Commit | Line | Data |
58cde26e |
1 | #!/usr/bin/perl -w |
2 | |
58cde26e |
3 | # The following hash values are internally used: |
4 | # _e: exponent (BigInt) |
5 | # _m: mantissa (absolute BigInt) |
6 | # sign: +,-,"NaN" if not a number |
7 | # _a: accuracy |
8 | # _p: precision |
0716bf9b |
9 | # _f: flags, used to signal MBI not to touch our private parts |
58cde26e |
10 | # _cow: Copy-On-Write (NRY) |
11 | |
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12 | package Math::BigFloat; |
13 | |
0716bf9b |
14 | $VERSION = 1.16; |
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15 | require 5.005; |
16 | use Exporter; |
0716bf9b |
17 | use Math::BigInt qw/objectify/; |
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18 | @ISA = qw( Exporter Math::BigInt); |
19 | # can not export bneg/babs since the are only in MBI |
20 | @EXPORT_OK = qw( |
21 | bcmp |
22 | badd bmul bdiv bmod bnorm bsub |
23 | bgcd blcm bround bfround |
24 | bpow bnan bzero bfloor bceil |
25 | bacmp bstr binc bdec bint binf |
0716bf9b |
26 | is_odd is_even is_nan is_inf is_positive is_negative |
58cde26e |
27 | is_zero is_one sign |
28 | ); |
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29 | |
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30 | #@EXPORT = qw( ); |
31 | use strict; |
32 | use vars qw/$AUTOLOAD $accuracy $precision $div_scale $rnd_mode/; |
33 | my $class = "Math::BigFloat"; |
a0d0e21e |
34 | |
a5f75d66 |
35 | use overload |
58cde26e |
36 | '<=>' => sub { |
37 | $_[2] ? |
38 | $class->bcmp($_[1],$_[0]) : |
39 | $class->bcmp($_[0],$_[1])}, |
0716bf9b |
40 | 'int' => sub { $_[0]->as_number() }, # 'trunc' to bigint |
a5f75d66 |
41 | ; |
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42 | |
0716bf9b |
43 | ############################################################################## |
44 | # global constants, flags and accessory |
45 | |
46 | use constant MB_NEVER_ROUND => 0x0001; |
47 | |
58cde26e |
48 | # are NaNs ok? |
49 | my $NaNOK=1; |
58cde26e |
50 | # constant for easier life |
51 | my $nan = 'NaN'; |
52 | my $ten = Math::BigInt->new(10); # shortcut for speed |
53 | |
54 | # Rounding modes one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc' |
55 | $rnd_mode = 'even'; |
56 | $accuracy = undef; |
57 | $precision = undef; |
58 | $div_scale = 40; |
59 | |
60 | { |
61 | # checks for AUTOLOAD |
62 | my %methods = map { $_ => 1 } |
63 | qw / fadd fsub fmul fdiv fround ffround fsqrt fmod fstr fsstr fpow fnorm |
64 | fabs fneg fint fcmp fzero fnan finc fdec |
65 | /; |
66 | |
67 | sub method_valid { return exists $methods{$_[0]||''}; } |
a0d0e21e |
68 | } |
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69 | |
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70 | ############################################################################## |
71 | # constructors |
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72 | |
58cde26e |
73 | sub new |
74 | { |
75 | # create a new BigFloat object from a string or another bigfloat object. |
76 | # _e: exponent |
77 | # _m: mantissa |
78 | # sign => sign (+/-), or "NaN" |
a0d0e21e |
79 | |
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80 | my $class = shift; |
81 | |
82 | my $wanted = shift; # avoid numify call by not using || here |
83 | return $class->bzero() if !defined $wanted; # default to 0 |
84 | return $wanted->copy() if ref($wanted) eq $class; |
a0d0e21e |
85 | |
58cde26e |
86 | my $round = shift; $round = 0 if !defined $round; # no rounding as default |
87 | my $self = {}; bless $self, $class; |
b22b3e31 |
88 | # shortcut for bigints and its subclasses |
0716bf9b |
89 | if ((ref($wanted)) && (ref($wanted) ne $class)) |
58cde26e |
90 | { |
0716bf9b |
91 | $self->{_m} = $wanted->as_number(); # get us a bigint copy |
58cde26e |
92 | $self->{_e} = Math::BigInt->new(0); |
93 | $self->{_m}->babs(); |
94 | $self->{sign} = $wanted->sign(); |
0716bf9b |
95 | return $self->bnorm(); |
58cde26e |
96 | } |
97 | # got string |
98 | # handle '+inf', '-inf' first |
99 | if ($wanted =~ /^[+-]inf$/) |
100 | { |
101 | $self->{_e} = Math::BigInt->new(0); |
102 | $self->{_m} = Math::BigInt->new(0); |
103 | $self->{sign} = $wanted; |
0716bf9b |
104 | return $self->bnorm(); |
58cde26e |
105 | } |
106 | #print "new string '$wanted'\n"; |
107 | my ($mis,$miv,$mfv,$es,$ev) = Math::BigInt::_split(\$wanted); |
108 | if (!ref $mis) |
109 | { |
110 | die "$wanted is not a number initialized to $class" if !$NaNOK; |
111 | $self->{_e} = Math::BigInt->new(0); |
112 | $self->{_m} = Math::BigInt->new(0); |
113 | $self->{sign} = $nan; |
114 | } |
115 | else |
116 | { |
117 | # make integer from mantissa by adjusting exp, then convert to bigint |
118 | $self->{_e} = Math::BigInt->new("$$es$$ev"); # exponent |
119 | $self->{_m} = Math::BigInt->new("$$mis$$miv$$mfv"); # create mantissa |
120 | # 3.123E0 = 3123E-3, and 3.123E-2 => 3123E-5 |
121 | $self->{_e} -= CORE::length($$mfv); |
122 | $self->{sign} = $self->{_m}->sign(); $self->{_m}->babs(); |
123 | } |
0716bf9b |
124 | #print "$wanted => $self->{sign} $self->{value}\n"; |
58cde26e |
125 | $self->bnorm(); # first normalize |
126 | # if any of the globals is set, round to them and thus store them insid $self |
127 | $self->round($accuracy,$precision,$rnd_mode) |
128 | if defined $accuracy || defined $precision; |
129 | return $self; |
130 | } |
a0d0e21e |
131 | |
58cde26e |
132 | # some shortcuts for easier life |
133 | sub bfloat |
134 | { |
135 | # exportable version of new |
58cde26e |
136 | return $class->new(@_); |
137 | } |
138 | |
139 | sub bint |
140 | { |
141 | # exportable version of new |
58cde26e |
142 | return $class->new(@_,0)->bround(0,'trunc'); |
143 | } |
144 | |
145 | sub bnan |
146 | { |
147 | # create a bigfloat 'NaN', if given a BigFloat, set it to 'NaN' |
148 | my $self = shift; |
149 | $self = $class if !defined $self; |
150 | if (!ref($self)) |
288d023a |
151 | { |
58cde26e |
152 | my $c = $self; $self = {}; bless $self, $c; |
a0d0e21e |
153 | } |
58cde26e |
154 | $self->{_e} = new Math::BigInt 0; |
155 | $self->{_m} = new Math::BigInt 0; |
156 | $self->{sign} = $nan; |
58cde26e |
157 | return $self; |
158 | } |
a0d0e21e |
159 | |
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160 | sub binf |
161 | { |
