Commit | Line | Data |
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; |
bd05a461 |
8 | use vars qw/@ISA $VERSION/; |
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9 | @ISA = qw(Exporter); |
10 | |
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11 | $VERSION = '0.16'; |
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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 $nan = 'NaN'; |
ee15d750 |
33 | my ($BASE,$RBASE,$BASE_LEN,$MAX_VAL); |
34 | |
35 | sub _base_len |
36 | { |
dccbb853 |
37 | # set/get the BASE_LEN and assorted other, connected values |
38 | # used only be the testsuite, set is used only by the BEGIN block below |
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39 | my $b = shift; |
40 | if (defined $b) |
41 | { |
dccbb853 |
42 | $b = 8 if $b > 8; # cap, for VMS, OS/390 and other 64 bit |
ee15d750 |
43 | $BASE_LEN = $b; |
44 | $BASE = int("1e".$BASE_LEN); |
45 | $RBASE = abs('1e-'.$BASE_LEN); # see USE_MUL |
46 | $MAX_VAL = $BASE-1; |
47 | # print "BASE_LEN: $BASE_LEN MAX_VAL: $MAX_VAL\n"; |
48 | # print "int: ",int($BASE * $RBASE),"\n"; |
49 | if (int($BASE * $RBASE) == 0) # should be 1 |
50 | { |
51 | # must USE_MUL |
ee15d750 |
52 | *{_mul} = \&_mul_use_mul; |
53 | *{_div} = \&_div_use_mul; |
54 | } |
55 | else |
56 | { |
ee15d750 |
57 | # can USE_DIV instead |
58 | *{_mul} = \&_mul_use_div; |
59 | *{_div} = \&_div_use_div; |
60 | } |
61 | } |
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62 | $BASE_LEN; |
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63 | } |
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64 | |
65 | BEGIN |
66 | { |
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67 | # from Daniel Pfeiffer: determine largest group of digits that is precisely |
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68 | # multipliable with itself plus carry |
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69 | # Test now changed to expect the proper pattern, not a result off by 1 or 2 |
70 | my ($e, $num) = 3; # lowest value we will use is 3+1-1 = 3 |
bd05a461 |
71 | do |
72 | { |
73 | $num = ('9' x ++$e) + 0; |
574bacfe |
74 | $num *= $num + 1; |
dccbb853 |
75 | # print "$num $e\n"; |
76 | } while ("$num" =~ /9{$e}0{$e}/); # must be a certain pattern |
77 | # last test failed, so retract one step: |
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78 | _base_len($e-1); |
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79 | } |
80 | |
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81 | ############################################################################## |
82 | # create objects from various representations |
83 | |
84 | sub _new |
85 | { |
86 | # (string) return ref to num_array |
87 | # Convert a number from string format to internal base 100000 format. |
88 | # Assumes normalized value as input. |
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89 | my $d = $_[1]; |
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90 | my $il = CORE::length($$d)-1; |
91 | # these leaves '00000' instead of int 0 and will be corrected after any op |
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92 | return [ reverse(unpack("a" . ($il % $BASE_LEN+1) |
93 | . ("a$BASE_LEN" x ($il / $BASE_LEN)), $$d)) ]; |
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94 | } |
95 | |
96 | sub _zero |
97 | { |
98 | # create a zero |
99 | return [ 0 ]; |
100 | } |
101 | |
102 | sub _one |
103 | { |
104 | # create a one |
105 | return [ 1 ]; |
106 | } |
107 | |
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108 | sub _two |
109 | { |
110 | # create a two (for _pow) |
111 | return [ 2 ]; |
112 | } |
113 | |
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114 | sub _copy |
115 | { |
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116 | return [ @{$_[1]} ]; |
0716bf9b |
117 | } |
118 | |
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119 | # catch and throw away |
120 | sub import { } |
121 | |
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122 | ############################################################################## |
123 | # convert back to string and number |
124 | |
125 | sub _str |
126 | { |
127 | # (ref to BINT) return num_str |
128 | # Convert number from internal base 100000 format to string format. |
129 | # internal format is always normalized (no leading zeros, "-0" => "+0") |
574bacfe |
130 | my $ar = $_[1]; |
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131 | my $ret = ""; |
