  prev_reg = curr_reg;

                  /* curr_reg = (region_list *)safe_malloc(sizeof(region_list)); */
                  curr_reg = allocate(1, region_list);
                  curr_reg->start = mid + 1;
                  curr_reg->end = end;
                  curr_reg->type = RGN_PLAIN;
                  curr_reg->next = NULL;
                  prev_reg->next = curr_reg;
                  prev_reg = curr_reg;

                  curr_reg->next = saved_next;
                  continue;
                }
            }

            if (prev_reg == NULL)
                regions = curr_reg;
            else
                prev_reg->next = curr_reg;
            prev_reg = curr_reg;
          }
      }
    }

    free(junk);
    return(regions);
}


static point_list *lialg_compute_dompts(point_list *pts, region_list *regions) {
    point_list *dpts = NULL;
    int ndpts;
    int *cas = NULL;
    int nonplain;
    region_list *r;

    /* Compute contour angle set. */
    cas = lialg_compute_contour_angle_set(pts, regions);
/*    assert(cas != NULL);*/

    /* Dominant points include:  start_pt, end_pt, extrema_of_non_plain_regions, midpts of the preceding. */
    nonplain = 0;
    for (r = regions; r != NULL; r = r->next)
      if (r->type != RGN_PLAIN) nonplain++;
    ndpts = 2 * (2 + nonplain) - 1;
    /* dpts = (point_list *)safe_malloc(sizeof(point_list)); */
    dpts = allocate(1, point_list);
    dpts->pts = make_pen_point_array(ndpts);
    if (dpts->pts == NULL) {
      free(dpts);
      return(NULL);
    }
    dpts->npts = ndpts;
    dpts->next = NULL;

    /* Pick out dominant points. */
    {
      region_list *curr;
      int dp;
      int previx;
      int currix;

      /* Record start point. */
      dp = 0;
      previx = 0;
      dpts->pts[dp++] = pts->pts[previx];

      for (curr = regions; curr != NULL; curr = curr->next)
          if (curr->type != RGN_PLAIN) {
            int max_v = 0;
            int min_v = MAXINT;
            int max_ix = -1;
            int min_ix = -1;
            int i;

            for (i = curr->start; i <= curr->end; i++) {
                int v = cas[i];
                if (v > max_v) { max_v = v; max_ix = i; }
                if (v < min_v) { min_v = v; min_ix = i; }
                if (lidebug > 1)
                  fprintf(stderr, "  %d\n", v);
            }

            currix = (curr->type == RGN_CONVEX ? max_ix : min_ix);

            /* Record midpoint. */
            dpts->pts[dp++] = pts->pts[previx + (currix - previx) / 2];

            /* Record extreme point. */
            dpts->pts[dp++] = pts->pts[currix];

            previx = currix;
          }

      /* Record last mid-point and end point. */
      currix = pts->npts - 1;
      dpts->pts[dp++] = pts->pts[previx + (currix - previx) / 2];
      dpts->pts[dp++] = pts->pts[currix];
    }

    /* Compute chain-code. */
    lialg_compute_chain_code(dpts);

    free(cas);
    return(dpts);
}


static int *lialg_compute_contour_angle_set(point_list *pts,
                                     region_list *regions) {
    int *V = NULL;
    region_list *curr_reg, *prev_reg;
    int i;

    /*    V = (int *)safe_malloc(pts->npts * sizeof(int));*/
    V = allocate(pts->npts, int);

