src/backend/utils/adt/int8.c

/*-------------------------------------------------------------------------
 *
 * int8.c
 *	  Internal 64-bit integer operations
 *
 * Portions Copyright (c) 1996-2023, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 * IDENTIFICATION
 *	  src/backend/utils/adt/int8.c
 *
 *-------------------------------------------------------------------------
 */
#include "postgres.h"

#include <ctype.h>
#include <limits.h>
#include <math.h>

#include "common/int.h"
#include "funcapi.h"
#include "libpq/pqformat.h"
#include "nodes/nodeFuncs.h"
#include "nodes/supportnodes.h"
#include "optimizer/optimizer.h"
#include "utils/builtins.h"
#include "utils/lsyscache.h"


typedef struct
{
	int64		current;
	int64		finish;
	int64		step;
} generate_series_fctx;


/***********************************************************************
 **
 **		Routines for 64-bit integers.
 **
 ***********************************************************************/

/*----------------------------------------------------------
 * Formatting and conversion routines.
 *---------------------------------------------------------*/

/* int8in()
 */
Datum
int8in(PG_FUNCTION_ARGS)
{
	char	   *num = PG_GETARG_CSTRING(0);

	PG_RETURN_INT64(pg_strtoint64_safe(num, fcinfo->context));
}


/* int8out()
 */
Datum
int8out(PG_FUNCTION_ARGS)
{
	int64		val = PG_GETARG_INT64(0);
	char		buf[MAXINT8LEN + 1];
	char	   *result;
	int			len;

	len = pg_lltoa(val, buf) + 1;

	/*
	 * Since the length is already known, we do a manual palloc() and memcpy()
	 * to avoid the strlen() call that would otherwise be done in pstrdup().
	 */
	result = palloc(len);
	memcpy(result, buf, len);
	PG_RETURN_CSTRING(result);
}

/*
 *		int8recv			- converts external binary format to int8
 */
Datum
int8recv(PG_FUNCTION_ARGS)
{
	StringInfo	buf = (StringInfo) PG_GETARG_POINTER(0);

	PG_RETURN_INT64(pq_getmsgint64(buf));
}

/*
 *		int8send			- converts int8 to binary format
 */
Datum
int8send(PG_FUNCTION_ARGS)
{
	int64		arg1 = PG_GETARG_INT64(0);
	StringInfoData buf;

	pq_begintypsend(&buf);
	pq_sendint64(&buf, arg1);
	PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
}


/*----------------------------------------------------------
 *	Relational operators for int8s, including cross-data-type comparisons.
 *---------------------------------------------------------*/

/* int8relop()
 * Is val1 relop val2?
 */
Datum
int8eq(PG_FUNCTION_ARGS)
{
	int64		val1 = PG_GETARG_INT64(0);
	int64		val2 = PG_GETARG_INT64(1);

	PG_RETURN_BOOL(val1 == val2);
}

Datum
int8ne(PG_FUNCTION_ARGS)
{
	int64		val1 = PG_GETARG_INT64(0);
	int64		val2 = PG_GETARG_INT64(1);

	PG_RETURN_BOOL(val1 != val2);
}

Datum
int8lt(PG_FUNCTION_ARGS)
{
	int64		val1 = PG_GETARG_INT64(0);
	int64		val2 = PG_GETARG_INT64(1);

	PG_RETURN_BOOL(val1 < val2);
}

Datum
int8gt(PG_FUNCTION_ARGS)
{
	int64		val1 = PG_GETARG_INT64(0);
	int64		val2 = PG_GETARG_INT64(1);

	PG_RETURN_BOOL(val1 > val2);
}

Datum
int8le(PG_FUNCTION_ARGS)
{
	int64		val1 = PG_GETARG_INT64(0);
	int64		val2 = PG_GETARG_INT64(1);

	PG_RETURN_BOOL(val1 <= val2);
}

Datum
int8ge(PG_FUNCTION_ARGS)
{
	int64		val1 = PG_GETARG_INT64(0);
	int64		val2 = PG_GETARG_INT64(1);

	PG_RETURN_BOOL(val1 >= val2);
}

/* int84relop()
 * Is 64-bit val1 relop 32-bit val2?
 */
Datum
int84eq(PG_FUNCTION_ARGS)
{
	int64		val1 = PG_GETARG_INT64(0);
	int32		val2 = PG_GETARG_INT32(1);

	PG_RETURN_BOOL(val1 == val2);
}

Datum
int84ne(PG_FUNCTION_ARGS)
{
	int64		val1 = PG_GETARG_INT64(0);
	int32		val2 = PG_GETARG_INT32(1);

	PG_RETURN_BOOL(val1 != val2);
}

Datum
int84lt(PG_FUNCTION_ARGS)
{
	int64		val1 = PG_GETARG_INT64(0);
	int32		val2 = PG_GETARG_INT32(1);

	PG_RETURN_BOOL(val1 < val2);
}

Datum
int84gt(PG_FUNCTION_ARGS)
{
	int64		val1 = PG_GETARG_INT64(0);
	int32		val2 = PG_GETARG_INT32(1);

	PG_RETURN_BOOL(val1 > val2);
}

Datum
int84le(PG_FUNCTION_ARGS)
{
	int64		val1 = PG_GETARG_INT64(0);
	int32		val2 = PG_GETARG_INT32(1);

