Commit | Line | Data |
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0716bf9b JH |
1 | package Math::BigInt::Calc; |
2 | ||
3 | use 5.005; | |
4 | use strict; | |
574bacfe | 5 | # use warnings; # dont use warnings for older Perls |
0716bf9b JH |
6 | |
7 | require Exporter; | |
bd05a461 | 8 | use vars qw/@ISA $VERSION/; |
0716bf9b JH |
9 | @ISA = qw(Exporter); |
10 | ||
13a12e00 | 11 | $VERSION = '0.23'; |
0716bf9b JH |
12 | |
13 | # Package to store unsigned big integers in decimal and do math with them | |
14 | ||
15 | # Internally the numbers are stored in an array with at least 1 element, no | |
027dc388 JH |
16 | # leading zero parts (except the first) and in base 1eX where X is determined |
17 | # automatically at loading time to be the maximum possible value | |
0716bf9b JH |
18 | |
19 | # todo: | |
20 | # - fully remove funky $# stuff (maybe) | |
0716bf9b JH |
21 | |
22 | # USE_MUL: due to problems on certain os (os390, posix-bc) "* 1e-5" is used | |
ee15d750 JH |
23 | # instead of "/ 1e5" at some places, (marked with USE_MUL). Other platforms |
24 | # BS2000, some Crays need USE_DIV instead. | |
bd05a461 JH |
25 | # The BEGIN block is used to determine which of the two variants gives the |
26 | # correct result. | |
0716bf9b JH |
27 | |
28 | ############################################################################## | |
29 | # global constants, flags and accessory | |
30 | ||
31 | # constants for easier life | |
32 | my $nan = 'NaN'; | |
61f5c3f5 | 33 | my ($MBASE,$BASE,$RBASE,$BASE_LEN,$MAX_VAL,$BASE_LEN2,$BASE_LEN_SMALL); |
394e6ffb JH |
34 | my ($AND_BITS,$XOR_BITS,$OR_BITS); |
35 | my ($AND_MASK,$XOR_MASK,$OR_MASK); | |
61f5c3f5 | 36 | my ($LEN_CONVERT); |
ee15d750 JH |
37 | |
38 | sub _base_len | |
39 | { | |
dccbb853 JH |
40 | # set/get the BASE_LEN and assorted other, connected values |
41 | # used only be the testsuite, set is used only by the BEGIN block below | |
394e6ffb JH |
42 | shift; |
43 | ||
ee15d750 JH |
44 | my $b = shift; |
45 | if (defined $b) | |
46 | { | |
61f5c3f5 T |
47 | # find whether we can use mul or div or none in mul()/div() |
48 | # (in last case reduce BASE_LEN_SMALL) | |
49 | $BASE_LEN_SMALL = $b+1; | |
50 | my $caught = 0; | |
51 | while (--$BASE_LEN_SMALL > 5) | |
394e6ffb | 52 | { |
61f5c3f5 T |
53 | $MBASE = int("1e".$BASE_LEN_SMALL); |
54 | $RBASE = abs('1e-'.$BASE_LEN_SMALL); # see USE_MUL | |
394e6ffb | 55 | $caught = 0; |
61f5c3f5 T |
56 | $caught += 1 if (int($MBASE * $RBASE) != 1); # should be 1 |
57 | $caught += 2 if (int($MBASE / $MBASE) != 1); # should be 1 | |
394e6ffb JH |
58 | last if $caught != 3; |
59 | } | |
61f5c3f5 T |
60 | # BASE_LEN is used for anything else than mul()/div() |
61 | $BASE_LEN = $BASE_LEN_SMALL; | |
62 | $BASE_LEN = shift if (defined $_[0]); # one more arg? | |
ee15d750 | 63 | $BASE = int("1e".$BASE_LEN); |
61f5c3f5 T |
64 | |
65 | $BASE_LEN2 = int($BASE_LEN_SMALL / 2); # for mul shortcut | |
66 | $MBASE = int("1e".$BASE_LEN_SMALL); | |
67 | $RBASE = abs('1e-'.$BASE_LEN_SMALL); # see USE_MUL | |
68 | $MAX_VAL = $MBASE-1; | |
69 | $LEN_CONVERT = 0; | |
70 | $LEN_CONVERT = 1 if $BASE_LEN_SMALL != $BASE_LEN; | |
71 | ||
72 | #print "BASE_LEN: $BASE_LEN MAX_VAL: $MAX_VAL BASE: $BASE RBASE: $RBASE "; | |
73 | #print "BASE_LEN_SMALL: $BASE_LEN_SMALL MBASE: $MBASE\n"; | |
74 | ||
394e6ffb | 75 | if ($caught & 1 != 0) |
ee15d750 JH |
76 | { |
77 | # must USE_MUL | |
ee15d750 JH |
78 | *{_mul} = \&_mul_use_mul; |
79 | *{_div} = \&_div_use_mul; | |
80 | } | |
394e6ffb | 81 | else # $caught must be 2, since it can't be 1 nor 3 |
ee15d750 | 82 | { |
ee15d750 JH |
83 | # can USE_DIV instead |
84 | *{_mul} = \&_mul_use_div; | |
85 | *{_div} = \&_div_use_div; | |
86 | } | |
87 | } | |
61f5c3f5 T |
88 | return $BASE_LEN unless wantarray; |
89 | return ($BASE_LEN, $AND_BITS, $XOR_BITS, $OR_BITS, $BASE_LEN_SMALL, $MAX_VAL); | |
ee15d750 | 90 | } |
574bacfe JH |
91 | |
92 | BEGIN | |
93 | { | |
bd05a461 | 94 | # from Daniel Pfeiffer: determine largest group of digits that is precisely |
574bacfe | 95 | # multipliable with itself plus carry |
dccbb853 JH |
96 | # Test now changed to expect the proper pattern, not a result off by 1 or 2 |
97 | my ($e, $num) = 3; # lowest value we will use is 3+1-1 = 3 | |
bd05a461 JH |
98 | do |
99 | { | |
100 | $num = ('9' x ++$e) + 0; | |
394e6ffb | 101 | $num *= $num + 1.0; |
394e6ffb JH |
102 | } while ("$num" =~ /9{$e}0{$e}/); # must be a certain pattern |
103 | $e--; # last test failed, so retract one step | |
104 | # the limits below brush the problems with the test above under the rug: | |
105 | # the test should be able to find the proper $e automatically | |
106 | $e = 5 if $^O =~ /^uts/; # UTS get's some special treatment | |
107 | $e = 5 if $^O =~ /^unicos/; # unicos is also problematic (6 seems to work | |
108 | # there, but we play safe) | |
109 | $e = 8 if $e > 8; # cap, for VMS, OS/390 and other 64 bit systems | |
110 | ||
61f5c3f5 T |
111 | # determine how many digits fit into an integer and can be safely added |
112 | # together plus carry w/o causing an overflow | |
113 | ||
114 | # this below detects 15 on a 64 bit system, because after that it becomes | |
115 | # 1e16 and not 1000000 :/ I can make it detect 18, but then I get a lot of | |
116 | # test failures. Ugh! (Tomake detect 18: uncomment lines marked with *) | |
117 | use integer; | |
118 | my $bi = 5; # approx. 16 bit | |
119 | $num = int('9' x $bi); | |
120 | # $num = 99999; # * | |
121 | # while ( ($num+$num+1) eq '1' . '9' x $bi) # * | |
122 | while ( int($num+$num+1) eq '1' . '9' x $bi) | |
123 | { | |
124 | $bi++; $num = int('9' x $bi); | |
125 | # $bi++; $num *= 10; $num += 9; # * | |
126 | } | |
127 | $bi--; # back off one step | |
128 | # by setting them equal, we ignore the findings and use the default | |
129 | # one-size-fits-all approach from former versions | |
130 | $bi = $e; # XXX, this should work always | |
131 | ||
132 | __PACKAGE__->_base_len($e,$bi); # set and store | |
394e6ffb JH |
133 | |
134 | # find out how many bits _and, _or and _xor can take (old default = 16) | |
135 | # I don't think anybody has yet 128 bit scalars, so let's play safe. | |
394e6ffb JH |
136 | local $^W = 0; # don't warn about 'nonportable number' |
137 | $AND_BITS = 15; $XOR_BITS = 15; $OR_BITS = 15; | |
138 | ||
139 | # find max bits, we will not go higher than numberofbits that fit into $BASE | |
140 | # to make _and etc simpler (and faster for smaller, slower for large numbers) | |
141 | my $max = 16; | |
142 | while (2 ** $max < $BASE) { $max++; } | |
143 | my ($x,$y,$z); | |
144 | do { | |
145 | $AND_BITS++; | |
146 | $x = oct('0b' . '1' x $AND_BITS); $y = $x & $x; | |
147 | $z = (2 ** $AND_BITS) - 1; | |
148 | } while ($AND_BITS < $max && $x == $z && $y == $x); | |
149 | $AND_BITS --; # retreat one step | |
150 | do { | |
151 | $XOR_BITS++; | |
152 | $x = oct('0b' . '1' x $XOR_BITS); $y = $x ^ 0; | |
153 | $z = (2 ** $XOR_BITS) - 1; | |
154 | } while ($XOR_BITS < $max && $x == $z && $y == $x); | |
155 | $XOR_BITS --; # retreat one step | |
156 | do { | |
157 | $OR_BITS++; | |
158 | $x = oct('0b' . '1' x $OR_BITS); $y = $x | $x; | |
159 | $z = (2 ** $OR_BITS) - 1; | |
160 | } while ($OR_BITS < $max && $x == $z && $y == $x); | |
161 | $OR_BITS --; # retreat one step | |
162 | ||
574bacfe JH |
163 | } |
164 | ||
0716bf9b | 165 | ############################################################################## |
61f5c3f5 T |
166 | # convert between the "small" and the "large" representation |
167 | ||
168 | sub _to_large | |
169 | { | |
170 | # take an array in base $BASE_LEN_SMALL and convert it in-place to $BASE_LEN | |
171 | my ($c,$x) = @_; | |
172 | ||
173 | # print "_to_large $BASE_LEN_SMALL => $BASE_LEN\n"; | |
