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0716bf9b |
1 | package Math::BigInt::Calc; |
2 | |
3 | use 5.005; |
4 | use strict; |
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5 | # use warnings; # dont use warnings for older Perls |
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6 | |
7 | require Exporter; |
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8 | use vars qw/@ISA $VERSION/; |
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9 | @ISA = qw(Exporter); |
10 | |
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11 | $VERSION = '0.17'; |
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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 |
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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 |
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18 | |
19 | # todo: |
20 | # - fully remove funky $# stuff (maybe) |
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21 | |
22 | # USE_MUL: due to problems on certain os (os390, posix-bc) "* 1e-5" is used |
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23 | # instead of "/ 1e5" at some places, (marked with USE_MUL). Other platforms |
24 | # BS2000, some Crays need USE_DIV instead. |
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25 | # The BEGIN block is used to determine which of the two variants gives the |
26 | # correct result. |
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27 | |
28 | ############################################################################## |
29 | # global constants, flags and accessory |
30 | |
31 | # constants for easier life |
32 | my $nan = 'NaN'; |
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33 | my ($BASE,$RBASE,$BASE_LEN,$MAX_VAL,$BASE_LEN2); |
34 | my ($AND_BITS,$XOR_BITS,$OR_BITS); |
35 | my ($AND_MASK,$XOR_MASK,$OR_MASK); |
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36 | |
37 | sub _base_len |
38 | { |
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39 | # set/get the BASE_LEN and assorted other, connected values |
40 | # used only be the testsuite, set is used only by the BEGIN block below |
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41 | shift; |
42 | |
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43 | my $b = shift; |
44 | if (defined $b) |
45 | { |
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46 | $b = 5 if $^O =~ /^uts/; # UTS needs 5, because 6 and 7 break |
47 | $BASE_LEN = $b+1; |
48 | my $caught; |
49 | while (--$BASE_LEN > 5) |
50 | { |
51 | $BASE = int("1e".$BASE_LEN); |
52 | $RBASE = abs('1e-'.$BASE_LEN); # see USE_MUL |
53 | $caught = 0; |
54 | $caught += 1 if (int($BASE * $RBASE) != 1); # should be 1 |
55 | $caught += 2 if (int($BASE / $BASE) != 1); # should be 1 |
56 | # print "caught $caught\n"; |
57 | last if $caught != 3; |
58 | } |
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59 | $BASE = int("1e".$BASE_LEN); |
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60 | $RBASE = abs('1e-'.$BASE_LEN); # see USE_MUL |
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61 | $MAX_VAL = $BASE-1; |
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62 | $BASE_LEN2 = int($BASE_LEN / 2); # for mul shortcut |
63 | # print "BASE_LEN: $BASE_LEN MAX_VAL: $MAX_VAL BASE: $BASE RBASE: $RBASE\n"; |
64 | |
65 | if ($caught & 1 != 0) |
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66 | { |
67 | # must USE_MUL |
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68 | *{_mul} = \&_mul_use_mul; |
69 | *{_div} = \&_div_use_mul; |
70 | } |
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71 | else # $caught must be 2, since it can't be 1 nor 3 |
ee15d750 |
72 | { |
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73 | # can USE_DIV instead |
74 | *{_mul} = \&_mul_use_div; |
75 | *{_div} = \&_div_use_div; |
76 | } |
77 | } |
394e6ffb |
78 | if (wantarray) |
79 | { |
80 | return ($BASE_LEN, $AND_BITS, $XOR_BITS, $OR_BITS); |
81 | } |
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82 | $BASE_LEN; |
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83 | } |
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84 | |
85 | BEGIN |
86 | { |
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87 | # from Daniel Pfeiffer: determine largest group of digits that is precisely |
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88 | # multipliable with itself plus carry |
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89 | # Test now changed to expect the proper pattern, not a result off by 1 or 2 |
90 | my ($e, $num) = 3; # lowest value we will use is 3+1-1 = 3 |
bd05a461 |
91 | do |
92 | { |
93 | $num = ('9' x ++$e) + 0; |
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94 | $num *= $num + 1.0; |
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95 | # print "$num $e\n"; |
394e6ffb |
96 | } while ("$num" =~ /9{$e}0{$e}/); # must be a certain pattern |
97 | $e--; # last test failed, so retract one step |
98 | # the limits below brush the problems with the test above under the rug: |
99 | # the test should be able to find the proper $e automatically |
100 | $e = 5 if $^O =~ /^uts/; # UTS get's some special treatment |
101 | $e = 5 if $^O =~ /^unicos/; # unicos is also problematic (6 seems to work |
102 | # there, but we play safe) |
103 | $e = 8 if $e > 8; # cap, for VMS, OS/390 and other 64 bit systems |
104 | |
105 | __PACKAGE__->_base_len($e); # set and store |
106 | |
107 | # find out how many bits _and, _or and _xor can take (old default = 16) |
108 | # I don't think anybody has yet 128 bit scalars, so let's play safe. |
109 | use integer; |
110 | local $^W = 0; # don't warn about 'nonportable number' |
111 | $AND_BITS = 15; $XOR_BITS = 15; $OR_BITS = 15; |
112 | |
113 | # find max bits, we will not go higher than numberofbits that fit into $BASE |
114 | # to make _and etc simpler (and faster for smaller, slower for large numbers) |
115 | my $max = 16; |
116 | while (2 ** $max < $BASE) { $max++; } |
117 | my ($x,$y,$z); |
118 | do { |
119 | $AND_BITS++; |