132 | my $l = scalar @$ar; # number of parts |
133 | return $nan if $l < 1; # should not happen |
134 | # handle first one different to strip leading zeros from it (there are no |
135 | # leading zero parts in internal representation) |
136 | $l --; $ret .= $ar->[$l]; $l--; |
137 | # Interestingly, the pre-padd method uses more time |
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138 | # the old grep variant takes longer (14 to 10 sec) |
139 | my $z = '0' x ($BASE_LEN-1); |
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140 | while ($l >= 0) |
141 | { |
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142 | $ret .= substr($z.$ar->[$l],-$BASE_LEN); # fastest way I could think of |
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143 | $l--; |
144 | } |
145 | return \$ret; |
146 | } |
147 | |
148 | sub _num |
149 | { |
150 | # Make a number (scalar int/float) from a BigInt object |
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151 | my $x = $_[1]; |
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152 | return $x->[0] if scalar @$x == 1; # below $BASE |
153 | my $fac = 1; |
154 | my $num = 0; |
155 | foreach (@$x) |
156 | { |
157 | $num += $fac*$_; $fac *= $BASE; |
158 | } |
159 | return $num; |
160 | } |
161 | |
162 | ############################################################################## |
163 | # actual math code |
164 | |
165 | sub _add |
166 | { |
167 | # (ref to int_num_array, ref to int_num_array) |
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168 | # routine to add two base 1eX numbers |
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169 | # stolen from Knuth Vol 2 Algorithm A pg 231 |
b22b3e31 |
170 | # there are separate routines to add and sub as per Knuth pg 233 |
0716bf9b |
171 | # This routine clobbers up array x, but not y. |
172 | |
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173 | my ($c,$x,$y) = @_; |
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174 | |
175 | # for each in Y, add Y to X and carry. If after that, something is left in |
176 | # X, foreach in X add carry to X and then return X, carry |
177 | # Trades one "$j++" for having to shift arrays, $j could be made integer |
b22b3e31 |
178 | # but this would impose a limit to number-length of 2**32. |
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179 | my $i; my $car = 0; my $j = 0; |
180 | for $i (@$y) |
181 | { |
e745a66c |
182 | $x->[$j] -= $BASE if $car = (($x->[$j] += $i + $car) >= $BASE) ? 1 : 0; |
0716bf9b |
183 | $j++; |
184 | } |
185 | while ($car != 0) |
186 | { |
187 | $x->[$j] -= $BASE if $car = (($x->[$j] += $car) >= $BASE) ? 1 : 0; $j++; |
188 | } |
e745a66c |
189 | return $x; |
190 | } |
191 | |
192 | sub _inc |
193 | { |
194 | # (ref to int_num_array, ref to int_num_array) |
195 | # routine to add 1 to a base 1eX numbers |
196 | # This routine clobbers up array x, but not y. |
197 | my ($c,$x) = @_; |
198 | |
199 | for my $i (@$x) |
200 | { |
201 | return $x if (($i += 1) < $BASE); # early out |
202 | $i -= $BASE; |
203 | } |
204 | if ($x->[-1] == 0) # last overflowed |
205 | { |
206 | push @$x,1; # extend |
207 | } |
208 | return $x; |
209 | } |
210 | |
211 | sub _dec |
212 | { |
213 | # (ref to int_num_array, ref to int_num_array) |
214 | # routine to add 1 to a base 1eX numbers |
215 | # This routine clobbers up array x, but not y. |
216 | my ($c,$x) = @_; |
217 | |
218 | for my $i (@$x) |
219 | { |
220 | last if (($i -= 1) >= 0); # early out |
221 | $i = $MAX_VAL; |
222 | } |
223 | pop @$x if $x->[-1] == 0 && @$x > 1; # last overflowed (but leave 0) |
224 | return $x; |
0716bf9b |
225 | } |
226 | |
227 | sub _sub |
228 | { |
229 | # (ref to int_num_array, ref to int_num_array) |
574bacfe |
230 | # subtract base 1eX numbers -- stolen from Knuth Vol 2 pg 232, $x > $y |
b22b3e31 |
231 | # subtract Y from X (X is always greater/equal!) by modifying x in place |
574bacfe |
232 | my ($c,$sx,$sy,$s) = @_; |
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233 | |
234 | my $car = 0; my $i; my $j = 0; |
235 | if (!$s) |
236 | { |
237 | #print "case 2\n"; |
238 | for $i (@$sx) |
239 | { |
240 | last unless defined $sy->[$j] || $car; |
0716bf9b |
241 | $i += $BASE if $car = (($i -= ($sy->[$j] || 0) + $car) < 0); $j++; |
0716bf9b |
242 | } |
243 | # might leave leading zeros, so fix that |
244 | __strip_zeros($sx); |
245 | return $sx; |
246 | } |
247 | else |
248 | { |
249 | #print "case 1 (swap)\n"; |