    V[0] = 18000;
    for (curr_reg = regions; curr_reg != NULL;
          prev_reg = curr_reg, curr_reg = curr_reg->next) {
      for (i = curr_reg->start; i <= curr_reg->end; i++) {
          if (curr_reg->type == RGN_PLAIN) {
            V[i] = 18000;
          }
          else {
#ifdef      notdef
            /* XXX - eliminate floating point */
            region_list *next_reg = curr_reg->next;
            int b = curr_reg->start;
            int h = prev_reg->start;
            int t = next_reg->end;
            int pts_before = i - h;
            int pts_after = t - i;
            int min_pts = (pts_before < pts_after)
              ? pts_before
              : pts_after;
            int k = (min_pts < T_ONE)
              ? T_ONE
              : (min_pts > T_TWO)
              ? T_TWO
              : min_pts;
            float sum = 0.0;

            for (j = 1; j <= k; j++) {
                int ptA = i - j;
                int ptB = i + j - 1;
                int d_A = pts->pts[ptA].chaincode;
                int d_B = pts->pts[ptB].chaincode;
                int a_i;

                if (d_A < d_B)
                  d_A += 8;

                a_i = (d_A - d_B) % 8;

                /* convert to radians */
                if (a_i == 4 && curr_reg->type == RGN_CONVEX)
                  sum += M_2_PI;
                else
                  sum += (float)((12 - a_i) % 8) / 4.0 * M_PI;
            }
            V[i] = sum / (float)k;
#else
            /* For now, simply choose the mid-point. */
            int isMidPt = (i == (curr_reg->start +
                             (curr_reg->end - curr_reg->start) / 2));
            V[i] = (curr_reg->type == RGN_CONVEX)
              ? (isMidPt ? 18000 : 0)
              : (isMidPt ? 0 : 18000);
#endif
          }
      }
    }
    V[pts->npts - 1] = 18000;

    return(V);
}


/*
 *  First compute the similarity between the two strings.
 *  If it's above a threshold, compute the distance between
 *  the two and return it as the ``score.''
 *  Otherwise, return the constant WORST_SCORE.
 *
 */
static void lialg_score_stroke(point_list *input_dompts, point_list *curr_dompts, int *sim, int *dist) {
    *sim = MIN_SIM;
    *dist = MAX_DIST;

    *sim = lialg_compute_similarity(input_dompts, curr_dompts);
    if (*sim < SIM_THLD) goto done;

    *dist = lialg_compute_distance(input_dompts, curr_dompts);

done:
    if (lidebug)
      fprintf(stderr, "%d, %d\n", *sim, *dist);
}


static int lialg_compute_similarity(point_list *input_dompts,
                             point_list *curr_dompts) {
    int sim = 0;
    point_list *A, *B;
    int N, M;
    int **G = NULL;
    int *junk = NULL;
    int i, j;

    /* A is the   longer sequence, length N. */
    /* B is the shorter sequence, length M. */
    if (input_dompts->npts >= curr_dompts->npts) {
      A = input_dompts;
      N = input_dompts->npts;
      B = curr_dompts;
      M = curr_dompts->npts;
    }
    else {
      A = curr_dompts;
      N = curr_dompts->npts;
      B = input_dompts;
      M = input_dompts->npts;
    }

    /* Allocate and initialize the Gain matrix, G. */
    /* The size of G is M x (N + 1). */
    /* Note that row 0 is unused. */
    /* Similarities are x 10. */
    {
        /*  G = (int **)safe_malloc(M * sizeof(int *));*/
        G = allocate(M, int *);
        /*  junk = (int *)safe_malloc(M * (N + 1) * sizeof(int)); */
      junk = allocate(M * (N + 1), int);
      for (i = 0; i < M; i++)
          G[i] = junk + (i * (N + 1));

      for (i = 1; i < M; i++) {
          int bval = B->pts[i-1].chaincode;

          /* Source column. */
          G[i][0] = 0;

          for (j = 1; j < N; j++) {
            int aval = A->pts[j-1].chaincode;
            int diff = abs(bval - aval);
            if (diff > 4) diff = 8 - diff;

            G[i][j] = (diff == 0)
              ? 10
              : (diff == 1)
              ? 6
              : 0;
          }

