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: |
8 | # _e: exponent (BigInt) |
9 | # _m: mantissa (absolute BigInt) |
990fb837 |
10 | # sign: +,-,+inf,-inf, or "NaN" if not a number |
58cde26e |
11 | # _a: accuracy |
12 | # _p: precision |
0716bf9b |
13 | # _f: flags, used to signal MBI not to touch our private parts |
58cde26e |
14 | |
990fb837 |
15 | $VERSION = '1.39'; |
58cde26e |
16 | require 5.005; |
17 | use Exporter; |
2ab5f49d |
18 | @ISA = qw(Exporter Math::BigInt); |
394e6ffb |
19 | |
58cde26e |
20 | use strict; |
027dc388 |
21 | use vars qw/$AUTOLOAD $accuracy $precision $div_scale $round_mode $rnd_mode/; |
8f675a64 |
22 | use vars qw/$upgrade $downgrade/; |
990fb837 |
23 | # the following are internal and should never be accessed from the outside |
24 | use vars qw/$_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; |
8f675a64 |
48 | my $MBI = 'Math::BigInt'; # the package we are using for our private parts |
49 | # changable by use Math::BigFloat with => 'package' |
b3abae2a |
50 | |
990fb837 |
51 | # the following are private and not to be used from the outside: |
52 | |
53 | use constant MB_NEVER_ROUND => 0x0001; |
54 | |
55 | # are NaNs ok? (otherwise it dies when encountering an NaN) set w/ config() |
56 | $_trap_nan = 0; |
57 | # the same for infs |
58 | $_trap_inf = 0; |
59 | |
60 | # constant for easier life |
61 | my $nan = 'NaN'; |
62 | |
63 | my $IMPORT = 0; # was import() called yet? |
64 | # used to make require work |
65 | |
66 | # some digits of accuracy for blog(undef,10); which we use in blog() for speed |
67 | my $LOG_10 = |
68 | '2.3025850929940456840179914546843642076011014886287729760333279009675726097'; |
69 | my $LOG_10_A = length($LOG_10)-1; |
70 | # ditto for log(2) |
71 | my $LOG_2 = |
72 | '0.6931471805599453094172321214581765680755001343602552541206800094933936220'; |
73 | my $LOG_2_A = length($LOG_2)-1; |
74 | |
027dc388 |
75 | ############################################################################## |
76 | # the old code had $rnd_mode, so we need to support it, too |
77 | |
027dc388 |
78 | sub TIESCALAR { my ($class) = @_; bless \$round_mode, $class; } |
79 | sub FETCH { return $round_mode; } |
80 | sub STORE { $rnd_mode = $_[0]->round_mode($_[1]); } |
81 | |
56b9c951 |
82 | BEGIN |
990fb837 |
83 | { |
84 | # when someone set's $rnd_mode, we catch this and check the value to see |
85 | # whether it is valid or not. |
86 | $rnd_mode = 'even'; tie $rnd_mode, 'Math::BigFloat'; |
56b9c951 |
87 | } |
027dc388 |
88 | |
89 | ############################################################################## |
90 | |
574bacfe |
91 | # in case we call SUPER::->foo() and this wants to call modify() |
92 | # sub modify () { 0; } |
93 | |
58cde26e |
94 | { |
ee15d750 |
95 | # valid method aliases for AUTOLOAD |
58cde26e |
96 | my %methods = map { $_ => 1 } |
97 | qw / fadd fsub fmul fdiv fround ffround fsqrt fmod fstr fsstr fpow fnorm |
b3abae2a |
98 | fint facmp fcmp fzero fnan finf finc fdec flog ffac |
990fb837 |
99 | fceil ffloor frsft flsft fone flog froot |
ee15d750 |
100 | /; |
61f5c3f5 |
101 | # valid method's that can be hand-ed up (for AUTOLOAD) |
ee15d750 |
102 | my %hand_ups = map { $_ => 1 } |
103 | qw / is_nan is_inf is_negative is_positive |
990fb837 |
104 | accuracy precision div_scale round_mode fneg fabs fnot |
28df3e88 |
105 | objectify upgrade downgrade |
13a12e00 |
106 | bone binf bnan bzero |
58cde26e |
107 | /; |
108 | |
ee15d750 |
109 | sub method_alias { return exists $methods{$_[0]||''}; } |
110 | sub method_hand_up { return exists $hand_ups{$_[0]||''}; } |
a0d0e21e |
111 | } |
0e8b9368 |
112 | |
58cde26e |
113 | ############################################################################## |
114 | # constructors |
a0d0e21e |
115 | |
58cde26e |
116 | sub new |
117 | { |
118 | # create a new BigFloat object from a string or another bigfloat object. |
119 | # _e: exponent |
120 | # _m: mantissa |
121 | # sign => sign (+/-), or "NaN" |
a0d0e21e |
122 | |
61f5c3f5 |
123 | my ($class,$wanted,@r) = @_; |
b3abae2a |
124 | |
61f5c3f5 |
125 | # avoid numify-calls by not using || on $wanted! |
126 | return $class->bzero() if !defined $wanted; # default to 0 |
127 | return $wanted->copy() if UNIVERSAL::isa($wanted,'Math::BigFloat'); |
a0d0e21e |
128 | |
990fb837 |
129 | $class->import() if $IMPORT == 0; # make require work |
130 | |
58cde26e |
131 | my $self = {}; bless $self, $class; |
b22b3e31 |
132 | # shortcut for bigints and its subclasses |
0716bf9b |
133 | if ((ref($wanted)) && (ref($wanted) ne $class)) |
58cde26e |
134 | { |
0716bf9b |
135 | $self->{_m} = $wanted->as_number(); # get us a bigint copy |
56b9c951 |
136 | $self->{_e} = $MBI->bzero(); |
58cde26e |
137 | $self->{_m}->babs(); |
138 | $self->{sign} = $wanted->sign(); |
0716bf9b |
139 | return $self->bnorm(); |
58cde26e |
140 | } |
141 | # got string |
142 | # handle '+inf', '-inf' first |
ee15d750 |
143 | if ($wanted =~ /^[+-]?inf$/) |
58cde26e |
144 | { |
28df3e88 |
145 | return $downgrade->new($wanted) if $downgrade; |
146 | |
56b9c951 |
147 | $self->{_e} = $MBI->bzero(); |
148 | $self->{_m} = $MBI->bzero(); |
58cde26e |
149 | $self->{sign} = $wanted; |
ee15d750 |
150 | $self->{sign} = '+inf' if $self->{sign} eq 'inf'; |
0716bf9b |
151 | return $self->bnorm(); |
58cde26e |
152 | } |
153 | #print "new string '$wanted'\n"; |
154 | my ($mis,$miv,$mfv,$es,$ev) = Math::BigInt::_split(\$wanted); |
155 | if (!ref $mis) |
156 | { |
990fb837 |
157 | if ($_trap_nan) |
158 | { |
159 | require Carp; |
160 | Carp::croak ("$wanted is not a number initialized to $class"); |
161 | } |
28df3e88 |
162 | |
163 | return $downgrade->bnan() if $downgrade; |
164 | |
56b9c951 |
165 | $self->{_e} = $MBI->bzero(); |
166 | $self->{_m} = $MBI->bzero(); |
58cde26e |
167 | $self->{sign} = $nan; |
168 | } |
169 | else |
170 | { |
171 | # make integer from mantissa by adjusting exp, then convert to bigint |
61f5c3f5 |
172 | # undef,undef to signal MBI that we don't need no bloody rounding |
56b9c951 |
173 | $self->{_e} = $MBI->new("$$es$$ev",undef,undef); # exponent |
174 | $self->{_m} = $MBI->new("$$miv$$mfv",undef,undef); # create mant. |
58cde26e |
175 | # 3.123E0 = 3123E-3, and 3.123E-2 => 3123E-5 |
027dc388 |
176 | $self->{_e} -= CORE::length($$mfv) if CORE::length($$mfv) != 0; |
177 | $self->{sign} = $$mis; |
58cde26e |
178 | } |
28df3e88 |
179 | # if downgrade, inf, NaN or integers go down |
180 | |
181 | if ($downgrade && $self->{_e}->{sign} eq '+') |
182 | { |
990fb837 |
183 | #print "downgrading $$miv$$mfv"."E$$es$$ev"; |
28df3e88 |
184 | if ($self->{_e}->is_zero()) |
185 | { |
186 | $self->{_m}->{sign} = $$mis; # negative if wanted |
187 | return $downgrade->new($self->{_m}); |
188 | } |
189 | return $downgrade->new("$$mis$$miv$$mfv"."E$$es$$ev"); |
190 | } |
990fb837 |
191 | #print "mbf new $self->{sign} $self->{_m} e $self->{_e} ",ref($self),"\n"; |
192 | $self->bnorm()->round(@r); # first normalize, then round |
58cde26e |
193 | } |
a0d0e21e |
194 | |
13a12e00 |
195 | sub _bnan |
58cde26e |
196 | { |
990fb837 |
197 | # used by parent class bone() to initialize number to NaN |
58cde26e |
198 | my $self = shift; |
990fb837 |
199 | |
200 | if ($_trap_nan) |
201 | { |
202 | require Carp; |
203 | my $class = ref($self); |
204 | Carp::croak ("Tried to set $self to NaN in $class\::_bnan()"); |
205 | } |
206 | |
207 | $IMPORT=1; # call our import only once |
56b9c951 |
208 | $self->{_m} = $MBI->bzero(); |
209 | $self->{_e} = $MBI->bzero(); |
58cde26e |
210 | } |
a0d0e21e |
211 | |
13a12e00 |
212 | sub _binf |
58cde26e |
213 | { |
990fb837 |
214 | # used by parent class bone() to initialize number to +-inf |
58cde26e |
215 | my $self = shift; |
990fb837 |
216 | |
217 | if ($_trap_inf) |
218 | { |
219 | require Carp; |
220 | my $class = ref($self); |
221 | Carp::croak ("Tried to set $self to +-inf in $class\::_binf()"); |
222 | } |
223 | |
224 | $IMPORT=1; # call our import only once |
56b9c951 |
225 | $self->{_m} = $MBI->bzero(); |
226 | $self->{_e} = $MBI->bzero(); |
58cde26e |
227 | } |
a0d0e21e |
228 | |
13a12e00 |
229 | sub _bone |
574bacfe |
230 | { |
13a12e00 |
231 | # used by parent class bone() to initialize number to 1 |
574bacfe |
232 | my $self = shift; |
990fb837 |
233 | $IMPORT=1; # call our import only once |
56b9c951 |
234 | $self->{_m} = $MBI->bone(); |
235 | $self->{_e} = $MBI->bzero(); |
574bacfe |
236 | } |
237 | |
13a12e00 |
238 | sub _bzero |
58cde26e |
239 | { |
990fb837 |
240 | # used by parent class bone() to initialize number to 0 |
58cde26e |
241 | my $self = shift; |
990fb837 |
242 | $IMPORT=1; # call our import only once |
56b9c951 |
243 | $self->{_m} = $MBI->bzero(); |
244 | $self->{_e} = $MBI->bone(); |
58cde26e |
245 | } |
246 | |
9393ace2 |
247 | sub isa |
248 | { |
249 | my ($self,$class) = @_; |
56b9c951 |
250 | return if $class =~ /^Math::BigInt/; # we aren't one of these |
251 | UNIVERSAL::isa($self,$class); |
9393ace2 |
252 | } |
253 | |
8f675a64 |
254 | sub config |
255 | { |
256 | # return (later set?) configuration data as hash ref |
257 | my $class = shift || 'Math::BigFloat'; |
258 | |
990fb837 |
259 | my $cfg = $class->SUPER::config(@_); |
8f675a64 |
260 | |
990fb837 |
261 | # now we need only to override the ones that are different from our parent |
8f675a64 |
262 | $cfg->{class} = $class; |
263 | $cfg->{with} = $MBI; |
8f675a64 |
264 | $cfg; |
265 | } |
266 | |
58cde26e |
267 | ############################################################################## |
268 | # string conversation |
269 | |
270 | sub bstr |
271 | { |
272 | # (ref to BFLOAT or num_str ) return num_str |
273 | # Convert number from internal format to (non-scientific) string format. |
274 | # internal format is always normalized (no leading zeros, "-0" => "+0") |
ee15d750 |
275 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
276 | #my $x = shift; my $class = ref($x) || $x; |
277 | #$x = $class->new(shift) unless ref($x); |
58cde26e |
278 | |
574bacfe |
279 | if ($x->{sign} !~ /^[+-]$/) |
58cde26e |
280 | { |
574bacfe |
281 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN |
282 | return 'inf'; # +inf |
58cde26e |
283 | } |
284 | |
574bacfe |
285 | my $es = '0'; my $len = 1; my $cad = 0; my $dot = '.'; |
286 | |
28df3e88 |
287 | my $not_zero = ! $x->is_zero(); |
574bacfe |
288 | if ($not_zero) |
58cde26e |
289 | { |
574bacfe |
290 | $es = $x->{_m}->bstr(); |
291 | $len = CORE::length($es); |
292 | if (!$x->{_e}->is_zero()) |
58cde26e |
293 | { |
574bacfe |
294 | if ($x->{_e}->sign() eq '-') |
295 | { |
296 | $dot = ''; |
297 | if ($x->{_e} <= -$len) |
298 | { |
990fb837 |
299 | #print "style: 0.xxxx\n"; |
574bacfe |
300 | my $r = $x->{_e}->copy(); $r->babs()->bsub( CORE::length($es) ); |
301 | $es = '0.'. ('0' x $r) . $es; $cad = -($len+$r); |
302 | } |
303 | else |
304 | { |
990fb837 |
305 | #print "insert '.' at $x->{_e} in '$es'\n"; |
574bacfe |
306 | substr($es,$x->{_e},0) = '.'; $cad = $x->{_e}; |
307 | } |
308 | } |
309 | else |
310 | { |
311 | # expand with zeros |
312 | $es .= '0' x $x->{_e}; $len += $x->{_e}; $cad = 0; |
313 | } |
82cf049f |
314 | } |
574bacfe |
315 | } # if not zero |
316 | $es = $x->{sign}.$es if $x->{sign} eq '-'; |
317 | # if set accuracy or precision, pad with zeros |
318 | if ((defined $x->{_a}) && ($not_zero)) |
319 | { |
320 | # 123400 => 6, 0.1234 => 4, 0.001234 => 4 |
321 | my $zeros = $x->{_a} - $cad; # cad == 0 => 12340 |
322 | $zeros = $x->{_a} - $len if $cad != $len; |
574bacfe |
323 | $es .= $dot.'0' x $zeros if $zeros > 0; |
82cf049f |
324 | } |
574bacfe |
325 | elsif ($x->{_p} || 0 < 0) |
58cde26e |
326 | { |
574bacfe |
327 | # 123400 => 6, 0.1234 => 4, 0.001234 => 6 |
328 | my $zeros = -$x->{_p} + $cad; |
574bacfe |
329 | $es .= $dot.'0' x $zeros if $zeros > 0; |
58cde26e |
330 | } |
56b9c951 |
331 | $es; |
82cf049f |
332 | } |
f216259d |
333 | |
58cde26e |
334 | sub bsstr |
335 | { |
336 | # (ref to BFLOAT or num_str ) return num_str |
337 | # Convert number from internal format to scientific string format. |
338 | # internal format is always normalized (no leading zeros, "-0E0" => "+0E0") |
ee15d750 |
339 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
340 | #my $x = shift; my $class = ref($x) || $x; |
341 | #$x = $class->new(shift) unless ref($x); |
a0d0e21e |
342 | |
574bacfe |
343 | if ($x->{sign} !~ /^[+-]$/) |
344 | { |
345 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN |
346 | return 'inf'; # +inf |
347 | } |
56d9de68 |
348 | my $esign = $x->{_e}->{sign}; $esign = '' if $esign eq '-'; |
349 | my $sep = 'e'.$esign; |
350 | my $sign = $x->{sign}; $sign = '' if $sign eq '+'; |
351 | $sign . $x->{_m}->bstr() . $sep . $x->{_e}->bstr(); |
58cde26e |
352 | } |
353 | |
354 | sub numify |
355 | { |
356 | # Make a number from a BigFloat object |
574bacfe |
357 | # simple return string and let Perl's atoi()/atof() handle the rest |
ee15d750 |
358 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
56b9c951 |
359 | $x->bsstr(); |
58cde26e |
360 | } |
a0d0e21e |
361 | |
58cde26e |
362 | ############################################################################## |
363 | # public stuff (usually prefixed with "b") |
364 | |
574bacfe |
365 | # tels 2001-08-04 |
366 | # todo: this must be overwritten and return NaN for non-integer values |
367 | # band(), bior(), bxor(), too |
58cde26e |
368 | #sub bnot |
369 | # { |
370 | # $class->SUPER::bnot($class,@_); |
371 | # } |
372 | |
373 | sub bcmp |
374 | { |
