like_support.c

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/*-------------------------------------------------------------------------
 *
 * like_support.c
 *    Planner support functions for LIKE, regex, and related operators.
 *
 * These routines handle special optimization of operators that can be
 * used with index scans even though they are not known to the executor's
 * indexscan machinery.  The key idea is that these operators allow us
 * to derive approximate indexscan qual clauses, such that any tuples
 * that pass the operator clause itself must also satisfy the simpler
 * indexscan condition(s).  Then we can use the indexscan machinery
 * to avoid scanning as much of the table as we'd otherwise have to,
 * while applying the original operator as a qpqual condition to ensure
 * we deliver only the tuples we want.  (In essence, we're using a regular
 * index as if it were a lossy index.)
 *
 * An example of what we're doing is
 *          textfield LIKE 'abc%def'
 * from which we can generate the indexscanable conditions
 *          textfield >= 'abc' AND textfield < 'abd'
 * which allow efficient scanning of an index on textfield.
 * (In reality, character set and collation issues make the transformation
 * from LIKE to indexscan limits rather harder than one might think ...
 * but that's the basic idea.)
 *
 * Portions Copyright (c) 1996-2023, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 *
 * IDENTIFICATION
 *    src/backend/utils/adt/like_support.c
 *
 *-------------------------------------------------------------------------
 */
#include "postgres.h"
 
#include <math.h>
 
#include "access/htup_details.h"
#include "access/stratnum.h"
#include "catalog/pg_collation.h"
#include "catalog/pg_operator.h"
#include "catalog/pg_opfamily.h"
#include "catalog/pg_statistic.h"
#include "catalog/pg_type.h"
#include "mb/pg_wchar.h"
#include "miscadmin.h"
#include "nodes/makefuncs.h"
#include "nodes/nodeFuncs.h"
#include "nodes/supportnodes.h"
#include "utils/builtins.h"
#include "utils/datum.h"
#include "utils/lsyscache.h"
#include "utils/pg_locale.h"
#include "utils/selfuncs.h"
#include "utils/varlena.h"
 
 
typedef enum
{
    Pattern_Type_Like,
    Pattern_Type_Like_IC,
    Pattern_Type_Regex,
    Pattern_Type_Regex_IC,
    Pattern_Type_Prefix
} Pattern_Type;
 
typedef enum
{
    Pattern_Prefix_None, Pattern_Prefix_Partial, Pattern_Prefix_Exact
} Pattern_Prefix_Status;
 
static Node *like_regex_support(Node *rawreq, Pattern_Type ptype);
static List *match_pattern_prefix(Node *leftop,
                                  Node *rightop,
                                  Pattern_Type ptype,
                                  Oid expr_coll,
                                  Oid opfamily,
                                  Oid indexcollation);
static double patternsel_common(PlannerInfo *root,
                                Oid oprid,
                                Oid opfuncid,
                                List *args,
                                int varRelid,
                                Oid collation,
                                Pattern_Type ptype,
                                bool negate);
static Pattern_Prefix_Status pattern_fixed_prefix(Const *patt,
                                                  Pattern_Type ptype,
                                                  Oid collation,
                                                  Const **prefix,
                                                  Selectivity *rest_selec);
static Selectivity prefix_selectivity(PlannerInfo *root,
                                      VariableStatData *vardata,
                                      Oid eqopr, Oid ltopr, Oid geopr,
                                      Oid collation,
                                      Const *prefixcon);
static Selectivity like_selectivity(const char *patt, int pattlen,
                                    bool case_insensitive);
static Selectivity regex_selectivity(const char *patt, int pattlen,
                                     bool case_insensitive,
                                     int fixed_prefix_len);
static int  pattern_char_isalpha(char c, bool is_multibyte,
                                 pg_locale_t locale, bool locale_is_c);
static Const *make_greater_string(const Const *str_const, FmgrInfo *ltproc,
                                  Oid collation);
static Datum string_to_datum(const char *str, Oid datatype);
static Const *string_to_const(const char *str, Oid datatype);
static Const *string_to_bytea_const(const char *str, size_t str_len);
 
 
/*
 * Planner support functions for LIKE, regex, and related operators
 */
Datum
textlike_support(PG_FUNCTION_ARGS)
{
    Node       *rawreq = (Node *) PG_GETARG_POINTER(0);
 
    PG_RETURN_POINTER(like_regex_support(rawreq, Pattern_Type_Like));
}
 
Datum
texticlike_support(PG_FUNCTION_ARGS)
{
    Node       *rawreq = (Node *) PG_GETARG_POINTER(0);
 
    PG_RETURN_POINTER(like_regex_support(rawreq, Pattern_Type_Like_IC));
}
 
Datum
textregexeq_support(PG_FUNCTION_ARGS)
{
    Node       *rawreq = (Node *) PG_GETARG_POINTER(0);
 
    PG_RETURN_POINTER(like_regex_support(rawreq, Pattern_Type_Regex));
}
 
Datum
texticregexeq_support(PG_FUNCTION_ARGS)
{
    Node       *rawreq = (Node *) PG_GETARG_POINTER(0);
 
    PG_RETURN_POINTER(like_regex_support(rawreq, Pattern_Type_Regex_IC));
}
 
Datum
text_starts_with_support(PG_FUNCTION_ARGS)
{
    Node       *rawreq = (Node *) PG_GETARG_POINTER(0);
 
    PG_RETURN_POINTER(like_regex_support(rawreq, Pattern_Type_Prefix));
}
 
/* Common code for the above */
static Node *
like_regex_support(Node *rawreq, Pattern_Type ptype)
{
    Node       *ret = NULL;
 
    if (IsA(rawreq, SupportRequestSelectivity))
    {
        /*
         * Make a selectivity estimate for a function call, just as we'd do if
         * the call was via the corresponding operator.
         */
        SupportRequestSelectivity *req = (SupportRequestSelectivity *) rawreq;
        Selectivity s1;
 
        if (req->is_join)
        {
            /*
             * For the moment we just punt.  If patternjoinsel is ever
             * improved to do better, this should be made to call it.
             */
            s1 = DEFAULT_MATCH_SEL;
        }
        else
        {
            /* Share code with operator restriction selectivity functions */
            s1 = patternsel_common(req->root,
                                   InvalidOid,
                                   req->funcid,
                                   req->args,
                                   req->varRelid,
                                   req->inputcollid,
                                   ptype,
                                   false);
        }
        req->selectivity = s1;
        ret = (Node *) req;
    }
    else if (IsA(rawreq, SupportRequestIndexCondition))
    {
        /* Try to convert operator/function call to index conditions */
        SupportRequestIndexCondition *req = (SupportRequestIndexCondition *) rawreq;
 
        /*
         * Currently we have no "reverse" match operators with the pattern on
         * the left, so we only need consider cases with the indexkey on the
         * left.
         */
        if (req->indexarg != 0)
            return NULL;
 
        if (is_opclause(req->node))
        {
            OpExpr     *clause = (OpExpr *) req->node;
 
            Assert(list_length(clause->args) == 2);
            ret = (Node *)
                match_pattern_prefix((Node *) linitial(clause->args),
                                     (Node *) lsecond(clause->args),
                                     ptype,
                                     clause->inputcollid,
                                     req->opfamily,
                                     req->indexcollation);
        }
        else if (is_funcclause(req->node))  /* be paranoid */
        {
            FuncExpr   *clause = (FuncExpr *) req->node;
 
