On Sun, Aug 11, 2024, at 22:04, Joel Jacobson wrote: >> Attachments: >> * v4-0001-Extend-mul_var_short-to-5-and-6-digit-inputs.patch >> * v4-0002-Optimise-numeric-multiplication-using-base-NBASE-.patch > > I've reviewed and tested both patches and think they are ready to be > committed.
In addition, I've also tested reduced rscale specifically, due to what you
wrote earlier:
> 2). Attempt to fix the formulae incorporating maxdigits mentioned
> above. This part really made my brain hurt, and I'm still not quite
> sure that I've got it right. In particular, it needs double-checking
> to ensure that it's not losing accuracy in the reduced-rscale case.
To test if there are any differences that actually matter in the result,
I patched mul_var to log what combinations that occur when running
the test suite:
```
if (rscale != var1->dscale + var2->dscale)
{
printf("NUMERIC_REDUCED_RSCALE %d,%d,%d,%d,%d\n", var1ndigits,
var2ndigits, var1->dscale, var2->dscale, rscale - (var1->dscale +
var2->dscale));
}
```
I also added a SQL-callable numeric_mul_rscale(var1, var2, rscale_adjustment)
function,
to be able to check for differences for the reduced rscale combinations.
I then ran the test suite against my db and extracted the seen combinations:
```
make installcheck
grep -E "^NUMERIC_REDUCED_RSCALE \d+,\d+,\d+,\d+,-\d+$" logfile | sort -u | awk
'{print $2}' > plausible_rscale_adjustments.csv
```
This test didn't produce any differences between HEAD and the two patches
applied.
% psql -f test-mul_var-verify.sql
CREATE TABLE
COPY 1413
var1ndigits | var2ndigits | var1dscale | var2dscale | rscale_adjustment | var1
| var2 | expected | numeric_mul_rscale
-------------+-------------+------------+------------+-------------------+------+------+----------+--------------------
(0 rows)
Attaching patch as .txt to not confuse cfbot.
Regards,
Joeldiff --git a/src/backend/utils/adt/numeric.c b/src/backend/utils/adt/numeric.c
index d0f0923710..94752fc343 100644
--- a/src/backend/utils/adt/numeric.c
+++ b/src/backend/utils/adt/numeric.c
@@ -3016,6 +3016,25 @@ numeric_mul(PG_FUNCTION_ARGS)
}
+/*
+ * numeric_mul_rscale() -
+ *
+ * Calculate the product of two numerics with reduced rscale.
+ */
+Datum
+numeric_mul_rscale(PG_FUNCTION_ARGS)
+{
+ Numeric num1 = PG_GETARG_NUMERIC(0);
+ Numeric num2 = PG_GETARG_NUMERIC(1);
+ int rscale_adjustment = PG_GETARG_INT32(2);
+ Numeric res;
+
+ res = numeric_mul_rscale_opt_error(num1, num2, NULL, rscale_adjustment);
+
+ PG_RETURN_NUMERIC(res);
+}
+
+
/*
* numeric_mul_opt_error() -
*
@@ -3119,6 +3138,108 @@ numeric_mul_opt_error(Numeric num1, Numeric num2, bool
*have_error)
}
+/*
+ * numeric_mul_rscale_opt_error() -
+ *
+ * Internal version of numeric_mul_rscale(). If "*have_error" flag is
provided,
+ * on error it's set to true, NULL returned. This is helpful when caller
+ * need to handle errors by itself.
+ */
+Numeric
+numeric_mul_rscale_opt_error(Numeric num1, Numeric num2, bool *have_error, int
rscale_adjustment)
+{
+ NumericVar arg1;
+ NumericVar arg2;
+ NumericVar result;
+ Numeric res;
+
+ /*
+ * Handle NaN and infinities
+ */
+ if (NUMERIC_IS_SPECIAL(num1) || NUMERIC_IS_SPECIAL(num2))
+ {
+ if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
+ return make_result(&const_nan);
+ if (NUMERIC_IS_PINF(num1))
+ {
+ switch (numeric_sign_internal(num2))
+ {
+ case 0:
+ return make_result(&const_nan); /* Inf
* 0 */
+ case 1:
+ return make_result(&const_pinf);
+ case -1:
+ return make_result(&const_ninf);
+ }
+ Assert(false);
+ }
+ if (NUMERIC_IS_NINF(num1))
+ {
+ switch (numeric_sign_internal(num2))
+ {
+ case 0:
+ return make_result(&const_nan); /* -Inf
* 0 */
+ case 1:
+ return make_result(&const_ninf);
+ case -1:
+ return make_result(&const_pinf);
+ }
+ Assert(false);
+ }
+ /* by here, num1 must be finite, so num2 is not */
+ if (NUMERIC_IS_PINF(num2))
+ {
+ switch (numeric_sign_internal(num1))
+ {
+ case 0:
+ return make_result(&const_nan); /* 0 *
Inf */
+ case 1:
+ return make_result(&const_pinf);
+ case -1:
+ return make_result(&const_ninf);
+ }
+ Assert(false);
+ }
+ Assert(NUMERIC_IS_NINF(num2));
+ switch (numeric_sign_internal(num1))
+ {
+ case 0:
+ return make_result(&const_nan); /* 0 * -Inf */
+ case 1:
+ return make_result(&const_ninf);
+ case -1:
+ return make_result(&const_pinf);
+ }
+ Assert(false);
+ }
+
+ /*
+ * Unpack the values, let mul_var() compute the result and return it.
