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86530b38 AT |
1 | package Math::BigFloat; |
2 | ||
3 | # | |
4 | # Mike grinned. 'Two down, infinity to go' - Mike Nostrus in 'Before and After' | |
5 | # | |
6 | ||
7 | # The following hash values are internally used: | |
8 | # _e: exponent (BigInt) | |
9 | # _m: mantissa (absolute BigInt) | |
10 | # sign: +,-,"NaN" if not a number | |
11 | # _a: accuracy | |
12 | # _p: precision | |
13 | # _f: flags, used to signal MBI not to touch our private parts | |
14 | ||
15 | $VERSION = '1.35'; | |
16 | require 5.005; | |
17 | use Exporter; | |
18 | use File::Spec; | |
19 | # use Math::BigInt; | |
20 | @ISA = qw( Exporter Math::BigInt); | |
21 | ||
22 | use strict; | |
23 | use vars qw/$AUTOLOAD $accuracy $precision $div_scale $round_mode $rnd_mode/; | |
24 | use vars qw/$upgrade $downgrade/; | |
25 | my $class = "Math::BigFloat"; | |
26 | ||
27 | use overload | |
28 | '<=>' => sub { $_[2] ? | |
29 | ref($_[0])->bcmp($_[1],$_[0]) : | |
30 | ref($_[0])->bcmp($_[0],$_[1])}, | |
31 | 'int' => sub { $_[0]->as_number() }, # 'trunc' to bigint | |
32 | ; | |
33 | ||
34 | ############################################################################## | |
35 | # global constants, flags and accessory | |
36 | ||
37 | use constant MB_NEVER_ROUND => 0x0001; | |
38 | ||
39 | # are NaNs ok? | |
40 | my $NaNOK=1; | |
41 | # constant for easier life | |
42 | my $nan = 'NaN'; | |
43 | ||
44 | # class constants, use Class->constant_name() to access | |
45 | $round_mode = 'even'; # one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc' | |
46 | $accuracy = undef; | |
47 | $precision = undef; | |
48 | $div_scale = 40; | |
49 | ||
50 | $upgrade = undef; | |
51 | $downgrade = undef; | |
52 | my $MBI = 'Math::BigInt'; # the package we are using for our private parts | |
53 | # changable by use Math::BigFloat with => 'package' | |
54 | ||
55 | ############################################################################## | |
56 | # the old code had $rnd_mode, so we need to support it, too | |
57 | ||
58 | sub TIESCALAR { my ($class) = @_; bless \$round_mode, $class; } | |
59 | sub FETCH { return $round_mode; } | |
60 | sub STORE { $rnd_mode = $_[0]->round_mode($_[1]); } | |
61 | ||
62 | BEGIN | |
63 | { | |
64 | $rnd_mode = 'even'; | |
65 | tie $rnd_mode, 'Math::BigFloat'; | |
66 | } | |
67 | ||
68 | ############################################################################## | |
69 | ||
70 | # in case we call SUPER::->foo() and this wants to call modify() | |
71 | # sub modify () { 0; } | |
72 | ||
73 | { | |
74 | # valid method aliases for AUTOLOAD | |
75 | my %methods = map { $_ => 1 } | |
76 | qw / fadd fsub fmul fdiv fround ffround fsqrt fmod fstr fsstr fpow fnorm | |
77 | fint facmp fcmp fzero fnan finf finc fdec flog ffac | |
78 | fceil ffloor frsft flsft fone flog | |
79 | /; | |
80 | # valid method's that can be hand-ed up (for AUTOLOAD) | |
81 | my %hand_ups = map { $_ => 1 } | |
82 | qw / is_nan is_inf is_negative is_positive | |
83 | accuracy precision div_scale round_mode fneg fabs babs fnot | |
84 | objectify upgrade downgrade | |
85 | bone binf bnan bzero | |
86 | /; | |
87 | ||
88 | sub method_alias { return exists $methods{$_[0]||''}; } | |
89 | sub method_hand_up { return exists $hand_ups{$_[0]||''}; } | |
90 | } | |
91 | ||
92 | ############################################################################## | |
93 | # constructors | |
94 | ||
95 | sub new | |
96 | { | |
97 | # create a new BigFloat object from a string or another bigfloat object. | |
98 | # _e: exponent | |
99 | # _m: mantissa | |
100 | # sign => sign (+/-), or "NaN" | |
101 | ||
102 | my ($class,$wanted,@r) = @_; | |
103 | ||
104 | # avoid numify-calls by not using || on $wanted! | |
105 | return $class->bzero() if !defined $wanted; # default to 0 | |
106 | return $wanted->copy() if UNIVERSAL::isa($wanted,'Math::BigFloat'); | |
107 | ||
108 | my $self = {}; bless $self, $class; | |
109 | # shortcut for bigints and its subclasses | |
110 | if ((ref($wanted)) && (ref($wanted) ne $class)) | |
111 | { | |
112 | $self->{_m} = $wanted->as_number(); # get us a bigint copy | |
113 | $self->{_e} = $MBI->bzero(); | |
114 | $self->{_m}->babs(); | |
115 | $self->{sign} = $wanted->sign(); | |
116 | return $self->bnorm(); | |
117 | } | |
118 | # got string | |
119 | # handle '+inf', '-inf' first | |
120 | if ($wanted =~ /^[+-]?inf$/) | |
121 | { | |
122 | return $downgrade->new($wanted) if $downgrade; | |
123 | ||
124 | $self->{_e} = $MBI->bzero(); | |
125 | $self->{_m} = $MBI->bzero(); | |
126 | $self->{sign} = $wanted; | |
127 | $self->{sign} = '+inf' if $self->{sign} eq 'inf'; | |
128 | return $self->bnorm(); | |
129 | } | |
130 | #print "new string '$wanted'\n"; | |
131 | my ($mis,$miv,$mfv,$es,$ev) = Math::BigInt::_split(\$wanted); | |
132 | if (!ref $mis) | |
133 | { | |
134 | die "$wanted is not a number initialized to $class" if !$NaNOK; | |
135 | ||
136 | return $downgrade->bnan() if $downgrade; | |
137 | ||
138 | $self->{_e} = $MBI->bzero(); | |
139 | $self->{_m} = $MBI->bzero(); | |
140 | $self->{sign} = $nan; | |
141 | } | |
142 | else | |
143 | { | |
144 | # make integer from mantissa by adjusting exp, then convert to bigint | |
145 | # undef,undef to signal MBI that we don't need no bloody rounding | |
146 | $self->{_e} = $MBI->new("$$es$$ev",undef,undef); # exponent | |
147 | $self->{_m} = $MBI->new("$$miv$$mfv",undef,undef); # create mant. | |
148 | # 3.123E0 = 3123E-3, and 3.123E-2 => 3123E-5 | |
149 | $self->{_e} -= CORE::length($$mfv) if CORE::length($$mfv) != 0; | |
150 | $self->{sign} = $$mis; | |
151 | } | |
152 | # if downgrade, inf, NaN or integers go down | |
153 | ||
154 | if ($downgrade && $self->{_e}->{sign} eq '+') | |
155 | { | |
156 | # print "downgrading $$miv$$mfv"."E$$es$$ev"; | |
157 | if ($self->{_e}->is_zero()) | |
158 | { | |
159 | $self->{_m}->{sign} = $$mis; # negative if wanted | |
160 | return $downgrade->new($self->{_m}); | |
161 | } | |
162 | return $downgrade->new("$$mis$$miv$$mfv"."E$$es$$ev"); | |
163 | } | |
164 | # print "mbf new $self->{sign} $self->{_m} e $self->{_e} ",ref($self),"\n"; | |
165 | $self->bnorm()->round(@r); # first normalize, then round | |
166 | } | |
167 | ||
168 | sub _bnan | |
169 | { | |
170 | # used by parent class bone() to initialize number to 1 | |
171 | my $self = shift; | |
172 | $self->{_m} = $MBI->bzero(); | |
173 | $self->{_e} = $MBI->bzero(); | |
174 | } | |
175 | ||
176 | sub _binf | |
177 | { | |
178 | # used by parent class bone() to initialize number to 1 | |
179 | my $self = shift; | |
180 | $self->{_m} = $MBI->bzero(); | |
181 | $self->{_e} = $MBI->bzero(); | |
182 | } | |
183 | ||
184 | sub _bone | |
185 | { | |
186 | # used by parent class bone() to initialize number to 1 | |
187 | my $self = shift; | |
188 | $self->{_m} = $MBI->bone(); | |
189 | $self->{_e} = $MBI->bzero(); | |
190 | } | |
191 | ||
192 | sub _bzero | |
193 | { | |
194 | # used by parent class bone() to initialize number to 1 | |
195 | my $self = shift; | |
196 | $self->{_m} = $MBI->bzero(); | |
197 | $self->{_e} = $MBI->bone(); | |
198 | } | |
199 | ||
200 | sub isa | |
201 | { | |
202 | my ($self,$class) = @_; | |
203 | return if $class =~ /^Math::BigInt/; # we aren't one of these | |
204 | UNIVERSAL::isa($self,$class); | |
205 | } | |
206 | ||
207 | sub config | |
208 | { | |
209 | # return (later set?) configuration data as hash ref | |
210 | my $class = shift || 'Math::BigFloat'; | |
211 | ||
212 | my $cfg = $MBI->config(); | |
213 | ||
214 | no strict 'refs'; | |
215 | $cfg->{class} = $class; | |
216 | $cfg->{with} = $MBI; | |
217 | foreach ( | |
218 | qw/upgrade downgrade precision accuracy round_mode VERSION div_scale/) | |
219 | { | |
220 | $cfg->{lc($_)} = ${"${class}::$_"}; | |
221 | }; | |
222 | $cfg; | |
223 | } | |
224 | ||
225 | ############################################################################## | |
226 | # string conversation | |
227 | ||
228 | sub bstr | |
229 | { | |
230 | # (ref to BFLOAT or num_str ) return num_str | |
231 | # Convert number from internal format to (non-scientific) string format. | |
232 | # internal format is always normalized (no leading zeros, "-0" => "+0") | |
233 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
234 | #my $x = shift; my $class = ref($x) || $x; | |
235 | #$x = $class->new(shift) unless ref($x); | |
236 | ||
237 | #die "Oups! e was $nan" if $x->{_e}->{sign} eq $nan; | |
238 | #die "Oups! m was $nan" if $x->{_m}->{sign} eq $nan; | |
239 | if ($x->{sign} !~ /^[+-]$/) | |
240 | { | |
241 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN | |
242 | return 'inf'; # +inf | |
243 | } | |
244 | ||
245 | my $es = '0'; my $len = 1; my $cad = 0; my $dot = '.'; | |
246 | ||
247 | my $not_zero = ! $x->is_zero(); | |
248 | if ($not_zero) | |
249 | { | |
250 | $es = $x->{_m}->bstr(); | |
251 | $len = CORE::length($es); | |
252 | if (!$x->{_e}->is_zero()) | |
253 | { | |
254 | if ($x->{_e}->sign() eq '-') | |
255 | { | |
256 | $dot = ''; | |
257 | if ($x->{_e} <= -$len) | |
258 | { | |
259 | # print "style: 0.xxxx\n"; | |
260 | my $r = $x->{_e}->copy(); $r->babs()->bsub( CORE::length($es) ); | |
261 | $es = '0.'. ('0' x $r) . $es; $cad = -($len+$r); | |
262 | } | |
263 | else | |
264 | { | |
265 | # print "insert '.' at $x->{_e} in '$es'\n"; | |
266 | substr($es,$x->{_e},0) = '.'; $cad = $x->{_e}; | |
267 | } | |
268 | } | |
269 | else | |
270 | { | |
271 | # expand with zeros | |
272 | $es .= '0' x $x->{_e}; $len += $x->{_e}; $cad = 0; | |
273 | } | |
274 | } | |
275 | } # if not zero | |
276 | $es = $x->{sign}.$es if $x->{sign} eq '-'; | |
277 | # if set accuracy or precision, pad with zeros | |
278 | if ((defined $x->{_a}) && ($not_zero)) | |
279 | { | |
280 | # 123400 => 6, 0.1234 => 4, 0.001234 => 4 | |
281 | my $zeros = $x->{_a} - $cad; # cad == 0 => 12340 | |
282 | $zeros = $x->{_a} - $len if $cad != $len; | |
283 | $es .= $dot.'0' x $zeros if $zeros > 0; | |
284 | } | |
285 | elsif ($x->{_p} || 0 < 0) | |
286 | { | |
287 | # 123400 => 6, 0.1234 => 4, 0.001234 => 6 | |
288 | my $zeros = -$x->{_p} + $cad; | |
289 | $es .= $dot.'0' x $zeros if $zeros > 0; | |
290 | } | |
291 | $es; | |
292 | } | |
293 | ||
294 | sub bsstr | |
295 | { | |
296 | # (ref to BFLOAT or num_str ) return num_str | |
297 | # Convert number from internal format to scientific string format. | |
298 | # internal format is always normalized (no leading zeros, "-0E0" => "+0E0") | |
299 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
300 | #my $x = shift; my $class = ref($x) || $x; | |
301 | #$x = $class->new(shift) unless ref($x); | |
302 | ||
303 | #die "Oups! e was $nan" if $x->{_e}->{sign} eq $nan; | |
304 | #die "Oups! m was $nan" if $x->{_m}->{sign} eq $nan; | |
305 | if ($x->{sign} !~ /^[+-]$/) | |
