/*-------------------------------------------------------------------------
 *
 * rangetypes.c
 *	  I/O functions, operators, and support functions for range types.
 *
 * The stored (serialized) format of a range value is:
 *
 *	4 bytes: varlena header
 *	4 bytes: range type's OID
 *	Lower boundary value, if any, aligned according to subtype's typalign
 *	Upper boundary value, if any, aligned according to subtype's typalign
 *	1 byte for flags
 *
 * This representation is chosen to avoid needing any padding before the
 * lower boundary value, even when it requires double alignment.  We can
 * expect that the varlena header is presented to us on a suitably aligned
 * boundary (possibly after detoasting), and then the lower boundary is too.
 * Note that this means we can't work with a packed (short varlena header)
 * value; we must detoast it first.
 *
 *
 * Portions Copyright (c) 1996-2012, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 *
 * IDENTIFICATION
 *	  src/backend/utils/adt/rangetypes.c
 *
 *-------------------------------------------------------------------------
 */
#include "postgres.h"

#include "access/hash.h"
#include "lib/stringinfo.h"
#include "libpq/pqformat.h"
#include "utils/builtins.h"
#include "utils/date.h"
#include "utils/int8.h"
#include "utils/lsyscache.h"
#include "utils/rangetypes.h"
#include "utils/timestamp.h"


#define RANGE_EMPTY_LITERAL "empty"

/* fn_extra cache entry for one of the range I/O functions */
typedef struct RangeIOData
{
	TypeCacheEntry *typcache;	/* range type's typcache entry */
	Oid			typiofunc;		/* element type's I/O function */
	Oid			typioparam;		/* element type's I/O parameter */
	FmgrInfo	proc;			/* lookup result for typiofunc */
} RangeIOData;


static RangeIOData *get_range_io_data(FunctionCallInfo fcinfo, Oid rngtypid,
				  IOFuncSelector func);
static char range_parse_flags(const char *flags_str);
static void range_parse(const char *input_str, char *flags, char **lbound_str,
			char **ubound_str);
static const char *range_parse_bound(const char *string, const char *ptr,
				  char **bound_str, bool *infinite);
static char *range_deparse(char flags, const char *lbound_str,
			  const char *ubound_str);
static char *range_bound_escape(const char *value);
static Size datum_compute_size(Size sz, Datum datum, bool typbyval,
				   char typalign, int16 typlen, char typstorage);
static Pointer datum_write(Pointer ptr, Datum datum, bool typbyval,
			char typalign, int16 typlen, char typstorage);


/*
 *----------------------------------------------------------
 * I/O FUNCTIONS
 *----------------------------------------------------------
 */

Datum
range_in(PG_FUNCTION_ARGS)
{
	char	   *input_str = PG_GETARG_CSTRING(0);
	Oid			rngtypoid = PG_GETARG_OID(1);
	Oid			typmod = PG_GETARG_INT32(2);
	RangeType  *range;
	RangeIOData *cache;
	char		flags;
	char	   *lbound_str;
	char	   *ubound_str;
	RangeBound	lower;
	RangeBound	upper;

	cache = get_range_io_data(fcinfo, rngtypoid, IOFunc_input);

	/* parse */
	range_parse(input_str, &flags, &lbound_str, &ubound_str);

	/* call element type's input function */
	if (RANGE_HAS_LBOUND(flags))
		lower.val = InputFunctionCall(&cache->proc, lbound_str,
									  cache->typioparam, typmod);
	if (RANGE_HAS_UBOUND(flags))
		upper.val = InputFunctionCall(&cache->proc, ubound_str,
									  cache->typioparam, typmod);

	lower.infinite = (flags & RANGE_LB_INF) != 0;
	lower.inclusive = (flags & RANGE_LB_INC) != 0;
	lower.lower = true;
	upper.infinite = (flags & RANGE_UB_INF) != 0;
	upper.inclusive = (flags & RANGE_UB_INC) != 0;
	upper.lower = false;

	/* serialize and canonicalize */
	range = make_range(cache->typcache, &lower, &upper, flags & RANGE_EMPTY);

	PG_RETURN_RANGE(range);
}

Datum
range_out(PG_FUNCTION_ARGS)
{
	RangeType  *range = PG_GETARG_RANGE(0);
	char	   *output_str;
	RangeIOData *cache;
	char		flags;
	char	   *lbound_str = NULL;
	char	   *ubound_str = NULL;
	RangeBound	lower;
	RangeBound	upper;
	bool		empty;

	cache = get_range_io_data(fcinfo, RangeTypeGetOid(range), IOFunc_output);

	/* deserialize */
	range_deserialize(cache->typcache, range, &lower, &upper, &empty);
	flags = range_get_flags(range);

	/* call element type's output function */
	if (RANGE_HAS_LBOUND(flags))
		lbound_str = OutputFunctionCall(&cache->proc, lower.val);
	if (RANGE_HAS_UBOUND(flags))
		ubound_str = OutputFunctionCall(&cache->proc, upper.val);

	/* construct result string */
	output_str = range_deparse(flags, lbound_str, ubound_str);

	PG_RETURN_CSTRING(output_str);
}

/*
 * Binary representation: The first byte is the flags, then the lower bound
 * (if present), then the upper bound (if present).  Each bound is represented
 * by a 4-byte length header and the binary representation of that bound (as
 * returned by a call to the send function for the subtype).
 */

Datum
range_recv(PG_FUNCTION_ARGS)
{
	StringInfo	buf = (StringInfo) PG_GETARG_POINTER(0);
	Oid			rngtypoid = PG_GETARG_OID(1);
	int32		typmod = PG_GETARG_INT32(2);
	RangeType  *range;
	RangeIOData *cache;
	char		flags;
	RangeBound	lower;
	RangeBound	upper;

	cache = get_range_io_data(fcinfo, rngtypoid, IOFunc_receive);

	/* receive the flags... */
	flags = (unsigned char) pq_getmsgbyte(buf);

	/*
	 * Mask out any unsupported flags, particularly RANGE_xB_NULL which would
	 * confuse following tests.  Note that range_serialize will take care of
	 * cleaning up any inconsistencies in the remaining flags.
	 */
	flags &= (RANGE_EMPTY |
			  RANGE_LB_INC |
			  RANGE_LB_INF |
			  RANGE_UB_INC |
			  RANGE_UB_INF);

	/* receive the bounds ... */
	if (RANGE_HAS_LBOUND(flags))
	{
		uint32		bound_len = pq_getmsgint(buf, 4);
		const char *bound_data = pq_getmsgbytes(buf, bound_len);
		StringInfoData bound_buf;

		initStringInfo(&bound_buf);
		appendBinaryStringInfo(&bound_buf, bound_data, bound_len);

		lower.val = ReceiveFunctionCall(&cache->proc,
										&bound_buf,
										cache->typioparam,
										typmod);
		pfree(bound_buf.data);
	}
	else
		lower.val = (Datum) 0;

	if (RANGE_HAS_UBOUND(flags))
	{
		uint32		bound_len = pq_getmsgint(buf, 4);
		const char *bound_data = pq_getmsgbytes(buf, bound_len);
		StringInfoData bound_buf;

		initStringInfo(&bound_buf);
		appendBinaryStringInfo(&bound_buf, bound_data, bound_len);

		upper.val = ReceiveFunctionCall(&cache->proc,
										&bound_buf,
										cache->typioparam,
										typmod);
		pfree(bound_buf.data);
	}
	else
		upper.val = (Datum) 0;

	pq_getmsgend(buf);

	/* finish constructing RangeBound representation */
	lower.infinite = (flags & RANGE_LB_INF) != 0;
	lower.inclusive = (flags & RANGE_LB_INC) != 0;
	lower.lower = true;
	upper.infinite = (flags & RANGE_UB_INF) != 0;
	upper.inclusive = (flags & RANGE_UB_INC) != 0;
	upper.lower = false;

	/* serialize and canonicalize */
	range = make_range(cache->typcache, &lower, &upper, flags & RANGE_EMPTY);

	PG_RETURN_RANGE(range);
}

Datum
range_send(PG_FUNCTION_ARGS)
{
	RangeType  *range = PG_GETARG_RANGE(0);
	StringInfo	buf = makeStringInfo();
	RangeIOData *cache;
	char		flags;
	RangeBound	lower;
	RangeBound	upper;
	bool		empty;

	cache = get_range_io_data(fcinfo, RangeTypeGetOid(range), IOFunc_send);

	/* deserialize */
	range_deserialize(cache->typcache, range, &lower, &upper, &empty);
	flags = range_get_flags(range);

