numeric.c

PostgreSQL7.4.6 for Linux

/*-------------------------------------------------------------------------
 *
 * numeric.c
 *	  An exact numeric data type for the Postgres database system
 *
 * Original coding 1998, Jan Wieck.  Heavily revised 2003, Tom Lane.
 *
 * Many of the algorithmic ideas are borrowed from David M. Smith's "FM"
 * multiple-precision math library, most recently published as Algorithm
 * 786: Multiple-Precision Complex Arithmetic and Functions, ACM
 * Transactions on Mathematical Software, Vol. 24, No. 4, December 1998,
 * pages 359-367.
 *
 * Copyright (c) 1998-2003, PostgreSQL Global Development Group
 *
 * IDENTIFICATION
 *	  $Header: /cvsroot/pgsql/src/backend/utils/adt/numeric.c,v 1.67 2003/09/29 00:05:25 petere Exp $
 *
 *-------------------------------------------------------------------------
 */

#include "postgres.h"

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

#include "catalog/pg_type.h"
#include "libpq/pqformat.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
 *
 * Numeric values are represented in a base-NBASE floating point format.
 * Each "digit" ranges from 0 to NBASE-1.  The type NumericDigit is signed
 * and wide enough to store a digit.  We assume that NBASE*NBASE can fit in
 * an int.	Although the purely calculational routines could handle any even
 * NBASE that's less than sqrt(INT_MAX), in practice we are only interested
 * in NBASE a power of ten, so that I/O conversions and decimal rounding
 * are easy.  Also, it's actually more efficient if NBASE is rather less than
 * sqrt(INT_MAX), so that there is "headroom" for mul_var and div_var to
 * postpone processing carries.
 * ----------
 */

#if 0
#define NBASE		10
#define HALF_NBASE	5
#define DEC_DIGITS	1			/* decimal digits per NBASE digit */
#define MUL_GUARD_DIGITS	4	/* these are measured in NBASE digits */
#define DIV_GUARD_DIGITS	8

typedef signed char NumericDigit;
#endif

#if 0
#define NBASE		100
#define HALF_NBASE	50
#define DEC_DIGITS	2			/* decimal digits per NBASE digit */
#define MUL_GUARD_DIGITS	3	/* these are measured in NBASE digits */
#define DIV_GUARD_DIGITS	6

typedef signed char NumericDigit;
#endif

#if 1
#define NBASE		10000
#define HALF_NBASE	5000
#define DEC_DIGITS	4			/* decimal digits per NBASE digit */
#define MUL_GUARD_DIGITS	2	/* these are measured in NBASE digits */
#define DIV_GUARD_DIGITS	4

typedef int16 NumericDigit;
#endif


/* ----------
 * The value represented by a NumericVar is determined by the sign, weight,
 * ndigits, and digits[] array.
 * Note: the first digit of a NumericVar's value is assumed to be multiplied
 * by NBASE ** weight.	Another way to say it is that there are weight+1
 * digits before the decimal point.  It is possible to have weight < 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 digit 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.
 * (There is no such extra space in a numeric value stored in the database,
 * only in a NumericVar in memory.)
 *
 * 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.
 *
 * dscale, or display scale, is the nominal precision expressed as number
 * of digits after the decimal point (it must always be >= 0 at present).
 * dscale may be more than the number of physically stored fractional digits,
 * implying that we have suppressed storage of significant trailing zeroes.
 * It should never be less than the number of stored digits, since that would
 * imply hiding digits that are present.  NOTE that dscale is always expressed
 * in *decimal* digits, and so it may correspond to a fractional number of
 * base-NBASE digits --- divide by DEC_DIGITS to convert to NBASE digits.
 *
 * rscale, or result scale, is the target precision for a computation.
 * Like dscale it is expressed as number of *decimal* digits after the decimal
 * point, and is always >= 0 at present.
 * Note that rscale is not stored in variables --- it's figured on-the-fly
 * from the dscales of the inputs.
 *
 * 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 struct NumericVar
{
	int			ndigits;		/* # of digits in digits[] - can be 0! */
	int			weight;			/* weight of first digit */
	int			sign;			/* NUMERIC_POS, NUMERIC_NEG, or
								 * NUMERIC_NAN */
	int			dscale;			/* display scale */
	NumericDigit *buf;			/* start of palloc'd space for digits[] */
	NumericDigit *digits;		/* base-NBASE digits */
} NumericVar;


