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58cde26e JH |
1 | #!/usr/bin/perl -w |
2 | ||
58cde26e JH |
3 | # The following hash values are internally used: |
4 | # _e: exponent (BigInt) | |
5 | # _m: mantissa (absolute BigInt) | |
6 | # sign: +,-,"NaN" if not a number | |
7 | # _a: accuracy | |
8 | # _p: precision | |
0716bf9b | 9 | # _f: flags, used to signal MBI not to touch our private parts |
58cde26e JH |
10 | # _cow: Copy-On-Write (NRY) |
11 | ||
a0d0e21e LW |
12 | package Math::BigFloat; |
13 | ||
ee15d750 | 14 | $VERSION = '1.23'; |
58cde26e JH |
15 | require 5.005; |
16 | use Exporter; | |
0716bf9b | 17 | use Math::BigInt qw/objectify/; |
58cde26e JH |
18 | @ISA = qw( Exporter Math::BigInt); |
19 | # can not export bneg/babs since the are only in MBI | |
20 | @EXPORT_OK = qw( | |
21 | bcmp | |
22 | badd bmul bdiv bmod bnorm bsub | |
23 | bgcd blcm bround bfround | |
24 | bpow bnan bzero bfloor bceil | |
574bacfe | 25 | bacmp bstr binc bdec binf |
0716bf9b | 26 | is_odd is_even is_nan is_inf is_positive is_negative |
58cde26e JH |
27 | is_zero is_one sign |
28 | ); | |
a0d0e21e | 29 | |
58cde26e JH |
30 | #@EXPORT = qw( ); |
31 | use strict; | |
ee15d750 | 32 | use vars qw/$AUTOLOAD $accuracy $precision $div_scale $round_mode/; |
58cde26e | 33 | my $class = "Math::BigFloat"; |
a0d0e21e | 34 | |
a5f75d66 | 35 | use overload |
bd05a461 JH |
36 | '<=>' => sub { $_[2] ? |
37 | ref($_[0])->bcmp($_[1],$_[0]) : | |
38 | ref($_[0])->bcmp($_[0],$_[1])}, | |
0716bf9b | 39 | 'int' => sub { $_[0]->as_number() }, # 'trunc' to bigint |
a5f75d66 | 40 | ; |
a0d0e21e | 41 | |
0716bf9b JH |
42 | ############################################################################## |
43 | # global constants, flags and accessory | |
44 | ||
45 | use constant MB_NEVER_ROUND => 0x0001; | |
46 | ||
58cde26e JH |
47 | # are NaNs ok? |
48 | my $NaNOK=1; | |
58cde26e JH |
49 | # constant for easier life |
50 | my $nan = 'NaN'; | |
58cde26e | 51 | |
ee15d750 JH |
52 | # class constants, use Class->constant_name() to access |
53 | $round_mode = 'even'; # one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc' | |
54 | $accuracy = undef; | |
55 | $precision = undef; | |
56 | $div_scale = 40; | |
58cde26e | 57 | |
574bacfe JH |
58 | # in case we call SUPER::->foo() and this wants to call modify() |
59 | # sub modify () { 0; } | |
60 | ||
58cde26e | 61 | { |
ee15d750 | 62 | # valid method aliases for AUTOLOAD |
58cde26e JH |
63 | my %methods = map { $_ => 1 } |
64 | qw / fadd fsub fmul fdiv fround ffround fsqrt fmod fstr fsstr fpow fnorm | |
ee15d750 JH |
65 | fneg fint facmp fcmp fzero fnan finf finc fdec |
66 | fceil ffloor | |
67 | /; | |
68 | # valid method's that need to be hand-ed up (for AUTOLOAD) | |
69 | my %hand_ups = map { $_ => 1 } | |
70 | qw / is_nan is_inf is_negative is_positive | |
71 | accuracy precision div_scale round_mode fabs babs | |
58cde26e JH |
72 | /; |
73 | ||
ee15d750 JH |
74 | sub method_alias { return exists $methods{$_[0]||''}; } |
75 | sub method_hand_up { return exists $hand_ups{$_[0]||''}; } | |
a0d0e21e | 76 | } |
0e8b9368 | 77 | |
58cde26e JH |
78 | ############################################################################## |
79 | # constructors | |
a0d0e21e | 80 | |
58cde26e JH |
81 | sub new |
82 | { | |
83 | # create a new BigFloat object from a string or another bigfloat object. | |
84 | # _e: exponent | |
85 | # _m: mantissa | |
86 | # sign => sign (+/-), or "NaN" | |
a0d0e21e | 87 | |
58cde26e JH |
88 | my $class = shift; |
89 | ||
90 | my $wanted = shift; # avoid numify call by not using || here | |
91 | return $class->bzero() if !defined $wanted; # default to 0 | |
92 | return $wanted->copy() if ref($wanted) eq $class; | |
a0d0e21e | 93 | |
58cde26e JH |
94 | my $round = shift; $round = 0 if !defined $round; # no rounding as default |
95 | my $self = {}; bless $self, $class; | |
b22b3e31 | 96 | # shortcut for bigints and its subclasses |
0716bf9b | 97 | if ((ref($wanted)) && (ref($wanted) ne $class)) |
58cde26e | 98 | { |
0716bf9b | 99 | $self->{_m} = $wanted->as_number(); # get us a bigint copy |
58cde26e JH |
100 | $self->{_e} = Math::BigInt->new(0); |
101 | $self->{_m}->babs(); | |
102 | $self->{sign} = $wanted->sign(); | |
0716bf9b | 103 | return $self->bnorm(); |
58cde26e JH |
104 | } |
105 | # got string | |
106 | # handle '+inf', '-inf' first | |
ee15d750 | 107 | if ($wanted =~ /^[+-]?inf$/) |
58cde26e JH |
108 | { |
109 | $self->{_e} = Math::BigInt->new(0); | |
110 | $self->{_m} = Math::BigInt->new(0); | |
111 | $self->{sign} = $wanted; | |
ee15d750 | 112 | $self->{sign} = '+inf' if $self->{sign} eq 'inf'; |
0716bf9b | 113 | return $self->bnorm(); |
58cde26e JH |
114 | } |
115 | #print "new string '$wanted'\n"; | |
116 | my ($mis,$miv,$mfv,$es,$ev) = Math::BigInt::_split(\$wanted); | |
117 | if (!ref $mis) | |
118 | { | |
119 | die "$wanted is not a number initialized to $class" if !$NaNOK; | |
120 | $self->{_e} = Math::BigInt->new(0); | |
121 | $self->{_m} = Math::BigInt->new(0); | |
122 | $self->{sign} = $nan; | |
123 | } | |
124 | else | |
125 | { | |
126 | # make integer from mantissa by adjusting exp, then convert to bigint | |
127 | $self->{_e} = Math::BigInt->new("$$es$$ev"); # exponent | |
128 | $self->{_m} = Math::BigInt->new("$$mis$$miv$$mfv"); # create mantissa | |
129 | # 3.123E0 = 3123E-3, and 3.123E-2 => 3123E-5 | |
130 | $self->{_e} -= CORE::length($$mfv); | |
131 | $self->{sign} = $self->{_m}->sign(); $self->{_m}->babs(); | |
132 | } | |
0716bf9b | 133 | #print "$wanted => $self->{sign} $self->{value}\n"; |
58cde26e JH |
134 | $self->bnorm(); # first normalize |
135 | # if any of the globals is set, round to them and thus store them insid $self | |
ee15d750 | 136 | $self->round($accuracy,$precision,$class->round_mode) |
58cde26e JH |
137 | if defined $accuracy || defined $precision; |
138 | return $self; | |
139 | } | |
a0d0e21e | 140 | |
58cde26e JH |
141 | sub bnan |
142 | { | |
143 | # create a bigfloat 'NaN', if given a BigFloat, set it to 'NaN' | |
144 | my $self = shift; | |
145 | $self = $class if !defined $self; | |
146 | if (!ref($self)) | |
288d023a | 147 | { |
58cde26e | 148 | my $c = $self; $self = {}; bless $self, $c; |
a0d0e21e | 149 | } |
574bacfe JH |
150 | $self->{_m} = Math::BigInt->bzero(); |
151 | $self->{_e} = Math::BigInt->bzero(); | |
58cde26e | 152 | $self->{sign} = $nan; |
58cde26e JH |
153 | return $self; |
154 | } | |
a0d0e21e | 155 | |
58cde26e JH |
156 | sub binf |
157 | { | |
158 | # create a bigfloat '+-inf', if given a BigFloat, set it to '+-inf' | |
159 | my $self = shift; | |
160 | my $sign = shift; $sign = '+' if !defined $sign || $sign ne '-'; | |
a0d0e21e | 161 | |
58cde26e JH |
162 | $self = $class if !defined $self; |
163 | if (!ref($self)) | |
164 | { | |
165 | my $c = $self; $self = {}; bless $self, $c; | |
166 | } | |
574bacfe JH |
167 | $self->{_m} = Math::BigInt->bzero(); |
168 | $self->{_e} = Math::BigInt->bzero(); | |
58cde26e | 169 | $self->{sign} = $sign.'inf'; |
58cde26e JH |
170 | return $self; |
171 | } | |
a0d0e21e | 172 | |
574bacfe JH |
173 | sub bone |
174 | { | |
175 | # create a bigfloat '+-1', if given a BigFloat, set it to '+-1' | |
176 | my $self = shift; | |
177 | my $sign = shift; $sign = '+' if !defined $sign || $sign ne '-'; | |
178 | ||
179 | $self = $class if !defined $self; | |
180 | if (!ref($self)) | |
181 | { | |
182 | my $c = $self; $self = {}; bless $self, $c; | |
183 | } | |
184 | $self->{_m} = Math::BigInt->bone(); | |
185 | $self->{_e} = Math::BigInt->bzero(); | |
186 | $self->{sign} = $sign; | |
187 | return $self; | |
188 | } | |
189 | ||
58cde26e JH |
190 | sub bzero |
191 | { | |
192 | # create a bigfloat '+0', if given a BigFloat, set it to 0 | |
193 | my $self = shift; | |
194 | $self = $class if !defined $self; | |
195 | if (!ref($self)) | |
196 | { | |
