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1 | package Math::BigInt; |
2 | |
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3 | use overload |
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4 | '+' => sub {new Math::BigInt &badd}, |
5 | '-' => sub {new Math::BigInt |
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6 | $_[2]? bsub($_[1],${$_[0]}) : bsub(${$_[0]},$_[1])}, |
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7 | '<=>' => sub {new Math::BigInt |
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8 | $_[2]? bcmp($_[1],${$_[0]}) : bcmp(${$_[0]},$_[1])}, |
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9 | 'cmp' => sub {new Math::BigInt |
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10 | $_[2]? ($_[1] cmp ${$_[0]}) : (${$_[0]} cmp $_[1])}, |
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11 | '*' => sub {new Math::BigInt &bmul}, |
12 | '/' => sub {new Math::BigInt |
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13 | $_[2]? scalar bdiv($_[1],${$_[0]}) : |
14 | scalar bdiv(${$_[0]},$_[1])}, |
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15 | '%' => sub {new Math::BigInt |
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16 | $_[2]? bmod($_[1],${$_[0]}) : bmod(${$_[0]},$_[1])}, |
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17 | '**' => sub {new Math::BigInt |
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18 | $_[2]? bpow($_[1],${$_[0]}) : bpow(${$_[0]},$_[1])}, |
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19 | 'neg' => sub {new Math::BigInt &bneg}, |
20 | 'abs' => sub {new Math::BigInt &babs}, |
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21 | |
22 | qw( |
23 | "" stringify |
24 | 0+ numify) # Order of arguments unsignificant |
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25 | ; |
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26 | |
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27 | $NaNOK=1; |
28 | |
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29 | sub new { |
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30 | my($class) = shift; |
31 | my($foo) = bnorm(shift); |
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32 | die "Not a number initialized to Math::BigInt" if !$NaNOK && $foo eq "NaN"; |
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33 | bless \$foo, $class; |
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34 | } |
35 | sub stringify { "${$_[0]}" } |
36 | sub numify { 0 + "${$_[0]}" } # Not needed, additional overhead |
37 | # comparing to direct compilation based on |
38 | # stringify |
39 | |
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40 | $zero = 0; |
41 | |
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42 | |
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43 | # normalize string form of number. Strip leading zeros. Strip any |
44 | # white space and add a sign, if missing. |
45 | # Strings that are not numbers result the value 'NaN'. |
46 | |
47 | sub bnorm { #(num_str) return num_str |
48 | local($_) = @_; |
49 | s/\s+//g; # strip white space |
50 | if (s/^([+-]?)0*(\d+)$/$1$2/) { # test if number |
51 | substr($_,$[,0) = '+' unless $1; # Add missing sign |
52 | s/^-0/+0/; |
53 | $_; |
54 | } else { |
55 | 'NaN'; |
56 | } |
57 | } |
58 | |
59 | # Convert a number from string format to internal base 100000 format. |
60 | # Assumes normalized value as input. |
61 | sub internal { #(num_str) return int_num_array |
62 | local($d) = @_; |
63 | ($is,$il) = (substr($d,$[,1),length($d)-2); |
64 | substr($d,$[,1) = ''; |
