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; |
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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 = '0.10'; |
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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 |
16 | # leading zero parts (except the first) and in base 100000 |
17 | |
18 | # todo: |
19 | # - fully remove funky $# stuff (maybe) |
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20 | |
21 | # USE_MUL: due to problems on certain os (os390, posix-bc) "* 1e-5" is used |
7f01e9eb |
22 | # instead of "/ 1e5" at some places, (marked with USE_MUL). |
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23 | # The BEGIN block is used to determine which of the two variants gives the |
24 | # correct result. |
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25 | |
26 | ############################################################################## |
27 | # global constants, flags and accessory |
28 | |
29 | # constants for easier life |
30 | my $nan = 'NaN'; |
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31 | |
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32 | my $BASE_LEN = 7; |
33 | my $BASE = int("1e".$BASE_LEN); # var for trying to change it to 1e7 |
34 | my $RBASE = abs('1e-'.$BASE_LEN); # see USE_MUL |
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35 | |
36 | BEGIN |
37 | { |
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38 | # from Daniel Pfeiffer: determine largest group of digits that is precisely |
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39 | # multipliable with itself plus carry |
40 | my ($e, $num) = 4; |
bd05a461 |
41 | do |
42 | { |
43 | $num = ('9' x ++$e) + 0; |
574bacfe |
44 | $num *= $num + 1; |
bd05a461 |
45 | } until ($num == $num - 1 or $num - 1 == $num - 2); |
574bacfe |
46 | $BASE_LEN = $e-1; |
47 | $BASE = int("1e".$BASE_LEN); |
48 | $RBASE = abs('1e-'.$BASE_LEN); # see USE_MUL |
49 | } |
50 | |
51 | # for quering and setting, to debug/benchmark things |
52 | sub _base_len |
53 | { |
54 | my $b = shift; |
55 | if (defined $b) |
56 | { |
57 | $BASE_LEN = $b; |
58 | $BASE = int("1e".$BASE_LEN); |
59 | $RBASE = abs('1e-'.$BASE_LEN); # see USE_MUL |
60 | } |
61 | $BASE_LEN; |
62 | } |
0716bf9b |
63 | |
64 | ############################################################################## |
65 | # create objects from various representations |
66 | |
67 | sub _new |
68 | { |
69 | # (string) return ref to num_array |
70 | # Convert a number from string format to internal base 100000 format. |
71 | # Assumes normalized value as input. |
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72 | my $d = $_[1]; |
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73 | # print "_new $d $$d\n"; |
74 | my $il = CORE::length($$d)-1; |
75 | # these leaves '00000' instead of int 0 and will be corrected after any op |
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76 | return [ reverse(unpack("a" . ($il % $BASE_LEN+1) |
77 | . ("a$BASE_LEN" x ($il / $BASE_LEN)), $$d)) ]; |
0716bf9b |
78 | } |
79 | |
80 | sub _zero |
81 | { |
82 | # create a zero |
83 | return [ 0 ]; |
84 | } |
85 | |
86 | sub _one |
87 | { |
88 | # create a one |
89 | return [ 1 ]; |
90 | } |
91 | |
92 | sub _copy |
93 | { |
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94 | return [ @{$_[1]} ]; |
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95 | } |
96 | |
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97 | # catch and throw away |