	/* construct output */
	pq_begintypsend(buf);

	pq_sendbyte(buf, flags);

	if (RANGE_HAS_LBOUND(flags))
	{
		Datum		bound = PointerGetDatum(SendFunctionCall(&cache->proc,
															 lower.val));
		uint32		bound_len = VARSIZE(bound) - VARHDRSZ;
		char	   *bound_data = VARDATA(bound);

		pq_sendint(buf, bound_len, 4);
		pq_sendbytes(buf, bound_data, bound_len);
	}

	if (RANGE_HAS_UBOUND(flags))
	{
		Datum		bound = PointerGetDatum(SendFunctionCall(&cache->proc,
															 upper.val));
		uint32		bound_len = VARSIZE(bound) - VARHDRSZ;
		char	   *bound_data = VARDATA(bound);

		pq_sendint(buf, bound_len, 4);
		pq_sendbytes(buf, bound_data, bound_len);
	}

	PG_RETURN_BYTEA_P(pq_endtypsend(buf));
}

/*
 * get_range_io_data: get cached information needed for range type I/O
 *
 * The range I/O functions need a bit more cached info than other range
 * functions, so they store a RangeIOData struct in fn_extra, not just a
 * pointer to a type cache entry.
 */
static RangeIOData *
get_range_io_data(FunctionCallInfo fcinfo, Oid rngtypid, IOFuncSelector func)
{
	RangeIOData *cache = (RangeIOData *) fcinfo->flinfo->fn_extra;

	if (cache == NULL || cache->typcache->type_id != rngtypid)
	{
		int16		typlen;
		bool		typbyval;
		char		typalign;
		char		typdelim;

		cache = (RangeIOData *) MemoryContextAlloc(fcinfo->flinfo->fn_mcxt,
												   sizeof(RangeIOData));
		cache->typcache = lookup_type_cache(rngtypid, TYPECACHE_RANGE_INFO);
		if (cache->typcache->rngelemtype == NULL)
			elog(ERROR, "type %u is not a range type", rngtypid);

		/* get_type_io_data does more than we need, but is convenient */
		get_type_io_data(cache->typcache->rngelemtype->type_id,
						 func,
						 &typlen,
						 &typbyval,
						 &typalign,
						 &typdelim,
						 &cache->typioparam,
						 &cache->typiofunc);

		if (!OidIsValid(cache->typiofunc))
		{
			/* this could only happen for receive or send */
			if (func == IOFunc_receive)
				ereport(ERROR,
						(errcode(ERRCODE_UNDEFINED_FUNCTION),
					 errmsg("no binary input function available for type %s",
					format_type_be(cache->typcache->rngelemtype->type_id))));
			else
				ereport(ERROR,
						(errcode(ERRCODE_UNDEFINED_FUNCTION),
					errmsg("no binary output function available for type %s",
					format_type_be(cache->typcache->rngelemtype->type_id))));
		}
		fmgr_info_cxt(cache->typiofunc, &cache->proc,
					  fcinfo->flinfo->fn_mcxt);

		fcinfo->flinfo->fn_extra = (void *) cache;
	}

	return cache;
}


/*
 *----------------------------------------------------------
 * GENERIC FUNCTIONS
 *----------------------------------------------------------
 */

/* Construct standard-form range value from two arguments */
Datum
range_constructor2(PG_FUNCTION_ARGS)
{
	Datum		arg1 = PG_GETARG_DATUM(0);
	Datum		arg2 = PG_GETARG_DATUM(1);
	Oid			rngtypid = get_fn_expr_rettype(fcinfo->flinfo);
	RangeType  *range;
	TypeCacheEntry *typcache;
	RangeBound	lower;
	RangeBound	upper;

	typcache = range_get_typcache(fcinfo, rngtypid);

	lower.val = PG_ARGISNULL(0) ? (Datum) 0 : arg1;
	lower.infinite = PG_ARGISNULL(0);
	lower.inclusive = true;
	lower.lower = true;

	upper.val = PG_ARGISNULL(1) ? (Datum) 0 : arg2;
	upper.infinite = PG_ARGISNULL(1);
	upper.inclusive = false;
	upper.lower = false;

	range = make_range(typcache, &lower, &upper, false);

	PG_RETURN_RANGE(range);
}

/* Construct general range value from three arguments */
Datum
range_constructor3(PG_FUNCTION_ARGS)
{
	Datum		arg1 = PG_GETARG_DATUM(0);
	Datum		arg2 = PG_GETARG_DATUM(1);
	Oid			rngtypid = get_fn_expr_rettype(fcinfo->flinfo);
	RangeType  *range;
	TypeCacheEntry *typcache;
	RangeBound	lower;
	RangeBound	upper;
	char		flags;

	typcache = range_get_typcache(fcinfo, rngtypid);

	if (PG_ARGISNULL(2))
		ereport(ERROR,
				(errcode(ERRCODE_DATA_EXCEPTION),
			   errmsg("range constructor flags argument must not be NULL")));

	flags = range_parse_flags(text_to_cstring(PG_GETARG_TEXT_P(2)));

	lower.val = PG_ARGISNULL(0) ? (Datum) 0 : arg1;
	lower.infinite = PG_ARGISNULL(0);
	lower.inclusive = (flags & RANGE_LB_INC) != 0;
	lower.lower = true;

	upper.val = PG_ARGISNULL(1) ? (Datum) 0 : arg2;
	upper.infinite = PG_ARGISNULL(1);
	upper.inclusive = (flags & RANGE_UB_INC) != 0;
	upper.lower = false;

	range = make_range(typcache, &lower, &upper, false);

	PG_RETURN_RANGE(range);
}


/* range -> subtype functions */

/* extract lower bound value */
Datum
range_lower(PG_FUNCTION_ARGS)
{
	RangeType  *r1 = PG_GETARG_RANGE(0);
	TypeCacheEntry *typcache;
	RangeBound	lower;
	RangeBound	upper;
	bool		empty;

	typcache = range_get_typcache(fcinfo, RangeTypeGetOid(r1));

	range_deserialize(typcache, r1, &lower, &upper, &empty);

	/* Return NULL if there's no finite lower bound */
	if (empty || lower.infinite)
		PG_RETURN_NULL();

	PG_RETURN_DATUM(lower.val);
}

/* extract upper bound value */
Datum
range_upper(PG_FUNCTION_ARGS)
{
	RangeType  *r1 = PG_GETARG_RANGE(0);
	TypeCacheEntry *typcache;
	RangeBound	lower;
	RangeBound	upper;
	bool		empty;

	typcache = range_get_typcache(fcinfo, RangeTypeGetOid(r1));

	range_deserialize(typcache, r1, &lower, &upper, &empty);

	/* Return NULL if there's no finite upper bound */
	if (empty || upper.infinite)
		PG_RETURN_NULL();

	PG_RETURN_DATUM(upper.val);
}


/* range -> bool functions */

/* is range empty? */
Datum
range_empty(PG_FUNCTION_ARGS)
{
	RangeType  *r1 = PG_GETARG_RANGE(0);
	char		flags = range_get_flags(r1);

	PG_RETURN_BOOL(flags & RANGE_EMPTY);
}

/* is lower bound inclusive? */
Datum
range_lower_inc(PG_FUNCTION_ARGS)
{
	RangeType  *r1 = PG_GETARG_RANGE(0);
	char		flags = range_get_flags(r1);

	PG_RETURN_BOOL(flags & RANGE_LB_INC);
}

/* is upper bound inclusive? */
Datum
range_upper_inc(PG_FUNCTION_ARGS)
{
	RangeType  *r1 = PG_GETARG_RANGE(0);
	char		flags = range_get_flags(r1);

	PG_RETURN_BOOL(flags & RANGE_UB_INC);
}

/* is lower bound infinite? */
Datum
range_lower_inf(PG_FUNCTION_ARGS)
{
	RangeType  *r1 = PG_GETARG_RANGE(0);
	char		flags = range_get_flags(r1);

	PG_RETURN_BOOL(flags & RANGE_LB_INF);
}

/* is upper bound infinite? */
Datum
range_upper_inf(PG_FUNCTION_ARGS)
{
	RangeType  *r1 = PG_GETARG_RANGE(0);
	char		flags = range_get_flags(r1);

	PG_RETURN_BOOL(flags & RANGE_UB_INF);
}


/* range, element -> bool functions */

/* contains? */
Datum
range_contains_elem(PG_FUNCTION_ARGS)
{
	RangeType  *r = PG_GETARG_RANGE(0);
	Datum		val = PG_GETARG_DATUM(1);
	TypeCacheEntry *typcache;

	typcache = range_get_typcache(fcinfo, RangeTypeGetOid(r));

	PG_RETURN_BOOL(range_contains_elem_internal(typcache, r, val));
}

/* contained by? */
Datum
elem_contained_by_range(PG_FUNCTION_ARGS)
{
	Datum		val = PG_GETARG_DATUM(0);
	RangeType  *r = PG_GETARG_RANGE(1);
	TypeCacheEntry *typcache;

	typcache = range_get_typcache(fcinfo, RangeTypeGetOid(r));

	PG_RETURN_BOOL(range_contains_elem_internal(typcache, r, val));
}


/* range, range -> bool functions */

/* equality (internal version) */
bool
range_eq_internal(TypeCacheEntry *typcache, RangeType *r1, RangeType *r2)
{
	RangeBound	lower1,
				lower2;
	RangeBound	upper1,
				upper2;
	bool		empty1,
				empty2;

	/* Different types should be prevented by ANYRANGE matching rules */
	if (RangeTypeGetOid(r1) != RangeTypeGetOid(r2))
		elog(ERROR, "range types do not match");

	range_deserialize(typcache, r1, &lower1, &upper1, &empty1);
	range_deserialize(typcache, r2, &lower2, &upper2, &empty2);

	if (empty1 && empty2)
		return true;
	if (empty1 != empty2)
		return false;

	if (range_cmp_bounds(typcache, &lower1, &lower2) != 0)
		return false;

	if (range_cmp_bounds(typcache, &upper1, &upper2) != 0)
		return false;

	return true;
}

/* equality */
Datum
range_eq(PG_FUNCTION_ARGS)
{
	RangeType  *r1 = PG_GETARG_RANGE(0);
	RangeType  *r2 = PG_GETARG_RANGE(1);
	TypeCacheEntry *typcache;

	typcache = range_get_typcache(fcinfo, RangeTypeGetOid(r1));

