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Revision add0f69b

Von Moritz Bunkus vor mehr als 10 Jahren hinzugefügt

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.

Unterschiede anzeigen:

SL/Form.pm
952 952 

  		




  953
  953
  
    
  # Rounding like "Kaufmannsrunden" (see http://de.wikipedia.org/wiki/Rundung )


  		




  954
  954
  
    

  		




  955
  
  
    
  # Round amounts to eight places before rounding to the requested


  		




  956
  
  
    
  # number of places. This gets rid of errors due to internal floating


  		




  957
  
  
    
  # point representation.


  		




  958
  
  
    
  $amount   = $self->round_amount($amount, 8) if $places < 8;


  		




  959
  
  
    

  		




  960
  
  
    
  # Remember the amount's sign but calculate in positive values only.


  		




  961
  
  
    
  my $sign  = $amount <=> 0;


  		




  962
  
  
    
  $amount   = abs $amount;


  		




  963
  
  
    

  		




  964
  
  
    
  # Shift the amount left by $places+1 decimal places and truncate it


  		




  965
  
  
    
  # to integer. Then to the integer equivalent of rounding to the next


  		




  966
  
  
    
  # multiple of 10: first add half of it (5). Then truncate it back to


  		




  967
  
  
    
  # the lower multiple of 10 by subtracting $amount modulo 10.


  		




  968
  
  
    
  my $shift = 10 ** ($places + 1);


  		




  969
  
  
    
  $amount   = int($amount * $shift) + 5;


  		




  970
  
  
    
  $amount  -= $amount % 10;


  		




  971
  
  
    

  		




  972
  
  
    
  # Lastly shift the amount back right by $places+1 decimal places and


  		




  973
  
  
    
  # restore its sign. Then we're done.


  		




  974
  
  
    
  $amount   = ($amount / $shift) * $sign;


  		




  
  955
  
    
  # If you search for rounding in Perl, you'll likely get the first version of


  		




  
  956
  
    
  # this algorithm:


  		




  
  957
  
    
  #


  		




  
  958
  
    
  # ($amount <=> 0) * int(abs($amount) * 10**$places) + .5) / 10**$places


  		




  
  959
  
    
  #


  		




  
  960
  
    
  # That doesn't work. It falls apart for certain values that are exactly 0.5


  		




  
  961
  
    
  # over the cutoff, because the internal IEEE754 representation is slightly


  		




  
  962
  
    
  # below the cutoff. Perl makes matters worse in that it really, really tries to


  		




  
  963
  
    
  # recognize exact values for presentation to you, even if they are not.


  		




  
  964
  
    
  #


  		




  
  965
  
    
  # Example: take the value 64.475 and round to 2 places.


  		




  
  966
  
    
  #


  		




  
  967
  
    
  # printf("%.20f\n", 64.475) gives you 64.47499999999999431566


  		




  
  968
  
    
  #


  		




  
  969
  
    
  # Then 64.475 * 100 + 0.5 is 6447.99999999999909050530, and


  		




  
  970
  
    
  # int(64.475 * 100 + 0.5) / 100 = 64.47


  		




  
  971
  
    
  #


  		




  
  972
  
    
  # Trying to round with more precision first only shifts the problem to rarer


  		




  
  973
  
    
  # cases, which nevertheless exist.


  		




  
  974
  
    
  #


  		




  
  975
  
    
  # Now we exploit the presentation rounding of Perl. Since it really tries hard


  		




  
  976
  
    
  # to recognize integers, we double $amount, and let Perl give us a representation.


  		




  
  977
  
    
  # If Perl recognizes it as a slightly too small integer, and rounds up to the


  		




  
  978
  
    
  # next odd integer, we follow suit and treat the fraction as .5 or greater.


  		




  
  979
  
    

  		




  
  980
  
    
  my $sign               = $amount <=> 0;


  		




  
  981
  
    
  $amount                = abs $amount;


  		




  
  982
  
    

  		




  
  983
  
    
  my $shift              = 10 ** ($places);


  		




  
  984
  
    
  my $shifted_and_double = $amount * $shift * 2;


  		




  
  985
  
    
  my $rounding_bias      = sprintf('%f', $shifted_and_double) % 2;


  		




  
  986
  
    
  $amount                = int($amount * $shift) + $rounding_bias;


  		




  
  987
  
    
  $amount                = $amount / $shift * $sign;


  		




  975
  988
  
    

  		




  976
  989
  
    
  return $amount;


  		




  977
  990
  
    
}


  		












  

    
      t/form/round_amount.t
    
  





  23
  23
  
    
is($::form->round_amount(33.675, 1), '33.7',  '33.675 @ 1');


  		




  24
  24
  
    
is($::form->round_amount(33.675, 0), '34',    '33.675 @ 0');


  		




  25
  25
  
    

  		




  
  26
  
    
is($::form->round_amount(64.475, 2), '64.48', '64.475 @ 2');


  		




  
  27
  
    
is($::form->round_amount(64.475, 1), '64.5',  '64.475 @ 1');


  		




  
  28
  
    
is($::form->round_amount(64.475, 0), '64',    '64.475 @ 0');


  		




  
  29
  
    

  		




  
  30
  
    
is($::form->round_amount(64.475499, 5), '64.4755', '64.475499 @ 5');


  		




  
  31
  
    
is($::form->round_amount(64.475499, 4), '64.4755', '64.475499 @ 4');


  		




  
  32
  
    
is($::form->round_amount(64.475499, 3), '64.475',  '64.475499 @ 3');


  		




  
  33
  
    
is($::form->round_amount(64.475499, 2), '64.48',   '64.475499 @ 2');


  		




  
  34
  
    
is($::form->round_amount(64.475499, 1), '64.5',    '64.475499 @ 1');


  		




  
  35
  
    
is($::form->round_amount(64.475499, 0), '64',      '64.475499 @ 0');


  		




  
  36
  
    

  		




  
  37
  
    
is($::form->round_amount(64.475999, 5), '64.476', '64.475999 @ 5');


  		




  
  38
  
    
is($::form->round_amount(64.475999, 4), '64.476', '64.475999 @ 4');


  		




  
  39
  
    
is($::form->round_amount(64.475999, 3), '64.476', '64.475999 @ 3');


  		




  
  40
  
    
is($::form->round_amount(64.475999, 2), '64.48',  '64.475999 @ 2');


  		




  
  41
  
    
is($::form->round_amount(64.475999, 1), '64.5',   '64.475999 @ 1');


  		




  
  42
  
    
is($::form->round_amount(64.475999, 0), '64',     '64.475999 @ 0');


  		




  
  43
  
    

  		




  26
  44
  
    
is($::form->round_amount(44.9 * 0.75, 2), '33.68', '44.9 * 0.75 @ 2');


  		




  27
  45
  
    
is($::form->round_amount(44.9 * 0.75, 1), '33.7',  '44.9 * 0.75 @ 1');


  		




  28
  46
  
    
is($::form->round_amount(44.9 * 0.75, 0), '34',    '44.9 * 0.75 @ 0');


  		












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