	PG_RETURN_BOOL(val1 <= val2);
}

Datum
int84ge(PG_FUNCTION_ARGS)
{
	int64		val1 = PG_GETARG_INT64(0);
	int32		val2 = PG_GETARG_INT32(1);

	PG_RETURN_BOOL(val1 >= val2);
}

/* int48relop()
 * Is 32-bit val1 relop 64-bit val2?
 */
Datum
int48eq(PG_FUNCTION_ARGS)
{
	int32		val1 = PG_GETARG_INT32(0);
	int64		val2 = PG_GETARG_INT64(1);

	PG_RETURN_BOOL(val1 == val2);
}

Datum
int48ne(PG_FUNCTION_ARGS)
{
	int32		val1 = PG_GETARG_INT32(0);
	int64		val2 = PG_GETARG_INT64(1);

	PG_RETURN_BOOL(val1 != val2);
}

Datum
int48lt(PG_FUNCTION_ARGS)
{
	int32		val1 = PG_GETARG_INT32(0);
	int64		val2 = PG_GETARG_INT64(1);

	PG_RETURN_BOOL(val1 < val2);
}

Datum
int48gt(PG_FUNCTION_ARGS)
{
	int32		val1 = PG_GETARG_INT32(0);
	int64		val2 = PG_GETARG_INT64(1);

	PG_RETURN_BOOL(val1 > val2);
}

Datum
int48le(PG_FUNCTION_ARGS)
{
	int32		val1 = PG_GETARG_INT32(0);
	int64		val2 = PG_GETARG_INT64(1);

	PG_RETURN_BOOL(val1 <= val2);
}

Datum
int48ge(PG_FUNCTION_ARGS)
{
	int32		val1 = PG_GETARG_INT32(0);
	int64		val2 = PG_GETARG_INT64(1);

	PG_RETURN_BOOL(val1 >= val2);
}

/* int82relop()
 * Is 64-bit val1 relop 16-bit val2?
 */
Datum
int82eq(PG_FUNCTION_ARGS)
{
	int64		val1 = PG_GETARG_INT64(0);
	int16		val2 = PG_GETARG_INT16(1);

	PG_RETURN_BOOL(val1 == val2);
}

Datum
int82ne(PG_FUNCTION_ARGS)
{
	int64		val1 = PG_GETARG_INT64(0);
	int16		val2 = PG_GETARG_INT16(1);

	PG_RETURN_BOOL(val1 != val2);
}

Datum
int82lt(PG_FUNCTION_ARGS)
{
	int64		val1 = PG_GETARG_INT64(0);
	int16		val2 = PG_GETARG_INT16(1);

	PG_RETURN_BOOL(val1 < val2);
}

Datum
int82gt(PG_FUNCTION_ARGS)
{
	int64		val1 = PG_GETARG_INT64(0);
	int16		val2 = PG_GETARG_INT16(1);

	PG_RETURN_BOOL(val1 > val2);
}

Datum
int82le(PG_FUNCTION_ARGS)
{
	int64		val1 = PG_GETARG_INT64(0);
	int16		val2 = PG_GETARG_INT16(1);

	PG_RETURN_BOOL(val1 <= val2);
}

Datum
int82ge(PG_FUNCTION_ARGS)
{
	int64		val1 = PG_GETARG_INT64(0);
	int16		val2 = PG_GETARG_INT16(1);

	PG_RETURN_BOOL(val1 >= val2);
}

/* int28relop()
 * Is 16-bit val1 relop 64-bit val2?
 */
Datum
int28eq(PG_FUNCTION_ARGS)
{
	int16		val1 = PG_GETARG_INT16(0);
	int64		val2 = PG_GETARG_INT64(1);

	PG_RETURN_BOOL(val1 == val2);
}

Datum
int28ne(PG_FUNCTION_ARGS)
{
	int16		val1 = PG_GETARG_INT16(0);
	int64		val2 = PG_GETARG_INT64(1);

	PG_RETURN_BOOL(val1 != val2);
}

Datum
int28lt(PG_FUNCTION_ARGS)
{
	int16		val1 = PG_GETARG_INT16(0);
	int64		val2 = PG_GETARG_INT64(1);

	PG_RETURN_BOOL(val1 < val2);
}

Datum
int28gt(PG_FUNCTION_ARGS)
{
	int16		val1 = PG_GETARG_INT16(0);
	int64		val2 = PG_GETARG_INT64(1);

	PG_RETURN_BOOL(val1 > val2);
}

Datum
int28le(PG_FUNCTION_ARGS)
{
	int16		val1 = PG_GETARG_INT16(0);
	int64		val2 = PG_GETARG_INT64(1);

	PG_RETURN_BOOL(val1 <= val2);
}

Datum
int28ge(PG_FUNCTION_ARGS)
{
	int16		val1 = PG_GETARG_INT16(0);
	int64		val2 = PG_GETARG_INT64(1);