174 | ||
175 | return $x if $LEN_CONVERT == 0 || # nothing to converconvertor | |
176 | @$x == 1; # only one element => early out | |
177 | ||
178 | # 12345 67890 12345 67890 contents | |
179 | # to 3 2 1 0 index | |
180 | # 123456 7890123 4567890 contents | |
181 | ||
182 | # # faster variant | |
183 | # my @d; my $str = ''; | |
184 | # my $z = '0' x $BASE_LEN_SMALL; | |
185 | # foreach (@$x) | |
186 | # { | |
187 | # # ... . 04321 . 000321 | |
188 | # $str = substr($z.$_,-$BASE_LEN_SMALL,$BASE_LEN_SMALL) . $str; | |
189 | # if (length($str) > $BASE_LEN) | |
190 | # { | |
191 | # push @d, substr($str,-$BASE_LEN,$BASE_LEN); # extract one piece | |
192 | # substr($str,-$BASE_LEN,$BASE_LEN) = ''; # remove it | |
193 | # } | |
194 | # } | |
195 | # push @d, $str if $str !~ /^0*$/; # extract last piece | |
196 | # @$x = @d; | |
197 | # $x->[-1] = int($x->[-1]); # strip leading zero | |
198 | # $x; | |
199 | ||
200 | my $ret = ""; | |
201 | my $l = scalar @$x; # number of parts | |
202 | $l --; $ret .= int($x->[$l]); $l--; | |
203 | my $z = '0' x ($BASE_LEN_SMALL-1); | |
204 | while ($l >= 0) | |
205 | { | |
206 | $ret .= substr($z.$x->[$l],-$BASE_LEN_SMALL); | |
207 | $l--; | |
208 | } | |
209 | my $str = _new($c,\$ret); # make array | |
210 | @$x = @$str; # clobber contents of $x | |
211 | $x->[-1] = int($x->[-1]); # strip leading zero | |
212 | } | |
213 | ||
214 | sub _to_small | |
215 | { | |
216 | # take an array in base $BASE_LEN and convert it in-place to $BASE_LEN_SMALL | |
217 | my ($c,$x) = @_; | |
218 | ||
219 | return $x if $LEN_CONVERT == 0; # nothing to do | |
220 | return $x if @$x == 1 && length(int($x->[0])) <= $BASE_LEN_SMALL; | |
221 | ||
222 | my $d = _str($c,$x); | |
223 | my $il = length($$d)-1; | |
224 | ## this leaves '00000' instead of int 0 and will be corrected after any op | |
225 | # clobber contents of $x | |
226 | @$x = reverse(unpack("a" . ($il % $BASE_LEN_SMALL+1) | |
227 | . ("a$BASE_LEN_SMALL" x ($il / $BASE_LEN_SMALL)), $$d)); | |
228 | ||
229 | $x->[-1] = int($x->[-1]); # strip leading zero | |
230 | } | |
231 | ||
232 | ############################################################################### | |
0716bf9b JH |
233 | |
234 | sub _new | |
235 | { | |
394e6ffb | 236 | # (ref to string) return ref to num_array |
0716bf9b JH |
237 | # Convert a number from string format to internal base 100000 format. |
238 | # Assumes normalized value as input. | |
574bacfe | 239 | my $d = $_[1]; |
61f5c3f5 T |
240 | my $il = length($$d)-1; |
241 | # this leaves '00000' instead of int 0 and will be corrected after any op | |
242 | [ reverse(unpack("a" . ($il % $BASE_LEN+1) | |
574bacfe | 243 | . ("a$BASE_LEN" x ($il / $BASE_LEN)), $$d)) ]; |
0716bf9b | 244 | } |
394e6ffb JH |
245 | |
246 | BEGIN | |
247 | { | |
248 | $AND_MASK = __PACKAGE__->_new( \( 2 ** $AND_BITS )); | |
249 | $XOR_MASK = __PACKAGE__->_new( \( 2 ** $XOR_BITS )); | |
250 | $OR_MASK = __PACKAGE__->_new( \( 2 ** $OR_BITS )); | |
251 | } | |
0716bf9b JH |
252 | |
253 | sub _zero | |
254 | { | |
255 | # create a zero | |
61f5c3f5 | 256 | [ 0 ]; |
0716bf9b JH |
257 | } |
258 | ||
259 | sub _one | |
260 | { | |
261 | # create a one | |
61f5c3f5 | 262 | [ 1 ]; |
0716bf9b JH |
263 | } |
264 | ||
027dc388 JH |
265 | sub _two |
266 | { | |
267 | # create a two (for _pow) | |
61f5c3f5 | 268 | [ 2 ]; |
027dc388 JH |
269 | } |
270 | ||
0716bf9b JH |
271 | sub _copy |
272 | { | |
61f5c3f5 | 273 | [ @{$_[1]} ]; |
0716bf9b JH |
274 | } |
275 | ||
bd05a461 JH |
276 | # catch and throw away |
277 | sub import { } | |
278 | ||
0716bf9b JH |
279 | ############################################################################## |
280 | # convert back to string and number | |
281 | ||
282 | sub _str | |
283 | { | |
284 | # (ref to BINT) return num_str | |
285 | # Convert number from internal base 100000 format to string format. | |
286 | # internal format is always normalized (no leading zeros, "-0" => "+0") | |
574bacfe | 287 | my $ar = $_[1]; |
0716bf9b | 288 | my $ret = ""; |
61f5c3f5 T |
289 | |
290 | my $l = scalar @$ar; # number of parts | |
291 | return $nan if $l < 1; # should not happen | |
292 | ||
0716bf9b JH |
293 | # handle first one different to strip leading zeros from it (there are no |
294 | # leading zero parts in internal representation) | |
61f5c3f5 | 295 | $l --; $ret .= int($ar->[$l]); $l--; |
0716bf9b | 296 | # Interestingly, the pre-padd method uses more time |
574bacfe JH |
297 | # the old grep variant takes longer (14 to 10 sec) |
298 | my $z = '0' x ($BASE_LEN-1); | |
0716bf9b JH |
299 | while ($l >= 0) |
300 | { | |
574bacfe | 301 | $ret .= substr($z.$ar->[$l],-$BASE_LEN); # fastest way I could think of |
0716bf9b JH |
302 | $l--; |
303 | } | |
61f5c3f5 | 304 | \$ret; |
0716bf9b JH |
305 | } |
306 | ||
307 | sub _num | |
308 | { | |
309 | # Make a number (scalar int/float) from a BigInt object | |
574bacfe | 310 | my $x = $_[1]; |
0716bf9b JH |
311 | return $x->[0] if scalar @$x == 1; # below $BASE |
312 | my $fac = 1; | |
313 | my $num = 0; | |
314 | foreach (@$x) | |
315 | { | |
316 | $num += $fac*$_; $fac *= $BASE; | |
317 | } | |
61f5c3f5 | 318 | $num; |
0716bf9b JH |
319 | } |
320 | ||
321 | ############################################################################## | |
322 | # actual math code | |
323 | ||
324 | sub _add | |
325 | { | |
326 | # (ref to int_num_array, ref to int_num_array) | |
574bacfe | 327 | # routine to add two base 1eX numbers |
0716bf9b | 328 | # stolen from Knuth Vol 2 Algorithm A pg 231 |
b22b3e31 | 329 | # there are separate routines to add and sub as per Knuth pg 233 |
0716bf9b JH |
330 | # This routine clobbers up array x, but not y. |
331 | ||
574bacfe | 332 | my ($c,$x,$y) = @_; |
b3abae2a JH |
333 | |
334 | return $x if (@$y == 1) && $y->[0] == 0; # $x + 0 => $x | |
335 | if ((@$x == 1) && $x->[0] == 0) # 0 + $y => $y->copy | |
336 | { | |
337 | # twice as slow as $x = [ @$y ], but necc. to retain $x as ref :( | |
338 | @$x = @$y; return $x; | |
339 | } | |
0716bf9b JH |
340 | |
341 | # for each in Y, add Y to X and carry. If after that, something is left in | |
342 | # X, foreach in X add carry to X and then return X, carry | |
343 | # Trades one "$j++" for having to shift arrays, $j could be made integer | |
b22b3e31 | 344 | # but this would impose a limit to number-length of 2**32. |
0716bf9b JH |
345 | my $i; my $car = 0; my $j = 0; |
346 | for $i (@$y) | |
347 | { | |
e745a66c | 348 | $x->[$j] -= $BASE if $car = (($x->[$j] += $i + $car) >= $BASE) ? 1 : 0; |
0716bf9b JH |
349 | $j++; |
350 | } | |
351 | while ($car != 0) | |
352 | { | |
353 | $x->[$j] -= $BASE if $car = (($x->[$j] += $car) >= $BASE) ? 1 : 0; $j++; | |
354 | } | |
61f5c3f5 | 355 | $x; |
e745a66c JH |
356 | } |
357 | ||
358 | sub _inc | |
359 | { | |
360 | # (ref to int_num_array, ref to int_num_array) | |
361 | # routine to add 1 to a base 1eX numbers | |
362 | # This routine clobbers up array x, but not y. | |
363 | my ($c,$x) = @_; | |
364 | ||
365 | for my $i (@$x) | |
366 | { | |
367 | return $x if (($i += 1) < $BASE); # early out | |
61f5c3f5 | 368 | $i = 0; # overflow, next |
e745a66c | 369 | } |
61f5c3f5 T |
370 | push @$x,1 if ($x->[-1] == 0); # last overflowed, so extend |
371 | $x; | |
e745a66c JH |
372 | } |
373 | ||
374 | sub _dec | |
375 | { | |
376 | # (ref to int_num_array, ref to int_num_array) | |
377 | # routine to add 1 to a base 1eX numbers | |
378 | # This routine clobbers up array x, but not y. | |
379 | my ($c,$x) = @_; | |
380 | ||
61f5c3f5 | 381 | my $MAX = $BASE-1; # since MAX_VAL based on MBASE |
e745a66c JH |
382 | for my $i (@$x) |
383 | { | |
384 | last if (($i -= 1) >= 0); # early out | |
61f5c3f5 | 385 | $i = $MAX; # overflow, next |