          /* Sink column. */
          G[i][N] = 0;
      }
    }

    /* Do the DP algorithm. */
    /* Proceed in column order, from highest column to the lowest. */
    /* Within each column, proceed from the highest row to the lowest. */
    /* Skip the highest column. */
    {
      for (j = N - 1; j >= 0; j--)
          for (i = M - 1; i > 0; i--) {
            int max = G[i][j + 1];

            if (i < (M - 1)) {
                int tmp = G[i + 1][j + 1];
                if (tmp > max) max = tmp;
            }

            G[i][j] += max;
          }

      sim = (10 * G[1][0] + (N - 1) / 2) / (N - 1);
    }

    if (G != NULL) free(G);
    if (junk != NULL) free(junk);
    return(sim);
}


static int lialg_compute_distance(point_list *input_dompts,
                           point_list *curr_dompts) {
    int dist = MAX_DIST;
    point_list *A, *B;
    int N, M;
    int **C = NULL;
    int *junk = NULL;
    int *BE = NULL;
    int *TE = NULL;
    int i, j;

    /* A is the   longer sequence, length N. */
    /* B is the shorter sequence, length M. */
    if (input_dompts->npts >= curr_dompts->npts) {
      A = input_dompts;
      N = input_dompts->npts;
      B = curr_dompts;
      M = curr_dompts->npts;
    }
    else {
      A = curr_dompts;
      N = curr_dompts->npts;
      B = input_dompts;
      M = input_dompts->npts;
    }

    /* Construct the helper vectors, BE and TE, which say for each column */
    /* what are the ``bottom'' and ``top'' rows of interest. */
    {
        /*  BE = (int *)safe_malloc((N + 1) * sizeof(int));*/
      BE = allocate((N + 1), int);
      /*    TE = (int *)safe_malloc((N + 1) * sizeof(int)); */
      TE = allocate((N + 1), int);

      for (j = 1; j <= N; j++) {
          int bot, top;

          bot = j + (M - DP_BAND);
          if (bot > M) bot = M;
          BE[j] = bot;

          top = j - (N - DP_BAND);
          if (top < 1) top = 1;
          TE[j] = top;
      }
    }

    /* Allocate and initialize the Cost matrix, C. */
    /* The size of C is (M + 1) x (N + 1). */
    /* Note that row and column 0 are unused. */
    /* Costs are x 100. */
    {
        /*  C = (int **)safe_malloc((M + 1) * sizeof(int *)); */
      C = allocate((M + 1), int *);
      /*    junk = (int *)safe_malloc((M + 1) * (N + 1) * sizeof(int)); */
      junk = allocate((M + 1) * (N + 1), int);
      for (i = 0; i <= M; i++)
          C[i] = junk + (i * (N + 1));

      for (i = 1; i <= M; i++) {
          int bx = B->pts[i-1].x;
          int by = B->pts[i-1].y;

          for (j = 1; j <= N; j++) {
            int ax = A->pts[j-1].x;
            int ay = A->pts[j-1].y;
            int dx = bx - ax;
            int dy = by - ay;
            int dist = isqrt(10000 * (dx * dx + dy * dy));

            C[i][j] = dist;
          }
      }
    }

    /* Do the DP algorithm. */
    /* Proceed in column order, from highest column to the lowest. */
    /* Within each column, proceed from the highest row to the lowest. */
    {
      for (j = N; j > 0; j--)
          for (i = M; i > 0; i--) {
            int min = MAX_DIST;

            if (i > BE[j] || i < TE[j] || (j == N && i == M))
                continue;

            if (j < N) {
                if (i >= TE[j+1]) {
                  int tmp = C[i][j+1];
                  if (tmp < min) min = tmp;
                }

                if (i < M) {
                  int tmp = C[i+1][j+1];
                  if (tmp < min) min = tmp;
                }
            }

            if (i < BE[j]) {
                int tmp = C[i+1][j];
                if (tmp < min) min = tmp;
            }

