Tadashi Okoshi
slash****@users*****
2005年 10月 25日 (火) 04:20:51 JST
Index: affelio_farm/admin/skelton/affelio/extlib/Math/BigInt/Calc.pm
diff -u affelio_farm/admin/skelton/affelio/extlib/Math/BigInt/Calc.pm:1.1.1.1 affelio_farm/admin/skelton/affelio/extlib/Math/BigInt/Calc.pm:removed
--- affelio_farm/admin/skelton/affelio/extlib/Math/BigInt/Calc.pm:1.1.1.1 Tue Oct 25 04:14:40 2005
+++ affelio_farm/admin/skelton/affelio/extlib/Math/BigInt/Calc.pm Tue Oct 25 04:20:51 2005
@@ -1,2102 +0,0 @@
-package Math::BigInt::Calc;
-
-use 5.005;
-use strict;
-# use warnings; # dont use warnings for older Perls
-
-use vars qw/$VERSION/;
-
-$VERSION = '0.47';
-
-# Package to store unsigned big integers in decimal and do math with them
-
-# Internally the numbers are stored in an array with at least 1 element, no
-# leading zero parts (except the first) and in base 1eX where X is determined
-# automatically at loading time to be the maximum possible value
-
-# todo:
-# - fully remove funky $# stuff in div() (maybe - that code scares me...)
-
-# USE_MUL: due to problems on certain os (os390, posix-bc) "* 1e-5" is used
-# instead of "/ 1e5" at some places, (marked with USE_MUL). Other platforms
-# BS2000, some Crays need USE_DIV instead.
-# The BEGIN block is used to determine which of the two variants gives the
-# correct result.
-
-# Beware of things like:
-# $i = $i * $y + $car; $car = int($i / $MBASE); $i = $i % $MBASE;
-# This works on x86, but fails on ARM (SA1100, iPAQ) due to whoknows what
-# reasons. So, use this instead (slower, but correct):
-# $i = $i * $y + $car; $car = int($i / $MBASE); $i -= $MBASE * $car;
-
-##############################################################################
-# global constants, flags and accessory
-
-# announce that we are compatible with MBI v1.70 and up
-sub api_version () { 1; }
-
-# constants for easier life
-my ($BASE,$BASE_LEN,$MBASE,$RBASE,$MAX_VAL,$BASE_LEN_SMALL);
-my ($AND_BITS,$XOR_BITS,$OR_BITS);
-my ($AND_MASK,$XOR_MASK,$OR_MASK);
-
-sub _base_len
- {
- # set/get the BASE_LEN and assorted other, connected values
- # used only be the testsuite, set is used only by the BEGIN block below
- shift;
-
- my $b = shift;
- if (defined $b)
- {
- # find whether we can use mul or div or none in mul()/div()
- # (in last case reduce BASE_LEN_SMALL)
- $BASE_LEN_SMALL = $b+1;
- my $caught = 0;
- while (--$BASE_LEN_SMALL > 5)
- {
- $MBASE = int("1e".$BASE_LEN_SMALL);
- $RBASE = abs('1e-'.$BASE_LEN_SMALL); # see USE_MUL
- $caught = 0;
- $caught += 1 if (int($MBASE * $RBASE) != 1); # should be 1
- $caught += 2 if (int($MBASE / $MBASE) != 1); # should be 1
- last if $caught != 3;
- }
- # BASE_LEN is used for anything else than mul()/div()
- $BASE_LEN = $BASE_LEN_SMALL;
- $BASE_LEN = shift if (defined $_[0]); # one more arg?
- $BASE = int("1e".$BASE_LEN);
-
- $MBASE = int("1e".$BASE_LEN_SMALL);
- $RBASE = abs('1e-'.$BASE_LEN_SMALL); # see USE_MUL
- $MAX_VAL = $MBASE-1;
-
- # avoid redefinitions
-
- undef &_mul;
- undef &_div;
-
- # $caught & 1 != 0 => cannot use MUL
- # $caught & 2 != 0 => cannot use DIV
- # The parens around ($caught & 1) were important, indeed, if we would use
- # & here.
- if ($caught == 2) # 2
- {
- # must USE_MUL since we cannot use DIV
- *{_mul} = \&_mul_use_mul;
- *{_div} = \&_div_use_mul;
- }
- else # 0 or 1
- {
- # can USE_DIV instead
- *{_mul} = \&_mul_use_div;
- *{_div} = \&_div_use_div;
- }
- }
- return $BASE_LEN unless wantarray;
- return ($BASE_LEN, $AND_BITS, $XOR_BITS, $OR_BITS, $BASE_LEN_SMALL, $MAX_VAL, $BASE);
- }
-
-sub _new
- {
- # (ref to string) return ref to num_array
- # Convert a number from string format (without sign) to internal base
- # 1ex format. Assumes normalized value as input.
- my $il = length($_[1])-1;
-
- # < BASE_LEN due len-1 above
- return [ int($_[1]) ] if $il < $BASE_LEN; # shortcut for short numbers
-
- # this leaves '00000' instead of int 0 and will be corrected after any op
- [ reverse(unpack("a" . ($il % $BASE_LEN+1)
- . ("a$BASE_LEN" x ($il / $BASE_LEN)), $_[1])) ];
- }
-
-BEGIN
- {
- # from Daniel Pfeiffer: determine largest group of digits that is precisely
- # multipliable with itself plus carry
- # Test now changed to expect the proper pattern, not a result off by 1 or 2
- my ($e, $num) = 3; # lowest value we will use is 3+1-1 = 3
- do
- {
- $num = ('9' x ++$e) + 0;
- $num *= $num + 1.0;
- } while ("$num" =~ /9{$e}0{$e}/); # must be a certain pattern
- $e--; # last test failed, so retract one step
- # the limits below brush the problems with the test above under the rug:
- # the test should be able to find the proper $e automatically
- $e = 5 if $^O =~ /^uts/; # UTS get's some special treatment
- $e = 5 if $^O =~ /^unicos/; # unicos is also problematic (6 seems to work
- # there, but we play safe)
- $e = 5 if $] < 5.006; # cap, for older Perls
- $e = 7 if $e > 7; # cap, for VMS, OS/390 and other 64 bit systems
- # 8 fails inside random testsuite, so take 7
-
- __PACKAGE__->_base_len($e); # set and store
-
- use integer;
- # find out how many bits _and, _or and _xor can take (old default = 16)
- # I don't think anybody has yet 128 bit scalars, so let's play safe.
- local $^W = 0; # don't warn about 'nonportable number'
- $AND_BITS = 15; $XOR_BITS = 15; $OR_BITS = 15;
-
- # find max bits, we will not go higher than numberofbits that fit into $BASE
- # to make _and etc simpler (and faster for smaller, slower for large numbers)
- my $max = 16;
- while (2 ** $max < $BASE) { $max++; }
- {
- no integer;
- $max = 16 if $] < 5.006; # older Perls might not take >16 too well
- }
- my ($x,$y,$z);
- do {
- $AND_BITS++;
- $x = oct('0b' . '1' x $AND_BITS); $y = $x & $x;
- $z = (2 ** $AND_BITS) - 1;
- } while ($AND_BITS < $max && $x == $z && $y == $x);
- $AND_BITS --; # retreat one step
- do {
- $XOR_BITS++;
- $x = oct('0b' . '1' x $XOR_BITS); $y = $x ^ 0;
- $z = (2 ** $XOR_BITS) - 1;
- } while ($XOR_BITS < $max && $x == $z && $y == $x);
- $XOR_BITS --; # retreat one step
- do {
- $OR_BITS++;
- $x = oct('0b' . '1' x $OR_BITS); $y = $x | $x;
- $z = (2 ** $OR_BITS) - 1;
- } while ($OR_BITS < $max && $x == $z && $y == $x);
- $OR_BITS --; # retreat one step
-
- $AND_MASK = __PACKAGE__->_new( ( 2 ** $AND_BITS ));
- $XOR_MASK = __PACKAGE__->_new( ( 2 ** $XOR_BITS ));
- $OR_MASK = __PACKAGE__->_new( ( 2 ** $OR_BITS ));
- }
-
-###############################################################################
-
-sub _zero
- {
- # create a zero
- [ 0 ];
- }
-
-sub _one
- {
- # create a one
- [ 1 ];
- }
-
-sub _two
- {
- # create a two (used internally for shifting)
- [ 2 ];
- }
-
-sub _ten
- {
- # create a 10 (used internally for shifting)
- [ 10 ];
- }
-
-sub _copy
- {
- # make a true copy
- [ @{$_[1]} ];
- }
-
-# catch and throw away
-sub import { }
-
-##############################################################################
-# convert back to string and number
-
-sub _str
- {
- # (ref to BINT) return num_str
- # Convert number from internal base 100000 format to string format.
- # internal format is always normalized (no leading zeros, "-0" => "+0")
- my $ar = $_[1];
-
- my $l = scalar @$ar; # number of parts
- if ($l < 1) # should not happen
- {
- require Carp;
- Carp::croak("$_[1] has no elements");
- }
-
- my $ret = "";
- # handle first one different to strip leading zeros from it (there are no
- # leading zero parts in internal representation)
- $l --; $ret .= int($ar->[$l]); $l--;
- # Interestingly, the pre-padd method uses more time
- # the old grep variant takes longer (14 vs. 10 sec)
- my $z = '0' x ($BASE_LEN-1);
- while ($l >= 0)
- {
- $ret .= substr($z.$ar->[$l],-$BASE_LEN); # fastest way I could think of
- $l--;
- }
- $ret;
- }
-
-sub _num
- {
- # Make a number (scalar int/float) from a BigInt object
- my $x = $_[1];
-
- return 0+$x->[0] if scalar @$x == 1; # below $BASE
- my $fac = 1;
- my $num = 0;
- foreach (@$x)
- {
- $num += $fac*$_; $fac *= $BASE;
- }
- $num;
- }
-
-##############################################################################
-# actual math code
-
-sub _add
- {
- # (ref to int_num_array, ref to int_num_array)
- # routine to add two base 1eX numbers
- # stolen from Knuth Vol 2 Algorithm A pg 231
- # there are separate routines to add and sub as per Knuth pg 233
- # This routine clobbers up array x, but not y.