120 | $x = oct('0b' . '1' x $AND_BITS); $y = $x & $x; |
121 | $z = (2 ** $AND_BITS) - 1; |
122 | } while ($AND_BITS < $max && $x == $z && $y == $x); |
123 | $AND_BITS --; # retreat one step |
124 | do { |
125 | $XOR_BITS++; |
126 | $x = oct('0b' . '1' x $XOR_BITS); $y = $x ^ 0; |
127 | $z = (2 ** $XOR_BITS) - 1; |
128 | } while ($XOR_BITS < $max && $x == $z && $y == $x); |
129 | $XOR_BITS --; # retreat one step |
130 | do { |
131 | $OR_BITS++; |
132 | $x = oct('0b' . '1' x $OR_BITS); $y = $x | $x; |
133 | $z = (2 ** $OR_BITS) - 1; |
134 | } while ($OR_BITS < $max && $x == $z && $y == $x); |
135 | $OR_BITS --; # retreat one step |
136 | |
137 | # print "AND $AND_BITS XOR $XOR_BITS OR $OR_BITS\n"; |
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138 | } |
139 | |
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140 | ############################################################################## |
141 | # create objects from various representations |
142 | |
143 | sub _new |
144 | { |
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145 | # (ref to string) return ref to num_array |
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146 | # Convert a number from string format to internal base 100000 format. |
147 | # Assumes normalized value as input. |
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148 | my $d = $_[1]; |
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149 | my $il = CORE::length($$d)-1; |
150 | # these leaves '00000' instead of int 0 and will be corrected after any op |
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151 | return [ reverse(unpack("a" . ($il % $BASE_LEN+1) |
152 | . ("a$BASE_LEN" x ($il / $BASE_LEN)), $$d)) ]; |
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153 | } |
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154 | |
155 | BEGIN |
156 | { |
157 | $AND_MASK = __PACKAGE__->_new( \( 2 ** $AND_BITS )); |
158 | $XOR_MASK = __PACKAGE__->_new( \( 2 ** $XOR_BITS )); |
159 | $OR_MASK = __PACKAGE__->_new( \( 2 ** $OR_BITS )); |
160 | } |
0716bf9b |
161 | |
162 | sub _zero |
163 | { |
164 | # create a zero |
165 | return [ 0 ]; |
166 | } |
167 | |
168 | sub _one |
169 | { |
170 | # create a one |
171 | return [ 1 ]; |
172 | } |
173 | |
027dc388 |
174 | sub _two |
175 | { |
176 | # create a two (for _pow) |
177 | return [ 2 ]; |
178 | } |
179 | |
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180 | sub _copy |
181 | { |
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182 | return [ @{$_[1]} ]; |
0716bf9b |
183 | } |
184 | |
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185 | # catch and throw away |
186 | sub import { } |
187 | |
0716bf9b |
188 | ############################################################################## |
189 | # convert back to string and number |
190 | |
191 | sub _str |
192 | { |
193 | # (ref to BINT) return num_str |
194 | # Convert number from internal base 100000 format to string format. |
195 | # internal format is always normalized (no leading zeros, "-0" => "+0") |
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196 | my $ar = $_[1]; |
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197 | my $ret = ""; |
198 | my $l = scalar @$ar; # number of parts |
199 | return $nan if $l < 1; # should not happen |
200 | # handle first one different to strip leading zeros from it (there are no |
201 | # leading zero parts in internal representation) |
202 | $l --; $ret .= $ar->[$l]; $l--; |
203 | # Interestingly, the pre-padd method uses more time |
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204 | # the old grep variant takes longer (14 to 10 sec) |
205 | my $z = '0' x ($BASE_LEN-1); |
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206 | while ($l >= 0) |
207 | { |
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208 | $ret .= substr($z.$ar->[$l],-$BASE_LEN); # fastest way I could think of |
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209 | $l--; |
210 | } |
211 | return \$ret; |
212 | } |
213 | |
214 | sub _num |
215 | { |
216 | # Make a number (scalar int/float) from a BigInt object |
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217 | my $x = $_[1]; |
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218 | return $x->[0] if scalar @$x == 1; # below $BASE |
219 | my $fac = 1; |
220 | my $num = 0; |
221 | foreach (@$x) |
222 | { |
223 | $num += $fac*$_; $fac *= $BASE; |
224 | } |
225 | return $num; |
226 | } |
227 | |
228 | ############################################################################## |
229 | # actual math code |
230 | |
231 | sub _add |
232 | { |
233 | # (ref to int_num_array, ref to int_num_array) |
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234 | # routine to add two base 1eX numbers |
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235 | # stolen from Knuth Vol 2 Algorithm A pg 231 |
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236 | # there are separate routines to add and sub as per Knuth pg 233 |
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237 | # This routine clobbers up array x, but not y. |
238 | |
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239 | my ($c,$x,$y) = @_; |
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240 | |
241 | # for each in Y, add Y to X and carry. If after that, something is left in |
242 | # X, foreach in X add carry to X and then return X, carry |
243 | # Trades one "$j++" for having to shift arrays, $j could be made integer |
b22b3e31 |
244 | # but this would impose a limit to number-length of 2**32. |
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245 | my $i; my $car = 0; my $j = 0; |
246 | for $i (@$y) |
247 | { |
e745a66c |
248 | $x->[$j] -= $BASE if $car = (($x->[$j] += $i + $car) >= $BASE) ? 1 : 0; |
0716bf9b |
249 | $j++; |
250 | } |
251 | while ($car != 0) |
252 | { |
253 | $x->[$j] -= $BASE if $car = (($x->[$j] += $car) >= $BASE) ? 1 : 0; $j++; |
254 | } |
e745a66c |
255 | return $x; |
256 | } |
257 | |
258 | sub _inc |
259 | { |
260 | # (ref to int_num_array, ref to int_num_array) |
