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bigint.pl
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package bigint; # # This library is no longer being maintained, and is included for backward # compatibility with Perl 4 programs which may require it. # # In particular, this should not be used as an example of modern Perl # programming techniques. # # Suggested alternative: Math::BigInt # # arbitrary size integer math package # # by Mark Biggar # # Canonical Big integer value are strings of the form # /^[+-]\d+$/ with leading zeros suppressed # Input values to these routines may be strings of the form # /^\s*[+-]?[\d\s]+$/. # Examples: # '+0' canonical zero value # ' -123 123 123' canonical value '-123123123' # '1 23 456 7890' canonical value '+1234567890' # Output values always in canonical form # # Actual math is done in an internal format consisting of an array # whose first element is the sign (/^[+-]$/) and whose remaining # elements are base 100000 digits with the least significant digit first. # The string 'NaN' is used to represent the result when input arguments # are not numbers, as well as the result of dividing by zero # # routines provided are: # # bneg(BINT) return BINT negation # babs(BINT) return BINT absolute value # bcmp(BINT,BINT) return CODE compare numbers (undef,<0,=0,>0) # badd(BINT,BINT) return BINT addition # bsub(BINT,BINT) return BINT subtraction # bmul(BINT,BINT) return BINT multiplication # bdiv(BINT,BINT) return (BINT,BINT) division (quo,rem) just quo if scalar # bmod(BINT,BINT) return BINT modulus # bgcd(BINT,BINT) return BINT greatest common divisor # bnorm(BINT) return BINT normalization # # overcome a floating point problem on certain osnames (posix-bc, os390) BEGIN { my $x = 100000.0; my $use_mult = int($x*1e-5)*1e5 == $x ? 1 : 0; } $zero = 0; # normalize string form of number. Strip leading zeros. Strip any # white space and add a sign, if missing. # Strings that are not numbers result the value 'NaN'. sub main'bnorm { #(num_str) return num_str local($_) = @_; s/\s+//g; # strip white space if (s/^([+-]?)0*(\d+)$/$1$2/) { # test if number substr($_,0,0) = '+' unless $1; # Add missing sign s/^-0/+0/; $_; } else { 'NaN'; } } # Convert a number from string format to internal base 100000 format. # Assumes normalized value as input. sub internal { #(num_str) return int_num_array local($d) = @_; ($is,$il) = (substr($d,0,1),length($d)-2); substr($d,0,1) = ''; ($is, reverse(unpack("a" . ($il%5+1) . ("a5" x ($il/5)), $d))); } # Convert a number from internal base 100000 format to string format. # This routine scribbles all over input array. sub external { #(int_num_array) return num_str $es = shift; grep($_ > 9999 || ($_ = substr('0000'.$_,-5)), @_); # zero pad &'bnorm(join('', $es, reverse(@_))); # reverse concat and normalize } # Negate input value. sub main'bneg { #(num_str) return num_str local($_) = &'bnorm(@_); vec($_,0,8) ^= ord('+') ^ ord('-') unless $_ eq '+0'; s/^./N/ unless /^[-+]/; # works both in ASCII and EBCDIC $_; } # Returns the absolute value of the input. sub main'babs { #(num_str) return num_str &abs(&'bnorm(@_)); } sub abs { # post-normalized abs for internal use local($_) = @_; s/^-/+/; $_; } # Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort) sub main'bcmp { #(num_str, num_str) return cond_code local($x,$y) = (&'bnorm($_[0]),&'bnorm($_[1])); if ($x eq 'NaN') { undef; } elsif ($y eq 'NaN') { undef; } else { &cmp($x,$y); } } sub cmp { # post-normalized compare for internal use local($cx, $cy) = @_; return 0 if ($cx eq $cy); local($sx, $sy) = (substr($cx, 0, 1), substr($cy, 0, 1)); local($ld); if ($sx eq '+') { return 1 if ($sy eq '-' || $cy eq '+0'); $ld = length($cx) - length($cy); return $ld if ($ld); return $cx cmp $cy; } else { # $sx eq '-' return -1 if ($sy eq '+'); $ld = length($cy) - length($cx); return $ld if ($ld); return $cy cmp $cx; } } sub main'badd { #(num_str, num_str) return num_str