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postgresql/src/backend/optimizer/path/clausesel.c

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/*-------------------------------------------------------------------------
*
* clausesel.c
* Routines to compute clause selectivities
*
* Portions Copyright (c) 1996-2019, PostgreSQL Global Development Group
* Portions Copyright (c) 1994, Regents of the University of California
*
*
* IDENTIFICATION
* src/backend/optimizer/path/clausesel.c
*
*-------------------------------------------------------------------------
*/
#include "postgres.h"
#include "nodes/makefuncs.h"
#include "nodes/nodeFuncs.h"
#include "optimizer/clauses.h"
#include "optimizer/cost.h"
#include "optimizer/optimizer.h"
#include "optimizer/pathnode.h"
#include "optimizer/plancat.h"
#include "statistics/statistics.h"
#include "utils/fmgroids.h"
#include "utils/lsyscache.h"
#include "utils/selfuncs.h"
/*
* Data structure for accumulating info about possible range-query
* clause pairs in clauselist_selectivity.
*/
typedef struct RangeQueryClause
{
struct RangeQueryClause *next; /* next in linked list */
Node *var; /* The common variable of the clauses */
bool have_lobound; /* found a low-bound clause yet? */
bool have_hibound; /* found a high-bound clause yet? */
Selectivity lobound; /* Selectivity of a var > something clause */
Selectivity hibound; /* Selectivity of a var < something clause */
} RangeQueryClause;
static void addRangeClause(RangeQueryClause **rqlist, Node *clause,
bool varonleft, bool isLTsel, Selectivity s2);
static RelOptInfo *find_single_rel_for_clauses(PlannerInfo *root,
List *clauses);
/****************************************************************************
* ROUTINES TO COMPUTE SELECTIVITIES
****************************************************************************/
/*
* clauselist_selectivity -
* Compute the selectivity of an implicitly-ANDed list of boolean
* expression clauses. The list can be empty, in which case 1.0
* must be returned. List elements may be either RestrictInfos
* or bare expression clauses --- the former is preferred since
* it allows caching of results.
*
* See clause_selectivity() for the meaning of the additional parameters.
*
* The basic approach is to apply extended statistics first, on as many
* clauses as possible, in order to capture cross-column dependencies etc.
* The remaining clauses are then estimated using regular statistics tracked
* for individual columns. This is done by simply passing the clauses to
* clauselist_selectivity_simple.
*/
Selectivity
clauselist_selectivity(PlannerInfo *root,
List *clauses,
int varRelid,
JoinType jointype,
SpecialJoinInfo *sjinfo)
{
Selectivity s1 = 1.0;
RelOptInfo *rel;
Bitmapset *estimatedclauses = NULL;
/*
* Determine if these clauses reference a single relation. If so, and if
* it has extended statistics, try to apply those.
*/
rel = find_single_rel_for_clauses(root, clauses);
if (rel && rel->rtekind == RTE_RELATION && rel->statlist != NIL)
{
/*
* Estimate as many clauses as possible using extended statistics.
*
* 'estimatedclauses' tracks the 0-based list position index of
* clauses that we've estimated using extended statistics, and that
* should be ignored.
*/
s1 *= statext_clauselist_selectivity(root, clauses, varRelid,
jointype, sjinfo, rel,
&estimatedclauses);
}
/*
* Apply normal selectivity estimates for the remaining clauses, passing
* 'estimatedclauses' so that it skips already estimated ones.
*/
return s1 * clauselist_selectivity_simple(root, clauses, varRelid,
jointype, sjinfo,
estimatedclauses);
}
/*
* clauselist_selectivity_simple -
* Compute the selectivity of an implicitly-ANDed list of boolean
* expression clauses. The list can be empty, in which case 1.0
* must be returned. List elements may be either RestrictInfos
* or bare expression clauses --- the former is preferred since
* it allows caching of results. The estimatedclauses bitmap tracks
* clauses that have already been estimated by other means.
*
* See clause_selectivity() for the meaning of the additional parameters.
*
* Our basic approach is to take the product of the selectivities of the
* subclauses. However, that's only right if the subclauses have independent
* probabilities, and in reality they are often NOT independent. So,
* we want to be smarter where we can.