98 | sub import { } |
99 | |
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100 | ############################################################################## |
101 | # convert back to string and number |
102 | |
103 | sub _str |
104 | { |
105 | # (ref to BINT) return num_str |
106 | # Convert number from internal base 100000 format to string format. |
107 | # internal format is always normalized (no leading zeros, "-0" => "+0") |
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108 | my $ar = $_[1]; |
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109 | my $ret = ""; |
110 | my $l = scalar @$ar; # number of parts |
111 | return $nan if $l < 1; # should not happen |
112 | # handle first one different to strip leading zeros from it (there are no |
113 | # leading zero parts in internal representation) |
114 | $l --; $ret .= $ar->[$l]; $l--; |
115 | # Interestingly, the pre-padd method uses more time |
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116 | # the old grep variant takes longer (14 to 10 sec) |
117 | my $z = '0' x ($BASE_LEN-1); |
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118 | while ($l >= 0) |
119 | { |
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120 | $ret .= substr($z.$ar->[$l],-$BASE_LEN); # fastest way I could think of |
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121 | $l--; |
122 | } |
123 | return \$ret; |
124 | } |
125 | |
126 | sub _num |
127 | { |
128 | # Make a number (scalar int/float) from a BigInt object |
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129 | my $x = $_[1]; |
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130 | return $x->[0] if scalar @$x == 1; # below $BASE |
131 | my $fac = 1; |
132 | my $num = 0; |
133 | foreach (@$x) |
134 | { |
135 | $num += $fac*$_; $fac *= $BASE; |
136 | } |
137 | return $num; |
138 | } |
139 | |
140 | ############################################################################## |
141 | # actual math code |
142 | |
143 | sub _add |
144 | { |
145 | # (ref to int_num_array, ref to int_num_array) |
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146 | # routine to add two base 1eX numbers |
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147 | # stolen from Knuth Vol 2 Algorithm A pg 231 |
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148 | # there are separate routines to add and sub as per Knuth pg 233 |
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149 | # This routine clobbers up array x, but not y. |
150 | |
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151 | my ($c,$x,$y) = @_; |
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152 | |
153 | # for each in Y, add Y to X and carry. If after that, something is left in |
154 | # X, foreach in X add carry to X and then return X, carry |
155 | # Trades one "$j++" for having to shift arrays, $j could be made integer |
b22b3e31 |
156 | # but this would impose a limit to number-length of 2**32. |
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157 | my $i; my $car = 0; my $j = 0; |
158 | for $i (@$y) |
159 | { |
160 | $x->[$j] -= $BASE |
161 | if $car = (($x->[$j] += $i + $car) >= $BASE) ? 1 : 0; |
162 | $j++; |
163 | } |
164 | while ($car != 0) |
165 | { |
166 | $x->[$j] -= $BASE if $car = (($x->[$j] += $car) >= $BASE) ? 1 : 0; $j++; |
167 | } |
168 | return $x; |
169 | } |
170 | |
171 | sub _sub |
172 | { |
173 | # (ref to int_num_array, ref to int_num_array) |
574bacfe |
