From d996d648f333b04ae3da3c5853120f6f37601fb2 Mon Sep 17 00:00:00 2001
From: Dean Rasheed <dean.a.rasheed@gmail.com>
Date: Sun, 27 Feb 2022 10:41:12 +0000
Subject: [PATCH] Simplify the inner loop of numeric division in div_var().

In the standard numeric division algorithm, the inner loop multiplies
the divisor by the next quotient digit and subtracts that from the
working dividend. As suggested by the original code comment, the
separate "carry" and "borrow" variables (from the multiplication and
subtraction steps respectively) can be folded together into a single
variable. Doing so significantly improves performance, as well as
simplifying the code.

Dean Rasheed, reviewed by Tom Lane.

Discussion: https://postgr.es/m/CAEZATCVwsBi-ND-t82Cuuh1=8ee6jdOpzsmGN+CUZB6yjLg9jw@mail.gmail.com
---
 src/backend/utils/adt/numeric.c | 36 ++++++++++++++-------------------
 1 file changed, 15 insertions(+), 21 deletions(-)

diff --git a/src/backend/utils/adt/numeric.c b/src/backend/utils/adt/numeric.c
index effc4b886c..47475bf695 100644
--- a/src/backend/utils/adt/numeric.c
+++ b/src/backend/utils/adt/numeric.c
@@ -8605,31 +8605,25 @@ div_var(const NumericVar *var1, const NumericVar *var2, NumericVar *result,
 			/* As above, need do nothing more when quotient digit is 0 */
 			if (qhat > 0)
 			{
+				NumericDigit *dividend_j = &dividend[j];
+
 				/*
 				 * Multiply the divisor by qhat, and subtract that from the
-				 * working dividend.  "carry" tracks the multiplication,
-				 * "borrow" the subtraction (could we fold these together?)
+				 * working dividend.  The multiplication and subtraction are
+				 * folded together here, noting that qhat <= NBASE (since it
+				 * might be one too large), and so the intermediate result
+				 * "tmp_result" is in the range [-NBASE^2, NBASE - 1], and
+				 * "borrow" is in the range [0, NBASE].
 				 */
-				carry = 0;
 				borrow = 0;
 				for (i = var2ndigits; i >= 0; i--)
 				{
-					carry += divisor[i] * qhat;
-					borrow -= carry % NBASE;
-					carry = carry / NBASE;
-					borrow += dividend[j + i];
-					if (borrow < 0)
-					{
-						dividend[j + i] = borrow + NBASE;
-						borrow = -1;
-					}
-					else
-					{
-						dividend[j + i] = borrow;
-						borrow = 0;
-					}
+					int			tmp_result;
+
+					tmp_result = dividend_j[i] - borrow - divisor[i] * qhat;
+					borrow = (NBASE - 1 - tmp_result) / NBASE;
+					dividend_j[i] = tmp_result + borrow * NBASE;
 				}
-				Assert(carry == 0);
 
 				/*
 				 * If we got a borrow out of the top dividend digit, then
@@ -8645,15 +8639,15 @@ div_var(const NumericVar *var1, const NumericVar *var2, NumericVar *result,
 					carry = 0;
 					for (i = var2ndigits; i >= 0; i--)
 					{
-						carry += dividend[j + i] + divisor[i];
+						carry += dividend_j[i] + divisor[i];
 						if (carry >= NBASE)
 						{
-							dividend[j + i] = carry - NBASE;
+							dividend_j[i] = carry - NBASE;
 							carry = 1;
 						}
 						else
 						{
-							dividend[j + i] = carry;
+							dividend_j[i] = carry;
 							carry = 0;
 						}
 					}