Commit | Line | Data |
13a12e00 |
1 | package Math::BigFloat; |
2 | |
3 | # |
d614cd8b |
4 | # Mike grinned. 'Two down, infinity to go' - Mike Nostrus in 'Before and After' |
13a12e00 |
5 | # |
6 | |
58cde26e |
7 | # The following hash values are internally used: |
9b924220 |
8 | # _e : exponent (ref to $CALC object) |
9 | # _m : mantissa (ref to $CALC object) |
10 | # _es : sign of _e |
11 | # sign : +,-,+inf,-inf, or "NaN" if not a number |
12 | # _a : accuracy |
13 | # _p : precision |
14 | |
2d2b2744 |
15 | $VERSION = '1.47'; |
58cde26e |
16 | require 5.005; |
3a427a11 |
17 | |
18 | require Exporter; |
2ab5f49d |
19 | @ISA = qw(Exporter Math::BigInt); |
394e6ffb |
20 | |
58cde26e |
21 | use strict; |
03874afe |
22 | # $_trap_inf/$_trap_nan are internal and should never be accessed from outside |
b282a552 |
23 | use vars qw/$AUTOLOAD $accuracy $precision $div_scale $round_mode $rnd_mode |
24 | $upgrade $downgrade $_trap_nan $_trap_inf/; |
58cde26e |
25 | my $class = "Math::BigFloat"; |
a0d0e21e |
26 | |
a5f75d66 |
27 | use overload |
bd05a461 |
28 | '<=>' => sub { $_[2] ? |
29 | ref($_[0])->bcmp($_[1],$_[0]) : |
30 | ref($_[0])->bcmp($_[0],$_[1])}, |
0716bf9b |
31 | 'int' => sub { $_[0]->as_number() }, # 'trunc' to bigint |
a5f75d66 |
32 | ; |
a0d0e21e |
33 | |
0716bf9b |
34 | ############################################################################## |
990fb837 |
35 | # global constants, flags and assorted stuff |
0716bf9b |
36 | |
990fb837 |
37 | # the following are public, but their usage is not recommended. Use the |
38 | # accessor methods instead. |
58cde26e |
39 | |
ee15d750 |
40 | # class constants, use Class->constant_name() to access |
41 | $round_mode = 'even'; # one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc' |
42 | $accuracy = undef; |
43 | $precision = undef; |
44 | $div_scale = 40; |
58cde26e |
45 | |
b3abae2a |
46 | $upgrade = undef; |
47 | $downgrade = undef; |
9b924220 |
48 | # the package we are using for our private parts, defaults to: |
49 | # Math::BigInt->config()->{lib} |
50 | my $MBI = 'Math::BigInt::Calc'; |
990fb837 |
51 | |
52 | # are NaNs ok? (otherwise it dies when encountering an NaN) set w/ config() |
53 | $_trap_nan = 0; |
9b924220 |
54 | # the same for infinity |
990fb837 |
55 | $_trap_inf = 0; |
56 | |
57 | # constant for easier life |
58 | my $nan = 'NaN'; |
59 | |
9b924220 |
60 | my $IMPORT = 0; # was import() called yet? used to make require work |
990fb837 |
61 | |
62 | # some digits of accuracy for blog(undef,10); which we use in blog() for speed |
63 | my $LOG_10 = |
64 | '2.3025850929940456840179914546843642076011014886287729760333279009675726097'; |
65 | my $LOG_10_A = length($LOG_10)-1; |
66 | # ditto for log(2) |
67 | my $LOG_2 = |
68 | '0.6931471805599453094172321214581765680755001343602552541206800094933936220'; |
69 | my $LOG_2_A = length($LOG_2)-1; |
27e7b8bb |
70 | my $HALF = '0.5'; # made into an object if necc. |
990fb837 |
71 | |
027dc388 |
72 | ############################################################################## |
73 | # the old code had $rnd_mode, so we need to support it, too |
74 | |
027dc388 |
75 | sub TIESCALAR { my ($class) = @_; bless \$round_mode, $class; } |
76 | sub FETCH { return $round_mode; } |
77 | sub STORE { $rnd_mode = $_[0]->round_mode($_[1]); } |
78 | |
56b9c951 |
79 | BEGIN |
990fb837 |
80 | { |
81 | # when someone set's $rnd_mode, we catch this and check the value to see |
82 | # whether it is valid or not. |
83 | $rnd_mode = 'even'; tie $rnd_mode, 'Math::BigFloat'; |
56b9c951 |
84 | } |
027dc388 |
85 | |
86 | ############################################################################## |
87 | |
58cde26e |
88 | { |
ee15d750 |
89 | # valid method aliases for AUTOLOAD |
58cde26e |
90 | my %methods = map { $_ => 1 } |
91 | qw / fadd fsub fmul fdiv fround ffround fsqrt fmod fstr fsstr fpow fnorm |
b3abae2a |
92 | fint facmp fcmp fzero fnan finf finc fdec flog ffac |
990fb837 |
93 | fceil ffloor frsft flsft fone flog froot |
ee15d750 |
94 | /; |
61f5c3f5 |
95 | # valid method's that can be hand-ed up (for AUTOLOAD) |
ee15d750 |
96 | my %hand_ups = map { $_ => 1 } |
ef9466ea |
97 | qw / is_nan is_inf is_negative is_positive is_pos is_neg |
990fb837 |
98 | accuracy precision div_scale round_mode fneg fabs fnot |
28df3e88 |
99 | objectify upgrade downgrade |
13a12e00 |
100 | bone binf bnan bzero |
58cde26e |
101 | /; |
102 | |
ef9466ea |
103 | sub method_alias { exists $methods{$_[0]||''}; } |
104 | sub method_hand_up { exists $hand_ups{$_[0]||''}; } |
a0d0e21e |
105 | } |
0e8b9368 |
106 | |
58cde26e |
107 | ############################################################################## |
108 | # constructors |
a0d0e21e |
109 | |
58cde26e |
110 | sub new |
111 | { |
112 | # create a new BigFloat object from a string or another bigfloat object. |
113 | # _e: exponent |
114 | # _m: mantissa |
115 | # sign => sign (+/-), or "NaN" |
a0d0e21e |
116 | |
61f5c3f5 |
117 | my ($class,$wanted,@r) = @_; |
b3abae2a |
118 | |
61f5c3f5 |
119 | # avoid numify-calls by not using || on $wanted! |
120 | return $class->bzero() if !defined $wanted; # default to 0 |
121 | return $wanted->copy() if UNIVERSAL::isa($wanted,'Math::BigFloat'); |
a0d0e21e |
122 | |
990fb837 |
123 | $class->import() if $IMPORT == 0; # make require work |
124 | |
58cde26e |
125 | my $self = {}; bless $self, $class; |
b22b3e31 |
126 | # shortcut for bigints and its subclasses |
0716bf9b |
127 | if ((ref($wanted)) && (ref($wanted) ne $class)) |
58cde26e |
128 | { |
9b924220 |
129 | $self->{_m} = $wanted->as_number()->{value}; # get us a bigint copy |
130 | $self->{_e} = $MBI->_zero(); |
131 | $self->{_es} = '+'; |
58cde26e |
132 | $self->{sign} = $wanted->sign(); |
0716bf9b |
133 | return $self->bnorm(); |
58cde26e |
134 | } |
2d2b2744 |
135 | # else: got a string |
136 | |
58cde26e |
137 | # handle '+inf', '-inf' first |
ee15d750 |
138 | if ($wanted =~ /^[+-]?inf$/) |
58cde26e |
139 | { |
28df3e88 |
140 | return $downgrade->new($wanted) if $downgrade; |
141 | |
9b924220 |
142 | $self->{_e} = $MBI->_zero(); |
143 | $self->{_es} = '+'; |
144 | $self->{_m} = $MBI->_zero(); |
58cde26e |
145 | $self->{sign} = $wanted; |
ee15d750 |
146 | $self->{sign} = '+inf' if $self->{sign} eq 'inf'; |
0716bf9b |
147 | return $self->bnorm(); |
58cde26e |
148 | } |
b282a552 |
149 | |
2d2b2744 |
150 | # shortcut for simple forms like '12' that neither have trailing nor leading |
151 | # zeros |
152 | if ($wanted =~ /^([+-]?)([1-9][0-9]*[1-9])$/) |
153 | { |
154 | $self->{_e} = $MBI->_zero(); |
155 | $self->{_es} = '+'; |
156 | $self->{sign} = $1 || '+'; |
157 | $self->{_m} = $MBI->_new($2); |
158 | return $self->round(@r) if !$downgrade; |
159 | } |
160 | |
9b924220 |
161 | my ($mis,$miv,$mfv,$es,$ev) = Math::BigInt::_split($wanted); |
58cde26e |
162 | if (!ref $mis) |
163 | { |
990fb837 |
164 | if ($_trap_nan) |
165 | { |
166 | require Carp; |
167 | Carp::croak ("$wanted is not a number initialized to $class"); |
168 | } |
28df3e88 |
169 | |
170 | return $downgrade->bnan() if $downgrade; |
171 | |
9b924220 |
172 | $self->{_e} = $MBI->_zero(); |
173 | $self->{_es} = '+'; |
174 | $self->{_m} = $MBI->_zero(); |
58cde26e |
175 | $self->{sign} = $nan; |
176 | } |
177 | else |
178 | { |
9b924220 |
179 | # make integer from mantissa by adjusting exp, then convert to int |
180 | $self->{_e} = $MBI->_new($$ev); # exponent |
181 | $self->{_es} = $$es || '+'; |
182 | my $mantissa = "$$miv$$mfv"; # create mant. |
183 | $mantissa =~ s/^0+(\d)/$1/; # strip leading zeros |
184 | $self->{_m} = $MBI->_new($mantissa); # create mant. |
b282a552 |
185 | |
58cde26e |
186 | # 3.123E0 = 3123E-3, and 3.123E-2 => 3123E-5 |
9b924220 |
187 | if (CORE::length($$mfv) != 0) |
188 | { |
189 | my $len = $MBI->_new( CORE::length($$mfv)); |
190 | ($self->{_e}, $self->{_es}) = |
191 | _e_sub ($self->{_e}, $len, $self->{_es}, '+'); |
192 | } |
2d2b2744 |
193 | # we can only have trailing zeros on the mantissa if $$mfv eq '' |
194 | else |
b282a552 |
195 | { |
2d2b2744 |
196 | # Use a regexp to count the trailing zeros in $$miv instead of _zeros() |
197 | # because that is faster, especially when _m is not stored in base 10. |
198 | my $zeros = 0; $zeros = CORE::length($1) if $$miv =~ /[1-9](0*)$/; |
b282a552 |
199 | if ($zeros != 0) |
200 | { |
9b924220 |
201 | my $z = $MBI->_new($zeros); |
2d2b2744 |
202 | # turn '120e2' into '12e3' |
9b924220 |
203 | $MBI->_rsft ( $self->{_m}, $z, 10); |
204 | _e_add ( $self->{_e}, $z, $self->{_es}, '+'); |
b282a552 |
205 | } |
206 | } |
2d2b2744 |
207 | $self->{sign} = $$mis; |
208 | |
9b924220 |
209 | # for something like 0Ey, set y to 1, and -0 => +0 |
2d2b2744 |
210 | # Check $$miv for beeing '0' and $$mfv eq '', because otherwise _m could not |
211 | # have become 0. That's faster than to call $MBI->_is_zero(). |
9b924220 |
212 | $self->{sign} = '+', $self->{_e} = $MBI->_one() |
2d2b2744 |
213 | if $$miv eq '0' and $$mfv eq ''; |
214 | |
b282a552 |
215 | return $self->round(@r) if !$downgrade; |
58cde26e |
216 | } |
28df3e88 |
217 | # if downgrade, inf, NaN or integers go down |
218 | |
9b924220 |
219 | if ($downgrade && $self->{_es} eq '+') |
28df3e88 |
220 | { |
9b924220 |
221 | if ($MBI->_is_zero( $self->{_e} )) |
28df3e88 |
222 | { |
9b924220 |
223 | return $downgrade->new($$mis . $MBI->_str( $self->{_m} )); |
28df3e88 |
224 | } |
8df1e0a2 |
225 | return $downgrade->new($self->bsstr()); |
28df3e88 |
226 | } |
990fb837 |
227 | $self->bnorm()->round(@r); # first normalize, then round |
58cde26e |
228 | } |
a0d0e21e |
229 | |
9b924220 |
230 | sub copy |
231 | { |
232 | my ($c,$x); |
233 | if (@_ > 1) |
234 | { |
235 | # if two arguments, the first one is the class to "swallow" subclasses |
236 | ($c,$x) = @_; |
237 | } |
238 | else |
239 | { |
240 | $x = shift; |
241 | $c = ref($x); |
242 | } |
243 | return unless ref($x); # only for objects |
244 | |
245 | my $self = {}; bless $self,$c; |
246 | |
247 | $self->{sign} = $x->{sign}; |
248 | $self->{_es} = $x->{_es}; |
249 | $self->{_m} = $MBI->_copy($x->{_m}); |
250 | $self->{_e} = $MBI->_copy($x->{_e}); |
251 | $self->{_a} = $x->{_a} if defined $x->{_a}; |
252 | $self->{_p} = $x->{_p} if defined $x->{_p}; |
253 | $self; |
254 | } |
255 | |
13a12e00 |
256 | sub _bnan |
58cde26e |
257 | { |
990fb837 |
258 | # used by parent class bone() to initialize number to NaN |
58cde26e |
259 | my $self = shift; |
990fb837 |
260 | |
261 | if ($_trap_nan) |
262 | { |
263 | require Carp; |
264 | my $class = ref($self); |
265 | Carp::croak ("Tried to set $self to NaN in $class\::_bnan()"); |
266 | } |
267 | |
268 | $IMPORT=1; # call our import only once |
9b924220 |
269 | $self->{_m} = $MBI->_zero(); |
270 | $self->{_e} = $MBI->_zero(); |
271 | $self->{_es} = '+'; |
58cde26e |
272 | } |
a0d0e21e |
273 | |
13a12e00 |
274 | sub _binf |
58cde26e |
275 | { |
990fb837 |
276 | # used by parent class bone() to initialize number to +-inf |
58cde26e |
277 | my $self = shift; |
990fb837 |
278 | |
279 | if ($_trap_inf) |
280 | { |
281 | require Carp; |
282 | my $class = ref($self); |
283 | Carp::croak ("Tried to set $self to +-inf in $class\::_binf()"); |
284 | } |
285 | |
286 | $IMPORT=1; # call our import only once |
9b924220 |
287 | $self->{_m} = $MBI->_zero(); |
288 | $self->{_e} = $MBI->_zero(); |
289 | $self->{_es} = '+'; |
58cde26e |
290 | } |
a0d0e21e |
291 | |
13a12e00 |
292 | sub _bone |
574bacfe |
293 | { |
13a12e00 |
294 | # used by parent class bone() to initialize number to 1 |
574bacfe |
295 | my $self = shift; |
990fb837 |
296 | $IMPORT=1; # call our import only once |
9b924220 |
297 | $self->{_m} = $MBI->_one(); |
298 | $self->{_e} = $MBI->_zero(); |
299 | $self->{_es} = '+'; |
574bacfe |
300 | } |
301 | |
13a12e00 |
302 | sub _bzero |
58cde26e |
303 | { |
990fb837 |
304 | # used by parent class bone() to initialize number to 0 |
58cde26e |
305 | my $self = shift; |
990fb837 |
306 | $IMPORT=1; # call our import only once |
9b924220 |
307 | $self->{_m} = $MBI->_zero(); |
308 | $self->{_e} = $MBI->_one(); |
309 | $self->{_es} = '+'; |
58cde26e |
310 | } |
311 | |
9393ace2 |
312 | sub isa |
313 | { |
314 | my ($self,$class) = @_; |
56b9c951 |
315 | return if $class =~ /^Math::BigInt/; # we aren't one of these |
316 | UNIVERSAL::isa($self,$class); |
9393ace2 |
317 | } |
318 | |
8f675a64 |
319 | sub config |
320 | { |
321 | # return (later set?) configuration data as hash ref |
322 | my $class = shift || 'Math::BigFloat'; |
323 | |
990fb837 |
324 | my $cfg = $class->SUPER::config(@_); |
8f675a64 |
325 | |
990fb837 |
326 | # now we need only to override the ones that are different from our parent |
8f675a64 |
327 | $cfg->{class} = $class; |
328 | $cfg->{with} = $MBI; |
8f675a64 |
329 | $cfg; |
330 | } |
331 | |
58cde26e |
332 | ############################################################################## |
333 | # string conversation |
334 | |
335 | sub bstr |
336 | { |
337 | # (ref to BFLOAT or num_str ) return num_str |
338 | # Convert number from internal format to (non-scientific) string format. |
339 | # internal format is always normalized (no leading zeros, "-0" => "+0") |
ee15d750 |
340 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
341 | |
574bacfe |
342 | if ($x->{sign} !~ /^[+-]$/) |
58cde26e |
343 | { |
574bacfe |
344 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN |
345 | return 'inf'; # +inf |
58cde26e |
346 | } |
c38b2de2 |
347 | |
574bacfe |
348 | my $es = '0'; my $len = 1; my $cad = 0; my $dot = '.'; |
349 | |
c38b2de2 |
350 | # $x is zero? |
9b924220 |
351 | my $not_zero = !($x->{sign} eq '+' && $MBI->_is_zero($x->{_m})); |
574bacfe |
352 | if ($not_zero) |
58cde26e |
353 | { |
9b924220 |
354 | $es = $MBI->_str($x->{_m}); |
574bacfe |
355 | $len = CORE::length($es); |
9b924220 |
356 | my $e = $MBI->_num($x->{_e}); |
357 | $e = -$e if $x->{_es} eq '-'; |
c38b2de2 |
358 | if ($e < 0) |
58cde26e |
359 | { |
c38b2de2 |
360 | $dot = ''; |
361 | # if _e is bigger than a scalar, the following will blow your memory |
362 | if ($e <= -$len) |
574bacfe |
363 | { |
c38b2de2 |
364 | my $r = abs($e) - $len; |
365 | $es = '0.'. ('0' x $r) . $es; $cad = -($len+$r); |
574bacfe |
366 | } |
367 | else |
368 | { |
9b924220 |
369 | substr($es,$e,0) = '.'; $cad = $MBI->_num($x->{_e}); |
370 | $cad = -$cad if $x->{_es} eq '-'; |
574bacfe |
371 | } |
82cf049f |
372 | } |
c38b2de2 |
373 | elsif ($e > 0) |
374 | { |
375 | # expand with zeros |
376 | $es .= '0' x $e; $len += $e; $cad = 0; |
377 | } |
574bacfe |
378 | } # if not zero |
9b924220 |
379 | |
c38b2de2 |
380 | $es = '-'.$es if $x->{sign} eq '-'; |
381 | # if set accuracy or precision, pad with zeros on the right side |
574bacfe |
382 | if ((defined $x->{_a}) && ($not_zero)) |
383 | { |
384 | # 123400 => 6, 0.1234 => 4, 0.001234 => 4 |
385 | my $zeros = $x->{_a} - $cad; # cad == 0 => 12340 |
386 | $zeros = $x->{_a} - $len if $cad != $len; |
574bacfe |
387 | $es .= $dot.'0' x $zeros if $zeros > 0; |
