/*====================================================================*
 -  Copyright (C) 2001 Leptonica.  All rights reserved.
 -
 -  Redistribution and use in source and binary forms, with or without
 -  modification, are permitted provided that the following conditions
 -  are met:
 -  1. Redistributions of source code must retain the above copyright
 -     notice, this list of conditions and the following disclaimer.
 -  2. Redistributions in binary form must reproduce the above
 -     copyright notice, this list of conditions and the following
 -     disclaimer in the documentation and/or other materials
 -     provided with the distribution.
 -
 -  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
 -  ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
 -  LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
 -  A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL ANY
 -  CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
 -  EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
 -  PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
 -  PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
 -  OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
 -  NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
 -  SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 *====================================================================*/

/*!
 * \file dnahash_remnant.c.notused
 * <pre>
 *
 *                                     NOTE
 *       ==================================================================
 *       This code has been retired from the library.  It is just
 *       documentation.  It contains dnahash functionality that is no
 *       longer in use.  The only current use of dnahash (in dnahash.c)
 *       is for fast template lookup in the jbig2 classifier (jbclass.c).
 *
 *       The functions in this file hash strings, points and doubles.
 *       Most of them have been replaced by analogous ones using the more
 *       general hashmap.  They are saved here for pedagogical purposes;
 *       mostly, to show how misguided one can be trying to implement a
 *       general hashing function using only an array of doubles.  (Yes, it can
 *       be done, but it's a lot of work for relatively little functionality.)
 *
 *       The new hashmap (in hashmap.c) has a much simpler lookup and
 *       add mechanism.  It also has a rehashing function to allow the hash
 *       array to grow as items are added.  Unlike the simple dnahash,
 *       the hashmap stores the key in the hashitem, so it doesn't require
 *       an auxiliary array to do lookup with checking and creating.
 *       (It does however require the auxiliary array to retrieve the
 *       original data, which is not stored in the hashitem.  This may
 *       be changed in the future.)
 *       ==================================================================
 *
 *      DnaHash: Accessors
 *          l_int32      l_dnaHashGetCount()
 *          l_int32      l_dnaHashGetTotalCount()
 *
 *      Set operations on dna
 *          L_DNAHASH   *l_dnaHashCreateFromDna()
 *          l_int32      l_dnaRemoveDupsByHash()
 *          l_int32      l_dnaMakeHistoByHash()
 *          L_DNA       *l_dnaIntersectionByHash()
 *          l_int32      l_dnaFindValByHash()
 *
 *      Set operations on pta
 *           PTA        *ptaUnionByHash()
 *           l_int32     ptaRemoveDupsByHash()
 *           PTA        *ptaIntersectionByHash();
 *           l_int32     ptaFindPtByHash()
 *           L_DNAHASH  *l_dnaHashCreateFromPta()
 *
 *      Set operations on sarray
 *          l_int32     sarrayRemoveDupsByHash()
 *          SARRAY     *sarrayIntersectionByHash()
 *          l_int32     sarrayFindStringByHash()
 *          L_DNAHASH  *l_dnaHashCreateFromSarray()
 *
 *    (1) The DnaHash is an array of Dna.  It can be used for fast
 *        storage and lookup for sets and maps.  If the set or map
 *        is on a Dna itself, the hash can be a simple casting from
 *        a double to a l_uint64. For a string or a (x,y) point, we
 *        use a hash to a l_uint64.  The result of the hash is
 *        a "key", which is then used with the mod function to select
 *        which Dna array is to be used.
 *    (2) The number of arrays in a DnaHash is a prime number.
 *        If there are N items, we set up the DnaHash array to have
 *        approximately N/20 Dna, so the average size of these arrays
 *        will be about 20 when fully populated.  The number 20 was
 *        found empirically to be in a broad maximum of efficiency.
 *    (3) Note that the word "hash" is overloaded.  There are actually
 *        two hashing steps: the first hashes the object to a l_uint64,
 *        called the "key", and the second uses the mod function to
 *        "hash" the "key" to the index of a particular Dna in the
 *        DnaHash array.
 *    (4) Insertion and lookup time for DnaHash is O(1).  Hash collisions
 *        into the dna array are expected (we might choose to have an average
 *        of 20 for each key).  This can be contrasted with using rbtree
 *        for sets and maps, where insertion and lookup are O(logN).
 *    (5) Hash functions that map points and strings to l_uint64 are
 *        given in utils1.c.
 *    (6) This is a very simple implementation, that expects that you
 *        know approximately (i.e., within a factor of 2 or 3) how many
 *        items are to be stored when you initialize the DnaHash.
 *        It cannot modify the size of the Dna array as the occupation grows.
 * </pre>
 */

