This commit was manufactured by cvs2git to create branch 'ecpg_big_bison'.

Sprout from master 2002-06-20 20:29:54 UTC Bruce Momjian <bruce@momjian.us> 'Update copyright to 2002.'
Delete:
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diff --git a/src/backend/utils/adt/numeric.c b/src/backend/utils/adt/numeric.c
deleted file mode 100644
index 1af7402fb38..00000000000
--- a/src/backend/utils/adt/numeric.c
+++ /dev/null
@@ -1,3997 +0,0 @@
-/* ----------
- * numeric.c
- *
- *	An exact numeric data type for the Postgres database system
- *
- *	1998 Jan Wieck
- *
- * $Header: /cvsroot/pgsql/src/backend/utils/adt/numeric.c,v 1.50 2002/02/18 14:25:40 momjian Exp $
- *
- * ----------
- */
-
-#include "postgres.h"
-
-#include <ctype.h>
-#include <float.h>
-#include <math.h>
-#include <errno.h>
-#include <sys/types.h>
-
-#include "utils/array.h"
-#include "utils/builtins.h"
-#include "utils/int8.h"
-#include "utils/numeric.h"
-
-/* ----------
- * Uncomment the following to enable compilation of dump_numeric()
- * and dump_var() and to get a dump of any result produced by make_result().
- * ----------
-#define NUMERIC_DEBUG
- */
-
-
-/* ----------
- * Local definitions
- * ----------
- */
-#ifndef NAN
-#define NAN		(0.0/0.0)
-#endif
-
-
-/* ----------
- * Local data types
- *
- * Note: the first digit of a NumericVar's value is assumed to be multiplied
- * by 10 ** weight.  Another way to say it is that there are weight+1 digits
- * before the decimal point.  It is possible to have weight < 0.
- *
- * The value represented by a NumericVar is determined by the sign, weight,
- * ndigits, and digits[] array.  The rscale and dscale are carried along,
- * but they are just auxiliary information until rounding is done before
- * final storage or display.  (Scales are the number of digits wanted
- * *after* the decimal point.  Scales are always >= 0.)
- *
- * buf points at the physical start of the palloc'd digit buffer for the
- * NumericVar.	digits points at the first digit in actual use (the one
- * with the specified weight).	We normally leave an unused byte or two
- * (preset to zeroes) between buf and digits, so that there is room to store
- * a carry out of the top digit without special pushups.  We just need to
- * decrement digits (and increment weight) to make room for the carry digit.
- *
- * If buf is NULL then the digit buffer isn't actually palloc'd and should
- * not be freed --- see the constants below for an example.
- *
- * NB: All the variable-level functions are written in a style that makes it
- * possible to give one and the same variable as argument and destination.
- * This is feasible because the digit buffer is separate from the variable.
- * ----------
- */
-typedef unsigned char NumericDigit;
-
-typedef struct NumericVar
-{
-	int			ndigits;		/* number of digits in digits[] - can be
-								 * 0! */
-	int			weight;			/* weight of first digit */
-	int			rscale;			/* result scale */
-	int			dscale;			/* display scale */
-	int			sign;			/* NUMERIC_POS, NUMERIC_NEG, or
-								 * NUMERIC_NAN */
-	NumericDigit *buf;			/* start of palloc'd space for digits[] */
-	NumericDigit *digits;		/* decimal digits */
-} NumericVar;
-
-
-/* ----------
- * Local data
- * ----------
- */
-static int	global_rscale = NUMERIC_MIN_RESULT_SCALE;
-
-/* ----------
- * Some preinitialized variables we need often
- * ----------
- */
-static NumericDigit const_zero_data[1] = {0};
-static NumericVar const_zero =
-{0, 0, 0, 0, NUMERIC_POS, NULL, const_zero_data};
-
-static NumericDigit const_one_data[1] = {1};
-static NumericVar const_one =
-{1, 0, 0, 0, NUMERIC_POS, NULL, const_one_data};
-
-static NumericDigit const_two_data[1] = {2};
-static NumericVar const_two =
-{1, 0, 0, 0, NUMERIC_POS, NULL, const_two_data};
-
-static NumericVar const_nan =
-{0, 0, 0, 0, NUMERIC_NAN, NULL, NULL};
-
-
-
-/* ----------
- * Local functions
- * ----------
- */
-
-#ifdef NUMERIC_DEBUG
-static void dump_numeric(char *str, Numeric num);
-static void dump_var(char *str, NumericVar *var);
-
-#else
-#define dump_numeric(s,n)
-#define dump_var(s,v)
-#endif
-
-#define digitbuf_alloc(size)  ((NumericDigit *) palloc(size))
-#define digitbuf_free(buf)	\
-	do { \
-		 if ((buf) != NULL) \
-			 pfree(buf); \
-	} while (0)
-
-#define init_var(v)		memset(v,0,sizeof(NumericVar))
-static void alloc_var(NumericVar *var, int ndigits);
-static void free_var(NumericVar *var);
-static void zero_var(NumericVar *var);
-
-static void set_var_from_str(char *str, NumericVar *dest);
-static void set_var_from_num(Numeric value, NumericVar *dest);
-static void set_var_from_var(NumericVar *value, NumericVar *dest);
-static char *get_str_from_var(NumericVar *var, int dscale);
-
-static Numeric make_result(NumericVar *var);
-
-static void apply_typmod(NumericVar *var, int32 typmod);
-
-static int	cmp_numerics(Numeric num1, Numeric num2);
-static int	cmp_var(NumericVar *var1, NumericVar *var2);
-static void add_var(NumericVar *var1, NumericVar *var2, NumericVar *result);
-static void sub_var(NumericVar *var1, NumericVar *var2, NumericVar *result);
-static void mul_var(NumericVar *var1, NumericVar *var2, NumericVar *result);
-static void div_var(NumericVar *var1, NumericVar *var2, NumericVar *result);
-static int select_div_scale(NumericVar *var1, NumericVar *var2);
-static void mod_var(NumericVar *var1, NumericVar *var2, NumericVar *result);
-static void ceil_var(NumericVar *var, NumericVar *result);
-static void floor_var(NumericVar *var, NumericVar *result);
-
-static void sqrt_var(NumericVar *arg, NumericVar *result);
-static void exp_var(NumericVar *arg, NumericVar *result);
-static void ln_var(NumericVar *arg, NumericVar *result);
-static void log_var(NumericVar *base, NumericVar *num, NumericVar *result);
-static void power_var(NumericVar *base, NumericVar *exp, NumericVar *result);
-
-static int	cmp_abs(NumericVar *var1, NumericVar *var2);
-static void add_abs(NumericVar *var1, NumericVar *var2, NumericVar *result);
-static void sub_abs(NumericVar *var1, NumericVar *var2, NumericVar *result);
-
-
-
-/* ----------------------------------------------------------------------
- *
- * Input-, output- and rounding-functions
- *
- * ----------------------------------------------------------------------
- */
-
-
-/* ----------
- * numeric_in() -
- *
- *	Input function for numeric data type
- * ----------
- */
-Datum
-numeric_in(PG_FUNCTION_ARGS)
-{
-	char	   *str = PG_GETARG_CSTRING(0);
-
-#ifdef NOT_USED
-	Oid			typelem = PG_GETARG_OID(1);
-#endif
-	int32		typmod = PG_GETARG_INT32(2);
-	NumericVar	value;
-	Numeric		res;
-
-	/*
-	 * Check for NaN
-	 */
-	if (strcmp(str, "NaN") == 0)
-		PG_RETURN_NUMERIC(make_result(&const_nan));
-
-	/*
-	 * Use set_var_from_str() to parse the input string and return it in
-	 * the packed DB storage format
-	 */
-	init_var(&value);
-	set_var_from_str(str, &value);
-
-	apply_typmod(&value, typmod);
-
-	res = make_result(&value);
-	free_var(&value);
-
-	PG_RETURN_NUMERIC(res);
-}
-
-
-/* ----------
- * numeric_out() -
- *
- *	Output function for numeric data type
- * ----------
- */
-Datum
-numeric_out(PG_FUNCTION_ARGS)
-{
-	Numeric		num = PG_GETARG_NUMERIC(0);
-	NumericVar	x;
-	char	   *str;
-
-	/*
-	 * Handle NaN
-	 */
-	if (NUMERIC_IS_NAN(num))
-		PG_RETURN_CSTRING(pstrdup("NaN"));
-
-	/*
-	 * Get the number in the variable format.
-	 *
-	 * Even if we didn't need to change format, we'd still need to copy the
-	 * value to have a modifiable copy for rounding.  set_var_from_num()
-	 * also guarantees there is extra digit space in case we produce a
-	 * carry out from rounding.
-	 */
-	init_var(&x);
-	set_var_from_num(num, &x);
-
-	str = get_str_from_var(&x, x.dscale);
-
-	free_var(&x);
-
-	PG_RETURN_CSTRING(str);
-}
-
-
-/* ----------
- * numeric() -
- *
- *	This is a special function called by the Postgres database system
- *	before a value is stored in a tuples attribute. The precision and
- *	scale of the attribute have to be applied on the value.
- * ----------
- */
-Datum
-numeric(PG_FUNCTION_ARGS)
-{
-	Numeric		num = PG_GETARG_NUMERIC(0);
-	int32		typmod = PG_GETARG_INT32(1);
-	Numeric		new;
-	int32		tmp_typmod;
-	int			precision;
-	int			scale;
-	int			maxweight;
-	NumericVar	var;
-
-	/*
-	 * Handle NaN
-	 */
-	if (NUMERIC_IS_NAN(num))
-		PG_RETURN_NUMERIC(make_result(&const_nan));
-
-	/*
-	 * If the value isn't a valid type modifier, simply return a copy of
-	 * the input value
-	 */
-	if (typmod < (int32) (VARHDRSZ))
-	{
-		new = (Numeric) palloc(num->varlen);
-		memcpy(new, num, num->varlen);
-		PG_RETURN_NUMERIC(new);
-	}
-
-	/*
-	 * Get the precision and scale out of the typmod value
-	 */
-	tmp_typmod = typmod - VARHDRSZ;
-	precision = (tmp_typmod >> 16) & 0xffff;
-	scale = tmp_typmod & 0xffff;
-	maxweight = precision - scale;
-
-	/*
-	 * If the number is in bounds and due to the present result scale no
-	 * rounding could be necessary, just make a copy of the input and
-	 * modify its scale fields.
-	 */
-	if (num->n_weight < maxweight && scale >= num->n_rscale)
-	{
-		new = (Numeric) palloc(num->varlen);
-		memcpy(new, num, num->varlen);
-		new->n_rscale = scale;
-		new->n_sign_dscale = NUMERIC_SIGN(new) |
-			((uint16) scale & NUMERIC_DSCALE_MASK);
-		PG_RETURN_NUMERIC(new);
-	}
-
-	/*
-	 * We really need to fiddle with things - unpack the number into a
-	 * variable and let apply_typmod() do it.
-	 */
-	init_var(&var);
-
-	set_var_from_num(num, &var);
-	apply_typmod(&var, typmod);
-	new = make_result(&var);
-
-	free_var(&var);
-
-	PG_RETURN_NUMERIC(new);
-}
-
-
-/* ----------------------------------------------------------------------
- *
- * Sign manipulation, rounding and the like
- *
- * ----------------------------------------------------------------------
- */
-
-Datum
-numeric_abs(PG_FUNCTION_ARGS)
-{
-	Numeric		num = PG_GETARG_NUMERIC(0);
-	Numeric		res;
-
-	/*
-	 * Handle NaN
-	 */
-	if (NUMERIC_IS_NAN(num))
-		PG_RETURN_NUMERIC(make_result(&const_nan));
-
-	/*
-	 * Do it the easy way directly on the packed format
-	 */
-	res = (Numeric) palloc(num->varlen);
-	memcpy(res, num, num->varlen);
-
-	res->n_sign_dscale = NUMERIC_POS | NUMERIC_DSCALE(num);
-
-	PG_RETURN_NUMERIC(res);
-}
-
-
-Datum
-numeric_uminus(PG_FUNCTION_ARGS)
-{
-	Numeric		num = PG_GETARG_NUMERIC(0);
-	Numeric		res;
-
-	/*
-	 * Handle NaN
-	 */
-	if (NUMERIC_IS_NAN(num))
-		PG_RETURN_NUMERIC(make_result(&const_nan));
-
-	/*
-	 * Do it the easy way directly on the packed format
-	 */
-	res = (Numeric) palloc(num->varlen);
-	memcpy(res, num, num->varlen);
-
-	/*
-	 * The packed format is known to be totally zero digit trimmed always.
-	 * So we can identify a ZERO by the fact that there are no digits at
-	 * all.  Do nothing to a zero.
-	 */
-	if (num->varlen != NUMERIC_HDRSZ)
-	{
-		/* Else, flip the sign */
-		if (NUMERIC_SIGN(num) == NUMERIC_POS)
-			res->n_sign_dscale = NUMERIC_NEG | NUMERIC_DSCALE(num);
-		else
-			res->n_sign_dscale = NUMERIC_POS | NUMERIC_DSCALE(num);
-	}
-
-	PG_RETURN_NUMERIC(res);
-}
-
-
-Datum
-numeric_uplus(PG_FUNCTION_ARGS)
-{
-	Numeric		num = PG_GETARG_NUMERIC(0);
-	Numeric		res;
-
-	res = (Numeric) palloc(num->varlen);
-	memcpy(res, num, num->varlen);
-
-	PG_RETURN_NUMERIC(res);
-}
-
-
-Datum
-numeric_sign(PG_FUNCTION_ARGS)
-{
-	Numeric		num = PG_GETARG_NUMERIC(0);
-	Numeric		res;
-	NumericVar	result;
-
-	/*
-	 * Handle NaN
-	 */
-	if (NUMERIC_IS_NAN(num))
-		PG_RETURN_NUMERIC(make_result(&const_nan));
-
-	init_var(&result);
-
-	/*
-	 * The packed format is known to be totally zero digit trimmed always.
-	 * So we can identify a ZERO by the fact that there are no digits at
-	 * all.
-	 */
-	if (num->varlen == NUMERIC_HDRSZ)
-		set_var_from_var(&const_zero, &result);
-	else
-	{
-		/*
-		 * And if there are some, we return a copy of ONE with the sign of
-		 * our argument
-		 */
-		set_var_from_var(&const_one, &result);
-		result.sign = NUMERIC_SIGN(num);
-	}
-
-	res = make_result(&result);
-	free_var(&result);
-
-	PG_RETURN_NUMERIC(res);
-}
-
-
-/* ----------
- * numeric_round() -
- *
- *	Round a value to have 'scale' digits after the decimal point.