82cf049f |
388 | } |
c38b2de2 |
389 | elsif ((($x->{_p} || 0) < 0)) |
58cde26e |
390 | { |
574bacfe |
391 | # 123400 => 6, 0.1234 => 4, 0.001234 => 6 |
392 | my $zeros = -$x->{_p} + $cad; |
574bacfe |
393 | $es .= $dot.'0' x $zeros if $zeros > 0; |
58cde26e |
394 | } |
56b9c951 |
395 | $es; |
82cf049f |
396 | } |
f216259d |
397 | |
58cde26e |
398 | sub bsstr |
399 | { |
400 | # (ref to BFLOAT or num_str ) return num_str |
401 | # Convert number from internal format to scientific string format. |
402 | # internal format is always normalized (no leading zeros, "-0E0" => "+0E0") |
ee15d750 |
403 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
a0d0e21e |
404 | |
574bacfe |
405 | if ($x->{sign} !~ /^[+-]$/) |
406 | { |
407 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN |
408 | return 'inf'; # +inf |
409 | } |
9b924220 |
410 | my $sep = 'e'.$x->{_es}; |
56d9de68 |
411 | my $sign = $x->{sign}; $sign = '' if $sign eq '+'; |
9b924220 |
412 | $sign . $MBI->_str($x->{_m}) . $sep . $MBI->_str($x->{_e}); |
58cde26e |
413 | } |
414 | |
415 | sub numify |
416 | { |
417 | # Make a number from a BigFloat object |
b282a552 |
418 | # simple return a string and let Perl's atoi()/atof() handle the rest |
419 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
56b9c951 |
420 | $x->bsstr(); |
58cde26e |
421 | } |
a0d0e21e |
422 | |
58cde26e |
423 | ############################################################################## |
424 | # public stuff (usually prefixed with "b") |
425 | |
574bacfe |
426 | # tels 2001-08-04 |
b282a552 |
427 | # XXX TODO this must be overwritten and return NaN for non-integer values |
574bacfe |
428 | # band(), bior(), bxor(), too |
58cde26e |
429 | #sub bnot |
430 | # { |
431 | # $class->SUPER::bnot($class,@_); |
432 | # } |
433 | |
434 | sub bcmp |
435 | { |
436 | # Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort) |
f9a08e12 |
437 | |
438 | # set up parameters |
439 | my ($self,$x,$y) = (ref($_[0]),@_); |
440 | # objectify is costly, so avoid it |
441 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
442 | { |
443 | ($self,$x,$y) = objectify(2,@_); |
444 | } |
58cde26e |
445 | |
56d9de68 |
446 | return $upgrade->bcmp($x,$y) if defined $upgrade && |
447 | ((!$x->isa($self)) || (!$y->isa($self))); |
448 | |
0716bf9b |
449 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
450 | { |
451 | # handle +-inf and NaN |
452 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
453 | return 0 if ($x->{sign} eq $y->{sign}) && ($x->{sign} =~ /^[+-]inf$/); |
454 | return +1 if $x->{sign} eq '+inf'; |
455 | return -1 if $x->{sign} eq '-inf'; |
456 | return -1 if $y->{sign} eq '+inf'; |
b3abae2a |
457 | return +1; |
0716bf9b |
458 | } |
459 | |
460 | # check sign for speed first |
574bacfe |
461 | return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y |
58cde26e |
462 | return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0 |
463 | |
574bacfe |
464 | # shortcut |
465 | my $xz = $x->is_zero(); |
466 | my $yz = $y->is_zero(); |
467 | return 0 if $xz && $yz; # 0 <=> 0 |
468 | return -1 if $xz && $y->{sign} eq '+'; # 0 <=> +y |
469 | return 1 if $yz && $x->{sign} eq '+'; # +x <=> 0 |
58cde26e |
470 | |
471 | # adjust so that exponents are equal |
9b924220 |
472 | my $lxm = $MBI->_len($x->{_m}); |
473 | my $lym = $MBI->_len($y->{_m}); |
28df3e88 |
474 | # the numify somewhat limits our length, but makes it much faster |
9b924220 |
475 | my ($xes,$yes) = (1,1); |
476 | $xes = -1 if $x->{_es} ne '+'; |
477 | $yes = -1 if $y->{_es} ne '+'; |
478 | my $lx = $lxm + $xes * $MBI->_num($x->{_e}); |
479 | my $ly = $lym + $yes * $MBI->_num($y->{_e}); |
28df3e88 |
480 | my $l = $lx - $ly; $l = -$l if $x->{sign} eq '-'; |
bd05a461 |
481 | return $l <=> 0 if $l != 0; |
58cde26e |
482 | |
bd05a461 |
483 | # lengths (corrected by exponent) are equal |
28df3e88 |
484 | # so make mantissa equal length by padding with zero (shift left) |
bd05a461 |
485 | my $diff = $lxm - $lym; |
486 | my $xm = $x->{_m}; # not yet copy it |
487 | my $ym = $y->{_m}; |
488 | if ($diff > 0) |
489 | { |
9b924220 |
490 | $ym = $MBI->_copy($y->{_m}); |
491 | $ym = $MBI->_lsft($ym, $MBI->_new($diff), 10); |
bd05a461 |
492 | } |
493 | elsif ($diff < 0) |
494 | { |
9b924220 |
495 | $xm = $MBI->_copy($x->{_m}); |
496 | $xm = $MBI->_lsft($xm, $MBI->_new(-$diff), 10); |
bd05a461 |
497 | } |
9b924220 |
498 | my $rc = $MBI->_acmp($xm,$ym); |
58cde26e |
499 | $rc = -$rc if $x->{sign} eq '-'; # -124 < -123 |
b3abae2a |
500 | $rc <=> 0; |
58cde26e |
501 | } |
502 | |
503 | sub bacmp |
504 | { |
505 | # Compares 2 values, ignoring their signs. |
506 | # Returns one of undef, <0, =0, >0. (suitable for sort) |
f9a08e12 |
507 | |
508 | # set up parameters |
509 | my ($self,$x,$y) = (ref($_[0]),@_); |
510 | # objectify is costly, so avoid it |
511 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
512 | { |
513 | ($self,$x,$y) = objectify(2,@_); |
514 | } |
ee15d750 |
515 | |
56d9de68 |
516 | return $upgrade->bacmp($x,$y) if defined $upgrade && |
517 | ((!$x->isa($self)) || (!$y->isa($self))); |
518 | |
ee15d750 |
519 | # handle +-inf and NaN's |
abcfbf51 |
520 | if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/) |
ee15d750 |
521 | { |
522 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
523 | return 0 if ($x->is_inf() && $y->is_inf()); |
524 | return 1 if ($x->is_inf() && !$y->is_inf()); |
b3abae2a |
525 | return -1; |
ee15d750 |
526 | } |
527 | |
528 | # shortcut |
529 | my $xz = $x->is_zero(); |
530 | my $yz = $y->is_zero(); |
531 | return 0 if $xz && $yz; # 0 <=> 0 |
532 | return -1 if $xz && !$yz; # 0 <=> +y |
533 | return 1 if $yz && !$xz; # +x <=> 0 |
534 | |
535 | # adjust so that exponents are equal |
9b924220 |
536 | my $lxm = $MBI->_len($x->{_m}); |
537 | my $lym = $MBI->_len($y->{_m}); |
538 | my ($xes,$yes) = (1,1); |
539 | $xes = -1 if $x->{_es} ne '+'; |
540 | $yes = -1 if $y->{_es} ne '+'; |
28df3e88 |
541 | # the numify somewhat limits our length, but makes it much faster |
9b924220 |
542 | my $lx = $lxm + $xes * $MBI->_num($x->{_e}); |
543 | my $ly = $lym + $yes * $MBI->_num($y->{_e}); |
394e6ffb |
544 | my $l = $lx - $ly; |
ee15d750 |
545 | return $l <=> 0 if $l != 0; |
58cde26e |
546 | |
ee15d750 |
547 | # lengths (corrected by exponent) are equal |
394e6ffb |
548 | # so make mantissa equal-length by padding with zero (shift left) |
ee15d750 |
549 | my $diff = $lxm - $lym; |
550 | my $xm = $x->{_m}; # not yet copy it |
551 | my $ym = $y->{_m}; |
552 | if ($diff > 0) |
553 | { |
9b924220 |
554 | $ym = $MBI->_copy($y->{_m}); |
555 | $ym = $MBI->_lsft($ym, $MBI->_new($diff), 10); |
ee15d750 |
556 | } |
557 | elsif ($diff < 0) |
558 | { |
9b924220 |
559 | $xm = $MBI->_copy($x->{_m}); |
560 | $xm = $MBI->_lsft($xm, $MBI->_new(-$diff), 10); |
ee15d750 |
561 | } |
9b924220 |
562 | $MBI->_acmp($xm,$ym); |
58cde26e |
563 | } |
a0d0e21e |
564 | |
58cde26e |
565 | sub badd |
566 | { |
567 | # add second arg (BFLOAT or string) to first (BFLOAT) (modifies first) |
568 | # return result as BFLOAT |
f9a08e12 |
569 | |
570 | # set up parameters |
571 | my ($self,$x,$y,$a,$p,$r) = (ref($_[0]),@_); |
572 | # objectify is costly, so avoid it |
573 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
574 | { |
575 | ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
576 | } |
58cde26e |
577 | |
574bacfe |
578 | # inf and NaN handling |
579 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
580 | { |
581 | # NaN first |
582 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
13a12e00 |
583 | # inf handling |
574bacfe |
584 | if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) |
585 | { |
13a12e00 |
586 | # +inf++inf or -inf+-inf => same, rest is NaN |
587 | return $x if $x->{sign} eq $y->{sign}; |
588 | return $x->bnan(); |
574bacfe |
589 | } |
56b9c951 |
590 | # +-inf + something => +inf; something +-inf => +-inf |
574bacfe |
591 | $x->{sign} = $y->{sign}, return $x if $y->{sign} =~ /^[+-]inf$/; |
592 | return $x; |
593 | } |
594 | |
8f675a64 |
595 | return $upgrade->badd($x,$y,$a,$p,$r) if defined $upgrade && |
596 | ((!$x->isa($self)) || (!$y->isa($self))); |
597 | |
58cde26e |
598 | # speed: no add for 0+y or x+0 |
28df3e88 |
599 | return $x->bround($a,$p,$r) if $y->is_zero(); # x+0 |
58cde26e |
600 | if ($x->is_zero()) # 0+y |
601 | { |
602 | # make copy, clobbering up x (modify in place!) |
9b924220 |
603 | $x->{_e} = $MBI->_copy($y->{_e}); |
604 | $x->{_es} = $y->{_es}; |
605 | $x->{_m} = $MBI->_copy($y->{_m}); |
58cde26e |
606 | $x->{sign} = $y->{sign} || $nan; |
607 | return $x->round($a,$p,$r,$y); |
a0d0e21e |
608 | } |
58cde26e |
609 | |
610 | # take lower of the two e's and adapt m1 to it to match m2 |
28df3e88 |
611 | my $e = $y->{_e}; |
9b924220 |
612 | $e = $MBI->_zero() if !defined $e; # if no BFLOAT? |
613 | $e = $MBI->_copy($e); # make copy (didn't do it yet) |
614 | |
615 | my $es; |
616 | |
617 | ($e,$es) = _e_sub($e, $x->{_e}, $y->{_es} || '+', $x->{_es}); |
618 | |
619 | my $add = $MBI->_copy($y->{_m}); |
620 | |
621 | if ($es eq '-') # < 0 |
58cde26e |
622 | { |
9b924220 |
623 | $MBI->_lsft( $x->{_m}, $e, 10); |
624 | ($x->{_e},$x->{_es}) = _e_add($x->{_e}, $e, $x->{_es}, $es); |
58cde26e |
625 | } |
9b924220 |
626 | elsif (!$MBI->_is_zero($e)) # > 0 |
58cde26e |
627 | { |
9b924220 |
628 | $MBI->_lsft($add, $e, 10); |
58cde26e |
629 | } |
61f5c3f5 |
630 | # else: both e are the same, so just leave them |
9b924220 |
631 | |
632 | if ($x->{sign} eq $y->{sign}) |
633 | { |
634 | # add |
635 | $x->{_m} = $MBI->_add($x->{_m}, $add); |
636 | } |
637 | else |
638 | { |
639 | ($x->{_m}, $x->{sign}) = |
640 | _e_add($x->{_m}, $add, $x->{sign}, $y->{sign}); |
641 | } |
642 | |
61f5c3f5 |
643 | # delete trailing zeros, then round |
091c87b1 |
644 | $x->bnorm()->round($a,$p,$r,$y); |
58cde26e |
645 | } |
646 | |
03874afe |
647 | # sub bsub is inherited from Math::BigInt! |
58cde26e |
648 | |
649 | sub binc |
650 | { |
651 | # increment arg by one |
b282a552 |
652 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
e745a66c |
653 | |
9b924220 |
654 | if ($x->{_es} eq '-') |
e745a66c |
655 | { |
b282a552 |
656 | return $x->badd($self->bone(),@r); # digits after dot |
e745a66c |
657 | } |
658 | |
9b924220 |
659 | if (!$MBI->_is_zero($x->{_e})) # _e == 0 for NaN, inf, -inf |
e745a66c |
660 | { |
b282a552 |
661 | # 1e2 => 100, so after the shift below _m has a '0' as last digit |
9b924220 |
662 | $x->{_m} = $MBI->_lsft($x->{_m}, $x->{_e},10); # 1e2 => 100 |
663 | $x->{_e} = $MBI->_zero(); # normalize |
664 | $x->{_es} = '+'; |
b282a552 |
665 | # we know that the last digit of $x will be '1' or '9', depending on the |
666 | # sign |
e745a66c |
667 | } |
668 | # now $x->{_e} == 0 |
669 | if ($x->{sign} eq '+') |
670 | { |
9b924220 |
671 | $MBI->_inc($x->{_m}); |
b282a552 |
672 | return $x->bnorm()->bround(@r); |
e745a66c |
673 | } |
674 | elsif ($x->{sign} eq '-') |
675 | { |
9b924220 |
676 | $MBI->_dec($x->{_m}); |
677 | $x->{sign} = '+' if $MBI->_is_zero($x->{_m}); # -1 +1 => -0 => +0 |
b282a552 |
678 | return $x->bnorm()->bround(@r); |
e745a66c |
679 | } |
680 | # inf, nan handling etc |
b282a552 |
681 | $x->badd($self->bone(),@r); # badd() does round |
58cde26e |
682 | } |
683 | |
684 | sub bdec |
685 | { |
686 | # decrement arg by one |
b282a552 |
687 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
e745a66c |
688 | |
9b924220 |
689 | if ($x->{_es} eq '-') |
e745a66c |
690 | { |
b282a552 |
691 | return $x->badd($self->bone('-'),@r); # digits after dot |
e745a66c |
692 | } |
693 | |
9b924220 |
694 | if (!$MBI->_is_zero($x->{_e})) |
e745a66c |
695 | { |
9b924220 |
696 | $x->{_m} = $MBI->_lsft($x->{_m}, $x->{_e},10); # 1e2 => 100 |
697 | $x->{_e} = $MBI->_zero(); # normalize |
698 | $x->{_es} = '+'; |
e745a66c |
699 | } |
700 | # now $x->{_e} == 0 |
701 | my $zero = $x->is_zero(); |
702 | # <= 0 |
703 | if (($x->{sign} eq '-') || $zero) |
704 | { |
9b924220 |
705 | $MBI->_inc($x->{_m}); |
706 | $x->{sign} = '-' if $zero; # 0 => 1 => -1 |
707 | $x->{sign} = '+' if $MBI->_is_zero($x->{_m}); # -1 +1 => -0 => +0 |
b282a552 |
708 | return $x->bnorm()->round(@r); |
e745a66c |
709 | } |
710 | # > 0 |
711 | elsif ($x->{sign} eq '+') |
712 | { |
9b924220 |
713 | $MBI->_dec($x->{_m}); |
b282a552 |
714 | return $x->bnorm()->round(@r); |
e745a66c |
715 | } |
716 | # inf, nan handling etc |
9b924220 |
717 | $x->badd($self->bone('-'),@r); # does round |
58cde26e |
718 | } |
719 | |
990fb837 |
720 | sub DEBUG () { 0; } |
721 | |
61f5c3f5 |
722 | sub blog |
723 | { |
990fb837 |
724 | my ($self,$x,$base,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
61f5c3f5 |
725 | |
990fb837 |
726 | # $base > 0, $base != 1; if $base == undef default to $base == e |
727 | # $x >= 0 |
9393ace2 |
728 | |
b3abae2a |
729 | # we need to limit the accuracy to protect against overflow |
730 | my $fallback = 0; |
990fb837 |
731 | my ($scale,@params); |
732 | ($x,@params) = $x->_find_round_parameters($a,$p,$r); |
61f5c3f5 |
733 | |
990fb837 |
734 | # also takes care of the "error in _find_round_parameters?" case |
735 | return $x->bnan() if $x->{sign} ne '+' || $x->is_zero(); |
091c87b1 |
736 | |
9b924220 |
737 | |
b3abae2a |
738 | # no rounding at all, so must use fallback |
990fb837 |
739 | if (scalar @params == 0) |
b3abae2a |
740 | { |
741 | # simulate old behaviour |
990fb837 |
742 | $params[0] = $self->div_scale(); # and round to it as accuracy |
743 | $params[1] = undef; # P = undef |
744 | $scale = $params[0]+4; # at least four more for proper round |
745 | $params[2] = $r; # round mode by caller or undef |
b3abae2a |
746 | $fallback = 1; # to clear a/p afterwards |
747 | } |
748 | else |
749 | { |
750 | # the 4 below is empirical, and there might be cases where it is not |
751 | # enough... |
990fb837 |
752 | $scale = abs($params[0] || $params[1]) + 4; # take whatever is defined |
b3abae2a |
753 | } |
61f5c3f5 |
754 | |
b3abae2a |
755 | return $x->bzero(@params) if $x->is_one(); |
990fb837 |
756 | # base not defined => base == Euler's constant e |
757 | if (defined $base) |
758 | { |
091c87b1 |
759 | # make object, since we don't feed it through objectify() to still get the |
990fb837 |
760 | # case of $base == undef |
761 | $base = $self->new($base) unless ref($base); |
762 | # $base > 0; $base != 1 |
763 | return $x->bnan() if $base->is_zero() || $base->is_one() || |
764 | $base->{sign} ne '+'; |
091c87b1 |
765 | # if $x == $base, we know the result must be 1.0 |
90d1b129 |
766 | if ($x->bcmp($base) == 0) |
767 | { |
768 | $x->bone('+',@params); |
769 | if ($fallback) |
770 | { |
771 | # clear a/p after round, since user did not request it |
772 | delete $x->{_a}; delete $x->{_p}; |
773 | } |
774 | return $x; |
775 | } |
990fb837 |
776 | } |
61f5c3f5 |
777 | |
b3abae2a |
778 | # when user set globals, they would interfere with our calculation, so |
56d9de68 |
779 | # disable them and later re-enable them |
b3abae2a |
780 | no strict 'refs'; |
