Commit | Line | Data |
a0d0e21e |
1 | package Math::BigInt; |
3deb277d |
2 | $VERSION='0.01'; |
a0d0e21e |
3 | |
a5f75d66 |
4 | use overload |
748a9306 |
5 | '+' => sub {new Math::BigInt &badd}, |
6 | '-' => sub {new Math::BigInt |
a0d0e21e |
7 | $_[2]? bsub($_[1],${$_[0]}) : bsub(${$_[0]},$_[1])}, |
5d7098d5 |
8 | '<=>' => sub {$_[2]? bcmp($_[1],${$_[0]}) : bcmp(${$_[0]},$_[1])}, |
9 | 'cmp' => sub {$_[2]? ($_[1] cmp ${$_[0]}) : (${$_[0]} cmp $_[1])}, |
748a9306 |
10 | '*' => sub {new Math::BigInt &bmul}, |
11 | '/' => sub {new Math::BigInt |
a0d0e21e |
12 | $_[2]? scalar bdiv($_[1],${$_[0]}) : |
13 | scalar bdiv(${$_[0]},$_[1])}, |
748a9306 |
14 | '%' => sub {new Math::BigInt |
a0d0e21e |
15 | $_[2]? bmod($_[1],${$_[0]}) : bmod(${$_[0]},$_[1])}, |
748a9306 |
16 | '**' => sub {new Math::BigInt |
a0d0e21e |
17 | $_[2]? bpow($_[1],${$_[0]}) : bpow(${$_[0]},$_[1])}, |
748a9306 |
18 | 'neg' => sub {new Math::BigInt &bneg}, |
19 | 'abs' => sub {new Math::BigInt &babs}, |
e16b8f49 |
20 | '<<' => sub {new Math::BigInt |
21 | $_[2]? blsft($_[1],${$_[0]}) : blsft(${$_[0]},$_[1])}, |
22 | '>>' => sub {new Math::BigInt |
23 | $_[2]? brsft($_[1],${$_[0]}) : brsft(${$_[0]},$_[1])}, |
24 | '&' => sub {new Math::BigInt &band}, |
25 | '|' => sub {new Math::BigInt &bior}, |
26 | '^' => sub {new Math::BigInt &bxor}, |
27 | '~' => sub {new Math::BigInt &bnot}, |
f216259d |
28 | 'int' => sub { shift }, |
a0d0e21e |
29 | |
30 | qw( |
31 | "" stringify |
32 | 0+ numify) # Order of arguments unsignificant |
a5f75d66 |
33 | ; |
a0d0e21e |
34 | |
748a9306 |
35 | $NaNOK=1; |
36 | |
a0d0e21e |
37 | sub new { |
a5f75d66 |
38 | my($class) = shift; |
39 | my($foo) = bnorm(shift); |
748a9306 |
40 | die "Not a number initialized to Math::BigInt" if !$NaNOK && $foo eq "NaN"; |
a5f75d66 |
41 | bless \$foo, $class; |
a0d0e21e |
42 | } |
43 | sub stringify { "${$_[0]}" } |
44 | sub numify { 0 + "${$_[0]}" } # Not needed, additional overhead |
45 | # comparing to direct compilation based on |
46 | # stringify |
b3ac6de7 |
47 | sub import { |
48 | shift; |
49 | return unless @_; |
50 | die "unknown import: @_" unless @_ == 1 and $_[0] eq ':constant'; |
51 | overload::constant integer => sub {Math::BigInt->new(shift)}; |
52 | } |
a0d0e21e |
53 | |
a0d0e21e |
54 | $zero = 0; |
55 | |
1f45ae4a |
56 | # overcome a floating point problem on certain osnames (posix-bc, os390) |
57 | BEGIN { |
58 | my $x = 100000.0; |
59 | my $use_mult = int($x*1e-5)*1e5 == $x ? 1 : 0; |
60 | } |
a5f75d66 |
61 | |
a0d0e21e |
62 | # normalize string form of number. Strip leading zeros. Strip any |
63 | # white space and add a sign, if missing. |
64 | # Strings that are not numbers result the value 'NaN'. |
65 | |
66 | sub bnorm { #(num_str) return num_str |
67 | local($_) = @_; |
68 | s/\s+//g; # strip white space |
69 | if (s/^([+-]?)0*(\d+)$/$1$2/) { # test if number |
70 | substr($_,$[,0) = '+' unless $1; # Add missing sign |
