source: trunk/third/perl/lib/bigint.pl @ 14545

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 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
#

$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) = '+' 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,$[,1),length($d)-2);
    substr($d,$[,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($_[$[]),&'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, $y) = (&'bnorm($_[$[]),&'bnorm($_[$[+1]));
    if ($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($_[$[],&'bneg($_[$[+1]));    
}

# GCD -- Euclids algorithm Knuth Vol 2 pg 296
sub main'bgcd { #(num_str, num_str) return num_str
    local($x,$y) = (&'bnorm($_[$[]),&'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, $y) = (&'bnorm($_[$[]), &'bnorm($_[$[+1]));
    if ($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, $[);
            for $y (@y) {
                $prod = $x * $y + $prod[$cty] + $car;
                $prod[$cty++] =
                    $prod - ($car = int($prod * 1e-5)) * 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, $y) = (&'bnorm($_[$[]), &'bnorm($_[$[+1]));
    return wantarray ? ('NaN','NaN') : 'NaN'
        if ($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 = $y[$[];
    $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;
            $x -= ($car = int($x * 1e-5)) * 1e5;
        }
        push(@x, $car); $car = 0;
        for $y (@y) {
            $y = $y * $dd + $car;
            $y -= ($car = int($y * 1e-5)) * 1e5;
        }
    }
    else {
        push(@x, 0);
    }
    @q = (); ($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 = $[, $x = $#x-$#y+$[-1; $y <= $#y; ++$y,++$x) {
                $prd = $q * $y[$y] + $car;
                $prd -= ($car = int($prd * 1e-5)) * 1e5;
                $x[$x] += 1e5 if ($bar = (($x[$x] -= $prd + $bar) < 0));
            }
            if ($x[$#x] < $car + $bar) {
                $car = 0; --$q;
                for ($y = $[, $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;