250 | for $i (@$sx) |
251 | { |
252 | last unless defined $sy->[$j] || $car; |
0716bf9b |
253 | $sy->[$j] += $BASE |
254 | if $car = (($sy->[$j] = $i-($sy->[$j]||0) - $car) < 0); |
0716bf9b |
255 | $j++; |
256 | } |
257 | # might leave leading zeros, so fix that |
258 | __strip_zeros($sy); |
259 | return $sy; |
260 | } |
261 | } |
262 | |
ee15d750 |
263 | sub _mul_use_mul |
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264 | { |
265 | # (BINT, BINT) return nothing |
266 | # multiply two numbers in internal representation |
b22b3e31 |
267 | # modifies first arg, second need not be different from first |
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268 | my ($c,$xv,$yv) = @_; |
dccbb853 |
269 | |
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270 | my @prod = (); my ($prod,$car,$cty,$xi,$yi); |
271 | # since multiplying $x with $x fails, make copy in this case |
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272 | $yv = [@$xv] if "$xv" eq "$yv"; # same references? |
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273 | for $xi (@$xv) |
274 | { |
275 | $car = 0; $cty = 0; |
574bacfe |
276 | |
277 | # slow variant |
278 | # for $yi (@$yv) |
279 | # { |
280 | # $prod = $xi * $yi + ($prod[$cty] || 0) + $car; |
281 | # $prod[$cty++] = |
282 | # $prod - ($car = int($prod * RBASE)) * $BASE; # see USE_MUL |
283 | # } |
284 | # $prod[$cty] += $car if $car; # need really to check for 0? |
285 | # $xi = shift @prod; |
286 | |
287 | # faster variant |
288 | # looping through this if $xi == 0 is silly - so optimize it away! |
289 | $xi = (shift @prod || 0), next if $xi == 0; |
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290 | for $yi (@$yv) |
291 | { |
292 | $prod = $xi * $yi + ($prod[$cty] || 0) + $car; |
574bacfe |
293 | ## this is actually a tad slower |
294 | ## $prod = $prod[$cty]; $prod += ($car + $xi * $yi); # no ||0 here |
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295 | $prod[$cty++] = |
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296 | $prod - ($car = int($prod * $RBASE)) * $BASE; # see USE_MUL |
0716bf9b |
297 | } |
298 | $prod[$cty] += $car if $car; # need really to check for 0? |
027dc388 |
299 | $xi = shift @prod || 0; # || 0 makes v5.005_3 happy |
0716bf9b |
300 | } |
0716bf9b |
301 | push @$xv, @prod; |
302 | __strip_zeros($xv); |
303 | # normalize (handled last to save check for $y->is_zero() |
304 | return $xv; |
305 | } |
306 | |
ee15d750 |
307 | sub _mul_use_div |
308 | { |
309 | # (BINT, BINT) return nothing |
310 | # multiply two numbers in internal representation |
311 | # modifies first arg, second need not be different from first |
312 | my ($c,$xv,$yv) = @_; |
313 | |
314 | my @prod = (); my ($prod,$car,$cty,$xi,$yi); |
315 | # since multiplying $x with $x fails, make copy in this case |
316 | $yv = [@$xv] if "$xv" eq "$yv"; # same references? |
317 | for $xi (@$xv) |
318 | { |
319 | $car = 0; $cty = 0; |
320 | # looping through this if $xi == 0 is silly - so optimize it away! |
321 | $xi = (shift @prod || 0), next if $xi == 0; |
322 | for $yi (@$yv) |
323 | { |
324 | $prod = $xi * $yi + ($prod[$cty] || 0) + $car; |
325 | $prod[$cty++] = |
326 | $prod - ($car = int($prod / $BASE)) * $BASE; |
327 | } |
328 | $prod[$cty] += $car if $car; # need really to check for 0? |
027dc388 |
329 | $xi = shift @prod || 0; # || 0 makes v5.005_3 happy |
ee15d750 |
330 | } |
331 | push @$xv, @prod; |
332 | __strip_zeros($xv); |
333 | # normalize (handled last to save check for $y->is_zero() |
334 | return $xv; |
335 | } |
336 | |
337 | sub _div_use_mul |
0716bf9b |
338 | { |
b22b3e31 |
339 | # ref to array, ref to array, modify first array and return remainder if |
0716bf9b |
340 | # in list context |
b22b3e31 |
341 | # no longer handles sign |
574bacfe |
342 | my ($c,$x,$yorg) = @_; |
0716bf9b |
343 | my ($car,$bar,$prd,$dd,$xi,$yi,@q,$v2,$v1); |
344 | |
345 | my (@d,$tmp,$q,$u2,$u1,$u0); |
346 | |
347 | $car = $bar = $prd = 0; |
348 | |
349 | my $y = [ @$yorg ]; |
350 | if (($dd = int($BASE/($y->[-1]+1))) != 1) |
351 | { |
352 | for $xi (@$x) |
353 | { |
354 | $xi = $xi * $dd + $car; |
355 | $xi -= ($car = int($xi * $RBASE)) * $BASE; # see USE_MUL |
356 | } |
357 | push(@$x, $car); $car = 0; |
358 | for $yi (@$y) |
359 | { |
360 | $yi = $yi * $dd + $car; |
361 | $yi -= ($car = int($yi * $RBASE)) * $BASE; # see USE_MUL |
362 | } |
363 | } |
364 | else |
365 | { |
366 | push(@$x, 0); |
367 | } |
368 | @q = (); ($v2,$v1) = @$y[-2,-1]; |