197 | my $c = $self; $self = {}; bless $self, $c; | |
198 | } | |
574bacfe JH |
199 | $self->{_m} = Math::BigInt->bzero(); |
200 | $self->{_e} = Math::BigInt->bone(); | |
58cde26e | 201 | $self->{sign} = '+'; |
58cde26e JH |
202 | return $self; |
203 | } | |
204 | ||
205 | ############################################################################## | |
206 | # string conversation | |
207 | ||
208 | sub bstr | |
209 | { | |
210 | # (ref to BFLOAT or num_str ) return num_str | |
211 | # Convert number from internal format to (non-scientific) string format. | |
212 | # internal format is always normalized (no leading zeros, "-0" => "+0") | |
ee15d750 JH |
213 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
214 | #my $x = shift; my $class = ref($x) || $x; | |
215 | #$x = $class->new(shift) unless ref($x); | |
58cde26e | 216 | |
574bacfe JH |
217 | #die "Oups! e was $nan" if $x->{_e}->{sign} eq $nan; |
218 | #die "Oups! m was $nan" if $x->{_m}->{sign} eq $nan; | |
219 | if ($x->{sign} !~ /^[+-]$/) | |
58cde26e | 220 | { |
574bacfe JH |
221 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN |
222 | return 'inf'; # +inf | |
58cde26e JH |
223 | } |
224 | ||
574bacfe JH |
225 | my $es = '0'; my $len = 1; my $cad = 0; my $dot = '.'; |
226 | ||
227 | my $not_zero = !$x->is_zero(); | |
228 | if ($not_zero) | |
58cde26e | 229 | { |
574bacfe JH |
230 | $es = $x->{_m}->bstr(); |
231 | $len = CORE::length($es); | |
232 | if (!$x->{_e}->is_zero()) | |
233 | # { | |
234 | # $es = $x->{sign}.$es if $x->{sign} eq '-'; | |
235 | # } | |
236 | # else | |
58cde26e | 237 | { |
574bacfe JH |
238 | if ($x->{_e}->sign() eq '-') |
239 | { | |
240 | $dot = ''; | |
241 | if ($x->{_e} <= -$len) | |
242 | { | |
243 | # print "style: 0.xxxx\n"; | |
244 | my $r = $x->{_e}->copy(); $r->babs()->bsub( CORE::length($es) ); | |
245 | $es = '0.'. ('0' x $r) . $es; $cad = -($len+$r); | |
246 | } | |
247 | else | |
248 | { | |
249 | # print "insert '.' at $x->{_e} in '$es'\n"; | |
250 | substr($es,$x->{_e},0) = '.'; $cad = $x->{_e}; | |
251 | } | |
252 | } | |
253 | else | |
254 | { | |
255 | # expand with zeros | |
256 | $es .= '0' x $x->{_e}; $len += $x->{_e}; $cad = 0; | |
257 | } | |
82cf049f | 258 | } |
574bacfe JH |
259 | } # if not zero |
260 | $es = $x->{sign}.$es if $x->{sign} eq '-'; | |
261 | # if set accuracy or precision, pad with zeros | |
262 | if ((defined $x->{_a}) && ($not_zero)) | |
263 | { | |
264 | # 123400 => 6, 0.1234 => 4, 0.001234 => 4 | |
265 | my $zeros = $x->{_a} - $cad; # cad == 0 => 12340 | |
266 | $zeros = $x->{_a} - $len if $cad != $len; | |
267 | #print "acc padd $x->{_a} $zeros (len $len cad $cad)\n"; | |
268 | $es .= $dot.'0' x $zeros if $zeros > 0; | |
82cf049f | 269 | } |
574bacfe | 270 | elsif ($x->{_p} || 0 < 0) |
58cde26e | 271 | { |
574bacfe JH |
272 | # 123400 => 6, 0.1234 => 4, 0.001234 => 6 |
273 | my $zeros = -$x->{_p} + $cad; | |
274 | #print "pre padd $x->{_p} $zeros (len $len cad $cad)\n"; | |
275 | $es .= $dot.'0' x $zeros if $zeros > 0; | |
58cde26e | 276 | } |
58cde26e | 277 | return $es; |
82cf049f | 278 | } |
f216259d | 279 | |
58cde26e JH |
280 | sub bsstr |
281 | { | |
282 | # (ref to BFLOAT or num_str ) return num_str | |
283 | # Convert number from internal format to scientific string format. | |
284 | # internal format is always normalized (no leading zeros, "-0E0" => "+0E0") | |
ee15d750 JH |
285 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
286 | #my $x = shift; my $class = ref($x) || $x; | |
287 | #$x = $class->new(shift) unless ref($x); | |
a0d0e21e | 288 | |
574bacfe JH |
289 | #die "Oups! e was $nan" if $x->{_e}->{sign} eq $nan; |
290 | #die "Oups! m was $nan" if $x->{_m}->{sign} eq $nan; | |
291 | if ($x->{sign} !~ /^[+-]$/) | |
292 | { | |
293 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN | |
294 | return 'inf'; # +inf | |
295 | } | |
58cde26e JH |
296 | my $sign = $x->{_e}->{sign}; $sign = '' if $sign eq '-'; |
297 | my $sep = 'e'.$sign; | |
298 | return $x->{_m}->bstr().$sep.$x->{_e}->bstr(); | |
299 | } | |
300 | ||
301 | sub numify | |
302 | { | |
303 | # Make a number from a BigFloat object | |
574bacfe | 304 | # simple return string and let Perl's atoi()/atof() handle the rest |
ee15d750 | 305 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e JH |
306 | return $x->bsstr(); |
307 | } | |
a0d0e21e | 308 | |
58cde26e JH |
309 | ############################################################################## |
310 | # public stuff (usually prefixed with "b") | |
311 | ||
312 | # really? Just for exporting them is not what I had in mind | |
313 | #sub babs | |
314 | # { | |
315 | # $class->SUPER::babs($class,@_); | |
316 | # } | |
317 | #sub bneg | |
318 | # { | |
319 | # $class->SUPER::bneg($class,@_); | |
320 | # } | |
574bacfe JH |
321 | |
322 | # tels 2001-08-04 | |
323 | # todo: this must be overwritten and return NaN for non-integer values | |
324 | # band(), bior(), bxor(), too | |
58cde26e JH |
325 | #sub bnot |
326 | # { | |
327 | # $class->SUPER::bnot($class,@_); | |
328 | # } | |
329 | ||
330 | sub bcmp | |
331 | { | |
332 | # Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort) | |
333 | # (BFLOAT or num_str, BFLOAT or num_str) return cond_code | |
334 | my ($self,$x,$y) = objectify(2,@_); | |
58cde26e | 335 | |
0716bf9b JH |
336 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
337 | { | |
338 | # handle +-inf and NaN | |
339 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); | |
340 | return 0 if ($x->{sign} eq $y->{sign}) && ($x->{sign} =~ /^[+-]inf$/); | |
341 | return +1 if $x->{sign} eq '+inf'; | |
342 | return -1 if $x->{sign} eq '-inf'; | |
343 | return -1 if $y->{sign} eq '+inf'; | |
344 | return +1 if $y->{sign} eq '-inf'; | |
345 | } | |
346 | ||
347 | # check sign for speed first | |
574bacfe | 348 | return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y |
58cde26e JH |
349 | return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0 |
350 | ||
574bacfe JH |
351 | # shortcut |
352 | my $xz = $x->is_zero(); | |
353 | my $yz = $y->is_zero(); | |
354 | return 0 if $xz && $yz; # 0 <=> 0 | |
355 | return -1 if $xz && $y->{sign} eq '+'; # 0 <=> +y | |
356 | return 1 if $yz && $x->{sign} eq '+'; # +x <=> 0 | |
58cde26e JH |
357 | |
358 | # adjust so that exponents are equal | |
bd05a461 JH |
359 | my $lxm = $x->{_m}->length(); |
360 | my $lym = $y->{_m}->length(); | |
361 | my $lx = $lxm + $x->{_e}; | |
362 | my $ly = $lym + $y->{_e}; | |
58cde26e JH |
363 | # print "x $x y $y lx $lx ly $ly\n"; |
364 | my $l = $lx - $ly; $l = -$l if $x->{sign} eq '-'; | |
365 | # print "$l $x->{sign}\n"; | |
bd05a461 | 366 | return $l <=> 0 if $l != 0; |
58cde26e | 367 | |
bd05a461 JH |
368 | # lengths (corrected by exponent) are equal |
369 | # so make mantissa euqal length by padding with zero (shift left) | |
370 | my $diff = $lxm - $lym; | |
371 | my $xm = $x->{_m}; # not yet copy it | |
372 | my $ym = $y->{_m}; | |
373 | if ($diff > 0) | |
374 | { | |
375 | $ym = $y->{_m}->copy()->blsft($diff,10); | |
376 | } | |
377 | elsif ($diff < 0) | |
378 | { | |
379 | $xm = $x->{_m}->copy()->blsft(-$diff,10); | |
380 | } | |
381 | my $rc = $xm->bcmp($ym); | |
58cde26e | 382 | $rc = -$rc if $x->{sign} eq '-'; # -124 < -123 |
bd05a461 | 383 | return $rc <=> 0; |
58cde26e JH |
384 | } |
385 | ||
386 | sub bacmp | |
387 | { | |
388 | # Compares 2 values, ignoring their signs. | |
389 | # Returns one of undef, <0, =0, >0. (suitable for sort) | |
390 | # (BFLOAT or num_str, BFLOAT or num_str) return cond_code | |
391 | my ($self,$x,$y) = objectify(2,@_); | |
ee15d750 JH |
392 | |
393 | # handle +-inf and NaN's | |
394 | if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]/) | |
395 | { | |
396 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); | |
397 | return 0 if ($x->is_inf() && $y->is_inf()); | |
398 | return 1 if ($x->is_inf() && !$y->is_inf()); | |