306 | { | |
307 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN | |
308 | return 'inf'; # +inf | |
309 | } | |
310 | my $sign = $x->{_e}->{sign}; $sign = '' if $sign eq '-'; | |
311 | my $sep = 'e'.$sign; | |
312 | $x->{_m}->bstr().$sep.$x->{_e}->bstr(); | |
313 | } | |
314 | ||
315 | sub numify | |
316 | { | |
317 | # Make a number from a BigFloat object | |
318 | # simple return string and let Perl's atoi()/atof() handle the rest | |
319 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
320 | $x->bsstr(); | |
321 | } | |
322 | ||
323 | ############################################################################## | |
324 | # public stuff (usually prefixed with "b") | |
325 | ||
326 | # tels 2001-08-04 | |
327 | # todo: this must be overwritten and return NaN for non-integer values | |
328 | # band(), bior(), bxor(), too | |
329 | #sub bnot | |
330 | # { | |
331 | # $class->SUPER::bnot($class,@_); | |
332 | # } | |
333 | ||
334 | sub bcmp | |
335 | { | |
336 | # Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort) | |
337 | # (BFLOAT or num_str, BFLOAT or num_str) return cond_code | |
338 | ||
339 | # set up parameters | |
340 | my ($self,$x,$y) = (ref($_[0]),@_); | |
341 | # objectify is costly, so avoid it | |
342 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
343 | { | |
344 | ($self,$x,$y) = objectify(2,@_); | |
345 | } | |
346 | ||
347 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) | |
348 | { | |
349 | # handle +-inf and NaN | |
350 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); | |
351 | return 0 if ($x->{sign} eq $y->{sign}) && ($x->{sign} =~ /^[+-]inf$/); | |
352 | return +1 if $x->{sign} eq '+inf'; | |
353 | return -1 if $x->{sign} eq '-inf'; | |
354 | return -1 if $y->{sign} eq '+inf'; | |
355 | return +1; | |
356 | } | |
357 | ||
358 | # check sign for speed first | |
359 | return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y | |
360 | return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0 | |
361 | ||
362 | # shortcut | |
363 | my $xz = $x->is_zero(); | |
364 | my $yz = $y->is_zero(); | |
365 | return 0 if $xz && $yz; # 0 <=> 0 | |
366 | return -1 if $xz && $y->{sign} eq '+'; # 0 <=> +y | |
367 | return 1 if $yz && $x->{sign} eq '+'; # +x <=> 0 | |
368 | ||
369 | # adjust so that exponents are equal | |
370 | my $lxm = $x->{_m}->length(); | |
371 | my $lym = $y->{_m}->length(); | |
372 | # the numify somewhat limits our length, but makes it much faster | |
373 | my $lx = $lxm + $x->{_e}->numify(); | |
374 | my $ly = $lym + $y->{_e}->numify(); | |
375 | my $l = $lx - $ly; $l = -$l if $x->{sign} eq '-'; | |
376 | return $l <=> 0 if $l != 0; | |
377 | ||
378 | # lengths (corrected by exponent) are equal | |
379 | # so make mantissa equal length by padding with zero (shift left) | |
380 | my $diff = $lxm - $lym; | |
381 | my $xm = $x->{_m}; # not yet copy it | |
382 | my $ym = $y->{_m}; | |
383 | if ($diff > 0) | |
384 | { | |
385 | $ym = $y->{_m}->copy()->blsft($diff,10); | |
386 | } | |
387 | elsif ($diff < 0) | |
388 | { | |
389 | $xm = $x->{_m}->copy()->blsft(-$diff,10); | |
390 | } | |
391 | my $rc = $xm->bacmp($ym); | |
392 | $rc = -$rc if $x->{sign} eq '-'; # -124 < -123 | |
393 | $rc <=> 0; | |
394 | } | |
395 | ||
396 | sub bacmp | |
397 | { | |
398 | # Compares 2 values, ignoring their signs. | |
399 | # Returns one of undef, <0, =0, >0. (suitable for sort) | |
400 | # (BFLOAT or num_str, BFLOAT or num_str) return cond_code | |
401 | ||
402 | # set up parameters | |
403 | my ($self,$x,$y) = (ref($_[0]),@_); | |
404 | # objectify is costly, so avoid it | |
405 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
406 | { | |
407 | ($self,$x,$y) = objectify(2,@_); | |
408 | } | |
409 | ||
410 | # handle +-inf and NaN's | |
411 | if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/) | |
412 | { | |
413 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); | |
414 | return 0 if ($x->is_inf() && $y->is_inf()); | |
415 | return 1 if ($x->is_inf() && !$y->is_inf()); | |
416 | return -1; | |
417 | } | |
418 | ||
419 | # shortcut | |
420 | my $xz = $x->is_zero(); | |
421 | my $yz = $y->is_zero(); | |
422 | return 0 if $xz && $yz; # 0 <=> 0 | |
423 | return -1 if $xz && !$yz; # 0 <=> +y | |
424 | return 1 if $yz && !$xz; # +x <=> 0 | |
425 | ||
426 | # adjust so that exponents are equal | |
427 | my $lxm = $x->{_m}->length(); | |
428 | my $lym = $y->{_m}->length(); | |
429 | # the numify somewhat limits our length, but makes it much faster | |
430 | my $lx = $lxm + $x->{_e}->numify(); | |
431 | my $ly = $lym + $y->{_e}->numify(); | |
432 | my $l = $lx - $ly; | |
433 | return $l <=> 0 if $l != 0; | |
434 | ||
435 | # lengths (corrected by exponent) are equal | |
436 | # so make mantissa equal-length by padding with zero (shift left) | |
437 | my $diff = $lxm - $lym; | |
438 | my $xm = $x->{_m}; # not yet copy it | |
439 | my $ym = $y->{_m}; | |
440 | if ($diff > 0) | |
441 | { | |
442 | $ym = $y->{_m}->copy()->blsft($diff,10); | |
443 | } | |
444 | elsif ($diff < 0) | |
445 | { | |
446 | $xm = $x->{_m}->copy()->blsft(-$diff,10); | |
447 | } | |
448 | $xm->bacmp($ym) <=> 0; | |
449 | } | |
450 | ||
451 | sub badd | |
452 | { | |
453 | # add second arg (BFLOAT or string) to first (BFLOAT) (modifies first) | |
454 | # return result as BFLOAT | |
455 | ||
456 | # set up parameters | |
457 | my ($self,$x,$y,$a,$p,$r) = (ref($_[0]),@_); | |
458 | # objectify is costly, so avoid it | |
459 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
460 | { | |
461 | ($self,$x,$y,$a,$p,$r) = objectify(2,@_); | |
462 | } | |
463 | ||
464 | # inf and NaN handling | |
465 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) | |
466 | { | |
467 | # NaN first | |
468 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); | |
469 | # inf handling | |
470 | if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) | |
471 | { | |
472 | # +inf++inf or -inf+-inf => same, rest is NaN | |
473 | return $x if $x->{sign} eq $y->{sign}; | |
474 | return $x->bnan(); | |
475 | } | |
476 | # +-inf + something => +inf; something +-inf => +-inf | |
477 | $x->{sign} = $y->{sign}, return $x if $y->{sign} =~ /^[+-]inf$/; | |
478 | return $x; | |
479 | } | |
480 | ||
481 | return $upgrade->badd($x,$y,$a,$p,$r) if defined $upgrade && | |
482 | ((!$x->isa($self)) || (!$y->isa($self))); | |
483 | ||
484 | # speed: no add for 0+y or x+0 | |
485 | return $x->bround($a,$p,$r) if $y->is_zero(); # x+0 | |
486 | if ($x->is_zero()) # 0+y | |
487 | { | |
488 | # make copy, clobbering up x (modify in place!) | |
489 | $x->{_e} = $y->{_e}->copy(); | |
490 | $x->{_m} = $y->{_m}->copy(); | |
491 | $x->{sign} = $y->{sign} || $nan; | |
492 | return $x->round($a,$p,$r,$y); | |
493 | } | |
494 | ||
495 | # take lower of the two e's and adapt m1 to it to match m2 | |
496 | my $e = $y->{_e}; | |
497 | $e = $MBI->bzero() if !defined $e; # if no BFLOAT ? | |
498 | $e = $e->copy(); # make copy (didn't do it yet) | |
499 | $e->bsub($x->{_e}); | |
500 | my $add = $y->{_m}->copy(); | |
501 | if ($e->{sign} eq '-') # < 0 | |
502 | { | |
503 | my $e1 = $e->copy()->babs(); | |
504 | #$x->{_m} *= (10 ** $e1); | |
505 | $x->{_m}->blsft($e1,10); | |
506 | $x->{_e} += $e; # need the sign of e | |
507 | } | |
508 | elsif (!$e->is_zero()) # > 0 | |
509 | { | |
510 | #$add *= (10 ** $e); | |
511 | $add->blsft($e,10); | |
512 | } | |
513 | # else: both e are the same, so just leave them | |
514 | $x->{_m}->{sign} = $x->{sign}; # fiddle with signs | |
515 | $add->{sign} = $y->{sign}; | |
516 | $x->{_m} += $add; # finally do add/sub | |
517 | $x->{sign} = $x->{_m}->{sign}; # re-adjust signs | |
518 | $x->{_m}->{sign} = '+'; # mantissa always positiv | |
519 | # delete trailing zeros, then round | |
520 | return $x->bnorm()->round($a,$p,$r,$y); | |
521 | } | |
522 | ||
523 | sub bsub | |
524 | { | |
525 | # (BigFloat or num_str, BigFloat or num_str) return BigFloat | |
526 | # subtract second arg from first, modify first | |
527 | ||
528 | # set up parameters | |
529 | my ($self,$x,$y,$a,$p,$r) = (ref($_[0]),@_); | |
530 | # objectify is costly, so avoid it | |
531 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
532 | { | |
533 | ($self,$x,$y,$a,$p,$r) = objectify(2,@_); | |
534 | } | |
535 | ||
536 | if ($y->is_zero()) # still round for not adding zero | |
537 | { | |
538 | return $x->round($a,$p,$r); | |
539 | } | |
540 | ||
541 | $y->{sign} =~ tr/+\-/-+/; # does nothing for NaN | |
542 | $x->badd($y,$a,$p,$r); # badd does not leave internal zeros | |
543 | $y->{sign} =~ tr/+\-/-+/; # refix $y (does nothing for NaN) | |
544 | $x; # already rounded by badd() | |
545 | } | |
546 | ||
547 | sub binc | |
548 | { | |
549 | # increment arg by one | |
550 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); | |
551 | ||
552 | if ($x->{_e}->sign() eq '-') | |
553 | { | |
554 | return $x->badd($self->bone(),$a,$p,$r); # digits after dot | |
555 | } | |
556 | ||
557 | if (!$x->{_e}->is_zero()) | |
558 | { | |
559 | $x->{_m}->blsft($x->{_e},10); # 1e2 => 100 | |
560 | $x->{_e}->bzero(); | |
561 | } | |
562 | # now $x->{_e} == 0 | |
563 | if ($x->{sign} eq '+') | |
564 | { | |
565 | $x->{_m}->binc(); | |
566 | return $x->bnorm()->bround($a,$p,$r); | |
567 | } | |
568 | elsif ($x->{sign} eq '-') | |
569 | { | |
570 | $x->{_m}->bdec(); | |
571 | $x->{sign} = '+' if $x->{_m}->is_zero(); # -1 +1 => -0 => +0 | |
572 | return $x->bnorm()->bround($a,$p,$r); | |
573 | } | |
574 | # inf, nan handling etc | |
575 | $x->badd($self->__one(),$a,$p,$r); # does round | |
576 | } | |
577 | ||
578 | sub bdec | |
579 | { | |
580 | # decrement arg by one | |
581 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); | |
582 | ||
583 | if ($x->{_e}->sign() eq '-') | |
584 | { | |
585 | return $x->badd($self->bone('-'),$a,$p,$r); # digits after dot | |
586 | } | |
587 | ||
588 | if (!$x->{_e}->is_zero()) | |
589 | { | |
590 | $x->{_m}->blsft($x->{_e},10); # 1e2 => 100 | |
591 | $x->{_e}->bzero(); | |
592 | } | |
593 | # now $x->{_e} == 0 | |
594 | my $zero = $x->is_zero(); | |
595 | # <= 0 | |
596 | if (($x->{sign} eq '-') || $zero) | |
597 | { | |
598 | $x->{_m}->binc(); | |
599 | $x->{sign} = '-' if $zero; # 0 => 1 => -1 | |
600 | $x->{sign} = '+' if $x->{_m}->is_zero(); # -1 +1 => -0 => +0 | |
601 | return $x->bnorm()->round($a,$p,$r); | |
602 | } | |
603 | # > 0 | |
604 | elsif ($x->{sign} eq '+') | |
605 | { | |
606 | $x->{_m}->bdec(); | |
607 | return $x->bnorm()->round($a,$p,$r); | |
608 | } | |
609 | # inf, nan handling etc | |
610 | $x->badd($self->bone('-'),$a,$p,$r); # does round | |
611 | } | |
612 | ||
613 | sub blog | |
614 | { | |
615 | my ($self,$x,$base,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(2,@_); | |
616 | ||
617 | # http://www.efunda.com/math/taylor_series/logarithmic.cfm?search_string=log | |
618 | ||