            Assert(list_length(clause->args) == 2);
            ret = (Node *)
                match_pattern_prefix((Node *) linitial(clause->args),
                                     (Node *) lsecond(clause->args),
                                     ptype,
                                     clause->inputcollid,
                                     req->opfamily,
                                     req->indexcollation);
        }
    }
 
    return ret;
}
 
/*
 * match_pattern_prefix
 *    Try to generate an indexqual for a LIKE or regex operator.
 */
static List *
match_pattern_prefix(Node *leftop,
                     Node *rightop,
                     Pattern_Type ptype,
                     Oid expr_coll,
                     Oid opfamily,
                     Oid indexcollation)
{
    List       *result;
    Const      *patt;
    Const      *prefix;
    Pattern_Prefix_Status pstatus;
    Oid         ldatatype;
    Oid         rdatatype;
    Oid         eqopr;
    Oid         ltopr;
    Oid         geopr;
    Oid         preopr = InvalidOid;
    bool        collation_aware;
    Expr       *expr;
    FmgrInfo    ltproc;
    Const      *greaterstr;
 
    /*
     * Can't do anything with a non-constant or NULL pattern argument.
     *
     * Note that since we restrict ourselves to cases with a hard constant on
     * the RHS, it's a-fortiori a pseudoconstant, and we don't need to worry
     * about verifying that.
     */
    if (!IsA(rightop, Const) ||
        ((Const *) rightop)->constisnull)
        return NIL;
    patt = (Const *) rightop;
 
    /*
     * Not supported if the expression collation is nondeterministic.  The
     * optimized equality or prefix tests use bytewise comparisons, which is
     * not consistent with nondeterministic collations.  The actual
     * pattern-matching implementation functions will later error out that
     * pattern-matching is not supported with nondeterministic collations. (We
     * could also error out here, but by doing it later we get more precise
     * error messages.)  (It should be possible to support at least
     * Pattern_Prefix_Exact, but no point as long as the actual
     * pattern-matching implementations don't support it.)
     *
     * expr_coll is not set for a non-collation-aware data type such as bytea.
     */
    if (expr_coll && !get_collation_isdeterministic(expr_coll))
        return NIL;
 
    /*
     * Try to extract a fixed prefix from the pattern.
     */
    pstatus = pattern_fixed_prefix(patt, ptype, expr_coll,
                                   &prefix, NULL);
 
    /* fail if no fixed prefix */
    if (pstatus == Pattern_Prefix_None)
        return NIL;
 
    /*
     * Identify the operators we want to use, based on the type of the
     * left-hand argument.  Usually these are just the type's regular
     * comparison operators, but if we are considering one of the semi-legacy
     * "pattern" opclasses, use the "pattern" operators instead.  Those are
     * not collation-sensitive but always use C collation, as we want.  The
     * selected operators also determine the needed type of the prefix
     * constant.
     */
    ldatatype = exprType(leftop);
    switch (ldatatype)
    {
        case TEXTOID:
            if (opfamily == TEXT_PATTERN_BTREE_FAM_OID)
            {
                eqopr = TextEqualOperator;
                ltopr = TextPatternLessOperator;
                geopr = TextPatternGreaterEqualOperator;
                collation_aware = false;
            }
            else if (opfamily == TEXT_SPGIST_FAM_OID)
            {
                eqopr = TextEqualOperator;
                ltopr = TextPatternLessOperator;
                geopr = TextPatternGreaterEqualOperator;
                /* This opfamily has direct support for prefixing */
                preopr = TextPrefixOperator;
                collation_aware = false;
            }
            else
            {
                eqopr = TextEqualOperator;
                ltopr = TextLessOperator;
                geopr = TextGreaterEqualOperator;
                collation_aware = true;
            }
            rdatatype = TEXTOID;
            break;
        case NAMEOID:
 
            /*
             * Note that here, we need the RHS type to be text, so that the
             * comparison value isn't improperly truncated to NAMEDATALEN.
             */
            eqopr = NameEqualTextOperator;
            ltopr = NameLessTextOperator;
            geopr = NameGreaterEqualTextOperator;
            collation_aware = true;
            rdatatype = TEXTOID;
            break;
        case BPCHAROID:
            if (opfamily == BPCHAR_PATTERN_BTREE_FAM_OID)
            {
                eqopr = BpcharEqualOperator;
                ltopr = BpcharPatternLessOperator;
                geopr = BpcharPatternGreaterEqualOperator;
                collation_aware = false;
            }
            else
            {
                eqopr = BpcharEqualOperator;
                ltopr = BpcharLessOperator;
                geopr = BpcharGreaterEqualOperator;
                collation_aware = true;
            }
            rdatatype = BPCHAROID;
            break;
        case BYTEAOID:
            eqopr = ByteaEqualOperator;
            ltopr = ByteaLessOperator;
            geopr = ByteaGreaterEqualOperator;
            collation_aware = false;
            rdatatype = BYTEAOID;
            break;
        default:
            /* Can't get here unless we're attached to the wrong operator */
            return NIL;
    }
 
    /*
     * If necessary, coerce the prefix constant to the right type.  The given
     * prefix constant is either text or bytea type, therefore the only case
     * where we need to do anything is when converting text to bpchar.  Those
     * two types are binary-compatible, so relabeling the Const node is
     * sufficient.
     */
    if (prefix->consttype != rdatatype)
    {
        Assert(prefix->consttype == TEXTOID &&
               rdatatype == BPCHAROID);
        prefix->consttype = rdatatype;
    }
 
    /*
     * If we found an exact-match pattern, generate an "=" indexqual.
     *
     * Here and below, check to see whether the desired operator is actually
     * supported by the index opclass, and fail quietly if not.  This allows
     * us to not be concerned with specific opclasses (except for the legacy
     * "pattern" cases); any index that correctly implements the operators
     * will work.
     */
    if (pstatus == Pattern_Prefix_Exact)
    {
        if (!op_in_opfamily(eqopr, opfamily))
            return NIL;
        expr = make_opclause(eqopr, BOOLOID, false,
                             (Expr *) leftop, (Expr *) prefix,
                             InvalidOid, indexcollation);
        result = list_make1(expr);
        return result;
    }
 
    /*
     * Otherwise, we have a nonempty required prefix of the values.  Some
     * opclasses support prefix checks directly, otherwise we'll try to
     * generate a range constraint.
     */
    if (OidIsValid(preopr) && op_in_opfamily(preopr, opfamily))
    {
        expr = make_opclause(preopr, BOOLOID, false,
                             (Expr *) leftop, (Expr *) prefix,
                             InvalidOid, indexcollation);
        result = list_make1(expr);
        return result;
    }
 
    /*
     * Since we need a range constraint, it's only going to work reliably if
     * the index is collation-insensitive or has "C" collation.  Note that
     * here we are looking at the index's collation, not the expression's
     * collation -- this test is *not* dependent on the LIKE/regex operator's
     * collation.
     */
    if (collation_aware &&
        !lc_collate_is_c(indexcollation))
        return NIL;
 
