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1 | #!/usr/bin/perl -w |
2 | |
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3 | # Qs: what exactly happens on numify of HUGE numbers? overflow? |
4 | # $a = -$a is much slower (making copy of $a) than $a->bneg(), hm!? |
5 | # (copy_on_write will help there, but that is not yet implemented) |
6 | |
7 | # The following hash values are used: |
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8 | # value: unsigned int with actual value (as a Math::BigInt::Calc or similiar) |
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9 | # sign : +,-,NaN,+inf,-inf |
10 | # _a : accuracy |
11 | # _p : precision |
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12 | # _f : flags, used by MBF to flag parts of a float as untouchable |
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13 | # _cow : copy on write: number of objects that share the data (NRY) |
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14 | |
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15 | # Remember not to take shortcuts ala $xs = $x->{value}; $CALC->foo($xs); since |
16 | # underlying lib might change the reference! |
17 | |
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18 | package Math::BigInt; |
19 | my $class = "Math::BigInt"; |
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20 | require 5.005; |
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21 | |
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22 | $VERSION = '1.44'; |
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23 | use Exporter; |
24 | @ISA = qw( Exporter ); |
25 | @EXPORT_OK = qw( bneg babs bcmp badd bmul bdiv bmod bnorm bsub |
26 | bgcd blcm |
27 | bround |
28 | blsft brsft band bior bxor bnot bpow bnan bzero |
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29 | bacmp bstr bsstr binc bdec binf bfloor bceil |
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30 | is_odd is_even is_zero is_one is_nan is_inf sign |
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31 | is_positive is_negative |
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32 | length as_number |
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33 | objectify _swap |
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34 | ); |
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35 | #@EXPORT = qw( ); |
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36 | use vars qw/$round_mode $accuracy $precision $div_scale/; |
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37 | use strict; |
38 | |
39 | # Inside overload, the first arg is always an object. If the original code had |
40 | # it reversed (like $x = 2 * $y), then the third paramater indicates this |
41 | # swapping. To make it work, we use a helper routine which not only reswaps the |
42 | # params, but also makes a new object in this case. See _swap() for details, |
43 | # especially the cases of operators with different classes. |
44 | |
45 | # For overloaded ops with only one argument we simple use $_[0]->copy() to |
46 | # preserve the argument. |
47 | |
48 | # Thus inheritance of overload operators becomes possible and transparent for |
49 | # our subclasses without the need to repeat the entire overload section there. |
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50 | |
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51 | use overload |
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52 | '=' => sub { $_[0]->copy(); }, |
53 | |
54 | # '+' and '-' do not use _swap, since it is a triffle slower. If you want to |
55 | # override _swap (if ever), then override overload of '+' and '-', too! |
56 | # for sub it is a bit tricky to keep b: b-a => -a+b |
57 | '-' => sub { my $c = $_[0]->copy; $_[2] ? |
58 | $c->bneg()->badd($_[1]) : |
59 | $c->bsub( $_[1]) }, |
60 | '+' => sub { $_[0]->copy()->badd($_[1]); }, |
61 | |
62 | # some shortcuts for speed (assumes that reversed order of arguments is routed |
63 | # to normal '+' and we thus can always modify first arg. If this is changed, |
64 | # this breaks and must be adjusted.) |
65 | '+=' => sub { $_[0]->badd($_[1]); }, |
66 | '-=' => sub { $_[0]->bsub($_[1]); }, |
67 | '*=' => sub { $_[0]->bmul($_[1]); }, |
68 | '/=' => sub { scalar $_[0]->bdiv($_[1]); }, |
69 | '**=' => sub { $_[0]->bpow($_[1]); }, |
70 | |
71 | '<=>' => sub { $_[2] ? |
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72 | ref($_[0])->bcmp($_[1],$_[0]) : |
73 | ref($_[0])->bcmp($_[0],$_[1])}, |
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74 | 'cmp' => sub { |
75 | $_[2] ? |
76 | $_[1] cmp $_[0]->bstr() : |
77 | $_[0]->bstr() cmp $_[1] }, |
78 | |
79 | 'int' => sub { $_[0]->copy(); }, |
80 | 'neg' => sub { $_[0]->copy()->bneg(); }, |
81 | 'abs' => sub { $_[0]->copy()->babs(); }, |
82 | '~' => sub { $_[0]->copy()->bnot(); }, |
83 | |
84 | '*' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bmul($a[1]); }, |
85 | '/' => sub { my @a = ref($_[0])->_swap(@_);scalar $a[0]->bdiv($a[1]);}, |
86 | '%' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bmod($a[1]); }, |
87 | '**' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bpow($a[1]); }, |
88 | '<<' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->blsft($a[1]); }, |
89 | '>>' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->brsft($a[1]); }, |
90 | |
91 | '&' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->band($a[1]); }, |
92 | '|' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bior($a[1]); }, |
93 | '^' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bxor($a[1]); }, |
94 | |
95 | # can modify arg of ++ and --, so avoid a new-copy for speed, but don't |
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96 | # use $_[0]->__one(), it modifies $_[0] to be 1! |
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97 | '++' => sub { $_[0]->binc() }, |
98 | '--' => sub { $_[0]->bdec() }, |
99 | |
100 | # if overloaded, O(1) instead of O(N) and twice as fast for small numbers |
101 | 'bool' => sub { |
102 | # this kludge is needed for perl prior 5.6.0 since returning 0 here fails :-/ |
103 | # v5.6.1 dumps on that: return !$_[0]->is_zero() || undef; :-( |
104 | my $t = !$_[0]->is_zero(); |
105 | undef $t if $t == 0; |
106 | return $t; |
107 | }, |
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108 | |
109 | qw( |
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110 | "" bstr |
111 | 0+ numify), # Order of arguments unsignificant |
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112 | ; |
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113 | |
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114 | ############################################################################## |
115 | # global constants, flags and accessory |
116 | |
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117 | use constant MB_NEVER_ROUND => 0x0001; |
118 | |
119 | my $NaNOK=1; # are NaNs ok? |
120 | my $nan = 'NaN'; # constants for easier life |
121 | |
122 | my $CALC = 'Math::BigInt::Calc'; # module to do low level math |
123 | sub _core_lib () { return $CALC; } # for test suite |
124 | |
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125 | $round_mode = 'even'; # one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc' |
126 | $accuracy = undef; |
127 | $precision = undef; |
128 | $div_scale = 40; |
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129 | |
130 | sub round_mode |
131 | { |
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132 | no strict 'refs'; |
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133 | # make Class->round_mode() work |
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134 | my $self = shift; |
135 | my $class = ref($self) || $self || __PACKAGE__; |
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136 | if (defined $_[0]) |
137 | { |
138 | my $m = shift; |
139 | die "Unknown round mode $m" |
140 | if $m !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/; |
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141 | ${"${class}::round_mode"} = $m; return $m; |
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142 | } |
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143 | return ${"${class}::round_mode"}; |
144 | } |
145 | |
146 | sub div_scale |
147 | { |
148 | no strict 'refs'; |
149 | # make Class->round_mode() work |
150 | my $self = shift; |
151 | my $class = ref($self) || $self || __PACKAGE__; |
152 | if (defined $_[0]) |
153 | { |
154 | die ('div_scale must be greater than zero') if $_[0] < 0; |
155 | ${"${class}::div_scale"} = shift; |
156 | } |
157 | return ${"${class}::div_scale"}; |
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158 | } |
159 | |
160 | sub accuracy |
161 | { |
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162 | # $x->accuracy($a); ref($x) $a |
163 | # $x->accuracy(); ref($x) |
164 | # Class->accuracy(); class |
165 | # Class->accuracy($a); class $a |
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166 | |
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167 | my $x = shift; |
168 | my $class = ref($x) || $x || __PACKAGE__; |
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169 | |
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170 | no strict 'refs'; |
171 | # need to set new value? |
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172 | if (@_ > 0) |
173 | { |
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174 | my $a = shift; |
175 | die ('accuracy must not be zero') if defined $a && $a == 0; |
176 | if (ref($x)) |
177 | { |
178 | # $object->accuracy() or fallback to global |
179 | $x->bround($a) if defined $a; |
180 | $x->{_a} = $a; # set/overwrite, even if not rounded |
181 | $x->{_p} = undef; # clear P |
182 | } |
183 | else |
184 | { |
185 | # set global |
186 | ${"${class}::accuracy"} = $a; |
187 | } |
188 | return $a; # shortcut |
189 | } |
190 | |
191 | if (ref($x)) |
192 | { |
193 | # $object->accuracy() or fallback to global |
194 | return $x->{_a} || ${"${class}::accuracy"}; |
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195 | } |
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196 | return ${"${class}::accuracy"}; |
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197 | } |
198 | |
199 | sub precision |
200 | { |
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201 | # $x->precision($p); ref($x) $p |
202 | # $x->precision(); ref($x) |
203 | # Class->precision(); class |
204 | # Class->precision($p); class $p |
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205 | |
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206 | my $x = shift; |
207 | my $class = ref($x) || $x || __PACKAGE__; |
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208 | |
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209 | no strict 'refs'; |
210 | # need to set new value? |
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211 | if (@_ > 0) |
212 | { |
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213 | my $p = shift; |
214 | if (ref($x)) |
215 | { |
216 | # $object->precision() or fallback to global |
217 | $x->bfround($p) if defined $p; |
218 | $x->{_p} = $p; # set/overwrite, even if not rounded |
219 | $x->{_a} = undef; # clear P |
220 | } |
221 | else |
222 | { |
223 | # set global |
224 | ${"${class}::precision"} = $p; |
225 | } |
226 | return $p; # shortcut |
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227 | } |
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228 | |
229 | if (ref($x)) |
230 | { |
231 | # $object->precision() or fallback to global |
232 | return $x->{_p} || ${"${class}::precision"}; |
233 | } |
234 | return ${"${class}::precision"}; |
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235 | } |
236 | |
237 | sub _scale_a |
238 | { |
239 | # select accuracy parameter based on precedence, |
240 | # used by bround() and bfround(), may return undef for scale (means no op) |
241 | my ($x,$s,$m,$scale,$mode) = @_; |
242 | $scale = $x->{_a} if !defined $scale; |
243 | $scale = $s if (!defined $scale); |
244 | $mode = $m if !defined $mode; |
245 | return ($scale,$mode); |
246 | } |
247 | |
248 | sub _scale_p |
249 | { |
250 | # select precision parameter based on precedence, |
251 | # used by bround() and bfround(), may return undef for scale (means no op) |
252 | my ($x,$s,$m,$scale,$mode) = @_; |
253 | $scale = $x->{_p} if !defined $scale; |
254 | $scale = $s if (!defined $scale); |
255 | $mode = $m if !defined $mode; |
256 | return ($scale,$mode); |
257 | } |
258 | |
259 | ############################################################################## |
260 | # constructors |
261 | |
262 | sub copy |
263 | { |
264 | my ($c,$x); |
265 | if (@_ > 1) |
266 | { |
267 | # if two arguments, the first one is the class to "swallow" subclasses |
268 | ($c,$x) = @_; |
269 | } |
270 | else |
271 | { |
272 | $x = shift; |
273 | $c = ref($x); |
274 | } |
275 | return unless ref($x); # only for objects |
276 | |
277 | my $self = {}; bless $self,$c; |
278 | foreach my $k (keys %$x) |
279 | { |
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280 | if ($k eq 'value') |
281 | { |
282 | $self->{$k} = $CALC->_copy($x->{$k}); |
283 | } |
284 | elsif (ref($x->{$k}) eq 'SCALAR') |
285 | { |
286 | $self->{$k} = \${$x->{$k}}; |
287 | } |
288 | elsif (ref($x->{$k}) eq 'ARRAY') |
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289 | { |
290 | $self->{$k} = [ @{$x->{$k}} ]; |
291 | } |
292 | elsif (ref($x->{$k}) eq 'HASH') |
293 | { |
294 | # only one level deep! |
295 | foreach my $h (keys %{$x->{$k}}) |
296 | { |
297 | $self->{$k}->{$h} = $x->{$k}->{$h}; |
298 | } |
299 | } |
300 | elsif (ref($x->{$k})) |
301 | { |
302 | my $c = ref($x->{$k}); |
303 | $self->{$k} = $c->new($x->{$k}); # no copy() due to deep rec |
304 | } |
305 | else |
306 | { |
307 | $self->{$k} = $x->{$k}; |
308 | } |
309 | } |
310 | $self; |
311 | } |
312 | |
313 | sub new |
314 | { |
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315 | # create a new BigInt object from a string or another BigInt object. |
0716bf9b |
316 | # see hash keys documented at top |
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317 | |
318 | # the argument could be an object, so avoid ||, && etc on it, this would |
b22b3e31 |
319 | # cause costly overloaded code to be called. The only allowed ops are |
320 | # ref() and defined. |
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321 | |
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322 | my $class = shift; |
323 | |
324 | my $wanted = shift; # avoid numify call by not using || here |
325 | return $class->bzero() if !defined $wanted; # default to 0 |
326 | return $class->copy($wanted) if ref($wanted); |
327 | |
328 | my $self = {}; bless $self, $class; |
329 | # handle '+inf', '-inf' first |
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330 | if ($wanted =~ /^[+-]?inf$/) |
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331 | { |
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332 | $self->{value} = $CALC->_zero(); |
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333 | $self->{sign} = $wanted; $self->{sign} = '+inf' if $self->{sign} eq 'inf'; |
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334 | return $self; |
335 | } |
336 | # split str in m mantissa, e exponent, i integer, f fraction, v value, s sign |
337 | my ($mis,$miv,$mfv,$es,$ev) = _split(\$wanted); |
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338 | if (!ref $mis) |
339 | { |
340 | die "$wanted is not a number initialized to $class" if !$NaNOK; |
