/*-------------------------------------------------------------------------
 *
 * float.c
 *	  Functions for the built-in floating-point types.
 *
 * Portions Copyright (c) 1996-2003, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 *
 * IDENTIFICATION
 *	  $PostgreSQL: pgsql/src/backend/utils/adt/float.c,v 1.100 2004/03/14 05:22:52 neilc Exp $
 *
 *-------------------------------------------------------------------------
 */
/*----------
 * OLD COMMENTS
 *		Basic float4 ops:
 *		 float4in, float4out, float4recv, float4send
 *		 float4abs, float4um, float4up
 *		Basic float8 ops:
 *		 float8in, float8out, float8recv, float8send
 *		 float8abs, float8um, float8up
 *		Arithmetic operators:
 *		 float4pl, float4mi, float4mul, float4div
 *		 float8pl, float8mi, float8mul, float8div
 *		Comparison operators:
 *		 float4eq, float4ne, float4lt, float4le, float4gt, float4ge, float4cmp
 *		 float8eq, float8ne, float8lt, float8le, float8gt, float8ge, float8cmp
 *		Conversion routines:
 *		 ftod, dtof, i4tod, dtoi4, i2tod, dtoi2, itof, ftoi, i2tof, ftoi2
 *
 *		Random float8 ops:
 *		 dround, dtrunc, dsqrt, dcbrt, dpow, dexp, dlog1
 *		Arithmetic operators:
 *		 float48pl, float48mi, float48mul, float48div
 *		 float84pl, float84mi, float84mul, float84div
 *		Comparison operators:
 *		 float48eq, float48ne, float48lt, float48le, float48gt, float48ge
 *		 float84eq, float84ne, float84lt, float84le, float84gt, float84ge
 *
 *		(You can do the arithmetic and comparison stuff using conversion
 *		 routines, but then you pay the overhead of invoking a separate
 *		 conversion function...)
 *
 * XXX GLUESOME STUFF. FIX IT! -AY '94
 *
 *		Added some additional conversion routines and cleaned up
 *		 a bit of the existing code. Need to change the error checking
 *		 for calls to pow(), exp() since on some machines (my Linux box
 *		 included) these routines do not set errno. - tgl 97/05/10
 *----------
 */
#include "postgres.h"

#include <ctype.h>
#include <errno.h>
#include <float.h>				/* faked on sunos4 */
#include <math.h>

#include <limits.h>
/* for finite() on Solaris */
#ifdef HAVE_IEEEFP_H
#include <ieeefp.h>
#endif

#include "catalog/pg_type.h"
#include "fmgr.h"
#include "libpq/pqformat.h"
#include "utils/array.h"
#include "utils/builtins.h"


#ifndef HAVE_CBRT
static double cbrt(double x);
#endif   /* HAVE_CBRT */

#ifndef M_PI
/* from my RH5.2 gcc math.h file - thomas 2000-04-03 */
#define M_PI 3.14159265358979323846
#endif

#ifndef NAN
#define NAN		(0.0/0.0)
#endif

#ifndef SHRT_MAX
#define SHRT_MAX 32767
#endif
#ifndef SHRT_MIN
#define SHRT_MIN (-32768)
#endif

/* not sure what the following should be, but better to make it over-sufficient */
#define MAXFLOATWIDTH	64
#define MAXDOUBLEWIDTH	128

/* ========== USER I/O ROUTINES ========== */


#define FLOAT4_MAX		 FLT_MAX
#define FLOAT4_MIN		 FLT_MIN
#define FLOAT8_MAX		 DBL_MAX
#define FLOAT8_MIN		 DBL_MIN


/* Configurable GUC parameter */
int			extra_float_digits = 0;		/* Added to DBL_DIG or FLT_DIG */


static void CheckFloat4Val(double val);
static void CheckFloat8Val(double val);
static int	is_infinite(double val);
static int	float4_cmp_internal(float4 a, float4 b);
static int	float8_cmp_internal(float8 a, float8 b);

/*
 * Returns -1 if 'val' represents negative infinity, 1 if 'val'
 * represents (positive) infinity, and 0 otherwise. On some platforms,
 * this is equivalent to the isinf() macro, but not everywhere: C99
 * does not specify that isinf() needs to distinguish between positive
 * and negative infinity.
 */
static int
is_infinite(double val)
{
	int inf = isinf(val);

	if (inf == 0)
		return 0;

	if (val > 0)
		return 1;

	return -1;
}

/*
 * check to see if a float4 val is outside of the FLOAT4_MIN,
 * FLOAT4_MAX bounds.
 *
 * raise an ereport() error if it is
 */
static void
CheckFloat4Val(double val)
{
	if (fabs(val) > FLOAT4_MAX)
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("type \"real\" value out of range: overflow")));
	if (val != 0.0 && fabs(val) < FLOAT4_MIN)
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("type \"real\" value out of range: underflow")));
}

/*
 * check to see if a float8 val is outside of the FLOAT8_MIN,
 * FLOAT8_MAX bounds.
 *
 * raise an ereport() error if it is
 */
static void
CheckFloat8Val(double val)
{
	if (fabs(val) > FLOAT8_MAX)
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("type \"double precision\" value out of range: overflow")));
	if (val != 0.0 && fabs(val) < FLOAT8_MIN)
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("type \"double precision\" value out of range: underflow")));
}

/*
 *		float4in		- converts "num" to float
 *						  restricted syntax:
 *						  {<sp>} [+|-] {digit} [.{digit}] [<exp>]
 *						  where <sp> is a space, digit is 0-9,
 *						  <exp> is "e" or "E" followed by an integer.
 */
Datum
float4in(PG_FUNCTION_ARGS)
{
	char	   *num = PG_GETARG_CSTRING(0);
	char	   *orig_num;
	double		val;
	char	   *endptr;

	/*
	 * endptr points to the first character _after_ the sequence we
	 * recognized as a valid floating point number. orig_num points to
	 * the original input string.
	 */
	orig_num = num;

	/*
	 * Check for an empty-string input to begin with, to avoid
	 * the vagaries of strtod() on different platforms.
	 *
	 * In releases prior to 7.5, we accepted an empty string as valid
	 * input (yielding a float4 of 0). In 7.5, we accept empty
	 * strings, but emit a warning noting that the feature is
	 * deprecated. In 7.6+, the warning should be replaced by an
	 * error.
	 */
	if (*num == '\0')
	{
		ereport(WARNING,
				(errcode(ERRCODE_WARNING_DEPRECATED_FEATURE),
				 errmsg("deprecated input syntax for type real: \"\""),
				 errdetail("This input will be rejected in "
						   "a future release of PostgreSQL.")));
		PG_RETURN_FLOAT4((float4) 0.0);
	}