162 | # create a bigfloat '+-inf', if given a BigFloat, set it to '+-inf' |
163 | my $self = shift; |
164 | my $sign = shift; $sign = '+' if !defined $sign || $sign ne '-'; |
a0d0e21e |
165 | |
58cde26e |
166 | $self = $class if !defined $self; |
167 | if (!ref($self)) |
168 | { |
169 | my $c = $self; $self = {}; bless $self, $c; |
170 | } |
171 | $self->{_e} = new Math::BigInt 0; |
172 | $self->{_m} = new Math::BigInt 0; |
173 | $self->{sign} = $sign.'inf'; |
58cde26e |
174 | return $self; |
175 | } |
a0d0e21e |
176 | |
58cde26e |
177 | sub bzero |
178 | { |
179 | # create a bigfloat '+0', if given a BigFloat, set it to 0 |
180 | my $self = shift; |
181 | $self = $class if !defined $self; |
182 | if (!ref($self)) |
183 | { |
184 | my $c = $self; $self = {}; bless $self, $c; |
185 | } |
186 | $self->{_m} = new Math::BigInt 0; |
187 | $self->{_e} = new Math::BigInt 1; |
188 | $self->{sign} = '+'; |
58cde26e |
189 | return $self; |
190 | } |
191 | |
192 | ############################################################################## |
193 | # string conversation |
194 | |
195 | sub bstr |
196 | { |
197 | # (ref to BFLOAT or num_str ) return num_str |
198 | # Convert number from internal format to (non-scientific) string format. |
199 | # internal format is always normalized (no leading zeros, "-0" => "+0") |
58cde26e |
200 | my ($self,$x) = objectify(1,@_); |
201 | |
202 | #return "Oups! e was $nan" if $x->{_e}->{sign} eq $nan; |
203 | #return "Oups! m was $nan" if $x->{_m}->{sign} eq $nan; |
204 | return $x->{sign} if $x->{sign} !~ /^[+-]$/; |
205 | return '0' if $x->is_zero(); |
206 | |
207 | my $es = $x->{_m}->bstr(); |
208 | if ($x->{_e}->is_zero()) |
209 | { |
210 | $es = $x->{sign}.$es if $x->{sign} eq '-'; |
211 | return $es; |
212 | } |
213 | |
214 | if ($x->{_e}->sign() eq '-') |
215 | { |
216 | if ($x->{_e} <= -CORE::length($es)) |
217 | { |
218 | # print "style: 0.xxxx\n"; |
219 | my $r = $x->{_e}->copy(); $r->babs()->bsub( CORE::length($es) ); |
220 | $es = '0.'. ('0' x $r) . $es; |
221 | } |
222 | else |
223 | { |
224 | # print "insert '.' at $x->{_e} in '$es'\n"; |
225 | substr($es,$x->{_e},0) = '.'; |
82cf049f |
226 | } |
82cf049f |
227 | } |
58cde26e |
228 | else |
229 | { |
230 | # expand with zeros |
231 | $es .= '0' x $x->{_e}; |
232 | } |
233 | $es = $x->{sign}.$es if $x->{sign} eq '-'; |
234 | return $es; |
82cf049f |
235 | } |
f216259d |
236 | |
58cde26e |
237 | sub bsstr |
238 | { |
239 | # (ref to BFLOAT or num_str ) return num_str |
240 | # Convert number from internal format to scientific string format. |
241 | # internal format is always normalized (no leading zeros, "-0E0" => "+0E0") |
58cde26e |
242 | my ($self,$x) = objectify(1,@_); |
a0d0e21e |
243 | |
58cde26e |
244 | return "Oups! e was $nan" if $x->{_e}->{sign} eq $nan; |
245 | return "Oups! m was $nan" if $x->{_m}->{sign} eq $nan; |
246 | return $x->{sign} if $x->{sign} !~ /^[+-]$/; |
247 | my $sign = $x->{_e}->{sign}; $sign = '' if $sign eq '-'; |
248 | my $sep = 'e'.$sign; |
249 | return $x->{_m}->bstr().$sep.$x->{_e}->bstr(); |
250 | } |
251 | |
252 | sub numify |
253 | { |
254 | # Make a number from a BigFloat object |
255 | # simple return string and let Perl's atoi() handle the rest |
58cde26e |
256 | my ($self,$x) = objectify(1,@_); |
257 | return $x->bsstr(); |
258 | } |
a0d0e21e |
259 | |
58cde26e |
260 | ############################################################################## |
261 | # public stuff (usually prefixed with "b") |
262 | |
263 | # really? Just for exporting them is not what I had in mind |
264 | #sub babs |
265 | # { |
266 | # $class->SUPER::babs($class,@_); |
267 | # } |
268 | #sub bneg |
269 | # { |
270 | # $class->SUPER::bneg($class,@_); |
271 | # } |
272 | #sub bnot |
273 | # { |
274 | # $class->SUPER::bnot($class,@_); |
275 | # } |
276 | |
277 | sub bcmp |
278 | { |
279 | # Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort) |
280 | # (BFLOAT or num_str, BFLOAT or num_str) return cond_code |
281 | my ($self,$x,$y) = objectify(2,@_); |
58cde26e |
282 | |
0716bf9b |
283 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
284 | { |
285 | # handle +-inf and NaN |
286 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
287 | return 0 if ($x->{sign} eq $y->{sign}) && ($x->{sign} =~ /^[+-]inf$/); |
288 | return +1 if $x->{sign} eq '+inf'; |
289 | return -1 if $x->{sign} eq '-inf'; |
290 | return -1 if $y->{sign} eq '+inf'; |
291 | return +1 if $y->{sign} eq '-inf'; |
292 | } |
293 | |
294 | # check sign for speed first |
58cde26e |
295 | return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; |
296 | return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0 |
297 | |
298 | return 0 if $x->is_zero() && $y->is_zero(); # 0 <=> 0 |
299 | return -1 if $x->is_zero() && $y->{sign} eq '+'; # 0 <=> +y |
300 | return 1 if $y->is_zero() && $x->{sign} eq '+'; # +x <=> 0 |
301 | |
302 | # adjust so that exponents are equal |
303 | my $lx = $x->{_m}->length() + $x->{_e}; |
304 | my $ly = $y->{_m}->length() + $y->{_e}; |
305 | # print "x $x y $y lx $lx ly $ly\n"; |
306 | my $l = $lx - $ly; $l = -$l if $x->{sign} eq '-'; |
307 | # print "$l $x->{sign}\n"; |
308 | return $l if $l != 0; |
309 | |
0716bf9b |
310 | # lengths are equal, so compare mantissa, if equal, compare exponents |
b22b3e31 |
311 | # this assumes normalized numbers (no trailing zeros etc!) |
58cde26e |
312 | my $rc = $x->{_m} <=> $y->{_m} || $x->{_e} <=> $y->{_e}; |
313 | $rc = -$rc if $x->{sign} eq '-'; # -124 < -123 |
314 | return $rc; |
315 | } |
316 | |
317 | sub bacmp |
318 | { |
319 | # Compares 2 values, ignoring their signs. |
320 | # Returns one of undef, <0, =0, >0. (suitable for sort) |
321 | # (BFLOAT or num_str, BFLOAT or num_str) return cond_code |
322 | my ($self,$x,$y) = objectify(2,@_); |
323 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
324 | |
325 | # signs are ignored, so check length |
326 | # length(x) is length(m)+e aka length of non-fraction part |
327 | # the longer one is bigger |
328 | my $l = $x->length() - $y->length(); |
329 | #print "$l\n"; |
330 | return $l if $l != 0; |
331 | #print "equal lengths\n"; |
332 | |
333 | # if both are equal long, make full compare |
334 | # first compare only the mantissa |