174 | # subtract base 1eX numbers -- stolen from Knuth Vol 2 pg 232, $x > $y |
b22b3e31 |
175 | # subtract Y from X (X is always greater/equal!) by modifying x in place |
574bacfe |
176 | my ($c,$sx,$sy,$s) = @_; |
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177 | |
178 | my $car = 0; my $i; my $j = 0; |
179 | if (!$s) |
180 | { |
181 | #print "case 2\n"; |
182 | for $i (@$sx) |
183 | { |
184 | last unless defined $sy->[$j] || $car; |
185 | #print "x: $i y: $sy->[$j] c: $car\n"; |
186 | $i += $BASE if $car = (($i -= ($sy->[$j] || 0) + $car) < 0); $j++; |
187 | #print "x: $i y: $sy->[$j-1] c: $car\n"; |
188 | } |
189 | # might leave leading zeros, so fix that |
190 | __strip_zeros($sx); |
191 | return $sx; |
192 | } |
193 | else |
194 | { |
195 | #print "case 1 (swap)\n"; |
196 | for $i (@$sx) |
197 | { |
198 | last unless defined $sy->[$j] || $car; |
199 | #print "$sy->[$j] $i $car => $sx->[$j]\n"; |
200 | $sy->[$j] += $BASE |
201 | if $car = (($sy->[$j] = $i-($sy->[$j]||0) - $car) < 0); |
202 | #print "$sy->[$j] $i $car => $sy->[$j]\n"; |
203 | $j++; |
204 | } |
205 | # might leave leading zeros, so fix that |
206 | __strip_zeros($sy); |
207 | return $sy; |
208 | } |
209 | } |
210 | |
7f01e9eb |
211 | sub _mul |
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212 | { |
213 | # (BINT, BINT) return nothing |
214 | # multiply two numbers in internal representation |
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215 | # modifies first arg, second need not be different from first |
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216 | my ($c,$xv,$yv) = @_; |
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217 | |
218 | my @prod = (); my ($prod,$car,$cty,$xi,$yi); |
219 | # since multiplying $x with $x fails, make copy in this case |
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220 | $yv = [@$xv] if "$xv" eq "$yv"; # same references? |
0716bf9b |
221 | for $xi (@$xv) |
222 | { |
223 | $car = 0; $cty = 0; |
574bacfe |
224 | |
225 | # slow variant |
226 | # for $yi (@$yv) |
227 | # { |
228 | # $prod = $xi * $yi + ($prod[$cty] || 0) + $car; |
229 | # $prod[$cty++] = |
230 | # $prod - ($car = int($prod * RBASE)) * $BASE; # see USE_MUL |
231 | # } |
232 | # $prod[$cty] += $car if $car; # need really to check for 0? |
233 | # $xi = shift @prod; |
234 | |
235 | # faster variant |
236 | # looping through this if $xi == 0 is silly - so optimize it away! |
237 | $xi = (shift @prod || 0), next if $xi == 0; |
0716bf9b |
238 | for $yi (@$yv) |
239 | { |
240 | $prod = $xi * $yi + ($prod[$cty] || 0) + $car; |
574bacfe |
241 | ## this is actually a tad slower |
242 | ## $prod = $prod[$cty]; $prod += ($car + $xi * $yi); # no ||0 here |
0716bf9b |
243 | $prod[$cty++] = |
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244 | $prod - ($car = int($prod * $RBASE)) * $BASE; # see USE_MUL |
0716bf9b |
245 | } |
246 | $prod[$cty] += $car if $car; # need really to check for 0? |
247 | $xi = shift @prod; |
248 | } |
0716bf9b |
249 | push @$xv, @prod; |
250 | __strip_zeros($xv); |
251 | # normalize (handled last to save check for $y->is_zero() |
252 | return $xv; |
253 | } |
254 | |
255 | sub _div |
256 | { |
b22b3e31 |
257 | # ref to array, ref to array, modify first array and return remainder if |
0716bf9b |
258 | # in list context |
b22b3e31 |
259 | # no longer handles sign |
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260 | my ($c,$x,$yorg) = @_; |
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261 | my ($car,$bar,$prd,$dd,$xi,$yi,@q,$v2,$v1); |
262 | |