	/* skip leading whitespace */
	while (*num != '\0' && isspace(*num))
		num++;

	errno = 0;
	val = strtod(num, &endptr);

	if (errno == ERANGE)
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("\"%s\" is out of range for type real",
						orig_num)));

	/* did we not see anything that looks like a double? */
	if (num == endptr)
	{
		/*
		 * C99 requires that strtod() accept NaN and [-]Infinity, but
		 * not all platforms support that yet. Therefore, we check for
		 * these inputs ourselves.
		 */
		if (strncasecmp(num, "NaN", 3) == 0)
		{
			val = NAN;
			endptr = num + 3;
		}
		else if (strncasecmp(num, "Infinity", 8) == 0)
		{
			val = HUGE_VAL;
			endptr = num + 8;
		}
		else if (strncasecmp(num, "-Infinity", 9) == 0)
		{
			val = -HUGE_VAL;
			endptr = num + 9;
		}
		else
			ereport(ERROR,
					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
					 errmsg("invalid input syntax for type real: \"%s\"",
							orig_num)));
	}

	/* skip trailing whitespace */
	while (*endptr != '\0' && isspace(*endptr))
		endptr++;

	/* if there is any junk left at the end of the string, bail out */
	if (*endptr != '\0')
		ereport(ERROR,
				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
				 errmsg("invalid input syntax for type real: \"%s\"",
						orig_num)));

	/*
	 * if we get here, we have a legal double, still need to check to see
	 * if it's a legal float4
	 */
	if (!isinf(val))
		CheckFloat4Val(val);

	PG_RETURN_FLOAT4((float4) val);
}

/*
 *		float4out		- converts a float4 number to a string
 *						  using a standard output format
 */
Datum
float4out(PG_FUNCTION_ARGS)
{
	float4		num = PG_GETARG_FLOAT4(0);
	char	   *ascii = (char *) palloc(MAXFLOATWIDTH + 1);

	if (isnan(num))
		PG_RETURN_CSTRING(strcpy(ascii, "NaN"));

	switch (is_infinite(num))
	{
		case 1:
			strcpy(ascii, "Infinity");
			break;
		case -1:
			strcpy(ascii, "-Infinity");
			break;
		default:
		{
			int ndig = FLT_DIG + extra_float_digits;
			if (ndig < 1)
				ndig = 1;

			sprintf(ascii, "%.*g", ndig, num);
		}
	}

	PG_RETURN_CSTRING(ascii);
}

/*
 *		float4recv			- converts external binary format to float4
 */
Datum
float4recv(PG_FUNCTION_ARGS)
{
	StringInfo	buf = (StringInfo) PG_GETARG_POINTER(0);

	PG_RETURN_FLOAT4(pq_getmsgfloat4(buf));
}

/*
 *		float4send			- converts float4 to binary format
 */
Datum
float4send(PG_FUNCTION_ARGS)
{
	float4		num = PG_GETARG_FLOAT4(0);
	StringInfoData buf;

	pq_begintypsend(&buf);
	pq_sendfloat4(&buf, num);
	PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
}

/*
 *		float8in		- converts "num" to float8
 *						  restricted syntax:
 *						  {<sp>} [+|-] {digit} [.{digit}] [<exp>]
 *						  where <sp> is a space, digit is 0-9,
 *						  <exp> is "e" or "E" followed by an integer.
 */
Datum
float8in(PG_FUNCTION_ARGS)
{
	char	   *num = PG_GETARG_CSTRING(0);
	char	   *orig_num;
	double		val;
	char	   *endptr;

	/*
	 * endptr points to the first character _after_ the sequence we
	 * recognized as a valid floating point number. orig_num points to
	 * the original input string.
	 */
	orig_num = num;

	/*
	 * Check for an empty-string input to begin with, to avoid
	 * the vagaries of strtod() on different platforms.
	 *
	 * In releases prior to 7.5, we accepted an empty string as valid
	 * input (yielding a float8 of 0). In 7.5, we accept empty
	 * strings, but emit a warning noting that the feature is
	 * deprecated. In 7.6+, the warning should be replaced by an
	 * error.
	 */
	if (*num == '\0')
	{
		ereport(WARNING,
				(errcode(ERRCODE_WARNING_DEPRECATED_FEATURE),
				 errmsg("deprecated input syntax for type double precision: \"\""),
				 errdetail("This input will be rejected in "
						   "a future release of PostgreSQL.")));
		PG_RETURN_FLOAT8(0.0);
	}

	/* skip leading whitespace */
	while (*num != '\0' && isspace(*num))
		num++;

	errno = 0;
	val = strtod(num, &endptr);

	if (errno == ERANGE)
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("\"%s\" is out of range for type double precision",
						orig_num)));

	/* did we not see anything that looks like a double? */
	if (num == endptr)
	{
		/*
		 * C99 requires that strtod() accept NaN and [-]Infinity, but
		 * not all platforms support that yet. Therefore, we check for
		 * these inputs ourselves.
		 */
		if (strncasecmp(num, "NaN", 3) == 0)
		{
			val = NAN;
			endptr = num + 3;
		}
		else if (strncasecmp(num, "Infinity", 8) == 0)
		{
			val = HUGE_VAL;
			endptr = num + 8;
		}
		else if (strncasecmp(num, "-Infinity", 9) == 0)
		{
			val = -HUGE_VAL;
			endptr = num + 9;
		}
		else
			ereport(ERROR,
					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
					 errmsg("invalid input syntax for type double precision: \"%s\"",
							orig_num)));
	}

	/* skip trailing whitespace */
	while (*endptr != '\0' && isspace(*endptr))
		endptr++;

	/* if there is any junk left at the end of the string, bail out */
	if (*endptr != '\0')
		ereport(ERROR,
				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
				 errmsg("invalid input syntax for type double precision: \"%s\"",
						orig_num)));

	if (!isinf(val))
		CheckFloat8Val(val);

	PG_RETURN_FLOAT8(val);
}

/*
 *		float8out		- converts float8 number to a string
 *						  using a standard output format
 */
Datum
float8out(PG_FUNCTION_ARGS)
{
	float8		num = PG_GETARG_FLOAT8(0);
	char	   *ascii = (char *) palloc(MAXDOUBLEWIDTH + 1);

	if (isnan(num))
		PG_RETURN_CSTRING(strcpy(ascii, "NaN"));

	switch (is_infinite(num))
	{
		case 1:
			strcpy(ascii, "Infinity");
			break;
		case -1:
			strcpy(ascii, "-Infinity");
			break;
		default:
		{
			int ndig = DBL_DIG + extra_float_digits;
			if (ndig < 1)
				ndig = 1;

			sprintf(ascii, "%.*g", ndig, num);
		}
	}

	PG_RETURN_CSTRING(ascii);
}

/*
 *		float8recv			- converts external binary format to float8
 */
Datum
float8recv(PG_FUNCTION_ARGS)
{
	StringInfo	buf = (StringInfo) PG_GETARG_POINTER(0);