261 | # routine to add 1 to a base 1eX numbers |
262 | # This routine clobbers up array x, but not y. |
263 | my ($c,$x) = @_; |
264 | |
265 | for my $i (@$x) |
266 | { |
267 | return $x if (($i += 1) < $BASE); # early out |
268 | $i -= $BASE; |
269 | } |
270 | if ($x->[-1] == 0) # last overflowed |
271 | { |
272 | push @$x,1; # extend |
273 | } |
274 | return $x; |
275 | } |
276 | |
277 | sub _dec |
278 | { |
279 | # (ref to int_num_array, ref to int_num_array) |
280 | # routine to add 1 to a base 1eX numbers |
281 | # This routine clobbers up array x, but not y. |
282 | my ($c,$x) = @_; |
283 | |
284 | for my $i (@$x) |
285 | { |
286 | last if (($i -= 1) >= 0); # early out |
287 | $i = $MAX_VAL; |
288 | } |
289 | pop @$x if $x->[-1] == 0 && @$x > 1; # last overflowed (but leave 0) |
290 | return $x; |
0716bf9b |
291 | } |
292 | |
293 | sub _sub |
294 | { |
295 | # (ref to int_num_array, ref to int_num_array) |
574bacfe |
296 | # subtract base 1eX numbers -- stolen from Knuth Vol 2 pg 232, $x > $y |
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297 | # subtract Y from X (X is always greater/equal!) by modifying x in place |
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298 | my ($c,$sx,$sy,$s) = @_; |
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299 | |
300 | my $car = 0; my $i; my $j = 0; |
301 | if (!$s) |
302 | { |
303 | #print "case 2\n"; |
304 | for $i (@$sx) |
305 | { |
306 | last unless defined $sy->[$j] || $car; |
0716bf9b |
307 | $i += $BASE if $car = (($i -= ($sy->[$j] || 0) + $car) < 0); $j++; |
0716bf9b |
308 | } |
309 | # might leave leading zeros, so fix that |
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310 | return __strip_zeros($sx); |
0716bf9b |
311 | } |
394e6ffb |
312 | #print "case 1 (swap)\n"; |
313 | for $i (@$sx) |
0716bf9b |
314 | { |
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315 | last unless defined $sy->[$j] || $car; |
316 | $sy->[$j] += $BASE |
317 | if $car = (($sy->[$j] = $i-($sy->[$j]||0) - $car) < 0); |
318 | $j++; |
0716bf9b |
319 | } |
394e6ffb |
320 | # might leave leading zeros, so fix that |
321 | __strip_zeros($sy); |
0716bf9b |
322 | } |
323 | |
ee15d750 |
324 | sub _mul_use_mul |
0716bf9b |
325 | { |
326 | # (BINT, BINT) return nothing |
327 | # multiply two numbers in internal representation |
b22b3e31 |
328 | # modifies first arg, second need not be different from first |
574bacfe |
329 | my ($c,$xv,$yv) = @_; |
dccbb853 |
330 | |
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331 | # shortcut for two very short numbers |
332 | # +0 since part maybe string '00001' from new() |
333 | if ((@$xv == 1) && (@$yv == 1) |
334 | && (length($xv->[0]+0) <= $BASE_LEN2) |
335 | && (length($yv->[0]+0) <= $BASE_LEN2)) |
336 | { |
337 | $xv->[0] *= $yv->[0]; |
338 | return $xv; |
339 | } |
340 | |
0716bf9b |
341 | my @prod = (); my ($prod,$car,$cty,$xi,$yi); |
342 | # since multiplying $x with $x fails, make copy in this case |
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343 | $yv = [@$xv] if "$xv" eq "$yv"; # same references? |
0716bf9b |
344 | for $xi (@$xv) |
345 | { |
346 | $car = 0; $cty = 0; |
574bacfe |
347 | |
348 | # slow variant |
349 | # for $yi (@$yv) |
350 | # { |
351 | # $prod = $xi * $yi + ($prod[$cty] || 0) + $car; |
352 | # $prod[$cty++] = |
353 | # $prod - ($car = int($prod * RBASE)) * $BASE; # see USE_MUL |
354 | # } |
355 | # $prod[$cty] += $car if $car; # need really to check for 0? |
356 | # $xi = shift @prod; |
357 | |
358 | # faster variant |
359 | # looping through this if $xi == 0 is silly - so optimize it away! |
360 | $xi = (shift @prod || 0), next if $xi == 0; |
0716bf9b |
361 | for $yi (@$yv) |
362 | { |
363 | $prod = $xi * $yi + ($prod[$cty] || 0) + $car; |
574bacfe |
364 | ## this is actually a tad slower |
365 | ## $prod = $prod[$cty]; $prod += ($car + $xi * $yi); # no ||0 here |
0716bf9b |
366 | $prod[$cty++] = |
574bacfe |
367 | $prod - ($car = int($prod * $RBASE)) * $BASE; # see USE_MUL |
0716bf9b |
368 | } |
369 | $prod[$cty] += $car if $car; # need really to check for 0? |
027dc388 |
370 | $xi = shift @prod || 0; # || 0 makes v5.005_3 happy |
0716bf9b |
371 | } |
0716bf9b |
372 | push @$xv, @prod; |
373 | __strip_zeros($xv); |
0716bf9b |
374 | } |
375 | |
ee15d750 |
376 | sub _mul_use_div |
377 | { |
378 | # (BINT, BINT) return nothing |
379 | # multiply two numbers in internal representation |
380 | # modifies first arg, second need not be different from first |
381 | my ($c,$xv,$yv) = @_; |
382 | |
394e6ffb |
383 | # shortcut for two very short numbers |
384 | # +0 since part maybe string '00001' from new() |
385 | if ((@$xv == 1) && (@$yv == 1) |
386 | && (length($xv->[0]+0) <= $BASE_LEN2) |
387 | && (length($yv->[0]+0) <= $BASE_LEN2)) |
388 | { |
389 | $xv->[0] *= $yv->[0]; |
390 | return $xv; |
391 | } |
392 | |
ee15d750 |
393 | my @prod = (); my ($prod,$car,$cty,$xi,$yi); |
394 | # since multiplying $x with $x fails, make copy in this case |
395 | $yv = [@$xv] if "$xv" eq "$yv"; # same references? |
396 | for $xi (@$xv) |
397 | { |
398 | $car = 0; $cty = 0; |
399 | # looping through this if $xi == 0 is silly - so optimize it away! |
400 | $xi = (shift @prod || 0), next if $xi == 0; |
401 | for $yi (@$yv) |
402 | { |
403 | $prod = $xi * $yi + ($prod[$cty] || 0) + $car; |
404 | $prod[$cty++] = |
405 | $prod - ($car = int($prod / $BASE)) * $BASE; |
406 | } |
407 | $prod[$cty] += $car if $car; # need really to check for 0? |
027dc388 |
408 | $xi = shift @prod || 0; # || 0 makes v5.005_3 happy |
ee15d750 |
409 | } |
410 | push @$xv, @prod; |
411 | __strip_zeros($xv); |
ee15d750 |
412 | } |
413 | |
414 | sub _div_use_mul |
0716bf9b |
415 | { |
b22b3e31 |
416 | # ref to array, ref to array, modify first array and return remainder if |
0716bf9b |
417 | # in list context |
574bacfe |
418 | my ($c,$x,$yorg) = @_; |
0716bf9b |
419 | my ($car,$bar,$prd,$dd,$xi,$yi,@q,$v2,$v1); |
420 | |
421 | my (@d,$tmp,$q,$u2,$u1,$u0); |
422 | |
423 | $car = $bar = $prd = 0; |
424 | |
425 | my $y = [ @$yorg ]; |
426 | if (($dd = int($BASE/($y->[-1]+1))) != 1) |