71 | s/^-0/+0/; |
72 | $_; |
73 | } else { |
74 | 'NaN'; |
75 | } |
76 | } |
77 | |
78 | # Convert a number from string format to internal base 100000 format. |
79 | # Assumes normalized value as input. |
80 | sub internal { #(num_str) return int_num_array |
81 | local($d) = @_; |
82 | ($is,$il) = (substr($d,$[,1),length($d)-2); |
83 | substr($d,$[,1) = ''; |
84 | ($is, reverse(unpack("a" . ($il%5+1) . ("a5" x ($il/5)), $d))); |
85 | } |
86 | |
87 | # Convert a number from internal base 100000 format to string format. |
88 | # This routine scribbles all over input array. |
89 | sub external { #(int_num_array) return num_str |
90 | $es = shift; |
91 | grep($_ > 9999 || ($_ = substr('0000'.$_,-5)), @_); # zero pad |
92 | &bnorm(join('', $es, reverse(@_))); # reverse concat and normalize |
93 | } |
94 | |
95 | # Negate input value. |
96 | sub bneg { #(num_str) return num_str |
97 | local($_) = &bnorm(@_); |
e3c7ef20 |
98 | return $_ if $_ eq '+0' or $_ eq 'NaN'; |
99 | vec($_,0,8) ^= ord('+') ^ ord('-'); |
a0d0e21e |
100 | $_; |
101 | } |
102 | |
103 | # Returns the absolute value of the input. |
104 | sub babs { #(num_str) return num_str |
105 | &abs(&bnorm(@_)); |
106 | } |
107 | |
108 | sub abs { # post-normalized abs for internal use |
109 | local($_) = @_; |
110 | s/^-/+/; |
111 | $_; |
112 | } |
a5f75d66 |
113 | |
a0d0e21e |
114 | # Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort) |
115 | sub bcmp { #(num_str, num_str) return cond_code |
116 | local($x,$y) = (&bnorm($_[$[]),&bnorm($_[$[+1])); |
117 | if ($x eq 'NaN') { |
118 | undef; |
119 | } elsif ($y eq 'NaN') { |
120 | undef; |
121 | } else { |
e3c7ef20 |
122 | &cmp($x,$y) <=> 0; |
a0d0e21e |
123 | } |
124 | } |
125 | |
126 | sub cmp { # post-normalized compare for internal use |
127 | local($cx, $cy) = @_; |
1e2e1ae8 |
128 | |
129 | return 0 if ($cx eq $cy); |
130 | |
131 | local($sx, $sy) = (substr($cx, 0, 1), substr($cy, 0, 1)); |
132 | local($ld); |
133 | |
134 | if ($sx eq '+') { |
135 | return 1 if ($sy eq '-' || $cy eq '+0'); |
136 | $ld = length($cx) - length($cy); |
137 | return $ld if ($ld); |
138 | return $cx cmp $cy; |
139 | } else { # $sx eq '-' |
140 | return -1 if ($sy eq '+'); |
141 | $ld = length($cy) - length($cx); |
142 | return $ld if ($ld); |
143 | return $cy cmp $cx; |
144 | } |
a0d0e21e |
145 | } |
146 | |
147 | sub badd { #(num_str, num_str) return num_str |
148 | local(*x, *y); ($x, $y) = (&bnorm($_[$[]),&bnorm($_[$[+1])); |
149 | if ($x eq 'NaN') { |
150 | 'NaN'; |
151 | } elsif ($y eq 'NaN') { |
152 | 'NaN'; |
153 | } else { |
154 | @x = &internal($x); # convert to internal form |
155 | @y = &internal($y); |
156 | local($sx, $sy) = (shift @x, shift @y); # get signs |
157 | if ($sx eq $sy) { |
158 | &external($sx, &add(*x, *y)); # if same sign add |
159 | } else { |
160 | ($x, $y) = (&abs($x),&abs($y)); # make abs |
161 | if (&cmp($y,$x) > 0) { |
