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numeric_in accepts exponents; numeric to int4 rounds; float4/8 to numeric
authorTom Lane <tgl@sss.pgh.pa.us>
Tue, 18 Jan 2000 03:44:41 +0000 (03:44 +0000)
committerTom Lane <tgl@sss.pgh.pa.us>
Tue, 18 Jan 2000 03:44:41 +0000 (03:44 +0000)
is considerably more robust and accurate than it used to be.
Also, get rid of numeric's private allocation freelist, which is no longer
a win since Jan rewrote palloc.

src/backend/utils/adt/numeric.c

index 46e67f3..20b2a00 100644 (file)
@@ -5,18 +5,19 @@
  *
  *     1998 Jan Wieck
  *
- * $Header: /cvsroot/pgsql/src/backend/utils/adt/numeric.c,v 1.22 2000/01/15 23:42:49 tgl Exp $
+ * $Header: /cvsroot/pgsql/src/backend/utils/adt/numeric.c,v 1.23 2000/01/18 03:44:41 tgl Exp $
  *
  * ----------
  */
 
+#include "postgres.h"
+
 #include <ctype.h>
 #include <float.h>
 #include <math.h>
 #include <errno.h>
 #include <sys/types.h>
 
-#include "postgres.h"
 #include "utils/builtins.h"
 #include "utils/numeric.h"
 
@@ -32,9 +33,6 @@
  * Local definitions
  * ----------
  */
-#define NUMERIC_MIN_BUFSIZE            2048
-#define NUMERIC_MAX_FREEBUFS   20
-
 #ifndef MIN
 #define MIN(a,b) (((a)<(b)) ? (a) : (b))
 #endif
  * 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 NumericDigitBuf
-{
-       struct NumericDigitBuf *prev;
-       struct NumericDigitBuf *next;
-       int                     size;
-} NumericDigitBuf;
-
 typedef struct NumericVar
 {
        int                     ndigits;                /* number of digits in digits[] - can be 0! */
@@ -77,7 +82,7 @@ typedef struct NumericVar
        int                     rscale;                 /* result scale */
        int                     dscale;                 /* display scale */
        int                     sign;                   /* NUMERIC_POS, NUMERIC_NEG, or NUMERIC_NAN */
-       NumericDigitBuf *buf;
+       NumericDigit *buf;                      /* start of palloc'd space for digits[] */
        NumericDigit *digits;           /* decimal digits */
 } NumericVar;
 
@@ -86,9 +91,6 @@ typedef struct NumericVar
  * Local data
  * ----------
  */
-static NumericDigitBuf *digitbuf_freelist = NULL;
-static NumericDigitBuf *digitbuf_usedlist = NULL;
-static int     digitbuf_nfree = 0;
 static int     global_rscale = NUMERIC_MIN_RESULT_SCALE;
 
 /* ----------
@@ -120,22 +122,28 @@ static NumericVar const_nan =
 #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
 
-static NumericDigitBuf *digitbuf_alloc(int size);
-static void digitbuf_free(NumericDigitBuf *buf);
+#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 free_allvars(void);
+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);
@@ -224,11 +232,8 @@ numeric_in(char *str, int dummy, int32 typmod)
 char *
 numeric_out(Numeric num)
 {
-       char       *str;
-       char       *cp;
        NumericVar      x;
-       int                     i;
-       int                     d;
+       char       *str;
 
        /* ----------
         * Handle NULL
@@ -256,92 +261,10 @@ numeric_out(Numeric num)
        init_var(&x);
        set_var_from_num(num, &x);
 