369 | $v2 = 0 unless $v2; |
370 | while ($#$x > $#$y) |
371 | { |
372 | ($u2,$u1,$u0) = @$x[-3..-1]; |
373 | $u2 = 0 unless $u2; |
374 | #warn "oups v1 is 0, u0: $u0 $y->[-2] $y->[-1] l ",scalar @$y,"\n" |
375 | # if $v1 == 0; |
ee15d750 |
376 | # $q = (($u0 == $v1) ? 99999 : int(($u0*$BASE+$u1)/$v1)); |
377 | $q = (($u0 == $v1) ? $MAX_VAL : int(($u0*$BASE+$u1)/$v1)); |
574bacfe |
378 | --$q while ($v2*$q > ($u0*$BASE+$u1-$q*$v1)*$BASE+$u2); |
0716bf9b |
379 | if ($q) |
380 | { |
381 | ($car, $bar) = (0,0); |
382 | for ($yi = 0, $xi = $#$x-$#$y-1; $yi <= $#$y; ++$yi,++$xi) |
383 | { |
384 | $prd = $q * $y->[$yi] + $car; |
385 | $prd -= ($car = int($prd * $RBASE)) * $BASE; # see USE_MUL |
574bacfe |
386 | $x->[$xi] += $BASE if ($bar = (($x->[$xi] -= $prd + $bar) < 0)); |
0716bf9b |
387 | } |
388 | if ($x->[-1] < $car + $bar) |
389 | { |
390 | $car = 0; --$q; |
391 | for ($yi = 0, $xi = $#$x-$#$y-1; $yi <= $#$y; ++$yi,++$xi) |
392 | { |
574bacfe |
393 | $x->[$xi] -= $BASE |
0716bf9b |
394 | if ($car = (($x->[$xi] += $y->[$yi] + $car) > $BASE)); |
395 | } |
396 | } |
397 | } |
398 | pop(@$x); unshift(@q, $q); |
399 | } |
400 | if (wantarray) |
401 | { |
402 | @d = (); |
403 | if ($dd != 1) |
404 | { |
405 | $car = 0; |
406 | for $xi (reverse @$x) |
407 | { |
408 | $prd = $car * $BASE + $xi; |
409 | $car = $prd - ($tmp = int($prd / $dd)) * $dd; # see USE_MUL |
410 | unshift(@d, $tmp); |
411 | } |
412 | } |
413 | else |
414 | { |
415 | @d = @$x; |
416 | } |
417 | @$x = @q; |
418 | __strip_zeros($x); |
419 | __strip_zeros(\@d); |
420 | return ($x,\@d); |
421 | } |
422 | @$x = @q; |
423 | __strip_zeros($x); |
424 | return $x; |
425 | } |
426 | |
ee15d750 |
427 | sub _div_use_div |
428 | { |
429 | # ref to array, ref to array, modify first array and return remainder if |
430 | # in list context |
431 | # no longer handles sign |
432 | my ($c,$x,$yorg) = @_; |
433 | my ($car,$bar,$prd,$dd,$xi,$yi,@q,$v2,$v1); |
434 | |
435 | my (@d,$tmp,$q,$u2,$u1,$u0); |
436 | |
437 | $car = $bar = $prd = 0; |
438 | |
439 | my $y = [ @$yorg ]; |
440 | if (($dd = int($BASE/($y->[-1]+1))) != 1) |
441 | { |
442 | for $xi (@$x) |
443 | { |
444 | $xi = $xi * $dd + $car; |
445 | $xi -= ($car = int($xi / $BASE)) * $BASE; |
446 | } |
447 | push(@$x, $car); $car = 0; |
448 | for $yi (@$y) |
449 | { |
450 | $yi = $yi * $dd + $car; |
451 | $yi -= ($car = int($yi / $BASE)) * $BASE; |
452 | } |
453 | } |
454 | else |
455 | { |
456 | push(@$x, 0); |
457 | } |
458 | @q = (); ($v2,$v1) = @$y[-2,-1]; |
459 | $v2 = 0 unless $v2; |
460 | while ($#$x > $#$y) |
461 | { |
462 | ($u2,$u1,$u0) = @$x[-3..-1]; |
463 | $u2 = 0 unless $u2; |
464 | #warn "oups v1 is 0, u0: $u0 $y->[-2] $y->[-1] l ",scalar @$y,"\n" |
465 | # if $v1 == 0; |
466 | # $q = (($u0 == $v1) ? 99999 : int(($u0*$BASE+$u1)/$v1)); |
467 | $q = (($u0 == $v1) ? $MAX_VAL : int(($u0*$BASE+$u1)/$v1)); |
468 | --$q while ($v2*$q > ($u0*$BASE+$u1-$q*$v1)*$BASE+$u2); |
469 | if ($q) |
470 | { |
471 | ($car, $bar) = (0,0); |
472 | for ($yi = 0, $xi = $#$x-$#$y-1; $yi <= $#$y; ++$yi,++$xi) |
473 | { |
474 | $prd = $q * $y->[$yi] + $car; |
475 | $prd -= ($car = int($prd / $BASE)) * $BASE; |
476 | $x->[$xi] += $BASE if ($bar = (($x->[$xi] -= $prd + $bar) < 0)); |
477 | } |
478 | if ($x->[-1] < $car + $bar) |
479 | { |
480 | $car = 0; --$q; |
481 | for ($yi = 0, $xi = $#$x-$#$y-1; $yi <= $#$y; ++$yi,++$xi) |
482 | { |
483 | $x->[$xi] -= $BASE |
484 | if ($car = (($x->[$xi] += $y->[$yi] + $car) > $BASE)); |
485 | } |
486 | } |
487 | } |
488 | pop(@$x); unshift(@q, $q); |
489 | } |
490 | if (wantarray) |
491 | { |
492 | @d = (); |
493 | if ($dd != 1) |
494 | { |
495 | $car = 0; |
496 | for $xi (reverse @$x) |
497 | { |
498 | $prd = $car * $BASE + $xi; |
499 | $car = $prd - ($tmp = int($prd / $dd)) * $dd; |
500 | unshift(@d, $tmp); |
501 | } |
502 | } |
503 | else |
504 | { |
505 | @d = @$x; |
506 | } |
507 | @$x = @q; |
508 | __strip_zeros($x); |
509 | __strip_zeros(\@d); |
510 | return ($x,\@d); |
511 | } |
512 | @$x = @q; |
513 | __strip_zeros($x); |
514 | return $x; |
515 | } |
516 | |
dccbb853 |
517 | sub _mod |
518 | { |
519 | # if possible, use mod shortcut |
520 | my ($c,$x,$yo) = @_; |
521 | |
522 | # slow way since $y to big |
523 | if (scalar @$yo > 1) |
524 | { |
525 | my ($xo,$rem) = _div($c,$x,$yo); |
526 | return $rem; |
527 | } |
528 | my $y = $yo->[0]; |
027dc388 |
529 | # both are single element arrays |
dccbb853 |
530 | if (scalar @$x == 1) |
531 | { |