375 | # Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort) |
376 | # (BFLOAT or num_str, BFLOAT or num_str) return cond_code |
f9a08e12 |
377 | |
378 | # set up parameters |
379 | my ($self,$x,$y) = (ref($_[0]),@_); |
380 | # objectify is costly, so avoid it |
381 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
382 | { |
383 | ($self,$x,$y) = objectify(2,@_); |
384 | } |
58cde26e |
385 | |
56d9de68 |
386 | return $upgrade->bcmp($x,$y) if defined $upgrade && |
387 | ((!$x->isa($self)) || (!$y->isa($self))); |
388 | |
0716bf9b |
389 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
390 | { |
391 | # handle +-inf and NaN |
392 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
393 | return 0 if ($x->{sign} eq $y->{sign}) && ($x->{sign} =~ /^[+-]inf$/); |
394 | return +1 if $x->{sign} eq '+inf'; |
395 | return -1 if $x->{sign} eq '-inf'; |
396 | return -1 if $y->{sign} eq '+inf'; |
b3abae2a |
397 | return +1; |
0716bf9b |
398 | } |
399 | |
400 | # check sign for speed first |
574bacfe |
401 | return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y |
58cde26e |
402 | return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0 |
403 | |
574bacfe |
404 | # shortcut |
405 | my $xz = $x->is_zero(); |
406 | my $yz = $y->is_zero(); |
407 | return 0 if $xz && $yz; # 0 <=> 0 |
408 | return -1 if $xz && $y->{sign} eq '+'; # 0 <=> +y |
409 | return 1 if $yz && $x->{sign} eq '+'; # +x <=> 0 |
58cde26e |
410 | |
411 | # adjust so that exponents are equal |
bd05a461 |
412 | my $lxm = $x->{_m}->length(); |
413 | my $lym = $y->{_m}->length(); |
28df3e88 |
414 | # the numify somewhat limits our length, but makes it much faster |
415 | my $lx = $lxm + $x->{_e}->numify(); |
416 | my $ly = $lym + $y->{_e}->numify(); |
417 | my $l = $lx - $ly; $l = -$l if $x->{sign} eq '-'; |
bd05a461 |
418 | return $l <=> 0 if $l != 0; |
58cde26e |
419 | |
bd05a461 |
420 | # lengths (corrected by exponent) are equal |
28df3e88 |
421 | # so make mantissa equal length by padding with zero (shift left) |
bd05a461 |
422 | my $diff = $lxm - $lym; |
423 | my $xm = $x->{_m}; # not yet copy it |
424 | my $ym = $y->{_m}; |
425 | if ($diff > 0) |
426 | { |
427 | $ym = $y->{_m}->copy()->blsft($diff,10); |
428 | } |
429 | elsif ($diff < 0) |
430 | { |
431 | $xm = $x->{_m}->copy()->blsft(-$diff,10); |
432 | } |
28df3e88 |
433 | my $rc = $xm->bacmp($ym); |
58cde26e |
434 | $rc = -$rc if $x->{sign} eq '-'; # -124 < -123 |
b3abae2a |
435 | $rc <=> 0; |
58cde26e |
436 | } |
437 | |
438 | sub bacmp |
439 | { |
440 | # Compares 2 values, ignoring their signs. |
441 | # Returns one of undef, <0, =0, >0. (suitable for sort) |
442 | # (BFLOAT or num_str, BFLOAT or num_str) return cond_code |
f9a08e12 |
443 | |
444 | # set up parameters |
445 | my ($self,$x,$y) = (ref($_[0]),@_); |
446 | # objectify is costly, so avoid it |
447 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
448 | { |
449 | ($self,$x,$y) = objectify(2,@_); |
450 | } |
ee15d750 |
451 | |
56d9de68 |
452 | return $upgrade->bacmp($x,$y) if defined $upgrade && |
453 | ((!$x->isa($self)) || (!$y->isa($self))); |
454 | |
ee15d750 |
455 | # handle +-inf and NaN's |
abcfbf51 |
456 | if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/) |
ee15d750 |
457 | { |
458 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
459 | return 0 if ($x->is_inf() && $y->is_inf()); |
460 | return 1 if ($x->is_inf() && !$y->is_inf()); |
b3abae2a |
461 | return -1; |
ee15d750 |
462 | } |
463 | |
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 && !$yz; # 0 <=> +y |
469 | return 1 if $yz && !$xz; # +x <=> 0 |
470 | |
471 | # adjust so that exponents are equal |
472 | my $lxm = $x->{_m}->length(); |
473 | my $lym = $y->{_m}->length(); |
28df3e88 |
474 | # the numify somewhat limits our length, but makes it much faster |
475 | my $lx = $lxm + $x->{_e}->numify(); |
476 | my $ly = $lym + $y->{_e}->numify(); |
394e6ffb |
477 | my $l = $lx - $ly; |
ee15d750 |
478 | return $l <=> 0 if $l != 0; |
58cde26e |
479 | |
ee15d750 |
480 | # lengths (corrected by exponent) are equal |
394e6ffb |
481 | # so make mantissa equal-length by padding with zero (shift left) |
ee15d750 |
482 | my $diff = $lxm - $lym; |
483 | my $xm = $x->{_m}; # not yet copy it |
484 | my $ym = $y->{_m}; |
485 | if ($diff > 0) |
486 | { |
487 | $ym = $y->{_m}->copy()->blsft($diff,10); |
488 | } |
489 | elsif ($diff < 0) |
490 | { |
491 | $xm = $x->{_m}->copy()->blsft(-$diff,10); |
492 | } |
28df3e88 |
493 | $xm->bacmp($ym) <=> 0; |
58cde26e |
494 | } |
a0d0e21e |
495 | |
58cde26e |
496 | sub badd |
497 | { |
498 | # add second arg (BFLOAT or string) to first (BFLOAT) (modifies first) |
499 | # return result as BFLOAT |
f9a08e12 |
500 | |
501 | # set up parameters |
502 | my ($self,$x,$y,$a,$p,$r) = (ref($_[0]),@_); |
503 | # objectify is costly, so avoid it |
504 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
505 | { |
506 | ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
507 | } |
58cde26e |
508 | |
574bacfe |
509 | # inf and NaN handling |
510 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
511 | { |
512 | # NaN first |
513 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
13a12e00 |
514 | # inf handling |
574bacfe |
515 | if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) |
516 | { |
13a12e00 |
517 | # +inf++inf or -inf+-inf => same, rest is NaN |
518 | return $x if $x->{sign} eq $y->{sign}; |
519 | return $x->bnan(); |
574bacfe |
520 | } |
56b9c951 |
521 | # +-inf + something => +inf; something +-inf => +-inf |
574bacfe |
522 | $x->{sign} = $y->{sign}, return $x if $y->{sign} =~ /^[+-]inf$/; |
523 | return $x; |
524 | } |
525 | |
8f675a64 |
526 | return $upgrade->badd($x,$y,$a,$p,$r) if defined $upgrade && |
527 | ((!$x->isa($self)) || (!$y->isa($self))); |
528 | |
58cde26e |
529 | # speed: no add for 0+y or x+0 |
28df3e88 |
530 | return $x->bround($a,$p,$r) if $y->is_zero(); # x+0 |
58cde26e |
531 | if ($x->is_zero()) # 0+y |
532 | { |
533 | # make copy, clobbering up x (modify in place!) |
534 | $x->{_e} = $y->{_e}->copy(); |
535 | $x->{_m} = $y->{_m}->copy(); |
536 | $x->{sign} = $y->{sign} || $nan; |
537 | return $x->round($a,$p,$r,$y); |
a0d0e21e |
538 | } |
58cde26e |
539 | |
540 | # take lower of the two e's and adapt m1 to it to match m2 |
28df3e88 |
541 | my $e = $y->{_e}; |
56b9c951 |
542 | $e = $MBI->bzero() if !defined $e; # if no BFLOAT ? |
543 | $e = $e->copy(); # make copy (didn't do it yet) |
28df3e88 |
544 | $e->bsub($x->{_e}); |
58cde26e |
545 | my $add = $y->{_m}->copy(); |
28df3e88 |
546 | if ($e->{sign} eq '-') # < 0 |
58cde26e |
547 | { |
58cde26e |
548 | my $e1 = $e->copy()->babs(); |
28df3e88 |
549 | #$x->{_m} *= (10 ** $e1); |
550 | $x->{_m}->blsft($e1,10); |
58cde26e |
551 | $x->{_e} += $e; # need the sign of e |
58cde26e |
552 | } |
28df3e88 |
553 | elsif (!$e->is_zero()) # > 0 |
58cde26e |
554 | { |
28df3e88 |
555 | #$add *= (10 ** $e); |
556 | $add->blsft($e,10); |
58cde26e |
557 | } |
61f5c3f5 |
558 | # else: both e are the same, so just leave them |
559 | $x->{_m}->{sign} = $x->{sign}; # fiddle with signs |
58cde26e |
560 | $add->{sign} = $y->{sign}; |
61f5c3f5 |
561 | $x->{_m} += $add; # finally do add/sub |
562 | $x->{sign} = $x->{_m}->{sign}; # re-adjust signs |
563 | $x->{_m}->{sign} = '+'; # mantissa always positiv |
564 | # delete trailing zeros, then round |
565 | return $x->bnorm()->round($a,$p,$r,$y); |
58cde26e |
566 | } |
567 | |
568 | sub bsub |
569 | { |
0716bf9b |
570 | # (BigFloat or num_str, BigFloat or num_str) return BigFloat |
58cde26e |
571 | # subtract second arg from first, modify first |
f9a08e12 |
572 | |
573 | # set up parameters |
574 | my ($self,$x,$y,$a,$p,$r) = (ref($_[0]),@_); |
575 | # objectify is costly, so avoid it |
576 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
577 | { |
578 | ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
579 | } |
a0d0e21e |
580 | |
28df3e88 |
581 | if ($y->is_zero()) # still round for not adding zero |
e745a66c |
582 | { |
28df3e88 |
583 | return $x->round($a,$p,$r); |
e745a66c |
584 | } |
28df3e88 |
585 | |
586 | $y->{sign} =~ tr/+\-/-+/; # does nothing for NaN |
587 | $x->badd($y,$a,$p,$r); # badd does not leave internal zeros |
588 | $y->{sign} =~ tr/+\-/-+/; # refix $y (does nothing for NaN) |
e745a66c |
589 | $x; # already rounded by badd() |
58cde26e |
590 | } |
591 | |
592 | sub binc |
593 | { |
594 | # increment arg by one |
ee15d750 |
595 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
e745a66c |
596 | |
597 | if ($x->{_e}->sign() eq '-') |
598 | { |
599 | return $x->badd($self->bone(),$a,$p,$r); # digits after dot |
600 | } |
601 | |
602 | if (!$x->{_e}->is_zero()) |
603 | { |
604 | $x->{_m}->blsft($x->{_e},10); # 1e2 => 100 |
605 | $x->{_e}->bzero(); |
606 | } |
607 | # now $x->{_e} == 0 |
608 | if ($x->{sign} eq '+') |
609 | { |
610 | $x->{_m}->binc(); |
611 | return $x->bnorm()->bround($a,$p,$r); |
612 | } |
613 | elsif ($x->{sign} eq '-') |
614 | { |
615 | $x->{_m}->bdec(); |
616 | $x->{sign} = '+' if $x->{_m}->is_zero(); # -1 +1 => -0 => +0 |
617 | return $x->bnorm()->bround($a,$p,$r); |
618 | } |
619 | # inf, nan handling etc |
620 | $x->badd($self->__one(),$a,$p,$r); # does round |
58cde26e |
621 | } |
622 | |
623 | sub bdec |
624 | { |
625 | # decrement arg by one |
ee15d750 |
626 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
e745a66c |
627 | |
628 | if ($x->{_e}->sign() eq '-') |
629 | { |
630 | return $x->badd($self->bone('-'),$a,$p,$r); # digits after dot |
631 | } |
632 | |
633 | if (!$x->{_e}->is_zero()) |
634 | { |
635 | $x->{_m}->blsft($x->{_e},10); # 1e2 => 100 |
636 | $x->{_e}->bzero(); |
637 | } |
638 | # now $x->{_e} == 0 |
639 | my $zero = $x->is_zero(); |
640 | # <= 0 |
641 | if (($x->{sign} eq '-') || $zero) |
642 | { |
643 | $x->{_m}->binc(); |
644 | $x->{sign} = '-' if $zero; # 0 => 1 => -1 |
645 | $x->{sign} = '+' if $x->{_m}->is_zero(); # -1 +1 => -0 => +0 |
646 | return $x->bnorm()->round($a,$p,$r); |
647 | } |
648 | # > 0 |
649 | elsif ($x->{sign} eq '+') |
650 | { |
651 | $x->{_m}->bdec(); |
652 | return $x->bnorm()->round($a,$p,$r); |
653 | } |
654 | # inf, nan handling etc |
655 | $x->badd($self->bone('-'),$a,$p,$r); # does round |
58cde26e |
656 | } |
657 | |
990fb837 |
658 | sub DEBUG () { 0; } |
659 | |
61f5c3f5 |
660 | sub blog |
661 | { |
990fb837 |
662 | my ($self,$x,$base,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
61f5c3f5 |
663 | |
990fb837 |
664 | # $base > 0, $base != 1; if $base == undef default to $base == e |
665 | # $x >= 0 |
9393ace2 |
666 | |
b3abae2a |
667 | # we need to limit the accuracy to protect against overflow |
668 | my $fallback = 0; |
990fb837 |
669 | my ($scale,@params); |
670 | ($x,@params) = $x->_find_round_parameters($a,$p,$r); |
61f5c3f5 |
671 | |
990fb837 |
672 | # also takes care of the "error in _find_round_parameters?" case |
673 | return $x->bnan() if $x->{sign} ne '+' || $x->is_zero(); |
674 | |
b3abae2a |
675 | # no rounding at all, so must use fallback |
990fb837 |
676 | if (scalar @params == 0) |
b3abae2a |
677 | { |
678 | # simulate old behaviour |
990fb837 |
679 | $params[0] = $self->div_scale(); # and round to it as accuracy |
680 | $params[1] = undef; # P = undef |
681 | $scale = $params[0]+4; # at least four more for proper round |
682 | $params[2] = $r; # round mode by caller or undef |
b3abae2a |
683 | $fallback = 1; # to clear a/p afterwards |
684 | } |
685 | else |
686 | { |
687 | # the 4 below is empirical, and there might be cases where it is not |
688 | # enough... |
990fb837 |
689 | $scale = abs($params[0] || $params[1]) + 4; # take whatever is defined |
b3abae2a |
690 | } |
61f5c3f5 |
691 | |
b3abae2a |
692 | return $x->bzero(@params) if $x->is_one(); |
990fb837 |
693 | # base not defined => base == Euler's constant e |
694 | if (defined $base) |
695 | { |
696 | # make object, since we don't feed it trough objectify() to still get the |
697 | # case of $base == undef |
698 | $base = $self->new($base) unless ref($base); |
699 | # $base > 0; $base != 1 |
700 | return $x->bnan() if $base->is_zero() || $base->is_one() || |
701 | $base->{sign} ne '+'; |
702 | return $x->bone('+',@params) if $x->bcmp($base) == 0; |
703 | } |
61f5c3f5 |
704 | |
b3abae2a |
705 | # when user set globals, they would interfere with our calculation, so |
56d9de68 |
706 | # disable them and later re-enable them |
b3abae2a |
707 | no strict 'refs'; |
708 | my $abr = "$self\::accuracy"; my $ab = $$abr; $$abr = undef; |
709 | my $pbr = "$self\::precision"; my $pb = $$pbr; $$pbr = undef; |
710 | # we also need to disable any set A or P on $x (_find_round_parameters took |
711 | # them already into account), since these would interfere, too |
712 | delete $x->{_a}; delete $x->{_p}; |
9393ace2 |
713 | # need to disable $upgrade in BigInt, to avoid deep recursion |
b3abae2a |
714 | local $Math::BigInt::upgrade = undef; |
93c87d9d |
715 | local $Math::BigFloat::downgrade = undef; |
990fb837 |
716 | |
717 | # upgrade $x if $x is not a BigFloat (handle BigInt input) |
718 | if (!$x->isa('Math::BigFloat')) |
719 | { |
720 | $x = Math::BigFloat->new($x); |
721 | $self = ref($x); |
722 | } |
723 | # first calculate the log to base e (using reduction by 10 (and probably 2)) |
724 | $self->_log_10($x,$scale); |
9393ace2 |
725 | |
990fb837 |
726 | # and if a different base was requested, convert it |
727 | if (defined $base) |
9393ace2 |
728 | { |
93c87d9d |
729 | $base = Math::BigFloat->new($base) unless $base->isa('Math::BigFloat'); |