-       /* ----------
-        * Check if we must round up before printing the value and
-        * do so.
-        * ----------
-        */
-       i = x.dscale + x.weight + 1;
-       if (i >= 0 && x.ndigits > i)
-       {
-               int             carry = (x.digits[i] > 4) ? 1 : 0;
-
-               x.ndigits = i;
-
-               while (carry)
-               {
-                       carry += x.digits[--i];
-                       x.digits[i] = carry % 10;
-                       carry /= 10;
-               }
-
-               if (i < 0)
-               {
-                       Assert(i == -1);        /* better not have added more than 1 digit */
-                       Assert(x.digits > (NumericDigit *) (x.buf + 1));
-                       x.digits--;
-                       x.ndigits++;
-                       x.weight++;
-               }
-       }
-       else
-               x.ndigits = MAX(0, MIN(i, x.ndigits));
-
-       /* ----------
-        * Allocate space for the result
-        * ----------
-        */
-       str = palloc(MAX(0, x.dscale) + MAX(0, x.weight) + 4);
-       cp = str;
-
-       /* ----------
-        * Output a dash for negative values
-        * ----------
-        */
-       if (x.sign == NUMERIC_NEG)
-               *cp++ = '-';
-
-       /* ----------
-        * Output all digits before the decimal point
-        * ----------
-        */
-       i = MAX(x.weight, 0);
-       d = 0;
-
-       while (i >= 0)
-       {
-               if (i <= x.weight && d < x.ndigits)
-                       *cp++ = x.digits[d++] + '0';
-               else
-                       *cp++ = '0';
-               i--;
-       }
-
-       /* ----------
-        * If requested, output a decimal point and all the digits
-        * that follow it.
-        * ----------
-        */
-       if (x.dscale > 0)
-       {
-               *cp++ = '.';
-               while (i >= -x.dscale)
-               {
-                       if (i <= x.weight && d < x.ndigits)
-                               *cp++ = x.digits[d++] + '0';
-                       else
-                               *cp++ = '0';
-                       i--;
-               }
-       }
+       str = get_str_from_var(&x, x.dscale);
 
-       /* ----------
-        * Get rid of the variable, terminate the string and return it
-        * ----------
-        */
        free_var(&x);
 
-       *cp = '\0';
        return str;
 }
 
@@ -551,11 +474,8 @@ numeric_round(Numeric num, int32 scale)
         * ----------
         */
        if (scale < 0 || scale > NUMERIC_MAX_DISPLAY_SCALE)
-       {
-               free_allvars();
                elog(ERROR, "illegal numeric scale %d - must be between 0 and %d",
                         scale, NUMERIC_MAX_DISPLAY_SCALE);
-       }
 
        /* ----------
         * Let numeric() and in turn apply_typmod() do the job
@@ -598,11 +518,8 @@ numeric_trunc(Numeric num, int32 scale)
         * ----------
         */
        if (scale < 0 || scale > NUMERIC_MAX_DISPLAY_SCALE)
-       {
-               free_allvars();
                elog(ERROR, "illegal numeric scale %d - must be between 0 and %d",
                         scale, NUMERIC_MAX_DISPLAY_SCALE);
-       }
 
        /* ----------
         * Unpack the argument and truncate it
@@ -1702,7 +1619,8 @@ int4_numeric(int32 val)
 int32
 numeric_int4(Numeric num)
 {
-       char       *tmp;
+       NumericVar      x;
+       char       *str;
        int32           result;
 
        if (num == NULL)
@@ -1711,9 +1629,19 @@ numeric_int4(Numeric num)
        if (NUMERIC_IS_NAN(num))
                return 0;
 
-       tmp = numeric_out(num);
-       result = int4in(tmp);
-       pfree(tmp);
+       /* ----------
+        * 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 = int4in(str);
+       pfree(str);
 
        return result;
 }
@@ -1724,7 +1652,7 @@ float8_numeric(float64 val)
 {
        Numeric         res;
        NumericVar      result;
-       char            buf[512];
+       char            buf[DBL_DIG + 100];
 
        if (val == NULL)
                return NULL;
@@ -1732,9 +1660,10 @@ float8_numeric(float64 val)
        if (isnan(*val))
                return make_result(&const_nan);
 
+       sprintf(buf, "%.*g", DBL_DIG, *val);
+
        init_var(&result);
 
