[perl5.git] / lib / bigint.pl

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.
# This legacy library is deprecated and will be removed in a future
# release of perl.
#
# Suggested alternative:  Math::BigInt

warn( "The 'bigint.pl' legacy library is deprecated and will be"
      . " removed in the next major release of perl. Please use the"
      . " Math::BigInt module instead." );

# 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;

\f
# 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/^-/+/;
    $_;
}
\f
# Compares 2 values.  Returns one of undef, <0, =0, >0. (suitable for sort)
sub main'bcmp { #(num_str, num_str) return cond_code
    local($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;
    }
}
\f
# 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] + $car;
                if ($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(@_))[$[+1];
}
\f
sub main'bdiv { #(dividend: num_str, divisor: num_str) return num_str
    local (*x, *y); ($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 + $car;
            if ($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 = $[, $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 = $[, $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;
Commit	Line	Data
5303340c	1	package bigint;
a6d71656 GS	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.
b6dbc3e0 S	8	# This legacy library is deprecated and will be removed in a future
b6dbc3e0 S	9	# release of perl.
a6d71656 GS	10	#
a6d71656 GS	11	# Suggested alternative: Math::BigInt
b6dbc3e0 S	12
	13	warn( "The 'bigint.pl' legacy library is deprecated and will be"
	14	. " removed in the next major release of perl. Please use the"
	15	. " Math::BigInt module instead." );
	16
5303340c LW	17	# arbitrary size integer math package
	18	#
	19	# by Mark Biggar
	20	#
	21	# Canonical Big integer value are strings of the form
	22	# /^[+-]\d+$/ with leading zeros suppressed
	23	# Input values to these routines may be strings of the form
	24	# /^\s*[+-]?[\d\s]+$/.
	25	# Examples:
	26	# '+0' canonical zero value
	27	# ' -123 123 123' canonical value '-123123123'
	28	# '1 23 456 7890' canonical value '+1234567890'
d1be9408	29	# Output values always in canonical form
5303340c LW	30	#
	31	# Actual math is done in an internal format consisting of an array
	32	# whose first element is the sign (/^[+-]$/) and whose remaining
	33	# elements are base 100000 digits with the least significant digit first.
	34	# The string 'NaN' is used to represent the result when input arguments
	35	# are not numbers, as well as the result of dividing by zero
	36	#
	37	# routines provided are:
	38	#
	39	# bneg(BINT) return BINT negation
	40	# babs(BINT) return BINT absolute value
	41	# bcmp(BINT,BINT) return CODE compare numbers (undef,<0,=0,>0)
	42	# badd(BINT,BINT) return BINT addition
	43	# bsub(BINT,BINT) return BINT subtraction
	44	# bmul(BINT,BINT) return BINT multiplication
	45	# bdiv(BINT,BINT) return (BINT,BINT) division (quo,rem) just quo if scalar
	46	# bmod(BINT,BINT) return BINT modulus
	47	# bgcd(BINT,BINT) return BINT greatest common divisor
	48	# bnorm(BINT) return BINT normalization
	49	#
8990e307	50
1f45ae4a PP	51	# overcome a floating point problem on certain osnames (posix-bc, os390)
	52	BEGIN {
	53	my $x = 100000.0;
	54	my $use_mult = int($x1e-5)1e5 == $x ? 1 : 0;
	55	}
	56
8990e307 LW	57	$zero = 0;
8990e307 LW	58
5303340c LW	59	\f
	60	# normalize string form of number. Strip leading zeros. Strip any
	61	# white space and add a sign, if missing.
	62	# Strings that are not numbers result the value 'NaN'.
8990e307	63
5303340c LW	64	sub main'bnorm { #(num_str) return num_str
	65	local($_) = @_;
	66	s/\s+//g; # strip white space
	67	if (s/^([+-]?)0*(\d+)$/$1$2/) { # test if number
79072805	68	substr($_,$[,0) = '+' unless $1; # Add missing sign
5303340c LW	69	s/^-0/+0/;
	70	$_;
	71	} else {
	72	'NaN';
	73	}
	74	}
	75
	76	# Convert a number from string format to internal base 100000 format.
	77	# Assumes normalized value as input.
	78	sub internal { #(num_str) return int_num_array
	79	local($d) = @_;
79072805 LW	80	($is,$il) = (substr($d,$[,1),length($d)-2);
79072805 LW	81	substr($d,$[,1) = '';
5303340c LW	82	($is, reverse(unpack("a" . ($il%5+1) . ("a5" x ($il/5)), $d)));
	83	}
	84
	85	# Convert a number from internal base 100000 format to string format.
	86	# This routine scribbles all over input array.
	87	sub external { #(int_num_array) return num_str
	88	$es = shift;
	89	grep($_ > 9999 \|\| ($_ = substr('0000'.$_,-5)), @_); # zero pad
	90	&'bnorm(join('', $es, reverse(@_))); # reverse concat and normalize
	91	}
	92
	93	# Negate input value.