781 | my $abr = "$self\::accuracy"; my $ab = $$abr; $$abr = undef; |
782 | my $pbr = "$self\::precision"; my $pb = $$pbr; $$pbr = undef; |
783 | # we also need to disable any set A or P on $x (_find_round_parameters took |
784 | # them already into account), since these would interfere, too |
785 | delete $x->{_a}; delete $x->{_p}; |
9393ace2 |
786 | # need to disable $upgrade in BigInt, to avoid deep recursion |
b3abae2a |
787 | local $Math::BigInt::upgrade = undef; |
93c87d9d |
788 | local $Math::BigFloat::downgrade = undef; |
990fb837 |
789 | |
790 | # upgrade $x if $x is not a BigFloat (handle BigInt input) |
791 | if (!$x->isa('Math::BigFloat')) |
792 | { |
793 | $x = Math::BigFloat->new($x); |
794 | $self = ref($x); |
795 | } |
b282a552 |
796 | |
797 | my $done = 0; |
798 | |
799 | # If the base is defined and an integer, try to calculate integer result |
800 | # first. This is very fast, and in case the real result was found, we can |
801 | # stop right here. |
802 | if (defined $base && $base->is_int() && $x->is_int()) |
803 | { |
9b924220 |
804 | my $i = $MBI->_copy( $x->{_m} ); |
805 | $MBI->_lsft( $i, $x->{_e}, 10 ) unless $MBI->_is_zero($x->{_e}); |
806 | my $int = Math::BigInt->bzero(); |
807 | $int->{value} = $i; |
b282a552 |
808 | $int->blog($base->as_number()); |
809 | # if ($exact) |
9b924220 |
810 | if ($base->as_number()->bpow($int) == $x) |
b282a552 |
811 | { |
812 | # found result, return it |
9b924220 |
813 | $x->{_m} = $int->{value}; |
814 | $x->{_e} = $MBI->_zero(); |
815 | $x->{_es} = '+'; |
b282a552 |
816 | $x->bnorm(); |
817 | $done = 1; |
818 | } |
819 | } |
820 | |
821 | if ($done == 0) |
9393ace2 |
822 | { |
b282a552 |
823 | # first calculate the log to base e (using reduction by 10 (and probably 2)) |
824 | $self->_log_10($x,$scale); |
9b924220 |
825 | |
b282a552 |
826 | # and if a different base was requested, convert it |
827 | if (defined $base) |
828 | { |
829 | $base = Math::BigFloat->new($base) unless $base->isa('Math::BigFloat'); |
830 | # not ln, but some other base (don't modify $base) |
831 | $x->bdiv( $base->copy()->blog(undef,$scale), $scale ); |
832 | } |
9393ace2 |
833 | } |
990fb837 |
834 | |
091c87b1 |
835 | # shortcut to not run through _find_round_parameters again |
990fb837 |
836 | if (defined $params[0]) |
b3abae2a |
837 | { |
990fb837 |
838 | $x->bround($params[0],$params[2]); # then round accordingly |
b3abae2a |
839 | } |
840 | else |
841 | { |
990fb837 |
842 | $x->bfround($params[1],$params[2]); # then round accordingly |
b3abae2a |
843 | } |
844 | if ($fallback) |
845 | { |
846 | # clear a/p after round, since user did not request it |
ef9466ea |
847 | delete $x->{_a}; delete $x->{_p}; |
b3abae2a |
848 | } |
849 | # restore globals |
850 | $$abr = $ab; $$pbr = $pb; |
851 | |
852 | $x; |
61f5c3f5 |
853 | } |
854 | |
990fb837 |
855 | sub _log |
856 | { |
091c87b1 |
857 | # internal log function to calculate ln() based on Taylor series. |
990fb837 |
858 | # Modifies $x in place. |
859 | my ($self,$x,$scale) = @_; |
860 | |
091c87b1 |
861 | # in case of $x == 1, result is 0 |
862 | return $x->bzero() if $x->is_one(); |
863 | |
990fb837 |
864 | # http://www.efunda.com/math/taylor_series/logarithmic.cfm?search_string=log |
865 | |
866 | # u = x-1, v = x+1 |
867 | # _ _ |
868 | # Taylor: | u 1 u^3 1 u^5 | |
869 | # ln (x) = 2 | --- + - * --- + - * --- + ... | x > 0 |
870 | # |_ v 3 v^3 5 v^5 _| |
871 | |
872 | # This takes much more steps to calculate the result and is thus not used |
873 | # u = x-1 |
874 | # _ _ |
875 | # Taylor: | u 1 u^2 1 u^3 | |
876 | # ln (x) = 2 | --- + - * --- + - * --- + ... | x > 1/2 |
877 | # |_ x 2 x^2 3 x^3 _| |
878 | |
990fb837 |
879 | my ($limit,$v,$u,$below,$factor,$two,$next,$over,$f); |
880 | |
881 | $v = $x->copy(); $v->binc(); # v = x+1 |
882 | $x->bdec(); $u = $x->copy(); # u = x-1; x = x-1 |
883 | $x->bdiv($v,$scale); # first term: u/v |
884 | $below = $v->copy(); |
885 | $over = $u->copy(); |
886 | $u *= $u; $v *= $v; # u^2, v^2 |
887 | $below->bmul($v); # u^3, v^3 |
888 | $over->bmul($u); |
889 | $factor = $self->new(3); $f = $self->new(2); |
890 | |
891 | my $steps = 0 if DEBUG; |
892 | $limit = $self->new("1E-". ($scale-1)); |
893 | while (3 < 5) |
894 | { |
895 | # we calculate the next term, and add it to the last |
896 | # when the next term is below our limit, it won't affect the outcome |
897 | # anymore, so we stop |
898 | |
899 | # calculating the next term simple from over/below will result in quite |
900 | # a time hog if the input has many digits, since over and below will |
901 | # accumulate more and more digits, and the result will also have many |
902 | # digits, but in the end it is rounded to $scale digits anyway. So if we |
903 | # round $over and $below first, we save a lot of time for the division |
904 | # (not with log(1.2345), but try log (123**123) to see what I mean. This |
905 | # can introduce a rounding error if the division result would be f.i. |
906 | # 0.1234500000001 and we round it to 5 digits it would become 0.12346, but |
091c87b1 |
907 | # if we truncated $over and $below we might get 0.12345. Does this matter |
908 | # for the end result? So we give $over and $below 4 more digits to be |
909 | # on the safe side (unscientific error handling as usual... :+D |
990fb837 |
910 | |
911 | $next = $over->copy->bround($scale+4)->bdiv( |
912 | $below->copy->bmul($factor)->bround($scale+4), |
913 | $scale); |
914 | |
915 | ## old version: |
916 | ## $next = $over->copy()->bdiv($below->copy()->bmul($factor),$scale); |
917 | |
918 | last if $next->bacmp($limit) <= 0; |
919 | |
920 | delete $next->{_a}; delete $next->{_p}; |
921 | $x->badd($next); |
990fb837 |
922 | # calculate things for the next term |
923 | $over *= $u; $below *= $v; $factor->badd($f); |
924 | if (DEBUG) |
925 | { |
926 | $steps++; print "step $steps = $x\n" if $steps % 10 == 0; |
927 | } |
928 | } |
929 | $x->bmul($f); # $x *= 2 |
930 | print "took $steps steps\n" if DEBUG; |
931 | } |
932 | |
933 | sub _log_10 |
934 | { |
091c87b1 |
935 | # Internal log function based on reducing input to the range of 0.1 .. 9.99 |
936 | # and then "correcting" the result to the proper one. Modifies $x in place. |
990fb837 |
937 | my ($self,$x,$scale) = @_; |
938 | |
939 | # taking blog() from numbers greater than 10 takes a *very long* time, so we |
940 | # break the computation down into parts based on the observation that: |
941 | # blog(x*y) = blog(x) + blog(y) |
942 | # We set $y here to multiples of 10 so that $x is below 1 (the smaller $x is |
943 | # the faster it get's, especially because 2*$x takes about 10 times as long, |
944 | # so by dividing $x by 10 we make it at least factor 100 faster...) |
945 | |
946 | # The same observation is valid for numbers smaller than 0.1 (e.g. computing |
947 | # log(1) is fastest, and the farther away we get from 1, the longer it takes) |
948 | # so we also 'break' this down by multiplying $x with 10 and subtract the |
949 | # log(10) afterwards to get the correct result. |
950 | |
951 | # calculate nr of digits before dot |
9b924220 |
952 | my $dbd = $MBI->_num($x->{_e}); |
953 | $dbd = -$dbd if $x->{_es} eq '-'; |
954 | $dbd += $MBI->_len($x->{_m}); |
990fb837 |
955 | |
956 | # more than one digit (e.g. at least 10), but *not* exactly 10 to avoid |
957 | # infinite recursion |
958 | |
959 | my $calc = 1; # do some calculation? |
960 | |
961 | # disable the shortcut for 10, since we need log(10) and this would recurse |
962 | # infinitely deep |
9b924220 |
963 | if ($x->{_es} eq '+' && $MBI->_is_one($x->{_e}) && $MBI->_is_one($x->{_m})) |
990fb837 |
964 | { |
965 | $dbd = 0; # disable shortcut |
966 | # we can use the cached value in these cases |
967 | if ($scale <= $LOG_10_A) |
968 | { |
969 | $x->bzero(); $x->badd($LOG_10); |
970 | $calc = 0; # no need to calc, but round |
971 | } |
972 | } |
091c87b1 |
973 | else |
990fb837 |
974 | { |
091c87b1 |
975 | # disable the shortcut for 2, since we maybe have it cached |
9b924220 |
976 | if (($MBI->_is_zero($x->{_e}) && $MBI->_is_two($x->{_m}))) |
990fb837 |
977 | { |
091c87b1 |
978 | $dbd = 0; # disable shortcut |
979 | # we can use the cached value in these cases |
980 | if ($scale <= $LOG_2_A) |
981 | { |
982 | $x->bzero(); $x->badd($LOG_2); |
983 | $calc = 0; # no need to calc, but round |
984 | } |
990fb837 |
985 | } |
986 | } |
987 | |
988 | # if $x = 0.1, we know the result must be 0-log(10) |
9b924220 |
989 | if ($calc != 0 && $x->{_es} eq '-' && $MBI->_is_one($x->{_e}) && |
990 | $MBI->_is_one($x->{_m})) |
990fb837 |
991 | { |
992 | $dbd = 0; # disable shortcut |
993 | # we can use the cached value in these cases |
994 | if ($scale <= $LOG_10_A) |
995 | { |
996 | $x->bzero(); $x->bsub($LOG_10); |
997 | $calc = 0; # no need to calc, but round |
998 | } |
999 | } |
1000 | |
091c87b1 |
1001 | return if $calc == 0; # already have the result |
1002 | |
990fb837 |
1003 | # default: these correction factors are undef and thus not used |
1004 | my $l_10; # value of ln(10) to A of $scale |
1005 | my $l_2; # value of ln(2) to A of $scale |
1006 | |
1007 | # $x == 2 => 1, $x == 13 => 2, $x == 0.1 => 0, $x == 0.01 => -1 |
1008 | # so don't do this shortcut for 1 or 0 |
1009 | if (($dbd > 1) || ($dbd < 0)) |
1010 | { |
1011 | # convert our cached value to an object if not already (avoid doing this |
1012 | # at import() time, since not everybody needs this) |
1013 | $LOG_10 = $self->new($LOG_10,undef,undef) unless ref $LOG_10; |
1014 | |
1015 | #print "x = $x, dbd = $dbd, calc = $calc\n"; |
1016 | # got more than one digit before the dot, or more than one zero after the |
1017 | # dot, so do: |
1018 | # log(123) == log(1.23) + log(10) * 2 |
1019 | # log(0.0123) == log(1.23) - log(10) * 2 |
1020 | |
1021 | if ($scale <= $LOG_10_A) |
1022 | { |
1023 | # use cached value |
990fb837 |
1024 | $l_10 = $LOG_10->copy(); # copy for mul |
1025 | } |
1026 | else |
1027 | { |
1028 | # else: slower, compute it (but don't cache it, because it could be big) |
1029 | # also disable downgrade for this code path |
1030 | local $Math::BigFloat::downgrade = undef; |
990fb837 |
1031 | $l_10 = $self->new(10)->blog(undef,$scale); # scale+4, actually |
1032 | } |
1033 | $dbd-- if ($dbd > 1); # 20 => dbd=2, so make it dbd=1 |
9b924220 |
1034 | $l_10->bmul( $self->new($dbd)); # log(10) * (digits_before_dot-1) |
1035 | my $dbd_sign = '+'; |
1036 | if ($dbd < 0) |
1037 | { |
1038 | $dbd = -$dbd; |
1039 | $dbd_sign = '-'; |
1040 | } |
1041 | ($x->{_e}, $x->{_es}) = |
1042 | _e_sub( $x->{_e}, $MBI->_new($dbd), $x->{_es}, $dbd_sign); # 123 => 1.23 |
990fb837 |
1043 | |
1044 | } |
1045 | |
1046 | # Now: 0.1 <= $x < 10 (and possible correction in l_10) |
1047 | |
1048 | ### Since $x in the range 0.5 .. 1.5 is MUCH faster, we do a repeated div |
1049 | ### or mul by 2 (maximum times 3, since x < 10 and x > 0.1) |
1050 | |
27e7b8bb |
1051 | $HALF = $self->new($HALF) unless ref($HALF); |
1052 | |
091c87b1 |
1053 | my $twos = 0; # default: none (0 times) |
1054 | my $two = $self->new(2); |
27e7b8bb |
1055 | while ($x->bacmp($HALF) <= 0) |
990fb837 |
1056 | { |
091c87b1 |
1057 | $twos--; $x->bmul($two); |
1058 | } |
1059 | while ($x->bacmp($two) >= 0) |
1060 | { |
1061 | $twos++; $x->bdiv($two,$scale+4); # keep all digits |
1062 | } |
091c87b1 |
1063 | # $twos > 0 => did mul 2, < 0 => did div 2 (never both) |
1064 | # calculate correction factor based on ln(2) |
1065 | if ($twos != 0) |
1066 | { |
1067 | $LOG_2 = $self->new($LOG_2,undef,undef) unless ref $LOG_2; |
1068 | if ($scale <= $LOG_2_A) |
990fb837 |
1069 | { |
091c87b1 |
1070 | # use cached value |
091c87b1 |
1071 | $l_2 = $LOG_2->copy(); # copy for mul |
990fb837 |
1072 | } |
091c87b1 |
1073 | else |
990fb837 |
1074 | { |
091c87b1 |
1075 | # else: slower, compute it (but don't cache it, because it could be big) |
1076 | # also disable downgrade for this code path |
1077 | local $Math::BigFloat::downgrade = undef; |
091c87b1 |
1078 | $l_2 = $two->blog(undef,$scale); # scale+4, actually |
990fb837 |
1079 | } |
091c87b1 |
1080 | $l_2->bmul($twos); # * -2 => subtract, * 2 => add |
990fb837 |
1081 | } |
1082 | |
091c87b1 |
1083 | $self->_log($x,$scale); # need to do the "normal" way |
1084 | $x->badd($l_10) if defined $l_10; # correct it by ln(10) |
1085 | $x->badd($l_2) if defined $l_2; # and maybe by ln(2) |
990fb837 |
1086 | # all done, $x contains now the result |
1087 | } |
1088 | |
58cde26e |
1089 | sub blcm |
1090 | { |
ee15d750 |
1091 | # (BFLOAT or num_str, BFLOAT or num_str) return BFLOAT |
58cde26e |
1092 | # does not modify arguments, but returns new object |
1093 | # Lowest Common Multiplicator |
58cde26e |
1094 | |
1095 | my ($self,@arg) = objectify(0,@_); |
1096 | my $x = $self->new(shift @arg); |
1097 | while (@arg) { $x = _lcm($x,shift @arg); } |
1098 | $x; |
1099 | } |
1100 | |
1101 | sub bgcd |
1102 | { |
ee15d750 |
1103 | # (BFLOAT or num_str, BFLOAT or num_str) return BINT |
58cde26e |
1104 | # does not modify arguments, but returns new object |
1105 | # GCD -- Euclids algorithm Knuth Vol 2 pg 296 |
58cde26e |
1106 | |
1107 | my ($self,@arg) = objectify(0,@_); |
1108 | my $x = $self->new(shift @arg); |
1109 | while (@arg) { $x = _gcd($x,shift @arg); } |
1110 | $x; |
1111 | } |
1112 | |
9b924220 |
1113 | ############################################################################## |
b3abae2a |
1114 | |
9b924220 |
1115 | sub _e_add |
091c87b1 |
1116 | { |
9b924220 |
1117 | # Internal helper sub to take two positive integers and their signs and |
1118 | # then add them. Input ($CALC,$CALC,('+'|'-'),('+'|'-')), |
1119 | # output ($CALC,('+'|'-')) |
1120 | my ($x,$y,$xs,$ys) = @_; |
1121 | |
1122 | # if the signs are equal we can add them (-5 + -3 => -(5 + 3) => -8) |
1123 | if ($xs eq $ys) |
1124 | { |
1125 | $x = $MBI->_add ($x, $y ); # a+b |
1126 | # the sign follows $xs |
1127 | return ($x, $xs); |
1128 | } |
091c87b1 |
1129 | |
9b924220 |
1130 | my $a = $MBI->_acmp($x,$y); |
1131 | if ($a > 0) |
1132 | { |
1133 | $x = $MBI->_sub ($x , $y); # abs sub |
1134 | } |
1135 | elsif ($a == 0) |
1136 | { |
1137 | $x = $MBI->_zero(); # result is 0 |
1138 | $xs = '+'; |
1139 | } |
1140 | else # a < 0 |
1141 | { |
1142 | $x = $MBI->_sub ( $y, $x, 1 ); # abs sub |
1143 | $xs = $ys; |
1144 | } |
1145 | ($x,$xs); |
091c87b1 |
1146 | } |
1147 | |
9b924220 |
1148 | sub _e_sub |
1149 | { |
1150 | # Internal helper sub to take two positive integers and their signs and |
1151 | # then subtract them. Input ($CALC,$CALC,('+'|'-'),('+'|'-')), |
1152 | # output ($CALC,('+'|'-')) |
1153 | my ($x,$y,$xs,$ys) = @_; |
1154 | |
1155 | # flip sign |
1156 | $ys =~ tr/+-/-+/; |
1157 | _e_add($x,$y,$xs,$ys); # call add (does subtract now) |
1158 | } |
1159 | |
1160 | ############################################################################### |
1161 | # is_foo methods (is_negative, is_positive are inherited from BigInt) |
1162 | |
b3abae2a |
1163 | sub is_int |