            C[i][j] += min;
          }

      dist = (C[1][1] + N / 2) / N;
    }

    if (C != NULL) free(C);
    if (junk != NULL) free(junk);
    if (BE != NULL) free(BE);
    if (TE != NULL) free(TE);
    return(dist);
}


/*************************************************************

  Digest-processing routines

 *************************************************************/

static int lialg_read_classifier_digest(rClassifier *rec) {
    int nclasses;
    FILE *fp = NULL;

    /* Try to open the corresponding digest file. */
    {
      char *clx_path;
      char *dot;

      /* Get a copy of the filename, with some room on the end. */
      /*    clx_path = safe_malloc(strlen(rec->file_name) + 5); */
      clx_path = allocate(strlen(rec->file_name) + 5, char);
      strcpy(clx_path, rec->file_name);

      /* Truncate the path after the last dot. */
      dot = strrchr(clx_path, '.');
      if (dot == NULL) { free(clx_path); return(-1); }
      *(dot + 1) = 0;

      /* Append the classifier-digest extension. */
      strcat(clx_path, "clx");

      fp = fopen(clx_path, "r");
      if (fp == NULL) { free(clx_path); return(-1); }

      free(clx_path);
    }

    /* Read-in the name and dominant points for each class. */
    for (nclasses = 0; !feof(fp); nclasses++) {
      point_list *dpts = NULL;
      char class[BUFSIZ];
      int npts;
      int j;

      if (fscanf(fp, "%s %d", class, &npts) != 2) {
          if (feof(fp)) break;

          goto failed;
      }
      rec->cnames[nclasses] = strdup(class);

      /* Allocate a dominant-points list. */
      /* dpts = (point_list *)safe_malloc(sizeof(point_list)); */
      dpts = allocate(1, point_list);
      dpts->pts = make_pen_point_array(npts);
      if (dpts->pts == NULL) goto failed;
      dpts->npts = npts;
      dpts->next = NULL;

      /* Read in each point. */
      for (j = 0; j < npts; j++) {
          int x, y;

          if (fscanf(fp, "%d %d", &x, &y) != 2) goto failed;
          dpts->pts[j].x = x;
          dpts->pts[j].y = y;
      }

      /* Compute the chain-code. */
      lialg_compute_chain_code(dpts);

      /* Store the list in the rec data structure. */
      rec->dompts[nclasses] = dpts;

      continue;

failed:
      fprintf(stderr, "read_classifier_digest failed...\n");
      for (; nclasses >= 0; nclasses--) {
          if (rec->cnames[nclasses] != NULL) {
            free(rec->cnames[nclasses]);
            rec->cnames[nclasses] = NULL;
          }
          if (rec->dompts[nclasses] != NULL) {
            delete_examples(rec->dompts[nclasses]);
            rec->dompts[nclasses] = NULL;
          }
      }
      if (dpts != NULL)
          delete_examples(dpts);
      fclose(fp);
      return(-1);
    }

    fclose(fp);
    return(0);
}


/*************************************************************

  Canonicalization routines

 *************************************************************/

static int lialg_canonicalize_examples(rClassifier *rec) {
    int i;
    int nclasses;

    if (lidebug) {
        fprintf(stderr, "lialg_canonicalize_examples working on %s\n",
            rec->file_name);
    }
    /* Initialize canonical-example arrays. */
    for (i = 0; i < MAXSCLASSES; i++) {
      rec->canonex[i] = NULL;
    }

    /* Figure out number of classes. */
    for (nclasses = 0;
        nclasses < MAXSCLASSES && rec->cnames[nclasses] != NULL;
        nclasses++)
      ;