341 | #print "NaN 1\n"; |
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342 | $self->{value} = $CALC->_zero(); |
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343 | $self->{sign} = $nan; |
344 | return $self; |
345 | } |
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346 | if (!ref $miv) |
347 | { |
348 | # _from_hex or _from_bin |
349 | $self->{value} = $mis->{value}; |
350 | $self->{sign} = $mis->{sign}; |
351 | return $self; # throw away $mis |
352 | } |
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353 | # make integer from mantissa by adjusting exp, then convert to bigint |
354 | $self->{sign} = $$mis; # store sign |
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355 | $self->{value} = $CALC->_zero(); # for all the NaN cases |
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356 | my $e = int("$$es$$ev"); # exponent (avoid recursion) |
357 | if ($e > 0) |
358 | { |
359 | my $diff = $e - CORE::length($$mfv); |
360 | if ($diff < 0) # Not integer |
361 | { |
362 | #print "NOI 1\n"; |
363 | $self->{sign} = $nan; |
364 | } |
365 | else # diff >= 0 |
366 | { |
367 | # adjust fraction and add it to value |
368 | # print "diff > 0 $$miv\n"; |
369 | $$miv = $$miv . ($$mfv . '0' x $diff); |
370 | } |
371 | } |
372 | else |
373 | { |
374 | if ($$mfv ne '') # e <= 0 |
375 | { |
376 | # fraction and negative/zero E => NOI |
377 | #print "NOI 2 \$\$mfv '$$mfv'\n"; |
378 | $self->{sign} = $nan; |
379 | } |
380 | elsif ($e < 0) |
381 | { |
382 | # xE-y, and empty mfv |
383 | #print "xE-y\n"; |
384 | $e = abs($e); |
385 | if ($$miv !~ s/0{$e}$//) # can strip so many zero's? |
386 | { |
387 | #print "NOI 3\n"; |
388 | $self->{sign} = $nan; |
389 | } |
390 | } |
391 | } |
392 | $self->{sign} = '+' if $$miv eq '0'; # normalize -0 => +0 |
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393 | $self->{value} = $CALC->_new($miv) if $self->{sign} =~ /^[+-]$/; |
394 | #print "$wanted => $self->{sign}\n"; |
395 | # if any of the globals is set, use them to round and store them inside $self |
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396 | $self->round($accuracy,$precision,$round_mode) |
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397 | if defined $accuracy || defined $precision; |
398 | return $self; |
399 | } |
400 | |
58cde26e |
401 | sub bnan |
402 | { |
403 | # create a bigint 'NaN', if given a BigInt, set it to 'NaN' |
b4f14daa |
404 | my $self = shift; |
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405 | $self = $class if !defined $self; |
406 | if (!ref($self)) |
407 | { |
408 | my $c = $self; $self = {}; bless $self, $c; |
409 | } |
410 | return if $self->modify('bnan'); |
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411 | $self->{value} = $CALC->_zero(); |
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412 | $self->{sign} = $nan; |
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413 | return $self; |
b4f14daa |
414 | } |
58cde26e |
415 | |
416 | sub binf |
417 | { |
418 | # create a bigint '+-inf', if given a BigInt, set it to '+-inf' |
419 | # the sign is either '+', or if given, used from there |
420 | my $self = shift; |
421 | my $sign = shift; $sign = '+' if !defined $sign || $sign ne '-'; |
422 | $self = $class if !defined $self; |
423 | if (!ref($self)) |
424 | { |
425 | my $c = $self; $self = {}; bless $self, $c; |
426 | } |
427 | return if $self->modify('binf'); |
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428 | $self->{value} = $CALC->_zero(); |
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429 | $self->{sign} = $sign.'inf'; |
58cde26e |
430 | return $self; |
431 | } |
432 | |
433 | sub bzero |
434 | { |
435 | # create a bigint '+0', if given a BigInt, set it to 0 |
436 | my $self = shift; |
437 | $self = $class if !defined $self; |
0716bf9b |
438 | |
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439 | if (!ref($self)) |
440 | { |
441 | my $c = $self; $self = {}; bless $self, $c; |
442 | } |
443 | return if $self->modify('bzero'); |
0716bf9b |
444 | $self->{value} = $CALC->_zero(); |
58cde26e |
445 | $self->{sign} = '+'; |
0716bf9b |
446 | #print "result: $self\n"; |
58cde26e |
447 | return $self; |
448 | } |
449 | |
574bacfe |
450 | sub bone |
451 | { |
452 | # create a bigint '+1' (or -1 if given sign '-'), |
453 | # if given a BigInt, set it to +1 or -1, respecively |
454 | my $self = shift; |
455 | my $sign = shift; $sign = '+' if !defined $sign || $sign ne '-'; |
456 | $self = $class if !defined $self; |
457 | #print "bone $self\n"; |
458 | |
459 | if (!ref($self)) |
460 | { |
461 | my $c = $self; $self = {}; bless $self, $c; |
462 | } |
463 | return if $self->modify('bone'); |
464 | $self->{value} = $CALC->_one(); |
465 | $self->{sign} = $sign; |
466 | #print "result: $self\n"; |
467 | return $self; |
468 | } |
469 | |
58cde26e |
470 | ############################################################################## |
471 | # string conversation |
472 | |
473 | sub bsstr |
474 | { |
475 | # (ref to BFLOAT or num_str ) return num_str |
476 | # Convert number from internal format to scientific string format. |
477 | # internal format is always normalized (no leading zeros, "-0E0" => "+0E0") |
ee15d750 |
478 | # print "bsstr $_[0] $_[1]\n"; |
479 | # my $x = shift; $class = ref($x) || $x; |
480 | # print "class $class $x (",ref($x),") $_[0]\n"; |
481 | # $x = $class->new(shift) if !ref($x); |
482 | # |
483 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
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484 | |
574bacfe |
485 | if ($x->{sign} !~ /^[+-]$/) |
486 | { |
487 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN |
488 | return 'inf'; # +inf |
489 | } |
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490 | my ($m,$e) = $x->parts(); |
574bacfe |
491 | # e can only be positive |
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492 | my $sign = 'e+'; |
493 | # MBF: my $s = $e->{sign}; $s = '' if $s eq '-'; my $sep = 'e'.$s; |
494 | return $m->bstr().$sign.$e->bstr(); |
495 | } |
496 | |
497 | sub bstr |
498 | { |
0716bf9b |
499 | # make a string from bigint object |
ee15d750 |
500 | my $x = shift; $class = ref($x) || $x; $x = $class->new(shift) if !ref($x); |
501 | # my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
502 | |
574bacfe |
503 | if ($x->{sign} !~ /^[+-]$/) |
504 | { |
505 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN |
506 | return 'inf'; # +inf |
507 | } |
0716bf9b |
508 | my $es = ''; $es = $x->{sign} if $x->{sign} eq '-'; |
509 | return $es.${$CALC->_str($x->{value})}; |
58cde26e |
510 | } |
511 | |
512 | sub numify |
513 | { |
514 | # Make a number from a BigInt object |
58cde26e |
515 | my $x = shift; $x = $class->new($x) unless ref $x; |
0716bf9b |
516 | return $x->{sign} if $x->{sign} !~ /^[+-]$/; |
517 | my $num = $CALC->_num($x->{value}); |
518 | return -$num if $x->{sign} eq '-'; |
58cde26e |
519 | return $num; |
520 | } |
521 | |
522 | ############################################################################## |
523 | # public stuff (usually prefixed with "b") |
524 | |
525 | sub sign |
526 | { |
527 | # return the sign of the number: +/-/NaN |
ee15d750 |
528 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
529 | |
58cde26e |
530 | return $x->{sign}; |
531 | } |
532 | |
ee15d750 |
533 | sub _find_round_parameters |
58cde26e |
534 | { |
535 | # After any operation or when calling round(), the result is rounded by |
536 | # regarding the A & P from arguments, local parameters, or globals. |
537 | # The result's A or P are set by the rounding, but not inspected beforehand |
538 | # (aka only the arguments enter into it). This works because the given |
539 | # 'first' argument is both the result and true first argument with unchanged |
540 | # A and P settings. |
541 | # This does not yet handle $x with A, and $y with P (which should be an |
542 | # error). |
543 | my $self = shift; |
544 | my $a = shift; # accuracy, if given by caller |
545 | my $p = shift; # precision, if given by caller |
546 | my $r = shift; # round_mode, if given by caller |
547 | my @args = @_; # all 'other' arguments (0 for unary, 1 for binary ops) |
548 | |
574bacfe |
549 | $self = new($self) unless ref($self); # if not object, make one |
ee15d750 |
550 | my $c = ref($self); # find out class of argument(s) |
574bacfe |
551 | unshift @args,$self; # add 'first' argument |
552 | |
17baacb7 |
553 | # leave bigfloat parts alone |
ee15d750 |
554 | return ($self) if exists $self->{_f} && $self->{_f} & MB_NEVER_ROUND != 0; |
17baacb7 |
555 | |
574bacfe |
556 | no strict 'refs'; |
574bacfe |
557 | |
58cde26e |
558 | # now pick $a or $p, but only if we have got "arguments" |
559 | if ((!defined $a) && (!defined $p) && (@args > 0)) |
560 | { |
561 | foreach (@args) |
562 | { |
563 | # take the defined one, or if both defined, the one that is smaller |
564 | $a = $_->{_a} if (defined $_->{_a}) && (!defined $a || $_->{_a} < $a); |
565 | } |
566 | if (!defined $a) # if it still is not defined, take p |
567 | { |
568 | foreach (@args) |
569 | { |
ee15d750 |
570 | # take the defined one, or if both defined, the one that is bigger |
571 | # -2 > -3, and 3 > 2 |
572 | $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} > $p); |
1f45ae4a |
573 | } |
58cde26e |
574 | # if none defined, use globals (#2) |
575 | if (!defined $p) |
576 | { |
ee15d750 |
577 | my $z = "$c\::accuracy"; my $a = $$z; |
578 | if (!defined $a) |
579 | { |
580 | $z = "$c\::precision"; $p = $$z; |
581 | } |
1f45ae4a |
582 | } |
58cde26e |
583 | } # endif !$a |
584 | } # endif !$a || !$P && args > 0 |
ee15d750 |
585 | my @params = ($self); |
586 | if (defined $a || defined $p) |
587 | { |
588 | # print "r => ",$r||'r undef'," in $c\n"; |
589 | $r = $r || ${"$c\::round_mode"}; |
590 | die "Unknown round mode '$r'" |
591 | if $r !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/; |
592 | push @params, ($a,$p,$r); |
593 | } |
594 | return @params; |
595 | } |
596 | |
597 | sub round |
598 | { |
599 | # round $self according to given parameters, or given second argument's |
600 | # parameters or global defaults |
601 | my $self = shift; |
602 | |
603 | my @params = $self->_find_round_parameters(@_); |
604 | return $self->bnorm() if @params == 1; # no-op |
605 | |
58cde26e |
606 | # now round, by calling fround or ffround: |
ee15d750 |
607 | if (defined $params[1]) |
58cde26e |
608 | { |
ee15d750 |
609 | $self->bround($params[1],$params[3]); |
58cde26e |
610 | } |
ee15d750 |
611 | else |
58cde26e |
612 | { |
ee15d750 |
613 | $self->bfround($params[2],$params[3]); |
58cde26e |
614 | } |
ee15d750 |
615 | return $self->bnorm(); # after round, normalize |
58cde26e |
616 | } |
617 | |
17baacb7 |
618 | sub bnorm |
58cde26e |
619 | { |
ee15d750 |
620 | # (numstr or or BINT) return BINT |
58cde26e |
621 | # Normalize number -- no-op here |
ee15d750 |
622 | return Math::BigInt->new($_[0]) if !ref($_[0]); |
574bacfe |
623 | return $_[0]; |
58cde26e |
624 | } |
625 | |
626 | sub babs |
627 | { |
628 | # (BINT or num_str) return BINT |
629 | # make number absolute, or return absolute BINT from string |
ee15d750 |
630 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
631 | |
58cde26e |
632 | return $x if $x->modify('babs'); |
633 | # post-normalized abs for internal use (does nothing for NaN) |
634 | $x->{sign} =~ s/^-/+/; |
635 | $x; |
636 | } |
637 | |
638 | sub bneg |
639 | { |
640 | # (BINT or num_str) return BINT |
641 | # negate number or make a negated number from string |
ee15d750 |
642 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
643 | |
58cde26e |
644 | return $x if $x->modify('bneg'); |
645 | # for +0 dont negate (to have always normalized) |
646 | return $x if $x->is_zero(); |
647 | $x->{sign} =~ tr/+\-/-+/; # does nothing for NaN |
58cde26e |
648 | $x; |
649 | } |
650 | |
651 | sub bcmp |
652 | { |
653 | # Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort) |
654 | # (BINT or num_str, BINT or num_str) return cond_code |
655 | my ($self,$x,$y) = objectify(2,@_); |
0716bf9b |
656 | |
657 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
658 | { |
659 | # handle +-inf and NaN |
660 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
574bacfe |
661 | return 0 if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/; |
0716bf9b |
662 | return +1 if $x->{sign} eq '+inf'; |
663 | return -1 if $x->{sign} eq '-inf'; |
664 | return -1 if $y->{sign} eq '+inf'; |
665 | return +1 if $y->{sign} eq '-inf'; |
666 | } |
574bacfe |
667 | # check sign for speed first |
668 | return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y |
669 | return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0 |
670 | |
671 | # shortcut |
672 | my $xz = $x->is_zero(); |
673 | my $yz = $y->is_zero(); |
674 | return 0 if $xz && $yz; # 0 <=> 0 |
675 | return -1 if $xz && $y->{sign} eq '+'; # 0 <=> +y |
676 | return 1 if $yz && $x->{sign} eq '+'; # +x <=> 0 |
0716bf9b |
677 | # normal compare now |
58cde26e |
678 | &cmp($x->{value},$y->{value},$x->{sign},$y->{sign}) <=> 0; |
679 | } |
680 | |
681 | sub bacmp |
682 | { |
683 | # Compares 2 values, ignoring their signs. |
684 | # Returns one of undef, <0, =0, >0. (suitable for sort) |
685 | # (BINT, BINT) return cond_code |
686 | my ($self,$x,$y) = objectify(2,@_); |
574bacfe |
687 | |
688 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
689 | { |
690 | # handle +-inf and NaN |
691 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
692 | return 0 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} =~ /^[+-]inf$/; |
693 | return +1; # inf is always bigger |
694 | } |
0716bf9b |
695 | $CALC->_acmp($x->{value},$y->{value}) <=> 0; |
58cde26e |
696 | } |
697 | |
698 | sub badd |
699 | { |
700 | # add second arg (BINT or string) to first (BINT) (modifies first) |
701 | # return result as BINT |
58cde26e |
702 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
703 | |
704 | return $x if $x->modify('badd'); |
58cde26e |
705 | |
574bacfe |
706 | # inf and NaN handling |
707 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
708 | { |
709 | # NaN first |
710 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
711 | # inf handline |
712 | if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) |
713 | { |
714 | # + and + => +, - and - => -, + and - => 0, - and + => 0 |
715 | return $x->bzero() if $x->{sign} ne $y->{sign}; |
716 | return $x; |
717 | } |
718 | # +-inf + something => +inf |
719 | # something +-inf => +-inf |
720 | $x->{sign} = $y->{sign}, return $x if $y->{sign} =~ /^[+-]inf$/; |
721 | return $x; |
722 | } |
723 | |
0716bf9b |
724 | my @bn = ($a,$p,$r,$y); # make array for round calls |
58cde26e |
725 | # speed: no add for 0+y or x+0 |
0716bf9b |
726 | return $x->round(@bn) if $y->is_zero(); # x+0 |
58cde26e |
727 | if ($x->is_zero()) # 0+y |
728 | { |
729 | # make copy, clobbering up x |
0716bf9b |
730 | $x->{value} = $CALC->_copy($y->{value}); |
58cde26e |
731 | $x->{sign} = $y->{sign} || $nan; |
732 | return $x->round(@bn); |
733 | } |
734 | |
58cde26e |
735 | my ($sx, $sy) = ( $x->{sign}, $y->{sign} ); # get signs |
736 | |
737 | if ($sx eq $sy) |
738 | { |
574bacfe |
739 | $x->{value} = $CALC->_add($x->{value},$y->{value}); # same sign, abs add |
58cde26e |
740 | $x->{sign} = $sx; |
741 | } |
742 | else |
743 | { |
574bacfe |
744 | my $a = $CALC->_acmp ($y->{value},$x->{value}); # absolute compare |
58cde26e |
745 | if ($a > 0) |
746 | { |
747 | #print "swapped sub (a=$a)\n"; |
574bacfe |
748 | $x->{value} = $CALC->_sub($y->{value},$x->{value},1); # abs sub w/ swap |
58cde26e |
