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) |
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 | |
1ddff52a |
15 | $VERSION = '1.34'; |
58cde26e |
16 | require 5.005; |
17 | use Exporter; |
56b9c951 |
18 | use File::Spec; |
19 | # use Math::BigInt; |
58cde26e |
20 | @ISA = qw( Exporter Math::BigInt); |
394e6ffb |
21 | |
58cde26e |
22 | use strict; |
027dc388 |
23 | use vars qw/$AUTOLOAD $accuracy $precision $div_scale $round_mode $rnd_mode/; |
8f675a64 |
24 | use vars qw/$upgrade $downgrade/; |
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 | ############################################################################## |
35 | # global constants, flags and accessory |
36 | |
37 | use constant MB_NEVER_ROUND => 0x0001; |
38 | |
58cde26e |
39 | # are NaNs ok? |
40 | my $NaNOK=1; |
58cde26e |
41 | # constant for easier life |
42 | my $nan = 'NaN'; |
58cde26e |
43 | |
ee15d750 |
44 | # class constants, use Class->constant_name() to access |
45 | $round_mode = 'even'; # one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc' |
46 | $accuracy = undef; |
47 | $precision = undef; |
48 | $div_scale = 40; |
58cde26e |
49 | |
b3abae2a |
50 | $upgrade = undef; |
51 | $downgrade = undef; |
8f675a64 |
52 | my $MBI = 'Math::BigInt'; # the package we are using for our private parts |
53 | # changable by use Math::BigFloat with => 'package' |
b3abae2a |
54 | |
027dc388 |
55 | ############################################################################## |
56 | # the old code had $rnd_mode, so we need to support it, too |
57 | |
027dc388 |
58 | sub TIESCALAR { my ($class) = @_; bless \$round_mode, $class; } |
59 | sub FETCH { return $round_mode; } |
60 | sub STORE { $rnd_mode = $_[0]->round_mode($_[1]); } |
61 | |
56b9c951 |
62 | BEGIN |
63 | { |
64 | $rnd_mode = 'even'; |
65 | tie $rnd_mode, 'Math::BigFloat'; |
66 | } |
027dc388 |
67 | |
68 | ############################################################################## |
69 | |
574bacfe |
70 | # in case we call SUPER::->foo() and this wants to call modify() |
71 | # sub modify () { 0; } |
72 | |
58cde26e |
73 | { |
ee15d750 |
74 | # valid method aliases for AUTOLOAD |
58cde26e |
75 | my %methods = map { $_ => 1 } |
76 | qw / fadd fsub fmul fdiv fround ffround fsqrt fmod fstr fsstr fpow fnorm |
b3abae2a |
77 | fint facmp fcmp fzero fnan finf finc fdec flog ffac |
61f5c3f5 |
78 | fceil ffloor frsft flsft fone flog |
ee15d750 |
79 | /; |
61f5c3f5 |
80 | # valid method's that can be hand-ed up (for AUTOLOAD) |
ee15d750 |
81 | my %hand_ups = map { $_ => 1 } |
82 | qw / is_nan is_inf is_negative is_positive |
394e6ffb |
83 | accuracy precision div_scale round_mode fneg fabs babs fnot |
28df3e88 |
84 | objectify upgrade downgrade |
13a12e00 |
85 | bone binf bnan bzero |
58cde26e |
86 | /; |
87 | |
ee15d750 |
88 | sub method_alias { return exists $methods{$_[0]||''}; } |
89 | sub method_hand_up { return exists $hand_ups{$_[0]||''}; } |
a0d0e21e |
90 | } |
0e8b9368 |
91 | |
58cde26e |
92 | ############################################################################## |
93 | # constructors |
a0d0e21e |
94 | |
58cde26e |
95 | sub new |
96 | { |
97 | # create a new BigFloat object from a string or another bigfloat object. |
98 | # _e: exponent |
99 | # _m: mantissa |
100 | # sign => sign (+/-), or "NaN" |
a0d0e21e |
101 | |
61f5c3f5 |
102 | my ($class,$wanted,@r) = @_; |
b3abae2a |
103 | |
61f5c3f5 |
104 | # avoid numify-calls by not using || on $wanted! |
105 | return $class->bzero() if !defined $wanted; # default to 0 |
106 | return $wanted->copy() if UNIVERSAL::isa($wanted,'Math::BigFloat'); |
a0d0e21e |
107 | |
58cde26e |
108 | my $self = {}; bless $self, $class; |
b22b3e31 |
109 | # shortcut for bigints and its subclasses |
0716bf9b |
110 | if ((ref($wanted)) && (ref($wanted) ne $class)) |
58cde26e |
111 | { |
0716bf9b |
112 | $self->{_m} = $wanted->as_number(); # get us a bigint copy |
56b9c951 |
113 | $self->{_e} = $MBI->bzero(); |
58cde26e |
114 | $self->{_m}->babs(); |
115 | $self->{sign} = $wanted->sign(); |
0716bf9b |
116 | return $self->bnorm(); |
58cde26e |
117 | } |
118 | # got string |
119 | # handle '+inf', '-inf' first |
ee15d750 |
120 | if ($wanted =~ /^[+-]?inf$/) |
58cde26e |
121 | { |
28df3e88 |
122 | return $downgrade->new($wanted) if $downgrade; |
123 | |
56b9c951 |
124 | $self->{_e} = $MBI->bzero(); |
125 | $self->{_m} = $MBI->bzero(); |
58cde26e |
126 | $self->{sign} = $wanted; |
ee15d750 |
127 | $self->{sign} = '+inf' if $self->{sign} eq 'inf'; |
0716bf9b |
128 | return $self->bnorm(); |
58cde26e |
129 | } |
130 | #print "new string '$wanted'\n"; |
131 | my ($mis,$miv,$mfv,$es,$ev) = Math::BigInt::_split(\$wanted); |
132 | if (!ref $mis) |
133 | { |
134 | die "$wanted is not a number initialized to $class" if !$NaNOK; |
28df3e88 |
135 | |
136 | return $downgrade->bnan() if $downgrade; |
137 | |
56b9c951 |
138 | $self->{_e} = $MBI->bzero(); |
139 | $self->{_m} = $MBI->bzero(); |
58cde26e |
140 | $self->{sign} = $nan; |
141 | } |
142 | else |
143 | { |
144 | # make integer from mantissa by adjusting exp, then convert to bigint |
61f5c3f5 |
145 | # undef,undef to signal MBI that we don't need no bloody rounding |
56b9c951 |
146 | $self->{_e} = $MBI->new("$$es$$ev",undef,undef); # exponent |
147 | $self->{_m} = $MBI->new("$$miv$$mfv",undef,undef); # create mant. |
58cde26e |
148 | # 3.123E0 = 3123E-3, and 3.123E-2 => 3123E-5 |
027dc388 |
149 | $self->{_e} -= CORE::length($$mfv) if CORE::length($$mfv) != 0; |
150 | $self->{sign} = $$mis; |
58cde26e |
151 | } |
28df3e88 |
152 | # if downgrade, inf, NaN or integers go down |
153 | |
154 | if ($downgrade && $self->{_e}->{sign} eq '+') |
155 | { |
156 | # print "downgrading $$miv$$mfv"."E$$es$$ev"; |
157 | if ($self->{_e}->is_zero()) |
158 | { |
159 | $self->{_m}->{sign} = $$mis; # negative if wanted |
160 | return $downgrade->new($self->{_m}); |
161 | } |
162 | return $downgrade->new("$$mis$$miv$$mfv"."E$$es$$ev"); |
163 | } |
9393ace2 |
164 | # print "mbf new $self->{sign} $self->{_m} e $self->{_e} ",ref($self),"\n"; |
61f5c3f5 |
165 | $self->bnorm()->round(@r); # first normalize, then round |
58cde26e |
166 | } |
a0d0e21e |
167 | |
13a12e00 |
168 | sub _bnan |
58cde26e |
169 | { |
13a12e00 |
170 | # used by parent class bone() to initialize number to 1 |
58cde26e |
171 | my $self = shift; |
56b9c951 |
172 | $self->{_m} = $MBI->bzero(); |
173 | $self->{_e} = $MBI->bzero(); |
58cde26e |
174 | } |
a0d0e21e |
175 | |
13a12e00 |
176 | sub _binf |
58cde26e |
177 | { |
13a12e00 |
178 | # used by parent class bone() to initialize number to 1 |
58cde26e |
179 | my $self = shift; |
56b9c951 |
180 | $self->{_m} = $MBI->bzero(); |
181 | $self->{_e} = $MBI->bzero(); |
58cde26e |
182 | } |
a0d0e21e |
183 | |
13a12e00 |
184 | sub _bone |
574bacfe |
185 | { |
13a12e00 |
186 | # used by parent class bone() to initialize number to 1 |
574bacfe |
187 | my $self = shift; |
56b9c951 |
188 | $self->{_m} = $MBI->bone(); |
189 | $self->{_e} = $MBI->bzero(); |
574bacfe |
190 | } |
191 | |
13a12e00 |
192 | sub _bzero |
58cde26e |
193 | { |
13a12e00 |
194 | # used by parent class bone() to initialize number to 1 |
58cde26e |
195 | my $self = shift; |
56b9c951 |
196 | $self->{_m} = $MBI->bzero(); |
197 | $self->{_e} = $MBI->bone(); |
58cde26e |
198 | } |
199 | |
9393ace2 |
200 | sub isa |
201 | { |
202 | my ($self,$class) = @_; |
56b9c951 |
203 | return if $class =~ /^Math::BigInt/; # we aren't one of these |
204 | UNIVERSAL::isa($self,$class); |
9393ace2 |
205 | } |
206 | |
8f675a64 |
207 | sub config |
208 | { |
209 | # return (later set?) configuration data as hash ref |
210 | my $class = shift || 'Math::BigFloat'; |
211 | |
212 | my $cfg = $MBI->config(); |
213 | |
214 | no strict 'refs'; |
215 | $cfg->{class} = $class; |
216 | $cfg->{with} = $MBI; |
217 | foreach ( |
218 | qw/upgrade downgrade precision accuracy round_mode VERSION div_scale/) |
219 | { |
220 | $cfg->{lc($_)} = ${"${class}::$_"}; |
221 | }; |
222 | $cfg; |
223 | } |
224 | |
58cde26e |
225 | ############################################################################## |
226 | # string conversation |
227 | |
228 | sub bstr |
229 | { |
230 | # (ref to BFLOAT or num_str ) return num_str |
231 | # Convert number from internal format to (non-scientific) string format. |
232 | # internal format is always normalized (no leading zeros, "-0" => "+0") |
ee15d750 |
233 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
234 | #my $x = shift; my $class = ref($x) || $x; |
235 | #$x = $class->new(shift) unless ref($x); |
58cde26e |
236 | |
574bacfe |
237 | #die "Oups! e was $nan" if $x->{_e}->{sign} eq $nan; |
238 | #die "Oups! m was $nan" if $x->{_m}->{sign} eq $nan; |
239 | if ($x->{sign} !~ /^[+-]$/) |
58cde26e |
240 | { |
574bacfe |
241 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN |
242 | return 'inf'; # +inf |
58cde26e |
243 | } |
244 | |
574bacfe |
245 | my $es = '0'; my $len = 1; my $cad = 0; my $dot = '.'; |
246 | |
28df3e88 |
247 | my $not_zero = ! $x->is_zero(); |
574bacfe |
248 | if ($not_zero) |
58cde26e |
249 | { |
574bacfe |
250 | $es = $x->{_m}->bstr(); |
251 | $len = CORE::length($es); |
252 | if (!$x->{_e}->is_zero()) |
58cde26e |
253 | { |
574bacfe |
254 | if ($x->{_e}->sign() eq '-') |
255 | { |
256 | $dot = ''; |
257 | if ($x->{_e} <= -$len) |
258 | { |
259 | # print "style: 0.xxxx\n"; |
260 | my $r = $x->{_e}->copy(); $r->babs()->bsub( CORE::length($es) ); |
261 | $es = '0.'. ('0' x $r) . $es; $cad = -($len+$r); |
262 | } |
263 | else |
264 | { |
265 | # print "insert '.' at $x->{_e} in '$es'\n"; |
266 | substr($es,$x->{_e},0) = '.'; $cad = $x->{_e}; |
267 | } |
268 | } |
269 | else |
270 | { |
271 | # expand with zeros |
272 | $es .= '0' x $x->{_e}; $len += $x->{_e}; $cad = 0; |
273 | } |
82cf049f |
274 | } |
574bacfe |
275 | } # if not zero |
276 | $es = $x->{sign}.$es if $x->{sign} eq '-'; |
277 | # if set accuracy or precision, pad with zeros |
278 | if ((defined $x->{_a}) && ($not_zero)) |
279 | { |
280 | # 123400 => 6, 0.1234 => 4, 0.001234 => 4 |
281 | my $zeros = $x->{_a} - $cad; # cad == 0 => 12340 |
282 | $zeros = $x->{_a} - $len if $cad != $len; |
574bacfe |
283 | $es .= $dot.'0' x $zeros if $zeros > 0; |
82cf049f |
284 | } |
574bacfe |
285 | elsif ($x->{_p} || 0 < 0) |
58cde26e |
286 | { |
574bacfe |
287 | # 123400 => 6, 0.1234 => 4, 0.001234 => 6 |
288 | my $zeros = -$x->{_p} + $cad; |
574bacfe |
289 | $es .= $dot.'0' x $zeros if $zeros > 0; |
58cde26e |
290 | } |
56b9c951 |
291 | $es; |
82cf049f |
292 | } |
f216259d |
293 | |
58cde26e |
294 | sub bsstr |
295 | { |
296 | # (ref to BFLOAT or num_str ) return num_str |
297 | # Convert number from internal format to scientific string format. |
298 | # internal format is always normalized (no leading zeros, "-0E0" => "+0E0") |
ee15d750 |
