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1 | #!/usr/bin/perl -w |
2 | |
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3 | # The following hash values are used: |
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4 | # value: unsigned int with actual value (as a Math::BigInt::Calc or similiar) |
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5 | # sign : +,-,NaN,+inf,-inf |
6 | # _a : accuracy |
7 | # _p : precision |
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8 | # _f : flags, used by MBF to flag parts of a float as untouchable |
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9 | |
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10 | # Remember not to take shortcuts ala $xs = $x->{value}; $CALC->foo($xs); since |
11 | # underlying lib might change the reference! |
12 | |
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13 | package Math::BigInt; |
14 | my $class = "Math::BigInt"; |
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15 | require 5.005; |
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16 | |
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17 | $VERSION = '1.48'; |
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18 | use Exporter; |
19 | @ISA = qw( Exporter ); |
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20 | # no longer export stuff (it doesn't work with subclasses anyway) |
21 | # bneg babs bcmp badd bmul bdiv bmod bnorm bsub |
22 | # bgcd blcm bround |
23 | # blsft brsft band bior bxor bnot bpow bnan bzero |
24 | # bacmp bstr bsstr binc bdec binf bfloor bceil |
25 | # is_odd is_even is_zero is_one is_nan is_inf sign |
26 | # is_positive is_negative |
27 | # length as_number |
28 | @EXPORT_OK = qw( |
29 | objectify _swap |
30 | bgcd blcm |
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31 | ); |
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32 | use vars qw/$round_mode $accuracy $precision $div_scale $rnd_mode/; |
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33 | use strict; |
34 | |
35 | # Inside overload, the first arg is always an object. If the original code had |
36 | # it reversed (like $x = 2 * $y), then the third paramater indicates this |
37 | # swapping. To make it work, we use a helper routine which not only reswaps the |
38 | # params, but also makes a new object in this case. See _swap() for details, |
39 | # especially the cases of operators with different classes. |
40 | |
41 | # For overloaded ops with only one argument we simple use $_[0]->copy() to |
42 | # preserve the argument. |
43 | |
44 | # Thus inheritance of overload operators becomes possible and transparent for |
45 | # our subclasses without the need to repeat the entire overload section there. |
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46 | |
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47 | use overload |
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48 | '=' => sub { $_[0]->copy(); }, |
49 | |
50 | # '+' and '-' do not use _swap, since it is a triffle slower. If you want to |
51 | # override _swap (if ever), then override overload of '+' and '-', too! |
52 | # for sub it is a bit tricky to keep b: b-a => -a+b |
53 | '-' => sub { my $c = $_[0]->copy; $_[2] ? |
54 | $c->bneg()->badd($_[1]) : |
55 | $c->bsub( $_[1]) }, |
56 | '+' => sub { $_[0]->copy()->badd($_[1]); }, |
57 | |
58 | # some shortcuts for speed (assumes that reversed order of arguments is routed |
59 | # to normal '+' and we thus can always modify first arg. If this is changed, |
60 | # this breaks and must be adjusted.) |
61 | '+=' => sub { $_[0]->badd($_[1]); }, |
62 | '-=' => sub { $_[0]->bsub($_[1]); }, |
63 | '*=' => sub { $_[0]->bmul($_[1]); }, |
64 | '/=' => sub { scalar $_[0]->bdiv($_[1]); }, |
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65 | '%=' => sub { $_[0]->bmod($_[1]); }, |
66 | '^=' => sub { $_[0]->bxor($_[1]); }, |
67 | '&=' => sub { $_[0]->band($_[1]); }, |
68 | '|=' => sub { $_[0]->bior($_[1]); }, |
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69 | '**=' => sub { $_[0]->bpow($_[1]); }, |
70 | |
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71 | '..' => \&_pointpoint, |
72 | |
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73 | '<=>' => sub { $_[2] ? |
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74 | ref($_[0])->bcmp($_[1],$_[0]) : |
75 | ref($_[0])->bcmp($_[0],$_[1])}, |
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76 | 'cmp' => sub { |
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77 | $_[2] ? |
78 | $_[1] cmp $_[0]->bstr() : |
79 | $_[0]->bstr() cmp $_[1] }, |
80 | |
81 | 'int' => sub { $_[0]->copy(); }, |
82 | 'neg' => sub { $_[0]->copy()->bneg(); }, |
83 | 'abs' => sub { $_[0]->copy()->babs(); }, |
84 | '~' => sub { $_[0]->copy()->bnot(); }, |
85 | |
86 | '*' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bmul($a[1]); }, |
87 | '/' => sub { my @a = ref($_[0])->_swap(@_);scalar $a[0]->bdiv($a[1]);}, |
88 | '%' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bmod($a[1]); }, |
89 | '**' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bpow($a[1]); }, |
90 | '<<' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->blsft($a[1]); }, |
91 | '>>' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->brsft($a[1]); }, |
92 | |
93 | '&' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->band($a[1]); }, |
94 | '|' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bior($a[1]); }, |
95 | '^' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bxor($a[1]); }, |
96 | |
97 | # can modify arg of ++ and --, so avoid a new-copy for speed, but don't |
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98 | # use $_[0]->__one(), it modifies $_[0] to be 1! |
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99 | '++' => sub { $_[0]->binc() }, |
100 | '--' => sub { $_[0]->bdec() }, |
101 | |
102 | # if overloaded, O(1) instead of O(N) and twice as fast for small numbers |
103 | 'bool' => sub { |
104 | # this kludge is needed for perl prior 5.6.0 since returning 0 here fails :-/ |
105 | # v5.6.1 dumps on that: return !$_[0]->is_zero() || undef; :-( |
106 | my $t = !$_[0]->is_zero(); |
107 | undef $t if $t == 0; |
108 | return $t; |
109 | }, |
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110 | |
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111 | # the original qw() does not work with the TIESCALAR below, why? |
112 | # Order of arguments unsignificant |
113 | '""' => sub { $_[0]->bstr(); }, |
114 | '0+' => sub { $_[0]->numify(); } |
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115 | ; |
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116 | |
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117 | ############################################################################## |
118 | # global constants, flags and accessory |
119 | |
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120 | use constant MB_NEVER_ROUND => 0x0001; |
121 | |
122 | my $NaNOK=1; # are NaNs ok? |
123 | my $nan = 'NaN'; # constants for easier life |
124 | |
125 | my $CALC = 'Math::BigInt::Calc'; # module to do low level math |
126 | sub _core_lib () { return $CALC; } # for test suite |
127 | |
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128 | $round_mode = 'even'; # one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc' |
129 | $accuracy = undef; |
130 | $precision = undef; |
131 | $div_scale = 40; |
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132 | |
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133 | ############################################################################## |
134 | # the old code had $rnd_mode, so we need to support it, too |
135 | |
136 | $rnd_mode = 'even'; |
137 | sub TIESCALAR { my ($class) = @_; bless \$round_mode, $class; } |
138 | sub FETCH { return $round_mode; } |
139 | sub STORE { $rnd_mode = $_[0]->round_mode($_[1]); } |
140 | |
141 | BEGIN { tie $rnd_mode, 'Math::BigInt'; } |
142 | |
143 | ############################################################################## |
144 | |
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145 | sub round_mode |
146 | { |
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147 | no strict 'refs'; |
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148 | # make Class->round_mode() work |
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149 | my $self = shift; |
150 | my $class = ref($self) || $self || __PACKAGE__; |
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151 | if (defined $_[0]) |
152 | { |
153 | my $m = shift; |
154 | die "Unknown round mode $m" |
155 | if $m !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/; |
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156 | ${"${class}::round_mode"} = $m; return $m; |
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157 | } |
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158 | return ${"${class}::round_mode"}; |
159 | } |
160 | |
161 | sub div_scale |
162 | { |
163 | no strict 'refs'; |
164 | # make Class->round_mode() work |
165 | my $self = shift; |
166 | my $class = ref($self) || $self || __PACKAGE__; |
167 | if (defined $_[0]) |
168 | { |
169 | die ('div_scale must be greater than zero') if $_[0] < 0; |
170 | ${"${class}::div_scale"} = shift; |
171 | } |
172 | return ${"${class}::div_scale"}; |
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173 | } |
174 | |
175 | sub accuracy |
176 | { |
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177 | # $x->accuracy($a); ref($x) $a |
178 | # $x->accuracy(); ref($x) |
179 | # Class->accuracy(); class |
180 | # Class->accuracy($a); class $a |
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181 | |
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182 | my $x = shift; |
183 | my $class = ref($x) || $x || __PACKAGE__; |
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184 | |
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185 | no strict 'refs'; |
186 | # need to set new value? |
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187 | if (@_ > 0) |
188 | { |
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189 | my $a = shift; |
190 | die ('accuracy must not be zero') if defined $a && $a == 0; |
191 | if (ref($x)) |
192 | { |
193 | # $object->accuracy() or fallback to global |
194 | $x->bround($a) if defined $a; |
195 | $x->{_a} = $a; # set/overwrite, even if not rounded |
196 | $x->{_p} = undef; # clear P |
197 | } |
198 | else |
199 | { |
200 | # set global |
201 | ${"${class}::accuracy"} = $a; |
202 | } |
203 | return $a; # shortcut |
204 | } |
205 | |
206 | if (ref($x)) |
207 | { |
208 | # $object->accuracy() or fallback to global |
209 | return $x->{_a} || ${"${class}::accuracy"}; |
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210 | } |
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211 | return ${"${class}::accuracy"}; |
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212 | } |
213 | |
214 | sub precision |
215 | { |
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216 | # $x->precision($p); ref($x) $p |
217 | # $x->precision(); ref($x) |
218 | # Class->precision(); class |
219 | # Class->precision($p); class $p |
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220 | |
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221 | my $x = shift; |
222 | my $class = ref($x) || $x || __PACKAGE__; |
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223 | |
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224 | no strict 'refs'; |
225 | # need to set new value? |
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226 | if (@_ > 0) |
227 | { |
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228 | my $p = shift; |
229 | if (ref($x)) |
230 | { |
231 | # $object->precision() or fallback to global |
232 | $x->bfround($p) if defined $p; |
233 | $x->{_p} = $p; # set/overwrite, even if not rounded |
234 | $x->{_a} = undef; # clear P |
235 | } |
236 | else |
237 | { |
238 | # set global |
239 | ${"${class}::precision"} = $p; |
240 | } |
241 | return $p; # shortcut |
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242 | } |
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243 | |
244 | if (ref($x)) |
245 | { |
246 | # $object->precision() or fallback to global |
247 | return $x->{_p} || ${"${class}::precision"}; |
248 | } |
249 | return ${"${class}::precision"}; |
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250 | } |
251 | |
252 | sub _scale_a |
253 | { |
254 | # select accuracy parameter based on precedence, |
255 | # used by bround() and bfround(), may return undef for scale (means no op) |
256 | my ($x,$s,$m,$scale,$mode) = @_; |
257 | $scale = $x->{_a} if !defined $scale; |
258 | $scale = $s if (!defined $scale); |
259 | $mode = $m if !defined $mode; |
260 | return ($scale,$mode); |
261 | } |
262 | |
263 | sub _scale_p |
264 | { |
265 | # select precision parameter based on precedence, |
266 | # used by bround() and bfround(), may return undef for scale (means no op) |
267 | my ($x,$s,$m,$scale,$mode) = @_; |
268 | $scale = $x->{_p} if !defined $scale; |
269 | $scale = $s if (!defined $scale); |
270 | $mode = $m if !defined $mode; |
271 | return ($scale,$mode); |
272 | } |
273 | |
274 | ############################################################################## |
275 | # constructors |
276 | |
277 | sub copy |
278 | { |
279 | my ($c,$x); |
280 | if (@_ > 1) |
281 | { |
282 | # if two arguments, the first one is the class to "swallow" subclasses |
283 | ($c,$x) = @_; |
284 | } |
285 | else |
286 | { |
287 | $x = shift; |
288 | $c = ref($x); |
289 | } |
290 | return unless ref($x); # only for objects |
291 | |
292 | my $self = {}; bless $self,$c; |
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293 | my $r; |
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294 | foreach my $k (keys %$x) |
295 | { |
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296 | if ($k eq 'value') |
297 | { |
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298 | $self->{value} = $CALC->_copy($x->{value}); next; |
299 | } |
300 | if (!($r = ref($x->{$k}))) |
301 | { |
302 | $self->{$k} = $x->{$k}; next; |
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303 | } |
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304 | if ($r eq 'SCALAR') |
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305 | { |
306 | $self->{$k} = \${$x->{$k}}; |
307 | } |
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308 | elsif ($r eq 'ARRAY') |
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309 | { |
310 | $self->{$k} = [ @{$x->{$k}} ]; |
311 | } |
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312 | elsif ($r eq 'HASH') |
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313 | { |
314 | # only one level deep! |
315 | foreach my $h (keys %{$x->{$k}}) |
316 | { |
317 | $self->{$k}->{$h} = $x->{$k}->{$h}; |
318 | } |
319 | } |
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320 | else # normal ref |
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321 | { |
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322 | my $xk = $x->{$k}; |
323 | if ($xk->can('copy')) |
324 | { |
325 | $self->{$k} = $xk->copy(); |
326 | } |
327 | else |
328 | { |
329 | $self->{$k} = $xk->new($xk); |
330 | } |
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331 | } |
332 | } |
333 | $self; |
334 | } |
335 | |
336 | sub new |
337 | { |
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338 | # create a new BigInt object from a string or another BigInt object. |
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339 | # see hash keys documented at top |
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340 | |
341 | # the argument could be an object, so avoid ||, && etc on it, this would |
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342 | # cause costly overloaded code to be called. The only allowed ops are |
343 | # ref() and defined. |
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344 | |
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345 | my $class = shift; |
346 | |
347 | my $wanted = shift; # avoid numify call by not using || here |
348 | return $class->bzero() if !defined $wanted; # default to 0 |
349 | return $class->copy($wanted) if ref($wanted); |
350 | |
351 | my $self = {}; bless $self, $class; |
352 | # handle '+inf', '-inf' first |
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353 | if ($wanted =~ /^[+-]?inf$/) |
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354 | { |
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355 | $self->{value} = $CALC->_zero(); |
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356 | $self->{sign} = $wanted; $self->{sign} = '+inf' if $self->{sign} eq 'inf'; |