335 | # if mantissa are equal, compare fractions |
336 | |
337 | return $x->{_m} <=> $y->{_m} || $x->{_e} <=> $y->{_e}; |
338 | } |
a0d0e21e |
339 | |
58cde26e |
340 | sub badd |
341 | { |
342 | # add second arg (BFLOAT or string) to first (BFLOAT) (modifies first) |
343 | # return result as BFLOAT |
58cde26e |
344 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
345 | |
58cde26e |
346 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
0716bf9b |
347 | |
58cde26e |
348 | # speed: no add for 0+y or x+0 |
349 | return $x if $y->is_zero(); # x+0 |
350 | if ($x->is_zero()) # 0+y |
351 | { |
352 | # make copy, clobbering up x (modify in place!) |
353 | $x->{_e} = $y->{_e}->copy(); |
354 | $x->{_m} = $y->{_m}->copy(); |
355 | $x->{sign} = $y->{sign} || $nan; |
356 | return $x->round($a,$p,$r,$y); |
a0d0e21e |
357 | } |
58cde26e |
358 | |
359 | # take lower of the two e's and adapt m1 to it to match m2 |
360 | my $e = $y->{_e}; $e = Math::BigInt::bzero() if !defined $e; # if no BFLOAT |
361 | $e = $e - $x->{_e}; |
362 | my $add = $y->{_m}->copy(); |
363 | if ($e < 0) |
364 | { |
0716bf9b |
365 | # print "e < 0\n"; |
58cde26e |
366 | #print "\$x->{_m}: $x->{_m} "; |
367 | #print "\$x->{_e}: $x->{_e}\n"; |
368 | my $e1 = $e->copy()->babs(); |
369 | $x->{_m} *= (10 ** $e1); |
370 | $x->{_e} += $e; # need the sign of e |
371 | #$x->{_m} += $y->{_m}; |
372 | #print "\$x->{_m}: $x->{_m} "; |
373 | #print "\$x->{_e}: $x->{_e}\n"; |
374 | } |
375 | elsif ($e > 0) |
376 | { |
0716bf9b |
377 | # print "e > 0\n"; |
58cde26e |
378 | #print "\$x->{_m}: $x->{_m} \$y->{_m}: $y->{_m} \$e: $e ",ref($e),"\n"; |
379 | $add *= (10 ** $e); |
380 | #$x->{_m} += $y->{_m} * (10 ** $e); |
381 | #print "\$x->{_m}: $x->{_m}\n"; |
382 | } |
383 | # else: both e are same, so leave them |
384 | #print "badd $x->{sign}$x->{_m} + $y->{sign}$add\n"; |
385 | # fiddle with signs |
386 | $x->{_m}->{sign} = $x->{sign}; |
387 | $add->{sign} = $y->{sign}; |
388 | # finally do add/sub |
389 | $x->{_m} += $add; |
390 | # re-adjust signs |
391 | $x->{sign} = $x->{_m}->{sign}; |
392 | $x->{_m}->{sign} = '+'; |
0716bf9b |
393 | #$x->bnorm(); # delete trailing zeros |
58cde26e |
394 | return $x->round($a,$p,$r,$y); |
395 | } |
396 | |
397 | sub bsub |
398 | { |
0716bf9b |
399 | # (BigFloat or num_str, BigFloat or num_str) return BigFloat |
58cde26e |
400 | # subtract second arg from first, modify first |
401 | my ($self,$x,$y) = objectify(2,@_); |
a0d0e21e |
402 | |
58cde26e |
403 | $x->badd($y->bneg()); # badd does not leave internal zeros |
404 | $y->bneg(); # refix y, assumes no one reads $y in between |
0716bf9b |
405 | return $x; # badd() already normalized and rounded |
58cde26e |
406 | } |
407 | |
408 | sub binc |
409 | { |
410 | # increment arg by one |
411 | my ($self,$x,$a,$p,$r) = objectify(1,@_); |
58cde26e |
412 | $x->badd($self->_one())->round($a,$p,$r); |
413 | } |
414 | |
415 | sub bdec |
416 | { |
417 | # decrement arg by one |
418 | my ($self,$x,$a,$p,$r) = objectify(1,@_); |
58cde26e |
419 | $x->badd($self->_one('-'))->round($a,$p,$r); |
420 | } |
421 | |
422 | sub blcm |
423 | { |
424 | # (BINT or num_str, BINT or num_str) return BINT |
425 | # does not modify arguments, but returns new object |
426 | # Lowest Common Multiplicator |
58cde26e |
427 | |
428 | my ($self,@arg) = objectify(0,@_); |
429 | my $x = $self->new(shift @arg); |
430 | while (@arg) { $x = _lcm($x,shift @arg); } |
431 | $x; |
432 | } |
433 | |
434 | sub bgcd |
435 | { |
436 | # (BINT or num_str, BINT or num_str) return BINT |
437 | # does not modify arguments, but returns new object |
438 | # GCD -- Euclids algorithm Knuth Vol 2 pg 296 |
58cde26e |
439 | |
440 | my ($self,@arg) = objectify(0,@_); |
441 | my $x = $self->new(shift @arg); |
442 | while (@arg) { $x = _gcd($x,shift @arg); } |
443 | $x; |
444 | } |
445 | |
446 | sub is_zero |
447 | { |
448 | # return true if arg (BINT or num_str) is zero (array '+', '0') |
449 | my $x = shift; $x = $class->new($x) unless ref $x; |
450 | #my ($self,$x) = objectify(1,@_); |
58cde26e |
451 | return ($x->{sign} ne $nan && $x->{_m}->is_zero()); |
452 | } |
453 | |
454 | sub is_one |
455 | { |
456 | # return true if arg (BINT or num_str) is +1 (array '+', '1') |
457 | # or -1 if signis given |
458 | my $x = shift; $x = $class->new($x) unless ref $x; |
459 | #my ($self,$x) = objectify(1,@_); |
460 | my $sign = $_[2] || '+'; |
461 | return ($x->{sign} eq $sign && $x->{_e}->is_zero() && $x->{_m}->is_one()); |
462 | } |
463 | |
464 | sub is_odd |
465 | { |
b22b3e31 |
466 | # return true if arg (BINT or num_str) is odd or false if even |
58cde26e |
467 | my $x = shift; $x = $class->new($x) unless ref $x; |
468 | #my ($self,$x) = objectify(1,@_); |
0716bf9b |
469 | |
470 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
471 | return ($x->{_e}->is_zero() && $x->{_m}->is_odd()); |
58cde26e |
472 | } |
473 | |
474 | sub is_even |
475 | { |
b22b3e31 |
476 | # return true if arg (BINT or num_str) is even or false if odd |
58cde26e |
477 | my $x = shift; $x = $class->new($x) unless ref $x; |
478 | #my ($self,$x) = objectify(1,@_); |
0716bf9b |
479 | |
480 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
481 | return 1 if $x->{_m}->is_zero(); # 0e1 is even |
482 | return ($x->{_e}->is_zero() && $x->{_m}->is_even()); # 123.45 is never |
58cde26e |
483 | } |
484 | |
485 | sub bmul |
486 | { |
487 | # multiply two numbers -- stolen from Knuth Vol 2 pg 233 |
488 | # (BINT or num_str, BINT or num_str) return BINT |
489 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
58cde26e |
490 | |
0716bf9b |
491 | # print "mbf bmul $x->{_m}e$x->{_e} $y->{_m}e$y->{_e}\n"; |
58cde26e |
492 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
493 | |
58cde26e |
494 | # aEb * cEd = (a*c)E(b+d) |
495 | $x->{_m} = $x->{_m} * $y->{_m}; |
496 | #print "m: $x->{_m}\n"; |
497 | $x->{_e} = $x->{_e} + $y->{_e}; |
498 | #print "e: $x->{_m}\n"; |
499 | # adjust sign: |
500 | $x->{sign} = $x->{sign} ne $y->{sign} ? '-' : '+'; |
501 | #print "s: $x->{sign}\n"; |
0716bf9b |
502 | $x->bnorm(); |
58cde26e |
503 | return $x->round($a,$p,$r,$y); |
504 | } |
505 | |
506 | sub bdiv |
507 | { |
508 | # (dividend: BFLOAT or num_str, divisor: BFLOAT or num_str) return |