    /* Canonicalize the examples for each class. */
    for (i = 0; i < nclasses; i++) {
      int j, k;
      int nex;
      point_list *pts, *tmp, *avg;
      int maxxrange, maxyrange;
      int minx, miny, maxx, maxy;
      int avgxrange, avgyrange, avgxoff, avgyoff, avgscale;

      
      if (lidebug) {
          fprintf(stderr, "lialg_canonicalize_examples working on class %s\n",
                rec->cnames[i]);
      }
      /* Make a copy of the examples. */
      pts = NULL;
      tmp = rec->ex[i];
      for (nex = 0; tmp != NULL; nex++, tmp = tmp->next) {
          if ((pts = add_example(pts, tmp->npts, tmp->pts)) == NULL) {
            delete_examples(pts);
            return(-1);
          }
      }

      /* Canonicalize each example, and derive the max x and y ranges. */
      maxxrange = 0;
      maxyrange = 0;
      for (j = 0, tmp = pts; j < nex; j++, tmp = tmp->next) {
          if (lialg_canonicalize_example_stroke(tmp) != 0) {
              if (lidebug) {
                fprintf(stderr, "lialg_canonicalize_example_stroke returned error\n");
            }
            return(-1);
          }

          if (tmp->xrange > maxxrange) maxxrange = tmp->xrange;
          if (tmp->yrange > maxyrange) maxyrange = tmp->yrange;
      }

      /* Normalize max ranges. */
      if (((100 * maxxrange + CANONICAL_X / 2) / CANONICAL_X) >
          ((100 * maxyrange + CANONICAL_Y / 2) / CANONICAL_Y)) {
          maxyrange = (maxyrange * CANONICAL_X + maxxrange / 2) / maxxrange;
          maxxrange = CANONICAL_X;
      }
      else {
          maxxrange = (maxxrange * CANONICAL_Y + maxyrange / 2) / maxyrange;
          maxyrange = CANONICAL_Y;
      }

      /* Re-scale each example to max ranges. */
      for (j = 0, tmp = pts; j < nex; j++, tmp = tmp->next) {
          int scalex = (tmp->xrange == 0) ? 100 : (100 * maxxrange + tmp->xrange / 2) / tmp->xrange;
          int scaley = (tmp->yrange == 0) ? 100 : (100 * maxyrange + tmp->yrange / 2) / tmp->yrange;
          if (lialg_translate_points(tmp, 0, 0, scalex, scaley) != 0) {
            delete_examples(pts);
            return(-1);
          }
      }

      /* Average the examples; leave average in first example. */
      avg = pts;                    /* careful aliasing!! */
      for (k = 0; k < NCANONICAL; k++) {
          int xsum = 0;
          int ysum = 0;

          for (j = 0, tmp = pts; j < nex; j++, tmp = tmp->next) {
            xsum += tmp->pts[k].x;
            ysum += tmp->pts[k].y;
          }

          avg->pts[k].x = (xsum + j / 2) / j;
          avg->pts[k].y = (ysum + j / 2) / j;
      }

      /* Compute BB of averaged stroke and re-scale. */
      lialg_get_bounding_box(avg, &minx, &miny, &maxx, &maxy);
      avgxrange = maxx - minx;
      avgyrange = maxy - miny;
      avgscale = (((100 * avgxrange + CANONICAL_X / 2) / CANONICAL_X) >
                ((100 * avgyrange + CANONICAL_Y / 2) / CANONICAL_Y))
        ? (100 * CANONICAL_X + avgxrange / 2) / avgxrange
        : (100 * CANONICAL_Y + avgyrange / 2) / avgyrange;
      if (lialg_translate_points(avg, minx, miny, avgscale, avgscale) != 0) {
          delete_examples(pts);
          return(-1);
      }

      /* Re-compute the x and y ranges and center the stroke. */
      lialg_get_bounding_box(avg, &minx, &miny, &maxx, &maxy);
      avgxrange = maxx - minx;
      avgyrange = maxy - miny;
      avgxoff = -((CANONICAL_X - avgxrange + 1) / 2);
      avgyoff = -((CANONICAL_Y - avgyrange + 1) / 2);
      if (lialg_translate_points(avg, avgxoff, avgyoff, 100, 100) != 0) {
          delete_examples(pts);
          return(-1);
      }