299 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
300 | #my $x = shift; my $class = ref($x) || $x; |
301 | #$x = $class->new(shift) unless ref($x); |
a0d0e21e |
302 | |
574bacfe |
303 | #die "Oups! e was $nan" if $x->{_e}->{sign} eq $nan; |
304 | #die "Oups! m was $nan" if $x->{_m}->{sign} eq $nan; |
305 | if ($x->{sign} !~ /^[+-]$/) |
306 | { |
307 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN |
308 | return 'inf'; # +inf |
309 | } |
58cde26e |
310 | my $sign = $x->{_e}->{sign}; $sign = '' if $sign eq '-'; |
311 | my $sep = 'e'.$sign; |
56b9c951 |
312 | $x->{_m}->bstr().$sep.$x->{_e}->bstr(); |
58cde26e |
313 | } |
314 | |
315 | sub numify |
316 | { |
317 | # Make a number from a BigFloat object |
574bacfe |
318 | # simple return string and let Perl's atoi()/atof() handle the rest |
ee15d750 |
319 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
56b9c951 |
320 | $x->bsstr(); |
58cde26e |
321 | } |
a0d0e21e |
322 | |
58cde26e |
323 | ############################################################################## |
324 | # public stuff (usually prefixed with "b") |
325 | |
574bacfe |
326 | # tels 2001-08-04 |
327 | # todo: this must be overwritten and return NaN for non-integer values |
328 | # band(), bior(), bxor(), too |
58cde26e |
329 | #sub bnot |
330 | # { |
331 | # $class->SUPER::bnot($class,@_); |
332 | # } |
333 | |
334 | sub bcmp |
335 | { |
336 | # Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort) |
337 | # (BFLOAT or num_str, BFLOAT or num_str) return cond_code |
338 | my ($self,$x,$y) = objectify(2,@_); |
58cde26e |
339 | |
0716bf9b |
340 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
341 | { |
342 | # handle +-inf and NaN |
343 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
344 | return 0 if ($x->{sign} eq $y->{sign}) && ($x->{sign} =~ /^[+-]inf$/); |
345 | return +1 if $x->{sign} eq '+inf'; |
346 | return -1 if $x->{sign} eq '-inf'; |
347 | return -1 if $y->{sign} eq '+inf'; |
b3abae2a |
348 | return +1; |
0716bf9b |
349 | } |
350 | |
351 | # check sign for speed first |
574bacfe |
352 | return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y |
58cde26e |
353 | return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0 |
354 | |
574bacfe |
355 | # shortcut |
356 | my $xz = $x->is_zero(); |
357 | my $yz = $y->is_zero(); |
358 | return 0 if $xz && $yz; # 0 <=> 0 |
359 | return -1 if $xz && $y->{sign} eq '+'; # 0 <=> +y |
360 | return 1 if $yz && $x->{sign} eq '+'; # +x <=> 0 |
58cde26e |
361 | |
362 | # adjust so that exponents are equal |
bd05a461 |
363 | my $lxm = $x->{_m}->length(); |
364 | my $lym = $y->{_m}->length(); |
28df3e88 |
365 | # the numify somewhat limits our length, but makes it much faster |
366 | my $lx = $lxm + $x->{_e}->numify(); |
367 | my $ly = $lym + $y->{_e}->numify(); |
368 | my $l = $lx - $ly; $l = -$l if $x->{sign} eq '-'; |
bd05a461 |
369 | return $l <=> 0 if $l != 0; |
58cde26e |
370 | |
bd05a461 |
371 | # lengths (corrected by exponent) are equal |
28df3e88 |
372 | # so make mantissa equal length by padding with zero (shift left) |
bd05a461 |
373 | my $diff = $lxm - $lym; |
374 | my $xm = $x->{_m}; # not yet copy it |
375 | my $ym = $y->{_m}; |
376 | if ($diff > 0) |
377 | { |
378 | $ym = $y->{_m}->copy()->blsft($diff,10); |
379 | } |
380 | elsif ($diff < 0) |
381 | { |
382 | $xm = $x->{_m}->copy()->blsft(-$diff,10); |
383 | } |
28df3e88 |
384 | my $rc = $xm->bacmp($ym); |
58cde26e |
385 | $rc = -$rc if $x->{sign} eq '-'; # -124 < -123 |
b3abae2a |
386 | $rc <=> 0; |
58cde26e |
387 | } |
388 | |
389 | sub bacmp |
390 | { |
391 | # Compares 2 values, ignoring their signs. |
392 | # Returns one of undef, <0, =0, >0. (suitable for sort) |
393 | # (BFLOAT or num_str, BFLOAT or num_str) return cond_code |
394 | my ($self,$x,$y) = objectify(2,@_); |
ee15d750 |
395 | |
396 | # handle +-inf and NaN's |
abcfbf51 |
397 | if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/) |
ee15d750 |
398 | { |
399 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
400 | return 0 if ($x->is_inf() && $y->is_inf()); |
401 | return 1 if ($x->is_inf() && !$y->is_inf()); |
b3abae2a |
402 | return -1; |
ee15d750 |
403 | } |
404 | |
405 | # shortcut |
406 | my $xz = $x->is_zero(); |
407 | my $yz = $y->is_zero(); |
408 | return 0 if $xz && $yz; # 0 <=> 0 |
409 | return -1 if $xz && !$yz; # 0 <=> +y |
410 | return 1 if $yz && !$xz; # +x <=> 0 |
411 | |
412 | # adjust so that exponents are equal |
413 | my $lxm = $x->{_m}->length(); |
414 | my $lym = $y->{_m}->length(); |
28df3e88 |
415 | # the numify somewhat limits our length, but makes it much faster |
416 | my $lx = $lxm + $x->{_e}->numify(); |
417 | my $ly = $lym + $y->{_e}->numify(); |
394e6ffb |
418 | my $l = $lx - $ly; |
ee15d750 |
419 | return $l <=> 0 if $l != 0; |
58cde26e |
420 | |
ee15d750 |
421 | # lengths (corrected by exponent) are equal |
394e6ffb |
422 | # so make mantissa equal-length by padding with zero (shift left) |
ee15d750 |
423 | my $diff = $lxm - $lym; |
424 | my $xm = $x->{_m}; # not yet copy it |
425 | my $ym = $y->{_m}; |
426 | if ($diff > 0) |
427 | { |
428 | $ym = $y->{_m}->copy()->blsft($diff,10); |
429 | } |
430 | elsif ($diff < 0) |
431 | { |
432 | $xm = $x->{_m}->copy()->blsft(-$diff,10); |
433 | } |
28df3e88 |
434 | $xm->bacmp($ym) <=> 0; |
58cde26e |
435 | } |
a0d0e21e |
436 | |
58cde26e |
437 | sub badd |
438 | { |
439 | # add second arg (BFLOAT or string) to first (BFLOAT) (modifies first) |
440 | # return result as BFLOAT |
58cde26e |
441 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
442 | |
574bacfe |
443 | # inf and NaN handling |
444 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
445 | { |
446 | # NaN first |
447 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
13a12e00 |
448 | # inf handling |
574bacfe |
449 | if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) |
450 | { |
13a12e00 |
451 | # +inf++inf or -inf+-inf => same, rest is NaN |
452 | return $x if $x->{sign} eq $y->{sign}; |
453 | return $x->bnan(); |
574bacfe |
454 | } |
56b9c951 |
455 | # +-inf + something => +inf; something +-inf => +-inf |
574bacfe |
456 | $x->{sign} = $y->{sign}, return $x if $y->{sign} =~ /^[+-]inf$/; |
457 | return $x; |
458 | } |
459 | |
8f675a64 |
460 | return $upgrade->badd($x,$y,$a,$p,$r) if defined $upgrade && |
461 | ((!$x->isa($self)) || (!$y->isa($self))); |
462 | |
58cde26e |
463 | # speed: no add for 0+y or x+0 |
28df3e88 |
464 | return $x->bround($a,$p,$r) if $y->is_zero(); # x+0 |
58cde26e |
465 | if ($x->is_zero()) # 0+y |
466 | { |
467 | # make copy, clobbering up x (modify in place!) |
468 | $x->{_e} = $y->{_e}->copy(); |
469 | $x->{_m} = $y->{_m}->copy(); |
470 | $x->{sign} = $y->{sign} || $nan; |
471 | return $x->round($a,$p,$r,$y); |
a0d0e21e |
472 | } |
58cde26e |
473 | |
474 | # take lower of the two e's and adapt m1 to it to match m2 |
28df3e88 |
475 | my $e = $y->{_e}; |
56b9c951 |
476 | $e = $MBI->bzero() if !defined $e; # if no BFLOAT ? |
477 | $e = $e->copy(); # make copy (didn't do it yet) |
28df3e88 |
478 | $e->bsub($x->{_e}); |
58cde26e |
479 | my $add = $y->{_m}->copy(); |
28df3e88 |
480 | if ($e->{sign} eq '-') # < 0 |
58cde26e |
481 | { |
58cde26e |
482 | my $e1 = $e->copy()->babs(); |
28df3e88 |
483 | #$x->{_m} *= (10 ** $e1); |
484 | $x->{_m}->blsft($e1,10); |
58cde26e |
485 | $x->{_e} += $e; # need the sign of e |
58cde26e |
486 | } |
28df3e88 |
487 | elsif (!$e->is_zero()) # > 0 |
58cde26e |
488 | { |
28df3e88 |
489 | #$add *= (10 ** $e); |
490 | $add->blsft($e,10); |
58cde26e |
491 | } |
61f5c3f5 |
492 | # else: both e are the same, so just leave them |
493 | $x->{_m}->{sign} = $x->{sign}; # fiddle with signs |
58cde26e |
494 | $add->{sign} = $y->{sign}; |
61f5c3f5 |
495 | $x->{_m} += $add; # finally do add/sub |
496 | $x->{sign} = $x->{_m}->{sign}; # re-adjust signs |
497 | $x->{_m}->{sign} = '+'; # mantissa always positiv |
498 | # delete trailing zeros, then round |
499 | return $x->bnorm()->round($a,$p,$r,$y); |
58cde26e |
500 | } |
501 | |
502 | sub bsub |
503 | { |
0716bf9b |
504 | # (BigFloat or num_str, BigFloat or num_str) return BigFloat |
58cde26e |
505 | # subtract second arg from first, modify first |
e745a66c |
506 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
a0d0e21e |
507 | |
28df3e88 |
508 | if ($y->is_zero()) # still round for not adding zero |
e745a66c |
509 | { |
28df3e88 |
510 | return $x->round($a,$p,$r); |
e745a66c |
511 | } |
28df3e88 |
512 | |
513 | $y->{sign} =~ tr/+\-/-+/; # does nothing for NaN |
514 | $x->badd($y,$a,$p,$r); # badd does not leave internal zeros |
515 | $y->{sign} =~ tr/+\-/-+/; # refix $y (does nothing for NaN) |
e745a66c |
516 | $x; # already rounded by badd() |
58cde26e |
517 | } |
518 | |
519 | sub binc |
520 | { |
521 | # increment arg by one |
ee15d750 |
522 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
e745a66c |
523 | |
524 | if ($x->{_e}->sign() eq '-') |
525 | { |
526 | return $x->badd($self->bone(),$a,$p,$r); # digits after dot |
527 | } |
528 | |
529 | if (!$x->{_e}->is_zero()) |
530 | { |
531 | $x->{_m}->blsft($x->{_e},10); # 1e2 => 100 |
532 | $x->{_e}->bzero(); |
533 | } |
534 | # now $x->{_e} == 0 |
535 | if ($x->{sign} eq '+') |
536 | { |
537 | $x->{_m}->binc(); |
538 | return $x->bnorm()->bround($a,$p,$r); |
539 | } |
540 | elsif ($x->{sign} eq '-') |
541 | { |
542 | $x->{_m}->bdec(); |
543 | $x->{sign} = '+' if $x->{_m}->is_zero(); # -1 +1 => -0 => +0 |
544 | return $x->bnorm()->bround($a,$p,$r); |
545 | } |
546 | # inf, nan handling etc |
547 | $x->badd($self->__one(),$a,$p,$r); # does round |
58cde26e |
548 | } |
549 | |
550 | sub bdec |
551 | { |
552 | # decrement arg by one |
ee15d750 |
553 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
e745a66c |
554 | |
555 | if ($x->{_e}->sign() eq '-') |
556 | { |
557 | return $x->badd($self->bone('-'),$a,$p,$r); # digits after dot |
558 | } |
559 | |
560 | if (!$x->{_e}->is_zero()) |
561 | { |
562 | $x->{_m}->blsft($x->{_e},10); # 1e2 => 100 |
563 | $x->{_e}->bzero(); |
564 | } |
565 | # now $x->{_e} == 0 |
566 | my $zero = $x->is_zero(); |
567 | # <= 0 |
568 | if (($x->{sign} eq '-') || $zero) |
569 | { |
570 | $x->{_m}->binc(); |
571 | $x->{sign} = '-' if $zero; # 0 => 1 => -1 |
572 | $x->{sign} = '+' if $x->{_m}->is_zero(); # -1 +1 => -0 => +0 |
573 | return $x->bnorm()->round($a,$p,$r); |
574 | } |
575 | # > 0 |
576 | elsif ($x->{sign} eq '+') |
577 | { |
578 | $x->{_m}->bdec(); |
579 | return $x->bnorm()->round($a,$p,$r); |
580 | } |
581 | # inf, nan handling etc |
582 | $x->badd($self->bone('-'),$a,$p,$r); # does round |
58cde26e |
583 | } |
584 | |
61f5c3f5 |
585 | sub blog |
586 | { |
b3abae2a |
587 | my ($self,$x,$base,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(2,@_); |
61f5c3f5 |
588 | |
589 | # http://www.efunda.com/math/taylor_series/logarithmic.cfm?search_string=log |
590 | |
9393ace2 |
