*
* 1998 Jan Wieck
*
- * $Header: /cvsroot/pgsql/src/backend/utils/adt/numeric.c,v 1.21 2000/01/05 18:23:50 momjian Exp $
+ * $Header: /cvsroot/pgsql/src/backend/utils/adt/numeric.c,v 1.22 2000/01/15 23:42:49 tgl Exp $
*
* ----------
*/
/* ----------
* Local data types
+ *
+ * Note: the first digit of a NumericVar's value is assumed to be multiplied
+ * by 10 ** weight. Another way to say it is that there are weight+1 digits
+ * before the decimal point. It is possible to have weight < 0.
+ *
+ * The value represented by a NumericVar is determined by the sign, weight,
+ * ndigits, and digits[] array. The rscale and dscale are carried along,
+ * 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.)
* ----------
*/
typedef unsigned char NumericDigit;
typedef struct NumericVar
{
- int ndigits;
- int weight;
- int rscale;
- int dscale;
- int sign;
+ int ndigits; /* number of digits in digits[] - can be 0! */
+ int weight; /* weight of first digit */
+ int rscale; /* result scale */
+ int dscale; /* display scale */
+ int sign; /* NUMERIC_POS, NUMERIC_NEG, or NUMERIC_NAN */
NumericDigitBuf *buf;
- NumericDigit *digits;
+ NumericDigit *digits; /* decimal digits */
} NumericVar;
* ----------
*/
if (num == NULL)
- {
- str = palloc(5);
- strcpy(str, "NULL");
- return str;
- }
+ return pstrdup("NULL");
/* ----------
* Handle NaN
* ----------
*/
if (NUMERIC_IS_NAN(num))
- {
- str = palloc(4);
- strcpy(str, "NaN");
- return str;
- }
+ return pstrdup("NaN");
/* ----------
- * Get the number in the variable format
+ * 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);
/* ----------
- * Allocate space for the result
- * ----------
- */
- str = palloc(x.dscale + MAX(0, x.weight) + 5);
- cp = str;
-
- /* ----------
- * Output a dash for negative values
- * ----------
- */
- if (x.sign == NUMERIC_NEG)
- *cp++ = '-';
-
- /* ----------
* Check if we must round up before printing the value and
* do so.
* ----------
*/
- if (x.dscale < x.rscale && (x.dscale + x.weight + 1) < x.ndigits)
+ i = x.dscale + x.weight + 1;
+ if (i >= 0 && x.ndigits > i)
{
- int j;
- int carry;
+ int carry = (x.digits[i] > 4) ? 1 : 0;
- j = x.dscale + x.weight + 1;
- carry = (x.digits[j] > 4) ? 1 : 0;
+ x.ndigits = i;
while (carry)
{
- j--;
- carry += x.digits[j];
- x.digits[j] = carry % 10;
+ carry += x.digits[--i];
+ x.digits[i] = carry % 10;
carry /= 10;
}
- if (j < 0)
+
+ 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
/* ----------
* If the number is in bounds and due to the present result scale
- * no rounding could be necessary, make a copy of the input and
- * modify its header fields.
+ * no rounding could be necessary, just make a copy of the input
+ * and modify its scale fields.
* ----------
*/
if (num->n_weight < maxweight && scale >= num->n_rscale)
memcpy(new, num, num->varlen);
new->n_rscale = scale;
new->n_sign_dscale = NUMERIC_SIGN(new) |
- ((uint16) scale & ~NUMERIC_SIGN_MASK);
+ ((uint16) scale & NUMERIC_DSCALE_MASK);
return new;
}
/* ----------
* The packed format is known to be totally zero digit trimmed
- * allways. So we can identify a ZERO by the fact that there
+ * always. So we can identify a ZERO by the fact that there
* are no digits at all.
* ----------
*/
arg.dscale = scale;
arg.ndigits = MIN(arg.ndigits, MAX(0, arg.weight + scale + 1));
- while (arg.ndigits > 0 && arg.digits[arg.ndigits - 1] == 0)
- arg.ndigits--;
/* ----------
* Return the truncated result
/* ----------------------------------------------------------------------
*
- * Comparision functions
+ * Comparison functions
*
* ----------------------------------------------------------------------
*/
* The minimum and maximum scales are compile time options from
* numeric.h):
*
- * DR = MIN(MAX(D1 + D2, MIN_DISPLAY_SCALE))
+ * DR = MIN(MAX(D1 + D2, MIN_DISPLAY_SCALE), MAX_DISPLAY_SCALE)
* SR = MIN(MAX(MAX(S1 + S2, MIN_RESULT_SCALE), DR + 4), MAX_RESULT_SCALE)
*
* By default, any result is computed with a minimum of 34 digits
if (*cp == 'e' || *cp == 'E')
{
- /* Handle ...Ennn */
+ /* XXX Should handle ...Ennn */
+ elog(ERROR, "Bad numeric input format '%s'", str);
}
while (dest->ndigits > 0 && *(dest->digits) == 0)
int i;
int n;
- n = num->varlen - NUMERIC_HDRSZ;
+ 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;
for (i = 0; i < n; i++)
{
- *digit++ = (num->n_data[i] >> 4) & 0x0f;
- *digit++ = num->n_data[i] & 0x0f;
+ unsigned char digitpair = num->n_data[i];
+ *digit++ = (digitpair >> 4) & 0x0f;
+ *digit++ = digitpair & 0x0f;
}
}
NumericDigitBuf *newbuf;
NumericDigit *newdigits;
+ /* XXX shouldn't we provide a spare digit for rounding here? */
+
newbuf = digitbuf_alloc(value->ndigits);
newdigits = ((NumericDigit *) newbuf) + sizeof(NumericDigitBuf);
memcpy(newdigits, value->digits, value->ndigits);
* make_result() -
*
* Create the packed db numeric format in palloc()'d memory from
- * a variable.