*
* We also recognize "range queries", such as "x > 34 AND x < 42". Clauses
* are recognized as possible range query components if they are restriction
* opclauses whose operators have scalarltsel or a related function as their
* restriction selectivity estimator. We pair up clauses of this form that
* refer to the same variable. An unpairable clause of this kind is simply
* multiplied into the selectivity product in the normal way. But when we
* find a pair, we know that the selectivities represent the relative
* positions of the low and high bounds within the column's range, so instead
* of figuring the selectivity as hisel * losel, we can figure it as hisel +
* losel - 1. (To visualize this, see that hisel is the fraction of the range
* below the high bound, while losel is the fraction above the low bound; so
* hisel can be interpreted directly as a 0..1 value but we need to convert
* losel to 1-losel before interpreting it as a value. Then the available
* range is 1-losel to hisel. However, this calculation double-excludes
* nulls, so really we need hisel + losel + null_frac - 1.)
*
* If either selectivity is exactly DEFAULT_INEQ_SEL, we forget this equation
* and instead use DEFAULT_RANGE_INEQ_SEL. The same applies if the equation
* yields an impossible (negative) result.
*
* A free side-effect is that we can recognize redundant inequalities such
* as "x < 4 AND x < 5"; only the tighter constraint will be counted.
*
* Of course this is all very dependent on the behavior of the inequality
* selectivity functions; perhaps some day we can generalize the approach.
*/
Selectivity
clauselist_selectivity_simple(PlannerInfo *root,
List *clauses,
int varRelid,
JoinType jointype,
SpecialJoinInfo *sjinfo,
Bitmapset *estimatedclauses)
{
Selectivity s1 = 1.0;
RangeQueryClause *rqlist = NULL;
ListCell *l;
int listidx;
/*
* If there's exactly one clause (and it was not estimated yet), just go
* directly to clause_selectivity(). None of what we might do below is
* relevant.
*/
if ((list_length(clauses) == 1) &&
bms_num_members(estimatedclauses) == 0)
return clause_selectivity(root, (Node *) linitial(clauses),
varRelid, jointype, sjinfo);
/*
* Anything that doesn't look like a potential rangequery clause gets
* multiplied into s1 and forgotten. Anything that does gets inserted into
* an rqlist entry.
*/
listidx = -1;
foreach(l, clauses)
{
Node *clause = (Node *) lfirst(l);
RestrictInfo *rinfo;
Selectivity s2;
listidx++;
/*
* Skip this clause if it's already been estimated by some other
* statistics above.
*/
if (bms_is_member(listidx, estimatedclauses))
continue;
/* Always compute the selectivity using clause_selectivity */
s2 = clause_selectivity(root, clause, varRelid, jointype, sjinfo);
/*
* Check for being passed a RestrictInfo.
*
* If it's a pseudoconstant RestrictInfo, then s2 is either 1.0 or
* 0.0; just use that rather than looking for range pairs.
*/
if (IsA(clause, RestrictInfo))
{
rinfo = (RestrictInfo *) clause;
if (rinfo->pseudoconstant)
{
s1 = s1 * s2;
continue;
}
clause = (Node *) rinfo->clause;
}
else
rinfo = NULL;
/*
* See if it looks like a restriction clause with a pseudoconstant on
* one side. (Anything more complicated than that might not behave in
* the simple way we are expecting.) Most of the tests here can be
* done more efficiently with rinfo than without.
*/
if (is_opclause(clause) && list_length(((OpExpr *) clause)->args) == 2)
{
OpExpr *expr = (OpExpr *) clause;
bool varonleft = true;
bool ok;
if (rinfo)
{
ok = (bms_membership(rinfo->clause_relids) == BMS_SINGLETON) &&
(is_pseudo_constant_clause_relids(lsecond(expr->args),
rinfo->right_relids) ||
(varonleft = false,
is_pseudo_constant_clause_relids(linitial(expr->args),
rinfo->left_relids)));
}
else
{
ok = (NumRelids(clause) == 1) &&
(is_pseudo_constant_clause(lsecond(expr->args)) ||
(varonleft = false,
is_pseudo_constant_clause(linitial(expr->args))));
}
if (ok)
{
/*
* If it's not a "<"/"<="/">"/">=" operator, just merge the
* selectivity in generically. But if it's the right oprrest,
* add the clause to rqlist for later processing.