532 | $x->[0] %= $y; |
533 | return $x; |
534 | } |
535 | |
027dc388 |
536 | # @y is single element, but @x has more than one |
dccbb853 |
537 | my $b = $BASE % $y; |
538 | if ($b == 0) |
539 | { |
540 | # when BASE % Y == 0 then (B * BASE) % Y == 0 |
541 | # (B * BASE) % $y + A % Y => A % Y |
542 | # so need to consider only last element: O(1) |
543 | $x->[0] %= $y; |
544 | } |
027dc388 |
545 | elsif ($b == 1) |
546 | { |
547 | # else need to go trough all elements: O(N), but loop is a bit simplified |
548 | my $r = 0; |
549 | foreach (@$x) |
550 | { |
551 | $r += $_ % $y; |
552 | $r %= $y; |
553 | } |
554 | $r = 0 if $r == $y; |
555 | $x->[0] = $r; |
556 | } |
dccbb853 |
557 | else |
558 | { |
027dc388 |
559 | # else need to go trough all elements: O(N) |
560 | my $r = 0; my $bm = 1; |
561 | foreach (@$x) |
562 | { |
563 | $r += ($_ % $y) * $bm; |
564 | $bm *= $b; |
565 | $bm %= $y; |
566 | $r %= $y; |
567 | } |
568 | $r = 0 if $r == $y; |
569 | $x->[0] = $r; |
dccbb853 |
570 | } |
571 | splice (@$x,1); |
572 | return $x; |
573 | } |
574 | |
0716bf9b |
575 | ############################################################################## |
574bacfe |
576 | # shifts |
577 | |
578 | sub _rsft |
579 | { |
580 | my ($c,$x,$y,$n) = @_; |
581 | |
582 | if ($n != 10) |
583 | { |
584 | return; # we cant do this here, due to now _pow, so signal failure |
585 | } |
586 | else |
587 | { |
588 | # shortcut (faster) for shifting by 10) |
589 | # multiples of $BASE_LEN |
590 | my $dst = 0; # destination |
591 | my $src = _num($c,$y); # as normal int |
dccbb853 |
592 | my $rem = $src % $BASE_LEN; # remainder to shift |
574bacfe |
593 | $src = int($src / $BASE_LEN); # source |
594 | if ($rem == 0) |
595 | { |
596 | splice (@$x,0,$src); # even faster, 38.4 => 39.3 |
597 | } |
598 | else |
599 | { |
600 | my $len = scalar @$x - $src; # elems to go |
601 | my $vd; my $z = '0'x $BASE_LEN; |
602 | $x->[scalar @$x] = 0; # avoid || 0 test inside loop |
603 | while ($dst < $len) |
604 | { |
605 | $vd = $z.$x->[$src]; |
574bacfe |
606 | $vd = substr($vd,-$BASE_LEN,$BASE_LEN-$rem); |
574bacfe |
607 | $src++; |
608 | $vd = substr($z.$x->[$src],-$rem,$rem) . $vd; |
574bacfe |
609 | $vd = substr($vd,-$BASE_LEN,$BASE_LEN) if length($vd) > $BASE_LEN; |
610 | $x->[$dst] = int($vd); |
611 | $dst++; |
612 | } |
613 | splice (@$x,$dst) if $dst > 0; # kill left-over array elems |
614 | pop @$x if $x->[-1] == 0; # kill last element if 0 |
615 | } # else rem == 0 |
616 | } |
617 | $x; |
618 | } |
619 | |
620 | sub _lsft |
621 | { |
622 | my ($c,$x,$y,$n) = @_; |
623 | |
624 | if ($n != 10) |
625 | { |
626 | return; # we cant do this here, due to now _pow, so signal failure |
627 | } |
628 | else |
629 | { |
630 | # shortcut (faster) for shifting by 10) since we are in base 10eX |
631 | # multiples of $BASE_LEN: |
632 | my $src = scalar @$x; # source |
633 | my $len = _num($c,$y); # shift-len as normal int |
dccbb853 |
634 | my $rem = $len % $BASE_LEN; # remainder to shift |
574bacfe |
635 | my $dst = $src + int($len/$BASE_LEN); # destination |
636 | my $vd; # further speedup |
574bacfe |
637 | $x->[$src] = 0; # avoid first ||0 for speed |
638 | my $z = '0' x $BASE_LEN; |
639 | while ($src >= 0) |
640 | { |
641 | $vd = $x->[$src]; $vd = $z.$vd; |
574bacfe |
642 | $vd = substr($vd,-$BASE_LEN+$rem,$BASE_LEN-$rem); |
574bacfe |
643 | $vd .= $src > 0 ? substr($z.$x->[$src-1],-$BASE_LEN,$rem) : '0' x $rem; |
574bacfe |
644 | $vd = substr($vd,-$BASE_LEN,$BASE_LEN) if length($vd) > $BASE_LEN; |
574bacfe |
645 | $x->[$dst] = int($vd); |
646 | $dst--; $src--; |
647 | } |
648 | # set lowest parts to 0 |
649 | while ($dst >= 0) { $x->[$dst--] = 0; } |
650 | # fix spurios last zero element |
651 | splice @$x,-1 if $x->[-1] == 0; |
574bacfe |
652 | } |
653 | $x; |
654 | } |
655 | |
027dc388 |
656 | sub _pow |
657 | { |
658 | # power of $x to $y |
659 | # ref to array, ref to array, return ref to array |
660 | my ($c,$cx,$cy) = @_; |
661 | |
662 | my $pow2 = _one(); |
663 | my $two = _two(); |
664 | my $y1 = _copy($c,$cy); |
665 | while (!_is_one($c,$y1)) |
666 | { |
667 | _mul($c,$pow2,$cx) if _is_odd($c,$y1); |
668 | _div($c,$y1,$two); |
669 | _mul($c,$cx,$cx); |
670 | } |
671 | _mul($c,$cx,$pow2) unless _is_one($c,$pow2); |
672 | return $cx; |
673 | } |
674 | |
574bacfe |
675 | ############################################################################## |
0716bf9b |
676 | # testing |
677 | |
678 | sub _acmp |
679 | { |