    /*
     * We can always say "x >= prefix".
     */
    if (!op_in_opfamily(geopr, opfamily))
        return NIL;
    expr = make_opclause(geopr, BOOLOID, false,
                         (Expr *) leftop, (Expr *) prefix,
                         InvalidOid, indexcollation);
    result = list_make1(expr);
 
    /*-------
     * If we can create a string larger than the prefix, we can say
     * "x < greaterstr".  NB: we rely on make_greater_string() to generate
     * a guaranteed-greater string, not just a probably-greater string.
     * In general this is only guaranteed in C locale, so we'd better be
     * using a C-locale index collation.
     *-------
     */
    if (!op_in_opfamily(ltopr, opfamily))
        return result;
    fmgr_info(get_opcode(ltopr), &ltproc);
    greaterstr = make_greater_string(prefix, &ltproc, indexcollation);
    if (greaterstr)
    {
        expr = make_opclause(ltopr, BOOLOID, false,
                             (Expr *) leftop, (Expr *) greaterstr,
                             InvalidOid, indexcollation);
        result = lappend(result, expr);
    }
 
    return result;
}
 
 
/*
 * patternsel_common - generic code for pattern-match restriction selectivity.
 *
 * To support using this from either the operator or function paths, caller
 * may pass either operator OID or underlying function OID; we look up the
 * latter from the former if needed.  (We could just have patternsel() call
 * get_opcode(), but the work would be wasted if we don't have a need to
 * compare a fixed prefix to the pg_statistic data.)
 *
 * Note that oprid and/or opfuncid should be for the positive-match operator
 * even when negate is true.
 */
static double
patternsel_common(PlannerInfo *root,
                  Oid oprid,
                  Oid opfuncid,
                  List *args,
                  int varRelid,
                  Oid collation,
                  Pattern_Type ptype,
                  bool negate)
{
    VariableStatData vardata;
    Node       *other;
    bool        varonleft;
    Datum       constval;
    Oid         consttype;
    Oid         vartype;
    Oid         rdatatype;
    Oid         eqopr;
    Oid         ltopr;
    Oid         geopr;
    Pattern_Prefix_Status pstatus;
    Const      *patt;
    Const      *prefix = NULL;
    Selectivity rest_selec = 0;
    double      nullfrac = 0.0;
    double      result;
 
    /*
     * Initialize result to the appropriate default estimate depending on
     * whether it's a match or not-match operator.
     */
    if (negate)
        result = 1.0 - DEFAULT_MATCH_SEL;
    else
        result = DEFAULT_MATCH_SEL;
 
    /*
     * If expression is not variable op constant, then punt and return the
     * default estimate.
     */
    if (!get_restriction_variable(root, args, varRelid,
                                  &vardata, &other, &varonleft))
        return result;
    if (!varonleft || !IsA(other, Const))
    {
        ReleaseVariableStats(vardata);
        return result;
    }
 
    /*
     * If the constant is NULL, assume operator is strict and return zero, ie,
     * operator will never return TRUE.  (It's zero even for a negator op.)
     */
    if (((Const *) other)->constisnull)
    {
        ReleaseVariableStats(vardata);
        return 0.0;
    }
    constval = ((Const *) other)->constvalue;
    consttype = ((Const *) other)->consttype;
 
    /*
     * The right-hand const is type text or bytea for all supported operators.
     * We do not expect to see binary-compatible types here, since
     * const-folding should have relabeled the const to exactly match the
     * operator's declared type.
     */
    if (consttype != TEXTOID && consttype != BYTEAOID)
    {
        ReleaseVariableStats(vardata);
        return result;
    }
 
    /*
     * Similarly, the exposed type of the left-hand side should be one of
     * those we know.  (Do not look at vardata.atttype, which might be
     * something binary-compatible but different.)  We can use it to identify
     * the comparison operators and the required type of the comparison
     * constant, much as in match_pattern_prefix().
     */
    vartype = vardata.vartype;
 
    switch (vartype)
    {
        case TEXTOID:
            eqopr = TextEqualOperator;
            ltopr = TextLessOperator;
            geopr = TextGreaterEqualOperator;
            rdatatype = TEXTOID;
            break;
        case NAMEOID:
 
            /*
             * Note that here, we need the RHS type to be text, so that the
             * comparison value isn't improperly truncated to NAMEDATALEN.
             */
            eqopr = NameEqualTextOperator;
            ltopr = NameLessTextOperator;
            geopr = NameGreaterEqualTextOperator;
            rdatatype = TEXTOID;
            break;
        case BPCHAROID:
            eqopr = BpcharEqualOperator;
            ltopr = BpcharLessOperator;
            geopr = BpcharGreaterEqualOperator;
            rdatatype = BPCHAROID;
            break;
        case BYTEAOID:
            eqopr = ByteaEqualOperator;
            ltopr = ByteaLessOperator;
            geopr = ByteaGreaterEqualOperator;
            rdatatype = BYTEAOID;
            break;
        default:
            /* Can't get here unless we're attached to the wrong operator */
            ReleaseVariableStats(vardata);
            return result;
    }
 
    /*
     * Grab the nullfrac for use below.
     */
    if (HeapTupleIsValid(vardata.statsTuple))
    {
        Form_pg_statistic stats;
 
        stats = (Form_pg_statistic) GETSTRUCT(vardata.statsTuple);
        nullfrac = stats->stanullfrac;
    }
 
    /*
     * Pull out any fixed prefix implied by the pattern, and estimate the
     * fractional selectivity of the remainder of the pattern.  Unlike many
     * other selectivity estimators, we use the pattern operator's actual
     * collation for this step.  This is not because we expect the collation
     * to make a big difference in the selectivity estimate (it seldom would),
     * but because we want to be sure we cache compiled regexps under the
     * right cache key, so that they can be re-used at runtime.
     */
    patt = (Const *) other;
    pstatus = pattern_fixed_prefix(patt, ptype, collation,
                                   &prefix, &rest_selec);
 
    /*
     * If necessary, coerce the prefix constant to the right type.  The only
     * case where we need to do anything is when converting text to bpchar.
     * Those two types are binary-compatible, so relabeling the Const node is
     * sufficient.
     */
    if (prefix && prefix->consttype != rdatatype)
    {
        Assert(prefix->consttype == TEXTOID &&
               rdatatype == BPCHAROID);
        prefix->consttype = rdatatype;
    }
 
    if (pstatus == Pattern_Prefix_Exact)
    {
        /*
         * Pattern specifies an exact match, so estimate as for '='
         */
        result = var_eq_const(&vardata, eqopr, collation, prefix->constvalue,
                              false, true, false);
    }
    else
    {
        /*
         * Not exact-match pattern.  If we have a sufficiently large
         * histogram, estimate selectivity for the histogram part of the
         * population by counting matches in the histogram.  If not, estimate
         * selectivity of the fixed prefix and remainder of pattern
         * separately, then combine the two to get an estimate of the
         * selectivity for the part of the column population represented by
         * the histogram.  (For small histograms, we combine these
         * approaches.)
         *
         * We then add up data for any most-common-values values; these are
         * not in the histogram population, and we can get exact answers for
         * them by applying the pattern operator, so there's no reason to
         * approximate.  (If the MCVs cover a significant part of the total
         * population, this gives us a big leg up in accuracy.)
         */
        Selectivity selec;
        int         hist_size;
        FmgrInfo    opproc;
        double      mcv_selec,
                    sumcommon;
 