990fb837 |
730 | # not ln, but some other base |
731 | $x->bdiv( $base->copy()->blog(undef,$scale), $scale ); |
9393ace2 |
732 | } |
990fb837 |
733 | |
b3abae2a |
734 | # shortcut to not run trough _find_round_parameters again |
990fb837 |
735 | if (defined $params[0]) |
b3abae2a |
736 | { |
990fb837 |
737 | $x->bround($params[0],$params[2]); # then round accordingly |
b3abae2a |
738 | } |
739 | else |
740 | { |
990fb837 |
741 | $x->bfround($params[1],$params[2]); # then round accordingly |
b3abae2a |
742 | } |
743 | if ($fallback) |
744 | { |
745 | # clear a/p after round, since user did not request it |
746 | $x->{_a} = undef; $x->{_p} = undef; |
747 | } |
748 | # restore globals |
749 | $$abr = $ab; $$pbr = $pb; |
750 | |
751 | $x; |
61f5c3f5 |
752 | } |
753 | |
990fb837 |
754 | sub _log |
755 | { |
756 | # internal log function to calculate log based on Taylor. |
757 | # Modifies $x in place. |
758 | my ($self,$x,$scale) = @_; |
759 | |
760 | # http://www.efunda.com/math/taylor_series/logarithmic.cfm?search_string=log |
761 | |
762 | # u = x-1, v = x+1 |
763 | # _ _ |
764 | # Taylor: | u 1 u^3 1 u^5 | |
765 | # ln (x) = 2 | --- + - * --- + - * --- + ... | x > 0 |
766 | # |_ v 3 v^3 5 v^5 _| |
767 | |
768 | # This takes much more steps to calculate the result and is thus not used |
769 | # u = x-1 |
770 | # _ _ |
771 | # Taylor: | u 1 u^2 1 u^3 | |
772 | # ln (x) = 2 | --- + - * --- + - * --- + ... | x > 1/2 |
773 | # |_ x 2 x^2 3 x^3 _| |
774 | |
775 | # "normal" log algorithmn |
776 | |
777 | my ($limit,$v,$u,$below,$factor,$two,$next,$over,$f); |
778 | |
779 | $v = $x->copy(); $v->binc(); # v = x+1 |
780 | $x->bdec(); $u = $x->copy(); # u = x-1; x = x-1 |
781 | $x->bdiv($v,$scale); # first term: u/v |
782 | $below = $v->copy(); |
783 | $over = $u->copy(); |
784 | $u *= $u; $v *= $v; # u^2, v^2 |
785 | $below->bmul($v); # u^3, v^3 |
786 | $over->bmul($u); |
787 | $factor = $self->new(3); $f = $self->new(2); |
788 | |
789 | my $steps = 0 if DEBUG; |
790 | $limit = $self->new("1E-". ($scale-1)); |
791 | while (3 < 5) |
792 | { |
793 | # we calculate the next term, and add it to the last |
794 | # when the next term is below our limit, it won't affect the outcome |
795 | # anymore, so we stop |
796 | |
797 | # calculating the next term simple from over/below will result in quite |
798 | # a time hog if the input has many digits, since over and below will |
799 | # accumulate more and more digits, and the result will also have many |
800 | # digits, but in the end it is rounded to $scale digits anyway. So if we |
801 | # round $over and $below first, we save a lot of time for the division |
802 | # (not with log(1.2345), but try log (123**123) to see what I mean. This |
803 | # can introduce a rounding error if the division result would be f.i. |
804 | # 0.1234500000001 and we round it to 5 digits it would become 0.12346, but |
805 | # if we truncated the $over and $below we might get 0.12345. Does this |
806 | # matter for the end result? So we give over and below 4 more digits to be |
807 | # on the safe side (unscientific error handling as usual...) |
808 | # Makes blog(1.23) *slightly* slower, but try blog(123*123) w/o it :o) |
809 | |
810 | $next = $over->copy->bround($scale+4)->bdiv( |
811 | $below->copy->bmul($factor)->bround($scale+4), |
812 | $scale); |
813 | |
814 | ## old version: |
815 | ## $next = $over->copy()->bdiv($below->copy()->bmul($factor),$scale); |
816 | |
817 | last if $next->bacmp($limit) <= 0; |
818 | |
819 | delete $next->{_a}; delete $next->{_p}; |
820 | $x->badd($next); |
821 | #print "step $x\n ($next - $limit = ",$next - $limit,")\n"; |
822 | # calculate things for the next term |
823 | $over *= $u; $below *= $v; $factor->badd($f); |
824 | if (DEBUG) |
825 | { |
826 | $steps++; print "step $steps = $x\n" if $steps % 10 == 0; |
827 | } |
828 | } |
829 | $x->bmul($f); # $x *= 2 |
830 | print "took $steps steps\n" if DEBUG; |
831 | } |
832 | |
833 | sub _log_10 |
834 | { |
835 | # internal log function based on reducing input to the range of 0.1 .. 9.99 |
836 | my ($self,$x,$scale) = @_; |
837 | |
838 | # taking blog() from numbers greater than 10 takes a *very long* time, so we |
839 | # break the computation down into parts based on the observation that: |
840 | # blog(x*y) = blog(x) + blog(y) |
841 | # We set $y here to multiples of 10 so that $x is below 1 (the smaller $x is |
842 | # the faster it get's, especially because 2*$x takes about 10 times as long, |
843 | # so by dividing $x by 10 we make it at least factor 100 faster...) |
844 | |
845 | # The same observation is valid for numbers smaller than 0.1 (e.g. computing |
846 | # log(1) is fastest, and the farther away we get from 1, the longer it takes) |
847 | # so we also 'break' this down by multiplying $x with 10 and subtract the |
848 | # log(10) afterwards to get the correct result. |
849 | |
850 | # calculate nr of digits before dot |
851 | my $dbd = $x->{_m}->length() + $x->{_e}->numify(); |
852 | |
853 | # more than one digit (e.g. at least 10), but *not* exactly 10 to avoid |
854 | # infinite recursion |
855 | |
856 | my $calc = 1; # do some calculation? |
857 | |
858 | # disable the shortcut for 10, since we need log(10) and this would recurse |
859 | # infinitely deep |
860 | if ($x->{_e}->is_one() && $x->{_m}->is_one()) |
861 | { |
862 | $dbd = 0; # disable shortcut |
863 | # we can use the cached value in these cases |
864 | if ($scale <= $LOG_10_A) |
865 | { |
866 | $x->bzero(); $x->badd($LOG_10); |
867 | $calc = 0; # no need to calc, but round |
868 | } |
869 | } |
870 | # disable the shortcut for 2, since we maybe have it cached |
871 | my $two = $self->new(2); # also used later on |
872 | if ($x->{_e}->is_zero() && $x->{_m}->bcmp($two) == 0) |
873 | { |
874 | $dbd = 0; # disable shortcut |
875 | # we can use the cached value in these cases |
876 | if ($scale <= $LOG_2_A) |
877 | { |
878 | $x->bzero(); $x->badd($LOG_2); |
879 | $calc = 0; # no need to calc, but round |
880 | } |
881 | } |
882 | |
883 | # if $x = 0.1, we know the result must be 0-log(10) |
884 | if ($x->{_e}->is_one('-') && $x->{_m}->is_one()) |
885 | { |
886 | $dbd = 0; # disable shortcut |
887 | # we can use the cached value in these cases |
888 | if ($scale <= $LOG_10_A) |
889 | { |
890 | $x->bzero(); $x->bsub($LOG_10); |
891 | $calc = 0; # no need to calc, but round |
892 | } |
893 | } |
894 | |
895 | # default: these correction factors are undef and thus not used |
896 | my $l_10; # value of ln(10) to A of $scale |
897 | my $l_2; # value of ln(2) to A of $scale |
898 | |
899 | # $x == 2 => 1, $x == 13 => 2, $x == 0.1 => 0, $x == 0.01 => -1 |
900 | # so don't do this shortcut for 1 or 0 |
901 | if (($dbd > 1) || ($dbd < 0)) |
902 | { |
903 | # convert our cached value to an object if not already (avoid doing this |
904 | # at import() time, since not everybody needs this) |
905 | $LOG_10 = $self->new($LOG_10,undef,undef) unless ref $LOG_10; |
906 | |
907 | #print "x = $x, dbd = $dbd, calc = $calc\n"; |
908 | # got more than one digit before the dot, or more than one zero after the |
909 | # dot, so do: |
910 | # log(123) == log(1.23) + log(10) * 2 |
911 | # log(0.0123) == log(1.23) - log(10) * 2 |
912 | |
913 | if ($scale <= $LOG_10_A) |
914 | { |
915 | # use cached value |
916 | #print "using cached value for l_10\n"; |
917 | $l_10 = $LOG_10->copy(); # copy for mul |
918 | } |
919 | else |
920 | { |
921 | # else: slower, compute it (but don't cache it, because it could be big) |
922 | # also disable downgrade for this code path |
923 | local $Math::BigFloat::downgrade = undef; |
924 | #print "l_10 = $l_10 (self = $self', |
925 | # ", ref(l_10) = ",ref($l_10)," scale $scale)\n"; |
926 | #print "calculating value for l_10, scale $scale\n"; |
927 | $l_10 = $self->new(10)->blog(undef,$scale); # scale+4, actually |
928 | } |
929 | $dbd-- if ($dbd > 1); # 20 => dbd=2, so make it dbd=1 |
930 | # make object |
931 | $dbd = $self->new($dbd); |
932 | #print "dbd $dbd\n"; |
933 | $l_10->bmul($dbd); # log(10) * (digits_before_dot-1) |
934 | #print "l_10 = $l_10\n"; |
935 | #print "x = $x"; |
936 | $x->{_e}->bsub($dbd); # 123 => 1.23 |
937 | #print " => $x\n"; |
938 | #print "calculating log($x) with scale=$scale\n"; |
939 | |
940 | } |
941 | |
942 | # Now: 0.1 <= $x < 10 (and possible correction in l_10) |
943 | |
944 | ### Since $x in the range 0.5 .. 1.5 is MUCH faster, we do a repeated div |
945 | ### or mul by 2 (maximum times 3, since x < 10 and x > 0.1) |
946 | |
947 | if ($calc != 0) |
948 | { |
949 | my $half = $self->new('0.5'); |
950 | my $twos = 0; # default: none (0 times) |
951 | while ($x->bacmp($half) < 0) |
952 | { |
953 | #print "$x\n"; |
954 | $twos--; $x->bmul($two); |
955 | } |
956 | while ($x->bacmp($two) > 0) |
957 | { |
958 | #print "$x\n"; |
959 | $twos++; $x->bdiv($two,$scale+4); # keep all digits |
960 | } |
961 | #print "$twos\n"; |
962 | # $twos > 0 => did mul 2, < 0 => did div 2 (never both) |
963 | # calculate correction factor based on ln(2) |
964 | if ($twos != 0) |
965 | { |
966 | $LOG_2 = $self->new($LOG_2,undef,undef) unless ref $LOG_2; |
967 | if ($scale <= $LOG_2_A) |
968 | { |
969 | # use cached value |
970 | #print "using cached value for l_10\n"; |
971 | $l_2 = $LOG_2->copy(); # copy for mul |
972 | } |
973 | else |
974 | { |
975 | # else: slower, compute it (but don't cache it, because it could be big) |
976 | # also disable downgrade for this code path |
977 | local $Math::BigFloat::downgrade = undef; |
978 | #print "calculating value for l_2, scale $scale\n"; |
979 | $l_2 = $two->blog(undef,$scale); # scale+4, actually |
980 | } |
981 | #print "$l_2 => \n"; |
982 | $l_2->bmul($twos); # * -2 => subtract, * 2 => add |
983 | #print "$l_2\n"; |
984 | } |
985 | } |
986 | |
987 | if ($calc != 0) |
988 | { |
989 | $self->_log($x,$scale); # need to do the "normal" way |
990 | #print "log(x) = $x\n"; |
991 | $x->badd($l_10) if defined $l_10; # correct it by ln(10) |
992 | #print "result = $x\n"; |
993 | $x->badd($l_2) if defined $l_2; # and maybe by ln(2) |
994 | #print "result = $x\n"; |
995 | } |
996 | # all done, $x contains now the result |
997 | } |
998 | |
58cde26e |
999 | sub blcm |
1000 | { |
ee15d750 |
1001 | # (BFLOAT or num_str, BFLOAT or num_str) return BFLOAT |
58cde26e |
1002 | # does not modify arguments, but returns new object |
1003 | # Lowest Common Multiplicator |
58cde26e |
1004 | |
1005 | my ($self,@arg) = objectify(0,@_); |
1006 | my $x = $self->new(shift @arg); |
1007 | while (@arg) { $x = _lcm($x,shift @arg); } |
1008 | $x; |
1009 | } |
1010 | |
1011 | sub bgcd |
1012 | { |
ee15d750 |
1013 | # (BFLOAT or num_str, BFLOAT or num_str) return BINT |
58cde26e |
1014 | # does not modify arguments, but returns new object |
1015 | # GCD -- Euclids algorithm Knuth Vol 2 pg 296 |
58cde26e |
1016 | |
1017 | my ($self,@arg) = objectify(0,@_); |
1018 | my $x = $self->new(shift @arg); |
1019 | while (@arg) { $x = _gcd($x,shift @arg); } |
1020 | $x; |
1021 | } |
1022 | |
b3abae2a |
1023 | ############################################################################### |
1024 | # is_foo methods (is_negative, is_positive are inherited from BigInt) |
1025 | |
1026 | sub is_int |
1027 | { |
1028 | # return true if arg (BFLOAT or num_str) is an integer |
1029 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
1030 | |
1031 | return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN and +-inf aren't |
1032 | $x->{_e}->{sign} eq '+'; # 1e-1 => no integer |
1033 | 0; |
1034 | } |
1035 | |
58cde26e |
1036 | sub is_zero |
1037 | { |
b3abae2a |
1038 | # return true if arg (BFLOAT or num_str) is zero |
ee15d750 |
1039 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
574bacfe |
1040 | |
1041 | return 1 if $x->{sign} eq '+' && $x->{_m}->is_zero(); |
b3abae2a |
1042 | 0; |
58cde26e |
1043 | } |
1044 | |
1045 | sub is_one |
1046 | { |
b3abae2a |
1047 | # return true if arg (BFLOAT or num_str) is +1 or -1 if signis given |
990fb837 |
1048 | my ($self,$x,$sign) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
ee15d750 |
1049 | |
990fb837 |
1050 | $sign = '+' if !defined $sign || $sign ne '-'; |
ee15d750 |
1051 | return 1 |
1052 | if ($x->{sign} eq $sign && $x->{_e}->is_zero() && $x->{_m}->is_one()); |
b3abae2a |
1053 | 0; |
58cde26e |
1054 | } |
1055 | |
1056 | sub is_odd |
1057 | { |
ee15d750 |
1058 | # return true if arg (BFLOAT or num_str) is odd or false if even |
1059 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
0716bf9b |
1060 | |
b3abae2a |
1061 | return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN & +-inf aren't |
1062 | ($x->{_e}->is_zero() && $x->{_m}->is_odd()); |
1063 | 0; |
58cde26e |
1064 | } |
1065 | |
1066 | sub is_even |
1067 | { |
b22b3e31 |
1068 | # return true if arg (BINT or num_str) is even or false if odd |
ee15d750 |
1069 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
0716bf9b |
1070 | |
1071 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
b3abae2a |
1072 | return 1 if ($x->{_e}->{sign} eq '+' # 123.45 is never |
1073 | && $x->{_m}->is_even()); # but 1200 is |
1074 | 0; |
58cde26e |
1075 | } |
1076 | |
1077 | sub bmul |
1078 | { |
1079 | # multiply two numbers -- stolen from Knuth Vol 2 pg 233 |
1080 | # (BINT or num_str, BINT or num_str) return BINT |
f9a08e12 |
1081 | |
1082 | # set up parameters |
1083 | my ($self,$x,$y,$a,$p,$r) = (ref($_[0]),@_); |
1084 | # objectify is costly, so avoid it |