427 | { |
428 | for $xi (@$x) |
429 | { |
430 | $xi = $xi * $dd + $car; |
431 | $xi -= ($car = int($xi * $RBASE)) * $BASE; # see USE_MUL |
432 | } |
433 | push(@$x, $car); $car = 0; |
434 | for $yi (@$y) |
435 | { |
436 | $yi = $yi * $dd + $car; |
437 | $yi -= ($car = int($yi * $RBASE)) * $BASE; # see USE_MUL |
438 | } |
439 | } |
440 | else |
441 | { |
442 | push(@$x, 0); |
443 | } |
444 | @q = (); ($v2,$v1) = @$y[-2,-1]; |
445 | $v2 = 0 unless $v2; |
446 | while ($#$x > $#$y) |
447 | { |
448 | ($u2,$u1,$u0) = @$x[-3..-1]; |
449 | $u2 = 0 unless $u2; |
450 | #warn "oups v1 is 0, u0: $u0 $y->[-2] $y->[-1] l ",scalar @$y,"\n" |
451 | # if $v1 == 0; |
ee15d750 |
452 | # $q = (($u0 == $v1) ? 99999 : int(($u0*$BASE+$u1)/$v1)); |
453 | $q = (($u0 == $v1) ? $MAX_VAL : int(($u0*$BASE+$u1)/$v1)); |
574bacfe |
454 | --$q while ($v2*$q > ($u0*$BASE+$u1-$q*$v1)*$BASE+$u2); |
0716bf9b |
455 | if ($q) |
456 | { |
457 | ($car, $bar) = (0,0); |
458 | for ($yi = 0, $xi = $#$x-$#$y-1; $yi <= $#$y; ++$yi,++$xi) |
459 | { |
460 | $prd = $q * $y->[$yi] + $car; |
461 | $prd -= ($car = int($prd * $RBASE)) * $BASE; # see USE_MUL |
574bacfe |
462 | $x->[$xi] += $BASE if ($bar = (($x->[$xi] -= $prd + $bar) < 0)); |
0716bf9b |
463 | } |
464 | if ($x->[-1] < $car + $bar) |
465 | { |
466 | $car = 0; --$q; |
467 | for ($yi = 0, $xi = $#$x-$#$y-1; $yi <= $#$y; ++$yi,++$xi) |
468 | { |
574bacfe |
469 | $x->[$xi] -= $BASE |
0716bf9b |
470 | if ($car = (($x->[$xi] += $y->[$yi] + $car) > $BASE)); |
471 | } |
472 | } |
473 | } |
474 | pop(@$x); unshift(@q, $q); |
475 | } |
476 | if (wantarray) |
477 | { |
478 | @d = (); |
479 | if ($dd != 1) |
480 | { |
481 | $car = 0; |
482 | for $xi (reverse @$x) |
483 | { |
484 | $prd = $car * $BASE + $xi; |
485 | $car = $prd - ($tmp = int($prd / $dd)) * $dd; # see USE_MUL |
486 | unshift(@d, $tmp); |
487 | } |
488 | } |
489 | else |
490 | { |
491 | @d = @$x; |
492 | } |
493 | @$x = @q; |
494 | __strip_zeros($x); |
495 | __strip_zeros(\@d); |
394e6ffb |
496 | _check('',$x); |
497 | _check('',\@d); |
0716bf9b |
498 | return ($x,\@d); |
499 | } |
500 | @$x = @q; |
501 | __strip_zeros($x); |
394e6ffb |
502 | _check('',$x); |
0716bf9b |
503 | } |
504 | |
ee15d750 |
505 | sub _div_use_div |
506 | { |
507 | # ref to array, ref to array, modify first array and return remainder if |
508 | # in list context |
ee15d750 |
509 | my ($c,$x,$yorg) = @_; |
510 | my ($car,$bar,$prd,$dd,$xi,$yi,@q,$v2,$v1); |
511 | |
512 | my (@d,$tmp,$q,$u2,$u1,$u0); |
513 | |
514 | $car = $bar = $prd = 0; |
515 | |
516 | my $y = [ @$yorg ]; |
517 | if (($dd = int($BASE/($y->[-1]+1))) != 1) |
518 | { |
519 | for $xi (@$x) |
520 | { |
521 | $xi = $xi * $dd + $car; |
522 | $xi -= ($car = int($xi / $BASE)) * $BASE; |
523 | } |
524 | push(@$x, $car); $car = 0; |
525 | for $yi (@$y) |
526 | { |
527 | $yi = $yi * $dd + $car; |
528 | $yi -= ($car = int($yi / $BASE)) * $BASE; |
529 | } |
530 | } |
531 | else |
532 | { |
533 | push(@$x, 0); |
534 | } |
535 | @q = (); ($v2,$v1) = @$y[-2,-1]; |
536 | $v2 = 0 unless $v2; |
537 | while ($#$x > $#$y) |
538 | { |
539 | ($u2,$u1,$u0) = @$x[-3..-1]; |
540 | $u2 = 0 unless $u2; |
541 | #warn "oups v1 is 0, u0: $u0 $y->[-2] $y->[-1] l ",scalar @$y,"\n" |
542 | # if $v1 == 0; |
543 | # $q = (($u0 == $v1) ? 99999 : int(($u0*$BASE+$u1)/$v1)); |
544 | $q = (($u0 == $v1) ? $MAX_VAL : int(($u0*$BASE+$u1)/$v1)); |
545 | --$q while ($v2*$q > ($u0*$BASE+$u1-$q*$v1)*$BASE+$u2); |
546 | if ($q) |
547 | { |
548 | ($car, $bar) = (0,0); |
549 | for ($yi = 0, $xi = $#$x-$#$y-1; $yi <= $#$y; ++$yi,++$xi) |
550 | { |
551 | $prd = $q * $y->[$yi] + $car; |
552 | $prd -= ($car = int($prd / $BASE)) * $BASE; |
553 | $x->[$xi] += $BASE if ($bar = (($x->[$xi] -= $prd + $bar) < 0)); |
554 | } |
555 | if ($x->[-1] < $car + $bar) |
556 | { |
557 | $car = 0; --$q; |
558 | for ($yi = 0, $xi = $#$x-$#$y-1; $yi <= $#$y; ++$yi,++$xi) |
559 | { |
560 | $x->[$xi] -= $BASE |
561 | if ($car = (($x->[$xi] += $y->[$yi] + $car) > $BASE)); |
562 | } |
563 | } |
564 | } |
565 | pop(@$x); unshift(@q, $q); |
566 | } |
567 | if (wantarray) |
568 | { |
569 | @d = (); |
570 | if ($dd != 1) |
571 | { |
572 | $car = 0; |
573 | for $xi (reverse @$x) |
574 | { |
575 | $prd = $car * $BASE + $xi; |
576 | $car = $prd - ($tmp = int($prd / $dd)) * $dd; |
577 | unshift(@d, $tmp); |
578 | } |
579 | } |
580 | else |
581 | { |
582 | @d = @$x; |
583 | } |
584 | @$x = @q; |
585 | __strip_zeros($x); |
586 | __strip_zeros(\@d); |
587 | return ($x,\@d); |
588 | } |
589 | @$x = @q; |
590 | __strip_zeros($x); |
ee15d750 |
591 | } |
592 | |
394e6ffb |
593 | ############################################################################## |
594 | # testing |
595 | |
596 | sub _acmp |
597 | { |
598 | # internal absolute post-normalized compare (ignore signs) |
599 | # ref to array, ref to array, return <0, 0, >0 |
600 | # arrays must have at least one entry; this is not checked for |
601 | |
602 | my ($c,$cx,$cy) = @_; |
603 | |
604 | # fat comp based on array elements |
605 | my $lxy = scalar @$cx - scalar @$cy; |
606 | return -1 if $lxy < 0; # already differs, ret |
607 | return 1 if $lxy > 0; # ditto |
608 | |
609 | # now calculate length based on digits, not parts |
610 | $lxy = _len($c,$cx) - _len($c,$cy); # difference |
611 | return -1 if $lxy < 0; |
612 | return 1 if $lxy > 0; |
613 | |
614 | # hm, same lengths, but same contents? |
615 | my $i = 0; my $a; |
616 | # first way takes 5.49 sec instead of 4.87, but has the early out advantage |
617 | # so grep is slightly faster, but more inflexible. hm. $_ instead of $k |
618 | # yields 5.6 instead of 5.5 sec huh? |
619 | # manual way (abort if unequal, good for early ne) |
620 | my $j = scalar @$cx - 1; |
621 | while ($j >= 0) |
622 | { |
623 | last if ($a = $cx->[$j] - $cy->[$j]); $j--; |
624 | } |
625 | return 1 if $a > 0; |
626 | return -1 if $a < 0; |
627 | return 0; # equal |
628 | # while it early aborts, it is even slower than the manual variant |
629 | #grep { return $a if ($a = $_ - $cy->[$i++]); } @$cx; |
630 | # grep way, go trough all (bad for early ne) |