1164 | { |
1165 | # return true if arg (BFLOAT or num_str) is an integer |
091c87b1 |
1166 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
b3abae2a |
1167 | |
1168 | return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN and +-inf aren't |
9b924220 |
1169 | $x->{_es} eq '+'; # 1e-1 => no integer |
b3abae2a |
1170 | 0; |
1171 | } |
1172 | |
58cde26e |
1173 | sub is_zero |
1174 | { |
b3abae2a |
1175 | # return true if arg (BFLOAT or num_str) is zero |
091c87b1 |
1176 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
574bacfe |
1177 | |
9b924220 |
1178 | return 1 if $x->{sign} eq '+' && $MBI->_is_zero($x->{_m}); |
b3abae2a |
1179 | 0; |
58cde26e |
1180 | } |
1181 | |
1182 | sub is_one |
1183 | { |
b3abae2a |
1184 | # return true if arg (BFLOAT or num_str) is +1 or -1 if signis given |
091c87b1 |
1185 | my ($self,$x,$sign) = ref($_[0]) ? (undef,@_) : objectify(1,@_); |
ee15d750 |
1186 | |
990fb837 |
1187 | $sign = '+' if !defined $sign || $sign ne '-'; |
ee15d750 |
1188 | return 1 |
9b924220 |
1189 | if ($x->{sign} eq $sign && |
1190 | $MBI->_is_zero($x->{_e}) && $MBI->_is_one($x->{_m})); |
b3abae2a |
1191 | 0; |
58cde26e |
1192 | } |
1193 | |
1194 | sub is_odd |
1195 | { |
ee15d750 |
1196 | # return true if arg (BFLOAT or num_str) is odd or false if even |
091c87b1 |
1197 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
0716bf9b |
1198 | |
b3abae2a |
1199 | return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN & +-inf aren't |
9b924220 |
1200 | ($MBI->_is_zero($x->{_e}) && $MBI->_is_odd($x->{_m})); |
b3abae2a |
1201 | 0; |
58cde26e |
1202 | } |
1203 | |
1204 | sub is_even |
1205 | { |
b22b3e31 |
1206 | # return true if arg (BINT or num_str) is even or false if odd |
091c87b1 |
1207 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
0716bf9b |
1208 | |
1209 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
9b924220 |
1210 | return 1 if ($x->{_es} eq '+' # 123.45 is never |
1211 | && $MBI->_is_even($x->{_m})); # but 1200 is |
b3abae2a |
1212 | 0; |
58cde26e |
1213 | } |
1214 | |
1215 | sub bmul |
1216 | { |
1217 | # multiply two numbers -- stolen from Knuth Vol 2 pg 233 |
1218 | # (BINT or num_str, BINT or num_str) return BINT |
f9a08e12 |
1219 | |
1220 | # set up parameters |
1221 | my ($self,$x,$y,$a,$p,$r) = (ref($_[0]),@_); |
1222 | # objectify is costly, so avoid it |
1223 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1224 | { |
1225 | ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
1226 | } |
58cde26e |
1227 | |
58cde26e |
1228 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
1229 | |
574bacfe |
1230 | # inf handling |
1231 | if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) |
1232 | { |
13a12e00 |
1233 | return $x->bnan() if $x->is_zero() || $y->is_zero(); |
574bacfe |
1234 | # result will always be +-inf: |
1235 | # +inf * +/+inf => +inf, -inf * -/-inf => +inf |
1236 | # +inf * -/-inf => -inf, -inf * +/+inf => -inf |
1237 | return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); |
1238 | return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); |
1239 | return $x->binf('-'); |
1240 | } |
13a12e00 |
1241 | # handle result = 0 |
1242 | return $x->bzero() if $x->is_zero() || $y->is_zero(); |
8f675a64 |
1243 | |
1244 | return $upgrade->bmul($x,$y,$a,$p,$r) if defined $upgrade && |
1245 | ((!$x->isa($self)) || (!$y->isa($self))); |
574bacfe |
1246 | |
58cde26e |
1247 | # aEb * cEd = (a*c)E(b+d) |
9b924220 |
1248 | $MBI->_mul($x->{_m},$y->{_m}); |
1249 | ($x->{_e}, $x->{_es}) = _e_add($x->{_e}, $y->{_e}, $x->{_es}, $y->{_es}); |
1250 | |
58cde26e |
1251 | # adjust sign: |
1252 | $x->{sign} = $x->{sign} ne $y->{sign} ? '-' : '+'; |
394e6ffb |
1253 | return $x->bnorm()->round($a,$p,$r,$y); |
58cde26e |
1254 | } |
1255 | |
1256 | sub bdiv |
1257 | { |
1258 | # (dividend: BFLOAT or num_str, divisor: BFLOAT or num_str) return |
9393ace2 |
1259 | # (BFLOAT,BFLOAT) (quo,rem) or BFLOAT (only rem) |
f9a08e12 |
1260 | |
1261 | # set up parameters |
1262 | my ($self,$x,$y,$a,$p,$r) = (ref($_[0]),@_); |
1263 | # objectify is costly, so avoid it |
1264 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1265 | { |
1266 | ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
1267 | } |
58cde26e |
1268 | |
13a12e00 |
1269 | return $self->_div_inf($x,$y) |
1270 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()); |
574bacfe |
1271 | |
13a12e00 |
1272 | # x== 0 # also: or y == 1 or y == -1 |
394e6ffb |
1273 | return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero(); |
0716bf9b |
1274 | |
9393ace2 |
1275 | # upgrade ? |
1276 | return $upgrade->bdiv($upgrade->new($x),$y,$a,$p,$r) if defined $upgrade; |
13a12e00 |
1277 | |
58cde26e |
1278 | # we need to limit the accuracy to protect against overflow |
574bacfe |
1279 | my $fallback = 0; |
990fb837 |
1280 | my (@params,$scale); |
1281 | ($x,@params) = $x->_find_round_parameters($a,$p,$r,$y); |
1282 | |
1283 | return $x if $x->is_nan(); # error in _find_round_parameters? |
ee15d750 |
1284 | |
1285 | # no rounding at all, so must use fallback |
990fb837 |
1286 | if (scalar @params == 0) |
58cde26e |
1287 | { |
0716bf9b |
1288 | # simulate old behaviour |
990fb837 |
1289 | $params[0] = $self->div_scale(); # and round to it as accuracy |
1290 | $scale = $params[0]+4; # at least four more for proper round |
1291 | $params[2] = $r; # round mode by caller or undef |
ee15d750 |
1292 | $fallback = 1; # to clear a/p afterwards |
1293 | } |
1294 | else |
1295 | { |
1296 | # the 4 below is empirical, and there might be cases where it is not |
1297 | # enough... |
990fb837 |
1298 | $scale = abs($params[0] || $params[1]) + 4; # take whatever is defined |
a0d0e21e |
1299 | } |
03874afe |
1300 | |
1301 | my $rem; $rem = $self->bzero() if wantarray; |
1302 | |
1303 | $y = $self->new($y) unless $y->isa('Math::BigFloat'); |
1304 | |
9b924220 |
1305 | my $lx = $MBI->_len($x->{_m}); my $ly = $MBI->_len($y->{_m}); |
58cde26e |
1306 | $scale = $lx if $lx > $scale; |
58cde26e |
1307 | $scale = $ly if $ly > $scale; |
0716bf9b |
1308 | my $diff = $ly - $lx; |
1309 | $scale += $diff if $diff > 0; # if lx << ly, but not if ly << lx! |
03874afe |
1310 | |
1311 | # cases like $x /= $x (but not $x /= $y!) were wrong due to modifying $x |
1312 | # twice below) |
ae161977 |
1313 | require Scalar::Util; |
1314 | if (Scalar::Util::refaddr($x) == Scalar::Util::refaddr($y)) |
b3abae2a |
1315 | { |
03874afe |
1316 | $x->bone(); # x/x => 1, rem 0 |
b3abae2a |
1317 | } |
03874afe |
1318 | else |
58cde26e |
1319 | { |
03874afe |
1320 | |
1321 | # make copy of $x in case of list context for later reminder calculation |
1322 | if (wantarray && !$y->is_one()) |
1323 | { |
1324 | $rem = $x->copy(); |
1325 | } |
394e6ffb |
1326 | |
03874afe |
1327 | $x->{sign} = $x->{sign} ne $y->sign() ? '-' : '+'; |
9b924220 |
1328 | |
03874afe |
1329 | # check for / +-1 ( +/- 1E0) |
1330 | if (!$y->is_one()) |
1331 | { |
1332 | # promote BigInts and it's subclasses (except when already a BigFloat) |
1333 | $y = $self->new($y) unless $y->isa('Math::BigFloat'); |
1334 | |
1335 | # calculate the result to $scale digits and then round it |
1336 | # a * 10 ** b / c * 10 ** d => a/c * 10 ** (b-d) |
1337 | $MBI->_lsft($x->{_m},$MBI->_new($scale),10); |
1338 | $MBI->_div ($x->{_m},$y->{_m}); # a/c |
1339 | |
1340 | # correct exponent of $x |
1341 | ($x->{_e},$x->{_es}) = _e_sub($x->{_e}, $y->{_e}, $x->{_es}, $y->{_es}); |
1342 | # correct for 10**scale |
1343 | ($x->{_e},$x->{_es}) = _e_sub($x->{_e}, $MBI->_new($scale), $x->{_es}, '+'); |
1344 | $x->bnorm(); # remove trailing 0's |
1345 | } |
1346 | } # ende else $x != $y |
a5f75d66 |
1347 | |
091c87b1 |
1348 | # shortcut to not run through _find_round_parameters again |
990fb837 |
1349 | if (defined $params[0]) |
ee15d750 |
1350 | { |
ef9466ea |
1351 | delete $x->{_a}; # clear before round |
990fb837 |
1352 | $x->bround($params[0],$params[2]); # then round accordingly |
ee15d750 |
1353 | } |
1354 | else |
1355 | { |
ef9466ea |
1356 | delete $x->{_p}; # clear before round |
990fb837 |
1357 | $x->bfround($params[1],$params[2]); # then round accordingly |
ee15d750 |
1358 | } |
574bacfe |
1359 | if ($fallback) |
1360 | { |
1361 | # clear a/p after round, since user did not request it |
ef9466ea |
1362 | delete $x->{_a}; delete $x->{_p}; |
574bacfe |
1363 | } |
03874afe |
1364 | |
58cde26e |
1365 | if (wantarray) |
1366 | { |
394e6ffb |
1367 | if (!$y->is_one()) |
1368 | { |
990fb837 |
1369 | $rem->bmod($y,@params); # copy already done |
394e6ffb |
1370 | } |
574bacfe |
1371 | if ($fallback) |
1372 | { |
1373 | # clear a/p after round, since user did not request it |
ef9466ea |
1374 | delete $rem->{_a}; delete $rem->{_p}; |
574bacfe |
1375 | } |
0716bf9b |
1376 | return ($x,$rem); |
58cde26e |
1377 | } |
9393ace2 |
1378 | $x; |
58cde26e |
1379 | } |
a0d0e21e |
1380 | |
58cde26e |
1381 | sub bmod |
1382 | { |
1383 | # (dividend: BFLOAT or num_str, divisor: BFLOAT or num_str) return reminder |
f9a08e12 |
1384 | |
1385 | # set up parameters |
1386 | my ($self,$x,$y,$a,$p,$r) = (ref($_[0]),@_); |
1387 | # objectify is costly, so avoid it |
1388 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1389 | { |
1390 | ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
1391 | } |
a0d0e21e |
1392 | |
9b924220 |
1393 | # handle NaN, inf, -inf |
61f5c3f5 |
1394 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
1395 | { |
1396 | my ($d,$re) = $self->SUPER::_div_inf($x,$y); |
f9a08e12 |
1397 | $x->{sign} = $re->{sign}; |
1398 | $x->{_e} = $re->{_e}; |
1399 | $x->{_m} = $re->{_m}; |
1400 | return $x->round($a,$p,$r,$y); |
61f5c3f5 |
1401 | } |
9b924220 |
1402 | if ($y->is_zero()) |
1403 | { |
1404 | return $x->bnan() if $x->is_zero(); |
1405 | return $x; |
1406 | } |
61f5c3f5 |
1407 | return $x->bzero() if $y->is_one() || $x->is_zero(); |
58cde26e |
1408 | |
61f5c3f5 |
1409 | my $cmp = $x->bacmp($y); # equal or $x < $y? |
1410 | return $x->bzero($a,$p) if $cmp == 0; # $x == $y => result 0 |
1411 | |
1412 | # only $y of the operands negative? |
1413 | my $neg = 0; $neg = 1 if $x->{sign} ne $y->{sign}; |
1414 | |
1415 | $x->{sign} = $y->{sign}; # calc sign first |
1416 | return $x->round($a,$p,$r) if $cmp < 0 && $neg == 0; # $x < $y => result $x |
1417 | |
9b924220 |
1418 | my $ym = $MBI->_copy($y->{_m}); |
61f5c3f5 |
1419 | |
1420 | # 2e1 => 20 |
9b924220 |
1421 | $MBI->_lsft( $ym, $y->{_e}, 10) |
1422 | if $y->{_es} eq '+' && !$MBI->_is_zero($y->{_e}); |
61f5c3f5 |
1423 | |
1424 | # if $y has digits after dot |
1425 | my $shifty = 0; # correct _e of $x by this |
9b924220 |
1426 | if ($y->{_es} eq '-') # has digits after dot |
61f5c3f5 |
1427 | { |
1428 | # 123 % 2.5 => 1230 % 25 => 5 => 0.5 |
9b924220 |
1429 | $shifty = $MBI->_num($y->{_e}); # no more digits after dot |
1430 | $MBI->_lsft($x->{_m}, $y->{_e}, 10);# 123 => 1230, $y->{_m} is already 25 |
61f5c3f5 |
1431 | } |
1432 | # $ym is now mantissa of $y based on exponent 0 |
b3abae2a |
1433 | |
61f5c3f5 |
1434 | my $shiftx = 0; # correct _e of $x by this |
9b924220 |
1435 | if ($x->{_es} eq '-') # has digits after dot |
61f5c3f5 |
1436 | { |
1437 | # 123.4 % 20 => 1234 % 200 |
9b924220 |
1438 | $shiftx = $MBI->_num($x->{_e}); # no more digits after dot |
1439 | $MBI->_lsft($ym, $x->{_e}, 10); # 123 => 1230 |
61f5c3f5 |
1440 | } |
1441 | # 123e1 % 20 => 1230 % 20 |
9b924220 |
1442 | if ($x->{_es} eq '+' && !$MBI->_is_zero($x->{_e})) |
61f5c3f5 |
1443 | { |
9b924220 |
1444 | $MBI->_lsft( $x->{_m}, $x->{_e},10); # es => '+' here |
61f5c3f5 |
1445 | } |
9b924220 |
1446 | |
1447 | $x->{_e} = $MBI->_new($shiftx); |
1448 | $x->{_es} = '+'; |
1449 | $x->{_es} = '-' if $shiftx != 0 || $shifty != 0; |
1450 | $MBI->_add( $x->{_e}, $MBI->_new($shifty)) if $shifty != 0; |
61f5c3f5 |
1451 | |
1452 | # now mantissas are equalized, exponent of $x is adjusted, so calc result |
b3abae2a |
1453 | |
9b924220 |
1454 | $x->{_m} = $MBI->_mod( $x->{_m}, $ym); |
61f5c3f5 |
1455 | |
9b924220 |
1456 | $x->{sign} = '+' if $MBI->_is_zero($x->{_m}); # fix sign for -0 |
61f5c3f5 |
1457 | $x->bnorm(); |
1458 | |
1459 | if ($neg != 0) # one of them negative => correct in place |
1460 | { |
1461 | my $r = $y - $x; |
1462 | $x->{_m} = $r->{_m}; |
1463 | $x->{_e} = $r->{_e}; |
9b924220 |
1464 | $x->{_es} = $r->{_es}; |
1465 | $x->{sign} = '+' if $MBI->_is_zero($x->{_m}); # fix sign for -0 |
61f5c3f5 |
1466 | $x->bnorm(); |
1467 | } |
1468 | |
1469 | $x->round($a,$p,$r,$y); # round and return |
58cde26e |
1470 | } |
1471 | |
990fb837 |
1472 | sub broot |
1473 | { |
1474 | # calculate $y'th root of $x |
3a427a11 |
1475 | |
1476 | # set up parameters |
1477 | my ($self,$x,$y,$a,$p,$r) = (ref($_[0]),@_); |
1478 | # objectify is costly, so avoid it |
1479 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1480 | { |
1481 | ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
1482 | } |
990fb837 |
1483 | |
1484 | # NaN handling: $x ** 1/0, x or y NaN, or y inf/-inf or y == 0 |
1485 | return $x->bnan() if $x->{sign} !~ /^\+/ || $y->is_zero() || |
1486 | $y->{sign} !~ /^\+$/; |
1487 | |
1488 | return $x if $x->is_zero() || $x->is_one() || $x->is_inf() || $y->is_one(); |
1489 | |
1490 | # we need to limit the accuracy to protect against overflow |
1491 | my $fallback = 0; |
1492 | my (@params,$scale); |
1493 | ($x,@params) = $x->_find_round_parameters($a,$p,$r); |
1494 | |
1495 | return $x if $x->is_nan(); # error in _find_round_parameters? |
1496 | |
1497 | # no rounding at all, so must use fallback |
1498 | if (scalar @params == 0) |
1499 | { |
1500 | # simulate old behaviour |
1501 | $params[0] = $self->div_scale(); # and round to it as accuracy |
1502 | $scale = $params[0]+4; # at least four more for proper round |
9b924220 |
1503 | $params[2] = $r; # iound mode by caller or undef |
990fb837 |
1504 | $fallback = 1; # to clear a/p afterwards |
1505 | } |
1506 | else |
1507 | { |
1508 | # the 4 below is empirical, and there might be cases where it is not |
1509 | # enough... |
1510 | $scale = abs($params[0] || $params[1]) + 4; # take whatever is defined |
1511 | } |
1512 | |
1513 | # when user set globals, they would interfere with our calculation, so |
1514 | # disable them and later re-enable them |
1515 | no strict 'refs'; |
1516 | my $abr = "$self\::accuracy"; my $ab = $$abr; $$abr = undef; |
1517 | my $pbr = "$self\::precision"; my $pb = $$pbr; $$pbr = undef; |
1518 | # we also need to disable any set A or P on $x (_find_round_parameters took |
1519 | # them already into account), since these would interfere, too |
1520 | delete $x->{_a}; delete $x->{_p}; |
1521 | # need to disable $upgrade in BigInt, to avoid deep recursion |
1522 | local $Math::BigInt::upgrade = undef; # should be really parent class vs MBI |
1523 | |
1524 | # remember sign and make $x positive, since -4 ** (1/2) => -2 |
27e7b8bb |
1525 | my $sign = 0; $sign = 1 if $x->{sign} eq '-'; $x->{sign} = '+'; |
1526 | |
1527 | my $is_two = 0; |
1528 | if ($y->isa('Math::BigFloat')) |