1085 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1086 | { |
1087 | ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
1088 | } |
58cde26e |
1089 | |
58cde26e |
1090 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
1091 | |
574bacfe |
1092 | # inf handling |
1093 | if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) |
1094 | { |
13a12e00 |
1095 | return $x->bnan() if $x->is_zero() || $y->is_zero(); |
574bacfe |
1096 | # result will always be +-inf: |
1097 | # +inf * +/+inf => +inf, -inf * -/-inf => +inf |
1098 | # +inf * -/-inf => -inf, -inf * +/+inf => -inf |
1099 | return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); |
1100 | return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); |
1101 | return $x->binf('-'); |
1102 | } |
13a12e00 |
1103 | # handle result = 0 |
1104 | return $x->bzero() if $x->is_zero() || $y->is_zero(); |
8f675a64 |
1105 | |
1106 | return $upgrade->bmul($x,$y,$a,$p,$r) if defined $upgrade && |
1107 | ((!$x->isa($self)) || (!$y->isa($self))); |
574bacfe |
1108 | |
58cde26e |
1109 | # aEb * cEd = (a*c)E(b+d) |
394e6ffb |
1110 | $x->{_m}->bmul($y->{_m}); |
1111 | $x->{_e}->badd($y->{_e}); |
58cde26e |
1112 | # adjust sign: |
1113 | $x->{sign} = $x->{sign} ne $y->{sign} ? '-' : '+'; |
394e6ffb |
1114 | return $x->bnorm()->round($a,$p,$r,$y); |
58cde26e |
1115 | } |
1116 | |
1117 | sub bdiv |
1118 | { |
1119 | # (dividend: BFLOAT or num_str, divisor: BFLOAT or num_str) return |
9393ace2 |
1120 | # (BFLOAT,BFLOAT) (quo,rem) or BFLOAT (only rem) |
f9a08e12 |
1121 | |
1122 | # set up parameters |
1123 | my ($self,$x,$y,$a,$p,$r) = (ref($_[0]),@_); |
1124 | # objectify is costly, so avoid it |
1125 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1126 | { |
1127 | ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
1128 | } |
58cde26e |
1129 | |
13a12e00 |
1130 | return $self->_div_inf($x,$y) |
1131 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()); |
574bacfe |
1132 | |
13a12e00 |
1133 | # x== 0 # also: or y == 1 or y == -1 |
394e6ffb |
1134 | return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero(); |
0716bf9b |
1135 | |
9393ace2 |
1136 | # upgrade ? |
1137 | return $upgrade->bdiv($upgrade->new($x),$y,$a,$p,$r) if defined $upgrade; |
13a12e00 |
1138 | |
58cde26e |
1139 | # we need to limit the accuracy to protect against overflow |
574bacfe |
1140 | my $fallback = 0; |
990fb837 |
1141 | my (@params,$scale); |
1142 | ($x,@params) = $x->_find_round_parameters($a,$p,$r,$y); |
1143 | |
1144 | return $x if $x->is_nan(); # error in _find_round_parameters? |
ee15d750 |
1145 | |
1146 | # no rounding at all, so must use fallback |
990fb837 |
1147 | if (scalar @params == 0) |
58cde26e |
1148 | { |
0716bf9b |
1149 | # simulate old behaviour |
990fb837 |
1150 | $params[0] = $self->div_scale(); # and round to it as accuracy |
1151 | $scale = $params[0]+4; # at least four more for proper round |
1152 | $params[2] = $r; # round mode by caller or undef |
ee15d750 |
1153 | $fallback = 1; # to clear a/p afterwards |
1154 | } |
1155 | else |
1156 | { |
1157 | # the 4 below is empirical, and there might be cases where it is not |
1158 | # enough... |
990fb837 |
1159 | $scale = abs($params[0] || $params[1]) + 4; # take whatever is defined |
a0d0e21e |
1160 | } |
0716bf9b |
1161 | my $lx = $x->{_m}->length(); my $ly = $y->{_m}->length(); |
58cde26e |
1162 | $scale = $lx if $lx > $scale; |
58cde26e |
1163 | $scale = $ly if $ly > $scale; |
0716bf9b |
1164 | my $diff = $ly - $lx; |
1165 | $scale += $diff if $diff > 0; # if lx << ly, but not if ly << lx! |
b3abae2a |
1166 | |
1167 | # make copy of $x in case of list context for later reminder calculation |
1168 | my $rem; |
1169 | if (wantarray && !$y->is_one()) |
1170 | { |
1171 | $rem = $x->copy(); |
1172 | } |
a0d0e21e |
1173 | |
58cde26e |
1174 | $x->{sign} = $x->{sign} ne $y->sign() ? '-' : '+'; |
a0d0e21e |
1175 | |
58cde26e |
1176 | # check for / +-1 ( +/- 1E0) |
394e6ffb |
1177 | if (!$y->is_one()) |
58cde26e |
1178 | { |
394e6ffb |
1179 | # promote BigInts and it's subclasses (except when already a BigFloat) |
1180 | $y = $self->new($y) unless $y->isa('Math::BigFloat'); |
1181 | |
9393ace2 |
1182 | # need to disable $upgrade in BigInt, to avoid deep recursion |
1183 | local $Math::BigInt::upgrade = undef; # should be parent class vs MBI |
1184 | |
394e6ffb |
1185 | # calculate the result to $scale digits and then round it |
1186 | # a * 10 ** b / c * 10 ** d => a/c * 10 ** (b-d) |
1187 | $x->{_m}->blsft($scale,10); |
1188 | $x->{_m}->bdiv( $y->{_m} ); # a/c |
1189 | $x->{_e}->bsub( $y->{_e} ); # b-d |
1190 | $x->{_e}->bsub($scale); # correct for 10**scale |
1191 | $x->bnorm(); # remove trailing 0's |
a0d0e21e |
1192 | } |
a5f75d66 |
1193 | |
ee15d750 |
1194 | # shortcut to not run trough _find_round_parameters again |
990fb837 |
1195 | if (defined $params[0]) |
ee15d750 |
1196 | { |
56d9de68 |
1197 | $x->{_a} = undef; # clear before round |
990fb837 |
1198 | $x->bround($params[0],$params[2]); # then round accordingly |
ee15d750 |
1199 | } |
1200 | else |
1201 | { |
56d9de68 |
1202 | $x->{_p} = undef; # clear before round |
990fb837 |
1203 | $x->bfround($params[1],$params[2]); # then round accordingly |
ee15d750 |
1204 | } |
574bacfe |
1205 | if ($fallback) |
1206 | { |
1207 | # clear a/p after round, since user did not request it |
ee15d750 |
1208 | $x->{_a} = undef; $x->{_p} = undef; |
574bacfe |
1209 | } |
0716bf9b |
1210 | |
58cde26e |
1211 | if (wantarray) |
1212 | { |
394e6ffb |
1213 | if (!$y->is_one()) |
1214 | { |
990fb837 |
1215 | $rem->bmod($y,@params); # copy already done |
394e6ffb |
1216 | } |
1217 | else |
1218 | { |
1219 | $rem = $self->bzero(); |
1220 | } |
574bacfe |
1221 | if ($fallback) |
1222 | { |
1223 | # clear a/p after round, since user did not request it |
ee15d750 |
1224 | $rem->{_a} = undef; $rem->{_p} = undef; |
574bacfe |
1225 | } |
0716bf9b |
1226 | return ($x,$rem); |
58cde26e |
1227 | } |
9393ace2 |
1228 | $x; |
58cde26e |
1229 | } |
a0d0e21e |
1230 | |
58cde26e |
1231 | sub bmod |
1232 | { |
1233 | # (dividend: BFLOAT or num_str, divisor: BFLOAT or num_str) return reminder |
f9a08e12 |
1234 | |
1235 | # set up parameters |
1236 | my ($self,$x,$y,$a,$p,$r) = (ref($_[0]),@_); |
1237 | # objectify is costly, so avoid it |
1238 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1239 | { |
1240 | ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
1241 | } |
a0d0e21e |
1242 | |
61f5c3f5 |
1243 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
1244 | { |
1245 | my ($d,$re) = $self->SUPER::_div_inf($x,$y); |
f9a08e12 |
1246 | $x->{sign} = $re->{sign}; |
1247 | $x->{_e} = $re->{_e}; |
1248 | $x->{_m} = $re->{_m}; |
1249 | return $x->round($a,$p,$r,$y); |
61f5c3f5 |
1250 | } |
1251 | return $x->bnan() if $x->is_zero() && $y->is_zero(); |
1252 | return $x if $y->is_zero(); |
1253 | return $x->bnan() if $x->is_nan() || $y->is_nan(); |
1254 | return $x->bzero() if $y->is_one() || $x->is_zero(); |
58cde26e |
1255 | |
61f5c3f5 |
1256 | # inf handling is missing here |
1257 | |
1258 | my $cmp = $x->bacmp($y); # equal or $x < $y? |
1259 | return $x->bzero($a,$p) if $cmp == 0; # $x == $y => result 0 |
1260 | |
1261 | # only $y of the operands negative? |
1262 | my $neg = 0; $neg = 1 if $x->{sign} ne $y->{sign}; |
1263 | |
1264 | $x->{sign} = $y->{sign}; # calc sign first |
1265 | return $x->round($a,$p,$r) if $cmp < 0 && $neg == 0; # $x < $y => result $x |
1266 | |
1267 | my $ym = $y->{_m}->copy(); |
1268 | |
1269 | # 2e1 => 20 |
1270 | $ym->blsft($y->{_e},10) if $y->{_e}->{sign} eq '+' && !$y->{_e}->is_zero(); |
1271 | |
1272 | # if $y has digits after dot |
1273 | my $shifty = 0; # correct _e of $x by this |
1274 | if ($y->{_e}->{sign} eq '-') # has digits after dot |
1275 | { |
1276 | # 123 % 2.5 => 1230 % 25 => 5 => 0.5 |
1277 | $shifty = $y->{_e}->copy()->babs(); # no more digits after dot |
1278 | $x->blsft($shifty,10); # 123 => 1230, $y->{_m} is already 25 |
1279 | } |
1280 | # $ym is now mantissa of $y based on exponent 0 |
b3abae2a |
1281 | |
61f5c3f5 |
1282 | my $shiftx = 0; # correct _e of $x by this |
1283 | if ($x->{_e}->{sign} eq '-') # has digits after dot |
1284 | { |
1285 | # 123.4 % 20 => 1234 % 200 |
1286 | $shiftx = $x->{_e}->copy()->babs(); # no more digits after dot |
1287 | $ym->blsft($shiftx,10); |
1288 | } |
1289 | # 123e1 % 20 => 1230 % 20 |
1290 | if ($x->{_e}->{sign} eq '+' && !$x->{_e}->is_zero()) |
1291 | { |
1292 | $x->{_m}->blsft($x->{_e},10); |
1293 | } |
56b9c951 |
1294 | $x->{_e} = $MBI->bzero() unless $x->{_e}->is_zero(); |
61f5c3f5 |
1295 | |
1296 | $x->{_e}->bsub($shiftx) if $shiftx != 0; |
1297 | $x->{_e}->bsub($shifty) if $shifty != 0; |
1298 | |
1299 | # now mantissas are equalized, exponent of $x is adjusted, so calc result |
b3abae2a |
1300 | |
61f5c3f5 |
1301 | $x->{_m}->bmod($ym); |
1302 | |
1303 | $x->{sign} = '+' if $x->{_m}->is_zero(); # fix sign for -0 |
1304 | $x->bnorm(); |
1305 | |
1306 | if ($neg != 0) # one of them negative => correct in place |
1307 | { |
1308 | my $r = $y - $x; |
1309 | $x->{_m} = $r->{_m}; |
1310 | $x->{_e} = $r->{_e}; |
1311 | $x->{sign} = '+' if $x->{_m}->is_zero(); # fix sign for -0 |
1312 | $x->bnorm(); |
1313 | } |
1314 | |
1315 | $x->round($a,$p,$r,$y); # round and return |
58cde26e |
1316 | } |
1317 | |
990fb837 |
1318 | sub broot |
1319 | { |
1320 | # calculate $y'th root of $x |
1321 | my ($self,$x,$y,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(2,@_); |
1322 | |
1323 | # NaN handling: $x ** 1/0, x or y NaN, or y inf/-inf or y == 0 |
1324 | return $x->bnan() if $x->{sign} !~ /^\+/ || $y->is_zero() || |
1325 | $y->{sign} !~ /^\+$/; |
1326 | |
1327 | return $x if $x->is_zero() || $x->is_one() || $x->is_inf() || $y->is_one(); |
1328 | |
1329 | # we need to limit the accuracy to protect against overflow |
1330 | my $fallback = 0; |
1331 | my (@params,$scale); |
1332 | ($x,@params) = $x->_find_round_parameters($a,$p,$r); |
1333 | |
1334 | return $x if $x->is_nan(); # error in _find_round_parameters? |
1335 | |
1336 | # no rounding at all, so must use fallback |
1337 | if (scalar @params == 0) |
1338 | { |
1339 | # simulate old behaviour |
1340 | $params[0] = $self->div_scale(); # and round to it as accuracy |
1341 | $scale = $params[0]+4; # at least four more for proper round |
1342 | $params[2] = $r; # round mode by caller or undef |
1343 | $fallback = 1; # to clear a/p afterwards |
1344 | } |
1345 | else |
1346 | { |
1347 | # the 4 below is empirical, and there might be cases where it is not |
1348 | # enough... |
1349 | $scale = abs($params[0] || $params[1]) + 4; # take whatever is defined |
1350 | } |
1351 | |
1352 | # when user set globals, they would interfere with our calculation, so |
1353 | # disable them and later re-enable them |
1354 | no strict 'refs'; |
1355 | my $abr = "$self\::accuracy"; my $ab = $$abr; $$abr = undef; |
1356 | my $pbr = "$self\::precision"; my $pb = $$pbr; $$pbr = undef; |
1357 | # we also need to disable any set A or P on $x (_find_round_parameters took |
1358 | # them already into account), since these would interfere, too |
1359 | delete $x->{_a}; delete $x->{_p}; |
1360 | # need to disable $upgrade in BigInt, to avoid deep recursion |
1361 | local $Math::BigInt::upgrade = undef; # should be really parent class vs MBI |
1362 | |
1363 | # remember sign and make $x positive, since -4 ** (1/2) => -2 |
1364 | my $sign = 0; $sign = 1 if $x->is_negative(); $x->babs(); |
1365 | |
1366 | if ($y->bcmp(2) == 0) # normal square root |
1367 | { |
1368 | $x->bsqrt($scale+4); |
1369 | } |
1370 | elsif ($y->is_one('-')) |
1371 | { |
1372 | # $x ** -1 => 1/$x |
1373 | my $u = $self->bone()->bdiv($x,$scale); |
1374 | # copy private parts over |
1375 | $x->{_m} = $u->{_m}; |
1376 | $x->{_e} = $u->{_e}; |
1377 | } |
1378 | else |
1379 | { |
1380 | my $u = $self->bone()->bdiv($y,$scale+4); |
1381 | delete $u->{_a}; delete $u->{_p}; # otherwise it conflicts |
1382 | $x->bpow($u,$scale+4); # el cheapo |
1383 | } |
1384 | $x->bneg() if $sign == 1; |
1385 | |
1386 | # shortcut to not run trough _find_round_parameters again |
1387 | if (defined $params[0]) |
1388 | { |
1389 | $x->bround($params[0],$params[2]); # then round accordingly |
1390 | } |
1391 | else |
1392 | { |
1393 | $x->bfround($params[1],$params[2]); # then round accordingly |
1394 | } |
1395 | if ($fallback) |
1396 | { |
1397 | # clear a/p after round, since user did not request it |
1398 | $x->{_a} = undef; $x->{_p} = undef; |
1399 | } |
1400 | # restore globals |
1401 | $$abr = $ab; $$pbr = $pb; |
1402 | $x; |
1403 | } |
1404 | |
58cde26e |
1405 | sub bsqrt |
1406 | { |
990fb837 |
1407 | # calculate square root |
ee15d750 |
1408 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e |
1409 | |
990fb837 |
1410 | return $x->bnan() if $x->{sign} !~ /^[+]/; # NaN, -inf or < 0 |
1411 | return $x if $x->{sign} eq '+inf'; # sqrt(inf) == inf |
1412 | return $x->round($a,$p,$r) if $x->is_zero() || $x->is_one(); |
58cde26e |
1413 | |
61f5c3f5 |
1414 | # we need to limit the accuracy to protect against overflow |
574bacfe |
1415 | my $fallback = 0; |
990fb837 |
1416 | my (@params,$scale); |
1417 | ($x,@params) = $x->_find_round_parameters($a,$p,$r); |
1418 | |
1419 | return $x if $x->is_nan(); # error in _find_round_parameters? |
61f5c3f5 |
1420 | |
1421 | # no rounding at all, so must use fallback |
990fb837 |
1422 | if (scalar @params == 0) |
0716bf9b |
1423 | { |
1424 | # simulate old behaviour |