        /* Try to use the histogram entries to get selectivity */
        if (!OidIsValid(opfuncid))
            opfuncid = get_opcode(oprid);
        fmgr_info(opfuncid, &opproc);
 
        selec = histogram_selectivity(&vardata, &opproc, collation,
                                      constval, true,
                                      10, 1, &hist_size);
 
        /* If not at least 100 entries, use the heuristic method */
        if (hist_size < 100)
        {
            Selectivity heursel;
            Selectivity prefixsel;
 
            if (pstatus == Pattern_Prefix_Partial)
                prefixsel = prefix_selectivity(root, &vardata,
                                               eqopr, ltopr, geopr,
                                               collation,
                                               prefix);
            else
                prefixsel = 1.0;
            heursel = prefixsel * rest_selec;
 
            if (selec < 0)      /* fewer than 10 histogram entries? */
                selec = heursel;
            else
            {
                /*
                 * For histogram sizes from 10 to 100, we combine the
                 * histogram and heuristic selectivities, putting increasingly
                 * more trust in the histogram for larger sizes.
                 */
                double      hist_weight = hist_size / 100.0;
 
                selec = selec * hist_weight + heursel * (1.0 - hist_weight);
            }
        }
 
        /* In any case, don't believe extremely small or large estimates. */
        if (selec < 0.0001)
            selec = 0.0001;
        else if (selec > 0.9999)
            selec = 0.9999;
 
        /*
         * If we have most-common-values info, add up the fractions of the MCV
         * entries that satisfy MCV OP PATTERN.  These fractions contribute
         * directly to the result selectivity.  Also add up the total fraction
         * represented by MCV entries.
         */
        mcv_selec = mcv_selectivity(&vardata, &opproc, collation,
                                    constval, true,
                                    &sumcommon);
 
        /*
         * Now merge the results from the MCV and histogram calculations,
         * realizing that the histogram covers only the non-null values that
         * are not listed in MCV.
         */
        selec *= 1.0 - nullfrac - sumcommon;
        selec += mcv_selec;
        result = selec;
    }
 
    /* now adjust if we wanted not-match rather than match */
    if (negate)
        result = 1.0 - result - nullfrac;
 
    /* result should be in range, but make sure... */
    CLAMP_PROBABILITY(result);
 
    if (prefix)
    {
        pfree(DatumGetPointer(prefix->constvalue));
        pfree(prefix);
    }
 
    ReleaseVariableStats(vardata);
 
    return result;
}
 
/*
 * Fix impedance mismatch between SQL-callable functions and patternsel_common
 */
static double
patternsel(PG_FUNCTION_ARGS, Pattern_Type ptype, bool negate)
{
    PlannerInfo *root = (PlannerInfo *) PG_GETARG_POINTER(0);
    Oid         operator = PG_GETARG_OID(1);
    List       *args = (List *) PG_GETARG_POINTER(2);
    int         varRelid = PG_GETARG_INT32(3);
    Oid         collation = PG_GET_COLLATION();
 
    /*
     * If this is for a NOT LIKE or similar operator, get the corresponding
     * positive-match operator and work with that.
     */
    if (negate)
    {
        operator = get_negator(operator);
        if (!OidIsValid(operator))
            elog(ERROR, "patternsel called for operator without a negator");
    }
 
    return patternsel_common(root,
                             operator,
                             InvalidOid,
                             args,
                             varRelid,
                             collation,
                             ptype,
                             negate);
}
 
/*
 *      regexeqsel      - Selectivity of regular-expression pattern match.
 */
Datum
regexeqsel(PG_FUNCTION_ARGS)
{
    PG_RETURN_FLOAT8(patternsel(fcinfo, Pattern_Type_Regex, false));
}
 
/*
 *      icregexeqsel    - Selectivity of case-insensitive regex match.
 */
Datum
icregexeqsel(PG_FUNCTION_ARGS)
{
    PG_RETURN_FLOAT8(patternsel(fcinfo, Pattern_Type_Regex_IC, false));
}
 
/*
 *      likesel         - Selectivity of LIKE pattern match.
 */
Datum
likesel(PG_FUNCTION_ARGS)
{
    PG_RETURN_FLOAT8(patternsel(fcinfo, Pattern_Type_Like, false));
}
 
/*
 *      prefixsel           - selectivity of prefix operator
 */
Datum
prefixsel(PG_FUNCTION_ARGS)
{
    PG_RETURN_FLOAT8(patternsel(fcinfo, Pattern_Type_Prefix, false));
}
 
/*
 *
 *      iclikesel           - Selectivity of ILIKE pattern match.
 */
Datum
iclikesel(PG_FUNCTION_ARGS)
{
    PG_RETURN_FLOAT8(patternsel(fcinfo, Pattern_Type_Like_IC, false));
}
 
/*
 *      regexnesel      - Selectivity of regular-expression pattern non-match.
 */
Datum
regexnesel(PG_FUNCTION_ARGS)
{
    PG_RETURN_FLOAT8(patternsel(fcinfo, Pattern_Type_Regex, true));
}
 
/*
 *      icregexnesel    - Selectivity of case-insensitive regex non-match.
 */
Datum
icregexnesel(PG_FUNCTION_ARGS)
{
    PG_RETURN_FLOAT8(patternsel(fcinfo, Pattern_Type_Regex_IC, true));
}
 
/*
 *      nlikesel        - Selectivity of LIKE pattern non-match.
 */
Datum
nlikesel(PG_FUNCTION_ARGS)
{
    PG_RETURN_FLOAT8(patternsel(fcinfo, Pattern_Type_Like, true));
}
 
/*
 *      icnlikesel      - Selectivity of ILIKE pattern non-match.
 */
Datum
icnlikesel(PG_FUNCTION_ARGS)
{
    PG_RETURN_FLOAT8(patternsel(fcinfo, Pattern_Type_Like_IC, true));
}
 
/*
 * patternjoinsel       - Generic code for pattern-match join selectivity.
 */
static double
patternjoinsel(PG_FUNCTION_ARGS, Pattern_Type ptype, bool negate)
{
    /* For the moment we just punt. */
    return negate ? (1.0 - DEFAULT_MATCH_SEL) : DEFAULT_MATCH_SEL;
}
 
/*
 *      regexeqjoinsel  - Join selectivity of regular-expression pattern match.
 */
Datum
regexeqjoinsel(PG_FUNCTION_ARGS)
{
    PG_RETURN_FLOAT8(patternjoinsel(fcinfo, Pattern_Type_Regex, false));
}
 
/*
 *      icregexeqjoinsel    - Join selectivity of case-insensitive regex match.
 */
Datum
icregexeqjoinsel(PG_FUNCTION_ARGS)
{
    PG_RETURN_FLOAT8(patternjoinsel(fcinfo, Pattern_Type_Regex_IC, false));
}
 
/*
 *      likejoinsel         - Join selectivity of LIKE pattern match.
 */
Datum
likejoinsel(PG_FUNCTION_ARGS)
{
    PG_RETURN_FLOAT8(patternjoinsel(fcinfo, Pattern_Type_Like, false));
}
 