1529 | { |
1530 | $is_two = ($y->{sign} eq '+' && $MBI->_is_two($y->{_m}) && $MBI->_is_zero($y->{_e})); |
1531 | } |
1532 | else |
1533 | { |
1534 | $is_two = ($y == 2); |
1535 | } |
990fb837 |
1536 | |
27e7b8bb |
1537 | # normal square root if $y == 2: |
1538 | if ($is_two) |
990fb837 |
1539 | { |
1540 | $x->bsqrt($scale+4); |
1541 | } |
1542 | elsif ($y->is_one('-')) |
1543 | { |
1544 | # $x ** -1 => 1/$x |
1545 | my $u = $self->bone()->bdiv($x,$scale); |
1546 | # copy private parts over |
1547 | $x->{_m} = $u->{_m}; |
1548 | $x->{_e} = $u->{_e}; |
9b924220 |
1549 | $x->{_es} = $u->{_es}; |
990fb837 |
1550 | } |
1551 | else |
1552 | { |
3a427a11 |
1553 | # calculate the broot() as integer result first, and if it fits, return |
1554 | # it rightaway (but only if $x and $y are integer): |
1555 | |
1556 | my $done = 0; # not yet |
1557 | if ($y->is_int() && $x->is_int()) |
1558 | { |
9b924220 |
1559 | my $i = $MBI->_copy( $x->{_m} ); |
1560 | $MBI->_lsft( $i, $x->{_e}, 10 ) unless $MBI->_is_zero($x->{_e}); |
1561 | my $int = Math::BigInt->bzero(); |
1562 | $int->{value} = $i; |
3a427a11 |
1563 | $int->broot($y->as_number()); |
1564 | # if ($exact) |
1565 | if ($int->copy()->bpow($y) == $x) |
1566 | { |
1567 | # found result, return it |
9b924220 |
1568 | $x->{_m} = $int->{value}; |
1569 | $x->{_e} = $MBI->_zero(); |
1570 | $x->{_es} = '+'; |
3a427a11 |
1571 | $x->bnorm(); |
1572 | $done = 1; |
1573 | } |
1574 | } |
1575 | if ($done == 0) |
1576 | { |
1577 | my $u = $self->bone()->bdiv($y,$scale+4); |
1578 | delete $u->{_a}; delete $u->{_p}; # otherwise it conflicts |
1579 | $x->bpow($u,$scale+4); # el cheapo |
1580 | } |
990fb837 |
1581 | } |
1582 | $x->bneg() if $sign == 1; |
1583 | |
091c87b1 |
1584 | # shortcut to not run through _find_round_parameters again |
990fb837 |
1585 | if (defined $params[0]) |
1586 | { |
1587 | $x->bround($params[0],$params[2]); # then round accordingly |
1588 | } |
1589 | else |
1590 | { |
1591 | $x->bfround($params[1],$params[2]); # then round accordingly |
1592 | } |
1593 | if ($fallback) |
1594 | { |
1595 | # clear a/p after round, since user did not request it |
ef9466ea |
1596 | delete $x->{_a}; delete $x->{_p}; |
990fb837 |
1597 | } |
1598 | # restore globals |
1599 | $$abr = $ab; $$pbr = $pb; |
1600 | $x; |
1601 | } |
1602 | |
58cde26e |
1603 | sub bsqrt |
1604 | { |
990fb837 |
1605 | # calculate square root |
ee15d750 |
1606 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e |
1607 | |
990fb837 |
1608 | return $x->bnan() if $x->{sign} !~ /^[+]/; # NaN, -inf or < 0 |
1609 | return $x if $x->{sign} eq '+inf'; # sqrt(inf) == inf |
1610 | return $x->round($a,$p,$r) if $x->is_zero() || $x->is_one(); |
58cde26e |
1611 | |
61f5c3f5 |
1612 | # we need to limit the accuracy to protect against overflow |
574bacfe |
1613 | my $fallback = 0; |
990fb837 |
1614 | my (@params,$scale); |
1615 | ($x,@params) = $x->_find_round_parameters($a,$p,$r); |
1616 | |
1617 | return $x if $x->is_nan(); # error in _find_round_parameters? |
61f5c3f5 |
1618 | |
1619 | # no rounding at all, so must use fallback |
990fb837 |
1620 | if (scalar @params == 0) |
0716bf9b |
1621 | { |
1622 | # simulate old behaviour |
990fb837 |
1623 | $params[0] = $self->div_scale(); # and round to it as accuracy |
1624 | $scale = $params[0]+4; # at least four more for proper round |
1625 | $params[2] = $r; # round mode by caller or undef |
ee15d750 |
1626 | $fallback = 1; # to clear a/p afterwards |
0716bf9b |
1627 | } |
61f5c3f5 |
1628 | else |
1629 | { |
1630 | # the 4 below is empirical, and there might be cases where it is not |
1631 | # enough... |
990fb837 |
1632 | $scale = abs($params[0] || $params[1]) + 4; # take whatever is defined |
61f5c3f5 |
1633 | } |
1634 | |
1635 | # when user set globals, they would interfere with our calculation, so |
9393ace2 |
1636 | # disable them and later re-enable them |
61f5c3f5 |
1637 | no strict 'refs'; |
1638 | my $abr = "$self\::accuracy"; my $ab = $$abr; $$abr = undef; |
b3abae2a |
1639 | my $pbr = "$self\::precision"; my $pb = $$pbr; $$pbr = undef; |
61f5c3f5 |
1640 | # we also need to disable any set A or P on $x (_find_round_parameters took |
1641 | # them already into account), since these would interfere, too |
1642 | delete $x->{_a}; delete $x->{_p}; |
9393ace2 |
1643 | # need to disable $upgrade in BigInt, to avoid deep recursion |
1644 | local $Math::BigInt::upgrade = undef; # should be really parent class vs MBI |
61f5c3f5 |
1645 | |
9b924220 |
1646 | my $i = $MBI->_copy( $x->{_m} ); |
1647 | $MBI->_lsft( $i, $x->{_e}, 10 ) unless $MBI->_is_zero($x->{_e}); |
1648 | my $xas = Math::BigInt->bzero(); |
1649 | $xas->{value} = $i; |
1650 | |
394e6ffb |
1651 | my $gs = $xas->copy()->bsqrt(); # some guess |
b3abae2a |
1652 | |
9b924220 |
1653 | if (($x->{_es} ne '-') # guess can't be accurate if there are |
394e6ffb |
1654 | # digits after the dot |
b3abae2a |
1655 | && ($xas->bacmp($gs * $gs) == 0)) # guess hit the nail on the head? |
394e6ffb |
1656 | { |
9b924220 |
1657 | # exact result, copy result over to keep $x |
1658 | $x->{_m} = $gs->{value}; $x->{_e} = $MBI->_zero(); $x->{_es} = '+'; |
1659 | $x->bnorm(); |
091c87b1 |
1660 | # shortcut to not run through _find_round_parameters again |
990fb837 |
1661 | if (defined $params[0]) |
61f5c3f5 |
1662 | { |
990fb837 |
1663 | $x->bround($params[0],$params[2]); # then round accordingly |
61f5c3f5 |
1664 | } |
1665 | else |
1666 | { |
990fb837 |
1667 | $x->bfround($params[1],$params[2]); # then round accordingly |
61f5c3f5 |
1668 | } |
1669 | if ($fallback) |
1670 | { |
1671 | # clear a/p after round, since user did not request it |
ef9466ea |
1672 | delete $x->{_a}; delete $x->{_p}; |
61f5c3f5 |
1673 | } |
9393ace2 |
1674 | # re-enable A and P, upgrade is taken care of by "local" |
b3abae2a |
1675 | ${"$self\::accuracy"} = $ab; ${"$self\::precision"} = $pb; |
61f5c3f5 |
1676 | return $x; |
394e6ffb |
1677 | } |
2ab5f49d |
1678 | |
1679 | # sqrt(2) = 1.4 because sqrt(2*100) = 1.4*10; so we can increase the accuracy |
1680 | # of the result by multipyling the input by 100 and then divide the integer |
1681 | # result of sqrt(input) by 10. Rounding afterwards returns the real result. |
9b924220 |
1682 | |
1683 | # The following steps will transform 123.456 (in $x) into 123456 (in $y1) |
1684 | my $y1 = $MBI->_copy($x->{_m}); |
1685 | |
1686 | my $length = $MBI->_len($y1); |
1687 | |
1688 | # Now calculate how many digits the result of sqrt(y1) would have |
1689 | my $digits = int($length / 2); |
1690 | |
1691 | # But we need at least $scale digits, so calculate how many are missing |
1692 | my $shift = $scale - $digits; |
1693 | |
1694 | # That should never happen (we take care of integer guesses above) |
1695 | # $shift = 0 if $shift < 0; |
1696 | |
1697 | # Multiply in steps of 100, by shifting left two times the "missing" digits |
1698 | my $s2 = $shift * 2; |
1699 | |
2ab5f49d |
1700 | # We now make sure that $y1 has the same odd or even number of digits than |
1701 | # $x had. So when _e of $x is odd, we must shift $y1 by one digit left, |
1702 | # because we always must multiply by steps of 100 (sqrt(100) is 10) and not |
1703 | # steps of 10. The length of $x does not count, since an even or odd number |
1704 | # of digits before the dot is not changed by adding an even number of digits |
1705 | # after the dot (the result is still odd or even digits long). |
9b924220 |
1706 | $s2++ if $MBI->_is_odd($x->{_e}); |
1707 | |
1708 | $MBI->_lsft( $y1, $MBI->_new($s2), 10); |
1709 | |
2ab5f49d |
1710 | # now take the square root and truncate to integer |
9b924220 |
1711 | $y1 = $MBI->_sqrt($y1); |
1712 | |
2ab5f49d |
1713 | # By "shifting" $y1 right (by creating a negative _e) we calculate the final |
1714 | # result, which is than later rounded to the desired scale. |
990fb837 |
1715 | |
1716 | # calculate how many zeros $x had after the '.' (or before it, depending |
9b924220 |
1717 | # on sign of $dat, the result should have half as many: |
1718 | my $dat = $MBI->_num($x->{_e}); |
1719 | $dat = -$dat if $x->{_es} eq '-'; |
1720 | $dat += $length; |
990fb837 |
1721 | |
1722 | if ($dat > 0) |
1723 | { |
1724 | # no zeros after the dot (e.g. 1.23, 0.49 etc) |
1725 | # preserve half as many digits before the dot than the input had |
1726 | # (but round this "up") |
1727 | $dat = int(($dat+1)/2); |
1728 | } |
1729 | else |
1730 | { |
1731 | $dat = int(($dat)/2); |
1732 | } |
9b924220 |
1733 | $dat -= $MBI->_len($y1); |
1734 | if ($dat < 0) |
1735 | { |
1736 | $dat = abs($dat); |
1737 | $x->{_e} = $MBI->_new( $dat ); |
1738 | $x->{_es} = '-'; |
1739 | } |
1740 | else |
1741 | { |
1742 | $x->{_e} = $MBI->_new( $dat ); |
1743 | $x->{_es} = '+'; |
1744 | } |
2ab5f49d |
1745 | $x->{_m} = $y1; |
9b924220 |
1746 | $x->bnorm(); |
61f5c3f5 |
1747 | |
091c87b1 |
1748 | # shortcut to not run through _find_round_parameters again |
990fb837 |
1749 | if (defined $params[0]) |
61f5c3f5 |
1750 | { |
990fb837 |
1751 | $x->bround($params[0],$params[2]); # then round accordingly |
61f5c3f5 |
1752 | } |
1753 | else |
1754 | { |
990fb837 |
1755 | $x->bfround($params[1],$params[2]); # then round accordingly |
61f5c3f5 |
1756 | } |
574bacfe |
1757 | if ($fallback) |
1758 | { |
1759 | # clear a/p after round, since user did not request it |
ef9466ea |
1760 | delete $x->{_a}; delete $x->{_p}; |
574bacfe |
1761 | } |
61f5c3f5 |
1762 | # restore globals |
b3abae2a |
1763 | $$abr = $ab; $$pbr = $pb; |
574bacfe |
1764 | $x; |
58cde26e |
1765 | } |
1766 | |
b3abae2a |
1767 | sub bfac |
1768 | { |
28df3e88 |
1769 | # (BFLOAT or num_str, BFLOAT or num_str) return BFLOAT |
091c87b1 |
1770 | # compute factorial number, modifies first argument |
b3abae2a |
1771 | |
b282a552 |
1772 | # set up parameters |
1773 | my ($self,$x,@r) = (ref($_[0]),@_); |
1774 | # objectify is costly, so avoid it |
1775 | ($self,$x,@r) = objectify(1,@_) if !ref($x); |
1776 | |
1777 | return $x if $x->{sign} eq '+inf'; # inf => inf |
28df3e88 |
1778 | return $x->bnan() |
1779 | if (($x->{sign} ne '+') || # inf, NaN, <0 etc => NaN |
9b924220 |
1780 | ($x->{_es} ne '+')); # digits after dot? |
b3abae2a |
1781 | |
b3abae2a |
1782 | # use BigInt's bfac() for faster calc |
9b924220 |
1783 | if (! $MBI->_is_zero($x->{_e})) |
091c87b1 |
1784 | { |
9b924220 |
1785 | $MBI->_lsft($x->{_m}, $x->{_e},10); # change 12e1 to 120e0 |
1786 | $x->{_e} = $MBI->_zero(); # normalize |
1787 | $x->{_es} = '+'; |
091c87b1 |
1788 | } |
9b924220 |
1789 | $MBI->_fac($x->{_m}); # calculate factorial |
091c87b1 |
1790 | $x->bnorm()->round(@r); # norm again and round result |
b3abae2a |
1791 | } |
1792 | |
9393ace2 |
1793 | sub _pow |
1794 | { |
1795 | # Calculate a power where $y is a non-integer, like 2 ** 0.5 |
1796 | my ($x,$y,$a,$p,$r) = @_; |
1797 | my $self = ref($x); |
1798 | |
1799 | # if $y == 0.5, it is sqrt($x) |
27e7b8bb |
1800 | $HALF = $self->new($HALF) unless ref($HALF); |
1801 | return $x->bsqrt($a,$p,$r,$y) if $y->bcmp($HALF) == 0; |
9393ace2 |
1802 | |
990fb837 |
1803 | # Using: |
1804 | # a ** x == e ** (x * ln a) |
1805 | |
9393ace2 |
1806 | # u = y * ln x |
990fb837 |
1807 | # _ _ |
1808 | # Taylor: | u u^2 u^3 | |
1809 | # x ** y = 1 + | --- + --- + ----- + ... | |
1810 | # |_ 1 1*2 1*2*3 _| |
9393ace2 |
1811 | |
1812 | # we need to limit the accuracy to protect against overflow |
1813 | my $fallback = 0; |
990fb837 |
1814 | my ($scale,@params); |
1815 | ($x,@params) = $x->_find_round_parameters($a,$p,$r); |
1816 | |
1817 | return $x if $x->is_nan(); # error in _find_round_parameters? |
9393ace2 |
1818 | |
1819 | # no rounding at all, so must use fallback |
990fb837 |
1820 | if (scalar @params == 0) |
9393ace2 |
1821 | { |
1822 | # simulate old behaviour |
990fb837 |
1823 | $params[0] = $self->div_scale(); # and round to it as accuracy |
1824 | $params[1] = undef; # disable P |
1825 | $scale = $params[0]+4; # at least four more for proper round |
1826 | $params[2] = $r; # round mode by caller or undef |
9393ace2 |
1827 | $fallback = 1; # to clear a/p afterwards |
1828 | } |
1829 | else |
1830 | { |
1831 | # the 4 below is empirical, and there might be cases where it is not |
1832 | # enough... |
990fb837 |
1833 | $scale = abs($params[0] || $params[1]) + 4; # take whatever is defined |
9393ace2 |
1834 | } |
1835 | |
1836 | # when user set globals, they would interfere with our calculation, so |
56d9de68 |
1837 | # disable them and later re-enable them |
9393ace2 |
1838 | no strict 'refs'; |
1839 | my $abr = "$self\::accuracy"; my $ab = $$abr; $$abr = undef; |
1840 | my $pbr = "$self\::precision"; my $pb = $$pbr; $$pbr = undef; |
1841 | # we also need to disable any set A or P on $x (_find_round_parameters took |
1842 | # them already into account), since these would interfere, too |
1843 | delete $x->{_a}; delete $x->{_p}; |
1844 | # need to disable $upgrade in BigInt, to avoid deep recursion |
1845 | local $Math::BigInt::upgrade = undef; |
1846 | |
1847 | my ($limit,$v,$u,$below,$factor,$next,$over); |
1848 | |
990fb837 |
1849 | $u = $x->copy()->blog(undef,$scale)->bmul($y); |
9393ace2 |
1850 | $v = $self->bone(); # 1 |
1851 | $factor = $self->new(2); # 2 |
1852 | $x->bone(); # first term: 1 |
1853 | |
1854 | $below = $v->copy(); |
1855 | $over = $u->copy(); |
ae161977 |
1856 | |
9393ace2 |
1857 | $limit = $self->new("1E-". ($scale-1)); |
1858 | #my $steps = 0; |
1859 | while (3 < 5) |
1860 | { |
1861 | # we calculate the next term, and add it to the last |
1862 | # when the next term is below our limit, it won't affect the outcome |
1863 | # anymore, so we stop |
1864 | $next = $over->copy()->bdiv($below,$scale); |
990fb837 |
1865 | last if $next->bacmp($limit) <= 0; |
9393ace2 |
1866 | $x->badd($next); |
9393ace2 |
1867 | # calculate things for the next term |
1868 | $over *= $u; $below *= $factor; $factor->binc(); |
9b924220 |
1869 | |
1870 | last if $x->{sign} !~ /^[-+]$/; |
1871 | |
9393ace2 |
1872 | #$steps++; |
1873 | } |
1874 | |
091c87b1 |
1875 | # shortcut to not run through _find_round_parameters again |
990fb837 |
1876 | if (defined $params[0]) |
9393ace2 |
1877 | { |
990fb837 |
1878 | $x->bround($params[0],$params[2]); # then round accordingly |
9393ace2 |
1879 | } |
1880 | else |
1881 | { |
990fb837 |
1882 | $x->bfround($params[1],$params[2]); # then round accordingly |
9393ace2 |
1883 | } |
1884 | if ($fallback) |
1885 | { |
1886 | # clear a/p after round, since user did not request it |
ef9466ea |
1887 | delete $x->{_a}; delete $x->{_p}; |
9393ace2 |
1888 | } |
1889 | # restore globals |
1890 | $$abr = $ab; $$pbr = $pb; |
1891 | $x; |
1892 | } |
1893 | |
58cde26e |
1894 | sub bpow |
1895 | { |
1896 | # (BFLOAT or num_str, BFLOAT or num_str) return BFLOAT |
1897 | # compute power of two numbers, second arg is used as integer |
1898 | # modifies first argument |
1899 | |
f9a08e12 |
1900 | # set up parameters |
1901 | my ($self,$x,$y,$a,$p,$r) = (ref($_[0]),@_); |
1902 | # objectify is costly, so avoid it |