263 | my (@d,$tmp,$q,$u2,$u1,$u0); |
264 | |
265 | $car = $bar = $prd = 0; |
266 | |
267 | my $y = [ @$yorg ]; |
268 | if (($dd = int($BASE/($y->[-1]+1))) != 1) |
269 | { |
270 | for $xi (@$x) |
271 | { |
272 | $xi = $xi * $dd + $car; |
273 | $xi -= ($car = int($xi * $RBASE)) * $BASE; # see USE_MUL |
274 | } |
275 | push(@$x, $car); $car = 0; |
276 | for $yi (@$y) |
277 | { |
278 | $yi = $yi * $dd + $car; |
279 | $yi -= ($car = int($yi * $RBASE)) * $BASE; # see USE_MUL |
280 | } |
281 | } |
282 | else |
283 | { |
284 | push(@$x, 0); |
285 | } |
286 | @q = (); ($v2,$v1) = @$y[-2,-1]; |
287 | $v2 = 0 unless $v2; |
288 | while ($#$x > $#$y) |
289 | { |
290 | ($u2,$u1,$u0) = @$x[-3..-1]; |
291 | $u2 = 0 unless $u2; |
292 | #warn "oups v1 is 0, u0: $u0 $y->[-2] $y->[-1] l ",scalar @$y,"\n" |
293 | # if $v1 == 0; |
294 | $q = (($u0 == $v1) ? 99999 : int(($u0*$BASE+$u1)/$v1)); |
574bacfe |
295 | --$q while ($v2*$q > ($u0*$BASE+$u1-$q*$v1)*$BASE+$u2); |
0716bf9b |
296 | if ($q) |
297 | { |
298 | ($car, $bar) = (0,0); |
299 | for ($yi = 0, $xi = $#$x-$#$y-1; $yi <= $#$y; ++$yi,++$xi) |
300 | { |
301 | $prd = $q * $y->[$yi] + $car; |
302 | $prd -= ($car = int($prd * $RBASE)) * $BASE; # see USE_MUL |
574bacfe |
303 | $x->[$xi] += $BASE if ($bar = (($x->[$xi] -= $prd + $bar) < 0)); |
0716bf9b |
304 | } |
305 | if ($x->[-1] < $car + $bar) |
306 | { |
307 | $car = 0; --$q; |
308 | for ($yi = 0, $xi = $#$x-$#$y-1; $yi <= $#$y; ++$yi,++$xi) |
309 | { |
574bacfe |
310 | $x->[$xi] -= $BASE |
0716bf9b |
311 | if ($car = (($x->[$xi] += $y->[$yi] + $car) > $BASE)); |
312 | } |
313 | } |
314 | } |
315 | pop(@$x); unshift(@q, $q); |
316 | } |
317 | if (wantarray) |
318 | { |
319 | @d = (); |
320 | if ($dd != 1) |
321 | { |
322 | $car = 0; |
323 | for $xi (reverse @$x) |
324 | { |
325 | $prd = $car * $BASE + $xi; |
326 | $car = $prd - ($tmp = int($prd / $dd)) * $dd; # see USE_MUL |
327 | unshift(@d, $tmp); |
328 | } |
329 | } |
330 | else |
331 | { |
332 | @d = @$x; |
333 | } |
334 | @$x = @q; |
335 | __strip_zeros($x); |
336 | __strip_zeros(\@d); |
337 | return ($x,\@d); |
338 | } |
339 | @$x = @q; |
340 | __strip_zeros($x); |
341 | return $x; |
342 | } |
343 | |
344 | ############################################################################## |
574bacfe |
345 | # shifts |
346 | |
347 | sub _rsft |
348 | { |
349 | my ($c,$x,$y,$n) = @_; |
350 | |
351 | if ($n != 10) |
352 | { |
353 | return; # we cant do this here, due to now _pow, so signal failure |
354 | } |
355 | else |
356 | { |
357 | # shortcut (faster) for shifting by 10) |
358 | # multiples of $BASE_LEN |
359 | my $dst = 0; # destination |
360 | my $src = _num($c,$y); # as normal int |
361 | my $rem = $src % $BASE_LEN; # reminder to shift |
362 | $src = int($src / $BASE_LEN); # source |
363 | if ($rem == 0) |
364 | { |
365 | splice (@$x,0,$src); # even faster, 38.4 => 39.3 |
366 | } |
367 | else |
368 | { |
369 | my $len = scalar @$x - $src; # elems to go |
370 | my $vd; my $z = '0'x $BASE_LEN; |
371 | $x->[scalar @$x] = 0; # avoid || 0 test inside loop |
372 | while ($dst < $len) |
373 | { |
374 | $vd = $z.$x->[$src]; |
375 | #print "$dst $src '$vd' "; |
376 | $vd = substr($vd,-$BASE_LEN,$BASE_LEN-$rem); |
377 | #print "'$vd' "; |
378 | $src++; |
379 | $vd = substr($z.$x->[$src],-$rem,$rem) . $vd; |
380 | #print "'$vd1' "; |
381 | #print "'$vd'\n"; |
382 | $vd = substr($vd,-$BASE_LEN,$BASE_LEN) if length($vd) > $BASE_LEN; |
383 | $x->[$dst] = int($vd); |
384 | $dst++; |
385 | } |