399 | return -1 if (!$x->is_inf() && $y->is_inf()); | |
400 | } | |
401 | ||
402 | # shortcut | |
403 | my $xz = $x->is_zero(); | |
404 | my $yz = $y->is_zero(); | |
405 | return 0 if $xz && $yz; # 0 <=> 0 | |
406 | return -1 if $xz && !$yz; # 0 <=> +y | |
407 | return 1 if $yz && !$xz; # +x <=> 0 | |
408 | ||
409 | # adjust so that exponents are equal | |
410 | my $lxm = $x->{_m}->length(); | |
411 | my $lym = $y->{_m}->length(); | |
412 | my $lx = $lxm + $x->{_e}; | |
413 | my $ly = $lym + $y->{_e}; | |
414 | # print "x $x y $y lx $lx ly $ly\n"; | |
415 | my $l = $lx - $ly; # $l = -$l if $x->{sign} eq '-'; | |
416 | # print "$l $x->{sign}\n"; | |
417 | return $l <=> 0 if $l != 0; | |
58cde26e | 418 | |
ee15d750 JH |
419 | # lengths (corrected by exponent) are equal |
420 | # so make mantissa euqal length by padding with zero (shift left) | |
421 | my $diff = $lxm - $lym; | |
422 | my $xm = $x->{_m}; # not yet copy it | |
423 | my $ym = $y->{_m}; | |
424 | if ($diff > 0) | |
425 | { | |
426 | $ym = $y->{_m}->copy()->blsft($diff,10); | |
427 | } | |
428 | elsif ($diff < 0) | |
429 | { | |
430 | $xm = $x->{_m}->copy()->blsft(-$diff,10); | |
431 | } | |
432 | my $rc = $xm->bcmp($ym); | |
433 | # $rc = -$rc if $x->{sign} eq '-'; # -124 < -123 | |
434 | return $rc <=> 0; | |
435 | ||
436 | # # signs are ignored, so check length | |
437 | # # length(x) is length(m)+e aka length of non-fraction part | |
438 | # # the longer one is bigger | |
439 | # my $l = $x->length() - $y->length(); | |
440 | # #print "$l\n"; | |
441 | # return $l if $l != 0; | |
442 | # #print "equal lengths\n"; | |
443 | # | |
444 | # # if both are equal long, make full compare | |
445 | # # first compare only the mantissa | |
446 | # # if mantissa are equal, compare fractions | |
447 | # | |
448 | # return $x->{_m} <=> $y->{_m} || $x->{_e} <=> $y->{_e}; | |
58cde26e | 449 | } |
a0d0e21e | 450 | |
58cde26e JH |
451 | sub badd |
452 | { | |
453 | # add second arg (BFLOAT or string) to first (BFLOAT) (modifies first) | |
454 | # return result as BFLOAT | |
58cde26e JH |
455 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
456 | ||
574bacfe JH |
457 | # inf and NaN handling |
458 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) | |
459 | { | |
460 | # NaN first | |
461 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); | |
462 | # inf handline | |
463 | if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) | |
464 | { | |
465 | # + and + => +, - and - => -, + and - => 0, - and + => 0 | |
466 | return $x->bzero() if $x->{sign} ne $y->{sign}; | |
467 | return $x; | |
468 | } | |
469 | # +-inf + something => +inf | |
470 | # something +-inf => +-inf | |
471 | $x->{sign} = $y->{sign}, return $x if $y->{sign} =~ /^[+-]inf$/; | |
472 | return $x; | |
473 | } | |
474 | ||
58cde26e JH |
475 | # speed: no add for 0+y or x+0 |
476 | return $x if $y->is_zero(); # x+0 | |
477 | if ($x->is_zero()) # 0+y | |
478 | { | |
479 | # make copy, clobbering up x (modify in place!) | |
480 | $x->{_e} = $y->{_e}->copy(); | |
481 | $x->{_m} = $y->{_m}->copy(); | |
482 | $x->{sign} = $y->{sign} || $nan; | |
483 | return $x->round($a,$p,$r,$y); | |
a0d0e21e | 484 | } |
58cde26e JH |
485 | |
486 | # take lower of the two e's and adapt m1 to it to match m2 | |
487 | my $e = $y->{_e}; $e = Math::BigInt::bzero() if !defined $e; # if no BFLOAT | |
488 | $e = $e - $x->{_e}; | |
489 | my $add = $y->{_m}->copy(); | |
490 | if ($e < 0) | |
491 | { | |
0716bf9b | 492 | # print "e < 0\n"; |
58cde26e JH |
493 | #print "\$x->{_m}: $x->{_m} "; |
494 | #print "\$x->{_e}: $x->{_e}\n"; | |
495 | my $e1 = $e->copy()->babs(); | |
496 | $x->{_m} *= (10 ** $e1); | |
497 | $x->{_e} += $e; # need the sign of e | |
498 | #$x->{_m} += $y->{_m}; | |
499 | #print "\$x->{_m}: $x->{_m} "; | |
500 | #print "\$x->{_e}: $x->{_e}\n"; | |
501 | } | |
502 | elsif ($e > 0) | |
503 | { | |
0716bf9b | 504 | # print "e > 0\n"; |
58cde26e JH |
505 | #print "\$x->{_m}: $x->{_m} \$y->{_m}: $y->{_m} \$e: $e ",ref($e),"\n"; |
506 | $add *= (10 ** $e); | |
507 | #$x->{_m} += $y->{_m} * (10 ** $e); | |
508 | #print "\$x->{_m}: $x->{_m}\n"; | |
509 | } | |
510 | # else: both e are same, so leave them | |
511 | #print "badd $x->{sign}$x->{_m} + $y->{sign}$add\n"; | |
512 | # fiddle with signs | |
513 | $x->{_m}->{sign} = $x->{sign}; | |
514 | $add->{sign} = $y->{sign}; | |
515 | # finally do add/sub | |
516 | $x->{_m} += $add; | |
517 | # re-adjust signs | |
518 | $x->{sign} = $x->{_m}->{sign}; | |
519 | $x->{_m}->{sign} = '+'; | |
0716bf9b | 520 | #$x->bnorm(); # delete trailing zeros |
58cde26e JH |
521 | return $x->round($a,$p,$r,$y); |
522 | } | |
523 | ||
524 | sub bsub | |
525 | { | |
0716bf9b | 526 | # (BigFloat or num_str, BigFloat or num_str) return BigFloat |
58cde26e JH |
527 | # subtract second arg from first, modify first |
528 | my ($self,$x,$y) = objectify(2,@_); | |
a0d0e21e | 529 | |
58cde26e JH |
530 | $x->badd($y->bneg()); # badd does not leave internal zeros |
531 | $y->bneg(); # refix y, assumes no one reads $y in between | |
0716bf9b | 532 | return $x; # badd() already normalized and rounded |
58cde26e JH |
533 | } |
534 | ||
535 | sub binc | |
536 | { | |
537 | # increment arg by one | |
ee15d750 JH |
538 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
539 | $x->badd($self->bone())->round($a,$p,$r); | |
58cde26e JH |
540 | } |
541 | ||
542 | sub bdec | |
543 | { | |
544 | # decrement arg by one | |
ee15d750 JH |
545 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
546 | $x->badd($self->bone('-'))->round($a,$p,$r); | |
58cde26e JH |
547 | } |
548 | ||
549 | sub blcm | |
550 | { | |
ee15d750 | 551 | # (BFLOAT or num_str, BFLOAT or num_str) return BFLOAT |
58cde26e JH |
552 | # does not modify arguments, but returns new object |
553 | # Lowest Common Multiplicator | |
58cde26e JH |
554 | |
555 | my ($self,@arg) = objectify(0,@_); | |
556 | my $x = $self->new(shift @arg); | |
557 | while (@arg) { $x = _lcm($x,shift @arg); } | |
558 | $x; | |
559 | } | |
560 | ||
561 | sub bgcd | |
562 | { | |
ee15d750 | 563 | # (BFLOAT or num_str, BFLOAT or num_str) return BINT |
58cde26e JH |
564 | # does not modify arguments, but returns new object |
565 | # GCD -- Euclids algorithm Knuth Vol 2 pg 296 | |
58cde26e JH |
566 | |
567 | my ($self,@arg) = objectify(0,@_); | |
568 | my $x = $self->new(shift @arg); | |
569 | while (@arg) { $x = _gcd($x,shift @arg); } | |
570 | $x; | |
571 | } | |
572 | ||
573 | sub is_zero | |
574 | { | |
ee15d750 JH |
575 | # return true if arg (BFLOAT or num_str) is zero (array '+', '0') |
576 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
574bacfe JH |
577 | |
578 | return 1 if $x->{sign} eq '+' && $x->{_m}->is_zero(); | |
579 | return 0; | |
58cde26e JH |
580 | } |
581 | ||
582 | sub is_one | |
583 | { | |
ee15d750 | 584 | # return true if arg (BFLOAT or num_str) is +1 (array '+', '1') |
58cde26e | 585 | # or -1 if signis given |
ee15d750 JH |
586 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
587 | ||
588 | my $sign = shift || ''; $sign = '+' if $sign ne '-'; | |
589 | return 1 | |
590 | if ($x->{sign} eq $sign && $x->{_e}->is_zero() && $x->{_m}->is_one()); | |
591 | return 0; | |
58cde26e JH |
592 | } |
593 | ||
594 | sub is_odd | |
595 | { | |
ee15d750 JH |
596 | # return true if arg (BFLOAT or num_str) is odd or false if even |
597 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
0716bf9b JH |
598 | |
599 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't | |
ee15d750 JH |
600 | return 1 if ($x->{_e}->is_zero() && $x->{_m}->is_odd()); |
601 | return 0; | |
58cde26e JH |
602 | } |
603 | ||
604 | sub is_even | |
605 | { | |
b22b3e31 | 606 | # return true if arg (BINT or num_str) is even or false if odd |
ee15d750 | 607 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
0716bf9b JH |
608 | |