631 | #grep { $a = $_ - $cy->[$i++]; } @$cx; |
632 | #return $a; |
633 | } |
634 | |
635 | sub _len |
636 | { |
637 | # compute number of digits in bigint, minus the sign |
638 | |
639 | # int() because add/sub sometimes leaves strings (like '00005') instead of |
640 | # '5' in this place, thus causing length() to report wrong length |
641 | my $cx = $_[1]; |
642 | |
643 | return (@$cx-1)*$BASE_LEN+length(int($cx->[-1])); |
644 | } |
645 | |
646 | sub _digit |
647 | { |
648 | # return the nth digit, negative values count backward |
649 | # zero is rightmost, so _digit(123,0) will give 3 |
650 | my ($c,$x,$n) = @_; |
651 | |
652 | my $len = _len('',$x); |
653 | |
654 | $n = $len+$n if $n < 0; # -1 last, -2 second-to-last |
655 | $n = abs($n); # if negative was too big |
656 | $len--; $n = $len if $n > $len; # n to big? |
657 | |
658 | my $elem = int($n / $BASE_LEN); # which array element |
659 | my $digit = $n % $BASE_LEN; # which digit in this element |
660 | $elem = '0000'.@$x[$elem]; # get element padded with 0's |
661 | return substr($elem,-$digit-1,1); |
662 | } |
663 | |
664 | sub _zeros |
665 | { |
666 | # return amount of trailing zeros in decimal |
667 | # check each array elem in _m for having 0 at end as long as elem == 0 |
668 | # Upon finding a elem != 0, stop |
669 | my $x = $_[1]; |
670 | my $zeros = 0; my $elem; |
671 | foreach my $e (@$x) |
672 | { |
673 | if ($e != 0) |
674 | { |
675 | $elem = "$e"; # preserve x |
676 | $elem =~ s/.*?(0*$)/$1/; # strip anything not zero |
677 | $zeros *= $BASE_LEN; # elems * 5 |
678 | $zeros += CORE::length($elem); # count trailing zeros |
679 | last; # early out |
680 | } |
681 | $zeros ++; # real else branch: 50% slower! |
682 | } |
683 | return $zeros; |
684 | } |
685 | |
686 | ############################################################################## |
687 | # _is_* routines |
688 | |
689 | sub _is_zero |
690 | { |
691 | # return true if arg (BINT or num_str) is zero (array '+', '0') |
692 | my $x = $_[1]; |
693 | return (((scalar @$x == 1) && ($x->[0] == 0))) <=> 0; |
694 | } |
695 | |
696 | sub _is_even |
697 | { |
698 | # return true if arg (BINT or num_str) is even |
699 | my $x = $_[1]; |
700 | return (!($x->[0] & 1)) <=> 0; |
701 | } |
702 | |
703 | sub _is_odd |
704 | { |
705 | # return true if arg (BINT or num_str) is even |
706 | my $x = $_[1]; |
707 | return (($x->[0] & 1)) <=> 0; |
708 | } |
709 | |
710 | sub _is_one |
711 | { |
712 | # return true if arg (BINT or num_str) is one (array '+', '1') |
713 | my $x = $_[1]; |
714 | return (scalar @$x == 1) && ($x->[0] == 1) <=> 0; |
715 | } |
716 | |
717 | sub __strip_zeros |
718 | { |
719 | # internal normalization function that strips leading zeros from the array |
720 | # args: ref to array |
721 | my $s = shift; |
722 | |
723 | my $cnt = scalar @$s; # get count of parts |
724 | my $i = $cnt-1; |
725 | push @$s,0 if $i < 0; # div might return empty results, so fix it |
726 | |
727 | #print "strip: cnt $cnt i $i\n"; |
728 | # '0', '3', '4', '0', '0', |
729 | # 0 1 2 3 4 |
730 | # cnt = 5, i = 4 |
731 | # i = 4 |
732 | # i = 3 |
733 | # => fcnt = cnt - i (5-2 => 3, cnt => 5-1 = 4, throw away from 4th pos) |
734 | # >= 1: skip first part (this can be zero) |
735 | while ($i > 0) { last if $s->[$i] != 0; $i--; } |
736 | $i++; splice @$s,$i if ($i < $cnt); # $i cant be 0 |
737 | $s; |
738 | } |
739 | |
740 | ############################################################################### |
741 | # check routine to test internal state of corruptions |
742 | |
743 | sub _check |
744 | { |
745 | # used by the test suite |
746 | my $x = $_[1]; |
747 | |
748 | return "$x is not a reference" if !ref($x); |
749 | |
750 | # are all parts are valid? |
751 | my $i = 0; my $j = scalar @$x; my ($e,$try); |
752 | while ($i < $j) |
753 | { |
754 | $e = $x->[$i]; $e = 'undef' unless defined $e; |
755 | $try = '=~ /^[\+]?[0-9]+\$/; '."($x, $e)"; |
756 | last if $e !~ /^[+]?[0-9]+$/; |
757 | $try = '=~ /^[\+]?[0-9]+\$/; '."($x, $e) (stringify)"; |
758 | last if "$e" !~ /^[+]?[0-9]+$/; |
759 | $try = '=~ /^[\+]?[0-9]+\$/; '."($x, $e) (cat-stringify)"; |
760 | last if '' . "$e" !~ /^[+]?[0-9]+$/; |
761 | $try = ' < 0 || >= $BASE; '."($x, $e)"; |
762 | last if $e <0 || $e >= $BASE; |
763 | # this test is disabled, since new/bnorm and certain ops (like early out |
764 | # in add/sub) are allowed/expected to leave '00000' in some elements |
765 | #$try = '=~ /^00+/; '."($x, $e)"; |
766 | #last if $e =~ /^00+/; |
767 | $i++; |
768 | } |
769 | return "Illegal part '$e' at pos $i (tested: $try)" if $i < $j; |
770 | return 0; |
771 | } |
772 | |
773 | |
774 | ############################################################################### |
775 | ############################################################################### |
776 | # some optional routines to make BigInt faster |
777 | |
dccbb853 |
778 | sub _mod |
779 | { |
780 | # if possible, use mod shortcut |
781 | my ($c,$x,$yo) = @_; |
782 | |
783 | # slow way since $y to big |
784 | if (scalar @$yo > 1) |
785 | { |
786 | my ($xo,$rem) = _div($c,$x,$yo); |
787 | return $rem; |
788 | } |
789 | my $y = $yo->[0]; |
027dc388 |
790 | # both are single element arrays |
dccbb853 |
791 | if (scalar @$x == 1) |
792 | { |
793 | $x->[0] %= $y; |
794 | return $x; |
795 | } |
796 | |
027dc388 |
797 | # @y is single element, but @x has more than one |
dccbb853 |
798 | my $b = $BASE % $y; |
799 | if ($b == 0) |
800 | { |
801 | # when BASE % Y == 0 then (B * BASE) % Y == 0 |
802 | # (B * BASE) % $y + A % Y => A % Y |
803 | # so need to consider only last element: O(1) |
804 | $x->[0] %= $y; |
805 | } |
027dc388 |
806 | elsif ($b == 1) |
807 | { |
808 | # else need to go trough all elements: O(N), but loop is a bit simplified |
809 | my $r = 0; |
810 | foreach (@$x) |
811 | { |
812 | $r += $_ % $y; |
813 | $r %= $y; |
814 | } |
815 | $r = 0 if $r == $y; |
816 | $x->[0] = $r; |
817 | } |
dccbb853 |
818 | else |
819 | { |
027dc388 |
820 | # else need to go trough all elements: O(N) |
821 | my $r = 0; my $bm = 1; |