749 | $x->{sign} = $sy; |
750 | } |
751 | elsif ($a == 0) |
752 | { |
753 | # speedup, if equal, set result to 0 |
0716bf9b |
754 | #print "equal sub, result = 0\n"; |
755 | $x->{value} = $CALC->_zero(); |
58cde26e |
756 | $x->{sign} = '+'; |
757 | } |
758 | else # a < 0 |
759 | { |
760 | #print "unswapped sub (a=$a)\n"; |
574bacfe |
761 | $x->{value} = $CALC->_sub($x->{value}, $y->{value}); # abs sub |
58cde26e |
762 | $x->{sign} = $sx; |
a0d0e21e |
763 | } |
a0d0e21e |
764 | } |
58cde26e |
765 | return $x->round(@bn); |
766 | } |
767 | |
768 | sub bsub |
769 | { |
770 | # (BINT or num_str, BINT or num_str) return num_str |
771 | # subtract second arg from first, modify first |
772 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
773 | |
58cde26e |
774 | return $x if $x->modify('bsub'); |
775 | $x->badd($y->bneg()); # badd does not leave internal zeros |
776 | $y->bneg(); # refix y, assumes no one reads $y in between |
777 | return $x->round($a,$p,$r,$y); |
778 | } |
779 | |
780 | sub binc |
781 | { |
782 | # increment arg by one |
ee15d750 |
783 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e |
784 | return $x if $x->modify('binc'); |
574bacfe |
785 | $x->badd($self->__one())->round($a,$p,$r); |
58cde26e |
786 | } |
787 | |
788 | sub bdec |
789 | { |
790 | # decrement arg by one |
ee15d750 |
791 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e |
792 | return $x if $x->modify('bdec'); |
574bacfe |
793 | $x->badd($self->__one('-'))->round($a,$p,$r); |
58cde26e |
794 | } |
795 | |
796 | sub blcm |
797 | { |
798 | # (BINT or num_str, BINT or num_str) return BINT |
799 | # does not modify arguments, but returns new object |
800 | # Lowest Common Multiplicator |
58cde26e |
801 | |
0716bf9b |
802 | my $y = shift; my ($x); |
803 | if (ref($y)) |
804 | { |
805 | $x = $y->copy(); |
806 | } |
807 | else |
808 | { |
809 | $x = $class->new($y); |
810 | } |
811 | while (@_) { $x = _lcm($x,shift); } |
58cde26e |
812 | $x; |
813 | } |
814 | |
815 | sub bgcd |
816 | { |
817 | # (BINT or num_str, BINT or num_str) return BINT |
818 | # does not modify arguments, but returns new object |
819 | # GCD -- Euclids algorithm, variant C (Knuth Vol 3, pg 341 ff) |
0716bf9b |
820 | |
821 | my $y = shift; my ($x); |
822 | if (ref($y)) |
58cde26e |
823 | { |
0716bf9b |
824 | $x = $y->copy(); |
825 | } |
826 | else |
827 | { |
828 | $x = $class->new($y); |
829 | } |
830 | |
831 | if ($CALC->can('_gcd')) |
832 | { |
833 | while (@_) |
834 | { |
835 | $y = shift; $y = $class->new($y) if !ref($y); |
836 | next if $y->is_zero(); |
837 | return $x->bnan() if $y->{sign} !~ /^[+-]$/; # y NaN? |
838 | $x->{value} = $CALC->_gcd($x->{value},$y->{value}); last if $x->is_one(); |
839 | } |
840 | } |
841 | else |
842 | { |
843 | while (@_) |
844 | { |
574bacfe |
845 | $x = __gcd($x,shift); last if $x->is_one(); # _gcd handles NaN |
0716bf9b |
846 | } |
847 | } |
848 | $x->babs(); |
58cde26e |
849 | } |
850 | |
851 | sub bmod |
852 | { |
853 | # modulus |
854 | # (BINT or num_str, BINT or num_str) return BINT |
855 | my ($self,$x,$y) = objectify(2,@_); |
856 | |
857 | return $x if $x->modify('bmod'); |
858 | (&bdiv($self,$x,$y))[1]; |
859 | } |
860 | |
861 | sub bnot |
862 | { |
863 | # (num_str or BINT) return BINT |
864 | # represent ~x as twos-complement number |
ee15d750 |
865 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
866 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (undef,@_) : objectify(1,@_); |
867 | |
58cde26e |
868 | return $x if $x->modify('bnot'); |
ee15d750 |
869 | $x->bneg(); $x->bdec(); # was: bsub(-1,$x);, time it someday |
870 | return $x->round($a,$p,$r); |
58cde26e |
871 | } |
872 | |
873 | sub is_zero |
874 | { |
875 | # return true if arg (BINT or num_str) is zero (array '+', '0') |
ee15d750 |
876 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
877 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
0716bf9b |
878 | |
574bacfe |
879 | return 0 if $x->{sign} !~ /^\+$/; # -, NaN & +-inf aren't |
17baacb7 |
880 | $CALC->_is_zero($x->{value}); |
58cde26e |
881 | } |
882 | |
883 | sub is_nan |
884 | { |
885 | # return true if arg (BINT or num_str) is NaN |
ee15d750 |
886 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
887 | |
888 | return 1 if $x->{sign} eq $nan; |
889 | return 0; |
58cde26e |
890 | } |
891 | |
892 | sub is_inf |
893 | { |
894 | # return true if arg (BINT or num_str) is +-inf |
ee15d750 |
895 | my ($self,$x,$sign) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
896 | |
897 | $sign = '' if !defined $sign; |
898 | return 0 if $sign !~ /^([+-]|)$/; |
58cde26e |
899 | |
ee15d750 |
900 | if ($sign eq '') |
901 | { |
902 | return 1 if ($x->{sign} =~ /^[+-]inf$/); |
903 | return 0; |
904 | } |
905 | $sign = quotemeta($sign.'inf'); |
906 | return 1 if ($x->{sign} =~ /^$sign$/); |
907 | return 0; |
58cde26e |
908 | } |
909 | |
910 | sub is_one |
911 | { |
b22b3e31 |
912 | # return true if arg (BINT or num_str) is +1 |
913 | # or -1 if sign is given |
ee15d750 |
914 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
915 | my ($self,$x,$sign) = ref($_[0]) ? (undef,@_) : objectify(1,@_); |
916 | |
917 | $sign = '' if !defined $sign; $sign = '+' if $sign ne '-'; |
0716bf9b |
918 | |
ee15d750 |
919 | return 0 if $x->{sign} ne $sign; # -1 != +1, NaN, +-inf aren't either |
0716bf9b |
920 | return $CALC->_is_one($x->{value}); |
58cde26e |
921 | } |
922 | |
923 | sub is_odd |
924 | { |
925 | # return true when arg (BINT or num_str) is odd, false for even |
ee15d750 |
926 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
927 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
0716bf9b |
928 | |
b22b3e31 |
929 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
0716bf9b |
930 | return $CALC->_is_odd($x->{value}); |
58cde26e |
931 | } |
932 | |
933 | sub is_even |
934 | { |
935 | # return true when arg (BINT or num_str) is even, false for odd |
ee15d750 |
936 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
937 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
0716bf9b |
938 | |
b22b3e31 |
939 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
0716bf9b |
940 | return $CALC->_is_even($x->{value}); |
0716bf9b |
941 | } |
942 | |
943 | sub is_positive |
944 | { |
945 | # return true when arg (BINT or num_str) is positive (>= 0) |
ee15d750 |
946 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
947 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
948 | |
949 | return 1 if $x->{sign} =~ /^\+/; |
950 | return 0; |
0716bf9b |
951 | } |
952 | |
953 | sub is_negative |
954 | { |
955 | # return true when arg (BINT or num_str) is negative (< 0) |
ee15d750 |
956 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
957 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
958 | |
959 | return 1 if ($x->{sign} =~ /^-/); |
960 | return 0; |
58cde26e |
961 | } |
962 | |
0716bf9b |
963 | ############################################################################### |
964 | |
58cde26e |
965 | sub bmul |
966 | { |
967 | # multiply two numbers -- stolen from Knuth Vol 2 pg 233 |
968 | # (BINT or num_str, BINT or num_str) return BINT |
969 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
0716bf9b |
970 | |
58cde26e |
971 | return $x if $x->modify('bmul'); |
574bacfe |
972 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
973 | # handle result = 0 |
974 | return $x if $x->is_zero(); |
975 | return $x->bzero() if $y->is_zero(); |
976 | # inf handling |
977 | if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) |
978 | { |
979 | # result will always be +-inf: |
980 | # +inf * +/+inf => +inf, -inf * -/-inf => +inf |
981 | # +inf * -/-inf => -inf, -inf * +/+inf => -inf |
982 | return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); |
983 | return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); |
984 | return $x->binf('-'); |
985 | } |
58cde26e |
986 | |
0716bf9b |
987 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; # +1 * +1 or -1 * -1 => + |
574bacfe |
988 | $x->{value} = $CALC->_mul($x->{value},$y->{value}); # do actual math |
58cde26e |
989 | return $x->round($a,$p,$r,$y); |
990 | } |
991 | |
992 | sub bdiv |
993 | { |
994 | # (dividend: BINT or num_str, divisor: BINT or num_str) return |
995 | # (BINT,BINT) (quo,rem) or BINT (only rem) |
58cde26e |
996 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
997 | |
998 | return $x if $x->modify('bdiv'); |
999 | |
574bacfe |
1000 | # x / +-inf => 0, reminder x |
1001 | return wantarray ? ($x->bzero(),$x->copy()) : $x->bzero() |
1002 | if $y->{sign} =~ /^[+-]inf$/; |
0716bf9b |
1003 | |
574bacfe |
1004 | # NaN if x == NaN or y == NaN or x==y==0 |
58cde26e |
1005 | return wantarray ? ($x->bnan(),bnan()) : $x->bnan() |
574bacfe |
1006 | if (($x->is_nan() || $y->is_nan()) || |
1007 | ($x->is_zero() && $y->is_zero())); |
1008 | |
1009 | # 5 / 0 => +inf, -6 / 0 => -inf |
1010 | return wantarray |
1011 | ? ($x->binf($x->{sign}),$self->bnan()) : $x->binf($x->{sign}) |
1012 | if ($x->{sign} =~ /^[+-]$/ && $y->is_zero()); |
1013 | |
1014 | # old code: always NaN if /0 |
1015 | #return wantarray ? ($x->bnan(),$self->bnan()) : $x->bnan() |
1016 | # if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/ || $y->is_zero()); |
58cde26e |
1017 | |
1018 | # 0 / something |
1019 | return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero(); |
1020 | |
1021 | # Is $x in the interval [0, $y) ? |
0716bf9b |
1022 | my $cmp = $CALC->_acmp($x->{value},$y->{value}); |
58cde26e |
1023 | if (($cmp < 0) and ($x->{sign} eq $y->{sign})) |
1024 | { |
1025 | return $x->bzero() unless wantarray; |
1026 | my $t = $x->copy(); # make copy first, because $x->bzero() clobbers $x |
1027 | return ($x->bzero(),$t); |
1028 | } |
1029 | elsif ($cmp == 0) |
1030 | { |
1031 | # shortcut, both are the same, so set to +/- 1 |
574bacfe |
1032 | $x->__one( ($x->{sign} ne $y->{sign} ? '-' : '+') ); |
58cde26e |
1033 | return $x unless wantarray; |
1034 | return ($x,$self->bzero()); |
1035 | } |
1036 | |
1037 | # calc new sign and in case $y == +/- 1, return $x |
1038 | $x->{sign} = ($x->{sign} ne $y->{sign} ? '-' : '+'); |
1039 | # check for / +-1 (cant use $y->is_one due to '-' |
0716bf9b |
1040 | if (($y == 1) || ($y == -1)) # slow! |
1041 | #if ((@{$y->{value}} == 1) && ($y->{value}->[0] == 1)) |
58cde26e |
1042 | { |
1043 | return wantarray ? ($x,$self->bzero()) : $x; |
1044 | } |
1045 | |
1046 | # call div here |
1047 | my $rem = $self->bzero(); |
1048 | $rem->{sign} = $y->{sign}; |
0716bf9b |
1049 | ($x->{value},$rem->{value}) = $CALC->_div($x->{value},$y->{value}); |
ee15d750 |
1050 | # do not leave reminder "-0"; |
0716bf9b |
1051 | # $rem->{sign} = '+' if (@{$rem->{value}} == 1) && ($rem->{value}->[0] == 0); |
1052 | $rem->{sign} = '+' if $CALC->_is_zero($rem->{value}); |
58cde26e |
1053 | if (($x->{sign} eq '-') and (!$rem->is_zero())) |
1054 | { |
1055 | $x->bdec(); |
1056 | } |
ee15d750 |
1057 | # print "in div round ",$a||'a undef'," ",$p|| 'p undef'," $r\n"; |
58cde26e |
1058 | $x->round($a,$p,$r,$y); |
1059 | if (wantarray) |
1060 | { |
1061 | $rem->round($a,$p,$r,$x,$y); |
1062 | return ($x,$y-$rem) if $x->{sign} eq '-'; # was $x,$rem |
1063 | return ($x,$rem); |
1064 | } |
1065 | return $x; |
1066 | } |
1067 | |
1068 | sub bpow |
1069 | { |
1070 | # (BINT or num_str, BINT or num_str) return BINT |
1071 | # compute power of two numbers -- stolen from Knuth Vol 2 pg 233 |
1072 | # modifies first argument |
58cde26e |
1073 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
1074 | |
1075 | return $x if $x->modify('bpow'); |
1076 | |
0716bf9b |
1077 | return $x if $x->{sign} =~ /^[+-]inf$/; # -inf/+inf ** x |
58cde26e |
1078 | return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan; |
574bacfe |
1079 | return $x->__one() if $y->is_zero(); |
58cde26e |
1080 | return $x if $x->is_one() || $y->is_one(); |
0716bf9b |
1081 | #if ($x->{sign} eq '-' && @{$x->{value}} == 1 && $x->{value}->[0] == 1) |
1082 | if ($x->{sign} eq '-' && $CALC->_is_one($x->{value})) |
58cde26e |
1083 | { |
1084 | # if $x == -1 and odd/even y => +1/-1 |
0716bf9b |
1085 | return $y->is_odd() ? $x : $x->babs(); |
574bacfe |
1086 | # my Casio FX-5500L has a bug here: -1 ** 2 is -1, but -1 * -1 is 1; |
58cde26e |
1087 | } |
574bacfe |
1088 | # 1 ** -y => 1 / (1 ** |y|) |
1089 | # so do test for negative $y after above's clause |
58cde26e |
1090 | return $x->bnan() if $y->{sign} eq '-'; |
1091 | return $x if $x->is_zero(); # 0**y => 0 (if not y <= 0) |
1092 | |
0716bf9b |
1093 | if ($CALC->can('_pow')) |
58cde26e |
1094 | { |
574bacfe |
1095 | $x->{value} = $CALC->_pow($x->{value},$y->{value}); |
0716bf9b |
1096 | return $x->round($a,$p,$r); |
58cde26e |
1097 | } |
0716bf9b |
1098 | # based on the assumption that shifting in base 10 is fast, and that mul |
1099 | # works faster if numbers are small: we count trailing zeros (this step is |
1100 | # O(1)..O(N), but in case of O(N) we save much more time due to this), |
1101 | # stripping them out of the multiplication, and add $count * $y zeros |
1102 | # afterwards like this: |
1103 | # 300 ** 3 == 300*300*300 == 3*3*3 . '0' x 2 * 3 == 27 . '0' x 6 |
1104 | # creates deep recursion? |
574bacfe |
1105 | # my $zeros = $x->_trailing_zeros(); |
1106 | # if ($zeros > 0) |
1107 | # { |
1108 | # $x->brsft($zeros,10); # remove zeros |
1109 | # $x->bpow($y); # recursion (will not branch into here again) |
1110 | # $zeros = $y * $zeros; # real number of zeros to add |
1111 | # $x->blsft($zeros,10); |
1112 | # return $x->round($a,$p,$r); |
1113 | # } |
1114 | |
1115 | my $pow2 = $self->__one(); |
58cde26e |
1116 | my $y1 = $class->new($y); |
1117 | my ($res); |
1118 | while (!$y1->is_one()) |
1119 | { |
1120 | #print "bpow: p2: $pow2 x: $x y: $y1 r: $res\n"; |
1121 | #print "len ",$x->length(),"\n"; |
1122 | ($y1,$res)=&bdiv($y1,2); |
1123 | if (!$res->is_zero()) { &bmul($pow2,$x); } |
1124 | if (!$y1->is_zero()) { &bmul($x,$x); } |
0716bf9b |
1125 | #print "$x $y\n"; |
58cde26e |
1126 | } |
1127 | #print "bpow: e p2: $pow2 x: $x y: $y1 r: $res\n"; |
1128 | &bmul($x,$pow2) if (!$pow2->is_one()); |
1129 | #print "bpow: e p2: $pow2 x: $x y: $y1 r: $res\n"; |
1130 | return $x->round($a,$p,$r); |
1131 | } |
1132 | |
1133 | sub blsft |
1134 | { |
1135 | # (BINT or num_str, BINT or num_str) return BINT |
1136 | # compute x << y, base n, y >= 0 |
1137 | my ($self,$x,$y,$n) = objectify(2,@_); |
1138 | |
1139 | return $x if $x->modify('blsft'); |
1140 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
1141 | |
574bacfe |
1142 | $n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-'; |
1143 | |
1144 | my $t = $CALC->_lsft($x->{value},$y->{value},$n) if $CALC->can('_lsft'); |
1145 | if (defined $t) |
1146 | { |
1147 | $x->{value} = $t; return $x; |
1148 | } |
1149 | # fallback |
1150 | return $x->bmul( $self->bpow($n, $y) ); |
58cde26e |
1151 | } |
1152 | |
1153 | sub brsft |
1154 | { |
1155 | # (BINT or num_str, BINT or num_str) return BINT |
1156 | # compute x >> y, base n, y >= 0 |
1157 | my ($self,$x,$y,$n) = objectify(2,@_); |
1158 | |
1159 | return $x if $x->modify('brsft'); |
1160 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
1161 | |
1162 | $n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-'; |
574bacfe |
1163 | |
1164 | my $t = $CALC->_rsft($x->{value},$y->{value},$n) if $CALC->can('_rsft'); |
1165 | if (defined $t) |
1166 | { |
1167 | $x->{value} = $t; return $x; |
1168 | } |
1169 | # fallback |
1170 | return scalar bdiv($x, $self->bpow($n, $y)); |
58cde26e |
1171 | } |
1172 | |
1173 | sub band |
1174 | { |