	PG_RETURN_BOOL(range_eq_internal(typcache, r1, r2));
}

/* inequality (internal version) */
bool
range_ne_internal(TypeCacheEntry *typcache, RangeType *r1, RangeType *r2)
{
	return (!range_eq_internal(typcache, r1, r2));
}

/* inequality */
Datum
range_ne(PG_FUNCTION_ARGS)
{
	RangeType  *r1 = PG_GETARG_RANGE(0);
	RangeType  *r2 = PG_GETARG_RANGE(1);
	TypeCacheEntry *typcache;

	typcache = range_get_typcache(fcinfo, RangeTypeGetOid(r1));

	PG_RETURN_BOOL(range_ne_internal(typcache, r1, r2));
}

/* contains? */
Datum
range_contains(PG_FUNCTION_ARGS)
{
	RangeType  *r1 = PG_GETARG_RANGE(0);
	RangeType  *r2 = PG_GETARG_RANGE(1);
	TypeCacheEntry *typcache;

	typcache = range_get_typcache(fcinfo, RangeTypeGetOid(r1));

	PG_RETURN_BOOL(range_contains_internal(typcache, r1, r2));
}

/* contained by? */
Datum
range_contained_by(PG_FUNCTION_ARGS)
{
	RangeType  *r1 = PG_GETARG_RANGE(0);
	RangeType  *r2 = PG_GETARG_RANGE(1);
	TypeCacheEntry *typcache;

	typcache = range_get_typcache(fcinfo, RangeTypeGetOid(r1));

	PG_RETURN_BOOL(range_contained_by_internal(typcache, r1, r2));
}

/* strictly left of? (internal version) */
bool
range_before_internal(TypeCacheEntry *typcache, RangeType *r1, RangeType *r2)
{
	RangeBound	lower1,
				lower2;
	RangeBound	upper1,
				upper2;
	bool		empty1,
				empty2;

	/* Different types should be prevented by ANYRANGE matching rules */
	if (RangeTypeGetOid(r1) != RangeTypeGetOid(r2))
		elog(ERROR, "range types do not match");

	range_deserialize(typcache, r1, &lower1, &upper1, &empty1);
	range_deserialize(typcache, r2, &lower2, &upper2, &empty2);

	/* An empty range is neither before nor after any other range */
	if (empty1 || empty2)
		return false;

	return (range_cmp_bounds(typcache, &upper1, &lower2) < 0);
}

/* strictly left of? */
Datum
range_before(PG_FUNCTION_ARGS)
{
	RangeType  *r1 = PG_GETARG_RANGE(0);
	RangeType  *r2 = PG_GETARG_RANGE(1);
	TypeCacheEntry *typcache;

	typcache = range_get_typcache(fcinfo, RangeTypeGetOid(r1));

	PG_RETURN_BOOL(range_before_internal(typcache, r1, r2));
}

/* strictly right of? (internal version) */
bool
range_after_internal(TypeCacheEntry *typcache, RangeType *r1, RangeType *r2)
{
	RangeBound	lower1,
				lower2;
	RangeBound	upper1,
				upper2;
	bool		empty1,
				empty2;

	/* Different types should be prevented by ANYRANGE matching rules */
	if (RangeTypeGetOid(r1) != RangeTypeGetOid(r2))
		elog(ERROR, "range types do not match");

	range_deserialize(typcache, r1, &lower1, &upper1, &empty1);
	range_deserialize(typcache, r2, &lower2, &upper2, &empty2);

	/* An empty range is neither before nor after any other range */
	if (empty1 || empty2)
		return false;

	return (range_cmp_bounds(typcache, &lower1, &upper2) > 0);
}

/* strictly right of? */
Datum
range_after(PG_FUNCTION_ARGS)
{
	RangeType  *r1 = PG_GETARG_RANGE(0);
	RangeType  *r2 = PG_GETARG_RANGE(1);
	TypeCacheEntry *typcache;

	typcache = range_get_typcache(fcinfo, RangeTypeGetOid(r1));

	PG_RETURN_BOOL(range_after_internal(typcache, r1, r2));
}

/* adjacent to (but not overlapping)? (internal version) */
bool
range_adjacent_internal(TypeCacheEntry *typcache, RangeType *r1, RangeType *r2)
{
	RangeBound	lower1,
				lower2;
	RangeBound	upper1,
				upper2;
	bool		empty1,
				empty2;
	RangeType  *r3;
	int			cmp;

	/* Different types should be prevented by ANYRANGE matching rules */
	if (RangeTypeGetOid(r1) != RangeTypeGetOid(r2))
		elog(ERROR, "range types do not match");

	range_deserialize(typcache, r1, &lower1, &upper1, &empty1);
	range_deserialize(typcache, r2, &lower2, &upper2, &empty2);

	/* An empty range is not adjacent to any other range */
	if (empty1 || empty2)
		return false;

	/*
	 * Given two ranges A..B and C..D, where B < C, the ranges are adjacent if
	 * and only if the range B..C is empty, where inclusivity of these two
	 * bounds is inverted compared to the original bounds.	For discrete
	 * ranges, we have to rely on the canonicalization function to normalize
	 * B..C to empty if it contains no elements of the subtype.  (If there is
	 * no canonicalization function, it's impossible for such a range to
	 * normalize to empty, so we needn't bother to try.)
	 *
	 * If B == C, the ranges are adjacent only if these bounds have different
	 * inclusive flags (i.e., exactly one of the ranges includes the common
	 * boundary point).
	 *
	 * And if B > C then the ranges cannot be adjacent in this order, but we
	 * must consider the other order (i.e., check D <= A).
	 */
	cmp = range_cmp_bound_values(typcache, &upper1, &lower2);
	if (cmp < 0)
	{
		/* in a continuous subtype, there are assumed to be points between */
		if (!OidIsValid(typcache->rng_canonical_finfo.fn_oid))
			return (false);
		/* flip the inclusion flags */
		upper1.inclusive = !upper1.inclusive;
		lower2.inclusive = !lower2.inclusive;
		/* change upper/lower labels to avoid Assert failures */
		upper1.lower = true;
		lower2.lower = false;
		r3 = make_range(typcache, &upper1, &lower2, false);
		return RangeIsEmpty(r3);
	}
	if (cmp == 0)
	{
		return (upper1.inclusive != lower2.inclusive);
	}

	cmp = range_cmp_bound_values(typcache, &upper2, &lower1);
	if (cmp < 0)
	{
		/* in a continuous subtype, there are assumed to be points between */
		if (!OidIsValid(typcache->rng_canonical_finfo.fn_oid))
			return (false);
		/* flip the inclusion flags */
		upper2.inclusive = !upper2.inclusive;
		lower1.inclusive = !lower1.inclusive;
		/* change upper/lower labels to avoid Assert failures */
		upper2.lower = true;
		lower1.lower = false;
		r3 = make_range(typcache, &upper2, &lower1, false);
		return RangeIsEmpty(r3);
	}
	if (cmp == 0)
	{
		return (upper2.inclusive != lower1.inclusive);
	}

	return false;
}

/* adjacent to (but not overlapping)? */
Datum
range_adjacent(PG_FUNCTION_ARGS)
{
	RangeType  *r1 = PG_GETARG_RANGE(0);
	RangeType  *r2 = PG_GETARG_RANGE(1);
	TypeCacheEntry *typcache;

	typcache = range_get_typcache(fcinfo, RangeTypeGetOid(r1));

	PG_RETURN_BOOL(range_adjacent_internal(typcache, r1, r2));
}

/* overlaps? (internal version) */
bool
range_overlaps_internal(TypeCacheEntry *typcache, RangeType *r1, RangeType *r2)
{
	RangeBound	lower1,
				lower2;
	RangeBound	upper1,
				upper2;
	bool		empty1,
				empty2;

	/* Different types should be prevented by ANYRANGE matching rules */
	if (RangeTypeGetOid(r1) != RangeTypeGetOid(r2))
		elog(ERROR, "range types do not match");

	range_deserialize(typcache, r1, &lower1, &upper1, &empty1);
	range_deserialize(typcache, r2, &lower2, &upper2, &empty2);

	/* An empty range does not overlap any other range */
	if (empty1 || empty2)
		return false;

	if (range_cmp_bounds(typcache, &lower1, &lower2) >= 0 &&
		range_cmp_bounds(typcache, &lower1, &upper2) <= 0)
		return true;

	if (range_cmp_bounds(typcache, &lower2, &lower1) >= 0 &&
		range_cmp_bounds(typcache, &lower2, &upper1) <= 0)
		return true;

	return false;
}

/* overlaps? */
Datum
range_overlaps(PG_FUNCTION_ARGS)
{
	RangeType  *r1 = PG_GETARG_RANGE(0);
	RangeType  *r2 = PG_GETARG_RANGE(1);
	TypeCacheEntry *typcache;

	typcache = range_get_typcache(fcinfo, RangeTypeGetOid(r1));