-       sprintf(buf, "%f", *val);
        set_var_from_str(buf, &result);
        res = make_result(&result);
 
@@ -1744,7 +1673,6 @@ float8_numeric(float64 val)
 }
 
 
-
 float64
 numeric_float8(Numeric num)
 {
@@ -1774,7 +1702,7 @@ float4_numeric(float32 val)
 {
        Numeric         res;
        NumericVar      result;
-       char       *tmp;
+       char            buf[FLT_DIG + 100];
 
        if (val == NULL)
                return NULL;
@@ -1782,14 +1710,14 @@ float4_numeric(float32 val)
        if (isnan(*val))
                return make_result(&const_nan);
 
+       sprintf(buf, "%.*g", FLT_DIG, *val);
+
        init_var(&result);
 
-       tmp = float4out(val);
-       set_var_from_str(tmp, &result);
+       set_var_from_str(buf, &result);
        res = make_result(&result);
 
        free_var(&result);
-       pfree(tmp);
 
        return res;
 }
@@ -1899,225 +1827,54 @@ dump_var(char *str, NumericVar *var)
 
 
 /* ----------
- * digitbuf_alloc() -
- *
- *     All variables used in the arithmetic functions hold some base
- *     information (sign, scales etc.) and a digit buffer for the
- *     value itself. All the variable level functions are written in
- *     a style that makes it possible to give one and the same variable
- *     as argument and result destination.
+ * alloc_var() -
  *
- *     The two functions below manage unused buffers in a free list
- *     as a try to reduce the number of malloc()/free() calls.
- * ----------
- */
-static NumericDigitBuf *
-digitbuf_alloc(int size)
-{
-       NumericDigitBuf *buf;
-       int                     asize;
-
-       /* ----------
-        * Lookup the free list if there is a digit buffer of
-        * the required size available
-        * ----------
-        */
-       for (buf = digitbuf_freelist; buf != NULL; buf = buf->next)
-       {
-               if (buf->size < size)
-                       continue;
-
-               /* ----------
-                * We found a free buffer that is big enough - remove it from
-                * the free list
-                * ----------
-                */
-               if (buf->prev == NULL)
-               {
-                       digitbuf_freelist = buf->next;
-                       if (buf->next != NULL)
-                               buf->next->prev = NULL;
-               }
-               else
-               {
-                       buf->prev->next = buf->next;
-                       if (buf->next != NULL)
-                               buf->next->prev = buf->prev;
-               }
-               digitbuf_nfree--;
-
-               /* ----------
-                * Put it onto the used list
-                * ----------
-                */
-               buf->prev = NULL;
-               buf->next = digitbuf_usedlist;
-               if (digitbuf_usedlist != NULL)
-                       digitbuf_usedlist->prev = buf;
-               digitbuf_usedlist = buf;
-
-               /* ----------
-                * Return this buffer
-                * ----------
-                */
-               return buf;
-       }
-
-       /* ----------
-        * There is no free buffer big enough - allocate a new one
-        * ----------
-        */