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357 | return $self; |
358 | } |
359 | # split str in m mantissa, e exponent, i integer, f fraction, v value, s sign |
360 | my ($mis,$miv,$mfv,$es,$ev) = _split(\$wanted); |
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361 | if (!ref $mis) |
362 | { |
363 | die "$wanted is not a number initialized to $class" if !$NaNOK; |
364 | #print "NaN 1\n"; |
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365 | $self->{value} = $CALC->_zero(); |
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366 | $self->{sign} = $nan; |
367 | return $self; |
368 | } |
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369 | if (!ref $miv) |
370 | { |
371 | # _from_hex or _from_bin |
372 | $self->{value} = $mis->{value}; |
373 | $self->{sign} = $mis->{sign}; |
374 | return $self; # throw away $mis |
375 | } |
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376 | # make integer from mantissa by adjusting exp, then convert to bigint |
377 | $self->{sign} = $$mis; # store sign |
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378 | $self->{value} = $CALC->_zero(); # for all the NaN cases |
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379 | my $e = int("$$es$$ev"); # exponent (avoid recursion) |
380 | if ($e > 0) |
381 | { |
382 | my $diff = $e - CORE::length($$mfv); |
383 | if ($diff < 0) # Not integer |
384 | { |
385 | #print "NOI 1\n"; |
386 | $self->{sign} = $nan; |
387 | } |
388 | else # diff >= 0 |
389 | { |
390 | # adjust fraction and add it to value |
391 | # print "diff > 0 $$miv\n"; |
392 | $$miv = $$miv . ($$mfv . '0' x $diff); |
393 | } |
394 | } |
395 | else |
396 | { |
397 | if ($$mfv ne '') # e <= 0 |
398 | { |
399 | # fraction and negative/zero E => NOI |
400 | #print "NOI 2 \$\$mfv '$$mfv'\n"; |
401 | $self->{sign} = $nan; |
402 | } |
403 | elsif ($e < 0) |
404 | { |
405 | # xE-y, and empty mfv |
406 | #print "xE-y\n"; |
407 | $e = abs($e); |
408 | if ($$miv !~ s/0{$e}$//) # can strip so many zero's? |
409 | { |
410 | #print "NOI 3\n"; |
411 | $self->{sign} = $nan; |
412 | } |
413 | } |
414 | } |
415 | $self->{sign} = '+' if $$miv eq '0'; # normalize -0 => +0 |
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416 | $self->{value} = $CALC->_new($miv) if $self->{sign} =~ /^[+-]$/; |
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417 | # if any of the globals is set, use them to round and store them inside $self |
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418 | $self->round($accuracy,$precision,$round_mode) |
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419 | if defined $accuracy || defined $precision; |
420 | return $self; |
421 | } |
422 | |
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423 | sub bnan |
424 | { |
425 | # create a bigint 'NaN', if given a BigInt, set it to 'NaN' |
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426 | my $self = shift; |
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427 | $self = $class if !defined $self; |
428 | if (!ref($self)) |
429 | { |
430 | my $c = $self; $self = {}; bless $self, $c; |
431 | } |
432 | return if $self->modify('bnan'); |
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433 | $self->{value} = $CALC->_zero(); |
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434 | $self->{sign} = $nan; |
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435 | delete $self->{_a}; delete $self->{_p}; # rounding NaN is silly |
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436 | return $self; |
b4f14daa |
437 | } |
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438 | |
439 | sub binf |
440 | { |
441 | # create a bigint '+-inf', if given a BigInt, set it to '+-inf' |
442 | # the sign is either '+', or if given, used from there |
443 | my $self = shift; |
444 | my $sign = shift; $sign = '+' if !defined $sign || $sign ne '-'; |
445 | $self = $class if !defined $self; |
446 | if (!ref($self)) |
447 | { |
448 | my $c = $self; $self = {}; bless $self, $c; |
449 | } |
450 | return if $self->modify('binf'); |
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451 | $self->{value} = $CALC->_zero(); |
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452 | $self->{sign} = $sign.'inf'; |
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453 | ($self->{_a},$self->{_p}) = @_; # take over requested rounding |
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454 | return $self; |
455 | } |
456 | |
457 | sub bzero |
458 | { |
459 | # create a bigint '+0', if given a BigInt, set it to 0 |
460 | my $self = shift; |
461 | $self = $class if !defined $self; |
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462 | |
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463 | if (!ref($self)) |
464 | { |
465 | my $c = $self; $self = {}; bless $self, $c; |
466 | } |
467 | return if $self->modify('bzero'); |
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468 | $self->{value} = $CALC->_zero(); |
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469 | $self->{sign} = '+'; |
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470 | ($self->{_a},$self->{_p}) = @_; # take over requested rounding |
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471 | return $self; |
472 | } |
473 | |
574bacfe |
474 | sub bone |
475 | { |
476 | # create a bigint '+1' (or -1 if given sign '-'), |
477 | # if given a BigInt, set it to +1 or -1, respecively |
478 | my $self = shift; |
479 | my $sign = shift; $sign = '+' if !defined $sign || $sign ne '-'; |
480 | $self = $class if !defined $self; |
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481 | |
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482 | if (!ref($self)) |
483 | { |
484 | my $c = $self; $self = {}; bless $self, $c; |
485 | } |
486 | return if $self->modify('bone'); |
487 | $self->{value} = $CALC->_one(); |
488 | $self->{sign} = $sign; |
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489 | ($self->{_a},$self->{_p}) = @_; # take over requested rounding |
574bacfe |
490 | return $self; |
491 | } |
492 | |
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493 | ############################################################################## |
494 | # string conversation |
495 | |
496 | sub bsstr |
497 | { |
498 | # (ref to BFLOAT or num_str ) return num_str |
499 | # Convert number from internal format to scientific string format. |
500 | # internal format is always normalized (no leading zeros, "-0E0" => "+0E0") |
dccbb853 |
501 | my $x = shift; $class = ref($x) || $x; $x = $class->new(shift) if !ref($x); |
502 | # my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
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503 | |
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504 | if ($x->{sign} !~ /^[+-]$/) |
505 | { |
506 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN |
507 | return 'inf'; # +inf |
508 | } |
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509 | my ($m,$e) = $x->parts(); |
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510 | # e can only be positive |
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511 | my $sign = 'e+'; |
512 | # MBF: my $s = $e->{sign}; $s = '' if $s eq '-'; my $sep = 'e'.$s; |
513 | return $m->bstr().$sign.$e->bstr(); |
514 | } |
515 | |
516 | sub bstr |
517 | { |
0716bf9b |
518 | # make a string from bigint object |
ee15d750 |
519 | my $x = shift; $class = ref($x) || $x; $x = $class->new(shift) if !ref($x); |
520 | # my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
027dc388 |
521 | |
574bacfe |
522 | if ($x->{sign} !~ /^[+-]$/) |
523 | { |
524 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN |
525 | return 'inf'; # +inf |
526 | } |
0716bf9b |
527 | my $es = ''; $es = $x->{sign} if $x->{sign} eq '-'; |
528 | return $es.${$CALC->_str($x->{value})}; |
58cde26e |
529 | } |
530 | |
531 | sub numify |
532 | { |
394e6ffb |
533 | # Make a "normal" scalar from a BigInt object |
58cde26e |
534 | my $x = shift; $x = $class->new($x) unless ref $x; |
0716bf9b |
535 | return $x->{sign} if $x->{sign} !~ /^[+-]$/; |
536 | my $num = $CALC->_num($x->{value}); |
537 | return -$num if $x->{sign} eq '-'; |
58cde26e |
538 | return $num; |
539 | } |
540 | |
541 | ############################################################################## |
542 | # public stuff (usually prefixed with "b") |
543 | |
544 | sub sign |
545 | { |
546 | # return the sign of the number: +/-/NaN |
ee15d750 |
547 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
548 | |
58cde26e |
549 | return $x->{sign}; |
550 | } |
551 | |
ee15d750 |
552 | sub _find_round_parameters |
58cde26e |
553 | { |
554 | # After any operation or when calling round(), the result is rounded by |
555 | # regarding the A & P from arguments, local parameters, or globals. |
556 | # The result's A or P are set by the rounding, but not inspected beforehand |
557 | # (aka only the arguments enter into it). This works because the given |
558 | # 'first' argument is both the result and true first argument with unchanged |
559 | # A and P settings. |
560 | # This does not yet handle $x with A, and $y with P (which should be an |
561 | # error). |
394e6ffb |
562 | my ($self,$a,$p,$r,@args) = @_; |
563 | # $a accuracy, if given by caller |
564 | # $p precision, if given by caller |
565 | # $r round_mode, if given by caller |
566 | # @args all 'other' arguments (0 for unary, 1 for binary ops) |
58cde26e |
567 | |
394e6ffb |
568 | # $self = new($self) unless ref($self); # if not object, make one |
574bacfe |
569 | |
17baacb7 |
570 | # leave bigfloat parts alone |
ee15d750 |
571 | return ($self) if exists $self->{_f} && $self->{_f} & MB_NEVER_ROUND != 0; |
17baacb7 |
572 | |
394e6ffb |
573 | unshift @args,$self; # add 'first' argument |
574 | my $c = ref($self); # find out class of argument(s) |
574bacfe |
575 | no strict 'refs'; |
574bacfe |
576 | |
58cde26e |
577 | # now pick $a or $p, but only if we have got "arguments" |
578 | if ((!defined $a) && (!defined $p) && (@args > 0)) |
579 | { |
580 | foreach (@args) |
581 | { |
582 | # take the defined one, or if both defined, the one that is smaller |
583 | $a = $_->{_a} if (defined $_->{_a}) && (!defined $a || $_->{_a} < $a); |
584 | } |
585 | if (!defined $a) # if it still is not defined, take p |
586 | { |
587 | foreach (@args) |
588 | { |
ee15d750 |
589 | # take the defined one, or if both defined, the one that is bigger |
590 | # -2 > -3, and 3 > 2 |
591 | $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} > $p); |
1f45ae4a |
592 | } |
58cde26e |
593 | # if none defined, use globals (#2) |
594 | if (!defined $p) |
595 | { |
ee15d750 |
596 | my $z = "$c\::accuracy"; my $a = $$z; |
597 | if (!defined $a) |
598 | { |
599 | $z = "$c\::precision"; $p = $$z; |
600 | } |
1f45ae4a |
601 | } |
58cde26e |
602 | } # endif !$a |
603 | } # endif !$a || !$P && args > 0 |
ee15d750 |
604 | my @params = ($self); |
605 | if (defined $a || defined $p) |
606 | { |
ee15d750 |
607 | $r = $r || ${"$c\::round_mode"}; |
608 | die "Unknown round mode '$r'" |
609 | if $r !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/; |
610 | push @params, ($a,$p,$r); |
611 | } |
612 | return @params; |
613 | } |
614 | |
615 | sub round |
616 | { |
617 | # round $self according to given parameters, or given second argument's |
618 | # parameters or global defaults |
619 | my $self = shift; |
620 | |
621 | my @params = $self->_find_round_parameters(@_); |
622 | return $self->bnorm() if @params == 1; # no-op |
623 | |
58cde26e |
624 | # now round, by calling fround or ffround: |
ee15d750 |
625 | if (defined $params[1]) |
58cde26e |
626 | { |
ee15d750 |
627 | $self->bround($params[1],$params[3]); |
58cde26e |
628 | } |
ee15d750 |
629 | else |
58cde26e |
630 | { |
ee15d750 |
631 | $self->bfround($params[2],$params[3]); |
58cde26e |
632 | } |
ee15d750 |
633 | return $self->bnorm(); # after round, normalize |
58cde26e |
634 | } |
635 | |
17baacb7 |
636 | sub bnorm |
58cde26e |
637 | { |
027dc388 |
638 | # (numstr or BINT) return BINT |
58cde26e |
639 | # Normalize number -- no-op here |
dccbb853 |
640 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
641 | return $x; |
58cde26e |
642 | } |
643 | |
644 | sub babs |
645 | { |
646 | # (BINT or num_str) return BINT |
647 | # make number absolute, or return absolute BINT from string |
ee15d750 |
648 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
649 | |
58cde26e |
650 | return $x if $x->modify('babs'); |
651 | # post-normalized abs for internal use (does nothing for NaN) |
652 | $x->{sign} =~ s/^-/+/; |
653 | $x; |
654 | } |
655 | |
656 | sub bneg |
657 | { |
658 | # (BINT or num_str) return BINT |
659 | # negate number or make a negated number from string |
ee15d750 |
660 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
661 | |
58cde26e |
662 | return $x if $x->modify('bneg'); |
663 | # for +0 dont negate (to have always normalized) |
664 | return $x if $x->is_zero(); |
394e6ffb |
665 | $x->{sign} =~ tr/+-/-+/; # does nothing for NaN |
58cde26e |
666 | $x; |
667 | } |
668 | |
669 | sub bcmp |
670 | { |
671 | # Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort) |
672 | # (BINT or num_str, BINT or num_str) return cond_code |
673 | my ($self,$x,$y) = objectify(2,@_); |
0716bf9b |
674 | |
675 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
676 | { |
677 | # handle +-inf and NaN |
678 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
574bacfe |
679 | return 0 if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/; |
0716bf9b |
680 | return +1 if $x->{sign} eq '+inf'; |
681 | return -1 if $x->{sign} eq '-inf'; |
682 | return -1 if $y->{sign} eq '+inf'; |
683 | return +1 if $y->{sign} eq '-inf'; |
684 | } |
574bacfe |
685 | # check sign for speed first |
686 | return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y |
687 | return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0 |
688 | |
689 | # shortcut |
690 | my $xz = $x->is_zero(); |
691 | my $yz = $y->is_zero(); |
692 | return 0 if $xz && $yz; # 0 <=> 0 |
693 | return -1 if $xz && $y->{sign} eq '+'; # 0 <=> +y |
694 | return 1 if $yz && $x->{sign} eq '+'; # +x <=> 0 |
dccbb853 |
695 | |
696 | # post-normalized compare for internal use (honors signs) |
697 | if ($x->{sign} eq '+') |
698 | { |
699 | return 1 if $y->{sign} eq '-'; # 0 check handled above |
700 | return $CALC->_acmp($x->{value},$y->{value}); |
701 | } |
702 | |
703 | # $x->{sign} eq '-' |
704 | return -1 if $y->{sign} eq '+'; |
705 | return $CALC->_acmp($y->{value},$x->{value}); # swaped |
706 | |
707 | # &cmp($x->{value},$y->{value},$x->{sign},$y->{sign}) <=> 0; |
58cde26e |
708 | } |
709 | |
710 | sub bacmp |
711 | { |
712 | # Compares 2 values, ignoring their signs. |
713 | # Returns one of undef, <0, =0, >0. (suitable for sort) |
714 | # (BINT, BINT) return cond_code |
715 | my ($self,$x,$y) = objectify(2,@_); |
574bacfe |
716 | |
717 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
718 | { |
719 | # handle +-inf and NaN |
720 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
721 | return 0 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} =~ /^[+-]inf$/; |
722 | return +1; # inf is always bigger |
723 | } |
0716bf9b |
724 | $CALC->_acmp($x->{value},$y->{value}) <=> 0; |
58cde26e |
725 | } |
726 | |
727 | sub badd |
728 | { |
729 | # add second arg (BINT or string) to first (BINT) (modifies first) |
730 | # return result as BINT |
58cde26e |
731 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
732 | |
733 | return $x if $x->modify('badd'); |
58cde26e |
734 | |
574bacfe |
735 | # inf and NaN handling |
736 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
737 | { |
738 | # NaN first |
739 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
740 | # inf handline |
741 | if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) |
742 | { |
743 | # + and + => +, - and - => -, + and - => 0, - and + => 0 |
744 | return $x->bzero() if $x->{sign} ne $y->{sign}; |
745 | return $x; |
746 | } |
747 | # +-inf + something => +inf |
748 | # something +-inf => +-inf |
749 | $x->{sign} = $y->{sign}, return $x if $y->{sign} =~ /^[+-]inf$/; |
750 | return $x; |
751 | } |
752 | |
0716bf9b |
753 | my @bn = ($a,$p,$r,$y); # make array for round calls |
58cde26e |
754 | # speed: no add for 0+y or x+0 |
0716bf9b |
755 | return $x->round(@bn) if $y->is_zero(); # x+0 |
58cde26e |
756 | if ($x->is_zero()) # 0+y |
757 | { |
758 | # make copy, clobbering up x |
0716bf9b |
759 | $x->{value} = $CALC->_copy($y->{value}); |
58cde26e |
760 | $x->{sign} = $y->{sign} || $nan; |
761 | return $x->round(@bn); |
762 | } |
763 | |
58cde26e |
