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   1  package bigint;
   2  #
   3  # This library is no longer being maintained, and is included for backward
   4  # compatibility with Perl 4 programs which may require it.
   5  #
   6  # In particular, this should not be used as an example of modern Perl
   7  # programming techniques.
   8  #
   9  # Suggested alternative:  Math::BigInt
  10  #
  11  # arbitrary size integer math package
  12  #
  13  # by Mark Biggar
  14  #
  15  # Canonical Big integer value are strings of the form
  16  #       /^[+-]\d+$/ with leading zeros suppressed
  17  # Input values to these routines may be strings of the form
  18  #       /^\s*[+-]?[\d\s]+$/.
  19  # Examples:
  20  #   '+0'                            canonical zero value
  21  #   '   -123 123 123'               canonical value '-123123123'
  22  #   '1 23 456 7890'                 canonical value '+1234567890'
  23  # Output values always in canonical form
  24  #
  25  # Actual math is done in an internal format consisting of an array
  26  #   whose first element is the sign (/^[+-]$/) and whose remaining 
  27  #   elements are base 100000 digits with the least significant digit first.
  28  # The string 'NaN' is used to represent the result when input arguments 
  29  #   are not numbers, as well as the result of dividing by zero
  30  #
  31  # routines provided are:
  32  #
  33  #   bneg(BINT) return BINT              negation
  34  #   babs(BINT) return BINT              absolute value
  35  #   bcmp(BINT,BINT) return CODE         compare numbers (undef,<0,=0,>0)
  36  #   badd(BINT,BINT) return BINT         addition
  37  #   bsub(BINT,BINT) return BINT         subtraction
  38  #   bmul(BINT,BINT) return BINT         multiplication
  39  #   bdiv(BINT,BINT) return (BINT,BINT)  division (quo,rem) just quo if scalar
  40  #   bmod(BINT,BINT) return BINT         modulus
  41  #   bgcd(BINT,BINT) return BINT         greatest common divisor
  42  #   bnorm(BINT) return BINT             normalization
  43  #
  44  
  45  # overcome a floating point problem on certain osnames (posix-bc, os390)
  46  BEGIN {
  47      my $x = 100000.0;
  48      my $use_mult = int($x*1e-5)*1e5 == $x ? 1 : 0;
  49  }
  50  
  51  $zero = 0;
  52  
  53  
  54  # normalize string form of number.   Strip leading zeros.  Strip any
  55  #   white space and add a sign, if missing.
  56  # Strings that are not numbers result the value 'NaN'.
  57  
  58  sub main'bnorm { #(num_str) return num_str
  59      local($_) = @_;
  60      s/\s+//g;                           # strip white space
  61      if (s/^([+-]?)0*(\d+)$/$1$2/) {     # test if number
  62      substr($_,$[,0) = '+' unless $1; # Add missing sign
  63      s/^-0/+0/;
  64      $_;
  65      } else {
  66      'NaN';
  67      }
  68  }
  69  
  70  # Convert a number from string format to internal base 100000 format.
  71  #   Assumes normalized value as input.
  72  sub internal { #(num_str) return int_num_array
  73      local($d) = @_;
  74      ($is,$il) = (substr($d,$[,1),length($d)-2);
  75      substr($d,$[,1) = '';
  76      ($is, reverse(unpack("a" . ($il%5+1) . ("a5" x ($il/5)), $d)));
  77  }
  78  
  79  # Convert a number from internal base 100000 format to string format.
  80  #   This routine scribbles all over input array.
  81  sub external { #(int_num_array) return num_str
  82      $es = shift;
  83      grep($_ > 9999 || ($_ = substr('0000'.$_,-5)), @_);   # zero pad
  84      &'bnorm(join('', $es, reverse(@_)));    # reverse concat and normalize
  85  }
  86  
  87  # Negate input value.
  88  sub main'bneg { #(num_str) return num_str
  89      local($_) = &'bnorm(@_);
  90      vec($_,0,8) ^= ord('+') ^ ord('-') unless $_ eq '+0';
  91      s/^./N/ unless /^[-+]/; # works both in ASCII and EBCDIC
  92      $_;
  93  }
  94  
  95  # Returns the absolute value of the input.
