On Fri, 5 Jul 2024 at 18:37, Joel Jacobson <[email protected]> wrote:
>
> On Fri, Jul 5, 2024, at 18:42, Joel Jacobson wrote:
> > Very nice, v7-optimize-numeric-mul_var-small-var1-arbitrary-var2.patch
> > is now the winner on all my CPUs:
>
> I thought it would be interesting to also measure the isolated effect
> on just numeric_mul() without the query overhead.
>
> Impressive speed-up, between 25% - 81%.
>
Cool. I think we should go with the mul_var_small() patch then, since
it's more generally applicable.
I also did some testing with much larger var2 values, and saw similar
speed-ups. One high-level function that benefits from that is
factorial(), which accepts inputs up to 32177, and so uses both the
1-digit and 2-digit code with very large var2 values. I doubt anyone
actually uses it with such large inputs, but it's interesting
nonetheless:
SELECT factorial(32177);
Time: 923.117 ms -- HEAD
Time: 534.375 ms -- mul_var_small() patch
I did one more round of (mostly cosmetic) copy-editing. Aside from
improving some of the comments, it occurred to me that there's no need
to pass rscale to mul_var_small(), or for it to call round_var(),
since it's always computing the exact result. That shaves off a few
more cycles.
Additionally, I didn't like how res_weight and res_ndigits were being
set 1 higher than they needed to be. That makes sense in mul_var()
because it may round the result, causing a non-zero carry to propagate
into the next digit up, but it's just confusing in mul_var_small(). So
I've reduced those by 1, which makes the look much more logical. To be
clear, this doesn't change how many digits we're calculating. But now
res_ndigits is actually the number of digits being calculated, whereas
before, res_ndigits was 1 larger and we were calculating res_ndigits -
1 digits, which was confusing.
I think this is good to go, so unless there are any further comments,
I plan to commit it soon.
Possible future work would be to try extending it to larger var1
values. I have a feeling that might work quite well for 5 or 6 digits,
but at some point, we'll start seeing diminishing returns, and the
code bloat won't be worth it.
Regards,
Dean
diff --git a/src/backend/utils/adt/numeric.c b/src/backend/utils/adt/numeric.c
new file mode 100644
index 5510a20..b556861
--- a/src/backend/utils/adt/numeric.c
+++ b/src/backend/utils/adt/numeric.c
@@ -551,6 +551,8 @@ static void sub_var(const NumericVar *va
static void mul_var(const NumericVar *var1, const NumericVar *var2,
NumericVar *result,
int rscale);
+static void mul_var_small(const NumericVar *var1, const NumericVar *var2,
+ NumericVar *result);
static void div_var(const NumericVar *var1, const NumericVar *var2,
NumericVar *result,
int rscale, bool round);
@@ -8707,7 +8709,7 @@ mul_var(const NumericVar *var1, const Nu
var1digits = var1->digits;
var2digits = var2->digits;
- if (var1ndigits == 0 || var2ndigits == 0)
+ if (var1ndigits == 0)
{
/* one or both inputs is zero; so is result */
zero_var(result);
@@ -8715,6 +8717,16 @@ mul_var(const NumericVar *var1, const Nu
return;
}
+ /*
+ * If var1 has 1-4 digits and the exact result was requested, delegate to
+ * mul_var_small() which uses a faster direct multiplication algorithm.
+ */
+ if (var1ndigits <= 4 && rscale == var1->dscale + var2->dscale)
+ {
+ mul_var_small(var1, var2, result);
+ return;
+ }
+
/* Determine result sign and (maximum possible) weight */
if (var1->sign == var2->sign)
res_sign = NUMERIC_POS;
@@ -8862,6 +8874,212 @@ mul_var(const NumericVar *var1, const Nu
/* Strip leading and trailing zeroes */
strip_var(result);
+}
+
+
+/*
+ * mul_var_small() -
+ *
+ * Special-case multiplication function used when var1 has 1-4 digits, var2
+ * has at least as many digits as var1, and the exact product var1 * var2 is
+ * requested.