591 | # u = x-1, v = x+1 |
61f5c3f5 |
592 | # _ _ |
9393ace2 |
593 | # Taylor: | u 1 u^3 1 u^5 | |
61f5c3f5 |
594 | # ln (x) = 2 | --- + - * --- + - * --- + ... | x > 0 |
b3abae2a |
595 | # |_ v 3 v^3 5 v^5 _| |
61f5c3f5 |
596 | |
9393ace2 |
597 | # This takes much more steps to calculate the result: |
598 | # u = x-1 |
599 | # _ _ |
600 | # Taylor: | u 1 u^2 1 u^3 | |
601 | # ln (x) = 2 | --- + - * --- + - * --- + ... | x > 1/2 |
602 | # |_ x 2 x^2 3 x^3 _| |
603 | |
b3abae2a |
604 | # we need to limit the accuracy to protect against overflow |
605 | my $fallback = 0; |
606 | my $scale = 0; |
607 | my @params = $x->_find_round_parameters($a,$p,$r); |
61f5c3f5 |
608 | |
b3abae2a |
609 | # no rounding at all, so must use fallback |
610 | if (scalar @params == 1) |
611 | { |
612 | # simulate old behaviour |
613 | $params[1] = $self->div_scale(); # and round to it as accuracy |
614 | $scale = $params[1]+4; # at least four more for proper round |
615 | $params[3] = $r; # round mode by caller or undef |
616 | $fallback = 1; # to clear a/p afterwards |
617 | } |
618 | else |
619 | { |
620 | # the 4 below is empirical, and there might be cases where it is not |
621 | # enough... |
622 | $scale = abs($params[1] || $params[2]) + 4; # take whatever is defined |
623 | } |
61f5c3f5 |
624 | |
b3abae2a |
625 | return $x->bzero(@params) if $x->is_one(); |
626 | return $x->bnan() if $x->{sign} ne '+' || $x->is_zero(); |
627 | #return $x->bone('+',@params) if $x->bcmp($base) == 0; |
61f5c3f5 |
628 | |
b3abae2a |
629 | # when user set globals, they would interfere with our calculation, so |
630 | # disable then and later re-enable them |
631 | no strict 'refs'; |
632 | my $abr = "$self\::accuracy"; my $ab = $$abr; $$abr = undef; |
633 | my $pbr = "$self\::precision"; my $pb = $$pbr; $$pbr = undef; |
634 | # we also need to disable any set A or P on $x (_find_round_parameters took |
635 | # them already into account), since these would interfere, too |
636 | delete $x->{_a}; delete $x->{_p}; |
9393ace2 |
637 | # need to disable $upgrade in BigInt, to avoid deep recursion |
b3abae2a |
638 | local $Math::BigInt::upgrade = undef; |
9393ace2 |
639 | |
640 | my ($case,$limit,$v,$u,$below,$factor,$two,$next,$over,$f); |
641 | |
642 | if (3 < 5) |
643 | #if ($x <= Math::BigFloat->new("0.5")) |
644 | { |
645 | $case = 0; |
646 | # print "case $case $x < 0.5\n"; |
647 | $v = $x->copy(); $v->binc(); # v = x+1 |
648 | $x->bdec(); $u = $x->copy(); # u = x-1; x = x-1 |
649 | $x->bdiv($v,$scale); # first term: u/v |
650 | $below = $v->copy(); |
651 | $over = $u->copy(); |
652 | $u *= $u; $v *= $v; # u^2, v^2 |
653 | $below->bmul($v); # u^3, v^3 |
654 | $over->bmul($u); |
655 | $factor = $self->new(3); $f = $self->new(2); |
61f5c3f5 |
656 | } |
9393ace2 |
657 | #else |
658 | # { |
659 | # $case = 1; |
660 | # print "case 1 $x > 0.5\n"; |
661 | # $v = $x->copy(); # v = x |
662 | # $u = $x->copy(); $u->bdec(); # u = x-1; |
663 | # $x->bdec(); $x->bdiv($v,$scale); # first term: x-1/x |
664 | # $below = $v->copy(); |
665 | # $over = $u->copy(); |
666 | # $below->bmul($v); # u^2, v^2 |
667 | # $over->bmul($u); |
668 | # $factor = $self->new(2); $f = $self->bone(); |
669 | # } |
670 | $limit = $self->new("1E-". ($scale-1)); |
671 | #my $steps = 0; |
672 | while (3 < 5) |
673 | { |
674 | # we calculate the next term, and add it to the last |
675 | # when the next term is below our limit, it won't affect the outcome |
676 | # anymore, so we stop |
677 | $next = $over->copy()->bdiv($below->copy()->bmul($factor),$scale); |
678 | last if $next->bcmp($limit) <= 0; |
679 | $x->badd($next); |
d614cd8b |
680 | # print "step $x\n"; |
9393ace2 |
681 | # calculate things for the next term |
682 | $over *= $u; $below *= $v; $factor->badd($f); |
683 | #$steps++; |
684 | } |
685 | $x->bmul(2) if $case == 0; |
686 | #print "took $steps steps\n"; |
b3abae2a |
687 | |
688 | # shortcut to not run trough _find_round_parameters again |
689 | if (defined $params[1]) |
690 | { |
691 | $x->bround($params[1],$params[3]); # then round accordingly |
692 | } |
693 | else |
694 | { |
695 | $x->bfround($params[2],$params[3]); # then round accordingly |
696 | } |
697 | if ($fallback) |
698 | { |
699 | # clear a/p after round, since user did not request it |
700 | $x->{_a} = undef; $x->{_p} = undef; |
701 | } |
702 | # restore globals |
703 | $$abr = $ab; $$pbr = $pb; |
704 | |
705 | $x; |
61f5c3f5 |
706 | } |
707 | |
58cde26e |
708 | sub blcm |
709 | { |
ee15d750 |
710 | # (BFLOAT or num_str, BFLOAT or num_str) return BFLOAT |
58cde26e |
711 | # does not modify arguments, but returns new object |
712 | # Lowest Common Multiplicator |
58cde26e |
713 | |
714 | my ($self,@arg) = objectify(0,@_); |
715 | my $x = $self->new(shift @arg); |
716 | while (@arg) { $x = _lcm($x,shift @arg); } |
717 | $x; |
718 | } |
719 | |
720 | sub bgcd |
721 | { |
ee15d750 |
722 | # (BFLOAT or num_str, BFLOAT or num_str) return BINT |
58cde26e |
723 | # does not modify arguments, but returns new object |
724 | # GCD -- Euclids algorithm Knuth Vol 2 pg 296 |
58cde26e |
725 | |
726 | my ($self,@arg) = objectify(0,@_); |
727 | my $x = $self->new(shift @arg); |
728 | while (@arg) { $x = _gcd($x,shift @arg); } |
729 | $x; |
730 | } |
731 | |
b3abae2a |
732 | ############################################################################### |
733 | # is_foo methods (is_negative, is_positive are inherited from BigInt) |
734 | |
735 | sub is_int |
736 | { |
737 | # return true if arg (BFLOAT or num_str) is an integer |
738 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
739 | |
740 | return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN and +-inf aren't |
741 | $x->{_e}->{sign} eq '+'; # 1e-1 => no integer |
742 | 0; |
743 | } |
744 | |
58cde26e |
745 | sub is_zero |
746 | { |
b3abae2a |
747 | # return true if arg (BFLOAT or num_str) is zero |
ee15d750 |
748 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
574bacfe |
749 | |
750 | return 1 if $x->{sign} eq '+' && $x->{_m}->is_zero(); |
b3abae2a |
751 | 0; |
58cde26e |
752 | } |
753 | |
754 | sub is_one |
755 | { |
b3abae2a |
756 | # return true if arg (BFLOAT or num_str) is +1 or -1 if signis given |
ee15d750 |
757 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
758 | |
759 | my $sign = shift || ''; $sign = '+' if $sign ne '-'; |
760 | return 1 |
761 | if ($x->{sign} eq $sign && $x->{_e}->is_zero() && $x->{_m}->is_one()); |
b3abae2a |
762 | 0; |
58cde26e |
763 | } |
764 | |
765 | sub is_odd |
766 | { |
ee15d750 |
767 | # return true if arg (BFLOAT or num_str) is odd or false if even |
768 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
0716bf9b |
769 | |
b3abae2a |
770 | return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN & +-inf aren't |
771 | ($x->{_e}->is_zero() && $x->{_m}->is_odd()); |
772 | 0; |
58cde26e |
773 | } |
774 | |
775 | sub is_even |
776 | { |
b22b3e31 |
777 | # return true if arg (BINT or num_str) is even or false if odd |
ee15d750 |
778 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
0716bf9b |
779 | |
780 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
b3abae2a |
781 | return 1 if ($x->{_e}->{sign} eq '+' # 123.45 is never |
782 | && $x->{_m}->is_even()); # but 1200 is |
783 | 0; |
58cde26e |
784 | } |
785 | |
786 | sub bmul |
787 | { |
788 | # multiply two numbers -- stolen from Knuth Vol 2 pg 233 |
789 | # (BINT or num_str, BINT or num_str) return BINT |
790 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
58cde26e |
791 | |
58cde26e |
792 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
793 | |
574bacfe |
794 | # inf handling |
795 | if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) |
796 | { |
13a12e00 |
797 | return $x->bnan() if $x->is_zero() || $y->is_zero(); |
574bacfe |
798 | # result will always be +-inf: |
799 | # +inf * +/+inf => +inf, -inf * -/-inf => +inf |
800 | # +inf * -/-inf => -inf, -inf * +/+inf => -inf |
801 | return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); |
802 | return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); |
803 | return $x->binf('-'); |
804 | } |
13a12e00 |
805 | # handle result = 0 |
806 | return $x->bzero() if $x->is_zero() || $y->is_zero(); |
8f675a64 |
807 | |
808 | return $upgrade->bmul($x,$y,$a,$p,$r) if defined $upgrade && |
809 | ((!$x->isa($self)) || (!$y->isa($self))); |
574bacfe |
810 | |
58cde26e |
811 | # aEb * cEd = (a*c)E(b+d) |
394e6ffb |
812 | $x->{_m}->bmul($y->{_m}); |
813 | $x->{_e}->badd($y->{_e}); |
58cde26e |
814 | # adjust sign: |
815 | $x->{sign} = $x->{sign} ne $y->{sign} ? '-' : '+'; |
394e6ffb |
816 | return $x->bnorm()->round($a,$p,$r,$y); |
58cde26e |
817 | } |
818 | |
819 | sub bdiv |
820 | { |
821 | # (dividend: BFLOAT or num_str, divisor: BFLOAT or num_str) return |
9393ace2 |
822 | # (BFLOAT,BFLOAT) (quo,rem) or BFLOAT (only rem) |
58cde26e |
823 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
824 | |
13a12e00 |
825 | return $self->_div_inf($x,$y) |
826 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()); |
574bacfe |
827 | |
13a12e00 |
828 | # x== 0 # also: or y == 1 or y == -1 |
394e6ffb |
829 | return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero(); |
0716bf9b |
830 | |
9393ace2 |
831 | # upgrade ? |
832 | return $upgrade->bdiv($upgrade->new($x),$y,$a,$p,$r) if defined $upgrade; |
13a12e00 |
833 | |
58cde26e |
834 | # we need to limit the accuracy to protect against overflow |
574bacfe |
835 | my $fallback = 0; |
ee15d750 |
836 | my $scale = 0; |
ee15d750 |
837 | my @params = $x->_find_round_parameters($a,$p,$r,$y); |
838 | |
839 | # no rounding at all, so must use fallback |
840 | if (scalar @params == 1) |
58cde26e |
841 | { |
0716bf9b |
842 | # simulate old behaviour |
ee15d750 |
843 | $params[1] = $self->div_scale(); # and round to it as accuracy |
61f5c3f5 |
844 | $scale = $params[1]+4; # at least four more for proper round |
ee15d750 |
845 | $params[3] = $r; # round mode by caller or undef |
846 | $fallback = 1; # to clear a/p afterwards |
847 | } |
848 | else |
849 | { |
850 | # the 4 below is empirical, and there might be cases where it is not |
851 | # enough... |
852 | $scale = abs($params[1] || $params[2]) + 4; # take whatever is defined |
a0d0e21e |
853 | } |
0716bf9b |
854 | my $lx = $x->{_m}->length(); my $ly = $y->{_m}->length(); |
58cde26e |
855 | $scale = $lx if $lx > $scale; |
58cde26e |
856 | $scale = $ly if $ly > $scale; |
0716bf9b |
857 | my $diff = $ly - $lx; |
858 | $scale += $diff if $diff > 0; # if lx << ly, but not if ly << lx! |
b3abae2a |
859 | |
860 | # make copy of $x in case of list context for later reminder calculation |
861 | my $rem; |
862 | if (wantarray && !$y->is_one()) |
863 | { |
864 | $rem = $x->copy(); |
865 | } |
a0d0e21e |
866 | |
58cde26e |
867 | $x->{sign} = $x->{sign} ne $y->sign() ? '-' : '+'; |
a0d0e21e |
868 | |