619 | # u = x-1, v = x+1 | |
620 | # _ _ | |
621 | # Taylor: | u 1 u^3 1 u^5 | | |
622 | # ln (x) = 2 | --- + - * --- + - * --- + ... | x > 0 | |
623 | # |_ v 3 v^3 5 v^5 _| | |
624 | ||
625 | # This takes much more steps to calculate the result: | |
626 | # u = x-1 | |
627 | # _ _ | |
628 | # Taylor: | u 1 u^2 1 u^3 | | |
629 | # ln (x) = 2 | --- + - * --- + - * --- + ... | x > 1/2 | |
630 | # |_ x 2 x^2 3 x^3 _| | |
631 | ||
632 | # we need to limit the accuracy to protect against overflow | |
633 | my $fallback = 0; | |
634 | my $scale = 0; | |
635 | my @params = $x->_find_round_parameters($a,$p,$r); | |
636 | ||
637 | # no rounding at all, so must use fallback | |
638 | if (scalar @params == 1) | |
639 | { | |
640 | # simulate old behaviour | |
641 | $params[1] = $self->div_scale(); # and round to it as accuracy | |
642 | $params[0] = undef; | |
643 | $scale = $params[1]+4; # at least four more for proper round | |
644 | $params[3] = $r; # round mode by caller or undef | |
645 | $fallback = 1; # to clear a/p afterwards | |
646 | } | |
647 | else | |
648 | { | |
649 | # the 4 below is empirical, and there might be cases where it is not | |
650 | # enough... | |
651 | $scale = abs($params[1] || $params[2]) + 4; # take whatever is defined | |
652 | } | |
653 | ||
654 | return $x->bzero(@params) if $x->is_one(); | |
655 | return $x->bnan() if $x->{sign} ne '+' || $x->is_zero(); | |
656 | return $x->bone('+',@params) if $x->bcmp($base) == 0; | |
657 | ||
658 | # when user set globals, they would interfere with our calculation, so | |
659 | # disable then and later re-enable them | |
660 | no strict 'refs'; | |
661 | my $abr = "$self\::accuracy"; my $ab = $$abr; $$abr = undef; | |
662 | my $pbr = "$self\::precision"; my $pb = $$pbr; $$pbr = undef; | |
663 | # we also need to disable any set A or P on $x (_find_round_parameters took | |
664 | # them already into account), since these would interfere, too | |
665 | delete $x->{_a}; delete $x->{_p}; | |
666 | # need to disable $upgrade in BigInt, to avoid deep recursion | |
667 | local $Math::BigInt::upgrade = undef; | |
668 | ||
669 | my ($case,$limit,$v,$u,$below,$factor,$two,$next,$over,$f); | |
670 | ||
671 | if (3 < 5) | |
672 | #if ($x <= Math::BigFloat->new("0.5")) | |
673 | { | |
674 | $case = 0; | |
675 | # print "case $case $x < 0.5\n"; | |
676 | $v = $x->copy(); $v->binc(); # v = x+1 | |
677 | $x->bdec(); $u = $x->copy(); # u = x-1; x = x-1 | |
678 | $x->bdiv($v,$scale); # first term: u/v | |
679 | $below = $v->copy(); | |
680 | $over = $u->copy(); | |
681 | $u *= $u; $v *= $v; # u^2, v^2 | |
682 | $below->bmul($v); # u^3, v^3 | |
683 | $over->bmul($u); | |
684 | $factor = $self->new(3); $f = $self->new(2); | |
685 | } | |
686 | #else | |
687 | # { | |
688 | # $case = 1; | |
689 | # print "case 1 $x > 0.5\n"; | |
690 | # $v = $x->copy(); # v = x | |
691 | # $u = $x->copy(); $u->bdec(); # u = x-1; | |
692 | # $x->bdec(); $x->bdiv($v,$scale); # first term: x-1/x | |
693 | # $below = $v->copy(); | |
694 | # $over = $u->copy(); | |
695 | # $below->bmul($v); # u^2, v^2 | |
696 | # $over->bmul($u); | |
697 | # $factor = $self->new(2); $f = $self->bone(); | |
698 | # } | |
699 | $limit = $self->new("1E-". ($scale-1)); | |
700 | #my $steps = 0; | |
701 | while (3 < 5) | |
702 | { | |
703 | # we calculate the next term, and add it to the last | |
704 | # when the next term is below our limit, it won't affect the outcome | |
705 | # anymore, so we stop | |
706 | $next = $over->copy()->bdiv($below->copy()->bmul($factor),$scale); | |
707 | last if $next->bcmp($limit) <= 0; | |
708 | $x->badd($next); | |
709 | # print "step $x\n"; | |
710 | # calculate things for the next term | |
711 | $over *= $u; $below *= $v; $factor->badd($f); | |
712 | #$steps++; | |
713 | } | |
714 | $x->bmul(2) if $case == 0; | |
715 | #print "took $steps steps\n"; | |
716 | ||
717 | # shortcut to not run trough _find_round_parameters again | |
718 | if (defined $params[1]) | |
719 | { | |
720 | $x->bround($params[1],$params[3]); # then round accordingly | |
721 | } | |
722 | else | |
723 | { | |
724 | $x->bfround($params[2],$params[3]); # then round accordingly | |
725 | } | |
726 | if ($fallback) | |
727 | { | |
728 | # clear a/p after round, since user did not request it | |
729 | $x->{_a} = undef; $x->{_p} = undef; | |
730 | } | |
731 | # restore globals | |
732 | $$abr = $ab; $$pbr = $pb; | |
733 | ||
734 | $x; | |
735 | } | |
736 | ||
737 | sub blcm | |
738 | { | |
739 | # (BFLOAT or num_str, BFLOAT or num_str) return BFLOAT | |
740 | # does not modify arguments, but returns new object | |
741 | # Lowest Common Multiplicator | |
742 | ||
743 | my ($self,@arg) = objectify(0,@_); | |
744 | my $x = $self->new(shift @arg); | |
745 | while (@arg) { $x = _lcm($x,shift @arg); } | |
746 | $x; | |
747 | } | |
748 | ||
749 | sub bgcd | |
750 | { | |
751 | # (BFLOAT or num_str, BFLOAT or num_str) return BINT | |
752 | # does not modify arguments, but returns new object | |
753 | # GCD -- Euclids algorithm Knuth Vol 2 pg 296 | |
754 | ||
755 | my ($self,@arg) = objectify(0,@_); | |
756 | my $x = $self->new(shift @arg); | |
757 | while (@arg) { $x = _gcd($x,shift @arg); } | |
758 | $x; | |
759 | } | |
760 | ||
761 | ############################################################################### | |
762 | # is_foo methods (is_negative, is_positive are inherited from BigInt) | |
763 | ||
764 | sub is_int | |
765 | { | |
766 | # return true if arg (BFLOAT or num_str) is an integer | |
767 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
768 | ||
769 | return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN and +-inf aren't | |
770 | $x->{_e}->{sign} eq '+'; # 1e-1 => no integer | |
771 | 0; | |
772 | } | |
773 | ||
774 | sub is_zero | |
775 | { | |
776 | # return true if arg (BFLOAT or num_str) is zero | |
777 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
778 | ||
779 | return 1 if $x->{sign} eq '+' && $x->{_m}->is_zero(); | |
780 | 0; | |
781 | } | |
782 | ||
783 | sub is_one | |
784 | { | |
785 | # return true if arg (BFLOAT or num_str) is +1 or -1 if signis given | |
786 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
787 | ||
788 | my $sign = shift || ''; $sign = '+' if $sign ne '-'; | |
789 | return 1 | |
790 | if ($x->{sign} eq $sign && $x->{_e}->is_zero() && $x->{_m}->is_one()); | |
791 | 0; | |
792 | } | |
793 | ||
794 | sub is_odd | |
795 | { | |
796 | # return true if arg (BFLOAT or num_str) is odd or false if even | |
797 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
798 | ||
799 | return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN & +-inf aren't | |
800 | ($x->{_e}->is_zero() && $x->{_m}->is_odd()); | |
801 | 0; | |
802 | } | |
803 | ||
804 | sub is_even | |
805 | { | |
806 | # return true if arg (BINT or num_str) is even or false if odd | |
807 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
808 | ||
809 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't | |
810 | return 1 if ($x->{_e}->{sign} eq '+' # 123.45 is never | |
811 | && $x->{_m}->is_even()); # but 1200 is | |
812 | 0; | |
813 | } | |
814 | ||
815 | sub bmul | |
816 | { | |
817 | # multiply two numbers -- stolen from Knuth Vol 2 pg 233 | |
818 | # (BINT or num_str, BINT or num_str) return BINT | |
819 | ||
820 | # set up parameters | |
821 | my ($self,$x,$y,$a,$p,$r) = (ref($_[0]),@_); | |
822 | # objectify is costly, so avoid it | |
823 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
824 | { | |
825 | ($self,$x,$y,$a,$p,$r) = objectify(2,@_); | |
826 | } | |
827 | ||
828 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); | |
829 | ||
830 | # inf handling | |
831 | if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) | |
832 | { | |
833 | return $x->bnan() if $x->is_zero() || $y->is_zero(); | |
834 | # result will always be +-inf: | |
835 | # +inf * +/+inf => +inf, -inf * -/-inf => +inf | |
836 | # +inf * -/-inf => -inf, -inf * +/+inf => -inf | |
837 | return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); | |
838 | return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); | |
839 | return $x->binf('-'); | |
840 | } | |
841 | # handle result = 0 | |
842 | return $x->bzero() if $x->is_zero() || $y->is_zero(); | |
843 | ||
844 | return $upgrade->bmul($x,$y,$a,$p,$r) if defined $upgrade && | |
845 | ((!$x->isa($self)) || (!$y->isa($self))); | |
846 | ||
847 | # aEb * cEd = (a*c)E(b+d) | |
848 | $x->{_m}->bmul($y->{_m}); | |
849 | $x->{_e}->badd($y->{_e}); | |
850 | # adjust sign: | |
851 | $x->{sign} = $x->{sign} ne $y->{sign} ? '-' : '+'; | |
852 | return $x->bnorm()->round($a,$p,$r,$y); | |
853 | } | |
854 | ||
855 | sub bdiv | |
856 | { | |
857 | # (dividend: BFLOAT or num_str, divisor: BFLOAT or num_str) return | |
858 | # (BFLOAT,BFLOAT) (quo,rem) or BFLOAT (only rem) | |
859 | ||
860 | # set up parameters | |
861 | my ($self,$x,$y,$a,$p,$r) = (ref($_[0]),@_); | |
862 | # objectify is costly, so avoid it | |
863 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
864 | { | |
865 | ($self,$x,$y,$a,$p,$r) = objectify(2,@_); | |
866 | } | |
867 | ||
868 | return $self->_div_inf($x,$y) | |
869 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()); | |
870 | ||
871 | # x== 0 # also: or y == 1 or y == -1 | |
872 | return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero(); | |
873 | ||
874 | # upgrade ? | |
875 | return $upgrade->bdiv($upgrade->new($x),$y,$a,$p,$r) if defined $upgrade; | |
876 | ||
877 | # we need to limit the accuracy to protect against overflow | |
878 | my $fallback = 0; | |
879 | my $scale = 0; | |
880 | my @params = $x->_find_round_parameters($a,$p,$r,$y); | |
881 | ||
882 | # no rounding at all, so must use fallback | |
883 | if (scalar @params == 1) | |
884 | { | |
885 | # simulate old behaviour | |
886 | $params[1] = $self->div_scale(); # and round to it as accuracy | |
887 | $scale = $params[1]+4; # at least four more for proper round | |
888 | $params[3] = $r; # round mode by caller or undef | |
889 | $fallback = 1; # to clear a/p afterwards | |
890 | } | |
891 | else | |
892 | { | |
893 | # the 4 below is empirical, and there might be cases where it is not | |
894 | # enough... | |
895 | $scale = abs($params[1] || $params[2]) + 4; # take whatever is defined | |
896 | } | |
897 | my $lx = $x->{_m}->length(); my $ly = $y->{_m}->length(); | |
898 | $scale = $lx if $lx > $scale; | |
899 | $scale = $ly if $ly > $scale; | |
900 | my $diff = $ly - $lx; | |
901 | $scale += $diff if $diff > 0; # if lx << ly, but not if ly << lx! | |
902 | ||
903 | # make copy of $x in case of list context for later reminder calculation | |
904 | my $rem; | |
905 | if (wantarray && !$y->is_one()) | |
906 | { | |
907 | $rem = $x->copy(); | |
908 | } | |
909 | ||
910 | $x->{sign} = $x->{sign} ne $y->sign() ? '-' : '+'; | |
911 | ||