#ifdef HAVE_CONFIG_H
#include <config_auto.h>
#endif  /* HAVE_CONFIG_H */

#include "allheaders.h"

/*--------------------------------------------------------------------------*
 *                   Dna hash: Accessors and modifiers                      *
 *--------------------------------------------------------------------------*/
/*!
 * \brief   l_dnaHashGetCount()
 *
 * \param[in]    dahash
 * \return  nbuckets allocated, or 0 on error
 */
l_int32
l_dnaHashGetCount(L_DNAHASH  *dahash)
{

    if (!dahash)
        return ERROR_INT("dahash not defined", __func__, 0);
    return dahash->nbuckets;
}


/*!
 * \brief   l_dnaHashGetTotalCount()
 *
 * \param[in]    dahash
 * \return  n number of numbers in all dna, or 0 on error
 */
l_int32
l_dnaHashGetTotalCount(L_DNAHASH  *dahash)
{
l_int32  i, n;
L_DNA   *da;

    if (!dahash)
        return ERROR_INT("dahash not defined", __func__, 0);

    for (i = 0, n = 0; i < dahash->nbuckets; i++) {
        da = l_dnaHashGetDna(dahash, i, L_NOCOPY);
        if (da)
            n += l_dnaGetCount(da);
    }

    return n;
}


/*--------------------------------------------------------------------------*
 *                   Set operations on dna using hashing                    *
 *--------------------------------------------------------------------------*/
/*!
 * \brief   l_dnaHashCreateFromDna()
 *
 * \param[in]    da
 * \return  dahash if OK; 1 on error
 *
 * <pre>
 * Notes:
 *      (1) The values stored in the %dahash are indices into %da;
 *          %dahash has no use without %da.
 * </pre>
 */
L_DNAHASH *
l_dnaHashCreateFromDna(L_DNA  *da)
{
l_int32     i, n;
l_uint32    nsize;
l_uint64    key;
l_float64   val;
L_DNAHASH  *dahash;

    if (!da)
        return (L_DNAHASH *)ERROR_PTR("da not defined", __func__, NULL);

    n = l_dnaGetCount(da);
    findNextLargerPrime(n / 20, &nsize);  /* buckets in hash table */

    dahash = l_dnaHashCreate(nsize, 8);
    for (i = 0; i < n; i++) {
        l_dnaGetDValue(da, i, &val);
        l_dnaHashAdd(dahash, (l_uint64)val, (l_float64)i);
    }

    return dahash;
}


/*!
 * \brief   l_dnaRemoveDupsByHash()
 *
 * \param[in]    das
 * \param[out]   pdad      hash set
 * \param[out]   pdahash   [optional] dnahash used for lookup
 * \return  0 if OK; 1 on error
 *
 * <pre>
 * Notes:
 *      (1) Generates a dna with unique values.
 *      (2) The dnahash is built up with dad to assure uniqueness.
 *          It can be used to find if an element is in the set:
 *              l_dnaFindValByHash(dad, dahash, val, &index)
 * </pre>
 */
l_ok
l_dnaRemoveDupsByHash(L_DNA       *das,
                      L_DNA      **pdad,
                      L_DNAHASH  **pdahash)
{
l_int32     i, n, index, items;
l_uint32    nsize;
l_uint64    key;
l_float64   val;
L_DNA      *dad;
L_DNAHASH  *dahash;

    if (pdahash) *pdahash = NULL;
    if (!pdad)
        return ERROR_INT("&dad not defined", __func__, 1);
    *pdad = NULL;
    if (!das)
        return ERROR_INT("das not defined", __func__, 1);

    n = l_dnaGetCount(das);
    findNextLargerPrime(n / 20, &nsize);  /* buckets in hash table */
    dahash = l_dnaHashCreate(nsize, 8);
    dad = l_dnaCreate(n);
    *pdad = dad;
    for (i = 0, items = 0; i < n; i++) {
        l_dnaGetDValue(das, i, &val);
        l_dnaFindValByHash(dad, dahash, val, &index);
        if (index < 0) {  /* not found */
            l_dnaHashAdd(dahash, (l_uint64)val, (l_float64)items);
            l_dnaAddNumber(dad, val);
            items++;
        }
    }

    if (pdahash)
        *pdahash = dahash;
    else
        l_dnaHashDestroy(&dahash);
    return 0;
}