/*
 *      prefixjoinsel           - Join selectivity of prefix operator
 */
Datum
prefixjoinsel(PG_FUNCTION_ARGS)
{
    PG_RETURN_FLOAT8(patternjoinsel(fcinfo, Pattern_Type_Prefix, false));
}
 
/*
 *      iclikejoinsel           - Join selectivity of ILIKE pattern match.
 */
Datum
iclikejoinsel(PG_FUNCTION_ARGS)
{
    PG_RETURN_FLOAT8(patternjoinsel(fcinfo, Pattern_Type_Like_IC, false));
}
 
/*
 *      regexnejoinsel  - Join selectivity of regex non-match.
 */
Datum
regexnejoinsel(PG_FUNCTION_ARGS)
{
    PG_RETURN_FLOAT8(patternjoinsel(fcinfo, Pattern_Type_Regex, true));
}
 
/*
 *      icregexnejoinsel    - Join selectivity of case-insensitive regex non-match.
 */
Datum
icregexnejoinsel(PG_FUNCTION_ARGS)
{
    PG_RETURN_FLOAT8(patternjoinsel(fcinfo, Pattern_Type_Regex_IC, true));
}
 
/*
 *      nlikejoinsel        - Join selectivity of LIKE pattern non-match.
 */
Datum
nlikejoinsel(PG_FUNCTION_ARGS)
{
    PG_RETURN_FLOAT8(patternjoinsel(fcinfo, Pattern_Type_Like, true));
}
 
/*
 *      icnlikejoinsel      - Join selectivity of ILIKE pattern non-match.
 */
Datum
icnlikejoinsel(PG_FUNCTION_ARGS)
{
    PG_RETURN_FLOAT8(patternjoinsel(fcinfo, Pattern_Type_Like_IC, true));
}
 
 
/*-------------------------------------------------------------------------
 *
 * Pattern analysis functions
 *
 * These routines support analysis of LIKE and regular-expression patterns
 * by the planner/optimizer.  It's important that they agree with the
 * regular-expression code in backend/regex/ and the LIKE code in
 * backend/utils/adt/like.c.  Also, the computation of the fixed prefix
 * must be conservative: if we report a string longer than the true fixed
 * prefix, the query may produce actually wrong answers, rather than just
 * getting a bad selectivity estimate!
 *
 *-------------------------------------------------------------------------
 */
 
/*
 * Extract the fixed prefix, if any, for a pattern.
 *
 * *prefix is set to a palloc'd prefix string (in the form of a Const node),
 *  or to NULL if no fixed prefix exists for the pattern.
 * If rest_selec is not NULL, *rest_selec is set to an estimate of the
 *  selectivity of the remainder of the pattern (without any fixed prefix).
 * The prefix Const has the same type (TEXT or BYTEA) as the input pattern.
 *
 * The return value distinguishes no fixed prefix, a partial prefix,
 * or an exact-match-only pattern.
 */
 
static Pattern_Prefix_Status
like_fixed_prefix(Const *patt_const, bool case_insensitive, Oid collation,
                  Const **prefix_const, Selectivity *rest_selec)
{
    char       *match;
    char       *patt;
    int         pattlen;
    Oid         typeid = patt_const->consttype;
    int         pos,
                match_pos;
    bool        is_multibyte = (pg_database_encoding_max_length() > 1);
    pg_locale_t locale = 0;
    bool        locale_is_c = false;
 
    /* the right-hand const is type text or bytea */
    Assert(typeid == BYTEAOID || typeid == TEXTOID);
 
    if (case_insensitive)
    {
        if (typeid == BYTEAOID)
            ereport(ERROR,
                    (errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
                     errmsg("case insensitive matching not supported on type bytea")));
 
        if (!OidIsValid(collation))
        {
            /*
             * This typically means that the parser could not resolve a
             * conflict of implicit collations, so report it that way.
             */
            ereport(ERROR,
                    (errcode(ERRCODE_INDETERMINATE_COLLATION),
                     errmsg("could not determine which collation to use for ILIKE"),
                     errhint("Use the COLLATE clause to set the collation explicitly.")));
        }
 
        /* If case-insensitive, we need locale info */
        if (lc_ctype_is_c(collation))
            locale_is_c = true;
        else
            locale = pg_newlocale_from_collation(collation);
    }
 
    if (typeid != BYTEAOID)
    {
        patt = TextDatumGetCString(patt_const->constvalue);
        pattlen = strlen(patt);
    }
    else
    {
        bytea      *bstr = DatumGetByteaPP(patt_const->constvalue);
 
        pattlen = VARSIZE_ANY_EXHDR(bstr);
        patt = (char *) palloc(pattlen);
        memcpy(patt, VARDATA_ANY(bstr), pattlen);
        Assert((Pointer) bstr == DatumGetPointer(patt_const->constvalue));
    }
 
    match = palloc(pattlen + 1);
    match_pos = 0;
    for (pos = 0; pos < pattlen; pos++)
    {
        /* % and _ are wildcard characters in LIKE */
        if (patt[pos] == '%' ||
            patt[pos] == '_')
            break;
 
        /* Backslash escapes the next character */
        if (patt[pos] == '\\')
        {
            pos++;
            if (pos >= pattlen)
                break;
        }
 
        /* Stop if case-varying character (it's sort of a wildcard) */
        if (case_insensitive &&
            pattern_char_isalpha(patt[pos], is_multibyte, locale, locale_is_c))
            break;
 
        match[match_pos++] = patt[pos];
    }
 
    match[match_pos] = '\0';
 
    if (typeid != BYTEAOID)
        *prefix_const = string_to_const(match, typeid);
    else
        *prefix_const = string_to_bytea_const(match, match_pos);
 
    if (rest_selec != NULL)
        *rest_selec = like_selectivity(&patt[pos], pattlen - pos,
                                       case_insensitive);
 
    pfree(patt);
    pfree(match);
 
    /* in LIKE, an empty pattern is an exact match! */
    if (pos == pattlen)
        return Pattern_Prefix_Exact;    /* reached end of pattern, so exact */
 
    if (match_pos > 0)
        return Pattern_Prefix_Partial;
 
    return Pattern_Prefix_None;
}
 
static Pattern_Prefix_Status
regex_fixed_prefix(Const *patt_const, bool case_insensitive, Oid collation,
                   Const **prefix_const, Selectivity *rest_selec)
{
    Oid         typeid = patt_const->consttype;
    char       *prefix;
    bool        exact;
 
    /*
     * Should be unnecessary, there are no bytea regex operators defined. As
     * such, it should be noted that the rest of this function has *not* been
     * made safe for binary (possibly NULL containing) strings.
     */
    if (typeid == BYTEAOID)
        ereport(ERROR,
                (errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
                 errmsg("regular-expression matching not supported on type bytea")));
 
    /* Use the regexp machinery to extract the prefix, if any */
    prefix = regexp_fixed_prefix(DatumGetTextPP(patt_const->constvalue),
                                 case_insensitive, collation,
                                 &exact);
 
    if (prefix == NULL)
    {
        *prefix_const = NULL;
 
        if (rest_selec != NULL)
        {
            char       *patt = TextDatumGetCString(patt_const->constvalue);
 