990fb837 |
1425 | $params[0] = $self->div_scale(); # and round to it as accuracy |
1426 | $scale = $params[0]+4; # at least four more for proper round |
1427 | $params[2] = $r; # round mode by caller or undef |
ee15d750 |
1428 | $fallback = 1; # to clear a/p afterwards |
0716bf9b |
1429 | } |
61f5c3f5 |
1430 | else |
1431 | { |
1432 | # the 4 below is empirical, and there might be cases where it is not |
1433 | # enough... |
990fb837 |
1434 | $scale = abs($params[0] || $params[1]) + 4; # take whatever is defined |
61f5c3f5 |
1435 | } |
1436 | |
1437 | # when user set globals, they would interfere with our calculation, so |
9393ace2 |
1438 | # disable them and later re-enable them |
61f5c3f5 |
1439 | no strict 'refs'; |
1440 | my $abr = "$self\::accuracy"; my $ab = $$abr; $$abr = undef; |
b3abae2a |
1441 | my $pbr = "$self\::precision"; my $pb = $$pbr; $$pbr = undef; |
61f5c3f5 |
1442 | # we also need to disable any set A or P on $x (_find_round_parameters took |
1443 | # them already into account), since these would interfere, too |
1444 | delete $x->{_a}; delete $x->{_p}; |
9393ace2 |
1445 | # need to disable $upgrade in BigInt, to avoid deep recursion |
1446 | local $Math::BigInt::upgrade = undef; # should be really parent class vs MBI |
61f5c3f5 |
1447 | |
394e6ffb |
1448 | my $xas = $x->as_number(); |
1449 | my $gs = $xas->copy()->bsqrt(); # some guess |
b3abae2a |
1450 | |
394e6ffb |
1451 | if (($x->{_e}->{sign} ne '-') # guess can't be accurate if there are |
1452 | # digits after the dot |
b3abae2a |
1453 | && ($xas->bacmp($gs * $gs) == 0)) # guess hit the nail on the head? |
394e6ffb |
1454 | { |
1455 | # exact result |
56b9c951 |
1456 | $x->{_m} = $gs; $x->{_e} = $MBI->bzero(); $x->bnorm(); |
61f5c3f5 |
1457 | # shortcut to not run trough _find_round_parameters again |
990fb837 |
1458 | if (defined $params[0]) |
61f5c3f5 |
1459 | { |
990fb837 |
1460 | $x->bround($params[0],$params[2]); # then round accordingly |
61f5c3f5 |
1461 | } |
1462 | else |
1463 | { |
990fb837 |
1464 | $x->bfround($params[1],$params[2]); # then round accordingly |
61f5c3f5 |
1465 | } |
1466 | if ($fallback) |
1467 | { |
1468 | # clear a/p after round, since user did not request it |
1469 | $x->{_a} = undef; $x->{_p} = undef; |
1470 | } |
9393ace2 |
1471 | # re-enable A and P, upgrade is taken care of by "local" |
b3abae2a |
1472 | ${"$self\::accuracy"} = $ab; ${"$self\::precision"} = $pb; |
61f5c3f5 |
1473 | return $x; |
394e6ffb |
1474 | } |
2ab5f49d |
1475 | |
1476 | # sqrt(2) = 1.4 because sqrt(2*100) = 1.4*10; so we can increase the accuracy |
1477 | # of the result by multipyling the input by 100 and then divide the integer |
1478 | # result of sqrt(input) by 10. Rounding afterwards returns the real result. |
1479 | # this will transform 123.456 (in $x) into 123456 (in $y1) |
1480 | my $y1 = $x->{_m}->copy(); |
1481 | # We now make sure that $y1 has the same odd or even number of digits than |
1482 | # $x had. So when _e of $x is odd, we must shift $y1 by one digit left, |
1483 | # because we always must multiply by steps of 100 (sqrt(100) is 10) and not |
1484 | # steps of 10. The length of $x does not count, since an even or odd number |
1485 | # of digits before the dot is not changed by adding an even number of digits |
1486 | # after the dot (the result is still odd or even digits long). |
990fb837 |
1487 | my $length = $y1->length(); |
2ab5f49d |
1488 | $y1->bmul(10) if $x->{_e}->is_odd(); |
1489 | # now calculate how many digits the result of sqrt(y1) would have |
990fb837 |
1490 | my $digits = int($length / 2); |
2ab5f49d |
1491 | # but we need at least $scale digits, so calculate how many are missing |
1492 | my $shift = $scale - $digits; |
1493 | # that should never happen (we take care of integer guesses above) |
1494 | # $shift = 0 if $shift < 0; |
1495 | # multiply in steps of 100, by shifting left two times the "missing" digits |
1496 | $y1->blsft($shift*2,10); |
1497 | # now take the square root and truncate to integer |
1498 | $y1->bsqrt(); |
1499 | # By "shifting" $y1 right (by creating a negative _e) we calculate the final |
1500 | # result, which is than later rounded to the desired scale. |
990fb837 |
1501 | |
1502 | # calculate how many zeros $x had after the '.' (or before it, depending |
1503 | # on sign of $dat, the result should have half as many: |
1504 | my $dat = $length + $x->{_e}->numify(); |
1505 | |
1506 | if ($dat > 0) |
1507 | { |
1508 | # no zeros after the dot (e.g. 1.23, 0.49 etc) |
1509 | # preserve half as many digits before the dot than the input had |
1510 | # (but round this "up") |
1511 | $dat = int(($dat+1)/2); |
1512 | } |
1513 | else |
1514 | { |
1515 | $dat = int(($dat)/2); |
1516 | } |
1517 | $x->{_e}= $MBI->new( $dat - $y1->length() ); |
1518 | |
2ab5f49d |
1519 | $x->{_m} = $y1; |
61f5c3f5 |
1520 | |
61f5c3f5 |
1521 | # shortcut to not run trough _find_round_parameters again |
990fb837 |
1522 | if (defined $params[0]) |
61f5c3f5 |
1523 | { |
990fb837 |
1524 | $x->bround($params[0],$params[2]); # then round accordingly |
61f5c3f5 |
1525 | } |
1526 | else |
1527 | { |
990fb837 |
1528 | $x->bfround($params[1],$params[2]); # then round accordingly |
61f5c3f5 |
1529 | } |
574bacfe |
1530 | if ($fallback) |
1531 | { |
1532 | # clear a/p after round, since user did not request it |
ee15d750 |
1533 | $x->{_a} = undef; $x->{_p} = undef; |
574bacfe |
1534 | } |
61f5c3f5 |
1535 | # restore globals |
b3abae2a |
1536 | $$abr = $ab; $$pbr = $pb; |
574bacfe |
1537 | $x; |
58cde26e |
1538 | } |
1539 | |
b3abae2a |
1540 | sub bfac |
1541 | { |
28df3e88 |
1542 | # (BFLOAT or num_str, BFLOAT or num_str) return BFLOAT |
b3abae2a |
1543 | # compute factorial numbers |
1544 | # modifies first argument |
1545 | my ($self,$x,@r) = objectify(1,@_); |
1546 | |
28df3e88 |
1547 | return $x->bnan() |
1548 | if (($x->{sign} ne '+') || # inf, NaN, <0 etc => NaN |
1549 | ($x->{_e}->{sign} ne '+')); # digits after dot? |
b3abae2a |
1550 | |
f9a08e12 |
1551 | return $x->bone('+',@r) if $x->is_zero() || $x->is_one(); # 0 or 1 => 1 |
b3abae2a |
1552 | |
1553 | # use BigInt's bfac() for faster calc |
1554 | $x->{_m}->blsft($x->{_e},10); # un-norm m |
1555 | $x->{_e}->bzero(); # norm $x again |
1556 | $x->{_m}->bfac(); # factorial |
28df3e88 |
1557 | $x->bnorm()->round(@r); |
b3abae2a |
1558 | } |
1559 | |
9393ace2 |
1560 | sub _pow |
1561 | { |
1562 | # Calculate a power where $y is a non-integer, like 2 ** 0.5 |
1563 | my ($x,$y,$a,$p,$r) = @_; |
1564 | my $self = ref($x); |
1565 | |
1566 | # if $y == 0.5, it is sqrt($x) |
1567 | return $x->bsqrt($a,$p,$r,$y) if $y->bcmp('0.5') == 0; |
1568 | |
990fb837 |
1569 | # Using: |
1570 | # a ** x == e ** (x * ln a) |
1571 | |
9393ace2 |
1572 | # u = y * ln x |
990fb837 |
1573 | # _ _ |
1574 | # Taylor: | u u^2 u^3 | |
1575 | # x ** y = 1 + | --- + --- + ----- + ... | |
1576 | # |_ 1 1*2 1*2*3 _| |
9393ace2 |
1577 | |
1578 | # we need to limit the accuracy to protect against overflow |
1579 | my $fallback = 0; |
990fb837 |
1580 | my ($scale,@params); |
1581 | ($x,@params) = $x->_find_round_parameters($a,$p,$r); |
1582 | |
1583 | return $x if $x->is_nan(); # error in _find_round_parameters? |
9393ace2 |
1584 | |
1585 | # no rounding at all, so must use fallback |
990fb837 |
1586 | if (scalar @params == 0) |
9393ace2 |
1587 | { |
1588 | # simulate old behaviour |
990fb837 |
1589 | $params[0] = $self->div_scale(); # and round to it as accuracy |
1590 | $params[1] = undef; # disable P |
1591 | $scale = $params[0]+4; # at least four more for proper round |
1592 | $params[2] = $r; # round mode by caller or undef |
9393ace2 |
1593 | $fallback = 1; # to clear a/p afterwards |
1594 | } |
1595 | else |
1596 | { |
1597 | # the 4 below is empirical, and there might be cases where it is not |
1598 | # enough... |
990fb837 |
1599 | $scale = abs($params[0] || $params[1]) + 4; # take whatever is defined |
9393ace2 |
1600 | } |
1601 | |
1602 | # when user set globals, they would interfere with our calculation, so |
56d9de68 |
1603 | # disable them and later re-enable them |
9393ace2 |
1604 | no strict 'refs'; |
1605 | my $abr = "$self\::accuracy"; my $ab = $$abr; $$abr = undef; |
1606 | my $pbr = "$self\::precision"; my $pb = $$pbr; $$pbr = undef; |
1607 | # we also need to disable any set A or P on $x (_find_round_parameters took |
1608 | # them already into account), since these would interfere, too |
1609 | delete $x->{_a}; delete $x->{_p}; |
1610 | # need to disable $upgrade in BigInt, to avoid deep recursion |
1611 | local $Math::BigInt::upgrade = undef; |
1612 | |
1613 | my ($limit,$v,$u,$below,$factor,$next,$over); |
1614 | |
990fb837 |
1615 | $u = $x->copy()->blog(undef,$scale)->bmul($y); |
9393ace2 |
1616 | $v = $self->bone(); # 1 |
1617 | $factor = $self->new(2); # 2 |
1618 | $x->bone(); # first term: 1 |
1619 | |
1620 | $below = $v->copy(); |
1621 | $over = $u->copy(); |
1622 | |
1623 | $limit = $self->new("1E-". ($scale-1)); |
1624 | #my $steps = 0; |
1625 | while (3 < 5) |
1626 | { |
1627 | # we calculate the next term, and add it to the last |
1628 | # when the next term is below our limit, it won't affect the outcome |
1629 | # anymore, so we stop |
1630 | $next = $over->copy()->bdiv($below,$scale); |
990fb837 |
1631 | last if $next->bacmp($limit) <= 0; |
9393ace2 |
1632 | $x->badd($next); |
9393ace2 |
1633 | # calculate things for the next term |
1634 | $over *= $u; $below *= $factor; $factor->binc(); |
1635 | #$steps++; |
1636 | } |
1637 | |
1638 | # shortcut to not run trough _find_round_parameters again |
990fb837 |
1639 | if (defined $params[0]) |
9393ace2 |
1640 | { |
990fb837 |
1641 | $x->bround($params[0],$params[2]); # then round accordingly |
9393ace2 |
1642 | } |
1643 | else |
1644 | { |
990fb837 |
1645 | $x->bfround($params[1],$params[2]); # then round accordingly |
9393ace2 |
1646 | } |
1647 | if ($fallback) |
1648 | { |
1649 | # clear a/p after round, since user did not request it |
1650 | $x->{_a} = undef; $x->{_p} = undef; |
1651 | } |
1652 | # restore globals |
1653 | $$abr = $ab; $$pbr = $pb; |
1654 | $x; |
1655 | } |
1656 | |
58cde26e |
1657 | sub bpow |
1658 | { |
1659 | # (BFLOAT or num_str, BFLOAT or num_str) return BFLOAT |
1660 | # compute power of two numbers, second arg is used as integer |
1661 | # modifies first argument |
1662 | |
f9a08e12 |
1663 | # set up parameters |
1664 | my ($self,$x,$y,$a,$p,$r) = (ref($_[0]),@_); |
1665 | # objectify is costly, so avoid it |
1666 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1667 | { |
1668 | ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
1669 | } |
58cde26e |
1670 | |
0716bf9b |
1671 | return $x if $x->{sign} =~ /^[+-]inf$/; |
58cde26e |
1672 | return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan; |
574bacfe |
1673 | return $x->bone() if $y->is_zero(); |
58cde26e |
1674 | return $x if $x->is_one() || $y->is_one(); |
9393ace2 |
1675 | |
d614cd8b |
1676 | return $x->_pow($y,$a,$p,$r) if !$y->is_int(); # non-integer power |
9393ace2 |
1677 | |
1678 | my $y1 = $y->as_number(); # make bigint |
394e6ffb |
1679 | # if ($x == -1) |
1680 | if ($x->{sign} eq '-' && $x->{_m}->is_one() && $x->{_e}->is_zero()) |
58cde26e |
1681 | { |
1682 | # if $x == -1 and odd/even y => +1/-1 because +-1 ^ (+-1) => +-1 |
0716bf9b |
1683 | return $y1->is_odd() ? $x : $x->babs(1); |
288d023a |
1684 | } |
28df3e88 |
1685 | if ($x->is_zero()) |
1686 | { |
1687 | return $x if $y->{sign} eq '+'; # 0**y => 0 (if not y <= 0) |
1688 | # 0 ** -y => 1 / (0 ** y) => / 0! (1 / 0 => +inf) |
1689 | $x->binf(); |
1690 | } |
58cde26e |
1691 | |
1692 | # calculate $x->{_m} ** $y and $x->{_e} * $y separately (faster) |
1693 | $y1->babs(); |
1694 | $x->{_m}->bpow($y1); |
1695 | $x->{_e}->bmul($y1); |
1696 | $x->{sign} = $nan if $x->{_m}->{sign} eq $nan || $x->{_e}->{sign} eq $nan; |
1697 | $x->bnorm(); |
1698 | if ($y->{sign} eq '-') |
1699 | { |
1700 | # modify $x in place! |
0716bf9b |
1701 | my $z = $x->copy(); $x->bzero()->binc(); |
58cde26e |
1702 | return $x->bdiv($z,$a,$p,$r); # round in one go (might ignore y's A!) |
a0d0e21e |
1703 | } |
28df3e88 |
1704 | $x->round($a,$p,$r,$y); |
58cde26e |
1705 | } |
1706 | |
1707 | ############################################################################### |
1708 | # rounding functions |
1709 | |
1710 | sub bfround |
1711 | { |
1712 | # precision: round to the $Nth digit left (+$n) or right (-$n) from the '.' |
1713 | # $n == 0 means round to integer |
1714 | # expects and returns normalized numbers! |
ee15d750 |
1715 | my $x = shift; my $self = ref($x) || $x; $x = $self->new(shift) if !ref($x); |
a0d0e21e |
1716 | |
58cde26e |
1717 | return $x if $x->modify('bfround'); |
1718 | |
ee15d750 |
1719 | my ($scale,$mode) = $x->_scale_p($self->precision(),$self->round_mode(),@_); |
58cde26e |
1720 | return $x if !defined $scale; # no-op |
1721 | |
574bacfe |
1722 | # never round a 0, +-inf, NaN |
61f5c3f5 |
1723 | if ($x->is_zero()) |
1724 | { |
1725 | $x->{_p} = $scale if !defined $x->{_p} || $x->{_p} < $scale; # -3 < -2 |
1726 | return $x; |
1727 | } |
1728 | return $x if $x->{sign} !~ /^[+-]$/; |
58cde26e |
1729 | |
ee15d750 |
1730 | # don't round if x already has lower precision |
1731 | return $x if (defined $x->{_p} && $x->{_p} < 0 && $scale < $x->{_p}); |
1732 | |
1733 | $x->{_p} = $scale; # remember round in any case |
1734 | $x->{_a} = undef; # and clear A |
58cde26e |
1735 | if ($scale < 0) |
1736 | { |
58cde26e |
1737 | # round right from the '.' |