/*!
 * \brief   l_dnaMakeHistoByHash()
 *
 * \param[in]    das
 * \param[out]   pdahash    hash map: val --> index
 * \param[out]   pdav       [optional] array of values: index --> val
 * \param[out]   pdac       [optional] histo array of counts: index --> count
 * \return  0 if OK; 1 on error
 *
 * <pre>
 * Notes:
 *      (1) Generates and returns a dna of occurrences (histogram),
 *          an aligned dna of values, and an associated hashmap.
 *          The hashmap takes %dav and a value, and points into the
 *          histogram in %dac.
 *      (2) The dna of values, %dav, is aligned with the histogram %dac,
 *          and is needed for fast lookup.  It is a hash set, because
 *          the values are unique.
 *      (3) If you only need to make a histogram and get the number of
 *          non-zero entries, here are two methods:
 *          (a) l_dnaMakeHistoByHash(da, &dahash, NULL, NULL);
 *              count = l_dnaHashGetTotalCount(dahash);
 *          (b) l_dnaRemoveDupsByHash(da, &da_nodups, NULL);
                count = l_dnaGetCount(da_nodups);
 *      (4) Lookup is simple:
 *              l_dnaFindValByHash(dav, dahash, val, &index);
 *              if (index >= 0)
 *                  l_dnaGetIValue(dac, index, &icount);
 *              else
 *                  icount = 0;
 * </pre>
 */
l_ok
l_dnaMakeHistoByHash(L_DNA       *das,
                     L_DNAHASH  **pdahash,
                     L_DNA      **pdav,
                     L_DNA      **pdac)
{
l_int32     i, n, nitems, index, count;
l_uint32    nsize;
l_uint64    key;
l_float64   val;
L_DNA      *dac, *dav;
L_DNAHASH  *dahash;

    if (pdahash) *pdahash = NULL;
    if (pdac) *pdac = NULL;
    if (pdav) *pdav = NULL;
    if (!pdahash)
        return ERROR_INT("&dahash not defined", __func__, 1);
    if (!das)
        return ERROR_INT("das not defined", __func__, 1);
    if ((n = l_dnaGetCount(das)) == 0)
        return ERROR_INT("no data in das", __func__, 1);

    findNextLargerPrime(n / 20, &nsize);  /* buckets in hash table */
    dahash = l_dnaHashCreate(nsize, 8);
    dac = l_dnaCreate(n);  /* histogram */
    dav = l_dnaCreate(n);  /* the values */
    for (i = 0, nitems = 0; i < n; i++) {
        l_dnaGetDValue(das, i, &val);
            /* Is this value already stored in dav? */
        l_dnaFindValByHash(dav, dahash, val, &index);
        if (index >= 0) {  /* found */
            l_dnaGetIValue(dac, (l_float64)index, &count);
            l_dnaSetValue(dac, (l_float64)index, count + 1);
        } else {  /* not found */
            l_dnaHashAdd(dahash, (l_uint64)val, (l_float64)nitems);
            l_dnaAddNumber(dav, val);
            l_dnaAddNumber(dac, 1);
            nitems++;
        }
    }

    *pdahash = dahash;
    if (pdac)
        *pdac = dac;
    else
        l_dnaDestroy(&dac);
    if (pdav)
        *pdav = dav;
    else
        l_dnaDestroy(&dav);
    return 0;
}