1903 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1904 | { |
1905 | ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
1906 | } |
58cde26e |
1907 | |
1908 | return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan; |
2d2b2744 |
1909 | return $x if $x->{sign} =~ /^[+-]inf$/; |
1910 | |
1911 | # -2 ** -2 => NaN |
1912 | return $x->bnan() if $x->{sign} eq '-' && $y->{sign} eq '-'; |
ae161977 |
1913 | |
1914 | # cache the result of is_zero |
1915 | my $y_is_zero = $y->is_zero(); |
1916 | return $x->bone() if $y_is_zero; |
58cde26e |
1917 | return $x if $x->is_one() || $y->is_one(); |
9393ace2 |
1918 | |
ae161977 |
1919 | my $x_is_zero = $x->is_zero(); |
2d2b2744 |
1920 | return $x->_pow($y,$a,$p,$r) if !$x_is_zero && !$y->is_int(); # non-integer power |
9393ace2 |
1921 | |
ae161977 |
1922 | my $y1 = $y->as_number()->{value}; # make MBI part |
9b924220 |
1923 | |
394e6ffb |
1924 | # if ($x == -1) |
9b924220 |
1925 | if ($x->{sign} eq '-' && $MBI->_is_one($x->{_m}) && $MBI->_is_zero($x->{_e})) |
58cde26e |
1926 | { |
1927 | # if $x == -1 and odd/even y => +1/-1 because +-1 ^ (+-1) => +-1 |
9b924220 |
1928 | return $MBI->_is_odd($y1) ? $x : $x->babs(1); |
288d023a |
1929 | } |
ae161977 |
1930 | if ($x_is_zero) |
28df3e88 |
1931 | { |
ae161977 |
1932 | return $x->bone() if $y_is_zero; |
28df3e88 |
1933 | return $x if $y->{sign} eq '+'; # 0**y => 0 (if not y <= 0) |
9b924220 |
1934 | # 0 ** -y => 1 / (0 ** y) => 1 / 0! (1 / 0 => +inf) |
1935 | return $x->binf(); |
28df3e88 |
1936 | } |
58cde26e |
1937 | |
9b924220 |
1938 | my $new_sign = '+'; |
ae161977 |
1939 | $new_sign = $MBI->_is_odd($y1) ? '-' : '+' if $x->{sign} ne '+'; |
9b924220 |
1940 | |
58cde26e |
1941 | # calculate $x->{_m} ** $y and $x->{_e} * $y separately (faster) |
9b924220 |
1942 | $x->{_m} = $MBI->_pow( $x->{_m}, $y1); |
ae161977 |
1943 | $x->{_e} = $MBI->_mul ($x->{_e}, $y1); |
9b924220 |
1944 | |
1945 | $x->{sign} = $new_sign; |
58cde26e |
1946 | $x->bnorm(); |
1947 | if ($y->{sign} eq '-') |
1948 | { |
1949 | # modify $x in place! |
ae161977 |
1950 | my $z = $x->copy(); $x->bone(); |
58cde26e |
1951 | return $x->bdiv($z,$a,$p,$r); # round in one go (might ignore y's A!) |
a0d0e21e |
1952 | } |
28df3e88 |
1953 | $x->round($a,$p,$r,$y); |
58cde26e |
1954 | } |
1955 | |
1956 | ############################################################################### |
1957 | # rounding functions |
1958 | |
1959 | sub bfround |
1960 | { |
1961 | # precision: round to the $Nth digit left (+$n) or right (-$n) from the '.' |
1962 | # $n == 0 means round to integer |
1963 | # expects and returns normalized numbers! |
ee15d750 |
1964 | my $x = shift; my $self = ref($x) || $x; $x = $self->new(shift) if !ref($x); |
a0d0e21e |
1965 | |
58cde26e |
1966 | return $x if $x->modify('bfround'); |
9b924220 |
1967 | |
ee15d750 |
1968 | my ($scale,$mode) = $x->_scale_p($self->precision(),$self->round_mode(),@_); |
58cde26e |
1969 | return $x if !defined $scale; # no-op |
1970 | |
574bacfe |
1971 | # never round a 0, +-inf, NaN |
61f5c3f5 |
1972 | if ($x->is_zero()) |
1973 | { |
1974 | $x->{_p} = $scale if !defined $x->{_p} || $x->{_p} < $scale; # -3 < -2 |
1975 | return $x; |
1976 | } |
1977 | return $x if $x->{sign} !~ /^[+-]$/; |
58cde26e |
1978 | |
ee15d750 |
1979 | # don't round if x already has lower precision |
1980 | return $x if (defined $x->{_p} && $x->{_p} < 0 && $scale < $x->{_p}); |
1981 | |
1982 | $x->{_p} = $scale; # remember round in any case |
ef9466ea |
1983 | delete $x->{_a}; # and clear A |
58cde26e |
1984 | if ($scale < 0) |
1985 | { |
58cde26e |
1986 | # round right from the '.' |
f9a08e12 |
1987 | |
9b924220 |
1988 | return $x if $x->{_es} eq '+'; # e >= 0 => nothing to round |
f9a08e12 |
1989 | |
58cde26e |
1990 | $scale = -$scale; # positive for simplicity |
9b924220 |
1991 | my $len = $MBI->_len($x->{_m}); # length of mantissa |
f9a08e12 |
1992 | |
1993 | # the following poses a restriction on _e, but if _e is bigger than a |
1994 | # scalar, you got other problems (memory etc) anyway |
9b924220 |
1995 | my $dad = -(0+ ($x->{_es}.$MBI->_num($x->{_e}))); # digits after dot |
58cde26e |
1996 | my $zad = 0; # zeros after dot |
f9a08e12 |
1997 | $zad = $dad - $len if (-$dad < -$len); # for 0.00..00xxx style |
9b924220 |
1998 | |
1999 | # p rint "scale $scale dad $dad zad $zad len $len\n"; |
58cde26e |
2000 | # number bsstr len zad dad |
2001 | # 0.123 123e-3 3 0 3 |
2002 | # 0.0123 123e-4 3 1 4 |
2003 | # 0.001 1e-3 1 2 3 |
2004 | # 1.23 123e-2 3 0 2 |
2005 | # 1.2345 12345e-4 5 0 4 |
2006 | |
2007 | # do not round after/right of the $dad |
2008 | return $x if $scale > $dad; # 0.123, scale >= 3 => exit |
2009 | |
ee15d750 |
2010 | # round to zero if rounding inside the $zad, but not for last zero like: |
2011 | # 0.0065, scale -2, round last '0' with following '65' (scale == zad case) |
2012 | return $x->bzero() if $scale < $zad; |
2013 | if ($scale == $zad) # for 0.006, scale -3 and trunc |
58cde26e |
2014 | { |
b3abae2a |
2015 | $scale = -$len; |
58cde26e |
2016 | } |
2017 | else |
2018 | { |
2019 | # adjust round-point to be inside mantissa |
2020 | if ($zad != 0) |
2021 | { |
2022 | $scale = $scale-$zad; |
2023 | } |
2024 | else |
2025 | { |
2026 | my $dbd = $len - $dad; $dbd = 0 if $dbd < 0; # digits before dot |
2027 | $scale = $dbd+$scale; |
2028 | } |
2029 | } |
a0d0e21e |
2030 | } |
58cde26e |
2031 | else |
2032 | { |
f9a08e12 |
2033 | # round left from the '.' |
2034 | |
58cde26e |
2035 | # 123 => 100 means length(123) = 3 - $scale (2) => 1 |
a5f75d66 |
2036 | |
9b924220 |
2037 | my $dbt = $MBI->_len($x->{_m}); |
b3abae2a |
2038 | # digits before dot |
9b924220 |
2039 | my $dbd = $dbt + ($x->{_es} . $MBI->_num($x->{_e})); |
b3abae2a |
2040 | # should be the same, so treat it as this |
2041 | $scale = 1 if $scale == 0; |
2042 | # shortcut if already integer |
2043 | return $x if $scale == 1 && $dbt <= $dbd; |
2044 | # maximum digits before dot |
2045 | ++$dbd; |
2046 | |
2047 | if ($scale > $dbd) |
2048 | { |
2049 | # not enough digits before dot, so round to zero |
2050 | return $x->bzero; |
2051 | } |
2052 | elsif ( $scale == $dbd ) |
2053 | { |
2054 | # maximum |
2055 | $scale = -$dbt; |
2056 | } |
58cde26e |
2057 | else |
b3abae2a |
2058 | { |
2059 | $scale = $dbd - $scale; |
2060 | } |
a0d0e21e |
2061 | } |
574bacfe |
2062 | # pass sign to bround for rounding modes '+inf' and '-inf' |
ae161977 |
2063 | my $m = bless { sign => $x->{sign}, value => $x->{_m} }, 'Math::BigInt'; |
9b924220 |
2064 | $m->bround($scale,$mode); |
2065 | $x->{_m} = $m->{value}; # get our mantissa back |
58cde26e |
2066 | $x->bnorm(); |
2067 | } |
2068 | |
2069 | sub bround |
2070 | { |
2071 | # accuracy: preserve $N digits, and overwrite the rest with 0's |
ee15d750 |
2072 | my $x = shift; my $self = ref($x) || $x; $x = $self->new(shift) if !ref($x); |
9b924220 |
2073 | |
990fb837 |
2074 | if (($_[0] || 0) < 0) |
2075 | { |
2076 | require Carp; Carp::croak ('bround() needs positive accuracy'); |
2077 | } |
58cde26e |
2078 | |
ee15d750 |
2079 | my ($scale,$mode) = $x->_scale_a($self->accuracy(),$self->round_mode(),@_); |
2080 | return $x if !defined $scale; # no-op |
61f5c3f5 |
2081 | |
58cde26e |
2082 | return $x if $x->modify('bround'); |
61f5c3f5 |
2083 | |
ee15d750 |
2084 | # scale is now either $x->{_a}, $accuracy, or the user parameter |
2085 | # test whether $x already has lower accuracy, do nothing in this case |
2086 | # but do round if the accuracy is the same, since a math operation might |
2087 | # want to round a number with A=5 to 5 digits afterwards again |
2088 | return $x if defined $_[0] && defined $x->{_a} && $x->{_a} < $_[0]; |
58cde26e |
2089 | |
61f5c3f5 |
2090 | # scale < 0 makes no sense |
2091 | # never round a +-inf, NaN |
2092 | return $x if ($scale < 0) || $x->{sign} !~ /^[+-]$/; |
58cde26e |
2093 | |
61f5c3f5 |
2094 | # 1: $scale == 0 => keep all digits |
2095 | # 2: never round a 0 |
2096 | # 3: if we should keep more digits than the mantissa has, do nothing |
9b924220 |
2097 | if ($scale == 0 || $x->is_zero() || $MBI->_len($x->{_m}) <= $scale) |
61f5c3f5 |
2098 | { |
2099 | $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; |
2100 | return $x; |
2101 | } |
f216259d |
2102 | |
58cde26e |
2103 | # pass sign to bround for '+inf' and '-inf' rounding modes |
ae161977 |
2104 | my $m = bless { sign => $x->{sign}, value => $x->{_m} }, 'Math::BigInt'; |
9b924220 |
2105 | |
2106 | $m->bround($scale,$mode); # round mantissa |
2107 | $x->{_m} = $m->{value}; # get our mantissa back |
ee15d750 |
2108 | $x->{_a} = $scale; # remember rounding |
ef9466ea |
2109 | delete $x->{_p}; # and clear P |
574bacfe |
2110 | $x->bnorm(); # del trailing zeros gen. by bround() |
58cde26e |
2111 | } |
2112 | |
2113 | sub bfloor |
2114 | { |
2115 | # return integer less or equal then $x |
ee15d750 |
2116 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e |
2117 | |
2118 | return $x if $x->modify('bfloor'); |
2119 | |
2120 | return $x if $x->{sign} !~ /^[+-]$/; # nan, +inf, -inf |
2121 | |
2122 | # if $x has digits after dot |
9b924220 |
2123 | if ($x->{_es} eq '-') |
58cde26e |
2124 | { |
9b924220 |
2125 | $x->{_m} = $MBI->_rsft($x->{_m},$x->{_e},10); # cut off digits after dot |
2126 | $x->{_e} = $MBI->_zero(); # trunc/norm |
2127 | $x->{_es} = '+'; # abs e |
2128 | $MBI->_inc($x->{_m}) if $x->{sign} eq '-'; # increment if negative |
f216259d |
2129 | } |
61f5c3f5 |
2130 | $x->round($a,$p,$r); |
58cde26e |
2131 | } |
288d023a |
2132 | |
58cde26e |
2133 | sub bceil |
2134 | { |
2135 | # return integer greater or equal then $x |
ee15d750 |
2136 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e |
2137 | |
2138 | return $x if $x->modify('bceil'); |
2139 | return $x if $x->{sign} !~ /^[+-]$/; # nan, +inf, -inf |
2140 | |
2141 | # if $x has digits after dot |
9b924220 |
2142 | if ($x->{_es} eq '-') |
58cde26e |
2143 | { |
9b924220 |
2144 | $x->{_m} = $MBI->_rsft($x->{_m},$x->{_e},10); # cut off digits after dot |
2145 | $x->{_e} = $MBI->_zero(); # trunc/norm |
2146 | $x->{_es} = '+'; # abs e |
2147 | $MBI->_inc($x->{_m}) if $x->{sign} eq '+'; # increment if positive |
a0d0e21e |
2148 | } |
61f5c3f5 |
2149 | $x->round($a,$p,$r); |
58cde26e |
2150 | } |
2151 | |
394e6ffb |
2152 | sub brsft |
2153 | { |
f9a08e12 |
2154 | # shift right by $y (divide by power of $n) |
2155 | |
2156 | # set up parameters |
2157 | my ($self,$x,$y,$n,$a,$p,$r) = (ref($_[0]),@_); |
2158 | # objectify is costly, so avoid it |
2159 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
2160 | { |
2161 | ($self,$x,$y,$n,$a,$p,$r) = objectify(2,@_); |
2162 | } |
394e6ffb |
2163 | |
2164 | return $x if $x->modify('brsft'); |
2165 | return $x if $x->{sign} !~ /^[+-]$/; # nan, +inf, -inf |
2166 | |
f9a08e12 |
2167 | $n = 2 if !defined $n; $n = $self->new($n); |
2168 | $x->bdiv($n->bpow($y),$a,$p,$r,$y); |
394e6ffb |
2169 | } |
2170 | |
2171 | sub blsft |
2172 | { |
f9a08e12 |
2173 | # shift left by $y (multiply by power of $n) |
2174 | |
2175 | # set up parameters |
2176 | my ($self,$x,$y,$n,$a,$p,$r) = (ref($_[0]),@_); |
2177 | # objectify is costly, so avoid it |
2178 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
2179 | { |
2180 | ($self,$x,$y,$n,$a,$p,$r) = objectify(2,@_); |
2181 | } |
394e6ffb |
2182 | |
f9a08e12 |
2183 | return $x if $x->modify('blsft'); |
394e6ffb |
2184 | return $x if $x->{sign} !~ /^[+-]$/; # nan, +inf, -inf |
2185 | |
f9a08e12 |
2186 | $n = 2 if !defined $n; $n = $self->new($n); |
2187 | $x->bmul($n->bpow($y),$a,$p,$r,$y); |
394e6ffb |
2188 | } |
2189 | |
58cde26e |
2190 | ############################################################################### |
a5f75d66 |
2191 | |
58cde26e |
2192 | sub DESTROY |
2193 | { |
b282a552 |
2194 | # going through AUTOLOAD for every DESTROY is costly, avoid it by empty sub |
58cde26e |
2195 | } |
2196 | |
2197 | sub AUTOLOAD |
2198 | { |
b3abae2a |
2199 | # make fxxx and bxxx both work by selectively mapping fxxx() to MBF::bxxx() |
2200 | # or falling back to MBI::bxxx() |
58cde26e |
2201 | my $name = $AUTOLOAD; |
2202 | |
ef9466ea |
2203 | $name =~ s/(.*):://; # split package |
2204 | my $c = $1 || $class; |
ee15d750 |
2205 | no strict 'refs'; |
ef9466ea |
2206 | $c->import() if $IMPORT == 0; |
ee15d750 |
2207 | if (!method_alias($name)) |
58cde26e |
2208 | { |
ee15d750 |
2209 | if (!defined $name) |
2210 | { |
2211 | # delayed load of Carp and avoid recursion |
2212 | require Carp; |
ef9466ea |
2213 | Carp::croak ("$c: Can't call a method without name"); |
ee15d750 |
2214 | } |
ee15d750 |
2215 | if (!method_hand_up($name)) |
2216 | { |
2217 | # delayed load of Carp and avoid recursion |
2218 | require Carp; |
ef9466ea |
2219 | Carp::croak ("Can't call $c\-\>$name, not a valid method"); |
ee15d750 |
2220 | } |
2221 | # try one level up, but subst. bxxx() for fxxx() since MBI only got bxxx() |
2222 | $name =~ s/^f/b/; |
9b924220 |
2223 | return &{"Math::BigInt"."::$name"}(@_); |
a0d0e21e |
2224 | } |
58cde26e |
2225 | my $bname = $name; $bname =~ s/^f/b/; |
ef9466ea |
2226 | $c .= "::$name"; |
2227 | *{$c} = \&{$bname}; |
2228 | &{$c}; # uses @_ |
58cde26e |
2229 | } |
2230 | |
2231 | sub exponent |
2232 | { |
2233 | # return a copy of the exponent |
ee15d750 |
2234 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
2235 | |
ee15d750 |
2236 | if ($x->{sign} !~ /^[+-]$/) |
2237 | { |
2238 | my $s = $x->{sign}; $s =~ s/^[+-]//; |
9b924220 |
2239 | return Math::BigInt->new($s); # -inf, +inf => +inf |
ee15d750 |
2240 | } |
9b924220 |
2241 | Math::BigInt->new( $x->{_es} . $MBI->_str($x->{_e})); |
58cde26e |
2242 | } |
2243 | |
2244 | sub mantissa |
2245 | { |
2246 | # return a copy of the mantissa |
ee15d750 |
2247 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
2248 | |
ee15d750 |
2249 | if ($x->{sign} !~ /^[+-]$/) |
2250 | { |
2251 | my $s = $x->{sign}; $s =~ s/^[+]//; |
9b924220 |
2252 | return Math::BigInt->new($s); # -inf, +inf => +inf |
ee15d750 |
2253 | } |
9b924220 |
2254 | my $m = Math::BigInt->new( $MBI->_str($x->{_m})); |
ee15d750 |
2255 | $m->bneg() if $x->{sign} eq '-'; |
58cde26e |
2256 | |
61f5c3f5 |
2257 | $m; |
58cde26e |
2258 | } |
2259 | |
2260 | sub parts |
2261 | { |
2262 | # return a copy of both the exponent and the mantissa |
ee15d750 |
2263 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
2264 | |
ee15d750 |
2265 | if ($x->{sign} !~ /^[+-]$/) |
2266 | { |
2267 | my $s = $x->{sign}; $s =~ s/^[+]//; my $se = $s; $se =~ s/^[-]//; |
2268 | return ($self->new($s),$self->new($se)); # +inf => inf and -inf,+inf => inf |
2269 | } |
9b924220 |
2270 | my $m = Math::BigInt->bzero(); |
2271 | $m->{value} = $MBI->_copy($x->{_m}); |
ee15d750 |
2272 | $m->bneg() if $x->{sign} eq '-'; |
9b924220 |
2273 | ($m, Math::BigInt->new( $x->{_es} . $MBI->_num($x->{_e}) )); |
58cde26e |
2274 | } |
2275 | |
2276 | ############################################################################## |