f9a08e12 |
1738 | |
1739 | return $x if $x->{_e}->{sign} eq '+'; # e >= 0 => nothing to round |
1740 | |
58cde26e |
1741 | $scale = -$scale; # positive for simplicity |
1742 | my $len = $x->{_m}->length(); # length of mantissa |
f9a08e12 |
1743 | |
1744 | # the following poses a restriction on _e, but if _e is bigger than a |
1745 | # scalar, you got other problems (memory etc) anyway |
1746 | my $dad = -($x->{_e}->numify()); # digits after dot |
58cde26e |
1747 | my $zad = 0; # zeros after dot |
f9a08e12 |
1748 | $zad = $dad - $len if (-$dad < -$len); # for 0.00..00xxx style |
1749 | |
ee15d750 |
1750 | #print "scale $scale dad $dad zad $zad len $len\n"; |
58cde26e |
1751 | # number bsstr len zad dad |
1752 | # 0.123 123e-3 3 0 3 |
1753 | # 0.0123 123e-4 3 1 4 |
1754 | # 0.001 1e-3 1 2 3 |
1755 | # 1.23 123e-2 3 0 2 |
1756 | # 1.2345 12345e-4 5 0 4 |
1757 | |
1758 | # do not round after/right of the $dad |
1759 | return $x if $scale > $dad; # 0.123, scale >= 3 => exit |
1760 | |
ee15d750 |
1761 | # round to zero if rounding inside the $zad, but not for last zero like: |
1762 | # 0.0065, scale -2, round last '0' with following '65' (scale == zad case) |
1763 | return $x->bzero() if $scale < $zad; |
1764 | if ($scale == $zad) # for 0.006, scale -3 and trunc |
58cde26e |
1765 | { |
b3abae2a |
1766 | $scale = -$len; |
58cde26e |
1767 | } |
1768 | else |
1769 | { |
1770 | # adjust round-point to be inside mantissa |
1771 | if ($zad != 0) |
1772 | { |
1773 | $scale = $scale-$zad; |
1774 | } |
1775 | else |
1776 | { |
1777 | my $dbd = $len - $dad; $dbd = 0 if $dbd < 0; # digits before dot |
1778 | $scale = $dbd+$scale; |
1779 | } |
1780 | } |
a0d0e21e |
1781 | } |
58cde26e |
1782 | else |
1783 | { |
f9a08e12 |
1784 | # round left from the '.' |
1785 | |
58cde26e |
1786 | # 123 => 100 means length(123) = 3 - $scale (2) => 1 |
a5f75d66 |
1787 | |
b3abae2a |
1788 | my $dbt = $x->{_m}->length(); |
1789 | # digits before dot |
f9a08e12 |
1790 | my $dbd = $dbt + $x->{_e}->numify(); |
b3abae2a |
1791 | # should be the same, so treat it as this |
1792 | $scale = 1 if $scale == 0; |
1793 | # shortcut if already integer |
1794 | return $x if $scale == 1 && $dbt <= $dbd; |
1795 | # maximum digits before dot |
1796 | ++$dbd; |
1797 | |
1798 | if ($scale > $dbd) |
1799 | { |
1800 | # not enough digits before dot, so round to zero |
1801 | return $x->bzero; |
1802 | } |
1803 | elsif ( $scale == $dbd ) |
1804 | { |
1805 | # maximum |
1806 | $scale = -$dbt; |
1807 | } |
58cde26e |
1808 | else |
b3abae2a |
1809 | { |
1810 | $scale = $dbd - $scale; |
1811 | } |
a0d0e21e |
1812 | } |
574bacfe |
1813 | # pass sign to bround for rounding modes '+inf' and '-inf' |
58cde26e |
1814 | $x->{_m}->{sign} = $x->{sign}; |
1815 | $x->{_m}->bround($scale,$mode); |
1816 | $x->{_m}->{sign} = '+'; # fix sign back |
1817 | $x->bnorm(); |
1818 | } |
1819 | |
1820 | sub bround |
1821 | { |
1822 | # accuracy: preserve $N digits, and overwrite the rest with 0's |
ee15d750 |
1823 | my $x = shift; my $self = ref($x) || $x; $x = $self->new(shift) if !ref($x); |
1824 | |
990fb837 |
1825 | if (($_[0] || 0) < 0) |
1826 | { |
1827 | require Carp; Carp::croak ('bround() needs positive accuracy'); |
1828 | } |
58cde26e |
1829 | |
ee15d750 |
1830 | my ($scale,$mode) = $x->_scale_a($self->accuracy(),$self->round_mode(),@_); |
1831 | return $x if !defined $scale; # no-op |
61f5c3f5 |
1832 | |
58cde26e |
1833 | return $x if $x->modify('bround'); |
61f5c3f5 |
1834 | |
ee15d750 |
1835 | # scale is now either $x->{_a}, $accuracy, or the user parameter |
1836 | # test whether $x already has lower accuracy, do nothing in this case |
1837 | # but do round if the accuracy is the same, since a math operation might |
1838 | # want to round a number with A=5 to 5 digits afterwards again |
1839 | return $x if defined $_[0] && defined $x->{_a} && $x->{_a} < $_[0]; |
58cde26e |
1840 | |
61f5c3f5 |
1841 | # scale < 0 makes no sense |
1842 | # never round a +-inf, NaN |
1843 | return $x if ($scale < 0) || $x->{sign} !~ /^[+-]$/; |
58cde26e |
1844 | |
61f5c3f5 |
1845 | # 1: $scale == 0 => keep all digits |
1846 | # 2: never round a 0 |
1847 | # 3: if we should keep more digits than the mantissa has, do nothing |
1848 | if ($scale == 0 || $x->is_zero() || $x->{_m}->length() <= $scale) |
1849 | { |
1850 | $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; |
1851 | return $x; |
1852 | } |
f216259d |
1853 | |
58cde26e |
1854 | # pass sign to bround for '+inf' and '-inf' rounding modes |
1855 | $x->{_m}->{sign} = $x->{sign}; |
1856 | $x->{_m}->bround($scale,$mode); # round mantissa |
1857 | $x->{_m}->{sign} = '+'; # fix sign back |
61f5c3f5 |
1858 | # $x->{_m}->{_a} = undef; $x->{_m}->{_p} = undef; |
ee15d750 |
1859 | $x->{_a} = $scale; # remember rounding |
1860 | $x->{_p} = undef; # and clear P |
574bacfe |
1861 | $x->bnorm(); # del trailing zeros gen. by bround() |
58cde26e |
1862 | } |
1863 | |
1864 | sub bfloor |
1865 | { |
1866 | # return integer less or equal then $x |
ee15d750 |
1867 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e |
1868 | |
1869 | return $x if $x->modify('bfloor'); |
1870 | |
1871 | return $x if $x->{sign} !~ /^[+-]$/; # nan, +inf, -inf |
1872 | |
1873 | # if $x has digits after dot |
1874 | if ($x->{_e}->{sign} eq '-') |
1875 | { |
28df3e88 |
1876 | $x->{_e}->{sign} = '+'; # negate e |
1877 | $x->{_m}->brsft($x->{_e},10); # cut off digits after dot |
1878 | $x->{_e}->bzero(); # trunc/norm |
1879 | $x->{_m}->binc() if $x->{sign} eq '-'; # decrement if negative |
f216259d |
1880 | } |
61f5c3f5 |
1881 | $x->round($a,$p,$r); |
58cde26e |
1882 | } |
288d023a |
1883 | |
58cde26e |
1884 | sub bceil |
1885 | { |
1886 | # return integer greater or equal then $x |
ee15d750 |
1887 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e |
1888 | |
1889 | return $x if $x->modify('bceil'); |
1890 | return $x if $x->{sign} !~ /^[+-]$/; # nan, +inf, -inf |
1891 | |
1892 | # if $x has digits after dot |
1893 | if ($x->{_e}->{sign} eq '-') |
1894 | { |
28df3e88 |
1895 | #$x->{_m}->brsft(-$x->{_e},10); |
1896 | #$x->{_e}->bzero(); |
1897 | #$x++ if $x->{sign} eq '+'; |
1898 | |
1899 | $x->{_e}->{sign} = '+'; # negate e |
1900 | $x->{_m}->brsft($x->{_e},10); # cut off digits after dot |
1901 | $x->{_e}->bzero(); # trunc/norm |
1902 | $x->{_m}->binc() if $x->{sign} eq '+'; # decrement if negative |
a0d0e21e |
1903 | } |
61f5c3f5 |
1904 | $x->round($a,$p,$r); |
58cde26e |
1905 | } |
1906 | |
394e6ffb |
1907 | sub brsft |
1908 | { |
f9a08e12 |
1909 | # shift right by $y (divide by power of $n) |
1910 | |
1911 | # set up parameters |
1912 | my ($self,$x,$y,$n,$a,$p,$r) = (ref($_[0]),@_); |
1913 | # objectify is costly, so avoid it |
1914 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1915 | { |
1916 | ($self,$x,$y,$n,$a,$p,$r) = objectify(2,@_); |
1917 | } |
394e6ffb |
1918 | |
1919 | return $x if $x->modify('brsft'); |
1920 | return $x if $x->{sign} !~ /^[+-]$/; # nan, +inf, -inf |
1921 | |
f9a08e12 |
1922 | $n = 2 if !defined $n; $n = $self->new($n); |
1923 | $x->bdiv($n->bpow($y),$a,$p,$r,$y); |
394e6ffb |
1924 | } |
1925 | |
1926 | sub blsft |
1927 | { |
f9a08e12 |
1928 | # shift left by $y (multiply by power of $n) |
1929 | |
1930 | # set up parameters |
1931 | my ($self,$x,$y,$n,$a,$p,$r) = (ref($_[0]),@_); |
1932 | # objectify is costly, so avoid it |
1933 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1934 | { |
1935 | ($self,$x,$y,$n,$a,$p,$r) = objectify(2,@_); |
1936 | } |
394e6ffb |
1937 | |
f9a08e12 |
1938 | return $x if $x->modify('blsft'); |
394e6ffb |
1939 | return $x if $x->{sign} !~ /^[+-]$/; # nan, +inf, -inf |
1940 | |
f9a08e12 |
1941 | $n = 2 if !defined $n; $n = $self->new($n); |
1942 | $x->bmul($n->bpow($y),$a,$p,$r,$y); |
394e6ffb |
1943 | } |
1944 | |
58cde26e |
1945 | ############################################################################### |
a5f75d66 |
1946 | |
58cde26e |
1947 | sub DESTROY |
1948 | { |
ee15d750 |
1949 | # going through AUTOLOAD for every DESTROY is costly, so avoid it by empty sub |
58cde26e |
1950 | } |
1951 | |
1952 | sub AUTOLOAD |
1953 | { |
b3abae2a |
1954 | # make fxxx and bxxx both work by selectively mapping fxxx() to MBF::bxxx() |
1955 | # or falling back to MBI::bxxx() |
58cde26e |
1956 | my $name = $AUTOLOAD; |
1957 | |
1958 | $name =~ s/.*:://; # split package |
ee15d750 |
1959 | no strict 'refs'; |
990fb837 |
1960 | $class->import() if $IMPORT == 0; |
ee15d750 |
1961 | if (!method_alias($name)) |
58cde26e |
1962 | { |
ee15d750 |
1963 | if (!defined $name) |
1964 | { |
1965 | # delayed load of Carp and avoid recursion |
1966 | require Carp; |
1967 | Carp::croak ("Can't call a method without name"); |
1968 | } |
ee15d750 |
1969 | if (!method_hand_up($name)) |
1970 | { |
1971 | # delayed load of Carp and avoid recursion |
1972 | require Carp; |
1973 | Carp::croak ("Can't call $class\-\>$name, not a valid method"); |
1974 | } |
1975 | # try one level up, but subst. bxxx() for fxxx() since MBI only got bxxx() |
1976 | $name =~ s/^f/b/; |
56b9c951 |
1977 | return &{"$MBI"."::$name"}(@_); |
a0d0e21e |
1978 | } |
58cde26e |
1979 | my $bname = $name; $bname =~ s/^f/b/; |
b3abae2a |
1980 | *{$class."::$name"} = \&$bname; |
58cde26e |
1981 | &$bname; # uses @_ |
1982 | } |
1983 | |
1984 | sub exponent |
1985 | { |
1986 | # return a copy of the exponent |
ee15d750 |
1987 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
1988 | |
ee15d750 |
1989 | if ($x->{sign} !~ /^[+-]$/) |
1990 | { |
1991 | my $s = $x->{sign}; $s =~ s/^[+-]//; |
1992 | return $self->new($s); # -inf, +inf => +inf |
1993 | } |
1994 | return $x->{_e}->copy(); |
58cde26e |
1995 | } |
1996 | |
1997 | sub mantissa |
1998 | { |
1999 | # return a copy of the mantissa |
ee15d750 |
2000 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
2001 | |
ee15d750 |
2002 | if ($x->{sign} !~ /^[+-]$/) |
2003 | { |
2004 | my $s = $x->{sign}; $s =~ s/^[+]//; |
2005 | return $self->new($s); # -inf, +inf => +inf |
2006 | } |
2007 | my $m = $x->{_m}->copy(); # faster than going via bstr() |
2008 | $m->bneg() if $x->{sign} eq '-'; |
58cde26e |
2009 | |
61f5c3f5 |
2010 | $m; |
58cde26e |
2011 | } |
2012 | |
2013 | sub parts |
2014 | { |
2015 | # return a copy of both the exponent and the mantissa |
ee15d750 |
2016 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
2017 | |
ee15d750 |
2018 | if ($x->{sign} !~ /^[+-]$/) |
2019 | { |
2020 | my $s = $x->{sign}; $s =~ s/^[+]//; my $se = $s; $se =~ s/^[-]//; |
2021 | return ($self->new($s),$self->new($se)); # +inf => inf and -inf,+inf => inf |
2022 | } |
2023 | my $m = $x->{_m}->copy(); # faster than going via bstr() |
2024 | $m->bneg() if $x->{sign} eq '-'; |
2025 | return ($m,$x->{_e}->copy()); |
58cde26e |
2026 | } |
2027 | |
2028 | ############################################################################## |
2029 | # private stuff (internal use only) |
2030 | |
58cde26e |
2031 | sub import |
2032 | { |
2033 | my $self = shift; |
8f675a64 |
2034 | my $l = scalar @_; |
2035 | my $lib = ''; my @a; |
990fb837 |
2036 | $IMPORT=1; |
8f675a64 |
2037 | for ( my $i = 0; $i < $l ; $i++) |
58cde26e |
2038 | { |
2039 | if ( $_[$i] eq ':constant' ) |
2040 | { |
2041 | # this rest causes overlord er load to step in |
58cde26e |
2042 | overload::constant float => sub { $self->new(shift); }; |
b3abae2a |
2043 | } |
2044 | elsif ($_[$i] eq 'upgrade') |
2045 | { |
2046 | # this causes upgrading |
28df3e88 |
2047 | $upgrade = $_[$i+1]; # or undef to disable |
8f675a64 |
2048 | $i++; |
28df3e88 |
2049 | } |
2050 | elsif ($_[$i] eq 'downgrade') |
2051 | { |
2052 | # this causes downgrading |
2053 | $downgrade = $_[$i+1]; # or undef to disable |
8f675a64 |
2054 | $i++; |
58cde26e |
2055 | } |
56b9c951 |
2056 | elsif ($_[$i] eq 'lib') |
2057 | { |
990fb837 |
2058 | # alternative library |
56b9c951 |
2059 | $lib = $_[$i+1] || ''; # default Calc |
8f675a64 |
2060 | $i++; |
56b9c951 |
2061 | } |
2062 | elsif ($_[$i] eq 'with') |
2063 | { |
990fb837 |
2064 | # alternative class for our private parts() |
56b9c951 |
2065 | $MBI = $_[$i+1] || 'Math::BigInt'; # default Math::BigInt |
8f675a64 |
2066 | $i++; |
2067 | } |
2068 | else |
2069 | { |
2070 | push @a, $_[$i]; |
56b9c951 |
2071 | } |
58cde26e |
2072 | } |
8f675a64 |
2073 | |
56b9c951 |
2074 | # let use Math::BigInt lib => 'GMP'; use Math::BigFloat; still work |
2075 | my $mbilib = eval { Math::BigInt->config()->{lib} }; |
8f675a64 |
2076 | if ((defined $mbilib) && ($MBI eq 'Math::BigInt')) |
2077 | { |
2078 | # MBI already loaded |
2079 | $MBI->import('lib',"$lib,$mbilib", 'objectify'); |
2080 | } |
2081 | else |
2082 | { |
2083 | # MBI not loaded, or with ne "Math::BigInt" |
2084 | $lib .= ",$mbilib" if defined $mbilib; |
07d34614 |
2085 | $lib =~ s/^,//; # don't leave empty |
990fb837 |
2086 | # replacement library can handle lib statement, but also could ignore it |
8f675a64 |
2087 | if ($] < 5.006) |
2088 | { |
2089 | # Perl < 5.6.0 dies with "out of memory!" when eval() and ':constant' is |
2090 | # used in the same script, or eval inside import(). |
2091 | my @parts = split /::/, $MBI; # Math::BigInt => Math BigInt |
2092 | my $file = pop @parts; $file .= '.pm'; # BigInt => BigInt.pm |
07d34614 |
2093 | require File::Spec; |
8f675a64 |
2094 | $file = File::Spec->catfile (@parts, $file); |
07d34614 |
2095 | eval { require "$file"; }; |
2096 | $MBI->import( lib => $lib, 'objectify' ); |
8f675a64 |
2097 | } |
2098 | else |
2099 | { |