509 | # (BFLOAT,BFLOAT) (quo,rem) or BINT (only rem) |
510 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
511 | |
512 | return wantarray ? ($x->bnan(),bnan()) : $x->bnan() |
513 | if ($x->{sign} eq $nan || $y->is_nan() || $y->is_zero()); |
0716bf9b |
514 | |
515 | $y = $class->new($y) if ref($y) ne $class; # promote bigints |
516 | |
517 | # print "mbf bdiv $x ",ref($x)," ",$y," ",ref($y),"\n"; |
58cde26e |
518 | # we need to limit the accuracy to protect against overflow |
0716bf9b |
519 | my ($scale) = $x->_scale_a($accuracy,$rnd_mode,$a,$r); # ignore $p |
58cde26e |
520 | if (!defined $scale) |
521 | { |
0716bf9b |
522 | # simulate old behaviour |
523 | $scale = $div_scale+1; # one more for proper riund |
524 | $a = $div_scale; # and round to it |
a0d0e21e |
525 | } |
0716bf9b |
526 | my $lx = $x->{_m}->length(); my $ly = $y->{_m}->length(); |
58cde26e |
527 | $scale = $lx if $lx > $scale; |
58cde26e |
528 | $scale = $ly if $ly > $scale; |
529 | #print "scale $scale $lx $ly\n"; |
0716bf9b |
530 | my $diff = $ly - $lx; |
531 | $scale += $diff if $diff > 0; # if lx << ly, but not if ly << lx! |
a0d0e21e |
532 | |
58cde26e |
533 | return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero(); |
534 | |
535 | $x->{sign} = $x->{sign} ne $y->sign() ? '-' : '+'; |
a0d0e21e |
536 | |
58cde26e |
537 | # check for / +-1 ( +/- 1E0) |
538 | if ($y->is_one()) |
539 | { |
540 | return wantarray ? ($x,$self->bzero()) : $x; |
a0d0e21e |
541 | } |
a5f75d66 |
542 | |
58cde26e |
543 | # a * 10 ** b / c * 10 ** d => a/c * 10 ** (b-d) |
544 | #print "self: $self x: $x ref(x) ", ref($x)," m: $x->{_m}\n"; |
545 | # my $scale_10 = 10 ** $scale; $x->{_m}->bmul($scale_10); |
546 | $x->{_m}->blsft($scale,10); |
0716bf9b |
547 | #print "m: $x->{_m} $y->{_m}\n"; |
58cde26e |
548 | $x->{_m}->bdiv( $y->{_m} ); # a/c |
549 | #print "m: $x->{_m}\n"; |
550 | #print "e: $x->{_e} $y->{_e}",$scale,"\n"; |
551 | $x->{_e}->bsub($y->{_e}); # b-d |
552 | #print "e: $x->{_e}\n"; |
553 | $x->{_e}->bsub($scale); # correct for 10**scale |
0716bf9b |
554 | #print "after div: m: $x->{_m} e: $x->{_e}\n"; |
555 | $x->bnorm(); # remove trailing 0's |
556 | #print "after div: m: $x->{_m} e: $x->{_e}\n"; |
557 | $x->round($a,$p,$r); # then round accordingly |
558 | |
58cde26e |
559 | if (wantarray) |
560 | { |
561 | my $rem = $x->copy(); |
562 | $rem->bmod($y,$a,$p,$r); |
0716bf9b |
563 | return ($x,$rem); |
58cde26e |
564 | } |
565 | return $x; |
566 | } |
a0d0e21e |
567 | |
58cde26e |
568 | sub bmod |
569 | { |
570 | # (dividend: BFLOAT or num_str, divisor: BFLOAT or num_str) return reminder |
571 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
a0d0e21e |
572 | |
58cde26e |
573 | return $x->bnan() if ($x->{sign} eq $nan || $y->is_nan() || $y->is_zero()); |
574 | return $x->bzero() if $y->is_one(); |
575 | |
576 | # XXX tels: not done yet |
577 | return $x->round($a,$p,$r,$y); |
578 | } |
579 | |
580 | sub bsqrt |
581 | { |
0716bf9b |
582 | # calculate square root; this should probably |
583 | # use a different test to see whether the accuracy we want is... |
58cde26e |
584 | my ($self,$x,$a,$p,$r) = objectify(1,@_); |
585 | |
0716bf9b |
586 | return $x->bnan() if $x->{sign} eq 'NaN' || $x->{sign} =~ /^-/; # <0, NaN |
587 | return $x if $x->{sign} eq '+inf'; # +inf |
58cde26e |
588 | return $x if $x->is_zero() || $x == 1; |
589 | |
0716bf9b |
590 | # we need to limit the accuracy to protect against overflow |
591 | my ($scale) = $x->_scale_a($accuracy,$rnd_mode,$a,$r); # ignore $p |
592 | if (!defined $scale) |
593 | { |
594 | # simulate old behaviour |
595 | $scale = $div_scale+1; # one more for proper riund |
596 | $a = $div_scale; # and round to it |
597 | } |
598 | my $lx = $x->{_m}->length(); |
599 | $scale = $lx if $scale < $lx; |
58cde26e |
600 | my $e = Math::BigFloat->new("1E-$scale"); # make test variable |
601 | return $x->bnan() if $e->sign() eq 'NaN'; |
602 | |
58cde26e |
603 | # start with some reasonable guess |
0716bf9b |
604 | #$x *= 10 ** ($len - $org->{_e}); $x /= 2; # !?!? |
605 | $lx = 1 if $lx < 1; |
606 | my $gs = Math::BigFloat->new('1'. ('0' x $lx)); |
607 | |
608 | # print "first guess: $gs (x $x) scale $scale\n"; |
58cde26e |
609 | |
610 | my $diff = $e; |
611 | my $y = $x->copy(); |
612 | my $two = Math::BigFloat->new(2); |
613 | $x = Math::BigFloat->new($x) if ref($x) ne $class; # promote BigInts |
614 | # $scale = 2; |
615 | while ($diff >= $e) |
616 | { |
58cde26e |
617 | return $x->bnan() if $gs->is_zero(); |
0716bf9b |
618 | $r = $y->copy(); $r->bdiv($gs,$scale); |
58cde26e |
619 | $x = ($r + $gs); |
0716bf9b |
620 | $x->bdiv($two,$scale); |
58cde26e |
621 | $diff = $x->copy()->bsub($gs)->babs(); |
58cde26e |
622 | $gs = $x->copy(); |
a0d0e21e |
623 | } |
0716bf9b |
624 | $x->round($a,$p,$r); |
58cde26e |
625 | } |
626 | |
627 | sub bpow |
628 | { |
629 | # (BFLOAT or num_str, BFLOAT or num_str) return BFLOAT |
630 | # compute power of two numbers, second arg is used as integer |
631 | # modifies first argument |
632 | |
633 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
634 | |
0716bf9b |
635 | return $x if $x->{sign} =~ /^[+-]inf$/; |
58cde26e |
636 | return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan; |
0716bf9b |
637 | return $x->bzero()->binc() if $y->is_zero(); |
58cde26e |
638 | return $x if $x->is_one() || $y->is_one(); |
639 | my $y1 = $y->as_number(); # make bigint |
640 | if ($x == -1) |
641 | { |
642 | # if $x == -1 and odd/even y => +1/-1 because +-1 ^ (+-1) => +-1 |
0716bf9b |
643 | return $y1->is_odd() ? $x : $x->babs(1); |
288d023a |
644 | } |
58cde26e |
645 | return $x if $x->is_zero() && $y->{sign} eq '+'; # 0**y => 0 (if not y <= 0) |
646 | # 0 ** -y => 1 / (0 ** y) => / 0! |
647 | return $x->bnan() if $x->is_zero() && $y->{sign} eq '-'; |
648 | |
649 | # calculate $x->{_m} ** $y and $x->{_e} * $y separately (faster) |
650 | $y1->babs(); |
651 | $x->{_m}->bpow($y1); |
652 | $x->{_e}->bmul($y1); |
653 | $x->{sign} = $nan if $x->{_m}->{sign} eq $nan || $x->{_e}->{sign} eq $nan; |
654 | $x->bnorm(); |
655 | if ($y->{sign} eq '-') |
656 | { |
657 | # modify $x in place! |
0716bf9b |
658 | my $z = $x->copy(); $x->bzero()->binc(); |
58cde26e |
659 | return $x->bdiv($z,$a,$p,$r); # round in one go (might ignore y's A!) |