65 | ($is, reverse(unpack("a" . ($il%5+1) . ("a5" x ($il/5)), $d))); |
66 | } |
67 | |
68 | # Convert a number from internal base 100000 format to string format. |
69 | # This routine scribbles all over input array. |
70 | sub external { #(int_num_array) return num_str |
71 | $es = shift; |
72 | grep($_ > 9999 || ($_ = substr('0000'.$_,-5)), @_); # zero pad |
73 | &bnorm(join('', $es, reverse(@_))); # reverse concat and normalize |
74 | } |
75 | |
76 | # Negate input value. |
77 | sub bneg { #(num_str) return num_str |
78 | local($_) = &bnorm(@_); |
79 | vec($_,0,8) ^= ord('+') ^ ord('-') unless $_ eq '+0'; |
80 | s/^H/N/; |
81 | $_; |
82 | } |
83 | |
84 | # Returns the absolute value of the input. |
85 | sub babs { #(num_str) return num_str |
86 | &abs(&bnorm(@_)); |
87 | } |
88 | |
89 | sub abs { # post-normalized abs for internal use |
90 | local($_) = @_; |
91 | s/^-/+/; |
92 | $_; |
93 | } |
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94 | |
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95 | # Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort) |
96 | sub bcmp { #(num_str, num_str) return cond_code |
97 | local($x,$y) = (&bnorm($_[$[]),&bnorm($_[$[+1])); |
98 | if ($x eq 'NaN') { |
99 | undef; |
100 | } elsif ($y eq 'NaN') { |
101 | undef; |
102 | } else { |
103 | &cmp($x,$y); |
104 | } |
105 | } |
106 | |
107 | sub cmp { # post-normalized compare for internal use |
108 | local($cx, $cy) = @_; |
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109 | |
110 | return 0 if ($cx eq $cy); |
111 | |
112 | local($sx, $sy) = (substr($cx, 0, 1), substr($cy, 0, 1)); |
113 | local($ld); |
114 | |
115 | if ($sx eq '+') { |
116 | return 1 if ($sy eq '-' || $cy eq '+0'); |
117 | $ld = length($cx) - length($cy); |
118 | return $ld if ($ld); |
119 | return $cx cmp $cy; |
120 | } else { # $sx eq '-' |
121 | return -1 if ($sy eq '+'); |
122 | $ld = length($cy) - length($cx); |
123 | return $ld if ($ld); |
124 | return $cy cmp $cx; |
125 | } |
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126 | } |
127 | |
128 | sub badd { #(num_str, num_str) return num_str |
129 | local(*x, *y); ($x, $y) = (&bnorm($_[$[]),&bnorm($_[$[+1])); |
130 | if ($x eq 'NaN') { |
131 | 'NaN'; |
132 | } elsif ($y eq 'NaN') { |
133 | 'NaN'; |
134 | } else { |
135 | @x = &internal($x); # convert to internal form |
136 | @y = &internal($y); |
137 | local($sx, $sy) = (shift @x, shift @y); # get signs |
138 | if ($sx eq $sy) { |
139 | &external($sx, &add(*x, *y)); # if same sign add |
140 | } else { |
141 | ($x, $y) = (&abs($x),&abs($y)); # make abs |
142 | if (&cmp($y,$x) > 0) { |
143 | &external($sy, &sub(*y, *x)); |
144 | } else { |
145 | &external($sx, &sub(*x, *y)); |
146 | } |
147 | } |
148 | } |
149 | } |
150 | |
151 | sub bsub { #(num_str, num_str) return num_str |
152 | &badd($_[$[],&bneg($_[$[+1])); |
153 | } |
154 | |
155 | # GCD -- Euclids algorithm Knuth Vol 2 pg 296 |
156 | sub bgcd { #(num_str, num_str) return num_str |
157 | local($x,$y) = (&bnorm($_[$[]),&bnorm($_[$[+1])); |
158 | if ($x eq 'NaN' || $y eq 'NaN') { |
159 | 'NaN'; |
160 | } else { |
161 | ($x, $y) = ($y,&bmod($x,$y)) while $y ne '+0'; |
162 | $x; |
163 | } |
164 | } |
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165 | |
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166 | # routine to add two base 1e5 numbers |
167 | # stolen from Knuth Vol 2 Algorithm A pg 231 |
168 | # there are separate routines to add and sub as per Kunth pg 233 |
169 | sub add { #(int_num_array, int_num_array) return int_num_array |
170 | local(*x, *y) = @_; |
171 | $car = 0; |