58cde26e |
869 | # check for / +-1 ( +/- 1E0) |
394e6ffb |
870 | if (!$y->is_one()) |
58cde26e |
871 | { |
394e6ffb |
872 | # promote BigInts and it's subclasses (except when already a BigFloat) |
873 | $y = $self->new($y) unless $y->isa('Math::BigFloat'); |
874 | |
9393ace2 |
875 | #print "bdiv $y ",ref($y),"\n"; |
876 | # need to disable $upgrade in BigInt, to avoid deep recursion |
877 | local $Math::BigInt::upgrade = undef; # should be parent class vs MBI |
878 | |
394e6ffb |
879 | # calculate the result to $scale digits and then round it |
880 | # a * 10 ** b / c * 10 ** d => a/c * 10 ** (b-d) |
881 | $x->{_m}->blsft($scale,10); |
882 | $x->{_m}->bdiv( $y->{_m} ); # a/c |
883 | $x->{_e}->bsub( $y->{_e} ); # b-d |
884 | $x->{_e}->bsub($scale); # correct for 10**scale |
885 | $x->bnorm(); # remove trailing 0's |
a0d0e21e |
886 | } |
a5f75d66 |
887 | |
ee15d750 |
888 | # shortcut to not run trough _find_round_parameters again |
889 | if (defined $params[1]) |
890 | { |
61f5c3f5 |
891 | $x->bround($params[1],$params[3]); # then round accordingly |
ee15d750 |
892 | } |
893 | else |
894 | { |
895 | $x->bfround($params[2],$params[3]); # then round accordingly |
896 | } |
574bacfe |
897 | if ($fallback) |
898 | { |
899 | # clear a/p after round, since user did not request it |
ee15d750 |
900 | $x->{_a} = undef; $x->{_p} = undef; |
574bacfe |
901 | } |
0716bf9b |
902 | |
58cde26e |
903 | if (wantarray) |
904 | { |
394e6ffb |
905 | if (!$y->is_one()) |
906 | { |
b3abae2a |
907 | $rem->bmod($y,$params[1],$params[2],$params[3]); # copy already done |
394e6ffb |
908 | } |
909 | else |
910 | { |
911 | $rem = $self->bzero(); |
912 | } |
574bacfe |
913 | if ($fallback) |
914 | { |
915 | # clear a/p after round, since user did not request it |
ee15d750 |
916 | $rem->{_a} = undef; $rem->{_p} = undef; |
574bacfe |
917 | } |
0716bf9b |
918 | return ($x,$rem); |
58cde26e |
919 | } |
9393ace2 |
920 | $x; |
58cde26e |
921 | } |
a0d0e21e |
922 | |
58cde26e |
923 | sub bmod |
924 | { |
925 | # (dividend: BFLOAT or num_str, divisor: BFLOAT or num_str) return reminder |
926 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
a0d0e21e |
927 | |
61f5c3f5 |
928 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
929 | { |
930 | my ($d,$re) = $self->SUPER::_div_inf($x,$y); |
931 | return $re->round($a,$p,$r,$y); |
932 | } |
933 | return $x->bnan() if $x->is_zero() && $y->is_zero(); |
934 | return $x if $y->is_zero(); |
935 | return $x->bnan() if $x->is_nan() || $y->is_nan(); |
936 | return $x->bzero() if $y->is_one() || $x->is_zero(); |
58cde26e |
937 | |
61f5c3f5 |
938 | # inf handling is missing here |
939 | |
940 | my $cmp = $x->bacmp($y); # equal or $x < $y? |
941 | return $x->bzero($a,$p) if $cmp == 0; # $x == $y => result 0 |
942 | |
943 | # only $y of the operands negative? |
944 | my $neg = 0; $neg = 1 if $x->{sign} ne $y->{sign}; |
945 | |
946 | $x->{sign} = $y->{sign}; # calc sign first |
947 | return $x->round($a,$p,$r) if $cmp < 0 && $neg == 0; # $x < $y => result $x |
948 | |
949 | my $ym = $y->{_m}->copy(); |
950 | |
951 | # 2e1 => 20 |
952 | $ym->blsft($y->{_e},10) if $y->{_e}->{sign} eq '+' && !$y->{_e}->is_zero(); |
953 | |
954 | # if $y has digits after dot |
955 | my $shifty = 0; # correct _e of $x by this |
956 | if ($y->{_e}->{sign} eq '-') # has digits after dot |
957 | { |
958 | # 123 % 2.5 => 1230 % 25 => 5 => 0.5 |
959 | $shifty = $y->{_e}->copy()->babs(); # no more digits after dot |
960 | $x->blsft($shifty,10); # 123 => 1230, $y->{_m} is already 25 |
961 | } |
962 | # $ym is now mantissa of $y based on exponent 0 |
b3abae2a |
963 | |
61f5c3f5 |
964 | my $shiftx = 0; # correct _e of $x by this |
965 | if ($x->{_e}->{sign} eq '-') # has digits after dot |
966 | { |
967 | # 123.4 % 20 => 1234 % 200 |
968 | $shiftx = $x->{_e}->copy()->babs(); # no more digits after dot |
969 | $ym->blsft($shiftx,10); |
970 | } |
971 | # 123e1 % 20 => 1230 % 20 |
972 | if ($x->{_e}->{sign} eq '+' && !$x->{_e}->is_zero()) |
973 | { |
974 | $x->{_m}->blsft($x->{_e},10); |
975 | } |
56b9c951 |
976 | $x->{_e} = $MBI->bzero() unless $x->{_e}->is_zero(); |
61f5c3f5 |
977 | |
978 | $x->{_e}->bsub($shiftx) if $shiftx != 0; |
979 | $x->{_e}->bsub($shifty) if $shifty != 0; |
980 | |
981 | # now mantissas are equalized, exponent of $x is adjusted, so calc result |
b3abae2a |
982 | |
61f5c3f5 |
983 | $x->{_m}->bmod($ym); |
984 | |
985 | $x->{sign} = '+' if $x->{_m}->is_zero(); # fix sign for -0 |
986 | $x->bnorm(); |
987 | |
988 | if ($neg != 0) # one of them negative => correct in place |
989 | { |
990 | my $r = $y - $x; |
991 | $x->{_m} = $r->{_m}; |
992 | $x->{_e} = $r->{_e}; |
993 | $x->{sign} = '+' if $x->{_m}->is_zero(); # fix sign for -0 |
994 | $x->bnorm(); |
995 | } |
996 | |
997 | $x->round($a,$p,$r,$y); # round and return |
58cde26e |
998 | } |
999 | |
1000 | sub bsqrt |
1001 | { |
0716bf9b |
1002 | # calculate square root; this should probably |
1003 | # use a different test to see whether the accuracy we want is... |
ee15d750 |
1004 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e |
1005 | |
0716bf9b |
1006 | return $x->bnan() if $x->{sign} eq 'NaN' || $x->{sign} =~ /^-/; # <0, NaN |
1007 | return $x if $x->{sign} eq '+inf'; # +inf |
394e6ffb |
1008 | return $x if $x->is_zero() || $x->is_one(); |
58cde26e |
1009 | |
61f5c3f5 |
1010 | # we need to limit the accuracy to protect against overflow |
574bacfe |
1011 | my $fallback = 0; |
61f5c3f5 |
1012 | my $scale = 0; |
1013 | my @params = $x->_find_round_parameters($a,$p,$r); |
1014 | |
1015 | # no rounding at all, so must use fallback |
1016 | if (scalar @params == 1) |
0716bf9b |
1017 | { |
1018 | # simulate old behaviour |
61f5c3f5 |
1019 | $params[1] = $self->div_scale(); # and round to it as accuracy |
1020 | $scale = $params[1]+4; # at least four more for proper round |
1021 | $params[3] = $r; # round mode by caller or undef |
ee15d750 |
1022 | $fallback = 1; # to clear a/p afterwards |
0716bf9b |
1023 | } |
61f5c3f5 |
1024 | else |
1025 | { |
1026 | # the 4 below is empirical, and there might be cases where it is not |
1027 | # enough... |
1028 | $scale = abs($params[1] || $params[2]) + 4; # take whatever is defined |
1029 | } |
1030 | |
1031 | # when user set globals, they would interfere with our calculation, so |
9393ace2 |
1032 | # disable them and later re-enable them |
61f5c3f5 |
1033 | no strict 'refs'; |
1034 | my $abr = "$self\::accuracy"; my $ab = $$abr; $$abr = undef; |
b3abae2a |
1035 | my $pbr = "$self\::precision"; my $pb = $$pbr; $$pbr = undef; |
61f5c3f5 |
1036 | # we also need to disable any set A or P on $x (_find_round_parameters took |
1037 | # them already into account), since these would interfere, too |
1038 | delete $x->{_a}; delete $x->{_p}; |
9393ace2 |
1039 | # need to disable $upgrade in BigInt, to avoid deep recursion |
1040 | local $Math::BigInt::upgrade = undef; # should be really parent class vs MBI |
61f5c3f5 |
1041 | |
394e6ffb |
1042 | my $xas = $x->as_number(); |
1043 | my $gs = $xas->copy()->bsqrt(); # some guess |
b3abae2a |
1044 | |
9393ace2 |
1045 | # print "guess $gs\n"; |
394e6ffb |
1046 | if (($x->{_e}->{sign} ne '-') # guess can't be accurate if there are |
1047 | # digits after the dot |
b3abae2a |
1048 | && ($xas->bacmp($gs * $gs) == 0)) # guess hit the nail on the head? |
394e6ffb |
1049 | { |
1050 | # exact result |
56b9c951 |
1051 | $x->{_m} = $gs; $x->{_e} = $MBI->bzero(); $x->bnorm(); |
61f5c3f5 |
1052 | # shortcut to not run trough _find_round_parameters again |
1053 | if (defined $params[1]) |
1054 | { |
1055 | $x->bround($params[1],$params[3]); # then round accordingly |
1056 | } |
1057 | else |
1058 | { |
1059 | $x->bfround($params[2],$params[3]); # then round accordingly |
1060 | } |
1061 | if ($fallback) |
1062 | { |
1063 | # clear a/p after round, since user did not request it |
1064 | $x->{_a} = undef; $x->{_p} = undef; |
1065 | } |
9393ace2 |
1066 | # re-enable A and P, upgrade is taken care of by "local" |
b3abae2a |
1067 | ${"$self\::accuracy"} = $ab; ${"$self\::precision"} = $pb; |
61f5c3f5 |
1068 | return $x; |
394e6ffb |
1069 | } |
61f5c3f5 |
1070 | $gs = $self->new( $gs ); # BigInt to BigFloat |
394e6ffb |
1071 | |
0716bf9b |
1072 | my $lx = $x->{_m}->length(); |
1073 | $scale = $lx if $scale < $lx; |
394e6ffb |
1074 | my $e = $self->new("1E-$scale"); # make test variable |
58cde26e |
1075 | |
58cde26e |
1076 | my $y = $x->copy(); |
394e6ffb |
1077 | my $two = $self->new(2); |
61f5c3f5 |
1078 | my $diff = $e; |
ee15d750 |
1079 | # promote BigInts and it's subclasses (except when already a BigFloat) |
1080 | $y = $self->new($y) unless $y->isa('Math::BigFloat'); |
61f5c3f5 |
1081 | |
ee15d750 |
1082 | my $rem; |
9393ace2 |
1083 | while ($diff->bacmp($e) >= 0) |
58cde26e |
1084 | { |
9393ace2 |
1085 | $rem = $y->copy()->bdiv($gs,$scale); |
61f5c3f5 |
1086 | $rem = $y->copy()->bdiv($gs,$scale)->badd($gs)->bdiv($two,$scale); |
9393ace2 |
1087 | $diff = $rem->copy()->bsub($gs); |
61f5c3f5 |
1088 | $gs = $rem->copy(); |
a0d0e21e |
1089 | } |
61f5c3f5 |
1090 | # copy over to modify $x |
1091 | $x->{_m} = $rem->{_m}; $x->{_e} = $rem->{_e}; |
1092 | |
1093 | # shortcut to not run trough _find_round_parameters again |
1094 | if (defined $params[1]) |
1095 | { |
1096 | $x->bround($params[1],$params[3]); # then round accordingly |
1097 | } |
1098 | else |
1099 | { |
1100 | $x->bfround($params[2],$params[3]); # then round accordingly |
1101 | } |
574bacfe |
1102 | if ($fallback) |
1103 | { |
1104 | # clear a/p after round, since user did not request it |
ee15d750 |
1105 | $x->{_a} = undef; $x->{_p} = undef; |
574bacfe |
1106 | } |
61f5c3f5 |
1107 | # restore globals |
b3abae2a |
1108 | $$abr = $ab; $$pbr = $pb; |
574bacfe |
1109 | $x; |
58cde26e |
1110 | } |
1111 | |
b3abae2a |
1112 | sub bfac |
1113 | { |
28df3e88 |
1114 | # (BFLOAT or num_str, BFLOAT or num_str) return BFLOAT |
b3abae2a |
1115 | # compute factorial numbers |
1116 | # modifies first argument |
1117 | my ($self,$x,@r) = objectify(1,@_); |
1118 | |
28df3e88 |
1119 | return $x->bnan() |
1120 | if (($x->{sign} ne '+') || # inf, NaN, <0 etc => NaN |
1121 | ($x->{_e}->{sign} ne '+')); # digits after dot? |
b3abae2a |
1122 | |
28df3e88 |
1123 | return $x->bone(@r) if $x->is_zero() || $x->is_one(); # 0 or 1 => 1 |
b3abae2a |
1124 | |
1125 | # use BigInt's bfac() for faster calc |
1126 | $x->{_m}->blsft($x->{_e},10); # un-norm m |
1127 | $x->{_e}->bzero(); # norm $x again |
1128 | $x->{_m}->bfac(); # factorial |
28df3e88 |
1129 | $x->bnorm()->round(@r); |
b3abae2a |
1130 | } |
1131 | |
56b9c951 |
1132 | sub _pow2 |
1133 | { |
1134 | # Calculate a power where $y is a non-integer, like 2 ** 0.5 |
1135 | my ($x,$y,$a,$p,$r) = @_; |
1136 | my $self = ref($x); |
1137 | |
1138 | # we need to limit the accuracy to protect against overflow |