-
- my ($c,$x,$y) = @_;
-
- return $x if (@$y == 1) && $y->[0] == 0; # $x + 0 => $x
- if ((@$x == 1) && $x->[0] == 0) # 0 + $y => $y->copy
- {
- # twice as slow as $x = [ @$y ], but necc. to retain $x as ref :(
- @$x = @$y; return $x;
- }
-
- # for each in Y, add Y to X and carry. If after that, something is left in
- # X, foreach in X add carry to X and then return X, carry
- # Trades one "$j++" for having to shift arrays
- my $i; my $car = 0; my $j = 0;
- for $i (@$y)
- {
- $x->[$j] -= $BASE if $car = (($x->[$j] += $i + $car) >= $BASE) ? 1 : 0;
- $j++;
- }
- while ($car != 0)
- {
- $x->[$j] -= $BASE if $car = (($x->[$j] += $car) >= $BASE) ? 1 : 0; $j++;
- }
- $x;
- }
-
-sub _inc
- {
- # (ref to int_num_array, ref to int_num_array)
- # Add 1 to $x, modify $x in place
- my ($c,$x) = @_;
-
- for my $i (@$x)
- {
- return $x if (($i += 1) < $BASE); # early out
- $i = 0; # overflow, next
- }
- push @$x,1 if (($x->[-1] || 0) == 0); # last overflowed, so extend
- $x;
- }
-
-sub _dec
- {
- # (ref to int_num_array, ref to int_num_array)
- # Sub 1 from $x, modify $x in place
- my ($c,$x) = @_;
-
- my $MAX = $BASE-1; # since MAX_VAL based on MBASE
- for my $i (@$x)
- {
- last if (($i -= 1) >= 0); # early out
- $i = $MAX; # underflow, next
- }
- pop @$x if $x->[-1] == 0 && @$x > 1; # last underflowed (but leave 0)
- $x;
- }
-
-sub _sub
- {
- # (ref to int_num_array, ref to int_num_array, swap)
- # subtract base 1eX numbers -- stolen from Knuth Vol 2 pg 232, $x > $y
- # subtract Y from X by modifying x in place
- my ($c,$sx,$sy,$s) = @_;
-
- my $car = 0; my $i; my $j = 0;
- if (!$s)
- {
- for $i (@$sx)
- {
- last unless defined $sy->[$j] || $car;
- $i += $BASE if $car = (($i -= ($sy->[$j] || 0) + $car) < 0); $j++;
- }
- # might leave leading zeros, so fix that
- return __strip_zeros($sx);
- }
- for $i (@$sx)
- {
- # we can't do an early out if $x is < than $y, since we
- # need to copy the high chunks from $y. Found by Bob Mathews.
- #last unless defined $sy->[$j] || $car;
- $sy->[$j] += $BASE
- if $car = (($sy->[$j] = $i-($sy->[$j]||0) - $car) < 0);
- $j++;
- }
- # might leave leading zeros, so fix that
- __strip_zeros($sy);
- }
-
-sub _mul_use_mul
- {
- # (ref to int_num_array, ref to int_num_array)
- # multiply two numbers in internal representation
- # modifies first arg, second need not be different from first
- my ($c,$xv,$yv) = @_;
-
- if (@$yv == 1)
- {
- # shortcut for two very short numbers (improved by Nathan Zook)
- # works also if xv and yv are the same reference, and handles also $x == 0
- if (@$xv == 1)
- {
- if (($xv->[0] *= $yv->[0]) >= $MBASE)
- {
- $xv->[0] = $xv->[0] - ($xv->[1] = int($xv->[0] * $RBASE)) * $MBASE;
- };
- return $xv;
- }
- # $x * 0 => 0
- if ($yv->[0] == 0)
- {
- @$xv = (0);
- return $xv;
- }
- # multiply a large number a by a single element one, so speed up
- my $y = $yv->[0]; my $car = 0;
- foreach my $i (@$xv)
- {
- $i = $i * $y + $car; $car = int($i * $RBASE); $i -= $car * $MBASE;
- }
- push @$xv, $car if $car != 0;
- return $xv;
- }
- # shortcut for result $x == 0 => result = 0
- return $xv if ( ((@$xv == 1) && ($xv->[0] == 0)) );
-
- # since multiplying $x with $x fails, make copy in this case
- $yv = [@$xv] if $xv == $yv; # same references?
-
- my @prod = (); my ($prod,$car,$cty,$xi,$yi);
-
- for $xi (@$xv)
- {
- $car = 0; $cty = 0;
-
- # slow variant
-# for $yi (@$yv)
-# {
-# $prod = $xi * $yi + ($prod[$cty] || 0) + $car;
-# $prod[$cty++] =
-# $prod - ($car = int($prod * RBASE)) * $MBASE; # see USE_MUL
-# }
-# $prod[$cty] += $car if $car; # need really to check for 0?
-# $xi = shift @prod;
-
- # faster variant
- # looping through this if $xi == 0 is silly - so optimize it away!
- $xi = (shift @prod || 0), next if $xi == 0;
- for $yi (@$yv)
- {
- $prod = $xi * $yi + ($prod[$cty] || 0) + $car;
-## this is actually a tad slower
-## $prod = $prod[$cty]; $prod += ($car + $xi * $yi); # no ||0 here
- $prod[$cty++] =
- $prod - ($car = int($prod * $RBASE)) * $MBASE; # see USE_MUL
- }
- $prod[$cty] += $car if $car; # need really to check for 0?
- $xi = shift @prod || 0; # || 0 makes v5.005_3 happy
- }
- push @$xv, @prod;
- __strip_zeros($xv);
- $xv;
- }
-
-sub _mul_use_div
- {
- # (ref to int_num_array, ref to int_num_array)
- # multiply two numbers in internal representation
- # modifies first arg, second need not be different from first
- my ($c,$xv,$yv) = @_;
-
- if (@$yv == 1)
- {
- # shortcut for two small numbers, also handles $x == 0
- if (@$xv == 1)
- {
- # shortcut for two very short numbers (improved by Nathan Zook)
- # works also if xv and yv are the same reference, and handles also $x == 0
- if (($xv->[0] *= $yv->[0]) >= $MBASE)
- {
- $xv->[0] =
- $xv->[0] - ($xv->[1] = int($xv->[0] / $MBASE)) * $MBASE;
- };
- return $xv;
- }
- # $x * 0 => 0
- if ($yv->[0] == 0)
- {
- @$xv = (0);
- return $xv;
- }
- # multiply a large number a by a single element one, so speed up
- my $y = $yv->[0]; my $car = 0;
- foreach my $i (@$xv)
- {
- $i = $i * $y + $car; $car = int($i / $MBASE); $i -= $car * $MBASE;
- }
- push @$xv, $car if $car != 0;
- return $xv;
- }
- # shortcut for result $x == 0 => result = 0
- return $xv if ( ((@$xv == 1) && ($xv->[0] == 0)) );
-
- # since multiplying $x with $x fails, make copy in this case
- $yv = [@$xv] if $xv == $yv; # same references?
-
- my @prod = (); my ($prod,$car,$cty,$xi,$yi);
- for $xi (@$xv)
- {
- $car = 0; $cty = 0;
- # looping through this if $xi == 0 is silly - so optimize it away!
- $xi = (shift @prod || 0), next if $xi == 0;
- for $yi (@$yv)
- {
- $prod = $xi * $yi + ($prod[$cty] || 0) + $car;
- $prod[$cty++] =
- $prod - ($car = int($prod / $MBASE)) * $MBASE;
- }
- $prod[$cty] += $car if $car; # need really to check for 0?
- $xi = shift @prod || 0; # || 0 makes v5.005_3 happy
- }
- push @$xv, @prod;
- __strip_zeros($xv);
- $xv;
- }
-
-sub _div_use_mul
- {
- # ref to array, ref to array, modify first array and return remainder if
- # in list context
-
- # see comments in _div_use_div() for more explanations
-
- my ($c,$x,$yorg) = @_;
-
- # the general div algorithmn here is about O(N*N) and thus quite slow, so
- # we first check for some special cases and use shortcuts to handle them.
-
- # This works, because we store the numbers in a chunked format where each
- # element contains 5..7 digits (depending on system).
-
- # if both numbers have only one element:
- if (@$x == 1 && @$yorg == 1)
- {
- # shortcut, $yorg and $x are two small numbers
- if (wantarray)
- {
- my $r = [ $x->[0] % $yorg->[0] ];
- $x->[0] = int($x->[0] / $yorg->[0]);
- return ($x,$r);
- }
- else
- {
- $x->[0] = int($x->[0] / $yorg->[0]);
- return $x;
- }
- }
-
- # if x has more than one, but y has only one element:
- if (@$yorg == 1)
- {
- my $rem;
- $rem = _mod($c,[ @$x ],$yorg) if wantarray;
-
- # shortcut, $y is < $BASE
- my $j = scalar @$x; my $r = 0;
- my $y = $yorg->[0]; my $b;
- while ($j-- > 0)
- {
- $b = $r * $MBASE + $x->[$j];
- $x->[$j] = int($b/$y);
- $r = $b % $y;
- }
- pop @$x if @$x > 1 && $x->[-1] == 0; # splice up a leading zero
- return ($x,$rem) if wantarray;
- return $x;
- }
-
- # now x and y have more than one element
-
- # check whether y has more elements than x, if yet, the result will be 0
- if (@$yorg > @$x)
- {
- my $rem;
- $rem = [@$x] if wantarray; # make copy
- splice (@$x,1); # keep ref to original array
- $x->[0] = 0; # set to 0
- return ($x,$rem) if wantarray; # including remainder?
- return $x; # only x, which is [0] now
- }
- # check whether the numbers have the same number of elements, in that case
- # the result will fit into one element and can be computed efficiently
- if (@$yorg == @$x)
- {
- my $rem;
- # if $yorg has more digits than $x (it's leading element is longer than
- # the one from $x), the result will also be 0:
- if (length(int($yorg->[-1])) > length(int($x->[-1])))
- {
- $rem = [@$x] if wantarray; # make copy
- splice (@$x,1); # keep ref to org array
- $x->[0] = 0; # set to 0
- return ($x,$rem) if wantarray; # including remainder?