1175 | #(BINT or num_str, BINT or num_str) return BINT |
1176 | # compute x & y |
0716bf9b |
1177 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
58cde26e |
1178 | |
1179 | return $x if $x->modify('band'); |
1180 | |
1181 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
1182 | return $x->bzero() if $y->is_zero(); |
0716bf9b |
1183 | |
574bacfe |
1184 | my $sign = 0; # sign of result |
1185 | $sign = 1 if ($x->{sign} eq '-') && ($y->{sign} eq '-'); |
1186 | my $sx = 1; $sx = -1 if $x->{sign} eq '-'; |
1187 | my $sy = 1; $sy = -1 if $y->{sign} eq '-'; |
1188 | |
1189 | if ($CALC->can('_and') && $sx == 1 && $sy == 1) |
0716bf9b |
1190 | { |
574bacfe |
1191 | $x->{value} = $CALC->_and($x->{value},$y->{value}); |
0716bf9b |
1192 | return $x->round($a,$p,$r); |
1193 | } |
574bacfe |
1194 | |
0716bf9b |
1195 | my $m = new Math::BigInt 1; my ($xr,$yr); |
574bacfe |
1196 | my $x10000 = new Math::BigInt (0x1000); |
1197 | my $y1 = copy(ref($x),$y); # make copy |
1198 | $y1->babs(); # and positive |
1199 | my $x1 = $x->copy()->babs(); $x->bzero(); # modify x in place! |
1200 | use integer; # need this for negative bools |
0716bf9b |
1201 | while (!$x1->is_zero() && !$y1->is_zero()) |
58cde26e |
1202 | { |
0716bf9b |
1203 | ($x1, $xr) = bdiv($x1, $x10000); |
58cde26e |
1204 | ($y1, $yr) = bdiv($y1, $x10000); |
574bacfe |
1205 | # make both op's numbers! |
1206 | $x->badd( bmul( $class->new( |
1207 | abs($sx*int($xr->numify()) & $sy*int($yr->numify()))), |
1208 | $m)); |
58cde26e |
1209 | $m->bmul($x10000); |
1210 | } |
574bacfe |
1211 | $x->bneg() if $sign; |
0716bf9b |
1212 | return $x->round($a,$p,$r); |
58cde26e |
1213 | } |
1214 | |
1215 | sub bior |
1216 | { |
1217 | #(BINT or num_str, BINT or num_str) return BINT |
1218 | # compute x | y |
0716bf9b |
1219 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
58cde26e |
1220 | |
1221 | return $x if $x->modify('bior'); |
1222 | |
1223 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
1224 | return $x if $y->is_zero(); |
574bacfe |
1225 | |
1226 | my $sign = 0; # sign of result |
1227 | $sign = 1 if ($x->{sign} eq '-') || ($y->{sign} eq '-'); |
1228 | my $sx = 1; $sx = -1 if $x->{sign} eq '-'; |
1229 | my $sy = 1; $sy = -1 if $y->{sign} eq '-'; |
1230 | |
1231 | # don't use lib for negative values |
1232 | if ($CALC->can('_or') && $sx == 1 && $sy == 1) |
0716bf9b |
1233 | { |
574bacfe |
1234 | $x->{value} = $CALC->_or($x->{value},$y->{value}); |
0716bf9b |
1235 | return $x->round($a,$p,$r); |
1236 | } |
1237 | |
1238 | my $m = new Math::BigInt 1; my ($xr,$yr); |
58cde26e |
1239 | my $x10000 = new Math::BigInt (0x10000); |
574bacfe |
1240 | my $y1 = copy(ref($x),$y); # make copy |
1241 | $y1->babs(); # and positive |
1242 | my $x1 = $x->copy()->babs(); $x->bzero(); # modify x in place! |
1243 | use integer; # need this for negative bools |
0716bf9b |
1244 | while (!$x1->is_zero() || !$y1->is_zero()) |
58cde26e |
1245 | { |
0716bf9b |
1246 | ($x1, $xr) = bdiv($x1,$x10000); |
58cde26e |
1247 | ($y1, $yr) = bdiv($y1,$x10000); |
574bacfe |
1248 | # make both op's numbers! |
1249 | $x->badd( bmul( $class->new( |
1250 | abs($sx*int($xr->numify()) | $sy*int($yr->numify()))), |
1251 | $m)); |
1252 | # $x->badd( bmul( $class->new(int($xr->numify()) | int($yr->numify())), $m)); |
58cde26e |
1253 | $m->bmul($x10000); |
1254 | } |
574bacfe |
1255 | $x->bneg() if $sign; |
0716bf9b |
1256 | return $x->round($a,$p,$r); |
58cde26e |
1257 | } |
1258 | |
1259 | sub bxor |
1260 | { |
1261 | #(BINT or num_str, BINT or num_str) return BINT |
1262 | # compute x ^ y |
0716bf9b |
1263 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
58cde26e |
1264 | |
1265 | return $x if $x->modify('bxor'); |
1266 | |
0716bf9b |
1267 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
58cde26e |
1268 | return $x if $y->is_zero(); |
1269 | return $x->bzero() if $x == $y; # shortcut |
0716bf9b |
1270 | |
574bacfe |
1271 | my $sign = 0; # sign of result |
1272 | $sign = 1 if $x->{sign} ne $y->{sign}; |
1273 | my $sx = 1; $sx = -1 if $x->{sign} eq '-'; |
1274 | my $sy = 1; $sy = -1 if $y->{sign} eq '-'; |
1275 | |
1276 | # don't use lib for negative values |
1277 | if ($CALC->can('_xor') && $sx == 1 && $sy == 1) |
0716bf9b |
1278 | { |
574bacfe |
1279 | $x->{value} = $CALC->_xor($x->{value},$y->{value}); |
0716bf9b |
1280 | return $x->round($a,$p,$r); |
1281 | } |
1282 | |
1283 | my $m = new Math::BigInt 1; my ($xr,$yr); |
58cde26e |
1284 | my $x10000 = new Math::BigInt (0x10000); |
1285 | my $y1 = copy(ref($x),$y); # make copy |
574bacfe |
1286 | $y1->babs(); # and positive |
1287 | my $x1 = $x->copy()->babs(); $x->bzero(); # modify x in place! |
1288 | use integer; # need this for negative bools |
0716bf9b |
1289 | while (!$x1->is_zero() || !$y1->is_zero()) |
58cde26e |
1290 | { |
0716bf9b |
1291 | ($x1, $xr) = bdiv($x1, $x10000); |
58cde26e |
1292 | ($y1, $yr) = bdiv($y1, $x10000); |
574bacfe |
1293 | # make both op's numbers! |
1294 | $x->badd( bmul( $class->new( |
1295 | abs($sx*int($xr->numify()) ^ $sy*int($yr->numify()))), |
1296 | $m)); |
1297 | # $x->badd( bmul( $class->new(int($xr->numify()) ^ int($yr->numify())), $m)); |
58cde26e |
1298 | $m->bmul($x10000); |
1299 | } |
574bacfe |
1300 | $x->bneg() if $sign; |
0716bf9b |
1301 | return $x->round($a,$p,$r); |
58cde26e |
1302 | } |
1303 | |
1304 | sub length |
1305 | { |
ee15d750 |
1306 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
1307 | |
0716bf9b |
1308 | my $e = $CALC->_len($x->{value}); |
1309 | # # fallback, since we do not know the underlying representation |
1310 | #my $es = "$x"; my $c = 0; $c = 1 if $es =~ /^[+-]/; # if lib returns '+123' |
1311 | #my $e = CORE::length($es)-$c; |
1312 | return wantarray ? ($e,0) : $e; |
58cde26e |
1313 | } |
1314 | |
1315 | sub digit |
1316 | { |
0716bf9b |
1317 | # return the nth decimal digit, negative values count backward, 0 is right |
58cde26e |
1318 | my $x = shift; |
1319 | my $n = shift || 0; |
1320 | |
0716bf9b |
1321 | return $CALC->_digit($x->{value},$n); |
58cde26e |
1322 | } |
1323 | |
1324 | sub _trailing_zeros |
1325 | { |
1326 | # return the amount of trailing zeros in $x |
1327 | my $x = shift; |
1328 | $x = $class->new($x) unless ref $x; |
1329 | |
bd05a461 |
1330 | #return 0 if $x->is_zero() || $x->is_odd() || $x->{sign} !~ /^[+-]$/; |
574bacfe |
1331 | return 0 if $x->is_zero() || $x->{sign} !~ /^[+-]$/; |
0716bf9b |
1332 | |
1333 | return $CALC->_zeros($x->{value}) if $CALC->can('_zeros'); |
1334 | |
b22b3e31 |
1335 | # if not: since we do not know underlying internal representation: |
0716bf9b |
1336 | my $es = "$x"; $es =~ /([0]*)$/; |
1337 | |
1338 | return 0 if !defined $1; # no zeros |
1339 | return CORE::length("$1"); # as string, not as +0! |
58cde26e |
1340 | } |
1341 | |
1342 | sub bsqrt |
1343 | { |
ee15d750 |
1344 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
1345 | |
1346 | return $x->bnan() if $x->{sign} =~ /\-|$nan/; # -x or NaN => NaN |
1347 | return $x->bzero() if $x->is_zero(); # 0 => 0 |
1348 | return $x if $x == 1; # 1 => 1 |
1349 | |
1350 | my $y = $x->copy(); # give us one more digit accur. |
1351 | my $l = int($x->length()/2); |
1352 | |
1353 | $x->bzero(); |
1354 | $x->binc(); # keep ref($x), but modify it |
1355 | $x *= 10 ** $l; |
1356 | |
1357 | # print "x: $y guess $x\n"; |
1358 | |
1359 | my $last = $self->bzero(); |
1360 | while ($last != $x) |
1361 | { |
1362 | $last = $x; |
1363 | $x += $y / $x; |
1364 | $x /= 2; |
1365 | } |
1366 | return $x; |
1367 | } |
1368 | |
1369 | sub exponent |
1370 | { |
1371 | # return a copy of the exponent (here always 0, NaN or 1 for $m == 0) |
ee15d750 |
1372 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
1373 | |
ee15d750 |
1374 | if ($x->{sign} !~ /^[+-]$/) |
1375 | { |
1376 | my $s = $x->{sign}; $s =~ s/^[+-]//; |
1377 | return $self->new($s); # -inf,+inf => inf |
1378 | } |
58cde26e |
1379 | my $e = $class->bzero(); |
1380 | return $e->binc() if $x->is_zero(); |
1381 | $e += $x->_trailing_zeros(); |
1382 | return $e; |
1383 | } |
1384 | |
1385 | sub mantissa |
1386 | { |
ee15d750 |
1387 | # return the mantissa (compatible to Math::BigFloat, e.g. reduced) |
1388 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
1389 | |
ee15d750 |
1390 | if ($x->{sign} !~ /^[+-]$/) |
1391 | { |
1392 | my $s = $x->{sign}; $s =~ s/^[+]//; |
1393 | return $self->new($s); # +inf => inf |
1394 | } |
58cde26e |
1395 | my $m = $x->copy(); |
1396 | # that's inefficient |
1397 | my $zeros = $m->_trailing_zeros(); |
1398 | $m /= 10 ** $zeros if $zeros != 0; |
1399 | return $m; |
1400 | } |
1401 | |
1402 | sub parts |
1403 | { |
ee15d750 |
1404 | # return a copy of both the exponent and the mantissa |
1405 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
1406 | |
ee15d750 |
1407 | return ($x->mantissa(),$x->exponent()); |
58cde26e |
1408 | } |
1409 | |
1410 | ############################################################################## |
1411 | # rounding functions |
1412 | |
1413 | sub bfround |
1414 | { |
1415 | # precision: round to the $Nth digit left (+$n) or right (-$n) from the '.' |
ee15d750 |
1416 | # $n == 0 || $n == 1 => round to integer |
58cde26e |
1417 | my $x = shift; $x = $class->new($x) unless ref $x; |
ee15d750 |
1418 | my ($scale,$mode) = $x->_scale_p($precision,$round_mode,@_); |
58cde26e |
1419 | return $x if !defined $scale; # no-op |
1420 | |
1421 | # no-op for BigInts if $n <= 0 |
ee15d750 |
1422 | if ($scale <= 0) |
1423 | { |
1424 | $x->{_p} = $scale; return $x; |
1425 | } |
58cde26e |
1426 | |
1427 | $x->bround( $x->length()-$scale, $mode); |
ee15d750 |
1428 | $x->{_a} = undef; # bround sets {_a} |
1429 | $x->{_p} = $scale; # so correct it |
1430 | $x; |
58cde26e |
1431 | } |
1432 | |
1433 | sub _scan_for_nonzero |
1434 | { |
1435 | my $x = shift; |
1436 | my $pad = shift; |
0716bf9b |
1437 | my $xs = shift; |
58cde26e |
1438 | |
1439 | my $len = $x->length(); |
1440 | return 0 if $len == 1; # '5' is trailed by invisible zeros |
1441 | my $follow = $pad - 1; |
1442 | return 0 if $follow > $len || $follow < 1; |
1443 | #print "checking $x $r\n"; |
0716bf9b |
1444 | |
b22b3e31 |
1445 | # since we do not know underlying represention of $x, use decimal string |
0716bf9b |
1446 | #my $r = substr ($$xs,-$follow); |
58cde26e |
1447 | my $r = substr ("$x",-$follow); |
1448 | return 1 if $r =~ /[^0]/; return 0; |
58cde26e |
1449 | } |
1450 | |
1451 | sub fround |
1452 | { |
1453 | # to make life easier for switch between MBF and MBI (autoload fxxx() |
1454 | # like MBF does for bxxx()?) |
1455 | my $x = shift; |
1456 | return $x->bround(@_); |
1457 | } |
1458 | |
1459 | sub bround |
1460 | { |
1461 | # accuracy: +$n preserve $n digits from left, |
1462 | # -$n preserve $n digits from right (f.i. for 0.1234 style in MBF) |
1463 | # no-op for $n == 0 |
1464 | # and overwrite the rest with 0's, return normalized number |
1465 | # do not return $x->bnorm(), but $x |
1466 | my $x = shift; $x = $class->new($x) unless ref $x; |
ee15d750 |
1467 | my ($scale,$mode) = $x->_scale_a($accuracy,$round_mode,@_); |
58cde26e |
1468 | return $x if !defined $scale; # no-op |
1469 | |
1470 | # print "MBI round: $x to $scale $mode\n"; |
574bacfe |
1471 | return $x if $x->{sign} !~ /^[+-]$/ || $x->is_zero() || $scale == 0; |
58cde26e |
1472 | |
1473 | # we have fewer digits than we want to scale to |
1474 | my $len = $x->length(); |
ee15d750 |
1475 | # print "$scale $len\n"; |
1476 | # scale < 0, but > -len (not >=!) |
1477 | if (($scale < 0 && $scale < -$len-1) || ($scale >= $len)) |
1478 | { |
1479 | $x->{_a} = $scale if !defined $x->{_a}; # if not yet defined overwrite |
1480 | return $x; |
1481 | } |
58cde26e |
1482 | |
1483 | # count of 0's to pad, from left (+) or right (-): 9 - +6 => 3, or |-6| => 6 |
1484 | my ($pad,$digit_round,$digit_after); |
1485 | $pad = $len - $scale; |
ee15d750 |
1486 | $pad = abs($scale-1) if $scale < 0; |
1487 | |
0716bf9b |
1488 | # do not use digit(), it is costly for binary => decimal |
1489 | #$digit_round = '0'; $digit_round = $x->digit($pad) if $pad < $len; |
1490 | #$digit_after = '0'; $digit_after = $x->digit($pad-1) if $pad > 0; |
ee15d750 |
1491 | |
0716bf9b |
1492 | my $xs = $CALC->_str($x->{value}); |
1493 | my $pl = -$pad-1; |
ee15d750 |
1494 | |
1495 | # print "pad $pad pl $pl scale $scale len $len\n"; |
0716bf9b |
1496 | # pad: 123: 0 => -1, at 1 => -2, at 2 => -3, at 3 => -4 |
1497 | # pad+1: 123: 0 => 0, at 1 => -1, at 2 => -2, at 3 => -3 |
1498 | $digit_round = '0'; $digit_round = substr($$xs,$pl,1) if $pad <= $len; |
1499 | $pl++; $pl ++ if $pad >= $len; |
1500 | $digit_after = '0'; $digit_after = substr($$xs,$pl,1) |
1501 | if $pad > 0; |
ee15d750 |
1502 | |
1503 | # print "$pad $pl $$xs dr $digit_round da $digit_after\n"; |
58cde26e |
1504 | |
1505 | # in case of 01234 we round down, for 6789 up, and only in case 5 we look |
1506 | # closer at the remaining digits of the original $x, remember decision |
1507 | my $round_up = 1; # default round up |
1508 | $round_up -- if |
1509 | ($mode eq 'trunc') || # trunc by round down |
1510 | ($digit_after =~ /[01234]/) || # round down anyway, |
1511 | # 6789 => round up |
1512 | ($digit_after eq '5') && # not 5000...0000 |
0716bf9b |
1513 | ($x->_scan_for_nonzero($pad,$xs) == 0) && |
58cde26e |
1514 | ( |
1515 | ($mode eq 'even') && ($digit_round =~ /[24680]/) || |
1516 | ($mode eq 'odd') && ($digit_round =~ /[13579]/) || |
1517 | ($mode eq '+inf') && ($x->{sign} eq '-') || |
1518 | ($mode eq '-inf') && ($x->{sign} eq '+') || |
1519 | ($mode eq 'zero') # round down if zero, sign adjusted below |
1520 | ); |
1521 | # allow rounding one place left of mantissa |
1522 | #print "$pad $len $scale\n"; |
1523 | # this is triggering warnings, and buggy for $scale < 0 |
1524 | #if (-$scale != $len) |
1525 | { |
b22b3e31 |
1526 | # old code, depend on internal representation |
0716bf9b |
1527 | # split mantissa at $pad and then pad with zeros |
1528 | #my $s5 = int($pad / 5); |
1529 | #my $i = 0; |
1530 | #while ($i < $s5) |
1531 | # { |
1532 | # $x->{value}->[$i++] = 0; # replace with 5 x 0 |
1533 | # } |
1534 | #$x->{value}->[$s5] = '00000'.$x->{value}->[$s5]; # pad with 0 |
1535 | #my $rem = $pad % 5; # so much left over |
1536 | #if ($rem > 0) |
1537 | # { |
1538 | # #print "remainder $rem\n"; |
1539 | ## #print "elem $x->{value}->[$s5]\n"; |
1540 | # substr($x->{value}->[$s5],-$rem,$rem) = '0' x $rem; # stamp w/ '0' |
1541 | # } |
1542 | #$x->{value}->[$s5] = int ($x->{value}->[$s5]); # str '05' => int '5' |
1543 | #print ${$CALC->_str($pad->{value})}," $len\n"; |
1544 | if (($pad > 0) && ($pad <= $len)) |
58cde26e |
1545 | { |
0716bf9b |
1546 | substr($$xs,-$pad,$pad) = '0' x $pad; |
1547 | $x->{value} = $CALC->_new($xs); # put back in |
58cde26e |
1548 | } |
0716bf9b |
1549 | elsif ($pad > $len) |
58cde26e |
1550 | { |
574bacfe |
1551 | $x->bzero(); # round to '0' |
58cde26e |
1552 | } |
ee15d750 |
1553 | # print "res $pad $len $x $$xs\n"; |
58cde26e |
1554 | } |
0716bf9b |
1555 | # move this later on after the inc of the string |
1556 | #$x->{value} = $CALC->_new($xs); # put back in |
58cde26e |
1557 | if ($round_up) # what gave test above? |
1558 | { |
ee15d750 |
1559 | #print " $pad => "; |
58cde26e |
1560 | $pad = $len if $scale < 0; # tlr: whack 0.51=>1.0 |
1561 | # modify $x in place, undef, undef to avoid rounding |
58cde26e |
1562 | # str creation much faster than 10 ** something |
ee15d750 |
1563 | #print " $pad, $x => "; |
0716bf9b |
1564 | $x->badd( Math::BigInt->new($x->{sign}.'1'.'0'x$pad) ); |
ee15d750 |
1565 | #print "$x\n"; |
0716bf9b |
