use Data::Dumper;
use Carp;
+use Config;
use CGI;
use Cwd;
use Encode;
use File::Copy;
use IO::File;
+use Math::BigInt;
use SL::Auth;
use SL::Auth::DB;
use SL::Auth::LDAP;
sub round_amount {
my ($self, $amount, $places) = @_;
- # Rounding like "Kaufmannsrunden" (see http://de.wikipedia.org/wiki/Rundung )
-
- # If you search for rounding in Perl, you'll likely get the first version of
- # this algorithm:
- #
- # ($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;
+ # We use Perl's knowledge of string representation for
+ # rounding. First, convert the floating point number to a string
+ # with a high number of places. Then split the string on the decimal
+ # sign and use integer calculation for rounding the decimal places
+ # part. If an overflow occurs then apply that overflow to the part
+ # before the decimal sign as well using integer arithmetic again.
+
+ my $amount_str = sprintf '%.*f', $places + 10, abs($amount);
+
+ return $amount unless $amount_str =~ m{^(\d+)\.(\d+)$};
+
+ my ($pre, $post) = ($1, $2);
+ my $decimals = '1' . substr($post, 0, $places);
+
+ my $propagation_limit = $Config{i32size} == 4 ? 7 : 18;
+ my $add_for_rounding = substr($post, $places, 1) >= 5 ? 1 : 0;
+
+ if ($places > $propagation_limit) {
+ $decimals = Math::BigInt->new($decimals)->badd($add_for_rounding);
+ $pre = Math::BigInt->new($decimals)->badd(1) if substr($decimals, 0, 1) eq '2';
+
+ } else {
+ $decimals += $add_for_rounding;
+ $pre += 1 if substr($decimals, 0, 1) eq '2';
+ }
+
+ $amount = ("${pre}." . substr($decimals, 1)) * ($amount <=> 0);
return $amount;
}
is($::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(143.20, 2), '143.2', '143.20 @ 2');
+is($::form->round_amount(143.20, 1), '143.2', '143.20 @ 1');
+is($::form->round_amount(143.20, 0), '143', '143.20 @ 0');
+
is($::form->round_amount(149.175, 2), '149.18', '149.175 @ 2');
is($::form->round_amount(149.175, 1), '149.2', '149.175 @ 1');
is($::form->round_amount(149.175, 0), '149', '149.175 @ 0');
is($::form->round_amount(-198.90 * 0.75, 1), '-149.2', '-198.90 * 0.75 @ 1');
is($::form->round_amount(-198.90 * 0.75, 0), '-149', '-198.90 * 0.75 @ 0');
+for my $sign (-1, 1) {
+ for ("00000".."09999") {
+ my $str = my $num = (99 * $sign) . $_;
+ $num /= 100; # shift decimal
+ $num /= 5; $num /= 3; # calc a bit around
+ $num *= 5; $num *= 3; # dumdidum
+
+ $str =~ s/(..)$/.$1/; # insert dot
+ $str =~ s/0+$//; # remove trailing 0
+ $str =~ s/\.$//; # remove trailing .
+
+ is $::form->round_amount($num, 2), $str, "round($num, 2) == $str";
+ }
+}
+
+# what about number that might occur scientific notation? yes we could just
+# check round_amount(1e-12, 2) and watch it blow up, but where's the fun? lets
+# check a few Cardano triplets. they are defined by:
+#
+# ∛(a + b√c) + ∛(a - b√c) - 1 = 0
+#
+# and the following are solutions for a,b,c:
+# (2,1,5)
+# (5,2,13)
+# (8,3,21)
+#
+# now calc that, and see what our round makes of the remaining number near zero
+#
+for ([2,1,5], [5,2,13], [8,3,21]) {
+ my ($a,$b,$c) = @$_;
+
+ my $result = ($a + $b * sqrt $c)**(1/3) - ($b * sqrt($c) - $a)**(1/3) - 1;
+
+ is $::form->round_amount($result, 2), '0', "$result => 0";
+}
+
+# round to any digit we like
+my $pi = atan2 0, -1;
+is $::form->round_amount($pi, 0), '3', "0 digits of π";
+is $::form->round_amount($pi, 1), '3.1', "1 digit of π";
+is $::form->round_amount($pi, 2), '3.14', "2 digits of π";
+is $::form->round_amount($pi, 3), '3.142', "3 digits of π";
+is $::form->round_amount($pi, 4), '3.1416', "4 digits of π";
+is $::form->round_amount($pi, 5), '3.14159', "5 digits of π";
+is $::form->round_amount($pi, 6), '3.141593', "6 digits of π";
+is $::form->round_amount($pi, 7), '3.1415927', "7 digits of π";
+is $::form->round_amount($pi, 8), '3.14159265', "8 digits of π";
+is $::form->round_amount($pi, 9), '3.141592654', "9 digits of π";
+is $::form->round_amount($pi, 10), '3.1415926536', "10 digits of π";
+
+# A LOT of places:
+is $::form->round_amount(1.2, 200), '1.2', '1.2 @ 200';
+
done_testing;
1;
projects / mfinanz.git / commitdiff