822 | foreach (@$x) |
823 | { |
824 | $r += ($_ % $y) * $bm; |
825 | $bm *= $b; |
826 | $bm %= $y; |
827 | $r %= $y; |
828 | } |
829 | $r = 0 if $r == $y; |
830 | $x->[0] = $r; |
dccbb853 |
831 | } |
832 | splice (@$x,1); |
833 | return $x; |
834 | } |
835 | |
0716bf9b |
836 | ############################################################################## |
574bacfe |
837 | # shifts |
838 | |
839 | sub _rsft |
840 | { |
841 | my ($c,$x,$y,$n) = @_; |
842 | |
843 | if ($n != 10) |
844 | { |
845 | return; # we cant do this here, due to now _pow, so signal failure |
846 | } |
847 | else |
848 | { |
849 | # shortcut (faster) for shifting by 10) |
850 | # multiples of $BASE_LEN |
851 | my $dst = 0; # destination |
852 | my $src = _num($c,$y); # as normal int |
dccbb853 |
853 | my $rem = $src % $BASE_LEN; # remainder to shift |
574bacfe |
854 | $src = int($src / $BASE_LEN); # source |
855 | if ($rem == 0) |
856 | { |
857 | splice (@$x,0,$src); # even faster, 38.4 => 39.3 |
858 | } |
859 | else |
860 | { |
861 | my $len = scalar @$x - $src; # elems to go |
862 | my $vd; my $z = '0'x $BASE_LEN; |
863 | $x->[scalar @$x] = 0; # avoid || 0 test inside loop |
864 | while ($dst < $len) |
865 | { |
866 | $vd = $z.$x->[$src]; |
574bacfe |
867 | $vd = substr($vd,-$BASE_LEN,$BASE_LEN-$rem); |
574bacfe |
868 | $src++; |
869 | $vd = substr($z.$x->[$src],-$rem,$rem) . $vd; |
574bacfe |
870 | $vd = substr($vd,-$BASE_LEN,$BASE_LEN) if length($vd) > $BASE_LEN; |
871 | $x->[$dst] = int($vd); |
872 | $dst++; |
873 | } |
874 | splice (@$x,$dst) if $dst > 0; # kill left-over array elems |
875 | pop @$x if $x->[-1] == 0; # kill last element if 0 |
876 | } # else rem == 0 |
877 | } |
878 | $x; |
879 | } |
880 | |
881 | sub _lsft |
882 | { |
883 | my ($c,$x,$y,$n) = @_; |
884 | |
885 | if ($n != 10) |
886 | { |
887 | return; # we cant do this here, due to now _pow, so signal failure |
888 | } |
889 | else |
890 | { |
891 | # shortcut (faster) for shifting by 10) since we are in base 10eX |
892 | # multiples of $BASE_LEN: |
893 | my $src = scalar @$x; # source |
894 | my $len = _num($c,$y); # shift-len as normal int |
dccbb853 |
895 | my $rem = $len % $BASE_LEN; # remainder to shift |
574bacfe |
896 | my $dst = $src + int($len/$BASE_LEN); # destination |
897 | my $vd; # further speedup |
574bacfe |
898 | $x->[$src] = 0; # avoid first ||0 for speed |
899 | my $z = '0' x $BASE_LEN; |
900 | while ($src >= 0) |
901 | { |
902 | $vd = $x->[$src]; $vd = $z.$vd; |
574bacfe |
903 | $vd = substr($vd,-$BASE_LEN+$rem,$BASE_LEN-$rem); |
574bacfe |
904 | $vd .= $src > 0 ? substr($z.$x->[$src-1],-$BASE_LEN,$rem) : '0' x $rem; |
574bacfe |
905 | $vd = substr($vd,-$BASE_LEN,$BASE_LEN) if length($vd) > $BASE_LEN; |
574bacfe |
906 | $x->[$dst] = int($vd); |
907 | $dst--; $src--; |
908 | } |
909 | # set lowest parts to 0 |
910 | while ($dst >= 0) { $x->[$dst--] = 0; } |
911 | # fix spurios last zero element |
912 | splice @$x,-1 if $x->[-1] == 0; |
574bacfe |
913 | } |
914 | $x; |
915 | } |
916 | |
027dc388 |
917 | sub _pow |
918 | { |
919 | # power of $x to $y |
920 | # ref to array, ref to array, return ref to array |
921 | my ($c,$cx,$cy) = @_; |
922 | |
923 | my $pow2 = _one(); |
924 | my $two = _two(); |
925 | my $y1 = _copy($c,$cy); |
926 | while (!_is_one($c,$y1)) |
927 | { |
928 | _mul($c,$pow2,$cx) if _is_odd($c,$y1); |
929 | _div($c,$y1,$two); |
930 | _mul($c,$cx,$cx); |
931 | } |
932 | _mul($c,$cx,$pow2) unless _is_one($c,$pow2); |
933 | return $cx; |
934 | } |
935 | |
394e6ffb |
936 | sub _sqrt |
0716bf9b |
937 | { |
394e6ffb |
938 | # square-root of $x |
939 | # ref to array, return ref to array |
940 | my ($c,$x) = @_; |
0716bf9b |
941 | |
394e6ffb |
942 | if (scalar @$x == 1) |
943 | { |
944 | # fit's into one Perl scalar |
945 | $x->[0] = int(sqrt($x->[0])); |
946 | return $x; |
947 | } |
948 | my $y = _copy($c,$x); |
949 | my $l = [ _len($c,$x) / 2 ]; |
0716bf9b |
950 | |
394e6ffb |
951 | splice @$x,0; $x->[0] = 1; # keep ref($x), but modify it |
0716bf9b |
952 | |
394e6ffb |
953 | _lsft($c,$x,$l,10); |
0716bf9b |
954 | |
394e6ffb |
955 | my $two = _two(); |
956 | my $last = _zero(); |
957 | my $lastlast = _zero(); |
958 | while (_acmp($c,$last,$x) != 0 && _acmp($c,$lastlast,$x) != 0) |
959 | { |
960 | $lastlast = _copy($c,$last); |
961 | $last = _copy($c,$x); |
962 | _add($c,$x, _div($c,_copy($c,$y),$x)); |
963 | _div($c,$x, $two ); |
964 | } |
965 | _dec($c,$x) if _acmp($c,$y,_mul($c,_copy($c,$x),$x)) < 0; # overshot? |
966 | $x; |
0716bf9b |
967 | } |
968 | |
394e6ffb |
969 | ############################################################################## |
970 | # binary stuff |
0716bf9b |
971 | |
394e6ffb |
972 | sub _and |
973 | { |
974 | my ($c,$x,$y) = @_; |
0716bf9b |
975 | |
394e6ffb |
976 | # the shortcut makes equal, large numbers _really_ fast, and makes only a |
977 | # very small performance drop for small numbers (e.g. something with less |
978 | # than 32 bit) Since we optimize for large numbers, this is enabled. |
979 | return $x if _acmp($c,$x,$y) == 0; # shortcut |
0716bf9b |
980 | |
394e6ffb |
981 | my $m = _one(); my ($xr,$yr); |
982 | my $mask = $AND_MASK; |
983 | |
984 | my $x1 = $x; |
985 | my $y1 = _copy($c,$y); # make copy |
986 | $x = _zero(); |
987 | my ($b,$xrr,$yrr); |
988 | use integer; |
989 | while (!_is_zero($c,$x1) && !_is_zero($c,$y1)) |
990 | { |
991 | ($x1, $xr) = _div($c,$x1,$mask); |
992 | ($y1, $yr) = _div($c,$y1,$mask); |
993 | |
994 | # make ints() from $xr, $yr |
995 | # this is when the AND_BITS are greater tahn $BASE and is slower for |
996 | # small (<256 bits) numbers, but faster for large numbers. Disabled |
997 | # due to KISS principle |
998 | |
999 | # $b = 1; $xrr = 0; foreach (@$xr) { $xrr += $_ * $b; $b *= $BASE; } |
1000 | # $b = 1; $yrr = 0; foreach (@$yr) { $yrr += $_ * $b; $b *= $BASE; } |
1001 | # _add($c,$x, _mul($c, _new( $c, \($xrr & $yrr) ), $m) ); |
1002 | |
1003 | _add($c,$x, _mul($c, [ $xr->[0] & $yr->[0] ], $m) ); |
1004 | _mul($c,$m,$mask); |
1005 | } |
1006 | $x; |
0716bf9b |
1007 | } |
1008 | |
394e6ffb |
1009 | sub _xor |