	PG_RETURN_FLOAT8(pq_getmsgfloat8(buf));
}

/*
 *		float8send			- converts float8 to binary format
 */
Datum
float8send(PG_FUNCTION_ARGS)
{
	float8		num = PG_GETARG_FLOAT8(0);
	StringInfoData buf;

	pq_begintypsend(&buf);
	pq_sendfloat8(&buf, num);
	PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
}


/* ========== PUBLIC ROUTINES ========== */


/*
 *		======================
 *		FLOAT4 BASE OPERATIONS
 *		======================
 */

/*
 *		float4abs		- returns |arg1| (absolute value)
 */
Datum
float4abs(PG_FUNCTION_ARGS)
{
	float4		arg1 = PG_GETARG_FLOAT4(0);

	PG_RETURN_FLOAT4((float4) fabs(arg1));
}

/*
 *		float4um		- returns -arg1 (unary minus)
 */
Datum
float4um(PG_FUNCTION_ARGS)
{
	float4		arg1 = PG_GETARG_FLOAT4(0);

	PG_RETURN_FLOAT4((float4) -arg1);
}

Datum
float4up(PG_FUNCTION_ARGS)
{
	float4		arg = PG_GETARG_FLOAT4(0);

	PG_RETURN_FLOAT4(arg);
}

Datum
float4larger(PG_FUNCTION_ARGS)
{
	float4		arg1 = PG_GETARG_FLOAT4(0);
	float4		arg2 = PG_GETARG_FLOAT4(1);
	float4		result;

	if (float4_cmp_internal(arg1, arg2) > 0)
		result = arg1;
	else
		result = arg2;
	PG_RETURN_FLOAT4(result);
}

Datum
float4smaller(PG_FUNCTION_ARGS)
{
	float4		arg1 = PG_GETARG_FLOAT4(0);
	float4		arg2 = PG_GETARG_FLOAT4(1);
	float4		result;

	if (float4_cmp_internal(arg1, arg2) < 0)
		result = arg1;
	else
		result = arg2;
	PG_RETURN_FLOAT4(result);
}

/*
 *		======================
 *		FLOAT8 BASE OPERATIONS
 *		======================
 */

/*
 *		float8abs		- returns |arg1| (absolute value)
 */
Datum
float8abs(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float8		result;

	result = fabs(arg1);

	CheckFloat8Val(result);
	PG_RETURN_FLOAT8(result);
}


/*
 *		float8um		- returns -arg1 (unary minus)
 */
Datum
float8um(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float8		result;

	result = ((arg1 != 0) ? -(arg1) : arg1);

	CheckFloat8Val(result);
	PG_RETURN_FLOAT8(result);
}

Datum
float8up(PG_FUNCTION_ARGS)
{
	float8		arg = PG_GETARG_FLOAT8(0);

	PG_RETURN_FLOAT8(arg);
}

Datum
float8larger(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float8		arg2 = PG_GETARG_FLOAT8(1);
	float8		result;

	if (float8_cmp_internal(arg1, arg2) > 0)
		result = arg1;
	else
		result = arg2;
	PG_RETURN_FLOAT8(result);
}

Datum
float8smaller(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float8		arg2 = PG_GETARG_FLOAT8(1);
	float8		result;

	if (float8_cmp_internal(arg1, arg2) < 0)
		result = arg1;
	else
		result = arg2;
	PG_RETURN_FLOAT8(result);
}


/*
 *		====================
 *		ARITHMETIC OPERATORS
 *		====================
 */

/*
 *		float4pl		- returns arg1 + arg2
 *		float4mi		- returns arg1 - arg2
 *		float4mul		- returns arg1 * arg2
 *		float4div		- returns arg1 / arg2
 */
Datum
float4pl(PG_FUNCTION_ARGS)
{
	float4		arg1 = PG_GETARG_FLOAT4(0);
	float4		arg2 = PG_GETARG_FLOAT4(1);
	double		result;

	result = arg1 + arg2;
	CheckFloat4Val(result);
	PG_RETURN_FLOAT4((float4) result);
}

Datum
float4mi(PG_FUNCTION_ARGS)
{
	float4		arg1 = PG_GETARG_FLOAT4(0);
	float4		arg2 = PG_GETARG_FLOAT4(1);
	double		result;

	result = arg1 - arg2;
	CheckFloat4Val(result);
	PG_RETURN_FLOAT4((float4) result);
}

Datum
float4mul(PG_FUNCTION_ARGS)
{
	float4		arg1 = PG_GETARG_FLOAT4(0);
	float4		arg2 = PG_GETARG_FLOAT4(1);
	double		result;

	result = arg1 * arg2;
	CheckFloat4Val(result);
	PG_RETURN_FLOAT4((float4) result);
}

Datum
float4div(PG_FUNCTION_ARGS)
{
	float4		arg1 = PG_GETARG_FLOAT4(0);
	float4		arg2 = PG_GETARG_FLOAT4(1);
	double		result;

	if (arg2 == 0.0)
		ereport(ERROR,
				(errcode(ERRCODE_DIVISION_BY_ZERO),
				 errmsg("division by zero")));

	/* Do division in float8, then check for overflow */
	result = (float8) arg1 / (float8) arg2;

	CheckFloat4Val(result);
	PG_RETURN_FLOAT4((float4) result);
}

/*
 *		float8pl		- returns arg1 + arg2
 *		float8mi		- returns arg1 - arg2
 *		float8mul		- returns arg1 * arg2
 *		float8div		- returns arg1 / arg2
 */
Datum
float8pl(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float8		arg2 = PG_GETARG_FLOAT8(1);
	float8		result;

	result = arg1 + arg2;

	CheckFloat8Val(result);
	PG_RETURN_FLOAT8(result);
}

Datum
float8mi(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float8		arg2 = PG_GETARG_FLOAT8(1);
	float8		result;

	result = arg1 - arg2;

	CheckFloat8Val(result);
	PG_RETURN_FLOAT8(result);
}

Datum
float8mul(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float8		arg2 = PG_GETARG_FLOAT8(1);
	float8		result;

	result = arg1 * arg2;