162 | &external($sy, &sub(*y, *x)); |
163 | } else { |
164 | &external($sx, &sub(*x, *y)); |
165 | } |
166 | } |
167 | } |
168 | } |
169 | |
170 | sub bsub { #(num_str, num_str) return num_str |
171 | &badd($_[$[],&bneg($_[$[+1])); |
172 | } |
173 | |
174 | # GCD -- Euclids algorithm Knuth Vol 2 pg 296 |
175 | sub bgcd { #(num_str, num_str) return num_str |
176 | local($x,$y) = (&bnorm($_[$[]),&bnorm($_[$[+1])); |
177 | if ($x eq 'NaN' || $y eq 'NaN') { |
178 | 'NaN'; |
179 | } else { |
180 | ($x, $y) = ($y,&bmod($x,$y)) while $y ne '+0'; |
181 | $x; |
182 | } |
183 | } |
a5f75d66 |
184 | |
a0d0e21e |
185 | # routine to add two base 1e5 numbers |
186 | # stolen from Knuth Vol 2 Algorithm A pg 231 |
187 | # there are separate routines to add and sub as per Kunth pg 233 |
188 | sub add { #(int_num_array, int_num_array) return int_num_array |
189 | local(*x, *y) = @_; |
190 | $car = 0; |
191 | for $x (@x) { |
192 | last unless @y || $car; |
20408e3c |
193 | $x -= 1e5 if $car = (($x += (@y ? shift(@y) : 0) + $car) >= 1e5) ? 1 : 0; |
a0d0e21e |
194 | } |
195 | for $y (@y) { |
196 | last unless $car; |
55497cff |
197 | $y -= 1e5 if $car = (($y += $car) >= 1e5) ? 1 : 0; |
a0d0e21e |
198 | } |
199 | (@x, @y, $car); |
200 | } |
201 | |
202 | # subtract base 1e5 numbers -- stolen from Knuth Vol 2 pg 232, $x > $y |
203 | sub sub { #(int_num_array, int_num_array) return int_num_array |
204 | local(*sx, *sy) = @_; |
205 | $bar = 0; |
206 | for $sx (@sx) { |
20408e3c |
207 | last unless @sy || $bar; |
208 | $sx += 1e5 if $bar = (($sx -= (@sy ? shift(@sy) : 0) + $bar) < 0); |
a0d0e21e |
209 | } |
210 | @sx; |
211 | } |
212 | |
213 | # multiply two numbers -- stolen from Knuth Vol 2 pg 233 |
214 | sub bmul { #(num_str, num_str) return num_str |
215 | local(*x, *y); ($x, $y) = (&bnorm($_[$[]), &bnorm($_[$[+1])); |
216 | if ($x eq 'NaN') { |
217 | 'NaN'; |
218 | } elsif ($y eq 'NaN') { |
219 | 'NaN'; |
220 | } else { |
221 | @x = &internal($x); |
222 | @y = &internal($y); |
223 | &external(&mul(*x,*y)); |
224 | } |
225 | } |
226 | |
227 | # multiply two numbers in internal representation |
228 | # destroys the arguments, supposes that two arguments are different |
229 | sub mul { #(*int_num_array, *int_num_array) return int_num_array |
230 | local(*x, *y) = (shift, shift); |
231 | local($signr) = (shift @x ne shift @y) ? '-' : '+'; |
232 | @prod = (); |
233 | for $x (@x) { |
234 | ($car, $cty) = (0, $[); |
235 | for $y (@y) { |
8b6a6e55 |
236 | $prod = $x * $y + ($prod[$cty] || 0) + $car; |
1f45ae4a |
237 | if ($use_mult) { |
a0d0e21e |
238 | $prod[$cty++] = |
239 | $prod - ($car = int($prod * 1e-5)) * 1e5; |
1f45ae4a |
240 | } |
241 | else { |
242 | $prod[$cty++] = |
243 | $prod - ($car = int($prod / 1e5)) * 1e5; |
244 | } |
a0d0e21e |
245 | } |
246 | $prod[$cty] += $car if $car; |
247 | $x = shift @prod; |
248 | } |
249 | ($signr, @x, @prod); |
250 | } |
251 | |
252 | # modulus |