1566 | # increment string in place, to avoid dec=>hex for the '1000...000' |
1567 | # $xs ...blah foo |
58cde26e |
1568 | } |
0716bf9b |
1569 | # to here: |
1570 | #$x->{value} = $CALC->_new($xs); # put back in |
ee15d750 |
1571 | |
1572 | $x->{_a} = $scale if $scale >= 0; |
1573 | if ($scale < 0) |
1574 | { |
1575 | $x->{_a} = $len+$scale; |
1576 | $x->{_a} = 0 if $scale < -$len; |
1577 | } |
58cde26e |
1578 | $x; |
1579 | } |
1580 | |
1581 | sub bfloor |
1582 | { |
1583 | # return integer less or equal then number, since it is already integer, |
1584 | # always returns $self |
ee15d750 |
1585 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e |
1586 | |
1587 | # not needed: return $x if $x->modify('bfloor'); |
58cde26e |
1588 | return $x->round($a,$p,$r); |
1589 | } |
1590 | |
1591 | sub bceil |
1592 | { |
1593 | # return integer greater or equal then number, since it is already integer, |
1594 | # always returns $self |
ee15d750 |
1595 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e |
1596 | |
1597 | # not needed: return $x if $x->modify('bceil'); |
58cde26e |
1598 | return $x->round($a,$p,$r); |
1599 | } |
1600 | |
1601 | ############################################################################## |
1602 | # private stuff (internal use only) |
1603 | |
574bacfe |
1604 | sub __one |
58cde26e |
1605 | { |
1606 | # internal speedup, set argument to 1, or create a +/- 1 |
1607 | my $self = shift; |
0716bf9b |
1608 | my $x = $self->bzero(); $x->{value} = $CALC->_one(); |
1609 | $x->{sign} = shift || '+'; |
1610 | return $x; |
58cde26e |
1611 | } |
1612 | |
1613 | sub _swap |
1614 | { |
1615 | # Overload will swap params if first one is no object ref so that the first |
1616 | # one is always an object ref. In this case, third param is true. |
1617 | # This routine is to overcome the effect of scalar,$object creating an object |
1618 | # of the class of this package, instead of the second param $object. This |
1619 | # happens inside overload, when the overload section of this package is |
1620 | # inherited by sub classes. |
1621 | # For overload cases (and this is used only there), we need to preserve the |
1622 | # args, hence the copy(). |
1623 | # You can override this method in a subclass, the overload section will call |
1624 | # $object->_swap() to make sure it arrives at the proper subclass, with some |
1625 | # exceptions like '+' and '-'. |
1626 | |
1627 | # object, (object|scalar) => preserve first and make copy |
1628 | # scalar, object => swapped, re-swap and create new from first |
1629 | # (using class of second object, not $class!!) |
1630 | my $self = shift; # for override in subclass |
1631 | #print "swap $self 0:$_[0] 1:$_[1] 2:$_[2]\n"; |
1632 | if ($_[2]) |
1633 | { |
1634 | my $c = ref ($_[0]) || $class; # fallback $class should not happen |
1635 | return ( $c->new($_[1]), $_[0] ); |
1636 | } |
17baacb7 |
1637 | return ( $_[0]->copy(), $_[1] ); |
58cde26e |
1638 | } |
1639 | |
1640 | sub objectify |
1641 | { |
1642 | # check for strings, if yes, return objects instead |
1643 | |
1644 | # the first argument is number of args objectify() should look at it will |
1645 | # return $count+1 elements, the first will be a classname. This is because |
1646 | # overloaded '""' calls bstr($object,undef,undef) and this would result in |
1647 | # useless objects beeing created and thrown away. So we cannot simple loop |
1648 | # over @_. If the given count is 0, all arguments will be used. |
1649 | |
1650 | # If the second arg is a ref, use it as class. |
1651 | # If not, try to use it as classname, unless undef, then use $class |
1652 | # (aka Math::BigInt). The latter shouldn't happen,though. |
1653 | |
1654 | # caller: gives us: |
1655 | # $x->badd(1); => ref x, scalar y |
1656 | # Class->badd(1,2); => classname x (scalar), scalar x, scalar y |
1657 | # Class->badd( Class->(1),2); => classname x (scalar), ref x, scalar y |
1658 | # Math::BigInt::badd(1,2); => scalar x, scalar y |
1659 | # In the last case we check number of arguments to turn it silently into |
574bacfe |
1660 | # $class,1,2. (We can not take '1' as class ;o) |
58cde26e |
1661 | # badd($class,1) is not supported (it should, eventually, try to add undef) |
1662 | # currently it tries 'Math::BigInt' + 1, which will not work. |
ee15d750 |
1663 | |
1664 | # some shortcut for the common cases |
1665 | |
1666 | # $x->unary_op(); |
1667 | return (ref($_[1]),$_[1]) if (@_ == 2) && ($_[0]||0 == 1) && ref($_[1]); |
1668 | # $x->binary_op($y); |
1669 | #return (ref($_[1]),$_[1],$_[2]) if (@_ == 3) && ($_[0]||0 == 2) |
1670 | # && ref($_[1]) && ref($_[2]); |
1671 | |
1672 | # print "obj '",join ("' '", @_),"'\n"; |
1673 | |
58cde26e |
1674 | my $count = abs(shift || 0); |
1675 | |
1676 | #print caller(),"\n"; |
1677 | |
1678 | my @a; # resulting array |
1679 | if (ref $_[0]) |
1680 | { |
1681 | # okay, got object as first |
1682 | $a[0] = ref $_[0]; |
1683 | } |
1684 | else |
1685 | { |
1686 | # nope, got 1,2 (Class->xxx(1) => Class,1 and not supported) |
1687 | $a[0] = $class; |
1688 | #print "@_\n"; sleep(1); |
1689 | $a[0] = shift if $_[0] =~ /^[A-Z].*::/; # classname as first? |
1690 | } |
1691 | #print caller(),"\n"; |
1692 | # print "Now in objectify, my class is today $a[0]\n"; |
1693 | my $k; |
1694 | if ($count == 0) |
1695 | { |
1696 | while (@_) |
1697 | { |
1698 | $k = shift; |
1699 | if (!ref($k)) |
1700 | { |
1701 | $k = $a[0]->new($k); |
1702 | } |
1703 | elsif (ref($k) ne $a[0]) |
1704 | { |
1705 | # foreign object, try to convert to integer |
1706 | $k->can('as_number') ? $k = $k->as_number() : $k = $a[0]->new($k); |
e16b8f49 |
1707 | } |
58cde26e |
1708 | push @a,$k; |
1709 | } |
1710 | } |
1711 | else |
1712 | { |
1713 | while ($count > 0) |
1714 | { |
1715 | #print "$count\n"; |
1716 | $count--; |
1717 | $k = shift; |
ee15d750 |
1718 | # print "$k (",ref($k),") => \n"; |
58cde26e |
1719 | if (!ref($k)) |
1720 | { |
1721 | $k = $a[0]->new($k); |
1722 | } |
1723 | elsif (ref($k) ne $a[0]) |
1724 | { |
1725 | # foreign object, try to convert to integer |
1726 | $k->can('as_number') ? $k = $k->as_number() : $k = $a[0]->new($k); |
e16b8f49 |
1727 | } |
ee15d750 |
1728 | # print "$k (",ref($k),")\n"; |
58cde26e |
1729 | push @a,$k; |
1730 | } |
1731 | push @a,@_; # return other params, too |
1732 | } |
1733 | #my $i = 0; |
1734 | #foreach (@a) |
1735 | # { |
1736 | # print "o $i $a[0]\n" if $i == 0; |
1737 | # print "o $i ",ref($_),"\n" if $i != 0; $i++; |
1738 | # } |
1739 | #print "objectify done: would return ",scalar @a," values\n"; |
1740 | #print caller(1),"\n" unless wantarray; |
1741 | die "$class objectify needs list context" unless wantarray; |
1742 | @a; |
1743 | } |
1744 | |
1745 | sub import |
1746 | { |
1747 | my $self = shift; |
1748 | #print "import $self @_\n"; |
0716bf9b |
1749 | my @a = @_; my $l = scalar @_; my $j = 0; |
1750 | for ( my $i = 0; $i < $l ; $i++,$j++ ) |
58cde26e |
1751 | { |
0716bf9b |
1752 | if ($_[$i] eq ':constant') |
58cde26e |
1753 | { |
0716bf9b |
1754 | # this causes overlord er load to step in |
58cde26e |
1755 | overload::constant integer => sub { $self->new(shift) }; |
0716bf9b |
1756 | splice @a, $j, 1; $j --; |
1757 | } |
1758 | elsif ($_[$i] =~ /^lib$/i) |
1759 | { |
1760 | # this causes a different low lib to take care... |
1761 | $CALC = $_[$i+1] || $CALC; |
574bacfe |
1762 | my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..." |
0716bf9b |
1763 | splice @a, $j, $s; $j -= $s; |
58cde26e |
1764 | } |
1765 | } |
1766 | # any non :constant stuff is handled by our parent, Exporter |
1767 | # even if @_ is empty, to give it a chance |
0716bf9b |
1768 | #$self->SUPER::import(@a); # does not work |
1769 | $self->export_to_level(1,$self,@a); # need this instead |
58cde26e |
1770 | |
574bacfe |
1771 | # try to load core math lib |
1772 | my @c = split /\s*,\s*/,$CALC; |
1773 | push @c,'Calc'; # if all fail, try this |
1774 | foreach my $lib (@c) |
1775 | { |
1776 | $lib = 'Math::BigInt::'.$lib if $lib !~ /^Math::BigInt/i; |
1777 | $lib =~ s/\.pm$//; |
1778 | if ($] < 5.6) |
1779 | { |
1780 | # Perl < 5.6.0 dies with "out of memory!" when eval() and ':constant' is |
1781 | # used in the same script, or eval inside import(). |
1782 | (my $mod = $lib . '.pm') =~ s!::!/!g; |
1783 | # require does not automatically :: => /, so portability problems arise |
bd05a461 |
1784 | eval { require $mod; $lib->import( @c ); } |
574bacfe |
1785 | } |
1786 | else |
1787 | { |
bd05a461 |
1788 | eval "use $lib @c;"; |
574bacfe |
1789 | } |
bd05a461 |
1790 | $CALC = $lib, last if $@ eq ''; # no error in loading lib? |
574bacfe |
1791 | } |
58cde26e |
1792 | } |
1793 | |
574bacfe |
1794 | sub __from_hex |
58cde26e |
1795 | { |
1796 | # convert a (ref to) big hex string to BigInt, return undef for error |
1797 | my $hs = shift; |
1798 | |
1799 | my $x = Math::BigInt->bzero(); |
1800 | return $x->bnan() if $$hs !~ /^[\-\+]?0x[0-9A-Fa-f]+$/; |
1801 | |
b22b3e31 |
1802 | my $sign = '+'; $sign = '-' if ($$hs =~ /^-/); |
58cde26e |
1803 | |
b22b3e31 |
1804 | $$hs =~ s/^[+-]//; # strip sign |
0716bf9b |
1805 | if ($CALC->can('_from_hex')) |
58cde26e |
1806 | { |
0716bf9b |
1807 | $x->{value} = $CALC->_from_hex($hs); |
58cde26e |
1808 | } |
0716bf9b |
1809 | else |
58cde26e |
1810 | { |
0716bf9b |
1811 | # fallback to pure perl |
1812 | my $mul = Math::BigInt->bzero(); $mul++; |
1813 | my $x65536 = Math::BigInt->new(65536); |
1814 | my $len = CORE::length($$hs)-2; |
1815 | $len = int($len/4); # 4-digit parts, w/o '0x' |
1816 | my $val; my $i = -4; |
1817 | while ($len >= 0) |
1818 | { |
1819 | $val = substr($$hs,$i,4); |
b22b3e31 |
1820 | $val =~ s/^[+-]?0x// if $len == 0; # for last part only because |
0716bf9b |
1821 | $val = hex($val); # hex does not like wrong chars |
1822 | # print "$val ",substr($$hs,$i,4),"\n"; |
1823 | $i -= 4; $len --; |
1824 | $x += $mul * $val if $val != 0; |
1825 | $mul *= $x65536 if $len >= 0; # skip last mul |
1826 | } |
58cde26e |
1827 | } |
0716bf9b |
1828 | $x->{sign} = $sign if !$x->is_zero(); # no '-0' |
58cde26e |
1829 | return $x; |
1830 | } |
1831 | |
574bacfe |
1832 | sub __from_bin |
58cde26e |
1833 | { |
1834 | # convert a (ref to) big binary string to BigInt, return undef for error |
1835 | my $bs = shift; |
1836 | |
1837 | my $x = Math::BigInt->bzero(); |
b22b3e31 |
1838 | return $x->bnan() if $$bs !~ /^[+-]?0b[01]+$/; |
58cde26e |
1839 | |
1840 | my $mul = Math::BigInt->bzero(); $mul++; |
1841 | my $x256 = Math::BigInt->new(256); |
1842 | |
0716bf9b |
1843 | my $sign = '+'; $sign = '-' if ($$bs =~ /^\-/); |
b22b3e31 |
1844 | $$bs =~ s/^[+-]//; # strip sign |
0716bf9b |
1845 | if ($CALC->can('_from_bin')) |
58cde26e |
1846 | { |
0716bf9b |
1847 | $x->{value} = $CALC->_from_bin($bs); |
58cde26e |
1848 | } |
0716bf9b |
1849 | else |
58cde26e |
1850 | { |
0716bf9b |
1851 | my $len = CORE::length($$bs)-2; |
1852 | $len = int($len/8); # 8-digit parts, w/o '0b' |
1853 | my $val; my $i = -8; |
1854 | while ($len >= 0) |
1855 | { |
1856 | $val = substr($$bs,$i,8); |
b22b3e31 |
1857 | $val =~ s/^[+-]?0b// if $len == 0; # for last part only |
1858 | #$val = oct('0b'.$val); # does not work on Perl prior to 5.6.0 |
0716bf9b |
1859 | $val = ('0' x (8-CORE::length($val))).$val if CORE::length($val) < 8; |
1860 | $val = ord(pack('B8',$val)); |
1861 | # print "$val ",substr($$bs,$i,16),"\n"; |
1862 | $i -= 8; $len --; |
1863 | $x += $mul * $val if $val != 0; |
1864 | $mul *= $x256 if $len >= 0; # skip last mul |
1865 | } |
58cde26e |
1866 | } |
1867 | $x->{sign} = $sign if !$x->is_zero(); |
1868 | return $x; |
1869 | } |
1870 | |
1871 | sub _split |
1872 | { |
1873 | # (ref to num_str) return num_str |
1874 | # internal, take apart a string and return the pieces |
574bacfe |
1875 | # strip leading/trailing whitespace, leading zeros, underscore, reject |
1876 | # invalid input |
58cde26e |
1877 | my $x = shift; |
1878 | |
574bacfe |
1879 | # strip white space at front, also extranous leading zeros |
1880 | $$x =~ s/^\s*([-]?)0*([0-9])/$1$2/g; # will not strip ' .2' |
1881 | $$x =~ s/^\s+//; # but this will |
58cde26e |
1882 | $$x =~ s/\s+$//g; # strip white space at end |
58cde26e |
1883 | |
574bacfe |
1884 | # shortcut, if nothing to split, return early |
1885 | if ($$x =~ /^[+-]?\d+$/) |
1886 | { |
1887 | $$x =~ s/^([+-])0*([0-9])/$2/; my $sign = $1 || '+'; |
1888 | return (\$sign, $x, \'', \'', \0); |
1889 | } |
58cde26e |
1890 | |
574bacfe |
1891 | # invalid starting char? |
1892 | return if $$x !~ /^[+-]?(\.?[0-9]|0b[0-1]|0x[0-9a-fA-F])/; |
58cde26e |
1893 | |
1894 | $$x =~ s/(\d)_(\d)/$1$2/g; # strip underscores between digits |
1895 | $$x =~ s/(\d)_(\d)/$1$2/g; # do twice for 1_2_3 |
1896 | |
574bacfe |
1897 | return __from_hex($x) if $$x =~ /^[\-\+]?0x/; # hex string |
1898 | return __from_bin($x) if $$x =~ /^[\-\+]?0b/; # binary string |
1899 | |
58cde26e |
1900 | # some possible inputs: |
1901 | # 2.1234 # 0.12 # 1 # 1E1 # 2.134E1 # 434E-10 # 1.02009E-2 |
1902 | # .2 # 1_2_3.4_5_6 # 1.4E1_2_3 # 1e3 # +.2 |
1903 | |
1904 | #print "input: '$$x' "; |
1905 | my ($m,$e) = split /[Ee]/,$$x; |
1906 | $e = '0' if !defined $e || $e eq ""; |
1907 | # print "m '$m' e '$e'\n"; |
1908 | # sign,value for exponent,mantint,mantfrac |
1909 | my ($es,$ev,$mis,$miv,$mfv); |
1910 | # valid exponent? |
1911 | if ($e =~ /^([+-]?)0*(\d+)$/) # strip leading zeros |
1912 | { |
1913 | $es = $1; $ev = $2; |
1914 | #print "'$m' '$e' e: $es $ev "; |
1915 | # valid mantissa? |
1916 | return if $m eq '.' || $m eq ''; |
1917 | my ($mi,$mf) = split /\./,$m; |
1918 | $mi = '0' if !defined $mi; |
1919 | $mi .= '0' if $mi =~ /^[\-\+]?$/; |
1920 | $mf = '0' if !defined $mf || $mf eq ''; |
1921 | if ($mi =~ /^([+-]?)0*(\d+)$/) # strip leading zeros |
1922 | { |
1923 | $mis = $1||'+'; $miv = $2; |
0716bf9b |
1924 | # print "$mis $miv"; |
58cde26e |
1925 | # valid, existing fraction part of mantissa? |
1926 | return unless ($mf =~ /^(\d*?)0*$/); # strip trailing zeros |
1927 | $mfv = $1; |
1928 | #print " split: $mis $miv . $mfv E $es $ev\n"; |
1929 | return (\$mis,\$miv,\$mfv,\$es,\$ev); |
1930 | } |
1931 | } |
1932 | return; # NaN, not a number |
1933 | } |
1934 | |
58cde26e |
1935 | sub as_number |
1936 | { |
1937 | # an object might be asked to return itself as bigint on certain overloaded |
1938 | # operations, this does exactly this, so that sub classes can simple inherit |
1939 | # it or override with their own integer conversion routine |
1940 | my $self = shift; |
1941 | |
17baacb7 |
1942 | $self->copy(); |
58cde26e |
1943 | } |
1944 | |
bd05a461 |
1945 | sub as_hex |
1946 | { |
1947 | # return as hex string, with prefixed 0x |
1948 | my $x = shift; $x = $class->new($x) if !ref($x); |
1949 | |
1950 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc |
1951 | return '0x0' if $x->is_zero(); |
1952 | |
1953 | my $es = ''; my $s = ''; |
1954 | $s = $x->{sign} if $x->{sign} eq '-'; |
bd05a461 |
1955 | if ($CALC->can('_as_hex')) |
1956 | { |
ee15d750 |
1957 | $es = ${$CALC->_as_hex($x->{value})}; |
bd05a461 |
1958 | } |
1959 | else |
1960 | { |
1961 | my $x1 = $x->copy()->babs(); my $xr; |
1962 | my $x100 = Math::BigInt->new (0x100); |
1963 | while (!$x1->is_zero()) |
1964 | { |
1965 | ($x1, $xr) = bdiv($x1,$x100); |
1966 | $es .= unpack('h2',pack('C',$xr->numify())); |
1967 | } |
1968 | $es = reverse $es; |
1969 | $es =~ s/^[0]+//; # strip leading zeros |
ee15d750 |
1970 | $s .= '0x'; |
bd05a461 |
1971 | } |
1972 | $s . $es; |
1973 | } |
1974 | |
1975 | sub as_bin |
1976 | { |
1977 | # return as binary string, with prefixed 0b |
1978 | my $x = shift; $x = $class->new($x) if !ref($x); |