	CheckFloat8Val(result);
	PG_RETURN_FLOAT8(result);
}

Datum
float8div(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float8		arg2 = PG_GETARG_FLOAT8(1);
	float8		result;

	if (arg2 == 0.0)
		ereport(ERROR,
				(errcode(ERRCODE_DIVISION_BY_ZERO),
				 errmsg("division by zero")));

	result = arg1 / arg2;

	CheckFloat8Val(result);
	PG_RETURN_FLOAT8(result);
}


/*
 *		====================
 *		COMPARISON OPERATORS
 *		====================
 */

/*
 *		float4{eq,ne,lt,le,gt,ge}		- float4/float4 comparison operations
 */
static int
float4_cmp_internal(float4 a, float4 b)
{
	/*
	 * 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 (isnan(a))
	{
		if (isnan(b))
			return 0;			/* NAN = NAN */
		else
			return 1;			/* NAN > non-NAN */
	}
	else if (isnan(b))
	{
		return -1;				/* non-NAN < NAN */
	}
	else
	{
		if (a > b)
			return 1;
		else if (a < b)
			return -1;
		else
			return 0;
	}
}

Datum
float4eq(PG_FUNCTION_ARGS)
{
	float4		arg1 = PG_GETARG_FLOAT4(0);
	float4		arg2 = PG_GETARG_FLOAT4(1);

	PG_RETURN_BOOL(float4_cmp_internal(arg1, arg2) == 0);
}

Datum
float4ne(PG_FUNCTION_ARGS)
{
	float4		arg1 = PG_GETARG_FLOAT4(0);
	float4		arg2 = PG_GETARG_FLOAT4(1);

	PG_RETURN_BOOL(float4_cmp_internal(arg1, arg2) != 0);
}

Datum
float4lt(PG_FUNCTION_ARGS)
{
	float4		arg1 = PG_GETARG_FLOAT4(0);
	float4		arg2 = PG_GETARG_FLOAT4(1);

	PG_RETURN_BOOL(float4_cmp_internal(arg1, arg2) < 0);
}

Datum
float4le(PG_FUNCTION_ARGS)
{
	float4		arg1 = PG_GETARG_FLOAT4(0);
	float4		arg2 = PG_GETARG_FLOAT4(1);

	PG_RETURN_BOOL(float4_cmp_internal(arg1, arg2) <= 0);
}

Datum
float4gt(PG_FUNCTION_ARGS)
{
	float4		arg1 = PG_GETARG_FLOAT4(0);
	float4		arg2 = PG_GETARG_FLOAT4(1);

	PG_RETURN_BOOL(float4_cmp_internal(arg1, arg2) > 0);
}

Datum
float4ge(PG_FUNCTION_ARGS)
{
	float4		arg1 = PG_GETARG_FLOAT4(0);
	float4		arg2 = PG_GETARG_FLOAT4(1);

	PG_RETURN_BOOL(float4_cmp_internal(arg1, arg2) >= 0);
}

Datum
btfloat4cmp(PG_FUNCTION_ARGS)
{
	float4		arg1 = PG_GETARG_FLOAT4(0);
	float4		arg2 = PG_GETARG_FLOAT4(1);

	PG_RETURN_INT32(float4_cmp_internal(arg1, arg2));
}

/*
 *		float8{eq,ne,lt,le,gt,ge}		- float8/float8 comparison operations
 */
static int
float8_cmp_internal(float8 a, float8 b)
{
	/*
	 * 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 (isnan(a))
	{
		if (isnan(b))
			return 0;			/* NAN = NAN */
		else
			return 1;			/* NAN > non-NAN */
	}
	else if (isnan(b))
	{
		return -1;				/* non-NAN < NAN */
	}
	else
	{
		if (a > b)
			return 1;
		else if (a < b)
			return -1;
		else
			return 0;
	}
}

Datum
float8eq(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float8		arg2 = PG_GETARG_FLOAT8(1);

	PG_RETURN_BOOL(float8_cmp_internal(arg1, arg2) == 0);
}

Datum
float8ne(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float8		arg2 = PG_GETARG_FLOAT8(1);

	PG_RETURN_BOOL(float8_cmp_internal(arg1, arg2) != 0);
}

Datum
float8lt(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float8		arg2 = PG_GETARG_FLOAT8(1);

	PG_RETURN_BOOL(float8_cmp_internal(arg1, arg2) < 0);
}

Datum
float8le(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float8		arg2 = PG_GETARG_FLOAT8(1);

	PG_RETURN_BOOL(float8_cmp_internal(arg1, arg2) <= 0);
}

Datum
float8gt(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float8		arg2 = PG_GETARG_FLOAT8(1);

	PG_RETURN_BOOL(float8_cmp_internal(arg1, arg2) > 0);
}

Datum
float8ge(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float8		arg2 = PG_GETARG_FLOAT8(1);

	PG_RETURN_BOOL(float8_cmp_internal(arg1, arg2) >= 0);
}

Datum
btfloat8cmp(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float8		arg2 = PG_GETARG_FLOAT8(1);

	PG_RETURN_INT32(float8_cmp_internal(arg1, arg2));
}

Datum
btfloat48cmp(PG_FUNCTION_ARGS)
{
	float4		arg1 = PG_GETARG_FLOAT4(0);
	float8		arg2 = PG_GETARG_FLOAT8(1);

	/* widen float4 to float8 and then compare */
	PG_RETURN_INT32(float8_cmp_internal(arg1, arg2));
}

Datum
btfloat84cmp(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float4		arg2 = PG_GETARG_FLOAT4(1);

	/* widen float4 to float8 and then compare */
	PG_RETURN_INT32(float8_cmp_internal(arg1, arg2));
}


/*
 *		===================
 *		CONVERSION ROUTINES
 *		===================
 */

/*
 *		ftod			- converts a float4 number to a float8 number
 */
Datum
ftod(PG_FUNCTION_ARGS)
{
	float4		num = PG_GETARG_FLOAT4(0);

	PG_RETURN_FLOAT8((float8) num);
}


/*
 *		dtof			- converts a float8 number to a float4 number
 */
Datum
dtof(PG_FUNCTION_ARGS)
{
	float8		num = PG_GETARG_FLOAT8(0);

	CheckFloat4Val(num);