2277 | # private stuff (internal use only) |
2278 | |
58cde26e |
2279 | sub import |
2280 | { |
2281 | my $self = shift; |
8f675a64 |
2282 | my $l = scalar @_; |
2283 | my $lib = ''; my @a; |
990fb837 |
2284 | $IMPORT=1; |
8f675a64 |
2285 | for ( my $i = 0; $i < $l ; $i++) |
58cde26e |
2286 | { |
2287 | if ( $_[$i] eq ':constant' ) |
2288 | { |
091c87b1 |
2289 | # This causes overlord er load to step in. 'binary' and 'integer' |
2290 | # are handled by BigInt. |
58cde26e |
2291 | overload::constant float => sub { $self->new(shift); }; |
b3abae2a |
2292 | } |
2293 | elsif ($_[$i] eq 'upgrade') |
2294 | { |
2295 | # this causes upgrading |
28df3e88 |
2296 | $upgrade = $_[$i+1]; # or undef to disable |
8f675a64 |
2297 | $i++; |
28df3e88 |
2298 | } |
2299 | elsif ($_[$i] eq 'downgrade') |
2300 | { |
2301 | # this causes downgrading |
2302 | $downgrade = $_[$i+1]; # or undef to disable |
8f675a64 |
2303 | $i++; |
58cde26e |
2304 | } |
56b9c951 |
2305 | elsif ($_[$i] eq 'lib') |
2306 | { |
990fb837 |
2307 | # alternative library |
56b9c951 |
2308 | $lib = $_[$i+1] || ''; # default Calc |
8f675a64 |
2309 | $i++; |
56b9c951 |
2310 | } |
2311 | elsif ($_[$i] eq 'with') |
2312 | { |
990fb837 |
2313 | # alternative class for our private parts() |
9b924220 |
2314 | # XXX: no longer supported |
2315 | # $MBI = $_[$i+1] || 'Math::BigInt'; |
8f675a64 |
2316 | $i++; |
2317 | } |
2318 | else |
2319 | { |
2320 | push @a, $_[$i]; |
56b9c951 |
2321 | } |
58cde26e |
2322 | } |
8f675a64 |
2323 | |
56b9c951 |
2324 | # let use Math::BigInt lib => 'GMP'; use Math::BigFloat; still work |
2325 | my $mbilib = eval { Math::BigInt->config()->{lib} }; |
9b924220 |
2326 | if ((defined $mbilib) && ($MBI eq 'Math::BigInt::Calc')) |
8f675a64 |
2327 | { |
2328 | # MBI already loaded |
9b924220 |
2329 | Math::BigInt->import('lib',"$lib,$mbilib", 'objectify'); |
8f675a64 |
2330 | } |
2331 | else |
2332 | { |
9b924220 |
2333 | # MBI not loaded, or with ne "Math::BigInt::Calc" |
8f675a64 |
2334 | $lib .= ",$mbilib" if defined $mbilib; |
07d34614 |
2335 | $lib =~ s/^,//; # don't leave empty |
12fc2493 |
2336 | |
990fb837 |
2337 | # replacement library can handle lib statement, but also could ignore it |
12fc2493 |
2338 | |
2339 | # Perl < 5.6.0 dies with "out of memory!" when eval() and ':constant' is |
2340 | # used in the same script, or eval inside import(). So we require MBI: |
2341 | require Math::BigInt; |
2342 | Math::BigInt->import( lib => $lib, 'objectify' ); |
8f675a64 |
2343 | } |
990fb837 |
2344 | if ($@) |
2345 | { |
9b924220 |
2346 | require Carp; Carp::croak ("Couldn't load $lib: $! $@"); |
990fb837 |
2347 | } |
9b924220 |
2348 | $MBI = Math::BigInt->config()->{lib}; |
56b9c951 |
2349 | |
58cde26e |
2350 | # any non :constant stuff is handled by our parent, Exporter |
2351 | # even if @_ is empty, to give it a chance |
b3abae2a |
2352 | $self->SUPER::import(@a); # for subclasses |
2353 | $self->export_to_level(1,$self,@a); # need this, too |
58cde26e |
2354 | } |
2355 | |
2356 | sub bnorm |
2357 | { |
2358 | # adjust m and e so that m is smallest possible |
2359 | # round number according to accuracy and precision settings |
9b924220 |
2360 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
58cde26e |
2361 | |
0716bf9b |
2362 | return $x if $x->{sign} !~ /^[+-]$/; # inf, nan etc |
58cde26e |
2363 | |
9b924220 |
2364 | my $zeros = $MBI->_zeros($x->{_m}); # correct for trailing zeros |
b282a552 |
2365 | if ($zeros != 0) |
2366 | { |
9b924220 |
2367 | my $z = $MBI->_new($zeros); |
2368 | $x->{_m} = $MBI->_rsft ($x->{_m}, $z, 10); |
2369 | if ($x->{_es} eq '-') |
2370 | { |
2371 | if ($MBI->_acmp($x->{_e},$z) >= 0) |
2372 | { |
2373 | $x->{_e} = $MBI->_sub ($x->{_e}, $z); |
27e7b8bb |
2374 | $x->{_es} = '+' if $MBI->_is_zero($x->{_e}); |
9b924220 |
2375 | } |
2376 | else |
2377 | { |
2378 | $x->{_e} = $MBI->_sub ( $MBI->_copy($z), $x->{_e}); |
2379 | $x->{_es} = '+'; |
2380 | } |
2381 | } |
2382 | else |
2383 | { |
2384 | $x->{_e} = $MBI->_add ($x->{_e}, $z); |
2385 | } |
b282a552 |
2386 | } |
2387 | else |
2388 | { |
2389 | # $x can only be 0Ey if there are no trailing zeros ('0' has 0 trailing |
2390 | # zeros). So, for something like 0Ey, set y to 1, and -0 => +0 |
9b924220 |
2391 | $x->{sign} = '+', $x->{_es} = '+', $x->{_e} = $MBI->_one() |
2392 | if $MBI->_is_zero($x->{_m}); |
b282a552 |
2393 | } |
2394 | |
61f5c3f5 |
2395 | $x; # MBI bnorm is no-op, so dont call it |
2396 | } |
58cde26e |
2397 | |
2398 | ############################################################################## |
56d9de68 |
2399 | |
2400 | sub as_hex |
2401 | { |
2402 | # return number as hexadecimal string (only for integers defined) |
2403 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
2404 | |
2405 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc |
2406 | return '0x0' if $x->is_zero(); |
2407 | |
9b924220 |
2408 | return $nan if $x->{_es} ne '+'; # how to do 1e-1 in hex!? |
56d9de68 |
2409 | |
9b924220 |
2410 | my $z = $MBI->_copy($x->{_m}); |
2411 | if (! $MBI->_is_zero($x->{_e})) # > 0 |
56d9de68 |
2412 | { |
9b924220 |
2413 | $MBI->_lsft( $z, $x->{_e},10); |
56d9de68 |
2414 | } |
9b924220 |
2415 | $z = Math::BigInt->new( $x->{sign} . $MBI->_num($z)); |
56d9de68 |
2416 | $z->as_hex(); |
2417 | } |
2418 | |
2419 | sub as_bin |
2420 | { |
2421 | # return number as binary digit string (only for integers defined) |
2422 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
2423 | |
2424 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc |
2425 | return '0b0' if $x->is_zero(); |
2426 | |
9b924220 |
2427 | return $nan if $x->{_es} ne '+'; # how to do 1e-1 in hex!? |
56d9de68 |
2428 | |
9b924220 |
2429 | my $z = $MBI->_copy($x->{_m}); |
2430 | if (! $MBI->_is_zero($x->{_e})) # > 0 |
56d9de68 |
2431 | { |
9b924220 |
2432 | $MBI->_lsft( $z, $x->{_e},10); |
56d9de68 |
2433 | } |
9b924220 |
2434 | $z = Math::BigInt->new( $x->{sign} . $MBI->_num($z)); |
56d9de68 |
2435 | $z->as_bin(); |
2436 | } |
58cde26e |
2437 | |
2438 | sub as_number |
2439 | { |
394e6ffb |
2440 | # return copy as a bigint representation of this BigFloat number |
2441 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
2442 | |
9b924220 |
2443 | my $z = $MBI->_copy($x->{_m}); |
2444 | if ($x->{_es} eq '-') # < 0 |
58cde26e |
2445 | { |
9b924220 |
2446 | $MBI->_rsft( $z, $x->{_e},10); |
0716bf9b |
2447 | } |
9b924220 |
2448 | elsif (! $MBI->_is_zero($x->{_e})) # > 0 |
0716bf9b |
2449 | { |
9b924220 |
2450 | $MBI->_lsft( $z, $x->{_e},10); |
58cde26e |
2451 | } |
9b924220 |
2452 | $z = Math::BigInt->new( $x->{sign} . $MBI->_num($z)); |
61f5c3f5 |
2453 | $z; |
58cde26e |
2454 | } |
2455 | |
2456 | sub length |
2457 | { |
ee15d750 |
2458 | my $x = shift; |
2459 | my $class = ref($x) || $x; |
2460 | $x = $class->new(shift) unless ref($x); |
58cde26e |
2461 | |
9b924220 |
2462 | return 1 if $MBI->_is_zero($x->{_m}); |
2463 | |
2464 | my $len = $MBI->_len($x->{_m}); |
2465 | $len += $MBI->_num($x->{_e}) if $x->{_es} eq '+'; |
58cde26e |
2466 | if (wantarray()) |
2467 | { |
9b924220 |
2468 | my $t = 0; |
2469 | $t = $MBI->_num($x->{_e}) if $x->{_es} eq '-'; |
2470 | return ($len, $t); |
58cde26e |
2471 | } |
61f5c3f5 |
2472 | $len; |
58cde26e |
2473 | } |
a0d0e21e |
2474 | |
2475 | 1; |
a5f75d66 |
2476 | __END__ |
2477 | |
2478 | =head1 NAME |
2479 | |
58cde26e |
2480 | Math::BigFloat - Arbitrary size floating point math package |
a5f75d66 |
2481 | |
2482 | =head1 SYNOPSIS |
2483 | |
a2008d6d |
2484 | use Math::BigFloat; |
58cde26e |
2485 | |
b3abae2a |
2486 | # Number creation |
2487 | $x = Math::BigFloat->new($str); # defaults to 0 |
2488 | $nan = Math::BigFloat->bnan(); # create a NotANumber |
2489 | $zero = Math::BigFloat->bzero(); # create a +0 |
2490 | $inf = Math::BigFloat->binf(); # create a +inf |
2491 | $inf = Math::BigFloat->binf('-'); # create a -inf |
2492 | $one = Math::BigFloat->bone(); # create a +1 |
2493 | $one = Math::BigFloat->bone('-'); # create a -1 |
58cde26e |
2494 | |
2495 | # Testing |
b3abae2a |
2496 | $x->is_zero(); # true if arg is +0 |
2497 | $x->is_nan(); # true if arg is NaN |
0716bf9b |
2498 | $x->is_one(); # true if arg is +1 |
2499 | $x->is_one('-'); # true if arg is -1 |
2500 | $x->is_odd(); # true if odd, false for even |
2501 | $x->is_even(); # true if even, false for odd |
ef9466ea |
2502 | $x->is_pos(); # true if >= 0 |
2503 | $x->is_neg(); # true if < 0 |
b3abae2a |
2504 | $x->is_inf(sign); # true if +inf, or -inf (default is '+') |
2505 | |
58cde26e |
2506 | $x->bcmp($y); # compare numbers (undef,<0,=0,>0) |
2507 | $x->bacmp($y); # compare absolutely (undef,<0,=0,>0) |
2508 | $x->sign(); # return the sign, either +,- or NaN |
b3abae2a |
2509 | $x->digit($n); # return the nth digit, counting from right |
2510 | $x->digit(-$n); # return the nth digit, counting from left |
58cde26e |
2511 | |
990fb837 |
2512 | # The following all modify their first argument. If you want to preserve |
2513 | # $x, use $z = $x->copy()->bXXX($y); See under L<CAVEATS> for why this is |
2514 | # neccessary when mixing $a = $b assigments with non-overloaded math. |
2515 | |
58cde26e |
2516 | # set |
2517 | $x->bzero(); # set $i to 0 |
2518 | $x->bnan(); # set $i to NaN |
b3abae2a |
2519 | $x->bone(); # set $x to +1 |
2520 | $x->bone('-'); # set $x to -1 |
2521 | $x->binf(); # set $x to inf |
2522 | $x->binf('-'); # set $x to -inf |
58cde26e |
2523 | |
2524 | $x->bneg(); # negation |
2525 | $x->babs(); # absolute value |
2526 | $x->bnorm(); # normalize (no-op) |
2527 | $x->bnot(); # two's complement (bit wise not) |
2528 | $x->binc(); # increment x by 1 |
2529 | $x->bdec(); # decrement x by 1 |
2530 | |
2531 | $x->badd($y); # addition (add $y to $x) |
2532 | $x->bsub($y); # subtraction (subtract $y from $x) |
2533 | $x->bmul($y); # multiplication (multiply $x by $y) |
990fb837 |
2534 | $x->bdiv($y); # divide, set $x to quotient |
58cde26e |
2535 | # return (quo,rem) or quo if scalar |
2536 | |
990fb837 |
2537 | $x->bmod($y); # modulus ($x % $y) |
2538 | $x->bpow($y); # power of arguments ($x ** $y) |
58cde26e |
2539 | $x->blsft($y); # left shift |
2540 | $x->brsft($y); # right shift |
2541 | # return (quo,rem) or quo if scalar |
2542 | |
990fb837 |
2543 | $x->blog(); # logarithm of $x to base e (Euler's number) |
2544 | $x->blog($base); # logarithm of $x to base $base (f.i. 2) |
61f5c3f5 |
2545 | |
58cde26e |
2546 | $x->band($y); # bit-wise and |
2547 | $x->bior($y); # bit-wise inclusive or |
2548 | $x->bxor($y); # bit-wise exclusive or |
2549 | $x->bnot(); # bit-wise not (two's complement) |
b3abae2a |
2550 | |
2551 | $x->bsqrt(); # calculate square-root |
990fb837 |
2552 | $x->broot($y); # $y'th root of $x (e.g. $y == 3 => cubic root) |
b3abae2a |
2553 | $x->bfac(); # factorial of $x (1*2*3*4*..$x) |
2554 | |
990fb837 |
2555 | $x->bround($N); # accuracy: preserve $N digits |
58cde26e |
2556 | $x->bfround($N); # precision: round to the $Nth digit |
2557 | |
990fb837 |
2558 | $x->bfloor(); # return integer less or equal than $x |
2559 | $x->bceil(); # return integer greater or equal than $x |
2560 | |
58cde26e |
2561 | # The following do not modify their arguments: |
990fb837 |
2562 | |
58cde26e |
2563 | bgcd(@values); # greatest common divisor |
2564 | blcm(@values); # lowest common multiplicator |
2565 | |
2566 | $x->bstr(); # return string |
2567 | $x->bsstr(); # return string in scientific notation |
ef9466ea |
2568 | |
2569 | $x->as_int(); # return $x as BigInt |
58cde26e |
2570 | $x->exponent(); # return exponent as BigInt |
2571 | $x->mantissa(); # return mantissa as BigInt |
2572 | $x->parts(); # return (mantissa,exponent) as BigInt |
2573 | |
2574 | $x->length(); # number of digits (w/o sign and '.') |
2575 | ($l,$f) = $x->length(); # number of digits, and length of fraction |
a5f75d66 |
2576 | |
f9a08e12 |
2577 | $x->precision(); # return P of $x (or global, if P of $x undef) |
2578 | $x->precision($n); # set P of $x to $n |
2579 | $x->accuracy(); # return A of $x (or global, if A of $x undef) |
723d369b |
2580 | $x->accuracy($n); # set A $x to $n |
f9a08e12 |
2581 | |
990fb837 |
2582 | # these get/set the appropriate global value for all BigFloat objects |
2583 | Math::BigFloat->precision(); # Precision |
2584 | Math::BigFloat->accuracy(); # Accuracy |
2585 | Math::BigFloat->round_mode(); # rounding mode |
f9a08e12 |
2586 | |
a5f75d66 |
2587 | =head1 DESCRIPTION |
2588 | |
58cde26e |
2589 | All operators (inlcuding basic math operations) are overloaded if you |
2590 | declare your big floating point numbers as |
a5f75d66 |
2591 | |
58cde26e |
2592 | $i = new Math::BigFloat '12_3.456_789_123_456_789E-2'; |
2593 | |
2594 | Operations with overloaded operators preserve the arguments, which is |
2595 | exactly what you expect. |
2596 | |
2597 | =head2 Canonical notation |
2598 | |
2599 | Input to these routines are either BigFloat objects, or strings of the |
2600 | following four forms: |
a5f75d66 |
2601 | |
2602 | =over 2 |
2603 | |
58cde26e |
2604 | =item * |
2605 | |
2606 | C</^[+-]\d+$/> |
a5f75d66 |
2607 | |
58cde26e |
2608 | =item * |
a5f75d66 |
2609 | |
58cde26e |
2610 | C</^[+-]\d+\.\d*$/> |
a5f75d66 |
2611 | |
58cde26e |
2612 | =item * |
a5f75d66 |
2613 | |
58cde26e |
2614 | C</^[+-]\d+E[+-]?\d+$/> |
a5f75d66 |
2615 | |
58cde26e |
2616 | =item * |
a5f75d66 |
2617 | |
58cde26e |
2618 | C</^[+-]\d*\.\d+E[+-]?\d+$/> |
5d7098d5 |
2619 | |
58cde26e |
2620 | =back |
2621 | |
2622 | all with optional leading and trailing zeros and/or spaces. Additonally, |
2623 | numbers are allowed to have an underscore between any two digits. |
2624 | |
2625 | Empty strings as well as other illegal numbers results in 'NaN'. |
2626 | |
2627 | bnorm() on a BigFloat object is now effectively a no-op, since the numbers |
2628 | are always stored in normalized form. On a string, it creates a BigFloat |
2629 | object. |
2630 | |
2631 | =head2 Output |
2632 | |
2633 | Output values are BigFloat objects (normalized), except for bstr() and bsstr(). |
2634 | |
2635 | The string output will always have leading and trailing zeros stripped and drop |
2636 | a plus sign. C<bstr()> will give you always the form with a decimal point, |
990fb837 |
2637 | while C<bsstr()> (s for scientific) gives you the scientific notation. |
58cde26e |
2638 | |
2639 | Input bstr() bsstr() |
2640 | '-0' '0' '0E1' |
2641 | ' -123 123 123' '-123123123' '-123123123E0' |
2642 | '00.0123' '0.0123' '123E-4' |
2643 | '123.45E-2' '1.2345' '12345E-4' |
2644 | '10E+3' '10000' '1E4' |
2645 | |
2646 | Some routines (C<is_odd()>, C<is_even()>, C<is_zero()>, C<is_one()>, |
2647 | C<is_nan()>) return true or false, while others (C<bcmp()>, C<bacmp()>) |
2648 | return either undef, <0, 0 or >0 and are suited for sort. |
2649 | |
990fb837 |
2650 | Actual math is done by using the class defined with C<with => Class;> (which |
2651 | defaults to BigInts) to represent the mantissa and exponent. |
2652 | |
58cde26e |
2653 | The sign C</^[+-]$/> is stored separately. The string 'NaN' is used to |