1979 | |
1980 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc |
1981 | return '0b0' if $x->is_zero(); |
1982 | |
1983 | my $es = ''; my $s = ''; |
1984 | $s = $x->{sign} if $x->{sign} eq '-'; |
bd05a461 |
1985 | if ($CALC->can('_as_bin')) |
1986 | { |
ee15d750 |
1987 | $es = ${$CALC->_as_bin($x->{value})}; |
bd05a461 |
1988 | } |
1989 | else |
1990 | { |
1991 | my $x1 = $x->copy()->babs(); my $xr; |
1992 | my $x100 = Math::BigInt->new (0x100); |
1993 | while (!$x1->is_zero()) |
1994 | { |
1995 | ($x1, $xr) = bdiv($x1,$x100); |
1996 | $es .= unpack('b8',pack('C',$xr->numify())); |
1997 | } |
1998 | $es = reverse $es; |
1999 | $es =~ s/^[0]+//; # strip leading zeros |
ee15d750 |
2000 | $s .= '0b'; |
bd05a461 |
2001 | } |
2002 | $s . $es; |
2003 | } |
2004 | |
58cde26e |
2005 | ############################################################################## |
0716bf9b |
2006 | # internal calculation routines (others are in Math::BigInt::Calc etc) |
58cde26e |
2007 | |
2008 | sub cmp |
2009 | { |
2010 | # post-normalized compare for internal use (honors signs) |
0716bf9b |
2011 | # input: ref to value, ref to value, sign, sign |
2012 | # output: <0, 0, >0 |
58cde26e |
2013 | my ($cx,$cy,$sx,$sy) = @_; |
2014 | |
58cde26e |
2015 | if ($sx eq '+') |
2016 | { |
2017 | return 1 if $sy eq '-'; # 0 check handled above |
0716bf9b |
2018 | return $CALC->_acmp($cx,$cy); |
58cde26e |
2019 | } |
2020 | else |
2021 | { |
2022 | # $sx eq '-' |
0716bf9b |
2023 | return -1 if $sy eq '+'; |
0716bf9b |
2024 | return $CALC->_acmp($cy,$cx); |
58cde26e |
2025 | } |
17baacb7 |
2026 | 0; # equal |
58cde26e |
2027 | } |
2028 | |
58cde26e |
2029 | sub _lcm |
2030 | { |
2031 | # (BINT or num_str, BINT or num_str) return BINT |
2032 | # does modify first argument |
2033 | # LCM |
2034 | |
2035 | my $x = shift; my $ty = shift; |
2036 | return $x->bnan() if ($x->{sign} eq $nan) || ($ty->{sign} eq $nan); |
2037 | return $x * $ty / bgcd($x,$ty); |
2038 | } |
2039 | |
574bacfe |
2040 | sub __gcd |
58cde26e |
2041 | { |
2042 | # (BINT or num_str, BINT or num_str) return BINT |
2043 | # does modify first arg |
2044 | # GCD -- Euclids algorithm E, Knuth Vol 2 pg 296 |
58cde26e |
2045 | |
0716bf9b |
2046 | my $x = shift; my $ty = $class->new(shift); # preserve y, but make class |
2047 | return $x->bnan() if $x->{sign} !~ /^[+-]$/ || $ty->{sign} !~ /^[+-]$/; |
58cde26e |
2048 | |
2049 | while (!$ty->is_zero()) |
2050 | { |
2051 | ($x, $ty) = ($ty,bmod($x,$ty)); |
2052 | } |
2053 | $x; |
2054 | } |
2055 | |
58cde26e |
2056 | ############################################################################### |
2057 | # this method return 0 if the object can be modified, or 1 for not |
2058 | # We use a fast use constant statement here, to avoid costly calls. Subclasses |
2059 | # may override it with special code (f.i. Math::BigInt::Constant does so) |
2060 | |
0716bf9b |
2061 | sub modify () { 0; } |
e16b8f49 |
2062 | |
a0d0e21e |
2063 | 1; |
a5f75d66 |
2064 | __END__ |
2065 | |
2066 | =head1 NAME |
2067 | |
2068 | Math::BigInt - Arbitrary size integer math package |
2069 | |
2070 | =head1 SYNOPSIS |
2071 | |
2072 | use Math::BigInt; |
58cde26e |
2073 | |
2074 | # Number creation |
574bacfe |
2075 | $x = Math::BigInt->new($str); # defaults to 0 |
2076 | $nan = Math::BigInt->bnan(); # create a NotANumber |
2077 | $zero = Math::BigInt->bzero(); # create a +0 |
2078 | $inf = Math::BigInt->binf(); # create a +inf |
2079 | $inf = Math::BigInt->binf('-'); # create a -inf |
2080 | $one = Math::BigInt->bone(); # create a +1 |
2081 | $one = Math::BigInt->bone('-'); # create a -1 |
58cde26e |
2082 | |
2083 | # Testing |
574bacfe |
2084 | $x->is_zero(); # true if arg is +0 |
2085 | $x->is_nan(); # true if arg is NaN |
0716bf9b |
2086 | $x->is_one(); # true if arg is +1 |
2087 | $x->is_one('-'); # true if arg is -1 |
2088 | $x->is_odd(); # true if odd, false for even |
2089 | $x->is_even(); # true if even, false for odd |
2090 | $x->is_positive(); # true if >= 0 |
2091 | $x->is_negative(); # true if < 0 |
2092 | $x->is_inf(sign); # true if +inf, or -inf (sign is default '+') |
2093 | |
58cde26e |
2094 | $x->bcmp($y); # compare numbers (undef,<0,=0,>0) |
2095 | $x->bacmp($y); # compare absolutely (undef,<0,=0,>0) |
2096 | $x->sign(); # return the sign, either +,- or NaN |
2097 | $x->digit($n); # return the nth digit, counting from right |
2098 | $x->digit(-$n); # return the nth digit, counting from left |
2099 | |
2100 | # The following all modify their first argument: |
2101 | |
2102 | # set |
2103 | $x->bzero(); # set $x to 0 |
2104 | $x->bnan(); # set $x to NaN |
574bacfe |
2105 | $x->bone(); # set $x to +1 |
2106 | $x->bone('-'); # set $x to -1 |
58cde26e |
2107 | |
2108 | $x->bneg(); # negation |
2109 | $x->babs(); # absolute value |
2110 | $x->bnorm(); # normalize (no-op) |
2111 | $x->bnot(); # two's complement (bit wise not) |
2112 | $x->binc(); # increment x by 1 |
2113 | $x->bdec(); # decrement x by 1 |
2114 | |
2115 | $x->badd($y); # addition (add $y to $x) |
2116 | $x->bsub($y); # subtraction (subtract $y from $x) |
2117 | $x->bmul($y); # multiplication (multiply $x by $y) |
2118 | $x->bdiv($y); # divide, set $x to quotient |
2119 | # return (quo,rem) or quo if scalar |
2120 | |
2121 | $x->bmod($y); # modulus (x % y) |
2122 | $x->bpow($y); # power of arguments (x ** y) |
2123 | $x->blsft($y); # left shift |
2124 | $x->brsft($y); # right shift |
2125 | $x->blsft($y,$n); # left shift, by base $n (like 10) |
2126 | $x->brsft($y,$n); # right shift, by base $n (like 10) |
2127 | |
2128 | $x->band($y); # bitwise and |
2129 | $x->bior($y); # bitwise inclusive or |
2130 | $x->bxor($y); # bitwise exclusive or |
2131 | $x->bnot(); # bitwise not (two's complement) |
2132 | |
2133 | $x->bsqrt(); # calculate square-root |
2134 | |
2135 | $x->round($A,$P,$round_mode); # round to accuracy or precision using mode $r |
2136 | $x->bround($N); # accuracy: preserve $N digits |
2137 | $x->bfround($N); # round to $Nth digit, no-op for BigInts |
2138 | |
2139 | # The following do not modify their arguments in BigInt, but do in BigFloat: |
2140 | $x->bfloor(); # return integer less or equal than $x |
2141 | $x->bceil(); # return integer greater or equal than $x |
2142 | |
2143 | # The following do not modify their arguments: |
2144 | |
2145 | bgcd(@values); # greatest common divisor |
2146 | blcm(@values); # lowest common multiplicator |
bd05a461 |
2147 | |
58cde26e |
2148 | $x->length(); # return number of digits in number |
bd05a461 |
2149 | ($x,$f) = $x->length(); # length of number and length of fraction part, |
2150 | # latter is always 0 digits long for BigInt's |
58cde26e |
2151 | |
2152 | $x->exponent(); # return exponent as BigInt |
ee15d750 |
2153 | $x->mantissa(); # return (signed) mantissa as BigInt |
58cde26e |
2154 | $x->parts(); # return (mantissa,exponent) as BigInt |
0716bf9b |
2155 | $x->copy(); # make a true copy of $x (unlike $y = $x;) |
2156 | $x->as_number(); # return as BigInt (in BigInt: same as copy()) |
bd05a461 |
2157 | |
2158 | # conversation to string |
2159 | $x->bstr(); # normalized string |
2160 | $x->bsstr(); # normalized string in scientific notation |
2161 | $x->as_hex(); # as signed hexadecimal string with prefixed 0x |
2162 | $x->as_bin(); # as signed binary string with prefixed 0b |
2163 | |
a5f75d66 |
2164 | =head1 DESCRIPTION |
2165 | |
58cde26e |
2166 | All operators (inlcuding basic math operations) are overloaded if you |
2167 | declare your big integers as |
a5f75d66 |
2168 | |
58cde26e |
2169 | $i = new Math::BigInt '123_456_789_123_456_789'; |
a5f75d66 |
2170 | |
58cde26e |
2171 | Operations with overloaded operators preserve the arguments which is |
2172 | exactly what you expect. |
a5f75d66 |
2173 | |
2174 | =over 2 |
2175 | |
2176 | =item Canonical notation |
2177 | |
58cde26e |
2178 | Big integer values are strings of the form C</^[+-]\d+$/> with leading |
a5f75d66 |
2179 | zeros suppressed. |
2180 | |
58cde26e |
2181 | '-0' canonical value '-0', normalized '0' |
2182 | ' -123_123_123' canonical value '-123123123' |
2183 | '1_23_456_7890' canonical value '1234567890' |
2184 | |
a5f75d66 |
2185 | =item Input |
2186 | |
58cde26e |
2187 | Input values to these routines may be either Math::BigInt objects or |
2188 | strings of the form C</^\s*[+-]?[\d]+\.?[\d]*E?[+-]?[\d]*$/>. |
2189 | |
2190 | You can include one underscore between any two digits. |
2191 | |
2192 | This means integer values like 1.01E2 or even 1000E-2 are also accepted. |
2193 | Non integer values result in NaN. |
2194 | |
2195 | Math::BigInt::new() defaults to 0, while Math::BigInt::new('') results |
2196 | in 'NaN'. |
2197 | |
2198 | bnorm() on a BigInt object is now effectively a no-op, since the numbers |
2199 | are always stored in normalized form. On a string, it creates a BigInt |
2200 | object. |
a5f75d66 |
2201 | |
2202 | =item Output |
2203 | |
58cde26e |
2204 | Output values are BigInt objects (normalized), except for bstr(), which |
2205 | returns a string in normalized form. |
2206 | Some routines (C<is_odd()>, C<is_even()>, C<is_zero()>, C<is_one()>, |
2207 | C<is_nan()>) return true or false, while others (C<bcmp()>, C<bacmp()>) |
2208 | return either undef, <0, 0 or >0 and are suited for sort. |
a5f75d66 |
2209 | |
2210 | =back |
2211 | |
0716bf9b |
2212 | =head1 ACCURACY and PRECISION |
2213 | |
b22b3e31 |
2214 | Since version v1.33, Math::BigInt and Math::BigFloat have full support for |
0716bf9b |
2215 | accuracy and precision based rounding, both automatically after every |
b22b3e31 |
2216 | operation as well as manually. |
0716bf9b |
2217 | |
2218 | This section describes the accuracy/precision handling in Math::Big* as it |
b22b3e31 |
2219 | used to be and as it is now, complete with an explanation of all terms and |
0716bf9b |
2220 | abbreviations. |
2221 | |
2222 | Not yet implemented things (but with correct description) are marked with '!', |
2223 | things that need to be answered are marked with '?'. |
2224 | |
2225 | In the next paragraph follows a short description of terms used here (because |
574bacfe |
2226 | these may differ from terms used by others people or documentation). |
0716bf9b |
2227 | |
b22b3e31 |
2228 | During the rest of this document, the shortcuts A (for accuracy), P (for |
0716bf9b |
2229 | precision), F (fallback) and R (rounding mode) will be used. |
2230 | |
2231 | =head2 Precision P |
2232 | |
2233 | A fixed number of digits before (positive) or after (negative) |
b22b3e31 |
2234 | the decimal point. For example, 123.45 has a precision of -2. 0 means an |
2235 | integer like 123 (or 120). A precision of 2 means two digits to the left |
2236 | of the decimal point are zero, so 123 with P = 1 becomes 120. Note that |
2237 | numbers with zeros before the decimal point may have different precisions, |
2238 | because 1200 can have p = 0, 1 or 2 (depending on what the inital value |
2239 | was). It could also have p < 0, when the digits after the decimal point |
2240 | are zero. |
0716bf9b |
2241 | |
574bacfe |
2242 | The string output (of floating point numbers) will be padded with zeros: |
2243 | |
2244 | Initial value P A Result String |
2245 | ------------------------------------------------------------ |
2246 | 1234.01 -3 1000 1000 |
2247 | 1234 -2 1200 1200 |
2248 | 1234.5 -1 1230 1230 |
2249 | 1234.001 1 1234 1234.0 |
2250 | 1234.01 0 1234 1234 |
2251 | 1234.01 2 1234.01 1234.01 |
2252 | 1234.01 5 1234.01 1234.01000 |
2253 | |
2254 | For BigInts, no padding occurs. |
0716bf9b |
2255 | |
2256 | =head2 Accuracy A |
2257 | |
2258 | Number of significant digits. Leading zeros are not counted. A |
2259 | number may have an accuracy greater than the non-zero digits |
b22b3e31 |
2260 | when there are zeros in it or trailing zeros. For example, 123.456 has |
2261 | A of 6, 10203 has 5, 123.0506 has 7, 123.450000 has 8 and 0.000123 has 3. |
0716bf9b |
2262 | |
574bacfe |
2263 | The string output (of floating point numbers) will be padded with zeros: |
2264 | |
2265 | Initial value P A Result String |
2266 | ------------------------------------------------------------ |
2267 | 1234.01 3 1230 1230 |
2268 | 1234.01 6 1234.01 1234.01 |
2269 | 1234.1 8 1234.1 1234.1000 |
2270 | |
2271 | For BigInts, no padding occurs. |
2272 | |
0716bf9b |
2273 | =head2 Fallback F |
a5f75d66 |
2274 | |
574bacfe |
2275 | When both A and P are undefined, this is used as a fallback accuracy when |
2276 | dividing numbers. |
0716bf9b |
2277 | |
2278 | =head2 Rounding mode R |
2279 | |
2280 | When rounding a number, different 'styles' or 'kinds' |
2281 | of rounding are possible. (Note that random rounding, as in |
2282 | Math::Round, is not implemented.) |
58cde26e |
2283 | |
2284 | =over 2 |
a5f75d66 |
2285 | |
0716bf9b |
2286 | =item 'trunc' |
2287 | |
2288 | truncation invariably removes all digits following the |
2289 | rounding place, replacing them with zeros. Thus, 987.65 rounded |
b22b3e31 |
2290 | to tens (P=1) becomes 980, and rounded to the fourth sigdig |
0716bf9b |
2291 | becomes 987.6 (A=4). 123.456 rounded to the second place after the |
b22b3e31 |
2292 | decimal point (P=-2) becomes 123.46. |
0716bf9b |
2293 | |
2294 | All other implemented styles of rounding attempt to round to the |
2295 | "nearest digit." If the digit D immediately to the right of the |
2296 | rounding place (skipping the decimal point) is greater than 5, the |
2297 | number is incremented at the rounding place (possibly causing a |
2298 | cascade of incrementation): e.g. when rounding to units, 0.9 rounds |
2299 | to 1, and -19.9 rounds to -20. If D < 5, the number is similarly |
2300 | truncated at the rounding place: e.g. when rounding to units, 0.4 |
2301 | rounds to 0, and -19.4 rounds to -19. |
2302 | |
2303 | However the results of other styles of rounding differ if the |
2304 | digit immediately to the right of the rounding place (skipping the |
2305 | decimal point) is 5 and if there are no digits, or no digits other |
2306 | than 0, after that 5. In such cases: |
2307 | |
2308 | =item 'even' |
2309 | |
2310 | rounds the digit at the rounding place to 0, 2, 4, 6, or 8 |
2311 | if it is not already. E.g., when rounding to the first sigdig, 0.45 |
2312 | becomes 0.4, -0.55 becomes -0.6, but 0.4501 becomes 0.5. |
2313 | |
2314 | =item 'odd' |
2315 | |
2316 | rounds the digit at the rounding place to 1, 3, 5, 7, or 9 if |
2317 | it is not already. E.g., when rounding to the first sigdig, 0.45 |
2318 | becomes 0.5, -0.55 becomes -0.5, but 0.5501 becomes 0.6. |
2319 | |
2320 | =item '+inf' |
2321 | |
2322 | round to plus infinity, i.e. always round up. E.g., when |
2323 | rounding to the first sigdig, 0.45 becomes 0.5, -0.55 becomes -0.5, |
b22b3e31 |
2324 | and 0.4501 also becomes 0.5. |
0716bf9b |
2325 | |
2326 | =item '-inf' |
2327 | |
2328 | round to minus infinity, i.e. always round down. E.g., when |
2329 | rounding to the first sigdig, 0.45 becomes 0.4, -0.55 becomes -0.6, |
2330 | but 0.4501 becomes 0.5. |
2331 | |
2332 | =item 'zero' |
2333 | |
2334 | round to zero, i.e. positive numbers down, negative ones up. |
2335 | E.g., when rounding to the first sigdig, 0.45 becomes 0.4, -0.55 |
2336 | becomes -0.5, but 0.4501 becomes 0.5. |
2337 | |
2338 | =back |
2339 | |
2340 | The handling of A & P in MBI/MBF (the old core code shipped with Perl |
2341 | versions <= 5.7.2) is like this: |
2342 | |
2343 | =over 2 |
a5f75d66 |
2344 | |
0716bf9b |
2345 | =item Precision |
2346 | |
b22b3e31 |
2347 | * ffround($p) is able to round to $p number of digits after the decimal |