a0d0e21e |
660 | } |
58cde26e |
661 | return $x->round($a,$p,$r,$y); |
662 | } |
663 | |
664 | ############################################################################### |
665 | # rounding functions |
666 | |
667 | sub bfround |
668 | { |
669 | # precision: round to the $Nth digit left (+$n) or right (-$n) from the '.' |
670 | # $n == 0 means round to integer |
671 | # expects and returns normalized numbers! |
672 | my $x = shift; $x = $class->new($x) unless ref $x; |
a0d0e21e |
673 | |
58cde26e |
674 | return $x if $x->modify('bfround'); |
675 | |
676 | my ($scale,$mode) = $x->_scale_p($precision,$rnd_mode,@_); |
677 | return $x if !defined $scale; # no-op |
678 | |
679 | # print "MBF bfround $x to scale $scale mode $mode\n"; |
680 | return $x if $x->is_nan() or $x->is_zero(); |
681 | |
682 | if ($scale < 0) |
683 | { |
684 | # print "bfround scale $scale e $x->{_e}\n"; |
685 | # round right from the '.' |
686 | return $x if $x->{_e} >= 0; # nothing to round |
687 | $scale = -$scale; # positive for simplicity |
688 | my $len = $x->{_m}->length(); # length of mantissa |
689 | my $dad = -$x->{_e}; # digits after dot |
690 | my $zad = 0; # zeros after dot |
691 | $zad = -$len-$x->{_e} if ($x->{_e} < -$len);# for 0.00..00xxx style |
692 | # print "scale $scale dad $dad zad $zad len $len\n"; |
693 | |
694 | # number bsstr len zad dad |
695 | # 0.123 123e-3 3 0 3 |
696 | # 0.0123 123e-4 3 1 4 |
697 | # 0.001 1e-3 1 2 3 |
698 | # 1.23 123e-2 3 0 2 |
699 | # 1.2345 12345e-4 5 0 4 |
700 | |
701 | # do not round after/right of the $dad |
702 | return $x if $scale > $dad; # 0.123, scale >= 3 => exit |
703 | |
704 | # round to zero if rounding inside the $zad, but not for last zero like: |
705 | # 0.0065, scale -2, round last '0' with following '65' (scale == zad case) |
706 | if ($scale < $zad) |
707 | { |
708 | $x->{_m} = Math::BigInt->new(0); |
709 | $x->{_e} = Math::BigInt->new(1); |
710 | $x->{sign} = '+'; |
711 | return $x; |
712 | } |
713 | if ($scale == $zad) # for 0.006, scale -2 and trunc |
714 | { |
715 | $scale = -$len; |
716 | } |
717 | else |
718 | { |
719 | # adjust round-point to be inside mantissa |
720 | if ($zad != 0) |
721 | { |
722 | $scale = $scale-$zad; |
723 | } |
724 | else |
725 | { |
726 | my $dbd = $len - $dad; $dbd = 0 if $dbd < 0; # digits before dot |
727 | $scale = $dbd+$scale; |
728 | } |
729 | } |
730 | # print "round to $x->{_m} to $scale\n"; |
a0d0e21e |
731 | } |
58cde26e |
732 | else |
733 | { |
734 | # 123 => 100 means length(123) = 3 - $scale (2) => 1 |
a5f75d66 |
735 | |
58cde26e |
736 | # calculate digits before dot |
737 | my $dbt = $x->{_m}->length(); $dbt += $x->{_e} if $x->{_e}->sign() eq '-'; |
738 | if (($scale > $dbt) && ($dbt < 0)) |
739 | { |
740 | # if not enough digits before dot, round to zero |
741 | $x->{_m} = Math::BigInt->new(0); |
742 | $x->{_e} = Math::BigInt->new(1); |
743 | $x->{sign} = '+'; |
744 | return $x; |
745 | } |
746 | if (($scale >= 0) && ($dbt == 0)) |
747 | { |
748 | # 0.49->bfround(1): scale == 1, dbt == 0: => 0.0 |
749 | # 0.51->bfround(0): scale == 0, dbt == 0: => 1.0 |
750 | # 0.5->bfround(0): scale == 0, dbt == 0: => 0 |
751 | # 0.05->bfround(0): scale == 0, dbt == 0: => 0 |
752 | # print "$scale $dbt $x->{_m}\n"; |
753 | $scale = -$x->{_m}->length(); |
754 | } |
755 | elsif ($dbt > 0) |
756 | { |
757 | # correct by subtracting scale |
758 | $scale = $dbt - $scale; |
759 | } |
760 | else |
761 | { |
762 | $scale = $x->{_m}->length() - $scale; |
763 | } |
a0d0e21e |
764 | } |
58cde26e |
765 | #print "using $scale for $x->{_m} with '$mode'\n"; |
766 | # pass sign to bround for '+inf' and '-inf' rounding modes |
767 | $x->{_m}->{sign} = $x->{sign}; |
768 | $x->{_m}->bround($scale,$mode); |
769 | $x->{_m}->{sign} = '+'; # fix sign back |
770 | $x->bnorm(); |
771 | } |
772 | |
773 | sub bround |
774 | { |
775 | # accuracy: preserve $N digits, and overwrite the rest with 0's |
776 | my $x = shift; $x = $class->new($x) unless ref $x; |
777 | my ($scale,$mode) = $x->_scale_a($accuracy,$rnd_mode,@_); |
778 | return $x if !defined $scale; # no-op |
779 | |
780 | return $x if $x->modify('bround'); |
781 | |
782 | # print "bround $scale $mode\n"; |
783 | # 0 => return all digits, scale < 0 makes no sense |
784 | return $x if ($scale <= 0); |
785 | return $x if $x->is_nan() or $x->is_zero(); # never round a 0 |
786 | |
787 | # if $e longer than $m, we have 0.0000xxxyyy style number, and must |
788 | # subtract the delta from scale, to simulate keeping the zeros |
789 | # -5 +5 => 1; -10 +5 => -4 |
790 | my $delta = $x->{_e} + $x->{_m}->length() + 1; |
791 | # removed by tlr, since causes problems with fraction tests: |
792 | # $scale += $delta if $delta < 0; |
793 | |
794 | # if we should keep more digits than the mantissa has, do nothing |
795 | return $x if $x->{_m}->length() <= $scale; |
f216259d |
796 | |
58cde26e |
797 | # pass sign to bround for '+inf' and '-inf' rounding modes |
798 | $x->{_m}->{sign} = $x->{sign}; |
799 | $x->{_m}->bround($scale,$mode); # round mantissa |
800 | $x->{_m}->{sign} = '+'; # fix sign back |
801 | return $x->bnorm(); # del trailing zeros gen. by bround() |
802 | } |
803 | |
804 | sub bfloor |
805 | { |
806 | # return integer less or equal then $x |
807 | my ($self,$x,$a,$p,$r) = objectify(1,@_); |
808 | |
809 | return $x if $x->modify('bfloor'); |
810 | |
811 | return $x if $x->{sign} !~ /^[+-]$/; # nan, +inf, -inf |
812 | |
813 | # if $x has digits after dot |
814 | if ($x->{_e}->{sign} eq '-') |
815 | { |
816 | $x->{_m}->brsft(-$x->{_e},10); |
817 | $x->{_e}->bzero(); |
818 | $x-- if $x->{sign} eq '-'; |
f216259d |
819 | } |
58cde26e |
820 | return $x->round($a,$p,$r); |
821 | } |
288d023a |
822 | |
58cde26e |
823 | sub bceil |
824 | { |
825 | # return integer greater or equal then $x |
826 | my ($self,$x,$a,$p,$r) = objectify(1,@_); |
827 | |
828 | return $x if $x->modify('bceil'); |
829 | return $x if $x->{sign} !~ /^[+-]$/; # nan, +inf, -inf |
830 | |
831 | # if $x has digits after dot |
832 | if ($x->{_e}->{sign} eq '-') |
833 | { |
834 | $x->{_m}->brsft(-$x->{_e},10); |
835 | $x->{_e}->bzero(); |
836 | $x++ if $x->{sign} eq '+'; |
a0d0e21e |
837 | } |
58cde26e |
838 | return $x->round($a,$p,$r); |
839 | } |
840 | |