764 | my ($sx, $sy) = ( $x->{sign}, $y->{sign} ); # get signs |
765 | |
766 | if ($sx eq $sy) |
767 | { |
574bacfe |
768 | $x->{value} = $CALC->_add($x->{value},$y->{value}); # same sign, abs add |
58cde26e |
769 | $x->{sign} = $sx; |
770 | } |
771 | else |
772 | { |
574bacfe |
773 | my $a = $CALC->_acmp ($y->{value},$x->{value}); # absolute compare |
58cde26e |
774 | if ($a > 0) |
775 | { |
776 | #print "swapped sub (a=$a)\n"; |
574bacfe |
777 | $x->{value} = $CALC->_sub($y->{value},$x->{value},1); # abs sub w/ swap |
58cde26e |
778 | $x->{sign} = $sy; |
779 | } |
780 | elsif ($a == 0) |
781 | { |
782 | # speedup, if equal, set result to 0 |
0716bf9b |
783 | #print "equal sub, result = 0\n"; |
784 | $x->{value} = $CALC->_zero(); |
58cde26e |
785 | $x->{sign} = '+'; |
786 | } |
787 | else # a < 0 |
788 | { |
789 | #print "unswapped sub (a=$a)\n"; |
574bacfe |
790 | $x->{value} = $CALC->_sub($x->{value}, $y->{value}); # abs sub |
58cde26e |
791 | $x->{sign} = $sx; |
a0d0e21e |
792 | } |
a0d0e21e |
793 | } |
58cde26e |
794 | return $x->round(@bn); |
795 | } |
796 | |
797 | sub bsub |
798 | { |
799 | # (BINT or num_str, BINT or num_str) return num_str |
800 | # subtract second arg from first, modify first |
801 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
802 | |
58cde26e |
803 | return $x if $x->modify('bsub'); |
e745a66c |
804 | |
805 | if (!$y->is_zero()) # don't need to do anything if $y is 0 |
806 | { |
807 | $y->{sign} =~ tr/+\-/-+/; # does nothing for NaN |
808 | $x->badd($y,$a,$p,$r); # badd does not leave internal zeros |
809 | $y->{sign} =~ tr/+\-/-+/; # refix $y (does nothing for NaN) |
810 | } |
811 | $x; # already rounded by badd() |
58cde26e |
812 | } |
813 | |
814 | sub binc |
815 | { |
816 | # increment arg by one |
ee15d750 |
817 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e |
818 | return $x if $x->modify('binc'); |
e745a66c |
819 | |
820 | if ($x->{sign} eq '+') |
821 | { |
822 | $x->{value} = $CALC->_inc($x->{value}); |
823 | return $x->round($a,$p,$r); |
824 | } |
825 | elsif ($x->{sign} eq '-') |
826 | { |
827 | $x->{value} = $CALC->_dec($x->{value}); |
828 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # -1 +1 => -0 => +0 |
829 | return $x->round($a,$p,$r); |
830 | } |
831 | # inf, nan handling etc |
832 | $x->badd($self->__one(),$a,$p,$r); # does round |
58cde26e |
833 | } |
834 | |
835 | sub bdec |
836 | { |
837 | # decrement arg by one |
ee15d750 |
838 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e |
839 | return $x if $x->modify('bdec'); |
e745a66c |
840 | |
841 | my $zero = $CALC->_is_zero($x->{value}) && $x->{sign} eq '+'; |
842 | # <= 0 |
843 | if (($x->{sign} eq '-') || $zero) |
844 | { |
845 | $x->{value} = $CALC->_inc($x->{value}); |
846 | $x->{sign} = '-' if $zero; # 0 => 1 => -1 |
847 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # -1 +1 => -0 => +0 |
848 | return $x->round($a,$p,$r); |
849 | } |
850 | # > 0 |
851 | elsif ($x->{sign} eq '+') |
852 | { |
853 | $x->{value} = $CALC->_dec($x->{value}); |
854 | return $x->round($a,$p,$r); |
855 | } |
856 | # inf, nan handling etc |
857 | $x->badd($self->__one('-'),$a,$p,$r); # does round |
58cde26e |
858 | } |
859 | |
860 | sub blcm |
861 | { |
862 | # (BINT or num_str, BINT or num_str) return BINT |
863 | # does not modify arguments, but returns new object |
864 | # Lowest Common Multiplicator |
58cde26e |
865 | |
0716bf9b |
866 | my $y = shift; my ($x); |
867 | if (ref($y)) |
868 | { |
869 | $x = $y->copy(); |
870 | } |
871 | else |
872 | { |
873 | $x = $class->new($y); |
874 | } |
dccbb853 |
875 | while (@_) { $x = __lcm($x,shift); } |
58cde26e |
876 | $x; |
877 | } |
878 | |
879 | sub bgcd |
880 | { |
881 | # (BINT or num_str, BINT or num_str) return BINT |
882 | # does not modify arguments, but returns new object |
883 | # GCD -- Euclids algorithm, variant C (Knuth Vol 3, pg 341 ff) |
0716bf9b |
884 | |
dccbb853 |
885 | my $y = shift; |
886 | $y = __PACKAGE__->new($y) if !ref($y); |
887 | my $self = ref($y); |
888 | my $x = $y->copy(); # keep arguments |
0716bf9b |
889 | if ($CALC->can('_gcd')) |
890 | { |
891 | while (@_) |
892 | { |
dccbb853 |
893 | $y = shift; $y = $self->new($y) if !ref($y); |
0716bf9b |
894 | next if $y->is_zero(); |
895 | return $x->bnan() if $y->{sign} !~ /^[+-]$/; # y NaN? |
896 | $x->{value} = $CALC->_gcd($x->{value},$y->{value}); last if $x->is_one(); |
897 | } |
898 | } |
899 | else |
900 | { |
901 | while (@_) |
902 | { |
dccbb853 |
903 | $y = shift; $y = $self->new($y) if !ref($y); |
904 | $x = __gcd($x,$y->copy()); last if $x->is_one(); # _gcd handles NaN |
0716bf9b |
905 | } |
906 | } |
907 | $x->babs(); |
58cde26e |
908 | } |
909 | |
58cde26e |
910 | sub bnot |
911 | { |
912 | # (num_str or BINT) return BINT |
913 | # represent ~x as twos-complement number |
ee15d750 |
914 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
915 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (undef,@_) : objectify(1,@_); |
916 | |
58cde26e |
917 | return $x if $x->modify('bnot'); |
ee15d750 |
918 | $x->bneg(); $x->bdec(); # was: bsub(-1,$x);, time it someday |
919 | return $x->round($a,$p,$r); |
58cde26e |
920 | } |
921 | |
922 | sub is_zero |
923 | { |
924 | # return true if arg (BINT or num_str) is zero (array '+', '0') |
ee15d750 |
925 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
926 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
0716bf9b |
927 | |
574bacfe |
928 | return 0 if $x->{sign} !~ /^\+$/; # -, NaN & +-inf aren't |
17baacb7 |
929 | $CALC->_is_zero($x->{value}); |
58cde26e |
930 | } |
931 | |
932 | sub is_nan |
933 | { |
934 | # return true if arg (BINT or num_str) is NaN |
ee15d750 |
935 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
936 | |
937 | return 1 if $x->{sign} eq $nan; |
938 | return 0; |
58cde26e |
939 | } |
940 | |
941 | sub is_inf |
942 | { |
943 | # return true if arg (BINT or num_str) is +-inf |
ee15d750 |
944 | my ($self,$x,$sign) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
945 | |
946 | $sign = '' if !defined $sign; |
947 | return 0 if $sign !~ /^([+-]|)$/; |
58cde26e |
948 | |
ee15d750 |
949 | if ($sign eq '') |
950 | { |
951 | return 1 if ($x->{sign} =~ /^[+-]inf$/); |
952 | return 0; |
953 | } |
954 | $sign = quotemeta($sign.'inf'); |
955 | return 1 if ($x->{sign} =~ /^$sign$/); |
956 | return 0; |
58cde26e |
957 | } |
958 | |
959 | sub is_one |
960 | { |
b22b3e31 |
961 | # return true if arg (BINT or num_str) is +1 |
962 | # or -1 if sign is given |
ee15d750 |
963 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
964 | my ($self,$x,$sign) = ref($_[0]) ? (undef,@_) : objectify(1,@_); |
965 | |
966 | $sign = '' if !defined $sign; $sign = '+' if $sign ne '-'; |
0716bf9b |
967 | |
ee15d750 |
968 | return 0 if $x->{sign} ne $sign; # -1 != +1, NaN, +-inf aren't either |
394e6ffb |
969 | $CALC->_is_one($x->{value}); |
58cde26e |
970 | } |
971 | |
972 | sub is_odd |
973 | { |
974 | # return true when arg (BINT or num_str) is odd, false for even |
ee15d750 |
975 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
976 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
0716bf9b |
977 | |
b22b3e31 |
978 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
394e6ffb |
979 | $CALC->_is_odd($x->{value}); |
58cde26e |
980 | } |
981 | |
982 | sub is_even |
983 | { |
984 | # return true when arg (BINT or num_str) is even, false for odd |
ee15d750 |
985 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
986 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
0716bf9b |
987 | |
b22b3e31 |
988 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
394e6ffb |
989 | $CALC->_is_even($x->{value}); |
0716bf9b |
990 | } |
991 | |
992 | sub is_positive |
993 | { |
994 | # return true when arg (BINT or num_str) is positive (>= 0) |
ee15d750 |
995 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
996 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
997 | |
998 | return 1 if $x->{sign} =~ /^\+/; |
394e6ffb |
999 | 0; |
0716bf9b |
1000 | } |
1001 | |
1002 | sub is_negative |
1003 | { |
1004 | # return true when arg (BINT or num_str) is negative (< 0) |
ee15d750 |
1005 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
1006 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
1007 | |
1008 | return 1 if ($x->{sign} =~ /^-/); |
394e6ffb |
1009 | 0; |
58cde26e |
1010 | } |
1011 | |
0716bf9b |
1012 | ############################################################################### |
1013 | |
58cde26e |
1014 | sub bmul |
1015 | { |
1016 | # multiply two numbers -- stolen from Knuth Vol 2 pg 233 |
1017 | # (BINT or num_str, BINT or num_str) return BINT |
1018 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
0716bf9b |
1019 | |
58cde26e |
1020 | return $x if $x->modify('bmul'); |
574bacfe |
1021 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
1022 | # handle result = 0 |
1023 | return $x if $x->is_zero(); |
1024 | return $x->bzero() if $y->is_zero(); |
1025 | # inf handling |
1026 | if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) |
1027 | { |
1028 | # result will always be +-inf: |
1029 | # +inf * +/+inf => +inf, -inf * -/-inf => +inf |
1030 | # +inf * -/-inf => -inf, -inf * +/+inf => -inf |
1031 | return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); |
1032 | return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); |
1033 | return $x->binf('-'); |
1034 | } |
58cde26e |
1035 | |
0716bf9b |
1036 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; # +1 * +1 or -1 * -1 => + |
dccbb853 |
1037 | |
574bacfe |
1038 | $x->{value} = $CALC->_mul($x->{value},$y->{value}); # do actual math |
58cde26e |
1039 | return $x->round($a,$p,$r,$y); |
dccbb853 |
1040 | } |
1041 | |
1042 | sub _div_inf |
1043 | { |
1044 | # helper function that handles +-inf cases for bdiv()/bmod() to reuse code |
1045 | my ($self,$x,$y) = @_; |
1046 | |
1047 | # NaN if x == NaN or y == NaN or x==y==0 |
1048 | return wantarray ? ($x->bnan(),$self->bnan()) : $x->bnan() |
1049 | if (($x->is_nan() || $y->is_nan()) || |
1050 | ($x->is_zero() && $y->is_zero())); |
1051 | |
1052 | # +inf / +inf == -inf / -inf == 1, remainder is 0 (A / A = 1, remainder 0) |
1053 | if (($x->{sign} eq $y->{sign}) && |
1054 | ($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) |
1055 | { |
1056 | return wantarray ? ($x->bone(),$self->bzero()) : $x->bone(); |
1057 | } |
1058 | # +inf / -inf == -inf / +inf == -1, remainder 0 |
1059 | if (($x->{sign} ne $y->{sign}) && |
1060 | ($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) |
1061 | { |
1062 | return wantarray ? ($x->bone('-'),$self->bzero()) : $x->bone('-'); |
1063 | } |
1064 | # x / +-inf => 0, remainder x (works even if x == 0) |
1065 | if ($y->{sign} =~ /^[+-]inf$/) |
1066 | { |
1067 | my $t = $x->copy(); # binf clobbers up $x |
1068 | return wantarray ? ($x->bzero(),$t) : $x->bzero() |
1069 | } |
1070 | |
1071 | # 5 / 0 => +inf, -6 / 0 => -inf |
1072 | # +inf / 0 = inf, inf, and -inf / 0 => -inf, -inf |
1073 | # exception: -8 / 0 has remainder -8, not 8 |
1074 | # exception: -inf / 0 has remainder -inf, not inf |
1075 | if ($y->is_zero()) |
1076 | { |
1077 | # +-inf / 0 => special case for -inf |
1078 | return wantarray ? ($x,$x->copy()) : $x if $x->is_inf(); |
1079 | if (!$x->is_zero() && !$x->is_inf()) |
1080 | { |
1081 | my $t = $x->copy(); # binf clobbers up $x |
1082 | return wantarray ? |
1083 | ($x->binf($x->{sign}),$t) : $x->binf($x->{sign}) |
1084 | } |
1085 | } |
1086 | |
1087 | # last case: +-inf / ordinary number |
1088 | my $sign = '+inf'; |
1089 | $sign = '-inf' if substr($x->{sign},0,1) ne $y->{sign}; |
1090 | $x->{sign} = $sign; |
1091 | return wantarray ? ($x,$self->bzero()) : $x; |
58cde26e |
1092 | } |
1093 | |
1094 | sub bdiv |
1095 | { |
1096 | # (dividend: BINT or num_str, divisor: BINT or num_str) return |
1097 | # (BINT,BINT) (quo,rem) or BINT (only rem) |
58cde26e |
1098 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
1099 | |
1100 | return $x if $x->modify('bdiv'); |
1101 | |
dccbb853 |
1102 | return $self->_div_inf($x,$y) |
1103 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()); |
58cde26e |
1104 | |
1105 | # 0 / something |
1106 | return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero(); |
1107 | |
1108 | # Is $x in the interval [0, $y) ? |
0716bf9b |
1109 | my $cmp = $CALC->_acmp($x->{value},$y->{value}); |
58cde26e |
1110 | if (($cmp < 0) and ($x->{sign} eq $y->{sign})) |
1111 | { |
1112 | return $x->bzero() unless wantarray; |
1113 | my $t = $x->copy(); # make copy first, because $x->bzero() clobbers $x |
1114 | return ($x->bzero(),$t); |
1115 | } |
1116 | elsif ($cmp == 0) |
1117 | { |
1118 | # shortcut, both are the same, so set to +/- 1 |
574bacfe |
1119 | $x->__one( ($x->{sign} ne $y->{sign} ? '-' : '+') ); |
58cde26e |
1120 | return $x unless wantarray; |
1121 | return ($x,$self->bzero()); |
1122 | } |
1123 | |
1124 | # calc new sign and in case $y == +/- 1, return $x |
dccbb853 |
1125 | my $xsign = $x->{sign}; # keep |
58cde26e |
1126 | $x->{sign} = ($x->{sign} ne $y->{sign} ? '-' : '+'); |
1127 | # check for / +-1 (cant use $y->is_one due to '-' |
394e6ffb |
1128 | if ($CALC->_is_one($y->{value})) |
58cde26e |
1129 | { |
1130 | return wantarray ? ($x,$self->bzero()) : $x; |
1131 | } |
1132 | |
394e6ffb |
1133 | my $rem; |
58cde26e |
1134 | if (wantarray) |
1135 | { |
394e6ffb |
1136 | my $rem = $self->bzero(); |
1137 | ($x->{value},$rem->{value}) = $CALC->_div($x->{value},$y->{value}); |
1138 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); |
1139 | $x->round($a,$p,$r,$y); |
dccbb853 |
1140 | if (! $CALC->_is_zero($rem->{value})) |
1141 | { |
1142 | $rem->{sign} = $y->{sign}; |
1143 | $rem = $y-$rem if $xsign ne $y->{sign}; # one of them '-' |
1144 | } |
1145 | else |
1146 | { |
1147 | $rem->{sign} = '+'; # dont leave -0 |
1148 | } |
1149 | $rem->round($a,$p,$r,$x,$y); |
58cde26e |
1150 | return ($x,$rem); |
1151 | } |
394e6ffb |
1152 | |
1153 | $x->{value} = $CALC->_div($x->{value},$y->{value}); |
1154 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); |
1155 | $x->round($a,$p,$r,$y); |
58cde26e |
1156 | } |
1157 | |
dccbb853 |
1158 | sub bmod |
1159 | { |
1160 | # modulus (or remainder) |
1161 | # (BINT or num_str, BINT or num_str) return BINT |
1162 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
1163 | |
1164 | return $x if $x->modify('bmod'); |
1165 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()) |
1166 | { |
1167 | my ($d,$r) = $self->_div_inf($x,$y); |
1168 | return $r; |
1169 | } |
1170 | |
1171 | if ($CALC->can('_mod')) |
1172 | { |
1173 | # calc new sign and in case $y == +/- 1, return $x |
1174 | $x->{value} = $CALC->_mod($x->{value},$y->{value}); |
1175 | my $xsign = $x->{sign}; |
1176 | if (!$CALC->_is_zero($x->{value})) |
1177 | { |
1178 | $x->{sign} = $y->{sign}; |
1179 | $x = $y-$x if $xsign ne $y->{sign}; # one of them '-' |
1180 | } |
1181 | else |
1182 | { |
1183 | $x->{sign} = '+'; # dont leave -0 |
1184 | } |
1185 | } |
1186 | else |
1187 | { |
027dc388 |
1188 | $x = (&bdiv($self,$x,$y))[1]; # slow way |
dccbb853 |
1189 | } |
394e6ffb |
1190 | $x->round($a,$p,$r); |
dccbb853 |
1191 | } |
1192 | |
58cde26e |
1193 | sub bpow |
1194 | { |
1195 | # (BINT or num_str, BINT or num_str) return BINT |
1196 | # compute power of two numbers -- stolen from Knuth Vol 2 pg 233 |
1197 | # modifies first argument |
58cde26e |
1198 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
1199 | |
1200 | return $x if $x->modify('bpow'); |
1201 | |
0716bf9b |
1202 | return $x if $x->{sign} =~ /^[+-]inf$/; # -inf/+inf ** x |
58cde26e |
1203 | return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan; |
574bacfe |
1204 | return $x->__one() if $y->is_zero(); |
58cde26e |
1205 | return $x if $x->is_one() || $y->is_one(); |
0716bf9b |
1206 | if ($x->{sign} eq '-' && $CALC->_is_one($x->{value})) |
58cde26e |
1207 | { |
1208 | # if $x == -1 and odd/even y => +1/-1 |
0716bf9b |
1209 | return $y->is_odd() ? $x : $x->babs(); |
574bacfe |
1210 | # my Casio FX-5500L has a bug here: -1 ** 2 is -1, but -1 * -1 is 1; |
58cde26e |
1211 | } |
574bacfe |
1212 | # 1 ** -y => 1 / (1 ** |y|) |
1213 | # so do test for negative $y after above's clause |
58cde26e |
1214 | return $x->bnan() if $y->{sign} eq '-'; |
1215 | return $x if $x->is_zero(); # 0**y => 0 (if not y <= 0) |
1216 | |
0716bf9b |
1217 | if ($CALC->can('_pow')) |
58cde26e |
1218 | { |
574bacfe |
1219 | $x->{value} = $CALC->_pow($x->{value},$y->{value}); |
0716bf9b |
1220 | return $x->round($a,$p,$r); |
58cde26e |
1221 | } |
027dc388 |
1222 | |
1223 | # based on the assumption that shifting in base 10 is fast, and that mul |
1224 | # works faster if numbers are small: we count trailing zeros (this step is |
