[perl5.git] / lib / bigint.pl

warn "Legacy library @{[(caller(0))[6]]} will be removed from the Perl core distribution in the next major release. Please install it from the CPAN distribution Perl4::CoreLibs. It is being used at @{[(caller)[1]]}, line @{[(caller)[2]]}.\n";

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

# 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$2/) {     # test if number
	substr($_,0,0) = '+' unless $1; # Add missing sign
	s/^-0/+0/;
	$_;
    } else {
	'NaN';
    }
}

# Convert a number from string format to internal base 100000 format.
#   Assumes normalized value as input.
sub internal { #(num_str) return int_num_array
    local($d) = @_;
    ($is,$il) = (substr($d,0,1),length($d)-2);
    substr($d,0,1) = '';
    ($is, reverse(unpack("a" . ($il%5+1) . ("a5" x ($il/5)), $d)));
}

# Convert a number from internal base 100000 format to string format.
#   This routine scribbles all over input array.
sub external { #(int_num_array) return num_str
    $es = shift;
    grep($_ > 9999 || ($_ = substr('0000'.$_,-5)), @_);   # zero pad
    &'bnorm(join('', $es, reverse(@_)));    # reverse concat and normalize
}

# Negate input value.
sub main'bneg { #(num_str) return num_str
    local($_) = &'bnorm(@_);
    vec($_,0,8) ^= ord('+') ^ ord('-') unless $_ eq '+0';
    s/^./N/ unless /^[-+]/; # works both in ASCII and EBCDIC
    $_;
}

# Returns the absolute value of the input.
sub main'babs { #(num_str) return num_str
    &abs(&'bnorm(@_));
}

sub abs { # post-normalized abs for internal use
    local($_) = @_;
    s/^-/+/;
    $_;
}
\f
# Compares 2 values.  Returns one of undef, <0, =0, >0. (suitable for sort)
sub main'bcmp { #(num_str, num_str) return cond_code
    local($x,$y) = (&'bnorm($_[0]),&'bnorm($_[1]));
    if ($x eq 'NaN') {
	undef;
    } elsif ($y eq 'NaN') {
	undef;
    } else {
	&cmp($x,$y);
    }
}

sub cmp { # post-normalized compare for internal use
    local($cx, $cy) = @_;
    return 0 if ($cx eq $cy);

    local($sx, $sy) = (substr($cx, 0, 1), substr($cy, 0, 1));
    local($ld);

    if ($sx eq '+') {
      return  1 if ($sy eq '-' || $cy eq '+0');
      $ld = length($cx) - length($cy);
      return $ld if ($ld);
      return $cx cmp $cy;
    } else { # $sx eq '-'
      return -1 if ($sy eq '+');
      $ld = length($cy) - length($cx);
      return $ld if ($ld);
      return $cy cmp $cx;
    }

}

sub main'badd { #(num_str, num_str) return num_str
    local(*x, *y); ($x, $y) = (&'bnorm($_[0]),&'bnorm($_[1]));
    if ($x eq 'NaN') {
	'NaN';
    } elsif ($y eq 'NaN') {
	'NaN';
    } else {
	@x = &internal($x);             # convert to internal form
	@y = &internal($y);
	local($sx, $sy) = (shift @x, shift @y); # get signs
	if ($sx eq $sy) {
	    &external($sx, &add(*x, *y)); # if same sign add
	} else {
	    ($x, $y) = (&abs($x),&abs($y)); # make abs
	    if (&cmp($y,$x) > 0) {
		&external($sy, &sub(*y, *x));
	    } else {
		&external($sx, &sub(*x, *y));
	    }
	}
    }
}

sub main'bsub { #(num_str, num_str) return num_str
    &'badd($_[0],&'bneg($_[1]));    
}

# GCD -- Euclids algorithm Knuth Vol 2 pg 296
sub main'bgcd { #(num_str, num_str) return num_str
    local($x,$y) = (&'bnorm($_[0]),&'bnorm($_[1]));
    if ($x eq 'NaN' || $y eq 'NaN') {
	'NaN';
    } else {
	($x, $y) = ($y,&'bmod($x,$y)) while $y ne '+0';
	$x;
    }
}
\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, $y) = (&'bnorm($_[0]), &'bnorm($_[1]));
    if ($x eq 'NaN') {
	'NaN';
    } elsif ($y eq 'NaN') {
	'NaN';
    } else {
	@x = &internal($x);
	@y = &internal($y);
	local($signr) = (shift @x ne shift @y) ? '-' : '+';
	@prod = ();
	for $x (@x) {
	    ($car, $cty) = (0, 0);
	    for $y (@y) {
		$prod = $x * $y + $prod[$cty] + $car;
                if ($use_mult) {
		    $prod[$cty++] =
		        $prod - ($car = int($prod * 1e-5)) * 1e5;
                }
                else {
		    $prod[$cty++] =
		        $prod - ($car = int($prod / 1e5)) * 1e5;
                }
	    }
	    $prod[$cty] += $car if $car;
	    $x = shift @prod;
	}
	&external($signr, @x, @prod);
    }
}