841 | ############################################################################### |
a5f75d66 |
842 | |
58cde26e |
843 | sub DESTROY |
844 | { |
845 | # going trough AUTOLOAD for every DESTROY is costly, so avoid it by empty sub |
846 | } |
847 | |
848 | sub AUTOLOAD |
849 | { |
850 | # make fxxx and bxxx work |
851 | # my $self = $_[0]; |
852 | my $name = $AUTOLOAD; |
853 | |
854 | $name =~ s/.*:://; # split package |
855 | #print "$name\n"; |
856 | if (!method_valid($name)) |
857 | { |
858 | #no strict 'refs'; |
859 | ## try one level up |
860 | #&{$class."::SUPER->$name"}(@_); |
861 | # delayed load of Carp and avoid recursion |
862 | require Carp; |
863 | Carp::croak ("Can't call $class\-\>$name, not a valid method"); |
a0d0e21e |
864 | } |
58cde26e |
865 | no strict 'refs'; |
866 | my $bname = $name; $bname =~ s/^f/b/; |
867 | *{$class."\:\:$name"} = \&$bname; |
868 | &$bname; # uses @_ |
869 | } |
870 | |
871 | sub exponent |
872 | { |
873 | # return a copy of the exponent |
874 | my $self = shift; |
875 | $self = $class->new($self) unless ref $self; |
876 | |
877 | return bnan() if $self->is_nan(); |
878 | return $self->{_e}->copy(); |
879 | } |
880 | |
881 | sub mantissa |
882 | { |
883 | # return a copy of the mantissa |
884 | my $self = shift; |
885 | $self = $class->new($self) unless ref $self; |
886 | |
887 | return bnan() if $self->is_nan(); |
888 | my $m = $self->{_m}->copy(); # faster than going via bstr() |
889 | $m->bneg() if $self->{sign} eq '-'; |
890 | |
891 | return $m; |
892 | } |
893 | |
894 | sub parts |
895 | { |
896 | # return a copy of both the exponent and the mantissa |
897 | my $self = shift; |
898 | $self = $class->new($self) unless ref $self; |
899 | |
900 | return (bnan(),bnan()) if $self->is_nan(); |
901 | my $m = $self->{_m}->copy(); # faster than going via bstr() |
902 | $m->bneg() if $self->{sign} eq '-'; |
903 | return ($m,$self->{_e}->copy()); |
904 | } |
905 | |
906 | ############################################################################## |
907 | # private stuff (internal use only) |
908 | |
909 | sub _one |
910 | { |
911 | # internal speedup, set argument to 1, or create a +/- 1 |
0716bf9b |
912 | my $self = shift; $self = ref($self) if ref($self); |
913 | my $x = {}; bless $x, $self; |
914 | $x->{_m} = Math::BigInt->new(1); |
915 | $x->{_e} = Math::BigInt->new(0); |
58cde26e |
916 | $x->{sign} = shift || '+'; |
917 | return $x; |
918 | } |
919 | |
920 | sub import |
921 | { |
922 | my $self = shift; |
923 | #print "import $self\n"; |
924 | for ( my $i = 0; $i < @_ ; $i++ ) |
925 | { |
926 | if ( $_[$i] eq ':constant' ) |
927 | { |
928 | # this rest causes overlord er load to step in |
929 | # print "overload @_\n"; |
930 | overload::constant float => sub { $self->new(shift); }; |
931 | splice @_, $i, 1; last; |
932 | } |
933 | } |
934 | # any non :constant stuff is handled by our parent, Exporter |
935 | # even if @_ is empty, to give it a chance |
936 | #$self->SUPER::import(@_); # does not work (would call MBI) |
937 | $self->export_to_level(1,$self,@_); # need this instead |
938 | } |
939 | |
940 | sub bnorm |
941 | { |
942 | # adjust m and e so that m is smallest possible |
943 | # round number according to accuracy and precision settings |
944 | my $x = shift; |
945 | |
0716bf9b |
946 | return $x if $x->{sign} !~ /^[+-]$/; # inf, nan etc |
58cde26e |
947 | |
948 | my $zeros = $x->{_m}->_trailing_zeros(); # correct for trailing zeros |
949 | if ($zeros != 0) |
950 | { |
951 | $x->{_m}->brsft($zeros,10); $x->{_e} += $zeros; |
952 | } |
953 | # for something like 0Ey, set y to 1 |
954 | $x->{_e}->bzero()->binc() if $x->{_m}->is_zero(); |
0716bf9b |
955 | $x->{_m}->{_f} = MB_NEVER_ROUND; |
956 | $x->{_e}->{_f} = MB_NEVER_ROUND; |
957 | return $x; # MBI bnorm is no-op |
58cde26e |
958 | } |
959 | |
960 | ############################################################################## |
961 | # internal calculation routines |
962 | |
963 | sub as_number |
964 | { |
965 | # return a bigint representation of this BigFloat number |
966 | my ($self,$x) = objectify(1,@_); |
967 | |
968 | my $z; |
969 | if ($x->{_e}->is_zero()) |
970 | { |
971 | $z = $x->{_m}->copy(); |
972 | $z->{sign} = $x->{sign}; |
973 | return $z; |
974 | } |
0716bf9b |
975 | $z = $x->{_m}->copy(); |
58cde26e |
976 | if ($x->{_e} < 0) |
977 | { |
0716bf9b |
978 | $z->brsft(-$x->{_e},10); |
979 | } |
980 | else |
981 | { |
982 | $z->blsft($x->{_e},10); |
58cde26e |
983 | } |
58cde26e |
984 | $z->{sign} = $x->{sign}; |
985 | return $z; |
986 | } |
987 | |
988 | sub length |
989 | { |
990 | my $x = shift; $x = $class->new($x) unless ref $x; |
991 | |
992 | my $len = $x->{_m}->length(); |
993 | $len += $x->{_e} if $x->{_e}->sign() eq '+'; |
994 | if (wantarray()) |
995 | { |
996 | my $t = Math::BigInt::bzero(); |
997 | $t = $x->{_e}->copy()->babs() if $x->{_e}->sign() eq '-'; |
998 | return ($len,$t); |
999 | } |
1000 | return $len; |
1001 | } |
a0d0e21e |
1002 | |
1003 | 1; |
a5f75d66 |
1004 | __END__ |
1005 | |
1006 | =head1 NAME |
1007 | |
58cde26e |
1008 | Math::BigFloat - Arbitrary size floating point math package |
a5f75d66 |
1009 | |
1010 | =head1 SYNOPSIS |
1011 | |
a2008d6d |
1012 | use Math::BigFloat; |
58cde26e |
1013 | |
1014 | # Number creation |
1015 | $x = Math::BigInt->new($str); # defaults to 0 |
1016 | $nan = Math::BigInt->bnan(); # create a NotANumber |
1017 | $zero = Math::BigInt->bzero();# create a "+0" |
1018 | |
1019 | # Testing |
1020 | $x->is_zero(); # return whether arg is zero or not |
0716bf9b |
1021 | $x->is_nan(); # return whether arg is NaN or not |
1022 | $x->is_one(); # true if arg is +1 |
1023 | $x->is_one('-'); # true if arg is -1 |
1024 | $x->is_odd(); # true if odd, false for even |
1025 | $x->is_even(); # true if even, false for odd |
1026 | $x->is_positive(); # true if >= 0 |
1027 | $x->is_negative(); # true if < 0 |
1028 | $x->is_inf(sign) # true if +inf or -inf (sign default '+') |
58cde26e |
1029 | $x->bcmp($y); # compare numbers (undef,<0,=0,>0) |
1030 | $x->bacmp($y); # compare absolutely (undef,<0,=0,>0) |
1031 | $x->sign(); # return the sign, either +,- or NaN |
1032 | |
1033 | # The following all modify their first argument: |
1034 | |
1035 | # set |
1036 | $x->bzero(); # set $i to 0 |