            *rest_selec = regex_selectivity(patt, strlen(patt),
                                            case_insensitive,
                                            0);
            pfree(patt);
        }
 
        return Pattern_Prefix_None;
    }
 
    *prefix_const = string_to_const(prefix, typeid);
 
    if (rest_selec != NULL)
    {
        if (exact)
        {
            /* Exact match, so there's no additional selectivity */
            *rest_selec = 1.0;
        }
        else
        {
            char       *patt = TextDatumGetCString(patt_const->constvalue);
 
            *rest_selec = regex_selectivity(patt, strlen(patt),
                                            case_insensitive,
                                            strlen(prefix));
            pfree(patt);
        }
    }
 
    pfree(prefix);
 
    if (exact)
        return Pattern_Prefix_Exact;    /* pattern specifies exact match */
    else
        return Pattern_Prefix_Partial;
}
 
static Pattern_Prefix_Status
pattern_fixed_prefix(Const *patt, Pattern_Type ptype, Oid collation,
                     Const **prefix, Selectivity *rest_selec)
{
    Pattern_Prefix_Status result;
 
    switch (ptype)
    {
        case Pattern_Type_Like:
            result = like_fixed_prefix(patt, false, collation,
                                       prefix, rest_selec);
            break;
        case Pattern_Type_Like_IC:
            result = like_fixed_prefix(patt, true, collation,
                                       prefix, rest_selec);
            break;
        case Pattern_Type_Regex:
            result = regex_fixed_prefix(patt, false, collation,
                                        prefix, rest_selec);
            break;
        case Pattern_Type_Regex_IC:
            result = regex_fixed_prefix(patt, true, collation,
                                        prefix, rest_selec);
            break;
        case Pattern_Type_Prefix:
            /* Prefix type work is trivial.  */
            result = Pattern_Prefix_Partial;
            *prefix = makeConst(patt->consttype,
                                patt->consttypmod,
                                patt->constcollid,
                                patt->constlen,
                                datumCopy(patt->constvalue,
                                          patt->constbyval,
                                          patt->constlen),
                                patt->constisnull,
                                patt->constbyval);
            if (rest_selec != NULL)
                *rest_selec = 1.0;  /* all */
            break;
        default:
            elog(ERROR, "unrecognized ptype: %d", (int) ptype);
            result = Pattern_Prefix_None;   /* keep compiler quiet */
            break;
    }
    return result;
}
 
/*
 * Estimate the selectivity of a fixed prefix for a pattern match.
 *
 * A fixed prefix "foo" is estimated as the selectivity of the expression
 * "variable >= 'foo' AND variable < 'fop'".
 *
 * The selectivity estimate is with respect to the portion of the column
 * population represented by the histogram --- the caller must fold this
 * together with info about MCVs and NULLs.
 *
 * We use the given comparison operators and collation to do the estimation.
 * The given variable and Const must be of the associated datatype(s).
 *
 * XXX Note: we make use of the upper bound to estimate operator selectivity
 * even if the locale is such that we cannot rely on the upper-bound string.
 * The selectivity only needs to be approximately right anyway, so it seems
 * more useful to use the upper-bound code than not.
 */
static Selectivity
prefix_selectivity(PlannerInfo *root, VariableStatData *vardata,
                   Oid eqopr, Oid ltopr, Oid geopr,
                   Oid collation,
                   Const *prefixcon)
{
    Selectivity prefixsel;
    FmgrInfo    opproc;
    Const      *greaterstrcon;
    Selectivity eq_sel;
 
    /* Estimate the selectivity of "x >= prefix" */
    fmgr_info(get_opcode(geopr), &opproc);
 
    prefixsel = ineq_histogram_selectivity(root, vardata,
                                           geopr, &opproc, true, true,
                                           collation,
                                           prefixcon->constvalue,
                                           prefixcon->consttype);
 
    if (prefixsel < 0.0)
    {
        /* No histogram is present ... return a suitable default estimate */
        return DEFAULT_MATCH_SEL;
    }
 
    /*
     * If we can create a string larger than the prefix, say "x < greaterstr".
     */
    fmgr_info(get_opcode(ltopr), &opproc);
    greaterstrcon = make_greater_string(prefixcon, &opproc, collation);
    if (greaterstrcon)
    {
        Selectivity topsel;
 
        topsel = ineq_histogram_selectivity(root, vardata,
                                            ltopr, &opproc, false, false,
                                            collation,
                                            greaterstrcon->constvalue,
                                            greaterstrcon->consttype);
 
        /* ineq_histogram_selectivity worked before, it shouldn't fail now */
        Assert(topsel >= 0.0);
 
        /*
         * Merge the two selectivities in the same way as for a range query
         * (see clauselist_selectivity()).  Note that we don't need to worry
         * about double-exclusion of nulls, since ineq_histogram_selectivity
         * doesn't count those anyway.
         */
        prefixsel = topsel + prefixsel - 1.0;
    }
 
    /*
     * If the prefix is long then the two bounding values might be too close
     * together for the histogram to distinguish them usefully, resulting in a
     * zero estimate (plus or minus roundoff error). To avoid returning a
     * ridiculously small estimate, compute the estimated selectivity for
     * "variable = 'foo'", and clamp to that. (Obviously, the resultant
     * estimate should be at least that.)
     *
     * We apply this even if we couldn't make a greater string.  That case
     * suggests that the prefix is near the maximum possible, and thus
     * probably off the end of the histogram, and thus we probably got a very
     * small estimate from the >= condition; so we still need to clamp.
     */
    eq_sel = var_eq_const(vardata, eqopr, collation, prefixcon->constvalue,
                          false, true, false);
 
    prefixsel = Max(prefixsel, eq_sel);
 
    return prefixsel;
}
 
 
/*
 * Estimate the selectivity of a pattern of the specified type.
 * Note that any fixed prefix of the pattern will have been removed already,
 * so actually we may be looking at just a fragment of the pattern.
 *
 * For now, we use a very simplistic approach: fixed characters reduce the
 * selectivity a good deal, character ranges reduce it a little,
 * wildcards (such as % for LIKE or .* for regex) increase it.
 */
 
#define FIXED_CHAR_SEL  0.20    /* about 1/5 */
#define CHAR_RANGE_SEL  0.25
#define ANY_CHAR_SEL    0.9     /* not 1, since it won't match end-of-string */
#define FULL_WILDCARD_SEL 5.0
#define PARTIAL_WILDCARD_SEL 2.0
 
static Selectivity
like_selectivity(const char *patt, int pattlen, bool case_insensitive)
{
    Selectivity sel = 1.0;
    int         pos;
 