# modulus
sub main'bmod { #(num_str, num_str) return num_str
    (&'bdiv(@_))[1];
}
\f
sub main'bdiv { #(dividend: num_str, divisor: num_str) return num_str
    local (*x, *y); ($x, $y) = (&'bnorm($_[0]), &'bnorm($_[1]));
    return wantarray ? ('NaN','NaN') : 'NaN'
	if ($x eq 'NaN' || $y eq 'NaN' || $y eq '+0');
    return wantarray ? ('+0',$x) : '+0' if (&cmp(&abs($x),&abs($y)) < 0);
    @x = &internal($x); @y = &internal($y);
    $srem = $y[0];
    $sr = (shift @x ne shift @y) ? '-' : '+';
    $car = $bar = $prd = 0;
    if (($dd = int(1e5/($y[$#y]+1))) != 1) {
	for $x (@x) {
	    $x = $x * $dd + $car;
            if ($use_mult) {
	    $x -= ($car = int($x * 1e-5)) * 1e5;
            }
            else {
	    $x -= ($car = int($x / 1e5)) * 1e5;
            }
	}
	push(@x, $car); $car = 0;
	for $y (@y) {
	    $y = $y * $dd + $car;
            if ($use_mult) {
	    $y -= ($car = int($y * 1e-5)) * 1e5;
            }
            else {
	    $y -= ($car = int($y / 1e5)) * 1e5;
            }
	}
    }
    else {
	push(@x, 0);
    }
    @q = (); ($v2,$v1) = @y[-2,-1];
    while ($#x > $#y) {
	($u2,$u1,$u0) = @x[-3..-1];
	$q = (($u0 == $v1) ? 99999 : int(($u0*1e5+$u1)/$v1));
	--$q while ($v2*$q > ($u0*1e5+$u1-$q*$v1)*1e5+$u2);
	if ($q) {
	    ($car, $bar) = (0,0);
	    for ($y = 0, $x = $#x-$#y-1; $y <= $#y; ++$y,++$x) {
		$prd = $q * $y[$y] + $car;
                if ($use_mult) {
		$prd -= ($car = int($prd * 1e-5)) * 1e5;
                }
                else {
		$prd -= ($car = int($prd / 1e5)) * 1e5;
                }
		$x[$x] += 1e5 if ($bar = (($x[$x] -= $prd + $bar) < 0));
	    }
	    if ($x[$#x] < $car + $bar) {
		$car = 0; --$q;
		for ($y = 0, $x = $#x-$#y-1; $y <= $#y; ++$y,++$x) {
		    $x[$x] -= 1e5
			if ($car = (($x[$x] += $y[$y] + $car) > 1e5));
		}
	    }   
	}
	pop(@x); unshift(@q, $q);
    }
    if (wantarray) {
	@d = ();
	if ($dd != 1) {
	    $car = 0;
	    for $x (reverse @x) {
		$prd = $car * 1e5 + $x;
		$car = $prd - ($tmp = int($prd / $dd)) * $dd;
		unshift(@d, $tmp);
	    }
	}
	else {
	    @d = @x;
	}
	(&external($sr, @q), &external($srem, @d, $zero));
    } else {
	&external($sr, @q);
    }
}
1;
Commit	Line	Data
0111154e Z	1	warn "Legacy library @{[(caller(0))[6]]} will be removed from the Perl core distribution in the next major release. Please install it from the CPAN distribution Perl4::CoreLibs. It is being used at @{[(caller)[1]]}, line @{[(caller)[2]]}.\n";
0111154e Z	2
5303340c	3	package bigint;
a6d71656 GS	4	#
	5	# This library is no longer being maintained, and is included for backward
	6	# compatibility with Perl 4 programs which may require it.
	7	#
	8	# In particular, this should not be used as an example of modern Perl
	9	# programming techniques.
b6dbc3e0 S	10	# This legacy library is deprecated and will be removed in a future
b6dbc3e0 S	11	# release of perl.
a6d71656 GS	12	#
a6d71656 GS	13	# Suggested alternative: Math::BigInt
b6dbc3e0	14
5303340c LW	15	# arbitrary size integer math package
	16	#
	17	# by Mark Biggar
	18	#
	19	# Canonical Big integer value are strings of the form
	20	# /^[+-]\d+$/ with leading zeros suppressed
	21	# Input values to these routines may be strings of the form
