Commit | Line | Data |
13a12e00 |
1 | package Math::BigFloat; |
2 | |
3 | # |
4 | # Mike grinned. 'Two down, infinity to go' - Mike Nostrus in Before and After |
5 | # |
6 | |
58cde26e |
7 | # The following hash values are internally used: |
8 | # _e: exponent (BigInt) |
9 | # _m: mantissa (absolute BigInt) |
10 | # sign: +,-,"NaN" if not a number |
11 | # _a: accuracy |
12 | # _p: precision |
0716bf9b |
13 | # _f: flags, used to signal MBI not to touch our private parts |
58cde26e |
14 | |
28df3e88 |
15 | $VERSION = '1.30'; |
58cde26e |
16 | require 5.005; |
17 | use Exporter; |
0716bf9b |
18 | use Math::BigInt qw/objectify/; |
58cde26e |
19 | @ISA = qw( Exporter Math::BigInt); |
394e6ffb |
20 | |
58cde26e |
21 | use strict; |
027dc388 |
22 | use vars qw/$AUTOLOAD $accuracy $precision $div_scale $round_mode $rnd_mode/; |
b3abae2a |
23 | use vars qw/$upgrade $downgrade/; |
58cde26e |
24 | my $class = "Math::BigFloat"; |
a0d0e21e |
25 | |
a5f75d66 |
26 | use overload |
bd05a461 |
27 | '<=>' => sub { $_[2] ? |
28 | ref($_[0])->bcmp($_[1],$_[0]) : |
29 | ref($_[0])->bcmp($_[0],$_[1])}, |
0716bf9b |
30 | 'int' => sub { $_[0]->as_number() }, # 'trunc' to bigint |
a5f75d66 |
31 | ; |
a0d0e21e |
32 | |
0716bf9b |
33 | ############################################################################## |
34 | # global constants, flags and accessory |
35 | |
36 | use constant MB_NEVER_ROUND => 0x0001; |
37 | |
58cde26e |
38 | # are NaNs ok? |
39 | my $NaNOK=1; |
58cde26e |
40 | # constant for easier life |
41 | my $nan = 'NaN'; |
58cde26e |
42 | |
ee15d750 |
43 | # class constants, use Class->constant_name() to access |
44 | $round_mode = 'even'; # one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc' |
45 | $accuracy = undef; |
46 | $precision = undef; |
47 | $div_scale = 40; |
58cde26e |
48 | |
b3abae2a |
49 | $upgrade = undef; |
50 | $downgrade = undef; |
51 | |
027dc388 |
52 | ############################################################################## |
53 | # the old code had $rnd_mode, so we need to support it, too |
54 | |
55 | $rnd_mode = 'even'; |
56 | sub TIESCALAR { my ($class) = @_; bless \$round_mode, $class; } |
57 | sub FETCH { return $round_mode; } |
58 | sub STORE { $rnd_mode = $_[0]->round_mode($_[1]); } |
59 | |
60 | BEGIN { tie $rnd_mode, 'Math::BigFloat'; } |
61 | |
62 | ############################################################################## |
63 | |
574bacfe |
64 | # in case we call SUPER::->foo() and this wants to call modify() |
65 | # sub modify () { 0; } |
66 | |
58cde26e |
67 | { |
ee15d750 |
68 | # valid method aliases for AUTOLOAD |
58cde26e |
69 | my %methods = map { $_ => 1 } |
70 | qw / fadd fsub fmul fdiv fround ffround fsqrt fmod fstr fsstr fpow fnorm |
b3abae2a |
71 | fint facmp fcmp fzero fnan finf finc fdec flog ffac |
61f5c3f5 |
72 | fceil ffloor frsft flsft fone flog |
ee15d750 |
73 | /; |
61f5c3f5 |
74 | # valid method's that can be hand-ed up (for AUTOLOAD) |
ee15d750 |
75 | my %hand_ups = map { $_ => 1 } |
76 | qw / is_nan is_inf is_negative is_positive |
394e6ffb |
77 | accuracy precision div_scale round_mode fneg fabs babs fnot |
28df3e88 |
78 | objectify upgrade downgrade |
13a12e00 |
79 | bone binf bnan bzero |
58cde26e |
80 | /; |
81 | |
ee15d750 |
82 | sub method_alias { return exists $methods{$_[0]||''}; } |
83 | sub method_hand_up { return exists $hand_ups{$_[0]||''}; } |
a0d0e21e |
84 | } |
0e8b9368 |
85 | |
58cde26e |
86 | ############################################################################## |
87 | # constructors |
a0d0e21e |
88 | |
58cde26e |
89 | sub new |
90 | { |
91 | # create a new BigFloat object from a string or another bigfloat object. |
92 | # _e: exponent |
93 | # _m: mantissa |
94 | # sign => sign (+/-), or "NaN" |
a0d0e21e |
95 | |
61f5c3f5 |
96 | my ($class,$wanted,@r) = @_; |
b3abae2a |
97 | |
61f5c3f5 |
98 | # avoid numify-calls by not using || on $wanted! |
99 | return $class->bzero() if !defined $wanted; # default to 0 |
100 | return $wanted->copy() if UNIVERSAL::isa($wanted,'Math::BigFloat'); |
a0d0e21e |
101 | |
58cde26e |
102 | my $self = {}; bless $self, $class; |
b22b3e31 |
103 | # shortcut for bigints and its subclasses |
0716bf9b |
104 | if ((ref($wanted)) && (ref($wanted) ne $class)) |
58cde26e |
105 | { |
0716bf9b |
106 | $self->{_m} = $wanted->as_number(); # get us a bigint copy |
027dc388 |
107 | $self->{_e} = Math::BigInt->bzero(); |
58cde26e |
108 | $self->{_m}->babs(); |
109 | $self->{sign} = $wanted->sign(); |
0716bf9b |
110 | return $self->bnorm(); |
58cde26e |
111 | } |
112 | # got string |
113 | # handle '+inf', '-inf' first |
ee15d750 |
114 | if ($wanted =~ /^[+-]?inf$/) |
58cde26e |
115 | { |
28df3e88 |
116 | return $downgrade->new($wanted) if $downgrade; |
117 | |
027dc388 |
118 | $self->{_e} = Math::BigInt->bzero(); |
119 | $self->{_m} = Math::BigInt->bzero(); |
58cde26e |
120 | $self->{sign} = $wanted; |
ee15d750 |
121 | $self->{sign} = '+inf' if $self->{sign} eq 'inf'; |
0716bf9b |
122 | return $self->bnorm(); |
58cde26e |
123 | } |
124 | #print "new string '$wanted'\n"; |
125 | my ($mis,$miv,$mfv,$es,$ev) = Math::BigInt::_split(\$wanted); |
126 | if (!ref $mis) |
127 | { |
128 | die "$wanted is not a number initialized to $class" if !$NaNOK; |
28df3e88 |
129 | |
130 | return $downgrade->bnan() if $downgrade; |
131 | |
027dc388 |
132 | $self->{_e} = Math::BigInt->bzero(); |
133 | $self->{_m} = Math::BigInt->bzero(); |
58cde26e |
134 | $self->{sign} = $nan; |
135 | } |
136 | else |
137 | { |
138 | # make integer from mantissa by adjusting exp, then convert to bigint |
61f5c3f5 |
139 | # undef,undef to signal MBI that we don't need no bloody rounding |
140 | $self->{_e} = Math::BigInt->new("$$es$$ev",undef,undef); # exponent |
141 | $self->{_m} = Math::BigInt->new("$$miv$$mfv",undef,undef); # create mant. |
58cde26e |
142 | # 3.123E0 = 3123E-3, and 3.123E-2 => 3123E-5 |
027dc388 |
143 | $self->{_e} -= CORE::length($$mfv) if CORE::length($$mfv) != 0; |
144 | $self->{sign} = $$mis; |
58cde26e |
145 | } |
28df3e88 |
146 | # if downgrade, inf, NaN or integers go down |
147 | |
148 | if ($downgrade && $self->{_e}->{sign} eq '+') |
149 | { |
150 | # print "downgrading $$miv$$mfv"."E$$es$$ev"; |
151 | if ($self->{_e}->is_zero()) |
152 | { |
153 | $self->{_m}->{sign} = $$mis; # negative if wanted |
154 | return $downgrade->new($self->{_m}); |
155 | } |
156 | return $downgrade->new("$$mis$$miv$$mfv"."E$$es$$ev"); |
157 | } |
158 | |
b3abae2a |
159 | # print "mbf new $self->{sign} $self->{_m} e $self->{_e}\n"; |
61f5c3f5 |
160 | $self->bnorm()->round(@r); # first normalize, then round |
58cde26e |
161 | } |
a0d0e21e |
162 | |
13a12e00 |
163 | sub _bnan |
58cde26e |
164 | { |
13a12e00 |
165 | # used by parent class bone() to initialize number to 1 |
58cde26e |
166 | my $self = shift; |
574bacfe |
167 | $self->{_m} = Math::BigInt->bzero(); |
168 | $self->{_e} = Math::BigInt->bzero(); |
58cde26e |
169 | } |
a0d0e21e |
170 | |
13a12e00 |
171 | sub _binf |
58cde26e |
172 | { |
13a12e00 |
173 | # used by parent class bone() to initialize number to 1 |
58cde26e |
174 | my $self = shift; |
574bacfe |
175 | $self->{_m} = Math::BigInt->bzero(); |
176 | $self->{_e} = Math::BigInt->bzero(); |
58cde26e |
177 | } |
a0d0e21e |
178 | |
13a12e00 |
179 | sub _bone |
574bacfe |
180 | { |
13a12e00 |
181 | # used by parent class bone() to initialize number to 1 |
574bacfe |
182 | my $self = shift; |
574bacfe |
183 | $self->{_m} = Math::BigInt->bone(); |
184 | $self->{_e} = Math::BigInt->bzero(); |
574bacfe |
185 | } |
186 | |
13a12e00 |
187 | sub _bzero |
58cde26e |
188 | { |
13a12e00 |
189 | # used by parent class bone() to initialize number to 1 |
58cde26e |
190 | my $self = shift; |
574bacfe |
191 | $self->{_m} = Math::BigInt->bzero(); |
192 | $self->{_e} = Math::BigInt->bone(); |
58cde26e |
193 | } |
194 | |
195 | ############################################################################## |
196 | # string conversation |
197 | |
198 | sub bstr |
199 | { |
200 | # (ref to BFLOAT or num_str ) return num_str |
201 | # Convert number from internal format to (non-scientific) string format. |
202 | # internal format is always normalized (no leading zeros, "-0" => "+0") |
ee15d750 |
203 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
204 | #my $x = shift; my $class = ref($x) || $x; |
205 | #$x = $class->new(shift) unless ref($x); |
58cde26e |
206 | |
574bacfe |
207 | #die "Oups! e was $nan" if $x->{_e}->{sign} eq $nan; |
208 | #die "Oups! m was $nan" if $x->{_m}->{sign} eq $nan; |
209 | if ($x->{sign} !~ /^[+-]$/) |
58cde26e |
210 | { |
574bacfe |
211 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN |
212 | return 'inf'; # +inf |
58cde26e |
213 | } |
214 | |
574bacfe |
215 | my $es = '0'; my $len = 1; my $cad = 0; my $dot = '.'; |
216 | |
28df3e88 |
217 | my $not_zero = ! $x->is_zero(); |
574bacfe |
218 | if ($not_zero) |
58cde26e |
219 | { |
574bacfe |
220 | $es = $x->{_m}->bstr(); |
221 | $len = CORE::length($es); |
222 | if (!$x->{_e}->is_zero()) |
58cde26e |
223 | { |
574bacfe |