e745a66c JH |
386 | } |
387 | pop @$x if $x->[-1] == 0 && @$x > 1; # last overflowed (but leave 0) | |
61f5c3f5 | 388 | $x; |
0716bf9b JH |
389 | } |
390 | ||
391 | sub _sub | |
392 | { | |
393 | # (ref to int_num_array, ref to int_num_array) | |
574bacfe | 394 | # subtract base 1eX numbers -- stolen from Knuth Vol 2 pg 232, $x > $y |
b22b3e31 | 395 | # subtract Y from X (X is always greater/equal!) by modifying x in place |
574bacfe | 396 | my ($c,$sx,$sy,$s) = @_; |
0716bf9b JH |
397 | |
398 | my $car = 0; my $i; my $j = 0; | |
399 | if (!$s) | |
400 | { | |
401 | #print "case 2\n"; | |
402 | for $i (@$sx) | |
403 | { | |
404 | last unless defined $sy->[$j] || $car; | |
0716bf9b | 405 | $i += $BASE if $car = (($i -= ($sy->[$j] || 0) + $car) < 0); $j++; |
0716bf9b JH |
406 | } |
407 | # might leave leading zeros, so fix that | |
394e6ffb | 408 | return __strip_zeros($sx); |
0716bf9b | 409 | } |
394e6ffb JH |
410 | #print "case 1 (swap)\n"; |
411 | for $i (@$sx) | |
0716bf9b | 412 | { |
394e6ffb JH |
413 | last unless defined $sy->[$j] || $car; |
414 | $sy->[$j] += $BASE | |
415 | if $car = (($sy->[$j] = $i-($sy->[$j]||0) - $car) < 0); | |
416 | $j++; | |
0716bf9b | 417 | } |
394e6ffb JH |
418 | # might leave leading zeros, so fix that |
419 | __strip_zeros($sy); | |
0716bf9b JH |
420 | } |
421 | ||
ee15d750 | 422 | sub _mul_use_mul |
0716bf9b JH |
423 | { |
424 | # (BINT, BINT) return nothing | |
425 | # multiply two numbers in internal representation | |
b22b3e31 | 426 | # modifies first arg, second need not be different from first |
574bacfe | 427 | my ($c,$xv,$yv) = @_; |
dccbb853 | 428 | |
b3abae2a | 429 | # shortcut for two very short numbers (improved by Nathan Zook) |
61f5c3f5 | 430 | # works also if xv and yv are the same reference |
b3abae2a JH |
431 | if ((@$xv == 1) && (@$yv == 1)) |
432 | { | |
433 | if (($xv->[0] *= $yv->[0]) >= $MBASE) | |
434 | { | |
435 | $xv->[0] = $xv->[0] - ($xv->[1] = int($xv->[0] * $RBASE)) * $MBASE; | |
436 | }; | |
437 | return $xv; | |
438 | } | |
439 | # shortcut for result == 0 | |
440 | if ( ((@$xv == 1) && ($xv->[0] == 0)) || | |
441 | ((@$yv == 1) && ($yv->[0] == 0)) ) | |
442 | { | |
443 | @$xv = (0); | |
444 | return $xv; | |
445 | } | |
446 | ||
0716bf9b | 447 | # since multiplying $x with $x fails, make copy in this case |
574bacfe | 448 | $yv = [@$xv] if "$xv" eq "$yv"; # same references? |
61f5c3f5 T |
449 | if ($LEN_CONVERT != 0) |
450 | { | |
451 | $c->_to_small($xv); $c->_to_small($yv); | |
452 | } | |
453 | ||
454 | my @prod = (); my ($prod,$car,$cty,$xi,$yi); | |
455 | ||
0716bf9b JH |
456 | for $xi (@$xv) |
457 | { | |
458 | $car = 0; $cty = 0; | |
574bacfe JH |
459 | |
460 | # slow variant | |
461 | # for $yi (@$yv) | |
462 | # { | |
463 | # $prod = $xi * $yi + ($prod[$cty] || 0) + $car; | |
464 | # $prod[$cty++] = | |
61f5c3f5 | 465 | # $prod - ($car = int($prod * RBASE)) * $MBASE; # see USE_MUL |
574bacfe JH |
466 | # } |
467 | # $prod[$cty] += $car if $car; # need really to check for 0? | |
468 | # $xi = shift @prod; | |
469 | ||
470 | # faster variant | |
471 | # looping through this if $xi == 0 is silly - so optimize it away! | |
472 | $xi = (shift @prod || 0), next if $xi == 0; | |
0716bf9b JH |
473 | for $yi (@$yv) |
474 | { | |
475 | $prod = $xi * $yi + ($prod[$cty] || 0) + $car; | |
574bacfe JH |
476 | ## this is actually a tad slower |
477 | ## $prod = $prod[$cty]; $prod += ($car + $xi * $yi); # no ||0 here | |
0716bf9b | 478 | $prod[$cty++] = |
61f5c3f5 | 479 | $prod - ($car = int($prod * $RBASE)) * $MBASE; # see USE_MUL |
0716bf9b JH |
480 | } |
481 | $prod[$cty] += $car if $car; # need really to check for 0? | |
027dc388 | 482 | $xi = shift @prod || 0; # || 0 makes v5.005_3 happy |
0716bf9b | 483 | } |
0716bf9b | 484 | push @$xv, @prod; |
61f5c3f5 T |
485 | if ($LEN_CONVERT != 0) |
486 | { | |
487 | $c->_to_large($yv); | |
488 | $c->_to_large($xv); | |
489 | } | |
490 | else | |
491 | { | |
492 | __strip_zeros($xv); | |
493 | } | |
494 | $xv; | |
0716bf9b JH |
495 | } |
496 | ||
ee15d750 JH |
497 | sub _mul_use_div |
498 | { | |
499 | # (BINT, BINT) return nothing | |
500 | # multiply two numbers in internal representation | |
501 | # modifies first arg, second need not be different from first | |
502 | my ($c,$xv,$yv) = @_; | |
503 | ||
b3abae2a | 504 | # shortcut for two very short numbers (improved by Nathan Zook) |
61f5c3f5 | 505 | # works also if xv and yv are the same reference |
b3abae2a JH |
506 | if ((@$xv == 1) && (@$yv == 1)) |
507 | { | |
508 | if (($xv->[0] *= $yv->[0]) >= $MBASE) | |
509 | { | |
510 | $xv->[0] = | |
511 | $xv->[0] - ($xv->[1] = int($xv->[0] / $MBASE)) * $MBASE; | |
512 | }; | |
513 | return $xv; | |
514 | } | |
515 | # shortcut for result == 0 | |
516 | if ( ((@$xv == 1) && ($xv->[0] == 0)) || | |
517 | ((@$yv == 1) && ($yv->[0] == 0)) ) | |
518 | { | |
519 | @$xv = (0); | |
520 | return $xv; | |
521 | } | |
522 | ||
61f5c3f5 | 523 | |
ee15d750 JH |
524 | # since multiplying $x with $x fails, make copy in this case |
525 | $yv = [@$xv] if "$xv" eq "$yv"; # same references? | |
61f5c3f5 T |
526 | if ($LEN_CONVERT != 0) |
527 | { | |
528 | $c->_to_small($xv); $c->_to_small($yv); | |
529 | } | |
530 | ||
531 | my @prod = (); my ($prod,$car,$cty,$xi,$yi); | |
ee15d750 JH |
532 | for $xi (@$xv) |
533 | { | |
534 | $car = 0; $cty = 0; | |
535 | # looping through this if $xi == 0 is silly - so optimize it away! | |
536 | $xi = (shift @prod || 0), next if $xi == 0; | |
537 | for $yi (@$yv) | |
538 | { | |
539 | $prod = $xi * $yi + ($prod[$cty] || 0) + $car; | |
540 | $prod[$cty++] = | |
61f5c3f5 | 541 | $prod - ($car = int($prod / $MBASE)) * $MBASE; |
ee15d750 JH |
542 | } |
543 | $prod[$cty] += $car if $car; # need really to check for 0? | |
027dc388 | 544 | $xi = shift @prod || 0; # || 0 makes v5.005_3 happy |
ee15d750 JH |
545 | } |
546 | push @$xv, @prod; | |
61f5c3f5 T |
547 | if ($LEN_CONVERT != 0) |
548 | { | |
549 | $c->_to_large($yv); | |
550 | $c->_to_large($xv); | |
551 | } | |
552 | else | |
553 | { | |
554 | __strip_zeros($xv); | |
555 | } | |
556 | $xv; | |
ee15d750 JH |
557 | } |
558 | ||
559 | sub _div_use_mul | |
0716bf9b | 560 | { |
b22b3e31 | 561 | # ref to array, ref to array, modify first array and return remainder if |
0716bf9b | 562 | # in list context |
574bacfe | 563 | my ($c,$x,$yorg) = @_; |
0716bf9b | 564 | |
61f5c3f5 T |
565 | if (@$x == 1 && @$yorg == 1) |
566 | { | |
13a12e00 | 567 | # shortcut, $yorg and $x are two small numbers |
61f5c3f5 T |
568 | if (wantarray) |
569 | { | |
570 | my $r = [ $x->[0] % $yorg->[0] ]; | |
571 | $x->[0] = int($x->[0] / $yorg->[0]); | |
572 | return ($x,$r); | |
573 | } | |
574 | else | |
575 | { | |
576 | $x->[0] = int($x->[0] / $yorg->[0]); | |
577 | return $x; | |
578 | } | |
579 | } | |
13a12e00 JH |
580 | #if (@$yorg == 1) |
581 | # { | |
582 | # # shortcut, $y is < $BASE | |
583 | # | |
584 | # } | |
585 | ||
0716bf9b | 586 | |
0716bf9b | 587 | my $y = [ @$yorg ]; |
61f5c3f5 T |
588 | if ($LEN_CONVERT != 0) |
589 | { | |
590 | $c->_to_small($x); $c->_to_small($y); | |
591 | } | |
592 | ||
593 | my ($car,$bar,$prd,$dd,$xi,$yi,@q,$v2,$v1,@d,$tmp,$q,$u2,$u1,$u0); | |
594 | ||
595 | $car = $bar = $prd = 0; | |
596 | if (($dd = int($MBASE/($y->[-1]+1))) != 1) | |
0716bf9b JH |
597 | { |
598 | for $xi (@$x) | |
599 | { | |
600 | $xi = $xi * $dd + $car; | |
61f5c3f5 | 601 | $xi -= ($car = int($xi * $RBASE)) * $MBASE; # see USE_MUL |
0716bf9b JH |
602 | } |
603 | push(@$x, $car); $car = 0; | |
604 | for $yi (@$y) | |
605 | { | |
606 | $yi = $yi * $dd + $car; | |
61f5c3f5 | 607 | $yi -= ($car = int($yi * $RBASE)) * $MBASE; # see USE_MUL |
0716bf9b JH |
608 | } |
609 | } | |
610 | else | |
611 | { | |
612 | push(@$x, 0); | |