- return $x;
- }
- # now calculate $x / $yorg
- if (length(int($yorg->[-1])) == length(int($x->[-1])))
- {
- # same length, so make full compare
-
- my $a = 0; my $j = scalar @$x - 1;
- # manual way (abort if unequal, good for early ne)
- while ($j >= 0)
- {
- last if ($a = $x->[$j] - $yorg->[$j]); $j--;
- }
- # $a contains the result of the compare between X and Y
- # a < 0: x < y, a == 0: x == y, a > 0: x > y
- if ($a <= 0)
- {
- $rem = [ 0 ]; # a = 0 => x == y => rem 0
- $rem = [@$x] if $a != 0; # a < 0 => x < y => rem = x
- splice(@$x,1); # keep single element
- $x->[0] = 0; # if $a < 0
- $x->[0] = 1 if $a == 0; # $x == $y
- return ($x,$rem) if wantarray;
- return $x;
- }
- # $x >= $y, so proceed normally
- }
- }
-
- # all other cases:
-
- my $y = [ @$yorg ]; # always make copy to preserve
-
- my ($car,$bar,$prd,$dd,$xi,$yi, ＠ q,$v2,$v1, ＠ d,$tmp,$q,$u2,$u1,$u0);
-
- $car = $bar = $prd = 0;
- if (($dd = int($MBASE/($y->[-1]+1))) != 1)
- {
- for $xi (@$x)
- {
- $xi = $xi * $dd + $car;
- $xi -= ($car = int($xi * $RBASE)) * $MBASE; # see USE_MUL
- }
- push(@$x, $car); $car = 0;
- for $yi (@$y)
- {
- $yi = $yi * $dd + $car;
- $yi -= ($car = int($yi * $RBASE)) * $MBASE; # see USE_MUL
- }
- }
- else
- {
- push(@$x, 0);
- }
- @q = (); ($v2,$v1) = @$y[-2,-1];
- $v2 = 0 unless $v2;
- while ($#$x > $#$y)
- {
- ($u2,$u1,$u0) = @$x[-3..-1];
- $u2 = 0 unless $u2;
- #warn "oups v1 is 0, u0: $u0 $y->[-2] $y->[-1] l ",scalar @$y,"\n"
- # if $v1 == 0;
- $q = (($u0 == $v1) ? $MAX_VAL : int(($u0*$MBASE+$u1)/$v1));
- --$q while ($v2*$q > ($u0*$MBASE+$u1-$q*$v1)*$MBASE+$u2);
- if ($q)
- {
- ($car, $bar) = (0,0);
- for ($yi = 0, $xi = $#$x-$#$y-1; $yi <= $#$y; ++$yi,++$xi)
- {
- $prd = $q * $y->[$yi] + $car;
- $prd -= ($car = int($prd * $RBASE)) * $MBASE; # see USE_MUL
- $x->[$xi] += $MBASE if ($bar = (($x->[$xi] -= $prd + $bar) < 0));
- }
- if ($x->[-1] < $car + $bar)
- {
- $car = 0; --$q;
- for ($yi = 0, $xi = $#$x-$#$y-1; $yi <= $#$y; ++$yi,++$xi)
- {
- $x->[$xi] -= $MBASE
- if ($car = (($x->[$xi] += $y->[$yi] + $car) >= $MBASE));
- }
- }
- }
- pop(@$x);
- unshift(@q, $q);
- }
- if (wantarray)
- {
- @d = ();
- if ($dd != 1)
- {
- $car = 0;
- for $xi (reverse @$x)
- {
- $prd = $car * $MBASE + $xi;
- $car = $prd - ($tmp = int($prd / $dd)) * $dd; # see USE_MUL
- unshift(@d, $tmp);
- }
- }
- else
- {
- @d = @$x;
- }
- @$x = @q;
- my $d = \@d;
- __strip_zeros($x);
- __strip_zeros($d);
- return ($x,$d);
- }
- @$x = @q;
- __strip_zeros($x);
- $x;
- }
-
-sub _div_use_div
- {
- # ref to array, ref to array, modify first array and return remainder if
- # in list context
- my ($c,$x,$yorg) = @_;
-
- # the general div algorithmn here is about O(N*N) and thus quite slow, so
- # we first check for some special cases and use shortcuts to handle them.
-
- # This works, because we store the numbers in a chunked format where each
- # element contains 5..7 digits (depending on system).
-
- # if both numbers have only one element:
- if (@$x == 1 && @$yorg == 1)
- {
- # shortcut, $yorg and $x are two small numbers
- if (wantarray)
- {
- my $r = [ $x->[0] % $yorg->[0] ];
- $x->[0] = int($x->[0] / $yorg->[0]);
- return ($x,$r);
- }
- else
- {
- $x->[0] = int($x->[0] / $yorg->[0]);
- return $x;
- }
- }
- # if x has more than one, but y has only one element:
- if (@$yorg == 1)
- {
- my $rem;
- $rem = _mod($c,[ @$x ],$yorg) if wantarray;
-
- # shortcut, $y is < $BASE
- my $j = scalar @$x; my $r = 0;
- my $y = $yorg->[0]; my $b;
- while ($j-- > 0)
- {
- $b = $r * $MBASE + $x->[$j];
- $x->[$j] = int($b/$y);
- $r = $b % $y;
- }
- pop @$x if @$x > 1 && $x->[-1] == 0; # splice up a leading zero
- return ($x,$rem) if wantarray;
- return $x;
- }
- # now x and y have more than one element
-
- # check whether y has more elements than x, if yet, the result will be 0
- if (@$yorg > @$x)
- {
- my $rem;
- $rem = [@$x] if wantarray; # make copy
- splice (@$x,1); # keep ref to original array
- $x->[0] = 0; # set to 0
- return ($x,$rem) if wantarray; # including remainder?
- return $x; # only x, which is [0] now
- }
- # check whether the numbers have the same number of elements, in that case
- # the result will fit into one element and can be computed efficiently
- if (@$yorg == @$x)
- {
- my $rem;
- # if $yorg has more digits than $x (it's leading element is longer than
- # the one from $x), the result will also be 0:
- if (length(int($yorg->[-1])) > length(int($x->[-1])))
- {
- $rem = [@$x] if wantarray; # make copy
- splice (@$x,1); # keep ref to org array
- $x->[0] = 0; # set to 0
- return ($x,$rem) if wantarray; # including remainder?
- return $x;
- }
- # now calculate $x / $yorg
-
- if (length(int($yorg->[-1])) == length(int($x->[-1])))
- {
- # same length, so make full compare
-
- my $a = 0; my $j = scalar @$x - 1;
- # manual way (abort if unequal, good for early ne)
- while ($j >= 0)
- {
- last if ($a = $x->[$j] - $yorg->[$j]); $j--;
- }
- # $a contains the result of the compare between X and Y
- # a < 0: x < y, a == 0: x == y, a > 0: x > y
- if ($a <= 0)
- {
- $rem = [ 0 ]; # a = 0 => x == y => rem 0
- $rem = [@$x] if $a != 0; # a < 0 => x < y => rem = x
- splice(@$x,1); # keep single element
- $x->[0] = 0; # if $a < 0
- $x->[0] = 1 if $a == 0; # $x == $y
- return ($x,$rem) if wantarray; # including remainder?
- return $x;
- }
- # $x >= $y, so proceed normally
-
- }
- }
-
- # all other cases:
-
- my $y = [ @$yorg ]; # always make copy to preserve
-
- my ($car,$bar,$prd,$dd,$xi,$yi, ＠ q,$v2,$v1, ＠ d,$tmp,$q,$u2,$u1,$u0);
-
- $car = $bar = $prd = 0;
- if (($dd = int($MBASE/($y->[-1]+1))) != 1)
- {
- for $xi (@$x)
- {
- $xi = $xi * $dd + $car;
- $xi -= ($car = int($xi / $MBASE)) * $MBASE;
- }
- push(@$x, $car); $car = 0;
- for $yi (@$y)
- {
- $yi = $yi * $dd + $car;
- $yi -= ($car = int($yi / $MBASE)) * $MBASE;
- }
- }
- else
- {
- push(@$x, 0);
- }
-
- # @q will accumulate the final result, $q contains the current computed
- # part of the final result
-
- @q = (); ($v2,$v1) = @$y[-2,-1];
- $v2 = 0 unless $v2;
- while ($#$x > $#$y)
- {
- ($u2,$u1,$u0) = @$x[-3..-1];
- $u2 = 0 unless $u2;
- #warn "oups v1 is 0, u0: $u0 $y->[-2] $y->[-1] l ",scalar @$y,"\n"
- # if $v1 == 0;
- $q = (($u0 == $v1) ? $MAX_VAL : int(($u0*$MBASE+$u1)/$v1));
- --$q while ($v2*$q > ($u0*$MBASE+$u1-$q*$v1)*$MBASE+$u2);
- if ($q)
- {
- ($car, $bar) = (0,0);
- for ($yi = 0, $xi = $#$x-$#$y-1; $yi <= $#$y; ++$yi,++$xi)
- {
- $prd = $q * $y->[$yi] + $car;
- $prd -= ($car = int($prd / $MBASE)) * $MBASE;
- $x->[$xi] += $MBASE if ($bar = (($x->[$xi] -= $prd + $bar) < 0));
- }
- if ($x->[-1] < $car + $bar)
- {
- $car = 0; --$q;
- for ($yi = 0, $xi = $#$x-$#$y-1; $yi <= $#$y; ++$yi,++$xi)
- {
- $x->[$xi] -= $MBASE
- if ($car = (($x->[$xi] += $y->[$yi] + $car) >= $MBASE));
- }
- }
- }
- pop(@$x); unshift(@q, $q);
- }
- if (wantarray)
- {
- @d = ();
- if ($dd != 1)
- {
- $car = 0;
- for $xi (reverse @$x)
- {
- $prd = $car * $MBASE + $xi;
- $car = $prd - ($tmp = int($prd / $dd)) * $dd;
- unshift(@d, $tmp);
- }
- }
- else
- {
- @d = @$x;
- }
- @$x = @q;
- my $d = \@d;
- __strip_zeros($x);
- __strip_zeros($d);
- return ($x,$d);
- }
- @$x = @q;
- __strip_zeros($x);
- $x;
- }
-
-##############################################################################
-# testing
-
-sub _acmp
- {
- # internal absolute post-normalized compare (ignore signs)
- # ref to array, ref to array, return <0, 0, >0
- # arrays must have at least one entry; this is not checked for
- my ($c,$cx,$cy) = @_;
-
- # shortcut for short numbers
- return (($cx->[0] <=> $cy->[0]) <=> 0)
- if scalar @$cx == scalar @$cy && scalar @$cx == 1;
-
- # fast comp based on number of array elements (aka pseudo-length)
- my $lxy = (scalar @$cx - scalar @$cy)
- # or length of first element if same number of elements (aka difference 0)
- ||
- # need int() here because sometimes the last element is '00018' vs '18'
- (length(int($cx->[-1])) - length(int($cy->[-1])));
- return -1 if $lxy < 0; # already differs, ret
- return 1 if $lxy > 0; # ditto
-
- # manual way (abort if unequal, good for early ne)
- my $a; my $j = scalar @$cx;
- while (--$j >= 0)
- {
- last if ($a = $cx->[$j] - $cy->[$j]);
- }
- $a <=> 0;
- }
-
-sub _len
- {
- # compute number of digits
-
- # int() because add/sub sometimes leaves strings (like '00005') instead of
- # '5' in this place, thus causing length() to report wrong length
- my $cx = $_[1];
-
- (@$cx-1)*$BASE_LEN+length(int($cx->[-1]));
- }
-
-sub _digit
- {
- # return the nth digit, negative values count backward
- # zero is rightmost, so _digit(123,0) will give 3
- my ($c,$x,$n) = @_;
-
- my $len = _len('',$x);
-
- $n = $len+$n if $n < 0; # -1 last, -2 second-to-last
- $n = abs($n); # if negative was too big
- $len--; $n = $len if $n > $len; # n to big?