2100 | my $rc = "use $MBI lib => '$lib', 'objectify';"; |
2101 | eval $rc; |
2102 | } |
2103 | } |
990fb837 |
2104 | if ($@) |
2105 | { |
2106 | require Carp; Carp::croak ("Couldn't load $MBI: $! $@"); |
2107 | } |
56b9c951 |
2108 | |
58cde26e |
2109 | # any non :constant stuff is handled by our parent, Exporter |
2110 | # even if @_ is empty, to give it a chance |
b3abae2a |
2111 | $self->SUPER::import(@a); # for subclasses |
2112 | $self->export_to_level(1,$self,@a); # need this, too |
58cde26e |
2113 | } |
2114 | |
2115 | sub bnorm |
2116 | { |
2117 | # adjust m and e so that m is smallest possible |
2118 | # round number according to accuracy and precision settings |
ee15d750 |
2119 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
2120 | |
0716bf9b |
2121 | return $x if $x->{sign} !~ /^[+-]$/; # inf, nan etc |
58cde26e |
2122 | |
28df3e88 |
2123 | # if (!$x->{_m}->is_odd()) |
2124 | # { |
2125 | my $zeros = $x->{_m}->_trailing_zeros(); # correct for trailing zeros |
2126 | if ($zeros != 0) |
2127 | { |
2128 | $x->{_m}->brsft($zeros,10); $x->{_e}->badd($zeros); |
2129 | } |
2130 | # for something like 0Ey, set y to 1, and -0 => +0 |
2131 | $x->{sign} = '+', $x->{_e}->bone() if $x->{_m}->is_zero(); |
2132 | # } |
ee15d750 |
2133 | # this is to prevent automatically rounding when MBI's globals are set |
0716bf9b |
2134 | $x->{_m}->{_f} = MB_NEVER_ROUND; |
2135 | $x->{_e}->{_f} = MB_NEVER_ROUND; |
ee15d750 |
2136 | # 'forget' that mantissa was rounded via MBI::bround() in MBF's bfround() |
2137 | $x->{_m}->{_a} = undef; $x->{_e}->{_a} = undef; |
2138 | $x->{_m}->{_p} = undef; $x->{_e}->{_p} = undef; |
61f5c3f5 |
2139 | $x; # MBI bnorm is no-op, so dont call it |
2140 | } |
58cde26e |
2141 | |
2142 | ############################################################################## |
56d9de68 |
2143 | |
2144 | sub as_hex |
2145 | { |
2146 | # return number as hexadecimal string (only for integers defined) |
2147 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
2148 | |
2149 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc |
2150 | return '0x0' if $x->is_zero(); |
2151 | |
990fb837 |
2152 | return $nan if $x->{_e}->{sign} ne '+'; # how to do 1e-1 in hex!? |
56d9de68 |
2153 | |
2154 | my $z = $x->{_m}->copy(); |
2155 | if (!$x->{_e}->is_zero()) # > 0 |
2156 | { |
2157 | $z->blsft($x->{_e},10); |
2158 | } |
2159 | $z->{sign} = $x->{sign}; |
2160 | $z->as_hex(); |
2161 | } |
2162 | |
2163 | sub as_bin |
2164 | { |
2165 | # return number as binary digit string (only for integers defined) |
2166 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
2167 | |
2168 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc |
2169 | return '0b0' if $x->is_zero(); |
2170 | |
990fb837 |
2171 | return $nan if $x->{_e}->{sign} ne '+'; # how to do 1e-1 in hex!? |
56d9de68 |
2172 | |
2173 | my $z = $x->{_m}->copy(); |
2174 | if (!$x->{_e}->is_zero()) # > 0 |
2175 | { |
2176 | $z->blsft($x->{_e},10); |
2177 | } |
2178 | $z->{sign} = $x->{sign}; |
2179 | $z->as_bin(); |
2180 | } |
58cde26e |
2181 | |
2182 | sub as_number |
2183 | { |
394e6ffb |
2184 | # return copy as a bigint representation of this BigFloat number |
2185 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
2186 | |
28df3e88 |
2187 | my $z = $x->{_m}->copy(); |
2188 | if ($x->{_e}->{sign} eq '-') # < 0 |
58cde26e |
2189 | { |
28df3e88 |
2190 | $x->{_e}->{sign} = '+'; # flip |
2191 | $z->brsft($x->{_e},10); |
2192 | $x->{_e}->{sign} = '-'; # flip back |
0716bf9b |
2193 | } |
28df3e88 |
2194 | elsif (!$x->{_e}->is_zero()) # > 0 |
0716bf9b |
2195 | { |
2196 | $z->blsft($x->{_e},10); |
58cde26e |
2197 | } |
58cde26e |
2198 | $z->{sign} = $x->{sign}; |
61f5c3f5 |
2199 | $z; |
58cde26e |
2200 | } |
2201 | |
2202 | sub length |
2203 | { |
ee15d750 |
2204 | my $x = shift; |
2205 | my $class = ref($x) || $x; |
2206 | $x = $class->new(shift) unless ref($x); |
58cde26e |
2207 | |
ee15d750 |
2208 | return 1 if $x->{_m}->is_zero(); |
58cde26e |
2209 | my $len = $x->{_m}->length(); |
2210 | $len += $x->{_e} if $x->{_e}->sign() eq '+'; |
2211 | if (wantarray()) |
2212 | { |
56b9c951 |
2213 | my $t = $MBI->bzero(); |
58cde26e |
2214 | $t = $x->{_e}->copy()->babs() if $x->{_e}->sign() eq '-'; |
2215 | return ($len,$t); |
2216 | } |
61f5c3f5 |
2217 | $len; |
58cde26e |
2218 | } |
a0d0e21e |
2219 | |
2220 | 1; |
a5f75d66 |
2221 | __END__ |
2222 | |
2223 | =head1 NAME |
2224 | |
58cde26e |
2225 | Math::BigFloat - Arbitrary size floating point math package |
a5f75d66 |
2226 | |
2227 | =head1 SYNOPSIS |
2228 | |
a2008d6d |
2229 | use Math::BigFloat; |
58cde26e |
2230 | |
b3abae2a |
2231 | # Number creation |
2232 | $x = Math::BigFloat->new($str); # defaults to 0 |
2233 | $nan = Math::BigFloat->bnan(); # create a NotANumber |
2234 | $zero = Math::BigFloat->bzero(); # create a +0 |
2235 | $inf = Math::BigFloat->binf(); # create a +inf |
2236 | $inf = Math::BigFloat->binf('-'); # create a -inf |
2237 | $one = Math::BigFloat->bone(); # create a +1 |
2238 | $one = Math::BigFloat->bone('-'); # create a -1 |
58cde26e |
2239 | |
2240 | # Testing |
b3abae2a |
2241 | $x->is_zero(); # true if arg is +0 |
2242 | $x->is_nan(); # true if arg is NaN |
0716bf9b |
2243 | $x->is_one(); # true if arg is +1 |
2244 | $x->is_one('-'); # true if arg is -1 |
2245 | $x->is_odd(); # true if odd, false for even |
2246 | $x->is_even(); # true if even, false for odd |
2247 | $x->is_positive(); # true if >= 0 |
2248 | $x->is_negative(); # true if < 0 |
b3abae2a |
2249 | $x->is_inf(sign); # true if +inf, or -inf (default is '+') |
2250 | |
58cde26e |
2251 | $x->bcmp($y); # compare numbers (undef,<0,=0,>0) |
2252 | $x->bacmp($y); # compare absolutely (undef,<0,=0,>0) |
2253 | $x->sign(); # return the sign, either +,- or NaN |
b3abae2a |
2254 | $x->digit($n); # return the nth digit, counting from right |
2255 | $x->digit(-$n); # return the nth digit, counting from left |
58cde26e |
2256 | |
990fb837 |
2257 | # The following all modify their first argument. If you want to preserve |
2258 | # $x, use $z = $x->copy()->bXXX($y); See under L<CAVEATS> for why this is |
2259 | # neccessary when mixing $a = $b assigments with non-overloaded math. |
2260 | |
58cde26e |
2261 | # set |
2262 | $x->bzero(); # set $i to 0 |
2263 | $x->bnan(); # set $i to NaN |
b3abae2a |
2264 | $x->bone(); # set $x to +1 |
2265 | $x->bone('-'); # set $x to -1 |
2266 | $x->binf(); # set $x to inf |
2267 | $x->binf('-'); # set $x to -inf |
58cde26e |
2268 | |
2269 | $x->bneg(); # negation |
2270 | $x->babs(); # absolute value |
2271 | $x->bnorm(); # normalize (no-op) |
2272 | $x->bnot(); # two's complement (bit wise not) |
2273 | $x->binc(); # increment x by 1 |
2274 | $x->bdec(); # decrement x by 1 |
2275 | |
2276 | $x->badd($y); # addition (add $y to $x) |
2277 | $x->bsub($y); # subtraction (subtract $y from $x) |
2278 | $x->bmul($y); # multiplication (multiply $x by $y) |
990fb837 |
2279 | $x->bdiv($y); # divide, set $x to quotient |
58cde26e |
2280 | # return (quo,rem) or quo if scalar |
2281 | |
990fb837 |
2282 | $x->bmod($y); # modulus ($x % $y) |
2283 | $x->bpow($y); # power of arguments ($x ** $y) |
58cde26e |
2284 | $x->blsft($y); # left shift |
2285 | $x->brsft($y); # right shift |
2286 | # return (quo,rem) or quo if scalar |
2287 | |
990fb837 |
2288 | $x->blog(); # logarithm of $x to base e (Euler's number) |
2289 | $x->blog($base); # logarithm of $x to base $base (f.i. 2) |
61f5c3f5 |
2290 | |
58cde26e |
2291 | $x->band($y); # bit-wise and |
2292 | $x->bior($y); # bit-wise inclusive or |
2293 | $x->bxor($y); # bit-wise exclusive or |
2294 | $x->bnot(); # bit-wise not (two's complement) |
b3abae2a |
2295 | |
2296 | $x->bsqrt(); # calculate square-root |
990fb837 |
2297 | $x->broot($y); # $y'th root of $x (e.g. $y == 3 => cubic root) |
b3abae2a |
2298 | $x->bfac(); # factorial of $x (1*2*3*4*..$x) |
2299 | |
990fb837 |
2300 | $x->bround($N); # accuracy: preserve $N digits |
58cde26e |
2301 | $x->bfround($N); # precision: round to the $Nth digit |
2302 | |
990fb837 |
2303 | $x->bfloor(); # return integer less or equal than $x |
2304 | $x->bceil(); # return integer greater or equal than $x |
2305 | |
58cde26e |
2306 | # The following do not modify their arguments: |
990fb837 |
2307 | |
58cde26e |
2308 | bgcd(@values); # greatest common divisor |
2309 | blcm(@values); # lowest common multiplicator |
2310 | |
2311 | $x->bstr(); # return string |
2312 | $x->bsstr(); # return string in scientific notation |
b3abae2a |
2313 | |
58cde26e |
2314 | $x->exponent(); # return exponent as BigInt |
2315 | $x->mantissa(); # return mantissa as BigInt |
2316 | $x->parts(); # return (mantissa,exponent) as BigInt |
2317 | |
2318 | $x->length(); # number of digits (w/o sign and '.') |
2319 | ($l,$f) = $x->length(); # number of digits, and length of fraction |
a5f75d66 |
2320 | |
f9a08e12 |
2321 | $x->precision(); # return P of $x (or global, if P of $x undef) |
2322 | $x->precision($n); # set P of $x to $n |
2323 | $x->accuracy(); # return A of $x (or global, if A of $x undef) |
723d369b |
2324 | $x->accuracy($n); # set A $x to $n |
f9a08e12 |
2325 | |
990fb837 |
2326 | # these get/set the appropriate global value for all BigFloat objects |
2327 | Math::BigFloat->precision(); # Precision |
2328 | Math::BigFloat->accuracy(); # Accuracy |
2329 | Math::BigFloat->round_mode(); # rounding mode |
f9a08e12 |
2330 | |
a5f75d66 |
2331 | =head1 DESCRIPTION |
2332 | |
58cde26e |
2333 | All operators (inlcuding basic math operations) are overloaded if you |
2334 | declare your big floating point numbers as |
a5f75d66 |
2335 | |
58cde26e |
2336 | $i = new Math::BigFloat '12_3.456_789_123_456_789E-2'; |
2337 | |
2338 | Operations with overloaded operators preserve the arguments, which is |
2339 | exactly what you expect. |
2340 | |
2341 | =head2 Canonical notation |
2342 | |
2343 | Input to these routines are either BigFloat objects, or strings of the |
2344 | following four forms: |
a5f75d66 |
2345 | |
2346 | =over 2 |
2347 | |
58cde26e |
2348 | =item * |
2349 | |
2350 | C</^[+-]\d+$/> |
a5f75d66 |
2351 | |
58cde26e |
2352 | =item * |
a5f75d66 |
2353 | |
58cde26e |
2354 | C</^[+-]\d+\.\d*$/> |
a5f75d66 |
2355 | |
58cde26e |
2356 | =item * |
a5f75d66 |
2357 | |
58cde26e |
2358 | C</^[+-]\d+E[+-]?\d+$/> |
a5f75d66 |
2359 | |
58cde26e |
2360 | =item * |
a5f75d66 |
2361 | |
58cde26e |
2362 | C</^[+-]\d*\.\d+E[+-]?\d+$/> |
5d7098d5 |
2363 | |
58cde26e |
2364 | =back |
2365 | |
2366 | all with optional leading and trailing zeros and/or spaces. Additonally, |
2367 | numbers are allowed to have an underscore between any two digits. |
2368 | |
2369 | Empty strings as well as other illegal numbers results in 'NaN'. |
2370 | |
2371 | bnorm() on a BigFloat object is now effectively a no-op, since the numbers |
2372 | are always stored in normalized form. On a string, it creates a BigFloat |
2373 | object. |
2374 | |
2375 | =head2 Output |
2376 | |
2377 | Output values are BigFloat objects (normalized), except for bstr() and bsstr(). |
2378 | |
2379 | The string output will always have leading and trailing zeros stripped and drop |
2380 | a plus sign. C<bstr()> will give you always the form with a decimal point, |
990fb837 |
2381 | while C<bsstr()> (s for scientific) gives you the scientific notation. |
58cde26e |
2382 | |
2383 | Input bstr() bsstr() |
2384 | '-0' '0' '0E1' |
2385 | ' -123 123 123' '-123123123' '-123123123E0' |
2386 | '00.0123' '0.0123' '123E-4' |
2387 | '123.45E-2' '1.2345' '12345E-4' |
2388 | '10E+3' '10000' '1E4' |
2389 | |
2390 | Some routines (C<is_odd()>, C<is_even()>, C<is_zero()>, C<is_one()>, |
2391 | C<is_nan()>) return true or false, while others (C<bcmp()>, C<bacmp()>) |
2392 | return either undef, <0, 0 or >0 and are suited for sort. |
2393 | |
990fb837 |
2394 | Actual math is done by using the class defined with C<with => Class;> (which |
2395 | defaults to BigInts) to represent the mantissa and exponent. |
2396 | |
58cde26e |
2397 | The sign C</^[+-]$/> is stored separately. The string 'NaN' is used to |
2398 | represent the result when input arguments are not numbers, as well as |
2399 | the result of dividing by zero. |
2400 | |
2401 | =head2 C<mantissa()>, C<exponent()> and C<parts()> |
2402 | |
2403 | C<mantissa()> and C<exponent()> return the said parts of the BigFloat |
2404 | as BigInts such that: |
2405 | |
2406 | $m = $x->mantissa(); |
2407 | $e = $x->exponent(); |
2408 | $y = $m * ( 10 ** $e ); |
2409 | print "ok\n" if $x == $y; |
2410 | |
2411 | C<< ($m,$e) = $x->parts(); >> is just a shortcut giving you both of them. |
2412 | |
2413 | A zero is represented and returned as C<0E1>, B<not> C<0E0> (after Knuth). |
2414 | |
2415 | Currently the mantissa is reduced as much as possible, favouring higher |
2416 | exponents over lower ones (e.g. returning 1e7 instead of 10e6 or 10000000e0). |
2417 | This might change in the future, so do not depend on it. |
2418 | |
2419 | =head2 Accuracy vs. Precision |
2420 | |
2421 | See also: L<Rounding|Rounding>. |
2422 | |
027dc388 |
2423 | Math::BigFloat supports both precision and accuracy. For a full documentation, |
2424 | examples and tips on these topics please see the large section in |
2425 | L<Math::BigInt>. |
5d7098d5 |
2426 | |
58cde26e |
2427 | Since things like sqrt(2) or 1/3 must presented with a limited precision lest |
2428 | a operation consumes all resources, each operation produces no more than |
990fb837 |
2429 | the requested number of digits. |
2430 | |
