1package bigint;
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.
8#
9# Suggested alternative:  Math::BigInt
10#
11# arbitrary size integer math package
12#
13# by Mark Biggar
14#
15# Canonical Big integer value are strings of the form
16#       /^[+-]\d+$/ with leading zeros suppressed
17# Input values to these routines may be strings of the form
18#       /^\s*[+-]?[\d\s]+$/.
19# Examples:
20#   '+0'                            canonical zero value
21#   '   -123 123 123'               canonical value '-123123123'
22#   '1 23 456 7890'                 canonical value '+1234567890'
23# Output values always in canonical form
24#
25# Actual math is done in an internal format consisting of an array
26#   whose first element is the sign (/^[+-]$/) and whose remaining
27#   elements are base 100000 digits with the least significant digit first.
28# The string 'NaN' is used to represent the result when input arguments
29#   are not numbers, as well as the result of dividing by zero
30#
31# routines provided are:
32#
33#   bneg(BINT) return BINT              negation
34#   babs(BINT) return BINT              absolute value
35#   bcmp(BINT,BINT) return CODE         compare numbers (undef,<0,=0,>0)
36#   badd(BINT,BINT) return BINT         addition
37#   bsub(BINT,BINT) return BINT         subtraction
38#   bmul(BINT,BINT) return BINT         multiplication
39#   bdiv(BINT,BINT) return (BINT,BINT)  division (quo,rem) just quo if scalar
40#   bmod(BINT,BINT) return BINT         modulus
41#   bgcd(BINT,BINT) return BINT         greatest common divisor
42#   bnorm(BINT) return BINT             normalization
43#
44
45# overcome a floating point problem on certain osnames (posix-bc, os390)
46BEGIN {
47    my $x = 100000.0;
48    my $use_mult = int($x*1e-5)*1e5 == $x ? 1 : 0;
49}
50
51$zero = 0;
52
53
54# normalize string form of number.   Strip leading zeros.  Strip any
55#   white space and add a sign, if missing.
56# Strings that are not numbers result the value 'NaN'.
57
58sub main'bnorm { #(num_str) return num_str
59    local($_) = @_;
60    s/\s+//g;                           # strip white space
61    if (s/^([+-]?)0*(\d+)$/$1$2/) {     # test if number
62	substr($_,0,0) = '+' unless $1; # Add missing sign
63	s/^-0/+0/;
64	$_;
65    } else {
66	'NaN';
67    }
68}
69
70# Convert a number from string format to internal base 100000 format.
71#   Assumes normalized value as input.
72sub internal { #(num_str) return int_num_array
73    local($d) = @_;
74    ($is,$il) = (substr($d,0,1),length($d)-2);
75    substr($d,0,1) = '';
76    ($is, reverse(unpack("a" . ($il%5+1) . ("a5" x ($il/5)), $d)));
77}
78
79# Convert a number from internal base 100000 format to string format.
80#   This routine scribbles all over input array.
81sub external { #(int_num_array) return num_str
82    $es = shift;
83    grep($_ > 9999 || ($_ = substr('0000'.$_,-5)), @_);   # zero pad
84    &'bnorm(join('', $es, reverse(@_)));    # reverse concat and normalize
85}
86
87# Negate input value.
88sub main'bneg { #(num_str) return num_str
89    local($_) = &'bnorm(@_);
90    vec($_,0,8) ^= ord('+') ^ ord('-') unless $_ eq '+0';
91    s/^./N/ unless /^[-+]/; # works both in ASCII and EBCDIC
92    $_;
93}
94
95# Returns the absolute value of the input.