224 | if ($x->{_e}->sign() eq '-') |
225 | { |
226 | $dot = ''; |
227 | if ($x->{_e} <= -$len) |
228 | { |
229 | # print "style: 0.xxxx\n"; |
230 | my $r = $x->{_e}->copy(); $r->babs()->bsub( CORE::length($es) ); |
231 | $es = '0.'. ('0' x $r) . $es; $cad = -($len+$r); |
232 | } |
233 | else |
234 | { |
235 | # print "insert '.' at $x->{_e} in '$es'\n"; |
236 | substr($es,$x->{_e},0) = '.'; $cad = $x->{_e}; |
237 | } |
238 | } |
239 | else |
240 | { |
241 | # expand with zeros |
242 | $es .= '0' x $x->{_e}; $len += $x->{_e}; $cad = 0; |
243 | } |
82cf049f |
244 | } |
574bacfe |
245 | } # if not zero |
246 | $es = $x->{sign}.$es if $x->{sign} eq '-'; |
247 | # if set accuracy or precision, pad with zeros |
248 | if ((defined $x->{_a}) && ($not_zero)) |
249 | { |
250 | # 123400 => 6, 0.1234 => 4, 0.001234 => 4 |
251 | my $zeros = $x->{_a} - $cad; # cad == 0 => 12340 |
252 | $zeros = $x->{_a} - $len if $cad != $len; |
574bacfe |
253 | $es .= $dot.'0' x $zeros if $zeros > 0; |
82cf049f |
254 | } |
574bacfe |
255 | elsif ($x->{_p} || 0 < 0) |
58cde26e |
256 | { |
574bacfe |
257 | # 123400 => 6, 0.1234 => 4, 0.001234 => 6 |
258 | my $zeros = -$x->{_p} + $cad; |
574bacfe |
259 | $es .= $dot.'0' x $zeros if $zeros > 0; |
58cde26e |
260 | } |
58cde26e |
261 | return $es; |
82cf049f |
262 | } |
f216259d |
263 | |
58cde26e |
264 | sub bsstr |
265 | { |
266 | # (ref to BFLOAT or num_str ) return num_str |
267 | # Convert number from internal format to scientific string format. |
268 | # internal format is always normalized (no leading zeros, "-0E0" => "+0E0") |
ee15d750 |
269 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
270 | #my $x = shift; my $class = ref($x) || $x; |
271 | #$x = $class->new(shift) unless ref($x); |
a0d0e21e |
272 | |
574bacfe |
273 | #die "Oups! e was $nan" if $x->{_e}->{sign} eq $nan; |
274 | #die "Oups! m was $nan" if $x->{_m}->{sign} eq $nan; |
275 | if ($x->{sign} !~ /^[+-]$/) |
276 | { |
277 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN |
278 | return 'inf'; # +inf |
279 | } |
58cde26e |
280 | my $sign = $x->{_e}->{sign}; $sign = '' if $sign eq '-'; |
281 | my $sep = 'e'.$sign; |
282 | return $x->{_m}->bstr().$sep.$x->{_e}->bstr(); |
283 | } |
284 | |
285 | sub numify |
286 | { |
287 | # Make a number from a BigFloat object |
574bacfe |
288 | # simple return string and let Perl's atoi()/atof() handle the rest |
ee15d750 |
289 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
290 | return $x->bsstr(); |
291 | } |
a0d0e21e |
292 | |
58cde26e |
293 | ############################################################################## |
294 | # public stuff (usually prefixed with "b") |
295 | |
574bacfe |
296 | # tels 2001-08-04 |
297 | # todo: this must be overwritten and return NaN for non-integer values |
298 | # band(), bior(), bxor(), too |
58cde26e |
299 | #sub bnot |
300 | # { |
301 | # $class->SUPER::bnot($class,@_); |
302 | # } |
303 | |
304 | sub bcmp |
305 | { |
306 | # Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort) |
307 | # (BFLOAT or num_str, BFLOAT or num_str) return cond_code |
308 | my ($self,$x,$y) = objectify(2,@_); |
58cde26e |
309 | |
0716bf9b |
310 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
311 | { |
312 | # handle +-inf and NaN |
313 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
314 | return 0 if ($x->{sign} eq $y->{sign}) && ($x->{sign} =~ /^[+-]inf$/); |
315 | return +1 if $x->{sign} eq '+inf'; |
316 | return -1 if $x->{sign} eq '-inf'; |
317 | return -1 if $y->{sign} eq '+inf'; |
b3abae2a |
318 | return +1; |
0716bf9b |
319 | } |
320 | |
321 | # check sign for speed first |
574bacfe |
322 | return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y |
58cde26e |
323 | return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0 |
324 | |
574bacfe |
325 | # shortcut |
326 | my $xz = $x->is_zero(); |
327 | my $yz = $y->is_zero(); |
328 | return 0 if $xz && $yz; # 0 <=> 0 |
329 | return -1 if $xz && $y->{sign} eq '+'; # 0 <=> +y |
330 | return 1 if $yz && $x->{sign} eq '+'; # +x <=> 0 |
58cde26e |
331 | |
332 | # adjust so that exponents are equal |
bd05a461 |
333 | my $lxm = $x->{_m}->length(); |
334 | my $lym = $y->{_m}->length(); |
28df3e88 |
335 | # the numify somewhat limits our length, but makes it much faster |
336 | my $lx = $lxm + $x->{_e}->numify(); |
337 | my $ly = $lym + $y->{_e}->numify(); |
338 | my $l = $lx - $ly; $l = -$l if $x->{sign} eq '-'; |
bd05a461 |
339 | return $l <=> 0 if $l != 0; |
58cde26e |
340 | |
bd05a461 |
341 | # lengths (corrected by exponent) are equal |
28df3e88 |
342 | # so make mantissa equal length by padding with zero (shift left) |
bd05a461 |
343 | my $diff = $lxm - $lym; |
344 | my $xm = $x->{_m}; # not yet copy it |
345 | my $ym = $y->{_m}; |
346 | if ($diff > 0) |
347 | { |
348 | $ym = $y->{_m}->copy()->blsft($diff,10); |
349 | } |
350 | elsif ($diff < 0) |
351 | { |
352 | $xm = $x->{_m}->copy()->blsft(-$diff,10); |
353 | } |
28df3e88 |
354 | my $rc = $xm->bacmp($ym); |
58cde26e |
355 | $rc = -$rc if $x->{sign} eq '-'; # -124 < -123 |
b3abae2a |
356 | $rc <=> 0; |
58cde26e |
357 | } |
358 | |
359 | sub bacmp |
360 | { |
361 | # Compares 2 values, ignoring their signs. |
362 | # Returns one of undef, <0, =0, >0. (suitable for sort) |
363 | # (BFLOAT or num_str, BFLOAT or num_str) return cond_code |
364 | my ($self,$x,$y) = objectify(2,@_); |
ee15d750 |
365 | |
366 | # handle +-inf and NaN's |
abcfbf51 |
367 | if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/) |
ee15d750 |
368 | { |
369 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
370 | return 0 if ($x->is_inf() && $y->is_inf()); |
371 | return 1 if ($x->is_inf() && !$y->is_inf()); |
b3abae2a |
372 | return -1; |
ee15d750 |
373 | } |
374 | |
375 | # shortcut |
376 | my $xz = $x->is_zero(); |
377 | my $yz = $y->is_zero(); |
378 | return 0 if $xz && $yz; # 0 <=> 0 |
379 | return -1 if $xz && !$yz; # 0 <=> +y |
380 | return 1 if $yz && !$xz; # +x <=> 0 |
381 | |
382 | # adjust so that exponents are equal |
383 | my $lxm = $x->{_m}->length(); |
384 | my $lym = $y->{_m}->length(); |
28df3e88 |
385 | # the numify somewhat limits our length, but makes it much faster |
386 | my $lx = $lxm + $x->{_e}->numify(); |
387 | my $ly = $lym + $y->{_e}->numify(); |
394e6ffb |
388 | my $l = $lx - $ly; |
ee15d750 |
389 | return $l <=> 0 if $l != 0; |
58cde26e |
390 | |
ee15d750 |
391 | # lengths (corrected by exponent) are equal |
394e6ffb |
392 | # so make mantissa equal-length by padding with zero (shift left) |
ee15d750 |
393 | my $diff = $lxm - $lym; |
394 | my $xm = $x->{_m}; # not yet copy it |
395 | my $ym = $y->{_m}; |
396 | if ($diff > 0) |
397 | { |
398 | $ym = $y->{_m}->copy()->blsft($diff,10); |
399 | } |
400 | elsif ($diff < 0) |
401 | { |
402 | $xm = $x->{_m}->copy()->blsft(-$diff,10); |
403 | } |
28df3e88 |
404 | $xm->bacmp($ym) <=> 0; |
58cde26e |
405 | } |
a0d0e21e |
406 | |
58cde26e |
407 | sub badd |
408 | { |
409 | # add second arg (BFLOAT or string) to first (BFLOAT) (modifies first) |
410 | # return result as BFLOAT |
58cde26e |
411 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
412 | |
b3abae2a |
413 | #print "mbf badd $x $y\n"; |
574bacfe |
414 | # inf and NaN handling |
415 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
416 | { |
417 | # NaN first |
418 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
13a12e00 |
419 | # inf handling |
574bacfe |
420 | if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) |
421 | { |
13a12e00 |
422 | # +inf++inf or -inf+-inf => same, rest is NaN |
423 | return $x if $x->{sign} eq $y->{sign}; |
424 | return $x->bnan(); |
574bacfe |
425 | } |
426 | # +-inf + something => +inf |
427 | # something +-inf => +-inf |
428 | $x->{sign} = $y->{sign}, return $x if $y->{sign} =~ /^[+-]inf$/; |
429 | return $x; |
430 | } |
431 | |
58cde26e |
432 | # speed: no add for 0+y or x+0 |
28df3e88 |
433 | return $x->bround($a,$p,$r) if $y->is_zero(); # x+0 |
58cde26e |
434 | if ($x->is_zero()) # 0+y |
435 | { |
436 | # make copy, clobbering up x (modify in place!) |
437 | $x->{_e} = $y->{_e}->copy(); |
438 | $x->{_m} = $y->{_m}->copy(); |
439 | $x->{sign} = $y->{sign} || $nan; |
440 | return $x->round($a,$p,$r,$y); |
a0d0e21e |
441 | } |
58cde26e |
442 | |
443 | # take lower of the two e's and adapt m1 to it to match m2 |
28df3e88 |
444 | my $e = $y->{_e}; |
445 | $e = Math::BigInt::bzero() if !defined $e; # if no BFLOAT ? |
446 | $e = $e->copy(); # make copy (didn't do it yet) |
447 | $e->bsub($x->{_e}); |
58cde26e |
448 | my $add = $y->{_m}->copy(); |
28df3e88 |
449 | # if ($e < 0) # < 0 |
450 | if ($e->{sign} eq '-') # < 0 |
58cde26e |
451 | { |
58cde26e |
452 | my $e1 = $e->copy()->babs(); |
28df3e88 |
453 | #$x->{_m} *= (10 ** $e1); |
454 | $x->{_m}->blsft($e1,10); |
58cde26e |
455 | $x->{_e} += $e; # need the sign of e |
58cde26e |
456 | } |
28df3e88 |
457 | # if ($e > 0) # > 0 |
458 | elsif (!$e->is_zero()) # > 0 |
58cde26e |
459 | { |
28df3e88 |
460 | #$add *= (10 ** $e); |
461 | $add->blsft($e,10); |
58cde26e |
462 | } |
61f5c3f5 |