2654 | represent the result when input arguments are not numbers, as well as |
2655 | the result of dividing by zero. |
2656 | |
2657 | =head2 C<mantissa()>, C<exponent()> and C<parts()> |
2658 | |
2659 | C<mantissa()> and C<exponent()> return the said parts of the BigFloat |
2660 | as BigInts such that: |
2661 | |
2662 | $m = $x->mantissa(); |
2663 | $e = $x->exponent(); |
2664 | $y = $m * ( 10 ** $e ); |
2665 | print "ok\n" if $x == $y; |
2666 | |
2667 | C<< ($m,$e) = $x->parts(); >> is just a shortcut giving you both of them. |
2668 | |
2669 | A zero is represented and returned as C<0E1>, B<not> C<0E0> (after Knuth). |
2670 | |
2671 | Currently the mantissa is reduced as much as possible, favouring higher |
2672 | exponents over lower ones (e.g. returning 1e7 instead of 10e6 or 10000000e0). |
2673 | This might change in the future, so do not depend on it. |
2674 | |
2675 | =head2 Accuracy vs. Precision |
2676 | |
2677 | See also: L<Rounding|Rounding>. |
2678 | |
027dc388 |
2679 | Math::BigFloat supports both precision and accuracy. For a full documentation, |
2680 | examples and tips on these topics please see the large section in |
2681 | L<Math::BigInt>. |
5d7098d5 |
2682 | |
58cde26e |
2683 | Since things like sqrt(2) or 1/3 must presented with a limited precision lest |
2684 | a operation consumes all resources, each operation produces no more than |
990fb837 |
2685 | the requested number of digits. |
2686 | |
2687 | Please refer to BigInt's documentation for the precedence rules of which |
2688 | accuracy/precision setting will be used. |
2689 | |
2690 | If there is no gloabl precision set, B<and> the operation inquestion was not |
2691 | called with a requested precision or accuracy, B<and> the input $x has no |
2692 | accuracy or precision set, then a fallback parameter will be used. For |
2693 | historical reasons, it is called C<div_scale> and can be accessed via: |
2694 | |
2695 | $d = Math::BigFloat->div_scale(); # query |
2696 | Math::BigFloat->div_scale($n); # set to $n digits |
2697 | |
2698 | The default value is 40 digits. |
58cde26e |
2699 | |
2700 | In case the result of one operation has more precision than specified, |
2701 | it is rounded. The rounding mode taken is either the default mode, or the one |
2702 | supplied to the operation after the I<scale>: |
2703 | |
2704 | $x = Math::BigFloat->new(2); |
990fb837 |
2705 | Math::BigFloat->precision(5); # 5 digits max |
58cde26e |
2706 | $y = $x->copy()->bdiv(3); # will give 0.66666 |
2707 | $y = $x->copy()->bdiv(3,6); # will give 0.666666 |
2708 | $y = $x->copy()->bdiv(3,6,'odd'); # will give 0.666667 |
990fb837 |
2709 | Math::BigFloat->round_mode('zero'); |
58cde26e |
2710 | $y = $x->copy()->bdiv(3,6); # will give 0.666666 |
2711 | |
2712 | =head2 Rounding |
2713 | |
2714 | =over 2 |
2715 | |
5dc6f178 |
2716 | =item ffround ( +$scale ) |
58cde26e |
2717 | |
0716bf9b |
2718 | Rounds to the $scale'th place left from the '.', counting from the dot. |
2719 | The first digit is numbered 1. |
58cde26e |
2720 | |
5dc6f178 |
2721 | =item ffround ( -$scale ) |
58cde26e |
2722 | |
0716bf9b |
2723 | Rounds to the $scale'th place right from the '.', counting from the dot. |
58cde26e |
2724 | |
5dc6f178 |
2725 | =item ffround ( 0 ) |
2726 | |
0716bf9b |
2727 | Rounds to an integer. |
5dc6f178 |
2728 | |
2729 | =item fround ( +$scale ) |
2730 | |
0716bf9b |
2731 | Preserves accuracy to $scale digits from the left (aka significant digits) |
2732 | and pads the rest with zeros. If the number is between 1 and -1, the |
2733 | significant digits count from the first non-zero after the '.' |
5dc6f178 |
2734 | |
2735 | =item fround ( -$scale ) and fround ( 0 ) |
2736 | |
990fb837 |
2737 | These are effectively no-ops. |
5d7098d5 |
2738 | |
a5f75d66 |
2739 | =back |
2740 | |
0716bf9b |
2741 | All rounding functions take as a second parameter a rounding mode from one of |
2742 | the following: 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'. |
58cde26e |
2743 | |
2744 | The default rounding mode is 'even'. By using |
990fb837 |
2745 | C<< Math::BigFloat->round_mode($round_mode); >> you can get and set the default |
ee15d750 |
2746 | mode for subsequent rounding. The usage of C<$Math::BigFloat::$round_mode> is |
0716bf9b |
2747 | no longer supported. |
b22b3e31 |
2748 | The second parameter to the round functions then overrides the default |
0716bf9b |
2749 | temporarily. |
58cde26e |
2750 | |
990fb837 |
2751 | The C<as_number()> function returns a BigInt from a Math::BigFloat. It uses |
58cde26e |
2752 | 'trunc' as rounding mode to make it equivalent to: |
2753 | |
2754 | $x = 2.5; |
2755 | $y = int($x) + 2; |
2756 | |
2757 | You can override this by passing the desired rounding mode as parameter to |
2758 | C<as_number()>: |
2759 | |
2760 | $x = Math::BigFloat->new(2.5); |
2761 | $y = $x->as_number('odd'); # $y = 3 |
2762 | |
2763 | =head1 EXAMPLES |
2764 | |
58cde26e |
2765 | # not ready yet |
58cde26e |
2766 | |
2767 | =head1 Autocreating constants |
2768 | |
2769 | After C<use Math::BigFloat ':constant'> all the floating point constants |
2770 | in the given scope are converted to C<Math::BigFloat>. This conversion |
2771 | happens at compile time. |
2772 | |
2773 | In particular |
2774 | |
2775 | perl -MMath::BigFloat=:constant -e 'print 2E-100,"\n"' |
2776 | |
56b9c951 |
2777 | prints the value of C<2E-100>. Note that without conversion of |
58cde26e |
2778 | constants the expression 2E-100 will be calculated as normal floating point |
2779 | number. |
2780 | |
56b9c951 |
2781 | Please note that ':constant' does not affect integer constants, nor binary |
2782 | nor hexadecimal constants. Use L<bignum> or L<Math::BigInt> to get this to |
2783 | work. |
2784 | |
2785 | =head2 Math library |
2786 | |
2787 | Math with the numbers is done (by default) by a module called |
2788 | Math::BigInt::Calc. This is equivalent to saying: |
2789 | |
2790 | use Math::BigFloat lib => 'Calc'; |
2791 | |
2792 | You can change this by using: |
2793 | |
2794 | use Math::BigFloat lib => 'BitVect'; |
2795 | |
2796 | The following would first try to find Math::BigInt::Foo, then |
2797 | Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: |
2798 | |
2799 | use Math::BigFloat lib => 'Foo,Math::BigInt::Bar'; |
2800 | |
2801 | Calc.pm uses as internal format an array of elements of some decimal base |
2802 | (usually 1e7, but this might be differen for some systems) with the least |
2803 | significant digit first, while BitVect.pm uses a bit vector of base 2, most |
2804 | significant bit first. Other modules might use even different means of |
2805 | representing the numbers. See the respective module documentation for further |
2806 | details. |
2807 | |
2808 | Please note that Math::BigFloat does B<not> use the denoted library itself, |
2809 | but it merely passes the lib argument to Math::BigInt. So, instead of the need |
2810 | to do: |
2811 | |
2812 | use Math::BigInt lib => 'GMP'; |
2813 | use Math::BigFloat; |
2814 | |
2815 | you can roll it all into one line: |
2816 | |
2817 | use Math::BigFloat lib => 'GMP'; |
2818 | |
990fb837 |
2819 | It is also possible to just require Math::BigFloat: |
2820 | |
2821 | require Math::BigFloat; |
2822 | |
2823 | This will load the neccessary things (like BigInt) when they are needed, and |
2824 | automatically. |
2825 | |
2826 | Use the lib, Luke! And see L<Using Math::BigInt::Lite> for more details than |
2827 | you ever wanted to know about loading a different library. |
56b9c951 |
2828 | |
2829 | =head2 Using Math::BigInt::Lite |
2830 | |
2831 | It is possible to use L<Math::BigInt::Lite> with Math::BigFloat: |
2832 | |
2833 | # 1 |
2834 | use Math::BigFloat with => 'Math::BigInt::Lite'; |
2835 | |
2836 | There is no need to "use Math::BigInt" or "use Math::BigInt::Lite", but you |
2837 | can combine these if you want. For instance, you may want to use |
2838 | Math::BigInt objects in your main script, too. |
2839 | |
2840 | # 2 |
2841 | use Math::BigInt; |
2842 | use Math::BigFloat with => 'Math::BigInt::Lite'; |
2843 | |
2844 | Of course, you can combine this with the C<lib> parameter. |
2845 | |
2846 | # 3 |
2847 | use Math::BigFloat with => 'Math::BigInt::Lite', lib => 'GMP,Pari'; |
2848 | |
990fb837 |
2849 | There is no need for a "use Math::BigInt;" statement, even if you want to |
2850 | use Math::BigInt's, since Math::BigFloat will needs Math::BigInt and thus |
2851 | always loads it. But if you add it, add it B<before>: |
56b9c951 |
2852 | |
2853 | # 4 |
2854 | use Math::BigInt; |
2855 | use Math::BigFloat with => 'Math::BigInt::Lite', lib => 'GMP,Pari'; |
2856 | |
2857 | Notice that the module with the last C<lib> will "win" and thus |
2858 | it's lib will be used if the lib is available: |
2859 | |
2860 | # 5 |
2861 | use Math::BigInt lib => 'Bar,Baz'; |
2862 | use Math::BigFloat with => 'Math::BigInt::Lite', lib => 'Foo'; |
2863 | |
2864 | That would try to load Foo, Bar, Baz and Calc (in that order). Or in other |
2865 | words, Math::BigFloat will try to retain previously loaded libs when you |
990fb837 |
2866 | don't specify it onem but if you specify one, it will try to load them. |
56b9c951 |
2867 | |
2868 | Actually, the lib loading order would be "Bar,Baz,Calc", and then |
2869 | "Foo,Bar,Baz,Calc", but independend of which lib exists, the result is the |
990fb837 |
2870 | same as trying the latter load alone, except for the fact that one of Bar or |
2871 | Baz might be loaded needlessly in an intermidiate step (and thus hang around |
2872 | and waste memory). If neither Bar nor Baz exist (or don't work/compile), they |
2873 | will still be tried to be loaded, but this is not as time/memory consuming as |
2874 | actually loading one of them. Still, this type of usage is not recommended due |
2875 | to these issues. |
56b9c951 |
2876 | |
990fb837 |
2877 | The old way (loading the lib only in BigInt) still works though: |
56b9c951 |
2878 | |
2879 | # 6 |
2880 | use Math::BigInt lib => 'Bar,Baz'; |
2881 | use Math::BigFloat; |
2882 | |
990fb837 |
2883 | You can even load Math::BigInt afterwards: |
56b9c951 |
2884 | |
990fb837 |
2885 | # 7 |
2886 | use Math::BigFloat; |
2887 | use Math::BigInt lib => 'Bar,Baz'; |
a5f75d66 |
2888 | |
990fb837 |
2889 | But this has the same problems like #5, it will first load Calc |
2890 | (Math::BigFloat needs Math::BigInt and thus loads it) and then later Bar or |
2891 | Baz, depending on which of them works and is usable/loadable. Since this |
2892 | loads Calc unnecc., it is not recommended. |
58cde26e |
2893 | |
990fb837 |
2894 | Since it also possible to just require Math::BigFloat, this poses the question |
2895 | about what libary this will use: |
58cde26e |
2896 | |
990fb837 |
2897 | require Math::BigFloat; |
2898 | my $x = Math::BigFloat->new(123); $x += 123; |
58cde26e |
2899 | |
990fb837 |
2900 | It will use Calc. Please note that the call to import() is still done, but |
2901 | only when you use for the first time some Math::BigFloat math (it is triggered |
2902 | via any constructor, so the first time you create a Math::BigFloat, the load |
2903 | will happen in the background). This means: |
58cde26e |
2904 | |
990fb837 |
2905 | require Math::BigFloat; |
2906 | Math::BigFloat->import ( lib => 'Foo,Bar' ); |
58cde26e |
2907 | |
990fb837 |
2908 | would be the same as: |
58cde26e |
2909 | |
990fb837 |
2910 | use Math::BigFloat lib => 'Foo, Bar'; |
2911 | |
2912 | But don't try to be clever to insert some operations in between: |
2913 | |
2914 | require Math::BigFloat; |
2915 | my $x = Math::BigFloat->bone() + 4; # load BigInt and Calc |
2916 | Math::BigFloat->import( lib => 'Pari' ); # load Pari, too |
2917 | $x = Math::BigFloat->bone()+4; # now use Pari |
2918 | |
2919 | While this works, it loads Calc needlessly. But maybe you just wanted that? |
2920 | |
2921 | B<Examples #3 is highly recommended> for daily usage. |
2922 | |
2923 | =head1 BUGS |
2924 | |
2925 | Please see the file BUGS in the CPAN distribution Math::BigInt for known bugs. |
58cde26e |
2926 | |
990fb837 |
2927 | =head1 CAVEATS |
58cde26e |
2928 | |
2929 | =over 1 |
2930 | |
2931 | =item stringify, bstr() |
2932 | |
2933 | Both stringify and bstr() now drop the leading '+'. The old code would return |
2934 | '+1.23', the new returns '1.23'. See the documentation in L<Math::BigInt> for |
2935 | reasoning and details. |
2936 | |
2937 | =item bdiv |
2938 | |
2939 | The following will probably not do what you expect: |
2940 | |
2941 | print $c->bdiv(123.456),"\n"; |
2942 | |
2943 | It prints both quotient and reminder since print works in list context. Also, |
2944 | bdiv() will modify $c, so be carefull. You probably want to use |
2945 | |
2946 | print $c / 123.456,"\n"; |
2947 | print scalar $c->bdiv(123.456),"\n"; # or if you want to modify $c |
2948 | |
2949 | instead. |
2950 | |
2951 | =item Modifying and = |
2952 | |
2953 | Beware of: |
2954 | |
2955 | $x = Math::BigFloat->new(5); |
2956 | $y = $x; |
2957 | |
2958 | It will not do what you think, e.g. making a copy of $x. Instead it just makes |
2959 | a second reference to the B<same> object and stores it in $y. Thus anything |
990fb837 |
2960 | that modifies $x will modify $y (except overloaded math operators), and vice |
2961 | versa. See L<Math::BigInt> for details and how to avoid that. |
58cde26e |
2962 | |
2963 | =item bpow |
2964 | |
2965 | C<bpow()> now modifies the first argument, unlike the old code which left |
2966 | it alone and only returned the result. This is to be consistent with |
2967 | C<badd()> etc. The first will modify $x, the second one won't: |
2968 | |
2969 | print bpow($x,$i),"\n"; # modify $x |
2970 | print $x->bpow($i),"\n"; # ditto |
2971 | print $x ** $i,"\n"; # leave $x alone |
2972 | |
2973 | =back |
2974 | |
990fb837 |
2975 | =head1 SEE ALSO |
2976 | |
2977 | L<Math::BigInt>, L<Math::BigRat> and L<Math::Big> as well as |
2978 | L<Math::BigInt::BitVect>, L<Math::BigInt::Pari> and L<Math::BigInt::GMP>. |
2979 | |
2980 | The pragmas L<bignum>, L<bigint> and L<bigrat> might also be of interest |
2981 | because they solve the autoupgrading/downgrading issue, at least partly. |
2982 | |
2983 | The package at |
2984 | L<http://search.cpan.org/search?mode=module&query=Math%3A%3ABigInt> contains |
2985 | more documentation including a full version history, testcases, empty |
2986 | subclass files and benchmarks. |
2987 | |
58cde26e |
2988 | =head1 LICENSE |
a5f75d66 |
2989 | |
58cde26e |
2990 | This program is free software; you may redistribute it and/or modify it under |
2991 | the same terms as Perl itself. |
5d7098d5 |
2992 | |
58cde26e |
2993 | =head1 AUTHORS |
5d7098d5 |
2994 | |
58cde26e |
2995 | Mark Biggar, overloaded interface by Ilya Zakharevich. |
990fb837 |
2996 | Completely rewritten by Tels http://bloodgate.com in 2001, 2002, and still |
2997 | at it in 2003. |
a5f75d66 |
2998 | |
a5f75d66 |
2999 | =cut |