680 | # internal absolute post-normalized compare (ignore signs) |
681 | # ref to array, ref to array, return <0, 0, >0 |
b22b3e31 |
682 | # arrays must have at least one entry; this is not checked for |
0716bf9b |
683 | |
574bacfe |
684 | my ($c,$cx, $cy) = @_; |
0716bf9b |
685 | |
0716bf9b |
686 | my ($i,$a,$x,$y,$k); |
687 | # calculate length based on digits, not parts |
574bacfe |
688 | $x = _len('',$cx); $y = _len('',$cy); |
574bacfe |
689 | my $lxy = $x - $y; # if different in length |
690 | return -1 if $lxy < 0; |
691 | return 1 if $lxy > 0; |
0716bf9b |
692 | $i = 0; $a = 0; |
693 | # first way takes 5.49 sec instead of 4.87, but has the early out advantage |
b22b3e31 |
694 | # so grep is slightly faster, but more inflexible. hm. $_ instead of $k |
0716bf9b |
695 | # yields 5.6 instead of 5.5 sec huh? |
696 | # manual way (abort if unequal, good for early ne) |
697 | my $j = scalar @$cx - 1; |
698 | while ($j >= 0) |
699 | { |
700 | # print "$cx->[$j] $cy->[$j] $a",$cx->[$j]-$cy->[$j],"\n"; |
701 | last if ($a = $cx->[$j] - $cy->[$j]); $j--; |
702 | } |
574bacfe |
703 | return 1 if $a > 0; |
704 | return -1 if $a < 0; |
705 | return 0; # equal |
0716bf9b |
706 | # while it early aborts, it is even slower than the manual variant |
707 | #grep { return $a if ($a = $_ - $cy->[$i++]); } @$cx; |
708 | # grep way, go trough all (bad for early ne) |
709 | #grep { $a = $_ - $cy->[$i++]; } @$cx; |
710 | #return $a; |
711 | } |
712 | |
713 | sub _len |
714 | { |
dccbb853 |
715 | # compute number of digits in bigint, minus the sign |
b22b3e31 |
716 | # int() because add/sub sometimes leaves strings (like '00005') instead of |
dccbb853 |
717 | # int ('5') in this place, thus causing length() to report wrong length |
574bacfe |
718 | my $cx = $_[1]; |
0716bf9b |
719 | |
574bacfe |
720 | return (@$cx-1)*$BASE_LEN+length(int($cx->[-1])); |
0716bf9b |
721 | } |
722 | |
723 | sub _digit |
724 | { |
725 | # return the nth digit, negative values count backward |
726 | # zero is rightmost, so _digit(123,0) will give 3 |
574bacfe |
727 | my ($c,$x,$n) = @_; |
0716bf9b |
728 | |
574bacfe |
729 | my $len = _len('',$x); |
0716bf9b |
730 | |
731 | $n = $len+$n if $n < 0; # -1 last, -2 second-to-last |
732 | $n = abs($n); # if negative was too big |
733 | $len--; $n = $len if $n > $len; # n to big? |
734 | |
574bacfe |
735 | my $elem = int($n / $BASE_LEN); # which array element |
736 | my $digit = $n % $BASE_LEN; # which digit in this element |
0716bf9b |
737 | $elem = '0000'.@$x[$elem]; # get element padded with 0's |
738 | return substr($elem,-$digit-1,1); |
739 | } |
740 | |
741 | sub _zeros |
742 | { |
743 | # return amount of trailing zeros in decimal |
744 | # check each array elem in _m for having 0 at end as long as elem == 0 |
745 | # Upon finding a elem != 0, stop |
574bacfe |
746 | my $x = $_[1]; |
0716bf9b |
747 | my $zeros = 0; my $elem; |
748 | foreach my $e (@$x) |
749 | { |
750 | if ($e != 0) |
751 | { |
574bacfe |
752 | $elem = "$e"; # preserve x |
753 | $elem =~ s/.*?(0*$)/$1/; # strip anything not zero |
754 | $zeros *= $BASE_LEN; # elems * 5 |
755 | $zeros += CORE::length($elem); # count trailing zeros |
756 | last; # early out |
0716bf9b |
757 | } |
574bacfe |
758 | $zeros ++; # real else branch: 50% slower! |
0716bf9b |
759 | } |
760 | return $zeros; |
761 | } |
762 | |
763 | ############################################################################## |
764 | # _is_* routines |
765 | |
766 | sub _is_zero |
767 | { |
768 | # return true if arg (BINT or num_str) is zero (array '+', '0') |
574bacfe |
769 | my $x = $_[1]; |
0716bf9b |
770 | return (((scalar @$x == 1) && ($x->[0] == 0))) <=> 0; |
771 | } |
772 | |
773 | sub _is_even |
774 | { |
775 | # return true if arg (BINT or num_str) is even |
574bacfe |
776 | my $x = $_[1]; |
0716bf9b |
777 | return (!($x->[0] & 1)) <=> 0; |
778 | } |
779 | |
780 | sub _is_odd |
781 | { |
782 | # return true if arg (BINT or num_str) is even |
574bacfe |
783 | my $x = $_[1]; |
0716bf9b |
784 | return (($x->[0] & 1)) <=> 0; |
785 | } |
786 | |
787 | sub _is_one |
788 | { |
789 | # return true if arg (BINT or num_str) is one (array '+', '1') |
574bacfe |
790 | my $x = $_[1]; |
0716bf9b |
791 | return (scalar @$x == 1) && ($x->[0] == 1) <=> 0; |
792 | } |
793 | |
794 | sub __strip_zeros |
795 | { |
796 | # internal normalization function that strips leading zeros from the array |
797 | # args: ref to array |
0716bf9b |
798 | my $s = shift; |
799 | |