+ * Unlike add_var() and sub_var(), mul_var() will round its result. In
the
+ * case of numeric_mul(), which is invoked for the * operator on
numerics,
+ * we request exact representation for the product (rscale = sum(dscale
of
+ * arg1, dscale of arg2)). If the exact result has more digits after
the
+ * decimal point than can be stored in a numeric, we round it. Rounding
+ * after computing the exact result ensures that the final result is
+ * correctly rounded (rounding in mul_var() using a truncated product
+ * would not guarantee this).
+ */
+ init_var_from_num(num1, &arg1);
+ init_var_from_num(num2, &arg2);
+
+ init_var(&result);
+ mul_var(&arg1, &arg2, &result, arg1.dscale + arg2.dscale +
rscale_adjustment);
+
+ if (result.dscale > NUMERIC_DSCALE_MAX)
+ round_var(&result, NUMERIC_DSCALE_MAX);
+
+ res = make_result_opt_error(&result, have_error);
+
+ free_var(&result);
+
+ return res;
+}
+
/*
* numeric_div() -
*
@@ -8719,6 +8840,11 @@ mul_var(const NumericVar *var1, const NumericVar *var2,
NumericVar *result,
return;
}
+ if (rscale != var1->dscale + var2->dscale)
+ {
+ printf("NUMERIC_REDUCED_RSCALE %d,%d,%d,%d,%d\n", var1ndigits,
var2ndigits, var1->dscale, var2->dscale, rscale - (var1->dscale +
var2->dscale));
+ }
+
/*
* If var1 has 1-4 digits and the exact result was requested, delegate
to
* mul_var_short() which uses a faster direct multiplication algorithm.
diff --git a/src/include/catalog/pg_proc.dat b/src/include/catalog/pg_proc.dat
index d36f6001bb..a400ff2875 100644
--- a/src/include/catalog/pg_proc.dat
+++ b/src/include/catalog/pg_proc.dat
@@ -4498,6 +4498,9 @@
{ oid => '1726',
proname => 'numeric_mul', prorettype => 'numeric',
proargtypes => 'numeric numeric', prosrc => 'numeric_mul' },
+{ oid => '8000',
+ proname => 'numeric_mul_rscale', prorettype => 'numeric',
+ proargtypes => 'numeric numeric int4', prosrc => 'numeric_mul_rscale' },
{ oid => '1727',
proname => 'numeric_div', prorettype => 'numeric',
proargtypes => 'numeric numeric', prosrc => 'numeric_div' },
diff --git a/src/include/utils/numeric.h b/src/include/utils/numeric.h
index 43c75c436f..76794970d1 100644
--- a/src/include/utils/numeric.h
+++ b/src/include/utils/numeric.h
@@ -97,6 +97,8 @@ extern Numeric numeric_sub_opt_error(Numeric num1, Numeric
num2,
bool
*have_error);
extern Numeric numeric_mul_opt_error(Numeric num1, Numeric num2,
bool
*have_error);
+extern Numeric numeric_mul_rscale_opt_error(Numeric num1, Numeric num2,
+ bool
*have_error, int rscale_adjustment);
extern Numeric numeric_div_opt_error(Numeric num1, Numeric num2,
bool
*have_error);
extern Numeric numeric_mod_opt_error(Numeric num1, Numeric num2,
