Reimplement NUMERIC datatype using base-10000 arithmetic; also improve

some of the algorithms for higher functions.  I see about a factor of ten
speedup on the 'numeric' regression test, but it's unlikely that that test
is representative of real-world applications.
initdb forced due to change of on-disk representation for NUMERIC.

doc/src/sgml/release.sgml

 <!--
-$Header: /cvsroot/pgsql/doc/src/sgml/release.sgml,v 1.185 2003/02/05 17:41:32 tgl Exp $
+$Header: /cvsroot/pgsql/doc/src/sgml/release.sgml,v 1.186 2003/03/21 01:58:04 tgl Exp $
 -->
 
 <appendix id="release">
@@ -24,6 +24,7 @@ CDATA means the content is "SGML-free", so you can write without
 worries about funny characters.
 -->
 <literallayout><![CDATA[
+Reimplementation of NUMERIC datatype for more speed
 New regular expression package, many more regexp features (most of Perl5)
 Can now do EXPLAIN ... EXECUTE to see plan used for a prepared query
 Explicit JOINs no longer constrain query plan, unless JOIN_COLLAPSE_LIMIT = 1

src/include/catalog/catversion.h

@@ -37,7 +37,7 @@
  * Portions Copyright (c) 1996-2002, PostgreSQL Global Development Group
  * Portions Copyright (c) 1994, Regents of the University of California
  *
- * $Id: catversion.h,v 1.181 2003/03/20 03:34:56 momjian Exp $
+ * $Id: catversion.h,v 1.182 2003/03/21 01:58:04 tgl Exp $
  *
  *-------------------------------------------------------------------------
  */
@@ -53,6 +53,6 @@
  */
 
 /*							yyyymmddN */
-#define CATALOG_VERSION_NO	200303191
+#define CATALOG_VERSION_NO	200303201
 
 #endif

src/include/utils/numeric.h

-/* ----------
+/*-------------------------------------------------------------------------
+ *
  * numeric.h
+ *	  Definitions for the exact numeric data type of Postgres
  *
- *	Definitions for the exact numeric data type of Postgres
+ * Original coding 1998, Jan Wieck.  Heavily revised 2003, Tom Lane.
  *
- *	1998 Jan Wieck
+ * Copyright (c) 1998-2003, PostgreSQL Global Development Group
  *
- * $Id: numeric.h,v 1.16 2002/10/02 19:21:26 tgl Exp $
+ * $Id: numeric.h,v 1.17 2003/03/21 01:58:05 tgl Exp $
  *
- * ----------
+ *-------------------------------------------------------------------------
  */
-
 #ifndef _PG_NUMERIC_H_
 #define _PG_NUMERIC_H_
 
@@ -34,12 +35,6 @@
  */
 #define NUMERIC_MIN_SIG_DIGITS		16
 
-/*
- * Standard number of extra digits carried internally while doing
- * inexact calculations.
- */
-#define NUMERIC_EXTRA_DIGITS		4
-
 
 /*
  * Sign values and macros to deal with packing/unpacking n_sign_dscale
@@ -51,30 +46,29 @@
 #define NUMERIC_DSCALE_MASK 0x3FFF
 #define NUMERIC_SIGN(n)		((n)->n_sign_dscale & NUMERIC_SIGN_MASK)
 #define NUMERIC_DSCALE(n)	((n)->n_sign_dscale & NUMERIC_DSCALE_MASK)
-#define NUMERIC_IS_NAN(n)	(NUMERIC_SIGN(n) != NUMERIC_POS &&			\
-								NUMERIC_SIGN(n) != NUMERIC_NEG)
+#define NUMERIC_IS_NAN(n)	(NUMERIC_SIGN(n) != NUMERIC_POS &&	\
+							 NUMERIC_SIGN(n) != NUMERIC_NEG)
 
 
 /*
  * The Numeric data type stored in the database
  *
  * NOTE: by convention, values in the packed form have been stripped of
- * all leading and trailing zeroes (except there will be a trailing zero
- * in the last byte, if the number of digits is odd).  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.
+ * 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.
  */
 typedef struct NumericData
 {
-	int32		varlen;			/* Variable size		*/
+	int32		varlen;			/* Variable size (std varlena header) */
 	int16		n_weight;		/* Weight of 1st digit	*/
-	uint16		n_rscale;		/* Result scale			*/
 	uint16		n_sign_dscale;	/* Sign + display scale */
-	unsigned char n_data[1];	/* Digit data (2 decimal digits/byte) */
+	char		n_data[1];		/* Digits (really array of NumericDigit) */
 } NumericData;
+
 typedef NumericData *Numeric;
 
-#define NUMERIC_HDRSZ	(sizeof(int32) + sizeof(uint16) * 3)
+#define NUMERIC_HDRSZ	(sizeof(int32) + sizeof(int16) + sizeof(uint16))
 
 
 /*

src/test/regress/expected/aggregates.out

@@ -2,15 +2,15 @@
 -- AGGREGATES
 --
 SELECT avg(four) AS avg_1 FROM onek;
-        avg_1        
----------------------
- 1.50000000000000000
+       avg_1        
+--------------------
+ 1.5000000000000000
 (1 row)
 
 SELECT avg(a) AS avg_32 FROM aggtest WHERE a < 100;
-       avg_32       
---------------------
- 32.666666666666667
+       avg_32        
+---------------------
+ 32.6666666666666667
 (1 row)
 
 -- In 7.1, avg(float4) is computed using float8 arithmetic.
@@ -120,9 +120,9 @@ group by ten order by ten;
 (10 rows)
 
 SELECT newavg(four) AS avg_1 FROM onek;
-        avg_1        
----------------------
- 1.50000000000000000
+       avg_1        
+--------------------
+ 1.5000000000000000
 (1 row)
 
 SELECT newsum(four) AS sum_1500 FROM onek;

src/test/regress/expected/numeric.out

@@ -665,9 +665,9 @@ SELECT t1.id1, t1.result, t2.expected
 -- ******************************
 -- numeric AVG used to fail on some platforms
 SELECT AVG(val) FROM num_data;
-         avg          
-----------------------
- -13430913.5922423207
+          avg           
+------------------------
+ -13430913.592242320700
 (1 row)
 
 -- Check for appropriate rounding and overflow