912 | # check for / +-1 ( +/- 1E0) | |
913 | if (!$y->is_one()) | |
914 | { | |
915 | # promote BigInts and it's subclasses (except when already a BigFloat) | |
916 | $y = $self->new($y) unless $y->isa('Math::BigFloat'); | |
917 | ||
918 | #print "bdiv $y ",ref($y),"\n"; | |
919 | # need to disable $upgrade in BigInt, to avoid deep recursion | |
920 | local $Math::BigInt::upgrade = undef; # should be parent class vs MBI | |
921 | ||
922 | # calculate the result to $scale digits and then round it | |
923 | # a * 10 ** b / c * 10 ** d => a/c * 10 ** (b-d) | |
924 | $x->{_m}->blsft($scale,10); | |
925 | $x->{_m}->bdiv( $y->{_m} ); # a/c | |
926 | $x->{_e}->bsub( $y->{_e} ); # b-d | |
927 | $x->{_e}->bsub($scale); # correct for 10**scale | |
928 | $x->bnorm(); # remove trailing 0's | |
929 | } | |
930 | ||
931 | # shortcut to not run trough _find_round_parameters again | |
932 | if (defined $params[1]) | |
933 | { | |
934 | $x->bround($params[1],$params[3]); # then round accordingly | |
935 | } | |
936 | else | |
937 | { | |
938 | $x->bfround($params[2],$params[3]); # then round accordingly | |
939 | } | |
940 | if ($fallback) | |
941 | { | |
942 | # clear a/p after round, since user did not request it | |
943 | $x->{_a} = undef; $x->{_p} = undef; | |
944 | } | |
945 | ||
946 | if (wantarray) | |
947 | { | |
948 | if (!$y->is_one()) | |
949 | { | |
950 | $rem->bmod($y,$params[1],$params[2],$params[3]); # copy already done | |
951 | } | |
952 | else | |
953 | { | |
954 | $rem = $self->bzero(); | |
955 | } | |
956 | if ($fallback) | |
957 | { | |
958 | # clear a/p after round, since user did not request it | |
959 | $rem->{_a} = undef; $rem->{_p} = undef; | |
960 | } | |
961 | return ($x,$rem); | |
962 | } | |
963 | $x; | |
964 | } | |
965 | ||
966 | sub bmod | |
967 | { | |
968 | # (dividend: BFLOAT or num_str, divisor: BFLOAT or num_str) return reminder | |
969 | ||
970 | # set up parameters | |
971 | my ($self,$x,$y,$a,$p,$r) = (ref($_[0]),@_); | |
972 | # objectify is costly, so avoid it | |
973 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
974 | { | |
975 | ($self,$x,$y,$a,$p,$r) = objectify(2,@_); | |
976 | } | |
977 | ||
978 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) | |
979 | { | |
980 | my ($d,$re) = $self->SUPER::_div_inf($x,$y); | |
981 | $x->{sign} = $re->{sign}; | |
982 | $x->{_e} = $re->{_e}; | |
983 | $x->{_m} = $re->{_m}; | |
984 | return $x->round($a,$p,$r,$y); | |
985 | } | |
986 | return $x->bnan() if $x->is_zero() && $y->is_zero(); | |
987 | return $x if $y->is_zero(); | |
988 | return $x->bnan() if $x->is_nan() || $y->is_nan(); | |
989 | return $x->bzero() if $y->is_one() || $x->is_zero(); | |
990 | ||
991 | # inf handling is missing here | |
992 | ||
993 | my $cmp = $x->bacmp($y); # equal or $x < $y? | |
994 | return $x->bzero($a,$p) if $cmp == 0; # $x == $y => result 0 | |
995 | ||
996 | # only $y of the operands negative? | |
997 | my $neg = 0; $neg = 1 if $x->{sign} ne $y->{sign}; | |
998 | ||
999 | $x->{sign} = $y->{sign}; # calc sign first | |
1000 | return $x->round($a,$p,$r) if $cmp < 0 && $neg == 0; # $x < $y => result $x | |
1001 | ||
1002 | my $ym = $y->{_m}->copy(); | |
1003 | ||
1004 | # 2e1 => 20 | |
1005 | $ym->blsft($y->{_e},10) if $y->{_e}->{sign} eq '+' && !$y->{_e}->is_zero(); | |
1006 | ||
1007 | # if $y has digits after dot | |
1008 | my $shifty = 0; # correct _e of $x by this | |
1009 | if ($y->{_e}->{sign} eq '-') # has digits after dot | |
1010 | { | |
1011 | # 123 % 2.5 => 1230 % 25 => 5 => 0.5 | |
1012 | $shifty = $y->{_e}->copy()->babs(); # no more digits after dot | |
1013 | $x->blsft($shifty,10); # 123 => 1230, $y->{_m} is already 25 | |
1014 | } | |
1015 | # $ym is now mantissa of $y based on exponent 0 | |
1016 | ||
1017 | my $shiftx = 0; # correct _e of $x by this | |
1018 | if ($x->{_e}->{sign} eq '-') # has digits after dot | |
1019 | { | |
1020 | # 123.4 % 20 => 1234 % 200 | |
1021 | $shiftx = $x->{_e}->copy()->babs(); # no more digits after dot | |
1022 | $ym->blsft($shiftx,10); | |
1023 | } | |
1024 | # 123e1 % 20 => 1230 % 20 | |
1025 | if ($x->{_e}->{sign} eq '+' && !$x->{_e}->is_zero()) | |
1026 | { | |
1027 | $x->{_m}->blsft($x->{_e},10); | |
1028 | } | |
1029 | $x->{_e} = $MBI->bzero() unless $x->{_e}->is_zero(); | |
1030 | ||
1031 | $x->{_e}->bsub($shiftx) if $shiftx != 0; | |
1032 | $x->{_e}->bsub($shifty) if $shifty != 0; | |
1033 | ||
1034 | # now mantissas are equalized, exponent of $x is adjusted, so calc result | |
1035 | ||
1036 | $x->{_m}->bmod($ym); | |
1037 | ||
1038 | $x->{sign} = '+' if $x->{_m}->is_zero(); # fix sign for -0 | |
1039 | $x->bnorm(); | |
1040 | ||
1041 | if ($neg != 0) # one of them negative => correct in place | |
1042 | { | |
1043 | my $r = $y - $x; | |
1044 | $x->{_m} = $r->{_m}; | |
1045 | $x->{_e} = $r->{_e}; | |
1046 | $x->{sign} = '+' if $x->{_m}->is_zero(); # fix sign for -0 | |
1047 | $x->bnorm(); | |
1048 | } | |
1049 | ||
1050 | $x->round($a,$p,$r,$y); # round and return | |
1051 | } | |
1052 | ||
1053 | sub bsqrt | |
1054 | { | |
1055 | # calculate square root; this should probably | |
1056 | # use a different test to see whether the accuracy we want is... | |
1057 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); | |
1058 | ||
1059 | return $x->bnan() if $x->{sign} eq 'NaN' || $x->{sign} =~ /^-/; # <0, NaN | |
1060 | return $x if $x->{sign} eq '+inf'; # +inf | |
1061 | return $x if $x->is_zero() || $x->is_one(); | |
1062 | ||
1063 | # we need to limit the accuracy to protect against overflow | |
1064 | my $fallback = 0; | |
1065 | my $scale = 0; | |
1066 | my @params = $x->_find_round_parameters($a,$p,$r); | |
1067 | ||
1068 | # no rounding at all, so must use fallback | |
1069 | if (scalar @params == 1) | |
1070 | { | |
1071 | # simulate old behaviour | |
1072 | $params[1] = $self->div_scale(); # and round to it as accuracy | |
1073 | $scale = $params[1]+4; # at least four more for proper round | |
1074 | $params[3] = $r; # round mode by caller or undef | |
1075 | $fallback = 1; # to clear a/p afterwards | |
1076 | } | |
1077 | else | |
1078 | { | |
1079 | # the 4 below is empirical, and there might be cases where it is not | |
1080 | # enough... | |
1081 | $scale = abs($params[1] || $params[2]) + 4; # take whatever is defined | |
1082 | } | |
1083 | ||
1084 | # when user set globals, they would interfere with our calculation, so | |
1085 | # disable them and later re-enable them | |
1086 | no strict 'refs'; | |
1087 | my $abr = "$self\::accuracy"; my $ab = $$abr; $$abr = undef; | |
1088 | my $pbr = "$self\::precision"; my $pb = $$pbr; $$pbr = undef; | |
1089 | # we also need to disable any set A or P on $x (_find_round_parameters took | |
1090 | # them already into account), since these would interfere, too | |
1091 | delete $x->{_a}; delete $x->{_p}; | |
1092 | # need to disable $upgrade in BigInt, to avoid deep recursion | |
1093 | local $Math::BigInt::upgrade = undef; # should be really parent class vs MBI | |
1094 | ||
1095 | my $xas = $x->as_number(); | |
1096 | my $gs = $xas->copy()->bsqrt(); # some guess | |
1097 | ||
1098 | # print "guess $gs\n"; | |
1099 | if (($x->{_e}->{sign} ne '-') # guess can't be accurate if there are | |
1100 | # digits after the dot | |
1101 | && ($xas->bacmp($gs * $gs) == 0)) # guess hit the nail on the head? | |
1102 | { | |
1103 | # exact result | |
1104 | $x->{_m} = $gs; $x->{_e} = $MBI->bzero(); $x->bnorm(); | |
1105 | # shortcut to not run trough _find_round_parameters again | |
1106 | if (defined $params[1]) | |
1107 | { | |
1108 | $x->bround($params[1],$params[3]); # then round accordingly | |
1109 | } | |
1110 | else | |
1111 | { | |
1112 | $x->bfround($params[2],$params[3]); # then round accordingly | |
1113 | } | |
1114 | if ($fallback) | |
1115 | { | |
1116 | # clear a/p after round, since user did not request it | |
1117 | $x->{_a} = undef; $x->{_p} = undef; | |
1118 | } | |
1119 | # re-enable A and P, upgrade is taken care of by "local" | |
1120 | ${"$self\::accuracy"} = $ab; ${"$self\::precision"} = $pb; | |
1121 | return $x; | |
1122 | } | |
1123 | $gs = $self->new( $gs ); # BigInt to BigFloat | |
1124 | ||
1125 | my $lx = $x->{_m}->length(); | |
1126 | $scale = $lx if $scale < $lx; | |
1127 | my $e = $self->new("1E-$scale"); # make test variable | |
1128 | ||
1129 | my $y = $x->copy(); | |
1130 | my $two = $self->new(2); | |
1131 | my $diff = $e; | |
1132 | # promote BigInts and it's subclasses (except when already a BigFloat) | |
1133 | $y = $self->new($y) unless $y->isa('Math::BigFloat'); | |
1134 | ||
1135 | my $rem; | |
1136 | while ($diff->bacmp($e) >= 0) | |
1137 | { | |
1138 | $rem = $y->copy()->bdiv($gs,$scale); | |
1139 | $rem = $y->copy()->bdiv($gs,$scale)->badd($gs)->bdiv($two,$scale); | |
1140 | $diff = $rem->copy()->bsub($gs); | |
1141 | $gs = $rem->copy(); | |
1142 | } | |
1143 | # copy over to modify $x | |
1144 | $x->{_m} = $rem->{_m}; $x->{_e} = $rem->{_e}; | |
1145 | ||
1146 | # shortcut to not run trough _find_round_parameters again | |
1147 | if (defined $params[1]) | |
1148 | { | |
1149 | $x->bround($params[1],$params[3]); # then round accordingly | |
1150 | } | |
1151 | else | |
1152 | { | |
1153 | $x->bfround($params[2],$params[3]); # then round accordingly | |
1154 | } | |
1155 | if ($fallback) | |
1156 | { | |
1157 | # clear a/p after round, since user did not request it | |
1158 | $x->{_a} = undef; $x->{_p} = undef; | |
1159 | } | |
1160 | # restore globals | |
1161 | $$abr = $ab; $$pbr = $pb; | |
1162 | $x; | |
1163 | } | |
1164 | ||
1165 | sub bfac | |
1166 | { | |
1167 | # (BFLOAT or num_str, BFLOAT or num_str) return BFLOAT | |
1168 | # compute factorial numbers | |
1169 | # modifies first argument | |
1170 | my ($self,$x,@r) = objectify(1,@_); | |
1171 | ||
1172 | return $x->bnan() | |
1173 | if (($x->{sign} ne '+') || # inf, NaN, <0 etc => NaN | |
1174 | ($x->{_e}->{sign} ne '+')); # digits after dot? | |
1175 | ||
1176 | return $x->bone('+',@r) if $x->is_zero() || $x->is_one(); # 0 or 1 => 1 | |
1177 | ||
1178 | # use BigInt's bfac() for faster calc | |
1179 | $x->{_m}->blsft($x->{_e},10); # un-norm m | |
1180 | $x->{_e}->bzero(); # norm $x again | |
1181 | $x->{_m}->bfac(); # factorial | |
1182 | $x->bnorm()->round(@r); | |
1183 | } | |
1184 | ||
1185 | sub _pow2 | |
1186 | { | |
1187 | # Calculate a power where $y is a non-integer, like 2 ** 0.5 | |
1188 | my ($x,$y,$a,$p,$r) = @_; | |
1189 | my $self = ref($x); | |
1190 | ||
1191 | # we need to limit the accuracy to protect against overflow | |
1192 | my $fallback = 0; | |
1193 | my $scale = 0; | |
1194 | my @params = $x->_find_round_parameters($a,$p,$r); | |
1195 | ||
1196 | # no rounding at all, so must use fallback | |
1197 | if (scalar @params == 1) | |
1198 | { | |
1199 | # simulate old behaviour | |
1200 | $params[1] = $self->div_scale(); # and round to it as accuracy | |