- *	We allow negative 'scale', implying rounding before the decimal
- *	point --- Oracle interprets rounding that way.
- * ----------
- */
-Datum
-numeric_round(PG_FUNCTION_ARGS)
-{
-	Numeric		num = PG_GETARG_NUMERIC(0);
-	int32		scale = PG_GETARG_INT32(1);
-	Numeric		res;
-	NumericVar	arg;
-	int			i;
-
-	/*
-	 * Handle NaN
-	 */
-	if (NUMERIC_IS_NAN(num))
-		PG_RETURN_NUMERIC(make_result(&const_nan));
-
-	/*
-	 * Limit the scale value to avoid possible overflow in calculations
-	 * below.
-	 */
-	scale = Min(NUMERIC_MAX_RESULT_SCALE,
-				Max(-NUMERIC_MAX_RESULT_SCALE, scale));
-
-	/*
-	 * Unpack the argument and round it at the proper digit position
-	 */
-	init_var(&arg);
-	set_var_from_num(num, &arg);
-
-	i = arg.weight + scale + 1;
-
-	if (i < arg.ndigits)
-	{
-		/*
-		 * If i = 0, the value loses all digits, but could round up if its
-		 * first digit is more than 4.	If i < 0 the result must be 0.
-		 */
-		if (i < 0)
-			arg.ndigits = 0;
-		else
-		{
-			int			carry = (arg.digits[i] > 4) ? 1 : 0;
-
-			arg.ndigits = i;
-
-			while (carry)
-			{
-				carry += arg.digits[--i];
-				arg.digits[i] = carry % 10;
-				carry /= 10;
-			}
-
-			if (i < 0)
-			{
-				Assert(i == -1);	/* better not have added more than 1 digit */
-				Assert(arg.digits > arg.buf);
-				arg.digits--;
-				arg.ndigits++;
-				arg.weight++;
-			}
-		}
-	}
-
-	/*
-	 * Set result's scale to something reasonable.
-	 */
-	scale = Min(NUMERIC_MAX_DISPLAY_SCALE, Max(0, scale));
-	arg.rscale = scale;
-	arg.dscale = scale;
-
-	/*
-	 * Return the rounded result
-	 */
-	res = make_result(&arg);
-
-	free_var(&arg);
-	PG_RETURN_NUMERIC(res);
-}
-
-
-/* ----------
- * numeric_trunc() -
- *
- *	Truncate a value to have 'scale' digits after the decimal point.
- *	We allow negative 'scale', implying a truncation before the decimal
- *	point --- Oracle interprets truncation that way.
- * ----------
- */
-Datum
-numeric_trunc(PG_FUNCTION_ARGS)
-{
-	Numeric		num = PG_GETARG_NUMERIC(0);
-	int32		scale = PG_GETARG_INT32(1);
-	Numeric		res;
-	NumericVar	arg;
-
-	/*
-	 * Handle NaN
-	 */
-	if (NUMERIC_IS_NAN(num))
-		PG_RETURN_NUMERIC(make_result(&const_nan));
-
-	/*
-	 * Limit the scale value to avoid possible overflow in calculations
-	 * below.
-	 */
-	scale = Min(NUMERIC_MAX_RESULT_SCALE,
-				Max(-NUMERIC_MAX_RESULT_SCALE, scale));
-
-	/*
-	 * Unpack the argument and truncate it at the proper digit position
-	 */
-	init_var(&arg);
-	set_var_from_num(num, &arg);
-
-	arg.ndigits = Min(arg.ndigits, Max(0, arg.weight + scale + 1));
-
-	/*
-	 * Set result's scale to something reasonable.
-	 */
-	scale = Min(NUMERIC_MAX_DISPLAY_SCALE, Max(0, scale));
-	arg.rscale = scale;
-	arg.dscale = scale;
-
-	/*
-	 * Return the truncated result
-	 */
-	res = make_result(&arg);
-
-	free_var(&arg);
-	PG_RETURN_NUMERIC(res);
-}
-
-
-/* ----------
- * numeric_ceil() -
- *
- *	Return the smallest integer greater than or equal to the argument
- * ----------
- */
-Datum
-numeric_ceil(PG_FUNCTION_ARGS)
-{
-	Numeric		num = PG_GETARG_NUMERIC(0);
-	Numeric		res;
-	NumericVar	result;
-
-	if (NUMERIC_IS_NAN(num))
-		PG_RETURN_NUMERIC(make_result(&const_nan));
-
-	init_var(&result);
-
-	set_var_from_num(num, &result);
-	ceil_var(&result, &result);
-
-	result.dscale = 0;
-
-	res = make_result(&result);
-	free_var(&result);
-
-	PG_RETURN_NUMERIC(res);
-}
-
-
-/* ----------
- * numeric_floor() -
- *
- *	Return the largest integer equal to or less than the argument
- * ----------
- */
-Datum
-numeric_floor(PG_FUNCTION_ARGS)
-{
-	Numeric		num = PG_GETARG_NUMERIC(0);
-	Numeric		res;
-	NumericVar	result;
-
-	if (NUMERIC_IS_NAN(num))
-		PG_RETURN_NUMERIC(make_result(&const_nan));
-
-	init_var(&result);
-
-	set_var_from_num(num, &result);
-	floor_var(&result, &result);
-
-	result.dscale = 0;
-
-	res = make_result(&result);
-	free_var(&result);
-
-	PG_RETURN_NUMERIC(res);
-}
-
-
-/* ----------------------------------------------------------------------
- *
- * Comparison functions
- *
- * Note: btree indexes need these routines not to leak memory; therefore,
- * be careful to free working copies of toasted datums.  Most places don't
- * need to be so careful.
- * ----------------------------------------------------------------------
- */
-
-
-Datum
-numeric_cmp(PG_FUNCTION_ARGS)
-{
-	Numeric		num1 = PG_GETARG_NUMERIC(0);
-	Numeric		num2 = PG_GETARG_NUMERIC(1);
-	int			result;
-
-	result = cmp_numerics(num1, num2);
-
-	PG_FREE_IF_COPY(num1, 0);
-	PG_FREE_IF_COPY(num2, 1);
-
-	PG_RETURN_INT32(result);
-}
-
-
-Datum
-numeric_eq(PG_FUNCTION_ARGS)
-{
-	Numeric		num1 = PG_GETARG_NUMERIC(0);
-	Numeric		num2 = PG_GETARG_NUMERIC(1);
-	bool		result;
-
-	result = cmp_numerics(num1, num2) == 0;
-
-	PG_FREE_IF_COPY(num1, 0);
-	PG_FREE_IF_COPY(num2, 1);
-
-	PG_RETURN_BOOL(result);
-}
-
-Datum
-numeric_ne(PG_FUNCTION_ARGS)
-{
-	Numeric		num1 = PG_GETARG_NUMERIC(0);
-	Numeric		num2 = PG_GETARG_NUMERIC(1);
-	bool		result;
-
-	result = cmp_numerics(num1, num2) != 0;
-
-	PG_FREE_IF_COPY(num1, 0);
-	PG_FREE_IF_COPY(num2, 1);
-
-	PG_RETURN_BOOL(result);
-}
-
-Datum
-numeric_gt(PG_FUNCTION_ARGS)
-{
-	Numeric		num1 = PG_GETARG_NUMERIC(0);
-	Numeric		num2 = PG_GETARG_NUMERIC(1);
-	bool		result;
-
-	result = cmp_numerics(num1, num2) > 0;
-
-	PG_FREE_IF_COPY(num1, 0);
-	PG_FREE_IF_COPY(num2, 1);
-
-	PG_RETURN_BOOL(result);
-}
-
-Datum
-numeric_ge(PG_FUNCTION_ARGS)
-{
-	Numeric		num1 = PG_GETARG_NUMERIC(0);
-	Numeric		num2 = PG_GETARG_NUMERIC(1);
-	bool		result;
-
-	result = cmp_numerics(num1, num2) >= 0;
-
-	PG_FREE_IF_COPY(num1, 0);
-	PG_FREE_IF_COPY(num2, 1);
-
-	PG_RETURN_BOOL(result);
-}
-
-Datum
-numeric_lt(PG_FUNCTION_ARGS)
-{
-	Numeric		num1 = PG_GETARG_NUMERIC(0);
-	Numeric		num2 = PG_GETARG_NUMERIC(1);
-	bool		result;
-
-	result = cmp_numerics(num1, num2) < 0;
-
-	PG_FREE_IF_COPY(num1, 0);
-	PG_FREE_IF_COPY(num2, 1);
-
-	PG_RETURN_BOOL(result);
-}
-
-Datum
-numeric_le(PG_FUNCTION_ARGS)
-{
-	Numeric		num1 = PG_GETARG_NUMERIC(0);
-	Numeric		num2 = PG_GETARG_NUMERIC(1);
-	bool		result;
-
-	result = cmp_numerics(num1, num2) <= 0;
-
-	PG_FREE_IF_COPY(num1, 0);
-	PG_FREE_IF_COPY(num2, 1);
-
-	PG_RETURN_BOOL(result);
-}
-
-static int
-cmp_numerics(Numeric num1, Numeric num2)
-{
-	int			result;
-
-	/*
-	 * We consider all NANs to be equal and larger than any non-NAN. This
-	 * is somewhat arbitrary; the important thing is to have a consistent
-	 * sort order.
-	 */
-	if (NUMERIC_IS_NAN(num1))
-	{
-		if (NUMERIC_IS_NAN(num2))
-			result = 0;			/* NAN = NAN */
-		else
-			result = 1;			/* NAN > non-NAN */
-	}
-	else if (NUMERIC_IS_NAN(num2))
-	{
-		result = -1;			/* non-NAN < NAN */
-	}
-	else
-	{
-		NumericVar	arg1;
-		NumericVar	arg2;
-
-		init_var(&arg1);
-		init_var(&arg2);
-
-		set_var_from_num(num1, &arg1);
-		set_var_from_num(num2, &arg2);
-
-		result = cmp_var(&arg1, &arg2);
-
-		free_var(&arg1);
-		free_var(&arg2);
-	}
-
-	return result;
-}
-
-
-/* ----------------------------------------------------------------------
- *
- * Arithmetic base functions
- *
- * ----------------------------------------------------------------------
- */
-
-
-/* ----------
- * numeric_add() -
- *
- *	Add two numerics
- * ----------
- */
-Datum
-numeric_add(PG_FUNCTION_ARGS)
-{
-	Numeric		num1 = PG_GETARG_NUMERIC(0);
-	Numeric		num2 = PG_GETARG_NUMERIC(1);
-	NumericVar	arg1;
-	NumericVar	arg2;
-	NumericVar	result;
-	Numeric		res;
-
-	/*
-	 * Handle NaN
-	 */
-	if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
-		PG_RETURN_NUMERIC(make_result(&const_nan));
-
-	/*
-	 * Unpack the values, let add_var() compute the result and return it.
-	 * The internals of add_var() will automatically set the correct
-	 * result and display scales in the result.
-	 */
-	init_var(&arg1);
-	init_var(&arg2);
-	init_var(&result);
-
-	set_var_from_num(num1, &arg1);
-	set_var_from_num(num2, &arg2);
-
-	add_var(&arg1, &arg2, &result);
-	res = make_result(&result);
-
-	free_var(&arg1);
-	free_var(&arg2);
-	free_var(&result);
-
-	PG_RETURN_NUMERIC(res);
-}
-
-
-/* ----------
- * numeric_sub() -
- *
- *	Subtract one numeric from another
- * ----------
- */
-Datum
-numeric_sub(PG_FUNCTION_ARGS)
-{
-	Numeric		num1 = PG_GETARG_NUMERIC(0);
-	Numeric		num2 = PG_GETARG_NUMERIC(1);
-	NumericVar	arg1;
-	NumericVar	arg2;
-	NumericVar	result;
-	Numeric		res;
-
-	/*
-	 * Handle NaN
-	 */
-	if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
-		PG_RETURN_NUMERIC(make_result(&const_nan));
-
-	/*
-	 * Unpack the two arguments, let sub_var() compute the result and
-	 * return it.
-	 */
-	init_var(&arg1);
-	init_var(&arg2);
-	init_var(&result);
-
-	set_var_from_num(num1, &arg1);
-	set_var_from_num(num2, &arg2);
-
-	sub_var(&arg1, &arg2, &result);
-	res = make_result(&result);
-
-	free_var(&arg1);
-	free_var(&arg2);
-	free_var(&result);
-
-	PG_RETURN_NUMERIC(res);
-}
-
-
-/* ----------
- * numeric_mul() -
- *
- *	Calculate the product of two numerics
- * ----------
- */
-Datum
-numeric_mul(PG_FUNCTION_ARGS)
-{
-	Numeric		num1 = PG_GETARG_NUMERIC(0);
-	Numeric		num2 = PG_GETARG_NUMERIC(1);
-	NumericVar	arg1;
-	NumericVar	arg2;
-	NumericVar	result;
-	Numeric		res;
-
-	/*
-	 * Handle NaN
-	 */
-	if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
-		PG_RETURN_NUMERIC(make_result(&const_nan));
-
-	/*
-	 * Unpack the arguments, let mul_var() compute the result and return
-	 * it. Unlike add_var() and sub_var(), mul_var() will round the result
-	 * to the scale stored in global_rscale. In the case of numeric_mul(),
-	 * which is invoked for the * operator on numerics, we set it to the
-	 * exact representation for the product (rscale = sum(rscale of arg1,
-	 * rscale of arg2) and the same for the dscale).