local(*x, *y); ($x, $y) = (&'bnorm($_[0]),&'bnorm($_[1])); if ($x eq 'NaN') { 'NaN'; } elsif ($y eq 'NaN') { 'NaN'; } else { @x = &internal($x); # convert to internal form @y = &internal($y); local($sx, $sy) = (shift @x, shift @y); # get signs if ($sx eq $sy) { &external($sx, &add(*x, *y)); # if same sign add } else { ($x, $y) = (&abs($x),&abs($y)); # make abs if (&cmp($y,$x) > 0) { &external($sy, &sub(*y, *x)); } else { &external($sx, &sub(*x, *y)); } } } } sub main'bsub { #(num_str, num_str) return num_str &'badd($_[0],&'bneg($_[1])); } # GCD -- Euclids algorithm Knuth Vol 2 pg 296 sub main'bgcd { #(num_str, num_str) return num_str local($x,$y) = (&'bnorm($_[0]),&'bnorm($_[1])); if ($x eq 'NaN' || $y eq 'NaN') { 'NaN'; } else { ($x, $y) = ($y,&'bmod($x,$y)) while $y ne '+0'; $x; } } # routine to add two base 1e5 numbers # stolen from Knuth Vol 2 Algorithm A pg 231 # there are separate routines to add and sub as per Kunth pg 233 sub add { #(int_num_array, int_num_array) return int_num_array local(*x, *y) = @_; $car = 0; for $x (@x) { last unless @y || $car; $x -= 1e5 if $car = (($x += shift(@y) + $car) >= 1e5) ? 1 : 0; } for $y (@y) { last unless $car; $y -= 1e5 if $car = (($y += $car) >= 1e5) ? 1 : 0; } (@x, @y, $car); } # subtract base 1e5 numbers -- stolen from Knuth Vol 2 pg 232, $x > $y sub sub { #(int_num_array, int_num_array) return int_num_array local(*sx, *sy) = @_; $bar = 0; for $sx (@sx) { last unless @y || $bar; $sx += 1e5 if $bar = (($sx -= shift(@sy) + $bar) < 0); } @sx; } # multiply two numbers -- stolen from Knuth Vol 2 pg 233 sub main'bmul { #(num_str, num_str) return num_str local(*x, *y); ($x, $y) = (&'bnorm($_[0]), &'bnorm($_[1])); if ($x eq 'NaN') { 'NaN'; } elsif ($y eq 'NaN') { 'NaN'; } else { @x = &internal($x); @y = &internal($y); local($signr) = (shift @x ne shift @y) ? '-' : '+'; @prod = (); for $x (@x) { ($car, $cty) = (0, 0); for $y (@y) { $prod = $x * $y + $prod[$cty] + $car; if ($use_mult) { $prod[$cty++] = $prod - ($car = int($prod * 1e-5)) * 1e5; } else { $prod[$cty++] = $prod - ($car = int($prod / 1e5)) * 1e5; } } $prod[$cty] += $car if $car; $x = shift @prod; } &external($signr, @x, @prod); } } # modulus sub main'bmod { #(num_str, num_str) return num_str (&'bdiv(@_))[1]; } sub main'bdiv { #(dividend: num_str, divisor: num_str) return num_str local (*x, *y); ($x, $y) = (&'bnorm($_[0]), &'bnorm($_[1])); return wantarray ? ('NaN','NaN') : 'NaN' if ($x eq 'NaN' || $y eq 'NaN' || $y eq '+0'); return wantarray ? ('+0',$x) : '+0' if (&cmp(&abs($x),&abs($y)) < 0); @x = &internal($x); @y = &internal($y); $srem = $y[0]; $sr = (shift @x ne shift @y) ? '-' : '+'; $car = $bar = $prd = 0; if (($dd = int(1e5/($y[$#y]+1))) != 1) { for $x (@x) { $x = $x * $dd + $car; if ($use_mult) { $x -= ($car = int($x * 1e-5)) * 1e5; } else { $x -= ($car = int($x / 1e5)) * 1e5; } } push(@x, $car); $car = 0; for $y (@y) { $y = $y * $dd + $car; if ($use_mult) { $y -= ($car = int($y * 1e-5)) * 1e5; } else { $y -= ($car = int($y / 1e5)) * 1e5; } } } else { push(@x, 0); } @q = (); ($v2,$v1) = @y[-2,-1]; while ($#x > $#y) { ($u2,$u1,$u0) = @x[-3..-1]; $q = (($u0 == $v1) ? 99999 : int(($u0*1e5+$u1)/$v1)); --$q while ($v2*$q > ($u0*1e5+$u1-$q*$v1)*1e5+$u2); if ($q) { ($car, $bar) = (0,0); for ($y = 0, $x = $#x-$#y-1; $y <= $#y; ++$y,++$x) { $prd = $q * $y[$y] + $car; if ($use_mult) { $prd -= ($car = int($prd * 1e-5)) * 1e5; } else { $prd -= ($car = int($prd / 1e5)) * 1e5; } $x[$x] += 1e5 if ($bar = (($x[$x] -= $prd + $bar) < 0)); } if ($x[$#x] < $car + $bar) { $car = 0; --$q; for ($y = 0, $x = $#x-$#y-1; $y <= $#y; ++$y,++$x) { $x[$x] -= 1e5 if ($car = (($x[$x] += $y[$y] + $car) > 1e5)); } } } pop(@x); unshift(@q, $q); } if (wantarray) { @d = (); if ($dd != 1) { $car = 0; for $x (reverse @x) { $prd = $car * 1e5 + $x; $car = $prd - ($tmp = int($prd / $dd)) * $dd; unshift(@d, $tmp); } } else { @d = @x; } (&external($sr, @q), &external($srem, @d, $zero)); } else { &external($sr, @q); } } 1;