1139 | my $fallback = 0; |
1140 | my $scale = 0; |
1141 | my @params = $x->_find_round_parameters($a,$p,$r); |
1142 | |
1143 | # no rounding at all, so must use fallback |
1144 | if (scalar @params == 1) |
1145 | { |
1146 | # simulate old behaviour |
1147 | $params[1] = $self->div_scale(); # and round to it as accuracy |
1148 | $scale = $params[1]+4; # at least four more for proper round |
1149 | $params[3] = $r; # round mode by caller or undef |
1150 | $fallback = 1; # to clear a/p afterwards |
1151 | } |
1152 | else |
1153 | { |
1154 | # the 4 below is empirical, and there might be cases where it is not |
1155 | # enough... |
1156 | $scale = abs($params[1] || $params[2]) + 4; # take whatever is defined |
1157 | } |
1158 | |
1159 | # when user set globals, they would interfere with our calculation, so |
1160 | # disable then and later re-enable them |
1161 | no strict 'refs'; |
1162 | my $abr = "$self\::accuracy"; my $ab = $$abr; $$abr = undef; |
1163 | my $pbr = "$self\::precision"; my $pb = $$pbr; $$pbr = undef; |
1164 | # we also need to disable any set A or P on $x (_find_round_parameters took |
1165 | # them already into account), since these would interfere, too |
1166 | delete $x->{_a}; delete $x->{_p}; |
1167 | # need to disable $upgrade in BigInt, to avoid deep recursion |
1168 | local $Math::BigInt::upgrade = undef; |
1169 | |
1170 | # split the second argument into its integer and fraction part |
1171 | # we calculate the result then from these two parts, like in |
1172 | # 2 ** 2.4 == (2 ** 2) * (2 ** 0.4) |
1173 | my $c = $self->new($y->as_number()); # integer part |
1174 | my $d = $y-$c; # fractional part |
1175 | my $xc = $x->copy(); # a temp. copy |
1176 | |
1177 | # now calculate binary fraction from the decimal fraction on the fly |
1178 | # f.i. 0.654: |
1179 | # 0.654 * 2 = 1.308 > 1 => 0.1 ( 1.308 - 1 = 0.308) |
1180 | # 0.308 * 2 = 0.616 < 1 => 0.10 |
1181 | # 0.616 * 2 = 1.232 > 1 => 0.101 ( 1.232 - 1 = 0.232) |
1182 | # and so on... |
1183 | # The process stops when the result is exactly one, or when we have |
1184 | # enough accuracy |
1185 | |
1186 | # From the binary fraction we calculate the result as follows: |
1187 | # we assume the fraction ends in 1, and we remove this one first. |
1188 | # For each digit after the dot, assume 1 eq R and 0 eq XR, where R means |
1189 | # take square root and X multiply with the original X. |
1190 | |
1191 | my $i = 0; |
1192 | while ($i++ < 50) |
1193 | { |
1194 | $d->badd($d); # * 2 |
1195 | last if $d->is_one(); # == 1 |
1196 | $x->bsqrt(); # 0 |
1197 | if ($d > 1) |
1198 | { |
1199 | $x->bsqrt(); $x->bmul($xc); $d->bdec(); # 1 |
1200 | } |
56b9c951 |
1201 | } |
1202 | # assume fraction ends in 1 |
1203 | $x->bsqrt(); # 1 |
1204 | if (!$c->is_one()) |
1205 | { |
1206 | $x->bmul( $xc->bpow($c) ); |
1207 | } |
1208 | elsif (!$c->is_zero()) |
1209 | { |
1210 | $x->bmul( $xc ); |
1211 | } |
1212 | # done |
1213 | |
1214 | # shortcut to not run trough _find_round_parameters again |
1215 | if (defined $params[1]) |
1216 | { |
1217 | $x->bround($params[1],$params[3]); # then round accordingly |
1218 | } |
1219 | else |
1220 | { |
1221 | $x->bfround($params[2],$params[3]); # then round accordingly |
1222 | } |
1223 | if ($fallback) |
1224 | { |
1225 | # clear a/p after round, since user did not request it |
1226 | $x->{_a} = undef; $x->{_p} = undef; |
1227 | } |
1228 | # restore globals |
1229 | $$abr = $ab; $$pbr = $pb; |
1230 | $x; |
1231 | } |
1232 | |
9393ace2 |
1233 | sub _pow |
1234 | { |
1235 | # Calculate a power where $y is a non-integer, like 2 ** 0.5 |
1236 | my ($x,$y,$a,$p,$r) = @_; |
1237 | my $self = ref($x); |
1238 | |
1239 | # if $y == 0.5, it is sqrt($x) |
1240 | return $x->bsqrt($a,$p,$r,$y) if $y->bcmp('0.5') == 0; |
1241 | |
1242 | # u = y * ln x |
1243 | # _ _ |
1244 | # Taylor: | u u^2 u^3 | |
1245 | # x ** y = 1 + | --- + --- + * ----- + ... | |
1246 | # |_ 1 1*2 1*2*3 _| |
1247 | |
1248 | # we need to limit the accuracy to protect against overflow |
1249 | my $fallback = 0; |
1250 | my $scale = 0; |
1251 | my @params = $x->_find_round_parameters($a,$p,$r); |
1252 | |
1253 | # no rounding at all, so must use fallback |
1254 | if (scalar @params == 1) |
1255 | { |
1256 | # simulate old behaviour |
1257 | $params[1] = $self->div_scale(); # and round to it as accuracy |
1258 | $scale = $params[1]+4; # at least four more for proper round |
1259 | $params[3] = $r; # round mode by caller or undef |
1260 | $fallback = 1; # to clear a/p afterwards |
1261 | } |
1262 | else |
1263 | { |
1264 | # the 4 below is empirical, and there might be cases where it is not |
1265 | # enough... |
1266 | $scale = abs($params[1] || $params[2]) + 4; # take whatever is defined |
1267 | } |
1268 | |
1269 | # when user set globals, they would interfere with our calculation, so |
1270 | # disable then and later re-enable them |
1271 | no strict 'refs'; |
1272 | my $abr = "$self\::accuracy"; my $ab = $$abr; $$abr = undef; |
1273 | my $pbr = "$self\::precision"; my $pb = $$pbr; $$pbr = undef; |
1274 | # we also need to disable any set A or P on $x (_find_round_parameters took |
1275 | # them already into account), since these would interfere, too |
1276 | delete $x->{_a}; delete $x->{_p}; |
1277 | # need to disable $upgrade in BigInt, to avoid deep recursion |
1278 | local $Math::BigInt::upgrade = undef; |
1279 | |
1280 | my ($limit,$v,$u,$below,$factor,$next,$over); |
1281 | |
1282 | $u = $x->copy()->blog($scale)->bmul($y); |
1283 | $v = $self->bone(); # 1 |
1284 | $factor = $self->new(2); # 2 |
1285 | $x->bone(); # first term: 1 |
1286 | |
1287 | $below = $v->copy(); |
1288 | $over = $u->copy(); |
1289 | |
1290 | $limit = $self->new("1E-". ($scale-1)); |
1291 | #my $steps = 0; |
1292 | while (3 < 5) |
1293 | { |
1294 | # we calculate the next term, and add it to the last |
1295 | # when the next term is below our limit, it won't affect the outcome |
1296 | # anymore, so we stop |
1297 | $next = $over->copy()->bdiv($below,$scale); |
1298 | last if $next->bcmp($limit) <= 0; |
1299 | $x->badd($next); |
1300 | # print "at $x\n"; |
1301 | # calculate things for the next term |
1302 | $over *= $u; $below *= $factor; $factor->binc(); |
1303 | #$steps++; |
1304 | } |
1305 | |
1306 | # shortcut to not run trough _find_round_parameters again |
1307 | if (defined $params[1]) |
1308 | { |
1309 | $x->bround($params[1],$params[3]); # then round accordingly |
1310 | } |
1311 | else |
1312 | { |
1313 | $x->bfround($params[2],$params[3]); # then round accordingly |
1314 | } |
1315 | if ($fallback) |
1316 | { |
1317 | # clear a/p after round, since user did not request it |
1318 | $x->{_a} = undef; $x->{_p} = undef; |
1319 | } |
1320 | # restore globals |
1321 | $$abr = $ab; $$pbr = $pb; |
1322 | $x; |
1323 | } |
1324 | |
58cde26e |
1325 | sub bpow |
1326 | { |
1327 | # (BFLOAT or num_str, BFLOAT or num_str) return BFLOAT |
1328 | # compute power of two numbers, second arg is used as integer |
1329 | # modifies first argument |
1330 | |
1331 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
1332 | |
0716bf9b |
1333 | return $x if $x->{sign} =~ /^[+-]inf$/; |
58cde26e |
1334 | return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan; |
574bacfe |
1335 | return $x->bone() if $y->is_zero(); |
58cde26e |
1336 | return $x if $x->is_one() || $y->is_one(); |
9393ace2 |
1337 | |
d614cd8b |
1338 | return $x->_pow($y,$a,$p,$r) if !$y->is_int(); # non-integer power |
9393ace2 |
1339 | |
1340 | my $y1 = $y->as_number(); # make bigint |
394e6ffb |
1341 | # if ($x == -1) |
1342 | if ($x->{sign} eq '-' && $x->{_m}->is_one() && $x->{_e}->is_zero()) |
58cde26e |
1343 | { |
1344 | # if $x == -1 and odd/even y => +1/-1 because +-1 ^ (+-1) => +-1 |
0716bf9b |
1345 | return $y1->is_odd() ? $x : $x->babs(1); |
288d023a |
1346 | } |
28df3e88 |
1347 | if ($x->is_zero()) |
1348 | { |
1349 | return $x if $y->{sign} eq '+'; # 0**y => 0 (if not y <= 0) |
1350 | # 0 ** -y => 1 / (0 ** y) => / 0! (1 / 0 => +inf) |
1351 | $x->binf(); |
1352 | } |
58cde26e |
1353 | |
1354 | # calculate $x->{_m} ** $y and $x->{_e} * $y separately (faster) |
1355 | $y1->babs(); |
1356 | $x->{_m}->bpow($y1); |
1357 | $x->{_e}->bmul($y1); |
1358 | $x->{sign} = $nan if $x->{_m}->{sign} eq $nan || $x->{_e}->{sign} eq $nan; |
1359 | $x->bnorm(); |
1360 | if ($y->{sign} eq '-') |
1361 | { |
1362 | # modify $x in place! |
0716bf9b |
1363 | my $z = $x->copy(); $x->bzero()->binc(); |
58cde26e |
1364 | return $x->bdiv($z,$a,$p,$r); # round in one go (might ignore y's A!) |
a0d0e21e |
1365 | } |
28df3e88 |
1366 | $x->round($a,$p,$r,$y); |
58cde26e |
1367 | } |
1368 | |
1369 | ############################################################################### |
1370 | # rounding functions |
1371 | |
1372 | sub bfround |
1373 | { |
1374 | # precision: round to the $Nth digit left (+$n) or right (-$n) from the '.' |
1375 | # $n == 0 means round to integer |
1376 | # expects and returns normalized numbers! |
ee15d750 |
1377 | my $x = shift; my $self = ref($x) || $x; $x = $self->new(shift) if !ref($x); |
a0d0e21e |
1378 | |
58cde26e |
1379 | return $x if $x->modify('bfround'); |
1380 | |
ee15d750 |
1381 | my ($scale,$mode) = $x->_scale_p($self->precision(),$self->round_mode(),@_); |
58cde26e |
1382 | return $x if !defined $scale; # no-op |
1383 | |
574bacfe |
1384 | # never round a 0, +-inf, NaN |
61f5c3f5 |
1385 | if ($x->is_zero()) |
1386 | { |
1387 | $x->{_p} = $scale if !defined $x->{_p} || $x->{_p} < $scale; # -3 < -2 |
1388 | return $x; |
1389 | } |
1390 | return $x if $x->{sign} !~ /^[+-]$/; |
58cde26e |
1391 | # print "MBF bfround $x to scale $scale mode $mode\n"; |
58cde26e |
1392 | |
ee15d750 |
1393 | # don't round if x already has lower precision |
1394 | return $x if (defined $x->{_p} && $x->{_p} < 0 && $scale < $x->{_p}); |
1395 | |
1396 | $x->{_p} = $scale; # remember round in any case |
1397 | $x->{_a} = undef; # and clear A |
58cde26e |
1398 | if ($scale < 0) |
1399 | { |
1400 | # print "bfround scale $scale e $x->{_e}\n"; |
1401 | # round right from the '.' |
1402 | return $x if $x->{_e} >= 0; # nothing to round |
1403 | $scale = -$scale; # positive for simplicity |
1404 | my $len = $x->{_m}->length(); # length of mantissa |
1405 | my $dad = -$x->{_e}; # digits after dot |
1406 | my $zad = 0; # zeros after dot |
1407 | $zad = -$len-$x->{_e} if ($x->{_e} < -$len);# for 0.00..00xxx style |
ee15d750 |
1408 | #print "scale $scale dad $dad zad $zad len $len\n"; |
58cde26e |
1409 | |
1410 | # number bsstr len zad dad |
1411 | # 0.123 123e-3 3 0 3 |
1412 | # 0.0123 123e-4 3 1 4 |
1413 | # 0.001 1e-3 1 2 3 |
1414 | # 1.23 123e-2 3 0 2 |
1415 | # 1.2345 12345e-4 5 0 4 |
1416 | |
1417 | # do not round after/right of the $dad |
1418 | return $x if $scale > $dad; # 0.123, scale >= 3 => exit |
1419 | |
ee15d750 |