	PG_RETURN_BOOL(range_overlaps_internal(typcache, r1, r2));
}

/* does not extend to right of? (internal version) */
bool
range_overleft_internal(TypeCacheEntry *typcache, RangeType *r1, RangeType *r2)
{
	RangeBound	lower1,
				lower2;
	RangeBound	upper1,
				upper2;
	bool		empty1,
				empty2;

	/* Different types should be prevented by ANYRANGE matching rules */
	if (RangeTypeGetOid(r1) != RangeTypeGetOid(r2))
		elog(ERROR, "range types do not match");

	range_deserialize(typcache, r1, &lower1, &upper1, &empty1);
	range_deserialize(typcache, r2, &lower2, &upper2, &empty2);

	/* An empty range is neither before nor after any other range */
	if (empty1 || empty2)
		return false;

	if (range_cmp_bounds(typcache, &upper1, &upper2) <= 0)
		return true;

	return false;
}

/* does not extend to right of? */
Datum
range_overleft(PG_FUNCTION_ARGS)
{
	RangeType  *r1 = PG_GETARG_RANGE(0);
	RangeType  *r2 = PG_GETARG_RANGE(1);
	TypeCacheEntry *typcache;

	typcache = range_get_typcache(fcinfo, RangeTypeGetOid(r1));

	PG_RETURN_BOOL(range_overleft_internal(typcache, r1, r2));
}

/* does not extend to left of? (internal version) */
bool
range_overright_internal(TypeCacheEntry *typcache, RangeType *r1, RangeType *r2)
{
	RangeBound	lower1,
				lower2;
	RangeBound	upper1,
				upper2;
	bool		empty1,
				empty2;

	/* Different types should be prevented by ANYRANGE matching rules */
	if (RangeTypeGetOid(r1) != RangeTypeGetOid(r2))
		elog(ERROR, "range types do not match");

	range_deserialize(typcache, r1, &lower1, &upper1, &empty1);
	range_deserialize(typcache, r2, &lower2, &upper2, &empty2);

	/* An empty range is neither before nor after any other range */
	if (empty1 || empty2)
		PG_RETURN_BOOL(false);

	if (range_cmp_bounds(typcache, &lower1, &lower2) >= 0)
		PG_RETURN_BOOL(true);

	PG_RETURN_BOOL(false);
}

/* does not extend to left of? */
Datum
range_overright(PG_FUNCTION_ARGS)
{
	RangeType  *r1 = PG_GETARG_RANGE(0);
	RangeType  *r2 = PG_GETARG_RANGE(1);
	TypeCacheEntry *typcache;

	typcache = range_get_typcache(fcinfo, RangeTypeGetOid(r1));

	PG_RETURN_BOOL(range_overright_internal(typcache, r1, r2));
}


/* range, range -> range functions */

/* set difference */
Datum
range_minus(PG_FUNCTION_ARGS)
{
	RangeType  *r1 = PG_GETARG_RANGE(0);
	RangeType  *r2 = PG_GETARG_RANGE(1);
	TypeCacheEntry *typcache;
	RangeBound	lower1,
				lower2;
	RangeBound	upper1,
				upper2;
	bool		empty1,
				empty2;
	int			cmp_l1l2,
				cmp_l1u2,
				cmp_u1l2,
				cmp_u1u2;

	/* Different types should be prevented by ANYRANGE matching rules */
	if (RangeTypeGetOid(r1) != RangeTypeGetOid(r2))
		elog(ERROR, "range types do not match");

	typcache = range_get_typcache(fcinfo, RangeTypeGetOid(r1));

	range_deserialize(typcache, r1, &lower1, &upper1, &empty1);
	range_deserialize(typcache, r2, &lower2, &upper2, &empty2);

	/* if either is empty, r1 is the correct answer */
	if (empty1 || empty2)
		PG_RETURN_RANGE(r1);

	cmp_l1l2 = range_cmp_bounds(typcache, &lower1, &lower2);
	cmp_l1u2 = range_cmp_bounds(typcache, &lower1, &upper2);
	cmp_u1l2 = range_cmp_bounds(typcache, &upper1, &lower2);
	cmp_u1u2 = range_cmp_bounds(typcache, &upper1, &upper2);

	if (cmp_l1l2 < 0 && cmp_u1u2 > 0)
		ereport(ERROR,
				(errcode(ERRCODE_DATA_EXCEPTION),
			  errmsg("result of range difference would not be contiguous")));

	if (cmp_l1u2 > 0 || cmp_u1l2 < 0)
		PG_RETURN_RANGE(r1);

	if (cmp_l1l2 >= 0 && cmp_u1u2 <= 0)
		PG_RETURN_RANGE(make_empty_range(typcache));

	if (cmp_l1l2 <= 0 && cmp_u1l2 >= 0 && cmp_u1u2 <= 0)
	{
		lower2.inclusive = !lower2.inclusive;
		lower2.lower = false;	/* it will become the upper bound */
		PG_RETURN_RANGE(make_range(typcache, &lower1, &lower2, false));
	}

	if (cmp_l1l2 >= 0 && cmp_u1u2 >= 0 && cmp_l1u2 <= 0)
	{
		upper2.inclusive = !upper2.inclusive;
		upper2.lower = true;	/* it will become the lower bound */
		PG_RETURN_RANGE(make_range(typcache, &upper2, &upper1, false));
	}

	elog(ERROR, "unexpected case in range_minus");
	PG_RETURN_NULL();
}

/* set union */
Datum
range_union(PG_FUNCTION_ARGS)
{
	RangeType  *r1 = PG_GETARG_RANGE(0);
	RangeType  *r2 = PG_GETARG_RANGE(1);
	TypeCacheEntry *typcache;
	RangeBound	lower1,
				lower2;
	RangeBound	upper1,
				upper2;
	bool		empty1,
				empty2;
	RangeBound *result_lower;
	RangeBound *result_upper;

	/* Different types should be prevented by ANYRANGE matching rules */
	if (RangeTypeGetOid(r1) != RangeTypeGetOid(r2))
		elog(ERROR, "range types do not match");

	typcache = range_get_typcache(fcinfo, RangeTypeGetOid(r1));

	range_deserialize(typcache, r1, &lower1, &upper1, &empty1);
	range_deserialize(typcache, r2, &lower2, &upper2, &empty2);

	/* if either is empty, the other is the correct answer */
	if (empty1)
		PG_RETURN_RANGE(r2);
	if (empty2)
		PG_RETURN_RANGE(r1);

	if (!DatumGetBool(range_overlaps(fcinfo)) &&
		!DatumGetBool(range_adjacent(fcinfo)))
		ereport(ERROR,
				(errcode(ERRCODE_DATA_EXCEPTION),
				 errmsg("result of range union would not be contiguous")));

	if (range_cmp_bounds(typcache, &lower1, &lower2) < 0)
		result_lower = &lower1;
	else
		result_lower = &lower2;

	if (range_cmp_bounds(typcache, &upper1, &upper2) > 0)
		result_upper = &upper1;
	else
		result_upper = &upper2;

	PG_RETURN_RANGE(make_range(typcache, result_lower, result_upper, false));
}

/* set intersection */
Datum
range_intersect(PG_FUNCTION_ARGS)
{
	RangeType  *r1 = PG_GETARG_RANGE(0);
	RangeType  *r2 = PG_GETARG_RANGE(1);
	TypeCacheEntry *typcache;
	RangeBound	lower1,
				lower2;
	RangeBound	upper1,
				upper2;
	bool		empty1,
				empty2;
	RangeBound *result_lower;
	RangeBound *result_upper;

	/* Different types should be prevented by ANYRANGE matching rules */
	if (RangeTypeGetOid(r1) != RangeTypeGetOid(r2))
		elog(ERROR, "range types do not match");

	typcache = range_get_typcache(fcinfo, RangeTypeGetOid(r1));

	range_deserialize(typcache, r1, &lower1, &upper1, &empty1);
	range_deserialize(typcache, r2, &lower2, &upper2, &empty2);

	if (empty1 || empty2 || !DatumGetBool(range_overlaps(fcinfo)))
		PG_RETURN_RANGE(make_empty_range(typcache));

	if (range_cmp_bounds(typcache, &lower1, &lower2) >= 0)
		result_lower = &lower1;
	else
		result_lower = &lower2;

	if (range_cmp_bounds(typcache, &upper1, &upper2) <= 0)
		result_upper = &upper1;
	else
		result_upper = &upper2;

	PG_RETURN_RANGE(make_range(typcache, result_lower, result_upper, false));
}

/* Btree support */

/* btree comparator */
Datum
range_cmp(PG_FUNCTION_ARGS)
{
	RangeType  *r1 = PG_GETARG_RANGE(0);
	RangeType  *r2 = PG_GETARG_RANGE(1);
	TypeCacheEntry *typcache;
	RangeBound	lower1,
				lower2;
	RangeBound	upper1,
				upper2;
	bool		empty1,
				empty2;
	int			cmp;

	/* Different types should be prevented by ANYRANGE matching rules */
	if (RangeTypeGetOid(r1) != RangeTypeGetOid(r2))
		elog(ERROR, "range types do not match");

	typcache = range_get_typcache(fcinfo, RangeTypeGetOid(r1));

	range_deserialize(typcache, r1, &lower1, &upper1, &empty1);
	range_deserialize(typcache, r2, &lower2, &upper2, &empty2);