/* ----------
 * Some preinitialized constants
 * ----------
 */
static NumericDigit const_zero_data[1] = {0};
static NumericVar const_zero =
{0, 0, NUMERIC_POS, 0, NULL, const_zero_data};

static NumericDigit const_one_data[1] = {1};
static NumericVar const_one =
{1, 0, NUMERIC_POS, 0, NULL, const_one_data};

static NumericDigit const_two_data[1] = {2};
static NumericVar const_two =
{1, 0, NUMERIC_POS, 0, NULL, const_two_data};

#if DEC_DIGITS == 4
static NumericDigit const_zero_point_five_data[1] = {5000};

#elif DEC_DIGITS == 2
static NumericDigit const_zero_point_five_data[1] = {50};

#elif DEC_DIGITS == 1
static NumericDigit const_zero_point_five_data[1] = {5};
#endif
static NumericVar const_zero_point_five =
{1, -1, NUMERIC_POS, 1, NULL, const_zero_point_five_data};

#if DEC_DIGITS == 4
static NumericDigit const_zero_point_nine_data[1] = {9000};

#elif DEC_DIGITS == 2
static NumericDigit const_zero_point_nine_data[1] = {90};

#elif DEC_DIGITS == 1
static NumericDigit const_zero_point_nine_data[1] = {9};
#endif
static NumericVar const_zero_point_nine =
{1, -1, NUMERIC_POS, 1, NULL, const_zero_point_nine_data};

#if DEC_DIGITS == 4
static NumericDigit const_zero_point_01_data[1] = {100};
static NumericVar const_zero_point_01 =
{1, -1, NUMERIC_POS, 2, NULL, const_zero_point_01_data};

#elif DEC_DIGITS == 2
static NumericDigit const_zero_point_01_data[1] = {1};
static NumericVar const_zero_point_01 =
{1, -1, NUMERIC_POS, 2, NULL, const_zero_point_01_data};

#elif DEC_DIGITS == 1
static NumericDigit const_zero_point_01_data[1] = {1};
static NumericVar const_zero_point_01 =
{1, -2, NUMERIC_POS, 2, NULL, const_zero_point_01_data};
#endif

#if DEC_DIGITS == 4
static NumericDigit const_one_point_one_data[2] = {1, 1000};

#elif DEC_DIGITS == 2
static NumericDigit const_one_point_one_data[2] = {1, 10};

#elif DEC_DIGITS == 1
static NumericDigit const_one_point_one_data[2] = {1, 1};
#endif
static NumericVar const_one_point_one =
{2, 0, NUMERIC_POS, 1, NULL, const_one_point_one_data};

static NumericVar const_nan =
{0, 0, NUMERIC_NAN, 0, NULL, NULL};

#if DEC_DIGITS == 4
static const int round_powers[4] = {0, 1000, 100, 10};
#endif


/* ----------
 * Local functions
 * ----------
 */

#ifdef NUMERIC_DEBUG
static void dump_numeric(const char *str, Numeric num);
static void dump_var(const char *str, NumericVar *var);

#else
#define dump_numeric(s,n)
#define dump_var(s,v)
#endif

#define digitbuf_alloc(ndigits)  \
	((NumericDigit *) palloc((ndigits) * sizeof(NumericDigit)))
#define digitbuf_free(buf)	\
	do { \
		 if ((buf) != NULL) \
			 pfree(buf); \
	} while (0)

#define init_var(v)		MemSetAligned(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(const 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 bool numericvar_to_int8(NumericVar *var, int64 *result);
static void int8_to_numericvar(int64 val, NumericVar *var);
static double numeric_to_double_no_overflow(Numeric num);
static double numericvar_to_double_no_overflow(NumericVar *var);