613 | } | |
614 | @q = (); ($v2,$v1) = @$y[-2,-1]; | |
615 | $v2 = 0 unless $v2; | |
616 | while ($#$x > $#$y) | |
617 | { | |
618 | ($u2,$u1,$u0) = @$x[-3..-1]; | |
619 | $u2 = 0 unless $u2; | |
620 | #warn "oups v1 is 0, u0: $u0 $y->[-2] $y->[-1] l ",scalar @$y,"\n" | |
621 | # if $v1 == 0; | |
61f5c3f5 T |
622 | $q = (($u0 == $v1) ? $MAX_VAL : int(($u0*$MBASE+$u1)/$v1)); |
623 | --$q while ($v2*$q > ($u0*$MBASE+$u1-$q*$v1)*$MBASE+$u2); | |
0716bf9b JH |
624 | if ($q) |
625 | { | |
626 | ($car, $bar) = (0,0); | |
627 | for ($yi = 0, $xi = $#$x-$#$y-1; $yi <= $#$y; ++$yi,++$xi) | |
628 | { | |
629 | $prd = $q * $y->[$yi] + $car; | |
61f5c3f5 T |
630 | $prd -= ($car = int($prd * $RBASE)) * $MBASE; # see USE_MUL |
631 | $x->[$xi] += $MBASE if ($bar = (($x->[$xi] -= $prd + $bar) < 0)); | |
0716bf9b JH |
632 | } |
633 | if ($x->[-1] < $car + $bar) | |
634 | { | |
635 | $car = 0; --$q; | |
636 | for ($yi = 0, $xi = $#$x-$#$y-1; $yi <= $#$y; ++$yi,++$xi) | |
637 | { | |
61f5c3f5 T |
638 | $x->[$xi] -= $MBASE |
639 | if ($car = (($x->[$xi] += $y->[$yi] + $car) > $MBASE)); | |
0716bf9b JH |
640 | } |
641 | } | |
642 | } | |
643 | pop(@$x); unshift(@q, $q); | |
644 | } | |
645 | if (wantarray) | |
646 | { | |
647 | @d = (); | |
648 | if ($dd != 1) | |
649 | { | |
650 | $car = 0; | |
651 | for $xi (reverse @$x) | |
652 | { | |
61f5c3f5 | 653 | $prd = $car * $MBASE + $xi; |
0716bf9b JH |
654 | $car = $prd - ($tmp = int($prd / $dd)) * $dd; # see USE_MUL |
655 | unshift(@d, $tmp); | |
656 | } | |
657 | } | |
658 | else | |
659 | { | |
660 | @d = @$x; | |
661 | } | |
662 | @$x = @q; | |
61f5c3f5 T |
663 | my $d = \@d; |
664 | if ($LEN_CONVERT != 0) | |
665 | { | |
666 | $c->_to_large($x); $c->_to_large($d); | |
667 | } | |
668 | else | |
669 | { | |
670 | __strip_zeros($x); | |
671 | __strip_zeros($d); | |
672 | } | |
673 | return ($x,$d); | |
0716bf9b JH |
674 | } |
675 | @$x = @q; | |
61f5c3f5 T |
676 | if ($LEN_CONVERT != 0) |
677 | { | |
678 | $c->_to_large($x); | |
679 | } | |
680 | else | |
681 | { | |
682 | __strip_zeros($x); | |
683 | } | |
684 | $x; | |
0716bf9b JH |
685 | } |
686 | ||
ee15d750 JH |
687 | sub _div_use_div |
688 | { | |
689 | # ref to array, ref to array, modify first array and return remainder if | |
690 | # in list context | |
ee15d750 | 691 | my ($c,$x,$yorg) = @_; |
ee15d750 | 692 | |
61f5c3f5 T |
693 | if (@$x == 1 && @$yorg == 1) |
694 | { | |
13a12e00 | 695 | # shortcut, $yorg and $x are two small numbers |
61f5c3f5 T |
696 | if (wantarray) |
697 | { | |
698 | my $r = [ $x->[0] % $yorg->[0] ]; | |
699 | $x->[0] = int($x->[0] / $yorg->[0]); | |
700 | return ($x,$r); | |
701 | } | |
702 | else | |
703 | { | |
704 | $x->[0] = int($x->[0] / $yorg->[0]); | |
705 | return $x; | |
706 | } | |
707 | } | |
13a12e00 JH |
708 | # if (@$yorg == 1) |
709 | # { | |
710 | # # shortcut, $y is < $BASE | |
711 | # | |
712 | # } | |
ee15d750 | 713 | |
ee15d750 | 714 | my $y = [ @$yorg ]; |
61f5c3f5 T |
715 | if ($LEN_CONVERT != 0) |
716 | { | |
717 | $c->_to_small($x); $c->_to_small($y); | |
718 | } | |
719 | ||
720 | my ($car,$bar,$prd,$dd,$xi,$yi,@q,$v2,$v1,@d,$tmp,$q,$u2,$u1,$u0); | |
721 | ||
722 | $car = $bar = $prd = 0; | |
723 | if (($dd = int($MBASE/($y->[-1]+1))) != 1) | |
ee15d750 JH |
724 | { |
725 | for $xi (@$x) | |
726 | { | |
727 | $xi = $xi * $dd + $car; | |
61f5c3f5 | 728 | $xi -= ($car = int($xi / $MBASE)) * $MBASE; |
ee15d750 JH |
729 | } |
730 | push(@$x, $car); $car = 0; | |
731 | for $yi (@$y) | |
732 | { | |
733 | $yi = $yi * $dd + $car; | |
61f5c3f5 | 734 | $yi -= ($car = int($yi / $MBASE)) * $MBASE; |
ee15d750 JH |
735 | } |
736 | } | |
737 | else | |
738 | { | |
739 | push(@$x, 0); | |
740 | } | |
741 | @q = (); ($v2,$v1) = @$y[-2,-1]; | |
742 | $v2 = 0 unless $v2; | |
743 | while ($#$x > $#$y) | |
744 | { | |
745 | ($u2,$u1,$u0) = @$x[-3..-1]; | |
746 | $u2 = 0 unless $u2; | |
747 | #warn "oups v1 is 0, u0: $u0 $y->[-2] $y->[-1] l ",scalar @$y,"\n" | |
748 | # if $v1 == 0; | |
61f5c3f5 T |
749 | $q = (($u0 == $v1) ? $MAX_VAL : int(($u0*$MBASE+$u1)/$v1)); |
750 | --$q while ($v2*$q > ($u0*$MBASE+$u1-$q*$v1)*$MBASE+$u2); | |
ee15d750 JH |
751 | if ($q) |
752 | { | |
753 | ($car, $bar) = (0,0); | |
754 | for ($yi = 0, $xi = $#$x-$#$y-1; $yi <= $#$y; ++$yi,++$xi) | |
755 | { | |
756 | $prd = $q * $y->[$yi] + $car; | |
61f5c3f5 T |
757 | $prd -= ($car = int($prd / $MBASE)) * $MBASE; |
758 | $x->[$xi] += $MBASE if ($bar = (($x->[$xi] -= $prd + $bar) < 0)); | |
ee15d750 JH |
759 | } |
760 | if ($x->[-1] < $car + $bar) | |
761 | { | |
762 | $car = 0; --$q; | |
763 | for ($yi = 0, $xi = $#$x-$#$y-1; $yi <= $#$y; ++$yi,++$xi) | |
764 | { | |
61f5c3f5 T |
765 | $x->[$xi] -= $MBASE |
766 | if ($car = (($x->[$xi] += $y->[$yi] + $car) > $MBASE)); | |
ee15d750 JH |
767 | } |
768 | } | |
769 | } | |
61f5c3f5 | 770 | pop(@$x); unshift(@q, $q); |
ee15d750 JH |
771 | } |
772 | if (wantarray) | |
773 | { | |
774 | @d = (); | |
775 | if ($dd != 1) | |
776 | { | |
777 | $car = 0; | |
778 | for $xi (reverse @$x) | |
779 | { | |
61f5c3f5 | 780 | $prd = $car * $MBASE + $xi; |
ee15d750 JH |
781 | $car = $prd - ($tmp = int($prd / $dd)) * $dd; |
782 | unshift(@d, $tmp); | |
783 | } | |
784 | } | |
785 | else | |
786 | { | |
787 | @d = @$x; | |
788 | } | |
789 | @$x = @q; | |
61f5c3f5 T |
790 | my $d = \@d; |
791 | if ($LEN_CONVERT != 0) | |
792 | { | |
793 | $c->_to_large($x); $c->_to_large($d); | |
794 | } | |
795 | else | |
796 | { | |
797 | __strip_zeros($x); | |
798 | __strip_zeros($d); | |
799 | } | |
800 | return ($x,$d); | |
ee15d750 JH |
801 | } |
802 | @$x = @q; | |
61f5c3f5 T |
803 | if ($LEN_CONVERT != 0) |
804 | { | |
805 | $c->_to_large($x); | |
806 | } | |
807 | else | |
808 | { | |
809 | __strip_zeros($x); | |
810 | } | |
811 | $x; | |
ee15d750 JH |
812 | } |
813 | ||
394e6ffb JH |
814 | ############################################################################## |
815 | # testing | |
816 | ||
817 | sub _acmp | |
818 | { | |
819 | # internal absolute post-normalized compare (ignore signs) | |
820 | # ref to array, ref to array, return <0, 0, >0 | |
821 | # arrays must have at least one entry; this is not checked for | |
822 | ||
823 | my ($c,$cx,$cy) = @_; | |
824 | ||
61f5c3f5 | 825 | # fast comp based on array elements |
394e6ffb JH |
826 | my $lxy = scalar @$cx - scalar @$cy; |
827 | return -1 if $lxy < 0; # already differs, ret | |
828 | return 1 if $lxy > 0; # ditto | |
829 | ||
830 | # now calculate length based on digits, not parts | |
831 | $lxy = _len($c,$cx) - _len($c,$cy); # difference | |
832 | return -1 if $lxy < 0; | |
833 | return 1 if $lxy > 0; | |
834 | ||
835 | # hm, same lengths, but same contents? | |
836 | my $i = 0; my $a; | |
837 | # first way takes 5.49 sec instead of 4.87, but has the early out advantage | |
838 | # so grep is slightly faster, but more inflexible. hm. $_ instead of $k | |
839 | # yields 5.6 instead of 5.5 sec huh? | |
840 | # manual way (abort if unequal, good for early ne) | |
841 | my $j = scalar @$cx - 1; | |
842 | while ($j >= 0) | |
843 | { | |
844 | last if ($a = $cx->[$j] - $cy->[$j]); $j--; | |
845 | } | |
846 | return 1 if $a > 0; | |
847 | return -1 if $a < 0; | |
61f5c3f5 T |
848 | 0; # equal |
849 | ||
394e6ffb JH |
850 | # while it early aborts, it is even slower than the manual variant |
851 | #grep { return $a if ($a = $_ - $cy->[$i++]); } @$cx; | |
852 | # grep way, go trough all (bad for early ne) | |
853 | #grep { $a = $_ - $cy->[$i++]; } @$cx; | |
854 | #return $a; | |
855 | } | |
856 | ||
857 | sub _len | |
858 | { | |
859 | # compute number of digits in bigint, minus the sign | |
860 | ||
861 | # int() because add/sub sometimes leaves strings (like '00005') instead of | |
