round_amount: Perls Repräsentationsalgorithmus fürs exakte Runden nutzen

Als Erläuterung paste ich schlicht den relevanten Teil des Kommentars,
der nun auch in der Funktion steht:

Trying to round with more precision first only shifts the problem to rarer
cases, which nevertheless exist.

Now we exploit the presentation rounding of Perl. Since it really tries hard
to recognize integers, we double $amount, and let Perl give us a representation.
If Perl recognizes it as a slightly too small integer, and rounds up to the
next odd integer, we follow suit and treat the fraction as .5 or greater.

diff --git a/SL/Form.pm b/SL/Form.pm
index 1368df738a27461745b299b2a3a634ccd295c188..7cbf60f8cd1be951dd86ed391f9f4c527663c939 100644 (file)
--- a/SL/Form.pm
+++ b/SL/Form.pm
@@ -952,26 +952,39 @@ sub round_amount {
 
   # Rounding like "Kaufmannsrunden" (see http://de.wikipedia.org/wiki/Rundung )
 
 
   # Rounding like "Kaufmannsrunden" (see http://de.wikipedia.org/wiki/Rundung )
 

-  # Round amounts to eight places before rounding to the requested
-  # number of places. This gets rid of errors due to internal floating
-  # point representation.
-  $amount   = $self->round_amount($amount, 8) if $places < 8;
-
-  # Remember the amount's sign but calculate in positive values only.
-  my $sign  = $amount <=> 0;
-  $amount   = abs $amount;
-
-  # Shift the amount left by $places+1 decimal places and truncate it
-  # to integer. Then to the integer equivalent of rounding to the next
-  # multiple of 10: first add half of it (5). Then truncate it back to
-  # the lower multiple of 10 by subtracting $amount modulo 10.
-  my $shift = 10 ** ($places + 1);
-  $amount   = int($amount * $shift) + 5;
-  $amount  -= $amount % 10;
-
-  # Lastly shift the amount back right by $places+1 decimal places and
-  # restore its sign. Then we're done.
-  $amount   = ($amount / $shift) * $sign;
+  # If you search for rounding in Perl, you'll likely get the first version of
+  # this algorithm:
+  #
+  # ($amount <=> 0) * int(abs($amount) * 10**$places) + .5) / 10**$places
+  #
+  # That doesn't work. It falls apart for certain values that are exactly 0.5
+  # over the cutoff, because the internal IEEE754 representation is slightly
+  # below the cutoff. Perl makes matters worse in that it really, really tries to
+  # recognize exact values for presentation to you, even if they are not.
+  #
+  # Example: take the value 64.475 and round to 2 places.
+  #
+  # printf("%.20f\n", 64.475) gives you 64.47499999999999431566
+  #
+  # Then 64.475 * 100 + 0.5 is 6447.99999999999909050530, and
+  # int(64.475 * 100 + 0.5) / 100 = 64.47
+  #
+  # Trying to round with more precision first only shifts the problem to rarer
+  # cases, which nevertheless exist.
+  #
+  # Now we exploit the presentation rounding of Perl. Since it really tries hard
+  # to recognize integers, we double $amount, and let Perl give us a representation.
+  # If Perl recognizes it as a slightly too small integer, and rounds up to the
+  # next odd integer, we follow suit and treat the fraction as .5 or greater.
+
+  my $sign               = $amount <=> 0;
+  $amount                = abs $amount;
+
+  my $shift              = 10 ** ($places);
+  my $shifted_and_double = $amount * $shift * 2;
+  my $rounding_bias      = sprintf('%f', $shifted_and_double) % 2;
+  $amount                = int($amount * $shift) + $rounding_bias;
+  $amount                = $amount / $shift * $sign;

 
   return $amount;
 }
 
   return $amount;
 }

diff --git a/t/form/round_amount.t b/t/form/round_amount.t
index 2ba2334a26c858235ff0349454aef2af953fa85a..685013a44b76d5274ee0a4c2821854779d385c19 100644 (file)
--- a/t/form/round_amount.t
+++ b/t/form/round_amount.t
@@ -23,6 +23,24 @@ is($::form->round_amount(33.675, 2), '33.68', '33.675 @ 2');
 is($::form->round_amount(33.675, 1), '33.7',  '33.675 @ 1');
 is($::form->round_amount(33.675, 0), '34',    '33.675 @ 0');
 
 is($::form->round_amount(33.675, 1), '33.7',  '33.675 @ 1');
 is($::form->round_amount(33.675, 0), '34',    '33.675 @ 0');
 

+is($::form->round_amount(64.475, 2), '64.48', '64.475 @ 2');
+is($::form->round_amount(64.475, 1), '64.5',  '64.475 @ 1');
+is($::form->round_amount(64.475, 0), '64',    '64.475 @ 0');
+
+is($::form->round_amount(64.475499, 5), '64.4755', '64.475499 @ 5');
+is($::form->round_amount(64.475499, 4), '64.4755', '64.475499 @ 4');
+is($::form->round_amount(64.475499, 3), '64.475',  '64.475499 @ 3');
+is($::form->round_amount(64.475499, 2), '64.48',   '64.475499 @ 2');
+is($::form->round_amount(64.475499, 1), '64.5',    '64.475499 @ 1');
+is($::form->round_amount(64.475499, 0), '64',      '64.475499 @ 0');
+
+is($::form->round_amount(64.475999, 5), '64.476', '64.475999 @ 5');
+is($::form->round_amount(64.475999, 4), '64.476', '64.475999 @ 4');
+is($::form->round_amount(64.475999, 3), '64.476', '64.475999 @ 3');
+is($::form->round_amount(64.475999, 2), '64.48',  '64.475999 @ 2');
+is($::form->round_amount(64.475999, 1), '64.5',   '64.475999 @ 1');
+is($::form->round_amount(64.475999, 0), '64',     '64.475999 @ 0');
+

 is($::form->round_amount(44.9 * 0.75, 2), '33.68', '44.9 * 0.75 @ 2');
 is($::form->round_amount(44.9 * 0.75, 1), '33.7',  '44.9 * 0.75 @ 1');
 is($::form->round_amount(44.9 * 0.75, 0), '34',    '44.9 * 0.75 @ 0');
 is($::form->round_amount(44.9 * 0.75, 2), '33.68', '44.9 * 0.75 @ 2');
 is($::form->round_amount(44.9 * 0.75, 1), '33.7',  '44.9 * 0.75 @ 1');
 is($::form->round_amount(44.9 * 0.75, 0), '34',    '44.9 * 0.75 @ 0');