/*!
 * \brief   l_dnaIntersectionByHash()
 *
 * \param[in]    da1, da2
 * \return  dad   intersection of the number arrays, or NULL on error
 *
 * <pre>
 * Notes:
 *      (1) This uses the same method for building the intersection set
 *          as ptaIntersectionByHash() and sarrayIntersectionByHash().
 * </pre>
 */
L_DNA *
l_dnaIntersectionByHash(L_DNA  *da1,
                        L_DNA  *da2)
{
l_int32     n1, n2, nsmall, nbuckets, i, index1, index2;
l_uint32    nsize2;
l_uint64    key;
l_float64   val;
L_DNAHASH  *dahash1, *dahash2;
L_DNA      *da_small, *da_big, *dad;

    if (!da1)
        return (L_DNA *)ERROR_PTR("da1 not defined", __func__, NULL);
    if (!da2)
        return (L_DNA *)ERROR_PTR("da2 not defined", __func__, NULL);

        /* Put the elements of the biggest array into a dnahash */
    n1 = l_dnaGetCount(da1);
    n2 = l_dnaGetCount(da2);
    da_small = (n1 < n2) ? da1 : da2;   /* do not destroy da_small */
    da_big = (n1 < n2) ? da2 : da1;   /* do not destroy da_big */
    dahash1 = l_dnaHashCreateFromDna(da_big);

        /* Build up the intersection of numbers.  Add to %dad
         * if the number is in da_big (using dahash1) but hasn't
         * yet been seen in the traversal of da_small (using dahash2). */
    dad = l_dnaCreate(0);
    nsmall = l_dnaGetCount(da_small);
    findNextLargerPrime(nsmall / 20, &nsize2);  /* buckets in hash table */
    dahash2 = l_dnaHashCreate(nsize2, 0);
    nbuckets = l_dnaHashGetCount(dahash2);
    for (i = 0; i < nsmall; i++) {
        l_dnaGetDValue(da_small, i, &val);
        l_dnaFindValByHash(da_big, dahash1, val, &index1);
        if (index1 >= 0) {  /* found */
            l_dnaFindValByHash(da_small, dahash2, val, &index2);
            if (index2 == -1) {  /* not found */
                l_dnaAddNumber(dad, val);
                l_dnaHashAdd(dahash2, (l_uint64)val, (l_float64)i);
            }
        }
    }

    l_dnaHashDestroy(&dahash1);
    l_dnaHashDestroy(&dahash2);
    return dad;
}


/*!
 * \brief   l_dnaFindValByHash()
 *
 * \param[in]    da
 * \param[in]    dahash    containing indices into %da
 * \param[in]    val       searching for this number in %da
 * \param[out]   pindex    index into da if found; -1 otherwise
 * \return  0 if OK; 1 on error
 *
 * <pre>
 * Notes:
 *      (1) Algo: hash %val into a key; hash the key to get the dna
 *                in %dahash (that holds indices into %da); traverse
 *                the dna of indices looking for %val in %da.
 * </pre>
 */
l_ok
l_dnaFindValByHash(L_DNA      *da,
                   L_DNAHASH  *dahash,
                   l_float64   val,
                   l_int32    *pindex)
{
l_int32    i, nbuckets, nvals, indexval;
l_float64  vali;
l_uint64   key;
L_DNA     *da1;

    if (!pindex)
        return ERROR_INT("&index not defined", __func__, 1);
    *pindex = -1;
    if (!da)
        return ERROR_INT("da not defined", __func__, 1);
    if (!dahash)
        return ERROR_INT("dahash not defined", __func__, 1);

    nbuckets = l_dnaHashGetCount(dahash);
    da1 = l_dnaHashGetDna(dahash, (l_uint64)val, L_NOCOPY);
    if (!da1) return 0;

        /* Run through da1, looking for this %val */
    nvals = l_dnaGetCount(da1);
    for (i = 0; i < nvals; i++) {
        l_dnaGetIValue(da1, i, &indexval);
        l_dnaGetDValue(da, indexval, &vali);
        if (val == vali) {
            *pindex = indexval;
            return 0;
        }
    }

    return 0;
}


/*---------------------------------------------------------------------*
 *                Set operations on points using hashing               *
 *---------------------------------------------------------------------*/
/*!
 * \brief   ptaUnionByHash()
 *
 * \param[in]    pta1, pta2
 * \return  ptad with the union of the set of points, or NULL on error
 *
 * <pre>
 * Notes:
 *      (1) This is faster than ptaUnionByAset(), because the
 *          bucket lookup is O(n).  It should be used if the pts are
 *          integers (e.g., representing pixel positions).
 * </pre>
 */
PTA *
ptaUnionByHash(PTA  *pta1,
               PTA  *pta2)
{
PTA  *pta3, *ptad;

    if (!pta1)
        return (PTA *)ERROR_PTR("pta1 not defined", __func__, NULL);
    if (!pta2)
        return (PTA *)ERROR_PTR("pta2 not defined", __func__, NULL);