  96  sub main'babs { #(num_str) return num_str
  97      &abs(&'bnorm(@_));
  98  }
  99  
 100  sub abs { # post-normalized abs for internal use
 101      local($_) = @_;
 102      s/^-/+/;
 103      $_;
 104  }
 105  
 106  # Compares 2 values.  Returns one of undef, <0, =0, >0. (suitable for sort)
 107  sub main'bcmp { #(num_str, num_str) return cond_code
 108      local($x,$y) = (&'bnorm($_[$[]),&'bnorm($_[$[+1]));
 109      if ($x eq 'NaN') {
 110      undef;
 111      } elsif ($y eq 'NaN') {
 112      undef;
 113      } else {
 114      &cmp($x,$y);
 115      }
 116  }
 117  
 118  sub cmp { # post-normalized compare for internal use
 119      local($cx, $cy) = @_;
 120      return 0 if ($cx eq $cy);
 121  
 122      local($sx, $sy) = (substr($cx, 0, 1), substr($cy, 0, 1));
 123      local($ld);
 124  
 125      if ($sx eq '+') {
 126        return  1 if ($sy eq '-' || $cy eq '+0');
 127        $ld = length($cx) - length($cy);
 128        return $ld if ($ld);
 129        return $cx cmp $cy;
 130      } else { # $sx eq '-'
 131        return -1 if ($sy eq '+');
 132        $ld = length($cy) - length($cx);
 133        return $ld if ($ld);
 134        return $cy cmp $cx;
 135      }
 136  
 137  }
 138  
 139  sub main'badd { #(num_str, num_str) return num_str
 140      local(*x, *y); ($x, $y) = (&'bnorm($_[$[]),&'bnorm($_[$[+1]));
 141      if ($x eq 'NaN') {
 142      'NaN';
 143      } elsif ($y eq 'NaN') {
 144      'NaN';
 145      } else {
 146      @x = &internal($x);             # convert to internal form
 147      @y = &internal($y);
 148      local($sx, $sy) = (shift @x, shift @y); # get signs
 149      if ($sx eq $sy) {
 150          &external($sx, &add(*x, *y)); # if same sign add
 151      } else {
 152          ($x, $y) = (&abs($x),&abs($y)); # make abs
 153          if (&cmp($y,$x) > 0) {
 154          &external($sy, &sub(*y, *x));
 155          } else {
 156          &external($sx, &sub(*x, *y));
 157          }
 158      }
 159      }
 160  }
 161  
 162  sub main'bsub { #(num_str, num_str) return num_str
 163      &'badd($_[$[],&'bneg($_[$[+1]));    
 164  }
 165  
 166  # GCD -- Euclids algorithm Knuth Vol 2 pg 296
 167  sub main'bgcd { #(num_str, num_str) return num_str
 168      local($x,$y) = (&'bnorm($_[$[]),&'bnorm($_[$[+1]));
 169      if ($x eq 'NaN' || $y eq 'NaN') {
 170      'NaN';
 171      } else {
 172      ($x, $y) = ($y,&'bmod($x,$y)) while $y ne '+0';
 173      $x;
 174      }
 175  }
 176  
 177  # routine to add two base 1e5 numbers
 178  #   stolen from Knuth Vol 2 Algorithm A pg 231
 179  #   there are separate routines to add and sub as per Kunth pg 233
 180  sub add { #(int_num_array, int_num_array) return int_num_array
 181      local(*x, *y) = @_;
 182      $car = 0;
 183      for $x (@x) {
 184      last unless @y || $car;
 185      $x -= 1e5 if $car = (($x += shift(@y) + $car) >= 1e5) ? 1 : 0;
 186      }
 187      for $y (@y) {
 188      last unless $car;
 189      $y -= 1e5 if $car = (($y += $car) >= 1e5) ? 1 : 0;
 190      }
 191      (@x, @y, $car);
 192  }
 193  
 194  # subtract base 1e5 numbers -- stolen from Knuth Vol 2 pg 232, $x > $y
 195  sub sub { #(int_num_array, int_num_array) return int_num_array
 196      local(*sx, *sy) = @_;
 197      $bar = 0;
 198      for $sx (@sx) {
 199      last unless @y || $bar;
 200      $sx += 1e5 if $bar = (($sx -= shift(@sy) + $bar) < 0);
 201      }
 202      @sx;
 203  }
 204  
 205  # multiply two numbers -- stolen from Knuth Vol 2 pg 233
 206  sub main'bmul { #(num_str, num_str) return num_str
 207      local(*x, *y); ($x, $y) = (&'bnorm($_[$[]), &'bnorm($_[$[+1]));
 208      if ($x eq 'NaN') {
 209      'NaN';