1,1,11,1,-1 1,1,11,2,-2 1,1,11,3,-3 1,1,11,4,-8 1,1,13,1,-1 1,1,14,2,-2 1,1,15,3,-3 1,1,16,4,-8 1,1,32,30,-16 1,1,32,31,-17 1,1,32,32,-18 1,1,46,46,-46 1,1,8,8,-1 1,1,8,8,-2 1,1,8,8,-3 1,1,8,8,-4 1,1,8,8,-5 1,10,28,38,-38 1,12,0,46,-11 1,13,0,51,-9 1,13,51,51,-51 1,14,0,57,-9 1,17,0,67,-9 1,18,62,72,-72 1,2,26,8,-8 1,2,80,77,-77 1,25,0,97,-11 1,27,0,108,-11 1,27,108,108,-108 1,29,0,114,-11 1,29,0,114,-9 1,3,0,1016,-8 1,3,0,1072,-8 1,3,28,17,-17 1,3,68,17,-17 1,4,0,26,-8 1,4,26,26,-26 1,4,27,15,-15 1,4,28,15,-15 1,4,7,19,-19 1,5,0,17,-9 1,5,0,18,-10 1,5,17,17,-17 1,5,18,18,-18 1,5,7,36,-36 1,53,0,209,-9 1,53,0,210,-10 1,54,211,218,-218 1,55,0,218,-9 1,57,0,226,-9 1,57,0,228,-9 1,58,0,232,-9 1,58,220,229,-229 1,58,222,231,-231 1,58,232,232,-232 1,59,0,234,-9 1,59,0,235,-9 1,59,226,235,-235 1,59,228,237,-237 1,59,235,235,-235 1,6,0,25,-10 1,6,0,25,-9 1,6,28,28,-28 1,7,0,25,-10 1,7,0,25,-9 1,7,0,26,-10 1,7,0,26,-11 1,7,0,28,-8 1,7,26,26,-26 1,8,0,33,-9 1,8,26,33,-33 1,8,27,34,-34 1,8,33,33,-33 1,9,0,33,-10 1,9,0,33,-9 1,9,0,34,-10 1,9,0,34,-11 1,9,0,34,-9 1,9,0,35,-9 1,9,0,36,-8 1,9,0,37,-8 1,9,27,36,-36 1,9,33,33,-33 1,9,34,34,-34 1,9,35,35,-35 10,10,29,29,-37 10,10,36,36,-44 10,10,37,37,-37 10,10,38,38,-39 10,10,38,38,-48 10,10,61,61,-37 10,12,46,46,-46 10,13,51,51,-51 10,15,57,57,-57 10,17,67,67,-67 10,18,62,72,-72 10,25,97,97,-97 10,27,108,108,-108 10,29,114,114,-114 10,53,209,209,-209 10,53,210,210,-210 10,54,211,218,-218 10,55,218,218,-218 10,57,226,226,-226 10,57,228,228,-228 10,58,220,229,-229 10,58,222,231,-231 10,58,232,232,-232 10,59,226,235,-235 10,59,228,237,-237 10,59,234,234,-234 10,59,235,235,-235 10,60,229,239,-239 11,11,45,45,-37 11,11,53,45,-37 11,12,46,46,-46 11,13,51,51,-51 11,15,57,57,-57 11,17,67,67,-67 11,18,62,72,-72 11,25,97,97,-97 11,27,108,108,-108 11,29,114,114,-114 11,53,209,209,-209 11,53,210,210,-210 11,54,211,218,-218 11,55,218,218,-218 11,57,226,226,-226 11,57,228,228,-228 11,58,220,229,-229 11,58,222,231,-231 11,58,232,232,-232 11,59,226,235,-235 11,59,228,237,-237 11,59,234,234,-234 11,59,235,235,-235 11,60,229,239,-239 12,12,34,34,-42 12,12,45,45,-45 12,12,46,46,-46 12,13,38,26,-46 12,13,51,51,-51 12,15,57,57,-57 12,17,67,67,-67 12,18,62,72,-72 12,25,97,97,-97 12,27,108,108,-108 12,29,114,114,-114 12,53,209,209,-209 12,53,210,210,-210 12,54,211,218,-218 12,55,218,218,-218 12,57,226,226,-226 12,57,228,228,-228 12,58,220,229,-229 12,58,222,231,-231 12,58,232,232,-232 12,59,226,235,-235 12,59,228,237,-237 12,59,234,234,-234 12,59,235,235,-235 12,60,229,239,-239 13,13,40,40,-48 13,13,42,42,-50 13,13,46,46,-46 13,13,51,51,-51 13,15,57,57,-57 13,17,67,67,-67 13,18,62,72,-72 13,25,97,97,-97 13,27,108,108,-108 13,29,114,114,-114 13,53,209,209,-209 13,53,210,210,-210 13,54,211,218,-218 13,55,218,218,-218 13,57,226,226,-226 13,57,228,228,-228 13,58,220,229,-229 13,58,222,231,-231 13,58,232,232,-232 13,59,226,235,-235 13,59,228,237,-237 13,59,234,234,-234 13,59,235,235,-235 13,60,229,239,-239 136,136,354,354,-538 136,137,490,450,-542 137,137,170,398,-546 137,137,450,450,-546 137,137,498,498,-546 137,137,522,522,-546 