On Thu, 1 Jul 2021 at 14:17, Dean Rasheed <[email protected]> wrote:
>
> On Tue, 29 Jun 2021 at 12:08, Dean Rasheed <[email protected]> wrote:
> >
> > Numeric x^y is supported for x < 0 if y is an integer, but this
> > currently fails if y is outside the range of an int32
>
> I've been doing some more testing of this, and I spotted another
> problem with numeric_power().
>
> [loss of precision and overflow errors]
>
> I think we should attempt to avoid all such overflow errors,
> that are actually underflows, and return zero instead.
>
Finally getting back to this ... attached is an updated patch that now
includes a fix for the loss-of-precision bug and the overflow errors.
I don't think it's really worth trying to split these up, since
they're all somewhat interrelated.
Regards,
Dean
diff --git a/src/backend/utils/adt/numeric.c b/src/backend/utils/adt/numeric.c
new file mode 100644
index bc71326..1481538
--- a/src/backend/utils/adt/numeric.c
+++ b/src/backend/utils/adt/numeric.c
@@ -3937,11 +3937,6 @@ numeric_power(PG_FUNCTION_ARGS)
(errcode(ERRCODE_INVALID_ARGUMENT_FOR_POWER_FUNCTION),
errmsg("zero raised to a negative power is undefined")));
- if (sign1 < 0 && !numeric_is_integral(num2))
- ereport(ERROR,
- (errcode(ERRCODE_INVALID_ARGUMENT_FOR_POWER_FUNCTION),
- errmsg("a negative number raised to a non-integer power yields a complex result")));
-
/*
* Initialize things
*/
@@ -9754,12 +9749,18 @@ exp_var(const NumericVar *arg, NumericVa
*/
val = numericvar_to_double_no_overflow(&x);
- /* Guard against overflow */
+ /* Guard against overflow/underflow */
/* If you change this limit, see also power_var()'s limit */
if (Abs(val) >= NUMERIC_MAX_RESULT_SCALE * 3)
- ereport(ERROR,
- (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
- errmsg("value overflows numeric format")));
+ {
+ if (val > 0)
+ ereport(ERROR,
+ (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
+ errmsg("value overflows numeric format")));
+ zero_var(result);
+ result->dscale = rscale;
+ return;
+ }
/* decimal weight = log10(e^x) = x * log10(e) */
dweight = (int) (val * 0.434294481903252);
@@ -10117,6 +10118,8 @@ log_var(const NumericVar *base, const Nu
static void
power_var(const NumericVar *base, const NumericVar *exp, NumericVar *result)
{
+ int res_sign;
+ NumericVar abs_base;
NumericVar ln_base;
NumericVar ln_num;
int ln_dweight;
@@ -10160,9 +10163,37 @@ power_var(const NumericVar *base, const
return;
}
+ init_var(&abs_base);
init_var(&ln_base);
init_var(&ln_num);
+ /*
+ * If base is negative, insist that exp be an integer. The result is then
+ * positive if exp is even and negative if exp is odd.
+ */
+ if (base->sign == NUMERIC_NEG)
+ {
+ /* check that exp is an integer */
+ if (exp->ndigits > 0 && exp->ndigits > exp->weight + 1)
+ ereport(ERROR,
+ (errcode(ERRCODE_INVALID_ARGUMENT_FOR_POWER_FUNCTION),
+ errmsg("a negative number raised to a non-integer power yields a complex result")));
+
+ /* test if exp is odd or even */
+ if (exp->ndigits > 0 && exp->ndigits == exp->weight + 1 &&
+ (exp->digits[exp->ndigits - 1] & 1))
+ res_sign = NUMERIC_NEG;
+ else
+ res_sign = NUMERIC_POS;
+
+ /* then work with abs(base) below */
+ set_var_from_var(base, &abs_base);
+ abs_base.sign = NUMERIC_POS;
+ base = &abs_base;
+ }
+ else
+ res_sign = NUMERIC_POS;
+
/*----------
* Decide on the scale for the ln() calculation. For this we need an
* estimate of the weight of the result, which we obtain by doing an
@@ -10193,25 +10224,31 @@ power_var(const NumericVar *base, const
val = numericvar_to_double_no_overflow(&ln_num);
- /* initial overflow test with fuzz factor */
+ /* initial overflow/underflow test with fuzz factor */
if (Abs(val) > NUMERIC_MAX_RESULT_SCALE * 3.01)
- ereport(ERROR,
- (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
- errmsg("value overflows numeric format")));