1037 | $x->bnan(); # set $i to NaN |
1038 | |
1039 | $x->bneg(); # negation |
1040 | $x->babs(); # absolute value |
1041 | $x->bnorm(); # normalize (no-op) |
1042 | $x->bnot(); # two's complement (bit wise not) |
1043 | $x->binc(); # increment x by 1 |
1044 | $x->bdec(); # decrement x by 1 |
1045 | |
1046 | $x->badd($y); # addition (add $y to $x) |
1047 | $x->bsub($y); # subtraction (subtract $y from $x) |
1048 | $x->bmul($y); # multiplication (multiply $x by $y) |
1049 | $x->bdiv($y); # divide, set $i to quotient |
1050 | # return (quo,rem) or quo if scalar |
1051 | |
1052 | $x->bmod($y); # modulus |
1053 | $x->bpow($y); # power of arguments (a**b) |
1054 | $x->blsft($y); # left shift |
1055 | $x->brsft($y); # right shift |
1056 | # return (quo,rem) or quo if scalar |
1057 | |
1058 | $x->band($y); # bit-wise and |
1059 | $x->bior($y); # bit-wise inclusive or |
1060 | $x->bxor($y); # bit-wise exclusive or |
1061 | $x->bnot(); # bit-wise not (two's complement) |
1062 | |
1063 | $x->bround($N); # accuracy: preserver $N digits |
1064 | $x->bfround($N); # precision: round to the $Nth digit |
1065 | |
1066 | # The following do not modify their arguments: |
1067 | |
1068 | bgcd(@values); # greatest common divisor |
1069 | blcm(@values); # lowest common multiplicator |
1070 | |
1071 | $x->bstr(); # return string |
1072 | $x->bsstr(); # return string in scientific notation |
1073 | |
1074 | $x->exponent(); # return exponent as BigInt |
1075 | $x->mantissa(); # return mantissa as BigInt |
1076 | $x->parts(); # return (mantissa,exponent) as BigInt |
1077 | |
1078 | $x->length(); # number of digits (w/o sign and '.') |
1079 | ($l,$f) = $x->length(); # number of digits, and length of fraction |
a5f75d66 |
1080 | |
1081 | =head1 DESCRIPTION |
1082 | |
58cde26e |
1083 | All operators (inlcuding basic math operations) are overloaded if you |
1084 | declare your big floating point numbers as |
a5f75d66 |
1085 | |
58cde26e |
1086 | $i = new Math::BigFloat '12_3.456_789_123_456_789E-2'; |
1087 | |
1088 | Operations with overloaded operators preserve the arguments, which is |
1089 | exactly what you expect. |
1090 | |
1091 | =head2 Canonical notation |
1092 | |
1093 | Input to these routines are either BigFloat objects, or strings of the |
1094 | following four forms: |
a5f75d66 |
1095 | |
1096 | =over 2 |
1097 | |
58cde26e |
1098 | =item * |
1099 | |
1100 | C</^[+-]\d+$/> |
a5f75d66 |
1101 | |
58cde26e |
1102 | =item * |
a5f75d66 |
1103 | |
58cde26e |
1104 | C</^[+-]\d+\.\d*$/> |
a5f75d66 |
1105 | |
58cde26e |
1106 | =item * |
a5f75d66 |
1107 | |
58cde26e |
1108 | C</^[+-]\d+E[+-]?\d+$/> |
a5f75d66 |
1109 | |
58cde26e |
1110 | =item * |
a5f75d66 |
1111 | |
58cde26e |
1112 | C</^[+-]\d*\.\d+E[+-]?\d+$/> |
5d7098d5 |
1113 | |
58cde26e |
1114 | =back |
1115 | |
1116 | all with optional leading and trailing zeros and/or spaces. Additonally, |
1117 | numbers are allowed to have an underscore between any two digits. |
1118 | |
1119 | Empty strings as well as other illegal numbers results in 'NaN'. |
1120 | |
1121 | bnorm() on a BigFloat object is now effectively a no-op, since the numbers |
1122 | are always stored in normalized form. On a string, it creates a BigFloat |
1123 | object. |
1124 | |
1125 | =head2 Output |
1126 | |
1127 | Output values are BigFloat objects (normalized), except for bstr() and bsstr(). |
1128 | |
1129 | The string output will always have leading and trailing zeros stripped and drop |
1130 | a plus sign. C<bstr()> will give you always the form with a decimal point, |
1131 | while C<bsstr()> (for scientific) gives you the scientific notation. |
1132 | |
1133 | Input bstr() bsstr() |
1134 | '-0' '0' '0E1' |
1135 | ' -123 123 123' '-123123123' '-123123123E0' |
1136 | '00.0123' '0.0123' '123E-4' |
1137 | '123.45E-2' '1.2345' '12345E-4' |
1138 | '10E+3' '10000' '1E4' |
1139 | |
1140 | Some routines (C<is_odd()>, C<is_even()>, C<is_zero()>, C<is_one()>, |
1141 | C<is_nan()>) return true or false, while others (C<bcmp()>, C<bacmp()>) |
1142 | return either undef, <0, 0 or >0 and are suited for sort. |
1143 | |
1144 | Actual math is done by using BigInts to represent the mantissa and exponent. |
1145 | The sign C</^[+-]$/> is stored separately. The string 'NaN' is used to |
1146 | represent the result when input arguments are not numbers, as well as |
1147 | the result of dividing by zero. |
1148 | |
1149 | =head2 C<mantissa()>, C<exponent()> and C<parts()> |
1150 | |
1151 | C<mantissa()> and C<exponent()> return the said parts of the BigFloat |
1152 | as BigInts such that: |
1153 | |
1154 | $m = $x->mantissa(); |
1155 | $e = $x->exponent(); |
1156 | $y = $m * ( 10 ** $e ); |
1157 | print "ok\n" if $x == $y; |
1158 | |
1159 | C<< ($m,$e) = $x->parts(); >> is just a shortcut giving you both of them. |
1160 | |
1161 | A zero is represented and returned as C<0E1>, B<not> C<0E0> (after Knuth). |
1162 | |
1163 | Currently the mantissa is reduced as much as possible, favouring higher |
1164 | exponents over lower ones (e.g. returning 1e7 instead of 10e6 or 10000000e0). |
1165 | This might change in the future, so do not depend on it. |
1166 | |
1167 | =head2 Accuracy vs. Precision |
1168 | |
1169 | See also: L<Rounding|Rounding>. |
1170 | |
1171 | Math::BigFloat supports both precision and accuracy. (here should follow |
1172 | a short description of both). |
5d7098d5 |
1173 | |
58cde26e |
1174 | Precision: digits after the '.', laber, schwad |
1175 | Accuracy: Significant digits blah blah |
5d7098d5 |
1176 | |
58cde26e |
1177 | Since things like sqrt(2) or 1/3 must presented with a limited precision lest |
1178 | a operation consumes all resources, each operation produces no more than |
1179 | C<Math::BigFloat::precision()> digits. |
1180 | |
1181 | In case the result of one operation has more precision than specified, |
1182 | it is rounded. The rounding mode taken is either the default mode, or the one |
1183 | supplied to the operation after the I<scale>: |
1184 | |
1185 | $x = Math::BigFloat->new(2); |
1186 | Math::BigFloat::precision(5); # 5 digits max |
1187 | $y = $x->copy()->bdiv(3); # will give 0.66666 |
1188 | $y = $x->copy()->bdiv(3,6); # will give 0.666666 |
1189 | $y = $x->copy()->bdiv(3,6,'odd'); # will give 0.666667 |