1225 | # O(1)..O(N), but in case of O(N) we save much more time due to this), |
1226 | # stripping them out of the multiplication, and add $count * $y zeros |
1227 | # afterwards like this: |
1228 | # 300 ** 3 == 300*300*300 == 3*3*3 . '0' x 2 * 3 == 27 . '0' x 6 |
1229 | # creates deep recursion? |
574bacfe |
1230 | # my $zeros = $x->_trailing_zeros(); |
1231 | # if ($zeros > 0) |
1232 | # { |
1233 | # $x->brsft($zeros,10); # remove zeros |
1234 | # $x->bpow($y); # recursion (will not branch into here again) |
1235 | # $zeros = $y * $zeros; # real number of zeros to add |
1236 | # $x->blsft($zeros,10); |
1237 | # return $x->round($a,$p,$r); |
1238 | # } |
1239 | |
1240 | my $pow2 = $self->__one(); |
58cde26e |
1241 | my $y1 = $class->new($y); |
dccbb853 |
1242 | my $two = $self->new(2); |
58cde26e |
1243 | while (!$y1->is_one()) |
1244 | { |
dccbb853 |
1245 | $pow2->bmul($x) if $y1->is_odd(); |
1246 | $y1->bdiv($two); |
027dc388 |
1247 | $x->bmul($x); |
58cde26e |
1248 | } |
dccbb853 |
1249 | $x->bmul($pow2) unless $pow2->is_one(); |
58cde26e |
1250 | return $x->round($a,$p,$r); |
1251 | } |
1252 | |
1253 | sub blsft |
1254 | { |
1255 | # (BINT or num_str, BINT or num_str) return BINT |
1256 | # compute x << y, base n, y >= 0 |
1257 | my ($self,$x,$y,$n) = objectify(2,@_); |
1258 | |
1259 | return $x if $x->modify('blsft'); |
1260 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
1261 | |
574bacfe |
1262 | $n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-'; |
1263 | |
027dc388 |
1264 | my $t; $t = $CALC->_lsft($x->{value},$y->{value},$n) if $CALC->can('_lsft'); |
574bacfe |
1265 | if (defined $t) |
1266 | { |
1267 | $x->{value} = $t; return $x; |
1268 | } |
1269 | # fallback |
1270 | return $x->bmul( $self->bpow($n, $y) ); |
58cde26e |
1271 | } |
1272 | |
1273 | sub brsft |
1274 | { |
1275 | # (BINT or num_str, BINT or num_str) return BINT |
1276 | # compute x >> y, base n, y >= 0 |
1277 | my ($self,$x,$y,$n) = objectify(2,@_); |
1278 | |
1279 | return $x if $x->modify('brsft'); |
1280 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
1281 | |
1282 | $n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-'; |
574bacfe |
1283 | |
027dc388 |
1284 | my $t; $t = $CALC->_rsft($x->{value},$y->{value},$n) if $CALC->can('_rsft'); |
574bacfe |
1285 | if (defined $t) |
1286 | { |
1287 | $x->{value} = $t; return $x; |
1288 | } |
1289 | # fallback |
1290 | return scalar bdiv($x, $self->bpow($n, $y)); |
58cde26e |
1291 | } |
1292 | |
1293 | sub band |
1294 | { |
1295 | #(BINT or num_str, BINT or num_str) return BINT |
1296 | # compute x & y |
0716bf9b |
1297 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
58cde26e |
1298 | |
1299 | return $x if $x->modify('band'); |
1300 | |
1301 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
394e6ffb |
1302 | return $x->bzero() if $y->is_zero() || $x->is_zero(); |
0716bf9b |
1303 | |
574bacfe |
1304 | my $sign = 0; # sign of result |
1305 | $sign = 1 if ($x->{sign} eq '-') && ($y->{sign} eq '-'); |
1306 | my $sx = 1; $sx = -1 if $x->{sign} eq '-'; |
1307 | my $sy = 1; $sy = -1 if $y->{sign} eq '-'; |
1308 | |
1309 | if ($CALC->can('_and') && $sx == 1 && $sy == 1) |
0716bf9b |
1310 | { |
574bacfe |
1311 | $x->{value} = $CALC->_and($x->{value},$y->{value}); |
0716bf9b |
1312 | return $x->round($a,$p,$r); |
1313 | } |
574bacfe |
1314 | |
394e6ffb |
1315 | my $m = Math::BigInt->bone(); my ($xr,$yr); |
574bacfe |
1316 | my $x10000 = new Math::BigInt (0x1000); |
1317 | my $y1 = copy(ref($x),$y); # make copy |
1318 | $y1->babs(); # and positive |
1319 | my $x1 = $x->copy()->babs(); $x->bzero(); # modify x in place! |
1320 | use integer; # need this for negative bools |
0716bf9b |
1321 | while (!$x1->is_zero() && !$y1->is_zero()) |
58cde26e |
1322 | { |
0716bf9b |
1323 | ($x1, $xr) = bdiv($x1, $x10000); |
58cde26e |
1324 | ($y1, $yr) = bdiv($y1, $x10000); |
574bacfe |
1325 | # make both op's numbers! |
1326 | $x->badd( bmul( $class->new( |
1327 | abs($sx*int($xr->numify()) & $sy*int($yr->numify()))), |
1328 | $m)); |
58cde26e |
1329 | $m->bmul($x10000); |
1330 | } |
574bacfe |
1331 | $x->bneg() if $sign; |
0716bf9b |
1332 | return $x->round($a,$p,$r); |
58cde26e |
1333 | } |
1334 | |
1335 | sub bior |
1336 | { |
1337 | #(BINT or num_str, BINT or num_str) return BINT |
1338 | # compute x | y |
0716bf9b |
1339 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
58cde26e |
1340 | |
1341 | return $x if $x->modify('bior'); |
1342 | |
1343 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
1344 | return $x if $y->is_zero(); |
574bacfe |
1345 | |
1346 | my $sign = 0; # sign of result |
1347 | $sign = 1 if ($x->{sign} eq '-') || ($y->{sign} eq '-'); |
1348 | my $sx = 1; $sx = -1 if $x->{sign} eq '-'; |
1349 | my $sy = 1; $sy = -1 if $y->{sign} eq '-'; |
1350 | |
1351 | # don't use lib for negative values |
1352 | if ($CALC->can('_or') && $sx == 1 && $sy == 1) |
0716bf9b |
1353 | { |
574bacfe |
1354 | $x->{value} = $CALC->_or($x->{value},$y->{value}); |
0716bf9b |
1355 | return $x->round($a,$p,$r); |
1356 | } |
1357 | |
394e6ffb |
1358 | my $m = Math::BigInt->bone(); my ($xr,$yr); |
1359 | my $x10000 = Math::BigInt->new(0x10000); |
574bacfe |
1360 | my $y1 = copy(ref($x),$y); # make copy |
1361 | $y1->babs(); # and positive |
1362 | my $x1 = $x->copy()->babs(); $x->bzero(); # modify x in place! |
1363 | use integer; # need this for negative bools |
0716bf9b |
1364 | while (!$x1->is_zero() || !$y1->is_zero()) |
58cde26e |
1365 | { |
0716bf9b |
1366 | ($x1, $xr) = bdiv($x1,$x10000); |
58cde26e |
1367 | ($y1, $yr) = bdiv($y1,$x10000); |
574bacfe |
1368 | # make both op's numbers! |
1369 | $x->badd( bmul( $class->new( |
1370 | abs($sx*int($xr->numify()) | $sy*int($yr->numify()))), |
1371 | $m)); |
58cde26e |
1372 | $m->bmul($x10000); |
1373 | } |
574bacfe |
1374 | $x->bneg() if $sign; |
0716bf9b |
1375 | return $x->round($a,$p,$r); |
58cde26e |
1376 | } |
1377 | |
1378 | sub bxor |
1379 | { |
1380 | #(BINT or num_str, BINT or num_str) return BINT |
1381 | # compute x ^ y |
0716bf9b |
1382 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
58cde26e |
1383 | |
1384 | return $x if $x->modify('bxor'); |
1385 | |
0716bf9b |
1386 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
58cde26e |
1387 | return $x if $y->is_zero(); |
0716bf9b |
1388 | |
574bacfe |
1389 | my $sign = 0; # sign of result |
1390 | $sign = 1 if $x->{sign} ne $y->{sign}; |
1391 | my $sx = 1; $sx = -1 if $x->{sign} eq '-'; |
1392 | my $sy = 1; $sy = -1 if $y->{sign} eq '-'; |
1393 | |
1394 | # don't use lib for negative values |
1395 | if ($CALC->can('_xor') && $sx == 1 && $sy == 1) |
0716bf9b |
1396 | { |
574bacfe |
1397 | $x->{value} = $CALC->_xor($x->{value},$y->{value}); |
0716bf9b |
1398 | return $x->round($a,$p,$r); |
1399 | } |
1400 | |
394e6ffb |
1401 | my $m = $self->bone(); my ($xr,$yr); |
1402 | my $x10000 = Math::BigInt->new(0x10000); |
58cde26e |
1403 | my $y1 = copy(ref($x),$y); # make copy |
574bacfe |
1404 | $y1->babs(); # and positive |
1405 | my $x1 = $x->copy()->babs(); $x->bzero(); # modify x in place! |
1406 | use integer; # need this for negative bools |
0716bf9b |
1407 | while (!$x1->is_zero() || !$y1->is_zero()) |
58cde26e |
1408 | { |
0716bf9b |
1409 | ($x1, $xr) = bdiv($x1, $x10000); |
58cde26e |
1410 | ($y1, $yr) = bdiv($y1, $x10000); |
574bacfe |
1411 | # make both op's numbers! |
1412 | $x->badd( bmul( $class->new( |
1413 | abs($sx*int($xr->numify()) ^ $sy*int($yr->numify()))), |
1414 | $m)); |
58cde26e |
1415 | $m->bmul($x10000); |
1416 | } |
574bacfe |
1417 | $x->bneg() if $sign; |
0716bf9b |
1418 | return $x->round($a,$p,$r); |
58cde26e |
1419 | } |
1420 | |
1421 | sub length |
1422 | { |
ee15d750 |
1423 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
1424 | |
0716bf9b |
1425 | my $e = $CALC->_len($x->{value}); |
0716bf9b |
1426 | return wantarray ? ($e,0) : $e; |
58cde26e |
1427 | } |
1428 | |
1429 | sub digit |
1430 | { |
0716bf9b |
1431 | # return the nth decimal digit, negative values count backward, 0 is right |
58cde26e |
1432 | my $x = shift; |
1433 | my $n = shift || 0; |
1434 | |
0716bf9b |
1435 | return $CALC->_digit($x->{value},$n); |
58cde26e |
1436 | } |
1437 | |
1438 | sub _trailing_zeros |
1439 | { |
1440 | # return the amount of trailing zeros in $x |
1441 | my $x = shift; |
1442 | $x = $class->new($x) unless ref $x; |
1443 | |
dccbb853 |
1444 | return 0 if $x->is_zero() || $x->is_odd() || $x->{sign} !~ /^[+-]$/; |
0716bf9b |
1445 | |
1446 | return $CALC->_zeros($x->{value}) if $CALC->can('_zeros'); |
1447 | |
b22b3e31 |
1448 | # if not: since we do not know underlying internal representation: |
0716bf9b |
1449 | my $es = "$x"; $es =~ /([0]*)$/; |
1450 | |
1451 | return 0 if !defined $1; # no zeros |
1452 | return CORE::length("$1"); # as string, not as +0! |
58cde26e |
1453 | } |
1454 | |
1455 | sub bsqrt |
1456 | { |
394e6ffb |
1457 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
1458 | |
394e6ffb |
1459 | return $x->bnan() if $x->{sign} ne '+'; # -x or inf or NaN => NaN |
1460 | return $x->bzero($a,$p) if $x->is_zero(); # 0 => 0 |
1461 | return $x->round($a,$p,$r) if $x->is_one(); # 1 => 1 |
1462 | return $x->bone($a,$p) if $x < 4; # 2,3 => 1 |
58cde26e |
1463 | |
394e6ffb |
1464 | if ($CALC->can('_sqrt')) |
1465 | { |
1466 | $x->{value} = $CALC->_sqrt($x->{value}); |
1467 | return $x->round($a,$p,$r); |
1468 | } |
1469 | |
1470 | my $y = $x->copy(); |
58cde26e |
1471 | my $l = int($x->length()/2); |
1472 | |
394e6ffb |
1473 | $x->bone(); # keep ref($x), but modify it |
1474 | $x->blsft($l,10); |
58cde26e |
1475 | |
1476 | my $last = $self->bzero(); |
394e6ffb |
1477 | my $two = $self->new(2); |
1478 | my $lastlast = $x+$two; |
1479 | while ($last != $x && $lastlast != $x) |
58cde26e |
1480 | { |
394e6ffb |
1481 | $lastlast = $last; $last = $x; |
58cde26e |
1482 | $x += $y / $x; |
394e6ffb |
1483 | $x /= $two; |
58cde26e |
1484 | } |
394e6ffb |
1485 | $x-- if $x * $x > $y; # overshot? |
1486 | return $x->round($a,$p,$r); |
58cde26e |
1487 | } |
1488 | |
1489 | sub exponent |
1490 | { |
1491 | # return a copy of the exponent (here always 0, NaN or 1 for $m == 0) |
ee15d750 |
1492 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
1493 | |
ee15d750 |
1494 | if ($x->{sign} !~ /^[+-]$/) |
1495 | { |
1496 | my $s = $x->{sign}; $s =~ s/^[+-]//; |
1497 | return $self->new($s); # -inf,+inf => inf |
1498 | } |
58cde26e |
1499 | my $e = $class->bzero(); |
1500 | return $e->binc() if $x->is_zero(); |
1501 | $e += $x->_trailing_zeros(); |
1502 | return $e; |
1503 | } |
1504 | |
1505 | sub mantissa |
1506 | { |
ee15d750 |
1507 | # return the mantissa (compatible to Math::BigFloat, e.g. reduced) |
1508 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
1509 | |
ee15d750 |
1510 | if ($x->{sign} !~ /^[+-]$/) |
1511 | { |
1512 | my $s = $x->{sign}; $s =~ s/^[+]//; |
1513 | return $self->new($s); # +inf => inf |
1514 | } |
58cde26e |
1515 | my $m = $x->copy(); |
1516 | # that's inefficient |
1517 | my $zeros = $m->_trailing_zeros(); |
1518 | $m /= 10 ** $zeros if $zeros != 0; |
1519 | return $m; |
1520 | } |
1521 | |
1522 | sub parts |
1523 | { |
ee15d750 |
1524 | # return a copy of both the exponent and the mantissa |
1525 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
1526 | |
ee15d750 |
1527 | return ($x->mantissa(),$x->exponent()); |
58cde26e |
1528 | } |
1529 | |
1530 | ############################################################################## |
1531 | # rounding functions |
1532 | |
1533 | sub bfround |
1534 | { |
1535 | # precision: round to the $Nth digit left (+$n) or right (-$n) from the '.' |
ee15d750 |
1536 | # $n == 0 || $n == 1 => round to integer |
58cde26e |
1537 | my $x = shift; $x = $class->new($x) unless ref $x; |
dccbb853 |
1538 | my ($scale,$mode) = $x->_scale_p($x->precision(),$x->round_mode(),@_); |
58cde26e |
1539 | return $x if !defined $scale; # no-op |
1540 | |
1541 | # no-op for BigInts if $n <= 0 |
ee15d750 |
1542 | if ($scale <= 0) |
1543 | { |
1544 | $x->{_p} = $scale; return $x; |
1545 | } |
58cde26e |
1546 | |
1547 | $x->bround( $x->length()-$scale, $mode); |
ee15d750 |
1548 | $x->{_a} = undef; # bround sets {_a} |
1549 | $x->{_p} = $scale; # so correct it |
1550 | $x; |
58cde26e |
1551 | } |
1552 | |
1553 | sub _scan_for_nonzero |
1554 | { |
1555 | my $x = shift; |
1556 | my $pad = shift; |
0716bf9b |
1557 | my $xs = shift; |
58cde26e |
1558 | |
1559 | my $len = $x->length(); |
1560 | return 0 if $len == 1; # '5' is trailed by invisible zeros |
1561 | my $follow = $pad - 1; |
1562 | return 0 if $follow > $len || $follow < 1; |
1563 | #print "checking $x $r\n"; |
0716bf9b |
1564 | |
b22b3e31 |
1565 | # since we do not know underlying represention of $x, use decimal string |
0716bf9b |
1566 | #my $r = substr ($$xs,-$follow); |
58cde26e |
1567 | my $r = substr ("$x",-$follow); |
1568 | return 1 if $r =~ /[^0]/; return 0; |
58cde26e |
1569 | } |
1570 | |
1571 | sub fround |
1572 | { |
1573 | # to make life easier for switch between MBF and MBI (autoload fxxx() |
1574 | # like MBF does for bxxx()?) |
1575 | my $x = shift; |
1576 | return $x->bround(@_); |
1577 | } |
1578 | |
1579 | sub bround |
1580 | { |
1581 | # accuracy: +$n preserve $n digits from left, |
1582 | # -$n preserve $n digits from right (f.i. for 0.1234 style in MBF) |
1583 | # no-op for $n == 0 |
1584 | # and overwrite the rest with 0's, return normalized number |
1585 | # do not return $x->bnorm(), but $x |
1586 | my $x = shift; $x = $class->new($x) unless ref $x; |
dccbb853 |
1587 | my ($scale,$mode) = $x->_scale_a($x->accuracy(),$x->round_mode(),@_); |
58cde26e |
1588 | return $x if !defined $scale; # no-op |
1589 | |
1590 | # print "MBI round: $x to $scale $mode\n"; |
574bacfe |
1591 | return $x if $x->{sign} !~ /^[+-]$/ || $x->is_zero() || $scale == 0; |
58cde26e |
1592 | |
1593 | # we have fewer digits than we want to scale to |
1594 | my $len = $x->length(); |
ee15d750 |
1595 | # print "$scale $len\n"; |
1596 | # scale < 0, but > -len (not >=!) |
1597 | if (($scale < 0 && $scale < -$len-1) || ($scale >= $len)) |
1598 | { |
1599 | $x->{_a} = $scale if !defined $x->{_a}; # if not yet defined overwrite |
1600 | return $x; |
1601 | } |
58cde26e |
1602 | |
1603 | # count of 0's to pad, from left (+) or right (-): 9 - +6 => 3, or |-6| => 6 |
1604 | my ($pad,$digit_round,$digit_after); |
1605 | $pad = $len - $scale; |
ee15d750 |
1606 | $pad = abs($scale-1) if $scale < 0; |
1607 | |
0716bf9b |
1608 | # do not use digit(), it is costly for binary => decimal |
1609 | #$digit_round = '0'; $digit_round = $x->digit($pad) if $pad < $len; |
1610 | #$digit_after = '0'; $digit_after = $x->digit($pad-1) if $pad > 0; |
ee15d750 |
1611 | |
0716bf9b |
1612 | my $xs = $CALC->_str($x->{value}); |
1613 | my $pl = -$pad-1; |
ee15d750 |
1614 | |
1615 | # print "pad $pad pl $pl scale $scale len $len\n"; |
0716bf9b |
1616 | # pad: 123: 0 => -1, at 1 => -2, at 2 => -3, at 3 => -4 |
1617 | # pad+1: 123: 0 => 0, at 1 => -1, at 2 => -2, at 3 => -3 |
1618 | $digit_round = '0'; $digit_round = substr($$xs,$pl,1) if $pad <= $len; |
1619 | $pl++; $pl ++ if $pad >= $len; |
1620 | $digit_after = '0'; $digit_after = substr($$xs,$pl,1) |
1621 | if $pad > 0; |
ee15d750 |
1622 | |
1623 | # print "$pad $pl $$xs dr $digit_round da $digit_after\n"; |
58cde26e |
1624 | |
1625 | # in case of 01234 we round down, for 6789 up, and only in case 5 we look |
1626 | # closer at the remaining digits of the original $x, remember decision |
1627 | my $round_up = 1; # default round up |
1628 | $round_up -- if |
1629 | ($mode eq 'trunc') || # trunc by round down |
1630 | ($digit_after =~ /[01234]/) || # round down anyway, |
1631 | # 6789 => round up |
1632 | ($digit_after eq '5') && # not 5000...0000 |
0716bf9b |
1633 | ($x->_scan_for_nonzero($pad,$xs) == 0) && |
58cde26e |
1634 | ( |
1635 | ($mode eq 'even') && ($digit_round =~ /[24680]/) || |
1636 | ($mode eq 'odd') && ($digit_round =~ /[13579]/) || |
1637 | ($mode eq '+inf') && ($x->{sign} eq '-') || |
1638 | ($mode eq '-inf') && ($x->{sign} eq '+') || |
1639 | ($mode eq 'zero') # round down if zero, sign adjusted below |
1640 | ); |
1641 | # allow rounding one place left of mantissa |
1642 | #print "$pad $len $scale\n"; |
1643 | # this is triggering warnings, and buggy for $scale < 0 |
1644 | #if (-$scale != $len) |
1645 | { |
b22b3e31 |
1646 | # old code, depend on internal representation |
0716bf9b |
1647 | # split mantissa at $pad and then pad with zeros |
1648 | #my $s5 = int($pad / 5); |
1649 | #my $i = 0; |
1650 | #while ($i < $s5) |
1651 | # { |
1652 | # $x->{value}->[$i++] = 0; # replace with 5 x 0 |
1653 | # } |
1654 | #$x->{value}->[$s5] = '00000'.$x->{value}->[$s5]; # pad with 0 |