862 | # '5' in this place, thus causing length() to report wrong length | |
863 | my $cx = $_[1]; | |
864 | ||
865 | return (@$cx-1)*$BASE_LEN+length(int($cx->[-1])); | |
866 | } | |
867 | ||
868 | sub _digit | |
869 | { | |
870 | # return the nth digit, negative values count backward | |
871 | # zero is rightmost, so _digit(123,0) will give 3 | |
872 | my ($c,$x,$n) = @_; | |
873 | ||
874 | my $len = _len('',$x); | |
875 | ||
876 | $n = $len+$n if $n < 0; # -1 last, -2 second-to-last | |
877 | $n = abs($n); # if negative was too big | |
878 | $len--; $n = $len if $n > $len; # n to big? | |
879 | ||
880 | my $elem = int($n / $BASE_LEN); # which array element | |
881 | my $digit = $n % $BASE_LEN; # which digit in this element | |
882 | $elem = '0000'.@$x[$elem]; # get element padded with 0's | |
883 | return substr($elem,-$digit-1,1); | |
884 | } | |
885 | ||
886 | sub _zeros | |
887 | { | |
888 | # return amount of trailing zeros in decimal | |
889 | # check each array elem in _m for having 0 at end as long as elem == 0 | |
890 | # Upon finding a elem != 0, stop | |
891 | my $x = $_[1]; | |
892 | my $zeros = 0; my $elem; | |
893 | foreach my $e (@$x) | |
894 | { | |
895 | if ($e != 0) | |
896 | { | |
897 | $elem = "$e"; # preserve x | |
898 | $elem =~ s/.*?(0*$)/$1/; # strip anything not zero | |
899 | $zeros *= $BASE_LEN; # elems * 5 | |
61f5c3f5 | 900 | $zeros += length($elem); # count trailing zeros |
394e6ffb JH |
901 | last; # early out |
902 | } | |
903 | $zeros ++; # real else branch: 50% slower! | |
904 | } | |
61f5c3f5 | 905 | $zeros; |
394e6ffb JH |
906 | } |
907 | ||
908 | ############################################################################## | |
909 | # _is_* routines | |
910 | ||
911 | sub _is_zero | |
912 | { | |
913 | # return true if arg (BINT or num_str) is zero (array '+', '0') | |
914 | my $x = $_[1]; | |
61f5c3f5 T |
915 | |
916 | (((scalar @$x == 1) && ($x->[0] == 0))) <=> 0; | |
394e6ffb JH |
917 | } |
918 | ||
919 | sub _is_even | |
920 | { | |
921 | # return true if arg (BINT or num_str) is even | |
922 | my $x = $_[1]; | |
61f5c3f5 | 923 | (!($x->[0] & 1)) <=> 0; |
394e6ffb JH |
924 | } |
925 | ||
926 | sub _is_odd | |
927 | { | |
928 | # return true if arg (BINT or num_str) is even | |
929 | my $x = $_[1]; | |
61f5c3f5 T |
930 | |
931 | (($x->[0] & 1)) <=> 0; | |
394e6ffb JH |
932 | } |
933 | ||
934 | sub _is_one | |
935 | { | |
936 | # return true if arg (BINT or num_str) is one (array '+', '1') | |
937 | my $x = $_[1]; | |
61f5c3f5 T |
938 | |
939 | (scalar @$x == 1) && ($x->[0] == 1) <=> 0; | |
394e6ffb JH |
940 | } |
941 | ||
942 | sub __strip_zeros | |
943 | { | |
944 | # internal normalization function that strips leading zeros from the array | |
945 | # args: ref to array | |
946 | my $s = shift; | |
947 | ||
948 | my $cnt = scalar @$s; # get count of parts | |
949 | my $i = $cnt-1; | |
950 | push @$s,0 if $i < 0; # div might return empty results, so fix it | |
951 | ||
61f5c3f5 T |
952 | return $s if @$s == 1; # early out |
953 | ||
394e6ffb JH |
954 | #print "strip: cnt $cnt i $i\n"; |
955 | # '0', '3', '4', '0', '0', | |
956 | # 0 1 2 3 4 | |
957 | # cnt = 5, i = 4 | |
958 | # i = 4 | |
959 | # i = 3 | |
960 | # => fcnt = cnt - i (5-2 => 3, cnt => 5-1 = 4, throw away from 4th pos) | |
961 | # >= 1: skip first part (this can be zero) | |
962 | while ($i > 0) { last if $s->[$i] != 0; $i--; } | |
963 | $i++; splice @$s,$i if ($i < $cnt); # $i cant be 0 | |
964 | $s; | |
965 | } | |
966 | ||
967 | ############################################################################### | |
968 | # check routine to test internal state of corruptions | |
969 | ||
970 | sub _check | |
971 | { | |
972 | # used by the test suite | |
973 | my $x = $_[1]; | |
974 | ||
975 | return "$x is not a reference" if !ref($x); | |
976 | ||
977 | # are all parts are valid? | |
978 | my $i = 0; my $j = scalar @$x; my ($e,$try); | |
979 | while ($i < $j) | |
980 | { | |
981 | $e = $x->[$i]; $e = 'undef' unless defined $e; | |
982 | $try = '=~ /^[\+]?[0-9]+\$/; '."($x, $e)"; | |
983 | last if $e !~ /^[+]?[0-9]+$/; | |
984 | $try = '=~ /^[\+]?[0-9]+\$/; '."($x, $e) (stringify)"; | |
985 | last if "$e" !~ /^[+]?[0-9]+$/; | |
986 | $try = '=~ /^[\+]?[0-9]+\$/; '."($x, $e) (cat-stringify)"; | |
987 | last if '' . "$e" !~ /^[+]?[0-9]+$/; | |
988 | $try = ' < 0 || >= $BASE; '."($x, $e)"; | |
989 | last if $e <0 || $e >= $BASE; | |
990 | # this test is disabled, since new/bnorm and certain ops (like early out | |
991 | # in add/sub) are allowed/expected to leave '00000' in some elements | |
992 | #$try = '=~ /^00+/; '."($x, $e)"; | |
993 | #last if $e =~ /^00+/; | |
994 | $i++; | |
995 | } | |
996 | return "Illegal part '$e' at pos $i (tested: $try)" if $i < $j; | |
997 | return 0; | |
998 | } | |
999 | ||
1000 | ||
1001 | ############################################################################### | |
1002 | ############################################################################### | |
1003 | # some optional routines to make BigInt faster | |
1004 | ||
dccbb853 JH |
1005 | sub _mod |
1006 | { | |
1007 | # if possible, use mod shortcut | |
1008 | my ($c,$x,$yo) = @_; | |
1009 | ||
1010 | # slow way since $y to big | |
1011 | if (scalar @$yo > 1) | |
1012 | { | |
1013 | my ($xo,$rem) = _div($c,$x,$yo); | |
1014 | return $rem; | |
1015 | } | |
1016 | my $y = $yo->[0]; | |
027dc388 | 1017 | # both are single element arrays |
dccbb853 JH |
1018 | if (scalar @$x == 1) |
1019 | { | |
1020 | $x->[0] %= $y; | |
1021 | return $x; | |
1022 | } | |
1023 | ||
61f5c3f5 | 1024 | # @y is single element, but @x has more than one |
dccbb853 JH |
1025 | my $b = $BASE % $y; |
1026 | if ($b == 0) | |
1027 | { | |
1028 | # when BASE % Y == 0 then (B * BASE) % Y == 0 | |
1029 | # (B * BASE) % $y + A % Y => A % Y | |
1030 | # so need to consider only last element: O(1) | |
1031 | $x->[0] %= $y; | |
1032 | } | |
027dc388 JH |
1033 | elsif ($b == 1) |
1034 | { | |
1035 | # else need to go trough all elements: O(N), but loop is a bit simplified | |
1036 | my $r = 0; | |
1037 | foreach (@$x) | |
1038 | { | |
1039 | $r += $_ % $y; | |
1040 | $r %= $y; | |
1041 | } | |
1042 | $r = 0 if $r == $y; | |
1043 | $x->[0] = $r; | |
1044 | } | |
dccbb853 JH |
1045 | else |
1046 | { | |
027dc388 JH |
1047 | # else need to go trough all elements: O(N) |
1048 | my $r = 0; my $bm = 1; | |
1049 | foreach (@$x) | |
1050 | { | |
1051 | $r += ($_ % $y) * $bm; | |
1052 | $bm *= $b; | |
1053 | $bm %= $y; | |
1054 | $r %= $y; | |
1055 | } | |
1056 | $r = 0 if $r == $y; | |
1057 | $x->[0] = $r; | |
dccbb853 JH |
1058 | } |
1059 | splice (@$x,1); | |
61f5c3f5 | 1060 | $x; |
dccbb853 JH |
1061 | } |
1062 | ||
0716bf9b | 1063 | ############################################################################## |
574bacfe JH |
1064 | # shifts |
1065 | ||
1066 | sub _rsft | |
1067 | { | |
1068 | my ($c,$x,$y,$n) = @_; | |
1069 | ||
1070 | if ($n != 10) | |
1071 | { | |
61f5c3f5 T |
1072 | $n = _new($c,\$n); return _div($c,$x, _pow($c,$n,$y)); |
1073 | } | |
1074 | ||
1075 | # shortcut (faster) for shifting by 10) | |
1076 | # multiples of $BASE_LEN | |
1077 | my $dst = 0; # destination | |
1078 | my $src = _num($c,$y); # as normal int | |
1079 | my $rem = $src % $BASE_LEN; # remainder to shift | |
1080 | $src = int($src / $BASE_LEN); # source | |
1081 | if ($rem == 0) | |
1082 | { | |
1083 | splice (@$x,0,$src); # even faster, 38.4 => 39.3 | |
574bacfe JH |
1084 | } |
1085 | else | |
1086 | { | |
61f5c3f5 T |
1087 | my $len = scalar @$x - $src; # elems to go |
1088 | my $vd; my $z = '0'x $BASE_LEN; | |
1089 | $x->[scalar @$x] = 0; # avoid || 0 test inside loop | |
1090 | while ($dst < $len) | |
574bacfe | 1091 | { |
61f5c3f5 T |
1092 | $vd = $z.$x->[$src]; |