2348 | point |
0716bf9b |
2349 | * otherwise P is unused |
2350 | |
2351 | =item Accuracy (significant digits) |
2352 | |
2353 | * fround($a) rounds to $a significant digits |
2354 | * only fdiv() and fsqrt() take A as (optional) paramater |
b22b3e31 |
2355 | + other operations simply create the same number (fneg etc), or more (fmul) |
0716bf9b |
2356 | of digits |
2357 | + rounding/truncating is only done when explicitly calling one of fround |
2358 | or ffround, and never for BigInt (not implemented) |
b22b3e31 |
2359 | * fsqrt() simply hands its accuracy argument over to fdiv. |
0716bf9b |
2360 | * the documentation and the comment in the code indicate two different ways |
2361 | on how fdiv() determines the maximum number of digits it should calculate, |
2362 | and the actual code does yet another thing |
2363 | POD: |
2364 | max($Math::BigFloat::div_scale,length(dividend)+length(divisor)) |
2365 | Comment: |
2366 | result has at most max(scale, length(dividend), length(divisor)) digits |
2367 | Actual code: |
2368 | scale = max(scale, length(dividend)-1,length(divisor)-1); |
2369 | scale += length(divisior) - length(dividend); |
b22b3e31 |
2370 | So for lx = 3, ly = 9, scale = 10, scale will actually be 16 (10+9-3). |
0716bf9b |
2371 | Actually, the 'difference' added to the scale is calculated from the |
2372 | number of "significant digits" in dividend and divisor, which is derived |
2373 | by looking at the length of the mantissa. Which is wrong, since it includes |
2374 | the + sign (oups) and actually gets 2 for '+100' and 4 for '+101'. Oups |
2375 | again. Thus 124/3 with div_scale=1 will get you '41.3' based on the strange |
2376 | assumption that 124 has 3 significant digits, while 120/7 will get you |
2377 | '17', not '17.1' since 120 is thought to have 2 significant digits. |
2378 | The rounding after the division then uses the reminder and $y to determine |
2379 | wether it must round up or down. |
b22b3e31 |
2380 | ? I have no idea which is the right way. That's why I used a slightly more |
2381 | ? simple scheme and tweaked the few failing testcases to match it. |
58cde26e |
2382 | |
0716bf9b |
2383 | =back |
5dc6f178 |
2384 | |
0716bf9b |
2385 | This is how it works now: |
5dc6f178 |
2386 | |
0716bf9b |
2387 | =over 2 |
5dc6f178 |
2388 | |
0716bf9b |
2389 | =item Setting/Accessing |
2390 | |
2391 | * You can set the A global via $Math::BigInt::accuracy or |
2392 | $Math::BigFloat::accuracy or whatever class you are using. |
2393 | * You can also set P globally by using $Math::SomeClass::precision likewise. |
2394 | * Globals are classwide, and not inherited by subclasses. |
2395 | * to undefine A, use $Math::SomeCLass::accuracy = undef |
2396 | * to undefine P, use $Math::SomeClass::precision = undef |
2397 | * To be valid, A must be > 0, P can have any value. |
b22b3e31 |
2398 | * If P is negative, this means round to the P'th place to the right of the |
2399 | decimal point; positive values mean to the left of the decimal point. |
2400 | P of 0 means round to integer. |
0716bf9b |
2401 | * to find out the current global A, take $Math::SomeClass::accuracy |
2402 | * use $x->accuracy() for the local setting of $x. |
2403 | * to find out the current global P, take $Math::SomeClass::precision |
2404 | * use $x->precision() for the local setting |
2405 | |
2406 | =item Creating numbers |
2407 | |
b22b3e31 |
2408 | !* When you create a number, there should be a way to define its A & P |
0716bf9b |
2409 | * When a number without specific A or P is created, but the globals are |
b22b3e31 |
2410 | defined, these should be used to round the number immediately and also |
2411 | stored locally with the number. Thus changing the global defaults later on |
2412 | will not change the A or P of previously created numbers (i.e., A and P of |
0716bf9b |
2413 | $x will be what was in effect when $x was created) |
2414 | |
2415 | =item Usage |
2416 | |
b22b3e31 |
2417 | * If A or P are enabled/defined, they are used to round the result of each |
0716bf9b |
2418 | operation according to the rules below |
b22b3e31 |
2419 | * Negative P is ignored in Math::BigInt, since BigInts never have digits |
2420 | after the decimal point |
574bacfe |
2421 | * Math::BigFloat uses Math::BigInts internally, but setting A or P inside |
2422 | Math::BigInt as globals should not tamper with the parts of a BigFloat. |
2423 | Thus a flag is used to mark all Math::BigFloat numbers as 'never round' |
0716bf9b |
2424 | |
2425 | =item Precedence |
2426 | |
b22b3e31 |
2427 | * It only makes sense that a number has only one of A or P at a time. |
2428 | Since you can set/get both A and P, there is a rule that will practically |
2429 | enforce only A or P to be in effect at a time, even if both are set. |
2430 | This is called precedence. |
2431 | !* If two objects are involved in an operation, and one of them has A in |
0716bf9b |
2432 | ! effect, and the other P, this should result in a warning or an error, |
2433 | ! probably in NaN. |
2434 | * A takes precendence over P (Hint: A comes before P). If A is defined, it |
b22b3e31 |
2435 | is used, otherwise P is used. If neither of them is defined, nothing is |
2436 | used, i.e. the result will have as many digits as it can (with an |
2437 | exception for fdiv/fsqrt) and will not be rounded. |
2438 | * There is another setting for fdiv() (and thus for fsqrt()). If neither of |
2439 | A or P is defined, fdiv() will use a fallback (F) of $div_scale digits. |
2440 | If either the dividend's or the divisor's mantissa has more digits than |
2441 | the value of F, the higher value will be used instead of F. |
2442 | This is to limit the digits (A) of the result (just consider what would |
2443 | happen with unlimited A and P in the case of 1/3 :-) |
2444 | * fdiv will calculate 1 more digit than required (determined by |
0716bf9b |
2445 | A, P or F), and, if F is not used, round the result |
b22b3e31 |
2446 | (this will still fail in the case of a result like 0.12345000000001 with A |
574bacfe |
2447 | or P of 5, but this can not be helped - or can it?) |
b22b3e31 |
2448 | * Thus you can have the math done by on Math::Big* class in three modes: |
0716bf9b |
2449 | + never round (this is the default): |
2450 | This is done by setting A and P to undef. No math operation |
b22b3e31 |
2451 | will round the result, with fdiv() and fsqrt() as exceptions to guard |
0716bf9b |
2452 | against overflows. You must explicitely call bround(), bfround() or |
b22b3e31 |
2453 | round() (the latter with parameters). |
2454 | Note: Once you have rounded a number, the settings will 'stick' on it |
2455 | and 'infect' all other numbers engaged in math operations with it, since |
0716bf9b |
2456 | local settings have the highest precedence. So, to get SaferRound[tm], |
2457 | use a copy() before rounding like this: |
2458 | |
2459 | $x = Math::BigFloat->new(12.34); |
2460 | $y = Math::BigFloat->new(98.76); |
2461 | $z = $x * $y; # 1218.6984 |
2462 | print $x->copy()->fround(3); # 12.3 (but A is now 3!) |
2463 | $z = $x * $y; # still 1218.6984, without |
2464 | # copy would have been 1210! |
2465 | |
2466 | + round after each op: |
b22b3e31 |
2467 | After each single operation (except for testing like is_zero()), the |
2468 | method round() is called and the result is rounded appropriately. By |
0716bf9b |
2469 | setting proper values for A and P, you can have all-the-same-A or |
b22b3e31 |
2470 | all-the-same-P modes. For example, Math::Currency might set A to undef, |
2471 | and P to -2, globally. |
0716bf9b |
2472 | |
b22b3e31 |
2473 | ?Maybe an extra option that forbids local A & P settings would be in order, |
2474 | ?so that intermediate rounding does not 'poison' further math? |
0716bf9b |
2475 | |
2476 | =item Overriding globals |
2477 | |
2478 | * you will be able to give A, P and R as an argument to all the calculation |
b22b3e31 |
2479 | routines; the second parameter is A, the third one is P, and the fourth is |
0716bf9b |
2480 | R (shift place by one for binary operations like add). P is used only if |
b22b3e31 |
2481 | the first parameter (A) is undefined. These three parameters override the |
2482 | globals in the order detailed as follows, i.e. the first defined value |
0716bf9b |
2483 | wins: |
b22b3e31 |
2484 | (local: per object, global: global default, parameter: argument to sub) |
0716bf9b |
2485 | + parameter A |
2486 | + parameter P |
2487 | + local A (if defined on both of the operands: smaller one is taken) |
2488 | + local P (if defined on both of the operands: smaller one is taken) |
2489 | + global A |
2490 | + global P |
2491 | + global F |
b22b3e31 |
2492 | * fsqrt() will hand its arguments to fdiv(), as it used to, only now for two |
0716bf9b |
2493 | arguments (A and P) instead of one |
2494 | |
2495 | =item Local settings |
2496 | |
2497 | * You can set A and P locally by using $x->accuracy() and $x->precision() |
2498 | and thus force different A and P for different objects/numbers. |
b22b3e31 |
2499 | * Setting A or P this way immediately rounds $x to the new value. |
0716bf9b |
2500 | |
2501 | =item Rounding |
2502 | |
b22b3e31 |
2503 | * the rounding routines will use the respective global or local settings. |
0716bf9b |
2504 | fround()/bround() is for accuracy rounding, while ffround()/bfround() |
2505 | is for precision |
2506 | * the two rounding functions take as the second parameter one of the |
2507 | following rounding modes (R): |
2508 | 'even', 'odd', '+inf', '-inf', 'zero', 'trunc' |
2509 | * you can set and get the global R by using Math::SomeClass->round_mode() |
ee15d750 |
2510 | or by setting $Math::SomeClass::round_mode |
0716bf9b |
2511 | * after each operation, $result->round() is called, and the result may |
b22b3e31 |
2512 | eventually be rounded (that is, if A or P were set either locally, |
2513 | globally or as parameter to the operation) |
ee15d750 |
2514 | * to manually round a number, call $x->round($A,$P,$round_mode); |
b22b3e31 |
2515 | this will round the number by using the appropriate rounding function |
0716bf9b |
2516 | and then normalize it. |
b22b3e31 |
2517 | * rounding modifies the local settings of the number: |
0716bf9b |
2518 | |
2519 | $x = Math::BigFloat->new(123.456); |
2520 | $x->accuracy(5); |
2521 | $x->bround(4); |
2522 | |
2523 | Here 4 takes precedence over 5, so 123.5 is the result and $x->accuracy() |
2524 | will be 4 from now on. |
2525 | |
2526 | =item Default values |
2527 | |
2528 | * R: 'even' |
2529 | * F: 40 |
2530 | * A: undef |
2531 | * P: undef |
2532 | |
2533 | =item Remarks |
2534 | |
2535 | * The defaults are set up so that the new code gives the same results as |
2536 | the old code (except in a few cases on fdiv): |
2537 | + Both A and P are undefined and thus will not be used for rounding |
2538 | after each operation. |
2539 | + round() is thus a no-op, unless given extra parameters A and P |
58cde26e |
2540 | |
2541 | =back |
2542 | |
0716bf9b |
2543 | =head1 INTERNALS |
2544 | |
574bacfe |
2545 | The actual numbers are stored as unsigned big integers (with seperate sign). |
2546 | You should neither care about nor depend on the internal representation; it |
2547 | might change without notice. Use only method calls like C<< $x->sign(); >> |
2548 | instead relying on the internal hash keys like in C<< $x->{sign}; >>. |
2549 | |
2550 | =head2 MATH LIBRARY |
58cde26e |
2551 | |
574bacfe |
2552 | Math with the numbers is done (by default) by a module called |
2553 | Math::BigInt::Calc. This is equivalent to saying: |
2554 | |
2555 | use Math::BigInt lib => 'Calc'; |
58cde26e |
2556 | |
0716bf9b |
2557 | You can change this by using: |
58cde26e |
2558 | |
0716bf9b |
2559 | use Math::BigInt lib => 'BitVect'; |
58cde26e |
2560 | |
574bacfe |
2561 | The following would first try to find Math::BigInt::Foo, then |
2562 | Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: |
0716bf9b |
2563 | |
574bacfe |
2564 | use Math::BigInt lib => 'Foo,Math::BigInt::Bar'; |
58cde26e |
2565 | |
574bacfe |
2566 | Calc.pm uses as internal format an array of elements of some decimal base |
2567 | (usually 1e5, but this might change to 1e7) with the least significant digit |
2568 | first, while BitVect.pm uses a bit vector of base 2, most significant bit |
2569 | first. Other modules might use even different means of representing the |
2570 | numbers. See the respective module documentation for further details. |
58cde26e |
2571 | |
574bacfe |
2572 | =head2 SIGN |
2573 | |
2574 | The sign is either '+', '-', 'NaN', '+inf' or '-inf' and stored seperately. |
2575 | |
2576 | A sign of 'NaN' is used to represent the result when input arguments are not |
2577 | numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively |
2578 | minus infinity. You will get '+inf' when dividing a positive number by 0, and |
2579 | '-inf' when dividing any negative number by 0. |
58cde26e |
2580 | |
2581 | =head2 mantissa(), exponent() and parts() |
2582 | |
2583 | C<mantissa()> and C<exponent()> return the said parts of the BigInt such |
2584 | that: |
2585 | |
2586 | $m = $x->mantissa(); |
2587 | $e = $x->exponent(); |
2588 | $y = $m * ( 10 ** $e ); |
2589 | print "ok\n" if $x == $y; |
2590 | |
b22b3e31 |
2591 | C<< ($m,$e) = $x->parts() >> is just a shortcut that gives you both of them |
2592 | in one go. Both the returned mantissa and exponent have a sign. |
58cde26e |
2593 | |
574bacfe |
2594 | Currently, for BigInts C<$e> will be always 0, except for NaN, +inf and -inf, |
2595 | where it will be NaN; and for $x == 0, where it will be 1 |
2596 | (to be compatible with Math::BigFloat's internal representation of a zero as |
2597 | C<0E1>). |
58cde26e |
2598 | |
2599 | C<$m> will always be a copy of the original number. The relation between $e |
b22b3e31 |
2600 | and $m might change in the future, but will always be equivalent in a |
0716bf9b |
2601 | numerical sense, e.g. $m might get minimized. |
2602 | |
58cde26e |
2603 | =head1 EXAMPLES |
2604 | |
574bacfe |
2605 | use Math::BigInt qw(bstr); |
2606 | |
2607 | sub bint { Math::BigInt->new(shift); } |
2608 | |
58cde26e |
2609 | $x = bstr("1234") # string "1234" |
2610 | $x = "$x"; # same as bstr() |
2611 | $x = bneg("1234") # Bigint "-1234" |
2612 | $x = Math::BigInt->bneg("1234"); # Bigint "-1234" |
2613 | $x = Math::BigInt->babs("-12345"); # Bigint "12345" |
2614 | $x = Math::BigInt->bnorm("-0 00"); # BigInt "0" |
2615 | $x = bint(1) + bint(2); # BigInt "3" |
2616 | $x = bint(1) + "2"; # ditto (auto-BigIntify of "2") |
2617 | $x = bint(1); # BigInt "1" |
2618 | $x = $x + 5 / 2; # BigInt "3" |
2619 | $x = $x ** 3; # BigInt "27" |
2620 | $x *= 2; # BigInt "54" |
2621 | $x = new Math::BigInt; # BigInt "0" |
2622 | $x--; # BigInt "-1" |
2623 | $x = Math::BigInt->badd(4,5) # BigInt "9" |
2624 | $x = Math::BigInt::badd(4,5) # BigInt "9" |
2625 | print $x->bsstr(); # 9e+0 |
a5f75d66 |
2626 | |
0716bf9b |
2627 | Examples for rounding: |
2628 | |
2629 | use Math::BigFloat; |
2630 | use Test; |
2631 | |
2632 | $x = Math::BigFloat->new(123.4567); |
2633 | $y = Math::BigFloat->new(123.456789); |
2634 | $Math::BigFloat::accuracy = 4; # no more A than 4 |
2635 | |
2636 | ok ($x->copy()->fround(),123.4); # even rounding |
2637 | print $x->copy()->fround(),"\n"; # 123.4 |
2638 | Math::BigFloat->round_mode('odd'); # round to odd |
2639 | print $x->copy()->fround(),"\n"; # 123.5 |
2640 | $Math::BigFloat::accuracy = 5; # no more A than 5 |
2641 | Math::BigFloat->round_mode('odd'); # round to odd |
2642 | print $x->copy()->fround(),"\n"; # 123.46 |