1420 | # round to zero if rounding inside the $zad, but not for last zero like: |
1421 | # 0.0065, scale -2, round last '0' with following '65' (scale == zad case) |
1422 | return $x->bzero() if $scale < $zad; |
1423 | if ($scale == $zad) # for 0.006, scale -3 and trunc |
58cde26e |
1424 | { |
b3abae2a |
1425 | $scale = -$len; |
58cde26e |
1426 | } |
1427 | else |
1428 | { |
1429 | # adjust round-point to be inside mantissa |
1430 | if ($zad != 0) |
1431 | { |
1432 | $scale = $scale-$zad; |
1433 | } |
1434 | else |
1435 | { |
1436 | my $dbd = $len - $dad; $dbd = 0 if $dbd < 0; # digits before dot |
1437 | $scale = $dbd+$scale; |
1438 | } |
1439 | } |
1440 | # print "round to $x->{_m} to $scale\n"; |
a0d0e21e |
1441 | } |
58cde26e |
1442 | else |
1443 | { |
1444 | # 123 => 100 means length(123) = 3 - $scale (2) => 1 |
a5f75d66 |
1445 | |
b3abae2a |
1446 | my $dbt = $x->{_m}->length(); |
1447 | # digits before dot |
1448 | my $dbd = $dbt + $x->{_e}; |
1449 | # should be the same, so treat it as this |
1450 | $scale = 1 if $scale == 0; |
1451 | # shortcut if already integer |
1452 | return $x if $scale == 1 && $dbt <= $dbd; |
1453 | # maximum digits before dot |
1454 | ++$dbd; |
1455 | |
1456 | if ($scale > $dbd) |
1457 | { |
1458 | # not enough digits before dot, so round to zero |
1459 | return $x->bzero; |
1460 | } |
1461 | elsif ( $scale == $dbd ) |
1462 | { |
1463 | # maximum |
1464 | $scale = -$dbt; |
1465 | } |
58cde26e |
1466 | else |
b3abae2a |
1467 | { |
1468 | $scale = $dbd - $scale; |
1469 | } |
1470 | |
a0d0e21e |
1471 | } |
574bacfe |
1472 | # print "using $scale for $x->{_m} with '$mode'\n"; |
1473 | # pass sign to bround for rounding modes '+inf' and '-inf' |
58cde26e |
1474 | $x->{_m}->{sign} = $x->{sign}; |
1475 | $x->{_m}->bround($scale,$mode); |
1476 | $x->{_m}->{sign} = '+'; # fix sign back |
1477 | $x->bnorm(); |
1478 | } |
1479 | |
1480 | sub bround |
1481 | { |
1482 | # accuracy: preserve $N digits, and overwrite the rest with 0's |
ee15d750 |
1483 | my $x = shift; my $self = ref($x) || $x; $x = $self->new(shift) if !ref($x); |
1484 | |
1485 | die ('bround() needs positive accuracy') if ($_[0] || 0) < 0; |
58cde26e |
1486 | |
ee15d750 |
1487 | my ($scale,$mode) = $x->_scale_a($self->accuracy(),$self->round_mode(),@_); |
1488 | return $x if !defined $scale; # no-op |
61f5c3f5 |
1489 | |
58cde26e |
1490 | return $x if $x->modify('bround'); |
61f5c3f5 |
1491 | |
ee15d750 |
1492 | # scale is now either $x->{_a}, $accuracy, or the user parameter |
1493 | # test whether $x already has lower accuracy, do nothing in this case |
1494 | # but do round if the accuracy is the same, since a math operation might |
1495 | # want to round a number with A=5 to 5 digits afterwards again |
1496 | return $x if defined $_[0] && defined $x->{_a} && $x->{_a} < $_[0]; |
58cde26e |
1497 | |
61f5c3f5 |
1498 | # scale < 0 makes no sense |
1499 | # never round a +-inf, NaN |
1500 | return $x if ($scale < 0) || $x->{sign} !~ /^[+-]$/; |
58cde26e |
1501 | |
61f5c3f5 |
1502 | # 1: $scale == 0 => keep all digits |
1503 | # 2: never round a 0 |
1504 | # 3: if we should keep more digits than the mantissa has, do nothing |
1505 | if ($scale == 0 || $x->is_zero() || $x->{_m}->length() <= $scale) |
1506 | { |
1507 | $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; |
1508 | return $x; |
1509 | } |
f216259d |
1510 | |
58cde26e |
1511 | # pass sign to bround for '+inf' and '-inf' rounding modes |
1512 | $x->{_m}->{sign} = $x->{sign}; |
1513 | $x->{_m}->bround($scale,$mode); # round mantissa |
1514 | $x->{_m}->{sign} = '+'; # fix sign back |
61f5c3f5 |
1515 | # $x->{_m}->{_a} = undef; $x->{_m}->{_p} = undef; |
ee15d750 |
1516 | $x->{_a} = $scale; # remember rounding |
1517 | $x->{_p} = undef; # and clear P |
574bacfe |
1518 | $x->bnorm(); # del trailing zeros gen. by bround() |
58cde26e |
1519 | } |
1520 | |
1521 | sub bfloor |
1522 | { |
1523 | # return integer less or equal then $x |
ee15d750 |
1524 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e |
1525 | |
1526 | return $x if $x->modify('bfloor'); |
1527 | |
1528 | return $x if $x->{sign} !~ /^[+-]$/; # nan, +inf, -inf |
1529 | |
1530 | # if $x has digits after dot |
1531 | if ($x->{_e}->{sign} eq '-') |
1532 | { |
28df3e88 |
1533 | #$x->{_m}->brsft(-$x->{_e},10); |
1534 | #$x->{_e}->bzero(); |
1535 | #$x-- if $x->{sign} eq '-'; |
1536 | |
1537 | $x->{_e}->{sign} = '+'; # negate e |
1538 | $x->{_m}->brsft($x->{_e},10); # cut off digits after dot |
1539 | $x->{_e}->bzero(); # trunc/norm |
1540 | $x->{_m}->binc() if $x->{sign} eq '-'; # decrement if negative |
f216259d |
1541 | } |
61f5c3f5 |
1542 | $x->round($a,$p,$r); |
58cde26e |
1543 | } |
288d023a |
1544 | |
58cde26e |
1545 | sub bceil |
1546 | { |
1547 | # return integer greater or equal then $x |
ee15d750 |
1548 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e |
1549 | |
1550 | return $x if $x->modify('bceil'); |
1551 | return $x if $x->{sign} !~ /^[+-]$/; # nan, +inf, -inf |
1552 | |
1553 | # if $x has digits after dot |
1554 | if ($x->{_e}->{sign} eq '-') |
1555 | { |
28df3e88 |
1556 | #$x->{_m}->brsft(-$x->{_e},10); |
1557 | #$x->{_e}->bzero(); |
1558 | #$x++ if $x->{sign} eq '+'; |
1559 | |
1560 | $x->{_e}->{sign} = '+'; # negate e |
1561 | $x->{_m}->brsft($x->{_e},10); # cut off digits after dot |
1562 | $x->{_e}->bzero(); # trunc/norm |
1563 | $x->{_m}->binc() if $x->{sign} eq '+'; # decrement if negative |
a0d0e21e |
1564 | } |
61f5c3f5 |
1565 | $x->round($a,$p,$r); |
58cde26e |
1566 | } |
1567 | |
394e6ffb |
1568 | sub brsft |
1569 | { |
1570 | # shift right by $y (divide by power of 2) |
1571 | my ($self,$x,$y,$n,$a,$p,$r) = objectify(2,@_); |
1572 | |
1573 | return $x if $x->modify('brsft'); |
1574 | return $x if $x->{sign} !~ /^[+-]$/; # nan, +inf, -inf |
1575 | |
1576 | $n = 2 if !defined $n; $n = Math::BigFloat->new($n); |
1577 | $x->bdiv($n ** $y,$a,$p,$r,$y); |
1578 | } |
1579 | |
1580 | sub blsft |
1581 | { |
1582 | # shift right by $y (divide by power of 2) |
1583 | my ($self,$x,$y,$n,$a,$p,$r) = objectify(2,@_); |
1584 | |
1585 | return $x if $x->modify('brsft'); |
1586 | return $x if $x->{sign} !~ /^[+-]$/; # nan, +inf, -inf |
1587 | |
1588 | $n = 2 if !defined $n; $n = Math::BigFloat->new($n); |
1589 | $x->bmul($n ** $y,$a,$p,$r,$y); |
1590 | } |
1591 | |
58cde26e |
1592 | ############################################################################### |
a5f75d66 |
1593 | |
58cde26e |
1594 | sub DESTROY |
1595 | { |
ee15d750 |
1596 | # going through AUTOLOAD for every DESTROY is costly, so avoid it by empty sub |
58cde26e |
1597 | } |
1598 | |
1599 | sub AUTOLOAD |
1600 | { |
b3abae2a |
1601 | # make fxxx and bxxx both work by selectively mapping fxxx() to MBF::bxxx() |
1602 | # or falling back to MBI::bxxx() |
58cde26e |
1603 | my $name = $AUTOLOAD; |
1604 | |
1605 | $name =~ s/.*:://; # split package |
ee15d750 |
1606 | no strict 'refs'; |
1607 | if (!method_alias($name)) |
58cde26e |
1608 | { |
ee15d750 |
1609 | if (!defined $name) |
1610 | { |
1611 | # delayed load of Carp and avoid recursion |
1612 | require Carp; |
1613 | Carp::croak ("Can't call a method without name"); |
1614 | } |
ee15d750 |
1615 | if (!method_hand_up($name)) |
1616 | { |
1617 | # delayed load of Carp and avoid recursion |
1618 | require Carp; |
1619 | Carp::croak ("Can't call $class\-\>$name, not a valid method"); |
1620 | } |
1621 | # try one level up, but subst. bxxx() for fxxx() since MBI only got bxxx() |
1622 | $name =~ s/^f/b/; |
56b9c951 |
1623 | return &{"$MBI"."::$name"}(@_); |
a0d0e21e |
1624 | } |
58cde26e |
1625 | my $bname = $name; $bname =~ s/^f/b/; |
b3abae2a |
1626 | *{$class."::$name"} = \&$bname; |
58cde26e |
1627 | &$bname; # uses @_ |
1628 | } |
1629 | |
1630 | sub exponent |
1631 | { |
1632 | # return a copy of the exponent |
ee15d750 |
1633 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
1634 | |
ee15d750 |
1635 | if ($x->{sign} !~ /^[+-]$/) |
1636 | { |
1637 | my $s = $x->{sign}; $s =~ s/^[+-]//; |
1638 | return $self->new($s); # -inf, +inf => +inf |
1639 | } |
1640 | return $x->{_e}->copy(); |
58cde26e |
1641 | } |
1642 | |
1643 | sub mantissa |
1644 | { |
1645 | # return a copy of the mantissa |
ee15d750 |
1646 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
1647 | |
ee15d750 |
1648 | if ($x->{sign} !~ /^[+-]$/) |
1649 | { |
1650 | my $s = $x->{sign}; $s =~ s/^[+]//; |
1651 | return $self->new($s); # -inf, +inf => +inf |
1652 | } |
1653 | my $m = $x->{_m}->copy(); # faster than going via bstr() |
1654 | $m->bneg() if $x->{sign} eq '-'; |
58cde26e |
1655 | |
61f5c3f5 |
1656 | $m; |
58cde26e |
1657 | } |
1658 | |
1659 | sub parts |
1660 | { |
1661 | # return a copy of both the exponent and the mantissa |
ee15d750 |
1662 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
1663 | |
ee15d750 |
1664 | if ($x->{sign} !~ /^[+-]$/) |
1665 | { |
1666 | my $s = $x->{sign}; $s =~ s/^[+]//; my $se = $s; $se =~ s/^[-]//; |
1667 | return ($self->new($s),$self->new($se)); # +inf => inf and -inf,+inf => inf |
1668 | } |
1669 | my $m = $x->{_m}->copy(); # faster than going via bstr() |
1670 | $m->bneg() if $x->{sign} eq '-'; |
1671 | return ($m,$x->{_e}->copy()); |
58cde26e |
1672 | } |
1673 | |
1674 | ############################################################################## |
1675 | # private stuff (internal use only) |
1676 | |
58cde26e |
1677 | sub import |
1678 | { |
1679 | my $self = shift; |
8f675a64 |
1680 | my $l = scalar @_; |
1681 | my $lib = ''; my @a; |
1682 | for ( my $i = 0; $i < $l ; $i++) |
58cde26e |
1683 | { |
8f675a64 |
1684 | # print "at $_[$i] (",$_[$i+1]||'undef',")\n"; |
58cde26e |
1685 | if ( $_[$i] eq ':constant' ) |
1686 | { |
1687 | # this rest causes overlord er load to step in |
1688 | # print "overload @_\n"; |
1689 | overload::constant float => sub { $self->new(shift); }; |
b3abae2a |
1690 | } |
1691 | elsif ($_[$i] eq 'upgrade') |
1692 | { |
1693 | # this causes upgrading |
28df3e88 |
1694 | $upgrade = $_[$i+1]; # or undef to disable |
8f675a64 |
1695 | $i++; |
28df3e88 |
1696 | } |
1697 | elsif ($_[$i] eq 'downgrade') |
1698 | { |
1699 | # this causes downgrading |
1700 | $downgrade = $_[$i+1]; # or undef to disable |
8f675a64 |
1701 | $i++; |
58cde26e |
1702 | } |
56b9c951 |
1703 | elsif ($_[$i] eq 'lib') |
1704 | { |
1705 | $lib = $_[$i+1] || ''; # default Calc |
8f675a64 |
1706 | $i++; |
56b9c951 |
1707 | } |
1708 | elsif ($_[$i] eq 'with') |
1709 | { |
1710 | $MBI = $_[$i+1] || 'Math::BigInt'; # default Math::BigInt |
8f675a64 |
1711 | $i++; |
1712 | } |
1713 | else |
1714 | { |
1715 | push @a, $_[$i]; |
56b9c951 |
1716 | } |
58cde26e |
1717 | } |
8f675a64 |
1718 | |
56b9c951 |
1719 | # let use Math::BigInt lib => 'GMP'; use Math::BigFloat; still work |
1720 | my $mbilib = eval { Math::BigInt->config()->{lib} }; |
8f675a64 |
1721 | if ((defined $mbilib) && ($MBI eq 'Math::BigInt')) |