	/* For b-tree use, empty ranges sort before all else */
	if (empty1 && empty2)
		PG_RETURN_INT32(0);
	else if (empty1)
		PG_RETURN_INT32(-1);
	else if (empty2)
		PG_RETURN_INT32(1);

	if ((cmp = range_cmp_bounds(typcache, &lower1, &lower2)) != 0)
		PG_RETURN_INT32(cmp);

	PG_RETURN_INT32(range_cmp_bounds(typcache, &upper1, &upper2));
}

/* inequality operators using the range_cmp function */
Datum
range_lt(PG_FUNCTION_ARGS)
{
	int			cmp = range_cmp(fcinfo);

	PG_RETURN_BOOL(cmp < 0);
}

Datum
range_le(PG_FUNCTION_ARGS)
{
	int			cmp = range_cmp(fcinfo);

	PG_RETURN_BOOL(cmp <= 0);
}

Datum
range_ge(PG_FUNCTION_ARGS)
{
	int			cmp = range_cmp(fcinfo);

	PG_RETURN_BOOL(cmp >= 0);
}

Datum
range_gt(PG_FUNCTION_ARGS)
{
	int			cmp = range_cmp(fcinfo);

	PG_RETURN_BOOL(cmp > 0);
}

/* Hash support */

/* hash a range value */
Datum
hash_range(PG_FUNCTION_ARGS)
{
	RangeType  *r = PG_GETARG_RANGE(0);
	uint32		result;
	TypeCacheEntry *typcache;
	TypeCacheEntry *scache;
	RangeBound	lower;
	RangeBound	upper;
	bool		empty;
	char		flags;
	uint32		lower_hash;
	uint32		upper_hash;

	typcache = range_get_typcache(fcinfo, RangeTypeGetOid(r));

	/* deserialize */
	range_deserialize(typcache, r, &lower, &upper, &empty);
	flags = range_get_flags(r);

	/*
	 * Look up the element type's hash function, if not done already.
	 */
	scache = typcache->rngelemtype;
	if (!OidIsValid(scache->hash_proc_finfo.fn_oid))
	{
		scache = lookup_type_cache(scache->type_id, TYPECACHE_HASH_PROC_FINFO);
		if (!OidIsValid(scache->hash_proc_finfo.fn_oid))
			ereport(ERROR,
					(errcode(ERRCODE_UNDEFINED_FUNCTION),
					 errmsg("could not identify a hash function for type %s",
							format_type_be(scache->type_id))));
	}

	/*
	 * Apply the hash function to each bound.
	 */
	if (RANGE_HAS_LBOUND(flags))
		lower_hash = DatumGetUInt32(FunctionCall1Coll(&scache->hash_proc_finfo,
													  typcache->rng_collation,
													  lower.val));
	else
		lower_hash = 0;

	if (RANGE_HAS_UBOUND(flags))
		upper_hash = DatumGetUInt32(FunctionCall1Coll(&scache->hash_proc_finfo,
													  typcache->rng_collation,
													  upper.val));
	else
		upper_hash = 0;

	/* Merge hashes of flags and bounds */
	result = hash_uint32((uint32) flags);
	result ^= lower_hash;
	result = (result << 1) | (result >> 31);
	result ^= upper_hash;

	PG_RETURN_INT32(result);
}

/* ANALYZE support */

/* typanalyze function for range datatypes */
Datum
range_typanalyze(PG_FUNCTION_ARGS)
{
	/*
	 * For the moment, just punt and don't analyze range columns.  If we get
	 * close to release without having a better answer, we could consider
	 * letting std_typanalyze do what it can ... but those stats are probably
	 * next door to useless for most activity with range columns, so it's not
	 * clear it's worth gathering them.
	 */
	PG_RETURN_BOOL(false);
}


/*
 *----------------------------------------------------------
 * CANONICAL FUNCTIONS
 *
 *	 Functions for specific built-in range types.
 *----------------------------------------------------------
 */

Datum
int4range_canonical(PG_FUNCTION_ARGS)
{
	RangeType  *r = PG_GETARG_RANGE(0);
	TypeCacheEntry *typcache;
	RangeBound	lower;
	RangeBound	upper;
	bool		empty;

	typcache = range_get_typcache(fcinfo, RangeTypeGetOid(r));

	range_deserialize(typcache, r, &lower, &upper, &empty);

	if (empty)
		PG_RETURN_RANGE(r);

	if (!lower.infinite && !lower.inclusive)
	{
		lower.val = DirectFunctionCall2(int4pl, lower.val, Int32GetDatum(1));
		lower.inclusive = true;
	}

	if (!upper.infinite && upper.inclusive)
	{
		upper.val = DirectFunctionCall2(int4pl, upper.val, Int32GetDatum(1));
		upper.inclusive = false;
	}

	PG_RETURN_RANGE(range_serialize(typcache, &lower, &upper, false));
}

Datum
int8range_canonical(PG_FUNCTION_ARGS)
{
	RangeType  *r = PG_GETARG_RANGE(0);
	TypeCacheEntry *typcache;
	RangeBound	lower;
	RangeBound	upper;
	bool		empty;

	typcache = range_get_typcache(fcinfo, RangeTypeGetOid(r));

	range_deserialize(typcache, r, &lower, &upper, &empty);

	if (empty)
		PG_RETURN_RANGE(r);

	if (!lower.infinite && !lower.inclusive)
	{
		lower.val = DirectFunctionCall2(int8pl, lower.val, Int64GetDatum(1));
		lower.inclusive = true;
	}

	if (!upper.infinite && upper.inclusive)
	{
		upper.val = DirectFunctionCall2(int8pl, upper.val, Int64GetDatum(1));
		upper.inclusive = false;
	}

	PG_RETURN_RANGE(range_serialize(typcache, &lower, &upper, false));
}

Datum
daterange_canonical(PG_FUNCTION_ARGS)
{
	RangeType  *r = PG_GETARG_RANGE(0);
	TypeCacheEntry *typcache;
	RangeBound	lower;
	RangeBound	upper;
	bool		empty;

	typcache = range_get_typcache(fcinfo, RangeTypeGetOid(r));

	range_deserialize(typcache, r, &lower, &upper, &empty);

	if (empty)
		PG_RETURN_RANGE(r);

	if (!lower.infinite && !lower.inclusive)
	{
		lower.val = DirectFunctionCall2(date_pli, lower.val, Int32GetDatum(1));
		lower.inclusive = true;
	}

	if (!upper.infinite && upper.inclusive)
	{
		upper.val = DirectFunctionCall2(date_pli, upper.val, Int32GetDatum(1));
		upper.inclusive = false;
	}

	PG_RETURN_RANGE(range_serialize(typcache, &lower, &upper, false));
}

/*
 *----------------------------------------------------------
 * SUBTYPE_DIFF FUNCTIONS
 *
 * Functions for specific built-in range types.
 *
 * Note that subtype_diff does return the difference, not the absolute value
 * of the difference, and it must take care to avoid overflow.
 * (numrange_subdiff is at some risk there ...)
 *----------------------------------------------------------
 */

Datum
int4range_subdiff(PG_FUNCTION_ARGS)
{
	int32		v1 = PG_GETARG_INT32(0);
	int32		v2 = PG_GETARG_INT32(1);

	PG_RETURN_FLOAT8((float8) v1 - (float8) v2);
}

Datum
int8range_subdiff(PG_FUNCTION_ARGS)
{
	int64		v1 = PG_GETARG_INT64(0);
	int64		v2 = PG_GETARG_INT64(1);

	PG_RETURN_FLOAT8((float8) v1 - (float8) v2);
}

Datum
numrange_subdiff(PG_FUNCTION_ARGS)
{
	Datum		v1 = PG_GETARG_DATUM(0);
	Datum		v2 = PG_GETARG_DATUM(1);
	Datum		numresult;
	float8		floatresult;

	numresult = DirectFunctionCall2(numeric_sub, v1, v2);

	floatresult = DatumGetFloat8(DirectFunctionCall1(numeric_float8,
													 numresult));

	PG_RETURN_FLOAT8(floatresult);
}

Datum
daterange_subdiff(PG_FUNCTION_ARGS)
{
	int32		v1 = PG_GETARG_INT32(0);
	int32		v2 = PG_GETARG_INT32(1);

	PG_RETURN_FLOAT8((float8) v1 - (float8) v2);
}

Datum
tsrange_subdiff(PG_FUNCTION_ARGS)
{
	Timestamp	v1 = PG_GETARG_TIMESTAMP(0);
	Timestamp	v2 = PG_GETARG_TIMESTAMP(1);
	float8		result;

#ifdef HAVE_INT64_TIMESTAMP
	result = ((float8) v1 - (float8) v2) / USECS_PER_SEC;
#else
	result = v1 - v2;
#endif

	PG_RETURN_FLOAT8(result);
}

Datum
tstzrange_subdiff(PG_FUNCTION_ARGS)
{
	Timestamp	v1 = PG_GETARG_TIMESTAMP(0);
	Timestamp	v2 = PG_GETARG_TIMESTAMP(1);
	float8		result;

#ifdef HAVE_INT64_TIMESTAMP
	result = ((float8) v1 - (float8) v2) / USECS_PER_SEC;
#else
	result = v1 - v2;
#endif