	PG_RETURN_BOOL(val1 >= val2);
}

/*
 * in_range support function for int8.
 *
 * Note: we needn't supply int8_int4 or int8_int2 variants, as implicit
 * coercion of the offset value takes care of those scenarios just as well.
 */
Datum
in_range_int8_int8(PG_FUNCTION_ARGS)
{
	int64		val = PG_GETARG_INT64(0);
	int64		base = PG_GETARG_INT64(1);
	int64		offset = PG_GETARG_INT64(2);
	bool		sub = PG_GETARG_BOOL(3);
	bool		less = PG_GETARG_BOOL(4);
	int64		sum;

	if (offset < 0)
		ereport(ERROR,
				(errcode(ERRCODE_INVALID_PRECEDING_OR_FOLLOWING_SIZE),
				 errmsg("invalid preceding or following size in window function")));

	if (sub)
		offset = -offset;		/* cannot overflow */

	if (unlikely(pg_add_s64_overflow(base, offset, &sum)))
	{
		/*
		 * If sub is false, the true sum is surely more than val, so correct
		 * answer is the same as "less".  If sub is true, the true sum is
		 * surely less than val, so the answer is "!less".
		 */
		PG_RETURN_BOOL(sub ? !less : less);
	}

	if (less)
		PG_RETURN_BOOL(val <= sum);
	else
		PG_RETURN_BOOL(val >= sum);
}


/*----------------------------------------------------------
 *	Arithmetic operators on 64-bit integers.
 *---------------------------------------------------------*/

Datum
int8um(PG_FUNCTION_ARGS)
{
	int64		arg = PG_GETARG_INT64(0);
	int64		result;

	if (unlikely(arg == PG_INT64_MIN))
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("bigint out of range")));
	result = -arg;
	PG_RETURN_INT64(result);
}

Datum
int8up(PG_FUNCTION_ARGS)
{
	int64		arg = PG_GETARG_INT64(0);

	PG_RETURN_INT64(arg);
}

Datum
int8pl(PG_FUNCTION_ARGS)
{
	int64		arg1 = PG_GETARG_INT64(0);
	int64		arg2 = PG_GETARG_INT64(1);
	int64		result;

	if (unlikely(pg_add_s64_overflow(arg1, arg2, &result)))
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("bigint out of range")));
	PG_RETURN_INT64(result);
}

Datum
int8mi(PG_FUNCTION_ARGS)
{
	int64		arg1 = PG_GETARG_INT64(0);
	int64		arg2 = PG_GETARG_INT64(1);
	int64		result;

	if (unlikely(pg_sub_s64_overflow(arg1, arg2, &result)))
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("bigint out of range")));
	PG_RETURN_INT64(result);
}

Datum
int8mul(PG_FUNCTION_ARGS)
{
	int64		arg1 = PG_GETARG_INT64(0);
	int64		arg2 = PG_GETARG_INT64(1);
	int64		result;

	if (unlikely(pg_mul_s64_overflow(arg1, arg2, &result)))
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("bigint out of range")));
	PG_RETURN_INT64(result);
}

Datum
int8div(PG_FUNCTION_ARGS)
{
	int64		arg1 = PG_GETARG_INT64(0);
	int64		arg2 = PG_GETARG_INT64(1);
	int64		result;

	if (arg2 == 0)
	{
		ereport(ERROR,
				(errcode(ERRCODE_DIVISION_BY_ZERO),
				 errmsg("division by zero")));
		/* ensure compiler realizes we mustn't reach the division (gcc bug) */
		PG_RETURN_NULL();
	}

	/*
	 * INT64_MIN / -1 is problematic, since the result can't be represented on
	 * a two's-complement machine.  Some machines produce INT64_MIN, some
	 * produce zero, some throw an exception.  We can dodge the problem by
	 * recognizing that division by -1 is the same as negation.
	 */
	if (arg2 == -1)
	{
		if (unlikely(arg1 == PG_INT64_MIN))
			ereport(ERROR,
					(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
					 errmsg("bigint out of range")));
		result = -arg1;
		PG_RETURN_INT64(result);
	}

	/* No overflow is possible */

	result = arg1 / arg2;

	PG_RETURN_INT64(result);
}

/* int8abs()
 * Absolute value
 */
Datum
int8abs(PG_FUNCTION_ARGS)
{
	int64		arg1 = PG_GETARG_INT64(0);
	int64		result;

	if (unlikely(arg1 == PG_INT64_MIN))
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("bigint out of range")));
	result = (arg1 < 0) ? -arg1 : arg1;
	PG_RETURN_INT64(result);
}

/* int8mod()
 * Modulo operation.
 */
Datum
int8mod(PG_FUNCTION_ARGS)
{
	int64		arg1 = PG_GETARG_INT64(0);
	int64		arg2 = PG_GETARG_INT64(1);

	if (unlikely(arg2 == 0))
	{
		ereport(ERROR,
				(errcode(ERRCODE_DIVISION_BY_ZERO),
				 errmsg("division by zero")));
		/* ensure compiler realizes we mustn't reach the division (gcc bug) */
		PG_RETURN_NULL();
	}

	/*
	 * Some machines throw a floating-point exception for INT64_MIN % -1,
	 * which is a bit silly since the correct answer is perfectly
	 * well-defined, namely zero.
	 */
	if (arg2 == -1)
		PG_RETURN_INT64(0);

