lib/perl5/5.8.8/bigint.pl

   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 $zero = 0;
  52
  53 \f
  54 # normalize string form of number.   Strip leading zeros.  Strip any
  55 #   white space and add a sign, if missing.
  56 # Strings that are not numbers result the value 'NaN'.
  57
  58 sub main'bnorm { #(num_str) return num_str
  59     local($_) = @_;
  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     $_;
 104 }
 105 \f
 106 # Compares 2 values.  Returns one of undef, <0, =0, >0. (suitable for sort)
 107 sub main'bcmp { #(num_str, num_str) return cond_code
 108     local($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 \f
 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(@_))[$[+1];
 240 }
 241 \f
 242 sub main'bdiv { #(dividend: num_str, divisor: num_str) return num_str
 243     local (*x, *y); ($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;