609 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't | |
610 | return 1 if $x->{_m}->is_zero(); # 0e1 is even | |
ee15d750 JH |
611 | return 1 if ($x->{_e}->is_zero() && $x->{_m}->is_even()); # 123.45 is never |
612 | return 0; | |
58cde26e JH |
613 | } |
614 | ||
615 | sub bmul | |
616 | { | |
617 | # multiply two numbers -- stolen from Knuth Vol 2 pg 233 | |
618 | # (BINT or num_str, BINT or num_str) return BINT | |
619 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); | |
58cde26e | 620 | |
0716bf9b | 621 | # print "mbf bmul $x->{_m}e$x->{_e} $y->{_m}e$y->{_e}\n"; |
58cde26e JH |
622 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
623 | ||
574bacfe JH |
624 | # handle result = 0 |
625 | return $x->bzero() if $x->is_zero() || $y->is_zero(); | |
626 | # inf handling | |
627 | if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) | |
628 | { | |
629 | # result will always be +-inf: | |
630 | # +inf * +/+inf => +inf, -inf * -/-inf => +inf | |
631 | # +inf * -/-inf => -inf, -inf * +/+inf => -inf | |
632 | return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); | |
633 | return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); | |
634 | return $x->binf('-'); | |
635 | } | |
636 | ||
58cde26e JH |
637 | # aEb * cEd = (a*c)E(b+d) |
638 | $x->{_m} = $x->{_m} * $y->{_m}; | |
639 | #print "m: $x->{_m}\n"; | |
640 | $x->{_e} = $x->{_e} + $y->{_e}; | |
641 | #print "e: $x->{_m}\n"; | |
642 | # adjust sign: | |
643 | $x->{sign} = $x->{sign} ne $y->{sign} ? '-' : '+'; | |
644 | #print "s: $x->{sign}\n"; | |
0716bf9b | 645 | $x->bnorm(); |
58cde26e JH |
646 | return $x->round($a,$p,$r,$y); |
647 | } | |
648 | ||
649 | sub bdiv | |
650 | { | |
651 | # (dividend: BFLOAT or num_str, divisor: BFLOAT or num_str) return | |
652 | # (BFLOAT,BFLOAT) (quo,rem) or BINT (only rem) | |
653 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); | |
654 | ||
ee15d750 | 655 | |
574bacfe JH |
656 | # x / +-inf => 0, reminder x |
657 | return wantarray ? ($x->bzero(),$x->copy()) : $x->bzero() | |
658 | if $y->{sign} =~ /^[+-]inf$/; | |
659 | ||
660 | # NaN if x == NaN or y == NaN or x==y==0 | |
58cde26e | 661 | return wantarray ? ($x->bnan(),bnan()) : $x->bnan() |
574bacfe JH |
662 | if (($x->is_nan() || $y->is_nan()) || |
663 | ($x->is_zero() && $y->is_zero())); | |
664 | ||
665 | # 5 / 0 => +inf, -6 / 0 => -inf | |
666 | return wantarray | |
667 | ? ($x->binf($x->{sign}),$self->bnan()) : $x->binf($x->{sign}) | |
668 | if ($x->{sign} =~ /^[+-]$/ && $y->is_zero()); | |
0716bf9b | 669 | |
ee15d750 JH |
670 | # promote BigInts and it's subclasses (except when already a BigFloat) |
671 | $y = $self->new($y) unless $y->isa('Math::BigFloat'); | |
672 | ||
673 | # old, broken way | |
674 | # $y = $class->new($y) if ref($y) ne $self; # promote bigints | |
0716bf9b JH |
675 | |
676 | # print "mbf bdiv $x ",ref($x)," ",$y," ",ref($y),"\n"; | |
58cde26e | 677 | # we need to limit the accuracy to protect against overflow |
ee15d750 | 678 | |
574bacfe | 679 | my $fallback = 0; |
ee15d750 JH |
680 | my $scale = 0; |
681 | # print "s=$scale a=",$a||'undef'," p=",$p||'undef'," r=",$r||'undef',"\n"; | |
682 | my @params = $x->_find_round_parameters($a,$p,$r,$y); | |
683 | ||
684 | # no rounding at all, so must use fallback | |
685 | if (scalar @params == 1) | |
58cde26e | 686 | { |
0716bf9b | 687 | # simulate old behaviour |
ee15d750 JH |
688 | $scale = $self->div_scale()+1; # at least one more for proper round |
689 | $params[1] = $self->div_scale(); # and round to it as accuracy | |
690 | $params[3] = $r; # round mode by caller or undef | |
691 | $fallback = 1; # to clear a/p afterwards | |
692 | } | |
693 | else | |
694 | { | |
695 | # the 4 below is empirical, and there might be cases where it is not | |
696 | # enough... | |
697 | $scale = abs($params[1] || $params[2]) + 4; # take whatever is defined | |
a0d0e21e | 698 | } |
ee15d750 | 699 | # print "s=$scale a=",$params[1]||'undef'," p=",$params[2]||'undef'," f=$fallback\n"; |
0716bf9b | 700 | my $lx = $x->{_m}->length(); my $ly = $y->{_m}->length(); |
58cde26e | 701 | $scale = $lx if $lx > $scale; |
58cde26e | 702 | $scale = $ly if $ly > $scale; |
ee15d750 | 703 | # print "scale $scale $lx $ly\n"; |
0716bf9b JH |
704 | my $diff = $ly - $lx; |
705 | $scale += $diff if $diff > 0; # if lx << ly, but not if ly << lx! | |
a0d0e21e | 706 | |
58cde26e JH |
707 | return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero(); |
708 | ||
709 | $x->{sign} = $x->{sign} ne $y->sign() ? '-' : '+'; | |
a0d0e21e | 710 | |
58cde26e JH |
711 | # check for / +-1 ( +/- 1E0) |
712 | if ($y->is_one()) | |
713 | { | |
ee15d750 | 714 | return wantarray ? ($x,$self->bzero()) : $x; |
a0d0e21e | 715 | } |
a5f75d66 | 716 | |
ee15d750 | 717 | # calculate the result to $scale digits and then round it |
58cde26e | 718 | # a * 10 ** b / c * 10 ** d => a/c * 10 ** (b-d) |
ee15d750 | 719 | #$scale = 82; |
58cde26e | 720 | #print "self: $self x: $x ref(x) ", ref($x)," m: $x->{_m}\n"; |
58cde26e | 721 | $x->{_m}->blsft($scale,10); |
0716bf9b | 722 | #print "m: $x->{_m} $y->{_m}\n"; |
58cde26e JH |
723 | $x->{_m}->bdiv( $y->{_m} ); # a/c |
724 | #print "m: $x->{_m}\n"; | |
ee15d750 | 725 | #print "e: $x->{_e} $y->{_e} ",$scale,"\n"; |
58cde26e JH |
726 | $x->{_e}->bsub($y->{_e}); # b-d |
727 | #print "e: $x->{_e}\n"; | |
728 | $x->{_e}->bsub($scale); # correct for 10**scale | |
0716bf9b JH |
729 | #print "after div: m: $x->{_m} e: $x->{_e}\n"; |
730 | $x->bnorm(); # remove trailing 0's | |
ee15d750 JH |
731 | #print "after norm: m: $x->{_m} e: $x->{_e}\n"; |
732 | ||
733 | # shortcut to not run trough _find_round_parameters again | |
734 | if (defined $params[1]) | |
735 | { | |
736 | $x->bround($params[1],undef,$params[3]); # then round accordingly | |
737 | } | |
738 | else | |
739 | { | |
740 | $x->bfround($params[2],$params[3]); # then round accordingly | |
741 | } | |
574bacfe JH |
742 | if ($fallback) |
743 | { | |
744 | # clear a/p after round, since user did not request it | |
ee15d750 | 745 | $x->{_a} = undef; $x->{_p} = undef; |
574bacfe | 746 | } |
0716bf9b | 747 | |
58cde26e JH |
748 | if (wantarray) |
749 | { | |
750 | my $rem = $x->copy(); | |
ee15d750 | 751 | $rem->bmod($y,$params[1],$params[2],$params[3]); |
574bacfe JH |
752 | if ($fallback) |
753 | { | |
754 | # clear a/p after round, since user did not request it | |
ee15d750 | 755 | $rem->{_a} = undef; $rem->{_p} = undef; |
574bacfe | 756 | } |
0716bf9b | 757 | return ($x,$rem); |
58cde26e JH |
758 | } |
759 | return $x; | |
760 | } | |
a0d0e21e | 761 | |
58cde26e JH |
762 | sub bmod |
763 | { | |
764 | # (dividend: BFLOAT or num_str, divisor: BFLOAT or num_str) return reminder | |
765 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); | |
a0d0e21e | 766 | |
58cde26e JH |
767 | return $x->bnan() if ($x->{sign} eq $nan || $y->is_nan() || $y->is_zero()); |
768 | return $x->bzero() if $y->is_one(); | |
769 | ||
770 | # XXX tels: not done yet | |
771 | return $x->round($a,$p,$r,$y); | |
772 | } | |
773 | ||
774 | sub bsqrt | |
775 | { | |
0716bf9b JH |
776 | # calculate square root; this should probably |
777 | # use a different test to see whether the accuracy we want is... | |
ee15d750 | 778 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e | 779 | |
0716bf9b JH |
780 | return $x->bnan() if $x->{sign} eq 'NaN' || $x->{sign} =~ /^-/; # <0, NaN |
781 | return $x if $x->{sign} eq '+inf'; # +inf | |
58cde26e JH |
782 | return $x if $x->is_zero() || $x == 1; |
783 | ||
ee15d750 JH |
784 | # we need to limit the accuracy to protect against overflow (ignore $p) |
785 | my ($scale) = $x->_scale_a($self->accuracy(),$self->round_mode,$a,$r); | |
574bacfe | 786 | my $fallback = 0; |
0716bf9b JH |
787 | if (!defined $scale) |
788 | { | |
789 | # simulate old behaviour | |
ee15d750 JH |
790 | $scale = $self->div_scale()+1; # one more for proper riund |