386 | splice (@$x,$dst) if $dst > 0; # kill left-over array elems |
387 | pop @$x if $x->[-1] == 0; # kill last element if 0 |
388 | } # else rem == 0 |
389 | } |
390 | $x; |
391 | } |
392 | |
393 | sub _lsft |
394 | { |
395 | my ($c,$x,$y,$n) = @_; |
396 | |
397 | if ($n != 10) |
398 | { |
399 | return; # we cant do this here, due to now _pow, so signal failure |
400 | } |
401 | else |
402 | { |
403 | # shortcut (faster) for shifting by 10) since we are in base 10eX |
404 | # multiples of $BASE_LEN: |
405 | my $src = scalar @$x; # source |
406 | my $len = _num($c,$y); # shift-len as normal int |
407 | my $rem = $len % $BASE_LEN; # reminder to shift |
408 | my $dst = $src + int($len/$BASE_LEN); # destination |
409 | my $vd; # further speedup |
410 | #print "src $src:",$x->[$src]||0," dst $dst:",$v->[$dst]||0," rem $rem\n"; |
411 | $x->[$src] = 0; # avoid first ||0 for speed |
412 | my $z = '0' x $BASE_LEN; |
413 | while ($src >= 0) |
414 | { |
415 | $vd = $x->[$src]; $vd = $z.$vd; |
416 | #print "s $src d $dst '$vd' "; |
417 | $vd = substr($vd,-$BASE_LEN+$rem,$BASE_LEN-$rem); |
418 | #print "'$vd' "; |
419 | $vd .= $src > 0 ? substr($z.$x->[$src-1],-$BASE_LEN,$rem) : '0' x $rem; |
420 | #print "'$vd' "; |
421 | $vd = substr($vd,-$BASE_LEN,$BASE_LEN) if length($vd) > $BASE_LEN; |
422 | #print "'$vd'\n"; |
423 | $x->[$dst] = int($vd); |
424 | $dst--; $src--; |
425 | } |
426 | # set lowest parts to 0 |
427 | while ($dst >= 0) { $x->[$dst--] = 0; } |
428 | # fix spurios last zero element |
429 | splice @$x,-1 if $x->[-1] == 0; |
430 | #print "elems: "; my $i = 0; |
431 | #foreach (reverse @$v) { print "$i $_ "; $i++; } print "\n"; |
432 | } |
433 | $x; |
434 | } |
435 | |
436 | ############################################################################## |
0716bf9b |
437 | # testing |
438 | |
439 | sub _acmp |
440 | { |
441 | # internal absolute post-normalized compare (ignore signs) |
442 | # ref to array, ref to array, return <0, 0, >0 |
b22b3e31 |
443 | # arrays must have at least one entry; this is not checked for |
0716bf9b |
444 | |
574bacfe |
445 | my ($c,$cx, $cy) = @_; |
0716bf9b |
446 | |
447 | #print "$cx $cy\n"; |
448 | my ($i,$a,$x,$y,$k); |
449 | # calculate length based on digits, not parts |
574bacfe |
450 | $x = _len('',$cx); $y = _len('',$cy); |
0716bf9b |
451 | # print "length: ",($x-$y),"\n"; |
574bacfe |
452 | my $lxy = $x - $y; # if different in length |
453 | return -1 if $lxy < 0; |
454 | return 1 if $lxy > 0; |
0716bf9b |
455 | #print "full compare\n"; |
456 | $i = 0; $a = 0; |
457 | # first way takes 5.49 sec instead of 4.87, but has the early out advantage |
b22b3e31 |
458 | # so grep is slightly faster, but more inflexible. hm. $_ instead of $k |
0716bf9b |
459 | # yields 5.6 instead of 5.5 sec huh? |
460 | # manual way (abort if unequal, good for early ne) |
461 | my $j = scalar @$cx - 1; |
462 | while ($j >= 0) |
463 | { |
464 | # print "$cx->[$j] $cy->[$j] $a",$cx->[$j]-$cy->[$j],"\n"; |
465 | last if ($a = $cx->[$j] - $cy->[$j]); $j--; |
466 | } |
574bacfe |
467 | return 1 if $a > 0; |
468 | return -1 if $a < 0; |
469 | return 0; # equal |
0716bf9b |
470 | # while it early aborts, it is even slower than the manual variant |
471 | #grep { return $a if ($a = $_ - $cy->[$i++]); } @$cx; |
472 | # grep way, go trough all (bad for early ne) |
473 | #grep { $a = $_ - $cy->[$i++]; } @$cx; |
474 | #return $a; |
475 | } |
476 | |
477 | sub _len |
478 | { |
479 | # computer number of digits in bigint, minus the sign |
b22b3e31 |