    /* Skip any leading wildcard; it's already factored into initial sel */
    for (pos = 0; pos < pattlen; pos++)
    {
        if (patt[pos] != '%' && patt[pos] != '_')
            break;
    }
 
    for (; pos < pattlen; pos++)
    {
        /* % and _ are wildcard characters in LIKE */
        if (patt[pos] == '%')
            sel *= FULL_WILDCARD_SEL;
        else if (patt[pos] == '_')
            sel *= ANY_CHAR_SEL;
        else if (patt[pos] == '\\')
        {
            /* Backslash quotes the next character */
            pos++;
            if (pos >= pattlen)
                break;
            sel *= FIXED_CHAR_SEL;
        }
        else
            sel *= FIXED_CHAR_SEL;
    }
    /* Could get sel > 1 if multiple wildcards */
    if (sel > 1.0)
        sel = 1.0;
    return sel;
}
 
static Selectivity
regex_selectivity_sub(const char *patt, int pattlen, bool case_insensitive)
{
    Selectivity sel = 1.0;
    int         paren_depth = 0;
    int         paren_pos = 0;  /* dummy init to keep compiler quiet */
    int         pos;
 
    /* since this function recurses, it could be driven to stack overflow */
    check_stack_depth();
 
    for (pos = 0; pos < pattlen; pos++)
    {
        if (patt[pos] == '(')
        {
            if (paren_depth == 0)
                paren_pos = pos;    /* remember start of parenthesized item */
            paren_depth++;
        }
        else if (patt[pos] == ')' && paren_depth > 0)
        {
            paren_depth--;
            if (paren_depth == 0)
                sel *= regex_selectivity_sub(patt + (paren_pos + 1),
                                             pos - (paren_pos + 1),
                                             case_insensitive);
        }
        else if (patt[pos] == '|' && paren_depth == 0)
        {
            /*
             * If unquoted | is present at paren level 0 in pattern, we have
             * multiple alternatives; sum their probabilities.
             */
            sel += regex_selectivity_sub(patt + (pos + 1),
                                         pattlen - (pos + 1),
                                         case_insensitive);
            break;              /* rest of pattern is now processed */
        }
        else if (patt[pos] == '[')
        {
            bool        negclass = false;
 
            if (patt[++pos] == '^')
            {
                negclass = true;
                pos++;
            }
            if (patt[pos] == ']')   /* ']' at start of class is not special */
                pos++;
            while (pos < pattlen && patt[pos] != ']')
                pos++;
            if (paren_depth == 0)
                sel *= (negclass ? (1.0 - CHAR_RANGE_SEL) : CHAR_RANGE_SEL);
        }
        else if (patt[pos] == '.')
        {
            if (paren_depth == 0)
                sel *= ANY_CHAR_SEL;
        }
        else if (patt[pos] == '*' ||
                 patt[pos] == '?' ||
                 patt[pos] == '+')
        {
            /* Ought to be smarter about quantifiers... */
            if (paren_depth == 0)
                sel *= PARTIAL_WILDCARD_SEL;
        }
        else if (patt[pos] == '{')
        {
            while (pos < pattlen && patt[pos] != '}')
                pos++;
            if (paren_depth == 0)
                sel *= PARTIAL_WILDCARD_SEL;
        }
        else if (patt[pos] == '\\')
        {
            /* backslash quotes the next character */
            pos++;
            if (pos >= pattlen)
                break;
            if (paren_depth == 0)
                sel *= FIXED_CHAR_SEL;
        }
        else
        {
            if (paren_depth == 0)
                sel *= FIXED_CHAR_SEL;
        }
    }
    /* Could get sel > 1 if multiple wildcards */
    if (sel > 1.0)
        sel = 1.0;
    return sel;
}
 
static Selectivity
regex_selectivity(const char *patt, int pattlen, bool case_insensitive,
                  int fixed_prefix_len)
{
    Selectivity sel;
 
    /* If patt doesn't end with $, consider it to have a trailing wildcard */
    if (pattlen > 0 && patt[pattlen - 1] == '$' &&
        (pattlen == 1 || patt[pattlen - 2] != '\\'))
    {
        /* has trailing $ */
        sel = regex_selectivity_sub(patt, pattlen - 1, case_insensitive);
    }
    else
    {
        /* no trailing $ */
        sel = regex_selectivity_sub(patt, pattlen, case_insensitive);
        sel *= FULL_WILDCARD_SEL;
    }
 
    /*
     * If there's a fixed prefix, discount its selectivity.  We have to be
     * careful here since a very long prefix could result in pow's result
     * underflowing to zero (in which case "sel" probably has as well).
     */
    if (fixed_prefix_len > 0)
    {
        double      prefixsel = pow(FIXED_CHAR_SEL, fixed_prefix_len);
 
        if (prefixsel > 0.0)
            sel /= prefixsel;
    }
 
    /* Make sure result stays in range */
    CLAMP_PROBABILITY(sel);
    return sel;
}
 
/*
 * Check whether char is a letter (and, hence, subject to case-folding)
 *
 * In multibyte character sets or with ICU, we can't use isalpha, and it does
 * not seem worth trying to convert to wchar_t to use iswalpha or u_isalpha.
 * Instead, just assume any non-ASCII char is potentially case-varying, and
 * hard-wire knowledge of which ASCII chars are letters.
 */
static int
pattern_char_isalpha(char c, bool is_multibyte,
                     pg_locale_t locale, bool locale_is_c)
{
    if (locale_is_c)
        return (c >= 'A' && c <= 'Z') || (c >= 'a' && c <= 'z');
    else if (is_multibyte && IS_HIGHBIT_SET(c))
        return true;
    else if (locale && locale->provider == COLLPROVIDER_ICU)
        return IS_HIGHBIT_SET(c) ||
            (c >= 'A' && c <= 'Z') || (c >= 'a' && c <= 'z');
    else if (locale && locale->provider == COLLPROVIDER_LIBC)
        return isalpha_l((unsigned char) c, locale->info.lt);
    else
        return isalpha((unsigned char) c);
}
 
 
/*
 * For bytea, the increment function need only increment the current byte
 * (there are no multibyte characters to worry about).
 */
static bool
byte_increment(unsigned char *ptr, int len)
{
    if (*ptr >= 255)
        return false;
    (*ptr)++;
    return true;
}
 
/*
 * Try to generate a string greater than the given string or any
 * string it is a prefix of.  If successful, return a palloc'd string
 * in the form of a Const node; else return NULL.
 *
 * The caller must provide the appropriate "less than" comparison function
 * for testing the strings, along with the collation to use.
 *
 * The key requirement here is that given a prefix string, say "foo",
 * we must be able to generate another string "fop" that is greater than
 * all strings "foobar" starting with "foo".  We can test that we have
 * generated a string greater than the prefix string, but in non-C collations
 * that is not a bulletproof guarantee that an extension of the string might
 * not sort after it; an example is that "foo " is less than "foo!", but it
 * is not clear that a "dictionary" sort ordering will consider "foo!" less
 * than "foo bar".  CAUTION: Therefore, this function should be used only for
 * estimation purposes when working in a non-C collation.
 *
 * To try to catch most cases where an extended string might otherwise sort
 * before the result value, we determine which of the strings "Z", "z", "y",
 * and "9" is seen as largest by the collation, and append that to the given
 * prefix before trying to find a string that compares as larger.
 *
 * To search for a greater string, we repeatedly "increment" the rightmost
 * character, using an encoding-specific character incrementer function.
 * When it's no longer possible to increment the last character, we truncate
 * off that character and start incrementing the next-to-rightmost.
 * For example, if "z" were the last character in the sort order, then we
 * could produce "foo" as a string greater than "fonz".
 *
 * This could be rather slow in the worst case, but in most cases we
 * won't have to try more than one or two strings before succeeding.
 *
 * Note that it's important for the character incrementer not to be too anal
 * about producing every possible character code, since in some cases the only
 * way to get a larger string is to increment a previous character position.
 * So we don't want to spend too much time trying every possible character
 * code at the last position.  A good rule of thumb is to be sure that we
 * don't try more than 256*K values for a K-byte character (and definitely
 * not 256^K, which is what an exhaustive search would approach).
 */
static Const *
make_greater_string(const Const *str_const, FmgrInfo *ltproc, Oid collation)
{
    Oid         datatype = str_const->consttype;
    char       *workstr;
    int         len;
    Datum       cmpstr;
    char       *cmptxt = NULL;
    mbcharacter_incrementer charinc;
 