        /* Join */
    pta3 = ptaCopy(pta1);
    ptaJoin(pta3, pta2, 0, -1);

        /* Eliminate duplicates */
    ptaRemoveDupsByHash(pta3, &ptad, NULL);
    ptaDestroy(&pta3);
    return ptad;
}


/*!
 * \brief   ptaRemoveDupsByHash()
 *
 * \param[in]    ptas      assumed to be integer values
 * \param[out]   pptad     unique set of pts; duplicates removed
 * \param[out]   pdahash   [optional] dnahash used for lookup
 * \return  0 if OK, 1 on error
 *
 * <pre>
 * Notes:
 *      (1) Generates a pta with unique values.
 *      (2) The dnahash is built up with ptad to assure uniqueness.
 *          It can be used to find if a point is in the set:
 *              ptaFindPtByHash(ptad, dahash, x, y, &index)
 *      (3) The hash of the (x,y) location is simple and fast.  It scales
 *          up with the number of buckets to insure a fairly random
 *          bucket selection for adjacent points.
 *      (4) A Dna is used rather than a Numa because we need accurate
 *          representation of 32-bit integers that are indices into ptas.
 *          Integer --> float --> integer conversion makes errors for
 *          integers larger than 10M.
 *      (5) This is faster than ptaRemoveDupsByAset(), because the
 *          bucket lookup is O(n), although there is a double-loop
 *          lookup within the dna in each bucket.
 * </pre>
 */
l_ok
ptaRemoveDupsByHash(PTA         *ptas,
                    PTA        **pptad,
                    L_DNAHASH  **pdahash)
{
l_int32     i, n, index, items, x, y;
l_uint32    nsize;
l_uint64    key;
PTA        *ptad;
L_DNAHASH  *dahash;

    if (pdahash) *pdahash = NULL;
    if (!pptad)
        return ERROR_INT("&ptad not defined", __func__, 1);
    *pptad = NULL;
    if (!ptas)
        return ERROR_INT("ptas not defined", __func__, 1);

    n = ptaGetCount(ptas);
    findNextLargerPrime(n / 20, &nsize);  /* buckets in hash table */
    dahash = l_dnaHashCreate(nsize, 8);
    ptad = ptaCreate(n);
    *pptad = ptad;
    for (i = 0, items = 0; i < n; i++) {
        ptaGetIPt(ptas, i, &x, &y);
        ptaFindPtByHash(ptad, dahash, x, y, &index);
        if (index < 0) {  /* not found */
            l_hashPtToUint64(x, y, &key);
            l_dnaHashAdd(dahash, key, (l_float64)items);
            ptaAddPt(ptad, x, y);
            items++;
        }
    }

    if (pdahash)
        *pdahash = dahash;
    else
        l_dnaHashDestroy(&dahash);
    return 0;
}


/*!
 * \brief   ptaIntersectionByHash()
 *
 * \param[in]    pta1, pta2
 * \return  ptad intersection of the point sets, or NULL on error
 *
 * <pre>
 * Notes:
 *      (1) This is faster than ptaIntersectionByAset(), because the
 *          bucket lookup is O(n).  It should be used if the pts are
 *          integers (e.g., representing pixel positions).
 * </pre>
 */
PTA *
ptaIntersectionByHash(PTA  *pta1,
                      PTA  *pta2)
{
l_int32     n1, n2, nsmall, i, x, y, index1, index2;
l_uint32    nsize2;
l_uint64    key;
L_DNAHASH  *dahash1, *dahash2;
PTA        *pta_small, *pta_big, *ptad;

    if (!pta1)
        return (PTA *)ERROR_PTR("pta1 not defined", __func__, NULL);
    if (!pta2)
        return (PTA *)ERROR_PTR("pta2 not defined", __func__, NULL);