	22	# /^\s*[+-]?[\d\s]+$/.
	23	# Examples:
	24	# '+0' canonical zero value
	25	# ' -123 123 123' canonical value '-123123123'
	26	# '1 23 456 7890' canonical value '+1234567890'
d1be9408	27	# Output values always in canonical form
5303340c LW	28	#
	29	# Actual math is done in an internal format consisting of an array
	30	# whose first element is the sign (/^[+-]$/) and whose remaining
	31	# elements are base 100000 digits with the least significant digit first.
	32	# The string 'NaN' is used to represent the result when input arguments
	33	# are not numbers, as well as the result of dividing by zero
	34	#
	35	# routines provided are:
	36	#
	37	# bneg(BINT) return BINT negation
	38	# babs(BINT) return BINT absolute value
	39	# bcmp(BINT,BINT) return CODE compare numbers (undef,<0,=0,>0)
	40	# badd(BINT,BINT) return BINT addition
	41	# bsub(BINT,BINT) return BINT subtraction
	42	# bmul(BINT,BINT) return BINT multiplication
	43	# bdiv(BINT,BINT) return (BINT,BINT) division (quo,rem) just quo if scalar
	44	# bmod(BINT,BINT) return BINT modulus
	45	# bgcd(BINT,BINT) return BINT greatest common divisor
	46	# bnorm(BINT) return BINT normalization
	47	#
8990e307	48
1f45ae4a PP	49	# overcome a floating point problem on certain osnames (posix-bc, os390)
	50	BEGIN {
	51	my $x = 100000.0;
	52	my $use_mult = int($x1e-5)1e5 == $x ? 1 : 0;
	53	}
	54
8990e307 LW	55	$zero = 0;
8990e307 LW	56
5303340c LW	57	\f
	58	# normalize string form of number. Strip leading zeros. Strip any
	59	# white space and add a sign, if missing.
	60	# Strings that are not numbers result the value 'NaN'.
8990e307	61
5303340c LW	62	sub main'bnorm { #(num_str) return num_str
	63	local($_) = @_;
	64	s/\s+//g; # strip white space
	65	if (s/^([+-]?)0*(\d+)$/$1$2/) { # test if number
859172fe	66	substr($_,0,0) = '+' unless $1; # Add missing sign
5303340c LW	67	s/^-0/+0/;
	68	$_;
	69	} else {
	70	'NaN';
	71	}
	72	}
	73
	74	# Convert a number from string format to internal base 100000 format.
	75	# Assumes normalized value as input.
	76	sub internal { #(num_str) return int_num_array
	77	local($d) = @_;
859172fe Z	78	($is,$il) = (substr($d,0,1),length($d)-2);
859172fe Z	79	substr($d,0,1) = '';
5303340c LW	80	($is, reverse(unpack("a" . ($il%5+1) . ("a5" x ($il/5)), $d)));
	81	}
	82
	83	# Convert a number from internal base 100000 format to string format.
	84	# This routine scribbles all over input array.
	85	sub external { #(int_num_array) return num_str
	86	$es = shift;
	87	grep($_ > 9999 \|\| ($_ = substr('0000'.$_,-5)), @_); # zero pad
	88	&'bnorm(join('', $es, reverse(@_))); # reverse concat and normalize
	89	}
	90
	91	# Negate input value.
	92	sub main'bneg { #(num_str) return num_str
	93	local($_) = &'bnorm(@_);
	94	vec($_,0,8) ^= ord('+') ^ ord('-') unless $_ eq '+0';
9d116dd7	95	s/^./N/ unless /^[-+]/; # works both in ASCII and EBCDIC
5303340c LW	96	$_;
	97	}
	98
	99	# Returns the absolute value of the input.
	100	sub main'babs { #(num_str) return num_str
	101	&abs(&'bnorm(@_));
	102	}
	103
	104	sub abs { # post-normalized abs for internal use
	105	local($_) = @_;
	106	s/^-/+/;
	107	$_;
	108	}
	109	\f
	110	# Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort)