-
- my $elem = int($n / $BASE_LEN); # which array element
- my $digit = $n % $BASE_LEN; # which digit in this element
- $elem = '0' x $BASE_LEN . @$x[$elem]; # get element padded with 0's
- substr($elem,-$digit-1,1);
- }
-
-sub _zeros
- {
- # return amount of trailing zeros in decimal
- # check each array elem in _m for having 0 at end as long as elem == 0
- # Upon finding a elem != 0, stop
- my $x = $_[1];
-
- return 0 if scalar @$x == 1 && $x->[0] == 0;
-
- my $zeros = 0; my $elem;
- foreach my $e (@$x)
- {
- if ($e != 0)
- {
- $elem = "$e"; # preserve x
- $elem =~ s/.*?(0*$)/$1/; # strip anything not zero
- $zeros *= $BASE_LEN; # elems * 5
- $zeros += length($elem); # count trailing zeros
- last; # early out
- }
- $zeros ++; # real else branch: 50% slower!
- }
- $zeros;
- }
-
-##############################################################################
-# _is_* routines
-
-sub _is_zero
- {
- # return true if arg is zero
- (((scalar @{$_[1]} == 1) && ($_[1]->[0] == 0))) <=> 0;
- }
-
-sub _is_even
- {
- # return true if arg is even
- (!($_[1]->[0] & 1)) <=> 0;
- }
-
-sub _is_odd
- {
- # return true if arg is even
- (($_[1]->[0] & 1)) <=> 0;
- }
-
-sub _is_one
- {
- # return true if arg is one
- (scalar @{$_[1]} == 1) && ($_[1]->[0] == 1) <=> 0;
- }
-
-sub _is_two
- {
- # return true if arg is two
- (scalar @{$_[1]} == 1) && ($_[1]->[0] == 2) <=> 0;
- }
-
-sub _is_ten
- {
- # return true if arg is ten
- (scalar @{$_[1]} == 1) && ($_[1]->[0] == 10) <=> 0;
- }
-
-sub __strip_zeros
- {
- # internal normalization function that strips leading zeros from the array
- # args: ref to array
- my $s = shift;
-
- my $cnt = scalar @$s; # get count of parts
- my $i = $cnt-1;
- push @$s,0 if $i < 0; # div might return empty results, so fix it
-
- return $s if @$s == 1; # early out
-
- #print "strip: cnt $cnt i $i\n";
- # '0', '3', '4', '0', '0',
- # 0 1 2 3 4
- # cnt = 5, i = 4
- # i = 4
- # i = 3
- # => fcnt = cnt - i (5-2 => 3, cnt => 5-1 = 4, throw away from 4th pos)
- # >= 1: skip first part (this can be zero)
- while ($i > 0) { last if $s->[$i] != 0; $i--; }
- $i++; splice @$s,$i if ($i < $cnt); # $i cant be 0
- $s;
- }
-
-###############################################################################
-# check routine to test internal state for corruptions
-
-sub _check
- {
- # used by the test suite
- my $x = $_[1];
-
- return "$x is not a reference" if !ref($x);
-
- # are all parts are valid?
- my $i = 0; my $j = scalar @$x; my ($e,$try);
- while ($i < $j)
- {
- $e = $x->[$i]; $e = 'undef' unless defined $e;
- $try = '=~ /^[\+]?[0-9]+\$/; '."($x, $e)";
- last if $e !~ /^[+]?[0-9]+$/;
- $try = '=~ /^[\+]?[0-9]+\$/; '."($x, $e) (stringify)";
- last if "$e" !~ /^[+]?[0-9]+$/;
- $try = '=~ /^[\+]?[0-9]+\$/; '."($x, $e) (cat-stringify)";
- last if '' . "$e" !~ /^[+]?[0-9]+$/;
- $try = ' < 0 || >= $BASE; '."($x, $e)";
- last if $e <0 || $e >= $BASE;
- # this test is disabled, since new/bnorm and certain ops (like early out
- # in add/sub) are allowed/expected to leave '00000' in some elements
- #$try = '=~ /^00+/; '."($x, $e)";
- #last if $e =~ /^00+/;
- $i++;
- }
- return "Illegal part '$e' at pos $i (tested: $try)" if $i < $j;
- 0;
- }
-
-
-###############################################################################
-
-sub _mod
- {
- # if possible, use mod shortcut
- my ($c,$x,$yo) = @_;
-
- # slow way since $y to big
- if (scalar @$yo > 1)
- {
- my ($xo,$rem) = _div($c,$x,$yo);
- return $rem;
- }
-
- my $y = $yo->[0];
- # both are single element arrays
- if (scalar @$x == 1)
- {
- $x->[0] %= $y;
- return $x;
- }
-
- # @y is a single element, but @x has more than one element
- my $b = $BASE % $y;
- if ($b == 0)
- {
- # when BASE % Y == 0 then (B * BASE) % Y == 0
- # (B * BASE) % $y + A % Y => A % Y
- # so need to consider only last element: O(1)
- $x->[0] %= $y;
- }
- elsif ($b == 1)
- {
- # else need to go through all elements: O(N), but loop is a bit simplified
- my $r = 0;
- foreach (@$x)
- {
- $r = ($r + $_) % $y; # not much faster, but heh...
- #$r += $_ % $y; $r %= $y;
- }
- $r = 0 if $r == $y;
- $x->[0] = $r;
- }
- else
- {
- # else need to go through all elements: O(N)
- my $r = 0; my $bm = 1;
- foreach (@$x)
- {
- $r = ($_ * $bm + $r) % $y;
- $bm = ($bm * $b) % $y;
-
- #$r += ($_ % $y) * $bm;
- #$bm *= $b;
- #$bm %= $y;
- #$r %= $y;
- }
- $r = 0 if $r == $y;
- $x->[0] = $r;
- }
- splice (@$x,1); # keep one element of $x
- $x;
- }
-
-##############################################################################
-# shifts
-
-sub _rsft
- {
- my ($c,$x,$y,$n) = @_;
-
- if ($n != 10)
- {
- $n = _new($c,$n); return _div($c,$x, _pow($c,$n,$y));
- }
-
- # shortcut (faster) for shifting by 10)
- # multiples of $BASE_LEN
- my $dst = 0; # destination
- my $src = _num($c,$y); # as normal int
- my $xlen = (@$x-1)*$BASE_LEN+length(int($x->[-1])); # len of x in digits
- if ($src >= $xlen or ($src == $xlen and ! defined $x->[1]))
- {
- # 12345 67890 shifted right by more than 10 digits => 0
- splice (@$x,1); # leave only one element
- $x->[0] = 0; # set to zero
- return $x;
- }
- my $rem = $src % $BASE_LEN; # remainder to shift
- $src = int($src / $BASE_LEN); # source
- if ($rem == 0)
- {
- splice (@$x,0,$src); # even faster, 38.4 => 39.3
- }
- else
- {
- my $len = scalar @$x - $src; # elems to go
- my $vd; my $z = '0'x $BASE_LEN;
- $x->[scalar @$x] = 0; # avoid || 0 test inside loop
- while ($dst < $len)
- {
- $vd = $z.$x->[$src];
- $vd = substr($vd,-$BASE_LEN,$BASE_LEN-$rem);
- $src++;
- $vd = substr($z.$x->[$src],-$rem,$rem) . $vd;
- $vd = substr($vd,-$BASE_LEN,$BASE_LEN) if length($vd) > $BASE_LEN;
- $x->[$dst] = int($vd);
- $dst++;
- }
- splice (@$x,$dst) if $dst > 0; # kill left-over array elems
- pop @$x if $x->[-1] == 0 && @$x > 1; # kill last element if 0
- } # else rem == 0
- $x;
- }
-
-sub _lsft
- {
- my ($c,$x,$y,$n) = @_;
-
- if ($n != 10)
- {
- $n = _new($c,$n); return _mul($c,$x, _pow($c,$n,$y));
- }
-
- # shortcut (faster) for shifting by 10) since we are in base 10eX
- # multiples of $BASE_LEN:
- my $src = scalar @$x; # source
- my $len = _num($c,$y); # shift-len as normal int
- my $rem = $len % $BASE_LEN; # remainder to shift
- my $dst = $src + int($len/$BASE_LEN); # destination
- my $vd; # further speedup
- $x->[$src] = 0; # avoid first ||0 for speed
- my $z = '0' x $BASE_LEN;
- while ($src >= 0)
- {
- $vd = $x->[$src]; $vd = $z.$vd;
- $vd = substr($vd,-$BASE_LEN+$rem,$BASE_LEN-$rem);
- $vd .= $src > 0 ? substr($z.$x->[$src-1],-$BASE_LEN,$rem) : '0' x $rem;
- $vd = substr($vd,-$BASE_LEN,$BASE_LEN) if length($vd) > $BASE_LEN;
- $x->[$dst] = int($vd);
- $dst--; $src--;
- }
- # set lowest parts to 0
- while ($dst >= 0) { $x->[$dst--] = 0; }
- # fix spurios last zero element
- splice @$x,-1 if $x->[-1] == 0;
- $x;
- }
-
-sub _pow
- {
- # power of $x to $y
- # ref to array, ref to array, return ref to array
- my ($c,$cx,$cy) = @_;
-
- if (scalar @$cy == 1 && $cy->[0] == 0)
- {
- splice (@$cx,1); $cx->[0] = 1; # y == 0 => x => 1
- return $cx;
- }
- if ((scalar @$cx == 1 && $cx->[0] == 1) || # x == 1
- (scalar @$cy == 1 && $cy->[0] == 1)) # or y == 1
- {
- return $cx;
- }
- if (scalar @$cx == 1 && $cx->[0] == 0)
- {
- splice (@$cx,1); $cx->[0] = 0; # 0 ** y => 0 (if not y <= 0)
- return $cx;
- }
-
- my $pow2 = _one();
-
- my $y_bin = _as_bin($c,$cy); $y_bin =~ s/^0b//;
- my $len = length($y_bin);
- while (--$len > 0)
- {
- _mul($c,$pow2,$cx) if substr($y_bin,$len,1) eq '1'; # is odd?