	/* No overflow is possible */

	PG_RETURN_INT64(arg1 % arg2);
}

/*
 * Greatest Common Divisor
 *
 * Returns the largest positive integer that exactly divides both inputs.
 * Special cases:
 *   - gcd(x, 0) = gcd(0, x) = abs(x)
 *   		because 0 is divisible by anything
 *   - gcd(0, 0) = 0
 *   		complies with the previous definition and is a common convention
 *
 * Special care must be taken if either input is INT64_MIN ---
 * gcd(0, INT64_MIN), gcd(INT64_MIN, 0) and gcd(INT64_MIN, INT64_MIN) are
 * all equal to abs(INT64_MIN), which cannot be represented as a 64-bit signed
 * integer.
 */
static int64
int8gcd_internal(int64 arg1, int64 arg2)
{
	int64		swap;
	int64		a1,
				a2;

	/*
	 * Put the greater absolute value in arg1.
	 *
	 * This would happen automatically in the loop below, but avoids an
	 * expensive modulo operation, and simplifies the special-case handling
	 * for INT64_MIN below.
	 *
	 * We do this in negative space in order to handle INT64_MIN.
	 */
	a1 = (arg1 < 0) ? arg1 : -arg1;
	a2 = (arg2 < 0) ? arg2 : -arg2;
	if (a1 > a2)
	{
		swap = arg1;
		arg1 = arg2;
		arg2 = swap;
	}

	/* Special care needs to be taken with INT64_MIN.  See comments above. */
	if (arg1 == PG_INT64_MIN)
	{
		if (arg2 == 0 || arg2 == PG_INT64_MIN)
			ereport(ERROR,
					(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
					 errmsg("bigint out of range")));

		/*
		 * Some machines throw a floating-point exception for INT64_MIN % -1,
		 * which is a bit silly since the correct answer is perfectly
		 * well-defined, namely zero.  Guard against this and just return the
		 * result, gcd(INT64_MIN, -1) = 1.
		 */
		if (arg2 == -1)
			return 1;
	}

	/* Use the Euclidean algorithm to find the GCD */
	while (arg2 != 0)
	{
		swap = arg2;
		arg2 = arg1 % arg2;
		arg1 = swap;
	}

	/*
	 * Make sure the result is positive. (We know we don't have INT64_MIN
	 * anymore).
	 */
	if (arg1 < 0)
		arg1 = -arg1;

	return arg1;
}

Datum
int8gcd(PG_FUNCTION_ARGS)
{
	int64		arg1 = PG_GETARG_INT64(0);
	int64		arg2 = PG_GETARG_INT64(1);
	int64		result;

	result = int8gcd_internal(arg1, arg2);

	PG_RETURN_INT64(result);
}

/*
 * Least Common Multiple
 */
Datum
int8lcm(PG_FUNCTION_ARGS)
{
	int64		arg1 = PG_GETARG_INT64(0);
	int64		arg2 = PG_GETARG_INT64(1);
	int64		gcd;
	int64		result;

	/*
	 * Handle lcm(x, 0) = lcm(0, x) = 0 as a special case.  This prevents a
	 * division-by-zero error below when x is zero, and an overflow error from
	 * the GCD computation when x = INT64_MIN.
	 */
	if (arg1 == 0 || arg2 == 0)
		PG_RETURN_INT64(0);

	/* lcm(x, y) = abs(x / gcd(x, y) * y) */
	gcd = int8gcd_internal(arg1, arg2);
	arg1 = arg1 / gcd;

	if (unlikely(pg_mul_s64_overflow(arg1, arg2, &result)))
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("bigint out of range")));

	/* If the result is INT64_MIN, it cannot be represented. */
	if (unlikely(result == PG_INT64_MIN))
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("bigint out of range")));

	if (result < 0)
		result = -result;

	PG_RETURN_INT64(result);
}

Datum
int8inc(PG_FUNCTION_ARGS)
{
	/*
	 * When int8 is pass-by-reference, we provide this special case to avoid
	 * palloc overhead for COUNT(): when called as an aggregate, we know that
	 * the argument is modifiable local storage, so just update it in-place.
	 * (If int8 is pass-by-value, then of course this is useless as well as
	 * incorrect, so just ifdef it out.)
	 */
#ifndef USE_FLOAT8_BYVAL		/* controls int8 too */
	if (AggCheckCallContext(fcinfo, NULL))
	{
		int64	   *arg = (int64 *) PG_GETARG_POINTER(0);

		if (unlikely(pg_add_s64_overflow(*arg, 1, arg)))
			ereport(ERROR,
					(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
					 errmsg("bigint out of range")));

		PG_RETURN_POINTER(arg);
	}
	else
#endif
	{
		/* Not called as an aggregate, so just do it the dumb way */
		int64		arg = PG_GETARG_INT64(0);
		int64		result;

		if (unlikely(pg_add_s64_overflow(arg, 1, &result)))
			ereport(ERROR,
					(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
					 errmsg("bigint out of range")));

		PG_RETURN_INT64(result);
	}
}

Datum
int8dec(PG_FUNCTION_ARGS)
{
	/*
	 * When int8 is pass-by-reference, we provide this special case to avoid
	 * palloc overhead for COUNT(): when called as an aggregate, we know that
	 * the argument is modifiable local storage, so just update it in-place.
	 * (If int8 is pass-by-value, then of course this is useless as well as
	 * incorrect, so just ifdef it out.)
	 */
#ifndef USE_FLOAT8_BYVAL		/* controls int8 too */
	if (AggCheckCallContext(fcinfo, NULL))
	{
		int64	   *arg = (int64 *) PG_GETARG_POINTER(0);

		if (unlikely(pg_sub_s64_overflow(*arg, 1, arg)))
			ereport(ERROR,
					(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
					 errmsg("bigint out of range")));
		PG_RETURN_POINTER(arg);
	}
	else
#endif
	{
		/* Not called as an aggregate, so just do it the dumb way */
		int64		arg = PG_GETARG_INT64(0);
		int64		result;

		if (unlikely(pg_sub_s64_overflow(arg, 1, &result)))
			ereport(ERROR,
					(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
					 errmsg("bigint out of range")));