      /* Create a point list to serve as the ``canonical representation. */
      if ((rec->canonex[i] = add_example(NULL, avg->npts, avg->pts)) == NULL) {
          delete_examples(pts);
          return(-1);
      }
      (rec->canonex[i])->xrange = maxx - minx;
      (rec->canonex[i])->yrange = maxy - miny;

      if (lidebug) {
          fprintf(stderr, "%s, avgpts = %d\n", rec->cnames[i], avg->npts);
          for (j = 0; j < avg->npts; j++) {
            fprintf(stderr, "  (%d, %d)\n",
                  avg->pts[j].x, avg->pts[j].y);
          }
      }

      /* Compute dominant points of canonical representation. */
      rec->dompts[i] = lialg_compute_dominant_points(avg);

      /* Clean up. */
      delete_examples(pts);
    }

    /* Sanity check. */
    for (i = 0; i < nclasses; i++) {
      char *best_name = lialg_recognize_stroke(rec, rec->canonex[i]);

      if (best_name != rec->cnames[i])
          fprintf(stderr, "%s, best = %s\n", rec->cnames[i], best_name);
    }

    return(0);
}


static int lialg_canonicalize_example_stroke(point_list *points) {
    int minx, miny, maxx, maxy, xrange, yrange, scale;

    /* Filter out points that are too close. */
    if (lialg_filter_points(points) != 0) return(-1);

    /* Must be at least two points! */
    if (points->npts < 2) {
        if (lidebug) {
          fprintf(stderr, "lialg_canonicalize_example_stroke: npts=%d\n",
                points->npts);
      }
        return(-1);
    }

    /* Scale up to avoid conversion errors. */
    lialg_get_bounding_box(points, &minx, &miny, &maxx, &maxy);
    xrange = maxx - minx;
    yrange = maxy - miny;
    scale = (((100 * xrange + CANONICAL_X / 2) / CANONICAL_X) >
           ((100 * yrange + CANONICAL_Y / 2) / CANONICAL_Y))
      ? (100 * CANONICAL_X + xrange / 2) / xrange
      : (100 * CANONICAL_Y + yrange / 2) / yrange;
    if (lialg_translate_points(points, minx, miny, scale, scale) != 0) {
        if (lidebug) {
          fprintf(stderr, "lialg_translate_points (minx=%d,miny=%d,scale=%d) returned error\n", minx, miny, scale);
      }
      return(-1);
    }

    /* Compute an equivalent stroke with equi-distant points. */
    if (lialg_compute_equipoints(points) != 0) return(-1);

    /* Re-translate the points to the origin. */
    lialg_get_bounding_box(points, &minx, &miny, &maxx, &maxy);
    if (lialg_translate_points(points, minx, miny, 100, 100) != 0) {
        if (lidebug) {
          fprintf(stderr, "lialg_translate_points (minx=%d,miny=%d) returned error\n", minx, miny);
      }
        return(-1);
    }

    /* Store the x and y ranges in the point list. */
    xrange = maxx - minx;
    yrange = maxy - miny;
    points->xrange = xrange;
    points->yrange = yrange;

    if (lidebug) {
      int i;
      fprintf(stderr, "Canonicalized:   %d, %d, %d, %d\n", minx, miny, maxx, maxy);
      for (i = 0; i < points->npts; i++)
          fprintf(stderr, "      (%d %d)\n",
                points->pts[i].x, points->pts[i].y);
      fflush(stderr);
    }

    return(0);
}


static int lialg_compute_equipoints(point_list *points) {
    pen_point *equipoints = make_pen_point_array(NCANONICAL);
    int nequipoints = 0;
    int pathlen = lialg_compute_pathlen(points);
    int equidist = (pathlen + (NCANONICAL - 1) / 2) / (NCANONICAL - 1);
    int i;
    int dist_since_last_eqpt;
    int remaining_seglen;
    int dist_to_next_eqpt;

    if (equipoints == NULL) {
      error("can't allocate memory in lialg_compute_equipoints");
      return(-1);
    }

    if (lidebug) {
      fprintf(stderr, "compute_equipoints:  npts = %d, pathlen = %d, equidist = %d\n",
            points->npts, pathlen, equidist);
      fflush(stderr);
    }