-       for (asize = NUMERIC_MIN_BUFSIZE; asize < size; asize *= 2);
-       buf = (NumericDigitBuf *) malloc(sizeof(NumericDigitBuf) + asize);
-       buf->size = asize;
-
-       /* ----------
-        * Put it onto the used list
-        * ----------
-        */
-       buf->prev = NULL;
-       buf->next = digitbuf_usedlist;
-       if (digitbuf_usedlist != NULL)
-               digitbuf_usedlist->prev = buf;
-       digitbuf_usedlist = buf;
-
-       /* ----------
-        * Return the new buffer
-        * ----------
-        */
-       return buf;
-}
-
-
-/* ----------
- * digitbuf_free() -
+ *     Allocate a digit buffer of ndigits digits (plus a spare digit for rounding)
  * ----------
  */
 static void
-digitbuf_free(NumericDigitBuf *buf)
+alloc_var(NumericVar *var, int ndigits)
 {
-       NumericDigitBuf *smallest;
-
-       if (buf == NULL)
-               return;
-
-       /* ----------
-        * Remove the buffer from the used list
-        * ----------
-        */
-       if (buf->prev == NULL)
-       {
-               digitbuf_usedlist = buf->next;
-               if (buf->next != NULL)
-                       buf->next->prev = NULL;
-       }
-       else
-       {
-               buf->prev->next = buf->next;
-               if (buf->next != NULL)
-                       buf->next->prev = buf->prev;
-       }
-
-       /* ----------
-        * Put it onto the free list
-        * ----------
-        */
-       if (digitbuf_freelist != NULL)
-               digitbuf_freelist->prev = buf;
-       buf->prev = NULL;
-       buf->next = digitbuf_freelist;
-       digitbuf_freelist = buf;
-       digitbuf_nfree++;
-
-       /* ----------
-        * Check for maximum free buffers
-        * ----------
-        */
-       if (digitbuf_nfree <= NUMERIC_MAX_FREEBUFS)
-               return;
-
-       /* ----------
-        * Have too many free buffers - destroy the smallest one
-        * ----------
-        */
-       smallest = buf;
-       for (buf = digitbuf_freelist->next; buf != NULL; buf = buf->next)
-       {
-               if (buf->size < smallest->size)
-                       smallest = buf;
-       }
-
-       /* ----------
-        * Remove it from the free list
-        * ----------
-        */
-       if (smallest->prev == NULL)
-       {
-               digitbuf_freelist = smallest->next;
-               if (smallest->next != NULL)
-                       smallest->next->prev = NULL;
-       }
-       else
-       {
-               smallest->prev->next = smallest->next;
-               if (smallest->next != NULL)
-                       smallest->next->prev = smallest->prev;
-       }
-       digitbuf_nfree--;
-
-       /* ----------
-        * And destroy it
-        * ----------
-        */
-       free(smallest);
+       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 pool
+ *     Return the digit buffer of a variable to the free pool
  * ----------
  */
 static void
 free_var(NumericVar *var)
 {
-       if (var->buf != NULL)
-       {
-               digitbuf_free(var->buf);
-               var->buf = NULL;
-               var->digits = NULL;
-       }
+       digitbuf_free(var->buf);
+       var->buf = NULL;
+       var->digits = NULL;
        var->sign = NUMERIC_NAN;
 }
 