-	 */
-	init_var(&arg1);
-	init_var(&arg2);
-	init_var(&result);
-
-	set_var_from_num(num1, &arg1);
-	set_var_from_num(num2, &arg2);
-
-	global_rscale = arg1.rscale + arg2.rscale;
-
-	mul_var(&arg1, &arg2, &result);
-
-	result.dscale = arg1.dscale + arg2.dscale;
-
-	res = make_result(&result);
-
-	free_var(&arg1);
-	free_var(&arg2);
-	free_var(&result);
-
-	PG_RETURN_NUMERIC(res);
-}
-
-
-/* ----------
- * numeric_div() -
- *
- *	Divide one numeric into another
- * ----------
- */
-Datum
-numeric_div(PG_FUNCTION_ARGS)
-{
-	Numeric		num1 = PG_GETARG_NUMERIC(0);
-	Numeric		num2 = PG_GETARG_NUMERIC(1);
-	NumericVar	arg1;
-	NumericVar	arg2;
-	NumericVar	result;
-	Numeric		res;
-	int			res_dscale;
-
-	/*
-	 * Handle NaN
-	 */
-	if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
-		PG_RETURN_NUMERIC(make_result(&const_nan));
-
-	/*
-	 * Unpack the arguments
-	 */
-	init_var(&arg1);
-	init_var(&arg2);
-	init_var(&result);
-
-	set_var_from_num(num1, &arg1);
-	set_var_from_num(num2, &arg2);
-
-	res_dscale = select_div_scale(&arg1, &arg2);
-
-	/*
-	 * Do the divide, set the display scale and return the result
-	 */
-	div_var(&arg1, &arg2, &result);
-
-	result.dscale = res_dscale;
-
-	res = make_result(&result);
-
-	free_var(&arg1);
-	free_var(&arg2);
-	free_var(&result);
-
-	PG_RETURN_NUMERIC(res);
-}
-
-
-/* ----------
- * numeric_mod() -
- *
- *	Calculate the modulo of two numerics
- * ----------
- */
-Datum
-numeric_mod(PG_FUNCTION_ARGS)
-{
-	Numeric		num1 = PG_GETARG_NUMERIC(0);
-	Numeric		num2 = PG_GETARG_NUMERIC(1);
-	Numeric		res;
-	NumericVar	arg1;
-	NumericVar	arg2;
-	NumericVar	result;
-
-	if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
-		PG_RETURN_NUMERIC(make_result(&const_nan));
-
-	init_var(&arg1);
-	init_var(&arg2);
-	init_var(&result);
-
-	set_var_from_num(num1, &arg1);
-	set_var_from_num(num2, &arg2);
-
-	mod_var(&arg1, &arg2, &result);
-
-	res = make_result(&result);
-
-	free_var(&result);
-	free_var(&arg2);
-	free_var(&arg1);
-
-	PG_RETURN_NUMERIC(res);
-}
-
-
-/* ----------
- * numeric_inc() -
- *
- *	Increment a number by one
- * ----------
- */
-Datum
-numeric_inc(PG_FUNCTION_ARGS)
-{
-	Numeric		num = PG_GETARG_NUMERIC(0);
-	NumericVar	arg;
-	Numeric		res;
-
-	/*
-	 * Handle NaN
-	 */
-	if (NUMERIC_IS_NAN(num))
-		PG_RETURN_NUMERIC(make_result(&const_nan));
-
-	/*
-	 * Compute the result and return it
-	 */
-	init_var(&arg);
-
-	set_var_from_num(num, &arg);
-
-	add_var(&arg, &const_one, &arg);
-	res = make_result(&arg);
-
-	free_var(&arg);
-
-	PG_RETURN_NUMERIC(res);
-}
-
-
-/* ----------
- * numeric_smaller() -
- *
- *	Return the smaller of two numbers
- * ----------
- */
-Datum
-numeric_smaller(PG_FUNCTION_ARGS)
-{
-	Numeric		num1 = PG_GETARG_NUMERIC(0);
-	Numeric		num2 = PG_GETARG_NUMERIC(1);
-	NumericVar	arg1;
-	NumericVar	arg2;
-	Numeric		res;
-
-	/*
-	 * Handle NaN
-	 */
-	if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
-		PG_RETURN_NUMERIC(make_result(&const_nan));
-
-	/*
-	 * Unpack the values, and decide which is the smaller one
-	 */
-	init_var(&arg1);
-	init_var(&arg2);
-
-	set_var_from_num(num1, &arg1);
-	set_var_from_num(num2, &arg2);
-
-	if (cmp_var(&arg1, &arg2) <= 0)
-		res = make_result(&arg1);
-	else
-		res = make_result(&arg2);
-
-	free_var(&arg1);
-	free_var(&arg2);
-
-	PG_RETURN_NUMERIC(res);
-}
-
-
-/* ----------
- * numeric_larger() -
- *
- *	Return the larger of two numbers
- * ----------
- */
-Datum
-numeric_larger(PG_FUNCTION_ARGS)
-{
-	Numeric		num1 = PG_GETARG_NUMERIC(0);
-	Numeric		num2 = PG_GETARG_NUMERIC(1);
-	NumericVar	arg1;
-	NumericVar	arg2;
-	Numeric		res;
-
-	/*
-	 * Handle NaN
-	 */
-	if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
-		PG_RETURN_NUMERIC(make_result(&const_nan));
-
-	/*
-	 * Unpack the values, and decide which is the larger one
-	 */
-	init_var(&arg1);
-	init_var(&arg2);
-
-	set_var_from_num(num1, &arg1);
-	set_var_from_num(num2, &arg2);
-
-	if (cmp_var(&arg1, &arg2) >= 0)
-		res = make_result(&arg1);
-	else
-		res = make_result(&arg2);
-
-	free_var(&arg1);
-	free_var(&arg2);
-
-	PG_RETURN_NUMERIC(res);
-}
-
-
-/* ----------------------------------------------------------------------
- *
- * Complex math functions
- *
- * ----------------------------------------------------------------------
- */
-
-
-/* ----------
- * numeric_sqrt() -
- *
- *	Compute the square root of a numeric.
- * ----------
- */
-Datum
-numeric_sqrt(PG_FUNCTION_ARGS)
-{
-	Numeric		num = PG_GETARG_NUMERIC(0);
-	Numeric		res;
-	NumericVar	arg;
-	NumericVar	result;
-	int			res_dscale;
-
-	/*
-	 * Handle NaN
-	 */
-	if (NUMERIC_IS_NAN(num))
-		PG_RETURN_NUMERIC(make_result(&const_nan));
-
-	/*
-	 * Unpack the argument, determine the scales like for divide, let
-	 * sqrt_var() do the calculation and return the result.
-	 */
-	init_var(&arg);
-	init_var(&result);
-
-	set_var_from_num(num, &arg);
-
-	res_dscale = Max(arg.dscale, NUMERIC_MIN_DISPLAY_SCALE);
-	res_dscale = Min(res_dscale, NUMERIC_MAX_DISPLAY_SCALE);
-	global_rscale = Max(arg.rscale, NUMERIC_MIN_RESULT_SCALE);
-	global_rscale = Max(global_rscale, res_dscale + 4);
-	global_rscale = Min(global_rscale, NUMERIC_MAX_RESULT_SCALE);
-
-	sqrt_var(&arg, &result);
-
-	result.dscale = res_dscale;
-
-	res = make_result(&result);
-
-	free_var(&result);
-	free_var(&arg);
-
-	PG_RETURN_NUMERIC(res);
-}
-
-
-/* ----------
- * numeric_exp() -
- *
- *	Raise e to the power of x
- * ----------
- */
-Datum
-numeric_exp(PG_FUNCTION_ARGS)
-{
-	Numeric		num = PG_GETARG_NUMERIC(0);
-	Numeric		res;
-	NumericVar	arg;
-	NumericVar	result;
-	int			res_dscale;
-
-	/*
-	 * Handle NaN
-	 */
-	if (NUMERIC_IS_NAN(num))
-		PG_RETURN_NUMERIC(make_result(&const_nan));
-
-	/*
-	 * Same procedure like for sqrt().
-	 */
-	init_var(&arg);
-	init_var(&result);
-	set_var_from_num(num, &arg);
-
-	res_dscale = Max(arg.dscale, NUMERIC_MIN_DISPLAY_SCALE);
-	res_dscale = Min(res_dscale, NUMERIC_MAX_DISPLAY_SCALE);
-	global_rscale = Max(arg.rscale, NUMERIC_MIN_RESULT_SCALE);
-	global_rscale = Max(global_rscale, res_dscale + 4);
-	global_rscale = Min(global_rscale, NUMERIC_MAX_RESULT_SCALE);
-
-	exp_var(&arg, &result);
-
-	result.dscale = res_dscale;
-
-	res = make_result(&result);
-
-	free_var(&result);
-	free_var(&arg);
-
-	PG_RETURN_NUMERIC(res);
-}
-
-
-/* ----------
- * numeric_ln() -
- *
- *	Compute the natural logarithm of x
- * ----------
- */
-Datum
-numeric_ln(PG_FUNCTION_ARGS)
-{
-	Numeric		num = PG_GETARG_NUMERIC(0);
-	Numeric		res;
-	NumericVar	arg;
-	NumericVar	result;
-	int			res_dscale;
-
-	/*
-	 * Handle NaN
-	 */
-	if (NUMERIC_IS_NAN(num))
-		PG_RETURN_NUMERIC(make_result(&const_nan));
-
-	/*
-	 * Same procedure like for sqrt()
-	 */
-	init_var(&arg);
-	init_var(&result);
-	set_var_from_num(num, &arg);
-
-	res_dscale = Max(arg.dscale, NUMERIC_MIN_DISPLAY_SCALE);
-	res_dscale = Min(res_dscale, NUMERIC_MAX_DISPLAY_SCALE);
-	global_rscale = Max(arg.rscale, NUMERIC_MIN_RESULT_SCALE);
-	global_rscale = Max(global_rscale, res_dscale + 4);
-	global_rscale = Min(global_rscale, NUMERIC_MAX_RESULT_SCALE);
-
-	ln_var(&arg, &result);
-
-	result.dscale = res_dscale;
-
-	res = make_result(&result);
-
-	free_var(&result);
-	free_var(&arg);
-
-	PG_RETURN_NUMERIC(res);
-}
-
-
-/* ----------
- * numeric_log() -
- *
- *	Compute the logarithm of x in a given base
- * ----------
- */
-Datum
-numeric_log(PG_FUNCTION_ARGS)
-{
-	Numeric		num1 = PG_GETARG_NUMERIC(0);
-	Numeric		num2 = PG_GETARG_NUMERIC(1);
-	Numeric		res;
-	NumericVar	arg1;
-	NumericVar	arg2;
-	NumericVar	result;
-	int			res_dscale;
-
-	/*
-	 * Handle NaN
-	 */
-	if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
-		PG_RETURN_NUMERIC(make_result(&const_nan));
-
-	/*
-	 * Initialize things and calculate scales
-	 */
-	init_var(&arg1);
-	init_var(&arg2);
-	init_var(&result);
-	set_var_from_num(num1, &arg1);
-	set_var_from_num(num2, &arg2);
-
-	res_dscale = Max(arg1.dscale + arg2.dscale, NUMERIC_MIN_DISPLAY_SCALE);
-	res_dscale = Min(res_dscale, NUMERIC_MAX_DISPLAY_SCALE);
-	global_rscale = Max(arg1.rscale + arg2.rscale, NUMERIC_MIN_RESULT_SCALE);
-	global_rscale = Max(global_rscale, res_dscale + 4);
-	global_rscale = Min(global_rscale, NUMERIC_MAX_RESULT_SCALE);
-
-	/*
-	 * Call log_var() to compute and return the result
-	 */
-	log_var(&arg1, &arg2, &result);
-
-	result.dscale = res_dscale;
-
-	res = make_result(&result);
-
-	free_var(&result);
-	free_var(&arg2);
-	free_var(&arg1);
-
-	PG_RETURN_NUMERIC(res);
-}
-
-
-/* ----------
- * numeric_power() -
- *
- *	Raise m to the power of x
- * ----------
- */
-Datum
-numeric_power(PG_FUNCTION_ARGS)
-{
-	Numeric		num1 = PG_GETARG_NUMERIC(0);
-	Numeric		num2 = PG_GETARG_NUMERIC(1);
-	Numeric		res;
-	NumericVar	arg1;
-	NumericVar	arg2;
-	NumericVar	result;
-	int			res_dscale;
-
-	/*
-	 * Handle NaN
-	 */
-	if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
-		PG_RETURN_NUMERIC(make_result(&const_nan));
-
-	/*
-	 * Initialize things and calculate scales
-	 */
-	init_var(&arg1);
-	init_var(&arg2);
-	init_var(&result);
-	set_var_from_num(num1, &arg1);
-	set_var_from_num(num2, &arg2);
-
-	res_dscale = Max(arg1.dscale + arg2.dscale, NUMERIC_MIN_DISPLAY_SCALE);
-	res_dscale = Min(res_dscale, NUMERIC_MAX_DISPLAY_SCALE);
-	global_rscale = Max(arg1.rscale + arg2.rscale, NUMERIC_MIN_RESULT_SCALE);
-	global_rscale = Max(global_rscale, res_dscale + 4);
-	global_rscale = Min(global_rscale, NUMERIC_MAX_RESULT_SCALE);
-
-	/*
-	 * Call log_var() to compute and return the result
-	 */
-	power_var(&arg1, &arg2, &result);
-
-	result.dscale = res_dscale;
-
-	res = make_result(&result);
-
-	free_var(&result);
-	free_var(&arg2);
-	free_var(&arg1);
-
-	PG_RETURN_NUMERIC(res);
-}
-
-
-/* ----------------------------------------------------------------------
- *
- * Type conversion functions
- *
- * ----------------------------------------------------------------------
- */
-
-
-Datum
-int4_numeric(PG_FUNCTION_ARGS)
-{
-	int32		val = PG_GETARG_INT32(0);
-	Numeric		res;
-	NumericVar	result;
-	char	   *tmp;
-
-	init_var(&result);
-
-	tmp = DatumGetCString(DirectFunctionCall1(int4out,
-											  Int32GetDatum(val)));
-	set_var_from_str(tmp, &result);
-	res = make_result(&result);
-
-	free_var(&result);
-	pfree(tmp);
-
-	PG_RETURN_NUMERIC(res);
-}
-
-
-Datum
-numeric_int4(PG_FUNCTION_ARGS)
-{
-	Numeric		num = PG_GETARG_NUMERIC(0);
-	NumericVar	x;
-	char	   *str;
-	Datum		result;
-
-	/* XXX would it be better to return NULL? */
-	if (NUMERIC_IS_NAN(num))
-		elog(ERROR, "Cannot convert NaN to int4");
-
-	/*
-	 * Get the number in the variable format so we can round to integer.
