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=head1 NAME
Math::Decimal::FastPP  Fast purePerl decimal math
=head1 SYNOPSIS
use Math::Decimal::FastPP;
$a = dadd($a, "1.23"); # $a += 1.23
$c = dmul($a, $b); # $c = $a * $b
$a = drhtz($a); # Round half toward zero
=head1 DESCRIPTION
Math::Decimal::FastPP provides a few common decimal arithmetic and rounding
functions written in pure Perl. The functions are of course slower than Perl's
builtin binary floatingpoint math, but they're faster than L<Math::BigFloat>
and other commonly used decimal math modules.
This module is currently less complete than Perl's builtin math and other
decimal math modules. So far it only includes addition, multiplication, and two
rounding functions.
Despite the similar name and purpose, this module is not compatible with
L<Math::Decimal>.
=head1 PHILOSOPHY
This module is designed both to run fast and to be used fast. The functions are
written to be as short and fast as possible, at a small cost in readability.
For help reading the bodies of these functions, see L</THEORY> below.
The names and parameters of this module's functions are kept minimal to allow
them to be typed quickly and to take little space in calling code. After all, a
function to add two numbers shouldn't take much more typing than C<+>. The
names of the rounding functions may look strange, but they are simply
initialisms (or acronyms, if you're creative enough) of "decimal round toward
zero" and "decimal round (away) from zero".
=head1 THEORY
The binary operation functions (C<dadd()> and C<dmul()>) operate on two numbers,
C<a> and C<b>. And obviously the unary operation functions (C<drhtz()> and
C<drhfz()>) operate on one number, C<a>. The binary operation functions produce
a resulting number, C<c>.
The input numbers C<a> and C<b> are broken into their integer (C<i>) and
fractional (C<f>) parts, for example C<$ai> and C<$af>. All three numbers C<a>,
C<b>, and C<c> are comprised of a significand C<s> and (negated) exponent C<e>
and can be expressed as C<s * 10**(1*e)>.
The significand is all of the significant digits (although the digits are
preserved exactly as given, so leading zeroes are considered "significant") in
the form of an integer, with no radix point. It is formed simply by
concatenating the integer and fractional parts, e.g. C<$as = $ai . $af>. The
exponent is simply the number of digits in the fractional part, e.g.
C<$ae = length($af)>.
Multiplication is done simply be multiplying the integer significands and adding
the exponents. The resulting significand and exponent is converted back into a
string with integer and fractional parts.
Addition is a little more complicated. The exponents of the two input numbers
must match; if they don't, zeroes are appended to the significand of the number
with the smaller exponent to make the exponents match. The significands are
then added. The output number is converted from the resulting significand and
the common exponent of the input numbers.
=head1 FUNCTIONS
=cut
package Math::Decimal::FastPP;
use strict;
use warnings;
use Exporter qw(import);
our @EXPORT = qw(dadd dmul drhtz drhfz);
our $VERSION = "0.001";
=head2 dadd()
$c = dadd($a, $b);
Adds C<$a> and C<$b> and returns their sum.
=cut
sub dadd
{
my ($ai, $af) = split("\\.", $_[0]);
my ($bi, $bf) = split("\\.", $_[1]);
$af = "";
$bf = "";
my $ae = length($af);
my $be = length($bf);
my $ce;
if ($ae == $be) {
$ce = $ae;
} elsif ($ae < $be) {
$af .= "0" x ($be  $ae);
$ce = $be;
} else {
$bf .= "0" x ($ae  $be);
$ce = $ae;
}
my $as = $ai . $af;
my $bs = $bi . $bf;
my $cs = $as + $bs;
$cs = sprintf("%0${ce}i", $cs);
# The substr() code is 400% faster than this regular expression code.
#$cs =~ s/(.{$ce})$/.$1/;
#return $cs;
return substr($cs, 0, length($cs)  $ce) . "." .
substr($cs, length($cs)  $ce);
}
=head2 dmul()
$c = dmul($a, $b);
Multiplies C<$a> and C<$b> and returns their product.