        /* Put the elements of the biggest pta into a dnahash */
    n1 = ptaGetCount(pta1);
    n2 = ptaGetCount(pta2);
    pta_small = (n1 < n2) ? pta1 : pta2;   /* do not destroy pta_small */
    pta_big = (n1 < n2) ? pta2 : pta1;   /* do not destroy pta_big */
    dahash1 = l_dnaHashCreateFromPta(pta_big);

        /* Build up the intersection of points.  Add to ptad
         * if the point is in pta_big (using dahash1) but hasn't
         * yet been seen in the traversal of pta_small (using dahash2). */
    ptad = ptaCreate(0);
    nsmall = ptaGetCount(pta_small);
    findNextLargerPrime(nsmall / 20, &nsize2);  /* buckets in hash table */
    dahash2 = l_dnaHashCreate(nsize2, 0);
    for (i = 0; i < nsmall; i++) {
        ptaGetIPt(pta_small, i, &x, &y);
        ptaFindPtByHash(pta_big, dahash1, x, y, &index1);
        if (index1 >= 0) {  /* found */
            ptaFindPtByHash(pta_small, dahash2, x, y, &index2);
            if (index2 == -1) {  /* not found */
                ptaAddPt(ptad, x, y);
                l_hashPtToUint64(x, y, &key);
                l_dnaHashAdd(dahash2, key, (l_float64)i);
            }
        }
    }

    l_dnaHashDestroy(&dahash1);
    l_dnaHashDestroy(&dahash2);
    return ptad;
}


/*!
 * \brief   ptaFindPtByHash()
 *
 * \param[in]    pta
 * \param[in]    dahash     built from pta
 * \param[in]    x, y       arbitrary points
 * \param[out]   pindex     index into pta if (x,y) is in pta; -1 otherwise
 * \return  0 if OK, 1 on error
 *
 * <pre>
 * Notes:
 *      (1) Fast lookup in dnaHash associated with a pta, to see if a
 *          random point (x,y) is already stored in the hash table.
 *      (2) We use a strong hash function to minimize the chance that
 *          two different points hash to the same key value.
 *      (3) We select the number of buckets to be about 5% of the size
 *          of the input %pta, so that when fully populated, each
 *          bucket (dna) will have about 20 entries, each being an index
 *          into %pta.  In lookup, after hashing to the key, and then
 *          again to the bucket, we traverse the bucket (dna), using the
 *          index into %pta to check if the point (x,y) has been found before.
 * </pre>
 */
l_ok
ptaFindPtByHash(PTA        *pta,
                L_DNAHASH  *dahash,
                l_int32     x,
                l_int32     y,
                l_int32    *pindex)
{
l_int32   i, nvals, index, xi, yi;
l_uint64  key;
L_DNA    *da;

    if (!pindex)
        return ERROR_INT("&index not defined", __func__, 1);
    *pindex = -1;
    if (!pta)
        return ERROR_INT("pta not defined", __func__, 1);
    if (!dahash)
        return ERROR_INT("dahash not defined", __func__, 1);

    l_hashPtToUint64(x, y, &key);
    da = l_dnaHashGetDna(dahash, key, L_NOCOPY);
    if (!da) return 0;

        /* Run through the da, looking for this point */
    nvals = l_dnaGetCount(da);
    for (i = 0; i < nvals; i++) {
        l_dnaGetIValue(da, i, &index);
        ptaGetIPt(pta, index, &xi, &yi);
        if (x == xi && y == yi) {
            *pindex = index;
            return 0;
        }
    }

    return 0;
}


/*!
 * \brief   l_dnaHashCreateFromPta()
 *
 * \param[in]    pta
 * \return  dahash, or NULL on error
 */
L_DNAHASH *
l_dnaHashCreateFromPta(PTA  *pta)
{
l_int32     i, n, x, y;
l_uint32    nsize;
l_uint64    key;
L_DNAHASH  *dahash;

    if (!pta)
        return (L_DNAHASH *)ERROR_PTR("pta not defined", __func__, NULL);

        /* Build up dnaHash of indices, hashed by a key that is
         * a large linear combination of x and y values designed to
         * randomize the key.  Having about 20 pts in each bucket is
         * roughly optimal for speed for large sets. */
    n = ptaGetCount(pta);
    findNextLargerPrime(n / 20, &nsize);  /* buckets in hash table */