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,
		int rscale);
static void div_var(NumericVar *var1, NumericVar *var2, NumericVar *result,
		int rscale);
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, int rscale);
static void exp_var(NumericVar *arg, NumericVar *result, int rscale);
static void exp_var_internal(NumericVar *arg, NumericVar *result, int rscale);
static void ln_var(NumericVar *arg, NumericVar *result, int rscale);
static void log_var(NumericVar *base, NumericVar *num, NumericVar *result);
static void power_var(NumericVar *base, NumericVar *exp, NumericVar *result);
static void power_var_int(NumericVar *base, int exp, NumericVar *result,
			  int rscale);

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);
static void round_var(NumericVar *var, int rscale);
static void trunc_var(NumericVar *var, int rscale);
static void strip_var(NumericVar *var);


/* ----------------------------------------------------------------------
 *
 * 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 (strcasecmp(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_recv			- converts external binary format to numeric
 *
 * External format is a sequence of int16's:
 * ndigits, weight, sign, dscale, NumericDigits.
 */
Datum
numeric_recv(PG_FUNCTION_ARGS)
{
	StringInfo	buf = (StringInfo) PG_GETARG_POINTER(0);
	NumericVar	value;
	Numeric		res;
	int			len,
				i;

	init_var(&value);

	len = (uint16) pq_getmsgint(buf, sizeof(uint16));
	if (len < 0 || len > NUMERIC_MAX_PRECISION + NUMERIC_MAX_RESULT_SCALE)
		ereport(ERROR,
				(errcode(ERRCODE_INVALID_BINARY_REPRESENTATION),
				 errmsg("invalid length in external \"numeric\" value")));

	alloc_var(&value, len);

	value.weight = (int16) pq_getmsgint(buf, sizeof(int16));
	value.sign = (uint16) pq_getmsgint(buf, sizeof(uint16));
	if (!(value.sign == NUMERIC_POS ||
		  value.sign == NUMERIC_NEG ||
		  value.sign == NUMERIC_NAN))
		ereport(ERROR,
				(errcode(ERRCODE_INVALID_BINARY_REPRESENTATION),
				 errmsg("invalid sign in external \"numeric\" value")));

	value.dscale = (uint16) pq_getmsgint(buf, sizeof(uint16));
	for (i = 0; i < len; i++)
	{
		NumericDigit d = pq_getmsgint(buf, sizeof(NumericDigit));

		if (d < 0 || d >= NBASE)
			ereport(ERROR,
					(errcode(ERRCODE_INVALID_BINARY_REPRESENTATION),
					 errmsg("invalid digit in external \"numeric\" value")));
		value.digits[i] = d;
	}

	res = make_result(&value);
	free_var(&value);

	PG_RETURN_NUMERIC(res);
}

/*
 *		numeric_send			- converts numeric to binary format
 */
Datum
numeric_send(PG_FUNCTION_ARGS)
{
	Numeric		num = PG_GETARG_NUMERIC(0);
	NumericVar	x;
	StringInfoData buf;
	int			i;

	init_var(&x);
	set_var_from_num(num, &x);

	pq_begintypsend(&buf);

	pq_sendint(&buf, x.ndigits, sizeof(int16));
	pq_sendint(&buf, x.weight, sizeof(int16));
	pq_sendint(&buf, x.sign, sizeof(int16));
	pq_sendint(&buf, x.dscale, sizeof(int16));
	for (i = 0; i < x.ndigits; i++)
		pq_sendint(&buf, x.digits[i], sizeof(NumericDigit));

	free_var(&x);

	PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
}


/*
 * numeric() -
 *
 *	This is a special function called by the Postgres database system
 *	before a value is stored in a tuple's 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			ddigits;
	int			maxdigits;
	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;
	maxdigits = precision - scale;

	/*
	 * If the number is certainly in bounds and due to the target scale no
	 * rounding could be necessary, just make a copy of the input and
	 * modify its scale fields.  (Note we assume the existing dscale is
	 * honest...)
	 */
	ddigits = (num->n_weight + 1) * DEC_DIGITS;
	if (ddigits <= maxdigits && scale >= NUMERIC_DSCALE(num))
	{
		new = (Numeric) palloc(num->varlen);
		memcpy(new, num, num->varlen);
		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);