    /* First original point is an equipoint. */
    equipoints[0] = points->pts[0];
    nequipoints++;
    dist_since_last_eqpt = 0;

    for (i = 1; i < points->npts; i++) {
      int dx1 = points->pts[i].x - points->pts[i-1].x;
      int dy1 = points->pts[i].y - points->pts[i-1].y;
      int endx = 100 * points->pts[i-1].x;
      int endy = 100 * points->pts[i-1].y;
      remaining_seglen = isqrt(10000 * (dx1 * dx1 + dy1 * dy1));
      dist_to_next_eqpt = equidist - dist_since_last_eqpt;

      while (remaining_seglen >= dist_to_next_eqpt) {
          if (dx1 == 0) {
            /* x-coordinate stays the same */
            if (dy1 >= 0)
                endy += dist_to_next_eqpt;
            else
                endy -= dist_to_next_eqpt;
          }
          else {
            int slope = (100 * dy1 + dx1 / 2) / dx1;
            int tmp = isqrt(10000 + slope * slope);
            int dx = (100 * dist_to_next_eqpt + tmp / 2) / tmp;
            int dy = (slope * dx + 50) / 100;

            if (dy < 0) dy = -dy;
            if (dx1 >= 0)
                endx += dx;
            else
                endx -= dx;
            if (dy1 >= 0)
                endy += dy;
            else
                endy -= dy;
          }

          equipoints[nequipoints].x = (endx + 50) / 100;
          equipoints[nequipoints].y = (endy + 50) / 100;
          nequipoints++;
/*        assert(nequipoints <= NCANONICAL);*/
          dist_since_last_eqpt = 0;
          remaining_seglen -= dist_to_next_eqpt;
          dist_to_next_eqpt = equidist;
      }

      dist_since_last_eqpt += remaining_seglen;
    }

    /* Take care of last equipoint. */
    if (nequipoints == NCANONICAL) {
      /* Good. */
    } else if (nequipoints == (NCANONICAL - 1)) {
      /* Make last original point the last equipoint. */
      equipoints[nequipoints] = points->pts[points->npts - 1];
    } else {
      if (lidebug) {
        fprintf(stderr,"lialg_compute_equipoints: nequipoints = %d\n", 
            nequipoints);
      }
/*    assert(false);*/
      return(-1);
    }

    points->npts = NCANONICAL;
    delete_pen_point_array(points->pts);
    points->pts = equipoints;
    return(0);
}


/*************************************************************

  Utility routines

 *************************************************************/

/* Result is x 100. */
static int lialg_compute_pathlen(point_list *points) {
    return(lialg_compute_pathlen_subset(points, 0, points->npts - 1));
}


/* Result is x 100. */
static int lialg_compute_pathlen_subset(point_list *points,
                                 int start, int end) {
    int pathlen;
    int i;

    pathlen = 0;
    for (i = start + 1; i <= end; i++) {
      int dx = points->pts[i].x - points->pts[i-1].x;
      int dy = points->pts[i].y - points->pts[i-1].y;
      int dist = isqrt(10000 * (dx * dx + dy * dy));
      pathlen += dist;
    }

    return(pathlen);
}


/* Note that this does NOT update points->xrange and points->yrange! */
static int lialg_filter_points(point_list *points) {
    int filtered_npts;
    pen_point *filtered_pts = make_pen_point_array(points->npts);
    int i;

    if (filtered_pts == NULL) {
      error("can't allocate memory in lialg_filter_points");
      return(-1);
    }