	PG_RETURN_FLOAT4((float4) num);
}


/*
 *		dtoi4			- converts a float8 number to an int4 number
 */
Datum
dtoi4(PG_FUNCTION_ARGS)
{
	float8		num = PG_GETARG_FLOAT8(0);
	int32		result;

	if ((num < INT_MIN) || (num > INT_MAX))
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("integer out of range")));

	result = (int32) rint(num);
	PG_RETURN_INT32(result);
}


/*
 *		dtoi2			- converts a float8 number to an int2 number
 */
Datum
dtoi2(PG_FUNCTION_ARGS)
{
	float8		num = PG_GETARG_FLOAT8(0);
	int16		result;

	if ((num < SHRT_MIN) || (num > SHRT_MAX))
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("integer out of range")));

	result = (int16) rint(num);
	PG_RETURN_INT16(result);
}


/*
 *		i4tod			- converts an int4 number to a float8 number
 */
Datum
i4tod(PG_FUNCTION_ARGS)
{
	int32		num = PG_GETARG_INT32(0);
	float8		result;

	result = num;
	PG_RETURN_FLOAT8(result);
}


/*
 *		i2tod			- converts an int2 number to a float8 number
 */
Datum
i2tod(PG_FUNCTION_ARGS)
{
	int16		num = PG_GETARG_INT16(0);
	float8		result;

	result = num;
	PG_RETURN_FLOAT8(result);
}


/*
 *		ftoi4			- converts a float4 number to an int4 number
 */
Datum
ftoi4(PG_FUNCTION_ARGS)
{
	float4		num = PG_GETARG_FLOAT4(0);
	int32		result;

	if ((num < INT_MIN) || (num > INT_MAX))
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("integer out of range")));

	result = (int32) rint(num);
	PG_RETURN_INT32(result);
}


/*
 *		ftoi2			- converts a float4 number to an int2 number
 */
Datum
ftoi2(PG_FUNCTION_ARGS)
{
	float4		num = PG_GETARG_FLOAT4(0);
	int16		result;

	if ((num < SHRT_MIN) || (num > SHRT_MAX))
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("integer out of range")));

	result = (int16) rint(num);
	PG_RETURN_INT16(result);
}


/*
 *		i4tof			- converts an int4 number to a float8 number
 */
Datum
i4tof(PG_FUNCTION_ARGS)
{
	int32		num = PG_GETARG_INT32(0);
	float4		result;

	result = num;
	PG_RETURN_FLOAT4(result);
}


/*
 *		i2tof			- converts an int2 number to a float4 number
 */
Datum
i2tof(PG_FUNCTION_ARGS)
{
	int16		num = PG_GETARG_INT16(0);
	float4		result;

	result = num;
	PG_RETURN_FLOAT4(result);
}


/*
 *		float8_text		- converts a float8 number to a text string
 */
Datum
float8_text(PG_FUNCTION_ARGS)
{
	float8		num = PG_GETARG_FLOAT8(0);
	text	   *result;
	int			len;
	char	   *str;

	str = DatumGetCString(DirectFunctionCall1(float8out,
											  Float8GetDatum(num)));

	len = strlen(str) + VARHDRSZ;

	result = (text *) palloc(len);

	VARATT_SIZEP(result) = len;
	memcpy(VARDATA(result), str, (len - VARHDRSZ));

	pfree(str);

	PG_RETURN_TEXT_P(result);
}


/*
 *		text_float8		- converts a text string to a float8 number
 */
Datum
text_float8(PG_FUNCTION_ARGS)
{
	text	   *string = PG_GETARG_TEXT_P(0);
	Datum		result;
	int			len;
	char	   *str;

	len = (VARSIZE(string) - VARHDRSZ);
	str = palloc(len + 1);
	memcpy(str, VARDATA(string), len);
	*(str + len) = '\0';

	result = DirectFunctionCall1(float8in, CStringGetDatum(str));

	pfree(str);

	PG_RETURN_DATUM(result);
}


/*
 *		float4_text		- converts a float4 number to a text string
 */
Datum
float4_text(PG_FUNCTION_ARGS)
{
	float4		num = PG_GETARG_FLOAT4(0);
	text	   *result;
	int			len;
	char	   *str;

	str = DatumGetCString(DirectFunctionCall1(float4out,
											  Float4GetDatum(num)));

	len = strlen(str) + VARHDRSZ;

	result = (text *) palloc(len);

	VARATT_SIZEP(result) = len;
	memcpy(VARDATA(result), str, (len - VARHDRSZ));

	pfree(str);

	PG_RETURN_TEXT_P(result);
}


/*
 *		text_float4		- converts a text string to a float4 number
 */
Datum
text_float4(PG_FUNCTION_ARGS)
{
	text	   *string = PG_GETARG_TEXT_P(0);
	Datum		result;
	int			len;
	char	   *str;

	len = (VARSIZE(string) - VARHDRSZ);
	str = palloc(len + 1);
	memcpy(str, VARDATA(string), len);
	*(str + len) = '\0';

	result = DirectFunctionCall1(float4in, CStringGetDatum(str));

	pfree(str);

	PG_RETURN_DATUM(result);
}


/*
 *		=======================
 *		RANDOM FLOAT8 OPERATORS
 *		=======================
 */

/*
 *		dround			- returns	ROUND(arg1)
 */
Datum
dround(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float8		result;

	result = rint(arg1);

	PG_RETURN_FLOAT8(result);
}

/*
 *		dceil			- returns the smallest integer greater than or
 *						  equal to the specified float
 */
Datum
dceil(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);

	PG_RETURN_FLOAT8(ceil(arg1));
}

/*
 *		dfloor			- returns the largest integer lesser than or
 *						  equal to the specified float
 */
Datum
dfloor(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);

	PG_RETURN_FLOAT8(floor(arg1));
}

/*
 *		dsign			- returns -1 if the argument is less than 0, 0
 *						  if the argument is equal to 0, and 1 if the
 *						  argument is greater than zero.
 */
Datum
dsign(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float8		result;

	if (arg1 > 0)
		result = 1.0;
	else if (arg1 < 0)
		result = -1.0;
	else
		result = 0.0;

	PG_RETURN_FLOAT8(result);
}

/*
 *		dtrunc			- returns truncation-towards-zero of arg1,
 *						  arg1 >= 0 ... the greatest integer less
 *										than or equal to arg1
 *						  arg1 < 0	... the least integer greater
 *										than or equal to arg1
 */
Datum
dtrunc(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float8		result;

	if (arg1 >= 0)
		result = floor(arg1);
	else
		result = -floor(-arg1);

	PG_RETURN_FLOAT8(result);
}


/*
 *		dsqrt			- returns square root of arg1
 */
Datum
dsqrt(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float8		result;

	if (arg1 < 0)
		ereport(ERROR,
				(errcode(ERRCODE_FLOATING_POINT_EXCEPTION),
				 errmsg("cannot take square root of a negative number")));

	result = sqrt(arg1);