1093 | $vd = substr($vd,-$BASE_LEN,$BASE_LEN-$rem); | |
1094 | $src++; | |
1095 | $vd = substr($z.$x->[$src],-$rem,$rem) . $vd; | |
1096 | $vd = substr($vd,-$BASE_LEN,$BASE_LEN) if length($vd) > $BASE_LEN; | |
1097 | $x->[$dst] = int($vd); | |
1098 | $dst++; | |
574bacfe | 1099 | } |
61f5c3f5 T |
1100 | splice (@$x,$dst) if $dst > 0; # kill left-over array elems |
1101 | pop @$x if $x->[-1] == 0; # kill last element if 0 | |
1102 | } # else rem == 0 | |
574bacfe JH |
1103 | $x; |
1104 | } | |
1105 | ||
1106 | sub _lsft | |
1107 | { | |
1108 | my ($c,$x,$y,$n) = @_; | |
1109 | ||
1110 | if ($n != 10) | |
1111 | { | |
61f5c3f5 | 1112 | $n = _new($c,\$n); return _mul($c,$x, _pow($c,$n,$y)); |
574bacfe | 1113 | } |
61f5c3f5 T |
1114 | |
1115 | # shortcut (faster) for shifting by 10) since we are in base 10eX | |
1116 | # multiples of $BASE_LEN: | |
1117 | my $src = scalar @$x; # source | |
1118 | my $len = _num($c,$y); # shift-len as normal int | |
1119 | my $rem = $len % $BASE_LEN; # remainder to shift | |
1120 | my $dst = $src + int($len/$BASE_LEN); # destination | |
1121 | my $vd; # further speedup | |
1122 | $x->[$src] = 0; # avoid first ||0 for speed | |
1123 | my $z = '0' x $BASE_LEN; | |
1124 | while ($src >= 0) | |
574bacfe | 1125 | { |
61f5c3f5 T |
1126 | $vd = $x->[$src]; $vd = $z.$vd; |
1127 | $vd = substr($vd,-$BASE_LEN+$rem,$BASE_LEN-$rem); | |
1128 | $vd .= $src > 0 ? substr($z.$x->[$src-1],-$BASE_LEN,$rem) : '0' x $rem; | |
1129 | $vd = substr($vd,-$BASE_LEN,$BASE_LEN) if length($vd) > $BASE_LEN; | |
1130 | $x->[$dst] = int($vd); | |
1131 | $dst--; $src--; | |
574bacfe | 1132 | } |
61f5c3f5 T |
1133 | # set lowest parts to 0 |
1134 | while ($dst >= 0) { $x->[$dst--] = 0; } | |
1135 | # fix spurios last zero element | |
1136 | splice @$x,-1 if $x->[-1] == 0; | |
574bacfe JH |
1137 | $x; |
1138 | } | |
1139 | ||
027dc388 JH |
1140 | sub _pow |
1141 | { | |
1142 | # power of $x to $y | |
1143 | # ref to array, ref to array, return ref to array | |
1144 | my ($c,$cx,$cy) = @_; | |
1145 | ||
1146 | my $pow2 = _one(); | |
1147 | my $two = _two(); | |
1148 | my $y1 = _copy($c,$cy); | |
1149 | while (!_is_one($c,$y1)) | |
1150 | { | |
1151 | _mul($c,$pow2,$cx) if _is_odd($c,$y1); | |
1152 | _div($c,$y1,$two); | |
1153 | _mul($c,$cx,$cx); | |
1154 | } | |
1155 | _mul($c,$cx,$pow2) unless _is_one($c,$pow2); | |
61f5c3f5 | 1156 | $cx; |
027dc388 JH |
1157 | } |
1158 | ||
b3abae2a JH |
1159 | sub _fac |
1160 | { | |
1161 | # factorial of $x | |
1162 | # ref to array, return ref to array | |
1163 | my ($c,$cx) = @_; | |
1164 | ||
1165 | if ((@$cx == 1) && ($cx->[0] <= 2)) | |
1166 | { | |
1167 | $cx->[0] = 1 * ($cx->[0]||1); # 0,1 => 1, 2 => 2 | |
1168 | return $cx; | |
1169 | } | |
1170 | ||
1171 | # go forward until $base is exceeded | |
1172 | # limit is either $x or $base (x == 100 means as result too high) | |
1173 | my $steps = 100; $steps = $cx->[0] if @$cx == 1; | |
1174 | my $r = 2; my $cf = 3; my $step = 1; my $last = $r; | |
1175 | while ($r < $BASE && $step < $steps) | |
1176 | { | |
1177 | $last = $r; $r *= $cf++; $step++; | |
1178 | } | |
1179 | if ((@$cx == 1) && ($step == $cx->[0])) | |
1180 | { | |
1181 | # completely done | |
1182 | $cx = [$last]; | |
1183 | return $cx; | |
1184 | } | |
1185 | my $n = _copy($c,$cx); | |
1186 | $cx = [$last]; | |
1187 | ||
1188 | #$cx = _one(); | |
1189 | while (!(@$n == 1 && $n->[0] == $step)) | |
1190 | { | |
1191 | _mul($c,$cx,$n); _dec($c,$n); | |
1192 | } | |
1193 | $cx; | |
1194 | } | |
1195 | ||
1196 | use constant DEBUG => 0; | |
1197 | ||
1198 | my $steps = 0; | |
1199 | ||
1200 | sub steps { $steps }; | |
1201 | ||
1202 | sub _sqrt | |
0716bf9b | 1203 | { |
394e6ffb JH |
1204 | # square-root of $x |
1205 | # ref to array, return ref to array | |
1206 | my ($c,$x) = @_; | |
0716bf9b | 1207 | |
394e6ffb JH |
1208 | if (scalar @$x == 1) |
1209 | { | |
1210 | # fit's into one Perl scalar | |
1211 | $x->[0] = int(sqrt($x->[0])); | |
1212 | return $x; | |
1213 | } | |
1214 | my $y = _copy($c,$x); | |
b3abae2a JH |
1215 | # hopefully _len/2 is < $BASE, the -1 is to always undershot the guess |
1216 | # since our guess will "grow" | |
1217 | my $l = int((_len($c,$x)-1) / 2); | |
1218 | ||
1219 | my $lastelem = $x->[-1]; # for guess | |
1220 | my $elems = scalar @$x - 1; | |
1221 | # not enough digits, but could have more? | |
1222 | if ((length($lastelem) <= 3) && ($elems > 1)) | |
1223 | { | |
1224 | # right-align with zero pad | |
1225 | my $len = length($lastelem) & 1; | |
1226 | print "$lastelem => " if DEBUG; | |
1227 | $lastelem .= substr($x->[-2] . '0' x $BASE_LEN,0,$BASE_LEN); | |
1228 | # former odd => make odd again, or former even to even again | |
1229 | $lastelem = $lastelem / 10 if (length($lastelem) & 1) != $len; | |
1230 | print "$lastelem\n" if DEBUG; | |
1231 | } | |
0716bf9b | 1232 | |
61f5c3f5 T |
1233 | # construct $x (instead of _lsft($c,$x,$l,10) |
1234 | my $r = $l % $BASE_LEN; # 10000 00000 00000 00000 ($BASE_LEN=5) | |
1235 | $l = int($l / $BASE_LEN); | |
b3abae2a JH |
1236 | print "l = $l " if DEBUG; |
1237 | ||
1238 | splice @$x,$l; # keep ref($x), but modify it | |
1239 | ||
1240 | # we make the first part of the guess not '1000...0' but int(sqrt($lastelem)) | |
1241 | # that gives us: | |
1242 | # 14400 00000 => sqrt(14400) => 120 | |
1243 | # 144000 000000 => sqrt(144000) => 379 | |
1244 | ||
1245 | # $x->[$l--] = int('1' . '0' x $r); # old way of guessing | |
1246 | print "$lastelem (elems $elems) => " if DEBUG; | |
1247 | $lastelem = $lastelem / 10 if ($elems & 1 == 1); # odd or even? | |
1248 | my $g = sqrt($lastelem); $g =~ s/\.//; # 2.345 => 2345 | |
1249 | $r -= 1 if $elems & 1 == 0; # 70 => 7 | |
1250 | ||
1251 | # padd with zeros if result is too short | |
1252 | $x->[$l--] = int(substr($g . '0' x $r,0,$r+1)); | |
1253 | print "now ",$x->[-1] if DEBUG; | |
1254 | print " would have been ", int('1' . '0' x $r),"\n" if DEBUG; | |
1255 | ||
1256 | # If @$x > 1, we could compute the second elem of the guess, too, to create | |
1257 | # an even better guess. Not implemented yet. | |
1258 | $x->[$l--] = 0 while ($l >= 0); # all other digits of guess are zero | |
61f5c3f5 | 1259 | |
b3abae2a | 1260 | print "start x= ",${_str($c,$x)},"\n" if DEBUG; |
394e6ffb JH |
1261 | my $two = _two(); |
1262 | my $last = _zero(); | |
1263 | my $lastlast = _zero(); | |
b3abae2a | 1264 | $steps = 0 if DEBUG; |
394e6ffb JH |
1265 | while (_acmp($c,$last,$x) != 0 && _acmp($c,$lastlast,$x) != 0) |
1266 | { | |
b3abae2a | 1267 | $steps++ if DEBUG; |
394e6ffb JH |
1268 | $lastlast = _copy($c,$last); |
1269 | $last = _copy($c,$x); | |
1270 | _add($c,$x, _div($c,_copy($c,$y),$x)); | |
1271 | _div($c,$x, $two ); | |
b3abae2a | 1272 | print " x= ",${_str($c,$x)},"\n" if DEBUG; |
394e6ffb | 1273 | } |
b3abae2a | 1274 | print "\nsteps in sqrt: $steps, " if DEBUG; |
394e6ffb | 1275 | _dec($c,$x) if _acmp($c,$y,_mul($c,_copy($c,$x),$x)) < 0; # overshot? |
b3abae2a | 1276 | print " final ",$x->[-1],"\n" if DEBUG; |
394e6ffb | 1277 | $x; |
0716bf9b JH |
1278 | } |
1279 | ||
394e6ffb JH |
1280 | ############################################################################## |
1281 | # binary stuff | |
0716bf9b | 1282 | |
394e6ffb JH |
1283 | sub _and |
1284 | { | |
1285 | my ($c,$x,$y) = @_; | |
0716bf9b | 1286 | |
394e6ffb JH |
1287 | # the shortcut makes equal, large numbers _really_ fast, and makes only a |
1288 | # very small performance drop for small numbers (e.g. something with less | |
1289 | # than 32 bit) Since we optimize for large numbers, this is enabled. | |
1290 | return $x if _acmp($c,$x,$y) == 0; # shortcut | |
0716bf9b | 1291 | |
394e6ffb JH |
1292 | my $m = _one(); my ($xr,$yr); |