1201 | $scale = $params[1]+4; # at least four more for proper round | |
1202 | $params[3] = $r; # round mode by caller or undef | |
1203 | $fallback = 1; # to clear a/p afterwards | |
1204 | } | |
1205 | else | |
1206 | { | |
1207 | # the 4 below is empirical, and there might be cases where it is not | |
1208 | # enough... | |
1209 | $scale = abs($params[1] || $params[2]) + 4; # take whatever is defined | |
1210 | } | |
1211 | ||
1212 | # when user set globals, they would interfere with our calculation, so | |
1213 | # disable then and later re-enable them | |
1214 | no strict 'refs'; | |
1215 | my $abr = "$self\::accuracy"; my $ab = $$abr; $$abr = undef; | |
1216 | my $pbr = "$self\::precision"; my $pb = $$pbr; $$pbr = undef; | |
1217 | # we also need to disable any set A or P on $x (_find_round_parameters took | |
1218 | # them already into account), since these would interfere, too | |
1219 | delete $x->{_a}; delete $x->{_p}; | |
1220 | # need to disable $upgrade in BigInt, to avoid deep recursion | |
1221 | local $Math::BigInt::upgrade = undef; | |
1222 | ||
1223 | # split the second argument into its integer and fraction part | |
1224 | # we calculate the result then from these two parts, like in | |
1225 | # 2 ** 2.4 == (2 ** 2) * (2 ** 0.4) | |
1226 | my $c = $self->new($y->as_number()); # integer part | |
1227 | my $d = $y-$c; # fractional part | |
1228 | my $xc = $x->copy(); # a temp. copy | |
1229 | ||
1230 | # now calculate binary fraction from the decimal fraction on the fly | |
1231 | # f.i. 0.654: | |
1232 | # 0.654 * 2 = 1.308 > 1 => 0.1 ( 1.308 - 1 = 0.308) | |
1233 | # 0.308 * 2 = 0.616 < 1 => 0.10 | |
1234 | # 0.616 * 2 = 1.232 > 1 => 0.101 ( 1.232 - 1 = 0.232) | |
1235 | # and so on... | |
1236 | # The process stops when the result is exactly one, or when we have | |
1237 | # enough accuracy | |
1238 | ||
1239 | # From the binary fraction we calculate the result as follows: | |
1240 | # we assume the fraction ends in 1, and we remove this one first. | |
1241 | # For each digit after the dot, assume 1 eq R and 0 eq XR, where R means | |
1242 | # take square root and X multiply with the original X. | |
1243 | ||
1244 | my $i = 0; | |
1245 | while ($i++ < 50) | |
1246 | { | |
1247 | $d->badd($d); # * 2 | |
1248 | last if $d->is_one(); # == 1 | |
1249 | $x->bsqrt(); # 0 | |
1250 | if ($d > 1) | |
1251 | { | |
1252 | $x->bsqrt(); $x->bmul($xc); $d->bdec(); # 1 | |
1253 | } | |
1254 | } | |
1255 | # assume fraction ends in 1 | |
1256 | $x->bsqrt(); # 1 | |
1257 | if (!$c->is_one()) | |
1258 | { | |
1259 | $x->bmul( $xc->bpow($c) ); | |
1260 | } | |
1261 | elsif (!$c->is_zero()) | |
1262 | { | |
1263 | $x->bmul( $xc ); | |
1264 | } | |
1265 | # done | |
1266 | ||
1267 | # shortcut to not run trough _find_round_parameters again | |
1268 | if (defined $params[1]) | |
1269 | { | |
1270 | $x->bround($params[1],$params[3]); # then round accordingly | |
1271 | } | |
1272 | else | |
1273 | { | |
1274 | $x->bfround($params[2],$params[3]); # then round accordingly | |
1275 | } | |
1276 | if ($fallback) | |
1277 | { | |
1278 | # clear a/p after round, since user did not request it | |
1279 | $x->{_a} = undef; $x->{_p} = undef; | |
1280 | } | |
1281 | # restore globals | |
1282 | $$abr = $ab; $$pbr = $pb; | |
1283 | $x; | |
1284 | } | |
1285 | ||
1286 | sub _pow | |
1287 | { | |
1288 | # Calculate a power where $y is a non-integer, like 2 ** 0.5 | |
1289 | my ($x,$y,$a,$p,$r) = @_; | |
1290 | my $self = ref($x); | |
1291 | ||
1292 | # if $y == 0.5, it is sqrt($x) | |
1293 | return $x->bsqrt($a,$p,$r,$y) if $y->bcmp('0.5') == 0; | |
1294 | ||
1295 | # u = y * ln x | |
1296 | # _ _ | |
1297 | # Taylor: | u u^2 u^3 | | |
1298 | # x ** y = 1 + | --- + --- + * ----- + ... | | |
1299 | # |_ 1 1*2 1*2*3 _| | |
1300 | ||
1301 | # we need to limit the accuracy to protect against overflow | |
1302 | my $fallback = 0; | |
1303 | my $scale = 0; | |
1304 | my @params = $x->_find_round_parameters($a,$p,$r); | |
1305 | ||
1306 | # no rounding at all, so must use fallback | |
1307 | if (scalar @params == 1) | |
1308 | { | |
1309 | # simulate old behaviour | |
1310 | $params[1] = $self->div_scale(); # and round to it as accuracy | |
1311 | $scale = $params[1]+4; # at least four more for proper round | |
1312 | $params[3] = $r; # round mode by caller or undef | |
1313 | $fallback = 1; # to clear a/p afterwards | |
1314 | } | |
1315 | else | |
1316 | { | |
1317 | # the 4 below is empirical, and there might be cases where it is not | |
1318 | # enough... | |
1319 | $scale = abs($params[1] || $params[2]) + 4; # take whatever is defined | |
1320 | } | |
1321 | ||
1322 | # when user set globals, they would interfere with our calculation, so | |
1323 | # disable then and later re-enable them | |
1324 | no strict 'refs'; | |
1325 | my $abr = "$self\::accuracy"; my $ab = $$abr; $$abr = undef; | |
1326 | my $pbr = "$self\::precision"; my $pb = $$pbr; $$pbr = undef; | |
1327 | # we also need to disable any set A or P on $x (_find_round_parameters took | |
1328 | # them already into account), since these would interfere, too | |
1329 | delete $x->{_a}; delete $x->{_p}; | |
1330 | # need to disable $upgrade in BigInt, to avoid deep recursion | |
1331 | local $Math::BigInt::upgrade = undef; | |
1332 | ||
1333 | my ($limit,$v,$u,$below,$factor,$next,$over); | |
1334 | ||
1335 | $u = $x->copy()->blog($scale)->bmul($y); | |
1336 | $v = $self->bone(); # 1 | |
1337 | $factor = $self->new(2); # 2 | |
1338 | $x->bone(); # first term: 1 | |
1339 | ||
1340 | $below = $v->copy(); | |
1341 | $over = $u->copy(); | |
1342 | ||
1343 | $limit = $self->new("1E-". ($scale-1)); | |
1344 | #my $steps = 0; | |
1345 | while (3 < 5) | |
1346 | { | |
1347 | # we calculate the next term, and add it to the last | |
1348 | # when the next term is below our limit, it won't affect the outcome | |
1349 | # anymore, so we stop | |
1350 | $next = $over->copy()->bdiv($below,$scale); | |
1351 | last if $next->bcmp($limit) <= 0; | |
1352 | $x->badd($next); | |
1353 | # print "at $x\n"; | |
1354 | # calculate things for the next term | |
1355 | $over *= $u; $below *= $factor; $factor->binc(); | |
1356 | #$steps++; | |
1357 | } | |
1358 | ||
1359 | # shortcut to not run trough _find_round_parameters again | |
1360 | if (defined $params[1]) | |
1361 | { | |
1362 | $x->bround($params[1],$params[3]); # then round accordingly | |
1363 | } | |
1364 | else | |
1365 | { | |
1366 | $x->bfround($params[2],$params[3]); # then round accordingly | |
1367 | } | |
1368 | if ($fallback) | |
1369 | { | |
1370 | # clear a/p after round, since user did not request it | |
1371 | $x->{_a} = undef; $x->{_p} = undef; | |
1372 | } | |
1373 | # restore globals | |
1374 | $$abr = $ab; $$pbr = $pb; | |
1375 | $x; | |
1376 | } | |
1377 | ||
1378 | sub bpow | |
1379 | { | |
1380 | # (BFLOAT or num_str, BFLOAT or num_str) return BFLOAT | |
1381 | # compute power of two numbers, second arg is used as integer | |
1382 | # modifies first argument | |
1383 | ||
1384 | # set up parameters | |
1385 | my ($self,$x,$y,$a,$p,$r) = (ref($_[0]),@_); | |
1386 | # objectify is costly, so avoid it | |
1387 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1388 | { | |
1389 | ($self,$x,$y,$a,$p,$r) = objectify(2,@_); | |
1390 | } | |
1391 | ||
1392 | return $x if $x->{sign} =~ /^[+-]inf$/; | |
1393 | return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan; | |
1394 | return $x->bone() if $y->is_zero(); | |
1395 | return $x if $x->is_one() || $y->is_one(); | |
1396 | ||
1397 | return $x->_pow($y,$a,$p,$r) if !$y->is_int(); # non-integer power | |
1398 | ||
1399 | my $y1 = $y->as_number(); # make bigint | |
1400 | # if ($x == -1) | |
1401 | if ($x->{sign} eq '-' && $x->{_m}->is_one() && $x->{_e}->is_zero()) | |
1402 | { | |
1403 | # if $x == -1 and odd/even y => +1/-1 because +-1 ^ (+-1) => +-1 | |
1404 | return $y1->is_odd() ? $x : $x->babs(1); | |
1405 | } | |
1406 | if ($x->is_zero()) | |
1407 | { | |
1408 | return $x if $y->{sign} eq '+'; # 0**y => 0 (if not y <= 0) | |
1409 | # 0 ** -y => 1 / (0 ** y) => / 0! (1 / 0 => +inf) | |
1410 | $x->binf(); | |
1411 | } | |
1412 | ||
1413 | # calculate $x->{_m} ** $y and $x->{_e} * $y separately (faster) | |
1414 | $y1->babs(); | |
1415 | $x->{_m}->bpow($y1); | |
1416 | $x->{_e}->bmul($y1); | |
1417 | $x->{sign} = $nan if $x->{_m}->{sign} eq $nan || $x->{_e}->{sign} eq $nan; | |
1418 | $x->bnorm(); | |
1419 | if ($y->{sign} eq '-') | |
1420 | { | |
1421 | # modify $x in place! | |
1422 | my $z = $x->copy(); $x->bzero()->binc(); | |
1423 | return $x->bdiv($z,$a,$p,$r); # round in one go (might ignore y's A!) | |
1424 | } | |
1425 | $x->round($a,$p,$r,$y); | |
1426 | } | |
1427 | ||
1428 | ############################################################################### | |
1429 | # rounding functions | |
1430 | ||
1431 | sub bfround | |
1432 | { | |
1433 | # precision: round to the $Nth digit left (+$n) or right (-$n) from the '.' | |
1434 | # $n == 0 means round to integer | |
1435 | # expects and returns normalized numbers! | |
1436 | my $x = shift; my $self = ref($x) || $x; $x = $self->new(shift) if !ref($x); | |
1437 | ||
1438 | return $x if $x->modify('bfround'); | |
1439 | ||
1440 | my ($scale,$mode) = $x->_scale_p($self->precision(),$self->round_mode(),@_); | |
1441 | return $x if !defined $scale; # no-op | |
1442 | ||
1443 | # never round a 0, +-inf, NaN | |
1444 | if ($x->is_zero()) | |
1445 | { | |
1446 | $x->{_p} = $scale if !defined $x->{_p} || $x->{_p} < $scale; # -3 < -2 | |
1447 | return $x; | |
1448 | } | |
1449 | return $x if $x->{sign} !~ /^[+-]$/; | |
1450 | ||
1451 | # don't round if x already has lower precision | |
1452 | return $x if (defined $x->{_p} && $x->{_p} < 0 && $scale < $x->{_p}); | |
1453 | ||
1454 | $x->{_p} = $scale; # remember round in any case | |
1455 | $x->{_a} = undef; # and clear A | |
1456 | if ($scale < 0) | |
1457 | { | |
1458 | # round right from the '.' | |
1459 | ||
1460 | return $x if $x->{_e}->{sign} eq '+'; # e >= 0 => nothing to round | |
1461 | ||
1462 | $scale = -$scale; # positive for simplicity | |
1463 | my $len = $x->{_m}->length(); # length of mantissa | |
1464 | ||
1465 | # the following poses a restriction on _e, but if _e is bigger than a | |
1466 | # scalar, you got other problems (memory etc) anyway | |
1467 | my $dad = -($x->{_e}->numify()); # digits after dot | |
1468 | my $zad = 0; # zeros after dot | |
1469 | $zad = $dad - $len if (-$dad < -$len); # for 0.00..00xxx style | |
1470 | ||
1471 | #print "scale $scale dad $dad zad $zad len $len\n"; | |
1472 | # number bsstr len zad dad | |
1473 | # 0.123 123e-3 3 0 3 | |
1474 | # 0.0123 123e-4 3 1 4 | |
1475 | # 0.001 1e-3 1 2 3 | |
1476 | # 1.23 123e-2 3 0 2 | |
1477 | # 1.2345 12345e-4 5 0 4 | |
1478 | ||