	CheckFloat8Val(result);
	PG_RETURN_FLOAT8(result);
}


/*
 *		dcbrt			- returns cube root of arg1
 */
Datum
dcbrt(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float8		result;

	result = cbrt(arg1);
	PG_RETURN_FLOAT8(result);
}


/*
 *		dpow			- returns pow(arg1,arg2)
 */
Datum
dpow(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float8		arg2 = PG_GETARG_FLOAT8(1);
	float8		result;

	/*
	 * We must check both for errno getting set and for a NaN result, in
	 * order to deal with the vagaries of different platforms...
	 */
	errno = 0;
	result = pow(arg1, arg2);
	if (errno != 0
#ifdef HAVE_FINITE
		|| !finite(result)
#endif
		)
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("result is out of range")));

	CheckFloat8Val(result);
	PG_RETURN_FLOAT8(result);
}


/*
 *		dexp			- returns the exponential function of arg1
 */
Datum
dexp(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float8		result;

	/*
	 * We must check both for errno getting set and for a NaN result, in
	 * order to deal with the vagaries of different platforms. Also, a
	 * zero result implies unreported underflow.
	 */
	errno = 0;
	result = exp(arg1);
	if (errno != 0 || result == 0.0
#ifdef HAVE_FINITE
		|| !finite(result)
#endif
		)
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("result is out of range")));

	CheckFloat8Val(result);
	PG_RETURN_FLOAT8(result);
}


/*
 *		dlog1			- returns the natural logarithm of arg1
 *						  ("dlog" is already a logging routine...)
 */
Datum
dlog1(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float8		result;

	if (arg1 == 0.0)
		ereport(ERROR,
				(errcode(ERRCODE_FLOATING_POINT_EXCEPTION),
				 errmsg("cannot take logarithm of zero")));

	if (arg1 < 0)
		ereport(ERROR,
				(errcode(ERRCODE_FLOATING_POINT_EXCEPTION),
				 errmsg("cannot take logarithm of a negative number")));

	result = log(arg1);

	CheckFloat8Val(result);
	PG_RETURN_FLOAT8(result);
}


/*
 *		dlog10			- returns the base 10 logarithm of arg1
 */
Datum
dlog10(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float8		result;

	if (arg1 == 0.0)
		ereport(ERROR,
				(errcode(ERRCODE_FLOATING_POINT_EXCEPTION),
				 errmsg("cannot take logarithm of zero")));

	if (arg1 < 0)
		ereport(ERROR,
				(errcode(ERRCODE_FLOATING_POINT_EXCEPTION),
				 errmsg("cannot take logarithm of a negative number")));

	result = log10(arg1);

	CheckFloat8Val(result);
	PG_RETURN_FLOAT8(result);
}


/*
 *		dacos			- returns the arccos of arg1 (radians)
 */
Datum
dacos(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float8		result;

	errno = 0;
	result = acos(arg1);
	if (errno != 0
#ifdef HAVE_FINITE
		|| !finite(result)
#endif
		)
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("input is out of range")));

	CheckFloat8Val(result);
	PG_RETURN_FLOAT8(result);
}


/*
 *		dasin			- returns the arcsin of arg1 (radians)
 */
Datum
dasin(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float8		result;

	errno = 0;
	result = asin(arg1);
	if (errno != 0
#ifdef HAVE_FINITE
		|| !finite(result)
#endif
		)
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("input is out of range")));

	CheckFloat8Val(result);
	PG_RETURN_FLOAT8(result);
}


/*
 *		datan			- returns the arctan of arg1 (radians)
 */
Datum
datan(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float8		result;

	errno = 0;
	result = atan(arg1);
	if (errno != 0
#ifdef HAVE_FINITE
		|| !finite(result)
#endif
		)
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("input is out of range")));

	CheckFloat8Val(result);
	PG_RETURN_FLOAT8(result);
}


/*
 *		atan2			- returns the arctan2 of arg1 (radians)
 */
Datum
datan2(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float8		arg2 = PG_GETARG_FLOAT8(1);
	float8		result;

	errno = 0;
	result = atan2(arg1, arg2);
	if (errno != 0
#ifdef HAVE_FINITE
		|| !finite(result)
#endif
		)
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("input is out of range")));

	CheckFloat8Val(result);
	PG_RETURN_FLOAT8(result);
}


/*
 *		dcos			- returns the cosine of arg1 (radians)
 */
Datum
dcos(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float8		result;

	errno = 0;
	result = cos(arg1);
	if (errno != 0
#ifdef HAVE_FINITE
		|| !finite(result)
#endif
		)
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("input is out of range")));

	CheckFloat8Val(result);
	PG_RETURN_FLOAT8(result);
}


/*
 *		dcot			- returns the cotangent of arg1 (radians)
 */
Datum
dcot(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float8		result;

	errno = 0;
	result = tan(arg1);
	if (errno != 0 || result == 0.0
#ifdef HAVE_FINITE
		|| !finite(result)
#endif
		)
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("input is out of range")));

	result = 1.0 / result;
	CheckFloat8Val(result);
	PG_RETURN_FLOAT8(result);
}


/*
 *		dsin			- returns the sine of arg1 (radians)
 */
Datum
dsin(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float8		result;

	errno = 0;
	result = sin(arg1);
	if (errno != 0
#ifdef HAVE_FINITE
		|| !finite(result)
#endif
		)
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("input is out of range")));

	CheckFloat8Val(result);
	PG_RETURN_FLOAT8(result);
}


/*
 *		dtan			- returns the tangent of arg1 (radians)
 */
Datum
dtan(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float8		result;

	errno = 0;
	result = tan(arg1);
	if (errno != 0
#ifdef HAVE_FINITE
		|| !finite(result)
#endif
		)
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("input is out of range")));

	CheckFloat8Val(result);
	PG_RETURN_FLOAT8(result);
}


/*
 *		degrees		- returns degrees converted from radians
 */
Datum
degrees(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float8		result;

	result = arg1 * (180.0 / M_PI);

	CheckFloat8Val(result);
	PG_RETURN_FLOAT8(result);
}


/*
 *		dpi				- returns the constant PI
 */
Datum
dpi(PG_FUNCTION_ARGS)
{
	PG_RETURN_FLOAT8(M_PI);
}


/*
 *		radians		- returns radians converted from degrees
 */
Datum
radians(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float8		result;

	result = arg1 * (M_PI / 180.0);

	CheckFloat8Val(result);
	PG_RETURN_FLOAT8(result);
}


/*
 *		drandom		- returns a random number
 */
Datum
drandom(PG_FUNCTION_ARGS)
{
	float8		result;