463 | # else: both e are the same, so just leave them |
464 | $x->{_m}->{sign} = $x->{sign}; # fiddle with signs |
58cde26e |
465 | $add->{sign} = $y->{sign}; |
61f5c3f5 |
466 | $x->{_m} += $add; # finally do add/sub |
467 | $x->{sign} = $x->{_m}->{sign}; # re-adjust signs |
468 | $x->{_m}->{sign} = '+'; # mantissa always positiv |
469 | # delete trailing zeros, then round |
470 | return $x->bnorm()->round($a,$p,$r,$y); |
58cde26e |
471 | } |
472 | |
473 | sub bsub |
474 | { |
0716bf9b |
475 | # (BigFloat or num_str, BigFloat or num_str) return BigFloat |
58cde26e |
476 | # subtract second arg from first, modify first |
e745a66c |
477 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
a0d0e21e |
478 | |
28df3e88 |
479 | if ($y->is_zero()) # still round for not adding zero |
e745a66c |
480 | { |
28df3e88 |
481 | return $x->round($a,$p,$r); |
e745a66c |
482 | } |
28df3e88 |
483 | |
484 | $y->{sign} =~ tr/+\-/-+/; # does nothing for NaN |
485 | $x->badd($y,$a,$p,$r); # badd does not leave internal zeros |
486 | $y->{sign} =~ tr/+\-/-+/; # refix $y (does nothing for NaN) |
e745a66c |
487 | $x; # already rounded by badd() |
58cde26e |
488 | } |
489 | |
490 | sub binc |
491 | { |
492 | # increment arg by one |
ee15d750 |
493 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
e745a66c |
494 | |
495 | if ($x->{_e}->sign() eq '-') |
496 | { |
497 | return $x->badd($self->bone(),$a,$p,$r); # digits after dot |
498 | } |
499 | |
500 | if (!$x->{_e}->is_zero()) |
501 | { |
502 | $x->{_m}->blsft($x->{_e},10); # 1e2 => 100 |
503 | $x->{_e}->bzero(); |
504 | } |
505 | # now $x->{_e} == 0 |
506 | if ($x->{sign} eq '+') |
507 | { |
508 | $x->{_m}->binc(); |
509 | return $x->bnorm()->bround($a,$p,$r); |
510 | } |
511 | elsif ($x->{sign} eq '-') |
512 | { |
513 | $x->{_m}->bdec(); |
514 | $x->{sign} = '+' if $x->{_m}->is_zero(); # -1 +1 => -0 => +0 |
515 | return $x->bnorm()->bround($a,$p,$r); |
516 | } |
517 | # inf, nan handling etc |
518 | $x->badd($self->__one(),$a,$p,$r); # does round |
58cde26e |
519 | } |
520 | |
521 | sub bdec |
522 | { |
523 | # decrement arg by one |
ee15d750 |
524 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
e745a66c |
525 | |
526 | if ($x->{_e}->sign() eq '-') |
527 | { |
528 | return $x->badd($self->bone('-'),$a,$p,$r); # digits after dot |
529 | } |
530 | |
531 | if (!$x->{_e}->is_zero()) |
532 | { |
533 | $x->{_m}->blsft($x->{_e},10); # 1e2 => 100 |
534 | $x->{_e}->bzero(); |
535 | } |
536 | # now $x->{_e} == 0 |
537 | my $zero = $x->is_zero(); |
538 | # <= 0 |
539 | if (($x->{sign} eq '-') || $zero) |
540 | { |
541 | $x->{_m}->binc(); |
542 | $x->{sign} = '-' if $zero; # 0 => 1 => -1 |
543 | $x->{sign} = '+' if $x->{_m}->is_zero(); # -1 +1 => -0 => +0 |
544 | return $x->bnorm()->round($a,$p,$r); |
545 | } |
546 | # > 0 |
547 | elsif ($x->{sign} eq '+') |
548 | { |
549 | $x->{_m}->bdec(); |
550 | return $x->bnorm()->round($a,$p,$r); |
551 | } |
552 | # inf, nan handling etc |
553 | $x->badd($self->bone('-'),$a,$p,$r); # does round |
58cde26e |
554 | } |
555 | |
61f5c3f5 |
556 | sub blog |
557 | { |
b3abae2a |
558 | my ($self,$x,$base,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(2,@_); |
61f5c3f5 |
559 | |
560 | # http://www.efunda.com/math/taylor_series/logarithmic.cfm?search_string=log |
561 | |
562 | # u = x-1, v = x +1 |
563 | # _ _ |
564 | # taylor: | u 1 u^3 1 u^5 | |
565 | # ln (x) = 2 | --- + - * --- + - * --- + ... | x > 0 |
b3abae2a |
566 | # |_ v 3 v^3 5 v^5 _| |
61f5c3f5 |
567 | |
b3abae2a |
568 | # we need to limit the accuracy to protect against overflow |
569 | my $fallback = 0; |
570 | my $scale = 0; |
571 | my @params = $x->_find_round_parameters($a,$p,$r); |
61f5c3f5 |
572 | |
b3abae2a |
573 | # no rounding at all, so must use fallback |
574 | if (scalar @params == 1) |
575 | { |
576 | # simulate old behaviour |
577 | $params[1] = $self->div_scale(); # and round to it as accuracy |
578 | $scale = $params[1]+4; # at least four more for proper round |
579 | $params[3] = $r; # round mode by caller or undef |
580 | $fallback = 1; # to clear a/p afterwards |
581 | } |
582 | else |
583 | { |
584 | # the 4 below is empirical, and there might be cases where it is not |
585 | # enough... |
586 | $scale = abs($params[1] || $params[2]) + 4; # take whatever is defined |
587 | } |
61f5c3f5 |
588 | |
b3abae2a |
589 | return $x->bzero(@params) if $x->is_one(); |
590 | return $x->bnan() if $x->{sign} ne '+' || $x->is_zero(); |
591 | #return $x->bone('+',@params) if $x->bcmp($base) == 0; |
61f5c3f5 |
592 | |
b3abae2a |
593 | # when user set globals, they would interfere with our calculation, so |
594 | # disable then and later re-enable them |
595 | no strict 'refs'; |
596 | my $abr = "$self\::accuracy"; my $ab = $$abr; $$abr = undef; |
597 | my $pbr = "$self\::precision"; my $pb = $$pbr; $$pbr = undef; |
598 | # we also need to disable any set A or P on $x (_find_round_parameters took |
599 | # them already into account), since these would interfere, too |
600 | delete $x->{_a}; delete $x->{_p}; |
601 | # need to disable $upgrade in BigInt, to aoid deep recursion |
602 | local $Math::BigInt::upgrade = undef; |
603 | |
604 | my $v = $x->copy(); $v->binc(); # v = x+1 |
605 | $x->bdec(); my $u = $x->copy(); # u = x-1; x = x-1 |
606 | |
607 | $x->bdiv($v,$scale); # first term: u/v |
608 | |
609 | my $below = $v->copy(); |
610 | my $over = $u->copy(); |
611 | $u *= $u; $v *= $v; # u^2, v^2 |
612 | $below->bmul($v); # u^3, v^3 |
613 | $over->bmul($u); |
61f5c3f5 |
614 | my $factor = $self->new(3); my $two = $self->new(2); |
615 | |
616 | my $diff = $self->bone(); |
b3abae2a |
617 | my $limit = $self->new("1E-". ($scale-1)); my $last; |
61f5c3f5 |
618 | # print "diff $diff limit $limit\n"; |
b3abae2a |
619 | while ($diff->bcmp($limit) > 0) |
61f5c3f5 |
620 | { |
b3abae2a |
621 | #print "$x $over $below $factor\n"; |
61f5c3f5 |
622 | $diff = $x->copy()->bsub($last)->babs(); |
b3abae2a |
623 | #print "diff $diff $limit\n"; |
61f5c3f5 |
624 | $last = $x->copy(); |
b3abae2a |
625 | $x += $over->copy()->bdiv($below->copy()->bmul($factor),$scale); |
61f5c3f5 |
626 | $over *= $u; $below *= $v; $factor->badd($two); |
627 | } |
628 | $x->bmul($two); |
b3abae2a |
629 | |
630 | # shortcut to not run trough _find_round_parameters again |
631 | if (defined $params[1]) |
632 | { |
633 | $x->bround($params[1],$params[3]); # then round accordingly |
634 | } |
635 | else |
636 | { |
637 | $x->bfround($params[2],$params[3]); # then round accordingly |
638 | } |
639 | if ($fallback) |
640 | { |
641 | # clear a/p after round, since user did not request it |
642 | $x->{_a} = undef; $x->{_p} = undef; |
643 | } |
644 | # restore globals |
645 | $$abr = $ab; $$pbr = $pb; |
646 | |
647 | $x; |
61f5c3f5 |
648 | } |
649 | |
58cde26e |
650 | sub blcm |
651 | { |
ee15d750 |
652 | # (BFLOAT or num_str, BFLOAT or num_str) return BFLOAT |
58cde26e |
653 | # does not modify arguments, but returns new object |
654 | # Lowest Common Multiplicator |
58cde26e |
655 | |
656 | my ($self,@arg) = objectify(0,@_); |
657 | my $x = $self->new(shift @arg); |
658 | while (@arg) { $x = _lcm($x,shift @arg); } |
659 | $x; |
660 | } |
661 | |
662 | sub bgcd |
663 | { |
ee15d750 |
664 | # (BFLOAT or num_str, BFLOAT or num_str) return BINT |
58cde26e |
665 | # does not modify arguments, but returns new object |
666 | # GCD -- Euclids algorithm Knuth Vol 2 pg 296 |
58cde26e |
667 | |
668 | my ($self,@arg) = objectify(0,@_); |
669 | my $x = $self->new(shift @arg); |
670 | while (@arg) { $x = _gcd($x,shift @arg); } |
671 | $x; |
672 | } |
673 | |
b3abae2a |
674 | ############################################################################### |
675 | # is_foo methods (is_negative, is_positive are inherited from BigInt) |
676 | |
677 | sub is_int |
678 | { |
679 | # return true if arg (BFLOAT or num_str) is an integer |
680 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
681 | |
682 | return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN and +-inf aren't |
683 | $x->{_e}->{sign} eq '+'; # 1e-1 => no integer |
684 | 0; |
685 | } |
686 | |
58cde26e |
687 | sub is_zero |
688 | { |
b3abae2a |
689 | # return true if arg (BFLOAT or num_str) is zero |
ee15d750 |
690 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
574bacfe |
691 | |
692 | return 1 if $x->{sign} eq '+' && $x->{_m}->is_zero(); |
b3abae2a |
693 | 0; |
58cde26e |
694 | } |
695 | |
696 | sub is_one |
697 | { |
b3abae2a |
698 | # return true if arg (BFLOAT or num_str) is +1 or -1 if signis given |
ee15d750 |
699 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
700 | |
701 | my $sign = shift || ''; $sign = '+' if $sign ne '-'; |
702 | return 1 |
703 | if ($x->{sign} eq $sign && $x->{_e}->is_zero() && $x->{_m}->is_one()); |
b3abae2a |
704 | 0; |
58cde26e |
705 | } |
706 | |
707 | sub is_odd |
708 | { |
ee15d750 |
709 | # return true if arg (BFLOAT or num_str) is odd or false if even |
710 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
0716bf9b |
711 | |
b3abae2a |