1479 | # do not round after/right of the $dad | |
1480 | return $x if $scale > $dad; # 0.123, scale >= 3 => exit | |
1481 | ||
1482 | # round to zero if rounding inside the $zad, but not for last zero like: | |
1483 | # 0.0065, scale -2, round last '0' with following '65' (scale == zad case) | |
1484 | return $x->bzero() if $scale < $zad; | |
1485 | if ($scale == $zad) # for 0.006, scale -3 and trunc | |
1486 | { | |
1487 | $scale = -$len; | |
1488 | } | |
1489 | else | |
1490 | { | |
1491 | # adjust round-point to be inside mantissa | |
1492 | if ($zad != 0) | |
1493 | { | |
1494 | $scale = $scale-$zad; | |
1495 | } | |
1496 | else | |
1497 | { | |
1498 | my $dbd = $len - $dad; $dbd = 0 if $dbd < 0; # digits before dot | |
1499 | $scale = $dbd+$scale; | |
1500 | } | |
1501 | } | |
1502 | } | |
1503 | else | |
1504 | { | |
1505 | # round left from the '.' | |
1506 | ||
1507 | # 123 => 100 means length(123) = 3 - $scale (2) => 1 | |
1508 | ||
1509 | my $dbt = $x->{_m}->length(); | |
1510 | # digits before dot | |
1511 | my $dbd = $dbt + $x->{_e}->numify(); | |
1512 | # should be the same, so treat it as this | |
1513 | $scale = 1 if $scale == 0; | |
1514 | # shortcut if already integer | |
1515 | return $x if $scale == 1 && $dbt <= $dbd; | |
1516 | # maximum digits before dot | |
1517 | ++$dbd; | |
1518 | ||
1519 | if ($scale > $dbd) | |
1520 | { | |
1521 | # not enough digits before dot, so round to zero | |
1522 | return $x->bzero; | |
1523 | } | |
1524 | elsif ( $scale == $dbd ) | |
1525 | { | |
1526 | # maximum | |
1527 | $scale = -$dbt; | |
1528 | } | |
1529 | else | |
1530 | { | |
1531 | $scale = $dbd - $scale; | |
1532 | } | |
1533 | } | |
1534 | # pass sign to bround for rounding modes '+inf' and '-inf' | |
1535 | $x->{_m}->{sign} = $x->{sign}; | |
1536 | $x->{_m}->bround($scale,$mode); | |
1537 | $x->{_m}->{sign} = '+'; # fix sign back | |
1538 | $x->bnorm(); | |
1539 | } | |
1540 | ||
1541 | sub bround | |
1542 | { | |
1543 | # accuracy: preserve $N digits, and overwrite the rest with 0's | |
1544 | my $x = shift; my $self = ref($x) || $x; $x = $self->new(shift) if !ref($x); | |
1545 | ||
1546 | die ('bround() needs positive accuracy') if ($_[0] || 0) < 0; | |
1547 | ||
1548 | my ($scale,$mode) = $x->_scale_a($self->accuracy(),$self->round_mode(),@_); | |
1549 | return $x if !defined $scale; # no-op | |
1550 | ||
1551 | return $x if $x->modify('bround'); | |
1552 | ||
1553 | # scale is now either $x->{_a}, $accuracy, or the user parameter | |
1554 | # test whether $x already has lower accuracy, do nothing in this case | |
1555 | # but do round if the accuracy is the same, since a math operation might | |
1556 | # want to round a number with A=5 to 5 digits afterwards again | |
1557 | return $x if defined $_[0] && defined $x->{_a} && $x->{_a} < $_[0]; | |
1558 | ||
1559 | # scale < 0 makes no sense | |
1560 | # never round a +-inf, NaN | |
1561 | return $x if ($scale < 0) || $x->{sign} !~ /^[+-]$/; | |
1562 | ||
1563 | # 1: $scale == 0 => keep all digits | |
1564 | # 2: never round a 0 | |
1565 | # 3: if we should keep more digits than the mantissa has, do nothing | |
1566 | if ($scale == 0 || $x->is_zero() || $x->{_m}->length() <= $scale) | |
1567 | { | |
1568 | $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; | |
1569 | return $x; | |
1570 | } | |
1571 | ||
1572 | # pass sign to bround for '+inf' and '-inf' rounding modes | |
1573 | $x->{_m}->{sign} = $x->{sign}; | |
1574 | $x->{_m}->bround($scale,$mode); # round mantissa | |
1575 | $x->{_m}->{sign} = '+'; # fix sign back | |
1576 | # $x->{_m}->{_a} = undef; $x->{_m}->{_p} = undef; | |
1577 | $x->{_a} = $scale; # remember rounding | |
1578 | $x->{_p} = undef; # and clear P | |
1579 | $x->bnorm(); # del trailing zeros gen. by bround() | |
1580 | } | |
1581 | ||
1582 | sub bfloor | |
1583 | { | |
1584 | # return integer less or equal then $x | |
1585 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); | |
1586 | ||
1587 | return $x if $x->modify('bfloor'); | |
1588 | ||
1589 | return $x if $x->{sign} !~ /^[+-]$/; # nan, +inf, -inf | |
1590 | ||
1591 | # if $x has digits after dot | |
1592 | if ($x->{_e}->{sign} eq '-') | |
1593 | { | |
1594 | $x->{_e}->{sign} = '+'; # negate e | |
1595 | $x->{_m}->brsft($x->{_e},10); # cut off digits after dot | |
1596 | $x->{_e}->bzero(); # trunc/norm | |
1597 | $x->{_m}->binc() if $x->{sign} eq '-'; # decrement if negative | |
1598 | } | |
1599 | $x->round($a,$p,$r); | |
1600 | } | |
1601 | ||
1602 | sub bceil | |
1603 | { | |
1604 | # return integer greater or equal then $x | |
1605 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); | |
1606 | ||
1607 | return $x if $x->modify('bceil'); | |
1608 | return $x if $x->{sign} !~ /^[+-]$/; # nan, +inf, -inf | |
1609 | ||
1610 | # if $x has digits after dot | |
1611 | if ($x->{_e}->{sign} eq '-') | |
1612 | { | |
1613 | #$x->{_m}->brsft(-$x->{_e},10); | |
1614 | #$x->{_e}->bzero(); | |
1615 | #$x++ if $x->{sign} eq '+'; | |
1616 | ||
1617 | $x->{_e}->{sign} = '+'; # negate e | |
1618 | $x->{_m}->brsft($x->{_e},10); # cut off digits after dot | |
1619 | $x->{_e}->bzero(); # trunc/norm | |
1620 | $x->{_m}->binc() if $x->{sign} eq '+'; # decrement if negative | |
1621 | } | |
1622 | $x->round($a,$p,$r); | |
1623 | } | |
1624 | ||
1625 | sub brsft | |
1626 | { | |
1627 | # shift right by $y (divide by power of $n) | |
1628 | ||
1629 | # set up parameters | |
1630 | my ($self,$x,$y,$n,$a,$p,$r) = (ref($_[0]),@_); | |
1631 | # objectify is costly, so avoid it | |
1632 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1633 | { | |
1634 | ($self,$x,$y,$n,$a,$p,$r) = objectify(2,@_); | |
1635 | } | |
1636 | ||
1637 | return $x if $x->modify('brsft'); | |
1638 | return $x if $x->{sign} !~ /^[+-]$/; # nan, +inf, -inf | |
1639 | ||
1640 | $n = 2 if !defined $n; $n = $self->new($n); | |
1641 | $x->bdiv($n->bpow($y),$a,$p,$r,$y); | |
1642 | } | |
1643 | ||
1644 | sub blsft | |
1645 | { | |
1646 | # shift left by $y (multiply by power of $n) | |
1647 | ||
1648 | # set up parameters | |
1649 | my ($self,$x,$y,$n,$a,$p,$r) = (ref($_[0]),@_); | |
1650 | # objectify is costly, so avoid it | |
1651 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1652 | { | |
1653 | ($self,$x,$y,$n,$a,$p,$r) = objectify(2,@_); | |
1654 | } | |
1655 | ||
1656 | return $x if $x->modify('blsft'); | |
1657 | return $x if $x->{sign} !~ /^[+-]$/; # nan, +inf, -inf | |
1658 | ||
1659 | $n = 2 if !defined $n; $n = $self->new($n); | |
1660 | $x->bmul($n->bpow($y),$a,$p,$r,$y); | |
1661 | } | |
1662 | ||
1663 | ############################################################################### | |
1664 | ||
1665 | sub DESTROY | |
1666 | { | |
1667 | # going through AUTOLOAD for every DESTROY is costly, so avoid it by empty sub | |
1668 | } | |
1669 | ||
1670 | sub AUTOLOAD | |
1671 | { | |
1672 | # make fxxx and bxxx both work by selectively mapping fxxx() to MBF::bxxx() | |
1673 | # or falling back to MBI::bxxx() | |
1674 | my $name = $AUTOLOAD; | |
1675 | ||
1676 | $name =~ s/.*:://; # split package | |
1677 | no strict 'refs'; | |
1678 | if (!method_alias($name)) | |
1679 | { | |
1680 | if (!defined $name) | |
1681 | { | |
1682 | # delayed load of Carp and avoid recursion | |
1683 | require Carp; | |
1684 | Carp::croak ("Can't call a method without name"); | |
1685 | } | |
1686 | if (!method_hand_up($name)) | |
1687 | { | |
1688 | # delayed load of Carp and avoid recursion | |
1689 | require Carp; | |
1690 | Carp::croak ("Can't call $class\-\>$name, not a valid method"); | |
1691 | } | |
1692 | # try one level up, but subst. bxxx() for fxxx() since MBI only got bxxx() | |
1693 | $name =~ s/^f/b/; | |
1694 | return &{"$MBI"."::$name"}(@_); | |
1695 | } | |
1696 | my $bname = $name; $bname =~ s/^f/b/; | |
1697 | *{$class."::$name"} = \&$bname; | |
1698 | &$bname; # uses @_ | |
1699 | } | |
1700 | ||
1701 | sub exponent | |
1702 | { | |
1703 | # return a copy of the exponent | |
1704 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
1705 | ||
1706 | if ($x->{sign} !~ /^[+-]$/) | |
1707 | { | |
1708 | my $s = $x->{sign}; $s =~ s/^[+-]//; | |
1709 | return $self->new($s); # -inf, +inf => +inf | |
1710 | } | |
1711 | return $x->{_e}->copy(); | |
1712 | } | |
1713 | ||
1714 | sub mantissa | |
1715 | { | |
1716 | # return a copy of the mantissa | |
1717 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
1718 | ||
1719 | if ($x->{sign} !~ /^[+-]$/) | |
1720 | { | |
1721 | my $s = $x->{sign}; $s =~ s/^[+]//; | |
1722 | return $self->new($s); # -inf, +inf => +inf | |
1723 | } | |
1724 | my $m = $x->{_m}->copy(); # faster than going via bstr() | |
1725 | $m->bneg() if $x->{sign} eq '-'; | |
1726 | ||
1727 | $m; | |
1728 | } | |
1729 | ||
1730 | sub parts | |
1731 | { | |
1732 | # return a copy of both the exponent and the mantissa | |
1733 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
1734 | ||
1735 | if ($x->{sign} !~ /^[+-]$/) | |
1736 | { | |
1737 | my $s = $x->{sign}; $s =~ s/^[+]//; my $se = $s; $se =~ s/^[-]//; | |
1738 | return ($self->new($s),$self->new($se)); # +inf => inf and -inf,+inf => inf | |
1739 | } | |
1740 | my $m = $x->{_m}->copy(); # faster than going via bstr() | |
1741 | $m->bneg() if $x->{sign} eq '-'; | |
1742 | return ($m,$x->{_e}->copy()); | |
1743 | } | |
1744 | ||
1745 | ############################################################################## | |
1746 | # private stuff (internal use only) | |
1747 | ||
1748 | sub import | |
1749 | { | |
1750 | my $self = shift; | |
1751 | my $l = scalar @_; | |
1752 | my $lib = ''; my @a; | |
1753 | for ( my $i = 0; $i < $l ; $i++) | |
1754 | { | |
1755 | # print "at $_[$i] (",$_[$i+1]||'undef',")\n"; | |
1756 | if ( $_[$i] eq ':constant' ) | |
1757 | { | |
1758 | # this rest causes overlord er load to step in | |
1759 | # print "overload @_\n"; | |
1760 | overload::constant float => sub { $self->new(shift); }; | |
1761 | } | |
1762 | elsif ($_[$i] eq 'upgrade') | |
1763 | { | |
1764 | # this causes upgrading | |
1765 | $upgrade = $_[$i+1]; # or undef to disable | |
1766 | $i++; | |
1767 | } | |
1768 | elsif ($_[$i] eq 'downgrade') | |
1769 | { | |
1770 | # this causes downgrading | |
1771 | $downgrade = $_[$i+1]; # or undef to disable | |
1772 | $i++; | |
1773 | } | |
1774 | elsif ($_[$i] eq 'lib') | |
1775 | { | |
1776 | $lib = $_[$i+1] || ''; # default Calc | |
1777 | $i++; | |
1778 | } | |
1779 | elsif ($_[$i] eq 'with') | |
1780 | { | |
1781 | $MBI = $_[$i+1] || 'Math::BigInt'; # default Math::BigInt | |
1782 | $i++; | |
1783 | } | |
1784 | else | |
1785 | { | |
1786 | push @a, $_[$i]; | |
1787 | } | |
1788 | } | |
1789 | ||
1790 | # let use Math::BigInt lib => 'GMP'; use Math::BigFloat; still work | |
1791 | my $mbilib = eval { Math::BigInt->config()->{lib} }; | |
1792 | if ((defined $mbilib) && ($MBI eq 'Math::BigInt')) | |