-	 */
-	init_var(&x);
-	set_var_from_num(num, &x);
-
-	str = get_str_from_var(&x, 0);		/* dscale = 0 produces rounding */
-
-	free_var(&x);
-
-	result = DirectFunctionCall1(int4in, CStringGetDatum(str));
-	pfree(str);
-
-	PG_RETURN_DATUM(result);
-}
-
-
-Datum
-int8_numeric(PG_FUNCTION_ARGS)
-{
-	Datum		val = PG_GETARG_DATUM(0);
-	Numeric		res;
-	NumericVar	result;
-	char	   *tmp;
-
-	init_var(&result);
-
-	tmp = DatumGetCString(DirectFunctionCall1(int8out, val));
-	set_var_from_str(tmp, &result);
-	res = make_result(&result);
-
-	free_var(&result);
-	pfree(tmp);
-
-	PG_RETURN_NUMERIC(res);
-}
-
-
-Datum
-numeric_int8(PG_FUNCTION_ARGS)
-{
-	Numeric		num = PG_GETARG_NUMERIC(0);
-	NumericVar	x;
-	char	   *str;
-	Datum		result;
-
-	/* XXX would it be better to return NULL? */
-	if (NUMERIC_IS_NAN(num))
-		elog(ERROR, "Cannot convert NaN to int8");
-
-	/*
-	 * Get the number in the variable format so we can round to integer.
-	 */
-	init_var(&x);
-	set_var_from_num(num, &x);
-
-	str = get_str_from_var(&x, 0);		/* dscale = 0 produces rounding */
-
-	free_var(&x);
-
-	result = DirectFunctionCall1(int8in, CStringGetDatum(str));
-	pfree(str);
-
-	PG_RETURN_DATUM(result);
-}
-
-
-Datum
-int2_numeric(PG_FUNCTION_ARGS)
-{
-	int16		val = PG_GETARG_INT16(0);
-	Numeric		res;
-	NumericVar	result;
-	char	   *tmp;
-
-	init_var(&result);
-
-	tmp = DatumGetCString(DirectFunctionCall1(int2out,
-											  Int16GetDatum(val)));
-	set_var_from_str(tmp, &result);
-	res = make_result(&result);
-
-	free_var(&result);
-	pfree(tmp);
-
-	PG_RETURN_NUMERIC(res);
-}
-
-
-Datum
-numeric_int2(PG_FUNCTION_ARGS)
-{
-	Numeric		num = PG_GETARG_NUMERIC(0);
-	NumericVar	x;
-	char	   *str;
-	Datum		result;
-
-	/* XXX would it be better to return NULL? */
-	if (NUMERIC_IS_NAN(num))
-		elog(ERROR, "Cannot convert NaN to int2");
-
-	/*
-	 * Get the number in the variable format so we can round to integer.
-	 */
-	init_var(&x);
-	set_var_from_num(num, &x);
-
-	str = get_str_from_var(&x, 0);		/* dscale = 0 produces rounding */
-
-	free_var(&x);
-
-	result = DirectFunctionCall1(int2in, CStringGetDatum(str));
-	pfree(str);
-
-	return result;
-}
-
-
-Datum
-float8_numeric(PG_FUNCTION_ARGS)
-{
-	float8		val = PG_GETARG_FLOAT8(0);
-	Numeric		res;
-	NumericVar	result;
-	char		buf[DBL_DIG + 100];
-
-	if (isnan(val))
-		PG_RETURN_NUMERIC(make_result(&const_nan));
-
-	sprintf(buf, "%.*g", DBL_DIG, val);
-
-	init_var(&result);
-
-	set_var_from_str(buf, &result);
-	res = make_result(&result);
-
-	free_var(&result);
-
-	PG_RETURN_NUMERIC(res);
-}
-
-
-Datum
-numeric_float8(PG_FUNCTION_ARGS)
-{
-	Numeric		num = PG_GETARG_NUMERIC(0);
-	char	   *tmp;
-	Datum		result;
-
-	if (NUMERIC_IS_NAN(num))
-		PG_RETURN_FLOAT8(NAN);
-
-	tmp = DatumGetCString(DirectFunctionCall1(numeric_out,
-											  NumericGetDatum(num)));
-
-	result = DirectFunctionCall1(float8in, CStringGetDatum(tmp));
-
-	pfree(tmp);
-
-	PG_RETURN_DATUM(result);
-}
-
-
-/* Convert numeric to float8; if out of range, return +/- HUGE_VAL */
-Datum
-numeric_float8_no_overflow(PG_FUNCTION_ARGS)
-{
-	Numeric		num = PG_GETARG_NUMERIC(0);
-	char	   *tmp;
-	double		val;
-	char	   *endptr;
-
-	if (NUMERIC_IS_NAN(num))
-		PG_RETURN_FLOAT8(NAN);
-
-	tmp = DatumGetCString(DirectFunctionCall1(numeric_out,
-											  NumericGetDatum(num)));
-
-	/* unlike float8in, we ignore ERANGE from strtod */
-	val = strtod(tmp, &endptr);
-	if (*endptr != '\0')
-	{
-		/* shouldn't happen ... */
-		elog(ERROR, "Bad float8 input format '%s'", tmp);
-	}
-
-	pfree(tmp);
-
-	PG_RETURN_FLOAT8(val);
-}
-
-
-Datum
-float4_numeric(PG_FUNCTION_ARGS)
-{
-	float4		val = PG_GETARG_FLOAT4(0);
-	Numeric		res;
-	NumericVar	result;
-	char		buf[FLT_DIG + 100];
-
-	if (isnan(val))
-		PG_RETURN_NUMERIC(make_result(&const_nan));
-
-	sprintf(buf, "%.*g", FLT_DIG, val);
-
-	init_var(&result);
-
-	set_var_from_str(buf, &result);
-	res = make_result(&result);
-
-	free_var(&result);
-
-	PG_RETURN_NUMERIC(res);
-}
-
-
-Datum
-numeric_float4(PG_FUNCTION_ARGS)
-{
-	Numeric		num = PG_GETARG_NUMERIC(0);
-	char	   *tmp;
-	Datum		result;
-
-	if (NUMERIC_IS_NAN(num))
-		PG_RETURN_FLOAT4((float4) NAN);
-
-	tmp = DatumGetCString(DirectFunctionCall1(numeric_out,
-											  NumericGetDatum(num)));
-
-	result = DirectFunctionCall1(float4in, CStringGetDatum(tmp));
-
-	pfree(tmp);
-
-	PG_RETURN_DATUM(result);
-}
-
-
-/* ----------------------------------------------------------------------
- *
- * Aggregate functions
- *
- * The transition datatype for all these aggregates is a 3-element array
- * of Numeric, holding the values N, sum(X), sum(X*X) in that order.
- *
- * We represent N as a numeric mainly to avoid having to build a special
- * datatype; it's unlikely it'd overflow an int4, but ...
- *
- * ----------------------------------------------------------------------
- */
-
-static ArrayType *
-do_numeric_accum(ArrayType *transarray, Numeric newval)
-{
-	Datum	   *transdatums;
-	int			ndatums;
-	Datum		N,
-				sumX,
-				sumX2;
-	ArrayType  *result;
-
-	/* We assume the input is array of numeric */
-	deconstruct_array(transarray,
-					  false, -1, 'i',
-					  &transdatums, &ndatums);
-	if (ndatums != 3)
-		elog(ERROR, "do_numeric_accum: expected 3-element numeric array");
-	N = transdatums[0];
-	sumX = transdatums[1];
-	sumX2 = transdatums[2];
-
-	N = DirectFunctionCall1(numeric_inc, N);
-	sumX = DirectFunctionCall2(numeric_add, sumX,
-							   NumericGetDatum(newval));
-	sumX2 = DirectFunctionCall2(numeric_add, sumX2,
-								DirectFunctionCall2(numeric_mul,
-												 NumericGetDatum(newval),
-											   NumericGetDatum(newval)));
-
-	transdatums[0] = N;
-	transdatums[1] = sumX;
-	transdatums[2] = sumX2;
-
-	result = construct_array(transdatums, 3,
-							 false, -1, 'i');
-
-	return result;
-}
-
-Datum
-numeric_accum(PG_FUNCTION_ARGS)
-{
-	ArrayType  *transarray = PG_GETARG_ARRAYTYPE_P(0);
-	Numeric		newval = PG_GETARG_NUMERIC(1);
-
-	PG_RETURN_ARRAYTYPE_P(do_numeric_accum(transarray, newval));
-}
-
-/*
- * Integer data types all use Numeric accumulators to share code and
- * avoid risk of overflow.	For int2 and int4 inputs, Numeric accumulation
- * is overkill for the N and sum(X) values, but definitely not overkill
- * for the sum(X*X) value.	Hence, we use int2_accum and int4_accum only
- * for stddev/variance --- there are faster special-purpose accumulator
- * routines for SUM and AVG of these datatypes.
- */
-
-Datum
-int2_accum(PG_FUNCTION_ARGS)
-{
-	ArrayType  *transarray = PG_GETARG_ARRAYTYPE_P(0);
-	Datum		newval2 = PG_GETARG_DATUM(1);
-	Numeric		newval;
-
-	newval = DatumGetNumeric(DirectFunctionCall1(int2_numeric, newval2));
-
-	PG_RETURN_ARRAYTYPE_P(do_numeric_accum(transarray, newval));
-}
-
-Datum
-int4_accum(PG_FUNCTION_ARGS)
-{
-	ArrayType  *transarray = PG_GETARG_ARRAYTYPE_P(0);
-	Datum		newval4 = PG_GETARG_DATUM(1);
-	Numeric		newval;
-
-	newval = DatumGetNumeric(DirectFunctionCall1(int4_numeric, newval4));
-
-	PG_RETURN_ARRAYTYPE_P(do_numeric_accum(transarray, newval));
-}
-
-Datum
-int8_accum(PG_FUNCTION_ARGS)
-{
-	ArrayType  *transarray = PG_GETARG_ARRAYTYPE_P(0);
-	Datum		newval8 = PG_GETARG_DATUM(1);
-	Numeric		newval;
-
-	newval = DatumGetNumeric(DirectFunctionCall1(int8_numeric, newval8));
-
-	PG_RETURN_ARRAYTYPE_P(do_numeric_accum(transarray, newval));
-}
-
-Datum
-numeric_avg(PG_FUNCTION_ARGS)
-{
-	ArrayType  *transarray = PG_GETARG_ARRAYTYPE_P(0);
-	Datum	   *transdatums;
-	int			ndatums;
-	Numeric		N,
-				sumX;
-
-	/* We assume the input is array of numeric */
-	deconstruct_array(transarray,
-					  false, -1, 'i',
-					  &transdatums, &ndatums);
-	if (ndatums != 3)
-		elog(ERROR, "numeric_avg: expected 3-element numeric array");
-	N = DatumGetNumeric(transdatums[0]);
-	sumX = DatumGetNumeric(transdatums[1]);
-	/* ignore sumX2 */
-
-	/* SQL92 defines AVG of no values to be NULL */
-	/* N is zero iff no digits (cf. numeric_uminus) */
-	if (N->varlen == NUMERIC_HDRSZ)
-		PG_RETURN_NULL();
-
-	PG_RETURN_DATUM(DirectFunctionCall2(numeric_div,
-										NumericGetDatum(sumX),
-										NumericGetDatum(N)));
-}
-
-Datum
-numeric_variance(PG_FUNCTION_ARGS)
-{
-	ArrayType  *transarray = PG_GETARG_ARRAYTYPE_P(0);
-	Datum	   *transdatums;
-	int			ndatums;
-	Numeric		N,
-				sumX,
-				sumX2,
-				res;
-	NumericVar	vN,
-				vsumX,
-				vsumX2,
-				vNminus1;
-	int			div_dscale;
-
-	/* We assume the input is array of numeric */
-	deconstruct_array(transarray,
-					  false, -1, 'i',
-					  &transdatums, &ndatums);
-	if (ndatums != 3)
-		elog(ERROR, "numeric_variance: expected 3-element numeric array");
-	N = DatumGetNumeric(transdatums[0]);
-	sumX = DatumGetNumeric(transdatums[1]);
-	sumX2 = DatumGetNumeric(transdatums[2]);
-
-	if (NUMERIC_IS_NAN(N) || NUMERIC_IS_NAN(sumX) || NUMERIC_IS_NAN(sumX2))
-		PG_RETURN_NUMERIC(make_result(&const_nan));
-
-	/* We define VARIANCE of no values to be NULL, of 1 value to be 0 */
-	/* N is zero iff no digits (cf. numeric_uminus) */
-	if (N->varlen == NUMERIC_HDRSZ)
-		PG_RETURN_NULL();
-
-	init_var(&vN);
-	set_var_from_num(N, &vN);
-
-	init_var(&vNminus1);
-	sub_var(&vN, &const_one, &vNminus1);
-
-	if (cmp_var(&vNminus1, &const_zero) <= 0)
-	{
-		free_var(&vN);
-		free_var(&vNminus1);
-		PG_RETURN_NUMERIC(make_result(&const_zero));
-	}
-
-	init_var(&vsumX);
-	set_var_from_num(sumX, &vsumX);
-	init_var(&vsumX2);
-	set_var_from_num(sumX2, &vsumX2);
-
-	mul_var(&vsumX, &vsumX, &vsumX);	/* now vsumX contains sumX * sumX */
-	mul_var(&vN, &vsumX2, &vsumX2);		/* now vsumX2 contains N * sumX2 */
-	sub_var(&vsumX2, &vsumX, &vsumX2);	/* N * sumX2 - sumX * sumX */
-
-	if (cmp_var(&vsumX2, &const_zero) <= 0)
-	{
-		/* Watch out for roundoff error producing a negative numerator */
-		res = make_result(&const_zero);
-	}
-	else
-	{
-		mul_var(&vN, &vNminus1, &vNminus1);	/* N * (N - 1) */
-		div_dscale = select_div_scale(&vsumX2, &vNminus1);
-		div_var(&vsumX2, &vNminus1, &vsumX);	/* variance */
-		vsumX.dscale = div_dscale;
-
-		res = make_result(&vsumX);
-	}
-
-	free_var(&vN);
-	free_var(&vNminus1);
-	free_var(&vsumX);
-	free_var(&vsumX2);
-
-	PG_RETURN_NUMERIC(res);
-}
-
-Datum
-numeric_stddev(PG_FUNCTION_ARGS)
-{
-	ArrayType  *transarray = PG_GETARG_ARRAYTYPE_P(0);
-	Datum	   *transdatums;
-	int			ndatums;
-	Numeric		N,
-				sumX,
-				sumX2,
-				res;
-	NumericVar	vN,
-				vsumX,
-				vsumX2,
-				vNminus1;
-	int			div_dscale;
-
-	/* We assume the input is array of numeric */
-	deconstruct_array(transarray,
-					  false, -1, 'i',
-					  &transdatums, &ndatums);
-	if (ndatums != 3)
-		elog(ERROR, "numeric_stddev: expected 3-element numeric array");
-	N = DatumGetNumeric(transdatums[0]);
-	sumX = DatumGetNumeric(transdatums[1]);
-	sumX2 = DatumGetNumeric(transdatums[2]);
-
-	if (NUMERIC_IS_NAN(N) || NUMERIC_IS_NAN(sumX) || NUMERIC_IS_NAN(sumX2))
-		PG_RETURN_NUMERIC(make_result(&const_nan));
-
-	/* We define STDDEV of no values to be NULL, of 1 value to be 0 */
-	/* N is zero iff no digits (cf. numeric_uminus) */
-	if (N->varlen == NUMERIC_HDRSZ)
-		PG_RETURN_NULL();
-
-	init_var(&vN);
-	set_var_from_num(N, &vN);
-
-	init_var(&vNminus1);
-	sub_var(&vN, &const_one, &vNminus1);
-
-	if (cmp_var(&vNminus1, &const_zero) <= 0)
-	{
-		free_var(&vN);
-		free_var(&vNminus1);
-		PG_RETURN_NUMERIC(make_result(&const_zero));
-	}
-
-	init_var(&vsumX);
-	set_var_from_num(sumX, &vsumX);
-	init_var(&vsumX2);
-	set_var_from_num(sumX2, &vsumX2);
-
-	mul_var(&vsumX, &vsumX, &vsumX);	/* now vsumX contains sumX * sumX */
-	mul_var(&vN, &vsumX2, &vsumX2);		/* now vsumX2 contains N * sumX2 */
-	sub_var(&vsumX2, &vsumX, &vsumX2);	/* N * sumX2 - sumX * sumX */
-
-	if (cmp_var(&vsumX2, &const_zero) <= 0)
-	{
-		/* Watch out for roundoff error producing a negative numerator */
-		res = make_result(&const_zero);
-	}
-	else
-	{
-		mul_var(&vN, &vNminus1, &vNminus1); /* N * (N - 1) */
-		div_dscale = select_div_scale(&vsumX2, &vNminus1);
-		div_var(&vsumX2, &vNminus1, &vsumX);	/* variance */
-		vsumX.dscale = div_dscale;
-		sqrt_var(&vsumX, &vsumX);		/* stddev */
-
-		res = make_result(&vsumX);
-	}
-
-	free_var(&vN);
-	free_var(&vNminus1);
-	free_var(&vsumX);
-	free_var(&vsumX2);
-
-	PG_RETURN_NUMERIC(res);
-}
-
-
-/*
- * SUM transition functions for integer datatypes.