712 | return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN & +-inf aren't |
713 | ($x->{_e}->is_zero() && $x->{_m}->is_odd()); |
714 | 0; |
58cde26e |
715 | } |
716 | |
717 | sub is_even |
718 | { |
b22b3e31 |
719 | # return true if arg (BINT or num_str) is even or false if odd |
ee15d750 |
720 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
0716bf9b |
721 | |
722 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
b3abae2a |
723 | return 1 if ($x->{_e}->{sign} eq '+' # 123.45 is never |
724 | && $x->{_m}->is_even()); # but 1200 is |
725 | 0; |
58cde26e |
726 | } |
727 | |
728 | sub bmul |
729 | { |
730 | # multiply two numbers -- stolen from Knuth Vol 2 pg 233 |
731 | # (BINT or num_str, BINT or num_str) return BINT |
732 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
58cde26e |
733 | |
58cde26e |
734 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
735 | |
574bacfe |
736 | # inf handling |
737 | if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) |
738 | { |
13a12e00 |
739 | return $x->bnan() if $x->is_zero() || $y->is_zero(); |
574bacfe |
740 | # result will always be +-inf: |
741 | # +inf * +/+inf => +inf, -inf * -/-inf => +inf |
742 | # +inf * -/-inf => -inf, -inf * +/+inf => -inf |
743 | return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); |
744 | return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); |
745 | return $x->binf('-'); |
746 | } |
13a12e00 |
747 | # handle result = 0 |
748 | return $x->bzero() if $x->is_zero() || $y->is_zero(); |
574bacfe |
749 | |
58cde26e |
750 | # aEb * cEd = (a*c)E(b+d) |
394e6ffb |
751 | $x->{_m}->bmul($y->{_m}); |
752 | $x->{_e}->badd($y->{_e}); |
58cde26e |
753 | # adjust sign: |
754 | $x->{sign} = $x->{sign} ne $y->{sign} ? '-' : '+'; |
394e6ffb |
755 | return $x->bnorm()->round($a,$p,$r,$y); |
58cde26e |
756 | } |
757 | |
758 | sub bdiv |
759 | { |
760 | # (dividend: BFLOAT or num_str, divisor: BFLOAT or num_str) return |
761 | # (BFLOAT,BFLOAT) (quo,rem) or BINT (only rem) |
762 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
763 | |
13a12e00 |
764 | return $self->_div_inf($x,$y) |
765 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()); |
574bacfe |
766 | |
13a12e00 |
767 | # x== 0 # also: or y == 1 or y == -1 |
394e6ffb |
768 | return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero(); |
0716bf9b |
769 | |
13a12e00 |
770 | # upgrade |
771 | return $upgrade->bdiv($x,$y,$a,$p,$r) if defined $upgrade; |
772 | |
58cde26e |
773 | # we need to limit the accuracy to protect against overflow |
574bacfe |
774 | my $fallback = 0; |
ee15d750 |
775 | my $scale = 0; |
ee15d750 |
776 | my @params = $x->_find_round_parameters($a,$p,$r,$y); |
777 | |
778 | # no rounding at all, so must use fallback |
779 | if (scalar @params == 1) |
58cde26e |
780 | { |
0716bf9b |
781 | # simulate old behaviour |
ee15d750 |
782 | $params[1] = $self->div_scale(); # and round to it as accuracy |
61f5c3f5 |
783 | $scale = $params[1]+4; # at least four more for proper round |
ee15d750 |
784 | $params[3] = $r; # round mode by caller or undef |
785 | $fallback = 1; # to clear a/p afterwards |
786 | } |
787 | else |
788 | { |
789 | # the 4 below is empirical, and there might be cases where it is not |
790 | # enough... |
791 | $scale = abs($params[1] || $params[2]) + 4; # take whatever is defined |
a0d0e21e |
792 | } |
0716bf9b |
793 | my $lx = $x->{_m}->length(); my $ly = $y->{_m}->length(); |
58cde26e |
794 | $scale = $lx if $lx > $scale; |
58cde26e |
795 | $scale = $ly if $ly > $scale; |
0716bf9b |
796 | my $diff = $ly - $lx; |
797 | $scale += $diff if $diff > 0; # if lx << ly, but not if ly << lx! |
b3abae2a |
798 | |
799 | # make copy of $x in case of list context for later reminder calculation |
800 | my $rem; |
801 | if (wantarray && !$y->is_one()) |
802 | { |
803 | $rem = $x->copy(); |
804 | } |
a0d0e21e |
805 | |
58cde26e |
806 | $x->{sign} = $x->{sign} ne $y->sign() ? '-' : '+'; |
a0d0e21e |
807 | |
58cde26e |
808 | # check for / +-1 ( +/- 1E0) |
394e6ffb |
809 | if (!$y->is_one()) |
58cde26e |
810 | { |
394e6ffb |
811 | # promote BigInts and it's subclasses (except when already a BigFloat) |
812 | $y = $self->new($y) unless $y->isa('Math::BigFloat'); |
813 | |
814 | # calculate the result to $scale digits and then round it |
815 | # a * 10 ** b / c * 10 ** d => a/c * 10 ** (b-d) |
816 | $x->{_m}->blsft($scale,10); |
817 | $x->{_m}->bdiv( $y->{_m} ); # a/c |
818 | $x->{_e}->bsub( $y->{_e} ); # b-d |
819 | $x->{_e}->bsub($scale); # correct for 10**scale |
820 | $x->bnorm(); # remove trailing 0's |
a0d0e21e |
821 | } |
a5f75d66 |
822 | |
ee15d750 |
823 | # shortcut to not run trough _find_round_parameters again |
824 | if (defined $params[1]) |
825 | { |
61f5c3f5 |
826 | $x->bround($params[1],$params[3]); # then round accordingly |
ee15d750 |
827 | } |
828 | else |
829 | { |
830 | $x->bfround($params[2],$params[3]); # then round accordingly |
831 | } |
574bacfe |
832 | if ($fallback) |
833 | { |
834 | # clear a/p after round, since user did not request it |
ee15d750 |
835 | $x->{_a} = undef; $x->{_p} = undef; |
574bacfe |
836 | } |
0716bf9b |
837 | |
58cde26e |
838 | if (wantarray) |
839 | { |
394e6ffb |
840 | if (!$y->is_one()) |
841 | { |
b3abae2a |
842 | $rem->bmod($y,$params[1],$params[2],$params[3]); # copy already done |
394e6ffb |
843 | } |
844 | else |
845 | { |
846 | $rem = $self->bzero(); |
847 | } |
574bacfe |
848 | if ($fallback) |
849 | { |
850 | # clear a/p after round, since user did not request it |
ee15d750 |
851 | $rem->{_a} = undef; $rem->{_p} = undef; |
574bacfe |
852 | } |
0716bf9b |
853 | return ($x,$rem); |
58cde26e |
854 | } |
855 | return $x; |
856 | } |
a0d0e21e |
857 | |
58cde26e |
858 | sub bmod |
859 | { |
860 | # (dividend: BFLOAT or num_str, divisor: BFLOAT or num_str) return reminder |
861 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
a0d0e21e |
862 | |
61f5c3f5 |
863 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
864 | { |
865 | my ($d,$re) = $self->SUPER::_div_inf($x,$y); |
866 | return $re->round($a,$p,$r,$y); |
867 | } |
868 | return $x->bnan() if $x->is_zero() && $y->is_zero(); |
869 | return $x if $y->is_zero(); |
870 | return $x->bnan() if $x->is_nan() || $y->is_nan(); |
871 | return $x->bzero() if $y->is_one() || $x->is_zero(); |
58cde26e |
872 | |
61f5c3f5 |
873 | # inf handling is missing here |
874 | |
875 | my $cmp = $x->bacmp($y); # equal or $x < $y? |
876 | return $x->bzero($a,$p) if $cmp == 0; # $x == $y => result 0 |
877 | |
878 | # only $y of the operands negative? |
879 | my $neg = 0; $neg = 1 if $x->{sign} ne $y->{sign}; |
880 | |
881 | $x->{sign} = $y->{sign}; # calc sign first |
882 | return $x->round($a,$p,$r) if $cmp < 0 && $neg == 0; # $x < $y => result $x |
883 | |
884 | my $ym = $y->{_m}->copy(); |
885 | |
886 | # 2e1 => 20 |
887 | $ym->blsft($y->{_e},10) if $y->{_e}->{sign} eq '+' && !$y->{_e}->is_zero(); |
888 | |
889 | # if $y has digits after dot |
890 | my $shifty = 0; # correct _e of $x by this |
891 | if ($y->{_e}->{sign} eq '-') # has digits after dot |
892 | { |
893 | # 123 % 2.5 => 1230 % 25 => 5 => 0.5 |
894 | $shifty = $y->{_e}->copy()->babs(); # no more digits after dot |
895 | $x->blsft($shifty,10); # 123 => 1230, $y->{_m} is already 25 |
896 | } |
897 | # $ym is now mantissa of $y based on exponent 0 |
b3abae2a |
898 | |
61f5c3f5 |
899 | my $shiftx = 0; # correct _e of $x by this |
900 | if ($x->{_e}->{sign} eq '-') # has digits after dot |
901 | { |
902 | # 123.4 % 20 => 1234 % 200 |
903 | $shiftx = $x->{_e}->copy()->babs(); # no more digits after dot |
904 | $ym->blsft($shiftx,10); |
905 | } |
906 | # 123e1 % 20 => 1230 % 20 |
907 | if ($x->{_e}->{sign} eq '+' && !$x->{_e}->is_zero()) |
908 | { |
909 | $x->{_m}->blsft($x->{_e},10); |
910 | } |
911 | $x->{_e} = Math::BigInt->bzero() unless $x->{_e}->is_zero(); |
912 | |
913 | $x->{_e}->bsub($shiftx) if $shiftx != 0; |
914 | $x->{_e}->bsub($shifty) if $shifty != 0; |
915 | |
916 | # now mantissas are equalized, exponent of $x is adjusted, so calc result |
b3abae2a |
917 | # $ym->{sign} = '-' if $neg; # bmod() will make the correction for us |
918 | |
61f5c3f5 |
919 | $x->{_m}->bmod($ym); |
920 | |
921 | $x->{sign} = '+' if $x->{_m}->is_zero(); # fix sign for -0 |
922 | $x->bnorm(); |
923 | |
924 | if ($neg != 0) # one of them negative => correct in place |
925 | { |
926 | my $r = $y - $x; |
927 | $x->{_m} = $r->{_m}; |
928 | $x->{_e} = $r->{_e}; |
929 | $x->{sign} = '+' if $x->{_m}->is_zero(); # fix sign for -0 |
930 | $x->bnorm(); |
931 | } |
932 | |
933 | $x->round($a,$p,$r,$y); # round and return |
58cde26e |
934 | } |
935 | |
936 | sub bsqrt |
937 | { |
0716bf9b |
938 | # calculate square root; this should probably |
939 | # use a different test to see whether the accuracy we want is... |
ee15d750 |
940 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e |
941 | |
0716bf9b |
942 | return $x->bnan() if $x->{sign} eq 'NaN' || $x->{sign} =~ /^-/; # <0, NaN |
943 | return $x if $x->{sign} eq '+inf'; # +inf |
394e6ffb |
944 | return $x if $x->is_zero() || $x->is_one(); |
58cde26e |