791 | $a = $self->div_scale(); # and round to it | |
792 | $fallback = 1; # to clear a/p afterwards | |
0716bf9b JH |
793 | } |
794 | my $lx = $x->{_m}->length(); | |
795 | $scale = $lx if $scale < $lx; | |
58cde26e JH |
796 | my $e = Math::BigFloat->new("1E-$scale"); # make test variable |
797 | return $x->bnan() if $e->sign() eq 'NaN'; | |
798 | ||
58cde26e | 799 | # start with some reasonable guess |
0716bf9b | 800 | #$x *= 10 ** ($len - $org->{_e}); $x /= 2; # !?!? |
574bacfe | 801 | $lx = $lx+$x->{_e}; |
0716bf9b JH |
802 | $lx = 1 if $lx < 1; |
803 | my $gs = Math::BigFloat->new('1'. ('0' x $lx)); | |
804 | ||
ee15d750 | 805 | # print "first guess: $gs (x $x) scale $scale\n"; |
58cde26e JH |
806 | |
807 | my $diff = $e; | |
808 | my $y = $x->copy(); | |
809 | my $two = Math::BigFloat->new(2); | |
ee15d750 JH |
810 | # promote BigInts and it's subclasses (except when already a BigFloat) |
811 | $y = $self->new($y) unless $y->isa('Math::BigFloat'); | |
812 | # old, broken way | |
813 | # $x = Math::BigFloat->new($x) if ref($x) ne $class; # promote BigInts | |
814 | my $rem; | |
58cde26e JH |
815 | # $scale = 2; |
816 | while ($diff >= $e) | |
817 | { | |
58cde26e | 818 | return $x->bnan() if $gs->is_zero(); |
ee15d750 JH |
819 | $rem = $y->copy(); $rem->bdiv($gs,$scale); |
820 | #print "y $y gs $gs ($gs->{_a}) rem (y/gs)\n $rem\n"; | |
821 | $x = ($rem + $gs); | |
822 | #print "x $x rem $rem gs $gs gsa: $gs->{_a}\n"; | |
823 | $x->bdiv($two,$scale); | |
824 | #print "x $x (/2)\n"; | |
58cde26e | 825 | $diff = $x->copy()->bsub($gs)->babs(); |
58cde26e | 826 | $gs = $x->copy(); |
a0d0e21e | 827 | } |
ee15d750 | 828 | # print "before $x $x->{_a} ",$a||'a undef'," ",$p||'p undef',"\n"; |
0716bf9b | 829 | $x->round($a,$p,$r); |
ee15d750 | 830 | # print "after $x $x->{_a} ",$a||'a undef'," ",$p||'p undef',"\n"; |
574bacfe JH |
831 | if ($fallback) |
832 | { | |
833 | # clear a/p after round, since user did not request it | |
ee15d750 | 834 | $x->{_a} = undef; $x->{_p} = undef; |
574bacfe JH |
835 | } |
836 | $x; | |
58cde26e JH |
837 | } |
838 | ||
839 | sub bpow | |
840 | { | |
841 | # (BFLOAT or num_str, BFLOAT or num_str) return BFLOAT | |
842 | # compute power of two numbers, second arg is used as integer | |
843 | # modifies first argument | |
844 | ||
845 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); | |
846 | ||
0716bf9b | 847 | return $x if $x->{sign} =~ /^[+-]inf$/; |
58cde26e | 848 | return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan; |
574bacfe | 849 | return $x->bone() if $y->is_zero(); |
58cde26e | 850 | return $x if $x->is_one() || $y->is_one(); |
ee15d750 | 851 | my $y1 = $y->as_number(); # make bigint (trunc) |
58cde26e JH |
852 | if ($x == -1) |
853 | { | |
854 | # if $x == -1 and odd/even y => +1/-1 because +-1 ^ (+-1) => +-1 | |
0716bf9b | 855 | return $y1->is_odd() ? $x : $x->babs(1); |
288d023a | 856 | } |
58cde26e | 857 | return $x if $x->is_zero() && $y->{sign} eq '+'; # 0**y => 0 (if not y <= 0) |
574bacfe JH |
858 | # 0 ** -y => 1 / (0 ** y) => / 0! (1 / 0 => +inf) |
859 | return $x->binf() if $x->is_zero() && $y->{sign} eq '-'; | |
58cde26e JH |
860 | |
861 | # calculate $x->{_m} ** $y and $x->{_e} * $y separately (faster) | |
862 | $y1->babs(); | |
863 | $x->{_m}->bpow($y1); | |
864 | $x->{_e}->bmul($y1); | |
865 | $x->{sign} = $nan if $x->{_m}->{sign} eq $nan || $x->{_e}->{sign} eq $nan; | |
866 | $x->bnorm(); | |
867 | if ($y->{sign} eq '-') | |
868 | { | |
869 | # modify $x in place! | |
0716bf9b | 870 | my $z = $x->copy(); $x->bzero()->binc(); |
58cde26e | 871 | return $x->bdiv($z,$a,$p,$r); # round in one go (might ignore y's A!) |
a0d0e21e | 872 | } |
58cde26e JH |
873 | return $x->round($a,$p,$r,$y); |
874 | } | |
875 | ||
876 | ############################################################################### | |
877 | # rounding functions | |
878 | ||
879 | sub bfround | |
880 | { | |
881 | # precision: round to the $Nth digit left (+$n) or right (-$n) from the '.' | |
882 | # $n == 0 means round to integer | |
883 | # expects and returns normalized numbers! | |
ee15d750 | 884 | my $x = shift; my $self = ref($x) || $x; $x = $self->new(shift) if !ref($x); |
a0d0e21e | 885 | |
58cde26e JH |
886 | return $x if $x->modify('bfround'); |
887 | ||
ee15d750 | 888 | my ($scale,$mode) = $x->_scale_p($self->precision(),$self->round_mode(),@_); |
58cde26e JH |
889 | return $x if !defined $scale; # no-op |
890 | ||
574bacfe JH |
891 | # never round a 0, +-inf, NaN |
892 | return $x if $x->{sign} !~ /^[+-]$/ || $x->is_zero(); | |
58cde26e | 893 | # print "MBF bfround $x to scale $scale mode $mode\n"; |
58cde26e | 894 | |
ee15d750 JH |
895 | # don't round if x already has lower precision |
896 | return $x if (defined $x->{_p} && $x->{_p} < 0 && $scale < $x->{_p}); | |
897 | ||
898 | $x->{_p} = $scale; # remember round in any case | |
899 | $x->{_a} = undef; # and clear A | |
58cde26e JH |
900 | if ($scale < 0) |
901 | { | |
902 | # print "bfround scale $scale e $x->{_e}\n"; | |
903 | # round right from the '.' | |
904 | return $x if $x->{_e} >= 0; # nothing to round | |
905 | $scale = -$scale; # positive for simplicity | |
906 | my $len = $x->{_m}->length(); # length of mantissa | |
907 | my $dad = -$x->{_e}; # digits after dot | |
908 | my $zad = 0; # zeros after dot | |
909 | $zad = -$len-$x->{_e} if ($x->{_e} < -$len);# for 0.00..00xxx style | |
ee15d750 | 910 | #print "scale $scale dad $dad zad $zad len $len\n"; |
58cde26e JH |
911 | |
912 | # number bsstr len zad dad | |
913 | # 0.123 123e-3 3 0 3 | |
914 | # 0.0123 123e-4 3 1 4 | |
915 | # 0.001 1e-3 1 2 3 | |
916 | # 1.23 123e-2 3 0 2 | |
917 | # 1.2345 12345e-4 5 0 4 | |
918 | ||
919 | # do not round after/right of the $dad | |
920 | return $x if $scale > $dad; # 0.123, scale >= 3 => exit | |
921 | ||
ee15d750 JH |
922 | # round to zero if rounding inside the $zad, but not for last zero like: |
923 | # 0.0065, scale -2, round last '0' with following '65' (scale == zad case) | |
924 | return $x->bzero() if $scale < $zad; | |
925 | if ($scale == $zad) # for 0.006, scale -3 and trunc | |
58cde26e | 926 | { |
ee15d750 | 927 | $scale = -$len-1; |
58cde26e JH |
928 | } |
929 | else | |
930 | { | |
931 | # adjust round-point to be inside mantissa | |
932 | if ($zad != 0) | |
933 | { | |
934 | $scale = $scale-$zad; | |
935 | } | |
936 | else | |
937 | { | |
938 | my $dbd = $len - $dad; $dbd = 0 if $dbd < 0; # digits before dot | |
939 | $scale = $dbd+$scale; | |
940 | } | |
941 | } | |
942 | # print "round to $x->{_m} to $scale\n"; | |
a0d0e21e | 943 | } |
58cde26e JH |
944 | else |
945 | { | |
946 | # 123 => 100 means length(123) = 3 - $scale (2) => 1 | |
a5f75d66 | 947 | |
58cde26e JH |
948 | # calculate digits before dot |
949 | my $dbt = $x->{_m}->length(); $dbt += $x->{_e} if $x->{_e}->sign() eq '-'; | |
ee15d750 JH |
950 | # if not enough digits before dot, round to zero |
951 | return $x->bzero() if ($scale > $dbt) && ($dbt < 0); | |
952 | # scale always >= 0 here | |
953 | if ($dbt == 0) | |
58cde26e JH |
954 | { |
955 | # 0.49->bfround(1): scale == 1, dbt == 0: => 0.0 | |
956 | # 0.51->bfround(0): scale == 0, dbt == 0: => 1.0 | |
957 | # 0.5->bfround(0): scale == 0, dbt == 0: => 0 | |
958 | # 0.05->bfround(0): scale == 0, dbt == 0: => 0 | |
959 | # print "$scale $dbt $x->{_m}\n"; | |
960 | $scale = -$x->{_m}->length(); | |
961 | } | |
962 | elsif ($dbt > 0) | |
963 | { | |
964 | # correct by subtracting scale | |
965 | $scale = $dbt - $scale; | |
966 | } | |
967 | else | |
968 | { | |
969 | $scale = $x->{_m}->length() - $scale; | |
970 | } | |
a0d0e21e | 971 | } |
574bacfe JH |
972 | # print "using $scale for $x->{_m} with '$mode'\n"; |
973 | # pass sign to bround for rounding modes '+inf' and '-inf' | |
58cde26e JH |
974 | $x->{_m}->{sign} = $x->{sign}; |