2643 | $y = $x->copy()->fround(4),"\n"; # A = 4: 123.4 |
2644 | print "$y, ",$y->accuracy(),"\n"; # 123.4, 4 |
2645 | |
2646 | $Math::BigFloat::accuracy = undef; # A not important |
2647 | $Math::BigFloat::precision = 2; # P important |
2648 | print $x->copy()->bnorm(),"\n"; # 123.46 |
2649 | print $x->copy()->fround(),"\n"; # 123.46 |
2650 | |
bd05a461 |
2651 | Examples for converting: |
2652 | |
2653 | my $x = Math::BigInt->new('0b1'.'01' x 123); |
2654 | print "bin: ",$x->as_bin()," hex:",$x->as_hex()," dec: ",$x,"\n"; |
2655 | |
b3ac6de7 |
2656 | =head1 Autocreating constants |
2657 | |
58cde26e |
2658 | After C<use Math::BigInt ':constant'> all the B<integer> decimal constants |
2659 | in the given scope are converted to C<Math::BigInt>. This conversion |
b3ac6de7 |
2660 | happens at compile time. |
2661 | |
b22b3e31 |
2662 | In particular, |
b3ac6de7 |
2663 | |
58cde26e |
2664 | perl -MMath::BigInt=:constant -e 'print 2**100,"\n"' |
2665 | |
2666 | prints the integer value of C<2**100>. Note that without conversion of |
0716bf9b |
2667 | constants the expression 2**100 will be calculated as perl scalar. |
58cde26e |
2668 | |
2669 | Please note that strings and floating point constants are not affected, |
2670 | so that |
2671 | |
2672 | use Math::BigInt qw/:constant/; |
2673 | |
2674 | $x = 1234567890123456789012345678901234567890 |
2675 | + 123456789123456789; |
b22b3e31 |
2676 | $y = '1234567890123456789012345678901234567890' |
58cde26e |
2677 | + '123456789123456789'; |
b3ac6de7 |
2678 | |
b22b3e31 |
2679 | do not work. You need an explicit Math::BigInt->new() around one of the |
2680 | operands. |
58cde26e |
2681 | |
2682 | =head1 PERFORMANCE |
2683 | |
2684 | Using the form $x += $y; etc over $x = $x + $y is faster, since a copy of $x |
2685 | must be made in the second case. For long numbers, the copy can eat up to 20% |
b22b3e31 |
2686 | of the work (in the case of addition/subtraction, less for |
58cde26e |
2687 | multiplication/division). If $y is very small compared to $x, the form |
2688 | $x += $y is MUCH faster than $x = $x + $y since making the copy of $x takes |
2689 | more time then the actual addition. |
2690 | |
b22b3e31 |
2691 | With a technique called copy-on-write, the cost of copying with overload could |
58cde26e |
2692 | be minimized or even completely avoided. This is currently not implemented. |
2693 | |
2694 | The new version of this module is slower on new(), bstr() and numify(). Some |
2695 | operations may be slower for small numbers, but are significantly faster for |
2696 | big numbers. Other operations are now constant (O(1), like bneg(), babs() |
2697 | etc), instead of O(N) and thus nearly always take much less time. |
2698 | |
574bacfe |
2699 | If you find the Calc module to slow, try to install any of the replacement |
2700 | modules and see if they help you. |
b3ac6de7 |
2701 | |
574bacfe |
2702 | =head2 Alternative math libraries |
0716bf9b |
2703 | |
2704 | You can use an alternative library to drive Math::BigInt via: |
2705 | |
2706 | use Math::BigInt lib => 'Module'; |
2707 | |
574bacfe |
2708 | The default is called Math::BigInt::Calc and is a pure-perl implementation |
2709 | that consists mainly of the standard routine present in earlier versions of |
2710 | Math::BigInt. |
0716bf9b |
2711 | |
2712 | There are also Math::BigInt::Scalar (primarily for testing) and |
574bacfe |
2713 | Math::BigInt::BitVect; as well as Math::BigInt::Pari and likely others. |
2714 | All these can be found via L<http://search.cpan.org/>: |
0716bf9b |
2715 | |
2716 | use Math::BigInt lib => 'BitVect'; |
2717 | |
2718 | my $x = Math::BigInt->new(2); |
2719 | print $x ** (1024*1024); |
2720 | |
574bacfe |
2721 | For more benchmark results see http://bloodgate.com/perl/benchmarks.html |
2722 | |
a5f75d66 |
2723 | =head1 BUGS |
2724 | |
58cde26e |
2725 | =over 2 |
2726 | |
574bacfe |
2727 | =item Out of Memory! |
58cde26e |
2728 | |
2729 | Under Perl prior to 5.6.0 having an C<use Math::BigInt ':constant';> and |
2730 | C<eval()> in your code will crash with "Out of memory". This is probably an |
2731 | overload/exporter bug. You can workaround by not having C<eval()> |
574bacfe |
2732 | and ':constant' at the same time or upgrade your Perl to a newer version. |
2733 | |
2734 | =item Fails to load Calc on Perl prior 5.6.0 |
2735 | |
2736 | Since eval(' use ...') can not be used in conjunction with ':constant', BigInt |
2737 | will fall back to eval { require ... } when loading the math lib on Perls |
2738 | prior to 5.6.0. This simple replaces '::' with '/' and thus might fail on |
2739 | filesystems using a different seperator. |
58cde26e |
2740 | |
2741 | =back |
2742 | |
2743 | =head1 CAVEATS |
2744 | |
2745 | Some things might not work as you expect them. Below is documented what is |
2746 | known to be troublesome: |
2747 | |
2748 | =over 1 |
2749 | |
2750 | =item stringify, bstr(), bsstr() and 'cmp' |
2751 | |
2752 | Both stringify and bstr() now drop the leading '+'. The old code would return |
2753 | '+3', the new returns '3'. This is to be consistent with Perl and to make |
2754 | cmp (especially with overloading) to work as you expect. It also solves |
2755 | problems with Test.pm, it's ok() uses 'eq' internally. |
2756 | |
2757 | Mark said, when asked about to drop the '+' altogether, or make only cmp work: |
2758 | |
2759 | I agree (with the first alternative), don't add the '+' on positive |
2760 | numbers. It's not as important anymore with the new internal |
2761 | form for numbers. It made doing things like abs and neg easier, |
2762 | but those have to be done differently now anyway. |
2763 | |
2764 | So, the following examples will now work all as expected: |
2765 | |
2766 | use Test; |
2767 | BEGIN { plan tests => 1 } |
2768 | use Math::BigInt; |
2769 | |
2770 | my $x = new Math::BigInt 3*3; |
2771 | my $y = new Math::BigInt 3*3; |
2772 | |
2773 | ok ($x,3*3); |
2774 | print "$x eq 9" if $x eq $y; |
2775 | print "$x eq 9" if $x eq '9'; |
2776 | print "$x eq 9" if $x eq 3*3; |
2777 | |
2778 | Additionally, the following still works: |
2779 | |
2780 | print "$x == 9" if $x == $y; |
2781 | print "$x == 9" if $x == 9; |
2782 | print "$x == 9" if $x == 3*3; |
2783 | |
2784 | There is now a C<bsstr()> method to get the string in scientific notation aka |
2785 | C<1e+2> instead of C<100>. Be advised that overloaded 'eq' always uses bstr() |
2786 | for comparisation, but Perl will represent some numbers as 100 and others |
2787 | as 1e+308. If in doubt, convert both arguments to Math::BigInt before doing eq: |
2788 | |
2789 | use Test; |
2790 | BEGIN { plan tests => 3 } |
2791 | use Math::BigInt; |
2792 | |
2793 | $x = Math::BigInt->new('1e56'); $y = 1e56; |
2794 | ok ($x,$y); # will fail |
2795 | ok ($x->bsstr(),$y); # okay |
2796 | $y = Math::BigInt->new($y); |
2797 | ok ($x,$y); # okay |
2798 | |
574bacfe |
2799 | There is not yet a way to get a number automatically represented in exactly |
2800 | the way Perl represents it. |
2801 | |
58cde26e |
2802 | =item int() |
2803 | |
2804 | C<int()> will return (at least for Perl v5.7.1 and up) another BigInt, not a |
2805 | Perl scalar: |
2806 | |
2807 | $x = Math::BigInt->new(123); |
2808 | $y = int($x); # BigInt 123 |
2809 | $x = Math::BigFloat->new(123.45); |
2810 | $y = int($x); # BigInt 123 |
2811 | |
2812 | In all Perl versions you can use C<as_number()> for the same effect: |
2813 | |
2814 | $x = Math::BigFloat->new(123.45); |
2815 | $y = $x->as_number(); # BigInt 123 |
2816 | |
2817 | This also works for other subclasses, like Math::String. |
2818 | |
574bacfe |
2819 | It is yet unlcear whether overloaded int() should return a scalar or a BigInt. |
2820 | |
58cde26e |
2821 | =item bdiv |
2822 | |
2823 | The following will probably not do what you expect: |
2824 | |
bd05a461 |
2825 | $c = Math::BigInt->new(123); |
2826 | print $c->length(),"\n"; # prints 30 |
2827 | |
2828 | It prints both the number of digits in the number and in the fraction part |
2829 | since print calls C<length()> in list context. Use something like: |
2830 | |
2831 | print scalar $c->length(),"\n"; # prints 3 |
2832 | |
2833 | =item bdiv |
2834 | |
2835 | The following will probably not do what you expect: |
2836 | |
58cde26e |
2837 | print $c->bdiv(10000),"\n"; |
2838 | |
2839 | It prints both quotient and reminder since print calls C<bdiv()> in list |
2840 | context. Also, C<bdiv()> will modify $c, so be carefull. You probably want |
2841 | to use |
2842 | |
2843 | print $c / 10000,"\n"; |
2844 | print scalar $c->bdiv(10000),"\n"; # or if you want to modify $c |
2845 | |
2846 | instead. |
2847 | |
2848 | The quotient is always the greatest integer less than or equal to the |
2849 | real-valued quotient of the two operands, and the remainder (when it is |
2850 | nonzero) always has the same sign as the second operand; so, for |
2851 | example, |
2852 | |
574bacfe |
2853 | 1 / 4 => ( 0, 1) |
2854 | 1 / -4 => (-1,-3) |
58cde26e |
2855 | -3 / 4 => (-1, 1) |
2856 | -3 / -4 => ( 0,-3) |
2857 | |
2858 | As a consequence, the behavior of the operator % agrees with the |
2859 | behavior of Perl's built-in % operator (as documented in the perlop |
2860 | manpage), and the equation |
2861 | |
2862 | $x == ($x / $y) * $y + ($x % $y) |
2863 | |
2864 | holds true for any $x and $y, which justifies calling the two return |
2865 | values of bdiv() the quotient and remainder. |
2866 | |
2867 | Perl's 'use integer;' changes the behaviour of % and / for scalars, but will |
2868 | not change BigInt's way to do things. This is because under 'use integer' Perl |
2869 | will do what the underlying C thinks is right and this is different for each |
2870 | system. If you need BigInt's behaving exactly like Perl's 'use integer', bug |
2871 | the author to implement it ;) |
2872 | |
2873 | =item Modifying and = |
2874 | |
2875 | Beware of: |
2876 | |
2877 | $x = Math::BigFloat->new(5); |
2878 | $y = $x; |
2879 | |
2880 | It will not do what you think, e.g. making a copy of $x. Instead it just makes |
2881 | a second reference to the B<same> object and stores it in $y. Thus anything |
17baacb7 |
2882 | that modifies $x (except overloaded operators) will modify $y, and vice versa. |
2883 | Or in other words, C<=> is only safe if you modify your BigInts only via |
2884 | overloaded math. As soon as you use a method call it breaks: |
58cde26e |
2885 | |
2886 | $x->bmul(2); |
2887 | print "$x, $y\n"; # prints '10, 10' |
2888 | |
2889 | If you want a true copy of $x, use: |
2890 | |
2891 | $y = $x->copy(); |
2892 | |
17baacb7 |
2893 | You can also chain the calls like this, this will make first a copy and then |
2894 | multiply it by 2: |
2895 | |
2896 | $y = $x->copy()->bmul(2); |
2897 | |
b22b3e31 |
2898 | See also the documentation for overload.pm regarding C<=>. |
58cde26e |
2899 | |
2900 | =item bpow |
2901 | |
2902 | C<bpow()> (and the rounding functions) now modifies the first argument and |
574bacfe |
2903 | returns it, unlike the old code which left it alone and only returned the |
58cde26e |
2904 | result. This is to be consistent with C<badd()> etc. The first three will |
2905 | modify $x, the last one won't: |
2906 | |
2907 | print bpow($x,$i),"\n"; # modify $x |
2908 | print $x->bpow($i),"\n"; # ditto |
2909 | print $x **= $i,"\n"; # the same |
2910 | print $x ** $i,"\n"; # leave $x alone |
2911 | |
2912 | The form C<$x **= $y> is faster than C<$x = $x ** $y;>, though. |
2913 | |
2914 | =item Overloading -$x |
2915 | |
2916 | The following: |
2917 | |
2918 | $x = -$x; |
2919 | |
2920 | is slower than |
2921 | |
2922 | $x->bneg(); |
2923 | |
2924 | since overload calls C<sub($x,0,1);> instead of C<neg($x)>. The first variant |
2925 | needs to preserve $x since it does not know that it later will get overwritten. |
0716bf9b |
2926 | This makes a copy of $x and takes O(N), but $x->bneg() is O(1). |
58cde26e |
2927 | |
2928 | With Copy-On-Write, this issue will be gone. Stay tuned... |
2929 | |
2930 | =item Mixing different object types |
2931 | |
2932 | In Perl you will get a floating point value if you do one of the following: |
2933 | |
2934 | $float = 5.0 + 2; |
2935 | $float = 2 + 5.0; |
2936 | $float = 5 / 2; |
2937 | |
2938 | With overloaded math, only the first two variants will result in a BigFloat: |
2939 | |
2940 | use Math::BigInt; |
2941 | use Math::BigFloat; |
2942 | |
2943 | $mbf = Math::BigFloat->new(5); |
2944 | $mbi2 = Math::BigInteger->new(5); |
2945 | $mbi = Math::BigInteger->new(2); |
2946 | |
2947 | # what actually gets called: |
2948 | $float = $mbf + $mbi; # $mbf->badd() |
2949 | $float = $mbf / $mbi; # $mbf->bdiv() |
2950 | $integer = $mbi + $mbf; # $mbi->badd() |
2951 | $integer = $mbi2 / $mbi; # $mbi2->bdiv() |
2952 | $integer = $mbi2 / $mbf; # $mbi2->bdiv() |
2953 | |
2954 | This is because math with overloaded operators follows the first (dominating) |
2955 | operand, this one's operation is called and returns thus the result. So, |
2956 | Math::BigInt::bdiv() will always return a Math::BigInt, regardless whether |
2957 | the result should be a Math::BigFloat or the second operant is one. |
2958 | |
2959 | To get a Math::BigFloat you either need to call the operation manually, |
2960 | make sure the operands are already of the proper type or casted to that type |
2961 | via Math::BigFloat->new(): |
2962 | |
2963 | $float = Math::BigFloat->new($mbi2) / $mbi; # = 2.5 |
2964 | |
2965 | Beware of simple "casting" the entire expression, this would only convert |
2966 | the already computed result: |
2967 | |
2968 | $float = Math::BigFloat->new($mbi2 / $mbi); # = 2.0 thus wrong! |
2969 | |
0716bf9b |
2970 | Beware also of the order of more complicated expressions like: |
58cde26e |
2971 | |
2972 | $integer = ($mbi2 + $mbi) / $mbf; # int / float => int |
2973 | $integer = $mbi2 / Math::BigFloat->new($mbi); # ditto |
2974 | |
2975 | If in doubt, break the expression into simpler terms, or cast all operands |
2976 | to the desired resulting type. |
2977 | |
2978 | Scalar values are a bit different, since: |
2979 | |
2980 | $float = 2 + $mbf; |
2981 | $float = $mbf + 2; |
2982 | |
2983 | will both result in the proper type due to the way the overloaded math works. |
2984 | |
2985 | This section also applies to other overloaded math packages, like Math::String. |
2986 | |
2987 | =item bsqrt() |
2988 | |
2989 | C<bsqrt()> works only good if the result is an big integer, e.g. the square |
2990 | root of 144 is 12, but from 12 the square root is 3, regardless of rounding |
2991 | mode. |
2992 | |
2993 | If you want a better approximation of the square root, then use: |
2994 | |
2995 | $x = Math::BigFloat->new(12); |
2996 | $Math::BigFloat::precision = 0; |
2997 | Math::BigFloat->round_mode('even'); |
2998 | print $x->copy->bsqrt(),"\n"; # 4 |
2999 | |
3000 | $Math::BigFloat::precision = 2; |
3001 | print $x->bsqrt(),"\n"; # 3.46 |
3002 | print $x->bsqrt(3),"\n"; # 3.464 |
3003 | |
3004 | =back |
3005 | |
3006 | =head1 LICENSE |
3007 | |
3008 | This program is free software; you may redistribute it and/or modify it under |
3009 | the same terms as Perl itself. |
a5f75d66 |
3010 | |
0716bf9b |
3011 | =head1 SEE ALSO |
3012 | |
3013 | L<Math::BigFloat> and L<Math::Big>. |
3014 | |
574bacfe |
3015 | L<Math::BigInt::BitVect> and L<Math::BigInt::Pari>. |
3016 | |
58cde26e |
3017 | =head1 AUTHORS |
a5f75d66 |
3018 | |
58cde26e |
3019 | Original code by Mark Biggar, overloaded interface by Ilya Zakharevich. |
3020 | Completely rewritten by Tels http://bloodgate.com in late 2000, 2001. |
a5f75d66 |
3021 | |
3022 | =cut |