- _mul($c,$cx,$cx);
- }
-
- _mul($c,$cx,$pow2);
- $cx;
- }
-
-sub _fac
- {
- # factorial of $x
- # ref to array, return ref to array
- my ($c,$cx) = @_;
-
- if ((@$cx == 1) && ($cx->[0] <= 2))
- {
- $cx->[0] ||= 1; # 0 => 1, 1 => 1, 2 => 2
- return $cx;
- }
-
- # go forward until $base is exceeded
- # limit is either $x steps (steps == 100 means a result always too high) or
- # $base.
- my $steps = 100; $steps = $cx->[0] if @$cx == 1;
- my $r = 2; my $cf = 3; my $step = 2; my $last = $r;
- while ($r*$cf < $BASE && $step < $steps)
- {
- $last = $r; $r *= $cf++; $step++;
- }
- if ((@$cx == 1) && $step == $cx->[0])
- {
- # completely done, so keep reference to $x and return
- $cx->[0] = $r;
- return $cx;
- }
-
- # now we must do the left over steps
- my $n; # steps still to do
- if (scalar @$cx == 1)
- {
- $n = $cx->[0];
- }
- else
- {
- $n = _copy($c,$cx);
- }
-
- $cx->[0] = $last; splice (@$cx,1); # keep ref to $x
- my $zero_elements = 0;
-
- # do left-over steps fit into a scalar?
- if (ref $n eq 'ARRAY')
- {
- # No, so use slower inc() & cmp()
- $step = [$step];
- while (_acmp($step,$n) <= 0)
- {
- # as soon as the last element of $cx is 0, we split it up and remember
- # how many zeors we got so far. The reason is that n! will accumulate
- # zeros at the end rather fast.
- if ($cx->[0] == 0)
- {
- $zero_elements ++; shift @$cx;
- }
- _mul($c,$cx,$step); _inc($c,$step);
- }
- }
- else
- {
- # Yes, so we can speed it up slightly
- while ($step <= $n)
- {
- # When the last element of $cx is 0, we split it up and remember
- # how many we got so far. The reason is that n! will accumulate
- # zeros at the end rather fast.
- if ($cx->[0] == 0)
- {
- $zero_elements ++; shift @$cx;
- }
- _mul($c,$cx,[$step]); $step++;
- }
- }
- # multiply in the zeros again
- while ($zero_elements-- > 0)
- {
- unshift @$cx, 0;
- }
- $cx; # return result
- }
-
-#############################################################################
-
-sub _log_int
- {
- # calculate integer log of $x to base $base
- # ref to array, ref to array - return ref to array
- my ($c,$x,$base) = @_;
-
- # X == 0 => NaN
- return if (scalar @$x == 1 && $x->[0] == 0);
- # BASE 0 or 1 => NaN
- return if (scalar @$base == 1 && $base->[0] < 2);
- my $cmp = _acmp($c,$x,$base); # X == BASE => 1
- if ($cmp == 0)
- {
- splice (@$x,1); $x->[0] = 1;
- return ($x,1)
- }
- # X < BASE
- if ($cmp < 0)
- {
- splice (@$x,1); $x->[0] = 0;
- return ($x,undef);
- }
-
- # this trial multiplication is very fast, even for large counts (like for
- # 2 ** 1024, since this still requires only 1024 very fast steps
- # (multiplication of a large number by a very small number is very fast))
- my $x_org = _copy($c,$x); # preserve x
- splice(@$x,1); $x->[0] = 1; # keep ref to $x
-
- my $trial = _copy($c,$base);
-
- # XXX TODO this only works if $base has only one element
- if (scalar @$base == 1)
- {
- # compute int ( length_in_base_10(X) / ( log(base) / log(10) ) )
- my $len = _len($c,$x_org);
- my $res = int($len / (log($base->[0]) / log(10))) || 1; # avoid $res == 0
-
- $x->[0] = $res;
- $trial = _pow ($c, _copy($c, $base), $x);
- my $a = _acmp($x,$trial,$x_org);
- return ($x,1) if $a == 0;
- # we now know that $res is too small
- if ($res < 0)
- {
- _mul($c,$trial,$base); _add($c, $x, [1]);
- }
- else
- {
- # or too big
- _div($c,$trial,$base); _sub($c, $x, [1]);
- }
- # did we now get the right result?
- $a = _acmp($x,$trial,$x_org);
- return ($x,1) if $a == 0; # yes, exactly
- # still too big
- if ($a > 0)
- {
- _div($c,$trial,$base); _sub($c, $x, [1]);
- }
- }
-
- # simple loop that increments $x by two in each step, possible overstepping
- # the real result by one
-
- my $a;
- my $base_mul = _mul($c, _copy($c,$base), $base);
-
- while (($a = _acmp($c,$trial,$x_org)) < 0)
- {
- _mul($c,$trial,$base_mul); _add($c, $x, [2]);
- }
-
- my $exact = 1;
- if ($a > 0)
- {
- # overstepped the result
- _dec($c, $x);
- _div($c,$trial,$base);
- $a = _acmp($c,$trial,$x_org);
- if ($a > 0)
- {
- _dec($c, $x);
- }
- $exact = 0 if $a != 0;
- }
-
- ($x,$exact); # return result
- }
-
-# for debugging:
- use constant DEBUG => 0;
- my $steps = 0;
- sub steps { $steps };
-
-sub _sqrt
- {
- # square-root of $x in place
- # Compute a guess of the result (by rule of thumb), then improve it via
- # Newton's method.
- my ($c,$x) = @_;
-
- if (scalar @$x == 1)
- {
- # fit's into one Perl scalar, so result can be computed directly
- $x->[0] = int(sqrt($x->[0]));
- return $x;
- }
- my $y = _copy($c,$x);
- # hopefully _len/2 is < $BASE, the -1 is to always undershot the guess
- # since our guess will "grow"
- my $l = int((_len($c,$x)-1) / 2);
-
- my $lastelem = $x->[-1]; # for guess
- my $elems = scalar @$x - 1;
- # not enough digits, but could have more?
- if ((length($lastelem) <= 3) && ($elems > 1))
- {
- # right-align with zero pad
- my $len = length($lastelem) & 1;
- print "$lastelem => " if DEBUG;
- $lastelem .= substr($x->[-2] . '0' x $BASE_LEN,0,$BASE_LEN);
- # former odd => make odd again, or former even to even again
- $lastelem = $lastelem / 10 if (length($lastelem) & 1) != $len;
- print "$lastelem\n" if DEBUG;
- }
-
- # construct $x (instead of _lsft($c,$x,$l,10)
- my $r = $l % $BASE_LEN; # 10000 00000 00000 00000 ($BASE_LEN=5)
- $l = int($l / $BASE_LEN);
- print "l = $l " if DEBUG;
-
- splice @$x,$l; # keep ref($x), but modify it
-
- # we make the first part of the guess not '1000...0' but int(sqrt($lastelem))
- # that gives us:
- # 14400 00000 => sqrt(14400) => guess first digits to be 120
- # 144000 000000 => sqrt(144000) => guess 379
-
- print "$lastelem (elems $elems) => " if DEBUG;
- $lastelem = $lastelem / 10 if ($elems & 1 == 1); # odd or even?
- my $g = sqrt($lastelem); $g =~ s/\.//; # 2.345 => 2345
- $r -= 1 if $elems & 1 == 0; # 70 => 7
-
- # padd with zeros if result is too short
- $x->[$l--] = int(substr($g . '0' x $r,0,$r+1));
- print "now ",$x->[-1] if DEBUG;
- print " would have been ", int('1' . '0' x $r),"\n" if DEBUG;
-
- # If @$x > 1, we could compute the second elem of the guess, too, to create
- # an even better guess. Not implemented yet. Does it improve performance?
- $x->[$l--] = 0 while ($l >= 0); # all other digits of guess are zero
-
- print "start x= ",_str($c,$x),"\n" if DEBUG;
- my $two = _two();
- my $last = _zero();
- my $lastlast = _zero();
- $steps = 0 if DEBUG;
- while (_acmp($c,$last,$x) != 0 && _acmp($c,$lastlast,$x) != 0)
- {
- $steps++ if DEBUG;
- $lastlast = _copy($c,$last);
- $last = _copy($c,$x);
- _add($c,$x, _div($c,_copy($c,$y),$x));
- _div($c,$x, $two );
- print " x= ",_str($c,$x),"\n" if DEBUG;
- }
- print "\nsteps in sqrt: $steps, " if DEBUG;
- _dec($c,$x) if _acmp($c,$y,_mul($c,_copy($c,$x),$x)) < 0; # overshot?
- print " final ",$x->[-1],"\n" if DEBUG;
- $x;
- }
-
-sub _root
- {
- # take n'th root of $x in place (n >= 3)
- my ($c,$x,$n) = @_;
-
- if (scalar @$x == 1)
- {
- if (scalar @$n > 1)
- {
- # result will always be smaller than 2 so trunc to 1 at once
- $x->[0] = 1;
- }
- else
- {
- # fit's into one Perl scalar, so result can be computed directly
- # cannot use int() here, because it rounds wrongly (try
- # (81 ** 3) ** (1/3) to see what I mean)
- #$x->[0] = int( $x->[0] ** (1 / $n->[0]) );
- # round to 8 digits, then truncate result to integer
- $x->[0] = int ( sprintf ("%.8f", $x->[0] ** (1 / $n->[0]) ) );
- }
- return $x;
- }
-
- # we know now that X is more than one element long
-
- # if $n is a power of two, we can repeatedly take sqrt($X) and find the
- # proper result, because sqrt(sqrt($x)) == root($x,4)
- my $b = _as_bin($c,$n);
- if ($b =~ /0b1(0+)$/)
- {
- my $count = CORE::length($1); # 0b100 => len('00') => 2
- my $cnt = $count; # counter for loop
- unshift (@$x, 0); # add one element, together with one
- # more below in the loop this makes 2
- while ($cnt-- > 0)
- {
- # 'inflate' $X by adding one element, basically computing
- # $x * $BASE * $BASE. This gives us more $BASE_LEN digits for result
- # since len(sqrt($X)) approx == len($x) / 2.
- unshift (@$x, 0);
- # calculate sqrt($x), $x is now one element to big, again. In the next
- # round we make that two, again.
- _sqrt($c,$x);
- }
- # $x is now one element to big, so truncate result by removing it
- splice (@$x,0,1);
- }
- else
- {
- # trial computation by starting with 2,4,8,16 etc until we overstep
- my $step;
- my $trial = _two();
-
- # while still to do more than X steps
- do
- {
- $step = _two();
- while (_acmp($c, _pow($c, _copy($c, $trial), $n), $x) < 0)
- {
- _mul ($c, $step, [2]);
- _add ($c, $trial, $step);
- }
-
- # hit exactly?