+ * a variable. The var's rscale determines the number of digits kept.
* ----------
*/
static Numeric
{
Numeric result;
NumericDigit *digit = var->digits;
- int n;
int weight = var->weight;
int sign = var->sign;
+ int n;
int i,
j;
n = MAX(0, MIN(var->ndigits, var->weight + var->rscale + 1));
+ /* truncate leading zeroes */
while (n > 0 && *digit == 0)
{
digit++;
weight--;
n--;
}
+ /* truncate trailing zeroes */
while (n > 0 && digit[n - 1] == 0)
n--;
+ /* If zero result, force to weight=0 and positive sign */
if (n == 0)
{
weight = 0;
result->varlen = NUMERIC_HDRSZ + (n + 1) / 2;
result->n_weight = weight;
result->n_rscale = var->rscale;
- result->n_sign_dscale = sign | ((uint16) (var->dscale) & ~NUMERIC_SIGN_MASK);
+ result->n_sign_dscale = sign |
+ ((uint16) var->dscale & NUMERIC_DSCALE_MASK);
i = 0;
j = 0;
while (j < n)
{
- result->n_data[i] = digit[j++] << 4;
+ unsigned char digitpair = digit[j++] << 4;
if (j < n)
- result->n_data[i] |= digit[j++];
- i++;
+ digitpair |= digit[j++];
+ result->n_data[i++] = digitpair;
}
dump_numeric("make_result()", result);
int maxweight;
int i;
+ /* Do nothing if we have a default typmod (-1) */
if (typmod < (int32) (VARHDRSZ))
return;
scale = typmod & 0xffff;
maxweight = precision - scale;
- if (var->weight >= maxweight)
- {
- free_allvars();
- elog(ERROR, "overflow on numeric "
- "ABS(value) >= 10^%d for field with precision %d scale %d",
- var->weight, precision, scale);
- }
-
+ /* Round to target scale */
i = scale + var->weight + 1;
if (i >= 0 && var->ndigits > i)
{
- long carry = (var->digits[i] > 4) ? 1 : 0;
+ int carry = (var->digits[i] > 4) ? 1 : 0;
var->ndigits = i;
+
while (carry)
{
carry += var->digits[--i];
if (i < 0)
{
+ Assert(i == -1); /* better not have added more than 1 digit */
+ Assert(var->digits > (NumericDigit *) (var->buf + 1));
var->digits--;
var->ndigits++;
var->weight++;
var->ndigits = MAX(0, MIN(i, var->ndigits));
/* ----------
- * Check for overflow again - rounding could have raised the
- * weight.
+ * Check for overflow - note we can't do this before rounding,
+ * because rounding could raise the weight. Also note that the
+ * var's weight could be inflated by leading zeroes, which will
+ * be stripped before storage but perhaps might not have been yet.
+ * In any case, we must recognize a true zero, whose weight doesn't
+ * mean anything.
* ----------
*/
if (var->weight >= maxweight)
{
- free_allvars();
- elog(ERROR, "overflow on numeric "
- "ABS(value) >= 10^%d for field with precision %d scale %d",
- var->weight, precision, scale);
+ /* Determine true weight; and check for all-zero result */
+ int tweight = var->weight;
+
+ for (i = 0; i < var->ndigits; i++)
+ {
+ if (var->digits[i])
+ break;
+ tweight--;
+ }
+
+ 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;
result->ndigits = ri + 1;
if (ri == res_ndigits + 1)
{
- long carry = (res_digits[ri] > 4) ? 1 : 0;
+ int carry = (res_digits[ri] > 4) ? 1 : 0;
result->ndigits = ri;
res_digits[ri] = 0;
*
* 1998 Jan Wieck
*
- * $Header: /cvsroot/pgsql/src/include/utils/numeric.h,v 1.7 1999/07/14 01:20:30 momjian Exp $
+ * $Header: /cvsroot/pgsql/src/include/utils/numeric.h,v 1.8 2000/01/15 23:42:48 tgl Exp $
*
* ----------
*/
#define NUMERIC_DEFAULT_PRECISION 30
#define NUMERIC_DEFAULT_SCALE 6
+
+/* ----------
+ * Internal limits on the scales chosen for calculation results
+ * ----------
+ */
#define NUMERIC_MAX_DISPLAY_SCALE NUMERIC_MAX_PRECISION
-#define NUMERIC_MIN_DISPLAY_SCALE NUMERIC_DEFAULT_SCALE + 4
+#define NUMERIC_MIN_DISPLAY_SCALE (NUMERIC_DEFAULT_SCALE + 4)
#define NUMERIC_MAX_RESULT_SCALE (NUMERIC_MAX_PRECISION * 2)
#define NUMERIC_MIN_RESULT_SCALE (NUMERIC_DEFAULT_PRECISION + 4)
-#define NUMERIC_UNPACKED_DATASIZE (NUMERIC_MAX_PRECISION * 2 + 4)
-
/* ----------
- * Sign values and macros to deal with n_sign_dscale
+ * Sign values and macros to deal with packing/unpacking n_sign_dscale
* ----------
*/
#define NUMERIC_SIGN_MASK 0xC000
#define NUMERIC_POS 0x0000
#define NUMERIC_NEG 0x4000
#define NUMERIC_NAN 0xC000
+#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_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)
/* ----------
* 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 this case, but we normally set it to zero.
* ----------
*/
typedef struct NumericData
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 */
+ unsigned char n_data[1]; /* Digit data (2 decimal digits/byte) */
} NumericData;
typedef NumericData *Numeric;
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