0716bf9b |
1010 | { |
394e6ffb |
1011 | my ($c,$x,$y) = @_; |
1012 | |
1013 | return _zero() if _acmp($c,$x,$y) == 0; # shortcut (see -and) |
1014 | |
1015 | my $m = _one(); my ($xr,$yr); |
1016 | my $mask = $XOR_MASK; |
1017 | |
1018 | my $x1 = $x; |
1019 | my $y1 = _copy($c,$y); # make copy |
1020 | $x = _zero(); |
1021 | my ($b,$xrr,$yrr); |
1022 | use integer; |
1023 | while (!_is_zero($c,$x1) && !_is_zero($c,$y1)) |
0716bf9b |
1024 | { |
394e6ffb |
1025 | ($x1, $xr) = _div($c,$x1,$mask); |
1026 | ($y1, $yr) = _div($c,$y1,$mask); |
1027 | # make ints() from $xr, $yr (see _and()) |
1028 | #$b = 1; $xrr = 0; foreach (@$xr) { $xrr += $_ * $b; $b *= $BASE; } |
1029 | #$b = 1; $yrr = 0; foreach (@$yr) { $yrr += $_ * $b; $b *= $BASE; } |
1030 | #_add($c,$x, _mul($c, _new( $c, \($xrr ^ $yrr) ), $m) ); |
1031 | |
1032 | _add($c,$x, _mul($c, [ $xr->[0] ^ $yr->[0] ], $m) ); |
1033 | _mul($c,$m,$mask); |
0716bf9b |
1034 | } |
394e6ffb |
1035 | # the loop stops when the shorter of the two numbers is exhausted |
1036 | # the remainder of the longer one will survive bit-by-bit, so we simple |
1037 | # multiply-add it in |
1038 | _add($c,$x, _mul($c, $x1, $m) ) if !_is_zero($c,$x1); |
1039 | _add($c,$x, _mul($c, $y1, $m) ) if !_is_zero($c,$y1); |
1040 | |
1041 | $x; |
0716bf9b |
1042 | } |
1043 | |
394e6ffb |
1044 | sub _or |
0716bf9b |
1045 | { |
394e6ffb |
1046 | my ($c,$x,$y) = @_; |
0716bf9b |
1047 | |
394e6ffb |
1048 | return $x if _acmp($c,$x,$y) == 0; # shortcut (see _and) |
0716bf9b |
1049 | |
394e6ffb |
1050 | my $m = _one(); my ($xr,$yr); |
1051 | my $mask = $OR_MASK; |
0716bf9b |
1052 | |
394e6ffb |
1053 | my $x1 = $x; |
1054 | my $y1 = _copy($c,$y); # make copy |
1055 | $x = _zero(); |
1056 | my ($b,$xrr,$yrr); |
1057 | use integer; |
1058 | while (!_is_zero($c,$x1) && !_is_zero($c,$y1)) |
1059 | { |
1060 | ($x1, $xr) = _div($c,$x1,$mask); |
1061 | ($y1, $yr) = _div($c,$y1,$mask); |
1062 | # make ints() from $xr, $yr (see _and()) |
1063 | # $b = 1; $xrr = 0; foreach (@$xr) { $xrr += $_ * $b; $b *= $BASE; } |
1064 | # $b = 1; $yrr = 0; foreach (@$yr) { $yrr += $_ * $b; $b *= $BASE; } |
1065 | # _add($c,$x, _mul($c, _new( $c, \($xrr | $yrr) ), $m) ); |
1066 | |
1067 | _add($c,$x, _mul($c, [ $xr->[0] | $yr->[0] ], $m) ); |
1068 | _mul($c,$m,$mask); |
1069 | } |
1070 | # the loop stops when the shorter of the two numbers is exhausted |
1071 | # the remainder of the longer one will survive bit-by-bit, so we simple |
1072 | # multiply-add it in |
1073 | _add($c,$x, _mul($c, $x1, $m) ) if !_is_zero($c,$x1); |
1074 | _add($c,$x, _mul($c, $y1, $m) ) if !_is_zero($c,$y1); |
1075 | |
1076 | $x; |
0716bf9b |
1077 | } |
1078 | |
394e6ffb |
1079 | sub _from_hex |
0716bf9b |
1080 | { |
394e6ffb |
1081 | # convert a hex number to decimal (ref to string, return ref to array) |
1082 | my ($c,$hs) = @_; |
0716bf9b |
1083 | |
394e6ffb |
1084 | my $mul = _one(); |
1085 | my $m = [ 0x10000 ]; # 16 bit at a time |
1086 | my $x = _zero(); |
0716bf9b |
1087 | |
394e6ffb |
1088 | my $len = CORE::length($$hs)-2; |
1089 | $len = int($len/4); # 4-digit parts, w/o '0x' |
1090 | my $val; my $i = -4; |
1091 | while ($len >= 0) |
1092 | { |
1093 | $val = substr($$hs,$i,4); |
1094 | $val =~ s/^[+-]?0x// if $len == 0; # for last part only because |
1095 | $val = hex($val); # hex does not like wrong chars |
1096 | $i -= 4; $len --; |
1097 | _add ($c, $x, _mul ($c, [ $val ], $mul ) ) if $val != 0; |
1098 | _mul ($c, $mul, $m ) if $len >= 0; # skip last mul |
1099 | } |
1100 | $x; |
1101 | } |
1102 | |
1103 | sub _from_bin |
0716bf9b |
1104 | { |
394e6ffb |
1105 | # convert a hex number to decimal (ref to string, return ref to array) |
1106 | my ($c,$bs) = @_; |
0716bf9b |
1107 | |
394e6ffb |
1108 | my $mul = _one(); |
1109 | my $m = [ 0x100 ]; # 8 bit at a time |
1110 | my $x = _zero(); |
0716bf9b |
1111 | |
394e6ffb |
1112 | my $len = CORE::length($$bs)-2; |
1113 | $len = int($len/8); # 4-digit parts, w/o '0x' |
1114 | my $val; my $i = -8; |
1115 | while ($len >= 0) |
0716bf9b |
1116 | { |
394e6ffb |
1117 | $val = substr($$bs,$i,8); |
1118 | $val =~ s/^[+-]?0b// if $len == 0; # for last part only |
1119 | |
1120 | #$val = oct('0b'.$val); # does not work on Perl prior to 5.6.0 |
1121 | # $val = ('0' x (8-CORE::length($val))).$val if CORE::length($val) < 8; |
1122 | $val = ord(pack('B8',substr('00000000'.$val,-8,8))); |
1123 | |
1124 | $i -= 8; $len --; |
1125 | _add ($c, $x, _mul ($c, [ $val ], $mul ) ) if $val != 0; |
1126 | _mul ($c, $mul, $m ) if $len >= 0; # skip last mul |
0716bf9b |
1127 | } |
394e6ffb |
1128 | $x; |
0716bf9b |
1129 | } |
1130 | |
394e6ffb |
1131 | ############################################################################## |
1132 | ############################################################################## |
1133 | |
0716bf9b |
1134 | 1; |
1135 | __END__ |
1136 | |
1137 | =head1 NAME |
1138 | |
1139 | Math::BigInt::Calc - Pure Perl module to support Math::BigInt |
1140 | |
1141 | =head1 SYNOPSIS |
1142 | |
ee15d750 |
1143 | Provides support for big integer calculations. Not intended to be used by other |
1144 | modules (except Math::BigInt::Cached). Other modules which sport the same |
1145 | functions can also be used to support Math::Bigint, like Math::BigInt::Pari. |
0716bf9b |
1146 | |
1147 | =head1 DESCRIPTION |
1148 | |
027dc388 |
1149 | In order to allow for multiple big integer libraries, Math::BigInt was |
1150 | rewritten to use library modules for core math routines. Any module which |
1151 | follows the same API as this can be used instead by using the following: |
0716bf9b |
1152 | |
ee15d750 |
1153 | use Math::BigInt lib => 'libname'; |
0716bf9b |
1154 | |
027dc388 |
1155 | 'libname' is either the long name ('Math::BigInt::Pari'), or only the short |
1156 | version like 'Pari'. |
1157 | |
0716bf9b |
1158 | =head1 EXPORT |
1159 | |
027dc388 |
1160 | The following functions MUST be defined in order to support the use by |
1161 | Math::BigInt: |
0716bf9b |
1162 | |
1163 | _new(string) return ref to new object from ref to decimal string |
