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920dae64 AT |
1 | package 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) | |
46 | BEGIN { | |
47 | my $x = 100000.0; | |
48 | my $use_mult = int($x*1e-5)*1e5 == $x ? 1 : 0; | |
49 | } | |
50 | ||
51 | $zero = 0; | |
52 | ||
53 | \f | |
54 | # normalize string form of number. Strip leading zeros. Strip any | |
55 | # white space and add a sign, if missing. | |
56 | # Strings that are not numbers result the value 'NaN'. | |
57 | ||
58 | sub main'bnorm { #(num_str) return num_str | |
59 | local($_) = @_; | |
60 | s/\s+//g; # strip white space | |
61 | if (s/^([+-]?)0*(\d+)$/$1$2/) { # test if number | |
62 | substr($_,$[,0) = '+' unless $1; # Add missing sign | |
63 | s/^-0/+0/; | |
64 | $_; | |
65 | } else { | |
66 | 'NaN'; | |
67 | } | |
68 | } | |
69 | ||
70 | # Convert a number from string format to internal base 100000 format. | |
71 | # Assumes normalized value as input. | |
72 | sub internal { #(num_str) return int_num_array | |
73 | local($d) = @_; | |
74 | ($is,$il) = (substr($d,$[,1),length($d)-2); | |
75 | substr($d,$[,1) = ''; | |
76 | ($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. | |
81 | sub external { #(int_num_array) return num_str | |
82 | $es = shift; | |
83 | grep($_ > 9999 || ($_ = substr('0000'.$_,-5)), @_); # zero pad | |
84 | &'bnorm(join('', $es, reverse(@_))); # reverse concat and normalize | |
85 | } | |
86 | ||
87 | # Negate input value. | |
88 | sub main'bneg { #(num_str) return num_str | |
89 | local($_) = &'bnorm(@_); | |
90 | vec($_,0,8) ^= ord('+') ^ ord('-') unless $_ eq '+0'; | |
91 | s/^./N/ unless /^[-+]/; # works both in ASCII and EBCDIC | |
92 | $_; | |
93 | } | |
94 | ||
95 | # Returns the absolute value of the input. | |
96 | sub main'babs { #(num_str) return num_str | |
97 | &abs(&'bnorm(@_)); | |
98 | } | |
99 | ||
100 | sub abs { # post-normalized abs for internal use | |
101 | local($_) = @_; | |
102 | s/^-/+/; | |
103 | $_; | |
104 | } | |
105 | \f | |
106 | # Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort) | |
107 | sub main'bcmp { #(num_str, num_str) return cond_code | |
108 | local($x,$y) = (&'bnorm($_[$[]),&'bnorm($_[$[+1])); | |
109 | if ($x eq 'NaN') { | |
110 | undef; | |
111 | } elsif ($y eq 'NaN') { | |
112 | undef; | |
113 | } else { | |
114 | &cmp($x,$y); | |
115 | } | |
116 | } | |
117 | ||
118 | sub cmp { # post-normalized compare for internal use | |
119 | local($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 $cx; | |
135 | } | |
136 | ||
137 | } | |
138 | ||
139 | sub main'badd { #(num_str, num_str) return num_str | |
140 | local(*x, *y); ($x, $y) = (&'bnorm($_[$[]),&'bnorm($_[$[+1])); | |
141 | if ($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($sx, &sub(*x, *y)); | |
157 | } | |
158 | } | |
159 | } | |
160 | } | |
161 | ||
162 | sub main'bsub { #(num_str, num_str) return num_str | |
163 | &'badd($_[$[],&'bneg($_[$[+1])); | |
164 | } | |
165 | ||
166 | # GCD -- Euclids algorithm Knuth Vol 2 pg 296 | |
167 | sub main'bgcd { #(num_str, num_str) return num_str | |
168 | local($x,$y) = (&'bnorm($_[$[]),&'bnorm($_[$[+1])); | |
169 | if ($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 | \f | |
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 | |
180 | sub 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 | |
195 | sub 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) + $bar) < 0); | |
201 | } | |
202 | @sx; | |
203 | } | |
204 | ||
205 | # multiply two numbers -- stolen from Knuth Vol 2 pg 233 | |
206 | sub main'bmul { #(num_str, num_str) return num_str | |
207 | local(*x, *y); ($x, $y) = (&'bnorm($_[$[]), &'bnorm($_[$[+1])); | |
208 | if ($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, $[); | |
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 | |
238 | sub main'bmod { #(num_str, num_str) return num_str | |
239 | (&'bdiv(@_))[$[+1]; | |
240 | } | |
241 | \f | |
242 | sub main'bdiv { #(dividend: num_str, divisor: num_str) return num_str | |
243 | local (*x, *y); ($x, $y) = (&'bnorm($_[$[]), &'bnorm($_[$[+1])); | |
244 | return wantarray ? ('NaN','NaN') : 'NaN' | |
245 | if ($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 = $y[$[]; | |
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 = $[, $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 = $[, $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 | } | |
320 | 1; |