945 | |
61f5c3f5 |
946 | # we need to limit the accuracy to protect against overflow |
574bacfe |
947 | my $fallback = 0; |
61f5c3f5 |
948 | my $scale = 0; |
949 | my @params = $x->_find_round_parameters($a,$p,$r); |
950 | |
951 | # no rounding at all, so must use fallback |
952 | if (scalar @params == 1) |
0716bf9b |
953 | { |
954 | # simulate old behaviour |
61f5c3f5 |
955 | $params[1] = $self->div_scale(); # and round to it as accuracy |
956 | $scale = $params[1]+4; # at least four more for proper round |
957 | $params[3] = $r; # round mode by caller or undef |
ee15d750 |
958 | $fallback = 1; # to clear a/p afterwards |
0716bf9b |
959 | } |
61f5c3f5 |
960 | else |
961 | { |
962 | # the 4 below is empirical, and there might be cases where it is not |
963 | # enough... |
964 | $scale = abs($params[1] || $params[2]) + 4; # take whatever is defined |
965 | } |
966 | |
967 | # when user set globals, they would interfere with our calculation, so |
968 | # disable then and later re-enable them |
969 | no strict 'refs'; |
970 | my $abr = "$self\::accuracy"; my $ab = $$abr; $$abr = undef; |
b3abae2a |
971 | my $pbr = "$self\::precision"; my $pb = $$pbr; $$pbr = undef; |
61f5c3f5 |
972 | # we also need to disable any set A or P on $x (_find_round_parameters took |
973 | # them already into account), since these would interfere, too |
974 | delete $x->{_a}; delete $x->{_p}; |
b3abae2a |
975 | # need to disable $upgrade in BigInt, to aoid deep recursion |
976 | local $Math::BigInt::upgrade = undef; |
61f5c3f5 |
977 | |
394e6ffb |
978 | my $xas = $x->as_number(); |
979 | my $gs = $xas->copy()->bsqrt(); # some guess |
b3abae2a |
980 | |
394e6ffb |
981 | if (($x->{_e}->{sign} ne '-') # guess can't be accurate if there are |
982 | # digits after the dot |
b3abae2a |
983 | && ($xas->bacmp($gs * $gs) == 0)) # guess hit the nail on the head? |
394e6ffb |
984 | { |
985 | # exact result |
61f5c3f5 |
986 | $x->{_m} = $gs; $x->{_e} = Math::BigInt->bzero(); $x->bnorm(); |
987 | # shortcut to not run trough _find_round_parameters again |
988 | if (defined $params[1]) |
989 | { |
990 | $x->bround($params[1],$params[3]); # then round accordingly |
991 | } |
992 | else |
993 | { |
994 | $x->bfround($params[2],$params[3]); # then round accordingly |
995 | } |
996 | if ($fallback) |
997 | { |
998 | # clear a/p after round, since user did not request it |
999 | $x->{_a} = undef; $x->{_p} = undef; |
1000 | } |
b3abae2a |
1001 | ${"$self\::accuracy"} = $ab; ${"$self\::precision"} = $pb; |
61f5c3f5 |
1002 | return $x; |
394e6ffb |
1003 | } |
61f5c3f5 |
1004 | $gs = $self->new( $gs ); # BigInt to BigFloat |
394e6ffb |
1005 | |
0716bf9b |
1006 | my $lx = $x->{_m}->length(); |
1007 | $scale = $lx if $scale < $lx; |
394e6ffb |
1008 | my $e = $self->new("1E-$scale"); # make test variable |
b3abae2a |
1009 | # return $x->bnan() if $e->sign() eq 'NaN'; |
58cde26e |
1010 | |
58cde26e |
1011 | my $y = $x->copy(); |
394e6ffb |
1012 | my $two = $self->new(2); |
61f5c3f5 |
1013 | my $diff = $e; |
ee15d750 |
1014 | # promote BigInts and it's subclasses (except when already a BigFloat) |
1015 | $y = $self->new($y) unless $y->isa('Math::BigFloat'); |
61f5c3f5 |
1016 | |
ee15d750 |
1017 | my $rem; |
58cde26e |
1018 | while ($diff >= $e) |
1019 | { |
61f5c3f5 |
1020 | $rem = $y->copy()->bdiv($gs,$scale)->badd($gs)->bdiv($two,$scale); |
1021 | $diff = $rem->copy()->bsub($gs)->babs(); |
1022 | $gs = $rem->copy(); |
a0d0e21e |
1023 | } |
61f5c3f5 |
1024 | # copy over to modify $x |
1025 | $x->{_m} = $rem->{_m}; $x->{_e} = $rem->{_e}; |
1026 | |
1027 | # shortcut to not run trough _find_round_parameters again |
1028 | if (defined $params[1]) |
1029 | { |
1030 | $x->bround($params[1],$params[3]); # then round accordingly |
1031 | } |
1032 | else |
1033 | { |
1034 | $x->bfround($params[2],$params[3]); # then round accordingly |
1035 | } |
574bacfe |
1036 | if ($fallback) |
1037 | { |
1038 | # clear a/p after round, since user did not request it |
ee15d750 |
1039 | $x->{_a} = undef; $x->{_p} = undef; |
574bacfe |
1040 | } |
61f5c3f5 |
1041 | # restore globals |
b3abae2a |
1042 | $$abr = $ab; $$pbr = $pb; |
574bacfe |
1043 | $x; |
58cde26e |
1044 | } |
1045 | |
b3abae2a |
1046 | sub bfac |
1047 | { |
28df3e88 |
1048 | # (BFLOAT or num_str, BFLOAT or num_str) return BFLOAT |
b3abae2a |
1049 | # compute factorial numbers |
1050 | # modifies first argument |
1051 | my ($self,$x,@r) = objectify(1,@_); |
1052 | |
28df3e88 |
1053 | return $x->bnan() |
1054 | if (($x->{sign} ne '+') || # inf, NaN, <0 etc => NaN |
1055 | ($x->{_e}->{sign} ne '+')); # digits after dot? |
b3abae2a |
1056 | |
28df3e88 |
1057 | return $x->bone(@r) if $x->is_zero() || $x->is_one(); # 0 or 1 => 1 |
b3abae2a |
1058 | |
1059 | # use BigInt's bfac() for faster calc |
1060 | $x->{_m}->blsft($x->{_e},10); # un-norm m |
1061 | $x->{_e}->bzero(); # norm $x again |
1062 | $x->{_m}->bfac(); # factorial |
28df3e88 |
1063 | $x->bnorm()->round(@r); |
b3abae2a |
1064 | } |
1065 | |
58cde26e |
1066 | sub bpow |
1067 | { |
1068 | # (BFLOAT or num_str, BFLOAT or num_str) return BFLOAT |
1069 | # compute power of two numbers, second arg is used as integer |
1070 | # modifies first argument |
1071 | |
1072 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
1073 | |
0716bf9b |
1074 | return $x if $x->{sign} =~ /^[+-]inf$/; |
58cde26e |
1075 | return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan; |
574bacfe |
1076 | return $x->bone() if $y->is_zero(); |
58cde26e |
1077 | return $x if $x->is_one() || $y->is_one(); |
ee15d750 |
1078 | my $y1 = $y->as_number(); # make bigint (trunc) |
394e6ffb |
1079 | # if ($x == -1) |
1080 | if ($x->{sign} eq '-' && $x->{_m}->is_one() && $x->{_e}->is_zero()) |
58cde26e |
1081 | { |
1082 | # if $x == -1 and odd/even y => +1/-1 because +-1 ^ (+-1) => +-1 |
0716bf9b |
1083 | return $y1->is_odd() ? $x : $x->babs(1); |
288d023a |
1084 | } |
28df3e88 |
1085 | if ($x->is_zero()) |
1086 | { |
1087 | return $x if $y->{sign} eq '+'; # 0**y => 0 (if not y <= 0) |
1088 | # 0 ** -y => 1 / (0 ** y) => / 0! (1 / 0 => +inf) |
1089 | $x->binf(); |
1090 | } |
58cde26e |
1091 | |
1092 | # calculate $x->{_m} ** $y and $x->{_e} * $y separately (faster) |
1093 | $y1->babs(); |
1094 | $x->{_m}->bpow($y1); |
1095 | $x->{_e}->bmul($y1); |
1096 | $x->{sign} = $nan if $x->{_m}->{sign} eq $nan || $x->{_e}->{sign} eq $nan; |
1097 | $x->bnorm(); |
1098 | if ($y->{sign} eq '-') |
1099 | { |
1100 | # modify $x in place! |
0716bf9b |
1101 | my $z = $x->copy(); $x->bzero()->binc(); |
58cde26e |
1102 | return $x->bdiv($z,$a,$p,$r); # round in one go (might ignore y's A!) |
a0d0e21e |
1103 | } |
28df3e88 |
1104 | $x->round($a,$p,$r,$y); |
58cde26e |
1105 | } |
1106 | |
1107 | ############################################################################### |
1108 | # rounding functions |
1109 | |
1110 | sub bfround |
1111 | { |
1112 | # precision: round to the $Nth digit left (+$n) or right (-$n) from the '.' |
1113 | # $n == 0 means round to integer |
1114 | # expects and returns normalized numbers! |
ee15d750 |
1115 | my $x = shift; my $self = ref($x) || $x; $x = $self->new(shift) if !ref($x); |
a0d0e21e |
1116 | |
58cde26e |
1117 | return $x if $x->modify('bfround'); |
1118 | |
ee15d750 |
1119 | my ($scale,$mode) = $x->_scale_p($self->precision(),$self->round_mode(),@_); |
58cde26e |
1120 | return $x if !defined $scale; # no-op |
1121 | |
574bacfe |
1122 | # never round a 0, +-inf, NaN |
61f5c3f5 |
1123 | if ($x->is_zero()) |
1124 | { |
1125 | $x->{_p} = $scale if !defined $x->{_p} || $x->{_p} < $scale; # -3 < -2 |
1126 | return $x; |
1127 | } |
1128 | return $x if $x->{sign} !~ /^[+-]$/; |
58cde26e |
1129 | # print "MBF bfround $x to scale $scale mode $mode\n"; |
58cde26e |
1130 | |
ee15d750 |
1131 | # don't round if x already has lower precision |
1132 | return $x if (defined $x->{_p} && $x->{_p} < 0 && $scale < $x->{_p}); |
1133 | |
1134 | $x->{_p} = $scale; # remember round in any case |
1135 | $x->{_a} = undef; # and clear A |
58cde26e |
1136 | if ($scale < 0) |
1137 | { |
1138 | # print "bfround scale $scale e $x->{_e}\n"; |
1139 | # round right from the '.' |
1140 | return $x if $x->{_e} >= 0; # nothing to round |
1141 | $scale = -$scale; # positive for simplicity |
1142 | my $len = $x->{_m}->length(); # length of mantissa |
1143 | my $dad = -$x->{_e}; # digits after dot |
1144 | my $zad = 0; # zeros after dot |
1145 | $zad = -$len-$x->{_e} if ($x->{_e} < -$len);# for 0.00..00xxx style |
ee15d750 |
1146 | #print "scale $scale dad $dad zad $zad len $len\n"; |
58cde26e |
1147 | |
1148 | # number bsstr len zad dad |
1149 | # 0.123 123e-3 3 0 3 |
1150 | # 0.0123 123e-4 3 1 4 |
1151 | # 0.001 1e-3 1 2 3 |
1152 | # 1.23 123e-2 3 0 2 |
1153 | # 1.2345 12345e-4 5 0 4 |
1154 | |
1155 | # do not round after/right of the $dad |
1156 | return $x if $scale > $dad; # 0.123, scale >= 3 => exit |
1157 | |
ee15d750 |
1158 | # round to zero if rounding inside the $zad, but not for last zero like: |
1159 | # 0.0065, scale -2, round last '0' with following '65' (scale == zad case) |