		PG_RETURN_INT64(result);
	}
}


/*
 * These functions are exactly like int8inc/int8dec but are used for
 * aggregates that count only non-null values.  Since the functions are
 * declared strict, the null checks happen before we ever get here, and all we
 * need do is increment the state value.  We could actually make these pg_proc
 * entries point right at int8inc/int8dec, but then the opr_sanity regression
 * test would complain about mismatched entries for a built-in function.
 */

Datum
int8inc_any(PG_FUNCTION_ARGS)
{
	return int8inc(fcinfo);
}

Datum
int8inc_float8_float8(PG_FUNCTION_ARGS)
{
	return int8inc(fcinfo);
}

Datum
int8dec_any(PG_FUNCTION_ARGS)
{
	return int8dec(fcinfo);
}

/*
 * int8inc_support
 *		prosupport function for int8inc() and int8inc_any()
 */
Datum
int8inc_support(PG_FUNCTION_ARGS)
{
	Node	   *rawreq = (Node *) PG_GETARG_POINTER(0);

	if (IsA(rawreq, SupportRequestWFuncMonotonic))
	{
		SupportRequestWFuncMonotonic *req = (SupportRequestWFuncMonotonic *) rawreq;
		MonotonicFunction monotonic = MONOTONICFUNC_NONE;
		int			frameOptions = req->window_clause->frameOptions;
		WindowFunc *wfunc = req->window_func;

		if (list_length(wfunc->args) == 1)
		{
			Node *expr = eval_const_expressions(NULL, linitial(wfunc->args));

			/*
			 * Due to the Node representation of WindowClause runConditions in
			 * version prior to v17, we need to insist that the count arg is
			 * Const to allow safe application of the runCondition
			 * optimization.
			 */
			if (!IsA(expr, Const))
				PG_RETURN_POINTER(NULL);
		}

		/* No ORDER BY clause then all rows are peers */
		if (req->window_clause->orderClause == NIL)
			monotonic = MONOTONICFUNC_BOTH;
		else
		{
			/*
			 * Otherwise take into account the frame options.  When the frame
			 * bound is the start of the window then the resulting value can
			 * never decrease, therefore is monotonically increasing
			 */
			if (frameOptions & FRAMEOPTION_START_UNBOUNDED_PRECEDING)
				monotonic |= MONOTONICFUNC_INCREASING;

			/*
			 * Likewise, if the frame bound is the end of the window then the
			 * resulting value can never decrease.
			 */
			if (frameOptions & FRAMEOPTION_END_UNBOUNDED_FOLLOWING)
				monotonic |= MONOTONICFUNC_DECREASING;
		}

		req->monotonic = monotonic;
		PG_RETURN_POINTER(req);
	}

	PG_RETURN_POINTER(NULL);
}


Datum
int8larger(PG_FUNCTION_ARGS)
{
	int64		arg1 = PG_GETARG_INT64(0);
	int64		arg2 = PG_GETARG_INT64(1);
	int64		result;

	result = ((arg1 > arg2) ? arg1 : arg2);

	PG_RETURN_INT64(result);
}

Datum
int8smaller(PG_FUNCTION_ARGS)
{
	int64		arg1 = PG_GETARG_INT64(0);
	int64		arg2 = PG_GETARG_INT64(1);
	int64		result;

	result = ((arg1 < arg2) ? arg1 : arg2);

	PG_RETURN_INT64(result);
}

Datum
int84pl(PG_FUNCTION_ARGS)
{
	int64		arg1 = PG_GETARG_INT64(0);
	int32		arg2 = PG_GETARG_INT32(1);
	int64		result;

	if (unlikely(pg_add_s64_overflow(arg1, (int64) arg2, &result)))
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("bigint out of range")));
	PG_RETURN_INT64(result);
}

Datum
int84mi(PG_FUNCTION_ARGS)
{
	int64		arg1 = PG_GETARG_INT64(0);
	int32		arg2 = PG_GETARG_INT32(1);
	int64		result;

	if (unlikely(pg_sub_s64_overflow(arg1, (int64) arg2, &result)))
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("bigint out of range")));
	PG_RETURN_INT64(result);
}

Datum
int84mul(PG_FUNCTION_ARGS)
{
	int64		arg1 = PG_GETARG_INT64(0);
	int32		arg2 = PG_GETARG_INT32(1);
	int64		result;

	if (unlikely(pg_mul_s64_overflow(arg1, (int64) arg2, &result)))
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("bigint out of range")));
	PG_RETURN_INT64(result);
}

Datum
int84div(PG_FUNCTION_ARGS)
{
	int64		arg1 = PG_GETARG_INT64(0);
	int32		arg2 = PG_GETARG_INT32(1);
	int64		result;

	if (arg2 == 0)
	{
		ereport(ERROR,
				(errcode(ERRCODE_DIVISION_BY_ZERO),
				 errmsg("division by zero")));
		/* ensure compiler realizes we mustn't reach the division (gcc bug) */
		PG_RETURN_NULL();
	}