975 | $x->{_m}->bround($scale,$mode); | |
976 | $x->{_m}->{sign} = '+'; # fix sign back | |
977 | $x->bnorm(); | |
978 | } | |
979 | ||
980 | sub bround | |
981 | { | |
982 | # accuracy: preserve $N digits, and overwrite the rest with 0's | |
ee15d750 JH |
983 | my $x = shift; my $self = ref($x) || $x; $x = $self->new(shift) if !ref($x); |
984 | ||
985 | die ('bround() needs positive accuracy') if ($_[0] || 0) < 0; | |
58cde26e | 986 | |
ee15d750 JH |
987 | my ($scale,$mode) = $x->_scale_a($self->accuracy(),$self->round_mode(),@_); |
988 | return $x if !defined $scale; # no-op | |
989 | ||
58cde26e | 990 | return $x if $x->modify('bround'); |
ee15d750 JH |
991 | |
992 | # scale is now either $x->{_a}, $accuracy, or the user parameter | |
993 | # test whether $x already has lower accuracy, do nothing in this case | |
994 | # but do round if the accuracy is the same, since a math operation might | |
995 | # want to round a number with A=5 to 5 digits afterwards again | |
996 | return $x if defined $_[0] && defined $x->{_a} && $x->{_a} < $_[0]; | |
58cde26e JH |
997 | |
998 | # print "bround $scale $mode\n"; | |
999 | # 0 => return all digits, scale < 0 makes no sense | |
1000 | return $x if ($scale <= 0); | |
574bacfe JH |
1001 | # never round a 0, +-inf, NaN |
1002 | return $x if $x->{sign} !~ /^[+-]$/ || $x->is_zero(); | |
58cde26e JH |
1003 | |
1004 | # if $e longer than $m, we have 0.0000xxxyyy style number, and must | |
1005 | # subtract the delta from scale, to simulate keeping the zeros | |
1006 | # -5 +5 => 1; -10 +5 => -4 | |
1007 | my $delta = $x->{_e} + $x->{_m}->length() + 1; | |
58cde26e JH |
1008 | |
1009 | # if we should keep more digits than the mantissa has, do nothing | |
1010 | return $x if $x->{_m}->length() <= $scale; | |
f216259d | 1011 | |
58cde26e JH |
1012 | # pass sign to bround for '+inf' and '-inf' rounding modes |
1013 | $x->{_m}->{sign} = $x->{sign}; | |
1014 | $x->{_m}->bround($scale,$mode); # round mantissa | |
1015 | $x->{_m}->{sign} = '+'; # fix sign back | |
ee15d750 JH |
1016 | $x->{_a} = $scale; # remember rounding |
1017 | $x->{_p} = undef; # and clear P | |
574bacfe | 1018 | $x->bnorm(); # del trailing zeros gen. by bround() |
58cde26e JH |
1019 | } |
1020 | ||
1021 | sub bfloor | |
1022 | { | |
1023 | # return integer less or equal then $x | |
ee15d750 | 1024 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e JH |
1025 | |
1026 | return $x if $x->modify('bfloor'); | |
1027 | ||
1028 | return $x if $x->{sign} !~ /^[+-]$/; # nan, +inf, -inf | |
1029 | ||
1030 | # if $x has digits after dot | |
1031 | if ($x->{_e}->{sign} eq '-') | |
1032 | { | |
1033 | $x->{_m}->brsft(-$x->{_e},10); | |
1034 | $x->{_e}->bzero(); | |
1035 | $x-- if $x->{sign} eq '-'; | |
f216259d | 1036 | } |
58cde26e JH |
1037 | return $x->round($a,$p,$r); |
1038 | } | |
288d023a | 1039 | |
58cde26e JH |
1040 | sub bceil |
1041 | { | |
1042 | # return integer greater or equal then $x | |
ee15d750 | 1043 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e JH |
1044 | |
1045 | return $x if $x->modify('bceil'); | |
1046 | return $x if $x->{sign} !~ /^[+-]$/; # nan, +inf, -inf | |
1047 | ||
1048 | # if $x has digits after dot | |
1049 | if ($x->{_e}->{sign} eq '-') | |
1050 | { | |
1051 | $x->{_m}->brsft(-$x->{_e},10); | |
1052 | $x->{_e}->bzero(); | |
1053 | $x++ if $x->{sign} eq '+'; | |
a0d0e21e | 1054 | } |
58cde26e JH |
1055 | return $x->round($a,$p,$r); |
1056 | } | |
1057 | ||
1058 | ############################################################################### | |
a5f75d66 | 1059 | |
58cde26e JH |
1060 | sub DESTROY |
1061 | { | |
ee15d750 | 1062 | # going through AUTOLOAD for every DESTROY is costly, so avoid it by empty sub |
58cde26e JH |
1063 | } |
1064 | ||
1065 | sub AUTOLOAD | |
1066 | { | |
1067 | # make fxxx and bxxx work | |
1068 | # my $self = $_[0]; | |
1069 | my $name = $AUTOLOAD; | |
1070 | ||
1071 | $name =~ s/.*:://; # split package | |
1072 | #print "$name\n"; | |
ee15d750 JH |
1073 | no strict 'refs'; |
1074 | if (!method_alias($name)) | |
58cde26e | 1075 | { |
ee15d750 JH |
1076 | if (!defined $name) |
1077 | { | |
1078 | # delayed load of Carp and avoid recursion | |
1079 | require Carp; | |
1080 | Carp::croak ("Can't call a method without name"); | |
1081 | } | |
1082 | # try one level up, but subst. bxxx() for fxxx() since MBI only got bxxx() | |
1083 | if (!method_hand_up($name)) | |
1084 | { | |
1085 | # delayed load of Carp and avoid recursion | |
1086 | require Carp; | |
1087 | Carp::croak ("Can't call $class\-\>$name, not a valid method"); | |
1088 | } | |
1089 | # try one level up, but subst. bxxx() for fxxx() since MBI only got bxxx() | |
1090 | $name =~ s/^f/b/; | |
1091 | return &{'Math::BigInt'."::$name"}(@_); | |
a0d0e21e | 1092 | } |
58cde26e JH |
1093 | my $bname = $name; $bname =~ s/^f/b/; |
1094 | *{$class."\:\:$name"} = \&$bname; | |
1095 | &$bname; # uses @_ | |
1096 | } | |
1097 | ||
1098 | sub exponent | |
1099 | { | |
1100 | # return a copy of the exponent | |
ee15d750 | 1101 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e | 1102 | |
ee15d750 JH |
1103 | if ($x->{sign} !~ /^[+-]$/) |
1104 | { | |
1105 | my $s = $x->{sign}; $s =~ s/^[+-]//; | |
1106 | return $self->new($s); # -inf, +inf => +inf | |
1107 | } | |
1108 | return $x->{_e}->copy(); | |
58cde26e JH |
1109 | } |
1110 | ||
1111 | sub mantissa | |
1112 | { | |
1113 | # return a copy of the mantissa | |
ee15d750 | 1114 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e | 1115 | |
ee15d750 JH |
1116 | if ($x->{sign} !~ /^[+-]$/) |
1117 | { | |
1118 | my $s = $x->{sign}; $s =~ s/^[+]//; | |
1119 | return $self->new($s); # -inf, +inf => +inf | |
1120 | } | |
1121 | my $m = $x->{_m}->copy(); # faster than going via bstr() | |
1122 | $m->bneg() if $x->{sign} eq '-'; | |
58cde26e JH |
1123 | |
1124 | return $m; | |
1125 | } | |
1126 | ||
1127 | sub parts | |
1128 | { | |
1129 | # return a copy of both the exponent and the mantissa | |
ee15d750 | 1130 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e | 1131 | |
ee15d750 JH |
1132 | if ($x->{sign} !~ /^[+-]$/) |
1133 | { | |
1134 | my $s = $x->{sign}; $s =~ s/^[+]//; my $se = $s; $se =~ s/^[-]//; | |
1135 | return ($self->new($s),$self->new($se)); # +inf => inf and -inf,+inf => inf | |
1136 | } | |
1137 | my $m = $x->{_m}->copy(); # faster than going via bstr() | |
1138 | $m->bneg() if $x->{sign} eq '-'; | |
1139 | return ($m,$x->{_e}->copy()); | |
58cde26e JH |
1140 | } |
1141 | ||
1142 | ############################################################################## | |
1143 | # private stuff (internal use only) | |
1144 | ||
58cde26e JH |
1145 | sub import |
1146 | { | |
1147 | my $self = shift; | |
58cde26e JH |
1148 | for ( my $i = 0; $i < @_ ; $i++ ) |
1149 | { | |
1150 | if ( $_[$i] eq ':constant' ) | |
1151 | { | |
1152 | # this rest causes overlord er load to step in | |
1153 | # print "overload @_\n"; | |
1154 | overload::constant float => sub { $self->new(shift); }; | |
1155 | splice @_, $i, 1; last; | |
1156 | } | |
1157 | } | |
1158 | # any non :constant stuff is handled by our parent, Exporter | |
1159 | # even if @_ is empty, to give it a chance | |
1160 | #$self->SUPER::import(@_); # does not work (would call MBI) | |
1161 | $self->export_to_level(1,$self,@_); # need this instead | |
1162 | } | |
1163 | ||
1164 | sub bnorm | |
1165 | { | |
1166 | # adjust m and e so that m is smallest possible | |
1167 | # round number according to accuracy and precision settings | |
ee15d750 | 1168 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e | 1169 | |
0716bf9b | 1170 | return $x if $x->{sign} !~ /^[+-]$/; # inf, nan etc |
58cde26e JH |
1171 | |
1172 | my $zeros = $x->{_m}->_trailing_zeros(); # correct for trailing zeros | |
1173 | if ($zeros != 0) | |
1174 | { | |
1175 | $x->{_m}->brsft($zeros,10); $x->{_e} += $zeros; | |
1176 | } | |