 
 /* ----------
- * free_allvars() -
- *
- *     Put all the currently used buffers back into the pool.
+ * zero_var() -
  *
- *     Warning: the variables currently holding the buffers aren't
- *     cleaned! This function should only be used directly before
- *     a call to elog(ERROR,...) or if it is totally impossible that
- *     any other call to free_var() will occur. None of the variable
- *     level functions should call it if it might return later without
- *     an error.
+ *     Set a variable to ZERO.
+ *     Note: rscale and dscale are not touched.
  * ----------
  */
 static void
-free_allvars(void)
-{
-       NumericDigitBuf *buf;
-       NumericDigitBuf *next;
-
-       buf = digitbuf_usedlist;
-       while (buf != NULL)
-       {
-               next = buf->next;
-               digitbuf_free(buf);
-               buf = next;
-       }
+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... */
 }
 
 
@@ -2132,7 +1889,7 @@ set_var_from_str(char *str, NumericVar *dest)
 {
        char       *cp = str;
        bool            have_dp = FALSE;
-       int                     i = 1;
+       int                     i = 0;
 
        while (*cp)
        {
@@ -2141,29 +1898,13 @@ set_var_from_str(char *str, NumericVar *dest)
                cp++;
        }
 
-       digitbuf_free(dest->buf);
-
-       dest->buf = digitbuf_alloc(strlen(cp) + 2);
-       dest->digits = (NumericDigit *) (dest->buf) + sizeof(NumericDigitBuf);
-       dest->digits[0] = 0;
-       dest->weight = 0;
+       alloc_var(dest, strlen(cp));
+       dest->weight = -1;
        dest->dscale = 0;
+       dest->sign = NUMERIC_POS;
 
        switch (*cp)
        {
-               case '0':
-               case '1':
-               case '2':
-               case '3':
-               case '4':
-               case '5':
-               case '6':
-               case '7':
-               case '8':
-               case '9':
-                       dest->sign = NUMERIC_POS;
-                       break;
-
                case '+':
                        dest->sign = NUMERIC_POS;
                        cp++;
@@ -2173,92 +1914,76 @@ set_var_from_str(char *str, NumericVar *dest)
                        dest->sign = NUMERIC_NEG;
                        cp++;
                        break;
-
-               case '.':
-                       dest->sign = NUMERIC_POS;
-                       have_dp = TRUE;
-                       cp++;
-                       break;
-
-               default:
-                       free_allvars();
-                       elog(ERROR, "Bad numeric input format '%s'", str);
        }
 
        if (*cp == '.')
        {
-               if (have_dp)
-               {
-                       free_allvars();
-                       elog(ERROR, "Bad numeric input format '%s'", str);
-               }
-
                have_dp = TRUE;
                cp++;
        }
 
-       if (*cp < '0' && *cp > '9')
-       {
-               free_allvars();
+       if (! isdigit(*cp))
                elog(ERROR, "Bad numeric input format '%s'", str);
-       }
 
        while (*cp)
        {
-               if (isspace(*cp))
-                       break;
-
-               if (*cp == 'e' || *cp == 'E')
-                       break;
-
-               switch (*cp)
+               if (isdigit(*cp))
                {
-                       case '0':
-                       case '1':
-                       case '2':
-                       case '3':
-                       case '4':
-                       case '5':
-                       case '6':
-                       case '7':
-                       case '8':
-                       case '9':
-                               dest->digits[i++] = *cp++ - '0';
-                               if (!have_dp)
-                                       dest->weight++;
-                               else
-                                       dest->dscale++;
-                               break;
-
-                       case '.':
-                               if (have_dp)
-                               {
-                                       free_allvars();
-                                       elog(ERROR, "Bad numeric input format '%s'", str);
-                               }
-                               have_dp = TRUE;
-                               cp++;
-                               break;
-
-                       default:
-                               free_allvars();
+                       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')
        {
-               /* XXX Should handle ...Ennn */
-               elog(ERROR, "Bad numeric input format '%s'", str);
+               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(*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;
 }
@@ -2279,23 +2004,15 @@ set_var_from_num(Numeric num, NumericVar *dest)
 
        n = num->varlen - NUMERIC_HDRSZ; /* number of digit-pairs in packed fmt */
 
-       digitbuf_free(dest->buf);
-       dest->buf = digitbuf_alloc(n * 2 + 2);
-
-       digit = ((NumericDigit *) (dest->buf)) + sizeof(NumericDigitBuf);
-
-       /* We always leave an extra high-order digit pair for carry! */
-       *digit++ = 0;
-       *digit++ = 0;
-
-       dest->digits = digit;
-       dest->ndigits = n * 2;
+       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];
@@ -2314,19 +2031,122 @@ set_var_from_num(Numeric num, NumericVar *dest)
 static void
 set_var_from_var(NumericVar *value, NumericVar *dest)
 {
-       NumericDigitBuf *newbuf;
-       NumericDigit *newdigits;
-
-       /* XXX shouldn't we provide a spare digit for rounding here? */
+       NumericDigit *newbuf;
 
-       newbuf = digitbuf_alloc(value->ndigits);
-       newdigits = ((NumericDigit *) newbuf) + sizeof(NumericDigitBuf);
-       memcpy(newdigits, value->digits, value->ndigits);
+       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 = newdigits;
+       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;
 }
 