480 | # int() because add/sub sometimes leaves strings (like '00005') instead of |
0716bf9b |
481 | # int ('5') in this place, causing length to fail |
574bacfe |
482 | my $cx = $_[1]; |
0716bf9b |
483 | |
574bacfe |
484 | return (@$cx-1)*$BASE_LEN+length(int($cx->[-1])); |
0716bf9b |
485 | } |
486 | |
487 | sub _digit |
488 | { |
489 | # return the nth digit, negative values count backward |
490 | # zero is rightmost, so _digit(123,0) will give 3 |
574bacfe |
491 | my ($c,$x,$n) = @_; |
0716bf9b |
492 | |
574bacfe |
493 | my $len = _len('',$x); |
0716bf9b |
494 | |
495 | $n = $len+$n if $n < 0; # -1 last, -2 second-to-last |
496 | $n = abs($n); # if negative was too big |
497 | $len--; $n = $len if $n > $len; # n to big? |
498 | |
574bacfe |
499 | my $elem = int($n / $BASE_LEN); # which array element |
500 | my $digit = $n % $BASE_LEN; # which digit in this element |
0716bf9b |
501 | $elem = '0000'.@$x[$elem]; # get element padded with 0's |
502 | return substr($elem,-$digit-1,1); |
503 | } |
504 | |
505 | sub _zeros |
506 | { |
507 | # return amount of trailing zeros in decimal |
508 | # check each array elem in _m for having 0 at end as long as elem == 0 |
509 | # Upon finding a elem != 0, stop |
574bacfe |
510 | my $x = $_[1]; |
0716bf9b |
511 | my $zeros = 0; my $elem; |
512 | foreach my $e (@$x) |
513 | { |
514 | if ($e != 0) |
515 | { |
574bacfe |
516 | $elem = "$e"; # preserve x |
517 | $elem =~ s/.*?(0*$)/$1/; # strip anything not zero |
518 | $zeros *= $BASE_LEN; # elems * 5 |
519 | $zeros += CORE::length($elem); # count trailing zeros |
520 | last; # early out |
0716bf9b |
521 | } |
574bacfe |
522 | $zeros ++; # real else branch: 50% slower! |
0716bf9b |
523 | } |
524 | return $zeros; |
525 | } |
526 | |
527 | ############################################################################## |
528 | # _is_* routines |
529 | |
530 | sub _is_zero |
531 | { |
532 | # return true if arg (BINT or num_str) is zero (array '+', '0') |
574bacfe |
533 | my $x = $_[1]; |
0716bf9b |
534 | return (((scalar @$x == 1) && ($x->[0] == 0))) <=> 0; |
535 | } |
536 | |
537 | sub _is_even |
538 | { |
539 | # return true if arg (BINT or num_str) is even |
574bacfe |
540 | my $x = $_[1]; |
0716bf9b |
541 | return (!($x->[0] & 1)) <=> 0; |
542 | } |
543 | |
544 | sub _is_odd |
545 | { |
546 | # return true if arg (BINT or num_str) is even |
574bacfe |
547 | my $x = $_[1]; |
0716bf9b |
548 | return (($x->[0] & 1)) <=> 0; |
549 | } |
550 | |
551 | sub _is_one |
552 | { |
553 | # return true if arg (BINT or num_str) is one (array '+', '1') |
574bacfe |
554 | my $x = $_[1]; |
0716bf9b |
555 | return (scalar @$x == 1) && ($x->[0] == 1) <=> 0; |
556 | } |
557 | |
558 | sub __strip_zeros |
559 | { |
560 | # internal normalization function that strips leading zeros from the array |
561 | # args: ref to array |
0716bf9b |
562 | my $s = shift; |
563 | |
564 | my $cnt = scalar @$s; # get count of parts |
565 | my $i = $cnt-1; |
566 | #print "strip: cnt $cnt i $i\n"; |
567 | # '0', '3', '4', '0', '0', |
568 | # 0 1 2 3 4 |
569 | # cnt = 5, i = 4 |
570 | # i = 4 |
571 | # i = 3 |
572 | # => fcnt = cnt - i (5-2 => 3, cnt => 5-1 = 4, throw away from 4th pos) |
573 | # >= 1: skip first part (this can be zero) |
574 | while ($i > 0) { last if $s->[$i] != 0; $i--; } |
575 | $i++; splice @$s,$i if ($i < $cnt); # $i cant be 0 |
576 | return $s; |
577 | } |
578 | |
579 | ############################################################################### |
580 | # check routine to test internal state of corruptions |