1722 | { |
1723 | # MBI already loaded |
1724 | $MBI->import('lib',"$lib,$mbilib", 'objectify'); |
1725 | } |
1726 | else |
1727 | { |
1728 | # MBI not loaded, or with ne "Math::BigInt" |
1729 | $lib .= ",$mbilib" if defined $mbilib; |
07d34614 |
1730 | $lib =~ s/^,//; # don't leave empty |
8f675a64 |
1731 | if ($] < 5.006) |
1732 | { |
1733 | # Perl < 5.6.0 dies with "out of memory!" when eval() and ':constant' is |
1734 | # used in the same script, or eval inside import(). |
1735 | my @parts = split /::/, $MBI; # Math::BigInt => Math BigInt |
1736 | my $file = pop @parts; $file .= '.pm'; # BigInt => BigInt.pm |
07d34614 |
1737 | require File::Spec; |
8f675a64 |
1738 | $file = File::Spec->catfile (@parts, $file); |
07d34614 |
1739 | eval { require "$file"; }; |
1740 | $MBI->import( lib => $lib, 'objectify' ); |
8f675a64 |
1741 | } |
1742 | else |
1743 | { |
1744 | my $rc = "use $MBI lib => '$lib', 'objectify';"; |
1745 | eval $rc; |
1746 | } |
1747 | } |
1748 | die ("Couldn't load $MBI: $! $@") if $@; |
56b9c951 |
1749 | |
58cde26e |
1750 | # any non :constant stuff is handled by our parent, Exporter |
1751 | # even if @_ is empty, to give it a chance |
b3abae2a |
1752 | $self->SUPER::import(@a); # for subclasses |
1753 | $self->export_to_level(1,$self,@a); # need this, too |
58cde26e |
1754 | } |
1755 | |
1756 | sub bnorm |
1757 | { |
1758 | # adjust m and e so that m is smallest possible |
1759 | # round number according to accuracy and precision settings |
ee15d750 |
1760 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
1761 | |
0716bf9b |
1762 | return $x if $x->{sign} !~ /^[+-]$/; # inf, nan etc |
58cde26e |
1763 | |
28df3e88 |
1764 | # if (!$x->{_m}->is_odd()) |
1765 | # { |
1766 | my $zeros = $x->{_m}->_trailing_zeros(); # correct for trailing zeros |
1767 | if ($zeros != 0) |
1768 | { |
1769 | $x->{_m}->brsft($zeros,10); $x->{_e}->badd($zeros); |
1770 | } |
1771 | # for something like 0Ey, set y to 1, and -0 => +0 |
1772 | $x->{sign} = '+', $x->{_e}->bone() if $x->{_m}->is_zero(); |
1773 | # } |
ee15d750 |
1774 | # this is to prevent automatically rounding when MBI's globals are set |
0716bf9b |
1775 | $x->{_m}->{_f} = MB_NEVER_ROUND; |
1776 | $x->{_e}->{_f} = MB_NEVER_ROUND; |
ee15d750 |
1777 | # 'forget' that mantissa was rounded via MBI::bround() in MBF's bfround() |
1778 | $x->{_m}->{_a} = undef; $x->{_e}->{_a} = undef; |
1779 | $x->{_m}->{_p} = undef; $x->{_e}->{_p} = undef; |
61f5c3f5 |
1780 | $x; # MBI bnorm is no-op, so dont call it |
1781 | } |
58cde26e |
1782 | |
1783 | ############################################################################## |
1784 | # internal calculation routines |
1785 | |
1786 | sub as_number |
1787 | { |
394e6ffb |
1788 | # return copy as a bigint representation of this BigFloat number |
1789 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
1790 | |
28df3e88 |
1791 | my $z = $x->{_m}->copy(); |
1792 | if ($x->{_e}->{sign} eq '-') # < 0 |
58cde26e |
1793 | { |
28df3e88 |
1794 | $x->{_e}->{sign} = '+'; # flip |
1795 | $z->brsft($x->{_e},10); |
1796 | $x->{_e}->{sign} = '-'; # flip back |
0716bf9b |
1797 | } |
28df3e88 |
1798 | elsif (!$x->{_e}->is_zero()) # > 0 |
0716bf9b |
1799 | { |
1800 | $z->blsft($x->{_e},10); |
58cde26e |
1801 | } |
58cde26e |
1802 | $z->{sign} = $x->{sign}; |
61f5c3f5 |
1803 | $z; |
58cde26e |
1804 | } |
1805 | |
1806 | sub length |
1807 | { |
ee15d750 |
1808 | my $x = shift; |
1809 | my $class = ref($x) || $x; |
1810 | $x = $class->new(shift) unless ref($x); |
58cde26e |
1811 | |
ee15d750 |
1812 | return 1 if $x->{_m}->is_zero(); |
58cde26e |
1813 | my $len = $x->{_m}->length(); |
1814 | $len += $x->{_e} if $x->{_e}->sign() eq '+'; |
1815 | if (wantarray()) |
1816 | { |
56b9c951 |
1817 | my $t = $MBI->bzero(); |
58cde26e |
1818 | $t = $x->{_e}->copy()->babs() if $x->{_e}->sign() eq '-'; |
1819 | return ($len,$t); |
1820 | } |
61f5c3f5 |
1821 | $len; |
58cde26e |
1822 | } |
a0d0e21e |
1823 | |
1824 | 1; |
a5f75d66 |
1825 | __END__ |
1826 | |
1827 | =head1 NAME |
1828 | |
58cde26e |
1829 | Math::BigFloat - Arbitrary size floating point math package |
a5f75d66 |
1830 | |
1831 | =head1 SYNOPSIS |
1832 | |
a2008d6d |
1833 | use Math::BigFloat; |
58cde26e |
1834 | |
b3abae2a |
1835 | # Number creation |
1836 | $x = Math::BigFloat->new($str); # defaults to 0 |
1837 | $nan = Math::BigFloat->bnan(); # create a NotANumber |
1838 | $zero = Math::BigFloat->bzero(); # create a +0 |
1839 | $inf = Math::BigFloat->binf(); # create a +inf |
1840 | $inf = Math::BigFloat->binf('-'); # create a -inf |
1841 | $one = Math::BigFloat->bone(); # create a +1 |
1842 | $one = Math::BigFloat->bone('-'); # create a -1 |
58cde26e |
1843 | |
1844 | # Testing |
b3abae2a |
1845 | $x->is_zero(); # true if arg is +0 |
1846 | $x->is_nan(); # true if arg is NaN |
0716bf9b |
1847 | $x->is_one(); # true if arg is +1 |
1848 | $x->is_one('-'); # true if arg is -1 |
1849 | $x->is_odd(); # true if odd, false for even |
1850 | $x->is_even(); # true if even, false for odd |
1851 | $x->is_positive(); # true if >= 0 |
1852 | $x->is_negative(); # true if < 0 |
b3abae2a |
1853 | $x->is_inf(sign); # true if +inf, or -inf (default is '+') |
1854 | |
58cde26e |
1855 | $x->bcmp($y); # compare numbers (undef,<0,=0,>0) |
1856 | $x->bacmp($y); # compare absolutely (undef,<0,=0,>0) |
1857 | $x->sign(); # return the sign, either +,- or NaN |
b3abae2a |
1858 | $x->digit($n); # return the nth digit, counting from right |
1859 | $x->digit(-$n); # return the nth digit, counting from left |
58cde26e |
1860 | |
1861 | # The following all modify their first argument: |
b3abae2a |
1862 | |
58cde26e |
1863 | # set |
1864 | $x->bzero(); # set $i to 0 |
1865 | $x->bnan(); # set $i to NaN |
b3abae2a |
1866 | $x->bone(); # set $x to +1 |
1867 | $x->bone('-'); # set $x to -1 |
1868 | $x->binf(); # set $x to inf |
1869 | $x->binf('-'); # set $x to -inf |
58cde26e |
1870 | |
1871 | $x->bneg(); # negation |
1872 | $x->babs(); # absolute value |
1873 | $x->bnorm(); # normalize (no-op) |
1874 | $x->bnot(); # two's complement (bit wise not) |
1875 | $x->binc(); # increment x by 1 |
1876 | $x->bdec(); # decrement x by 1 |
1877 | |
1878 | $x->badd($y); # addition (add $y to $x) |
1879 | $x->bsub($y); # subtraction (subtract $y from $x) |
1880 | $x->bmul($y); # multiplication (multiply $x by $y) |
1881 | $x->bdiv($y); # divide, set $i to quotient |
1882 | # return (quo,rem) or quo if scalar |
1883 | |
1884 | $x->bmod($y); # modulus |
1885 | $x->bpow($y); # power of arguments (a**b) |
1886 | $x->blsft($y); # left shift |
1887 | $x->brsft($y); # right shift |
1888 | # return (quo,rem) or quo if scalar |
1889 | |
61f5c3f5 |
1890 | $x->blog($base); # logarithm of $x, base defaults to e |
1891 | # (other bases than e not supported yet) |
1892 | |
58cde26e |
1893 | $x->band($y); # bit-wise and |
1894 | $x->bior($y); # bit-wise inclusive or |
1895 | $x->bxor($y); # bit-wise exclusive or |
1896 | $x->bnot(); # bit-wise not (two's complement) |
b3abae2a |
1897 | |
1898 | $x->bsqrt(); # calculate square-root |
1899 | $x->bfac(); # factorial of $x (1*2*3*4*..$x) |
1900 | |
58cde26e |
1901 | $x->bround($N); # accuracy: preserver $N digits |
1902 | $x->bfround($N); # precision: round to the $Nth digit |
1903 | |
1904 | # The following do not modify their arguments: |
58cde26e |
1905 | bgcd(@values); # greatest common divisor |
1906 | blcm(@values); # lowest common multiplicator |
1907 | |
1908 | $x->bstr(); # return string |
1909 | $x->bsstr(); # return string in scientific notation |
b3abae2a |
1910 | |
1911 | $x->bfloor(); # return integer less or equal than $x |
1912 | $x->bceil(); # return integer greater or equal than $x |
1913 | |
58cde26e |
1914 | $x->exponent(); # return exponent as BigInt |
1915 | $x->mantissa(); # return mantissa as BigInt |
1916 | $x->parts(); # return (mantissa,exponent) as BigInt |
1917 | |
1918 | $x->length(); # number of digits (w/o sign and '.') |
1919 | ($l,$f) = $x->length(); # number of digits, and length of fraction |
a5f75d66 |
1920 | |
1921 | =head1 DESCRIPTION |
1922 | |
58cde26e |
1923 | All operators (inlcuding basic math operations) are overloaded if you |
1924 | declare your big floating point numbers as |
a5f75d66 |
1925 | |
58cde26e |
1926 | $i = new Math::BigFloat '12_3.456_789_123_456_789E-2'; |
1927 | |
1928 | Operations with overloaded operators preserve the arguments, which is |
1929 | exactly what you expect. |
1930 | |
1931 | =head2 Canonical notation |
1932 | |
1933 | Input to these routines are either BigFloat objects, or strings of the |
1934 | following four forms: |
a5f75d66 |
1935 | |
1936 | =over 2 |
1937 | |
58cde26e |
1938 | =item * |
1939 | |
1940 | C</^[+-]\d+$/> |
a5f75d66 |
1941 | |
58cde26e |
1942 | =item * |
a5f75d66 |
1943 | |
58cde26e |
1944 | C</^[+-]\d+\.\d*$/> |
a5f75d66 |
1945 | |
58cde26e |
1946 | =item * |
a5f75d66 |
1947 | |
58cde26e |
1948 | C</^[+-]\d+E[+-]?\d+$/> |
a5f75d66 |
1949 | |
58cde26e |
1950 | =item * |
a5f75d66 |
1951 | |
58cde26e |
1952 | C</^[+-]\d*\.\d+E[+-]?\d+$/> |
5d7098d5 |
1953 | |
58cde26e |
1954 | =back |
1955 | |
1956 | all with optional leading and trailing zeros and/or spaces. Additonally, |
1957 | numbers are allowed to have an underscore between any two digits. |
1958 | |
1959 | Empty strings as well as other illegal numbers results in 'NaN'. |
1960 | |
1961 | bnorm() on a BigFloat object is now effectively a no-op, since the numbers |
1962 | are always stored in normalized form. On a string, it creates a BigFloat |
1963 | object. |
1964 | |
1965 | =head2 Output |
1966 | |
1967 | Output values are BigFloat objects (normalized), except for bstr() and bsstr(). |
1968 | |
1969 | The string output will always have leading and trailing zeros stripped and drop |
1970 | a plus sign. C<bstr()> will give you always the form with a decimal point, |
1971 | while C<bsstr()> (for scientific) gives you the scientific notation. |
1972 | |
1973 | Input bstr() bsstr() |
1974 | '-0' '0' '0E1' |
1975 | ' -123 123 123' '-123123123' '-123123123E0' |
1976 | '00.0123' '0.0123' '123E-4' |
1977 | '123.45E-2' '1.2345' '12345E-4' |
1978 | '10E+3' '10000' '1E4' |
1979 | |
1980 | Some routines (C<is_odd()>, C<is_even()>, C<is_zero()>, C<is_one()>, |
1981 | C<is_nan()>) return true or false, while others (C<bcmp()>, C<bacmp()>) |
1982 | return either undef, <0, 0 or >0 and are suited for sort. |
1983 | |
1984 | Actual math is done by using BigInts to represent the mantissa and exponent. |
1985 | The sign C</^[+-]$/> is stored separately. The string 'NaN' is used to |
1986 | represent the result when input arguments are not numbers, as well as |
1987 | the result of dividing by zero. |
1988 | |
1989 | =head2 C<mantissa()>, C<exponent()> and C<parts()> |
1990 | |
1991 | C<mantissa()> and C<exponent()> return the said parts of the BigFloat |