*/
switch (get_oprrest(expr->opno))
{
case F_SCALARLTSEL:
case F_SCALARLESEL:
addRangeClause(&rqlist, clause,
varonleft, true, s2);
break;
case F_SCALARGTSEL:
case F_SCALARGESEL:
addRangeClause(&rqlist, clause,
varonleft, false, s2);
break;
default:
/* Just merge the selectivity in generically */
s1 = s1 * s2;
break;
}
continue; /* drop to loop bottom */
}
}
/* Not the right form, so treat it generically. */
s1 = s1 * s2;
}
/*
* Now scan the rangequery pair list.
*/
while (rqlist != NULL)
{
RangeQueryClause *rqnext;
if (rqlist->have_lobound && rqlist->have_hibound)
{
/* Successfully matched a pair of range clauses */
Selectivity s2;
/*
* Exact equality to the default value probably means the
* selectivity function punted. This is not airtight but should
* be good enough.
*/
if (rqlist->hibound == DEFAULT_INEQ_SEL ||
rqlist->lobound == DEFAULT_INEQ_SEL)
{
s2 = DEFAULT_RANGE_INEQ_SEL;
}
else
{
s2 = rqlist->hibound + rqlist->lobound - 1.0;
/* Adjust for double-exclusion of NULLs */
s2 += nulltestsel(root, IS_NULL, rqlist->var,
varRelid, jointype, sjinfo);
/*
* A zero or slightly negative s2 should be converted into a
* small positive value; we probably are dealing with a very
* tight range and got a bogus result due to roundoff errors.
* However, if s2 is very negative, then we probably have
* default selectivity estimates on one or both sides of the
* range that we failed to recognize above for some reason.
*/
if (s2 <= 0.0)
{
if (s2 < -0.01)
{
/*
* No data available --- use a default estimate that
* is small, but not real small.
*/
s2 = DEFAULT_RANGE_INEQ_SEL;
}
else
{
/*
* It's just roundoff error; use a small positive
* value
*/
s2 = 1.0e-10;
}
}
}
/* Merge in the selectivity of the pair of clauses */
s1 *= s2;
}
else
{
/* Only found one of a pair, merge it in generically */
if (rqlist->have_lobound)
s1 *= rqlist->lobound;
else
s1 *= rqlist->hibound;
}
/* release storage and advance */
rqnext = rqlist->next;
pfree(rqlist);
rqlist = rqnext;
}
return s1;
}
/*
* addRangeClause --- add a new range clause for clauselist_selectivity
*
* Here is where we try to match up pairs of range-query clauses
*/
static void
addRangeClause(RangeQueryClause **rqlist, Node *clause,
bool varonleft, bool isLTsel, Selectivity s2)
{
RangeQueryClause *rqelem;
Node *var;
bool is_lobound;
if (varonleft)
{
var = get_leftop((Expr *) clause);
is_lobound = !isLTsel; /* x < something is high bound */
}
else
{
var = get_rightop((Expr *) clause);
is_lobound = isLTsel; /* something < x is low bound */
}
for (rqelem = *rqlist; rqelem; rqelem = rqelem->next)
{
/*
* We use full equal() here because the "var" might be a function of
* one or more attributes of the same relation...
*/
if (!equal(var, rqelem->var))
continue;
/* Found the right group to put this clause in */
if (is_lobound)
{
if (!rqelem->have_lobound)
{
rqelem->have_lobound = true;
rqelem->lobound = s2;
}
else
{
/*------
* We have found two similar clauses, such as
* x < y AND x <= z.
* Keep only the more restrictive one.
*------
*/
if (rqelem->lobound > s2)
rqelem->lobound = s2;
}
}
else
{
if (!rqelem->have_hibound)
{
rqelem->have_hibound = true;
rqelem->hibound = s2;
}
else
{
/*------
* We have found two similar clauses, such as
* x > y AND x >= z.
* Keep only the more restrictive one.
*------
*/
if (rqelem->hibound > s2)
rqelem->hibound = s2;
}
}
return;
}
/* No matching var found, so make a new clause-pair data structure */
rqelem = (RangeQueryClause *) palloc(sizeof(RangeQueryClause));
rqelem->var = var;
if (is_lobound)
{
rqelem->have_lobound = true;
rqelem->have_hibound = false;
rqelem->lobound = s2;
}
else
{
rqelem->have_lobound = false;
rqelem->have_hibound = true;
rqelem->hibound = s2;
}
rqelem->next = *rqlist;
*rqlist = rqelem;
}
/*
* find_single_rel_for_clauses
* Examine each clause in 'clauses' and determine if all clauses
* reference only a single relation. If so return that relation,
* otherwise return NULL.