	PG_RETURN_FLOAT8(result);
}

/*
 *----------------------------------------------------------
 * SUPPORT FUNCTIONS
 *
 *	 These functions aren't in pg_proc, but are useful for
 *	 defining new generic range functions in C.
 *----------------------------------------------------------
 */

/*
 * range_get_typcache: get cached information about a range type
 *
 * This is for use by range-related functions that follow the convention
 * of using the fn_extra field as a pointer to the type cache entry for
 * the range type.	Functions that need to cache more information than
 * that must fend for themselves.
 */
TypeCacheEntry *
range_get_typcache(FunctionCallInfo fcinfo, Oid rngtypid)
{
	TypeCacheEntry *typcache = (TypeCacheEntry *) fcinfo->flinfo->fn_extra;

	if (typcache == NULL ||
		typcache->type_id != rngtypid)
	{
		typcache = lookup_type_cache(rngtypid, TYPECACHE_RANGE_INFO);
		if (typcache->rngelemtype == NULL)
			elog(ERROR, "type %u is not a range type", rngtypid);
		fcinfo->flinfo->fn_extra = (void *) typcache;
	}

	return typcache;
}

/*
 * range_serialize: construct a range value from bounds and empty-flag
 *
 * This does not force canonicalization of the range value.  In most cases,
 * external callers should only be canonicalization functions.	Note that
 * we perform some datatype-independent canonicalization checks anyway.
 */
RangeType *
range_serialize(TypeCacheEntry *typcache, RangeBound *lower, RangeBound *upper,
				bool empty)
{
	RangeType  *range;
	int			cmp;
	Size		msize;
	Pointer		ptr;
	int16		typlen;
	bool		typbyval;
	char		typalign;
	char		typstorage;
	char		flags = 0;

	/*
	 * Verify range is not invalid on its face, and construct flags value,
	 * preventing any non-canonical combinations such as infinite+inclusive.
	 */
	Assert(lower->lower);
	Assert(!upper->lower);

	if (empty)
		flags |= RANGE_EMPTY;
	else
	{
		cmp = range_cmp_bound_values(typcache, lower, upper);

		/* error check: if lower bound value is above upper, it's wrong */
		if (cmp > 0)
			ereport(ERROR,
					(errcode(ERRCODE_DATA_EXCEPTION),
					 errmsg("range lower bound must be less than or equal to range upper bound")));

		/* if bounds are equal, and not both inclusive, range is empty */
		if (cmp == 0 && !(lower->inclusive && upper->inclusive))
			flags |= RANGE_EMPTY;
		else
		{
			/* infinite boundaries are never inclusive */
			if (lower->infinite)
				flags |= RANGE_LB_INF;
			else if (lower->inclusive)
				flags |= RANGE_LB_INC;
			if (upper->infinite)
				flags |= RANGE_UB_INF;
			else if (upper->inclusive)
				flags |= RANGE_UB_INC;
		}
	}

	/* Fetch information about range's element type */
	typlen = typcache->rngelemtype->typlen;
	typbyval = typcache->rngelemtype->typbyval;
	typalign = typcache->rngelemtype->typalign;
	typstorage = typcache->rngelemtype->typstorage;

	/* Count space for varlena header and range type's OID */
	msize = sizeof(RangeType);
	Assert(msize == MAXALIGN(msize));

	/* Count space for bounds */
	if (RANGE_HAS_LBOUND(flags))
	{
		/*
		 * Make sure item to be inserted is not toasted.  It is essential that
		 * we not insert an out-of-line toast value pointer into a range
		 * object, for the same reasons that arrays and records can't contain
		 * them.  It would work to store a compressed-in-line value, but we
		 * prefer to decompress and then let compression be applied to the
		 * whole range object if necessary.  But, unlike arrays, we do allow
		 * short-header varlena objects to stay as-is.
		 */
		if (typlen == -1)
			lower->val = PointerGetDatum(PG_DETOAST_DATUM_PACKED(lower->val));

		msize = datum_compute_size(msize, lower->val, typbyval, typalign,
								   typlen, typstorage);
	}

	if (RANGE_HAS_UBOUND(flags))
	{
		/* Make sure item to be inserted is not toasted */
		if (typlen == -1)
			upper->val = PointerGetDatum(PG_DETOAST_DATUM_PACKED(upper->val));

		msize = datum_compute_size(msize, upper->val, typbyval, typalign,
								   typlen, typstorage);
	}

	/* Add space for flag byte */
	msize += sizeof(char);

	/* Note: zero-fill is required here, just as in heap tuples */
	range = (RangeType *) palloc0(msize);
	SET_VARSIZE(range, msize);

	/* Now fill in the datum */
	range->rangetypid = typcache->type_id;

	ptr = (char *) (range + 1);

	if (RANGE_HAS_LBOUND(flags))
	{
		Assert(lower->lower);
		ptr = datum_write(ptr, lower->val, typbyval, typalign, typlen,
						  typstorage);
	}

	if (RANGE_HAS_UBOUND(flags))
	{
		Assert(!upper->lower);
		ptr = datum_write(ptr, upper->val, typbyval, typalign, typlen,
						  typstorage);
	}

	*((char *) ptr) = flags;

	return range;
}

/*
 * range_deserialize: deconstruct a range value
 *
 * NB: the given range object must be fully detoasted; it cannot have a
 * short varlena header.
 *
 * Note that if the element type is pass-by-reference, the datums in the
 * RangeBound structs will be pointers into the given range object.
 */
void
range_deserialize(TypeCacheEntry *typcache, RangeType *range,
				  RangeBound *lower, RangeBound *upper, bool *empty)
{
	char		flags;
	int16		typlen;
	bool		typbyval;
	char		typalign;
	Pointer		ptr;
	Datum		lbound;
	Datum		ubound;

	/* assert caller passed the right typcache entry */
	Assert(RangeTypeGetOid(range) == typcache->type_id);

	/* fetch the flag byte from datum's last byte */
	flags = *((char *) range + VARSIZE(range) - 1);

	/* fetch information about range's element type */
	typlen = typcache->rngelemtype->typlen;
	typbyval = typcache->rngelemtype->typbyval;
	typalign = typcache->rngelemtype->typalign;

	/* initialize data pointer just after the range OID */
	ptr = (Pointer) (range + 1);

	/* fetch lower bound, if any */
	if (RANGE_HAS_LBOUND(flags))
	{
		/* att_align_pointer cannot be necessary here */
		lbound = fetch_att(ptr, typbyval, typlen);
		ptr = (Pointer) att_addlength_pointer(ptr, typlen, ptr);
	}
	else
		lbound = (Datum) 0;

	/* fetch upper bound, if any */
	if (RANGE_HAS_UBOUND(flags))
	{
		ptr = (Pointer) att_align_pointer(ptr, typalign, typlen, ptr);
		ubound = fetch_att(ptr, typbyval, typlen);
		/* no need for att_addlength_pointer */
	}
	else
		ubound = (Datum) 0;

	/* emit results */

	*empty = (flags & RANGE_EMPTY) != 0;

	lower->val = lbound;
	lower->infinite = (flags & RANGE_LB_INF) != 0;
	lower->inclusive = (flags & RANGE_LB_INC) != 0;
	lower->lower = true;

	upper->val = ubound;
	upper->infinite = (flags & RANGE_UB_INF) != 0;
	upper->inclusive = (flags & RANGE_UB_INC) != 0;
	upper->lower = false;
}

/*
 * range_get_flags: just get the flags from a RangeType value.
 *
 * This is frequently useful in places that only need the flags and not
 * the full results of range_deserialize.
 */
char
range_get_flags(RangeType *range)
{
	/* fetch the flag byte from datum's last byte */
	return *((char *) range + VARSIZE(range) - 1);
}

/*
 * range_set_contain_empty: set the RANGE_CONTAIN_EMPTY bit in the value.
 *
 * This is only needed in GiST operations, so we don't include a provision
 * for setting it in range_serialize; rather, this function must be applied
 * afterwards.
 */
void
range_set_contain_empty(RangeType *range)
{
	char	   *flagsp;

	/* flag byte is datum's last byte */
	flagsp = (char *) range + VARSIZE(range) - 1;

	*flagsp |= RANGE_CONTAIN_EMPTY;
}

/*
 * This both serializes and canonicalizes (if applicable) the range.
 * This should be used by most callers.
 */
RangeType *
make_range(TypeCacheEntry *typcache, RangeBound *lower, RangeBound *upper,
		   bool empty)
{
	RangeType  *range;

	range = range_serialize(typcache, lower, upper, empty);

	/* no need to call canonical on empty ranges ... */
	if (OidIsValid(typcache->rng_canonical_finfo.fn_oid) &&
		!RangeIsEmpty(range))
		range = DatumGetRangeType(FunctionCall1(&typcache->rng_canonical_finfo,
												RangeTypeGetDatum(range)));

	return range;
}

/*
 * Compare two range boundary points, returning <0, 0, or >0 according to
 * whether b1 is less than, equal to, or greater than b2.
 *
 * The boundaries can be any combination of upper and lower; so it's useful
 * for a variety of operators.
 *
 * The simple case is when b1 and b2 are both finite and inclusive, in which
 * case the result is just a comparison of the values held in b1 and b2.
 *
 * If a bound is exclusive, then we need to know whether it's a lower bound,
 * in which case we treat the boundary point as "just greater than" the held
 * value; or an upper bound, in which case we treat the boundary point as
 * "just less than" the held value.
 *
 * If a bound is infinite, it represents minus infinity (less than every other
 * point) if it's a lower bound; or plus infinity (greater than every other
 * point) if it's an upper bound.
 *
 * There is only one case where two boundaries compare equal but are not
 * identical: when both bounds are inclusive and hold the same finite value,
 * but one is an upper bound and the other a lower bound.
 */
int
range_cmp_bounds(TypeCacheEntry *typcache, RangeBound *b1, RangeBound *b2)
{
	int32		result;