253 | sub bmod { #(num_str, num_str) return num_str |
254 | (&bdiv(@_))[$[+1]; |
255 | } |
a5f75d66 |
256 | |
a0d0e21e |
257 | sub bdiv { #(dividend: num_str, divisor: num_str) return num_str |
258 | local (*x, *y); ($x, $y) = (&bnorm($_[$[]), &bnorm($_[$[+1])); |
259 | return wantarray ? ('NaN','NaN') : 'NaN' |
260 | if ($x eq 'NaN' || $y eq 'NaN' || $y eq '+0'); |
261 | return wantarray ? ('+0',$x) : '+0' if (&cmp(&abs($x),&abs($y)) < 0); |
262 | @x = &internal($x); @y = &internal($y); |
263 | $srem = $y[$[]; |
264 | $sr = (shift @x ne shift @y) ? '-' : '+'; |
265 | $car = $bar = $prd = 0; |
266 | if (($dd = int(1e5/($y[$#y]+1))) != 1) { |
267 | for $x (@x) { |
268 | $x = $x * $dd + $car; |
1f45ae4a |
269 | if ($use_mult) { |
a0d0e21e |
270 | $x -= ($car = int($x * 1e-5)) * 1e5; |
1f45ae4a |
271 | } |
272 | else { |
273 | $x -= ($car = int($x / 1e5)) * 1e5; |
274 | } |
a0d0e21e |
275 | } |
276 | push(@x, $car); $car = 0; |
277 | for $y (@y) { |
278 | $y = $y * $dd + $car; |
1f45ae4a |
279 | if ($use_mult) { |
a0d0e21e |
280 | $y -= ($car = int($y * 1e-5)) * 1e5; |
1f45ae4a |
281 | } |
282 | else { |
283 | $y -= ($car = int($y / 1e5)) * 1e5; |
284 | } |
a0d0e21e |
285 | } |
286 | } |
287 | else { |
288 | push(@x, 0); |
289 | } |
5d7098d5 |
290 | @q = (); ($v2,$v1) = @y[-2,-1]; |
0a6a0d52 |
291 | $v2 = 0 unless $v2; |
a0d0e21e |
292 | while ($#x > $#y) { |
5d7098d5 |
293 | ($u2,$u1,$u0) = @x[-3..-1]; |
0a6a0d52 |
294 | $u2 = 0 unless $u2; |
a0d0e21e |
295 | $q = (($u0 == $v1) ? 99999 : int(($u0*1e5+$u1)/$v1)); |
296 | --$q while ($v2*$q > ($u0*1e5+$u1-$q*$v1)*1e5+$u2); |
297 | if ($q) { |
298 | ($car, $bar) = (0,0); |
299 | for ($y = $[, $x = $#x-$#y+$[-1; $y <= $#y; ++$y,++$x) { |
300 | $prd = $q * $y[$y] + $car; |
1f45ae4a |
301 | if ($use_mult) { |
a0d0e21e |
302 | $prd -= ($car = int($prd * 1e-5)) * 1e5; |
1f45ae4a |
303 | } |
304 | else { |
305 | $prd -= ($car = int($prd / 1e5)) * 1e5; |
306 | } |
a0d0e21e |
307 | $x[$x] += 1e5 if ($bar = (($x[$x] -= $prd + $bar) < 0)); |
308 | } |
309 | if ($x[$#x] < $car + $bar) { |
310 | $car = 0; --$q; |
311 | for ($y = $[, $x = $#x-$#y+$[-1; $y <= $#y; ++$y,++$x) { |
312 | $x[$x] -= 1e5 |
313 | if ($car = (($x[$x] += $y[$y] + $car) > 1e5)); |
314 | } |
315 | } |
316 | } |
317 | pop(@x); unshift(@q, $q); |
318 | } |
319 | if (wantarray) { |
320 | @d = (); |
321 | if ($dd != 1) { |
322 | $car = 0; |
323 | for $x (reverse @x) { |
324 | $prd = $car * 1e5 + $x; |
325 | $car = $prd - ($tmp = int($prd / $dd)) * $dd; |
326 | unshift(@d, $tmp); |
327 | } |
328 | } |
329 | else { |
330 | @d = @x; |
331 | } |
332 | (&external($sr, @q), &external($srem, @d, $zero)); |
333 | } else { |
334 | &external($sr, @q); |
335 | } |
336 | } |
337 | |
338 | # compute power of two numbers -- stolen from Knuth Vol 2 pg 233 |
339 | sub bpow { #(num_str, num_str) return num_str |
340 | local(*x, *y); ($x, $y) = (&bnorm($_[$[]), &bnorm($_[$[+1])); |
