Fix precision and rounding issues in money multiplication and division.

The cash_div_intX functions applied rint() to the result of the division.
That's not merely useless (because the result is already an integer) but
it causes precision loss for values larger than 2^52 or so, because of
the forced conversion to float8.

On the other hand, the cash_mul_fltX functions neglected to apply rint() to
their multiplication results, thus possibly causing off-by-one outputs.

Per C standard, arithmetic between any integral value and a float value is
performed in float format.  Thus, cash_mul_flt4 and cash_div_flt4 produced
answers good to only about six digits, even when the float value is exact.
We can improve matters noticeably by widening the float inputs to double.
(It's tempting to consider using "long double" arithmetic if available,
but that's probably too much of a stretch for a back-patched fix.)

Also, document that cash_div_intX operators truncate rather than round.

Per bug #14663 from Richard Pistole.  Back-patch to all supported branches.

Discussion: https://postgr.es/m/22403.1495223615@sss.pgh.pa.us

doc/src/sgml/datatype.sgml

@@ -962,6 +962,11 @@ SELECT '52093.89'::money::numeric::float8;
    </para>
 
    <para>
+    Division of a <type>money</type> value by an integer value is performed
+    with truncation of the fractional part towards zero.  To get a rounded
+    result, divide by a floating-point value, or cast the <type>money</type>
+    value to <type>numeric</> before dividing and back to <type>money</type>
+    afterwards.  (The latter is preferable to avoid risking precision loss.)
     When a <type>money</type> value is divided by another <type>money</type>
     value, the result is <type>double precision</type> (i.e., a pure number,
     not money); the currency units cancel each other out in the division.

src/backend/utils/adt/cash.c

@@ -623,7 +623,7 @@ cash_mul_flt8(PG_FUNCTION_ARGS)
 	float8		f = PG_GETARG_FLOAT8(1);
 	Cash		result;
 
-	result = c * f;
+	result = rint(c * f);
 	PG_RETURN_CASH(result);
 }
 
@@ -638,7 +638,7 @@ flt8_mul_cash(PG_FUNCTION_ARGS)
 	Cash		c = PG_GETARG_CASH(1);
 	Cash		result;
 
-	result = f * c;
+	result = rint(f * c);
 	PG_RETURN_CASH(result);
 }
 
@@ -673,7 +673,7 @@ cash_mul_flt4(PG_FUNCTION_ARGS)
 	float4		f = PG_GETARG_FLOAT4(1);
 	Cash		result;
 
-	result = c * f;
+	result = rint(c * (float8) f);
 	PG_RETURN_CASH(result);
 }
 
@@ -688,7 +688,7 @@ flt4_mul_cash(PG_FUNCTION_ARGS)
 	Cash		c = PG_GETARG_CASH(1);
 	Cash		result;
 
-	result = f * c;
+	result = rint((float8) f * c);
 	PG_RETURN_CASH(result);
 }
 
@@ -709,7 +709,7 @@ cash_div_flt4(PG_FUNCTION_ARGS)
 				(errcode(ERRCODE_DIVISION_BY_ZERO),
 				 errmsg("division by zero")));
 
-	result = rint(c / f);
+	result = rint(c / (float8) f);
 	PG_RETURN_CASH(result);
 }
 
@@ -758,7 +758,7 @@ cash_div_int8(PG_FUNCTION_ARGS)
 				(errcode(ERRCODE_DIVISION_BY_ZERO),
 				 errmsg("division by zero")));
 
-	result = rint(c / i);
+	result = c / i;
 
 	PG_RETURN_CASH(result);
 }
@@ -810,7 +810,7 @@ cash_div_int4(PG_FUNCTION_ARGS)
 				(errcode(ERRCODE_DIVISION_BY_ZERO),
 				 errmsg("division by zero")));
 
-	result = rint(c / i);
+	result = c / i;
 
 	PG_RETURN_CASH(result);
 }
@@ -860,7 +860,7 @@ cash_div_int2(PG_FUNCTION_ARGS)
 				(errcode(ERRCODE_DIVISION_BY_ZERO),
 				 errmsg("division by zero")));
 
-	result = rint(c / s);
+	result = c / s;
 	PG_RETURN_CASH(result);
 }
 

src/test/regress/expected/money.out

@@ -185,6 +185,44 @@ SELECT * FROM money_data;
  $123.46
 (1 row)
 
+-- rounding vs. truncation in division
+SELECT '878.08'::money / 11::float8;
+ ?column? 
+----------
+   $79.83
+(1 row)
+
+SELECT '878.08'::money / 11::float4;
+ ?column? 
+----------
+   $79.83
+(1 row)
+
+SELECT '878.08'::money / 11::int;
+ ?column? 
+----------
+   $79.82
+(1 row)
+
+SELECT '878.08'::money / 11::smallint;
+ ?column? 
+----------
+   $79.82
+(1 row)
+
+-- check for precision loss in division
+SELECT '90000000000000099.00'::money / 10::int;
+         ?column?          
+---------------------------
+ $9,000,000,000,000,009.90
+(1 row)
+
+SELECT '90000000000000099.00'::money / 10::smallint;
+         ?column?          
+---------------------------
+ $9,000,000,000,000,009.90
+(1 row)
+
 -- Cast int4/int8 to money
 SELECT 1234567890::money;
        money       

src/test/regress/sql/money.sql

@@ -57,6 +57,16 @@ DELETE FROM money_data;
 INSERT INTO money_data VALUES ('$123.459');
 SELECT * FROM money_data;
 
+-- rounding vs. truncation in division
+SELECT '878.08'::money / 11::float8;
+SELECT '878.08'::money / 11::float4;
+SELECT '878.08'::money / 11::int;
+SELECT '878.08'::money / 11::smallint;
+
+-- check for precision loss in division
+SELECT '90000000000000099.00'::money / 10::int;
+SELECT '90000000000000099.00'::money / 10::smallint;
+
 -- Cast int4/int8 to money
 SELECT 1234567890::money;
 SELECT 12345678901234567::money;