1190 | Math::BigFloat::round_mode('zero'); |
1191 | $y = $x->copy()->bdiv(3,6); # will give 0.666666 |
1192 | |
1193 | =head2 Rounding |
1194 | |
1195 | =over 2 |
1196 | |
5dc6f178 |
1197 | =item ffround ( +$scale ) |
58cde26e |
1198 | |
0716bf9b |
1199 | Rounds to the $scale'th place left from the '.', counting from the dot. |
1200 | The first digit is numbered 1. |
58cde26e |
1201 | |
5dc6f178 |
1202 | =item ffround ( -$scale ) |
58cde26e |
1203 | |
0716bf9b |
1204 | Rounds to the $scale'th place right from the '.', counting from the dot. |
58cde26e |
1205 | |
5dc6f178 |
1206 | =item ffround ( 0 ) |
1207 | |
0716bf9b |
1208 | Rounds to an integer. |
5dc6f178 |
1209 | |
1210 | =item fround ( +$scale ) |
1211 | |
0716bf9b |
1212 | Preserves accuracy to $scale digits from the left (aka significant digits) |
1213 | and pads the rest with zeros. If the number is between 1 and -1, the |
1214 | significant digits count from the first non-zero after the '.' |
5dc6f178 |
1215 | |
1216 | =item fround ( -$scale ) and fround ( 0 ) |
1217 | |
0716bf9b |
1218 | These are effetively no-ops. |
5d7098d5 |
1219 | |
a5f75d66 |
1220 | =back |
1221 | |
0716bf9b |
1222 | All rounding functions take as a second parameter a rounding mode from one of |
1223 | the following: 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'. |
58cde26e |
1224 | |
1225 | The default rounding mode is 'even'. By using |
0716bf9b |
1226 | C<< Math::BigFloat::round_mode($rnd_mode); >> you can get and set the default |
1227 | mode for subsequent rounding. The usage of C<$Math::BigFloat::$rnd_mode> is |
1228 | no longer supported. |
b22b3e31 |
1229 | The second parameter to the round functions then overrides the default |
0716bf9b |
1230 | temporarily. |
58cde26e |
1231 | |
1232 | The C<< as_number() >> function returns a BigInt from a Math::BigFloat. It uses |
1233 | 'trunc' as rounding mode to make it equivalent to: |
1234 | |
1235 | $x = 2.5; |
1236 | $y = int($x) + 2; |
1237 | |
1238 | You can override this by passing the desired rounding mode as parameter to |
1239 | C<as_number()>: |
1240 | |
1241 | $x = Math::BigFloat->new(2.5); |
1242 | $y = $x->as_number('odd'); # $y = 3 |
1243 | |
1244 | =head1 EXAMPLES |
1245 | |
1246 | use Math::BigFloat qw(bstr bint); |
1247 | # not ready yet |
1248 | $x = bstr("1234") # string "1234" |
1249 | $x = "$x"; # same as bstr() |
1250 | $x = bneg("1234") # BigFloat "-1234" |
1251 | $x = Math::BigFloat->bneg("1234"); # BigFloat "1234" |
1252 | $x = Math::BigFloat->babs("-12345"); # BigFloat "12345" |
1253 | $x = Math::BigFloat->bnorm("-0 00"); # BigFloat "0" |
1254 | $x = bint(1) + bint(2); # BigFloat "3" |
1255 | $x = bint(1) + "2"; # ditto (auto-BigFloatify of "2") |
1256 | $x = bint(1); # BigFloat "1" |
1257 | $x = $x + 5 / 2; # BigFloat "3" |
1258 | $x = $x ** 3; # BigFloat "27" |
1259 | $x *= 2; # BigFloat "54" |
1260 | $x = new Math::BigFloat; # BigFloat "0" |
1261 | $x--; # BigFloat "-1" |
1262 | |
1263 | =head1 Autocreating constants |
1264 | |
1265 | After C<use Math::BigFloat ':constant'> all the floating point constants |
1266 | in the given scope are converted to C<Math::BigFloat>. This conversion |
1267 | happens at compile time. |
1268 | |
1269 | In particular |
1270 | |
1271 | perl -MMath::BigFloat=:constant -e 'print 2E-100,"\n"' |
1272 | |
1273 | prints the value of C<2E-100>. Note that without conversion of |
1274 | constants the expression 2E-100 will be calculated as normal floating point |
1275 | number. |
1276 | |
1277 | =head1 PERFORMANCE |
1278 | |
1279 | Greatly enhanced ;o) |
1280 | SectionNotReadyYet. |
1281 | |
a5f75d66 |
1282 | =head1 BUGS |
1283 | |
58cde26e |
1284 | =over 2 |
1285 | |
1286 | =item * |
1287 | |
1288 | The following does not work yet: |
1289 | |
1290 | $m = $x->mantissa(); |
1291 | $e = $x->exponent(); |
1292 | $y = $m * ( 10 ** $e ); |
1293 | print "ok\n" if $x == $y; |
1294 | |
1295 | =item * |
1296 | |
1297 | There is no fmod() function yet. |
1298 | |
1299 | =back |
1300 | |
1301 | =head1 CAVEAT |
1302 | |
1303 | =over 1 |
1304 | |
1305 | =item stringify, bstr() |
1306 | |
1307 | Both stringify and bstr() now drop the leading '+'. The old code would return |
1308 | '+1.23', the new returns '1.23'. See the documentation in L<Math::BigInt> for |
1309 | reasoning and details. |
1310 | |
1311 | =item bdiv |
1312 | |
1313 | The following will probably not do what you expect: |
1314 | |
1315 | print $c->bdiv(123.456),"\n"; |
1316 | |
1317 | It prints both quotient and reminder since print works in list context. Also, |
1318 | bdiv() will modify $c, so be carefull. You probably want to use |
1319 | |
1320 | print $c / 123.456,"\n"; |
1321 | print scalar $c->bdiv(123.456),"\n"; # or if you want to modify $c |
1322 | |
1323 | instead. |
1324 | |
1325 | =item Modifying and = |
1326 | |
1327 | Beware of: |
1328 | |
1329 | $x = Math::BigFloat->new(5); |
1330 | $y = $x; |
1331 | |
1332 | It will not do what you think, e.g. making a copy of $x. Instead it just makes |
1333 | a second reference to the B<same> object and stores it in $y. Thus anything |
1334 | that modifies $x will modify $y, and vice versa. |
1335 | |
1336 | $x->bmul(2); |
1337 | print "$x, $y\n"; # prints '10, 10' |
1338 | |
1339 | If you want a true copy of $x, use: |
1340 | |
1341 | $y = $x->copy(); |
1342 | |
1343 | See also the documentation in L<overload> regarding C<=>. |
1344 | |
1345 | =item bpow |
1346 | |
1347 | C<bpow()> now modifies the first argument, unlike the old code which left |
1348 | it alone and only returned the result. This is to be consistent with |
1349 | C<badd()> etc. The first will modify $x, the second one won't: |
1350 | |
1351 | print bpow($x,$i),"\n"; # modify $x |
1352 | print $x->bpow($i),"\n"; # ditto |
1353 | print $x ** $i,"\n"; # leave $x alone |
1354 | |
1355 | =back |
1356 | |
1357 | =head1 LICENSE |
a5f75d66 |
1358 | |
58cde26e |
1359 | This program is free software; you may redistribute it and/or modify it under |
1360 | the same terms as Perl itself. |
5d7098d5 |
1361 | |
58cde26e |
1362 | =head1 AUTHORS |
5d7098d5 |
1363 | |
58cde26e |
1364 | Mark Biggar, overloaded interface by Ilya Zakharevich. |
1365 | Completely rewritten by Tels http://bloodgate.com in 2001. |
a5f75d66 |
1366 | |
a5f75d66 |
1367 | =cut |