	/*
	 * First, handle cases involving infinity, which don't require invoking
	 * the comparison proc.
	 */
	if (b1->infinite && b2->infinite)
	{
		/*
		 * Both are infinity, so they are equal unless one is lower and the
		 * other not.
		 */
		if (b1->lower == b2->lower)
			return 0;
		else
			return b1->lower ? -1 : 1;
	}
	else if (b1->infinite)
		return b1->lower ? -1 : 1;
	else if (b2->infinite)
		return b2->lower ? 1 : -1;

	/*
	 * Both boundaries are finite, so compare the held values.
	 */
	result = DatumGetInt32(FunctionCall2Coll(&typcache->rng_cmp_proc_finfo,
											 typcache->rng_collation,
											 b1->val, b2->val));

	/*
	 * If the comparison is anything other than equal, we're done. If they
	 * compare equal though, we still have to consider whether the boundaries
	 * are inclusive or exclusive.
	 */
	if (result == 0)
	{
		if (!b1->inclusive && !b2->inclusive)
		{
			/* both are exclusive */
			if (b1->lower == b2->lower)
				return 0;
			else
				return b1->lower ? 1 : -1;
		}
		else if (!b1->inclusive)
			return b1->lower ? 1 : -1;
		else if (!b2->inclusive)
			return b2->lower ? -1 : 1;
		else
		{
			/*
			 * Both are inclusive and the values held are equal, so they are
			 * equal regardless of whether they are upper or lower boundaries,
			 * or a mix.
			 */
			return 0;
		}
	}

	return result;
}

/*
 * Compare two range boundary point values, returning <0, 0, or >0 according
 * to whether b1 is less than, equal to, or greater than b2.
 *
 * This is similar to but simpler than range_cmp_bounds().	We just compare
 * the values held in b1 and b2, ignoring inclusive/exclusive flags.  The
 * lower/upper flags only matter for infinities, where they tell us if the
 * infinity is plus or minus.
 */
int
range_cmp_bound_values(TypeCacheEntry *typcache, RangeBound *b1,
					   RangeBound *b2)
{
	/*
	 * First, handle cases involving infinity, which don't require invoking
	 * the comparison proc.
	 */
	if (b1->infinite && b2->infinite)
	{
		/*
		 * Both are infinity, so they are equal unless one is lower and the
		 * other not.
		 */
		if (b1->lower == b2->lower)
			return 0;
		else
			return b1->lower ? -1 : 1;
	}
	else if (b1->infinite)
		return b1->lower ? -1 : 1;
	else if (b2->infinite)
		return b2->lower ? 1 : -1;

	/*
	 * Both boundaries are finite, so compare the held values.
	 */
	return DatumGetInt32(FunctionCall2Coll(&typcache->rng_cmp_proc_finfo,
										   typcache->rng_collation,
										   b1->val, b2->val));
}

/*
 * Build an empty range value of the type indicated by the typcache entry.
 */
RangeType *
make_empty_range(TypeCacheEntry *typcache)
{
	RangeBound	lower;
	RangeBound	upper;

	lower.val = (Datum) 0;
	lower.infinite = false;
	lower.inclusive = false;
	lower.lower = true;

	upper.val = (Datum) 0;
	upper.infinite = false;
	upper.inclusive = false;
	upper.lower = false;

	return make_range(typcache, &lower, &upper, true);
}


/*
 *----------------------------------------------------------
 * STATIC FUNCTIONS
 *----------------------------------------------------------
 */

/*
 * Given a string representing the flags for the range type, return the flags
 * represented as a char.
 */
static char
range_parse_flags(const char *flags_str)
{
	char		flags = 0;

	if (flags_str[0] == '\0' ||
		flags_str[1] == '\0' ||
		flags_str[2] != '\0')
		ereport(ERROR,
				(errcode(ERRCODE_SYNTAX_ERROR),
				 errmsg("invalid range bound flags"),
				 errhint("Valid values are \"[]\", \"[)\", \"(]\", and \"()\".")));

	switch (flags_str[0])
	{
		case '[':
			flags |= RANGE_LB_INC;
			break;
		case '(':
			break;
		default:
			ereport(ERROR,
					(errcode(ERRCODE_SYNTAX_ERROR),
					 errmsg("invalid range bound flags"),
				   errhint("Valid values are '[]', '[)', '(]', and '()'.")));
	}

	switch (flags_str[1])
	{
		case ']':
			flags |= RANGE_UB_INC;
			break;
		case ')':
			break;
		default:
			ereport(ERROR,
					(errcode(ERRCODE_SYNTAX_ERROR),
					 errmsg("invalid range bound flags"),
				   errhint("Valid values are '[]', '[)', '(]', and '()'.")));
	}

	return flags;
}

/*
 * Parse range input.
 *
 * Input parameters:
 *	string: input string to be parsed
 * Output parameters:
 *	*flags: receives flags bitmask
 *	*lbound_str: receives palloc'd lower bound string, or NULL if none
 *	*ubound_str: receives palloc'd upper bound string, or NULL if none
 *
 * This is modeled somewhat after record_in in rowtypes.c.
 * The input syntax is:
 *	<range>   := EMPTY
 *			   | <lb-inc> <string>, <string> <ub-inc>
 *	<lb-inc>  := '[' | '('
 *	<ub-inc>  := ']' | ')'
 *
 * Whitespace before or after <range> is ignored.  Whitespace within a <string>
 * is taken literally and becomes part of the input string for that bound.
 *
 * A <string> of length zero is taken as "infinite" (i.e. no bound), unless it
 * is surrounded by double-quotes, in which case it is the literal empty
 * string.
 *
 * Within a <string>, special characters (such as comma, parenthesis, or
 * brackets) can be enclosed in double-quotes or escaped with backslash. Within
 * double-quotes, a double-quote can be escaped with double-quote or backslash.
 */
static void
range_parse(const char *string, char *flags, char **lbound_str,
			char **ubound_str)
{
	const char *ptr = string;
	bool		infinite;

	*flags = 0;

	/* consume whitespace */
	while (*ptr != '\0' && isspace((unsigned char) *ptr))
		ptr++;

	/* check for empty range */
	if (pg_strncasecmp(ptr, RANGE_EMPTY_LITERAL,
					   strlen(RANGE_EMPTY_LITERAL)) == 0)
	{
		*flags = RANGE_EMPTY;
		*lbound_str = NULL;
		*ubound_str = NULL;

		ptr += strlen(RANGE_EMPTY_LITERAL);

		/* the rest should be whitespace */
		while (*ptr != '\0' && isspace((unsigned char) *ptr))
			ptr++;

		/* should have consumed everything */
		if (*ptr != '\0')
			ereport(ERROR,
					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
					 errmsg("malformed range literal: \"%s\"",
							string),
					 errdetail("Junk after \"empty\" keyword.")));

		return;
	}

	if (*ptr == '[')
	{
		*flags |= RANGE_LB_INC;
		ptr++;
	}
	else if (*ptr == '(')
		ptr++;
	else
		ereport(ERROR,
				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
				 errmsg("malformed range literal: \"%s\"",
						string),
				 errdetail("Missing left parenthesis or bracket.")));

	ptr = range_parse_bound(string, ptr, lbound_str, &infinite);
	if (infinite)
		*flags |= RANGE_LB_INF;

	if (*ptr == ',')
		ptr++;
	else
		ereport(ERROR,
				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
				 errmsg("malformed range literal: \"%s\"",
						string),
				 errdetail("Missing comma after lower bound.")));

	ptr = range_parse_bound(string, ptr, ubound_str, &infinite);
	if (infinite)
		*flags |= RANGE_UB_INF;

	if (*ptr == ']')
	{
		*flags |= RANGE_UB_INC;
		ptr++;
	}
	else if (*ptr == ')')
		ptr++;
	else	/* must be a comma */
		ereport(ERROR,
				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
				 errmsg("malformed range literal: \"%s\"",
						string),
				 errdetail("Too many commas.")));

	/* consume whitespace */
	while (*ptr != '\0' && isspace((unsigned char) *ptr))
		ptr++;

	if (*ptr != '\0')
		ereport(ERROR,
				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
				 errmsg("malformed range literal: \"%s\"",
						string),
				 errdetail("Junk after right parenthesis or bracket.")));
}

/*
 * Helper for range_parse: parse and de-quote one bound string.
 *
 * We scan until finding comma, right parenthesis, or right bracket.
 *
 * Input parameters:
 *	string: entire input string (used only for error reports)
 *	ptr: where to start parsing bound
 * Output parameters:
 *	*bound_str: receives palloc'd bound string, or NULL if none
 *	*infinite: set true if no bound, else false
 *
 * The return value is the scan ptr, advanced past the bound string.
 */
static const char *
range_parse_bound(const char *string, const char *ptr,
				  char **bound_str, bool *infinite)
{
	StringInfoData buf;