- *
- * To avoid overflow, we use accumulators wider than the input datatype.
- * A Numeric accumulator is needed for int8 input; for int4 and int2
- * inputs, we use int8 accumulators which should be sufficient for practical
- * purposes.  (The latter two therefore don't really belong in this file,
- * but we keep them here anyway.)
- *
- * Because SQL92 defines the SUM() of no values to be NULL, not zero,
- * the initial condition of the transition data value needs to be NULL. This
- * means we can't rely on ExecAgg to automatically insert the first non-null
- * data value into the transition data: it doesn't know how to do the type
- * conversion.	The upshot is that these routines have to be marked non-strict
- * and handle substitution of the first non-null input themselves.
- */
-
-Datum
-int2_sum(PG_FUNCTION_ARGS)
-{
-	int64		oldsum;
-	int64		newval;
-
-	if (PG_ARGISNULL(0))
-	{
-		/* No non-null input seen so far... */
-		if (PG_ARGISNULL(1))
-			PG_RETURN_NULL();	/* still no non-null */
-		/* This is the first non-null input. */
-		newval = (int64) PG_GETARG_INT16(1);
-		PG_RETURN_INT64(newval);
-	}
-
-	oldsum = PG_GETARG_INT64(0);
-
-	/* Leave sum unchanged if new input is null. */
-	if (PG_ARGISNULL(1))
-		PG_RETURN_INT64(oldsum);
-
-	/* OK to do the addition. */
-	newval = oldsum + (int64) PG_GETARG_INT16(1);
-
-	PG_RETURN_INT64(newval);
-}
-
-Datum
-int4_sum(PG_FUNCTION_ARGS)
-{
-	int64		oldsum;
-	int64		newval;
-
-	if (PG_ARGISNULL(0))
-	{
-		/* No non-null input seen so far... */
-		if (PG_ARGISNULL(1))
-			PG_RETURN_NULL();	/* still no non-null */
-		/* This is the first non-null input. */
-		newval = (int64) PG_GETARG_INT32(1);
-		PG_RETURN_INT64(newval);
-	}
-
-	oldsum = PG_GETARG_INT64(0);
-
-	/* Leave sum unchanged if new input is null. */
-	if (PG_ARGISNULL(1))
-		PG_RETURN_INT64(oldsum);
-
-	/* OK to do the addition. */
-	newval = oldsum + (int64) PG_GETARG_INT32(1);
-
-	PG_RETURN_INT64(newval);
-}
-
-Datum
-int8_sum(PG_FUNCTION_ARGS)
-{
-	Numeric		oldsum;
-	Datum		newval;
-
-	if (PG_ARGISNULL(0))
-	{
-		/* No non-null input seen so far... */
-		if (PG_ARGISNULL(1))
-			PG_RETURN_NULL();	/* still no non-null */
-		/* This is the first non-null input. */
-		newval = DirectFunctionCall1(int8_numeric, PG_GETARG_DATUM(1));
-		PG_RETURN_DATUM(newval);
-	}
-
-	oldsum = PG_GETARG_NUMERIC(0);
-
-	/* Leave sum unchanged if new input is null. */
-	if (PG_ARGISNULL(1))
-		PG_RETURN_NUMERIC(oldsum);
-
-	/* OK to do the addition. */
-	newval = DirectFunctionCall1(int8_numeric, PG_GETARG_DATUM(1));
-
-	PG_RETURN_DATUM(DirectFunctionCall2(numeric_add,
-										NumericGetDatum(oldsum), newval));
-}
-
-
-/*
- * Routines for avg(int2) and avg(int4).  The transition datatype
- * is a two-element int8 array, holding count and sum.
- */
-
-typedef struct Int8TransTypeData
-{
-#ifndef INT64_IS_BUSTED
-	int64		count;
-	int64		sum;
-#else
-	/* "int64" isn't really 64 bits, so fake up properly-aligned fields */
-	int32		count;
-	int32		pad1;
-	int32		sum;
-	int32		pad2;
-#endif
-} Int8TransTypeData;
-
-Datum
-int2_avg_accum(PG_FUNCTION_ARGS)
-{
-	ArrayType  *transarray = PG_GETARG_ARRAYTYPE_P_COPY(0);
-	int16		newval = PG_GETARG_INT16(1);
-	Int8TransTypeData *transdata;
-
-	/*
-	 * We copied the input array, so it's okay to scribble on it directly.
-	 */
-	if (ARR_SIZE(transarray) != ARR_OVERHEAD(1) + sizeof(Int8TransTypeData))
-		elog(ERROR, "int2_avg_accum: expected 2-element int8 array");
-	transdata = (Int8TransTypeData *) ARR_DATA_PTR(transarray);
-
-	transdata->count++;
-	transdata->sum += newval;
-
-	PG_RETURN_ARRAYTYPE_P(transarray);
-}
-
-Datum
-int4_avg_accum(PG_FUNCTION_ARGS)
-{
-	ArrayType  *transarray = PG_GETARG_ARRAYTYPE_P_COPY(0);
-	int32		newval = PG_GETARG_INT32(1);
-	Int8TransTypeData *transdata;
-
-	/*
-	 * We copied the input array, so it's okay to scribble on it directly.
-	 */
-	if (ARR_SIZE(transarray) != ARR_OVERHEAD(1) + sizeof(Int8TransTypeData))
-		elog(ERROR, "int4_avg_accum: expected 2-element int8 array");
-	transdata = (Int8TransTypeData *) ARR_DATA_PTR(transarray);
-
-	transdata->count++;
-	transdata->sum += newval;
-
-	PG_RETURN_ARRAYTYPE_P(transarray);
-}
-
-Datum
-int8_avg(PG_FUNCTION_ARGS)
-{
-	ArrayType  *transarray = PG_GETARG_ARRAYTYPE_P(0);
-	Int8TransTypeData *transdata;
-	Datum		countd,
-				sumd;
-
-	if (ARR_SIZE(transarray) != ARR_OVERHEAD(1) + sizeof(Int8TransTypeData))
-		elog(ERROR, "int8_avg: expected 2-element int8 array");
-	transdata = (Int8TransTypeData *) ARR_DATA_PTR(transarray);
-
-	/* SQL92 defines AVG of no values to be NULL */
-	if (transdata->count == 0)
-		PG_RETURN_NULL();
-
-	countd = DirectFunctionCall1(int8_numeric,
-								 Int64GetDatumFast(transdata->count));
-	sumd = DirectFunctionCall1(int8_numeric,
-							   Int64GetDatumFast(transdata->sum));
-
-	PG_RETURN_DATUM(DirectFunctionCall2(numeric_div, sumd, countd));
-}
-
-
-/* ----------------------------------------------------------------------
- *
- * Local functions follow
- *
- * ----------------------------------------------------------------------
- */
-
-
-#ifdef NUMERIC_DEBUG
-
-/* ----------
- * dump_numeric() - Dump a value in the db storage format for debugging
- * ----------
- */
-static void
-dump_numeric(char *str, Numeric num)
-{
-	int			i;
-
-	printf("%s: NUMERIC w=%d r=%d d=%d ", str, num->n_weight, num->n_rscale,
-		   NUMERIC_DSCALE(num));
-	switch (NUMERIC_SIGN(num))
-	{
-		case NUMERIC_POS:
-			printf("POS");
-			break;
-		case NUMERIC_NEG:
-			printf("NEG");
-			break;
-		case NUMERIC_NAN:
-			printf("NaN");
-			break;
-		default:
-			printf("SIGN=0x%x", NUMERIC_SIGN(num));
-			break;
-	}
-
-	for (i = 0; i < num->varlen - NUMERIC_HDRSZ; i++)
-		printf(" %d %d", (num->n_data[i] >> 4) & 0x0f, num->n_data[i] & 0x0f);
-	printf("\n");
-}
-
-
-/* ----------
- * dump_var() - Dump a value in the variable format for debugging
- * ----------
- */
-static void
-dump_var(char *str, NumericVar *var)
-{
-	int			i;
-
-	printf("%s: VAR w=%d r=%d d=%d ", str, var->weight, var->rscale,
-		   var->dscale);
-	switch (var->sign)
-	{
-		case NUMERIC_POS:
-			printf("POS");
-			break;
-		case NUMERIC_NEG:
-			printf("NEG");
-			break;
-		case NUMERIC_NAN:
-			printf("NaN");
-			break;
-		default:
-			printf("SIGN=0x%x", var->sign);
-			break;
-	}
-
-	for (i = 0; i < var->ndigits; i++)
-		printf(" %d", var->digits[i]);
-
-	printf("\n");
-}
-#endif   /* NUMERIC_DEBUG */
-
-
-/* ----------
- * alloc_var() -
- *
- *	Allocate a digit buffer of ndigits digits (plus a spare digit for rounding)
- * ----------
- */
-static void
-alloc_var(NumericVar *var, int ndigits)
-{
-	digitbuf_free(var->buf);
-	var->buf = digitbuf_alloc(ndigits + 1);
-	var->buf[0] = 0;
-	var->digits = var->buf + 1;
-	var->ndigits = ndigits;
-}
-
-
-/* ----------
- * free_var() -
- *
- *	Return the digit buffer of a variable to the free pool
- * ----------
- */
-static void
-free_var(NumericVar *var)
-{
-	digitbuf_free(var->buf);
-	var->buf = NULL;
-	var->digits = NULL;
-	var->sign = NUMERIC_NAN;
-}
-
-
-/* ----------
- * zero_var() -
- *
- *	Set a variable to ZERO.
- *	Note: rscale and dscale are not touched.
- * ----------
- */
-static void
-zero_var(NumericVar *var)
-{
-	digitbuf_free(var->buf);
-	var->buf = NULL;
-	var->digits = NULL;
-	var->ndigits = 0;
-	var->weight = 0;			/* by convention; doesn't really matter */
-	var->sign = NUMERIC_POS;	/* anything but NAN... */
-}
-
-
-/* ----------
- * set_var_from_str()
- *
- *	Parse a string and put the number into a variable
- * ----------
- */
-static void
-set_var_from_str(char *str, NumericVar *dest)
-{
-	char	   *cp = str;
-	bool		have_dp = FALSE;
-	int			i = 0;
-
-	while (*cp)
-	{
-		if (!isspace((unsigned char) *cp))
-			break;
-		cp++;
-	}
-
-	alloc_var(dest, strlen(cp));
-	dest->weight = -1;
-	dest->dscale = 0;
-	dest->sign = NUMERIC_POS;
-
-	switch (*cp)
-	{
-		case '+':
-			dest->sign = NUMERIC_POS;
-			cp++;
-			break;
-
-		case '-':
-			dest->sign = NUMERIC_NEG;
-			cp++;
-			break;
-	}
-
-	if (*cp == '.')
-	{
-		have_dp = TRUE;
-		cp++;
-	}
-
-	if (!isdigit((unsigned char) *cp))
-		elog(ERROR, "Bad numeric input format '%s'", str);
-
-	while (*cp)
-	{
-		if (isdigit((unsigned char) *cp))
-		{
-			dest->digits[i++] = *cp++ - '0';
-			if (!have_dp)
-				dest->weight++;
-			else
-				dest->dscale++;
-		}
-		else if (*cp == '.')