1655 | #my $rem = $pad % 5; # so much left over |
1656 | #if ($rem > 0) |
1657 | # { |
1658 | # #print "remainder $rem\n"; |
1659 | ## #print "elem $x->{value}->[$s5]\n"; |
1660 | # substr($x->{value}->[$s5],-$rem,$rem) = '0' x $rem; # stamp w/ '0' |
1661 | # } |
1662 | #$x->{value}->[$s5] = int ($x->{value}->[$s5]); # str '05' => int '5' |
1663 | #print ${$CALC->_str($pad->{value})}," $len\n"; |
1664 | if (($pad > 0) && ($pad <= $len)) |
58cde26e |
1665 | { |
0716bf9b |
1666 | substr($$xs,-$pad,$pad) = '0' x $pad; |
1667 | $x->{value} = $CALC->_new($xs); # put back in |
58cde26e |
1668 | } |
0716bf9b |
1669 | elsif ($pad > $len) |
58cde26e |
1670 | { |
574bacfe |
1671 | $x->bzero(); # round to '0' |
58cde26e |
1672 | } |
ee15d750 |
1673 | # print "res $pad $len $x $$xs\n"; |
58cde26e |
1674 | } |
0716bf9b |
1675 | # move this later on after the inc of the string |
1676 | #$x->{value} = $CALC->_new($xs); # put back in |
58cde26e |
1677 | if ($round_up) # what gave test above? |
1678 | { |
ee15d750 |
1679 | #print " $pad => "; |
58cde26e |
1680 | $pad = $len if $scale < 0; # tlr: whack 0.51=>1.0 |
1681 | # modify $x in place, undef, undef to avoid rounding |
58cde26e |
1682 | # str creation much faster than 10 ** something |
ee15d750 |
1683 | #print " $pad, $x => "; |
0716bf9b |
1684 | $x->badd( Math::BigInt->new($x->{sign}.'1'.'0'x$pad) ); |
ee15d750 |
1685 | #print "$x\n"; |
0716bf9b |
1686 | # increment string in place, to avoid dec=>hex for the '1000...000' |
1687 | # $xs ...blah foo |
58cde26e |
1688 | } |
0716bf9b |
1689 | # to here: |
1690 | #$x->{value} = $CALC->_new($xs); # put back in |
ee15d750 |
1691 | |
1692 | $x->{_a} = $scale if $scale >= 0; |
1693 | if ($scale < 0) |
1694 | { |
1695 | $x->{_a} = $len+$scale; |
1696 | $x->{_a} = 0 if $scale < -$len; |
1697 | } |
58cde26e |
1698 | $x; |
1699 | } |
1700 | |
1701 | sub bfloor |
1702 | { |
1703 | # return integer less or equal then number, since it is already integer, |
1704 | # always returns $self |
ee15d750 |
1705 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e |
1706 | |
1707 | # not needed: return $x if $x->modify('bfloor'); |
58cde26e |
1708 | return $x->round($a,$p,$r); |
1709 | } |
1710 | |
1711 | sub bceil |
1712 | { |
1713 | # return integer greater or equal then number, since it is already integer, |
1714 | # always returns $self |
ee15d750 |
1715 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e |
1716 | |
1717 | # not needed: return $x if $x->modify('bceil'); |
58cde26e |
1718 | return $x->round($a,$p,$r); |
1719 | } |
1720 | |
1721 | ############################################################################## |
1722 | # private stuff (internal use only) |
1723 | |
574bacfe |
1724 | sub __one |
58cde26e |
1725 | { |
1726 | # internal speedup, set argument to 1, or create a +/- 1 |
1727 | my $self = shift; |
dccbb853 |
1728 | my $x = $self->bone(); # $x->{value} = $CALC->_one(); |
0716bf9b |
1729 | $x->{sign} = shift || '+'; |
1730 | return $x; |
58cde26e |
1731 | } |
1732 | |
1733 | sub _swap |
1734 | { |
1735 | # Overload will swap params if first one is no object ref so that the first |
1736 | # one is always an object ref. In this case, third param is true. |
1737 | # This routine is to overcome the effect of scalar,$object creating an object |
1738 | # of the class of this package, instead of the second param $object. This |
1739 | # happens inside overload, when the overload section of this package is |
1740 | # inherited by sub classes. |
1741 | # For overload cases (and this is used only there), we need to preserve the |
1742 | # args, hence the copy(). |
1743 | # You can override this method in a subclass, the overload section will call |
1744 | # $object->_swap() to make sure it arrives at the proper subclass, with some |
394e6ffb |
1745 | # exceptions like '+' and '-'. To make '+' and '-' work, you also need to |
1746 | # specify your own overload for them. |
58cde26e |
1747 | |
1748 | # object, (object|scalar) => preserve first and make copy |
1749 | # scalar, object => swapped, re-swap and create new from first |
1750 | # (using class of second object, not $class!!) |
1751 | my $self = shift; # for override in subclass |
58cde26e |
1752 | if ($_[2]) |
1753 | { |
1754 | my $c = ref ($_[0]) || $class; # fallback $class should not happen |
1755 | return ( $c->new($_[1]), $_[0] ); |
1756 | } |
17baacb7 |
1757 | return ( $_[0]->copy(), $_[1] ); |
58cde26e |
1758 | } |
1759 | |
1760 | sub objectify |
1761 | { |
1762 | # check for strings, if yes, return objects instead |
1763 | |
1764 | # the first argument is number of args objectify() should look at it will |
1765 | # return $count+1 elements, the first will be a classname. This is because |
1766 | # overloaded '""' calls bstr($object,undef,undef) and this would result in |
1767 | # useless objects beeing created and thrown away. So we cannot simple loop |
1768 | # over @_. If the given count is 0, all arguments will be used. |
1769 | |
1770 | # If the second arg is a ref, use it as class. |
1771 | # If not, try to use it as classname, unless undef, then use $class |
1772 | # (aka Math::BigInt). The latter shouldn't happen,though. |
1773 | |
1774 | # caller: gives us: |
1775 | # $x->badd(1); => ref x, scalar y |
1776 | # Class->badd(1,2); => classname x (scalar), scalar x, scalar y |
1777 | # Class->badd( Class->(1),2); => classname x (scalar), ref x, scalar y |
1778 | # Math::BigInt::badd(1,2); => scalar x, scalar y |
1779 | # In the last case we check number of arguments to turn it silently into |
574bacfe |
1780 | # $class,1,2. (We can not take '1' as class ;o) |
58cde26e |
1781 | # badd($class,1) is not supported (it should, eventually, try to add undef) |
1782 | # currently it tries 'Math::BigInt' + 1, which will not work. |
ee15d750 |
1783 | |
1784 | # some shortcut for the common cases |
1785 | |
1786 | # $x->unary_op(); |
1787 | return (ref($_[1]),$_[1]) if (@_ == 2) && ($_[0]||0 == 1) && ref($_[1]); |
1788 | # $x->binary_op($y); |
1789 | #return (ref($_[1]),$_[1],$_[2]) if (@_ == 3) && ($_[0]||0 == 2) |
1790 | # && ref($_[1]) && ref($_[2]); |
1791 | |
1792 | # print "obj '",join ("' '", @_),"'\n"; |
1793 | |
58cde26e |
1794 | my $count = abs(shift || 0); |
1795 | |
dccbb853 |
1796 | # print "MBI ",caller(),"\n"; |
58cde26e |
1797 | |
1798 | my @a; # resulting array |
1799 | if (ref $_[0]) |
1800 | { |
1801 | # okay, got object as first |
1802 | $a[0] = ref $_[0]; |
1803 | } |
1804 | else |
1805 | { |
1806 | # nope, got 1,2 (Class->xxx(1) => Class,1 and not supported) |
1807 | $a[0] = $class; |
1808 | #print "@_\n"; sleep(1); |
1809 | $a[0] = shift if $_[0] =~ /^[A-Z].*::/; # classname as first? |
1810 | } |
1811 | #print caller(),"\n"; |
1812 | # print "Now in objectify, my class is today $a[0]\n"; |
1813 | my $k; |
1814 | if ($count == 0) |
1815 | { |
1816 | while (@_) |
1817 | { |
1818 | $k = shift; |
1819 | if (!ref($k)) |
1820 | { |
1821 | $k = $a[0]->new($k); |
1822 | } |
1823 | elsif (ref($k) ne $a[0]) |
1824 | { |
1825 | # foreign object, try to convert to integer |
1826 | $k->can('as_number') ? $k = $k->as_number() : $k = $a[0]->new($k); |
e16b8f49 |
1827 | } |
58cde26e |
1828 | push @a,$k; |
1829 | } |
1830 | } |
1831 | else |
1832 | { |
1833 | while ($count > 0) |
1834 | { |
1835 | #print "$count\n"; |
1836 | $count--; |
1837 | $k = shift; |
dccbb853 |
1838 | # print "$k (",ref($k),") => \n"; |
58cde26e |
1839 | if (!ref($k)) |
1840 | { |
1841 | $k = $a[0]->new($k); |
1842 | } |
1843 | elsif (ref($k) ne $a[0]) |
1844 | { |
1845 | # foreign object, try to convert to integer |
1846 | $k->can('as_number') ? $k = $k->as_number() : $k = $a[0]->new($k); |
e16b8f49 |
1847 | } |
ee15d750 |
1848 | # print "$k (",ref($k),")\n"; |
58cde26e |
1849 | push @a,$k; |
1850 | } |
1851 | push @a,@_; # return other params, too |
1852 | } |
1853 | #my $i = 0; |
1854 | #foreach (@a) |
1855 | # { |
1856 | # print "o $i $a[0]\n" if $i == 0; |
1857 | # print "o $i ",ref($_),"\n" if $i != 0; $i++; |
1858 | # } |
1859 | #print "objectify done: would return ",scalar @a," values\n"; |
1860 | #print caller(1),"\n" unless wantarray; |
1861 | die "$class objectify needs list context" unless wantarray; |
1862 | @a; |
1863 | } |
1864 | |
1865 | sub import |
1866 | { |
1867 | my $self = shift; |
1868 | #print "import $self @_\n"; |
0716bf9b |
1869 | my @a = @_; my $l = scalar @_; my $j = 0; |
1870 | for ( my $i = 0; $i < $l ; $i++,$j++ ) |
58cde26e |
1871 | { |
0716bf9b |
1872 | if ($_[$i] eq ':constant') |
58cde26e |
1873 | { |
0716bf9b |
1874 | # this causes overlord er load to step in |
58cde26e |
1875 | overload::constant integer => sub { $self->new(shift) }; |
0716bf9b |
1876 | splice @a, $j, 1; $j --; |
1877 | } |
1878 | elsif ($_[$i] =~ /^lib$/i) |
1879 | { |
1880 | # this causes a different low lib to take care... |
1881 | $CALC = $_[$i+1] || $CALC; |
574bacfe |
1882 | my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..." |
0716bf9b |
1883 | splice @a, $j, $s; $j -= $s; |
58cde26e |
1884 | } |
1885 | } |
1886 | # any non :constant stuff is handled by our parent, Exporter |
1887 | # even if @_ is empty, to give it a chance |
dccbb853 |
1888 | $self->SUPER::import(@a); # need it for subclasses |
1889 | $self->export_to_level(1,$self,@a); # need it for MBF |
58cde26e |
1890 | |
574bacfe |
1891 | # try to load core math lib |
1892 | my @c = split /\s*,\s*/,$CALC; |
1893 | push @c,'Calc'; # if all fail, try this |
1894 | foreach my $lib (@c) |
1895 | { |
1896 | $lib = 'Math::BigInt::'.$lib if $lib !~ /^Math::BigInt/i; |
1897 | $lib =~ s/\.pm$//; |
1898 | if ($] < 5.6) |
1899 | { |
1900 | # Perl < 5.6.0 dies with "out of memory!" when eval() and ':constant' is |
1901 | # used in the same script, or eval inside import(). |
1902 | (my $mod = $lib . '.pm') =~ s!::!/!g; |
1903 | # require does not automatically :: => /, so portability problems arise |
bd05a461 |
1904 | eval { require $mod; $lib->import( @c ); } |
574bacfe |
1905 | } |
1906 | else |
1907 | { |
bd05a461 |
1908 | eval "use $lib @c;"; |
574bacfe |
1909 | } |
bd05a461 |
1910 | $CALC = $lib, last if $@ eq ''; # no error in loading lib? |
574bacfe |
1911 | } |
58cde26e |
1912 | } |
1913 | |
574bacfe |
1914 | sub __from_hex |
58cde26e |
1915 | { |
1916 | # convert a (ref to) big hex string to BigInt, return undef for error |
1917 | my $hs = shift; |
1918 | |
1919 | my $x = Math::BigInt->bzero(); |
394e6ffb |
1920 | |
1921 | # strip underscores |
1922 | $$hs =~ s/([0-9a-fA-F])_([0-9a-fA-F])/$1$2/g; |
1923 | $$hs =~ s/([0-9a-fA-F])_([0-9a-fA-F])/$1$2/g; |
1924 | |
58cde26e |
1925 | return $x->bnan() if $$hs !~ /^[\-\+]?0x[0-9A-Fa-f]+$/; |
1926 | |
b22b3e31 |
1927 | my $sign = '+'; $sign = '-' if ($$hs =~ /^-/); |
58cde26e |
1928 | |
b22b3e31 |
1929 | $$hs =~ s/^[+-]//; # strip sign |
0716bf9b |
1930 | if ($CALC->can('_from_hex')) |
58cde26e |
1931 | { |
0716bf9b |
1932 | $x->{value} = $CALC->_from_hex($hs); |
58cde26e |
1933 | } |
0716bf9b |
1934 | else |
58cde26e |
1935 | { |
0716bf9b |
1936 | # fallback to pure perl |
1937 | my $mul = Math::BigInt->bzero(); $mul++; |
1938 | my $x65536 = Math::BigInt->new(65536); |
1939 | my $len = CORE::length($$hs)-2; |
1940 | $len = int($len/4); # 4-digit parts, w/o '0x' |
1941 | my $val; my $i = -4; |
1942 | while ($len >= 0) |
1943 | { |
1944 | $val = substr($$hs,$i,4); |
b22b3e31 |
1945 | $val =~ s/^[+-]?0x// if $len == 0; # for last part only because |
0716bf9b |
1946 | $val = hex($val); # hex does not like wrong chars |
1947 | # print "$val ",substr($$hs,$i,4),"\n"; |
1948 | $i -= 4; $len --; |
1949 | $x += $mul * $val if $val != 0; |
1950 | $mul *= $x65536 if $len >= 0; # skip last mul |
1951 | } |
58cde26e |
1952 | } |
0716bf9b |
1953 | $x->{sign} = $sign if !$x->is_zero(); # no '-0' |
58cde26e |
1954 | return $x; |
1955 | } |
1956 | |
574bacfe |
1957 | sub __from_bin |
58cde26e |
1958 | { |
1959 | # convert a (ref to) big binary string to BigInt, return undef for error |
1960 | my $bs = shift; |
1961 | |
1962 | my $x = Math::BigInt->bzero(); |
394e6ffb |
1963 | # strip underscores |
1964 | $$bs =~ s/([01])_([01])/$1$2/g; |
1965 | $$bs =~ s/([01])_([01])/$1$2/g; |
b22b3e31 |
1966 | return $x->bnan() if $$bs !~ /^[+-]?0b[01]+$/; |
58cde26e |
1967 | |
1968 | my $mul = Math::BigInt->bzero(); $mul++; |
1969 | my $x256 = Math::BigInt->new(256); |
1970 | |
0716bf9b |
1971 | my $sign = '+'; $sign = '-' if ($$bs =~ /^\-/); |
b22b3e31 |
1972 | $$bs =~ s/^[+-]//; # strip sign |
0716bf9b |
1973 | if ($CALC->can('_from_bin')) |
58cde26e |
1974 | { |
0716bf9b |
1975 | $x->{value} = $CALC->_from_bin($bs); |
58cde26e |
1976 | } |
0716bf9b |
1977 | else |
58cde26e |
1978 | { |
0716bf9b |
1979 | my $len = CORE::length($$bs)-2; |
1980 | $len = int($len/8); # 8-digit parts, w/o '0b' |
1981 | my $val; my $i = -8; |
1982 | while ($len >= 0) |
1983 | { |
1984 | $val = substr($$bs,$i,8); |
b22b3e31 |
1985 | $val =~ s/^[+-]?0b// if $len == 0; # for last part only |
1986 | #$val = oct('0b'.$val); # does not work on Perl prior to 5.6.0 |
394e6ffb |
1987 | # slower: |
1988 | # $val = ('0' x (8-CORE::length($val))).$val if CORE::length($val) < 8; |
1989 | $val = ord(pack('B8',substr('00000000'.$val,-8,8))); |
0716bf9b |
1990 | $i -= 8; $len --; |
1991 | $x += $mul * $val if $val != 0; |
1992 | $mul *= $x256 if $len >= 0; # skip last mul |
1993 | } |
58cde26e |
1994 | } |
1995 | $x->{sign} = $sign if !$x->is_zero(); |
1996 | return $x; |
1997 | } |
1998 | |
1999 | sub _split |
2000 | { |
2001 | # (ref to num_str) return num_str |
2002 | # internal, take apart a string and return the pieces |
dccbb853 |
2003 | # strip leading/trailing whitespace, leading zeros, underscore and reject |
574bacfe |
2004 | # invalid input |
58cde26e |
2005 | my $x = shift; |
2006 | |
574bacfe |
2007 | # strip white space at front, also extranous leading zeros |
2008 | $$x =~ s/^\s*([-]?)0*([0-9])/$1$2/g; # will not strip ' .2' |
2009 | $$x =~ s/^\s+//; # but this will |
58cde26e |
2010 | $$x =~ s/\s+$//g; # strip white space at end |
58cde26e |
2011 | |
574bacfe |
2012 | # shortcut, if nothing to split, return early |
2013 | if ($$x =~ /^[+-]?\d+$/) |
2014 | { |
2015 | $$x =~ s/^([+-])0*([0-9])/$2/; my $sign = $1 || '+'; |
2016 | return (\$sign, $x, \'', \'', \0); |
2017 | } |
58cde26e |
2018 | |
574bacfe |
2019 | # invalid starting char? |
2020 | return if $$x !~ /^[+-]?(\.?[0-9]|0b[0-1]|0x[0-9a-fA-F])/; |
58cde26e |
2021 | |
574bacfe |
2022 | return __from_hex($x) if $$x =~ /^[\-\+]?0x/; # hex string |
2023 | return __from_bin($x) if $$x =~ /^[\-\+]?0b/; # binary string |
394e6ffb |
2024 | |
2025 | # strip underscores between digits |
2026 | $$x =~ s/(\d)_(\d)/$1$2/g; |
2027 | $$x =~ s/(\d)_(\d)/$1$2/g; # do twice for 1_2_3 |
574bacfe |
2028 | |
58cde26e |
2029 | # some possible inputs: |
2030 | # 2.1234 # 0.12 # 1 # 1E1 # 2.134E1 # 434E-10 # 1.02009E-2 |
2031 | # .2 # 1_2_3.4_5_6 # 1.4E1_2_3 # 1e3 # +.2 |
2032 | |
027dc388 |
2033 | return if $$x =~ /[Ee].*[Ee]/; # more than one E => error |
2034 | |
58cde26e |
2035 | my ($m,$e) = split /[Ee]/,$$x; |
2036 | $e = '0' if !defined $e || $e eq ""; |
2037 | # print "m '$m' e '$e'\n"; |
2038 | # sign,value for exponent,mantint,mantfrac |
2039 | my ($es,$ev,$mis,$miv,$mfv); |
2040 | # valid exponent? |
2041 | if ($e =~ /^([+-]?)0*(\d+)$/) # strip leading zeros |
2042 | { |
2043 | $es = $1; $ev = $2; |
2044 | #print "'$m' '$e' e: $es $ev "; |
2045 | # valid mantissa? |
2046 | return if $m eq '.' || $m eq ''; |
2047 | my ($mi,$mf) = split /\./,$m; |
2048 | $mi = '0' if !defined $mi; |
2049 | $mi .= '0' if $mi =~ /^[\-\+]?$/; |
2050 | $mf = '0' if !defined $mf || $mf eq ''; |
2051 | if ($mi =~ /^([+-]?)0*(\d+)$/) # strip leading zeros |
2052 | { |
2053 | $mis = $1||'+'; $miv = $2; |
0716bf9b |
2054 | # print "$mis $miv"; |
58cde26e |
2055 | # valid, existing fraction part of mantissa? |
2056 | return unless ($mf =~ /^(\d*?)0*$/); # strip trailing zeros |
2057 | $mfv = $1; |
2058 | #print " split: $mis $miv . $mfv E $es $ev\n"; |
2059 | return (\$mis,\$miv,\$mfv,\$es,\$ev); |
2060 | } |
2061 | } |
2062 | return; # NaN, not a number |
2063 | } |
2064 | |
58cde26e |
2065 | sub as_number |
2066 | { |
2067 | # an object might be asked to return itself as bigint on certain overloaded |
2068 | # operations, this does exactly this, so that sub classes can simple inherit |
2069 | # it or override with their own integer conversion routine |
2070 | my $self = shift; |
2071 | |
17baacb7 |
2072 | $self->copy(); |
58cde26e |
2073 | } |
2074 | |
bd05a461 |
2075 | sub as_hex |
2076 | { |
2077 | # return as hex string, with prefixed 0x |
2078 | my $x = shift; $x = $class->new($x) if !ref($x); |
2079 | |
2080 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc |
2081 | return '0x0' if $x->is_zero(); |
2082 | |
2083 | my $es = ''; my $s = ''; |
2084 | $s = $x->{sign} if $x->{sign} eq '-'; |
bd05a461 |
2085 | if ($CALC->can('_as_hex')) |
2086 | { |
ee15d750 |
2087 | $es = ${$CALC->_as_hex($x->{value})}; |
bd05a461 |
2088 | } |
2089 | else |
2090 | { |
2091 | my $x1 = $x->copy()->babs(); my $xr; |
2092 | my $x100 = Math::BigInt->new (0x100); |
2093 | while (!$x1->is_zero()) |
2094 | { |
2095 | ($x1, $xr) = bdiv($x1,$x100); |
2096 | $es .= unpack('h2',pack('C',$xr->numify())); |
2097 | } |
2098 | $es = reverse $es; |
2099 | $es =~ s/^[0]+//; # strip leading zeros |
ee15d750 |
2100 | $s .= '0x'; |
bd05a461 |
2101 | } |
2102 | $s . $es; |
2103 | } |
2104 | |
2105 | sub as_bin |
2106 | { |
2107 | # return as binary string, with prefixed 0b |
2108 | my $x = shift; $x = $class->new($x) if !ref($x); |
2109 | |
2110 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc |
2111 | return '0b0' if $x->is_zero(); |
2112 | |
2113 | my $es = ''; my $s = ''; |
2114 | $s = $x->{sign} if $x->{sign} eq '-'; |
bd05a461 |
2115 | if ($CALC->can('_as_bin')) |
2116 | { |
ee15d750 |
2117 | $es = ${$CALC->_as_bin($x->{value})}; |
bd05a461 |
2118 | } |
2119 | else |
2120 | { |
2121 | my $x1 = $x->copy()->babs(); my $xr; |
2122 | my $x100 = Math::BigInt->new (0x100); |
2123 | while (!$x1->is_zero()) |
2124 | { |
2125 | ($x1, $xr) = bdiv($x1,$x100); |
2126 | $es .= unpack('b8',pack('C',$xr->numify())); |
2127 | } |
2128 | $es = reverse $es; |
2129 | $es =~ s/^[0]+//; # strip leading zeros |
ee15d750 |
2130 | $s .= '0b'; |
bd05a461 |
2131 | } |
2132 | $s . $es; |
2133 | } |
2134 | |
58cde26e |
2135 | ############################################################################## |
0716bf9b |
2136 | # internal calculation routines (others are in Math::BigInt::Calc etc) |
58cde26e |
2137 | |
dccbb853 |
2138 | sub __lcm |
58cde26e |
2139 | { |
2140 | # (BINT or num_str, BINT or num_str) return BINT |
2141 | # does modify first argument |
2142 | # LCM |
2143 | |
2144 | my $x = shift; my $ty = shift; |
2145 | return $x->bnan() if ($x->{sign} eq $nan) || ($ty->{sign} eq $nan); |
2146 | return $x * $ty / bgcd($x,$ty); |
2147 | } |
2148 | |
574bacfe |
2149 | sub __gcd |
58cde26e |
2150 | { |
2151 | # (BINT or num_str, BINT or num_str) return BINT |
dccbb853 |
2152 | # does modify both arguments |
58cde26e |
2153 | # GCD -- Euclids algorithm E, Knuth Vol 2 pg 296 |
dccbb853 |
2154 | my ($x,$ty) = @_; |
2155 | |
0716bf9b |
2156 | return $x->bnan() if $x->{sign} !~ /^[+-]$/ || $ty->{sign} !~ /^[+-]$/; |
58cde26e |
2157 | |
2158 | while (!$ty->is_zero()) |
2159 | { |
2160 | ($x, $ty) = ($ty,bmod($x,$ty)); |
2161 | } |
2162 | $x; |
2163 | } |
2164 | |
58cde26e |
2165 | ############################################################################### |
2166 | # this method return 0 if the object can be modified, or 1 for not |
2167 | # We use a fast use constant statement here, to avoid costly calls. Subclasses |
2168 | # may override it with special code (f.i. Math::BigInt::Constant does so) |
2169 | |
0716bf9b |
2170 | sub modify () { 0; } |
e16b8f49 |
2171 | |
a0d0e21e |
2172 | 1; |
a5f75d66 |
2173 | __END__ |
2174 | |
2175 | =head1 NAME |
2176 | |
2177 | Math::BigInt - Arbitrary size integer math package |
2178 | |
2179 | =head1 SYNOPSIS |
2180 | |
2181 | use Math::BigInt; |
58cde26e |
2182 | |
2183 | # Number creation |
574bacfe |
2184 | $x = Math::BigInt->new($str); # defaults to 0 |
2185 | $nan = Math::BigInt->bnan(); # create a NotANumber |
2186 | $zero = Math::BigInt->bzero(); # create a +0 |
2187 | $inf = Math::BigInt->binf(); # create a +inf |
2188 | $inf = Math::BigInt->binf('-'); # create a -inf |
2189 | $one = Math::BigInt->bone(); # create a +1 |
2190 | $one = Math::BigInt->bone('-'); # create a -1 |
58cde26e |
2191 | |
2192 | # Testing |
574bacfe |
2193 | $x->is_zero(); # true if arg is +0 |
2194 | $x->is_nan(); # true if arg is NaN |
0716bf9b |
2195 | $x->is_one(); # true if arg is +1 |
2196 | $x->is_one('-'); # true if arg is -1 |
2197 | $x->is_odd(); # true if odd, false for even |
2198 | $x->is_even(); # true if even, false for odd |
2199 | $x->is_positive(); # true if >= 0 |
2200 | $x->is_negative(); # true if < 0 |
2201 | $x->is_inf(sign); # true if +inf, or -inf (sign is default '+') |
2202 | |
58cde26e |
2203 | $x->bcmp($y); # compare numbers (undef,<0,=0,>0) |
2204 | $x->bacmp($y); # compare absolutely (undef,<0,=0,>0) |
2205 | $x->sign(); # return the sign, either +,- or NaN |
2206 | $x->digit($n); # return the nth digit, counting from right |
2207 | $x->digit(-$n); # return the nth digit, counting from left |
2208 | |
2209 | # The following all modify their first argument: |
2210 | |
2211 | # set |
2212 | $x->bzero(); # set $x to 0 |
2213 | $x->bnan(); # set $x to NaN |
574bacfe |
2214 | $x->bone(); # set $x to +1 |
2215 | $x->bone('-'); # set $x to -1 |
58cde26e |
2216 | |
2217 | $x->bneg(); # negation |
2218 | $x->babs(); # absolute value |
2219 | $x->bnorm(); # normalize (no-op) |
2220 | $x->bnot(); # two's complement (bit wise not) |
2221 | $x->binc(); # increment x by 1 |
2222 | $x->bdec(); # decrement x by 1 |
2223 | |
2224 | $x->badd($y); # addition (add $y to $x) |
2225 | $x->bsub($y); # subtraction (subtract $y from $x) |
2226 | $x->bmul($y); # multiplication (multiply $x by $y) |
2227 | $x->bdiv($y); # divide, set $x to quotient |
2228 | # return (quo,rem) or quo if scalar |
2229 | |
2230 | $x->bmod($y); # modulus (x % y) |
2231 | $x->bpow($y); # power of arguments (x ** y) |
2232 | $x->blsft($y); # left shift |
2233 | $x->brsft($y); # right shift |
2234 | $x->blsft($y,$n); # left shift, by base $n (like 10) |
2235 | $x->brsft($y,$n); # right shift, by base $n (like 10) |
2236 | |
2237 | $x->band($y); # bitwise and |
2238 | $x->bior($y); # bitwise inclusive or |
2239 | $x->bxor($y); # bitwise exclusive or |
2240 | $x->bnot(); # bitwise not (two's complement) |
2241 | |
2242 | $x->bsqrt(); # calculate square-root |
2243 | |
2244 | $x->round($A,$P,$round_mode); # round to accuracy or precision using mode $r |
2245 | $x->bround($N); # accuracy: preserve $N digits |
2246 | $x->bfround($N); # round to $Nth digit, no-op for BigInts |
2247 | |
2248 | # The following do not modify their arguments in BigInt, but do in BigFloat: |
2249 | $x->bfloor(); # return integer less or equal than $x |
2250 | $x->bceil(); # return integer greater or equal than $x |
2251 | |
2252 | # The following do not modify their arguments: |
2253 | |
dccbb853 |
2254 | bgcd(@values); # greatest common divisor (no OO style) |
2255 | blcm(@values); # lowest common multiplicator (no OO style) |
bd05a461 |
2256 | |
58cde26e |
2257 | $x->length(); # return number of digits in number |
bd05a461 |
2258 | ($x,$f) = $x->length(); # length of number and length of fraction part, |
2259 | # latter is always 0 digits long for BigInt's |
58cde26e |
2260 | |
2261 | $x->exponent(); # return exponent as BigInt |
ee15d750 |
2262 | $x->mantissa(); # return (signed) mantissa as BigInt |
58cde26e |
2263 | $x->parts(); # return (mantissa,exponent) as BigInt |
0716bf9b |
2264 | $x->copy(); # make a true copy of $x (unlike $y = $x;) |
2265 | $x->as_number(); # return as BigInt (in BigInt: same as copy()) |
bd05a461 |
2266 | |
2267 | # conversation to string |
2268 | $x->bstr(); # normalized string |
2269 | $x->bsstr(); # normalized string in scientific notation |
2270 | $x->as_hex(); # as signed hexadecimal string with prefixed 0x |
2271 | $x->as_bin(); # as signed binary string with prefixed 0b |
2272 | |
a5f75d66 |
2273 | =head1 DESCRIPTION |
2274 | |
58cde26e |
2275 | All operators (inlcuding basic math operations) are overloaded if you |
2276 | declare your big integers as |
a5f75d66 |
2277 | |
58cde26e |
2278 | $i = new Math::BigInt '123_456_789_123_456_789'; |
a5f75d66 |
2279 | |
58cde26e |
2280 | Operations with overloaded operators preserve the arguments which is |
2281 | exactly what you expect. |
a5f75d66 |
2282 | |
2283 | =over 2 |
2284 | |
2285 | =item Canonical notation |
2286 | |
58cde26e |
2287 | Big integer values are strings of the form C</^[+-]\d+$/> with leading |
a5f75d66 |
2288 | zeros suppressed. |
2289 | |
58cde26e |
2290 | '-0' canonical value '-0', normalized '0' |
2291 | ' -123_123_123' canonical value '-123123123' |
2292 | '1_23_456_7890' canonical value '1234567890' |
2293 | |
a5f75d66 |
2294 | =item Input |
2295 | |
58cde26e |
2296 | Input values to these routines may be either Math::BigInt objects or |
2297 | strings of the form C</^\s*[+-]?[\d]+\.?[\d]*E?[+-]?[\d]*$/>. |
2298 | |
2299 | You can include one underscore between any two digits. |
2300 | |
2301 | This means integer values like 1.01E2 or even 1000E-2 are also accepted. |
2302 | Non integer values result in NaN. |
2303 | |
2304 | Math::BigInt::new() defaults to 0, while Math::BigInt::new('') results |
2305 | in 'NaN'. |
2306 | |
2307 | bnorm() on a BigInt object is now effectively a no-op, since the numbers |
2308 | are always stored in normalized form. On a string, it creates a BigInt |
2309 | object. |
a5f75d66 |
2310 | |
2311 | =item Output |
2312 | |
58cde26e |
2313 | Output values are BigInt objects (normalized), except for bstr(), which |
2314 | returns a string in normalized form. |
2315 | Some routines (C<is_odd()>, C<is_even()>, C<is_zero()>, C<is_one()>, |
2316 | C<is_nan()>) return true or false, while others (C<bcmp()>, C<bacmp()>) |
2317 | return either undef, <0, 0 or >0 and are suited for sort. |
a5f75d66 |
2318 | |
2319 | =back |
2320 | |
0716bf9b |
2321 | =head1 ACCURACY and PRECISION |
2322 | |
b22b3e31 |
2323 | Since version v1.33, Math::BigInt and Math::BigFloat have full support for |
0716bf9b |
2324 | accuracy and precision based rounding, both automatically after every |
b22b3e31 |
2325 | operation as well as manually. |
0716bf9b |
2326 | |
2327 | This section describes the accuracy/precision handling in Math::Big* as it |
b22b3e31 |
2328 | used to be and as it is now, complete with an explanation of all terms and |
0716bf9b |
2329 | abbreviations. |
2330 | |
2331 | Not yet implemented things (but with correct description) are marked with '!', |
2332 | things that need to be answered are marked with '?'. |
2333 | |
2334 | In the next paragraph follows a short description of terms used here (because |
574bacfe |
2335 | these may differ from terms used by others people or documentation). |
0716bf9b |
2336 | |
b22b3e31 |
2337 | During the rest of this document, the shortcuts A (for accuracy), P (for |
0716bf9b |
2338 | precision), F (fallback) and R (rounding mode) will be used. |
2339 | |
2340 | =head2 Precision P |
2341 | |
2342 | A fixed number of digits before (positive) or after (negative) |
b22b3e31 |
2343 | the decimal point. For example, 123.45 has a precision of -2. 0 means an |
2344 | integer like 123 (or 120). A precision of 2 means two digits to the left |
2345 | of the decimal point are zero, so 123 with P = 1 becomes 120. Note that |
2346 | numbers with zeros before the decimal point may have different precisions, |
2347 | because 1200 can have p = 0, 1 or 2 (depending on what the inital value |
2348 | was). It could also have p < 0, when the digits after the decimal point |
2349 | are zero. |
0716bf9b |
2350 | |
574bacfe |
2351 | The string output (of floating point numbers) will be padded with zeros: |
2352 | |
2353 | Initial value P A Result String |
2354 | ------------------------------------------------------------ |
2355 | 1234.01 -3 1000 1000 |
2356 | 1234 -2 1200 1200 |
2357 | 1234.5 -1 1230 1230 |
2358 | 1234.001 1 1234 1234.0 |
2359 | 1234.01 0 1234 1234 |
2360 | 1234.01 2 1234.01 1234.01 |
2361 | 1234.01 5 1234.01 1234.01000 |
2362 | |
2363 | For BigInts, no padding occurs. |
0716bf9b |
2364 | |
2365 | =head2 Accuracy A |
2366 | |
2367 | Number of significant digits. Leading zeros are not counted. A |
2368 | number may have an accuracy greater than the non-zero digits |
b22b3e31 |
2369 | when there are zeros in it or trailing zeros. For example, 123.456 has |
2370 | A of 6, 10203 has 5, 123.0506 has 7, 123.450000 has 8 and 0.000123 has 3. |
0716bf9b |
2371 | |
574bacfe |
2372 | The string output (of floating point numbers) will be padded with zeros: |
2373 | |
2374 | Initial value P A Result String |
2375 | ------------------------------------------------------------ |
2376 | 1234.01 3 1230 1230 |
2377 | 1234.01 6 1234.01 1234.01 |
2378 | 1234.1 8 1234.1 1234.1000 |
2379 | |
2380 | For BigInts, no padding occurs. |
2381 | |
0716bf9b |
2382 | =head2 Fallback F |
a5f75d66 |
2383 | |
574bacfe |
2384 | When both A and P are undefined, this is used as a fallback accuracy when |
2385 | dividing numbers. |
0716bf9b |
2386 | |
2387 | =head2 Rounding mode R |
2388 | |
2389 | When rounding a number, different 'styles' or 'kinds' |
2390 | of rounding are possible. (Note that random rounding, as in |
2391 | Math::Round, is not implemented.) |
58cde26e |
2392 | |
2393 | =over 2 |
a5f75d66 |
2394 | |
0716bf9b |
2395 | =item 'trunc' |
2396 | |
2397 | truncation invariably removes all digits following the |
2398 | rounding place, replacing them with zeros. Thus, 987.65 rounded |
b22b3e31 |
2399 | to tens (P=1) becomes 980, and rounded to the fourth sigdig |
0716bf9b |
2400 | becomes 987.6 (A=4). 123.456 rounded to the second place after the |
b22b3e31 |
2401 | decimal point (P=-2) becomes 123.46. |
0716bf9b |
2402 | |
2403 | All other implemented styles of rounding attempt to round to the |
2404 | "nearest digit." If the digit D immediately to the right of the |
2405 | rounding place (skipping the decimal point) is greater than 5, the |
2406 | number is incremented at the rounding place (possibly causing a |
2407 | cascade of incrementation): e.g. when rounding to units, 0.9 rounds |
2408 | to 1, and -19.9 rounds to -20. If D < 5, the number is similarly |
2409 | truncated at the rounding place: e.g. when rounding to units, 0.4 |
2410 | rounds to 0, and -19.4 rounds to -19. |
2411 | |
2412 | However the results of other styles of rounding differ if the |
2413 | digit immediately to the right of the rounding place (skipping the |
2414 | decimal point) is 5 and if there are no digits, or no digits other |
2415 | than 0, after that 5. In such cases: |
2416 | |
2417 | =item 'even' |
2418 | |
2419 | rounds the digit at the rounding place to 0, 2, 4, 6, or 8 |
2420 | if it is not already. E.g., when rounding to the first sigdig, 0.45 |
2421 | becomes 0.4, -0.55 becomes -0.6, but 0.4501 becomes 0.5. |
2422 | |
2423 | =item 'odd' |
2424 | |
2425 | rounds the digit at the rounding place to 1, 3, 5, 7, or 9 if |
2426 | it is not already. E.g., when rounding to the first sigdig, 0.45 |
2427 | becomes 0.5, -0.55 becomes -0.5, but 0.5501 becomes 0.6. |
2428 | |
2429 | =item '+inf' |
2430 | |
2431 | round to plus infinity, i.e. always round up. E.g., when |
2432 | rounding to the first sigdig, 0.45 becomes 0.5, -0.55 becomes -0.5, |
b22b3e31 |
2433 | and 0.4501 also becomes 0.5. |
0716bf9b |
2434 | |
2435 | =item '-inf' |
2436 | |
2437 | round to minus infinity, i.e. always round down. E.g., when |
2438 | rounding to the first sigdig, 0.45 becomes 0.4, -0.55 becomes -0.6, |
2439 | but 0.4501 becomes 0.5. |
2440 | |
2441 | =item 'zero' |
2442 | |
2443 | round to zero, i.e. positive numbers down, negative ones up. |
2444 | E.g., when rounding to the first sigdig, 0.45 becomes 0.4, -0.55 |
2445 | becomes -0.5, but 0.4501 becomes 0.5. |
2446 | |
2447 | =back |
2448 | |
2449 | The handling of A & P in MBI/MBF (the old core code shipped with Perl |
2450 | versions <= 5.7.2) is like this: |
2451 | |
2452 | =over 2 |
a5f75d66 |
2453 | |
0716bf9b |
2454 | =item Precision |
2455 | |
b22b3e31 |
2456 | * ffround($p) is able to round to $p number of digits after the decimal |
2457 | point |
0716bf9b |
2458 | * otherwise P is unused |
2459 | |
2460 | =item Accuracy (significant digits) |
2461 | |
2462 | * fround($a) rounds to $a significant digits |
2463 | * only fdiv() and fsqrt() take A as (optional) paramater |
b22b3e31 |
2464 | + other operations simply create the same number (fneg etc), or more (fmul) |
0716bf9b |
2465 | of digits |
2466 | + rounding/truncating is only done when explicitly calling one of fround |
2467 | or ffround, and never for BigInt (not implemented) |
b22b3e31 |
2468 | * fsqrt() simply hands its accuracy argument over to fdiv. |
0716bf9b |
2469 | * the documentation and the comment in the code indicate two different ways |
2470 | on how fdiv() determines the maximum number of digits it should calculate, |
2471 | and the actual code does yet another thing |
2472 | POD: |
2473 | max($Math::BigFloat::div_scale,length(dividend)+length(divisor)) |
2474 | Comment: |