- if (_acmp($c, _pow($c, _copy($c, $trial), $n), $x) == 0)
- {
- @$x = @$trial; # make copy while preserving ref to $x
- return $x;
- }
- # overstepped, so go back on step
- _sub($c, $trial, $step);
- } while (scalar @$step > 1 || $step->[0] > 128);
-
- # reset step to 2
- $step = _two();
- # add two, because $trial cannot be exactly the result (otherwise we would
- # alrady have found it)
- _add($c, $trial, $step);
-
- # and now add more and more (2,4,6,8,10 etc)
- while (_acmp($c, _pow($c, _copy($c, $trial), $n), $x) < 0)
- {
- _add ($c, $trial, $step);
- }
-
- # hit not exactly? (overstepped)
- if (_acmp($c, _pow($c, _copy($c, $trial), $n), $x) > 0)
- {
- _dec($c,$trial);
- }
-
- # hit not exactly? (overstepped)
- # 80 too small, 81 slightly too big, 82 too big
- if (_acmp($c, _pow($c, _copy($c, $trial), $n), $x) > 0)
- {
- _dec ($c, $trial);
- }
-
- @$x = @$trial; # make copy while preserving ref to $x
- return $x;
- }
- $x;
- }
-
-##############################################################################
-# binary stuff
-
-sub _and
- {
- my ($c,$x,$y) = @_;
-
- # the shortcut makes equal, large numbers _really_ fast, and makes only a
- # very small performance drop for small numbers (e.g. something with less
- # than 32 bit) Since we optimize for large numbers, this is enabled.
- return $x if _acmp($c,$x,$y) == 0; # shortcut
-
- my $m = _one(); my ($xr,$yr);
- my $mask = $AND_MASK;
-
- my $x1 = $x;
- my $y1 = _copy($c,$y); # make copy
- $x = _zero();
- my ($b,$xrr,$yrr);
- use integer;
- while (!_is_zero($c,$x1) && !_is_zero($c,$y1))
- {
- ($x1, $xr) = _div($c,$x1,$mask);
- ($y1, $yr) = _div($c,$y1,$mask);
-
- # make ints() from $xr, $yr
- # this is when the AND_BITS are greater than $BASE and is slower for
- # small (<256 bits) numbers, but faster for large numbers. Disabled
- # due to KISS principle
-
-# $b = 1; $xrr = 0; foreach (@$xr) { $xrr += $_ * $b; $b *= $BASE; }
-# $b = 1; $yrr = 0; foreach (@$yr) { $yrr += $_ * $b; $b *= $BASE; }
-# _add($c,$x, _mul($c, _new( $c, ($xrr & $yrr) ), $m) );
-
- # 0+ due to '&' doesn't work in strings
- _add($c,$x, _mul($c, [ 0+$xr->[0] & 0+$yr->[0] ], $m) );
- _mul($c,$m,$mask);
- }
- $x;
- }
-
-sub _xor
- {
- my ($c,$x,$y) = @_;
-
- return _zero() if _acmp($c,$x,$y) == 0; # shortcut (see -and)
-
- my $m = _one(); my ($xr,$yr);
- my $mask = $XOR_MASK;
-
- my $x1 = $x;
- my $y1 = _copy($c,$y); # make copy
- $x = _zero();
- my ($b,$xrr,$yrr);
- use integer;
- while (!_is_zero($c,$x1) && !_is_zero($c,$y1))
- {
- ($x1, $xr) = _div($c,$x1,$mask);
- ($y1, $yr) = _div($c,$y1,$mask);
- # make ints() from $xr, $yr (see _and())
- #$b = 1; $xrr = 0; foreach (@$xr) { $xrr += $_ * $b; $b *= $BASE; }
- #$b = 1; $yrr = 0; foreach (@$yr) { $yrr += $_ * $b; $b *= $BASE; }
- #_add($c,$x, _mul($c, _new( $c, ($xrr ^ $yrr) ), $m) );
-
- # 0+ due to '^' doesn't work in strings
- _add($c,$x, _mul($c, [ 0+$xr->[0] ^ 0+$yr->[0] ], $m) );
- _mul($c,$m,$mask);
- }
- # the loop stops when the shorter of the two numbers is exhausted
- # the remainder of the longer one will survive bit-by-bit, so we simple
- # multiply-add it in
- _add($c,$x, _mul($c, $x1, $m) ) if !_is_zero($c,$x1);
- _add($c,$x, _mul($c, $y1, $m) ) if !_is_zero($c,$y1);
-
- $x;
- }
-
-sub _or
- {
- my ($c,$x,$y) = @_;
-
- return $x if _acmp($c,$x,$y) == 0; # shortcut (see _and)
-
- my $m = _one(); my ($xr,$yr);
- my $mask = $OR_MASK;
-
- my $x1 = $x;
- my $y1 = _copy($c,$y); # make copy
- $x = _zero();
- my ($b,$xrr,$yrr);
- use integer;
- while (!_is_zero($c,$x1) && !_is_zero($c,$y1))
- {
- ($x1, $xr) = _div($c,$x1,$mask);
- ($y1, $yr) = _div($c,$y1,$mask);
- # make ints() from $xr, $yr (see _and())
-# $b = 1; $xrr = 0; foreach (@$xr) { $xrr += $_ * $b; $b *= $BASE; }
-# $b = 1; $yrr = 0; foreach (@$yr) { $yrr += $_ * $b; $b *= $BASE; }
-# _add($c,$x, _mul($c, _new( $c, ($xrr | $yrr) ), $m) );
-
- # 0+ due to '|' doesn't work in strings
- _add($c,$x, _mul($c, [ 0+$xr->[0] | 0+$yr->[0] ], $m) );
- _mul($c,$m,$mask);
- }
- # the loop stops when the shorter of the two numbers is exhausted
- # the remainder of the longer one will survive bit-by-bit, so we simple
- # multiply-add it in
- _add($c,$x, _mul($c, $x1, $m) ) if !_is_zero($c,$x1);
- _add($c,$x, _mul($c, $y1, $m) ) if !_is_zero($c,$y1);
-
- $x;
- }
-
-sub _as_hex
- {
- # convert a decimal number to hex (ref to array, return ref to string)
- my ($c,$x) = @_;
-
- # fit's into one element (handle also 0x0 case)
- return sprintf("0x%x",$x->[0]) if @$x == 1;
-
- my $x1 = _copy($c,$x);
-
- my $es = '';
- my ($xr, $h, $x10000);
- if ($] >= 5.006)
- {
- $x10000 = [ 0x10000 ]; $h = 'h4';
- }
- else
- {
- $x10000 = [ 0x1000 ]; $h = 'h3';
- }
- while (@$x1 != 1 || $x1->[0] != 0) # _is_zero()
- {
- ($x1, $xr) = _div($c,$x1,$x10000);
- $es .= unpack($h,pack('v',$xr->[0])); # XXX TODO: why pack('v',...)?
- }
- $es = reverse $es;
- $es =~ s/^[0]+//; # strip leading zeros
- '0x' . $es; # return result prepended with 0x
- }
-
-sub _as_bin
- {
- # convert a decimal number to bin (ref to array, return ref to string)
- my ($c,$x) = @_;
-
- # fit's into one element (and Perl recent enough), handle also 0b0 case
- # handle zero case for older Perls
- if ($] <= 5.005 && @$x == 1 && $x->[0] == 0)
- {
- my $t = '0b0'; return $t;
- }
- if (@$x == 1 && $] >= 5.006)
- {
- my $t = sprintf("0b%b",$x->[0]);
- return $t;
- }
- my $x1 = _copy($c,$x);
-
- my $es = '';
- my ($xr, $b, $x10000);
- if ($] >= 5.006)
- {
- $x10000 = [ 0x10000 ]; $b = 'b16';
- }
- else
- {
- $x10000 = [ 0x1000 ]; $b = 'b12';
- }
- while (!(@$x1 == 1 && $x1->[0] == 0)) # _is_zero()
- {
- ($x1, $xr) = _div($c,$x1,$x10000);
- $es .= unpack($b,pack('v',$xr->[0])); # XXX TODO: why pack('v',...)?
- # $es .= unpack($b,$xr->[0]);
- }
- $es = reverse $es;
- $es =~ s/^[0]+//; # strip leading zeros
- '0b' . $es; # return result prepended with 0b
- }
-
-sub _from_hex
- {
- # convert a hex number to decimal (ref to string, return ref to array)
- my ($c,$hs) = @_;
-
- my $m = _new($c, 0x10000000); # 28 bit at a time (<32 bit!)
- my $d = 7; # 7 digits at a time
- if ($] <= 5.006)
- {
- # for older Perls, play safe
- $m = [ 0x10000 ]; # 16 bit at a time (<32 bit!)
- $d = 4; # 4 digits at a time
- }
-
- my $mul = _one();
- my $x = _zero();
-
- my $len = int( (length($hs)-2)/$d ); # $d digit parts, w/o the '0x'
- my $val; my $i = -$d;
- while ($len >= 0)
- {
- $val = substr($hs,$i,$d); # get hex digits
- $val =~ s/^[+-]?0x// if $len == 0; # for last part only because
- $val = hex($val); # hex does not like wrong chars
- $i -= $d; $len --;
- my $adder = [ $val ];
- # if the resulting number was to big to fit into one element, create a
- # two-element version (bug found by Mark Lakata - Thanx!)
- if (CORE::length($val) > $BASE_LEN)
- {
- $adder = _new($c,$val);
- }
- _add ($c, $x, _mul ($c, $adder, $mul ) ) if $val != 0;
- _mul ($c, $mul, $m ) if $len >= 0; # skip last mul
- }
- $x;
- }
-
-sub _from_bin
- {
- # convert a hex number to decimal (ref to string, return ref to array)
- my ($c,$bs) = @_;
-
- # instead of converting X (8) bit at a time, it is faster to "convert" the
- # number to hex, and then call _from_hex.
-
- my $hs = $bs;
- $hs =~ s/^[+-]?0b//; # remove sign and 0b
- my $l = length($hs); # bits
- $hs = '0' x (8-($l % 8)) . $hs if ($l % 8) != 0; # padd left side w/ 0
- my $h = '0x' . unpack('H*', pack ('B*', $hs)); # repack as hex
-
- $c->_from_hex($h);
- }
-
-##############################################################################
-# special modulus functions
-
-sub _modinv
- {
- # modular inverse
- my ($c,$x,$y) = @_;
-
- my $u = _zero($c); my $u1 = _one($c);
- my $a = _copy($c,$y); my $b = _copy($c,$x);
-
- # Euclid's Algorithm for bgcd(), only that we calc bgcd() ($a) and the
- # result ($u) at the same time. See comments in BigInt for why this works.