=cut
sub dmul
{
my ($ai, $af) = split("\\.", $_[0]);
my ($bi, $bf) = split("\\.", $_[1]);
$af = "";
$bf = "";
my $as = $ai . $af;
my $ae = length($af);
my $bs = $bi . $bf;
my $be = length($bf);
my $cs = $as * $bs;
my $ce = $ae + $be;
$cs = sprintf("%0${ce}i", $cs);
# The substr() code is 400% faster than this regular expression code.
#$cs =~ s/(.{$ce})$/.$1/;
#return $cs;
return substr($cs, 0, length($cs)  $ce) . "." .
substr($cs, length($cs)  $ce);
}
=head2 drhtz()
$a = drhtz($a, $p);
Rounds C<$a> with precision C<$p>. Halves are rounded toward zero. For
example:
drhtz("23.5", 0); # Returns "23."
drhtz("2.35", 1); # Returns "2.3"
drhtz("23.5", 0); # Returns "23."
drhtz("2.35", 1); # Returns "2.3"
C<$p> is a nonnegative (i.e. zero or positive) integer representing the number
of significant digits right of the radix point.
=cut
sub drhtz
{
my ($ai, $af, $ad) = $_[0] =~ m/^(.*)\.(.{$_[1]})(.*)$/ or return;
my $as = $ai . $af;
if ($as >= 0) {
++$as if $ad > "5" . "0" x (length($ad)  1);
} else {
$as if $ad > "5" . "0" x (length($ad)  1);
}
$as = sprintf("%0$_[1]i", $as);
# The substr() code is 400% faster than this regular expression code.
#$as =~ s/(.{$_[1]})$/.$1/;
#return $cs;
return substr($as, 0, length($as)  $_[1]) . "." .
substr($as, length($as)  $_[1]);
}
=head2 drhfz()
$a = drhfz($a, $p);
Rounds C<$a> with precision C<$p>. Halves are rounded away from zero. For
example:
drhfz("23.5", 0); # Returns "24."
drhtz("2.35", 1); # Returns "2.4"
drhfz("23.5", 0); # Returns "24."
drhtz("2.35", 1); # Returns "2.4"
C<$p> is a nonnegative (i.e. zero or positive) integer representing the number
of significant digits right of the radix point.
=cut
sub drhfz
{
my ($ai, $af, $ad) = $_[0] =~ m/^(.*)\.(.{$_[1]})(.*)$/ or return;
my $as = $ai . $af;
if ($as >= 0) {
++$as if $ad >= "5" . "0" x (length($ad)  1);
} else {
$as if $ad >= "5" . "0" x (length($ad)  1);
}
$as = sprintf("%0$_[1]i", $as);
# The substr() code is 400% faster than this regular expression code.
#$as =~ s/(.{$_[1]})$/.$1/;
#return $as;
return substr($as, 0, length($as)  $_[1]) . "." .
substr($as, length($as)  $_[1]);
}
1;
__END__
=head1 CAVEATS
These arithmetic functions preserve all significant fractional digits, including
trailing zeroes. They also don't always add a leading zero before the radix
point for numbers with absolute values less than one. So the output numbers can
look "ugly", like ".123000". This is only an issue if the numbers (which are
returned as strings) are concatenated into other strings or printed without
formatting. If this is an issue in your code, use the outputs as numbers (e.g.
C<$c + 0>) or print with formatting (with C<printf>).
=head1 AUTHOR
Patrick McDermott L<mailto:patrick.mcdermott@libiquity.com>
=head1 SEE ALSO
L<Math::BigFloat>, L<Math::Decimal>
=head1 COPYRIGHT
Copyright (C) 2017 Patrick McDermott
=head1 LICENSE
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see L<http://www.gnu.org/licenses/>.
=cut