 
@@ -2445,7 +2265,7 @@ apply_typmod(NumericVar *var, int32 typmod)
                if (i < 0)
                {
                        Assert(i == -1);        /* better not have added more than 1 digit */
-                       Assert(var->digits > (NumericDigit *) (var->buf + 1));
+                       Assert(var->digits > var->buf);
                        var->digits--;
                        var->ndigits++;
                        var->weight++;
@@ -2476,12 +2296,9 @@ apply_typmod(NumericVar *var, int32 typmod)
                }
                
                if (tweight >= maxweight && i < var->ndigits)
-               {
-                       free_allvars();
                        elog(ERROR, "overflow on numeric "
                                 "ABS(value) >= 10^%d for field with precision %d scale %d",
                                 tweight, precision, scale);
-               }
        }
 
        var->rscale = scale;
@@ -2567,15 +2384,9 @@ add_var(NumericVar *var1, NumericVar *var2, NumericVar *result)
                                                                                                 * result = ZERO
                                                                                                 * ----------
                                                                                                 */
-                                       digitbuf_free(result->buf);
-                                       result->buf = digitbuf_alloc(0);
-                                       result->ndigits = 0;
-                                       result->digits = ((NumericDigit *) (result->buf)) +
-                                               sizeof(NumericDigitBuf);
-                                       result->weight = 0;
+                                       zero_var(result);
                                        result->rscale = MAX(var1->rscale, var2->rscale);
                                        result->dscale = MAX(var1->dscale, var2->dscale);
-                                       result->sign = NUMERIC_POS;
                                        break;
 
                                case 1: /* ----------
@@ -2614,15 +2425,9 @@ add_var(NumericVar *var1, NumericVar *var2, NumericVar *result)
                                                                                                 * result = ZERO
                                                                                                 * ----------
                                                                                                 */
-                                       digitbuf_free(result->buf);
-                                       result->buf = digitbuf_alloc(0);
-                                       result->ndigits = 0;
-                                       result->digits = ((NumericDigit *) (result->buf)) +
-                                               sizeof(NumericDigitBuf);
-                                       result->weight = 0;
+                                       zero_var(result);
                                        result->rscale = MAX(var1->rscale, var2->rscale);
                                        result->dscale = MAX(var1->dscale, var2->dscale);
-                                       result->sign = NUMERIC_POS;
                                        break;
 
                                case 1: /* ----------
@@ -2698,15 +2503,9 @@ sub_var(NumericVar *var1, NumericVar *var2, NumericVar *result)
                                                                                                 * result = ZERO
                                                                                                 * ----------
                                                                                                 */
-                                       digitbuf_free(result->buf);
-                                       result->buf = digitbuf_alloc(0);
-                                       result->ndigits = 0;
-                                       result->digits = ((NumericDigit *) (result->buf)) +
-                                               sizeof(NumericDigitBuf);
-                                       result->weight = 0;
+                                       zero_var(result);
                                        result->rscale = MAX(var1->rscale, var2->rscale);
                                        result->dscale = MAX(var1->dscale, var2->dscale);
-                                       result->sign = NUMERIC_POS;
                                        break;
 
                                case 1: /* ----------
@@ -2745,15 +2544,9 @@ sub_var(NumericVar *var1, NumericVar *var2, NumericVar *result)
                                                                                                 * result = ZERO
                                                                                                 * ----------
                                                                                                 */
-                                       digitbuf_free(result->buf);
-                                       result->buf = digitbuf_alloc(0);
-                                       result->ndigits = 0;
-                                       result->digits = ((NumericDigit *) (result->buf)) +
-                                               sizeof(NumericDigitBuf);
-                                       result->weight = 0;
+                                       zero_var(result);
                                        result->rscale = MAX(var1->rscale, var2->rscale);
                                        result->dscale = MAX(var1->dscale, var2->dscale);
-                                       result->sign = NUMERIC_POS;
                                        break;
 