*/
static RelOptInfo *
find_single_rel_for_clauses(PlannerInfo *root, List *clauses)
{
int lastrelid = 0;
ListCell *l;
foreach(l, clauses)
{
RestrictInfo *rinfo = (RestrictInfo *) lfirst(l);
int relid;
/*
* If we have a list of bare clauses rather than RestrictInfos, we
* could pull out their relids the hard way with pull_varnos().
* However, currently the extended-stats machinery won't do anything
* with non-RestrictInfo clauses anyway, so there's no point in
* spending extra cycles; just fail if that's what we have.
*/
if (!IsA(rinfo, RestrictInfo))
return NULL;
if (bms_is_empty(rinfo->clause_relids))
continue; /* we can ignore variable-free clauses */
if (!bms_get_singleton_member(rinfo->clause_relids, &relid))
return NULL; /* multiple relations in this clause */
if (lastrelid == 0)
lastrelid = relid; /* first clause referencing a relation */
else if (relid != lastrelid)
return NULL; /* relation not same as last one */
}
if (lastrelid != 0)
return find_base_rel(root, lastrelid);
return NULL; /* no clauses */
}
/*
* bms_is_subset_singleton
*
* Same result as bms_is_subset(s, bms_make_singleton(x)),
* but a little faster and doesn't leak memory.
*
* Is this of use anywhere else? If so move to bitmapset.c ...
*/
static bool
bms_is_subset_singleton(const Bitmapset *s, int x)
{
switch (bms_membership(s))
{
case BMS_EMPTY_SET:
return true;
case BMS_SINGLETON:
return bms_is_member(x, s);
case BMS_MULTIPLE:
return false;
}
/* can't get here... */
return false;
}
/*
* treat_as_join_clause -
* Decide whether an operator clause is to be handled by the
* restriction or join estimator. Subroutine for clause_selectivity().
*/
static inline bool
treat_as_join_clause(Node *clause, RestrictInfo *rinfo,
int varRelid, SpecialJoinInfo *sjinfo)
{
if (varRelid != 0)
{
/*
* Caller is forcing restriction mode (eg, because we are examining an
* inner indexscan qual).
*/
return false;
}
else if (sjinfo == NULL)
{
/*
* It must be a restriction clause, since it's being evaluated at a
* scan node.
*/
return false;
}
else
{
/*
* Otherwise, it's a join if there's more than one relation used. We
* can optimize this calculation if an rinfo was passed.
*
* XXX Since we know the clause is being evaluated at a join, the
* only way it could be single-relation is if it was delayed by outer
* joins. Although we can make use of the restriction qual estimators
* anyway, it seems likely that we ought to account for the
* probability of injected nulls somehow.
*/
if (rinfo)
return (bms_membership(rinfo->clause_relids) == BMS_MULTIPLE);
else
return (NumRelids(clause) > 1);
}
}
/*
* clause_selectivity -
* Compute the selectivity of a general boolean expression clause.
*
* The clause can be either a RestrictInfo or a plain expression. If it's
* a RestrictInfo, we try to cache the selectivity for possible re-use,
* so passing RestrictInfos is preferred.
*
* varRelid is either 0 or a rangetable index.
*
* When varRelid is not 0, only variables belonging to that relation are
* considered in computing selectivity; other vars are treated as constants
* of unknown values. This is appropriate for estimating the selectivity of
* a join clause that is being used as a restriction clause in a scan of a
* nestloop join's inner relation --- varRelid should then be the ID of the
* inner relation.
*
* When varRelid is 0, all variables are treated as variables. This
* is appropriate for ordinary join clauses and restriction clauses.
*
* jointype is the join type, if the clause is a join clause. Pass JOIN_INNER
* if the clause isn't a join clause.
*
* sjinfo is NULL for a non-join clause, otherwise it provides additional
* context information about the join being performed. There are some
* special cases:
* 1. For a special (not INNER) join, sjinfo is always a member of
* root->join_info_list.
* 2. For an INNER join, sjinfo is just a transient struct, and only the
* relids and jointype fields in it can be trusted.
