ex_numeric.h

#ifndef _EX_NUMERIC_H_
#define _EX_NUMERIC_H_

/*-------------------------------------------------------------------------
 *
 * 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) 1998-2015, PostgreSQL Global Development Group
 *
 * IDENTIFICATION
 *	  src/backend/utils/adt/numeric.c
 *
 *-------------------------------------------------------------------------
 */

/* ----------
 * 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_fast to
 * postpone processing carries.
 *
 * Values of NBASE other than 10000 are considered of historical interest only
 * and are no longer supported in any sense; no mechanism exists for the client
 * to discover the base, so every client supporting binary mode expects the
 * base-10000 format.  If you plan to change this, also note the numeric
 * abbreviation code, which assumes NBASE=10000.
 * ----------
 */

#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 Numeric type as stored on disk.
 *
 * If the high bits of the first word of a NumericChoice (n_header, or
 * n_short.n_header, or n_long.n_sign_dscale) are NUMERIC_SHORT, then the
 * numeric follows the NumericShort format; if they are NUMERIC_POS or
 * NUMERIC_NEG, it follows the NumericLong format.  If they are NUMERIC_NAN,
 * it is a NaN.  We currently always store a NaN using just two bytes (i.e.
 * only n_header), but previous releases used only the NumericLong format,
 * so we might find 4-byte NaNs on disk if a database has been migrated using
 * pg_upgrade.  In either case, when the high bits indicate a NaN, the
 * remaining bits are never examined.  Currently, we always initialize these
 * to zero, but it might be possible to use them for some other purpose in
 * the future.
 *
 * In the NumericShort format, the remaining 14 bits of the header word
 * (n_short.n_header) are allocated as follows: 1 for sign (positive or
 * negative), 6 for dynamic scale, and 7 for weight.  In practice, most
 * commonly-encountered values can be represented this way.
 *
 * In the NumericLong format, the remaining 14 bits of the header word
 * (n_long.n_sign_dscale) represent the display scale; and the weight is
 * stored separately in n_weight.
 *
 * NOTE: by convention, values in the packed form have been stripped of
 * all leading and trailing zero digits (where a "digit" is of base NBASE).
 * In particular, if the value is zero, there will be no digits at all!
 * The weight is arbitrary in that case, but we normally set it to zero.
 */

struct NumericShort
{
	uint16		n_header;		/* Sign + display scale + weight */
	NumericDigit n_data[FLEXIBLE_ARRAY_MEMBER]; /* Digits */
};

struct NumericLong
{
	uint16		n_sign_dscale;	/* Sign + display scale */
	int16		n_weight;		/* Weight of 1st digit	*/
	NumericDigit n_data[FLEXIBLE_ARRAY_MEMBER]; /* Digits */
};

union NumericChoice
{
	uint16		n_header;		/* Header word */
	struct NumericLong n_long;	/* Long form (4-byte header) */
	struct NumericShort n_short;	/* Short form (2-byte header) */
};

struct NumericData
{
	int32		vl_len_;		/* varlena header (do not touch directly!) */
	union NumericChoice choice; /* choice of format */
};


/*
 * Interpretation of high bits.
 */

#define NUMERIC_SIGN_MASK	0xC000
#define NUMERIC_POS			0x0000
#define NUMERIC_NEG			0x4000
#define NUMERIC_SHORT		0x8000
#define NUMERIC_NAN			0xC000

#define NUMERIC_FLAGBITS(n) ((n)->choice.n_header & NUMERIC_SIGN_MASK)
#define NUMERIC_IS_NAN(n)		(NUMERIC_FLAGBITS(n) == NUMERIC_NAN)
#define NUMERIC_IS_SHORT(n)		(NUMERIC_FLAGBITS(n) == NUMERIC_SHORT)

#define NUMERIC_HDRSZ	(VARHDRSZ + sizeof(uint16) + sizeof(int16))
#define NUMERIC_HDRSZ_SHORT (VARHDRSZ + sizeof(uint16))

/*
 * If the flag bits are NUMERIC_SHORT or NUMERIC_NAN, we want the short header;
 * otherwise, we want the long one.  Instead of testing against each value, we
 * can just look at the high bit, for a slight efficiency gain.
 */
#define NUMERIC_HEADER_IS_SHORT(n)	(((n)->choice.n_header & 0x8000) != 0)
#define NUMERIC_HEADER_SIZE(n) \
	(VARHDRSZ + sizeof(uint16) + \
	 (NUMERIC_HEADER_IS_SHORT(n) ? 0 : sizeof(int16)))

/*
 * Short format definitions.
 */

#define NUMERIC_SHORT_SIGN_MASK			0x2000
#define NUMERIC_SHORT_DSCALE_MASK		0x1F80
#define NUMERIC_SHORT_DSCALE_SHIFT		7
#define NUMERIC_SHORT_DSCALE_MAX		\
	(NUMERIC_SHORT_DSCALE_MASK >> NUMERIC_SHORT_DSCALE_SHIFT)
#define NUMERIC_SHORT_WEIGHT_SIGN_MASK	0x0040
#define NUMERIC_SHORT_WEIGHT_MASK		0x003F
#define NUMERIC_SHORT_WEIGHT_MAX		NUMERIC_SHORT_WEIGHT_MASK
#define NUMERIC_SHORT_WEIGHT_MIN		(-(NUMERIC_SHORT_WEIGHT_MASK+1))

/*
 * Extract sign, display scale, weight.
 */

#define NUMERIC_DSCALE_MASK			0x3FFF

#define NUMERIC_SIGN(n) \
	(NUMERIC_IS_SHORT(n) ? \
		(((n)->choice.n_short.n_header & NUMERIC_SHORT_SIGN_MASK) ? \
		NUMERIC_NEG : NUMERIC_POS) : NUMERIC_FLAGBITS(n))
#define NUMERIC_DSCALE(n)	(NUMERIC_HEADER_IS_SHORT((n)) ? \
	((n)->choice.n_short.n_header & NUMERIC_SHORT_DSCALE_MASK) \
		>> NUMERIC_SHORT_DSCALE_SHIFT \
	: ((n)->choice.n_long.n_sign_dscale & NUMERIC_DSCALE_MASK))
#define NUMERIC_WEIGHT(n)	(NUMERIC_HEADER_IS_SHORT((n)) ? \
	(((n)->choice.n_short.n_header & NUMERIC_SHORT_WEIGHT_SIGN_MASK ? \
		~NUMERIC_SHORT_WEIGHT_MASK : 0) \
	 | ((n)->choice.n_short.n_header & NUMERIC_SHORT_WEIGHT_MASK)) \
	: ((n)->choice.n_long.n_weight))

#define NUMERIC_DIGITS(num) (NUMERIC_HEADER_IS_SHORT(num) ? \
	(num)->choice.n_short.n_data : (num)->choice.n_long.n_data)
#define NUMERIC_NDIGITS(num) \
	((VARSIZE(num) - NUMERIC_HEADER_SIZE(num)) / sizeof(NumericDigit))

#endif /* #define _EX_NUMERIC_H_ */