2475 | result has at most max(scale, length(dividend), length(divisor)) digits |
2476 | Actual code: |
2477 | scale = max(scale, length(dividend)-1,length(divisor)-1); |
2478 | scale += length(divisior) - length(dividend); |
b22b3e31 |
2479 | So for lx = 3, ly = 9, scale = 10, scale will actually be 16 (10+9-3). |
0716bf9b |
2480 | Actually, the 'difference' added to the scale is calculated from the |
2481 | number of "significant digits" in dividend and divisor, which is derived |
2482 | by looking at the length of the mantissa. Which is wrong, since it includes |
2483 | the + sign (oups) and actually gets 2 for '+100' and 4 for '+101'. Oups |
2484 | again. Thus 124/3 with div_scale=1 will get you '41.3' based on the strange |
2485 | assumption that 124 has 3 significant digits, while 120/7 will get you |
2486 | '17', not '17.1' since 120 is thought to have 2 significant digits. |
dccbb853 |
2487 | The rounding after the division then uses the remainder and $y to determine |
0716bf9b |
2488 | wether it must round up or down. |
b22b3e31 |
2489 | ? I have no idea which is the right way. That's why I used a slightly more |
2490 | ? simple scheme and tweaked the few failing testcases to match it. |
58cde26e |
2491 | |
0716bf9b |
2492 | =back |
5dc6f178 |
2493 | |
0716bf9b |
2494 | This is how it works now: |
5dc6f178 |
2495 | |
0716bf9b |
2496 | =over 2 |
5dc6f178 |
2497 | |
0716bf9b |
2498 | =item Setting/Accessing |
2499 | |
2500 | * You can set the A global via $Math::BigInt::accuracy or |
2501 | $Math::BigFloat::accuracy or whatever class you are using. |
2502 | * You can also set P globally by using $Math::SomeClass::precision likewise. |
2503 | * Globals are classwide, and not inherited by subclasses. |
2504 | * to undefine A, use $Math::SomeCLass::accuracy = undef |
2505 | * to undefine P, use $Math::SomeClass::precision = undef |
2506 | * To be valid, A must be > 0, P can have any value. |
b22b3e31 |
2507 | * If P is negative, this means round to the P'th place to the right of the |
2508 | decimal point; positive values mean to the left of the decimal point. |
2509 | P of 0 means round to integer. |
0716bf9b |
2510 | * to find out the current global A, take $Math::SomeClass::accuracy |
2511 | * use $x->accuracy() for the local setting of $x. |
2512 | * to find out the current global P, take $Math::SomeClass::precision |
2513 | * use $x->precision() for the local setting |
2514 | |
2515 | =item Creating numbers |
2516 | |
b22b3e31 |
2517 | !* When you create a number, there should be a way to define its A & P |
0716bf9b |
2518 | * When a number without specific A or P is created, but the globals are |
b22b3e31 |
2519 | defined, these should be used to round the number immediately and also |
2520 | stored locally with the number. Thus changing the global defaults later on |
2521 | will not change the A or P of previously created numbers (i.e., A and P of |
0716bf9b |
2522 | $x will be what was in effect when $x was created) |
2523 | |
2524 | =item Usage |
2525 | |
b22b3e31 |
2526 | * If A or P are enabled/defined, they are used to round the result of each |
0716bf9b |
2527 | operation according to the rules below |
b22b3e31 |
2528 | * Negative P is ignored in Math::BigInt, since BigInts never have digits |
2529 | after the decimal point |
574bacfe |
2530 | * Math::BigFloat uses Math::BigInts internally, but setting A or P inside |
2531 | Math::BigInt as globals should not tamper with the parts of a BigFloat. |
2532 | Thus a flag is used to mark all Math::BigFloat numbers as 'never round' |
0716bf9b |
2533 | |
2534 | =item Precedence |
2535 | |
b22b3e31 |
2536 | * It only makes sense that a number has only one of A or P at a time. |
2537 | Since you can set/get both A and P, there is a rule that will practically |
2538 | enforce only A or P to be in effect at a time, even if both are set. |
2539 | This is called precedence. |
2540 | !* If two objects are involved in an operation, and one of them has A in |
0716bf9b |
2541 | ! effect, and the other P, this should result in a warning or an error, |
2542 | ! probably in NaN. |
2543 | * A takes precendence over P (Hint: A comes before P). If A is defined, it |
b22b3e31 |
2544 | is used, otherwise P is used. If neither of them is defined, nothing is |
2545 | used, i.e. the result will have as many digits as it can (with an |
2546 | exception for fdiv/fsqrt) and will not be rounded. |
2547 | * There is another setting for fdiv() (and thus for fsqrt()). If neither of |
2548 | A or P is defined, fdiv() will use a fallback (F) of $div_scale digits. |
2549 | If either the dividend's or the divisor's mantissa has more digits than |
2550 | the value of F, the higher value will be used instead of F. |
2551 | This is to limit the digits (A) of the result (just consider what would |
2552 | happen with unlimited A and P in the case of 1/3 :-) |
2553 | * fdiv will calculate 1 more digit than required (determined by |
0716bf9b |
2554 | A, P or F), and, if F is not used, round the result |
b22b3e31 |
2555 | (this will still fail in the case of a result like 0.12345000000001 with A |
574bacfe |
2556 | or P of 5, but this can not be helped - or can it?) |
b22b3e31 |
2557 | * Thus you can have the math done by on Math::Big* class in three modes: |
0716bf9b |
2558 | + never round (this is the default): |
2559 | This is done by setting A and P to undef. No math operation |
b22b3e31 |
2560 | will round the result, with fdiv() and fsqrt() as exceptions to guard |
0716bf9b |
2561 | against overflows. You must explicitely call bround(), bfround() or |
b22b3e31 |
2562 | round() (the latter with parameters). |
2563 | Note: Once you have rounded a number, the settings will 'stick' on it |
2564 | and 'infect' all other numbers engaged in math operations with it, since |
0716bf9b |
2565 | local settings have the highest precedence. So, to get SaferRound[tm], |
2566 | use a copy() before rounding like this: |
2567 | |
2568 | $x = Math::BigFloat->new(12.34); |
2569 | $y = Math::BigFloat->new(98.76); |
2570 | $z = $x * $y; # 1218.6984 |
2571 | print $x->copy()->fround(3); # 12.3 (but A is now 3!) |
2572 | $z = $x * $y; # still 1218.6984, without |
2573 | # copy would have been 1210! |
2574 | |
2575 | + round after each op: |
b22b3e31 |
2576 | After each single operation (except for testing like is_zero()), the |
2577 | method round() is called and the result is rounded appropriately. By |
0716bf9b |
2578 | setting proper values for A and P, you can have all-the-same-A or |
b22b3e31 |
2579 | all-the-same-P modes. For example, Math::Currency might set A to undef, |
2580 | and P to -2, globally. |
0716bf9b |
2581 | |
b22b3e31 |
2582 | ?Maybe an extra option that forbids local A & P settings would be in order, |
2583 | ?so that intermediate rounding does not 'poison' further math? |
0716bf9b |
2584 | |
2585 | =item Overriding globals |
2586 | |
2587 | * you will be able to give A, P and R as an argument to all the calculation |
b22b3e31 |
2588 | routines; the second parameter is A, the third one is P, and the fourth is |
0716bf9b |
2589 | R (shift place by one for binary operations like add). P is used only if |
b22b3e31 |
2590 | the first parameter (A) is undefined. These three parameters override the |
2591 | globals in the order detailed as follows, i.e. the first defined value |
0716bf9b |
2592 | wins: |
b22b3e31 |
2593 | (local: per object, global: global default, parameter: argument to sub) |
0716bf9b |
2594 | + parameter A |
2595 | + parameter P |
2596 | + local A (if defined on both of the operands: smaller one is taken) |
2597 | + local P (if defined on both of the operands: smaller one is taken) |
2598 | + global A |
2599 | + global P |
2600 | + global F |
b22b3e31 |
2601 | * fsqrt() will hand its arguments to fdiv(), as it used to, only now for two |
0716bf9b |
2602 | arguments (A and P) instead of one |
2603 | |
2604 | =item Local settings |
2605 | |
2606 | * You can set A and P locally by using $x->accuracy() and $x->precision() |
2607 | and thus force different A and P for different objects/numbers. |
b22b3e31 |
2608 | * Setting A or P this way immediately rounds $x to the new value. |
0716bf9b |
2609 | |
2610 | =item Rounding |
2611 | |
b22b3e31 |
2612 | * the rounding routines will use the respective global or local settings. |
0716bf9b |
2613 | fround()/bround() is for accuracy rounding, while ffround()/bfround() |
2614 | is for precision |
2615 | * the two rounding functions take as the second parameter one of the |
2616 | following rounding modes (R): |
2617 | 'even', 'odd', '+inf', '-inf', 'zero', 'trunc' |
2618 | * you can set and get the global R by using Math::SomeClass->round_mode() |
ee15d750 |
2619 | or by setting $Math::SomeClass::round_mode |
0716bf9b |
2620 | * after each operation, $result->round() is called, and the result may |
b22b3e31 |
2621 | eventually be rounded (that is, if A or P were set either locally, |
2622 | globally or as parameter to the operation) |
ee15d750 |
2623 | * to manually round a number, call $x->round($A,$P,$round_mode); |
b22b3e31 |
2624 | this will round the number by using the appropriate rounding function |
0716bf9b |
2625 | and then normalize it. |
b22b3e31 |
2626 | * rounding modifies the local settings of the number: |
0716bf9b |
2627 | |
2628 | $x = Math::BigFloat->new(123.456); |
2629 | $x->accuracy(5); |
2630 | $x->bround(4); |
2631 | |
2632 | Here 4 takes precedence over 5, so 123.5 is the result and $x->accuracy() |
2633 | will be 4 from now on. |
2634 | |
2635 | =item Default values |
2636 | |
2637 | * R: 'even' |
2638 | * F: 40 |
2639 | * A: undef |
2640 | * P: undef |
2641 | |
2642 | =item Remarks |
2643 | |
2644 | * The defaults are set up so that the new code gives the same results as |
2645 | the old code (except in a few cases on fdiv): |
2646 | + Both A and P are undefined and thus will not be used for rounding |
2647 | after each operation. |
2648 | + round() is thus a no-op, unless given extra parameters A and P |
58cde26e |
2649 | |
2650 | =back |
2651 | |
0716bf9b |
2652 | =head1 INTERNALS |
2653 | |
574bacfe |
2654 | The actual numbers are stored as unsigned big integers (with seperate sign). |
2655 | You should neither care about nor depend on the internal representation; it |
2656 | might change without notice. Use only method calls like C<< $x->sign(); >> |
2657 | instead relying on the internal hash keys like in C<< $x->{sign}; >>. |
2658 | |
2659 | =head2 MATH LIBRARY |
58cde26e |
2660 | |
574bacfe |
2661 | Math with the numbers is done (by default) by a module called |
2662 | Math::BigInt::Calc. This is equivalent to saying: |
2663 | |
2664 | use Math::BigInt lib => 'Calc'; |
58cde26e |
2665 | |
0716bf9b |
2666 | You can change this by using: |
58cde26e |
2667 | |
0716bf9b |
2668 | use Math::BigInt lib => 'BitVect'; |
58cde26e |
2669 | |
574bacfe |
2670 | The following would first try to find Math::BigInt::Foo, then |
2671 | Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: |
0716bf9b |
2672 | |
574bacfe |
2673 | use Math::BigInt lib => 'Foo,Math::BigInt::Bar'; |
58cde26e |
2674 | |
574bacfe |
2675 | Calc.pm uses as internal format an array of elements of some decimal base |
2676 | (usually 1e5, but this might change to 1e7) with the least significant digit |
2677 | first, while BitVect.pm uses a bit vector of base 2, most significant bit |
2678 | first. Other modules might use even different means of representing the |
2679 | numbers. See the respective module documentation for further details. |
58cde26e |
2680 | |
574bacfe |
2681 | =head2 SIGN |
2682 | |
2683 | The sign is either '+', '-', 'NaN', '+inf' or '-inf' and stored seperately. |
2684 | |
2685 | A sign of 'NaN' is used to represent the result when input arguments are not |
2686 | numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively |
2687 | minus infinity. You will get '+inf' when dividing a positive number by 0, and |
2688 | '-inf' when dividing any negative number by 0. |
58cde26e |
2689 | |
2690 | =head2 mantissa(), exponent() and parts() |
2691 | |
2692 | C<mantissa()> and C<exponent()> return the said parts of the BigInt such |
2693 | that: |
2694 | |
2695 | $m = $x->mantissa(); |
2696 | $e = $x->exponent(); |
2697 | $y = $m * ( 10 ** $e ); |
2698 | print "ok\n" if $x == $y; |
2699 | |
b22b3e31 |
2700 | C<< ($m,$e) = $x->parts() >> is just a shortcut that gives you both of them |
2701 | in one go. Both the returned mantissa and exponent have a sign. |
58cde26e |
2702 | |
574bacfe |
2703 | Currently, for BigInts C<$e> will be always 0, except for NaN, +inf and -inf, |
2704 | where it will be NaN; and for $x == 0, where it will be 1 |
2705 | (to be compatible with Math::BigFloat's internal representation of a zero as |
2706 | C<0E1>). |
58cde26e |
2707 | |
2708 | C<$m> will always be a copy of the original number. The relation between $e |
b22b3e31 |
2709 | and $m might change in the future, but will always be equivalent in a |
0716bf9b |
2710 | numerical sense, e.g. $m might get minimized. |
2711 | |
58cde26e |
2712 | =head1 EXAMPLES |
2713 | |
394e6ffb |
2714 | use Math::BigInt; |
574bacfe |
2715 | |
2716 | sub bint { Math::BigInt->new(shift); } |
2717 | |
394e6ffb |
2718 | $x = Math::BigInt->bstr("1234") # string "1234" |
58cde26e |
2719 | $x = "$x"; # same as bstr() |
58cde26e |
2720 | $x = Math::BigInt->bneg("1234"); # Bigint "-1234" |
2721 | $x = Math::BigInt->babs("-12345"); # Bigint "12345" |
2722 | $x = Math::BigInt->bnorm("-0 00"); # BigInt "0" |
2723 | $x = bint(1) + bint(2); # BigInt "3" |
2724 | $x = bint(1) + "2"; # ditto (auto-BigIntify of "2") |
2725 | $x = bint(1); # BigInt "1" |
2726 | $x = $x + 5 / 2; # BigInt "3" |
2727 | $x = $x ** 3; # BigInt "27" |
2728 | $x *= 2; # BigInt "54" |
394e6ffb |
2729 | $x = Math::BigInt->new(0); # BigInt "0" |
58cde26e |
2730 | $x--; # BigInt "-1" |
2731 | $x = Math::BigInt->badd(4,5) # BigInt "9" |
58cde26e |
2732 | print $x->bsstr(); # 9e+0 |
a5f75d66 |
2733 | |
0716bf9b |
2734 | Examples for rounding: |
2735 | |
2736 | use Math::BigFloat; |
2737 | use Test; |
2738 | |
2739 | $x = Math::BigFloat->new(123.4567); |
2740 | $y = Math::BigFloat->new(123.456789); |
394e6ffb |
2741 | Math::BigFloat->accuracy(4); # no more A than 4 |
0716bf9b |
2742 | |
2743 | ok ($x->copy()->fround(),123.4); # even rounding |
2744 | print $x->copy()->fround(),"\n"; # 123.4 |
2745 | Math::BigFloat->round_mode('odd'); # round to odd |
2746 | print $x->copy()->fround(),"\n"; # 123.5 |
394e6ffb |
2747 | Math::BigFloat->accuracy(5); # no more A than 5 |
0716bf9b |
2748 | Math::BigFloat->round_mode('odd'); # round to odd |
2749 | print $x->copy()->fround(),"\n"; # 123.46 |
2750 | $y = $x->copy()->fround(4),"\n"; # A = 4: 123.4 |
2751 | print "$y, ",$y->accuracy(),"\n"; # 123.4, 4 |
2752 | |
394e6ffb |
2753 | Math::BigFloat->accuracy(undef); # A not important now |
2754 | Math::BigFloat->precision(2); # P important |
2755 | print $x->copy()->bnorm(),"\n"; # 123.46 |
2756 | print $x->copy()->fround(),"\n"; # 123.46 |
0716bf9b |
2757 | |
bd05a461 |
2758 | Examples for converting: |
2759 | |
2760 | my $x = Math::BigInt->new('0b1'.'01' x 123); |
2761 | print "bin: ",$x->as_bin()," hex:",$x->as_hex()," dec: ",$x,"\n"; |
2762 | |
b3ac6de7 |
2763 | =head1 Autocreating constants |
2764 | |
58cde26e |
2765 | After C<use Math::BigInt ':constant'> all the B<integer> decimal constants |
2766 | in the given scope are converted to C<Math::BigInt>. This conversion |
b3ac6de7 |
2767 | happens at compile time. |
2768 | |
b22b3e31 |
2769 | In particular, |
b3ac6de7 |
2770 | |
58cde26e |
2771 | perl -MMath::BigInt=:constant -e 'print 2**100,"\n"' |
2772 | |
2773 | prints the integer value of C<2**100>. Note that without conversion of |
0716bf9b |
2774 | constants the expression 2**100 will be calculated as perl scalar. |
58cde26e |
2775 | |
2776 | Please note that strings and floating point constants are not affected, |
2777 | so that |
2778 | |
2779 | use Math::BigInt qw/:constant/; |
2780 | |
2781 | $x = 1234567890123456789012345678901234567890 |
2782 | + 123456789123456789; |
b22b3e31 |
2783 | $y = '1234567890123456789012345678901234567890' |
58cde26e |
2784 | + '123456789123456789'; |
b3ac6de7 |
2785 | |
b22b3e31 |
2786 | do not work. You need an explicit Math::BigInt->new() around one of the |
394e6ffb |
2787 | operands. You should also quote large constants to protect loss of precision: |
2788 | |
2789 | use Math::Bigint; |
2790 | |
2791 | $x = Math::BigInt->new('1234567889123456789123456789123456789'); |
2792 | |
2793 | Without the quotes Perl would convert the large number to a floating point |
2794 | constant at compile time and then hand the result to BigInt, which results in |