96sub main'babs { #(num_str) return num_str
97    &abs(&'bnorm(@_));
98}
99
100sub abs { # post-normalized abs for internal use
101    local($_) = @_;
102    s/^-/+/;
103    $_;
104}
105
106# Compares 2 values.  Returns one of undef, <0, =0, >0. (suitable for sort)
107sub main'bcmp { #(num_str, num_str) return cond_code
108    local($x,$y) = (&'bnorm($_[0]),&'bnorm($_[1]));
109    if ($x eq 'NaN') {
110	undef;
111    } elsif ($y eq 'NaN') {
112	undef;
113    } else {
114	&cmp($x,$y);
115    }
116}
117
118sub cmp { # post-normalized compare for internal use
119    local($cx, $cy) = @_;
120    return 0 if ($cx eq $cy);
121
122    local($sx, $sy) = (substr($cx, 0, 1), substr($cy, 0, 1));
123    local($ld);
124
125    if ($sx eq '+') {
126      return  1 if ($sy eq '-' || $cy eq '+0');
127      $ld = length($cx) - length($cy);
128      return $ld if ($ld);
129      return $cx cmp $cy;
130    } else { # $sx eq '-'
131      return -1 if ($sy eq '+');
132      $ld = length($cy) - length($cx);
133      return $ld if ($ld);
134      return $cy cmp $cx;
135    }
136
137}
138
139sub main'badd { #(num_str, num_str) return num_str
140    local(*x, *y); ($x, $y) = (&'bnorm($_[0]),&'bnorm($_[1]));
141    if ($x eq 'NaN') {
142	'NaN';
143    } elsif ($y eq 'NaN') {
144	'NaN';
145    } else {
146	@x = &internal($x);             # convert to internal form
147	@y = &internal($y);
148	local($sx, $sy) = (shift @x, shift @y); # get signs
149	if ($sx eq $sy) {
150	    &external($sx, &add(*x, *y)); # if same sign add
151	} else {
152	    ($x, $y) = (&abs($x),&abs($y)); # make abs
153	    if (&cmp($y,$x) > 0) {
154		&external($sy, &sub(*y, *x));
155	    } else {
156		&external($sx, &sub(*x, *y));
157	    }
158	}
159    }
160}
161
162sub main'bsub { #(num_str, num_str) return num_str
163    &'badd($_[0],&'bneg($_[1]));
164}
165
166# GCD -- Euclids algorithm Knuth Vol 2 pg 296
167sub main'bgcd { #(num_str, num_str) return num_str
168    local($x,$y) = (&'bnorm($_[0]),&'bnorm($_[1]));
169    if ($x eq 'NaN' || $y eq 'NaN') {
170	'NaN';
171    } else {
172	($x, $y) = ($y,&'bmod($x,$y)) while $y ne '+0';
173	$x;
174    }
175}
176
177# routine to add two base 1e5 numbers
178#   stolen from Knuth Vol 2 Algorithm A pg 231
179#   there are separate routines to add and sub as per Kunth pg 233
180sub add { #(int_num_array, int_num_array) return int_num_array
181    local(*x, *y) = @_;
182    $car = 0;
183    for $x (@x) {
184	last unless @y || $car;
185	$x -= 1e5 if $car = (($x += shift(@y) + $car) >= 1e5) ? 1 : 0;
186    }
187    for $y (@y) {
188	last unless $car;
189	$y -= 1e5 if $car = (($y += $car) >= 1e5) ? 1 : 0;
190    }
191    (@x, @y, $car);
192}
193
194# subtract base 1e5 numbers -- stolen from Knuth Vol 2 pg 232, $x > $y
195sub sub { #(int_num_array, int_num_array) return int_num_array
196    local(*sx, *sy) = @_;
197    $bar = 0;
198    for $sx (@sx) {
199	last unless @y || $bar;
200	$sx += 1e5 if $bar = (($sx -= shift(@sy) + $bar) < 0);
201    }
202    @sx;
203}
204
205# multiply two numbers -- stolen from Knuth Vol 2 pg 233
206sub main'bmul { #(num_str, num_str) return num_str
207    local(*x, *y); ($x, $y) = (&'bnorm($_[0]), &'bnorm($_[1]));