581 | |
582 | sub _check |
583 | { |
bd05a461 |
584 | # used by the test suite |
574bacfe |
585 | my $x = $_[1]; |
0716bf9b |
586 | |
0716bf9b |
587 | return "$x is not a reference" if !ref($x); |
588 | |
589 | # are all parts are valid? |
590 | my $i = 0; my $j = scalar @$x; my ($e,$try); |
591 | while ($i < $j) |
592 | { |
593 | $e = $x->[$i]; $e = 'undef' unless defined $e; |
594 | $try = '=~ /^[\+]?[0-9]+\$/; '."($x, $e)"; |
595 | last if $e !~ /^[+]?[0-9]+$/; |
596 | $try = ' < 0 || >= $BASE; '."($x, $e)"; |
597 | last if $e <0 || $e >= $BASE; |
598 | # this test is disabled, since new/bnorm and certain ops (like early out |
599 | # in add/sub) are allowed/expected to leave '00000' in some elements |
600 | #$try = '=~ /^00+/; '."($x, $e)"; |
601 | #last if $e =~ /^00+/; |
602 | $i++; |
603 | } |
604 | return "Illegal part '$e' at pos $i (tested: $try)" if $i < $j; |
605 | return 0; |
606 | } |
607 | |
608 | 1; |
609 | __END__ |
610 | |
611 | =head1 NAME |
612 | |
613 | Math::BigInt::Calc - Pure Perl module to support Math::BigInt |
614 | |
615 | =head1 SYNOPSIS |
616 | |
617 | Provides support for big integer calculations. Not intended |
618 | to be used by other modules. Other modules which export the |
619 | same functions can also be used to support Math::Bigint |
620 | |
621 | =head1 DESCRIPTION |
622 | |
623 | In order to allow for multiple big integer libraries, Math::BigInt |
624 | was rewritten to use library modules for core math routines. Any |
625 | module which follows the same API as this can be used instead by |
626 | using the following call: |
627 | |
574bacfe |
628 | use Math::BigInt lib => BigNum; |
0716bf9b |
629 | |
630 | =head1 EXPORT |
631 | |
bd05a461 |
632 | The following functions MUST be defined in order to support |
0716bf9b |
633 | the use by Math::BigInt: |
634 | |
635 | _new(string) return ref to new object from ref to decimal string |
636 | _zero() return a new object with value 0 |
637 | _one() return a new object with value 1 |
638 | |
639 | _str(obj) return ref to a string representing the object |
640 | _num(obj) returns a Perl integer/floating point number |
641 | NOTE: because of Perl numeric notation defaults, |
642 | the _num'ified obj may lose accuracy due to |
643 | machine-dependend floating point size limitations |
644 | |
645 | _add(obj,obj) Simple addition of two objects |
646 | _mul(obj,obj) Multiplication of two objects |
647 | _div(obj,obj) Division of the 1st object by the 2nd |
b22b3e31 |
648 | In list context, returns (result,remainder). |
649 | NOTE: this is integer math, so no |
650 | fractional part will be returned. |
651 | _sub(obj,obj) Simple subtraction of 1 object from another |
0716bf9b |
652 | a third, optional parameter indicates that the params |
653 | are swapped. In this case, the first param needs to |
654 | be preserved, while you can destroy the second. |
655 | sub (x,y,1) => return x - y and keep x intact! |
656 | |
657 | _acmp(obj,obj) <=> operator for objects (return -1, 0 or 1) |
658 | |
659 | _len(obj) returns count of the decimal digits of the object |
660 | _digit(obj,n) returns the n'th decimal digit of object |
661 | |
662 | _is_one(obj) return true if argument is +1 |
663 | _is_zero(obj) return true if argument is 0 |
664 | _is_even(obj) return true if argument is even (0,2,4,6..) |
665 | _is_odd(obj) return true if argument is odd (1,3,5,7..) |
666 | |
667 | _copy return a ref to a true copy of the object |
668 | |