-		{
-			if (have_dp)
-				elog(ERROR, "Bad numeric input format '%s'", str);
-			have_dp = TRUE;
-			cp++;
-		}
-		else
-			break;
-	}
-	dest->ndigits = i;
-
-	/* Handle exponent, if any */
-	if (*cp == 'e' || *cp == 'E')
-	{
-		long		exponent;
-		char	   *endptr;
-
-		cp++;
-		exponent = strtol(cp, &endptr, 10);
-		if (endptr == cp)
-			elog(ERROR, "Bad numeric input format '%s'", str);
-		cp = endptr;
-		if (exponent > NUMERIC_MAX_PRECISION ||
-			exponent < -NUMERIC_MAX_PRECISION)
-			elog(ERROR, "Bad numeric input format '%s'", str);
-		dest->weight += (int) exponent;
-		dest->dscale -= (int) exponent;
-		if (dest->dscale < 0)
-			dest->dscale = 0;
-	}
-
-	/* Should be nothing left but spaces */
-	while (*cp)
-	{
-		if (!isspace((unsigned char) *cp))
-			elog(ERROR, "Bad numeric input format '%s'", str);
-		cp++;
-	}
-
-	/* Strip any leading zeroes */
-	while (dest->ndigits > 0 && *(dest->digits) == 0)
-	{
-		(dest->digits)++;
-		(dest->weight)--;
-		(dest->ndigits)--;
-	}
-	if (dest->ndigits == 0)
-		dest->weight = 0;
-
-	dest->rscale = dest->dscale;
-}
-
-
-/*
- * set_var_from_num() -
- *
- *	Parse back the packed db format into a variable
- *
- */
-static void
-set_var_from_num(Numeric num, NumericVar *dest)
-{
-	NumericDigit *digit;
-	int			i;
-	int			n;
-
-	n = num->varlen - NUMERIC_HDRSZ;	/* number of digit-pairs in packed
-										 * fmt */
-
-	alloc_var(dest, n * 2);
-
-	dest->weight = num->n_weight;
-	dest->rscale = num->n_rscale;
-	dest->dscale = NUMERIC_DSCALE(num);
-	dest->sign = NUMERIC_SIGN(num);
-
-	digit = dest->digits;
-
-	for (i = 0; i < n; i++)
-	{
-		unsigned char digitpair = num->n_data[i];
-
-		*digit++ = (digitpair >> 4) & 0x0f;
-		*digit++ = digitpair & 0x0f;
-	}
-}
-
-
-/* ----------
- * set_var_from_var() -
- *
- *	Copy one variable into another
- * ----------
- */
-static void
-set_var_from_var(NumericVar *value, NumericVar *dest)
-{
-	NumericDigit *newbuf;
-
-	newbuf = digitbuf_alloc(value->ndigits + 1);
-	newbuf[0] = 0;				/* spare digit for rounding */
-	memcpy(newbuf + 1, value->digits, value->ndigits);
-
-	digitbuf_free(dest->buf);
-
-	memcpy(dest, value, sizeof(NumericVar));
-	dest->buf = newbuf;
-	dest->digits = newbuf + 1;
-}
-
-
-/* ----------
- * get_str_from_var() -
- *
- *	Convert a var to text representation (guts of numeric_out).
- *	CAUTION: var's contents may be modified by rounding!
- *	Caller must have checked for NaN case.
- *	Returns a palloc'd string.
- * ----------
- */
-static char *
-get_str_from_var(NumericVar *var, int dscale)
-{
-	char	   *str;
-	char	   *cp;
-	int			i;
-	int			d;
-
-	/*
-	 * Check if we must round up before printing the value and do so.
-	 */
-	i = dscale + var->weight + 1;
-	if (i >= 0 && var->ndigits > i)
-	{
-		int			carry = (var->digits[i] > 4) ? 1 : 0;
-
-		var->ndigits = i;
-
-		while (carry)
-		{
-			carry += var->digits[--i];
-			var->digits[i] = carry % 10;
-			carry /= 10;
-		}
-
-		if (i < 0)
-		{
-			Assert(i == -1);	/* better not have added more than 1 digit */
-			Assert(var->digits > var->buf);
-			var->digits--;
-			var->ndigits++;
-			var->weight++;
-		}
-	}
-	else
-		var->ndigits = Max(0, Min(i, var->ndigits));
-
-	/*
-	 * Allocate space for the result
-	 */
-	str = palloc(Max(0, dscale) + Max(0, var->weight) + 4);
-	cp = str;
-
-	/*
-	 * Output a dash for negative values
-	 */
-	if (var->sign == NUMERIC_NEG)
-		*cp++ = '-';
-
-	/*
-	 * Output all digits before the decimal point
-	 */
-	i = Max(var->weight, 0);
-	d = 0;
-
-	while (i >= 0)
-	{
-		if (i <= var->weight && d < var->ndigits)
-			*cp++ = var->digits[d++] + '0';
-		else
-			*cp++ = '0';
-		i--;
-	}
-
-	/*
-	 * If requested, output a decimal point and all the digits that follow
-	 * it.
-	 */
-	if (dscale > 0)
-	{
-		*cp++ = '.';
-		while (i >= -dscale)
-		{
-			if (i <= var->weight && d < var->ndigits)
-				*cp++ = var->digits[d++] + '0';
-			else
-				*cp++ = '0';
-			i--;
-		}
-	}
-
-	/*
-	 * terminate the string and return it
-	 */
-	*cp = '\0';
-	return str;
-}
-
-
-/* ----------
- * make_result() -
- *
- *	Create the packed db numeric format in palloc()'d memory from
- *	a variable.  The var's rscale determines the number of digits kept.
- * ----------
- */
-static Numeric
-make_result(NumericVar *var)
-{
-	Numeric		result;
-	NumericDigit *digit = var->digits;
-	int			weight = var->weight;
-	int			sign = var->sign;
-	int			n;
-	int			i,
-				j;
-
-	if (sign == NUMERIC_NAN)
-	{
-		result = (Numeric) palloc(NUMERIC_HDRSZ);
-
-		result->varlen = NUMERIC_HDRSZ;
-		result->n_weight = 0;
-		result->n_rscale = 0;
-		result->n_sign_dscale = NUMERIC_NAN;
-
-		dump_numeric("make_result()", result);
-		return result;
-	}
-
-	n = Max(0, Min(var->ndigits, var->weight + var->rscale + 1));
-
-	/* truncate leading zeroes */
-	while (n > 0 && *digit == 0)
-	{
-		digit++;
-		weight--;
-		n--;
-	}
-	/* truncate trailing zeroes */
-	while (n > 0 && digit[n - 1] == 0)
-		n--;
-
-	/* If zero result, force to weight=0 and positive sign */
-	if (n == 0)
-	{
-		weight = 0;
-		sign = NUMERIC_POS;
-	}
-
-	result = (Numeric) palloc(NUMERIC_HDRSZ + (n + 1) / 2);
-	result->varlen = NUMERIC_HDRSZ + (n + 1) / 2;
-	result->n_weight = weight;
-	result->n_rscale = var->rscale;
-	result->n_sign_dscale = sign |
-		((uint16) var->dscale & NUMERIC_DSCALE_MASK);
-
-	i = 0;
-	j = 0;
-	while (j < n)
-	{
-		unsigned char digitpair = digit[j++] << 4;
-
-		if (j < n)
-			digitpair |= digit[j++];
-		result->n_data[i++] = digitpair;
-	}
-
-	dump_numeric("make_result()", result);
-	return result;
-}
-
-
-/* ----------
- * apply_typmod() -
- *
- *	Do bounds checking and rounding according to the attributes
- *	typmod field.
- * ----------
- */
-static void
-apply_typmod(NumericVar *var, int32 typmod)
-{
-	int			precision;
-	int			scale;
-	int			maxweight;
-	int			i;
-
-	/* Do nothing if we have a default typmod (-1) */
-	if (typmod < (int32) (VARHDRSZ))
-		return;
-
-	typmod -= VARHDRSZ;
-	precision = (typmod >> 16) & 0xffff;
-	scale = typmod & 0xffff;
-	maxweight = precision - scale;
-
-	/* Round to target scale */
-	i = scale + var->weight + 1;
-	if (i >= 0 && var->ndigits > i)
-	{
-		int			carry = (var->digits[i] > 4) ? 1 : 0;
-
-		var->ndigits = i;
-
-		while (carry)
-		{
-			carry += var->digits[--i];
-			var->digits[i] = carry % 10;
-			carry /= 10;
-		}
-
-		if (i < 0)
-		{
-			Assert(i == -1);	/* better not have added more than 1 digit */
-			Assert(var->digits > var->buf);
-			var->digits--;
-			var->ndigits++;
-			var->weight++;
-		}
-	}
-	else
-		var->ndigits = Max(0, Min(i, var->ndigits));
-
-	/*
-	 * Check for overflow - note we can't do this before rounding, because
-	 * rounding could raise the weight.  Also note that the var's weight
-	 * could be inflated by leading zeroes, which will be stripped before
-	 * storage but perhaps might not have been yet. In any case, we must
-	 * recognize a true zero, whose weight doesn't mean anything.
-	 */
-	if (var->weight >= maxweight)
-	{
-		/* Determine true weight; and check for all-zero result */
-		int			tweight = var->weight;
-
-		for (i = 0; i < var->ndigits; i++)
-		{
-			if (var->digits[i])
-				break;
-			tweight--;
-		}
-
-		if (tweight >= maxweight && i < var->ndigits)
-			elog(ERROR, "overflow on numeric "
-			  "ABS(value) >= 10^%d for field with precision %d scale %d",
-				 tweight, precision, scale);
-	}
-
-	var->rscale = scale;
-	var->dscale = scale;
-}
-
-
-/* ----------
- * cmp_var() -
- *
- *	Compare two values on variable level
- * ----------
- */
-static int
-cmp_var(NumericVar *var1, NumericVar *var2)
-{
-	if (var1->ndigits == 0)
-	{
-		if (var2->ndigits == 0)
-			return 0;
-		if (var2->sign == NUMERIC_NEG)
-			return 1;
-		return -1;
-	}
-	if (var2->ndigits == 0)
-	{
-		if (var1->sign == NUMERIC_POS)
-			return 1;
-		return -1;
-	}
-
-	if (var1->sign == NUMERIC_POS)
-	{
-		if (var2->sign == NUMERIC_NEG)
-			return 1;
-		return cmp_abs(var1, var2);
-	}
-
-	if (var2->sign == NUMERIC_POS)
-		return -1;
-
-	return cmp_abs(var2, var1);
-}
-
-
-/* ----------
- * add_var() -
- *
- *	Full version of add functionality on variable level (handling signs).
- *	result might point to one of the operands too without danger.
- * ----------
- */
-static void
-add_var(NumericVar *var1, NumericVar *var2, NumericVar *result)
-{
-	/*
-	 * Decide on the signs of the two variables what to do
-	 */
-	if (var1->sign == NUMERIC_POS)
-	{
-		if (var2->sign == NUMERIC_POS)
-		{
-			/*
-			 * Both are positive result = +(ABS(var1) + ABS(var2))
-			 */
-			add_abs(var1, var2, result);
-			result->sign = NUMERIC_POS;
-		}
-		else
-		{
-			/*
-			 * var1 is positive, var2 is negative Must compare absolute
-			 * values
-			 */
-			switch (cmp_abs(var1, var2))
-			{
-				case 0:
-					/* ----------
-					 * ABS(var1) == ABS(var2)
-					 * result = ZERO
-					 * ----------
-					 */
-					zero_var(result);
-					result->rscale = Max(var1->rscale, var2->rscale);
-					result->dscale = Max(var1->dscale, var2->dscale);
-					break;
-
-				case 1:
-					/* ----------
-					 * ABS(var1) > ABS(var2)
-					 * result = +(ABS(var1) - ABS(var2))
-					 * ----------
-					 */
-					sub_abs(var1, var2, result);
-					result->sign = NUMERIC_POS;
-					break;
-
-				case -1:
-					/* ----------
-					 * ABS(var1) < ABS(var2)
-					 * result = -(ABS(var2) - ABS(var1))
-					 * ----------
-					 */
-					sub_abs(var2, var1, result);
-					result->sign = NUMERIC_NEG;
-					break;
-			}
-		}
-	}
-	else
-	{
-		if (var2->sign == NUMERIC_POS)
-		{
-			/* ----------
-			 * var1 is negative, var2 is positive
-			 * Must compare absolute values
-			 * ----------
-			 */
-			switch (cmp_abs(var1, var2))
-			{
-				case 0:
-					/* ----------
-					 * ABS(var1) == ABS(var2)
-					 * result = ZERO
-					 * ----------
-					 */
-					zero_var(result);
-					result->rscale = Max(var1->rscale, var2->rscale);
-					result->dscale = Max(var1->dscale, var2->dscale);
-					break;
-
-				case 1:
-					/* ----------
-					 * ABS(var1) > ABS(var2)
-					 * result = -(ABS(var1) - ABS(var2))
-					 * ----------
-					 */
-					sub_abs(var1, var2, result);
-					result->sign = NUMERIC_NEG;
-					break;
-
-				case -1:
-					/* ----------
-					 * ABS(var1) < ABS(var2)
-					 * result = +(ABS(var2) - ABS(var1))
-					 * ----------
-					 */
-					sub_abs(var2, var1, result);
-					result->sign = NUMERIC_POS;
-					break;
-			}
-		}
-		else
-		{
-			/* ----------
-			 * Both are negative
-			 * result = -(ABS(var1) + ABS(var2))
-			 * ----------
-			 */
-			add_abs(var1, var2, result);
-			result->sign = NUMERIC_NEG;
-		}
-	}
-}
-
-
-/* ----------
- * sub_var() -
- *
- *	Full version of sub functionality on variable level (handling signs).
- *	result might point to one of the operands too without danger.
- * ----------
- */
-static void
-sub_var(NumericVar *var1, NumericVar *var2, NumericVar *result)
-{
-	/*
-	 * Decide on the signs of the two variables what to do
-	 */
-	if (var1->sign == NUMERIC_POS)
-	{
-		if (var2->sign == NUMERIC_NEG)
-		{
-			/* ----------
-			 * var1 is positive, var2 is negative
-			 * result = +(ABS(var1) + ABS(var2))
-			 * ----------
-			 */
-			add_abs(var1, var2, result);
-			result->sign = NUMERIC_POS;
-		}
-		else
-		{
-			/* ----------
-			 * Both are positive
-			 * Must compare absolute values
-			 * ----------
-			 */
-			switch (cmp_abs(var1, var2))
-			{
-				case 0:
-					/* ----------
-					 * ABS(var1) == ABS(var2)
-					 * result = ZERO
-					 * ----------
-					 */
-					zero_var(result);
-					result->rscale = Max(var1->rscale, var2->rscale);
-					result->dscale = Max(var1->dscale, var2->dscale);
-					break;
-
-				case 1:
-					/* ----------
-					 * ABS(var1) > ABS(var2)
-					 * result = +(ABS(var1) - ABS(var2))
-					 * ----------
-					 */
-					sub_abs(var1, var2, result);
-					result->sign = NUMERIC_POS;
-					break;
-
-				case -1:
-					/* ----------
-					 * ABS(var1) < ABS(var2)
-					 * result = -(ABS(var2) - ABS(var1))
-					 * ----------
-					 */
-					sub_abs(var2, var1, result);
-					result->sign = NUMERIC_NEG;
-					break;
-			}
-		}
-	}
-	else
-	{
-		if (var2->sign == NUMERIC_NEG)
-		{
-			/* ----------
-			 * Both are negative
-			 * Must compare absolute values
-			 * ----------
-			 */
-			switch (cmp_abs(var1, var2))
-			{
-				case 0:
-					/* ----------
-					 * ABS(var1) == ABS(var2)
-					 * result = ZERO
-					 * ----------
-					 */
-					zero_var(result);
-					result->rscale = Max(var1->rscale, var2->rscale);
-					result->dscale = Max(var1->dscale, var2->dscale);
-					break;
-
-				case 1:
-					/* ----------
-					 * ABS(var1) > ABS(var2)
-					 * result = -(ABS(var1) - ABS(var2))
-					 * ----------
-					 */
-					sub_abs(var1, var2, result);
-					result->sign = NUMERIC_NEG;
-					break;
-
-				case -1:
-					/* ----------
-					 * ABS(var1) < ABS(var2)
-					 * result = +(ABS(var2) - ABS(var1))
-					 * ----------
-					 */
-					sub_abs(var2, var1, result);
-					result->sign = NUMERIC_POS;
-					break;
-			}
-		}
-		else
-		{
-			/* ----------
-			 * var1 is negative, var2 is positive
-			 * result = -(ABS(var1) + ABS(var2))
-			 * ----------
-			 */
-			add_abs(var1, var2, result);
-			result->sign = NUMERIC_NEG;
-		}
-	}
-}
-
-
-/* ----------
- * mul_var() -
- *
- *	Multiplication on variable level. Product of var1 * var2 is stored
- *	in result.