	/* result 0.0-1.0 */
	result = ((double) random()) / ((double) MAX_RANDOM_VALUE);

	PG_RETURN_FLOAT8(result);
}


/*
 *		setseed		- set seed for the random number generator
 */
Datum
setseed(PG_FUNCTION_ARGS)
{
	float8		seed = PG_GETARG_FLOAT8(0);
	int			iseed = (int) (seed * MAX_RANDOM_VALUE);

	srandom((unsigned int) iseed);

	PG_RETURN_INT32(iseed);
}



/*
 *		=========================
 *		FLOAT AGGREGATE OPERATORS
 *		=========================
 *
 *		float8_accum	- accumulate for AVG(), STDDEV(), etc
 *		float4_accum	- same, but input data is float4
 *		float8_avg		- produce final result for float AVG()
 *		float8_variance - produce final result for float VARIANCE()
 *		float8_stddev	- produce final result for float STDDEV()
 *
 * The transition datatype for all these aggregates is a 3-element array
 * of float8, holding the values N, sum(X), sum(X*X) in that order.
 *
 * Note that we represent N as a float to avoid having to build a special
 * datatype.  Given a reasonable floating-point implementation, there should
 * be no accuracy loss unless N exceeds 2 ^ 52 or so (by which time the
 * user will have doubtless lost interest anyway...)
 */

static float8 *
check_float8_array(ArrayType *transarray, const char *caller)
{
	/*
	 * We expect the input to be a 3-element float array; verify that. We
	 * don't need to use deconstruct_array() since the array data is just
	 * going to look like a C array of 3 float8 values.
	 */
	if (ARR_NDIM(transarray) != 1 ||
		ARR_DIMS(transarray)[0] != 3 ||
		ARR_ELEMTYPE(transarray) != FLOAT8OID)
		elog(ERROR, "%s: expected 3-element float8 array", caller);
	return (float8 *) ARR_DATA_PTR(transarray);
}

Datum
float8_accum(PG_FUNCTION_ARGS)
{
	ArrayType  *transarray = PG_GETARG_ARRAYTYPE_P(0);
	float8		newval = PG_GETARG_FLOAT8(1);
	float8	   *transvalues;
	float8		N,
				sumX,
				sumX2;
	Datum		transdatums[3];
	ArrayType  *result;

	transvalues = check_float8_array(transarray, "float8_accum");
	N = transvalues[0];
	sumX = transvalues[1];
	sumX2 = transvalues[2];

	N += 1.0;
	sumX += newval;
	sumX2 += newval * newval;

	transdatums[0] = Float8GetDatumFast(N);
	transdatums[1] = Float8GetDatumFast(sumX);
	transdatums[2] = Float8GetDatumFast(sumX2);

	result = construct_array(transdatums, 3,
							 FLOAT8OID,
						 sizeof(float8), false /* float8 byval */ , 'd');

	PG_RETURN_ARRAYTYPE_P(result);
}

Datum
float4_accum(PG_FUNCTION_ARGS)
{
	ArrayType  *transarray = PG_GETARG_ARRAYTYPE_P(0);
	float4		newval4 = PG_GETARG_FLOAT4(1);
	float8	   *transvalues;
	float8		N,
				sumX,
				sumX2,
				newval;
	Datum		transdatums[3];
	ArrayType  *result;

	transvalues = check_float8_array(transarray, "float4_accum");
	N = transvalues[0];
	sumX = transvalues[1];
	sumX2 = transvalues[2];

	/* Do arithmetic in float8 for best accuracy */
	newval = newval4;

	N += 1.0;
	sumX += newval;
	sumX2 += newval * newval;

	transdatums[0] = Float8GetDatumFast(N);
	transdatums[1] = Float8GetDatumFast(sumX);
	transdatums[2] = Float8GetDatumFast(sumX2);

	result = construct_array(transdatums, 3,
							 FLOAT8OID,
						 sizeof(float8), false /* float8 byval */ , 'd');

	PG_RETURN_ARRAYTYPE_P(result);
}

Datum
float8_avg(PG_FUNCTION_ARGS)
{
	ArrayType  *transarray = PG_GETARG_ARRAYTYPE_P(0);
	float8	   *transvalues;
	float8		N,
				sumX;

	transvalues = check_float8_array(transarray, "float8_avg");
	N = transvalues[0];
	sumX = transvalues[1];
	/* ignore sumX2 */

	/* SQL92 defines AVG of no values to be NULL */
	if (N == 0.0)
		PG_RETURN_NULL();

	PG_RETURN_FLOAT8(sumX / N);
}

Datum
float8_variance(PG_FUNCTION_ARGS)
{
	ArrayType  *transarray = PG_GETARG_ARRAYTYPE_P(0);
	float8	   *transvalues;
	float8		N,
				sumX,
				sumX2,
				numerator;

	transvalues = check_float8_array(transarray, "float8_variance");
	N = transvalues[0];
	sumX = transvalues[1];
	sumX2 = transvalues[2];

	/* Sample variance is undefined when N is 0 or 1, so return NULL */
	if (N <= 1.0)
		PG_RETURN_NULL();

	numerator = N * sumX2 - sumX * sumX;

	/* Watch out for roundoff error producing a negative numerator */
	if (numerator <= 0.0)
		PG_RETURN_FLOAT8(0.0);

	PG_RETURN_FLOAT8(numerator / (N * (N - 1.0)));
}

Datum
float8_stddev(PG_FUNCTION_ARGS)
{
	ArrayType  *transarray = PG_GETARG_ARRAYTYPE_P(0);
	float8	   *transvalues;
	float8		N,
				sumX,
				sumX2,
				numerator;

	transvalues = check_float8_array(transarray, "float8_stddev");
	N = transvalues[0];
	sumX = transvalues[1];
	sumX2 = transvalues[2];

	/* Sample stddev is undefined when N is 0 or 1, so return NULL */
	if (N <= 1.0)
		PG_RETURN_NULL();

	numerator = N * sumX2 - sumX * sumX;

	/* Watch out for roundoff error producing a negative numerator */
	if (numerator <= 0.0)
		PG_RETURN_FLOAT8(0.0);

	PG_RETURN_FLOAT8(sqrt(numerator / (N * (N - 1.0))));
}


/*
 *		====================================
 *		MIXED-PRECISION ARITHMETIC OPERATORS
 *		====================================
 */