1992 | as BigInts such that: |
1993 | |
1994 | $m = $x->mantissa(); |
1995 | $e = $x->exponent(); |
1996 | $y = $m * ( 10 ** $e ); |
1997 | print "ok\n" if $x == $y; |
1998 | |
1999 | C<< ($m,$e) = $x->parts(); >> is just a shortcut giving you both of them. |
2000 | |
2001 | A zero is represented and returned as C<0E1>, B<not> C<0E0> (after Knuth). |
2002 | |
2003 | Currently the mantissa is reduced as much as possible, favouring higher |
2004 | exponents over lower ones (e.g. returning 1e7 instead of 10e6 or 10000000e0). |
2005 | This might change in the future, so do not depend on it. |
2006 | |
2007 | =head2 Accuracy vs. Precision |
2008 | |
2009 | See also: L<Rounding|Rounding>. |
2010 | |
027dc388 |
2011 | Math::BigFloat supports both precision and accuracy. For a full documentation, |
2012 | examples and tips on these topics please see the large section in |
2013 | L<Math::BigInt>. |
5d7098d5 |
2014 | |
58cde26e |
2015 | Since things like sqrt(2) or 1/3 must presented with a limited precision lest |
2016 | a operation consumes all resources, each operation produces no more than |
2017 | C<Math::BigFloat::precision()> digits. |
2018 | |
2019 | In case the result of one operation has more precision than specified, |
2020 | it is rounded. The rounding mode taken is either the default mode, or the one |
2021 | supplied to the operation after the I<scale>: |
2022 | |
2023 | $x = Math::BigFloat->new(2); |
2024 | Math::BigFloat::precision(5); # 5 digits max |
2025 | $y = $x->copy()->bdiv(3); # will give 0.66666 |
2026 | $y = $x->copy()->bdiv(3,6); # will give 0.666666 |
2027 | $y = $x->copy()->bdiv(3,6,'odd'); # will give 0.666667 |
2028 | Math::BigFloat::round_mode('zero'); |
2029 | $y = $x->copy()->bdiv(3,6); # will give 0.666666 |
2030 | |
2031 | =head2 Rounding |
2032 | |
2033 | =over 2 |
2034 | |
5dc6f178 |
2035 | =item ffround ( +$scale ) |
58cde26e |
2036 | |
0716bf9b |
2037 | Rounds to the $scale'th place left from the '.', counting from the dot. |
2038 | The first digit is numbered 1. |
58cde26e |
2039 | |
5dc6f178 |
2040 | =item ffround ( -$scale ) |
58cde26e |
2041 | |
0716bf9b |
2042 | Rounds to the $scale'th place right from the '.', counting from the dot. |
58cde26e |
2043 | |
5dc6f178 |
2044 | =item ffround ( 0 ) |
2045 | |
0716bf9b |
2046 | Rounds to an integer. |
5dc6f178 |
2047 | |
2048 | =item fround ( +$scale ) |
2049 | |
0716bf9b |
2050 | Preserves accuracy to $scale digits from the left (aka significant digits) |
2051 | and pads the rest with zeros. If the number is between 1 and -1, the |
2052 | significant digits count from the first non-zero after the '.' |
5dc6f178 |
2053 | |
2054 | =item fround ( -$scale ) and fround ( 0 ) |
2055 | |
0716bf9b |
2056 | These are effetively no-ops. |
5d7098d5 |
2057 | |
a5f75d66 |
2058 | =back |
2059 | |
0716bf9b |
2060 | All rounding functions take as a second parameter a rounding mode from one of |
2061 | the following: 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'. |
58cde26e |
2062 | |
2063 | The default rounding mode is 'even'. By using |
ee15d750 |
2064 | C<< Math::BigFloat::round_mode($round_mode); >> you can get and set the default |
2065 | mode for subsequent rounding. The usage of C<$Math::BigFloat::$round_mode> is |
0716bf9b |
2066 | no longer supported. |
b22b3e31 |
2067 | The second parameter to the round functions then overrides the default |
0716bf9b |
2068 | temporarily. |
58cde26e |
2069 | |
2070 | The C<< as_number() >> function returns a BigInt from a Math::BigFloat. It uses |
2071 | 'trunc' as rounding mode to make it equivalent to: |
2072 | |
2073 | $x = 2.5; |
2074 | $y = int($x) + 2; |
2075 | |
2076 | You can override this by passing the desired rounding mode as parameter to |
2077 | C<as_number()>: |
2078 | |
2079 | $x = Math::BigFloat->new(2.5); |
2080 | $y = $x->as_number('odd'); # $y = 3 |
2081 | |
2082 | =head1 EXAMPLES |
2083 | |
58cde26e |
2084 | # not ready yet |
58cde26e |
2085 | |
2086 | =head1 Autocreating constants |
2087 | |
2088 | After C<use Math::BigFloat ':constant'> all the floating point constants |
2089 | in the given scope are converted to C<Math::BigFloat>. This conversion |
2090 | happens at compile time. |
2091 | |
2092 | In particular |
2093 | |
2094 | perl -MMath::BigFloat=:constant -e 'print 2E-100,"\n"' |
2095 | |
56b9c951 |
2096 | prints the value of C<2E-100>. Note that without conversion of |
58cde26e |
2097 | constants the expression 2E-100 will be calculated as normal floating point |
2098 | number. |
2099 | |
56b9c951 |
2100 | Please note that ':constant' does not affect integer constants, nor binary |
2101 | nor hexadecimal constants. Use L<bignum> or L<Math::BigInt> to get this to |
2102 | work. |
2103 | |
2104 | =head2 Math library |
2105 | |
2106 | Math with the numbers is done (by default) by a module called |
2107 | Math::BigInt::Calc. This is equivalent to saying: |
2108 | |
2109 | use Math::BigFloat lib => 'Calc'; |
2110 | |
2111 | You can change this by using: |
2112 | |
2113 | use Math::BigFloat lib => 'BitVect'; |
2114 | |
2115 | The following would first try to find Math::BigInt::Foo, then |
2116 | Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: |
2117 | |
2118 | use Math::BigFloat lib => 'Foo,Math::BigInt::Bar'; |
2119 | |
2120 | Calc.pm uses as internal format an array of elements of some decimal base |
2121 | (usually 1e7, but this might be differen for some systems) with the least |
2122 | significant digit first, while BitVect.pm uses a bit vector of base 2, most |
2123 | significant bit first. Other modules might use even different means of |
2124 | representing the numbers. See the respective module documentation for further |
2125 | details. |
2126 | |
2127 | Please note that Math::BigFloat does B<not> use the denoted library itself, |
2128 | but it merely passes the lib argument to Math::BigInt. So, instead of the need |
2129 | to do: |
2130 | |
2131 | use Math::BigInt lib => 'GMP'; |
2132 | use Math::BigFloat; |
2133 | |
2134 | you can roll it all into one line: |
2135 | |
2136 | use Math::BigFloat lib => 'GMP'; |
2137 | |
2138 | Use the lib, Luke! And see L<Using Math::BigInt::Lite> for more details. |
2139 | |
2140 | =head2 Using Math::BigInt::Lite |
2141 | |
2142 | It is possible to use L<Math::BigInt::Lite> with Math::BigFloat: |
2143 | |
2144 | # 1 |
2145 | use Math::BigFloat with => 'Math::BigInt::Lite'; |
2146 | |
2147 | There is no need to "use Math::BigInt" or "use Math::BigInt::Lite", but you |
2148 | can combine these if you want. For instance, you may want to use |
2149 | Math::BigInt objects in your main script, too. |
2150 | |
2151 | # 2 |
2152 | use Math::BigInt; |
2153 | use Math::BigFloat with => 'Math::BigInt::Lite'; |
2154 | |
2155 | Of course, you can combine this with the C<lib> parameter. |
2156 | |
2157 | # 3 |
2158 | use Math::BigFloat with => 'Math::BigInt::Lite', lib => 'GMP,Pari'; |
2159 | |
2160 | If you want to use Math::BigInt's, too, simple add a Math::BigInt B<before>: |
2161 | |
2162 | # 4 |
2163 | use Math::BigInt; |
2164 | use Math::BigFloat with => 'Math::BigInt::Lite', lib => 'GMP,Pari'; |
2165 | |
2166 | Notice that the module with the last C<lib> will "win" and thus |
2167 | it's lib will be used if the lib is available: |
2168 | |
2169 | # 5 |
2170 | use Math::BigInt lib => 'Bar,Baz'; |
2171 | use Math::BigFloat with => 'Math::BigInt::Lite', lib => 'Foo'; |
2172 | |
2173 | That would try to load Foo, Bar, Baz and Calc (in that order). Or in other |
2174 | words, Math::BigFloat will try to retain previously loaded libs when you |
2175 | don't specify it one. |
2176 | |
2177 | Actually, the lib loading order would be "Bar,Baz,Calc", and then |
2178 | "Foo,Bar,Baz,Calc", but independend of which lib exists, the result is the |
2179 | same as trying the latter load alone, except for the fact that Bar or Baz |
2180 | might be loaded needlessly in an intermidiate step |
2181 | |
2182 | The old way still works though: |
2183 | |
2184 | # 6 |
2185 | use Math::BigInt lib => 'Bar,Baz'; |
2186 | use Math::BigFloat; |
2187 | |
2188 | But B<examples #3 and #4 are recommended> for usage. |
2189 | |
a5f75d66 |
2190 | =head1 BUGS |
2191 | |
58cde26e |
2192 | =over 2 |
2193 | |
2194 | =item * |
2195 | |
2196 | The following does not work yet: |
2197 | |
2198 | $m = $x->mantissa(); |
2199 | $e = $x->exponent(); |
2200 | $y = $m * ( 10 ** $e ); |
2201 | print "ok\n" if $x == $y; |
2202 | |
2203 | =item * |
2204 | |
2205 | There is no fmod() function yet. |
2206 | |
2207 | =back |
2208 | |
2209 | =head1 CAVEAT |
2210 | |
2211 | =over 1 |
2212 | |
2213 | =item stringify, bstr() |
2214 | |
2215 | Both stringify and bstr() now drop the leading '+'. The old code would return |
2216 | '+1.23', the new returns '1.23'. See the documentation in L<Math::BigInt> for |
2217 | reasoning and details. |
2218 | |
2219 | =item bdiv |
2220 | |
2221 | The following will probably not do what you expect: |
2222 | |
2223 | print $c->bdiv(123.456),"\n"; |
2224 | |
2225 | It prints both quotient and reminder since print works in list context. Also, |
2226 | bdiv() will modify $c, so be carefull. You probably want to use |
2227 | |
2228 | print $c / 123.456,"\n"; |
2229 | print scalar $c->bdiv(123.456),"\n"; # or if you want to modify $c |
2230 | |
2231 | instead. |
2232 | |
2233 | =item Modifying and = |
2234 | |
2235 | Beware of: |
2236 | |
2237 | $x = Math::BigFloat->new(5); |
2238 | $y = $x; |
2239 | |
2240 | It will not do what you think, e.g. making a copy of $x. Instead it just makes |
2241 | a second reference to the B<same> object and stores it in $y. Thus anything |
2242 | that modifies $x will modify $y, and vice versa. |
2243 | |
2244 | $x->bmul(2); |
2245 | print "$x, $y\n"; # prints '10, 10' |
2246 | |
2247 | If you want a true copy of $x, use: |
2248 | |
2249 | $y = $x->copy(); |
2250 | |
2251 | See also the documentation in L<overload> regarding C<=>. |
2252 | |
2253 | =item bpow |
2254 | |
2255 | C<bpow()> now modifies the first argument, unlike the old code which left |
2256 | it alone and only returned the result. This is to be consistent with |
2257 | C<badd()> etc. The first will modify $x, the second one won't: |
2258 | |
2259 | print bpow($x,$i),"\n"; # modify $x |
2260 | print $x->bpow($i),"\n"; # ditto |
2261 | print $x ** $i,"\n"; # leave $x alone |
2262 | |
2263 | =back |
2264 | |
2265 | =head1 LICENSE |
a5f75d66 |
2266 | |
58cde26e |
2267 | This program is free software; you may redistribute it and/or modify it under |
2268 | the same terms as Perl itself. |
5d7098d5 |
2269 | |
58cde26e |
2270 | =head1 AUTHORS |
5d7098d5 |
2271 | |
58cde26e |
2272 | Mark Biggar, overloaded interface by Ilya Zakharevich. |
2273 | Completely rewritten by Tels http://bloodgate.com in 2001. |
a5f75d66 |
2274 | |
a5f75d66 |
2275 | =cut |