669 | _check(obj) check whether internal representation is still intact |
670 | return 0 for ok, otherwise error message as string |
671 | |
bd05a461 |
672 | The following functions are optional, and can be defined if the underlying lib |
0716bf9b |
673 | has a fast way to do them. If not defined, Math::BigInt will use a pure, but |
bd05a461 |
674 | slow, Perl way as fallback to emulate these: |
0716bf9b |
675 | |
676 | _from_hex(str) return ref to new object from ref to hexadecimal string |
677 | _from_bin(str) return ref to new object from ref to binary string |
678 | |
679 | _rsft(obj,N,B) shift object in base B by N 'digits' right |
680 | _lsft(obj,N,B) shift object in base B by N 'digits' left |
681 | |
682 | _xor(obj1,obj2) XOR (bit-wise) object 1 with object 2 |
683 | Mote: XOR, AND and OR pad with zeros if size mismatches |
684 | _and(obj1,obj2) AND (bit-wise) object 1 with object 2 |
685 | _or(obj1,obj2) OR (bit-wise) object 1 with object 2 |
686 | |
687 | _sqrt(obj) return the square root of object |
688 | _pow(obj,obj) return object 1 to the power of object 2 |
689 | _gcd(obj,obj) return Greatest Common Divisor of two objects |
690 | |
b22b3e31 |
691 | _zeros(obj) return number of trailing decimal zeros |
0716bf9b |
692 | |
693 | _dec(obj) decrement object by one (input is >= 1) |
694 | _inc(obj) increment object by one |
695 | |
b22b3e31 |
696 | Input strings come in as unsigned but with prefix (i.e. as '123', '0xabc' |
0716bf9b |
697 | or '0b1101'). |
698 | |
b22b3e31 |
699 | Testing of input parameter validity is done by the caller, so you need not |
574bacfe |
700 | worry about underflow (f.i. in C<_sub()>, C<_dec()>) nor about division by |
701 | zero or similar cases. |
702 | |
703 | The first parameter can be modified, that includes the possibility that you |
704 | return a reference to a completely different object instead. Although keeping |
bd05a461 |
705 | the reference is prefered over creating and returning a different one. |
574bacfe |
706 | |
707 | Return values are always references to objects or strings. Exceptions are |
708 | C<_lsft()> and C<_rsft()>, which return undef if they can not shift the |
709 | argument. This is used to delegate shifting of bases different than 10 back |
710 | to BigInt, which will use some generic code to calculate the result. |
711 | |
712 | =head1 WRAP YOUR OWN |
713 | |
714 | If you want to port your own favourite c-lib for big numbers to the |
715 | Math::BigInt interface, you can take any of the already existing modules as |
716 | a rough guideline. You should really wrap up the latest BigInt and BigFloat |
bd05a461 |
717 | testsuites with your module, and replace in them any of the following: |
574bacfe |
718 | |
719 | use Math::BigInt; |
720 | |
bd05a461 |
721 | by this: |
574bacfe |
722 | |
723 | use Math::BigInt lib => 'yourlib'; |
724 | |
725 | This way you ensure that your library really works 100% within Math::BigInt. |
0716bf9b |
726 | |
727 | =head1 LICENSE |
728 | |
729 | This program is free software; you may redistribute it and/or modify it under |
730 | the same terms as Perl itself. |
731 | |
732 | =head1 AUTHORS |
733 | |
734 | Original math code by Mark Biggar, rewritten by Tels L<http://bloodgate.com/> |
735 | in late 2000, 2001. |
736 | Seperated from BigInt and shaped API with the help of John Peacock. |
737 | |
738 | =head1 SEE ALSO |
739 | |
574bacfe |
740 | L<Math::BigInt>, L<Math::BigFloat>, L<Math::BigInt::BitVect> and |
741 | L<Math::BigInt::Pari>. |
0716bf9b |
742 | |
743 | =cut |