	/*
	 * INT64_MIN / -1 is problematic, since the result can't be represented on
	 * a two's-complement machine.  Some machines produce INT64_MIN, some
	 * produce zero, some throw an exception.  We can dodge the problem by
	 * recognizing that division by -1 is the same as negation.
	 */
	if (arg2 == -1)
	{
		if (unlikely(arg1 == PG_INT64_MIN))
			ereport(ERROR,
					(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
					 errmsg("bigint out of range")));
		result = -arg1;
		PG_RETURN_INT64(result);
	}

	/* No overflow is possible */

	result = arg1 / arg2;

	PG_RETURN_INT64(result);
}

Datum
int48pl(PG_FUNCTION_ARGS)
{
	int32		arg1 = PG_GETARG_INT32(0);
	int64		arg2 = PG_GETARG_INT64(1);
	int64		result;

	if (unlikely(pg_add_s64_overflow((int64) arg1, arg2, &result)))
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("bigint out of range")));
	PG_RETURN_INT64(result);
}

Datum
int48mi(PG_FUNCTION_ARGS)
{
	int32		arg1 = PG_GETARG_INT32(0);
	int64		arg2 = PG_GETARG_INT64(1);
	int64		result;

	if (unlikely(pg_sub_s64_overflow((int64) arg1, arg2, &result)))
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("bigint out of range")));
	PG_RETURN_INT64(result);
}

Datum
int48mul(PG_FUNCTION_ARGS)
{
	int32		arg1 = PG_GETARG_INT32(0);
	int64		arg2 = PG_GETARG_INT64(1);
	int64		result;

	if (unlikely(pg_mul_s64_overflow((int64) arg1, arg2, &result)))
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("bigint out of range")));
	PG_RETURN_INT64(result);
}

Datum
int48div(PG_FUNCTION_ARGS)
{
	int32		arg1 = PG_GETARG_INT32(0);
	int64		arg2 = PG_GETARG_INT64(1);

	if (unlikely(arg2 == 0))
	{
		ereport(ERROR,
				(errcode(ERRCODE_DIVISION_BY_ZERO),
				 errmsg("division by zero")));
		/* ensure compiler realizes we mustn't reach the division (gcc bug) */
		PG_RETURN_NULL();
	}

	/* No overflow is possible */
	PG_RETURN_INT64((int64) arg1 / arg2);
}

Datum
int82pl(PG_FUNCTION_ARGS)
{
	int64		arg1 = PG_GETARG_INT64(0);
	int16		arg2 = PG_GETARG_INT16(1);
	int64		result;

	if (unlikely(pg_add_s64_overflow(arg1, (int64) arg2, &result)))
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("bigint out of range")));
	PG_RETURN_INT64(result);
}

Datum
int82mi(PG_FUNCTION_ARGS)
{
	int64		arg1 = PG_GETARG_INT64(0);
	int16		arg2 = PG_GETARG_INT16(1);
	int64		result;

	if (unlikely(pg_sub_s64_overflow(arg1, (int64) arg2, &result)))
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("bigint out of range")));
	PG_RETURN_INT64(result);
}

Datum
int82mul(PG_FUNCTION_ARGS)
{
	int64		arg1 = PG_GETARG_INT64(0);
	int16		arg2 = PG_GETARG_INT16(1);
	int64		result;

	if (unlikely(pg_mul_s64_overflow(arg1, (int64) arg2, &result)))
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("bigint out of range")));
	PG_RETURN_INT64(result);
}

Datum
int82div(PG_FUNCTION_ARGS)
{
	int64		arg1 = PG_GETARG_INT64(0);
	int16		arg2 = PG_GETARG_INT16(1);
	int64		result;

	if (unlikely(arg2 == 0))
	{
		ereport(ERROR,
				(errcode(ERRCODE_DIVISION_BY_ZERO),
				 errmsg("division by zero")));
		/* ensure compiler realizes we mustn't reach the division (gcc bug) */
		PG_RETURN_NULL();
	}

	/*
	 * INT64_MIN / -1 is problematic, since the result can't be represented on
	 * a two's-complement machine.  Some machines produce INT64_MIN, some
	 * produce zero, some throw an exception.  We can dodge the problem by
	 * recognizing that division by -1 is the same as negation.
	 */
	if (arg2 == -1)
	{
		if (unlikely(arg1 == PG_INT64_MIN))
			ereport(ERROR,
					(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
					 errmsg("bigint out of range")));
		result = -arg1;
		PG_RETURN_INT64(result);
	}

	/* No overflow is possible */

	result = arg1 / arg2;

	PG_RETURN_INT64(result);
}

Datum
int28pl(PG_FUNCTION_ARGS)
{
	int16		arg1 = PG_GETARG_INT16(0);
	int64		arg2 = PG_GETARG_INT64(1);
	int64		result;

	if (unlikely(pg_add_s64_overflow((int64) arg1, arg2, &result)))
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("bigint out of range")));
	PG_RETURN_INT64(result);
}

Datum
int28mi(PG_FUNCTION_ARGS)
{
	int16		arg1 = PG_GETARG_INT16(0);
	int64		arg2 = PG_GETARG_INT64(1);
	int64		result;

	if (unlikely(pg_sub_s64_overflow((int64) arg1, arg2, &result)))
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("bigint out of range")));
	PG_RETURN_INT64(result);
}