        /* Add each point, using the hash as key and the index into
         * %ptas as the value.  Storing the index enables operations
         * that check for duplicates. */
    dahash = l_dnaHashCreate(nsize, 8);
    for (i = 0; i < n; i++) {
        ptaGetIPt(pta, i, &x, &y);
        l_hashPtToUint64(x, y, &key);
        l_dnaHashAdd(dahash, key, (l_float64)i);
    }

    return dahash;
}


/*----------------------------------------------------------------------*
 *               Set operations on sarray using hashing                 *
 *----------------------------------------------------------------------*/
/*!
 * \brief   sarrayRemoveDupsByHash()
 *
 * \param[in]    sas
 * \param[out]   psad      unique set of strings; duplicates removed
 * \param[out]   pdahash   [optional] dnahash used for lookup
 * \return  0 if OK, 1 on error
 *
 * <pre>
 * Notes:
 *      (1) Generates a sarray with unique values.
 *      (2) The dnahash is built up with sad to assure uniqueness.
 *          It can be used to find if a string is in the set:
 *              sarrayFindValByHash(sad, dahash, str, &index)
 *      (3) The hash of the string location is simple and fast.  It scales
 *          up with the number of buckets to insure a fairly random
 *          bucket selection input strings.
 *      (4) This is faster than sarrayRemoveDupsByAset(), because the
 *          bucket lookup is O(n), although there is a double-loop
 *          lookup within the dna in each bucket.
 * </pre>
 */
l_ok
sarrayRemoveDupsByHash(SARRAY      *sas,
                       SARRAY     **psad,
                       L_DNAHASH  **pdahash)
{
char       *str;
l_int32     i, n, index, items;
l_uint32    nsize;
l_uint64    key;
SARRAY     *sad;
L_DNAHASH  *dahash;

    if (pdahash) *pdahash = NULL;
    if (!psad)
        return ERROR_INT("&sad not defined", __func__, 1);
    *psad = NULL;
    if (!sas)
        return ERROR_INT("sas not defined", __func__, 1);

    n = sarrayGetCount(sas);
    findNextLargerPrime(n / 20, &nsize);  /* buckets in hash table */
    dahash = l_dnaHashCreate(nsize, 8);
    sad = sarrayCreate(n);
    *psad = sad;
    for (i = 0, items = 0; i < n; i++) {
        str = sarrayGetString(sas, i, L_NOCOPY);
        sarrayFindStringByHash(sad, dahash, str, &index);
        if (index < 0) {  /* not found */
            l_hashStringToUint64(str, &key);
            l_dnaHashAdd(dahash, key, (l_float64)items);
            sarrayAddString(sad, str, L_COPY);
            items++;
        }
    }

    if (pdahash)
        *pdahash = dahash;
    else
        l_dnaHashDestroy(&dahash);
    return 0;
}


/*!
 * \brief   sarrayIntersectionByHash()
 *
 * \param[in]    sa1, sa2
 * \return  sad  intersection of the strings, or NULL on error
 *
 * <pre>
 * Notes:
 *      (1) This is faster than sarrayIntersectionByAset(), because the
 *          bucket lookup is O(n).
 * </pre>
 */
SARRAY *
sarrayIntersectionByHash(SARRAY  *sa1,
                         SARRAY  *sa2)
{
char       *str;
l_int32     n1, n2, nsmall, i, index1, index2;
l_uint32    nsize2;
l_uint64    key;
L_DNAHASH  *dahash1, *dahash2;
SARRAY     *sa_small, *sa_big, *sad;

    if (!sa1)
        return (SARRAY *)ERROR_PTR("sa1 not defined", __func__, NULL);
    if (!sa2)
        return (SARRAY *)ERROR_PTR("sa2 not defined", __func__, NULL);

        /* Put the elements of the biggest sarray into a dnahash */
    n1 = sarrayGetCount(sa1);
    n2 = sarrayGetCount(sa2);
    sa_small = (n1 < n2) ? sa1 : sa2;   /* do not destroy sa_small */
    sa_big = (n1 < n2) ? sa2 : sa1;   /* do not destroy sa_big */
    dahash1 = l_dnaHashCreateFromSarray(sa_big);