1793 | { | |
1794 | # MBI already loaded | |
1795 | $MBI->import('lib',"$lib,$mbilib", 'objectify'); | |
1796 | } | |
1797 | else | |
1798 | { | |
1799 | # MBI not loaded, or with ne "Math::BigInt" | |
1800 | $lib .= ",$mbilib" if defined $mbilib; | |
1801 | $lib =~ s/^,//; # don't leave empty | |
1802 | if ($] < 5.006) | |
1803 | { | |
1804 | # Perl < 5.6.0 dies with "out of memory!" when eval() and ':constant' is | |
1805 | # used in the same script, or eval inside import(). | |
1806 | my @parts = split /::/, $MBI; # Math::BigInt => Math BigInt | |
1807 | my $file = pop @parts; $file .= '.pm'; # BigInt => BigInt.pm | |
1808 | require File::Spec; | |
1809 | $file = File::Spec->catfile (@parts, $file); | |
1810 | eval { require "$file"; }; | |
1811 | $MBI->import( lib => $lib, 'objectify' ); | |
1812 | } | |
1813 | else | |
1814 | { | |
1815 | my $rc = "use $MBI lib => '$lib', 'objectify';"; | |
1816 | eval $rc; | |
1817 | } | |
1818 | } | |
1819 | die ("Couldn't load $MBI: $! $@") if $@; | |
1820 | ||
1821 | # any non :constant stuff is handled by our parent, Exporter | |
1822 | # even if @_ is empty, to give it a chance | |
1823 | $self->SUPER::import(@a); # for subclasses | |
1824 | $self->export_to_level(1,$self,@a); # need this, too | |
1825 | } | |
1826 | ||
1827 | sub bnorm | |
1828 | { | |
1829 | # adjust m and e so that m is smallest possible | |
1830 | # round number according to accuracy and precision settings | |
1831 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
1832 | ||
1833 | return $x if $x->{sign} !~ /^[+-]$/; # inf, nan etc | |
1834 | ||
1835 | # if (!$x->{_m}->is_odd()) | |
1836 | # { | |
1837 | my $zeros = $x->{_m}->_trailing_zeros(); # correct for trailing zeros | |
1838 | if ($zeros != 0) | |
1839 | { | |
1840 | $x->{_m}->brsft($zeros,10); $x->{_e}->badd($zeros); | |
1841 | } | |
1842 | # for something like 0Ey, set y to 1, and -0 => +0 | |
1843 | $x->{sign} = '+', $x->{_e}->bone() if $x->{_m}->is_zero(); | |
1844 | # } | |
1845 | # this is to prevent automatically rounding when MBI's globals are set | |
1846 | $x->{_m}->{_f} = MB_NEVER_ROUND; | |
1847 | $x->{_e}->{_f} = MB_NEVER_ROUND; | |
1848 | # 'forget' that mantissa was rounded via MBI::bround() in MBF's bfround() | |
1849 | $x->{_m}->{_a} = undef; $x->{_e}->{_a} = undef; | |
1850 | $x->{_m}->{_p} = undef; $x->{_e}->{_p} = undef; | |
1851 | $x; # MBI bnorm is no-op, so dont call it | |
1852 | } | |
1853 | ||
1854 | ############################################################################## | |
1855 | # internal calculation routines | |
1856 | ||
1857 | sub as_number | |
1858 | { | |
1859 | # return copy as a bigint representation of this BigFloat number | |
1860 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
1861 | ||
1862 | my $z = $x->{_m}->copy(); | |
1863 | if ($x->{_e}->{sign} eq '-') # < 0 | |
1864 | { | |
1865 | $x->{_e}->{sign} = '+'; # flip | |
1866 | $z->brsft($x->{_e},10); | |
1867 | $x->{_e}->{sign} = '-'; # flip back | |
1868 | } | |
1869 | elsif (!$x->{_e}->is_zero()) # > 0 | |
1870 | { | |
1871 | $z->blsft($x->{_e},10); | |
1872 | } | |
1873 | $z->{sign} = $x->{sign}; | |
1874 | $z; | |
1875 | } | |
1876 | ||
1877 | sub length | |
1878 | { | |
1879 | my $x = shift; | |
1880 | my $class = ref($x) || $x; | |
1881 | $x = $class->new(shift) unless ref($x); | |
1882 | ||
1883 | return 1 if $x->{_m}->is_zero(); | |
1884 | my $len = $x->{_m}->length(); | |
1885 | $len += $x->{_e} if $x->{_e}->sign() eq '+'; | |
1886 | if (wantarray()) | |
1887 | { | |
1888 | my $t = $MBI->bzero(); | |
1889 | $t = $x->{_e}->copy()->babs() if $x->{_e}->sign() eq '-'; | |
1890 | return ($len,$t); | |
1891 | } | |
1892 | $len; | |
1893 | } | |
1894 | ||
1895 | 1; | |
1896 | __END__ | |
1897 | ||
1898 | =head1 NAME | |
1899 | ||
1900 | Math::BigFloat - Arbitrary size floating point math package | |
1901 | ||
1902 | =head1 SYNOPSIS | |
1903 | ||
1904 | use Math::BigFloat; | |
1905 | ||
1906 | # Number creation | |
1907 | $x = Math::BigFloat->new($str); # defaults to 0 | |
1908 | $nan = Math::BigFloat->bnan(); # create a NotANumber | |
1909 | $zero = Math::BigFloat->bzero(); # create a +0 | |
1910 | $inf = Math::BigFloat->binf(); # create a +inf | |
1911 | $inf = Math::BigFloat->binf('-'); # create a -inf | |
1912 | $one = Math::BigFloat->bone(); # create a +1 | |
1913 | $one = Math::BigFloat->bone('-'); # create a -1 | |
1914 | ||
1915 | # Testing | |
1916 | $x->is_zero(); # true if arg is +0 | |
1917 | $x->is_nan(); # true if arg is NaN | |
1918 | $x->is_one(); # true if arg is +1 | |
1919 | $x->is_one('-'); # true if arg is -1 | |
1920 | $x->is_odd(); # true if odd, false for even | |
1921 | $x->is_even(); # true if even, false for odd | |
1922 | $x->is_positive(); # true if >= 0 | |
1923 | $x->is_negative(); # true if < 0 | |
1924 | $x->is_inf(sign); # true if +inf, or -inf (default is '+') | |
1925 | ||
1926 | $x->bcmp($y); # compare numbers (undef,<0,=0,>0) | |
1927 | $x->bacmp($y); # compare absolutely (undef,<0,=0,>0) | |
1928 | $x->sign(); # return the sign, either +,- or NaN | |
1929 | $x->digit($n); # return the nth digit, counting from right | |
1930 | $x->digit(-$n); # return the nth digit, counting from left | |
1931 | ||
1932 | # The following all modify their first argument: | |
1933 | ||
1934 | # set | |
1935 | $x->bzero(); # set $i to 0 | |
1936 | $x->bnan(); # set $i to NaN | |
1937 | $x->bone(); # set $x to +1 | |
1938 | $x->bone('-'); # set $x to -1 | |
1939 | $x->binf(); # set $x to inf | |
1940 | $x->binf('-'); # set $x to -inf | |
1941 | ||
1942 | $x->bneg(); # negation | |
1943 | $x->babs(); # absolute value | |
1944 | $x->bnorm(); # normalize (no-op) | |
1945 | $x->bnot(); # two's complement (bit wise not) | |
1946 | $x->binc(); # increment x by 1 | |
1947 | $x->bdec(); # decrement x by 1 | |
1948 | ||
1949 | $x->badd($y); # addition (add $y to $x) | |
1950 | $x->bsub($y); # subtraction (subtract $y from $x) | |
1951 | $x->bmul($y); # multiplication (multiply $x by $y) | |
1952 | $x->bdiv($y); # divide, set $i to quotient | |
1953 | # return (quo,rem) or quo if scalar | |
1954 | ||
1955 | $x->bmod($y); # modulus | |
1956 | $x->bpow($y); # power of arguments (a**b) | |
1957 | $x->blsft($y); # left shift | |
1958 | $x->brsft($y); # right shift | |
1959 | # return (quo,rem) or quo if scalar | |
1960 | ||
1961 | $x->blog($base); # logarithm of $x, base defaults to e | |
1962 | # (other bases than e not supported yet) | |
1963 | ||
1964 | $x->band($y); # bit-wise and | |
1965 | $x->bior($y); # bit-wise inclusive or | |
1966 | $x->bxor($y); # bit-wise exclusive or | |
1967 | $x->bnot(); # bit-wise not (two's complement) | |
1968 | ||
1969 | $x->bsqrt(); # calculate square-root | |
1970 | $x->bfac(); # factorial of $x (1*2*3*4*..$x) | |
1971 | ||
1972 | $x->bround($N); # accuracy: preserver $N digits | |
1973 | $x->bfround($N); # precision: round to the $Nth digit | |
1974 | ||
1975 | # The following do not modify their arguments: | |
1976 | bgcd(@values); # greatest common divisor | |
1977 | blcm(@values); # lowest common multiplicator | |
1978 | ||
1979 | $x->bstr(); # return string | |
1980 | $x->bsstr(); # return string in scientific notation | |
1981 | ||
1982 | $x->bfloor(); # return integer less or equal than $x | |
1983 | $x->bceil(); # return integer greater or equal than $x | |
1984 | ||
1985 | $x->exponent(); # return exponent as BigInt | |
1986 | $x->mantissa(); # return mantissa as BigInt | |
1987 | $x->parts(); # return (mantissa,exponent) as BigInt | |
1988 | ||
1989 | $x->length(); # number of digits (w/o sign and '.') | |
1990 | ($l,$f) = $x->length(); # number of digits, and length of fraction | |
1991 | ||
1992 | $x->precision(); # return P of $x (or global, if P of $x undef) | |
1993 | $x->precision($n); # set P of $x to $n | |
1994 | $x->accuracy(); # return A of $x (or global, if A of $x undef) | |
1995 | $x->accuracy($n); # set A $x to $n | |
1996 | ||
1997 | Math::BigFloat->precision(); # get/set global P for all BigFloat objects | |
1998 | Math::BigFloat->accuracy(); # get/set global A for all BigFloat objects | |
1999 | ||
2000 | =head1 DESCRIPTION | |
2001 | ||
2002 | All operators (inlcuding basic math operations) are overloaded if you | |
2003 | declare your big floating point numbers as | |
2004 | ||
2005 | $i = new Math::BigFloat '12_3.456_789_123_456_789E-2'; | |
2006 | ||
2007 | Operations with overloaded operators preserve the arguments, which is | |
2008 | exactly what you expect. | |
2009 | ||
2010 | =head2 Canonical notation | |
2011 | ||
2012 | Input to these routines are either BigFloat objects, or strings of the | |
2013 | following four forms: | |
2014 | ||
2015 | =over 2 | |
2016 | ||
2017 | =item * | |
2018 | ||
2019 | C</^[+-]\d+$/> | |
2020 | ||
2021 | =item * | |
2022 | ||
2023 | C</^[+-]\d+\.\d*$/> | |
2024 | ||
2025 | =item * | |
2026 | ||
2027 | C</^[+-]\d+E[+-]?\d+$/> | |
2028 | ||
2029 | =item * | |
2030 | ||
2031 | C</^[+-]\d*\.\d+E[+-]?\d+$/> | |
2032 | ||
2033 | =back | |
2034 | ||
2035 | all with optional leading and trailing zeros and/or spaces. Additonally, | |
2036 | numbers are allowed to have an underscore between any two digits. | |
2037 | ||
2038 | Empty strings as well as other illegal numbers results in 'NaN'. | |
2039 | ||
2040 | bnorm() on a BigFloat object is now effectively a no-op, since the numbers | |
2041 | are always stored in normalized form. On a string, it creates a BigFloat | |
2042 | object. | |
2043 | ||
2044 | =head2 Output | |
2045 | ||
2046 | Output values are BigFloat objects (normalized), except for bstr() and bsstr(). | |
2047 | ||
2048 | The string output will always have leading and trailing zeros stripped and drop | |
2049 | a plus sign. C<bstr()> will give you always the form with a decimal point, | |
2050 | while C<bsstr()> (for scientific) gives you the scientific notation. | |
2051 | ||
2052 | Input bstr() bsstr() | |
2053 | '-0' '0' '0E1' | |
2054 | ' -123 123 123' '-123123123' '-123123123E0' | |
2055 | '00.0123' '0.0123' '123E-4' | |
2056 | '123.45E-2' '1.2345' '12345E-4' | |
2057 | '10E+3' '10000' '1E4' | |
2058 | ||
2059 | Some routines (C<is_odd()>, C<is_even()>, C<is_zero()>, C<is_one()>, | |
2060 | C<is_nan()>) return true or false, while others (C<bcmp()>, C<bacmp()>) | |
2061 | return either undef, <0, 0 or >0 and are suited for sort. | |
2062 | ||
2063 | Actual math is done by using BigInts to represent the mantissa and exponent. | |
2064 | The sign C</^[+-]$/> is stored separately. The string 'NaN' is used to | |
2065 | represent the result when input arguments are not numbers, as well as | |
2066 | the result of dividing by zero. | |
2067 | ||
2068 | =head2 C<mantissa()>, C<exponent()> and C<parts()> | |
2069 | ||
2070 | C<mantissa()> and C<exponent()> return the said parts of the BigFloat | |