Datum
int28mul(PG_FUNCTION_ARGS)
{
	int16		arg1 = PG_GETARG_INT16(0);
	int64		arg2 = PG_GETARG_INT64(1);
	int64		result;

	if (unlikely(pg_mul_s64_overflow((int64) arg1, arg2, &result)))
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("bigint out of range")));
	PG_RETURN_INT64(result);
}

Datum
int28div(PG_FUNCTION_ARGS)
{
	int16		arg1 = PG_GETARG_INT16(0);
	int64		arg2 = PG_GETARG_INT64(1);

	if (unlikely(arg2 == 0))
	{
		ereport(ERROR,
				(errcode(ERRCODE_DIVISION_BY_ZERO),
				 errmsg("division by zero")));
		/* ensure compiler realizes we mustn't reach the division (gcc bug) */
		PG_RETURN_NULL();
	}

	/* No overflow is possible */
	PG_RETURN_INT64((int64) arg1 / arg2);
}

/* Binary arithmetics
 *
 *		int8and		- returns arg1 & arg2
 *		int8or		- returns arg1 | arg2
 *		int8xor		- returns arg1 # arg2
 *		int8not		- returns ~arg1
 *		int8shl		- returns arg1 << arg2
 *		int8shr		- returns arg1 >> arg2
 */

Datum
int8and(PG_FUNCTION_ARGS)
{
	int64		arg1 = PG_GETARG_INT64(0);
	int64		arg2 = PG_GETARG_INT64(1);

	PG_RETURN_INT64(arg1 & arg2);
}

Datum
int8or(PG_FUNCTION_ARGS)
{
	int64		arg1 = PG_GETARG_INT64(0);
	int64		arg2 = PG_GETARG_INT64(1);

	PG_RETURN_INT64(arg1 | arg2);
}

Datum
int8xor(PG_FUNCTION_ARGS)
{
	int64		arg1 = PG_GETARG_INT64(0);
	int64		arg2 = PG_GETARG_INT64(1);

	PG_RETURN_INT64(arg1 ^ arg2);
}

Datum
int8not(PG_FUNCTION_ARGS)
{
	int64		arg1 = PG_GETARG_INT64(0);

	PG_RETURN_INT64(~arg1);
}

Datum
int8shl(PG_FUNCTION_ARGS)
{
	int64		arg1 = PG_GETARG_INT64(0);
	int32		arg2 = PG_GETARG_INT32(1);

	PG_RETURN_INT64(arg1 << arg2);
}

Datum
int8shr(PG_FUNCTION_ARGS)
{
	int64		arg1 = PG_GETARG_INT64(0);
	int32		arg2 = PG_GETARG_INT32(1);

	PG_RETURN_INT64(arg1 >> arg2);
}

/*----------------------------------------------------------
 *	Conversion operators.
 *---------------------------------------------------------*/

Datum
int48(PG_FUNCTION_ARGS)
{
	int32		arg = PG_GETARG_INT32(0);

	PG_RETURN_INT64((int64) arg);
}

Datum
int84(PG_FUNCTION_ARGS)
{
	int64		arg = PG_GETARG_INT64(0);

	if (unlikely(arg < PG_INT32_MIN) || unlikely(arg > PG_INT32_MAX))
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("integer out of range")));

	PG_RETURN_INT32((int32) arg);
}

Datum
int28(PG_FUNCTION_ARGS)
{
	int16		arg = PG_GETARG_INT16(0);

	PG_RETURN_INT64((int64) arg);
}

Datum
int82(PG_FUNCTION_ARGS)
{
	int64		arg = PG_GETARG_INT64(0);

	if (unlikely(arg < PG_INT16_MIN) || unlikely(arg > PG_INT16_MAX))
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("smallint out of range")));

	PG_RETURN_INT16((int16) arg);
}

Datum
i8tod(PG_FUNCTION_ARGS)
{
	int64		arg = PG_GETARG_INT64(0);
	float8		result;

	result = arg;

	PG_RETURN_FLOAT8(result);
}

/* dtoi8()
 * Convert float8 to 8-byte integer.
 */
Datum
dtoi8(PG_FUNCTION_ARGS)
{
	float8		num = PG_GETARG_FLOAT8(0);

	/*
	 * Get rid of any fractional part in the input.  This is so we don't fail
	 * on just-out-of-range values that would round into range.  Note
	 * assumption that rint() will pass through a NaN or Inf unchanged.
	 */
	num = rint(num);

	/* Range check */
	if (unlikely(isnan(num) || !FLOAT8_FITS_IN_INT64(num)))
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("bigint out of range")));

	PG_RETURN_INT64((int64) num);
}

Datum
i8tof(PG_FUNCTION_ARGS)
{
	int64		arg = PG_GETARG_INT64(0);
	float4		result;

	result = arg;

	PG_RETURN_FLOAT4(result);
}

/* ftoi8()
 * Convert float4 to 8-byte integer.
 */
Datum
ftoi8(PG_FUNCTION_ARGS)
{
	float4		num = PG_GETARG_FLOAT4(0);

	/*
	 * Get rid of any fractional part in the input.  This is so we don't fail
	 * on just-out-of-range values that would round into range.  Note
	 * assumption that rint() will pass through a NaN or Inf unchanged.
	 */
	num = rint(num);