2431 | Please refer to BigInt's documentation for the precedence rules of which |
2432 | accuracy/precision setting will be used. |
2433 | |
2434 | If there is no gloabl precision set, B<and> the operation inquestion was not |
2435 | called with a requested precision or accuracy, B<and> the input $x has no |
2436 | accuracy or precision set, then a fallback parameter will be used. For |
2437 | historical reasons, it is called C<div_scale> and can be accessed via: |
2438 | |
2439 | $d = Math::BigFloat->div_scale(); # query |
2440 | Math::BigFloat->div_scale($n); # set to $n digits |
2441 | |
2442 | The default value is 40 digits. |
58cde26e |
2443 | |
2444 | In case the result of one operation has more precision than specified, |
2445 | it is rounded. The rounding mode taken is either the default mode, or the one |
2446 | supplied to the operation after the I<scale>: |
2447 | |
2448 | $x = Math::BigFloat->new(2); |
990fb837 |
2449 | Math::BigFloat->precision(5); # 5 digits max |
58cde26e |
2450 | $y = $x->copy()->bdiv(3); # will give 0.66666 |
2451 | $y = $x->copy()->bdiv(3,6); # will give 0.666666 |
2452 | $y = $x->copy()->bdiv(3,6,'odd'); # will give 0.666667 |
990fb837 |
2453 | Math::BigFloat->round_mode('zero'); |
58cde26e |
2454 | $y = $x->copy()->bdiv(3,6); # will give 0.666666 |
2455 | |
2456 | =head2 Rounding |
2457 | |
2458 | =over 2 |
2459 | |
5dc6f178 |
2460 | =item ffround ( +$scale ) |
58cde26e |
2461 | |
0716bf9b |
2462 | Rounds to the $scale'th place left from the '.', counting from the dot. |
2463 | The first digit is numbered 1. |
58cde26e |
2464 | |
5dc6f178 |
2465 | =item ffround ( -$scale ) |
58cde26e |
2466 | |
0716bf9b |
2467 | Rounds to the $scale'th place right from the '.', counting from the dot. |
58cde26e |
2468 | |
5dc6f178 |
2469 | =item ffround ( 0 ) |
2470 | |
0716bf9b |
2471 | Rounds to an integer. |
5dc6f178 |
2472 | |
2473 | =item fround ( +$scale ) |
2474 | |
0716bf9b |
2475 | Preserves accuracy to $scale digits from the left (aka significant digits) |
2476 | and pads the rest with zeros. If the number is between 1 and -1, the |
2477 | significant digits count from the first non-zero after the '.' |
5dc6f178 |
2478 | |
2479 | =item fround ( -$scale ) and fround ( 0 ) |
2480 | |
990fb837 |
2481 | These are effectively no-ops. |
5d7098d5 |
2482 | |
a5f75d66 |
2483 | =back |
2484 | |
0716bf9b |
2485 | All rounding functions take as a second parameter a rounding mode from one of |
2486 | the following: 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'. |
58cde26e |
2487 | |
2488 | The default rounding mode is 'even'. By using |
990fb837 |
2489 | C<< Math::BigFloat->round_mode($round_mode); >> you can get and set the default |
ee15d750 |
2490 | mode for subsequent rounding. The usage of C<$Math::BigFloat::$round_mode> is |
0716bf9b |
2491 | no longer supported. |
b22b3e31 |
2492 | The second parameter to the round functions then overrides the default |
0716bf9b |
2493 | temporarily. |
58cde26e |
2494 | |
990fb837 |
2495 | The C<as_number()> function returns a BigInt from a Math::BigFloat. It uses |
58cde26e |
2496 | 'trunc' as rounding mode to make it equivalent to: |
2497 | |
2498 | $x = 2.5; |
2499 | $y = int($x) + 2; |
2500 | |
2501 | You can override this by passing the desired rounding mode as parameter to |
2502 | C<as_number()>: |
2503 | |
2504 | $x = Math::BigFloat->new(2.5); |
2505 | $y = $x->as_number('odd'); # $y = 3 |
2506 | |
2507 | =head1 EXAMPLES |
2508 | |
58cde26e |
2509 | # not ready yet |
58cde26e |
2510 | |
2511 | =head1 Autocreating constants |
2512 | |
2513 | After C<use Math::BigFloat ':constant'> all the floating point constants |
2514 | in the given scope are converted to C<Math::BigFloat>. This conversion |
2515 | happens at compile time. |
2516 | |
2517 | In particular |
2518 | |
2519 | perl -MMath::BigFloat=:constant -e 'print 2E-100,"\n"' |
2520 | |
56b9c951 |
2521 | prints the value of C<2E-100>. Note that without conversion of |
58cde26e |
2522 | constants the expression 2E-100 will be calculated as normal floating point |
2523 | number. |
2524 | |
56b9c951 |
2525 | Please note that ':constant' does not affect integer constants, nor binary |
2526 | nor hexadecimal constants. Use L<bignum> or L<Math::BigInt> to get this to |
2527 | work. |
2528 | |
2529 | =head2 Math library |
2530 | |
2531 | Math with the numbers is done (by default) by a module called |
2532 | Math::BigInt::Calc. This is equivalent to saying: |
2533 | |
2534 | use Math::BigFloat lib => 'Calc'; |
2535 | |
2536 | You can change this by using: |
2537 | |
2538 | use Math::BigFloat lib => 'BitVect'; |
2539 | |
2540 | The following would first try to find Math::BigInt::Foo, then |
2541 | Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: |
2542 | |
2543 | use Math::BigFloat lib => 'Foo,Math::BigInt::Bar'; |
2544 | |
2545 | Calc.pm uses as internal format an array of elements of some decimal base |
2546 | (usually 1e7, but this might be differen for some systems) with the least |
2547 | significant digit first, while BitVect.pm uses a bit vector of base 2, most |
2548 | significant bit first. Other modules might use even different means of |
2549 | representing the numbers. See the respective module documentation for further |
2550 | details. |
2551 | |
2552 | Please note that Math::BigFloat does B<not> use the denoted library itself, |
2553 | but it merely passes the lib argument to Math::BigInt. So, instead of the need |
2554 | to do: |
2555 | |
2556 | use Math::BigInt lib => 'GMP'; |
2557 | use Math::BigFloat; |
2558 | |
2559 | you can roll it all into one line: |
2560 | |
2561 | use Math::BigFloat lib => 'GMP'; |
2562 | |
990fb837 |
2563 | It is also possible to just require Math::BigFloat: |
2564 | |
2565 | require Math::BigFloat; |
2566 | |
2567 | This will load the neccessary things (like BigInt) when they are needed, and |
2568 | automatically. |
2569 | |
2570 | Use the lib, Luke! And see L<Using Math::BigInt::Lite> for more details than |
2571 | you ever wanted to know about loading a different library. |
56b9c951 |
2572 | |
2573 | =head2 Using Math::BigInt::Lite |
2574 | |
2575 | It is possible to use L<Math::BigInt::Lite> with Math::BigFloat: |
2576 | |
2577 | # 1 |
2578 | use Math::BigFloat with => 'Math::BigInt::Lite'; |
2579 | |
2580 | There is no need to "use Math::BigInt" or "use Math::BigInt::Lite", but you |
2581 | can combine these if you want. For instance, you may want to use |
2582 | Math::BigInt objects in your main script, too. |
2583 | |
2584 | # 2 |
2585 | use Math::BigInt; |
2586 | use Math::BigFloat with => 'Math::BigInt::Lite'; |
2587 | |
2588 | Of course, you can combine this with the C<lib> parameter. |
2589 | |
2590 | # 3 |
2591 | use Math::BigFloat with => 'Math::BigInt::Lite', lib => 'GMP,Pari'; |
2592 | |
990fb837 |
2593 | There is no need for a "use Math::BigInt;" statement, even if you want to |
2594 | use Math::BigInt's, since Math::BigFloat will needs Math::BigInt and thus |
2595 | always loads it. But if you add it, add it B<before>: |
56b9c951 |
2596 | |
2597 | # 4 |
2598 | use Math::BigInt; |
2599 | use Math::BigFloat with => 'Math::BigInt::Lite', lib => 'GMP,Pari'; |
2600 | |
2601 | Notice that the module with the last C<lib> will "win" and thus |
2602 | it's lib will be used if the lib is available: |
2603 | |
2604 | # 5 |
2605 | use Math::BigInt lib => 'Bar,Baz'; |
2606 | use Math::BigFloat with => 'Math::BigInt::Lite', lib => 'Foo'; |
2607 | |
2608 | That would try to load Foo, Bar, Baz and Calc (in that order). Or in other |
2609 | words, Math::BigFloat will try to retain previously loaded libs when you |
990fb837 |
2610 | don't specify it onem but if you specify one, it will try to load them. |
56b9c951 |
2611 | |
2612 | Actually, the lib loading order would be "Bar,Baz,Calc", and then |
2613 | "Foo,Bar,Baz,Calc", but independend of which lib exists, the result is the |
990fb837 |
2614 | same as trying the latter load alone, except for the fact that one of Bar or |
2615 | Baz might be loaded needlessly in an intermidiate step (and thus hang around |
2616 | and waste memory). If neither Bar nor Baz exist (or don't work/compile), they |
2617 | will still be tried to be loaded, but this is not as time/memory consuming as |
2618 | actually loading one of them. Still, this type of usage is not recommended due |
2619 | to these issues. |
56b9c951 |
2620 | |
990fb837 |
2621 | The old way (loading the lib only in BigInt) still works though: |
56b9c951 |
2622 | |
2623 | # 6 |
2624 | use Math::BigInt lib => 'Bar,Baz'; |
2625 | use Math::BigFloat; |
2626 | |
990fb837 |
2627 | You can even load Math::BigInt afterwards: |
56b9c951 |
2628 | |
990fb837 |
2629 | # 7 |
2630 | use Math::BigFloat; |
2631 | use Math::BigInt lib => 'Bar,Baz'; |
a5f75d66 |
2632 | |
990fb837 |
2633 | But this has the same problems like #5, it will first load Calc |
2634 | (Math::BigFloat needs Math::BigInt and thus loads it) and then later Bar or |
2635 | Baz, depending on which of them works and is usable/loadable. Since this |
2636 | loads Calc unnecc., it is not recommended. |
58cde26e |
2637 | |
990fb837 |
2638 | Since it also possible to just require Math::BigFloat, this poses the question |
2639 | about what libary this will use: |
58cde26e |
2640 | |
990fb837 |
2641 | require Math::BigFloat; |
2642 | my $x = Math::BigFloat->new(123); $x += 123; |
58cde26e |
2643 | |
990fb837 |
2644 | It will use Calc. Please note that the call to import() is still done, but |
2645 | only when you use for the first time some Math::BigFloat math (it is triggered |
2646 | via any constructor, so the first time you create a Math::BigFloat, the load |
2647 | will happen in the background). This means: |
58cde26e |
2648 | |
990fb837 |
2649 | require Math::BigFloat; |
2650 | Math::BigFloat->import ( lib => 'Foo,Bar' ); |
58cde26e |
2651 | |
990fb837 |
2652 | would be the same as: |
58cde26e |
2653 | |
990fb837 |
2654 | use Math::BigFloat lib => 'Foo, Bar'; |
2655 | |
2656 | But don't try to be clever to insert some operations in between: |
2657 | |
2658 | require Math::BigFloat; |
2659 | my $x = Math::BigFloat->bone() + 4; # load BigInt and Calc |
2660 | Math::BigFloat->import( lib => 'Pari' ); # load Pari, too |
2661 | $x = Math::BigFloat->bone()+4; # now use Pari |
2662 | |
2663 | While this works, it loads Calc needlessly. But maybe you just wanted that? |
2664 | |
2665 | B<Examples #3 is highly recommended> for daily usage. |
2666 | |
2667 | =head1 BUGS |
2668 | |
2669 | Please see the file BUGS in the CPAN distribution Math::BigInt for known bugs. |
58cde26e |
2670 | |
990fb837 |
2671 | =head1 CAVEATS |
58cde26e |
2672 | |
2673 | =over 1 |
2674 | |
2675 | =item stringify, bstr() |
2676 | |
2677 | Both stringify and bstr() now drop the leading '+'. The old code would return |
2678 | '+1.23', the new returns '1.23'. See the documentation in L<Math::BigInt> for |
2679 | reasoning and details. |
2680 | |
2681 | =item bdiv |
2682 | |
2683 | The following will probably not do what you expect: |
2684 | |
2685 | print $c->bdiv(123.456),"\n"; |
2686 | |
2687 | It prints both quotient and reminder since print works in list context. Also, |
2688 | bdiv() will modify $c, so be carefull. You probably want to use |
2689 | |
2690 | print $c / 123.456,"\n"; |
2691 | print scalar $c->bdiv(123.456),"\n"; # or if you want to modify $c |
2692 | |
2693 | instead. |
2694 | |
2695 | =item Modifying and = |
2696 | |
2697 | Beware of: |
2698 | |
2699 | $x = Math::BigFloat->new(5); |
2700 | $y = $x; |
2701 | |
2702 | It will not do what you think, e.g. making a copy of $x. Instead it just makes |
2703 | a second reference to the B<same> object and stores it in $y. Thus anything |
990fb837 |
2704 | that modifies $x will modify $y (except overloaded math operators), and vice |
2705 | versa. See L<Math::BigInt> for details and how to avoid that. |
58cde26e |
2706 | |
2707 | =item bpow |
2708 | |
2709 | C<bpow()> now modifies the first argument, unlike the old code which left |
2710 | it alone and only returned the result. This is to be consistent with |
2711 | C<badd()> etc. The first will modify $x, the second one won't: |
2712 | |
2713 | print bpow($x,$i),"\n"; # modify $x |
2714 | print $x->bpow($i),"\n"; # ditto |
2715 | print $x ** $i,"\n"; # leave $x alone |
2716 | |
2717 | =back |
2718 | |
990fb837 |
2719 | =head1 SEE ALSO |
2720 | |
2721 | L<Math::BigInt>, L<Math::BigRat> and L<Math::Big> as well as |
2722 | L<Math::BigInt::BitVect>, L<Math::BigInt::Pari> and L<Math::BigInt::GMP>. |
2723 | |
2724 | The pragmas L<bignum>, L<bigint> and L<bigrat> might also be of interest |
2725 | because they solve the autoupgrading/downgrading issue, at least partly. |
2726 | |
2727 | The package at |
2728 | L<http://search.cpan.org/search?mode=module&query=Math%3A%3ABigInt> contains |
2729 | more documentation including a full version history, testcases, empty |
2730 | subclass files and benchmarks. |
2731 | |
58cde26e |
2732 | =head1 LICENSE |
a5f75d66 |
2733 | |
58cde26e |
2734 | This program is free software; you may redistribute it and/or modify it under |
2735 | the same terms as Perl itself. |
5d7098d5 |
2736 | |
58cde26e |
2737 | =head1 AUTHORS |
5d7098d5 |
2738 | |
58cde26e |
2739 | Mark Biggar, overloaded interface by Ilya Zakharevich. |
990fb837 |
2740 | Completely rewritten by Tels http://bloodgate.com in 2001, 2002, and still |
2741 | at it in 2003. |
a5f75d66 |
2742 | |
a5f75d66 |
2743 | =cut |