172 | for $x (@x) { |
173 | last unless @y || $car; |
174 | $x -= 1e5 if $car = (($x += shift(@y) + $car) >= 1e5); |
175 | } |
176 | for $y (@y) { |
177 | last unless $car; |
178 | $y -= 1e5 if $car = (($y += $car) >= 1e5); |
179 | } |
180 | (@x, @y, $car); |
181 | } |
182 | |
183 | # subtract base 1e5 numbers -- stolen from Knuth Vol 2 pg 232, $x > $y |
184 | sub sub { #(int_num_array, int_num_array) return int_num_array |
185 | local(*sx, *sy) = @_; |
186 | $bar = 0; |
187 | for $sx (@sx) { |
188 | last unless @y || $bar; |
189 | $sx += 1e5 if $bar = (($sx -= shift(@sy) + $bar) < 0); |
190 | } |
191 | @sx; |
192 | } |
193 | |
194 | # multiply two numbers -- stolen from Knuth Vol 2 pg 233 |
195 | sub bmul { #(num_str, num_str) return num_str |
196 | local(*x, *y); ($x, $y) = (&bnorm($_[$[]), &bnorm($_[$[+1])); |
197 | if ($x eq 'NaN') { |
198 | 'NaN'; |
199 | } elsif ($y eq 'NaN') { |
200 | 'NaN'; |
201 | } else { |
202 | @x = &internal($x); |
203 | @y = &internal($y); |
204 | &external(&mul(*x,*y)); |
205 | } |
206 | } |
207 | |
208 | # multiply two numbers in internal representation |
209 | # destroys the arguments, supposes that two arguments are different |
210 | sub mul { #(*int_num_array, *int_num_array) return int_num_array |
211 | local(*x, *y) = (shift, shift); |
212 | local($signr) = (shift @x ne shift @y) ? '-' : '+'; |
213 | @prod = (); |
214 | for $x (@x) { |
215 | ($car, $cty) = (0, $[); |
216 | for $y (@y) { |
217 | $prod = $x * $y + $prod[$cty] + $car; |
218 | $prod[$cty++] = |
219 | $prod - ($car = int($prod * 1e-5)) * 1e5; |
220 | } |
221 | $prod[$cty] += $car if $car; |
222 | $x = shift @prod; |
223 | } |
224 | ($signr, @x, @prod); |
225 | } |
226 | |
227 | # modulus |
228 | sub bmod { #(num_str, num_str) return num_str |
229 | (&bdiv(@_))[$[+1]; |
230 | } |
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231 | |
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232 | sub bdiv { #(dividend: num_str, divisor: num_str) return num_str |
233 | local (*x, *y); ($x, $y) = (&bnorm($_[$[]), &bnorm($_[$[+1])); |
234 | return wantarray ? ('NaN','NaN') : 'NaN' |
235 | if ($x eq 'NaN' || $y eq 'NaN' || $y eq '+0'); |
236 | return wantarray ? ('+0',$x) : '+0' if (&cmp(&abs($x),&abs($y)) < 0); |
237 | @x = &internal($x); @y = &internal($y); |
238 | $srem = $y[$[]; |
239 | $sr = (shift @x ne shift @y) ? '-' : '+'; |
240 | $car = $bar = $prd = 0; |
241 | if (($dd = int(1e5/($y[$#y]+1))) != 1) { |
242 | for $x (@x) { |
243 | $x = $x * $dd + $car; |
244 | $x -= ($car = int($x * 1e-5)) * 1e5; |
245 | } |
246 | push(@x, $car); $car = 0; |
247 | for $y (@y) { |
248 | $y = $y * $dd + $car; |
249 | $y -= ($car = int($y * 1e-5)) * 1e5; |
250 | } |
251 | } |
252 | else { |
253 | push(@x, 0); |
254 | } |
255 | @q = (); ($v2,$v1) = @y[-2,-1]; |
256 | while ($#x > $#y) { |
257 | ($u2,$u1,$u0) = @x[-3..-1]; |
258 | $q = (($u0 == $v1) ? 99999 : int(($u0*1e5+$u1)/$v1)); |
259 | --$q while ($v2*$q > ($u0*1e5+$u1-$q*$v1)*1e5+$u2); |
260 | if ($q) { |
261 | ($car, $bar) = (0,0); |
262 | for ($y = $[, $x = $#x-$#y+$[-1; $y <= $#y; ++$y,++$x) { |
263 | $prd = $q * $y[$y] + $car; |
264 | $prd -= ($car = int($prd * 1e-5)) * 1e5; |
265 | $x[$x] += 1e5 if ($bar = (($x[$x] -= $prd + $bar) < 0)); |
266 | } |
267 | if ($x[$#x] < $car + $bar) { |
268 | $car = 0; --$q; |
269 | for ($y = $[, $x = $#x-$#y+$[-1; $y <= $#y; ++$y,++$x) { |
270 | $x[$x] -= 1e5 |
271 | if ($car = (($x[$x] += $y[$y] + $car) > 1e5)); |
272 | } |
273 | } |
274 | } |
275 | pop(@x); unshift(@q, $q); |
276 | } |
277 | if (wantarray) { |
278 | @d = (); |
279 | if ($dd != 1) { |