	/* Check for null: completely empty input means null */
	if (*ptr == ',' || *ptr == ')' || *ptr == ']')
	{
		*bound_str = NULL;
		*infinite = true;
	}
	else
	{
		/* Extract string for this bound */
		bool		inquote = false;

		initStringInfo(&buf);
		while (inquote || !(*ptr == ',' || *ptr == ')' || *ptr == ']'))
		{
			char		ch = *ptr++;

			if (ch == '\0')
				ereport(ERROR,
						(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
						 errmsg("malformed range literal: \"%s\"",
								string),
						 errdetail("Unexpected end of input.")));
			if (ch == '\\')
			{
				if (*ptr == '\0')
					ereport(ERROR,
							(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
							 errmsg("malformed range literal: \"%s\"",
									string),
							 errdetail("Unexpected end of input.")));
				appendStringInfoChar(&buf, *ptr++);
			}
			else if (ch == '\"')
			{
				if (!inquote)
					inquote = true;
				else if (*ptr == '\"')
				{
					/* doubled quote within quote sequence */
					appendStringInfoChar(&buf, *ptr++);
				}
				else
					inquote = false;
			}
			else
				appendStringInfoChar(&buf, ch);
		}

		*bound_str = buf.data;
		*infinite = false;
	}

	return ptr;
}

/*
 * Convert a deserialized range value to text form
 *
 * Inputs are the flags byte, and the two bound values already converted to
 * text (but not yet quoted).  If no bound value, pass NULL.
 *
 * Result is a palloc'd string
 */
static char *
range_deparse(char flags, const char *lbound_str, const char *ubound_str)
{
	StringInfoData buf;

	if (flags & RANGE_EMPTY)
		return pstrdup(RANGE_EMPTY_LITERAL);

	initStringInfo(&buf);

	appendStringInfoChar(&buf, (flags & RANGE_LB_INC) ? '[' : '(');

	if (RANGE_HAS_LBOUND(flags))
		appendStringInfoString(&buf, range_bound_escape(lbound_str));

	appendStringInfoChar(&buf, ',');

	if (RANGE_HAS_UBOUND(flags))
		appendStringInfoString(&buf, range_bound_escape(ubound_str));

	appendStringInfoChar(&buf, (flags & RANGE_UB_INC) ? ']' : ')');

	return buf.data;
}

/*
 * Helper for range_deparse: quote a bound value as needed
 *
 * Result is a palloc'd string
 */
static char *
range_bound_escape(const char *value)
{
	bool		nq;
	const char *ptr;
	StringInfoData buf;

	initStringInfo(&buf);

	/* Detect whether we need double quotes for this value */
	nq = (value[0] == '\0');	/* force quotes for empty string */
	for (ptr = value; *ptr; ptr++)
	{
		char		ch = *ptr;

		if (ch == '"' || ch == '\\' ||
			ch == '(' || ch == ')' ||
			ch == '[' || ch == ']' ||
			ch == ',' ||
			isspace((unsigned char) ch))
		{
			nq = true;
			break;
		}
	}

	/* And emit the string */
	if (nq)
		appendStringInfoChar(&buf, '"');
	for (ptr = value; *ptr; ptr++)
	{
		char		ch = *ptr;

		if (ch == '"' || ch == '\\')
			appendStringInfoChar(&buf, ch);
		appendStringInfoChar(&buf, ch);
	}
	if (nq)
		appendStringInfoChar(&buf, '"');

	return buf.data;
}

/*
 * Test whether range r1 contains range r2.
 *
 * Caller has already checked that they are the same range type, and looked up
 * the necessary typcache entry.
 */
bool
range_contains_internal(TypeCacheEntry *typcache, RangeType *r1, RangeType *r2)
{
	RangeBound	lower1;
	RangeBound	upper1;
	bool		empty1;
	RangeBound	lower2;
	RangeBound	upper2;
	bool		empty2;

	/* Different types should be prevented by ANYRANGE matching rules */
	if (RangeTypeGetOid(r1) != RangeTypeGetOid(r2))
		elog(ERROR, "range types do not match");

	range_deserialize(typcache, r1, &lower1, &upper1, &empty1);
	range_deserialize(typcache, r2, &lower2, &upper2, &empty2);

	/* If either range is empty, the answer is easy */
	if (empty2)
		return true;
	else if (empty1)
		return false;

	/* Else we must have lower1 <= lower2 and upper1 >= upper2 */
	if (range_cmp_bounds(typcache, &lower1, &lower2) > 0)
		return false;
	if (range_cmp_bounds(typcache, &upper1, &upper2) < 0)
		return false;

	return true;
}

bool
range_contained_by_internal(TypeCacheEntry *typcache, RangeType *r1, RangeType *r2)
{
	return range_contains_internal(typcache, r2, r1);
}

/*
 * Test whether range r contains a specific element value.
 */
bool
range_contains_elem_internal(TypeCacheEntry *typcache, RangeType *r, Datum val)
{
	RangeBound	lower;
	RangeBound	upper;
	bool		empty;
	int32		cmp;

	range_deserialize(typcache, r, &lower, &upper, &empty);

	if (empty)
		return false;

	if (!lower.infinite)
	{
		cmp = DatumGetInt32(FunctionCall2Coll(&typcache->rng_cmp_proc_finfo,
											  typcache->rng_collation,
											  lower.val, val));
		if (cmp > 0)
			return false;
		if (cmp == 0 && !lower.inclusive)
			return false;
	}

	if (!upper.infinite)
	{
		cmp = DatumGetInt32(FunctionCall2Coll(&typcache->rng_cmp_proc_finfo,
											  typcache->rng_collation,
											  upper.val, val));
		if (cmp < 0)
			return false;
		if (cmp == 0 && !upper.inclusive)
			return false;
	}

	return true;
}


/*
 * datum_compute_size() and datum_write() are used to insert the bound
 * values into a range object.	They are modeled after heaptuple.c's
 * heap_compute_data_size() and heap_fill_tuple(), but we need not handle
 * null values here.  TYPE_IS_PACKABLE must test the same conditions as
 * heaptuple.c's ATT_IS_PACKABLE macro.
 */

/* Does datatype allow packing into the 1-byte-header varlena format? */
#define TYPE_IS_PACKABLE(typlen, typstorage) \
	((typlen) == -1 && (typstorage) != 'p')

/*
 * Increment data_length by the space needed by the datum, including any
 * preceding alignment padding.
 */
static Size
datum_compute_size(Size data_length, Datum val, bool typbyval, char typalign,
				   int16 typlen, char typstorage)
{
	if (TYPE_IS_PACKABLE(typlen, typstorage) &&
		VARATT_CAN_MAKE_SHORT(DatumGetPointer(val)))
	{
		/*
		 * we're anticipating converting to a short varlena header, so adjust
		 * length and don't count any alignment
		 */
		data_length += VARATT_CONVERTED_SHORT_SIZE(DatumGetPointer(val));
	}
	else
	{
		data_length = att_align_datum(data_length, typalign, typlen, val);
		data_length = att_addlength_datum(data_length, typlen, val);
	}

	return data_length;
}

/*
 * Write the given datum beginning at ptr (after advancing to correct
 * alignment, if needed).  Return the pointer incremented by space used.
 */
static Pointer
datum_write(Pointer ptr, Datum datum, bool typbyval, char typalign,
			int16 typlen, char typstorage)
{
	Size		data_length;

	if (typbyval)
	{
		/* pass-by-value */
		ptr = (char *) att_align_nominal(ptr, typalign);
		store_att_byval(ptr, datum, typlen);
		data_length = typlen;
	}
	else if (typlen == -1)
	{
		/* varlena */
		Pointer		val = DatumGetPointer(datum);

		if (VARATT_IS_EXTERNAL(val))
		{
			/*
			 * Throw error, because we must never put a toast pointer inside a
			 * range object.  Caller should have detoasted it.
			 */
			elog(ERROR, "cannot store a toast pointer inside a range");
			data_length = 0;	/* keep compiler quiet */
		}
		else if (VARATT_IS_SHORT(val))
		{
			/* no alignment for short varlenas */
			data_length = VARSIZE_SHORT(val);
			memcpy(ptr, val, data_length);
		}
		else if (TYPE_IS_PACKABLE(typlen, typstorage) &&
				 VARATT_CAN_MAKE_SHORT(val))
		{
			/* convert to short varlena -- no alignment */
			data_length = VARATT_CONVERTED_SHORT_SIZE(val);
			SET_VARSIZE_SHORT(ptr, data_length);
			memcpy(ptr + 1, VARDATA(val), data_length - 1);
		}
		else
		{
			/* full 4-byte header varlena */
			ptr = (char *) att_align_nominal(ptr, typalign);
			data_length = VARSIZE(val);
			memcpy(ptr, val, data_length);
		}
	}
	else if (typlen == -2)
	{
		/* cstring ... never needs alignment */
		Assert(typalign == 'c');
		data_length = strlen(DatumGetCString(datum)) + 1;
		memcpy(ptr, DatumGetPointer(datum), data_length);
	}
	else
	{
		/* fixed-length pass-by-reference */
		ptr = (char *) att_align_nominal(ptr, typalign);
		Assert(typlen > 0);
		data_length = typlen;
		memcpy(ptr, DatumGetPointer(datum), data_length);
	}

	ptr += data_length;

	return ptr;
}