800 | my $cnt = scalar @$s; # get count of parts |
801 | my $i = $cnt-1; |
802 | #print "strip: cnt $cnt i $i\n"; |
803 | # '0', '3', '4', '0', '0', |
804 | # 0 1 2 3 4 |
805 | # cnt = 5, i = 4 |
806 | # i = 4 |
807 | # i = 3 |
808 | # => fcnt = cnt - i (5-2 => 3, cnt => 5-1 = 4, throw away from 4th pos) |
809 | # >= 1: skip first part (this can be zero) |
810 | while ($i > 0) { last if $s->[$i] != 0; $i--; } |
811 | $i++; splice @$s,$i if ($i < $cnt); # $i cant be 0 |
812 | return $s; |
813 | } |
814 | |
815 | ############################################################################### |
816 | # check routine to test internal state of corruptions |
817 | |
818 | sub _check |
819 | { |
bd05a461 |
820 | # used by the test suite |
574bacfe |
821 | my $x = $_[1]; |
0716bf9b |
822 | |
0716bf9b |
823 | return "$x is not a reference" if !ref($x); |
824 | |
825 | # are all parts are valid? |
826 | my $i = 0; my $j = scalar @$x; my ($e,$try); |
827 | while ($i < $j) |
828 | { |
829 | $e = $x->[$i]; $e = 'undef' unless defined $e; |
830 | $try = '=~ /^[\+]?[0-9]+\$/; '."($x, $e)"; |
831 | last if $e !~ /^[+]?[0-9]+$/; |
dccbb853 |
832 | $try = '=~ /^[\+]?[0-9]+\$/; '."($x, $e) (stringify)"; |
833 | last if "$e" !~ /^[+]?[0-9]+$/; |
834 | $try = '=~ /^[\+]?[0-9]+\$/; '."($x, $e) (cat-stringify)"; |
835 | last if '' . "$e" !~ /^[+]?[0-9]+$/; |
0716bf9b |
836 | $try = ' < 0 || >= $BASE; '."($x, $e)"; |
837 | last if $e <0 || $e >= $BASE; |
838 | # this test is disabled, since new/bnorm and certain ops (like early out |
839 | # in add/sub) are allowed/expected to leave '00000' in some elements |
840 | #$try = '=~ /^00+/; '."($x, $e)"; |
841 | #last if $e =~ /^00+/; |
842 | $i++; |
843 | } |
844 | return "Illegal part '$e' at pos $i (tested: $try)" if $i < $j; |
845 | return 0; |
846 | } |
847 | |
848 | 1; |
849 | __END__ |
850 | |
851 | =head1 NAME |
852 | |
853 | Math::BigInt::Calc - Pure Perl module to support Math::BigInt |
854 | |
855 | =head1 SYNOPSIS |
856 | |
ee15d750 |
857 | Provides support for big integer calculations. Not intended to be used by other |
858 | modules (except Math::BigInt::Cached). Other modules which sport the same |
859 | functions can also be used to support Math::Bigint, like Math::BigInt::Pari. |
0716bf9b |
860 | |
861 | =head1 DESCRIPTION |
862 | |
027dc388 |
863 | In order to allow for multiple big integer libraries, Math::BigInt was |
864 | rewritten to use library modules for core math routines. Any module which |
865 | follows the same API as this can be used instead by using the following: |
0716bf9b |
866 | |
ee15d750 |
867 | use Math::BigInt lib => 'libname'; |
0716bf9b |
868 | |
027dc388 |
869 | 'libname' is either the long name ('Math::BigInt::Pari'), or only the short |
870 | version like 'Pari'. |
871 | |
0716bf9b |
872 | =head1 EXPORT |
873 | |
027dc388 |
874 | The following functions MUST be defined in order to support the use by |
875 | Math::BigInt: |
0716bf9b |
876 | |
877 | _new(string) return ref to new object from ref to decimal string |
878 | _zero() return a new object with value 0 |
879 | _one() return a new object with value 1 |
880 | |
881 | _str(obj) return ref to a string representing the object |
882 | _num(obj) returns a Perl integer/floating point number |
883 | NOTE: because of Perl numeric notation defaults, |
884 | the _num'ified obj may lose accuracy due to |
885 | machine-dependend floating point size limitations |
886 | |
887 | _add(obj,obj) Simple addition of two objects |
888 | _mul(obj,obj) Multiplication of two objects |
889 | _div(obj,obj) Division of the 1st object by the 2nd |
b22b3e31 |
890 | In list context, returns (result,remainder). |
891 | NOTE: this is integer math, so no |
892 | fractional part will be returned. |
893 | _sub(obj,obj) Simple subtraction of 1 object from another |
0716bf9b |
894 | a third, optional parameter indicates that the params |
895 | are swapped. In this case, the first param needs to |
896 | be preserved, while you can destroy the second. |
897 | sub (x,y,1) => return x - y and keep x intact! |
e745a66c |
898 | _dec(obj) decrement object by one (input is garant. to be > 0) |
899 | _inc(obj) increment object by one |
900 | |
0716bf9b |
901 | |
902 | _acmp(obj,obj) <=> operator for objects (return -1, 0 or 1) |
903 | |
904 | _len(obj) returns count of the decimal digits of the object |
905 | _digit(obj,n) returns the n'th decimal digit of object |
906 | |
907 | _is_one(obj) return true if argument is +1 |