1293 | my $mask = $AND_MASK; | |
1294 | ||
1295 | my $x1 = $x; | |
1296 | my $y1 = _copy($c,$y); # make copy | |
1297 | $x = _zero(); | |
1298 | my ($b,$xrr,$yrr); | |
1299 | use integer; | |
1300 | while (!_is_zero($c,$x1) && !_is_zero($c,$y1)) | |
1301 | { | |
1302 | ($x1, $xr) = _div($c,$x1,$mask); | |
1303 | ($y1, $yr) = _div($c,$y1,$mask); | |
1304 | ||
1305 | # make ints() from $xr, $yr | |
1306 | # this is when the AND_BITS are greater tahn $BASE and is slower for | |
1307 | # small (<256 bits) numbers, but faster for large numbers. Disabled | |
1308 | # due to KISS principle | |
1309 | ||
1310 | # $b = 1; $xrr = 0; foreach (@$xr) { $xrr += $_ * $b; $b *= $BASE; } | |
1311 | # $b = 1; $yrr = 0; foreach (@$yr) { $yrr += $_ * $b; $b *= $BASE; } | |
1312 | # _add($c,$x, _mul($c, _new( $c, \($xrr & $yrr) ), $m) ); | |
1313 | ||
61f5c3f5 T |
1314 | # 0+ due to '&' doesn't work in strings |
1315 | _add($c,$x, _mul($c, [ 0+$xr->[0] & 0+$yr->[0] ], $m) ); | |
394e6ffb JH |
1316 | _mul($c,$m,$mask); |
1317 | } | |
1318 | $x; | |
0716bf9b JH |
1319 | } |
1320 | ||
394e6ffb | 1321 | sub _xor |
0716bf9b | 1322 | { |
394e6ffb JH |
1323 | my ($c,$x,$y) = @_; |
1324 | ||
1325 | return _zero() if _acmp($c,$x,$y) == 0; # shortcut (see -and) | |
1326 | ||
1327 | my $m = _one(); my ($xr,$yr); | |
1328 | my $mask = $XOR_MASK; | |
1329 | ||
1330 | my $x1 = $x; | |
1331 | my $y1 = _copy($c,$y); # make copy | |
1332 | $x = _zero(); | |
1333 | my ($b,$xrr,$yrr); | |
1334 | use integer; | |
1335 | while (!_is_zero($c,$x1) && !_is_zero($c,$y1)) | |
0716bf9b | 1336 | { |
394e6ffb JH |
1337 | ($x1, $xr) = _div($c,$x1,$mask); |
1338 | ($y1, $yr) = _div($c,$y1,$mask); | |
1339 | # make ints() from $xr, $yr (see _and()) | |
1340 | #$b = 1; $xrr = 0; foreach (@$xr) { $xrr += $_ * $b; $b *= $BASE; } | |
1341 | #$b = 1; $yrr = 0; foreach (@$yr) { $yrr += $_ * $b; $b *= $BASE; } | |
1342 | #_add($c,$x, _mul($c, _new( $c, \($xrr ^ $yrr) ), $m) ); | |
61f5c3f5 T |
1343 | |
1344 | # 0+ due to '^' doesn't work in strings | |
1345 | _add($c,$x, _mul($c, [ 0+$xr->[0] ^ 0+$yr->[0] ], $m) ); | |
394e6ffb | 1346 | _mul($c,$m,$mask); |
0716bf9b | 1347 | } |
394e6ffb JH |
1348 | # the loop stops when the shorter of the two numbers is exhausted |
1349 | # the remainder of the longer one will survive bit-by-bit, so we simple | |
1350 | # multiply-add it in | |
1351 | _add($c,$x, _mul($c, $x1, $m) ) if !_is_zero($c,$x1); | |
1352 | _add($c,$x, _mul($c, $y1, $m) ) if !_is_zero($c,$y1); | |
1353 | ||
1354 | $x; | |
0716bf9b JH |
1355 | } |
1356 | ||
394e6ffb | 1357 | sub _or |
0716bf9b | 1358 | { |
394e6ffb | 1359 | my ($c,$x,$y) = @_; |
0716bf9b | 1360 | |
394e6ffb | 1361 | return $x if _acmp($c,$x,$y) == 0; # shortcut (see _and) |
0716bf9b | 1362 | |
394e6ffb JH |
1363 | my $m = _one(); my ($xr,$yr); |
1364 | my $mask = $OR_MASK; | |
0716bf9b | 1365 | |
394e6ffb JH |
1366 | my $x1 = $x; |
1367 | my $y1 = _copy($c,$y); # make copy | |
1368 | $x = _zero(); | |
1369 | my ($b,$xrr,$yrr); | |
1370 | use integer; | |
1371 | while (!_is_zero($c,$x1) && !_is_zero($c,$y1)) | |
1372 | { | |
1373 | ($x1, $xr) = _div($c,$x1,$mask); | |
1374 | ($y1, $yr) = _div($c,$y1,$mask); | |
1375 | # make ints() from $xr, $yr (see _and()) | |
1376 | # $b = 1; $xrr = 0; foreach (@$xr) { $xrr += $_ * $b; $b *= $BASE; } | |
1377 | # $b = 1; $yrr = 0; foreach (@$yr) { $yrr += $_ * $b; $b *= $BASE; } | |
1378 | # _add($c,$x, _mul($c, _new( $c, \($xrr | $yrr) ), $m) ); | |
1379 | ||
61f5c3f5 T |
1380 | # 0+ due to '|' doesn't work in strings |
1381 | _add($c,$x, _mul($c, [ 0+$xr->[0] | 0+$yr->[0] ], $m) ); | |
394e6ffb JH |
1382 | _mul($c,$m,$mask); |
1383 | } | |
1384 | # the loop stops when the shorter of the two numbers is exhausted | |
1385 | # the remainder of the longer one will survive bit-by-bit, so we simple | |
1386 | # multiply-add it in | |
1387 | _add($c,$x, _mul($c, $x1, $m) ) if !_is_zero($c,$x1); | |
1388 | _add($c,$x, _mul($c, $y1, $m) ) if !_is_zero($c,$y1); | |
1389 | ||
1390 | $x; | |
0716bf9b JH |
1391 | } |
1392 | ||
61f5c3f5 T |
1393 | sub _as_hex |
1394 | { | |
1395 | # convert a decimal number to hex (ref to array, return ref to string) | |
1396 | my ($c,$x) = @_; | |
1397 | ||
1398 | my $x1 = _copy($c,$x); | |
1399 | ||
1400 | my $es = ''; | |
1401 | my $xr; | |
1402 | my $x10000 = [ 0x10000 ]; | |
1403 | while (! _is_zero($c,$x1)) | |
1404 | { | |
1405 | ($x1, $xr) = _div($c,$x1,$x10000); | |
1406 | $es .= unpack('h4',pack('v',$xr->[0])); | |
1407 | } | |
1408 | $es = reverse $es; | |
1409 | $es =~ s/^[0]+//; # strip leading zeros | |
1410 | $es = '0x' . $es; | |
1411 | \$es; | |
1412 | } | |
1413 | ||
1414 | sub _as_bin | |
1415 | { | |
1416 | # convert a decimal number to bin (ref to array, return ref to string) | |
1417 | my ($c,$x) = @_; | |
1418 | ||
1419 | my $x1 = _copy($c,$x); | |
1420 | ||
1421 | my $es = ''; | |
1422 | my $xr; | |
1423 | my $x10000 = [ 0x10000 ]; | |
1424 | while (! _is_zero($c,$x1)) | |
1425 | { | |
1426 | ($x1, $xr) = _div($c,$x1,$x10000); | |
1427 | $es .= unpack('b16',pack('v',$xr->[0])); | |
1428 | } | |
1429 | $es = reverse $es; | |
1430 | $es =~ s/^[0]+//; # strip leading zeros | |
1431 | $es = '0b' . $es; | |
1432 | \$es; | |
1433 | } | |
1434 | ||
394e6ffb | 1435 | sub _from_hex |
0716bf9b | 1436 | { |
394e6ffb JH |
1437 | # convert a hex number to decimal (ref to string, return ref to array) |
1438 | my ($c,$hs) = @_; | |
0716bf9b | 1439 | |
394e6ffb JH |
1440 | my $mul = _one(); |
1441 | my $m = [ 0x10000 ]; # 16 bit at a time | |
1442 | my $x = _zero(); | |
0716bf9b | 1443 | |
61f5c3f5 | 1444 | my $len = length($$hs)-2; |
394e6ffb JH |
1445 | $len = int($len/4); # 4-digit parts, w/o '0x' |
1446 | my $val; my $i = -4; | |
1447 | while ($len >= 0) | |
1448 | { | |
1449 | $val = substr($$hs,$i,4); | |
1450 | $val =~ s/^[+-]?0x// if $len == 0; # for last part only because | |
1451 | $val = hex($val); # hex does not like wrong chars | |
1452 | $i -= 4; $len --; | |
1453 | _add ($c, $x, _mul ($c, [ $val ], $mul ) ) if $val != 0; | |
1454 | _mul ($c, $mul, $m ) if $len >= 0; # skip last mul | |
1455 | } | |
1456 | $x; | |
1457 | } | |
1458 | ||
1459 | sub _from_bin | |
0716bf9b | 1460 | { |
394e6ffb JH |
1461 | # convert a hex number to decimal (ref to string, return ref to array) |
1462 | my ($c,$bs) = @_; | |
0716bf9b | 1463 | |
13a12e00 JH |
1464 | # instead of converting 8 bit at a time, it is faster to convert the |
1465 | # number to hex, and then call _from_hex. | |
1466 | ||
1467 | my $hs = $$bs; | |
1468 | $hs =~ s/^[+-]?0b//; # remove sign and 0b | |
1469 | my $l = length($hs); # bits | |
1470 | $hs = '0' x (8-($l % 8)) . $hs if ($l % 8) != 0; # padd left side w/ 0 | |
1471 | my $h = unpack('H*', pack ('B*', $hs)); # repack as hex | |
1472 | return $c->_from_hex(\('0x'.$h)); | |
1473 | ||
394e6ffb JH |
1474 | my $mul = _one(); |
1475 | my $m = [ 0x100 ]; # 8 bit at a time | |
1476 | my $x = _zero(); | |
0716bf9b | 1477 | |
61f5c3f5 | 1478 | my $len = length($$bs)-2; |
394e6ffb JH |
1479 | $len = int($len/8); # 4-digit parts, w/o '0x' |
1480 | my $val; my $i = -8; | |
1481 | while ($len >= 0) | |
0716bf9b | 1482 | { |
394e6ffb JH |
1483 | $val = substr($$bs,$i,8); |
1484 | $val =~ s/^[+-]?0b// if $len == 0; # for last part only | |
1485 | ||
394e6ffb JH |
1486 | $val = ord(pack('B8',substr('00000000'.$val,-8,8))); |
1487 | ||
1488 | $i -= 8; $len --; | |
1489 | _add ($c, $x, _mul ($c, [ $val ], $mul ) ) if $val != 0; | |
1490 | _mul ($c, $mul, $m ) if $len >= 0; # skip last mul | |
0716bf9b | 1491 | } |
394e6ffb | 1492 | $x; |
0716bf9b JH |
1493 | } |
1494 | ||
394e6ffb JH |
1495 | ############################################################################## |