1160 | return $x->bzero() if $scale < $zad; |
1161 | if ($scale == $zad) # for 0.006, scale -3 and trunc |
58cde26e |
1162 | { |
b3abae2a |
1163 | $scale = -$len; |
58cde26e |
1164 | } |
1165 | else |
1166 | { |
1167 | # adjust round-point to be inside mantissa |
1168 | if ($zad != 0) |
1169 | { |
1170 | $scale = $scale-$zad; |
1171 | } |
1172 | else |
1173 | { |
1174 | my $dbd = $len - $dad; $dbd = 0 if $dbd < 0; # digits before dot |
1175 | $scale = $dbd+$scale; |
1176 | } |
1177 | } |
1178 | # print "round to $x->{_m} to $scale\n"; |
a0d0e21e |
1179 | } |
58cde26e |
1180 | else |
1181 | { |
1182 | # 123 => 100 means length(123) = 3 - $scale (2) => 1 |
a5f75d66 |
1183 | |
b3abae2a |
1184 | my $dbt = $x->{_m}->length(); |
1185 | # digits before dot |
1186 | my $dbd = $dbt + $x->{_e}; |
1187 | # should be the same, so treat it as this |
1188 | $scale = 1 if $scale == 0; |
1189 | # shortcut if already integer |
1190 | return $x if $scale == 1 && $dbt <= $dbd; |
1191 | # maximum digits before dot |
1192 | ++$dbd; |
1193 | |
1194 | if ($scale > $dbd) |
1195 | { |
1196 | # not enough digits before dot, so round to zero |
1197 | return $x->bzero; |
1198 | } |
1199 | elsif ( $scale == $dbd ) |
1200 | { |
1201 | # maximum |
1202 | $scale = -$dbt; |
1203 | } |
58cde26e |
1204 | else |
b3abae2a |
1205 | { |
1206 | $scale = $dbd - $scale; |
1207 | } |
1208 | |
a0d0e21e |
1209 | } |
574bacfe |
1210 | # print "using $scale for $x->{_m} with '$mode'\n"; |
1211 | # pass sign to bround for rounding modes '+inf' and '-inf' |
58cde26e |
1212 | $x->{_m}->{sign} = $x->{sign}; |
1213 | $x->{_m}->bround($scale,$mode); |
1214 | $x->{_m}->{sign} = '+'; # fix sign back |
1215 | $x->bnorm(); |
1216 | } |
1217 | |
1218 | sub bround |
1219 | { |
1220 | # accuracy: preserve $N digits, and overwrite the rest with 0's |
ee15d750 |
1221 | my $x = shift; my $self = ref($x) || $x; $x = $self->new(shift) if !ref($x); |
1222 | |
1223 | die ('bround() needs positive accuracy') if ($_[0] || 0) < 0; |
58cde26e |
1224 | |
ee15d750 |
1225 | my ($scale,$mode) = $x->_scale_a($self->accuracy(),$self->round_mode(),@_); |
1226 | return $x if !defined $scale; # no-op |
61f5c3f5 |
1227 | |
58cde26e |
1228 | return $x if $x->modify('bround'); |
61f5c3f5 |
1229 | |
ee15d750 |
1230 | # scale is now either $x->{_a}, $accuracy, or the user parameter |
1231 | # test whether $x already has lower accuracy, do nothing in this case |
1232 | # but do round if the accuracy is the same, since a math operation might |
1233 | # want to round a number with A=5 to 5 digits afterwards again |
1234 | return $x if defined $_[0] && defined $x->{_a} && $x->{_a} < $_[0]; |
58cde26e |
1235 | |
61f5c3f5 |
1236 | # scale < 0 makes no sense |
1237 | # never round a +-inf, NaN |
1238 | return $x if ($scale < 0) || $x->{sign} !~ /^[+-]$/; |
58cde26e |
1239 | |
61f5c3f5 |
1240 | # 1: $scale == 0 => keep all digits |
1241 | # 2: never round a 0 |
1242 | # 3: if we should keep more digits than the mantissa has, do nothing |
1243 | if ($scale == 0 || $x->is_zero() || $x->{_m}->length() <= $scale) |
1244 | { |
1245 | $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; |
1246 | return $x; |
1247 | } |
f216259d |
1248 | |
58cde26e |
1249 | # pass sign to bround for '+inf' and '-inf' rounding modes |
1250 | $x->{_m}->{sign} = $x->{sign}; |
1251 | $x->{_m}->bround($scale,$mode); # round mantissa |
1252 | $x->{_m}->{sign} = '+'; # fix sign back |
61f5c3f5 |
1253 | # $x->{_m}->{_a} = undef; $x->{_m}->{_p} = undef; |
ee15d750 |
1254 | $x->{_a} = $scale; # remember rounding |
1255 | $x->{_p} = undef; # and clear P |
574bacfe |
1256 | $x->bnorm(); # del trailing zeros gen. by bround() |
58cde26e |
1257 | } |
1258 | |
1259 | sub bfloor |
1260 | { |
1261 | # return integer less or equal then $x |
ee15d750 |
1262 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e |
1263 | |
1264 | return $x if $x->modify('bfloor'); |
1265 | |
1266 | return $x if $x->{sign} !~ /^[+-]$/; # nan, +inf, -inf |
1267 | |
1268 | # if $x has digits after dot |
1269 | if ($x->{_e}->{sign} eq '-') |
1270 | { |
28df3e88 |
1271 | #$x->{_m}->brsft(-$x->{_e},10); |
1272 | #$x->{_e}->bzero(); |
1273 | #$x-- if $x->{sign} eq '-'; |
1274 | |
1275 | $x->{_e}->{sign} = '+'; # negate e |
1276 | $x->{_m}->brsft($x->{_e},10); # cut off digits after dot |
1277 | $x->{_e}->bzero(); # trunc/norm |
1278 | $x->{_m}->binc() if $x->{sign} eq '-'; # decrement if negative |
f216259d |
1279 | } |
61f5c3f5 |
1280 | $x->round($a,$p,$r); |
58cde26e |
1281 | } |
288d023a |
1282 | |
58cde26e |
1283 | sub bceil |
1284 | { |
1285 | # return integer greater or equal then $x |
ee15d750 |
1286 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e |
1287 | |
1288 | return $x if $x->modify('bceil'); |
1289 | return $x if $x->{sign} !~ /^[+-]$/; # nan, +inf, -inf |
1290 | |
1291 | # if $x has digits after dot |
1292 | if ($x->{_e}->{sign} eq '-') |
1293 | { |
28df3e88 |
1294 | #$x->{_m}->brsft(-$x->{_e},10); |
1295 | #$x->{_e}->bzero(); |
1296 | #$x++ if $x->{sign} eq '+'; |
1297 | |
1298 | $x->{_e}->{sign} = '+'; # negate e |
1299 | $x->{_m}->brsft($x->{_e},10); # cut off digits after dot |
1300 | $x->{_e}->bzero(); # trunc/norm |
1301 | $x->{_m}->binc() if $x->{sign} eq '+'; # decrement if negative |
a0d0e21e |
1302 | } |
61f5c3f5 |
1303 | $x->round($a,$p,$r); |
58cde26e |
1304 | } |
1305 | |
394e6ffb |
1306 | sub brsft |
1307 | { |
1308 | # shift right by $y (divide by power of 2) |
1309 | my ($self,$x,$y,$n,$a,$p,$r) = objectify(2,@_); |
1310 | |
1311 | return $x if $x->modify('brsft'); |
1312 | return $x if $x->{sign} !~ /^[+-]$/; # nan, +inf, -inf |
1313 | |
1314 | $n = 2 if !defined $n; $n = Math::BigFloat->new($n); |
1315 | $x->bdiv($n ** $y,$a,$p,$r,$y); |
1316 | } |
1317 | |
1318 | sub blsft |
1319 | { |
1320 | # shift right by $y (divide by power of 2) |
1321 | my ($self,$x,$y,$n,$a,$p,$r) = objectify(2,@_); |
1322 | |
1323 | return $x if $x->modify('brsft'); |
1324 | return $x if $x->{sign} !~ /^[+-]$/; # nan, +inf, -inf |
1325 | |
1326 | $n = 2 if !defined $n; $n = Math::BigFloat->new($n); |
1327 | $x->bmul($n ** $y,$a,$p,$r,$y); |
1328 | } |
1329 | |
58cde26e |
1330 | ############################################################################### |
a5f75d66 |
1331 | |
58cde26e |
1332 | sub DESTROY |
1333 | { |
ee15d750 |
1334 | # going through AUTOLOAD for every DESTROY is costly, so avoid it by empty sub |
58cde26e |
1335 | } |
1336 | |
1337 | sub AUTOLOAD |
1338 | { |
b3abae2a |
1339 | # make fxxx and bxxx both work by selectively mapping fxxx() to MBF::bxxx() |
1340 | # or falling back to MBI::bxxx() |
58cde26e |
1341 | my $name = $AUTOLOAD; |
1342 | |
1343 | $name =~ s/.*:://; # split package |
ee15d750 |
1344 | no strict 'refs'; |
1345 | if (!method_alias($name)) |
58cde26e |
1346 | { |
ee15d750 |
1347 | if (!defined $name) |
1348 | { |
1349 | # delayed load of Carp and avoid recursion |
1350 | require Carp; |
1351 | Carp::croak ("Can't call a method without name"); |
1352 | } |
ee15d750 |
1353 | if (!method_hand_up($name)) |
1354 | { |
1355 | # delayed load of Carp and avoid recursion |
1356 | require Carp; |
1357 | Carp::croak ("Can't call $class\-\>$name, not a valid method"); |
1358 | } |
1359 | # try one level up, but subst. bxxx() for fxxx() since MBI only got bxxx() |
1360 | $name =~ s/^f/b/; |
1361 | return &{'Math::BigInt'."::$name"}(@_); |
a0d0e21e |
1362 | } |
58cde26e |
1363 | my $bname = $name; $bname =~ s/^f/b/; |
b3abae2a |
1364 | *{$class."::$name"} = \&$bname; |
58cde26e |
1365 | &$bname; # uses @_ |
1366 | } |
1367 | |
1368 | sub exponent |
1369 | { |
1370 | # return a copy of the exponent |
ee15d750 |
1371 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
1372 | |
ee15d750 |
1373 | if ($x->{sign} !~ /^[+-]$/) |
1374 | { |
1375 | my $s = $x->{sign}; $s =~ s/^[+-]//; |
1376 | return $self->new($s); # -inf, +inf => +inf |
1377 | } |
1378 | return $x->{_e}->copy(); |
58cde26e |
1379 | } |
1380 | |
1381 | sub mantissa |
1382 | { |
1383 | # return a copy of the mantissa |
ee15d750 |
1384 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
1385 | |
ee15d750 |
1386 | if ($x->{sign} !~ /^[+-]$/) |
1387 | { |
1388 | my $s = $x->{sign}; $s =~ s/^[+]//; |
1389 | return $self->new($s); # -inf, +inf => +inf |
1390 | } |
1391 | my $m = $x->{_m}->copy(); # faster than going via bstr() |
1392 | $m->bneg() if $x->{sign} eq '-'; |
58cde26e |
1393 | |
61f5c3f5 |
1394 | $m; |
58cde26e |
1395 | } |
1396 | |
1397 | sub parts |
1398 | { |
1399 | # return a copy of both the exponent and the mantissa |
ee15d750 |
1400 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
1401 | |
ee15d750 |
1402 | if ($x->{sign} !~ /^[+-]$/) |
1403 | { |
1404 | my $s = $x->{sign}; $s =~ s/^[+]//; my $se = $s; $se =~ s/^[-]//; |
1405 | return ($self->new($s),$self->new($se)); # +inf => inf and -inf,+inf => inf |
1406 | } |
1407 | my $m = $x->{_m}->copy(); # faster than going via bstr() |
1408 | $m->bneg() if $x->{sign} eq '-'; |
1409 | return ($m,$x->{_e}->copy()); |
58cde26e |
1410 | } |