908 | _is_zero(obj) return true if argument is 0 |
909 | _is_even(obj) return true if argument is even (0,2,4,6..) |
910 | _is_odd(obj) return true if argument is odd (1,3,5,7..) |
911 | |
912 | _copy return a ref to a true copy of the object |
913 | |
914 | _check(obj) check whether internal representation is still intact |
915 | return 0 for ok, otherwise error message as string |
916 | |
bd05a461 |
917 | The following functions are optional, and can be defined if the underlying lib |
027dc388 |
918 | has a fast way to do them. If undefined, Math::BigInt will use pure Perl (hence |
919 | slow) fallback routines to emulate these: |
0716bf9b |
920 | |
921 | _from_hex(str) return ref to new object from ref to hexadecimal string |
922 | _from_bin(str) return ref to new object from ref to binary string |
923 | |
ee15d750 |
924 | _as_hex(str) return ref to scalar string containing the value as |
925 | unsigned hex string, with the '0x' prepended. |
926 | Leading zeros must be stripped. |
927 | _as_bin(str) Like as_hex, only as binary string containing only |
928 | zeros and ones. Leading zeros must be stripped and a |
929 | '0b' must be prepended. |
930 | |
0716bf9b |
931 | _rsft(obj,N,B) shift object in base B by N 'digits' right |
dccbb853 |
932 | For unsupported bases B, return undef to signal failure |
0716bf9b |
933 | _lsft(obj,N,B) shift object in base B by N 'digits' left |
dccbb853 |
934 | For unsupported bases B, return undef to signal failure |
0716bf9b |
935 | |
936 | _xor(obj1,obj2) XOR (bit-wise) object 1 with object 2 |
dccbb853 |
937 | Note: XOR, AND and OR pad with zeros if size mismatches |
0716bf9b |
938 | _and(obj1,obj2) AND (bit-wise) object 1 with object 2 |
939 | _or(obj1,obj2) OR (bit-wise) object 1 with object 2 |
940 | |
dccbb853 |
941 | _mod(obj,obj) Return remainder of div of the 1st by the 2nd object |
0716bf9b |
942 | _sqrt(obj) return the square root of object |
943 | _pow(obj,obj) return object 1 to the power of object 2 |
944 | _gcd(obj,obj) return Greatest Common Divisor of two objects |
945 | |
b22b3e31 |
946 | _zeros(obj) return number of trailing decimal zeros |
0716bf9b |
947 | |
b22b3e31 |
948 | Input strings come in as unsigned but with prefix (i.e. as '123', '0xabc' |
0716bf9b |
949 | or '0b1101'). |
950 | |
b22b3e31 |
951 | Testing of input parameter validity is done by the caller, so you need not |
574bacfe |
952 | worry about underflow (f.i. in C<_sub()>, C<_dec()>) nor about division by |
953 | zero or similar cases. |
954 | |
955 | The first parameter can be modified, that includes the possibility that you |
956 | return a reference to a completely different object instead. Although keeping |
dccbb853 |
957 | the reference and just changing it's contents is prefered over creating and |
958 | returning a different reference. |
574bacfe |
959 | |
960 | Return values are always references to objects or strings. Exceptions are |
961 | C<_lsft()> and C<_rsft()>, which return undef if they can not shift the |
027dc388 |
962 | argument. This is used to delegate shifting of bases different than the one |
963 | you can support back to Math::BigInt, which will use some generic code to |
964 | calculate the result. |
574bacfe |
965 | |
966 | =head1 WRAP YOUR OWN |
967 | |
968 | If you want to port your own favourite c-lib for big numbers to the |
969 | Math::BigInt interface, you can take any of the already existing modules as |
970 | a rough guideline. You should really wrap up the latest BigInt and BigFloat |
bd05a461 |
971 | testsuites with your module, and replace in them any of the following: |
574bacfe |
972 | |
973 | use Math::BigInt; |
974 | |
bd05a461 |
975 | by this: |
574bacfe |
976 | |
977 | use Math::BigInt lib => 'yourlib'; |
978 | |
979 | This way you ensure that your library really works 100% within Math::BigInt. |
0716bf9b |
980 | |
981 | =head1 LICENSE |
982 | |
983 | This program is free software; you may redistribute it and/or modify it under |
984 | the same terms as Perl itself. |
985 | |
986 | =head1 AUTHORS |
987 | |
988 | Original math code by Mark Biggar, rewritten by Tels L<http://bloodgate.com/> |
989 | in late 2000, 2001. |
990 | Seperated from BigInt and shaped API with the help of John Peacock. |
991 | |
992 | =head1 SEE ALSO |
993 | |
ee15d750 |
994 | L<Math::BigInt>, L<Math::BigFloat>, L<Math::BigInt::BitVect>, |
995 | L<Math::BigInt::GMP>, L<Math::BigInt::Cached> and L<Math::BigInt::Pari>. |
0716bf9b |
996 | |
997 | =cut |