+ */
+static void
+mul_var_small(const NumericVar *var1, const NumericVar *var2,
+ NumericVar *result)
+{
+ int var1ndigits = var1->ndigits;
+ int var2ndigits = var2->ndigits;
+ NumericDigit *var1digits = var1->digits;
+ NumericDigit *var2digits = var2->digits;
+ int res_sign;
+ int res_weight;
+ int res_ndigits;
+ NumericDigit *res_buf;
+ NumericDigit *res_digits;
+ uint32 carry;
+ uint32 term;
+
+ /* Check preconditions */
+ Assert(var1ndigits >= 1);
+ Assert(var1ndigits <= 4);
+ Assert(var2ndigits >= var1ndigits);
+
+ /*
+ * Determine the result sign, weight, and number of digits to calculate.
+ * The weight figured here is correct if the product has no leading zero
+ * digits; otherwise strip_var() will fix things up. Note that, unlike
+ * mul_var(), we do not need to allocate an extra output digit, because we
+ * are not rounding here.
+ */
+ if (var1->sign == var2->sign)
+ res_sign = NUMERIC_POS;
+ else
+ res_sign = NUMERIC_NEG;
+ res_weight = var1->weight + var2->weight + 1;
+ res_ndigits = var1ndigits + var2ndigits;
+
+ /* Allocate result digit array */
+ res_buf = digitbuf_alloc(res_ndigits + 1);
+ res_buf[0] = 0; /* spare digit for later rounding */
+ res_digits = res_buf + 1;
+
+ /*
+ * Compute the result digits in reverse, in one pass, propagating the
+ * carry up as we go. The i'th result digit consists of the sum of the
+ * products var1digits[i1] * var2digits[i2] for which i = i1 + i2 + 1.
+ */
+ switch (var1ndigits)
+ {
+ case 1:
+ /* ---------
+ * 1-digit case:
+ * var1ndigits = 1
+ * var2ndigits >= 1
+ * res_ndigits = var2ndigits + 1
+ * ----------
+ */
+ carry = 0;
+ for (int i = res_ndigits - 2; i >= 0; i--)
+ {
+ term = (uint32) var1digits[0] * var2digits[i] + carry;
+ res_digits[i + 1] = (NumericDigit) (term % NBASE);
+ carry = term / NBASE;
+ }
+ res_digits[0] = (NumericDigit) carry;
+ break;
+
+ case 2:
+ /* ---------
+ * 2-digit case:
+ * var1ndigits = 2
+ * var2ndigits >= 2
+ * res_ndigits = var2ndigits + 2
+ * ----------
+ */
+ /* last result digit and carry */
+ term = (uint32) var1digits[1] * var2digits[res_ndigits - 3];
+ res_digits[res_ndigits - 1] = (NumericDigit) (term % NBASE);
+ carry = term / NBASE;
+
+ /* remaining digits, except for the first two */
+ for (int i = res_ndigits - 3; i >= 1; i--)
+ {
+ term = (uint32) var1digits[0] * var2digits[i] +
+ (uint32) var1digits[1] * var2digits[i - 1] + carry;
+ res_digits[i + 1] = (NumericDigit) (term % NBASE);
+ carry = term / NBASE;
+ }
+
+ /* first two digits */
+ term = (uint32) var1digits[0] * var2digits[0] + carry;
+ res_digits[1] = (NumericDigit) (term % NBASE);
+ res_digits[0] = (NumericDigit) (term / NBASE);
+ break;
+
+ case 3:
+ /* ---------
+ * 3-digit case:
+ * var1ndigits = 3
+ * var2ndigits >= 3
+ * res_ndigits = var2ndigits + 3
+ * ----------
+ */
+ /* last two result digits */
+ term = (uint32) var1digits[2] * var2digits[res_ndigits - 4];
+ res_digits[res_ndigits - 1] = (NumericDigit) (term % NBASE);
+ carry = term / NBASE;
+