	111	sub main'bcmp { #(num_str, num_str) return cond_code
859172fe	112	local($x,$y) = (&'bnorm($_[0]),&'bnorm($_[1]));
5303340c LW	113	if ($x eq 'NaN') {
	114	undef;
	115	} elsif ($y eq 'NaN') {
	116	undef;
	117	} else {
	118	&cmp($x,$y);
	119	}
	120	}
	121
	122	sub cmp { # post-normalized compare for internal use
	123	local($cx, $cy) = @_;
1e2e1ae8 JH	124	return 0 if ($cx eq $cy);
	125
	126	local($sx, $sy) = (substr($cx, 0, 1), substr($cy, 0, 1));
	127	local($ld);
	128
	129	if ($sx eq '+') {
	130	return 1 if ($sy eq '-' \|\| $cy eq '+0');
	131	$ld = length($cx) - length($cy);
	132	return $ld if ($ld);
	133	return $cx cmp $cy;
	134	} else { # $sx eq '-'
	135	return -1 if ($sy eq '+');
	136	$ld = length($cy) - length($cx);
	137	return $ld if ($ld);
	138	return $cy cmp $cx;
	139	}
	140
5303340c LW	141	}
	142
	143	sub main'badd { #(num_str, num_str) return num_str
859172fe	144	local(x, y); ($x, $y) = (&'bnorm($_[0]),&'bnorm($_[1]));
5303340c LW	145	if ($x eq 'NaN') {
	146	'NaN';
	147	} elsif ($y eq 'NaN') {
	148	'NaN';
	149	} else {
	150	@x = &internal($x); # convert to internal form
	151	@y = &internal($y);
	152	local($sx, $sy) = (shift @x, shift @y); # get signs
	153	if ($sx eq $sy) {
	154	&external($sx, &add(x, y)); # if same sign add
	155	} else {
	156	($x, $y) = (&abs($x),&abs($y)); # make abs
	157	if (&cmp($y,$x) > 0) {
	158	&external($sy, &sub(y, x));
	159	} else {
	160	&external($sx, &sub(x, y));
	161	}
	162	}
	163	}
	164	}
	165
	166	sub main'bsub { #(num_str, num_str) return num_str
859172fe	167	&'badd($_[0],&'bneg($_[1]));
5303340c LW	168	}
	169
	170	# GCD -- Euclids algorithm Knuth Vol 2 pg 296
	171	sub main'bgcd { #(num_str, num_str) return num_str
859172fe	172	local($x,$y) = (&'bnorm($_[0]),&'bnorm($_[1]));
68decaef	173	if ($x eq 'NaN' \|\| $y eq 'NaN') {
5303340c	174	'NaN';
68decaef	175	} else {
5303340c LW	176	($x, $y) = ($y,&'bmod($x,$y)) while $y ne '+0';
	177	$x;
	178	}
	179	}
	180	\f
68decaef	181	# routine to add two base 1e5 numbers
5303340c LW	182	# stolen from Knuth Vol 2 Algorithm A pg 231
	183	# there are separate routines to add and sub as per Kunth pg 233
	184	sub add { #(int_num_array, int_num_array) return int_num_array
	185	local(x, y) = @_;
	186	$car = 0;
	187	for $x (@x) {
	188	last unless @y \|\| $car;
55497cff	189	$x -= 1e5 if $car = (($x += shift(@y) + $car) >= 1e5) ? 1 : 0;
5303340c LW	190	}
	191	for $y (@y) {
	192	last unless $car;
55497cff	193	$y -= 1e5 if $car = (($y += $car) >= 1e5) ? 1 : 0;
5303340c LW	194	}
	195	(@x, @y, $car);
	196	}
	197
68decaef	198	# subtract base 1e5 numbers -- stolen from Knuth Vol 2 pg 232, $x > $y
5303340c LW	199	sub sub { #(int_num_array, int_num_array) return int_num_array
	200	local(sx, sy) = @_;
	201	$bar = 0;
	202	for $sx (@sx) {
	203	last unless @y \|\| $bar;
e334a159	204	$sx += 1e5 if $bar = (($sx -= shift(@sy) + $bar) < 0);
5303340c LW	205	}
	206	@sx;
	207	}
	208
	209	# multiply two numbers -- stolen from Knuth Vol 2 pg 233
	210	sub main'bmul { #(num_str, num_str) return num_str
859172fe	211	local(x, y); ($x, $y) = (&'bnorm($_[0]), &'bnorm($_[1]));
5303340c LW	212	if ($x eq 'NaN') {
	213	'NaN';
	214	} elsif ($y eq 'NaN') {
	215	'NaN';
	216	} else {