                                case 1: /* ----------
@@ -2799,7 +2592,7 @@ sub_var(NumericVar *var1, NumericVar *var2, NumericVar *result)
 static void
 mul_var(NumericVar *var1, NumericVar *var2, NumericVar *result)
 {
-       NumericDigitBuf *res_buf;
+       NumericDigit *res_buf;
        NumericDigit *res_digits;
        int                     res_ndigits;
        int                     res_weight;
@@ -2818,7 +2611,7 @@ mul_var(NumericVar *var1, NumericVar *var2, NumericVar *result)
                res_sign = NUMERIC_NEG;
 
        res_buf = digitbuf_alloc(res_ndigits);
-       res_digits = ((NumericDigit *) res_buf) + sizeof(NumericDigitBuf);
+       res_digits = res_buf;
        memset(res_digits, 0, res_ndigits);
 
        ri = res_ndigits;
@@ -2907,10 +2700,7 @@ div_var(NumericVar *var1, NumericVar *var2, NumericVar *result)
         */
        ndigits_tmp = var2->ndigits + 1;
        if (ndigits_tmp == 1)
-       {
-               free_allvars();
                elog(ERROR, "division by zero on numeric");
-       }
 
        /* ----------
         * Determine the result sign, weight and number of digits to calculate
@@ -2922,6 +2712,8 @@ div_var(NumericVar *var1, NumericVar *var2, NumericVar *result)
                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
@@ -2929,13 +2721,8 @@ div_var(NumericVar *var1, NumericVar *var2, NumericVar *result)
         */
        if (var1->ndigits == 0)
        {
-               digitbuf_free(result->buf);
-               result->buf = digitbuf_alloc(0);
-               result->digits = ((NumericDigit *) (result->buf)) + sizeof(NumericDigitBuf);
-               result->ndigits = 0;
-               result->weight = 0;
+               zero_var(result);
                result->rscale = global_rscale;
-               result->sign = NUMERIC_POS;
                return;
        }
 
@@ -2947,7 +2734,6 @@ div_var(NumericVar *var1, NumericVar *var2, NumericVar *result)
        for (i = 1; i < 10; i++)
                init_var(&divisor[i]);
 
-
        /* ----------
         * Make a copy of the divisor which has one leading zero digit
         * ----------
@@ -2956,8 +2742,7 @@ div_var(NumericVar *var1, NumericVar *var2, NumericVar *result)
        divisor[1].rscale = var2->ndigits;
        divisor[1].sign = NUMERIC_POS;
        divisor[1].buf = digitbuf_alloc(ndigits_tmp);
-       divisor[1].digits = ((NumericDigit *) (divisor[1].buf)) +
-               sizeof(NumericDigitBuf);
+       divisor[1].digits = divisor[1].buf;
        divisor[1].digits[0] = 0;
        memcpy(&(divisor[1].digits[1]), var2->digits, ndigits_tmp - 1);
 
@@ -2970,7 +2755,7 @@ div_var(NumericVar *var1, NumericVar *var2, NumericVar *result)
        dividend.rscale = var1->ndigits;
        dividend.sign = NUMERIC_POS;
        dividend.buf = digitbuf_alloc(var1->ndigits);
-       dividend.digits = ((NumericDigit *) (dividend.buf)) + sizeof(NumericDigitBuf);
+       dividend.digits = dividend.buf;
        memcpy(dividend.digits, var1->digits, var1->ndigits);
 
        /* ----------
@@ -2979,7 +2764,7 @@ div_var(NumericVar *var1, NumericVar *var2, NumericVar *result)
         */
        digitbuf_free(result->buf);
        result->buf = digitbuf_alloc(res_ndigits + 2);
-       res_digits = ((NumericDigit *) (result->buf)) + sizeof(NumericDigitBuf);
+       res_digits = result->buf;
        result->digits = res_digits;
        result->ndigits = res_ndigits;
        result->weight = res_weight;
@@ -2997,7 +2782,7 @@ div_var(NumericVar *var1, NumericVar *var2, NumericVar *result)
        weight_tmp = 1;
        rscale_tmp = divisor[1].rscale;
 