208    if ($x eq 'NaN') {
209	'NaN';
210    } elsif ($y eq 'NaN') {
211	'NaN';
212    } else {
213	@x = &internal($x);
214	@y = &internal($y);
215	local($signr) = (shift @x ne shift @y) ? '-' : '+';
216	@prod = ();
217	for $x (@x) {
218	    ($car, $cty) = (0, 0);
219	    for $y (@y) {
220		$prod = $x * $y + $prod[$cty] + $car;
221                if ($use_mult) {
222		    $prod[$cty++] =
223		        $prod - ($car = int($prod * 1e-5)) * 1e5;
224                }
225                else {
226		    $prod[$cty++] =
227		        $prod - ($car = int($prod / 1e5)) * 1e5;
228                }
229	    }
230	    $prod[$cty] += $car if $car;
231	    $x = shift @prod;
232	}
233	&external($signr, @x, @prod);
234    }
235}
236
237# modulus
238sub main'bmod { #(num_str, num_str) return num_str
239    (&'bdiv(@_))[1];
240}
241
242sub main'bdiv { #(dividend: num_str, divisor: num_str) return num_str
243    local (*x, *y); ($x, $y) = (&'bnorm($_[0]), &'bnorm($_[1]));
244    return wantarray ? ('NaN','NaN') : 'NaN'
245	if ($x eq 'NaN' || $y eq 'NaN' || $y eq '+0');
246    return wantarray ? ('+0',$x) : '+0' if (&cmp(&abs($x),&abs($y)) < 0);
247    @x = &internal($x); @y = &internal($y);
248    $srem = $y[0];
249    $sr = (shift @x ne shift @y) ? '-' : '+';
250    $car = $bar = $prd = 0;
251    if (($dd = int(1e5/($y[$#y]+1))) != 1) {
252	for $x (@x) {
253	    $x = $x * $dd + $car;
254            if ($use_mult) {
255	    $x -= ($car = int($x * 1e-5)) * 1e5;
256            }
257            else {
258	    $x -= ($car = int($x / 1e5)) * 1e5;
259            }
260	}
261	push(@x, $car); $car = 0;
262	for $y (@y) {
263	    $y = $y * $dd + $car;
264            if ($use_mult) {
265	    $y -= ($car = int($y * 1e-5)) * 1e5;
266            }
267            else {
268	    $y -= ($car = int($y / 1e5)) * 1e5;
269            }
270	}
271    }
272    else {
273	push(@x, 0);
274    }
275    @q = (); ($v2,$v1) = @y[-2,-1];
276    while ($#x > $#y) {
277	($u2,$u1,$u0) = @x[-3..-1];
278	$q = (($u0 == $v1) ? 99999 : int(($u0*1e5+$u1)/$v1));
279	--$q while ($v2*$q > ($u0*1e5+$u1-$q*$v1)*1e5+$u2);
280	if ($q) {
281	    ($car, $bar) = (0,0);
282	    for ($y = 0, $x = $#x-$#y-1; $y <= $#y; ++$y,++$x) {
283		$prd = $q * $y[$y] + $car;
284                if ($use_mult) {
285		$prd -= ($car = int($prd * 1e-5)) * 1e5;
286                }
287                else {
288		$prd -= ($car = int($prd / 1e5)) * 1e5;
289                }
290		$x[$x] += 1e5 if ($bar = (($x[$x] -= $prd + $bar) < 0));
291	    }
292	    if ($x[$#x] < $car + $bar) {
293		$car = 0; --$q;
294		for ($y = 0, $x = $#x-$#y-1; $y <= $#y; ++$y,++$x) {
295		    $x[$x] -= 1e5
296			if ($car = (($x[$x] += $y[$y] + $car) > 1e5));
297		}
298	    }
299	}
300	pop(@x); unshift(@q, $q);
301    }
302    if (wantarray) {
303	@d = ();
304	if ($dd != 1) {
305	    $car = 0;
306	    for $x (reverse @x) {
307		$prd = $car * 1e5 + $x;
308		$car = $prd - ($tmp = int($prd / $dd)) * $dd;
309		unshift(@d, $tmp);
310	    }
311	}
312	else {
313	    @d = @x;
314	}
315	(&external($sr, @q), &external($srem, @d, $zero));
316    } else {
317	&external($sr, @q);
318    }
319}
3201;
321