- * ----------
- */
-static void
-mul_var(NumericVar *var1, NumericVar *var2, NumericVar *result)
-{
-	NumericDigit *res_buf;
-	NumericDigit *res_digits;
-	int			res_ndigits;
-	int			res_weight;
-	int			res_sign;
-	int			i,
-				ri,
-				i1,
-				i2;
-	long		sum = 0;
-
-	res_weight = var1->weight + var2->weight + 2;
-	res_ndigits = var1->ndigits + var2->ndigits + 1;
-	if (var1->sign == var2->sign)
-		res_sign = NUMERIC_POS;
-	else
-		res_sign = NUMERIC_NEG;
-
-	res_buf = digitbuf_alloc(res_ndigits);
-	res_digits = res_buf;
-	memset(res_digits, 0, res_ndigits);
-
-	ri = res_ndigits;
-	for (i1 = var1->ndigits - 1; i1 >= 0; i1--)
-	{
-		sum = 0;
-		i = --ri;
-
-		for (i2 = var2->ndigits - 1; i2 >= 0; i2--)
-		{
-			sum += res_digits[i] + var1->digits[i1] * var2->digits[i2];
-			res_digits[i--] = sum % 10;
-			sum /= 10;
-		}
-		res_digits[i] = sum;
-	}
-
-	i = res_weight + global_rscale + 2;
-	if (i >= 0 && i < res_ndigits)
-	{
-		sum = (res_digits[i] > 4) ? 1 : 0;
-		res_ndigits = i;
-		i--;
-		while (sum)
-		{
-			sum += res_digits[i];
-			res_digits[i--] = sum % 10;
-			sum /= 10;
-		}
-	}
-
-	while (res_ndigits > 0 && *res_digits == 0)
-	{
-		res_digits++;
-		res_weight--;
-		res_ndigits--;
-	}
-	while (res_ndigits > 0 && res_digits[res_ndigits - 1] == 0)
-		res_ndigits--;
-
-	if (res_ndigits == 0)
-	{
-		res_sign = NUMERIC_POS;
-		res_weight = 0;
-	}
-
-	digitbuf_free(result->buf);
-	result->buf = res_buf;
-	result->digits = res_digits;
-	result->ndigits = res_ndigits;
-	result->weight = res_weight;
-	result->rscale = global_rscale;
-	result->sign = res_sign;
-}
-
-
-/* ----------
- * div_var() -
- *
- *	Division on variable level.
- * ----------
- */
-static void
-div_var(NumericVar *var1, NumericVar *var2, NumericVar *result)
-{
-	NumericDigit *res_digits;
-	int			res_ndigits;
-	int			res_sign;
-	int			res_weight;
-	NumericVar	dividend;
-	NumericVar	divisor[10];
-	int			ndigits_tmp;
-	int			weight_tmp;
-	int			rscale_tmp;
-	int			ri;
-	int			i;
-	long		guess;
-	long		first_have;
-	long		first_div;
-	int			first_nextdigit;
-	int			stat = 0;
-
-	/*
-	 * First of all division by zero check
-	 */
-	ndigits_tmp = var2->ndigits + 1;
-	if (ndigits_tmp == 1)
-		elog(ERROR, "division by zero on numeric");
-
-	/*
-	 * Determine the result sign, weight and number of digits to calculate
-	 */
-	if (var1->sign == var2->sign)
-		res_sign = NUMERIC_POS;
-	else
-		res_sign = NUMERIC_NEG;
-	res_weight = var1->weight - var2->weight + 1;
-	res_ndigits = global_rscale + res_weight;
-	if (res_ndigits <= 0)
-		res_ndigits = 1;
-
-	/*
-	 * Now result zero check
-	 */
-	if (var1->ndigits == 0)
-	{
-		zero_var(result);
-		result->rscale = global_rscale;
-		return;
-	}
-
-	/*
-	 * Initialize local variables
-	 */
-	init_var(&dividend);
-	for (i = 1; i < 10; i++)
-		init_var(&divisor[i]);
-
-	/*
-	 * Make a copy of the divisor which has one leading zero digit
-	 */
-	divisor[1].ndigits = ndigits_tmp;
-	divisor[1].rscale = var2->ndigits;
-	divisor[1].sign = NUMERIC_POS;
-	divisor[1].buf = digitbuf_alloc(ndigits_tmp);
-	divisor[1].digits = divisor[1].buf;
-	divisor[1].digits[0] = 0;
-	memcpy(&(divisor[1].digits[1]), var2->digits, ndigits_tmp - 1);
-
-	/*
-	 * Make a copy of the dividend
-	 */
-	dividend.ndigits = var1->ndigits;
-	dividend.weight = 0;
-	dividend.rscale = var1->ndigits;
-	dividend.sign = NUMERIC_POS;
-	dividend.buf = digitbuf_alloc(var1->ndigits);
-	dividend.digits = dividend.buf;
-	memcpy(dividend.digits, var1->digits, var1->ndigits);
-
-	/*
-	 * Setup the result
-	 */
-	digitbuf_free(result->buf);
-	result->buf = digitbuf_alloc(res_ndigits + 2);
-	res_digits = result->buf;
-	result->digits = res_digits;
-	result->ndigits = res_ndigits;
-	result->weight = res_weight;
-	result->rscale = global_rscale;
-	result->sign = res_sign;
-	res_digits[0] = 0;
-
-	first_div = divisor[1].digits[1] * 10;
-	if (ndigits_tmp > 2)
-		first_div += divisor[1].digits[2];
-
-	first_have = 0;
-	first_nextdigit = 0;
-
-	weight_tmp = 1;
-	rscale_tmp = divisor[1].rscale;
-
-	for (ri = 0; ri <= res_ndigits; ri++)
-	{
-		first_have = first_have * 10;
-		if (first_nextdigit >= 0 && first_nextdigit < dividend.ndigits)
-			first_have += dividend.digits[first_nextdigit];
-		first_nextdigit++;
-
-		guess = (first_have * 10) / first_div + 1;
-		if (guess > 9)
-			guess = 9;
-
-		while (guess > 0)
-		{
-			if (divisor[guess].buf == NULL)
-			{
-				int			i;
-				long		sum = 0;
-
-				memcpy(&divisor[guess], &divisor[1], sizeof(NumericVar));
-				divisor[guess].buf = digitbuf_alloc(divisor[guess].ndigits);
-				divisor[guess].digits = divisor[guess].buf;
-				for (i = divisor[1].ndigits - 1; i >= 0; i--)
-				{
-					sum += divisor[1].digits[i] * guess;
-					divisor[guess].digits[i] = sum % 10;
-					sum /= 10;
-				}
-			}
-
-			divisor[guess].weight = weight_tmp;
-			divisor[guess].rscale = rscale_tmp;
-
-			stat = cmp_abs(&dividend, &divisor[guess]);
-			if (stat >= 0)
-				break;
-
-			guess--;
-		}
-
-		res_digits[ri + 1] = guess;
-		if (stat == 0)
-		{
-			ri++;
-			break;
-		}
-
-		weight_tmp--;
-		rscale_tmp++;
-
-		if (guess == 0)
-			continue;
-
-		sub_abs(&dividend, &divisor[guess], &dividend);
-
-		first_nextdigit = dividend.weight - weight_tmp;
-		first_have = 0;
-		if (first_nextdigit >= 0 && first_nextdigit < dividend.ndigits)
-			first_have = dividend.digits[first_nextdigit];
-		first_nextdigit++;
-	}
-
-	result->ndigits = ri + 1;
-	if (ri == res_ndigits + 1)
-	{
-		int			carry = (res_digits[ri] > 4) ? 1 : 0;
-
-		result->ndigits = ri;
-		res_digits[ri] = 0;
-
-		while (carry && ri > 0)
-		{
-			carry += res_digits[--ri];
-			res_digits[ri] = carry % 10;
-			carry /= 10;
-		}
-	}
-
-	while (result->ndigits > 0 && *(result->digits) == 0)
-	{
-		(result->digits)++;
-		(result->weight)--;
-		(result->ndigits)--;
-	}
-	while (result->ndigits > 0 && result->digits[result->ndigits - 1] == 0)
-		(result->ndigits)--;
-	if (result->ndigits == 0)
-		result->sign = NUMERIC_POS;
-
-	/*
-	 * Tidy up
-	 */
-	digitbuf_free(dividend.buf);
-	for (i = 1; i < 10; i++)
-		digitbuf_free(divisor[i].buf);
-}
-
-
-/*
- * Default scale selection for division
- *
- * Returns the appropriate display scale for the division result,
- * and sets global_rscale to the result scale to use during div_var.
- *
- * Note that this must be called before div_var.
- */
-static int
-select_div_scale(NumericVar *var1, NumericVar *var2)
-{
-	int			res_dscale;
-	int			res_rscale;
-
-	/* ----------
-	 * The result scale of a division isn't specified in any
-	 * SQL standard. For Postgres it is the following (where
-	 * SR, DR are the result- and display-scales of the returned
-	 * value, S1, D1, S2 and D2 are the scales of the two arguments,
-	 * The minimum and maximum scales are compile time options from
-	 * numeric.h):
-	 *
-	 *	DR = Min(Max(D1 + D2, MIN_DISPLAY_SCALE), MAX_DISPLAY_SCALE)
-	 *	SR = Min(Max(Max(S1 + S2, DR + 4), MIN_RESULT_SCALE), MAX_RESULT_SCALE)
-	 *
-	 * By default, any result is computed with a minimum of 34 digits
-	 * after the decimal point or at least with 4 digits more than
-	 * displayed.
-	 * ----------
-	 */
-	res_dscale = var1->dscale + var2->dscale;
-	res_dscale = Max(res_dscale, NUMERIC_MIN_DISPLAY_SCALE);
-	res_dscale = Min(res_dscale, NUMERIC_MAX_DISPLAY_SCALE);
-
-	res_rscale = var1->rscale + var2->rscale;
-	res_rscale = Max(res_rscale, res_dscale + 4);
-	res_rscale = Max(res_rscale, NUMERIC_MIN_RESULT_SCALE);
-	res_rscale = Min(res_rscale, NUMERIC_MAX_RESULT_SCALE);
-	global_rscale = res_rscale;
-
-	return res_dscale;
-}
-
-
-/* ----------
- * mod_var() -
- *
- *	Calculate the modulo of two numerics at variable level
- * ----------
- */
-static void
-mod_var(NumericVar *var1, NumericVar *var2, NumericVar *result)
-{
-	NumericVar	tmp;
-	int			save_global_rscale;
-	int			div_dscale;
-
-	init_var(&tmp);
-
-	/* ---------
-	 * We do this using the equation
-	 *		mod(x,y) = x - trunc(x/y)*y
-	 * We set global_rscale the same way numeric_div and numeric_mul do
-	 * to get the right answer from the equation.  The final result,
-	 * however, need not be displayed to more precision than the inputs.