- my $q;
- ($a, $q, $b) = ($b, _div($c,$a,$b)); # step 1
- my $sign = 1;
- while (!_is_zero($c,$b))
- {
- my $t = _add($c, # step 2:
- _mul($c,_copy($c,$u1), $q) , # t = u1 * q
- $u ); # + u
- $u = $u1; # u = u1, u1 = t
- $u1 = $t;
- $sign = -$sign;
- ($a, $q, $b) = ($b, _div($c,$a,$b)); # step 1
- }
-
- # if the gcd is not 1, then return NaN
- return (undef,undef) unless _is_one($c,$a);
-
- ($u1, $sign == 1 ? '+' : '-');
- }
-
-sub _modpow
- {
- # modulus of power ($x ** $y) % $z
- my ($c,$num,$exp,$mod) = @_;
-
- # in the trivial case,
- if (_is_one($c,$mod))
- {
- splice @$num,0,1; $num->[0] = 0;
- return $num;
- }
- if ((scalar @$num == 1) && (($num->[0] == 0) || ($num->[0] == 1)))
- {
- $num->[0] = 1;
- return $num;
- }
-
-# $num = _mod($c,$num,$mod); # this does not make it faster
-
- my $acc = _copy($c,$num); my $t = _one();
-
- my $expbin = _as_bin($c,$exp); $expbin =~ s/^0b//;
- my $len = length($expbin);
- while (--$len >= 0)
- {
- if ( substr($expbin,$len,1) eq '1') # is_odd
- {
- _mul($c,$t,$acc);
- $t = _mod($c,$t,$mod);
- }
- _mul($c,$acc,$acc);
- $acc = _mod($c,$acc,$mod);
- }
- @$num = @$t;
- $num;
- }
-
-sub _gcd
- {
- # greatest common divisor
- my ($c,$x,$y) = @_;
-
- while ( (scalar @$y != 1) || ($y->[0] != 0) ) # while ($y != 0)
- {
- my $t = _copy($c,$y);
- $y = _mod($c, $x, $y);
- $x = $t;
- }
- $x;
- }
-
-##############################################################################
-##############################################################################
-
-1;
-__END__
-
-=head1 NAME
-
-Math::BigInt::Calc - Pure Perl module to support Math::BigInt
-
-=head1 SYNOPSIS
-
-Provides support for big integer calculations. Not intended to be used by other
-modules. Other modules which sport the same functions can also be used to support
-Math::BigInt, like Math::BigInt::GMP or Math::BigInt::Pari.
-
-=head1 DESCRIPTION
-
-In order to allow for multiple big integer libraries, Math::BigInt was
-rewritten to use library modules for core math routines. Any module which
-follows the same API as this can be used instead by using the following:
-
- use Math::BigInt lib => 'libname';
-
-'libname' is either the long name ('Math::BigInt::Pari'), or only the short
-version like 'Pari'.
-
-=head1 STORAGE
-
-=head1 METHODS
-
-The following functions MUST be defined in order to support the use by
-Math::BigInt v1.70 or later:
-
- api_version() return API version, minimum 1 for v1.70
- _new(string) return ref to new object from ref to decimal string
- _zero() return a new object with value 0
- _one() return a new object with value 1
- _two() return a new object with value 2
- _ten() return a new object with value 10
-
- _str(obj) return ref to a string representing the object
- _num(obj) returns a Perl integer/floating point number
- NOTE: because of Perl numeric notation defaults,
- the _num'ified obj may lose accuracy due to
- machine-dependend floating point size limitations
-
- _add(obj,obj) Simple addition of two objects
- _mul(obj,obj) Multiplication of two objects
- _div(obj,obj) Division of the 1st object by the 2nd
- In list context, returns (result,remainder).
- NOTE: this is integer math, so no
- fractional part will be returned.
- The second operand will be not be 0, so no need to
- check for that.
- _sub(obj,obj) Simple subtraction of 1 object from another
- a third, optional parameter indicates that the params
- are swapped. In this case, the first param needs to
- be preserved, while you can destroy the second.
- sub (x,y,1) => return x - y and keep x intact!
- _dec(obj) decrement object by one (input is garant. to be > 0)
- _inc(obj) increment object by one
-
-
- _acmp(obj,obj) <=> operator for objects (return -1, 0 or 1)
-
- _len(obj) returns count of the decimal digits of the object
- _digit(obj,n) returns the n'th decimal digit of object
-
- _is_one(obj) return true if argument is 1
- _is_two(obj) return true if argument is 2
- _is_ten(obj) return true if argument is 10
- _is_zero(obj) return true if argument is 0
- _is_even(obj) return true if argument is even (0,2,4,6..)
- _is_odd(obj) return true if argument is odd (1,3,5,7..)
-
- _copy return a ref to a true copy of the object
-
- _check(obj) check whether internal representation is still intact
- return 0 for ok, otherwise error message as string
-
- _from_hex(str) return ref to new object from ref to hexadecimal string
- _from_bin(str) return ref to new object from ref to binary string
-
- _as_hex(str) return string containing the value as
- unsigned hex string, with the '0x' prepended.
- Leading zeros must be stripped.
- _as_bin(str) Like as_hex, only as binary string containing only
- zeros and ones. Leading zeros must be stripped and a
- '0b' must be prepended.
-
- _rsft(obj,N,B) shift object in base B by N 'digits' right
- _lsft(obj,N,B) shift object in base B by N 'digits' left
-
- _xor(obj1,obj2) XOR (bit-wise) object 1 with object 2
- Note: XOR, AND and OR pad with zeros if size mismatches
- _and(obj1,obj2) AND (bit-wise) object 1 with object 2
- _or(obj1,obj2) OR (bit-wise) object 1 with object 2
-
- _mod(obj,obj) Return remainder of div of the 1st by the 2nd object
- _sqrt(obj) return the square root of object (truncated to int)
- _root(obj) return the n'th (n >= 3) root of obj (truncated to int)
- _fac(obj) return factorial of object 1 (1*2*3*4..)
- _pow(obj,obj) return object 1 to the power of object 2
- return undef for NaN
- _zeros(obj) return number of trailing decimal zeros
- _modinv return inverse modulus
- _modpow return modulus of power ($x ** $y) % $z
- _log_int(X,N) calculate integer log() of X in base N
- X >= 0, N >= 0 (return undef for NaN)
- returns (RESULT, EXACT) where EXACT is:
- 1 : result is exactly RESULT
- 0 : result was truncated to RESULT
- undef : unknown whether result is exactly RESULT
- _gcd(obj,obj) return Greatest Common Divisor of two objects
-
-The following functions are optional, and can be defined if the underlying lib
-has a fast way to do them. If undefined, Math::BigInt will use pure Perl (hence
-slow) fallback routines to emulate these:
-
- _signed_or
- _signed_and
- _signed_xor
-
-
-Input strings come in as unsigned but with prefix (i.e. as '123', '0xabc'
-or '0b1101').
-
-So the library needs only to deal with unsigned big integers. Testing of input
-parameter validity is done by the caller, so you need not worry about
-underflow (f.i. in C<_sub()>, C<_dec()>) nor about division by zero or similar
-cases.
-
-The first parameter can be modified, that includes the possibility that you
-return a reference to a completely different object instead. Although keeping
-the reference and just changing it's contents is prefered over creating and
-returning a different reference.
-
-Return values are always references to objects, strings, or true/false for
-comparisation routines.
-
-=head1 WRAP YOUR OWN
-
-If you want to port your own favourite c-lib for big numbers to the
-Math::BigInt interface, you can take any of the already existing modules as
-a rough guideline. You should really wrap up the latest BigInt and BigFloat
-testsuites with your module, and replace in them any of the following:
-
- use Math::BigInt;
-
-by this:
-
- use Math::BigInt lib => 'yourlib';
-
-This way you ensure that your library really works 100% within Math::BigInt.
-
-=head1 LICENSE
-
-This program is free software; you may redistribute it and/or modify it under
-the same terms as Perl itself.
-
-=head1 AUTHORS
-
-Original math code by Mark Biggar, rewritten by Tels L<http://bloodgate.com/>
-in late 2000.
-Seperated from BigInt and shaped API with the help of John Peacock.
-
-Fixed, speed-up, streamlined and enhanced by Tels 2001 - 2005.
-
-=head1 SEE ALSO
-
-L<Math::BigInt>, L<Math::BigFloat>, L<Math::BigInt::BitVect>,
-L<Math::BigInt::GMP>, L<Math::BigInt::FastCalc> and L<Math::BigInt::Pari>.
-
-=cut
Index: affelio_farm/admin/skelton/affelio/extlib/Math/BigInt/CalcEmu.pm
diff -u affelio_farm/admin/skelton/affelio/extlib/Math/BigInt/CalcEmu.pm:1.1.1.1 affelio_farm/admin/skelton/affelio/extlib/Math/BigInt/CalcEmu.pm:removed
--- affelio_farm/admin/skelton/affelio/extlib/Math/BigInt/CalcEmu.pm:1.1.1.1 Tue Oct 25 04:14:40 2005
+++ affelio_farm/admin/skelton/affelio/extlib/Math/BigInt/CalcEmu.pm Tue Oct 25 04:20:51 2005
@@ -1,329 +0,0 @@
-package Math::BigInt::CalcEmu;
-
-use 5.005;
-use strict;
-# use warnings; # dont use warnings for older Perls
-use vars qw/$VERSION/;
-
-$VERSION = '0.05';
-
-package Math::BigInt;
-
-# See SYNOPSIS below.