1411 | |
1412 | ############################################################################## |
1413 | # private stuff (internal use only) |
1414 | |
58cde26e |
1415 | sub import |
1416 | { |
1417 | my $self = shift; |
b3abae2a |
1418 | my $l = scalar @_; my $j = 0; my @a = @_; |
1419 | for ( my $i = 0; $i < $l ; $i++, $j++) |
58cde26e |
1420 | { |
1421 | if ( $_[$i] eq ':constant' ) |
1422 | { |
1423 | # this rest causes overlord er load to step in |
1424 | # print "overload @_\n"; |
1425 | overload::constant float => sub { $self->new(shift); }; |
b3abae2a |
1426 | splice @a, $j, 1; $j--; |
1427 | } |
1428 | elsif ($_[$i] eq 'upgrade') |
1429 | { |
1430 | # this causes upgrading |
28df3e88 |
1431 | $upgrade = $_[$i+1]; # or undef to disable |
1432 | my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..." |
1433 | splice @a, $j, $s; $j -= $s; |
1434 | } |
1435 | elsif ($_[$i] eq 'downgrade') |
1436 | { |
1437 | # this causes downgrading |
1438 | $downgrade = $_[$i+1]; # or undef to disable |
b3abae2a |
1439 | my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..." |
1440 | splice @a, $j, $s; $j -= $s; |
58cde26e |
1441 | } |
1442 | } |
1443 | # any non :constant stuff is handled by our parent, Exporter |
1444 | # even if @_ is empty, to give it a chance |
b3abae2a |
1445 | $self->SUPER::import(@a); # for subclasses |
1446 | $self->export_to_level(1,$self,@a); # need this, too |
58cde26e |
1447 | } |
1448 | |
1449 | sub bnorm |
1450 | { |
1451 | # adjust m and e so that m is smallest possible |
1452 | # round number according to accuracy and precision settings |
ee15d750 |
1453 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
1454 | |
0716bf9b |
1455 | return $x if $x->{sign} !~ /^[+-]$/; # inf, nan etc |
58cde26e |
1456 | |
28df3e88 |
1457 | # if (!$x->{_m}->is_odd()) |
1458 | # { |
1459 | my $zeros = $x->{_m}->_trailing_zeros(); # correct for trailing zeros |
1460 | if ($zeros != 0) |
1461 | { |
1462 | $x->{_m}->brsft($zeros,10); $x->{_e}->badd($zeros); |
1463 | } |
1464 | # for something like 0Ey, set y to 1, and -0 => +0 |
1465 | $x->{sign} = '+', $x->{_e}->bone() if $x->{_m}->is_zero(); |
1466 | # } |
ee15d750 |
1467 | # this is to prevent automatically rounding when MBI's globals are set |
0716bf9b |
1468 | $x->{_m}->{_f} = MB_NEVER_ROUND; |
1469 | $x->{_e}->{_f} = MB_NEVER_ROUND; |
ee15d750 |
1470 | # 'forget' that mantissa was rounded via MBI::bround() in MBF's bfround() |
1471 | $x->{_m}->{_a} = undef; $x->{_e}->{_a} = undef; |
1472 | $x->{_m}->{_p} = undef; $x->{_e}->{_p} = undef; |
61f5c3f5 |
1473 | $x; # MBI bnorm is no-op, so dont call it |
1474 | } |
58cde26e |
1475 | |
1476 | ############################################################################## |
1477 | # internal calculation routines |
1478 | |
1479 | sub as_number |
1480 | { |
394e6ffb |
1481 | # return copy as a bigint representation of this BigFloat number |
1482 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
1483 | |
28df3e88 |
1484 | my $z = $x->{_m}->copy(); |
1485 | if ($x->{_e}->{sign} eq '-') # < 0 |
58cde26e |
1486 | { |
28df3e88 |
1487 | $x->{_e}->{sign} = '+'; # flip |
1488 | $z->brsft($x->{_e},10); |
1489 | $x->{_e}->{sign} = '-'; # flip back |
0716bf9b |
1490 | } |
28df3e88 |
1491 | elsif (!$x->{_e}->is_zero()) # > 0 |
0716bf9b |
1492 | { |
1493 | $z->blsft($x->{_e},10); |
58cde26e |
1494 | } |
58cde26e |
1495 | $z->{sign} = $x->{sign}; |
61f5c3f5 |
1496 | $z; |
58cde26e |
1497 | } |
1498 | |
1499 | sub length |
1500 | { |
ee15d750 |
1501 | my $x = shift; |
1502 | my $class = ref($x) || $x; |
1503 | $x = $class->new(shift) unless ref($x); |
58cde26e |
1504 | |
ee15d750 |
1505 | return 1 if $x->{_m}->is_zero(); |
58cde26e |
1506 | my $len = $x->{_m}->length(); |
1507 | $len += $x->{_e} if $x->{_e}->sign() eq '+'; |
1508 | if (wantarray()) |
1509 | { |
1510 | my $t = Math::BigInt::bzero(); |
1511 | $t = $x->{_e}->copy()->babs() if $x->{_e}->sign() eq '-'; |
1512 | return ($len,$t); |
1513 | } |
61f5c3f5 |
1514 | $len; |
58cde26e |
1515 | } |
a0d0e21e |
1516 | |
1517 | 1; |
a5f75d66 |
1518 | __END__ |
1519 | |
1520 | =head1 NAME |
1521 | |
58cde26e |
1522 | Math::BigFloat - Arbitrary size floating point math package |
a5f75d66 |
1523 | |
1524 | =head1 SYNOPSIS |
1525 | |
a2008d6d |
1526 | use Math::BigFloat; |
58cde26e |
1527 | |
b3abae2a |
1528 | # Number creation |
1529 | $x = Math::BigFloat->new($str); # defaults to 0 |
1530 | $nan = Math::BigFloat->bnan(); # create a NotANumber |
1531 | $zero = Math::BigFloat->bzero(); # create a +0 |
1532 | $inf = Math::BigFloat->binf(); # create a +inf |
1533 | $inf = Math::BigFloat->binf('-'); # create a -inf |
1534 | $one = Math::BigFloat->bone(); # create a +1 |
1535 | $one = Math::BigFloat->bone('-'); # create a -1 |
58cde26e |
1536 | |
1537 | # Testing |
b3abae2a |
1538 | $x->is_zero(); # true if arg is +0 |
1539 | $x->is_nan(); # true if arg is NaN |
0716bf9b |
1540 | $x->is_one(); # true if arg is +1 |
1541 | $x->is_one('-'); # true if arg is -1 |
1542 | $x->is_odd(); # true if odd, false for even |
1543 | $x->is_even(); # true if even, false for odd |
1544 | $x->is_positive(); # true if >= 0 |
1545 | $x->is_negative(); # true if < 0 |
b3abae2a |
1546 | $x->is_inf(sign); # true if +inf, or -inf (default is '+') |
1547 | |
58cde26e |
1548 | $x->bcmp($y); # compare numbers (undef,<0,=0,>0) |
1549 | $x->bacmp($y); # compare absolutely (undef,<0,=0,>0) |
1550 | $x->sign(); # return the sign, either +,- or NaN |
b3abae2a |
1551 | $x->digit($n); # return the nth digit, counting from right |
1552 | $x->digit(-$n); # return the nth digit, counting from left |
58cde26e |
1553 | |
1554 | # The following all modify their first argument: |
b3abae2a |
1555 | |
58cde26e |
1556 | # set |
1557 | $x->bzero(); # set $i to 0 |
1558 | $x->bnan(); # set $i to NaN |
b3abae2a |
1559 | $x->bone(); # set $x to +1 |
1560 | $x->bone('-'); # set $x to -1 |
1561 | $x->binf(); # set $x to inf |
1562 | $x->binf('-'); # set $x to -inf |
58cde26e |
1563 | |
1564 | $x->bneg(); # negation |
1565 | $x->babs(); # absolute value |
1566 | $x->bnorm(); # normalize (no-op) |
1567 | $x->bnot(); # two's complement (bit wise not) |
1568 | $x->binc(); # increment x by 1 |
1569 | $x->bdec(); # decrement x by 1 |
1570 | |
1571 | $x->badd($y); # addition (add $y to $x) |
1572 | $x->bsub($y); # subtraction (subtract $y from $x) |
1573 | $x->bmul($y); # multiplication (multiply $x by $y) |
1574 | $x->bdiv($y); # divide, set $i to quotient |
1575 | # return (quo,rem) or quo if scalar |
1576 | |
1577 | $x->bmod($y); # modulus |
1578 | $x->bpow($y); # power of arguments (a**b) |
1579 | $x->blsft($y); # left shift |
1580 | $x->brsft($y); # right shift |
1581 | # return (quo,rem) or quo if scalar |
1582 | |
61f5c3f5 |
1583 | $x->blog($base); # logarithm of $x, base defaults to e |
1584 | # (other bases than e not supported yet) |
1585 | |
58cde26e |
1586 | $x->band($y); # bit-wise and |
1587 | $x->bior($y); # bit-wise inclusive or |
1588 | $x->bxor($y); # bit-wise exclusive or |
1589 | $x->bnot(); # bit-wise not (two's complement) |
b3abae2a |
1590 | |
1591 | $x->bsqrt(); # calculate square-root |
1592 | $x->bfac(); # factorial of $x (1*2*3*4*..$x) |
1593 | |
58cde26e |
1594 | $x->bround($N); # accuracy: preserver $N digits |
1595 | $x->bfround($N); # precision: round to the $Nth digit |
1596 | |
1597 | # The following do not modify their arguments: |
58cde26e |
1598 | bgcd(@values); # greatest common divisor |
1599 | blcm(@values); # lowest common multiplicator |
1600 | |
1601 | $x->bstr(); # return string |
1602 | $x->bsstr(); # return string in scientific notation |
b3abae2a |
1603 | |
1604 | $x->bfloor(); # return integer less or equal than $x |
1605 | $x->bceil(); # return integer greater or equal than $x |
1606 | |
58cde26e |
1607 | $x->exponent(); # return exponent as BigInt |
1608 | $x->mantissa(); # return mantissa as BigInt |
1609 | $x->parts(); # return (mantissa,exponent) as BigInt |
1610 | |
1611 | $x->length(); # number of digits (w/o sign and '.') |
1612 | ($l,$f) = $x->length(); # number of digits, and length of fraction |
a5f75d66 |
1613 | |
1614 | =head1 DESCRIPTION |
1615 | |
58cde26e |
1616 | All operators (inlcuding basic math operations) are overloaded if you |
1617 | declare your big floating point numbers as |
a5f75d66 |
1618 | |
58cde26e |
1619 | $i = new Math::BigFloat '12_3.456_789_123_456_789E-2'; |
1620 | |
1621 | Operations with overloaded operators preserve the arguments, which is |
1622 | exactly what you expect. |
1623 | |
1624 | =head2 Canonical notation |
1625 | |
1626 | Input to these routines are either BigFloat objects, or strings of the |
1627 | following four forms: |
a5f75d66 |
1628 | |
1629 | =over 2 |
1630 | |
58cde26e |
1631 | =item * |
1632 | |
1633 | C</^[+-]\d+$/> |
a5f75d66 |
1634 | |
58cde26e |
1635 | =item * |
a5f75d66 |
1636 | |
58cde26e |
1637 | C</^[+-]\d+\.\d*$/> |
a5f75d66 |
1638 | |
58cde26e |
1639 | =item * |
a5f75d66 |
1640 | |
58cde26e |
1641 | C</^[+-]\d+E[+-]?\d+$/> |
a5f75d66 |
1642 | |
58cde26e |