14,15,57,57,-57 14,17,67,67,-67 14,18,62,72,-72 14,25,97,97,-97 14,27,108,108,-108 14,29,114,114,-114 14,53,209,209,-209 14,53,210,210,-210 14,54,211,218,-218 14,55,218,218,-218 14,57,226,226,-226 14,57,228,228,-228 14,58,220,229,-229 14,58,222,231,-231 14,58,232,232,-232 14,59,226,235,-235 14,59,228,237,-237 14,59,234,234,-234 14,59,235,235,-235 14,60,229,239,-239 140,140,490,490,-554 140,140,522,522,-554 140,140,538,538,-554 140,140,546,546,-554 140,140,553,553,-552 140,140,554,554,-554 141,141,290,290,-562 141,141,426,426,-562 141,141,554,554,-562 15,15,57,57,-57 15,17,67,67,-67 15,18,62,72,-72 15,25,97,97,-97 15,27,108,108,-108 15,29,114,114,-114 15,53,209,209,-209 15,53,210,210,-210 15,54,211,218,-218 15,55,218,218,-218 15,57,226,226,-226 15,57,228,228,-228 15,58,220,229,-229 15,58,222,231,-231 15,58,232,232,-232 15,59,226,235,-235 15,59,228,237,-237 15,59,234,234,-234 15,59,235,235,-235 15,60,229,239,-239 16,17,67,67,-67 16,25,97,97,-97 16,27,108,108,-108 16,29,114,114,-114 16,53,209,209,-209 16,53,210,210,-210 16,54,211,218,-218 16,55,218,218,-218 16,57,226,226,-226 16,57,228,228,-228 16,58,220,229,-229 16,58,222,231,-231 16,58,232,232,-232 16,59,226,235,-235 16,59,228,237,-237 16,59,234,234,-234 16,59,235,235,-235 17,17,39,39,-63 17,17,63,63,-63 17,17,67,67,-67 17,25,97,97,-97 17,27,108,108,-108 17,29,114,114,-114 17,53,209,209,-209 17,53,210,210,-210 17,54,211,218,-218 17,55,218,218,-218 17,57,226,226,-226 17,57,228,228,-228 17,58,220,229,-229 17,58,222,231,-231 17,58,232,232,-232 17,59,226,235,-235 17,59,228,237,-237 17,59,234,234,-234 17,59,235,235,-235 17,60,229,239,-239 18,18,1082,1082,-2086 18,18,55,55,-71 18,18,63,63,-71 18,18,68,68,-67 18,18,69,69,-69 18,18,72,72,-82 18,25,97,97,-97 18,27,108,108,-108 18,29,114,114,-114 18,53,209,209,-209 18,53,210,210,-210 18,54,211,218,-218 18,55,218,218,-218 18,57,226,226,-226 18,57,228,228,-228 18,58,220,229,-229 18,58,222,231,-231 18,58,232,232,-232 18,59,226,235,-235 18,59,228,237,-237 18,59,234,234,-234 18,59,235,235,-235 18,60,229,239,-239 19,19,102,102,-70 19,19,190,190,-70 19,19,310,310,-70 19,19,45,45,-69 19,19,69,69,-69 19,19,72,72,-81 19,19,78,78,-70 19,19,86,86,-70 19,25,97,97,-97 19,27,108,108,-108 19,29,114,114,-114 19,53,210,210,-210 19,54,211,218,-218 19,55,218,218,-218 19,57,226,226,-226 19,57,228,228,-228 19,58,220,229,-229 19,58,222,231,-231 19,58,232,232,-232 19,59,226,235,-235 19,59,228,237,-237 19,59,234,234,-234 19,59,235,235,-235 19,60,229,239,-239 2,10,28,38,-38 2,10,77,80,-77 2,11,77,80,-77 2,12,46,46,-46 2,12,77,80,-77 2,13,51,51,-51 2,13,77,80,-77 2,14,77,80,-77 2,15,57,57,-57 2,15,77,80,-77 2,16,1,58,-1 2,16,77,80,-77 2,17,67,67,-67 2,17,77,80,-77 2,18,62,72,-72 2,18,77,80,-77 2,19,77,80,-77 2,2,26,8,-8 2,2,77,77,-74 2,2,8,1,-1 2,2,80,77,-77 2,25,97,97,-97 2,27,108,108,-108 2,29,114,114,-114 2,3,1,8,-1 2,3,28,17,-17 2,3,68,17,-17 