    filtered_pts[0] = points->pts[0];
    filtered_npts = 1;
    for (i = 1; i < points->npts; i++) {
      int j = filtered_npts - 1;
      int dx = points->pts[i].x - filtered_pts[j].x;
      int dy = points->pts[i].y - filtered_pts[j].y;
      int magsq = dx * dx + dy * dy;

      if (magsq >= DIST_SQ_THRESHOLD) {
          filtered_pts[filtered_npts] = points->pts[i];
          filtered_npts++;
      }
    }

    points->npts = filtered_npts;
    delete_pen_point_array(points->pts);
    points->pts = filtered_pts;
    return(0);
}


/* scalex and scaley are x 100. */
/* Note that this does NOT update points->xrange and points->yrange! */
static int lialg_translate_points(point_list *points,
                           int minx, int miny,
                           int scalex, int scaley) {
    int i;

    for (i = 0; i < points->npts; i++) {
      points->pts[i].x = ((points->pts[i].x - minx) * scalex + 50) / 100;
      points->pts[i].y = ((points->pts[i].y - miny) * scaley + 50) / 100;
    }

    return(0);
}


static void lialg_get_bounding_box(point_list *points,
                            int *pminx, int *pminy,
                            int *pmaxx, int *pmaxy) {
    int minx, miny, maxx, maxy;
    int i;

    minx = maxx = points->pts[0].x;
    miny = maxy = points->pts[0].y;
    for (i = 1; i < points->npts; i++) {
      pen_point *pt = &(points->pts[i]);
      if (pt->x < minx) minx = pt->x;
      if (pt->x > maxx) maxx = pt->x;
      if (pt->y < miny) miny = pt->y;
      if (pt->y > maxy) maxy = pt->y;
    }

    *pminx = minx;
    *pminy = miny;
    *pmaxx = maxx;
    *pmaxy = maxy;
}

#ifdef __ECOS
float
expf(float x)
{
    return exp((double)x);
}
#endif


static void lialg_compute_lpf_parameters() {
    int i;

    for (i = LP_FILTER_WIDTH; i >= 0; i--) {
      float x = 0.04 * (i * i);
#if defined(ARM_LINUX) || !defined(__GLIBC__)
      double tmp = 100.0 * exp((double)x);
#else
      float tmp = 100.0 * expf(x);
#endif
      int wt = rint((double)tmp);

      lialg_lpfwts[LP_FILTER_WIDTH - i] = wt;
      lialg_lpfwts[LP_FILTER_WIDTH + i] = wt;
    }
    lialg_lpfconst = 0;
    for (i = 0; i < (2 * LP_FILTER_WIDTH + 1); i++) {
      lialg_lpfconst += lialg_lpfwts[i];
    }
}


/* Code from Joseph Hall (jnhall@sat.mot.com). */
static int isqrt(int n) {
    register int i;
    register long k0, k1, nn;

    for (nn = i = n, k0 = 2; i > 0; i >>= 2, k0 <<= 1)
      ;
    nn <<= 2;
    for (;;) {
      k1 = (nn / k0 + k0) >> 1;
      if (((k0 ^ k1) & ~1) == 0)
          break;
      k0 = k1;
    }
    return (int) ((k1 + 1) >> 1);
}


/* Helper routines from Mark Hayter. */
static int likeatan(int tantop, int tanbot) { 
    int t;
    /* Use tan(theta)=top/bot --> order for t */
    /* t in range 0..0x40000 */

    if ((tantop == 0) && (tanbot == 0)) 
      t = 0;
    else
    {
      t = (tantop << 16) / (abs(tantop) + abs(tanbot));
      if (tanbot < 0) 
          t = 0x20000 - t;
      else 
          if (tantop < 0) t = 0x40000 + t;
    }
    return t;
}


static int quadr(int t) {
    return (8 - (((t + 0x4000) >> 15) & 7)) & 7;
}

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