    /*
     * Get a modifiable copy of the prefix string in C-string format, and set
     * up the string we will compare to as a Datum.  In C locale this can just
     * be the given prefix string, otherwise we need to add a suffix.  Type
     * BYTEA sorts bytewise so it never needs a suffix either.
     */
    if (datatype == BYTEAOID)
    {
        bytea      *bstr = DatumGetByteaPP(str_const->constvalue);
 
        len = VARSIZE_ANY_EXHDR(bstr);
        workstr = (char *) palloc(len);
        memcpy(workstr, VARDATA_ANY(bstr), len);
        Assert((Pointer) bstr == DatumGetPointer(str_const->constvalue));
        cmpstr = str_const->constvalue;
    }
    else
    {
        if (datatype == NAMEOID)
            workstr = DatumGetCString(DirectFunctionCall1(nameout,
                                                          str_const->constvalue));
        else
            workstr = TextDatumGetCString(str_const->constvalue);
        len = strlen(workstr);
        if (lc_collate_is_c(collation) || len == 0)
            cmpstr = str_const->constvalue;
        else
        {
            /* If first time through, determine the suffix to use */
            static char suffixchar = 0;
            static Oid  suffixcollation = 0;
 
            if (!suffixchar || suffixcollation != collation)
            {
                char       *best;
 
                best = "Z";
                if (varstr_cmp(best, 1, "z", 1, collation) < 0)
                    best = "z";
                if (varstr_cmp(best, 1, "y", 1, collation) < 0)
                    best = "y";
                if (varstr_cmp(best, 1, "9", 1, collation) < 0)
                    best = "9";
                suffixchar = *best;
                suffixcollation = collation;
            }
 
            /* And build the string to compare to */
            if (datatype == NAMEOID)
            {
                cmptxt = palloc(len + 2);
                memcpy(cmptxt, workstr, len);
                cmptxt[len] = suffixchar;
                cmptxt[len + 1] = '\0';
                cmpstr = PointerGetDatum(cmptxt);
            }
            else
            {
                cmptxt = palloc(VARHDRSZ + len + 1);
                SET_VARSIZE(cmptxt, VARHDRSZ + len + 1);
                memcpy(VARDATA(cmptxt), workstr, len);
                *(VARDATA(cmptxt) + len) = suffixchar;
                cmpstr = PointerGetDatum(cmptxt);
            }
        }
    }
 
    /* Select appropriate character-incrementer function */
    if (datatype == BYTEAOID)
        charinc = byte_increment;
    else
        charinc = pg_database_encoding_character_incrementer();
 
    /* And search ... */
    while (len > 0)
    {
        int         charlen;
        unsigned char *lastchar;
 
        /* Identify the last character --- for bytea, just the last byte */
        if (datatype == BYTEAOID)
            charlen = 1;
        else
            charlen = len - pg_mbcliplen(workstr, len, len - 1);
        lastchar = (unsigned char *) (workstr + len - charlen);
 
        /*
         * Try to generate a larger string by incrementing the last character
         * (for BYTEA, we treat each byte as a character).
         *
         * Note: the incrementer function is expected to return true if it's
         * generated a valid-per-the-encoding new character, otherwise false.
         * The contents of the character on false return are unspecified.
         */
        while (charinc(lastchar, charlen))
        {
            Const      *workstr_const;
 
            if (datatype == BYTEAOID)
                workstr_const = string_to_bytea_const(workstr, len);
            else
                workstr_const = string_to_const(workstr, datatype);
 
            if (DatumGetBool(FunctionCall2Coll(ltproc,
                                               collation,
                                               cmpstr,
                                               workstr_const->constvalue)))
            {
                /* Successfully made a string larger than cmpstr */
                if (cmptxt)
                    pfree(cmptxt);
                pfree(workstr);
                return workstr_const;
            }
 
            /* No good, release unusable value and try again */
            pfree(DatumGetPointer(workstr_const->constvalue));
            pfree(workstr_const);
        }
 
        /*
         * No luck here, so truncate off the last character and try to
         * increment the next one.
         */
        len -= charlen;
        workstr[len] = '\0';
    }
 
    /* Failed... */
    if (cmptxt)
        pfree(cmptxt);
    pfree(workstr);
 
    return NULL;
}
 
/*
 * Generate a Datum of the appropriate type from a C string.
 * Note that all of the supported types are pass-by-ref, so the
 * returned value should be pfree'd if no longer needed.
 */
static Datum
string_to_datum(const char *str, Oid datatype)
{
    Assert(str != NULL);
 
    /*
     * We cheat a little by assuming that CStringGetTextDatum() will do for
     * bpchar and varchar constants too...
     */
    if (datatype == NAMEOID)
        return DirectFunctionCall1(namein, CStringGetDatum(str));
    else if (datatype == BYTEAOID)
        return DirectFunctionCall1(byteain, CStringGetDatum(str));
    else
        return CStringGetTextDatum(str);
}
 
/*
 * Generate a Const node of the appropriate type from a C string.
 */
static Const *
string_to_const(const char *str, Oid datatype)
{
    Datum       conval = string_to_datum(str, datatype);
    Oid         collation;
    int         constlen;
 
    /*
     * We only need to support a few datatypes here, so hard-wire properties
     * instead of incurring the expense of catalog lookups.
     */
    switch (datatype)
    {
        case TEXTOID:
        case VARCHAROID:
        case BPCHAROID:
            collation = DEFAULT_COLLATION_OID;
            constlen = -1;
            break;
 
        case NAMEOID:
            collation = C_COLLATION_OID;
            constlen = NAMEDATALEN;
            break;
 
        case BYTEAOID:
            collation = InvalidOid;
            constlen = -1;
            break;
 
        default:
            elog(ERROR, "unexpected datatype in string_to_const: %u",
                 datatype);
            return NULL;
    }
 
    return makeConst(datatype, -1, collation, constlen,
                     conval, false, false);
}
 
/*
 * Generate a Const node of bytea type from a binary C string and a length.
 */
static Const *
string_to_bytea_const(const char *str, size_t str_len)
{
    bytea      *bstr = palloc(VARHDRSZ + str_len);
    Datum       conval;
 
    memcpy(VARDATA(bstr), str, str_len);
    SET_VARSIZE(bstr, VARHDRSZ + str_len);
    conval = PointerGetDatum(bstr);
 
    return makeConst(BYTEAOID, -1, InvalidOid, -1, conval, false, false);
}