	94	sub main'bneg { #(num_str) return num_str
	95	local($_) = &'bnorm(@_);
	96	vec($_,0,8) ^= ord('+') ^ ord('-') unless $_ eq '+0';
9d116dd7	97	s/^./N/ unless /^[-+]/; # works both in ASCII and EBCDIC
5303340c LW	98	$_;
	99	}
	100
	101	# Returns the absolute value of the input.
	102	sub main'babs { #(num_str) return num_str
	103	&abs(&'bnorm(@_));
	104	}
	105
	106	sub abs { # post-normalized abs for internal use
	107	local($_) = @_;
	108	s/^-/+/;
	109	$_;
	110	}
	111	\f
	112	# Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort)
	113	sub main'bcmp { #(num_str, num_str) return cond_code
79072805	114	local($x,$y) = (&'bnorm($_[$[]),&'bnorm($_[$[+1]));
5303340c LW	115	if ($x eq 'NaN') {
	116	undef;
	117	} elsif ($y eq 'NaN') {
	118	undef;
	119	} else {
	120	&cmp($x,$y);
	121	}
	122	}
	123
	124	sub cmp { # post-normalized compare for internal use
	125	local($cx, $cy) = @_;
1e2e1ae8 JH	126	return 0 if ($cx eq $cy);
	127
	128	local($sx, $sy) = (substr($cx, 0, 1), substr($cy, 0, 1));
	129	local($ld);
	130
	131	if ($sx eq '+') {
	132	return 1 if ($sy eq '-' \|\| $cy eq '+0');
	133	$ld = length($cx) - length($cy);
	134	return $ld if ($ld);
	135	return $cx cmp $cy;
	136	} else { # $sx eq '-'
	137	return -1 if ($sy eq '+');
	138	$ld = length($cy) - length($cx);
	139	return $ld if ($ld);
	140	return $cy cmp $cx;
	141	}
	142
5303340c LW	143	}
	144
	145	sub main'badd { #(num_str, num_str) return num_str
79072805	146	local(x, y); ($x, $y) = (&'bnorm($_[$[]),&'bnorm($_[$[+1]));
5303340c LW	147	if ($x eq 'NaN') {
	148	'NaN';
	149	} elsif ($y eq 'NaN') {
	150	'NaN';
	151	} else {
	152	@x = &internal($x); # convert to internal form
	153	@y = &internal($y);
	154	local($sx, $sy) = (shift @x, shift @y); # get signs
	155	if ($sx eq $sy) {
	156	&external($sx, &add(x, y)); # if same sign add
	157	} else {
	158	($x, $y) = (&abs($x),&abs($y)); # make abs
	159	if (&cmp($y,$x) > 0) {
	160	&external($sy, &sub(y, x));
	161	} else {
	162	&external($sx, &sub(x, y));
	163	}
	164	}
	165	}
	166	}
	167
	168	sub main'bsub { #(num_str, num_str) return num_str
79072805	169	&'badd($_[$[],&'bneg($_[$[+1]));
5303340c LW	170	}
	171
	172	# GCD -- Euclids algorithm Knuth Vol 2 pg 296
	173	sub main'bgcd { #(num_str, num_str) return num_str
79072805	174	local($x,$y) = (&'bnorm($_[$[]),&'bnorm($_[$[+1]));
68decaef	175	if ($x eq 'NaN' \|\| $y eq 'NaN') {
5303340c	176	'NaN';
68decaef	177	} else {
5303340c LW	178	($x, $y) = ($y,&'bmod($x,$y)) while $y ne '+0';
	179	$x;
	180	}
	181	}
	182	\f
68decaef	183	# routine to add two base 1e5 numbers
5303340c LW	184	# stolen from Knuth Vol 2 Algorithm A pg 231
	185	# there are separate routines to add and sub as per Kunth pg 233
	186	sub add { #(int_num_array, int_num_array) return int_num_array
	187	local(x, y) = @_;
	188	$car = 0;
	189	for $x (@x) {
	190	last unless @y \|\| $car;
55497cff	191	$x -= 1e5 if $car = (($x += shift(@y) + $car) >= 1e5) ? 1 : 0;
5303340c LW	192	}
	193	for $y (@y) {
	194	last unless $car;
55497cff	195	$y -= 1e5 if $car = (($y += $car) >= 1e5) ? 1 : 0;
5303340c LW	196	}
	197	(@x, @y, $car);
	198	}
	199
68decaef	200	# subtract base 1e5 numbers -- stolen from Knuth Vol 2 pg 232, $x > $y
5303340c LW	201	sub sub { #(int_num_array, int_num_array) return int_num_array
	202	local(sx, sy) = @_;
	203	$bar = 0;
	204	for $sx (@sx) {
	205	last unless @y \|\| $bar;
e334a159	206	$sx += 1e5 if $bar = (($sx -= shift(@sy) + $bar) < 0);
5303340c LW	207	}
	208	@sx;
	209	}
	210