	/* Range check */
	if (unlikely(isnan(num) || !FLOAT4_FITS_IN_INT64(num)))
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("bigint out of range")));

	PG_RETURN_INT64((int64) num);
}

Datum
i8tooid(PG_FUNCTION_ARGS)
{
	int64		arg = PG_GETARG_INT64(0);

	if (unlikely(arg < 0) || unlikely(arg > PG_UINT32_MAX))
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("OID out of range")));

	PG_RETURN_OID((Oid) arg);
}

Datum
oidtoi8(PG_FUNCTION_ARGS)
{
	Oid			arg = PG_GETARG_OID(0);

	PG_RETURN_INT64((int64) arg);
}

/*
 * non-persistent numeric series generator
 */
Datum
generate_series_int8(PG_FUNCTION_ARGS)
{
	return generate_series_step_int8(fcinfo);
}

Datum
generate_series_step_int8(PG_FUNCTION_ARGS)
{
	FuncCallContext *funcctx;
	generate_series_fctx *fctx;
	int64		result;
	MemoryContext oldcontext;

	/* stuff done only on the first call of the function */
	if (SRF_IS_FIRSTCALL())
	{
		int64		start = PG_GETARG_INT64(0);
		int64		finish = PG_GETARG_INT64(1);
		int64		step = 1;

		/* see if we were given an explicit step size */
		if (PG_NARGS() == 3)
			step = PG_GETARG_INT64(2);
		if (step == 0)
			ereport(ERROR,
					(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
					 errmsg("step size cannot equal zero")));

		/* create a function context for cross-call persistence */
		funcctx = SRF_FIRSTCALL_INIT();

		/*
		 * switch to memory context appropriate for multiple function calls
		 */
		oldcontext = MemoryContextSwitchTo(funcctx->multi_call_memory_ctx);

		/* allocate memory for user context */
		fctx = (generate_series_fctx *) palloc(sizeof(generate_series_fctx));

		/*
		 * Use fctx to keep state from call to call. Seed current with the
		 * original start value
		 */
		fctx->current = start;
		fctx->finish = finish;
		fctx->step = step;

		funcctx->user_fctx = fctx;
		MemoryContextSwitchTo(oldcontext);
	}

	/* stuff done on every call of the function */
	funcctx = SRF_PERCALL_SETUP();

	/*
	 * get the saved state and use current as the result for this iteration
	 */
	fctx = funcctx->user_fctx;
	result = fctx->current;

	if ((fctx->step > 0 && fctx->current <= fctx->finish) ||
		(fctx->step < 0 && fctx->current >= fctx->finish))
	{
		/*
		 * Increment current in preparation for next iteration. If next-value
		 * computation overflows, this is the final result.
		 */
		if (pg_add_s64_overflow(fctx->current, fctx->step, &fctx->current))
			fctx->step = 0;

		/* do when there is more left to send */
		SRF_RETURN_NEXT(funcctx, Int64GetDatum(result));
	}
	else
		/* do when there is no more left */
		SRF_RETURN_DONE(funcctx);
}

/*
 * Planner support function for generate_series(int8, int8 [, int8])
 */
Datum
generate_series_int8_support(PG_FUNCTION_ARGS)
{
	Node	   *rawreq = (Node *) PG_GETARG_POINTER(0);
	Node	   *ret = NULL;

	if (IsA(rawreq, SupportRequestRows))
	{
		/* Try to estimate the number of rows returned */
		SupportRequestRows *req = (SupportRequestRows *) rawreq;

		if (is_funcclause(req->node))	/* be paranoid */
		{
			List	   *args = ((FuncExpr *) req->node)->args;
			Node	   *arg1,
					   *arg2,
					   *arg3;

			/* We can use estimated argument values here */
			arg1 = estimate_expression_value(req->root, linitial(args));
			arg2 = estimate_expression_value(req->root, lsecond(args));
			if (list_length(args) >= 3)
				arg3 = estimate_expression_value(req->root, lthird(args));
			else
				arg3 = NULL;

			/*
			 * If any argument is constant NULL, we can safely assume that
			 * zero rows are returned.  Otherwise, if they're all non-NULL
			 * constants, we can calculate the number of rows that will be
			 * returned.  Use double arithmetic to avoid overflow hazards.
			 */
			if ((IsA(arg1, Const) &&
				 ((Const *) arg1)->constisnull) ||
				(IsA(arg2, Const) &&
				 ((Const *) arg2)->constisnull) ||
				(arg3 != NULL && IsA(arg3, Const) &&
				 ((Const *) arg3)->constisnull))
			{
				req->rows = 0;
				ret = (Node *) req;
			}
			else if (IsA(arg1, Const) &&
					 IsA(arg2, Const) &&
					 (arg3 == NULL || IsA(arg3, Const)))
			{
				double		start,
							finish,
							step;

				start = DatumGetInt64(((Const *) arg1)->constvalue);
				finish = DatumGetInt64(((Const *) arg2)->constvalue);
				step = arg3 ? DatumGetInt64(((Const *) arg3)->constvalue) : 1;

				/* This equation works for either sign of step */
				if (step != 0)
				{
					req->rows = floor((finish - start + step) / step);
					ret = (Node *) req;
				}
			}
		}
	}

	PG_RETURN_POINTER(ret);
}