        /* Build up the intersection of strings.  Add to %sad
         * if the string is in sa_big (using dahash1) but hasn't
         * yet been seen in the traversal of sa_small (using dahash2). */
    sad = sarrayCreate(0);
    nsmall = sarrayGetCount(sa_small);
    findNextLargerPrime(nsmall / 20, &nsize2);  /* buckets in hash table */
    dahash2 = l_dnaHashCreate(nsize2, 0);
    for (i = 0; i < nsmall; i++) {
        str = sarrayGetString(sa_small, i, L_NOCOPY);
        sarrayFindStringByHash(sa_big, dahash1, str, &index1);
        if (index1 >= 0) {
            sarrayFindStringByHash(sa_small, dahash2, str, &index2);
            if (index2 == -1) {
                sarrayAddString(sad, str, L_COPY);
                l_hashStringToUint64(str, &key);
                l_dnaHashAdd(dahash2, key, (l_float64)i);
            }
        }
    }

    l_dnaHashDestroy(&dahash1);
    l_dnaHashDestroy(&dahash2);
    return sad;
}


/*!
 * \brief   sarrayFindStringByHash()
 *
 * \param[in]    sa
 * \param[in]    dahash   built from sa
 * \param[in]    str      arbitrary string
 * \param[out]   pindex   index into %sa if %str is in %sa; -1 otherwise
 * \return  0 if OK, 1 on error
 *
 * <pre>
 * Notes:
 *      (1) Fast lookup in dnaHash associated with a sarray, to see if a
 *          random string %str is already stored in the hash table.
 *      (2) We use a strong hash function to minimize the chance that
 *          two different strings hash to the same key value.
 *      (3) We select the number of buckets to be about 5% of the size
 *          of the input sarray, so that when fully populated, each
 *          bucket (dna) will have about 20 entries, each being an index
 *          into sa.  In lookup, after hashing to the key, and then
 *          again to the bucket, we traverse the bucket (dna), using the
 *          index into sa to check if %str has been found before.
 * </pre>
 */
l_ok
sarrayFindStringByHash(SARRAY      *sa,
                       L_DNAHASH   *dahash,
                       const char  *str,
                       l_int32     *pindex)
{
char     *stri;
l_int32   i, nvals, index;
l_uint64  key;
L_DNA    *da;

    if (!pindex)
        return ERROR_INT("&index not defined", __func__, 1);
    *pindex = -1;
    if (!sa)
        return ERROR_INT("sa not defined", __func__, 1);
    if (!dahash)
        return ERROR_INT("dahash not defined", __func__, 1);

    l_hashStringToUint64(str, &key);
    da = l_dnaHashGetDna(dahash, key, L_NOCOPY);
    if (!da) return 0;

        /* Run through the da, looking for this string */
    nvals = l_dnaGetCount(da);
    for (i = 0; i < nvals; i++) {
        l_dnaGetIValue(da, i, &index);
        stri = sarrayGetString(sa, index, L_NOCOPY);
        if (!strcmp(str, stri)) {  /* duplicate */
            *pindex = index;
            return 0;
        }
    }

    return 0;
}


/*!
 * \brief   l_dnaHashCreateFromSarray()
 *
 * \param[in]    sa
 * \return  dahash, or NULL on error
 */
L_DNAHASH *
l_dnaHashCreateFromSarray(SARRAY  *sa)
{
char       *str;
l_int32     i, n;
l_uint32    nsize;
l_uint64    key;
L_DNAHASH  *dahash;

        /* Build up dnaHash of indices, hashed by a 64-bit key that
         * should randomize the lower bits used in bucket selection.
         * Having about 20 pts in each bucket is roughly optimal. */
    n = sarrayGetCount(sa);
    findNextLargerPrime(n / 20, &nsize);  /* buckets in hash table */
/*    lept_stderr("Prime used: %d\n", nsize); */

        /* Add each string, using the hash as key and the index into %sa
         * as the value.  Storing the index enables operations that check
         * for duplicates.  */
    dahash = l_dnaHashCreate(nsize, 8);
    for (i = 0; i < n; i++) {
        str = sarrayGetString(sa, i, L_NOCOPY);
        l_hashStringToUint64(str, &key);
        l_dnaHashAdd(dahash, key, (l_float64)i);
    }

    return dahash;
}