+ term = (uint32) var1digits[1] * var2digits[res_ndigits - 4] +
+ (uint32) var1digits[2] * var2digits[res_ndigits - 5] + carry;
+ res_digits[res_ndigits - 2] = (NumericDigit) (term % NBASE);
+ carry = term / NBASE;
+
+ /* remaining digits, except for the first three */
+ for (int i = res_ndigits - 4; i >= 2; i--)
+ {
+ term = (uint32) var1digits[0] * var2digits[i] +
+ (uint32) var1digits[1] * var2digits[i - 1] +
+ (uint32) var1digits[2] * var2digits[i - 2] + carry;
+ res_digits[i + 1] = (NumericDigit) (term % NBASE);
+ carry = term / NBASE;
+ }
+
+ /* first three digits */
+ term = (uint32) var1digits[0] * var2digits[1] +
+ (uint32) var1digits[1] * var2digits[0] + carry;
+ res_digits[2] = (NumericDigit) (term % NBASE);
+ carry = term / NBASE;
+
+ term = (uint32) var1digits[0] * var2digits[0] + carry;
+ res_digits[1] = (NumericDigit) (term % NBASE);
+ res_digits[0] = (NumericDigit) (term / NBASE);
+ break;
+
+ case 4:
+ /* ---------
+ * 4-digit case:
+ * var1ndigits = 4
+ * var2ndigits >= 4
+ * res_ndigits = var2ndigits + 4
+ * ----------
+ */
+ /* last three result digits */
+ term = (uint32) var1digits[3] * var2digits[res_ndigits - 5];
+ res_digits[res_ndigits - 1] = (NumericDigit) (term % NBASE);
+ carry = term / NBASE;
+
+ term = (uint32) var1digits[2] * var2digits[res_ndigits - 5] +
+ (uint32) var1digits[3] * var2digits[res_ndigits - 6] + carry;
+ res_digits[res_ndigits - 2] = (NumericDigit) (term % NBASE);
+ carry = term / NBASE;
+
+ term = (uint32) var1digits[1] * var2digits[res_ndigits - 5] +
+ (uint32) var1digits[2] * var2digits[res_ndigits - 6] +
+ (uint32) var1digits[3] * var2digits[res_ndigits - 7] + carry;
+ res_digits[res_ndigits - 3] = (NumericDigit) (term % NBASE);
+ carry = term / NBASE;
+
+ /* remaining digits, except for the first four */
+ for (int i = res_ndigits - 5; i >= 3; i--)
+ {
+ term = (uint32) var1digits[0] * var2digits[i] +
+ (uint32) var1digits[1] * var2digits[i - 1] +
+ (uint32) var1digits[2] * var2digits[i - 2] +
+ (uint32) var1digits[3] * var2digits[i - 3] + carry;
+ res_digits[i + 1] = (NumericDigit) (term % NBASE);
+ carry = term / NBASE;
+ }
+
+ /* first four digits */
+ term = (uint32) var1digits[0] * var2digits[2] +
+ (uint32) var1digits[1] * var2digits[1] +
+ (uint32) var1digits[2] * var2digits[0] + carry;
+ res_digits[3] = (NumericDigit) (term % NBASE);
+ carry = term / NBASE;
+
+ term = (uint32) var1digits[0] * var2digits[1] +
+ (uint32) var1digits[1] * var2digits[0] + carry;
+ res_digits[2] = (NumericDigit) (term % NBASE);
+ carry = term / NBASE;
+
+ term = (uint32) var1digits[0] * var2digits[0] + carry;
+ res_digits[1] = (NumericDigit) (term % NBASE);
+ res_digits[0] = (NumericDigit) (term / NBASE);
+ break;
+ }
+
+ /* Store the product in result */
+ digitbuf_free(result->buf);
+ result->ndigits = res_ndigits;
+ result->buf = res_buf;
+ result->digits = res_digits;
+ result->weight = res_weight;
+ result->sign = res_sign;
+ result->dscale = var1->dscale + var2->dscale;
+
+ /* Strip leading and trailing zeroes */
+ strip_var(result);
}
