Re: [mv] Prorate discount script bug

["Bill Randle" <billr@exgate.tek.com>]

******    message to minivend-users from "Bill Randle" <billr@exgate.tek.com>     ******

Sydney,

Now I understand! I thought everything was being prorated down to $1.00
at the end of the month. This equation, though a bit more complicated,
should do the trick:

	$s - $s * (1 - 1 / $mon{$month}) * ($n - 1) / ($mon{$month} - 1);

[<start lesson> Derivation (from simple algebra):
  step 1, offset the days by 1 so they become zero-based as it
    simplifies the derivation
  step 2, draw a graph of price vs. time

	|
	|\   <-- starting price s
price	| \
	|  \
	|   \
	|    \ <-- ending price e
	|----------> day-in-month - 1
       day    ^
	0    day (mdays - 1)

  ending price (e) = starting price (s) / mdays
  slope of the line (m) = (e - s) / (mdays - 1)

  step 3, plug the numbers into the standard equation of a line: y = mx + b
    in this case, y is the price and x is the day number (zero-based); b is
    the value on day 0 (which is the initial price). So (using p for
    the price, n for the 1-based day number, mdays for days in a month),
	p = ((e - s) / (mdays - 1)) * (n - 1) + s
    substitue for e:
	p = ((s/mdays - s) / (mdays - 1)) * (n - 1) + s
    factor out -s:
	p = -s * ((-1/mdays + 1) / (mdays - 1)) * (n - 1) + s
    rearrange the order:
	p = s - s * (1 - 1/mdays) * (n - 1) / (mdays - 1)

<end of lesson>]

	-Bill


On Jun 30,  2:33pm, Sydney Urshan wrote:
} Subject: Re: [mv] Prorate discount script bug
} ******    message to minivend-users from Sydney Urshan
<urshan@nethollywood.net>     ******
}
} Bill,
}
} I just installed this script (at http://nethollywood.net) to check it
} out (on the last day of the month).  The new result is $1 no matter
} what the item costs.  (Which is better than $0!)
}
} Instead, a $20 item today should be $.67 and a $5 item should be
} $.17.  If this month had a different # days, then the results would
} be different by a few cents.  The example below was $1 on the last
} day because, for simplicity sake, it was a $30 item in a 30 day
} month.  Can you help me tweak it to get it working right?
}
} Thanks,
}
} Sydney
}
} >******    message to minivend-users from Bill Randle
} ><billr@exgate.tek.com>     ******
} >
} >Sydney,
} >
} >Try this for the calculation:
} >         $s - ($s - 1) * ($n - 1) / ($mon{$month} - 1);
} >
} >I tried it for a few test cases and it seems to work for me. You could,
} >of course, build the length-Of_month-1 value into your month table.
} >Also, for a little less overhead, you could use localtime() directly,
} >rather than calling $Tag->time(), as you don't need the formating. E.g.:
} >         my ($sec, $min, $hr, $mday, $mon) = localtime;
} >If you do that, remember that $mon goes from 0 to 11.
} >
} >         -Bill
} >
} >
} >Sydney Urshan wrote:
} >  >
} >  > Well, if it's a $30 item in a 30 day month, day 30 should be $1, day
} >  > 29 should be $2...day 2 should be $29, and the first day of the month
} >  > should be $30 with everything else in between adjusted accordingly.
} >  >
} >  > >Sydney Urshan wrote:
} >  > >>
} >  > >>  The following discount script works perfect until the last day of
the
} >  > >>  month at which time the result is 0.  Can someone help me out on
this
} >  > >>  one?
} >  > >>
} >  > >>  [loop list='2001 2002 3001 3002']
} >  > >>  [discount [loop-code]]
} >  > >>  my $bit = $Tag->time('', {}, '%m %d');
} >  > >>  my ($month, $n) = split /\s+/, $bit;
} >  > >>  $n =~ s/^0//;
} >  > >>  my %mon = (
} >  > >>          '01' => 31,
} >  > >>          '02' => 29,
} >  > >>          '03' => 31,
} >  > >>          '04' => 30,
} >  > >>          '05' => 31,
} >  > >>          '06' => 30,
} >  > >>          '07' => 31,
} >  > >>          '08' => 31,
} >  > >>          '09' => 30,
} >  > >>          '10' => 31,
} >  > >>          '11' => 30,
} >  > >>          '12' => 31,
} >  > >>  );
} >  > >>  if ($mon{$month} and $n > 1) {
} >  > >>             return ($s - ($s / $mon{$month} * $n));
} >  > >>  }
} >  > >>  return $s;
} >  > >>  [/discount]
} >  > >>  [/loop]
} >  > >>
} >  > >>  Thanks,
} >  > >>
} >  > >>  Sydney Urshan
} >  > >
} >  > >Look at your calculation again:
} >  > >       $s - ($s / days_in_month * day_of_month);
} >  > >This is equivalent to saying:
} >  > >       $s - $s * (days_in_month / day_of_month);
} >  > >when day_of_month is the same as days_in_month, you get
} >  > >       $s - $s * 1;
} >  > >which is 0.
} >  > >
} >  > >What did you intend the prorate to be at the end of the month?
} >  > >
} >  > >       -Bill
} -
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}-- End of excerpt from Sydney Urshan


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