2,3,77,80,-77 2,3,8,26,-8 2,4,27,15,-15 2,4,28,15,-15 2,4,77,80,-77 2,4,8,26,-8 2,5,17,17,-17 2,5,18,18,-18 2,5,553,21,-21 2,5,77,80,-77 2,5,8,26,-8 2,53,209,209,-209 2,53,210,210,-210 2,54,211,218,-218 2,55,218,218,-218 2,57,226,226,-226 2,57,228,228,-228 2,58,220,229,-229 2,58,222,231,-231 2,58,232,232,-232 2,59,226,235,-235 2,59,228,237,-237 2,59,234,234,-234 2,59,235,235,-235 2,6,1,24,-1 2,6,25,25,-25 2,6,77,80,-77 2,6,8,26,-8 2,60,229,239,-239 2,7,1,24,-1 2,7,25,25,-25 2,7,26,26,-26 2,7,69,1082,-1082 2,7,77,80,-77 2,8,26,33,-33 2,8,27,34,-34 2,8,33,33,-33 2,8,36,36,-36 2,8,37,37,-37 2,8,77,80,-77 2,9,27,36,-36 2,9,33,33,-33 2,9,34,34,-34 2,9,35,35,-35 2,9,77,80,-77 20,20,134,134,-78 20,20,550,550,-78 20,20,61,61,-77 20,20,69,69,-77 20,20,78,78,-78 20,25,97,97,-97 20,27,108,108,-108 20,29,114,114,-114 20,53,209,209,-209 20,53,210,210,-210 20,54,211,218,-218 20,55,218,218,-218 20,57,226,226,-226 20,57,228,228,-228 20,58,220,229,-229 20,58,222,231,-231 20,58,232,232,-232 20,59,226,235,-235 20,59,228,237,-237 20,59,234,234,-234 20,59,235,235,-235 20,60,229,239,-239 21,21,80,80,-79 21,21,81,81,-81 21,25,97,97,-97 21,27,108,108,-108 21,29,114,114,-114 21,53,209,209,-209 21,53,210,210,-210 21,54,211,218,-218 21,55,218,218,-218 21,57,226,226,-226 21,57,228,228,-228 21,58,220,229,-229 21,58,222,231,-231 21,58,232,232,-232 21,59,226,235,-235 21,59,228,237,-237 21,59,234,234,-234 21,59,235,235,-235 21,60,229,239,-239 22,22,81,81,-81 22,25,97,97,-97 22,27,108,108,-108 22,29,114,114,-114 22,53,209,209,-209 22,53,210,210,-210 22,54,211,218,-218 22,55,218,218,-218 22,57,226,226,-226 22,57,228,228,-228 22,58,220,229,-229 22,58,222,231,-231 22,58,232,232,-232 22,59,226,235,-235 22,59,228,237,-237 22,59,234,234,-234 22,59,235,235,-235 22,60,229,239,-239 23,25,97,97,-97 23,27,108,108,-108 23,29,114,114,-114 23,53,209,209,-209 23,53,210,210,-210 23,54,211,218,-218 23,55,218,218,-218 23,57,226,226,-226 23,57,228,228,-228 23,58,220,229,-229 23,58,222,231,-231 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8,8,28,28,-27 8,8,28,28,-28 8,8,32,32,-19 8,8,33,33,-33 8,8,33,33,-40 8,8,34,34,-41 8,8,36,36,-28 8,9,33,33,-33 8,9,34,34,-34 8,9,35,35,-35 8,9,36,36,-36 8,9,37,37,-37 9,12,46,46,-46 9,13,51,51,-51 9,15,57,57,-57 9,17,67,67,-67 9,18,62,72,-72 9,25,97,97,-97 9,27,108,108,-108 9,29,114,114,-114 9,53,209,209,-209 9,53,210,210,-210 9,54,211,218,-218 9,55,218,218,-218 9,57,226,226,-226 9,57,228,228,-228 9,58,220,229,-229 9,58,222,231,-231 9,58,232,232,-232 9,59,226,235,-235 9,59,228,237,-237 9,59,234,234,-234 9,59,235,235,-235 9,60,229,239,-239 9,9,28,28,-36 9,9,29,29,-29 9,9,32,32,-22 9,9,33,33,-33 9,9,33,33,-39 9,9,34,34,-34 9,9,34,34,-40 9,9,35,35,-35 9,9,36,36,-36 9,9,36,36,-45 9,9,37,37,-29 9,9,37,37,-37 9,9,45,45,-29 99,99,384,384,-246
test-mul_var-init.sql
Description: Binary data
test-mul_var-verify.sql
Description: Binary data