ee15d750 JH |
1177 | # for something like 0Ey, set y to 1, and -0 => +0 |
1178 | $x->{sign} = '+', $x->{_e}->bone() if $x->{_m}->is_zero(); | |
1179 | # this is to prevent automatically rounding when MBI's globals are set | |
0716bf9b JH |
1180 | $x->{_m}->{_f} = MB_NEVER_ROUND; |
1181 | $x->{_e}->{_f} = MB_NEVER_ROUND; | |
ee15d750 JH |
1182 | # 'forget' that mantissa was rounded via MBI::bround() in MBF's bfround() |
1183 | $x->{_m}->{_a} = undef; $x->{_e}->{_a} = undef; | |
1184 | $x->{_m}->{_p} = undef; $x->{_e}->{_p} = undef; | |
0716bf9b | 1185 | return $x; # MBI bnorm is no-op |
58cde26e JH |
1186 | } |
1187 | ||
1188 | ############################################################################## | |
1189 | # internal calculation routines | |
1190 | ||
1191 | sub as_number | |
1192 | { | |
1193 | # return a bigint representation of this BigFloat number | |
ee15d750 | 1194 | my $x = shift; my $class = ref($x) || $x; $x = $class->new(shift) unless ref($x); |
58cde26e JH |
1195 | |
1196 | my $z; | |
1197 | if ($x->{_e}->is_zero()) | |
1198 | { | |
1199 | $z = $x->{_m}->copy(); | |
1200 | $z->{sign} = $x->{sign}; | |
1201 | return $z; | |
1202 | } | |
0716bf9b | 1203 | $z = $x->{_m}->copy(); |
58cde26e JH |
1204 | if ($x->{_e} < 0) |
1205 | { | |
0716bf9b JH |
1206 | $z->brsft(-$x->{_e},10); |
1207 | } | |
1208 | else | |
1209 | { | |
1210 | $z->blsft($x->{_e},10); | |
58cde26e | 1211 | } |
58cde26e JH |
1212 | $z->{sign} = $x->{sign}; |
1213 | return $z; | |
1214 | } | |
1215 | ||
1216 | sub length | |
1217 | { | |
ee15d750 JH |
1218 | my $x = shift; |
1219 | my $class = ref($x) || $x; | |
1220 | $x = $class->new(shift) unless ref($x); | |
58cde26e | 1221 | |
ee15d750 | 1222 | return 1 if $x->{_m}->is_zero(); |
58cde26e JH |
1223 | my $len = $x->{_m}->length(); |
1224 | $len += $x->{_e} if $x->{_e}->sign() eq '+'; | |
1225 | if (wantarray()) | |
1226 | { | |
1227 | my $t = Math::BigInt::bzero(); | |
1228 | $t = $x->{_e}->copy()->babs() if $x->{_e}->sign() eq '-'; | |
1229 | return ($len,$t); | |
1230 | } | |
1231 | return $len; | |
1232 | } | |
a0d0e21e LW |
1233 | |
1234 | 1; | |
a5f75d66 AD |
1235 | __END__ |
1236 | ||
1237 | =head1 NAME | |
1238 | ||
58cde26e | 1239 | Math::BigFloat - Arbitrary size floating point math package |
a5f75d66 AD |
1240 | |
1241 | =head1 SYNOPSIS | |
1242 | ||
a2008d6d | 1243 | use Math::BigFloat; |
58cde26e JH |
1244 | |
1245 | # Number creation | |
1246 | $x = Math::BigInt->new($str); # defaults to 0 | |
1247 | $nan = Math::BigInt->bnan(); # create a NotANumber | |
1248 | $zero = Math::BigInt->bzero();# create a "+0" | |
1249 | ||
1250 | # Testing | |
1251 | $x->is_zero(); # return whether arg is zero or not | |
0716bf9b JH |
1252 | $x->is_nan(); # return whether arg is NaN or not |
1253 | $x->is_one(); # true if arg is +1 | |
1254 | $x->is_one('-'); # true if arg is -1 | |
1255 | $x->is_odd(); # true if odd, false for even | |
1256 | $x->is_even(); # true if even, false for odd | |
1257 | $x->is_positive(); # true if >= 0 | |
1258 | $x->is_negative(); # true if < 0 | |
1259 | $x->is_inf(sign) # true if +inf or -inf (sign default '+') | |
58cde26e JH |
1260 | $x->bcmp($y); # compare numbers (undef,<0,=0,>0) |
1261 | $x->bacmp($y); # compare absolutely (undef,<0,=0,>0) | |
1262 | $x->sign(); # return the sign, either +,- or NaN | |
1263 | ||
1264 | # The following all modify their first argument: | |
1265 | ||
1266 | # set | |
1267 | $x->bzero(); # set $i to 0 | |
1268 | $x->bnan(); # set $i to NaN | |
1269 | ||
1270 | $x->bneg(); # negation | |
1271 | $x->babs(); # absolute value | |
1272 | $x->bnorm(); # normalize (no-op) | |
1273 | $x->bnot(); # two's complement (bit wise not) | |
1274 | $x->binc(); # increment x by 1 | |
1275 | $x->bdec(); # decrement x by 1 | |
1276 | ||
1277 | $x->badd($y); # addition (add $y to $x) | |
1278 | $x->bsub($y); # subtraction (subtract $y from $x) | |
1279 | $x->bmul($y); # multiplication (multiply $x by $y) | |
1280 | $x->bdiv($y); # divide, set $i to quotient | |
1281 | # return (quo,rem) or quo if scalar | |
1282 | ||
1283 | $x->bmod($y); # modulus | |
1284 | $x->bpow($y); # power of arguments (a**b) | |
1285 | $x->blsft($y); # left shift | |
1286 | $x->brsft($y); # right shift | |
1287 | # return (quo,rem) or quo if scalar | |
1288 | ||
1289 | $x->band($y); # bit-wise and | |
1290 | $x->bior($y); # bit-wise inclusive or | |
1291 | $x->bxor($y); # bit-wise exclusive or | |
1292 | $x->bnot(); # bit-wise not (two's complement) | |
1293 | ||
1294 | $x->bround($N); # accuracy: preserver $N digits | |
1295 | $x->bfround($N); # precision: round to the $Nth digit | |
1296 | ||
1297 | # The following do not modify their arguments: | |
1298 | ||
1299 | bgcd(@values); # greatest common divisor | |
1300 | blcm(@values); # lowest common multiplicator | |
1301 | ||
1302 | $x->bstr(); # return string | |
1303 | $x->bsstr(); # return string in scientific notation | |
1304 | ||
1305 | $x->exponent(); # return exponent as BigInt | |
1306 | $x->mantissa(); # return mantissa as BigInt | |
1307 | $x->parts(); # return (mantissa,exponent) as BigInt | |
1308 | ||
1309 | $x->length(); # number of digits (w/o sign and '.') | |
1310 | ($l,$f) = $x->length(); # number of digits, and length of fraction | |
a5f75d66 AD |
1311 | |
1312 | =head1 DESCRIPTION | |
1313 | ||
58cde26e JH |
1314 | All operators (inlcuding basic math operations) are overloaded if you |
1315 | declare your big floating point numbers as | |
a5f75d66 | 1316 | |
58cde26e JH |
1317 | $i = new Math::BigFloat '12_3.456_789_123_456_789E-2'; |
1318 | ||
1319 | Operations with overloaded operators preserve the arguments, which is | |
1320 | exactly what you expect. | |
1321 | ||
1322 | =head2 Canonical notation | |
1323 | ||
1324 | Input to these routines are either BigFloat objects, or strings of the | |
1325 | following four forms: | |
a5f75d66 AD |
1326 | |
1327 | =over 2 | |
1328 | ||
58cde26e JH |
1329 | =item * |
1330 | ||
1331 | C</^[+-]\d+$/> | |
a5f75d66 | 1332 | |
58cde26e | 1333 | =item * |
a5f75d66 | 1334 | |
58cde26e | 1335 | C</^[+-]\d+\.\d*$/> |
a5f75d66 | 1336 | |
58cde26e | 1337 | =item * |
a5f75d66 | 1338 | |
58cde26e | 1339 | C</^[+-]\d+E[+-]?\d+$/> |
a5f75d66 | 1340 | |
58cde26e | 1341 | =item * |
a5f75d66 | 1342 | |
58cde26e | 1343 | C</^[+-]\d*\.\d+E[+-]?\d+$/> |
5d7098d5 | 1344 | |
58cde26e JH |
1345 | =back |
1346 | ||
1347 | all with optional leading and trailing zeros and/or spaces. Additonally, | |
1348 | numbers are allowed to have an underscore between any two digits. | |
1349 | ||
1350 | Empty strings as well as other illegal numbers results in 'NaN'. | |
1351 | ||
1352 | bnorm() on a BigFloat object is now effectively a no-op, since the numbers | |
1353 | are always stored in normalized form. On a string, it creates a BigFloat | |
1354 | object. | |
1355 | ||
1356 | =head2 Output | |
1357 | ||
1358 | Output values are BigFloat objects (normalized), except for bstr() and bsstr(). | |
1359 | ||
1360 | The string output will always have leading and trailing zeros stripped and drop | |
1361 | a plus sign. C<bstr()> will give you always the form with a decimal point, | |
1362 | while C<bsstr()> (for scientific) gives you the scientific notation. | |
1363 | ||
1364 | Input bstr() bsstr() | |
1365 | '-0' '0' '0E1' | |
1366 | ' -123 123 123' '-123123123' '-123123123E0' | |
1367 | '00.0123' '0.0123' '123E-4' | |
1368 | '123.45E-2' '1.2345' '12345E-4' | |
1369 | '10E+3' '10000' '1E4' | |
1370 | ||
1371 | Some routines (C<is_odd()>, C<is_even()>, C<is_zero()>, C<is_one()>, | |
1372 | C<is_nan()>) return true or false, while others (C<bcmp()>, C<bacmp()>) | |
1373 | return either undef, <0, 0 or >0 and are suited for sort. | |
1374 | ||
1375 | Actual math is done by using BigInts to represent the mantissa and exponent. | |
1376 | The sign C</^[+-]$/> is stored separately. The string 'NaN' is used to | |