1164 | _zero() return a new object with value 0 |
1165 | _one() return a new object with value 1 |
1166 | |
1167 | _str(obj) return ref to a string representing the object |
1168 | _num(obj) returns a Perl integer/floating point number |
1169 | NOTE: because of Perl numeric notation defaults, |
1170 | the _num'ified obj may lose accuracy due to |
1171 | machine-dependend floating point size limitations |
1172 | |
1173 | _add(obj,obj) Simple addition of two objects |
1174 | _mul(obj,obj) Multiplication of two objects |
1175 | _div(obj,obj) Division of the 1st object by the 2nd |
b22b3e31 |
1176 | In list context, returns (result,remainder). |
1177 | NOTE: this is integer math, so no |
1178 | fractional part will be returned. |
1179 | _sub(obj,obj) Simple subtraction of 1 object from another |
0716bf9b |
1180 | a third, optional parameter indicates that the params |
1181 | are swapped. In this case, the first param needs to |
1182 | be preserved, while you can destroy the second. |
1183 | sub (x,y,1) => return x - y and keep x intact! |
e745a66c |
1184 | _dec(obj) decrement object by one (input is garant. to be > 0) |
1185 | _inc(obj) increment object by one |
1186 | |
0716bf9b |
1187 | |
1188 | _acmp(obj,obj) <=> operator for objects (return -1, 0 or 1) |
1189 | |
1190 | _len(obj) returns count of the decimal digits of the object |
1191 | _digit(obj,n) returns the n'th decimal digit of object |
1192 | |
1193 | _is_one(obj) return true if argument is +1 |
1194 | _is_zero(obj) return true if argument is 0 |
1195 | _is_even(obj) return true if argument is even (0,2,4,6..) |
1196 | _is_odd(obj) return true if argument is odd (1,3,5,7..) |
1197 | |
1198 | _copy return a ref to a true copy of the object |
1199 | |
1200 | _check(obj) check whether internal representation is still intact |
1201 | return 0 for ok, otherwise error message as string |
1202 | |
bd05a461 |
1203 | The following functions are optional, and can be defined if the underlying lib |
027dc388 |
1204 | has a fast way to do them. If undefined, Math::BigInt will use pure Perl (hence |
1205 | slow) fallback routines to emulate these: |
0716bf9b |
1206 | |
1207 | _from_hex(str) return ref to new object from ref to hexadecimal string |
1208 | _from_bin(str) return ref to new object from ref to binary string |
1209 | |
ee15d750 |
1210 | _as_hex(str) return ref to scalar string containing the value as |
1211 | unsigned hex string, with the '0x' prepended. |
1212 | Leading zeros must be stripped. |
1213 | _as_bin(str) Like as_hex, only as binary string containing only |
1214 | zeros and ones. Leading zeros must be stripped and a |
1215 | '0b' must be prepended. |
1216 | |
0716bf9b |
1217 | _rsft(obj,N,B) shift object in base B by N 'digits' right |
dccbb853 |
1218 | For unsupported bases B, return undef to signal failure |
0716bf9b |
1219 | _lsft(obj,N,B) shift object in base B by N 'digits' left |
dccbb853 |
1220 | For unsupported bases B, return undef to signal failure |
0716bf9b |
1221 | |
1222 | _xor(obj1,obj2) XOR (bit-wise) object 1 with object 2 |
dccbb853 |
1223 | Note: XOR, AND and OR pad with zeros if size mismatches |
0716bf9b |
1224 | _and(obj1,obj2) AND (bit-wise) object 1 with object 2 |
1225 | _or(obj1,obj2) OR (bit-wise) object 1 with object 2 |
1226 | |
dccbb853 |
1227 | _mod(obj,obj) Return remainder of div of the 1st by the 2nd object |
394e6ffb |
1228 | _sqrt(obj) return the square root of object (truncate to int) |
0716bf9b |
1229 | _pow(obj,obj) return object 1 to the power of object 2 |
1230 | _gcd(obj,obj) return Greatest Common Divisor of two objects |
1231 | |
b22b3e31 |
1232 | _zeros(obj) return number of trailing decimal zeros |
0716bf9b |
1233 | |
b22b3e31 |
1234 | Input strings come in as unsigned but with prefix (i.e. as '123', '0xabc' |
0716bf9b |
1235 | or '0b1101'). |
1236 | |
b22b3e31 |
1237 | Testing of input parameter validity is done by the caller, so you need not |
574bacfe |
1238 | worry about underflow (f.i. in C<_sub()>, C<_dec()>) nor about division by |
1239 | zero or similar cases. |
1240 | |
1241 | The first parameter can be modified, that includes the possibility that you |
1242 | return a reference to a completely different object instead. Although keeping |
dccbb853 |
1243 | the reference and just changing it's contents is prefered over creating and |
1244 | returning a different reference. |
574bacfe |
1245 | |
1246 | Return values are always references to objects or strings. Exceptions are |
1247 | C<_lsft()> and C<_rsft()>, which return undef if they can not shift the |
027dc388 |
1248 | argument. This is used to delegate shifting of bases different than the one |
1249 | you can support back to Math::BigInt, which will use some generic code to |
1250 | calculate the result. |
574bacfe |
1251 | |
1252 | =head1 WRAP YOUR OWN |
1253 | |
1254 | If you want to port your own favourite c-lib for big numbers to the |
1255 | Math::BigInt interface, you can take any of the already existing modules as |
1256 | a rough guideline. You should really wrap up the latest BigInt and BigFloat |
bd05a461 |
1257 | testsuites with your module, and replace in them any of the following: |
574bacfe |
1258 | |
1259 | use Math::BigInt; |
1260 | |
bd05a461 |
1261 | by this: |
574bacfe |
1262 | |
1263 | use Math::BigInt lib => 'yourlib'; |
1264 | |
1265 | This way you ensure that your library really works 100% within Math::BigInt. |
0716bf9b |
1266 | |
1267 | =head1 LICENSE |
1268 | |
1269 | This program is free software; you may redistribute it and/or modify it under |
1270 | the same terms as Perl itself. |
1271 | |
1272 | =head1 AUTHORS |
1273 | |
1274 | Original math code by Mark Biggar, rewritten by Tels L<http://bloodgate.com/> |
1275 | in late 2000, 2001. |
1276 | Seperated from BigInt and shaped API with the help of John Peacock. |
1277 | |
1278 | =head1 SEE ALSO |
1279 | |
ee15d750 |
1280 | L<Math::BigInt>, L<Math::BigFloat>, L<Math::BigInt::BitVect>, |
1281 | L<Math::BigInt::GMP>, L<Math::BigInt::Cached> and L<Math::BigInt::Pari>. |
0716bf9b |
1282 | |
1283 | =cut |