2071 | as BigInts such that: | |
2072 | ||
2073 | $m = $x->mantissa(); | |
2074 | $e = $x->exponent(); | |
2075 | $y = $m * ( 10 ** $e ); | |
2076 | print "ok\n" if $x == $y; | |
2077 | ||
2078 | C<< ($m,$e) = $x->parts(); >> is just a shortcut giving you both of them. | |
2079 | ||
2080 | A zero is represented and returned as C<0E1>, B<not> C<0E0> (after Knuth). | |
2081 | ||
2082 | Currently the mantissa is reduced as much as possible, favouring higher | |
2083 | exponents over lower ones (e.g. returning 1e7 instead of 10e6 or 10000000e0). | |
2084 | This might change in the future, so do not depend on it. | |
2085 | ||
2086 | =head2 Accuracy vs. Precision | |
2087 | ||
2088 | See also: L<Rounding|Rounding>. | |
2089 | ||
2090 | Math::BigFloat supports both precision and accuracy. For a full documentation, | |
2091 | examples and tips on these topics please see the large section in | |
2092 | L<Math::BigInt>. | |
2093 | ||
2094 | Since things like sqrt(2) or 1/3 must presented with a limited precision lest | |
2095 | a operation consumes all resources, each operation produces no more than | |
2096 | C<Math::BigFloat::precision()> digits. | |
2097 | ||
2098 | In case the result of one operation has more precision than specified, | |
2099 | it is rounded. The rounding mode taken is either the default mode, or the one | |
2100 | supplied to the operation after the I<scale>: | |
2101 | ||
2102 | $x = Math::BigFloat->new(2); | |
2103 | Math::BigFloat::precision(5); # 5 digits max | |
2104 | $y = $x->copy()->bdiv(3); # will give 0.66666 | |
2105 | $y = $x->copy()->bdiv(3,6); # will give 0.666666 | |
2106 | $y = $x->copy()->bdiv(3,6,'odd'); # will give 0.666667 | |
2107 | Math::BigFloat::round_mode('zero'); | |
2108 | $y = $x->copy()->bdiv(3,6); # will give 0.666666 | |
2109 | ||
2110 | =head2 Rounding | |
2111 | ||
2112 | =over 2 | |
2113 | ||
2114 | =item ffround ( +$scale ) | |
2115 | ||
2116 | Rounds to the $scale'th place left from the '.', counting from the dot. | |
2117 | The first digit is numbered 1. | |
2118 | ||
2119 | =item ffround ( -$scale ) | |
2120 | ||
2121 | Rounds to the $scale'th place right from the '.', counting from the dot. | |
2122 | ||
2123 | =item ffround ( 0 ) | |
2124 | ||
2125 | Rounds to an integer. | |
2126 | ||
2127 | =item fround ( +$scale ) | |
2128 | ||
2129 | Preserves accuracy to $scale digits from the left (aka significant digits) | |
2130 | and pads the rest with zeros. If the number is between 1 and -1, the | |
2131 | significant digits count from the first non-zero after the '.' | |
2132 | ||
2133 | =item fround ( -$scale ) and fround ( 0 ) | |
2134 | ||
2135 | These are effetively no-ops. | |
2136 | ||
2137 | =back | |
2138 | ||
2139 | All rounding functions take as a second parameter a rounding mode from one of | |
2140 | the following: 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'. | |
2141 | ||
2142 | The default rounding mode is 'even'. By using | |
2143 | C<< Math::BigFloat::round_mode($round_mode); >> you can get and set the default | |
2144 | mode for subsequent rounding. The usage of C<$Math::BigFloat::$round_mode> is | |
2145 | no longer supported. | |
2146 | The second parameter to the round functions then overrides the default | |
2147 | temporarily. | |
2148 | ||
2149 | The C<< as_number() >> function returns a BigInt from a Math::BigFloat. It uses | |
2150 | 'trunc' as rounding mode to make it equivalent to: | |
2151 | ||
2152 | $x = 2.5; | |
2153 | $y = int($x) + 2; | |
2154 | ||
2155 | You can override this by passing the desired rounding mode as parameter to | |
2156 | C<as_number()>: | |
2157 | ||
2158 | $x = Math::BigFloat->new(2.5); | |
2159 | $y = $x->as_number('odd'); # $y = 3 | |
2160 | ||
2161 | =head1 EXAMPLES | |
2162 | ||
2163 | # not ready yet | |
2164 | ||
2165 | =head1 Autocreating constants | |
2166 | ||
2167 | After C<use Math::BigFloat ':constant'> all the floating point constants | |
2168 | in the given scope are converted to C<Math::BigFloat>. This conversion | |
2169 | happens at compile time. | |
2170 | ||
2171 | In particular | |
2172 | ||
2173 | perl -MMath::BigFloat=:constant -e 'print 2E-100,"\n"' | |
2174 | ||
2175 | prints the value of C<2E-100>. Note that without conversion of | |
2176 | constants the expression 2E-100 will be calculated as normal floating point | |
2177 | number. | |
2178 | ||
2179 | Please note that ':constant' does not affect integer constants, nor binary | |
2180 | nor hexadecimal constants. Use L<bignum> or L<Math::BigInt> to get this to | |
2181 | work. | |
2182 | ||
2183 | =head2 Math library | |
2184 | ||
2185 | Math with the numbers is done (by default) by a module called | |
2186 | Math::BigInt::Calc. This is equivalent to saying: | |
2187 | ||
2188 | use Math::BigFloat lib => 'Calc'; | |
2189 | ||
2190 | You can change this by using: | |
2191 | ||
2192 | use Math::BigFloat lib => 'BitVect'; | |
2193 | ||
2194 | The following would first try to find Math::BigInt::Foo, then | |
2195 | Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: | |
2196 | ||
2197 | use Math::BigFloat lib => 'Foo,Math::BigInt::Bar'; | |
2198 | ||
2199 | Calc.pm uses as internal format an array of elements of some decimal base | |
2200 | (usually 1e7, but this might be differen for some systems) with the least | |
2201 | significant digit first, while BitVect.pm uses a bit vector of base 2, most | |
2202 | significant bit first. Other modules might use even different means of | |
2203 | representing the numbers. See the respective module documentation for further | |
2204 | details. | |
2205 | ||
2206 | Please note that Math::BigFloat does B<not> use the denoted library itself, | |
2207 | but it merely passes the lib argument to Math::BigInt. So, instead of the need | |
2208 | to do: | |
2209 | ||
2210 | use Math::BigInt lib => 'GMP'; | |
2211 | use Math::BigFloat; | |
2212 | ||
2213 | you can roll it all into one line: | |
2214 | ||
2215 | use Math::BigFloat lib => 'GMP'; | |
2216 | ||
2217 | Use the lib, Luke! And see L<Using Math::BigInt::Lite> for more details. | |
2218 | ||
2219 | =head2 Using Math::BigInt::Lite | |
2220 | ||
2221 | It is possible to use L<Math::BigInt::Lite> with Math::BigFloat: | |
2222 | ||
2223 | # 1 | |
2224 | use Math::BigFloat with => 'Math::BigInt::Lite'; | |
2225 | ||
2226 | There is no need to "use Math::BigInt" or "use Math::BigInt::Lite", but you | |
2227 | can combine these if you want. For instance, you may want to use | |
2228 | Math::BigInt objects in your main script, too. | |
2229 | ||
2230 | # 2 | |
2231 | use Math::BigInt; | |
2232 | use Math::BigFloat with => 'Math::BigInt::Lite'; | |
2233 | ||
2234 | Of course, you can combine this with the C<lib> parameter. | |
2235 | ||
2236 | # 3 | |
2237 | use Math::BigFloat with => 'Math::BigInt::Lite', lib => 'GMP,Pari'; | |
2238 | ||
2239 | If you want to use Math::BigInt's, too, simple add a Math::BigInt B<before>: | |
2240 | ||
2241 | # 4 | |
2242 | use Math::BigInt; | |
2243 | use Math::BigFloat with => 'Math::BigInt::Lite', lib => 'GMP,Pari'; | |
2244 | ||
2245 | Notice that the module with the last C<lib> will "win" and thus | |
2246 | it's lib will be used if the lib is available: | |
2247 | ||
2248 | # 5 | |
2249 | use Math::BigInt lib => 'Bar,Baz'; | |
2250 | use Math::BigFloat with => 'Math::BigInt::Lite', lib => 'Foo'; | |
2251 | ||
2252 | That would try to load Foo, Bar, Baz and Calc (in that order). Or in other | |
2253 | words, Math::BigFloat will try to retain previously loaded libs when you | |
2254 | don't specify it one. | |
2255 | ||
2256 | Actually, the lib loading order would be "Bar,Baz,Calc", and then | |
2257 | "Foo,Bar,Baz,Calc", but independend of which lib exists, the result is the | |
2258 | same as trying the latter load alone, except for the fact that Bar or Baz | |
2259 | might be loaded needlessly in an intermidiate step | |
2260 | ||
2261 | The old way still works though: | |
2262 | ||
2263 | # 6 | |
2264 | use Math::BigInt lib => 'Bar,Baz'; | |
2265 | use Math::BigFloat; | |
2266 | ||
2267 | But B<examples #3 and #4 are recommended> for usage. | |
2268 | ||
2269 | =head1 BUGS | |
2270 | ||
2271 | =over 2 | |
2272 | ||
2273 | =item * | |
2274 | ||
2275 | The following does not work yet: | |
2276 | ||
2277 | $m = $x->mantissa(); | |
2278 | $e = $x->exponent(); | |
2279 | $y = $m * ( 10 ** $e ); | |
2280 | print "ok\n" if $x == $y; | |
2281 | ||
2282 | =item * | |
2283 | ||
2284 | There is no fmod() function yet. | |
2285 | ||
2286 | =back | |
2287 | ||
2288 | =head1 CAVEAT | |
2289 | ||
2290 | =over 1 | |
2291 | ||
2292 | =item stringify, bstr() | |
2293 | ||
2294 | Both stringify and bstr() now drop the leading '+'. The old code would return | |
2295 | '+1.23', the new returns '1.23'. See the documentation in L<Math::BigInt> for | |
2296 | reasoning and details. | |
2297 | ||
2298 | =item bdiv | |
2299 | ||
2300 | The following will probably not do what you expect: | |
2301 | ||
2302 | print $c->bdiv(123.456),"\n"; | |
2303 | ||
2304 | It prints both quotient and reminder since print works in list context. Also, | |
2305 | bdiv() will modify $c, so be carefull. You probably want to use | |
2306 | ||
2307 | print $c / 123.456,"\n"; | |
2308 | print scalar $c->bdiv(123.456),"\n"; # or if you want to modify $c | |
2309 | ||
2310 | instead. | |
2311 | ||
2312 | =item Modifying and = | |
2313 | ||
2314 | Beware of: | |
2315 | ||
2316 | $x = Math::BigFloat->new(5); | |
2317 | $y = $x; | |
2318 | ||
2319 | It will not do what you think, e.g. making a copy of $x. Instead it just makes | |
2320 | a second reference to the B<same> object and stores it in $y. Thus anything | |
2321 | that modifies $x will modify $y, and vice versa. | |
2322 | ||
2323 | $x->bmul(2); | |
2324 | print "$x, $y\n"; # prints '10, 10' | |
2325 | ||
2326 | If you want a true copy of $x, use: | |
2327 | ||
2328 | $y = $x->copy(); | |
2329 | ||
2330 | See also the documentation in L<overload> regarding C<=>. | |
2331 | ||
2332 | =item bpow | |
2333 | ||
2334 | C<bpow()> now modifies the first argument, unlike the old code which left | |
2335 | it alone and only returned the result. This is to be consistent with | |
2336 | C<badd()> etc. The first will modify $x, the second one won't: | |
2337 | ||
2338 | print bpow($x,$i),"\n"; # modify $x | |
2339 | print $x->bpow($i),"\n"; # ditto | |
2340 | print $x ** $i,"\n"; # leave $x alone | |
2341 | ||
2342 | =back | |
2343 | ||
2344 | =head1 LICENSE | |
2345 | ||
2346 | This program is free software; you may redistribute it and/or modify it under | |
2347 | the same terms as Perl itself. | |
2348 | ||
2349 | =head1 AUTHORS | |
2350 | ||
2351 | Mark Biggar, overloaded interface by Ilya Zakharevich. | |
2352 | Completely rewritten by Tels http://bloodgate.com in 2001. | |
2353 | ||
2354 | =cut |