1377 | represent the result when input arguments are not numbers, as well as | |
1378 | the result of dividing by zero. | |
1379 | ||
1380 | =head2 C<mantissa()>, C<exponent()> and C<parts()> | |
1381 | ||
1382 | C<mantissa()> and C<exponent()> return the said parts of the BigFloat | |
1383 | as BigInts such that: | |
1384 | ||
1385 | $m = $x->mantissa(); | |
1386 | $e = $x->exponent(); | |
1387 | $y = $m * ( 10 ** $e ); | |
1388 | print "ok\n" if $x == $y; | |
1389 | ||
1390 | C<< ($m,$e) = $x->parts(); >> is just a shortcut giving you both of them. | |
1391 | ||
1392 | A zero is represented and returned as C<0E1>, B<not> C<0E0> (after Knuth). | |
1393 | ||
1394 | Currently the mantissa is reduced as much as possible, favouring higher | |
1395 | exponents over lower ones (e.g. returning 1e7 instead of 10e6 or 10000000e0). | |
1396 | This might change in the future, so do not depend on it. | |
1397 | ||
1398 | =head2 Accuracy vs. Precision | |
1399 | ||
1400 | See also: L<Rounding|Rounding>. | |
1401 | ||
1402 | Math::BigFloat supports both precision and accuracy. (here should follow | |
1403 | a short description of both). | |
5d7098d5 | 1404 | |
58cde26e JH |
1405 | Precision: digits after the '.', laber, schwad |
1406 | Accuracy: Significant digits blah blah | |
5d7098d5 | 1407 | |
58cde26e JH |
1408 | Since things like sqrt(2) or 1/3 must presented with a limited precision lest |
1409 | a operation consumes all resources, each operation produces no more than | |
1410 | C<Math::BigFloat::precision()> digits. | |
1411 | ||
1412 | In case the result of one operation has more precision than specified, | |
1413 | it is rounded. The rounding mode taken is either the default mode, or the one | |
1414 | supplied to the operation after the I<scale>: | |
1415 | ||
1416 | $x = Math::BigFloat->new(2); | |
1417 | Math::BigFloat::precision(5); # 5 digits max | |
1418 | $y = $x->copy()->bdiv(3); # will give 0.66666 | |
1419 | $y = $x->copy()->bdiv(3,6); # will give 0.666666 | |
1420 | $y = $x->copy()->bdiv(3,6,'odd'); # will give 0.666667 | |
1421 | Math::BigFloat::round_mode('zero'); | |
1422 | $y = $x->copy()->bdiv(3,6); # will give 0.666666 | |
1423 | ||
1424 | =head2 Rounding | |
1425 | ||
1426 | =over 2 | |
1427 | ||
5dc6f178 | 1428 | =item ffround ( +$scale ) |
58cde26e | 1429 | |
0716bf9b JH |
1430 | Rounds to the $scale'th place left from the '.', counting from the dot. |
1431 | The first digit is numbered 1. | |
58cde26e | 1432 | |
5dc6f178 | 1433 | =item ffround ( -$scale ) |
58cde26e | 1434 | |
0716bf9b | 1435 | Rounds to the $scale'th place right from the '.', counting from the dot. |
58cde26e | 1436 | |
5dc6f178 JH |
1437 | =item ffround ( 0 ) |
1438 | ||
0716bf9b | 1439 | Rounds to an integer. |
5dc6f178 JH |
1440 | |
1441 | =item fround ( +$scale ) | |
1442 | ||
0716bf9b JH |
1443 | Preserves accuracy to $scale digits from the left (aka significant digits) |
1444 | and pads the rest with zeros. If the number is between 1 and -1, the | |
1445 | significant digits count from the first non-zero after the '.' | |
5dc6f178 JH |
1446 | |
1447 | =item fround ( -$scale ) and fround ( 0 ) | |
1448 | ||
0716bf9b | 1449 | These are effetively no-ops. |
5d7098d5 | 1450 | |
a5f75d66 AD |
1451 | =back |
1452 | ||
0716bf9b JH |
1453 | All rounding functions take as a second parameter a rounding mode from one of |
1454 | the following: 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'. | |
58cde26e JH |
1455 | |
1456 | The default rounding mode is 'even'. By using | |
ee15d750 JH |
1457 | C<< Math::BigFloat::round_mode($round_mode); >> you can get and set the default |
1458 | mode for subsequent rounding. The usage of C<$Math::BigFloat::$round_mode> is | |
0716bf9b | 1459 | no longer supported. |
b22b3e31 | 1460 | The second parameter to the round functions then overrides the default |
0716bf9b | 1461 | temporarily. |
58cde26e JH |
1462 | |
1463 | The C<< as_number() >> function returns a BigInt from a Math::BigFloat. It uses | |
1464 | 'trunc' as rounding mode to make it equivalent to: | |
1465 | ||
1466 | $x = 2.5; | |
1467 | $y = int($x) + 2; | |
1468 | ||
1469 | You can override this by passing the desired rounding mode as parameter to | |
1470 | C<as_number()>: | |
1471 | ||
1472 | $x = Math::BigFloat->new(2.5); | |
1473 | $y = $x->as_number('odd'); # $y = 3 | |
1474 | ||
1475 | =head1 EXAMPLES | |
1476 | ||
58cde26e | 1477 | # not ready yet |
58cde26e JH |
1478 | |
1479 | =head1 Autocreating constants | |
1480 | ||
1481 | After C<use Math::BigFloat ':constant'> all the floating point constants | |
1482 | in the given scope are converted to C<Math::BigFloat>. This conversion | |
1483 | happens at compile time. | |
1484 | ||
1485 | In particular | |
1486 | ||
1487 | perl -MMath::BigFloat=:constant -e 'print 2E-100,"\n"' | |
1488 | ||
1489 | prints the value of C<2E-100>. Note that without conversion of | |
1490 | constants the expression 2E-100 will be calculated as normal floating point | |
1491 | number. | |
1492 | ||
a5f75d66 AD |
1493 | =head1 BUGS |
1494 | ||
58cde26e JH |
1495 | =over 2 |
1496 | ||
1497 | =item * | |
1498 | ||
1499 | The following does not work yet: | |
1500 | ||
1501 | $m = $x->mantissa(); | |
1502 | $e = $x->exponent(); | |
1503 | $y = $m * ( 10 ** $e ); | |
1504 | print "ok\n" if $x == $y; | |
1505 | ||
1506 | =item * | |
1507 | ||
1508 | There is no fmod() function yet. | |
1509 | ||
1510 | =back | |
1511 | ||
1512 | =head1 CAVEAT | |
1513 | ||
1514 | =over 1 | |
1515 | ||
1516 | =item stringify, bstr() | |
1517 | ||
1518 | Both stringify and bstr() now drop the leading '+'. The old code would return | |
1519 | '+1.23', the new returns '1.23'. See the documentation in L<Math::BigInt> for | |
1520 | reasoning and details. | |
1521 | ||
1522 | =item bdiv | |
1523 | ||
1524 | The following will probably not do what you expect: | |
1525 | ||
1526 | print $c->bdiv(123.456),"\n"; | |
1527 | ||
1528 | It prints both quotient and reminder since print works in list context. Also, | |
1529 | bdiv() will modify $c, so be carefull. You probably want to use | |
1530 | ||
1531 | print $c / 123.456,"\n"; | |
1532 | print scalar $c->bdiv(123.456),"\n"; # or if you want to modify $c | |
1533 | ||
1534 | instead. | |
1535 | ||
1536 | =item Modifying and = | |
1537 | ||
1538 | Beware of: | |
1539 | ||
1540 | $x = Math::BigFloat->new(5); | |
1541 | $y = $x; | |
1542 | ||
1543 | It will not do what you think, e.g. making a copy of $x. Instead it just makes | |
1544 | a second reference to the B<same> object and stores it in $y. Thus anything | |
1545 | that modifies $x will modify $y, and vice versa. | |
1546 | ||
1547 | $x->bmul(2); | |
1548 | print "$x, $y\n"; # prints '10, 10' | |
1549 | ||
1550 | If you want a true copy of $x, use: | |
1551 | ||
1552 | $y = $x->copy(); | |
1553 | ||
1554 | See also the documentation in L<overload> regarding C<=>. | |
1555 | ||
1556 | =item bpow | |
1557 | ||
1558 | C<bpow()> now modifies the first argument, unlike the old code which left | |
1559 | it alone and only returned the result. This is to be consistent with | |
1560 | C<badd()> etc. The first will modify $x, the second one won't: | |
1561 | ||
1562 | print bpow($x,$i),"\n"; # modify $x | |
1563 | print $x->bpow($i),"\n"; # ditto | |
1564 | print $x ** $i,"\n"; # leave $x alone | |
1565 | ||
1566 | =back | |
1567 | ||
1568 | =head1 LICENSE | |
a5f75d66 | 1569 | |
58cde26e JH |
1570 | This program is free software; you may redistribute it and/or modify it under |
1571 | the same terms as Perl itself. | |
5d7098d5 | 1572 | |
58cde26e | 1573 | =head1 AUTHORS |
5d7098d5 | 1574 | |
58cde26e JH |
1575 | Mark Biggar, overloaded interface by Ilya Zakharevich. |
1576 | Completely rewritten by Tels http://bloodgate.com in 2001. | |
a5f75d66 | 1577 | |
a5f75d66 | 1578 | =cut |