	217	@x = &internal($x);
	218	@y = &internal($y);
	219	local($signr) = (shift @x ne shift @y) ? '-' : '+';
	220	@prod = ();
	221	for $x (@x) {
859172fe	222	($car, $cty) = (0, 0);
5303340c LW	223	for $y (@y) {
5303340c LW	224	$prod = $x * $y + $prod[$cty] + $car;
1f45ae4a PP	225	if ($use_mult) {
	226	$prod[$cty++] =
	227	$prod - ($car = int($prod * 1e-5)) * 1e5;
	228	}
	229	else {
	230	$prod[$cty++] =
	231	$prod - ($car = int($prod / 1e5)) * 1e5;
	232	}
5303340c LW	233	}
	234	$prod[$cty] += $car if $car;
	235	$x = shift @prod;
	236	}
	237	&external($signr, @x, @prod);
	238	}
	239	}
	240
	241	# modulus
	242	sub main'bmod { #(num_str, num_str) return num_str
859172fe	243	(&'bdiv(@_))[1];
5303340c LW	244	}
	245	\f
	246	sub main'bdiv { #(dividend: num_str, divisor: num_str) return num_str
859172fe	247	local (x, y); ($x, $y) = (&'bnorm($_[0]), &'bnorm($_[1]));
5303340c LW	248	return wantarray ? ('NaN','NaN') : 'NaN'
	249	if ($x eq 'NaN' \|\| $y eq 'NaN' \|\| $y eq '+0');
	250	return wantarray ? ('+0',$x) : '+0' if (&cmp(&abs($x),&abs($y)) < 0);
	251	@x = &internal($x); @y = &internal($y);
859172fe	252	$srem = $y[0];
5303340c LW	253	$sr = (shift @x ne shift @y) ? '-' : '+';
5303340c LW	254	$car = $bar = $prd = 0;
68decaef	255	if (($dd = int(1e5/($y[$#y]+1))) != 1) {
5303340c LW	256	for $x (@x) {
5303340c LW	257	$x = $x * $dd + $car;
1f45ae4a	258	if ($use_mult) {
68decaef	259	$x -= ($car = int($x * 1e-5)) * 1e5;
1f45ae4a PP	260	}
	261	else {
	262	$x -= ($car = int($x / 1e5)) * 1e5;
	263	}
5303340c LW	264	}
	265	push(@x, $car); $car = 0;
	266	for $y (@y) {
	267	$y = $y * $dd + $car;
1f45ae4a	268	if ($use_mult) {
68decaef	269	$y -= ($car = int($y * 1e-5)) * 1e5;
1f45ae4a PP	270	}
	271	else {
	272	$y -= ($car = int($y / 1e5)) * 1e5;
	273	}
5303340c LW	274	}
	275	}
	276	else {
	277	push(@x, 0);
	278	}
ed6116ce	279	@q = (); ($v2,$v1) = @y[-2,-1];
5303340c	280	while ($#x > $#y) {
ed6116ce	281	($u2,$u1,$u0) = @x[-3..-1];
68decaef LW	282	$q = (($u0 == $v1) ? 99999 : int(($u0*1e5+$u1)/$v1));
68decaef LW	283	--$q while ($v2$q > ($u01e5+$u1-$q$v1)1e5+$u2);
5303340c LW	284	if ($q) {
5303340c LW	285	($car, $bar) = (0,0);
859172fe	286	for ($y = 0, $x = $#x-$#y-1; $y <= $#y; ++$y,++$x) {
5303340c	287	$prd = $q * $y[$y] + $car;
1f45ae4a	288	if ($use_mult) {
68decaef	289	$prd -= ($car = int($prd * 1e-5)) * 1e5;
1f45ae4a PP	290	}
	291	else {
	292	$prd -= ($car = int($prd / 1e5)) * 1e5;
	293	}
68decaef	294	$x[$x] += 1e5 if ($bar = (($x[$x] -= $prd + $bar) < 0));
5303340c LW	295	}
	296	if ($x[$#x] < $car + $bar) {
	297	$car = 0; --$q;
859172fe	298	for ($y = 0, $x = $#x-$#y-1; $y <= $#y; ++$y,++$x) {
68decaef LW	299	$x[$x] -= 1e5
68decaef LW	300	if ($car = (($x[$x] += $y[$y] + $car) > 1e5));
5303340c LW	301	}
	302	}
	303	}
	304	pop(@x); unshift(@q, $q);
	305	}
	306	if (wantarray) {
	307	@d = ();
	308	if ($dd != 1) {
	309	$car = 0;
	310	for $x (reverse @x) {
68decaef	311	$prd = $car * 1e5 + $x;
5303340c LW	312	$car = $prd - ($tmp = int($prd / $dd)) * $dd;
	313	unshift(@d, $tmp);
	314	}
	315	}
	316	else {
	317	@d = @x;
	318	}
8990e307	319	(&external($sr, @q), &external($srem, @d, $zero));
5303340c LW	320	} else {
	321	&external($sr, @q);
	322	}
	323	}
	324	1;