341 | if ($x eq 'NaN') { |
342 | 'NaN'; |
343 | } elsif ($y eq 'NaN') { |
344 | 'NaN'; |
345 | } elsif ($x eq '+1') { |
346 | '+1'; |
347 | } elsif ($x eq '-1') { |
348 | &bmod($x,2) ? '-1': '+1'; |
349 | } elsif ($y =~ /^-/) { |
350 | 'NaN'; |
351 | } elsif ($x eq '+0' && $y eq '+0') { |
352 | 'NaN'; |
353 | } else { |
354 | @x = &internal($x); |
355 | local(@pow2)=@x; |
356 | local(@pow)=&internal("+1"); |
357 | local($y1,$res,@tmp1,@tmp2)=(1); # need tmp to send to mul |
358 | while ($y ne '+0') { |
359 | ($y,$res)=&bdiv($y,2); |
360 | if ($res ne '+0') {@tmp=@pow2; @pow=&mul(*pow,*tmp);} |
361 | if ($y ne '+0') {@tmp=@pow2;@pow2=&mul(*pow2,*tmp);} |
362 | } |
363 | &external(@pow); |
364 | } |
365 | } |
366 | |
e16b8f49 |
367 | # compute x << y, y >= 0 |
368 | sub blsft { #(num_str, num_str) return num_str |
369 | &bmul($_[$[], &bpow(2, $_[$[+1])); |
370 | } |
371 | |
372 | # compute x >> y, y >= 0 |
373 | sub brsft { #(num_str, num_str) return num_str |
374 | &bdiv($_[$[], &bpow(2, $_[$[+1])); |
375 | } |
376 | |
377 | # compute x & y |
378 | sub band { #(num_str, num_str) return num_str |
379 | local($x,$y,$r,$m,$xr,$yr) = (&bnorm($_[$[]),&bnorm($_[$[+1]),0,1); |
380 | if ($x eq 'NaN' || $y eq 'NaN') { |
381 | 'NaN'; |
382 | } else { |
383 | while ($x ne '+0' && $y ne '+0') { |
384 | ($x, $xr) = &bdiv($x, 0x10000); |
385 | ($y, $yr) = &bdiv($y, 0x10000); |
386 | $r = &badd(&bmul(int $xr & $yr, $m), $r); |
387 | $m = &bmul($m, 0x10000); |
388 | } |
389 | $r; |
390 | } |
391 | } |
392 | |
393 | # compute x | y |
394 | sub bior { #(num_str, num_str) return num_str |
395 | local($x,$y,$r,$m,$xr,$yr) = (&bnorm($_[$[]),&bnorm($_[$[+1]),0,1); |
396 | if ($x eq 'NaN' || $y eq 'NaN') { |
397 | 'NaN'; |
398 | } else { |
399 | while ($x ne '+0' || $y ne '+0') { |
400 | ($x, $xr) = &bdiv($x, 0x10000); |
401 | ($y, $yr) = &bdiv($y, 0x10000); |
402 | $r = &badd(&bmul(int $xr | $yr, $m), $r); |
403 | $m = &bmul($m, 0x10000); |
404 | } |
405 | $r; |
406 | } |
407 | } |
408 | |
409 | # compute x ^ y |
410 | sub bxor { #(num_str, num_str) return num_str |
411 | local($x,$y,$r,$m,$xr,$yr) = (&bnorm($_[$[]),&bnorm($_[$[+1]),0,1); |
412 | if ($x eq 'NaN' || $y eq 'NaN') { |
413 | 'NaN'; |
414 | } else { |
415 | while ($x ne '+0' || $y ne '+0') { |
416 | ($x, $xr) = &bdiv($x, 0x10000); |
417 | ($y, $yr) = &bdiv($y, 0x10000); |
418 | $r = &badd(&bmul(int $xr ^ $yr, $m), $r); |
419 | $m = &bmul($m, 0x10000); |
420 | } |
421 | $r; |
422 | } |
423 | } |
424 | |
425 | # represent ~x as twos-complement number |
426 | sub bnot { #(num_str) return num_str |
427 | &bsub(-1,$_[$[]); |
428 | } |
429 | |
a0d0e21e |
430 | 1; |
a5f75d66 |
431 | __END__ |
432 | |
433 | =head1 NAME |
434 | |
435 | Math::BigInt - Arbitrary size integer math package |
436 | |
437 | =head1 SYNOPSIS |
438 | |
439 | use Math::BigInt; |
440 | $i = Math::BigInt->new($string); |
441 | |
442 | $i->bneg return BINT negation |