1496 | ############################################################################## | |
1497 | ||
0716bf9b JH |
1498 | 1; |
1499 | __END__ | |
1500 | ||
1501 | =head1 NAME | |
1502 | ||
1503 | Math::BigInt::Calc - Pure Perl module to support Math::BigInt | |
1504 | ||
1505 | =head1 SYNOPSIS | |
1506 | ||
ee15d750 JH |
1507 | Provides support for big integer calculations. Not intended to be used by other |
1508 | modules (except Math::BigInt::Cached). Other modules which sport the same | |
1509 | functions can also be used to support Math::Bigint, like Math::BigInt::Pari. | |
0716bf9b JH |
1510 | |
1511 | =head1 DESCRIPTION | |
1512 | ||
027dc388 JH |
1513 | In order to allow for multiple big integer libraries, Math::BigInt was |
1514 | rewritten to use library modules for core math routines. Any module which | |
1515 | follows the same API as this can be used instead by using the following: | |
0716bf9b | 1516 | |
ee15d750 | 1517 | use Math::BigInt lib => 'libname'; |
0716bf9b | 1518 | |
027dc388 JH |
1519 | 'libname' is either the long name ('Math::BigInt::Pari'), or only the short |
1520 | version like 'Pari'. | |
1521 | ||
0716bf9b JH |
1522 | =head1 EXPORT |
1523 | ||
027dc388 JH |
1524 | The following functions MUST be defined in order to support the use by |
1525 | Math::BigInt: | |
0716bf9b JH |
1526 | |
1527 | _new(string) return ref to new object from ref to decimal string | |
1528 | _zero() return a new object with value 0 | |
1529 | _one() return a new object with value 1 | |
1530 | ||
1531 | _str(obj) return ref to a string representing the object | |
1532 | _num(obj) returns a Perl integer/floating point number | |
1533 | NOTE: because of Perl numeric notation defaults, | |
1534 | the _num'ified obj may lose accuracy due to | |
1535 | machine-dependend floating point size limitations | |
1536 | ||
1537 | _add(obj,obj) Simple addition of two objects | |
1538 | _mul(obj,obj) Multiplication of two objects | |
1539 | _div(obj,obj) Division of the 1st object by the 2nd | |
b22b3e31 PN |
1540 | In list context, returns (result,remainder). |
1541 | NOTE: this is integer math, so no | |
1542 | fractional part will be returned. | |
1543 | _sub(obj,obj) Simple subtraction of 1 object from another | |
0716bf9b JH |
1544 | a third, optional parameter indicates that the params |
1545 | are swapped. In this case, the first param needs to | |
1546 | be preserved, while you can destroy the second. | |
1547 | sub (x,y,1) => return x - y and keep x intact! | |
e745a66c JH |
1548 | _dec(obj) decrement object by one (input is garant. to be > 0) |
1549 | _inc(obj) increment object by one | |
1550 | ||
0716bf9b JH |
1551 | |
1552 | _acmp(obj,obj) <=> operator for objects (return -1, 0 or 1) | |
1553 | ||
1554 | _len(obj) returns count of the decimal digits of the object | |
1555 | _digit(obj,n) returns the n'th decimal digit of object | |
1556 | ||
1557 | _is_one(obj) return true if argument is +1 | |
1558 | _is_zero(obj) return true if argument is 0 | |
1559 | _is_even(obj) return true if argument is even (0,2,4,6..) | |
1560 | _is_odd(obj) return true if argument is odd (1,3,5,7..) | |
1561 | ||
1562 | _copy return a ref to a true copy of the object | |
1563 | ||
1564 | _check(obj) check whether internal representation is still intact | |
1565 | return 0 for ok, otherwise error message as string | |
1566 | ||
bd05a461 | 1567 | The following functions are optional, and can be defined if the underlying lib |
027dc388 JH |
1568 | has a fast way to do them. If undefined, Math::BigInt will use pure Perl (hence |
1569 | slow) fallback routines to emulate these: | |
0716bf9b JH |
1570 | |
1571 | _from_hex(str) return ref to new object from ref to hexadecimal string | |
1572 | _from_bin(str) return ref to new object from ref to binary string | |
1573 | ||
ee15d750 JH |
1574 | _as_hex(str) return ref to scalar string containing the value as |
1575 | unsigned hex string, with the '0x' prepended. | |
1576 | Leading zeros must be stripped. | |
1577 | _as_bin(str) Like as_hex, only as binary string containing only | |
1578 | zeros and ones. Leading zeros must be stripped and a | |
1579 | '0b' must be prepended. | |
1580 | ||
0716bf9b | 1581 | _rsft(obj,N,B) shift object in base B by N 'digits' right |
dccbb853 | 1582 | For unsupported bases B, return undef to signal failure |
0716bf9b | 1583 | _lsft(obj,N,B) shift object in base B by N 'digits' left |
dccbb853 | 1584 | For unsupported bases B, return undef to signal failure |
0716bf9b JH |
1585 | |
1586 | _xor(obj1,obj2) XOR (bit-wise) object 1 with object 2 | |
dccbb853 | 1587 | Note: XOR, AND and OR pad with zeros if size mismatches |
0716bf9b JH |
1588 | _and(obj1,obj2) AND (bit-wise) object 1 with object 2 |
1589 | _or(obj1,obj2) OR (bit-wise) object 1 with object 2 | |
1590 | ||
dccbb853 | 1591 | _mod(obj,obj) Return remainder of div of the 1st by the 2nd object |
394e6ffb | 1592 | _sqrt(obj) return the square root of object (truncate to int) |
b3abae2a | 1593 | _fac(obj) return factorial of object 1 (1*2*3*4..) |
0716bf9b JH |
1594 | _pow(obj,obj) return object 1 to the power of object 2 |
1595 | _gcd(obj,obj) return Greatest Common Divisor of two objects | |
1596 | ||
b22b3e31 | 1597 | _zeros(obj) return number of trailing decimal zeros |
0716bf9b | 1598 | |
b22b3e31 | 1599 | Input strings come in as unsigned but with prefix (i.e. as '123', '0xabc' |
0716bf9b JH |
1600 | or '0b1101'). |
1601 | ||
b22b3e31 | 1602 | Testing of input parameter validity is done by the caller, so you need not |
574bacfe JH |
1603 | worry about underflow (f.i. in C<_sub()>, C<_dec()>) nor about division by |
1604 | zero or similar cases. | |
1605 | ||
1606 | The first parameter can be modified, that includes the possibility that you | |
1607 | return a reference to a completely different object instead. Although keeping | |
dccbb853 JH |
1608 | the reference and just changing it's contents is prefered over creating and |
1609 | returning a different reference. | |
574bacfe JH |
1610 | |
1611 | Return values are always references to objects or strings. Exceptions are | |
1612 | C<_lsft()> and C<_rsft()>, which return undef if they can not shift the | |
027dc388 JH |
1613 | argument. This is used to delegate shifting of bases different than the one |
1614 | you can support back to Math::BigInt, which will use some generic code to | |
1615 | calculate the result. | |
574bacfe JH |
1616 | |
1617 | =head1 WRAP YOUR OWN | |
1618 | ||
1619 | If you want to port your own favourite c-lib for big numbers to the | |
1620 | Math::BigInt interface, you can take any of the already existing modules as | |
1621 | a rough guideline. You should really wrap up the latest BigInt and BigFloat | |
bd05a461 | 1622 | testsuites with your module, and replace in them any of the following: |
574bacfe JH |
1623 | |
1624 | use Math::BigInt; | |
1625 | ||
bd05a461 | 1626 | by this: |
574bacfe JH |
1627 | |
1628 | use Math::BigInt lib => 'yourlib'; | |
1629 | ||
1630 | This way you ensure that your library really works 100% within Math::BigInt. | |
0716bf9b JH |
1631 | |
1632 | =head1 LICENSE | |
1633 | ||
1634 | This program is free software; you may redistribute it and/or modify it under | |
1635 | the same terms as Perl itself. | |
1636 | ||
1637 | =head1 AUTHORS | |
1638 | ||
1639 | Original math code by Mark Biggar, rewritten by Tels L<http://bloodgate.com/> | |
1640 | in late 2000, 2001. | |
1641 | Seperated from BigInt and shaped API with the help of John Peacock. | |
1642 | ||
1643 | =head1 SEE ALSO | |
1644 | ||
ee15d750 JH |
1645 | L<Math::BigInt>, L<Math::BigFloat>, L<Math::BigInt::BitVect>, |
1646 | L<Math::BigInt::GMP>, L<Math::BigInt::Cached> and L<Math::BigInt::Pari>. | |
0716bf9b JH |
1647 | |
1648 | =cut |