2795 | an truncated result or a NaN. |
58cde26e |
2796 | |
2797 | =head1 PERFORMANCE |
2798 | |
2799 | Using the form $x += $y; etc over $x = $x + $y is faster, since a copy of $x |
2800 | must be made in the second case. For long numbers, the copy can eat up to 20% |
b22b3e31 |
2801 | of the work (in the case of addition/subtraction, less for |
58cde26e |
2802 | multiplication/division). If $y is very small compared to $x, the form |
2803 | $x += $y is MUCH faster than $x = $x + $y since making the copy of $x takes |
2804 | more time then the actual addition. |
2805 | |
b22b3e31 |
2806 | With a technique called copy-on-write, the cost of copying with overload could |
394e6ffb |
2807 | be minimized or even completely avoided. A test implementation of COW did show |
2808 | performance gains for overloaded math, but introduced a performance loss due |
2809 | to a constant overhead for all other operatons. |
2810 | |
2811 | The rewritten version of this module is slower on certain operations, like |
2812 | new(), bstr() and numify(). The reason are that it does now more work and |
2813 | handles more cases. The time spent in these operations is usually gained in |
2814 | the other operations so that programs on the average should get faster. If |
2815 | they don't, please contect the author. |
58cde26e |
2816 | |
394e6ffb |
2817 | Some operations may be slower for small numbers, but are significantly faster |
2818 | for big numbers. Other operations are now constant (O(1), like bneg(), babs() |
2819 | etc), instead of O(N) and thus nearly always take much less time. These |
2820 | optimizations were done on purpose. |
58cde26e |
2821 | |
574bacfe |
2822 | If you find the Calc module to slow, try to install any of the replacement |
2823 | modules and see if they help you. |
b3ac6de7 |
2824 | |
574bacfe |
2825 | =head2 Alternative math libraries |
0716bf9b |
2826 | |
2827 | You can use an alternative library to drive Math::BigInt via: |
2828 | |
2829 | use Math::BigInt lib => 'Module'; |
2830 | |
394e6ffb |
2831 | See L<MATH LIBRARY> for more information. |
0716bf9b |
2832 | |
394e6ffb |
2833 | For more benchmark results see L<http://bloodgate.com/perl/benchmarks.html>. |
574bacfe |
2834 | |
a5f75d66 |
2835 | =head1 BUGS |
2836 | |
58cde26e |
2837 | =over 2 |
2838 | |
574bacfe |
2839 | =item Out of Memory! |
58cde26e |
2840 | |
2841 | Under Perl prior to 5.6.0 having an C<use Math::BigInt ':constant';> and |
2842 | C<eval()> in your code will crash with "Out of memory". This is probably an |
2843 | overload/exporter bug. You can workaround by not having C<eval()> |
574bacfe |
2844 | and ':constant' at the same time or upgrade your Perl to a newer version. |
2845 | |
2846 | =item Fails to load Calc on Perl prior 5.6.0 |
2847 | |
2848 | Since eval(' use ...') can not be used in conjunction with ':constant', BigInt |
2849 | will fall back to eval { require ... } when loading the math lib on Perls |
2850 | prior to 5.6.0. This simple replaces '::' with '/' and thus might fail on |
2851 | filesystems using a different seperator. |
58cde26e |
2852 | |
2853 | =back |
2854 | |
2855 | =head1 CAVEATS |
2856 | |
2857 | Some things might not work as you expect them. Below is documented what is |
2858 | known to be troublesome: |
2859 | |
2860 | =over 1 |
2861 | |
2862 | =item stringify, bstr(), bsstr() and 'cmp' |
2863 | |
2864 | Both stringify and bstr() now drop the leading '+'. The old code would return |
2865 | '+3', the new returns '3'. This is to be consistent with Perl and to make |
2866 | cmp (especially with overloading) to work as you expect. It also solves |
2867 | problems with Test.pm, it's ok() uses 'eq' internally. |
2868 | |
2869 | Mark said, when asked about to drop the '+' altogether, or make only cmp work: |
2870 | |
2871 | I agree (with the first alternative), don't add the '+' on positive |
2872 | numbers. It's not as important anymore with the new internal |
2873 | form for numbers. It made doing things like abs and neg easier, |
2874 | but those have to be done differently now anyway. |
2875 | |
2876 | So, the following examples will now work all as expected: |
2877 | |
2878 | use Test; |
2879 | BEGIN { plan tests => 1 } |
2880 | use Math::BigInt; |
2881 | |
2882 | my $x = new Math::BigInt 3*3; |
2883 | my $y = new Math::BigInt 3*3; |
2884 | |
2885 | ok ($x,3*3); |
2886 | print "$x eq 9" if $x eq $y; |
2887 | print "$x eq 9" if $x eq '9'; |
2888 | print "$x eq 9" if $x eq 3*3; |
2889 | |
2890 | Additionally, the following still works: |
2891 | |
2892 | print "$x == 9" if $x == $y; |
2893 | print "$x == 9" if $x == 9; |
2894 | print "$x == 9" if $x == 3*3; |
2895 | |
2896 | There is now a C<bsstr()> method to get the string in scientific notation aka |
2897 | C<1e+2> instead of C<100>. Be advised that overloaded 'eq' always uses bstr() |
2898 | for comparisation, but Perl will represent some numbers as 100 and others |
2899 | as 1e+308. If in doubt, convert both arguments to Math::BigInt before doing eq: |
2900 | |
2901 | use Test; |
2902 | BEGIN { plan tests => 3 } |
2903 | use Math::BigInt; |
2904 | |
2905 | $x = Math::BigInt->new('1e56'); $y = 1e56; |
2906 | ok ($x,$y); # will fail |
2907 | ok ($x->bsstr(),$y); # okay |
2908 | $y = Math::BigInt->new($y); |
2909 | ok ($x,$y); # okay |
2910 | |
394e6ffb |
2911 | Alternatively, simple use <=> for comparisations, that will get it always |
2912 | right. There is not yet a way to get a number automatically represented as |
2913 | a string that matches exactly the way Perl represents it. |
574bacfe |
2914 | |
58cde26e |
2915 | =item int() |
2916 | |
2917 | C<int()> will return (at least for Perl v5.7.1 and up) another BigInt, not a |
2918 | Perl scalar: |
2919 | |
2920 | $x = Math::BigInt->new(123); |
2921 | $y = int($x); # BigInt 123 |
2922 | $x = Math::BigFloat->new(123.45); |
2923 | $y = int($x); # BigInt 123 |
2924 | |
2925 | In all Perl versions you can use C<as_number()> for the same effect: |
2926 | |
2927 | $x = Math::BigFloat->new(123.45); |
2928 | $y = $x->as_number(); # BigInt 123 |
2929 | |
2930 | This also works for other subclasses, like Math::String. |
2931 | |
574bacfe |
2932 | It is yet unlcear whether overloaded int() should return a scalar or a BigInt. |
2933 | |
dccbb853 |
2934 | =item length |
58cde26e |
2935 | |
2936 | The following will probably not do what you expect: |
2937 | |
bd05a461 |
2938 | $c = Math::BigInt->new(123); |
2939 | print $c->length(),"\n"; # prints 30 |
2940 | |
2941 | It prints both the number of digits in the number and in the fraction part |
2942 | since print calls C<length()> in list context. Use something like: |
2943 | |
2944 | print scalar $c->length(),"\n"; # prints 3 |
2945 | |
2946 | =item bdiv |
2947 | |
2948 | The following will probably not do what you expect: |
2949 | |
58cde26e |
2950 | print $c->bdiv(10000),"\n"; |
2951 | |
dccbb853 |
2952 | It prints both quotient and remainder since print calls C<bdiv()> in list |
58cde26e |
2953 | context. Also, C<bdiv()> will modify $c, so be carefull. You probably want |
2954 | to use |
2955 | |
2956 | print $c / 10000,"\n"; |
2957 | print scalar $c->bdiv(10000),"\n"; # or if you want to modify $c |
2958 | |
2959 | instead. |
2960 | |
2961 | The quotient is always the greatest integer less than or equal to the |
2962 | real-valued quotient of the two operands, and the remainder (when it is |
2963 | nonzero) always has the same sign as the second operand; so, for |
2964 | example, |
2965 | |
dccbb853 |
2966 | 1 / 4 => ( 0, 1) |
2967 | 1 / -4 => (-1,-3) |
2968 | -3 / 4 => (-1, 1) |
2969 | -3 / -4 => ( 0,-3) |
2970 | -11 / 2 => (-5,1) |
2971 | 11 /-2 => (-5,-1) |
58cde26e |
2972 | |
2973 | As a consequence, the behavior of the operator % agrees with the |
2974 | behavior of Perl's built-in % operator (as documented in the perlop |
2975 | manpage), and the equation |
2976 | |
2977 | $x == ($x / $y) * $y + ($x % $y) |
2978 | |
2979 | holds true for any $x and $y, which justifies calling the two return |
dccbb853 |
2980 | values of bdiv() the quotient and remainder. The only exception to this rule |
2981 | are when $y == 0 and $x is negative, then the remainder will also be |
2982 | negative. See below under "infinity handling" for the reasoning behing this. |
58cde26e |
2983 | |
2984 | Perl's 'use integer;' changes the behaviour of % and / for scalars, but will |
2985 | not change BigInt's way to do things. This is because under 'use integer' Perl |
2986 | will do what the underlying C thinks is right and this is different for each |
2987 | system. If you need BigInt's behaving exactly like Perl's 'use integer', bug |
2988 | the author to implement it ;) |
2989 | |
dccbb853 |
2990 | =item infinity handling |
2991 | |
2992 | Here are some examples that explain the reasons why certain results occur while |
2993 | handling infinity: |
2994 | |
2995 | The following table shows the result of the division and the remainder, so that |
2996 | the equation above holds true. Some "ordinary" cases are strewn in to show more |
2997 | clearly the reasoning: |
2998 | |
2999 | A / B = C, R so that C * B + R = A |
3000 | ========================================================= |
3001 | 5 / 8 = 0, 5 0 * 8 + 5 = 5 |
3002 | 0 / 8 = 0, 0 0 * 8 + 0 = 0 |
3003 | 0 / inf = 0, 0 0 * inf + 0 = 0 |
3004 | 0 /-inf = 0, 0 0 * -inf + 0 = 0 |
3005 | 5 / inf = 0, 5 0 * inf + 5 = 5 |
3006 | 5 /-inf = 0, 5 0 * -inf + 5 = 5 |
3007 | -5/ inf = 0, -5 0 * inf + -5 = -5 |
3008 | -5/-inf = 0, -5 0 * -inf + -5 = -5 |
3009 | inf/ 5 = inf, 0 inf * 5 + 0 = inf |
3010 | -inf/ 5 = -inf, 0 -inf * 5 + 0 = -inf |
3011 | inf/ -5 = -inf, 0 -inf * -5 + 0 = inf |
3012 | -inf/ -5 = inf, 0 inf * -5 + 0 = -inf |
3013 | 5/ 5 = 1, 0 1 * 5 + 0 = 5 |
3014 | -5/ -5 = 1, 0 1 * -5 + 0 = -5 |
3015 | inf/ inf = 1, 0 1 * inf + 0 = inf |
3016 | -inf/-inf = 1, 0 1 * -inf + 0 = -inf |
3017 | inf/-inf = -1, 0 -1 * -inf + 0 = inf |
3018 | -inf/ inf = -1, 0 1 * -inf + 0 = -inf |
3019 | 8/ 0 = inf, 8 inf * 0 + 8 = 8 |
3020 | inf/ 0 = inf, inf inf * 0 + inf = inf |
3021 | 0/ 0 = NaN |
3022 | |
3023 | These cases below violate the "remainder has the sign of the second of the two |
3024 | arguments", since they wouldn't match up otherwise. |
3025 | |
3026 | A / B = C, R so that C * B + R = A |
3027 | ======================================================== |
3028 | -inf/ 0 = -inf, -inf -inf * 0 + inf = -inf |
3029 | -8/ 0 = -inf, -8 -inf * 0 + 8 = -8 |
3030 | |
58cde26e |
3031 | =item Modifying and = |
3032 | |
3033 | Beware of: |
3034 | |
3035 | $x = Math::BigFloat->new(5); |
3036 | $y = $x; |
3037 | |
3038 | It will not do what you think, e.g. making a copy of $x. Instead it just makes |
3039 | a second reference to the B<same> object and stores it in $y. Thus anything |
17baacb7 |
3040 | that modifies $x (except overloaded operators) will modify $y, and vice versa. |
3041 | Or in other words, C<=> is only safe if you modify your BigInts only via |
3042 | overloaded math. As soon as you use a method call it breaks: |
58cde26e |
3043 | |
3044 | $x->bmul(2); |
3045 | print "$x, $y\n"; # prints '10, 10' |
3046 | |
3047 | If you want a true copy of $x, use: |
3048 | |
3049 | $y = $x->copy(); |
3050 | |
17baacb7 |
3051 | You can also chain the calls like this, this will make first a copy and then |
3052 | multiply it by 2: |
3053 | |
3054 | $y = $x->copy()->bmul(2); |
3055 | |
b22b3e31 |
3056 | See also the documentation for overload.pm regarding C<=>. |
58cde26e |
3057 | |
3058 | =item bpow |
3059 | |
3060 | C<bpow()> (and the rounding functions) now modifies the first argument and |
574bacfe |
3061 | returns it, unlike the old code which left it alone and only returned the |
58cde26e |
3062 | result. This is to be consistent with C<badd()> etc. The first three will |
3063 | modify $x, the last one won't: |
3064 | |
3065 | print bpow($x,$i),"\n"; # modify $x |
3066 | print $x->bpow($i),"\n"; # ditto |
3067 | print $x **= $i,"\n"; # the same |
3068 | print $x ** $i,"\n"; # leave $x alone |
3069 | |
3070 | The form C<$x **= $y> is faster than C<$x = $x ** $y;>, though. |
3071 | |
3072 | =item Overloading -$x |
3073 | |
3074 | The following: |
3075 | |
3076 | $x = -$x; |
3077 | |
3078 | is slower than |
3079 | |
3080 | $x->bneg(); |
3081 | |
3082 | since overload calls C<sub($x,0,1);> instead of C<neg($x)>. The first variant |
3083 | needs to preserve $x since it does not know that it later will get overwritten. |
0716bf9b |
3084 | This makes a copy of $x and takes O(N), but $x->bneg() is O(1). |
58cde26e |
3085 | |
394e6ffb |
3086 | With Copy-On-Write, this issue would be gone, but C-o-W is not implemented |
3087 | since it is slower for all other things. |
58cde26e |
3088 | |
3089 | =item Mixing different object types |
3090 | |
3091 | In Perl you will get a floating point value if you do one of the following: |
3092 | |
3093 | $float = 5.0 + 2; |
3094 | $float = 2 + 5.0; |
3095 | $float = 5 / 2; |
3096 | |
3097 | With overloaded math, only the first two variants will result in a BigFloat: |
3098 | |
3099 | use Math::BigInt; |
3100 | use Math::BigFloat; |
3101 | |
3102 | $mbf = Math::BigFloat->new(5); |
3103 | $mbi2 = Math::BigInteger->new(5); |
3104 | $mbi = Math::BigInteger->new(2); |
3105 | |
3106 | # what actually gets called: |
3107 | $float = $mbf + $mbi; # $mbf->badd() |
3108 | $float = $mbf / $mbi; # $mbf->bdiv() |
3109 | $integer = $mbi + $mbf; # $mbi->badd() |
3110 | $integer = $mbi2 / $mbi; # $mbi2->bdiv() |
3111 | $integer = $mbi2 / $mbf; # $mbi2->bdiv() |
3112 | |
3113 | This is because math with overloaded operators follows the first (dominating) |
394e6ffb |
3114 | operand, and the operation of that is called and returns thus the result. So, |
58cde26e |
3115 | Math::BigInt::bdiv() will always return a Math::BigInt, regardless whether |
3116 | the result should be a Math::BigFloat or the second operant is one. |
3117 | |
3118 | To get a Math::BigFloat you either need to call the operation manually, |
3119 | make sure the operands are already of the proper type or casted to that type |
3120 | via Math::BigFloat->new(): |
3121 | |
3122 | $float = Math::BigFloat->new($mbi2) / $mbi; # = 2.5 |
3123 | |
3124 | Beware of simple "casting" the entire expression, this would only convert |
3125 | the already computed result: |
3126 | |
3127 | $float = Math::BigFloat->new($mbi2 / $mbi); # = 2.0 thus wrong! |
3128 | |
0716bf9b |
3129 | Beware also of the order of more complicated expressions like: |
58cde26e |
3130 | |
3131 | $integer = ($mbi2 + $mbi) / $mbf; # int / float => int |
3132 | $integer = $mbi2 / Math::BigFloat->new($mbi); # ditto |
3133 | |
3134 | If in doubt, break the expression into simpler terms, or cast all operands |
3135 | to the desired resulting type. |
3136 | |
3137 | Scalar values are a bit different, since: |
3138 | |
3139 | $float = 2 + $mbf; |
3140 | $float = $mbf + 2; |
3141 | |
3142 | will both result in the proper type due to the way the overloaded math works. |
3143 | |
3144 | This section also applies to other overloaded math packages, like Math::String. |
3145 | |
3146 | =item bsqrt() |
3147 | |
394e6ffb |
3148 | C<bsqrt()> works only good if the result is a big integer, e.g. the square |
58cde26e |
3149 | root of 144 is 12, but from 12 the square root is 3, regardless of rounding |
3150 | mode. |
3151 | |
3152 | If you want a better approximation of the square root, then use: |
3153 | |
3154 | $x = Math::BigFloat->new(12); |
394e6ffb |
3155 | Math::BigFloat->precision(0); |
58cde26e |
3156 | Math::BigFloat->round_mode('even'); |
3157 | print $x->copy->bsqrt(),"\n"; # 4 |
3158 | |
394e6ffb |
3159 | Math::BigFloat->precision(2); |
58cde26e |
3160 | print $x->bsqrt(),"\n"; # 3.46 |
3161 | print $x->bsqrt(3),"\n"; # 3.464 |
3162 | |
3163 | =back |
3164 | |
3165 | =head1 LICENSE |
3166 | |
3167 | This program is free software; you may redistribute it and/or modify it under |
3168 | the same terms as Perl itself. |
a5f75d66 |
3169 | |
0716bf9b |
3170 | =head1 SEE ALSO |
3171 | |
027dc388 |
3172 | L<Math::BigFloat> and L<Math::Big> as well as L<Math::BigInt::BitVect>, |
3173 | L<Math::BigInt::Pari> and L<Math::BigInt::GMP>. |
0716bf9b |
3174 | |
027dc388 |
3175 | The package at |
3176 | L<http://search.cpan.org/search?mode=module&query=Math%3A%3ABigInt> contains |
3177 | more documentation including a full version history, testcases, empty |
3178 | subclass files and benchmarks. |
574bacfe |
3179 | |
58cde26e |
3180 | =head1 AUTHORS |
a5f75d66 |
3181 | |
58cde26e |
3182 | Original code by Mark Biggar, overloaded interface by Ilya Zakharevich. |
3183 | Completely rewritten by Tels http://bloodgate.com in late 2000, 2001. |
a5f75d66 |
3184 | |
3185 | =cut |