* It is possible for jointype to be different from sjinfo->jointype.
* This indicates we are considering a variant join: either with
* the LHS and RHS switched, or with one input unique-ified.
*
* Note: when passing nonzero varRelid, it's normally appropriate to set
* jointype == JOIN_INNER, sjinfo == NULL, even if the clause is really a
* join clause; because we aren't treating it as a join clause.
*/
Selectivity
clause_selectivity(PlannerInfo *root,
Node *clause,
int varRelid,
JoinType jointype,
SpecialJoinInfo *sjinfo)
{
Selectivity s1 = 0.5; /* default for any unhandled clause type */
RestrictInfo *rinfo = NULL;
bool cacheable = false;
if (clause == NULL) /* can this still happen? */
return s1;
if (IsA(clause, RestrictInfo))
{
rinfo = (RestrictInfo *) clause;
/*
* If the clause is marked pseudoconstant, then it will be used as a
* gating qual and should not affect selectivity estimates; hence
* return 1.0. The only exception is that a constant FALSE may be
* taken as having selectivity 0.0, since it will surely mean no rows
* out of the plan. This case is simple enough that we need not
* bother caching the result.
*/
if (rinfo->pseudoconstant)
{
if (!IsA(rinfo->clause, Const))
return (Selectivity) 1.0;
}
/*
* If the clause is marked redundant, always return 1.0.
*/
if (rinfo->norm_selec > 1)
return (Selectivity) 1.0;
/*
* If possible, cache the result of the selectivity calculation for
* the clause. We can cache if varRelid is zero or the clause
* contains only vars of that relid --- otherwise varRelid will affect
* the result, so mustn't cache. Outer join quals might be examined
* with either their join's actual jointype or JOIN_INNER, so we need
* two cache variables to remember both cases. Note: we assume the
* result won't change if we are switching the input relations or
* considering a unique-ified case, so we only need one cache variable
* for all non-JOIN_INNER cases.
*/
if (varRelid == 0 ||
bms_is_subset_singleton(rinfo->clause_relids, varRelid))
{
/* Cacheable --- do we already have the result? */
if (jointype == JOIN_INNER)
{
if (rinfo->norm_selec >= 0)
return rinfo->norm_selec;
}
else
{
if (rinfo->outer_selec >= 0)
return rinfo->outer_selec;
}
cacheable = true;
}
/*
* Proceed with examination of contained clause. If the clause is an
* OR-clause, we want to look at the variant with sub-RestrictInfos,
* so that per-subclause selectivities can be cached.
*/
if (rinfo->orclause)
clause = (Node *) rinfo->orclause;
else
clause = (Node *) rinfo->clause;
}
if (IsA(clause, Var))
{
Var *var = (Var *) clause;
/*
* We probably shouldn't ever see an uplevel Var here, but if we do,
* return the default selectivity...
*/
if (var->varlevelsup == 0 &&
(varRelid == 0 || varRelid == (int) var->varno))
{
/* Use the restriction selectivity function for a bool Var */
s1 = boolvarsel(root, (Node *) var, varRelid);
}
}
else if (IsA(clause, Const))
{
/* bool constant is pretty easy... */
Const *con = (Const *) clause;
s1 = con->constisnull ? 0.0 :
DatumGetBool(con->constvalue) ? 1.0 : 0.0;
}
else if (IsA(clause, Param))
{
/* see if we can replace the Param */
Node *subst = estimate_expression_value(root, clause);
if (IsA(subst, Const))
{
/* bool constant is pretty easy... */
Const *con = (Const *) subst;
s1 = con->constisnull ? 0.0 :
DatumGetBool(con->constvalue) ? 1.0 : 0.0;
}
else
{
/* XXX any way to do better than default? */
}
}
else if (is_notclause(clause))
{
/* inverse of the selectivity of the underlying clause */
s1 = 1.0 - clause_selectivity(root,
(Node *) get_notclausearg((Expr *) clause),
varRelid,
jointype,
sjinfo);
}
else if (is_andclause(clause))
{
/* share code with clauselist_selectivity() */
s1 = clauselist_selectivity(root,
((BoolExpr *) clause)->args,
varRelid,
jointype,
sjinfo);
}
else if (is_orclause(clause))
{
/*
* Selectivities for an OR clause are computed as s1+s2 - s1*s2 to
* account for the probable overlap of selected tuple sets.