-       for (ri = 0; ri < res_ndigits + 1; ri++)
+       for (ri = 0; ri <= res_ndigits; ri++)
        {
                first_have = first_have * 10;
                if (first_nextdigit >= 0 && first_nextdigit < dividend.ndigits)
@@ -3017,8 +2802,7 @@ div_var(NumericVar *var1, NumericVar *var2, NumericVar *result)
 
                                memcpy(&divisor[guess], &divisor[1], sizeof(NumericVar));
                                divisor[guess].buf = digitbuf_alloc(divisor[guess].ndigits);
-                               divisor[guess].digits = ((NumericDigit *) (divisor[guess].buf) +
-                                                                                sizeof(NumericDigitBuf));
+                               divisor[guess].digits = divisor[guess].buf;
                                for (i = divisor[1].ndigits - 1; i >= 0; i--)
                                {
                                        sum += divisor[1].digits[i] * guess;
@@ -3212,10 +2996,7 @@ sqrt_var(NumericVar *arg, NumericVar *result)
        }
 
        if (stat < 0)
-       {
-               free_allvars();
                elog(ERROR, "math error on numeric - cannot compute SQRT of negative value");
-       }
 
        init_var(&tmp_arg);
        init_var(&tmp_val);
@@ -3230,7 +3011,7 @@ sqrt_var(NumericVar *arg, NumericVar *result)
         */
        digitbuf_free(result->buf);
        result->buf = digitbuf_alloc(1);
-       result->digits = ((NumericDigit *) (result->buf)) + sizeof(NumericDigitBuf);
+       result->digits = result->buf;
        result->digits[0] = tmp_arg.digits[0] / 2;
        if (result->digits[0] == 0)
                result->digits[0] = 1;
@@ -3302,10 +3083,7 @@ exp_var(NumericVar *arg, NumericVar *result)
                if (d < x.ndigits)
                        global_rscale += x.digits[d];
                if (global_rscale >= 1000)
-               {
-                       free_allvars();
                        elog(ERROR, "argument for EXP() too big");
-               }
        }
 
        global_rscale = global_rscale / 2 + save_global_rscale + 8;
@@ -3372,10 +3150,7 @@ ln_var(NumericVar *arg, NumericVar *result)
        int                     save_global_rscale;
 
        if (cmp_var(arg, &const_zero) <= 0)
-       {
-               free_allvars();
                elog(ERROR, "math error on numeric - cannot compute LN of value <= zero");
-       }
 
        save_global_rscale = global_rscale;
        global_rscale += 8;
@@ -3572,7 +3347,7 @@ cmp_abs(NumericVar *var1, NumericVar *var2)
 static void
 add_abs(NumericVar *var1, NumericVar *var2, NumericVar *result)
 {
-       NumericDigitBuf *res_buf;
+       NumericDigit *res_buf;
        NumericDigit *res_digits;
        int                     res_ndigits;
        int                     res_weight;
@@ -3587,9 +3362,11 @@ add_abs(NumericVar *var1, NumericVar *var2, NumericVar *result)
        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 = ((NumericDigit *) res_buf) + sizeof(NumericDigitBuf);
+       res_digits = res_buf;
 
        i1 = res_rscale + var1->weight + 1;
        i2 = res_rscale + var2->weight + 1;
@@ -3641,7 +3418,7 @@ add_abs(NumericVar *var1, NumericVar *var2, NumericVar *result)
 static void
 sub_abs(NumericVar *var1, NumericVar *var2, NumericVar *result)
 {
-       NumericDigitBuf *res_buf;
+       NumericDigit *res_buf;
        NumericDigit *res_digits;
        int                     res_ndigits;
        int                     res_weight;
@@ -3656,9 +3433,11 @@ sub_abs(NumericVar *var1, NumericVar *var2, NumericVar *result)
        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 = ((NumericDigit *) res_buf) + sizeof(NumericDigitBuf);
+       res_digits = res_buf;
 
        i1 = res_rscale + var1->weight + 1;
        i2 = res_rscale + var2->weight + 1;