 210      } elsif ($y eq 'NaN') {
 211      'NaN';
 212      } else {
 213      @x = &internal($x);
 214      @y = &internal($y);
 215      local($signr) = (shift @x ne shift @y) ? '-' : '+';
 216      @prod = ();
 217      for $x (@x) {
 218          ($car, $cty) = (0, $[);
 219          for $y (@y) {
 220          $prod = $x * $y + $prod[$cty] + $car;
 221                  if ($use_mult) {
 222              $prod[$cty++] =
 223                  $prod - ($car = int($prod * 1e-5)) * 1e5;
 224                  }
 225                  else {
 226              $prod[$cty++] =
 227                  $prod - ($car = int($prod / 1e5)) * 1e5;
 228                  }
 229          }
 230          $prod[$cty] += $car if $car;
 231          $x = shift @prod;
 232      }
 233      &external($signr, @x, @prod);
 234      }
 235  }
 236  
 237  # modulus
 238  sub main'bmod { #(num_str, num_str) return num_str
 239      (&'bdiv(@_))[$[+1];
 240  }
 241  
 242  sub main'bdiv { #(dividend: num_str, divisor: num_str) return num_str
 243      local (*x, *y); ($x, $y) = (&'bnorm($_[$[]), &'bnorm($_[$[+1]));
 244      return wantarray ? ('NaN','NaN') : 'NaN'
 245      if ($x eq 'NaN' || $y eq 'NaN' || $y eq '+0');
 246      return wantarray ? ('+0',$x) : '+0' if (&cmp(&abs($x),&abs($y)) < 0);
 247      @x = &internal($x); @y = &internal($y);
 248      $srem = $y[$[];
 249      $sr = (shift @x ne shift @y) ? '-' : '+';
 250      $car = $bar = $prd = 0;
 251      if (($dd = int(1e5/($y[$#y]+1))) != 1) {
 252      for $x (@x) {
 253          $x = $x * $dd + $car;
 254              if ($use_mult) {
 255          $x -= ($car = int($x * 1e-5)) * 1e5;
 256              }
 257              else {
 258          $x -= ($car = int($x / 1e5)) * 1e5;
 259              }
 260      }
 261      push(@x, $car); $car = 0;
 262      for $y (@y) {
 263          $y = $y * $dd + $car;
 264              if ($use_mult) {
 265          $y -= ($car = int($y * 1e-5)) * 1e5;
 266              }
 267              else {
 268          $y -= ($car = int($y / 1e5)) * 1e5;
 269              }
 270      }
 271      }
 272      else {
 273      push(@x, 0);
 274      }
 275      @q = (); ($v2,$v1) = @y[-2,-1];
 276      while ($#x > $#y) {
 277      ($u2,$u1,$u0) = @x[-3..-1];
 278      $q = (($u0 == $v1) ? 99999 : int(($u0*1e5+$u1)/$v1));
 279      --$q while ($v2*$q > ($u0*1e5+$u1-$q*$v1)*1e5+$u2);
 280      if ($q) {
 281          ($car, $bar) = (0,0);
 282          for ($y = $[, $x = $#x-$#y+$[-1; $y <= $#y; ++$y,++$x) {
 283          $prd = $q * $y[$y] + $car;
 284                  if ($use_mult) {
 285          $prd -= ($car = int($prd * 1e-5)) * 1e5;
 286                  }
 287                  else {
 288          $prd -= ($car = int($prd / 1e5)) * 1e5;
 289                  }
 290          $x[$x] += 1e5 if ($bar = (($x[$x] -= $prd + $bar) < 0));
 291          }
 292          if ($x[$#x] < $car + $bar) {
 293          $car = 0; --$q;
 294          for ($y = $[, $x = $#x-$#y+$[-1; $y <= $#y; ++$y,++$x) {
 295              $x[$x] -= 1e5
 296              if ($car = (($x[$x] += $y[$y] + $car) > 1e5));
 297          }
 298          }   
 299      }
 300      pop(@x); unshift(@q, $q);
 301      }
 302      if (wantarray) {
 303      @d = ();
 304      if ($dd != 1) {
 305          $car = 0;
 306          for $x (reverse @x) {
 307          $prd = $car * 1e5 + $x;
 308          $car = $prd - ($tmp = int($prd / $dd)) * $dd;
 309          unshift(@d, $tmp);
 310          }
 311      }
 312      else {
 313          @d = @x;
 314      }
 315      (&external($sr, @q), &external($srem, @d, $zero));
 316      } else {
 317      &external($sr, @q);
 318      }
 319  }
 320  1;