*
* XXX is this too conservative?
*/
ListCell *arg;
s1 = 0.0;
foreach(arg, ((BoolExpr *) clause)->args)
{
Selectivity s2 = clause_selectivity(root,
(Node *) lfirst(arg),
varRelid,
jointype,
sjinfo);
s1 = s1 + s2 - s1 * s2;
}
}
else if (is_opclause(clause) || IsA(clause, DistinctExpr))
{
OpExpr *opclause = (OpExpr *) clause;
Oid opno = opclause->opno;
if (treat_as_join_clause(clause, rinfo, varRelid, sjinfo))
{
/* Estimate selectivity for a join clause. */
s1 = join_selectivity(root, opno,
opclause->args,
opclause->inputcollid,
jointype,
sjinfo);
}
else
{
/* Estimate selectivity for a restriction clause. */
s1 = restriction_selectivity(root, opno,
opclause->args,
opclause->inputcollid,
varRelid);
}
/*
* DistinctExpr has the same representation as OpExpr, but the
* contained operator is "=" not "<>", so we must negate the result.
* This estimation method doesn't give the right behavior for nulls,
* but it's better than doing nothing.
*/
if (IsA(clause, DistinctExpr))
s1 = 1.0 - s1;
}
else if (is_funcclause(clause))
{
FuncExpr *funcclause = (FuncExpr *) clause;
/* Try to get an estimate from the support function, if any */
s1 = function_selectivity(root,
funcclause->funcid,
funcclause->args,
funcclause->inputcollid,
treat_as_join_clause(clause, rinfo,
varRelid, sjinfo),
varRelid,
jointype,
sjinfo);
}
else if (IsA(clause, ScalarArrayOpExpr))
{
/* Use node specific selectivity calculation function */
s1 = scalararraysel(root,
(ScalarArrayOpExpr *) clause,
treat_as_join_clause(clause, rinfo,
varRelid, sjinfo),
varRelid,
jointype,
sjinfo);
}
else if (IsA(clause, RowCompareExpr))
{
/* Use node specific selectivity calculation function */
s1 = rowcomparesel(root,
(RowCompareExpr *) clause,
varRelid,
jointype,
sjinfo);
}
else if (IsA(clause, NullTest))
{
/* Use node specific selectivity calculation function */
s1 = nulltestsel(root,
((NullTest *) clause)->nulltesttype,
(Node *) ((NullTest *) clause)->arg,
varRelid,
jointype,
sjinfo);
}
else if (IsA(clause, BooleanTest))
{
/* Use node specific selectivity calculation function */
s1 = booltestsel(root,
((BooleanTest *) clause)->booltesttype,
(Node *) ((BooleanTest *) clause)->arg,
varRelid,
jointype,
sjinfo);
}
else if (IsA(clause, CurrentOfExpr))
{
/* CURRENT OF selects at most one row of its table */
CurrentOfExpr *cexpr = (CurrentOfExpr *) clause;
RelOptInfo *crel = find_base_rel(root, cexpr->cvarno);
if (crel->tuples > 0)
s1 = 1.0 / crel->tuples;
}
else if (IsA(clause, RelabelType))
{
/* Not sure this case is needed, but it can't hurt */
s1 = clause_selectivity(root,
(Node *) ((RelabelType *) clause)->arg,
varRelid,
jointype,
sjinfo);
}
else if (IsA(clause, CoerceToDomain))
{
/* Not sure this case is needed, but it can't hurt */
s1 = clause_selectivity(root,
(Node *) ((CoerceToDomain *) clause)->arg,
varRelid,
jointype,
sjinfo);
}
else
{
/*
* For anything else, see if we can consider it as a boolean variable.
* This only works if it's an immutable expression in Vars of a single
* relation; but there's no point in us checking that here because
* boolvarsel() will do it internally, and return a suitable default
* selectivity if not.
*/
s1 = boolvarsel(root, clause, varRelid);
}
/* Cache the result if possible */
if (cacheable)
{
if (jointype == JOIN_INNER)
rinfo->norm_selec = s1;
else
rinfo->outer_selec = s1;
}
#ifdef SELECTIVITY_DEBUG
elog(DEBUG4, "clause_selectivity: s1 %f", s1);
#endif /* SELECTIVITY_DEBUG */
return s1;
}
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