-
-my $CALC_EMU;
-
-BEGIN
- {
- $CALC_EMU = Math::BigInt->config()->{'lib'};
- # register us with MBI to get notified of future lib changes
- Math::BigInt::_register_callback( __PACKAGE__, sub { $CALC_EMU = $_[0]; } );
- }
-
-sub __emu_band
- {
- my ($self,$x,$y,$sx,$sy, ＠ r) = @_;
-
- return $x->bzero(@r) if $y->is_zero() || $x->is_zero();
-
- my $sign = 0; # sign of result
- $sign = 1 if $sx == -1 && $sy == -1;
-
- my ($bx,$by);
-
- if ($sx == -1) # if x is negative
- {
- # two's complement: inc and flip all "bits" in $bx
- $bx = $x->binc()->as_hex(); # -1 => 0, -2 => 1, -3 => 2 etc
- $bx =~ s/-?0x//;
- $bx =~ tr/0123456789abcdef/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
- }
- else
- {
- $bx = $x->as_hex(); # get binary representation
- $bx =~ s/-?0x//;
- $bx =~ tr/fedcba9876543210/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
- }
- if ($sy == -1) # if y is negative
- {
- # two's complement: inc and flip all "bits" in $by
- $by = $y->copy()->binc()->as_hex(); # -1 => 0, -2 => 1, -3 => 2 etc
- $by =~ s/-?0x//;
- $by =~ tr/0123456789abcdef/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
- }
- else
- {
- $by = $y->as_hex(); # get binary representation
- $by =~ s/-?0x//;
- $by =~ tr/fedcba9876543210/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
- }
- # now we have bit-strings from X and Y, reverse them for padding
- $bx = reverse $bx;
- $by = reverse $by;
-
- # padd the shorter string
- my $xx = "\x00"; $xx = "\x0f" if $sx == -1;
- my $yy = "\x00"; $yy = "\x0f" if $sy == -1;
- my $diff = CORE::length($bx) - CORE::length($by);
- if ($diff > 0)
- {
- # if $yy eq "\x00", we can cut $bx, otherwise we need to padd $by
- $by .= $yy x $diff;
- }
- elsif ($diff < 0)
- {
- # if $xx eq "\x00", we can cut $by, otherwise we need to padd $bx
- $bx .= $xx x abs($diff);
- }
-
- # and the strings together
- my $r = $bx & $by;
-
- # and reverse the result again
- $bx = reverse $r;
-
- # One of $x or $y was negative, so need to flip bits in the result.
- # In both cases (one or two of them negative, or both positive) we need
- # to get the characters back.
- if ($sign == 1)
- {
- $bx =~ tr/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/0123456789abcdef/;
- }
- else
- {
- $bx =~ tr/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/fedcba9876543210/;
- }
-
- # leading zeros will be stripped by _from_hex()
- $bx = '0x' . $bx;
- $x->{value} = $CALC_EMU->_from_hex( $bx );
-
- # calculate sign of result
- $x->{sign} = '+';
- $x->{sign} = '-' if $sign == 1 && !$x->is_zero();
-
- $x->bdec() if $sign == 1;
-
- $x->round(@r);
- }
-
-sub __emu_bior
- {
- my ($self,$x,$y,$sx,$sy, ＠ r) = @_;
-
- return $x->round(@r) if $y->is_zero();
-
- my $sign = 0; # sign of result
- $sign = 1 if ($sx == -1) || ($sy == -1);
-
- my ($bx,$by);
-
- if ($sx == -1) # if x is negative
- {
- # two's complement: inc and flip all "bits" in $bx
- $bx = $x->binc()->as_hex(); # -1 => 0, -2 => 1, -3 => 2 etc
- $bx =~ s/-?0x//;
- $bx =~ tr/0123456789abcdef/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
- }
- else
- {
- $bx = $x->as_hex(); # get binary representation
- $bx =~ s/-?0x//;
- $bx =~ tr/fedcba9876543210/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
- }
- if ($sy == -1) # if y is negative
- {
- # two's complement: inc and flip all "bits" in $by
- $by = $y->copy()->binc()->as_hex(); # -1 => 0, -2 => 1, -3 => 2 etc
- $by =~ s/-?0x//;
- $by =~ tr/0123456789abcdef/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
- }
- else
- {
- $by = $y->as_hex(); # get binary representation
- $by =~ s/-?0x//;
- $by =~ tr/fedcba9876543210/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
- }
- # now we have bit-strings from X and Y, reverse them for padding
- $bx = reverse $bx;
- $by = reverse $by;
-
- # padd the shorter string
- my $xx = "\x00"; $xx = "\x0f" if $sx == -1;
- my $yy = "\x00"; $yy = "\x0f" if $sy == -1;
- my $diff = CORE::length($bx) - CORE::length($by);
- if ($diff > 0)
- {
- $by .= $yy x $diff;
- }
- elsif ($diff < 0)
- {
- $bx .= $xx x abs($diff);
- }
-
- # or the strings together
- my $r = $bx | $by;
-
- # and reverse the result again
- $bx = reverse $r;
-
- # one of $x or $y was negative, so need to flip bits in the result
- # in both cases (one or two of them negative, or both positive) we need
- # to get the characters back.
- if ($sign == 1)
- {
- $bx =~ tr/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/0123456789abcdef/;
- }
- else
- {
- $bx =~ tr/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/fedcba9876543210/;
- }
-
- # leading zeros will be stripped by _from_hex()
- $bx = '0x' . $bx;
- $x->{value} = $CALC_EMU->_from_hex( $bx );
-
- # calculate sign of result
- $x->{sign} = '+';
- $x->{sign} = '-' if $sign == 1 && !$x->is_zero();
-
- # if one of X or Y was negative, we need to decrement result
- $x->bdec() if $sign == 1;
-
- $x->round(@r);
- }
-
-sub __emu_bxor
- {
- my ($self,$x,$y,$sx,$sy, ＠ r) = @_;
-
- return $x->round(@r) if $y->is_zero();
-
- my $sign = 0; # sign of result
- $sign = 1 if $x->{sign} ne $y->{sign};
-
- my ($bx,$by);
-
- if ($sx == -1) # if x is negative
- {
- # two's complement: inc and flip all "bits" in $bx
- $bx = $x->binc()->as_hex(); # -1 => 0, -2 => 1, -3 => 2 etc
- $bx =~ s/-?0x//;
- $bx =~ tr/0123456789abcdef/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
- }
- else
- {
- $bx = $x->as_hex(); # get binary representation
- $bx =~ s/-?0x//;
- $bx =~ tr/fedcba9876543210/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
- }
- if ($sy == -1) # if y is negative
- {
- # two's complement: inc and flip all "bits" in $by
- $by = $y->copy()->binc()->as_hex(); # -1 => 0, -2 => 1, -3 => 2 etc
- $by =~ s/-?0x//;
- $by =~ tr/0123456789abcdef/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
- }
- else
- {
- $by = $y->as_hex(); # get binary representation
- $by =~ s/-?0x//;
- $by =~ tr/fedcba9876543210/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
- }
- # now we have bit-strings from X and Y, reverse them for padding
- $bx = reverse $bx;
- $by = reverse $by;
-
- # padd the shorter string
- my $xx = "\x00"; $xx = "\x0f" if $sx == -1;
- my $yy = "\x00"; $yy = "\x0f" if $sy == -1;
- my $diff = CORE::length($bx) - CORE::length($by);
- if ($diff > 0)
- {
- $by .= $yy x $diff;
- }
- elsif ($diff < 0)
- {
- $bx .= $xx x abs($diff);
- }
-
- # xor the strings together
- my $r = $bx ^ $by;
-
- # and reverse the result again
- $bx = reverse $r;
-
- # one of $x or $y was negative, so need to flip bits in the result
- # in both cases (one or two of them negative, or both positive) we need
- # to get the characters back.
- if ($sign == 1)
- {
- $bx =~ tr/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/0123456789abcdef/;
- }
- else
- {
- $bx =~ tr/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/fedcba9876543210/;
- }
-
- # leading zeros will be stripped by _from_hex()
- $bx = '0x' . $bx;
- $x->{value} = $CALC_EMU->_from_hex( $bx );
-
- # calculate sign of result
- $x->{sign} = '+';
- $x->{sign} = '-' if $sx != $sy && !$x->is_zero();
-
- $x->bdec() if $sign == 1;
-
- $x->round(@r);
- }
-
-##############################################################################
-##############################################################################
-
-1;
-__END__
-
-=head1 NAME
-
-Math::BigInt::CalcEmu - Emulate low-level math with BigInt code
-
-=head1 SYNOPSIS
-
- use Math::BigInt::CalcEmu;
-
-=head1 DESCRIPTION
-
-Contains routines that emulate low-level math functions in BigInt, e.g.
-optional routines the low-level math package does not provide on it's own.
-
-Will be loaded on demand and called automatically by BigInt.
-
-Stuff here is really low-priority to optimize, since it is far better to
-implement the operation in the low-level math libary directly, possible even
-using a call to the native lib.
-
-=head1 METHODS
-
-=head2 __emu_bxor
-
-=head2 __emu_band
-
-=head2 __emu_bior
-
-=head1 LICENSE
-
-This program is free software; you may redistribute it and/or modify it under
-the same terms as Perl itself.
-
-=head1 AUTHORS
-
-(c) Tels http://bloodgate.com 2003, 2004 - based on BigInt code by
-Tels from 2001-2003.
-
-=head1 SEE ALSO
-
-L<Math::BigInt>, L<Math::BigFloat>, L<Math::BigInt::BitVect>,
-L<Math::BigInt::GMP> and L<Math::BigInt::Pari>.
-
-=cut
Index: affelio_farm/admin/skelton/affelio/extlib/Math/BigInt/Trace.pm
diff -u affelio_farm/admin/skelton/affelio/extlib/Math/BigInt/Trace.pm:1.1.1.1 affelio_farm/admin/skelton/affelio/extlib/Math/BigInt/Trace.pm:removed
--- affelio_farm/admin/skelton/affelio/extlib/Math/BigInt/Trace.pm:1.1.1.1 Tue Oct 25 04:14:40 2005
+++ affelio_farm/admin/skelton/affelio/extlib/Math/BigInt/Trace.pm Tue Oct 25 04:20:51 2005
@@ -1,47 +0,0 @@
-#!/usr/bin/perl -w
-
-package Math::BigInt::Trace;
-
-require 5.005_02;
-use strict;
-
-use Exporter;
-use Math::BigInt;
-use vars qw($VERSION @ISA $PACKAGE @EXPORT_OK
- $accuracy $precision $round_mode $div_scale);
-
- ＠ ISA = qw(Exporter Math::BigInt);
-
-$VERSION = 0.01;
-
-use overload; # inherit overload from BigInt
-
-# Globals
-$accuracy = $precision = undef;
-$round_mode = 'even';
-$div_scale = 40;
-
-sub new
-{
- my $proto = shift;
- my $class = ref($proto) || $proto;
-
- my $value = shift;
- my $a = $accuracy; $a = $_[0] if defined $_[0];
- my $p = $precision; $p = $_[1] if defined $_[1];
- my $self = Math::BigInt->new($value,$a,$p,$round_mode);
- bless $self,$class;
- print "MBI new '$value' => '$self' (",ref($self),")";
- return $self;
-}
-
-sub import
- {
- print "MBI import ",join(' ', ＠ _);
- my $self = shift;
- Math::BigInt::import($self, ＠ _); # need it for subclasses
-# $self->export_to_level(1,$self, ＠ _); # need this ?
- @_ = ();
- }
-
-1;