443 | $i->babs return BINT absolute value |
444 | $i->bcmp(BINT) return CODE compare numbers (undef,<0,=0,>0) |
445 | $i->badd(BINT) return BINT addition |
446 | $i->bsub(BINT) return BINT subtraction |
447 | $i->bmul(BINT) return BINT multiplication |
448 | $i->bdiv(BINT) return (BINT,BINT) division (quo,rem) just quo if scalar |
449 | $i->bmod(BINT) return BINT modulus |
450 | $i->bgcd(BINT) return BINT greatest common divisor |
451 | $i->bnorm return BINT normalization |
e16b8f49 |
452 | $i->blsft(BINT) return BINT left shift |
453 | $i->brsft(BINT) return (BINT,BINT) right shift (quo,rem) just quo if scalar |
454 | $i->band(BINT) return BINT bit-wise and |
455 | $i->bior(BINT) return BINT bit-wise inclusive or |
456 | $i->bxor(BINT) return BINT bit-wise exclusive or |
457 | $i->bnot return BINT bit-wise not |
a5f75d66 |
458 | |
459 | =head1 DESCRIPTION |
460 | |
461 | All basic math operations are overloaded if you declare your big |
462 | integers as |
463 | |
464 | $i = new Math::BigInt '123 456 789 123 456 789'; |
465 | |
466 | |
467 | =over 2 |
468 | |
469 | =item Canonical notation |
470 | |
471 | Big integer value are strings of the form C</^[+-]\d+$/> with leading |
472 | zeros suppressed. |
473 | |
474 | =item Input |
475 | |
476 | Input values to these routines may be strings of the form |
477 | C</^\s*[+-]?[\d\s]+$/>. |
478 | |
479 | =item Output |
480 | |
481 | Output values always always in canonical form |
482 | |
483 | =back |
484 | |
485 | Actual math is done in an internal format consisting of an array |
486 | whose first element is the sign (/^[+-]$/) and whose remaining |
487 | elements are base 100000 digits with the least significant digit first. |
488 | The string 'NaN' is used to represent the result when input arguments |
489 | are not numbers, as well as the result of dividing by zero. |
490 | |
491 | =head1 EXAMPLES |
492 | |
493 | '+0' canonical zero value |
494 | ' -123 123 123' canonical value '-123123123' |
495 | '1 23 456 7890' canonical value '+1234567890' |
496 | |
497 | |
b3ac6de7 |
498 | =head1 Autocreating constants |
499 | |
500 | After C<use Math::BigInt ':constant'> all the integer decimal constants |
e3c7ef20 |
501 | in the given scope are converted to C<Math::BigInt>. This conversion |
b3ac6de7 |
502 | happens at compile time. |
503 | |
504 | In particular |
505 | |
506 | perl -MMath::BigInt=:constant -e 'print 2**100' |
507 | |
8dcee03e |
508 | print the integer value of C<2**100>. Note that without conversion of |
509 | constants the expression 2**100 will be calculated as floating point number. |
b3ac6de7 |
510 | |
a5f75d66 |
511 | =head1 BUGS |
512 | |
513 | The current version of this module is a preliminary version of the |
514 | real thing that is currently (as of perl5.002) under development. |
515 | |
516 | =head1 AUTHOR |
517 | |
518 | Mark Biggar, overloaded interface by Ilya Zakharevich. |
519 | |
520 | =cut |