/*
 *		float48pl		- returns arg1 + arg2
 *		float48mi		- returns arg1 - arg2
 *		float48mul		- returns arg1 * arg2
 *		float48div		- returns arg1 / arg2
 */
Datum
float48pl(PG_FUNCTION_ARGS)
{
	float4		arg1 = PG_GETARG_FLOAT4(0);
	float8		arg2 = PG_GETARG_FLOAT8(1);
	float8		result;

	result = arg1 + arg2;
	CheckFloat8Val(result);
	PG_RETURN_FLOAT8(result);
}

Datum
float48mi(PG_FUNCTION_ARGS)
{
	float4		arg1 = PG_GETARG_FLOAT4(0);
	float8		arg2 = PG_GETARG_FLOAT8(1);
	float8		result;

	result = arg1 - arg2;
	CheckFloat8Val(result);
	PG_RETURN_FLOAT8(result);
}

Datum
float48mul(PG_FUNCTION_ARGS)
{
	float4		arg1 = PG_GETARG_FLOAT4(0);
	float8		arg2 = PG_GETARG_FLOAT8(1);
	float8		result;

	result = arg1 * arg2;
	CheckFloat8Val(result);
	PG_RETURN_FLOAT8(result);
}

Datum
float48div(PG_FUNCTION_ARGS)
{
	float4		arg1 = PG_GETARG_FLOAT4(0);
	float8		arg2 = PG_GETARG_FLOAT8(1);
	float8		result;

	if (arg2 == 0.0)
		ereport(ERROR,
				(errcode(ERRCODE_DIVISION_BY_ZERO),
				 errmsg("division by zero")));

	result = arg1 / arg2;
	CheckFloat8Val(result);
	PG_RETURN_FLOAT8(result);
}

/*
 *		float84pl		- returns arg1 + arg2
 *		float84mi		- returns arg1 - arg2
 *		float84mul		- returns arg1 * arg2
 *		float84div		- returns arg1 / arg2
 */
Datum
float84pl(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float4		arg2 = PG_GETARG_FLOAT4(1);
	float8		result;

	result = arg1 + arg2;

	CheckFloat8Val(result);
	PG_RETURN_FLOAT8(result);
}

Datum
float84mi(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float4		arg2 = PG_GETARG_FLOAT4(1);
	float8		result;

	result = arg1 - arg2;

	CheckFloat8Val(result);
	PG_RETURN_FLOAT8(result);
}

Datum
float84mul(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float4		arg2 = PG_GETARG_FLOAT4(1);
	float8		result;

	result = arg1 * arg2;

	CheckFloat8Val(result);
	PG_RETURN_FLOAT8(result);
}

Datum
float84div(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float4		arg2 = PG_GETARG_FLOAT4(1);
	float8		result;

	if (arg2 == 0.0)
		ereport(ERROR,
				(errcode(ERRCODE_DIVISION_BY_ZERO),
				 errmsg("division by zero")));

	result = arg1 / arg2;

	CheckFloat8Val(result);
	PG_RETURN_FLOAT8(result);
}

/*
 *		====================
 *		COMPARISON OPERATORS
 *		====================
 */

/*
 *		float48{eq,ne,lt,le,gt,ge}		- float4/float8 comparison operations
 */
Datum
float48eq(PG_FUNCTION_ARGS)
{
	float4		arg1 = PG_GETARG_FLOAT4(0);
	float8		arg2 = PG_GETARG_FLOAT8(1);

	PG_RETURN_BOOL(float8_cmp_internal(arg1, arg2) == 0);
}

Datum
float48ne(PG_FUNCTION_ARGS)
{
	float4		arg1 = PG_GETARG_FLOAT4(0);
	float8		arg2 = PG_GETARG_FLOAT8(1);

	PG_RETURN_BOOL(float8_cmp_internal(arg1, arg2) != 0);
}

Datum
float48lt(PG_FUNCTION_ARGS)
{
	float4		arg1 = PG_GETARG_FLOAT4(0);
	float8		arg2 = PG_GETARG_FLOAT8(1);

	PG_RETURN_BOOL(float8_cmp_internal(arg1, arg2) < 0);
}

Datum
float48le(PG_FUNCTION_ARGS)
{
	float4		arg1 = PG_GETARG_FLOAT4(0);
	float8		arg2 = PG_GETARG_FLOAT8(1);

	PG_RETURN_BOOL(float8_cmp_internal(arg1, arg2) <= 0);
}

Datum
float48gt(PG_FUNCTION_ARGS)
{
	float4		arg1 = PG_GETARG_FLOAT4(0);
	float8		arg2 = PG_GETARG_FLOAT8(1);

	PG_RETURN_BOOL(float8_cmp_internal(arg1, arg2) > 0);
}

Datum
float48ge(PG_FUNCTION_ARGS)
{
	float4		arg1 = PG_GETARG_FLOAT4(0);
	float8		arg2 = PG_GETARG_FLOAT8(1);

	PG_RETURN_BOOL(float8_cmp_internal(arg1, arg2) >= 0);
}

/*
 *		float84{eq,ne,lt,le,gt,ge}		- float8/float4 comparison operations
 */
Datum
float84eq(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float4		arg2 = PG_GETARG_FLOAT4(1);

	PG_RETURN_BOOL(float8_cmp_internal(arg1, arg2) == 0);
}

Datum
float84ne(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float4		arg2 = PG_GETARG_FLOAT4(1);

	PG_RETURN_BOOL(float8_cmp_internal(arg1, arg2) != 0);
}

Datum
float84lt(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float4		arg2 = PG_GETARG_FLOAT4(1);

	PG_RETURN_BOOL(float8_cmp_internal(arg1, arg2) < 0);
}

Datum
float84le(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float4		arg2 = PG_GETARG_FLOAT4(1);

	PG_RETURN_BOOL(float8_cmp_internal(arg1, arg2) <= 0);
}

Datum
float84gt(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float4		arg2 = PG_GETARG_FLOAT4(1);

	PG_RETURN_BOOL(float8_cmp_internal(arg1, arg2) > 0);
}

Datum
float84ge(PG_FUNCTION_ARGS)
{
	float8		arg1 = PG_GETARG_FLOAT8(0);
	float4		arg2 = PG_GETARG_FLOAT4(1);

	PG_RETURN_BOOL(float8_cmp_internal(arg1, arg2) >= 0);
}

/* ========== PRIVATE ROUTINES ========== */

#ifndef HAVE_CBRT
static double
cbrt(double x)
{
	int			isneg = (x < 0.0);
	double		tmpres = pow(fabs(x), (double) 1.0 / (double) 3.0);

	return isneg ? -tmpres : tmpres;
}

#endif   /* !HAVE_CBRT */