280 | $car = 0; |
281 | for $x (reverse @x) { |
282 | $prd = $car * 1e5 + $x; |
283 | $car = $prd - ($tmp = int($prd / $dd)) * $dd; |
284 | unshift(@d, $tmp); |
285 | } |
286 | } |
287 | else { |
288 | @d = @x; |
289 | } |
290 | (&external($sr, @q), &external($srem, @d, $zero)); |
291 | } else { |
292 | &external($sr, @q); |
293 | } |
294 | } |
295 | |
296 | # compute power of two numbers -- stolen from Knuth Vol 2 pg 233 |
297 | sub bpow { #(num_str, num_str) return num_str |
298 | local(*x, *y); ($x, $y) = (&bnorm($_[$[]), &bnorm($_[$[+1])); |
299 | if ($x eq 'NaN') { |
300 | 'NaN'; |
301 | } elsif ($y eq 'NaN') { |
302 | 'NaN'; |
303 | } elsif ($x eq '+1') { |
304 | '+1'; |
305 | } elsif ($x eq '-1') { |
306 | &bmod($x,2) ? '-1': '+1'; |
307 | } elsif ($y =~ /^-/) { |
308 | 'NaN'; |
309 | } elsif ($x eq '+0' && $y eq '+0') { |
310 | 'NaN'; |
311 | } else { |
312 | @x = &internal($x); |
313 | local(@pow2)=@x; |
314 | local(@pow)=&internal("+1"); |
315 | local($y1,$res,@tmp1,@tmp2)=(1); # need tmp to send to mul |
316 | while ($y ne '+0') { |
317 | ($y,$res)=&bdiv($y,2); |
318 | if ($res ne '+0') {@tmp=@pow2; @pow=&mul(*pow,*tmp);} |
319 | if ($y ne '+0') {@tmp=@pow2;@pow2=&mul(*pow2,*tmp);} |
320 | } |
321 | &external(@pow); |
322 | } |
323 | } |
324 | |
325 | 1; |
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326 | __END__ |
327 | |
328 | =head1 NAME |
329 | |
330 | Math::BigInt - Arbitrary size integer math package |
331 | |
332 | =head1 SYNOPSIS |
333 | |
334 | use Math::BigInt; |
335 | $i = Math::BigInt->new($string); |
336 | |
337 | $i->bneg return BINT negation |
338 | $i->babs return BINT absolute value |
339 | $i->bcmp(BINT) return CODE compare numbers (undef,<0,=0,>0) |
340 | $i->badd(BINT) return BINT addition |
341 | $i->bsub(BINT) return BINT subtraction |
342 | $i->bmul(BINT) return BINT multiplication |
343 | $i->bdiv(BINT) return (BINT,BINT) division (quo,rem) just quo if scalar |
344 | $i->bmod(BINT) return BINT modulus |
345 | $i->bgcd(BINT) return BINT greatest common divisor |
346 | $i->bnorm return BINT normalization |
347 | |
348 | =head1 DESCRIPTION |
349 | |
350 | All basic math operations are overloaded if you declare your big |
351 | integers as |
352 | |
353 | $i = new Math::BigInt '123 456 789 123 456 789'; |
354 | |
355 | |
356 | =over 2 |
357 | |
358 | =item Canonical notation |
359 | |
360 | Big integer value are strings of the form C</^[+-]\d+$/> with leading |
361 | zeros suppressed. |
362 | |
363 | =item Input |
364 | |
365 | Input values to these routines may be strings of the form |
366 | C</^\s*[+-]?[\d\s]+$/>. |
367 | |
368 | =item Output |
369 | |
370 | Output values always always in canonical form |
371 | |
372 | =back |
373 | |
374 | Actual math is done in an internal format consisting of an array |
375 | whose first element is the sign (/^[+-]$/) and whose remaining |
376 | elements are base 100000 digits with the least significant digit first. |
377 | The string 'NaN' is used to represent the result when input arguments |
378 | are not numbers, as well as the result of dividing by zero. |
379 | |
380 | =head1 EXAMPLES |
381 | |
382 | '+0' canonical zero value |
383 | ' -123 123 123' canonical value '-123123123' |
384 | '1 23 456 7890' canonical value '+1234567890' |
385 | |
386 | |
387 | =head1 BUGS |
388 | |
389 | The current version of this module is a preliminary version of the |
390 | real thing that is currently (as of perl5.002) under development. |
391 | |
392 | =head1 AUTHOR |
393 | |
394 | Mark Biggar, overloaded interface by Ilya Zakharevich. |
395 | |
396 | =cut |