-	 * ----------
-	 */
-	save_global_rscale = global_rscale;
-
-	div_dscale = select_div_scale(var1, var2);
-
-	div_var(var1, var2, &tmp);
-
-	tmp.dscale = div_dscale;
-
-	/* do trunc() by forgetting digits to the right of the decimal point */
-	tmp.ndigits = Max(0, Min(tmp.ndigits, tmp.weight + 1));
-
-	global_rscale = var2->rscale + tmp.rscale;
-
-	mul_var(var2, &tmp, &tmp);
-
-	sub_var(var1, &tmp, result);
-
-	result->dscale = Max(var1->dscale, var2->dscale);
-
-	global_rscale = save_global_rscale;
-	free_var(&tmp);
-}
-
-
-/* ----------
- * ceil_var() -
- *
- *	Return the smallest integer greater than or equal to the argument
- *	on variable level
- * ----------
- */
-static void
-ceil_var(NumericVar *var, NumericVar *result)
-{
-	NumericVar	tmp;
-
-	init_var(&tmp);
-	set_var_from_var(var, &tmp);
-
-	tmp.rscale = 0;
-	tmp.ndigits = Min(tmp.ndigits, Max(0, tmp.weight + 1));
-	if (tmp.sign == NUMERIC_POS && cmp_var(var, &tmp) != 0)
-		add_var(&tmp, &const_one, &tmp);
-
-	set_var_from_var(&tmp, result);
-	free_var(&tmp);
-}
-
-
-/* ----------
- * floor_var() -
- *
- *	Return the largest integer equal to or less than the argument
- *	on variable level
- * ----------
- */
-static void
-floor_var(NumericVar *var, NumericVar *result)
-{
-	NumericVar	tmp;
-
-	init_var(&tmp);
-	set_var_from_var(var, &tmp);
-
-	tmp.rscale = 0;
-	tmp.ndigits = Min(tmp.ndigits, Max(0, tmp.weight + 1));
-	if (tmp.sign == NUMERIC_NEG && cmp_var(var, &tmp) != 0)
-		sub_var(&tmp, &const_one, &tmp);
-
-	set_var_from_var(&tmp, result);
-	free_var(&tmp);
-}
-
-
-/* ----------
- * sqrt_var() -
- *
- *	Compute the square root of x using Newtons algorithm
- * ----------
- */
-static void
-sqrt_var(NumericVar *arg, NumericVar *result)
-{
-	NumericVar	tmp_arg;
-	NumericVar	tmp_val;
-	NumericVar	last_val;
-	int			res_rscale;
-	int			save_global_rscale;
-	int			stat;
-
-	save_global_rscale = global_rscale;
-	global_rscale += 8;
-	res_rscale = global_rscale;
-
-	stat = cmp_var(arg, &const_zero);
-	if (stat == 0)
-	{
-		set_var_from_var(&const_zero, result);
-		result->rscale = res_rscale;
-		result->sign = NUMERIC_POS;
-		return;
-	}
-
-	if (stat < 0)
-		elog(ERROR, "math error on numeric - cannot compute SQRT of negative value");
-
-	init_var(&tmp_arg);
-	init_var(&tmp_val);
-	init_var(&last_val);
-
-	set_var_from_var(arg, &tmp_arg);
-	set_var_from_var(result, &last_val);
-
-	/*
-	 * Initialize the result to the first guess
-	 */
-	digitbuf_free(result->buf);
-	result->buf = digitbuf_alloc(1);
-	result->digits = result->buf;
-	result->digits[0] = tmp_arg.digits[0] / 2;
-	if (result->digits[0] == 0)
-		result->digits[0] = 1;
-	result->ndigits = 1;
-	result->weight = tmp_arg.weight / 2;
-	result->rscale = res_rscale;
-	result->sign = NUMERIC_POS;
-
-	for (;;)
-	{
-		div_var(&tmp_arg, result, &tmp_val);
-
-		add_var(result, &tmp_val, result);
-		div_var(result, &const_two, result);
-
-		if (cmp_var(&last_val, result) == 0)
-			break;
-		set_var_from_var(result, &last_val);
-	}
-
-	free_var(&last_val);
-	free_var(&tmp_val);
-	free_var(&tmp_arg);
-
-	global_rscale = save_global_rscale;
-	div_var(result, &const_one, result);
-}
-
-
-/* ----------
- * exp_var() -
- *
- *	Raise e to the power of x
- * ----------
- */
-static void
-exp_var(NumericVar *arg, NumericVar *result)
-{
-	NumericVar	x;
-	NumericVar	xpow;
-	NumericVar	ifac;
-	NumericVar	elem;
-	NumericVar	ni;
-	int			d;
-	int			i;
-	int			ndiv2 = 0;
-	bool		xneg = FALSE;
-	int			save_global_rscale;
-
-	init_var(&x);
-	init_var(&xpow);
-	init_var(&ifac);
-	init_var(&elem);
-	init_var(&ni);
-
-	set_var_from_var(arg, &x);
-
-	if (x.sign == NUMERIC_NEG)
-	{
-		xneg = TRUE;
-		x.sign = NUMERIC_POS;
-	}
-
-	save_global_rscale = global_rscale;
-	global_rscale = 0;
-	for (i = x.weight, d = 0; i >= 0; i--, d++)
-	{
-		global_rscale *= 10;
-		if (d < x.ndigits)
-			global_rscale += x.digits[d];
-		if (global_rscale >= 1000)
-			elog(ERROR, "argument for EXP() too big");
-	}
-
-	global_rscale = global_rscale / 2 + save_global_rscale + 8;
-
-	while (cmp_var(&x, &const_one) > 0)
-	{
-		ndiv2++;
-		global_rscale++;
-		div_var(&x, &const_two, &x);
-	}
-
-	add_var(&const_one, &x, result);
-	set_var_from_var(&x, &xpow);
-	set_var_from_var(&const_one, &ifac);
-	set_var_from_var(&const_one, &ni);
-
-	for (i = 2;; i++)
-	{
-		add_var(&ni, &const_one, &ni);
-		mul_var(&xpow, &x, &xpow);
-		mul_var(&ifac, &ni, &ifac);
-		div_var(&xpow, &ifac, &elem);
-
-		if (elem.ndigits == 0)
-			break;
-
-		add_var(result, &elem, result);
-	}
-
-	while (ndiv2-- > 0)
-		mul_var(result, result, result);
-
-	global_rscale = save_global_rscale;
-	if (xneg)
-		div_var(&const_one, result, result);
-	else
-		div_var(result, &const_one, result);
-
-	result->sign = NUMERIC_POS;
-
-	free_var(&x);
-	free_var(&xpow);
-	free_var(&ifac);
-	free_var(&elem);
-	free_var(&ni);
-}
-
-
-/* ----------
- * ln_var() -
- *
- *	Compute the natural log of x
- * ----------
- */
-static void
-ln_var(NumericVar *arg, NumericVar *result)
-{
-	NumericVar	x;
-	NumericVar	xx;
-	NumericVar	ni;
-	NumericVar	elem;
-	NumericVar	fact;
-	int			i;
-	int			save_global_rscale;
-
-	if (cmp_var(arg, &const_zero) <= 0)
-		elog(ERROR, "math error on numeric - cannot compute LN of value <= zero");
-
-	save_global_rscale = global_rscale;
-	global_rscale += 8;
-
-	init_var(&x);
-	init_var(&xx);
-	init_var(&ni);
-	init_var(&elem);
-	init_var(&fact);
-
-	set_var_from_var(&const_two, &fact);
-	set_var_from_var(arg, &x);
-
-	while (cmp_var(&x, &const_two) >= 0)
-	{
-		sqrt_var(&x, &x);
-		mul_var(&fact, &const_two, &fact);
-	}
-	set_var_from_str("0.5", &elem);
-	while (cmp_var(&x, &elem) <= 0)
-	{
-		sqrt_var(&x, &x);
-		mul_var(&fact, &const_two, &fact);
-	}
-
-	sub_var(&x, &const_one, result);
-	add_var(&x, &const_one, &elem);
-	div_var(result, &elem, result);
-	set_var_from_var(result, &xx);
-	mul_var(result, result, &x);
-
-	set_var_from_var(&const_one, &ni);
-
-	for (i = 2;; i++)
-	{
-		add_var(&ni, &const_two, &ni);
-		mul_var(&xx, &x, &xx);
-		div_var(&xx, &ni, &elem);
-
-		if (cmp_var(&elem, &const_zero) == 0)
-			break;
-
-		add_var(result, &elem, result);
-	}
-
-	global_rscale = save_global_rscale;
-	mul_var(result, &fact, result);
-
-	free_var(&x);
-	free_var(&xx);
-	free_var(&ni);
-	free_var(&elem);
-	free_var(&fact);
-}
-
-
-/* ----------
- * log_var() -
- *
- *	Compute the logarithm of x in a given base
- * ----------
- */
-static void
-log_var(NumericVar *base, NumericVar *num, NumericVar *result)
-{
-	NumericVar	ln_base;
-	NumericVar	ln_num;
-
-	global_rscale += 8;
-
-	init_var(&ln_base);
-	init_var(&ln_num);
-
-	ln_var(base, &ln_base);
-	ln_var(num, &ln_num);
-
-	global_rscale -= 8;
-
-	div_var(&ln_num, &ln_base, result);
-
-	free_var(&ln_num);
-	free_var(&ln_base);
-}
-
-
-/* ----------
- * power_var() -
- *
- *	Raise base to the power of exp
- * ----------
- */
-static void
-power_var(NumericVar *base, NumericVar *exp, NumericVar *result)
-{
-	NumericVar	ln_base;
-	NumericVar	ln_num;
-	int			save_global_rscale;
-
-	save_global_rscale = global_rscale;
-	global_rscale += global_rscale / 3 + 8;
-
-	init_var(&ln_base);
-	init_var(&ln_num);
-
-	ln_var(base, &ln_base);
-	mul_var(&ln_base, exp, &ln_num);
-
-	global_rscale = save_global_rscale;
-
-	exp_var(&ln_num, result);
-
-	free_var(&ln_num);
-	free_var(&ln_base);
-
-}
-
-
-/* ----------------------------------------------------------------------
- *
- * Following are the lowest level functions that operate unsigned
- * on the variable level
- *
- * ----------------------------------------------------------------------
- */
-
-
-/* ----------
- * cmp_abs() -
- *
- *	Compare the absolute values of var1 and var2
- *	Returns:	-1 for ABS(var1) < ABS(var2)
- *				0  for ABS(var1) == ABS(var2)
- *				1  for ABS(var1) > ABS(var2)
- * ----------
- */
-static int
-cmp_abs(NumericVar *var1, NumericVar *var2)
-{
-	int			i1 = 0;
-	int			i2 = 0;
-	int			w1 = var1->weight;
-	int			w2 = var2->weight;
-	int			stat;
-
-	while (w1 > w2 && i1 < var1->ndigits)
-	{
-		if (var1->digits[i1++] != 0)
-			return 1;
-		w1--;
-	}
-	while (w2 > w1 && i2 < var2->ndigits)
-	{
-		if (var2->digits[i2++] != 0)
-			return -1;
-		w2--;
-	}
-
-	if (w1 == w2)
-	{
-		while (i1 < var1->ndigits && i2 < var2->ndigits)
-		{
-			stat = var1->digits[i1++] - var2->digits[i2++];
-			if (stat)
-			{
-				if (stat > 0)
-					return 1;
-				return -1;
-			}
-		}
-	}
-
-	while (i1 < var1->ndigits)
-	{
-		if (var1->digits[i1++] != 0)
-			return 1;
-	}
-	while (i2 < var2->ndigits)
-	{
-		if (var2->digits[i2++] != 0)
-			return -1;
-	}
-
-	return 0;
-}
-
-
-/* ----------
- * add_abs() -
- *
- *	Add the absolute values of two variables into result.
- *	result might point to one of the operands without danger.
- * ----------
- */
-static void
-add_abs(NumericVar *var1, NumericVar *var2, NumericVar *result)
-{
-	NumericDigit *res_buf;
-	NumericDigit *res_digits;
-	int			res_ndigits;
-	int			res_weight;
-	int			res_rscale;
-	int			res_dscale;
-	int			i,
-				i1,
-				i2;
-	int			carry = 0;
-
-	/* copy these values into local vars for speed in inner loop */
-	int			var1ndigits = var1->ndigits;
-	int			var2ndigits = var2->ndigits;
-	NumericDigit *var1digits = var1->digits;
-	NumericDigit *var2digits = var2->digits;
-
-	res_weight = Max(var1->weight, var2->weight) + 1;
-	res_rscale = Max(var1->rscale, var2->rscale);
-	res_dscale = Max(var1->dscale, var2->dscale);
-	res_ndigits = res_rscale + res_weight + 1;
-	if (res_ndigits <= 0)
-		res_ndigits = 1;
-
-	res_buf = digitbuf_alloc(res_ndigits);
-	res_digits = res_buf;
-
-	i1 = res_rscale + var1->weight + 1;
-	i2 = res_rscale + var2->weight + 1;
-	for (i = res_ndigits - 1; i >= 0; i--)
-	{
-		i1--;
-		i2--;
-		if (i1 >= 0 && i1 < var1ndigits)
-			carry += var1digits[i1];
-		if (i2 >= 0 && i2 < var2ndigits)
-			carry += var2digits[i2];
-
-		if (carry >= 10)
-		{
-			res_digits[i] = carry - 10;
-			carry = 1;
-		}
-		else
-		{
-			res_digits[i] = carry;
-			carry = 0;
-		}
-	}
-
-	Assert(carry == 0);			/* else we failed to allow for carry out */
-
-	while (res_ndigits > 0 && *res_digits == 0)
-	{
-		res_digits++;
-		res_weight--;
-		res_ndigits--;
-	}
-	while (res_ndigits > 0 && res_digits[res_ndigits - 1] == 0)
-		res_ndigits--;
-
-	if (res_ndigits == 0)
-		res_weight = 0;
-
-	digitbuf_free(result->buf);
-	result->ndigits = res_ndigits;
-	result->buf = res_buf;
-	result->digits = res_digits;
-	result->weight = res_weight;
-	result->rscale = res_rscale;
-	result->dscale = res_dscale;
-}
-
-
-/* ----------
- * sub_abs() -
- *
- *	Subtract the absolute value of var2 from the absolute value of var1
- *	and store in result. result might point to one of the operands
- *	without danger.
- *
- *	ABS(var1) MUST BE GREATER OR EQUAL ABS(var2) !!!
- * ----------
- */
-static void
-sub_abs(NumericVar *var1, NumericVar *var2, NumericVar *result)
-{
-	NumericDigit *res_buf;
-	NumericDigit *res_digits;
-	int			res_ndigits;
-	int			res_weight;
-	int			res_rscale;
-	int			res_dscale;
-	int			i,
-				i1,
-				i2;
-	int			borrow = 0;
-
-	/* copy these values into local vars for speed in inner loop */
-	int			var1ndigits = var1->ndigits;
-	int			var2ndigits = var2->ndigits;
-	NumericDigit *var1digits = var1->digits;
-	NumericDigit *var2digits = var2->digits;
-
-	res_weight = var1->weight;
-	res_rscale = Max(var1->rscale, var2->rscale);
-	res_dscale = Max(var1->dscale, var2->dscale);
-	res_ndigits = res_rscale + res_weight + 1;
-	if (res_ndigits <= 0)
-		res_ndigits = 1;
-
-	res_buf = digitbuf_alloc(res_ndigits);
-	res_digits = res_buf;
-
-	i1 = res_rscale + var1->weight + 1;
-	i2 = res_rscale + var2->weight + 1;
-	for (i = res_ndigits - 1; i >= 0; i--)
-	{
-		i1--;
-		i2--;
-		if (i1 >= 0 && i1 < var1ndigits)
-			borrow += var1digits[i1];
-		if (i2 >= 0 && i2 < var2ndigits)
-			borrow -= var2digits[i2];
-
-		if (borrow < 0)
-		{
-			res_digits[i] = borrow + 10;
-			borrow = -1;
-		}
-		else
-		{
-			res_digits[i] = borrow;
-			borrow = 0;
-		}
-	}
-
-	Assert(borrow == 0);		/* else caller gave us var1 < var2 */
-
-	while (res_ndigits > 0 && *res_digits == 0)
-	{
-		res_digits++;
-		res_weight--;
-		res_ndigits--;
-	}
-	while (res_ndigits > 0 && res_digits[res_ndigits - 1] == 0)
-		res_ndigits--;
-
-	if (res_ndigits == 0)
-		res_weight = 0;
-
-	digitbuf_free(result->buf);
-	result->ndigits = res_ndigits;
-	result->buf = res_buf;
-	result->digits = res_digits;
-	result->weight = res_weight;
-	result->rscale = res_rscale;
-	result->dscale = res_dscale;
-}