	211	# multiply two numbers -- stolen from Knuth Vol 2 pg 233
	212	sub main'bmul { #(num_str, num_str) return num_str
79072805	213	local(x, y); ($x, $y) = (&'bnorm($_[$[]), &'bnorm($_[$[+1]));
5303340c LW	214	if ($x eq 'NaN') {
	215	'NaN';
	216	} elsif ($y eq 'NaN') {
	217	'NaN';
	218	} else {
	219	@x = &internal($x);
	220	@y = &internal($y);
	221	local($signr) = (shift @x ne shift @y) ? '-' : '+';
	222	@prod = ();
	223	for $x (@x) {
79072805	224	($car, $cty) = (0, $[);
5303340c LW	225	for $y (@y) {
5303340c LW	226	$prod = $x * $y + $prod[$cty] + $car;
1f45ae4a PP	227	if ($use_mult) {
	228	$prod[$cty++] =
	229	$prod - ($car = int($prod * 1e-5)) * 1e5;
	230	}
	231	else {
	232	$prod[$cty++] =
	233	$prod - ($car = int($prod / 1e5)) * 1e5;
	234	}
5303340c LW	235	}
	236	$prod[$cty] += $car if $car;
	237	$x = shift @prod;
	238	}
	239	&external($signr, @x, @prod);
	240	}
	241	}
	242
	243	# modulus
	244	sub main'bmod { #(num_str, num_str) return num_str
79072805	245	(&'bdiv(@_))[$[+1];
5303340c LW	246	}
	247	\f
	248	sub main'bdiv { #(dividend: num_str, divisor: num_str) return num_str
79072805	249	local (x, y); ($x, $y) = (&'bnorm($_[$[]), &'bnorm($_[$[+1]));
5303340c LW	250	return wantarray ? ('NaN','NaN') : 'NaN'
	251	if ($x eq 'NaN' \|\| $y eq 'NaN' \|\| $y eq '+0');
	252	return wantarray ? ('+0',$x) : '+0' if (&cmp(&abs($x),&abs($y)) < 0);
	253	@x = &internal($x); @y = &internal($y);
79072805	254	$srem = $y[$[];
5303340c LW	255	$sr = (shift @x ne shift @y) ? '-' : '+';
5303340c LW	256	$car = $bar = $prd = 0;
68decaef	257	if (($dd = int(1e5/($y[$#y]+1))) != 1) {
5303340c LW	258	for $x (@x) {
5303340c LW	259	$x = $x * $dd + $car;
1f45ae4a	260	if ($use_mult) {
68decaef	261	$x -= ($car = int($x * 1e-5)) * 1e5;
1f45ae4a PP	262	}
	263	else {
	264	$x -= ($car = int($x / 1e5)) * 1e5;
	265	}
5303340c LW	266	}
	267	push(@x, $car); $car = 0;
	268	for $y (@y) {
	269	$y = $y * $dd + $car;
1f45ae4a	270	if ($use_mult) {
68decaef	271	$y -= ($car = int($y * 1e-5)) * 1e5;
1f45ae4a PP	272	}
	273	else {
	274	$y -= ($car = int($y / 1e5)) * 1e5;
	275	}
5303340c LW	276	}
	277	}
	278	else {
	279	push(@x, 0);
	280	}
ed6116ce	281	@q = (); ($v2,$v1) = @y[-2,-1];
5303340c	282	while ($#x > $#y) {
ed6116ce	283	($u2,$u1,$u0) = @x[-3..-1];
68decaef LW	284	$q = (($u0 == $v1) ? 99999 : int(($u0*1e5+$u1)/$v1));
68decaef LW	285	--$q while ($v2$q > ($u01e5+$u1-$q$v1)1e5+$u2);
5303340c LW	286	if ($q) {
5303340c LW	287	($car, $bar) = (0,0);
79072805	288	for ($y = $[, $x = $#x-$#y+$[-1; $y <= $#y; ++$y,++$x) {
5303340c	289	$prd = $q * $y[$y] + $car;
1f45ae4a	290	if ($use_mult) {
68decaef	291	$prd -= ($car = int($prd * 1e-5)) * 1e5;
1f45ae4a PP	292	}
	293	else {
	294	$prd -= ($car = int($prd / 1e5)) * 1e5;
	295	}
68decaef	296	$x[$x] += 1e5 if ($bar = (($x[$x] -= $prd + $bar) < 0));
5303340c LW	297	}
	298	if ($x[$#x] < $car + $bar) {
	299	$car = 0; --$q;
79072805	300	for ($y = $[, $x = $#x-$#y+$[-1; $y <= $#y; ++$y,++$x) {
68decaef LW	301	$x[$x] -= 1e5
68decaef LW	302	if ($car = (($x[$x] += $y[$y] + $car) > 1e5));
5303340c LW	303	}
	304	}
	305	}
	306	pop(@x); unshift(@q, $q);
	307	}
	308	if (wantarray) {
	309	@d = ();
	310	if ($dd != 1) {
	311	$car = 0;
	312	for $x (reverse @x) {
68decaef	313	$prd = $car * 1e5 + $x;
5303340c LW	314	$car = $prd - ($tmp = int($prd / $dd)) * $dd;
	315	unshift(@d, $tmp);
	316	}
	317	}
	318	else {
	319	@d = @x;
	320	}
8990e307	321	(&external($sr, @q), &external($srem, @d, $zero));
5303340c LW	322	} else {
	323	&external($sr, @q);
	324	}
	325	}
	326	1;