1643 | =item * |
a5f75d66 |
1644 | |
58cde26e |
1645 | C</^[+-]\d*\.\d+E[+-]?\d+$/> |
5d7098d5 |
1646 | |
58cde26e |
1647 | =back |
1648 | |
1649 | all with optional leading and trailing zeros and/or spaces. Additonally, |
1650 | numbers are allowed to have an underscore between any two digits. |
1651 | |
1652 | Empty strings as well as other illegal numbers results in 'NaN'. |
1653 | |
1654 | bnorm() on a BigFloat object is now effectively a no-op, since the numbers |
1655 | are always stored in normalized form. On a string, it creates a BigFloat |
1656 | object. |
1657 | |
1658 | =head2 Output |
1659 | |
1660 | Output values are BigFloat objects (normalized), except for bstr() and bsstr(). |
1661 | |
1662 | The string output will always have leading and trailing zeros stripped and drop |
1663 | a plus sign. C<bstr()> will give you always the form with a decimal point, |
1664 | while C<bsstr()> (for scientific) gives you the scientific notation. |
1665 | |
1666 | Input bstr() bsstr() |
1667 | '-0' '0' '0E1' |
1668 | ' -123 123 123' '-123123123' '-123123123E0' |
1669 | '00.0123' '0.0123' '123E-4' |
1670 | '123.45E-2' '1.2345' '12345E-4' |
1671 | '10E+3' '10000' '1E4' |
1672 | |
1673 | Some routines (C<is_odd()>, C<is_even()>, C<is_zero()>, C<is_one()>, |
1674 | C<is_nan()>) return true or false, while others (C<bcmp()>, C<bacmp()>) |
1675 | return either undef, <0, 0 or >0 and are suited for sort. |
1676 | |
1677 | Actual math is done by using BigInts to represent the mantissa and exponent. |
1678 | The sign C</^[+-]$/> is stored separately. The string 'NaN' is used to |
1679 | represent the result when input arguments are not numbers, as well as |
1680 | the result of dividing by zero. |
1681 | |
1682 | =head2 C<mantissa()>, C<exponent()> and C<parts()> |
1683 | |
1684 | C<mantissa()> and C<exponent()> return the said parts of the BigFloat |
1685 | as BigInts such that: |
1686 | |
1687 | $m = $x->mantissa(); |
1688 | $e = $x->exponent(); |
1689 | $y = $m * ( 10 ** $e ); |
1690 | print "ok\n" if $x == $y; |
1691 | |
1692 | C<< ($m,$e) = $x->parts(); >> is just a shortcut giving you both of them. |
1693 | |
1694 | A zero is represented and returned as C<0E1>, B<not> C<0E0> (after Knuth). |
1695 | |
1696 | Currently the mantissa is reduced as much as possible, favouring higher |
1697 | exponents over lower ones (e.g. returning 1e7 instead of 10e6 or 10000000e0). |
1698 | This might change in the future, so do not depend on it. |
1699 | |
1700 | =head2 Accuracy vs. Precision |
1701 | |
1702 | See also: L<Rounding|Rounding>. |
1703 | |
027dc388 |
1704 | Math::BigFloat supports both precision and accuracy. For a full documentation, |
1705 | examples and tips on these topics please see the large section in |
1706 | L<Math::BigInt>. |
5d7098d5 |
1707 | |
58cde26e |
1708 | Since things like sqrt(2) or 1/3 must presented with a limited precision lest |
1709 | a operation consumes all resources, each operation produces no more than |
1710 | C<Math::BigFloat::precision()> digits. |
1711 | |
1712 | In case the result of one operation has more precision than specified, |
1713 | it is rounded. The rounding mode taken is either the default mode, or the one |
1714 | supplied to the operation after the I<scale>: |
1715 | |
1716 | $x = Math::BigFloat->new(2); |
1717 | Math::BigFloat::precision(5); # 5 digits max |
1718 | $y = $x->copy()->bdiv(3); # will give 0.66666 |
1719 | $y = $x->copy()->bdiv(3,6); # will give 0.666666 |
1720 | $y = $x->copy()->bdiv(3,6,'odd'); # will give 0.666667 |
1721 | Math::BigFloat::round_mode('zero'); |
1722 | $y = $x->copy()->bdiv(3,6); # will give 0.666666 |
1723 | |
1724 | =head2 Rounding |
1725 | |
1726 | =over 2 |
1727 | |
5dc6f178 |
1728 | =item ffround ( +$scale ) |
58cde26e |
1729 | |
0716bf9b |
1730 | Rounds to the $scale'th place left from the '.', counting from the dot. |
1731 | The first digit is numbered 1. |
58cde26e |
1732 | |
5dc6f178 |
1733 | =item ffround ( -$scale ) |
58cde26e |
1734 | |
0716bf9b |
1735 | Rounds to the $scale'th place right from the '.', counting from the dot. |
58cde26e |
1736 | |
5dc6f178 |
1737 | =item ffround ( 0 ) |
1738 | |
0716bf9b |
1739 | Rounds to an integer. |
5dc6f178 |
1740 | |
1741 | =item fround ( +$scale ) |
1742 | |
0716bf9b |
1743 | Preserves accuracy to $scale digits from the left (aka significant digits) |
1744 | and pads the rest with zeros. If the number is between 1 and -1, the |
1745 | significant digits count from the first non-zero after the '.' |
5dc6f178 |
1746 | |
1747 | =item fround ( -$scale ) and fround ( 0 ) |
1748 | |
0716bf9b |
1749 | These are effetively no-ops. |
5d7098d5 |
1750 | |
a5f75d66 |
1751 | =back |
1752 | |
0716bf9b |
1753 | All rounding functions take as a second parameter a rounding mode from one of |
1754 | the following: 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'. |
58cde26e |
1755 | |
1756 | The default rounding mode is 'even'. By using |
ee15d750 |
1757 | C<< Math::BigFloat::round_mode($round_mode); >> you can get and set the default |
1758 | mode for subsequent rounding. The usage of C<$Math::BigFloat::$round_mode> is |
0716bf9b |
1759 | no longer supported. |
b22b3e31 |
1760 | The second parameter to the round functions then overrides the default |
0716bf9b |
1761 | temporarily. |
58cde26e |
1762 | |
1763 | The C<< as_number() >> function returns a BigInt from a Math::BigFloat. It uses |
1764 | 'trunc' as rounding mode to make it equivalent to: |
1765 | |
1766 | $x = 2.5; |
1767 | $y = int($x) + 2; |
1768 | |
1769 | You can override this by passing the desired rounding mode as parameter to |
1770 | C<as_number()>: |
1771 | |
1772 | $x = Math::BigFloat->new(2.5); |
1773 | $y = $x->as_number('odd'); # $y = 3 |
1774 | |
1775 | =head1 EXAMPLES |
1776 | |
58cde26e |
1777 | # not ready yet |
58cde26e |
1778 | |
1779 | =head1 Autocreating constants |
1780 | |
1781 | After C<use Math::BigFloat ':constant'> all the floating point constants |
1782 | in the given scope are converted to C<Math::BigFloat>. This conversion |
1783 | happens at compile time. |
1784 | |
1785 | In particular |
1786 | |
1787 | perl -MMath::BigFloat=:constant -e 'print 2E-100,"\n"' |
1788 | |
1789 | prints the value of C<2E-100>. Note that without conversion of |
1790 | constants the expression 2E-100 will be calculated as normal floating point |
1791 | number. |
1792 | |
a5f75d66 |
1793 | =head1 BUGS |
1794 | |
58cde26e |
1795 | =over 2 |
1796 | |
1797 | =item * |
1798 | |
1799 | The following does not work yet: |
1800 | |
1801 | $m = $x->mantissa(); |
1802 | $e = $x->exponent(); |
1803 | $y = $m * ( 10 ** $e ); |
1804 | print "ok\n" if $x == $y; |
1805 | |
1806 | =item * |
1807 | |
1808 | There is no fmod() function yet. |
1809 | |
1810 | =back |
1811 | |
1812 | =head1 CAVEAT |
1813 | |
1814 | =over 1 |
1815 | |
1816 | =item stringify, bstr() |
1817 | |
1818 | Both stringify and bstr() now drop the leading '+'. The old code would return |
1819 | '+1.23', the new returns '1.23'. See the documentation in L<Math::BigInt> for |
1820 | reasoning and details. |
1821 | |
1822 | =item bdiv |
1823 | |
1824 | The following will probably not do what you expect: |
1825 | |
1826 | print $c->bdiv(123.456),"\n"; |
1827 | |
1828 | It prints both quotient and reminder since print works in list context. Also, |
1829 | bdiv() will modify $c, so be carefull. You probably want to use |
1830 | |
1831 | print $c / 123.456,"\n"; |
1832 | print scalar $c->bdiv(123.456),"\n"; # or if you want to modify $c |
1833 | |
1834 | instead. |
1835 | |
1836 | =item Modifying and = |
1837 | |
1838 | Beware of: |
1839 | |
1840 | $x = Math::BigFloat->new(5); |
1841 | $y = $x; |
1842 | |
1843 | It will not do what you think, e.g. making a copy of $x. Instead it just makes |
1844 | a second reference to the B<same> object and stores it in $y. Thus anything |
1845 | that modifies $x will modify $y, and vice versa. |
1846 | |
1847 | $x->bmul(2); |
1848 | print "$x, $y\n"; # prints '10, 10' |
1849 | |
1850 | If you want a true copy of $x, use: |
1851 | |
1852 | $y = $x->copy(); |
1853 | |
1854 | See also the documentation in L<overload> regarding C<=>. |
1855 | |
1856 | =item bpow |
1857 | |
1858 | C<bpow()> now modifies the first argument, unlike the old code which left |
1859 | it alone and only returned the result. This is to be consistent with |
1860 | C<badd()> etc. The first will modify $x, the second one won't: |
1861 | |
1862 | print bpow($x,$i),"\n"; # modify $x |
1863 | print $x->bpow($i),"\n"; # ditto |
1864 | print $x ** $i,"\n"; # leave $x alone |
1865 | |
1866 | =back |
1867 | |
1868 | =head1 LICENSE |
a5f75d66 |
1869 | |
58cde26e |
1870 | This program is free software; you may redistribute it and/or modify it under |
1871 | the same terms as Perl itself. |
5d7098d5 |
1872 | |
58cde26e |
1873 | =head1 AUTHORS |
5d7098d5 |
1874 | |
58cde26e |
1875 | Mark Biggar, overloaded interface by Ilya Zakharevich. |
1876 | Completely rewritten by Tels http://bloodgate.com in 2001. |
a5f75d66 |
1877 | |
a5f75d66 |
1878 | =cut |