+ {
+ if (val > 0)
+ ereport(ERROR,
+ (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
+ errmsg("value overflows numeric format")));
+ zero_var(result);
+ result->dscale = NUMERIC_MAX_DISPLAY_SCALE;
+ return;
+ }
val *= 0.434294481903252; /* approximate decimal result weight */
- /* choose the result scale */
+ /* choose the result scale and the scale for the real calculation */
rscale = NUMERIC_MIN_SIG_DIGITS - (int) val;
rscale = Max(rscale, base->dscale);
rscale = Max(rscale, exp->dscale);
rscale = Max(rscale, NUMERIC_MIN_DISPLAY_SCALE);
- rscale = Min(rscale, NUMERIC_MAX_DISPLAY_SCALE);
- /* set the scale for the real exp * ln(base) calculation */
local_rscale = rscale + (int) val - ln_dweight + 8;
local_rscale = Max(local_rscale, NUMERIC_MIN_DISPLAY_SCALE);
+ rscale = Min(rscale, NUMERIC_MAX_DISPLAY_SCALE);
+
/* and do the real calculation */
ln_var(base, &ln_base, local_rscale);
@@ -10220,8 +10257,12 @@ power_var(const NumericVar *base, const
exp_var(&ln_num, result, rscale);
+ if (res_sign == NUMERIC_NEG && result->ndigits > 0)
+ result->sign = NUMERIC_NEG;
+
free_var(&ln_num);
free_var(&ln_base);
+ free_var(&abs_base);
}
/*
diff --git a/src/test/regress/expected/numeric.out b/src/test/regress/expected/numeric.out
new file mode 100644
index 4ad4851..01937b0
--- a/src/test/regress/expected/numeric.out
+++ b/src/test/regress/expected/numeric.out
@@ -2327,6 +2327,12 @@ select 1.000000000123 ^ (-2147483648);
0.7678656556403084
(1 row)
+select 0.9999999999 ^ 23300000000000 = 0 as rounds_to_zero;
+ rounds_to_zero
+----------------
+ t
+(1 row)
+
-- cases that used to error out
select 0.12 ^ (-25);
?column?
@@ -2340,6 +2346,43 @@ select 0.5678 ^ (-85);
782333637740774446257.7719390061997396
(1 row)
+select 0.9999999999 ^ 70000000000000 = 0 as underflows;
+ underflows
+------------
+ t
+(1 row)
+
+-- negative base to integer powers
+select (-1.0) ^ 2147483646;
+ ?column?
+--------------------
+ 1.0000000000000000
+(1 row)
+
+select (-1.0) ^ 2147483647;
+ ?column?
+---------------------
+ -1.0000000000000000
+(1 row)
+
+select (-1.0) ^ 2147483648;
+ ?column?
+--------------------
+ 1.0000000000000000
+(1 row)
+
+select (-1.0) ^ 1000000000000000;
+ ?column?
+--------------------
+ 1.0000000000000000
+(1 row)
+
+select (-1.0) ^ 1000000000000001;
+ ?column?
+---------------------
+ -1.0000000000000000
+(1 row)
+
--
-- Tests for raising to non-integer powers
--
@@ -2476,6 +2519,18 @@ select exp('-inf'::numeric);
0
(1 row)
+select exp(-5000::numeric) = 0 as rounds_to_zero;
+ rounds_to_zero
+----------------
+ t
+(1 row)
+
+select exp(-10000::numeric) = 0 as underflows;
+ underflows
+------------
+ t
+(1 row)
+
-- cases that used to generate inaccurate results
select exp(32.999);
exp
diff --git a/src/test/regress/sql/numeric.sql b/src/test/regress/sql/numeric.sql
new file mode 100644
index 3784c52..f040f0b
--- a/src/test/regress/sql/numeric.sql
+++ b/src/test/regress/sql/numeric.sql
@@ -1090,10 +1090,19 @@ select 3.789 ^ 35;
select 1.2 ^ 345;
select 0.12 ^ (-20);
select 1.000000000123 ^ (-2147483648);
+select 0.9999999999 ^ 23300000000000 = 0 as rounds_to_zero;
-- cases that used to error out
select 0.12 ^ (-25);
select 0.5678 ^ (-85);
+select 0.9999999999 ^ 70000000000000 = 0 as underflows;
+
+-- negative base to integer powers
+select (-1.0) ^ 2147483646;
+select (-1.0) ^ 2147483647;
+select (-1.0) ^ 2147483648;
+select (-1.0) ^ 1000000000000000;
+select (-1.0) ^ 1000000000000001;
--
-- Tests for raising to non-integer powers
@@ -1136,6 +1145,8 @@ select exp(1.0::numeric(71,70));
select exp('nan'::numeric);
select exp('inf'::numeric);
select exp('-inf'::numeric);
+select exp(-5000::numeric) = 0 as rounds_to_zero;
+select exp(-10000::numeric) = 0 as underflows;
-- cases that used to generate inaccurate results
select exp(32.999);
