Commit | Line | Data |
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1 | #!/usr/bin/perl -w |
2 | |
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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 |
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10 | # _cow: Copy-On-Write (NRY) |
11 | |
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12 | package Math::BigFloat; |
13 | |
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14 | $VERSION = '1.25'; |
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15 | require 5.005; |
16 | use Exporter; |
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17 | use Math::BigInt qw/objectify/; |
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18 | @ISA = qw( Exporter Math::BigInt); |
19 | # can not export bneg/babs since the are only in MBI |
20 | @EXPORT_OK = qw( |
21 | bcmp |
22 | badd bmul bdiv bmod bnorm bsub |
23 | bgcd blcm bround bfround |
24 | bpow bnan bzero bfloor bceil |
574bacfe |
25 | bacmp bstr binc bdec binf |
0716bf9b |
26 | is_odd is_even is_nan is_inf is_positive is_negative |
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27 | is_zero is_one sign |
28 | ); |
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29 | |
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30 | #@EXPORT = qw( ); |
31 | use strict; |
027dc388 |
32 | use vars qw/$AUTOLOAD $accuracy $precision $div_scale $round_mode $rnd_mode/; |
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33 | my $class = "Math::BigFloat"; |
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34 | |
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35 | use overload |
bd05a461 |
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 | ; |
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41 | |
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42 | ############################################################################## |
43 | # global constants, flags and accessory |
44 | |
45 | use constant MB_NEVER_ROUND => 0x0001; |
46 | |
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47 | # are NaNs ok? |
48 | my $NaNOK=1; |
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49 | # constant for easier life |
50 | my $nan = 'NaN'; |
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51 | |
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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; |
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57 | |
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58 | ############################################################################## |
59 | # the old code had $rnd_mode, so we need to support it, too |
60 | |
61 | $rnd_mode = 'even'; |
62 | sub TIESCALAR { my ($class) = @_; bless \$round_mode, $class; } |
63 | sub FETCH { return $round_mode; } |
64 | sub STORE { $rnd_mode = $_[0]->round_mode($_[1]); } |
65 | |
66 | BEGIN { tie $rnd_mode, 'Math::BigFloat'; } |
67 | |
68 | ############################################################################## |
69 | |
574bacfe |
70 | # in case we call SUPER::->foo() and this wants to call modify() |
71 | # sub modify () { 0; } |
72 | |
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73 | { |
ee15d750 |
74 | # valid method aliases for AUTOLOAD |
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75 | my %methods = map { $_ => 1 } |
76 | qw / fadd fsub fmul fdiv fround ffround fsqrt fmod fstr fsstr fpow fnorm |
ee15d750 |
77 | fneg fint facmp fcmp fzero fnan finf finc fdec |
78 | fceil ffloor |
79 | /; |
80 | # valid method's that need to be hand-ed up (for AUTOLOAD) |
81 | my %hand_ups = map { $_ => 1 } |
82 | qw / is_nan is_inf is_negative is_positive |
83 | accuracy precision div_scale round_mode fabs babs |
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84 | /; |
85 | |
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86 | sub method_alias { return exists $methods{$_[0]||''}; } |
87 | sub method_hand_up { return exists $hand_ups{$_[0]||''}; } |
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88 | } |
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89 | |
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90 | ############################################################################## |
91 | # constructors |
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92 | |
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93 | sub new |
94 | { |
95 | # create a new BigFloat object from a string or another bigfloat object. |
96 | # _e: exponent |
97 | # _m: mantissa |
98 | # sign => sign (+/-), or "NaN" |
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99 | |
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100 | my $class = shift; |
101 | |
102 | my $wanted = shift; # avoid numify call by not using || here |
103 | return $class->bzero() if !defined $wanted; # default to 0 |
104 | return $wanted->copy() if ref($wanted) eq $class; |
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105 | |
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106 | my $round = shift; $round = 0 if !defined $round; # no rounding as default |
107 | my $self = {}; bless $self, $class; |
b22b3e31 |
108 | # shortcut for bigints and its subclasses |
0716bf9b |
109 | if ((ref($wanted)) && (ref($wanted) ne $class)) |
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110 | { |
0716bf9b |
111 | $self->{_m} = $wanted->as_number(); # get us a bigint copy |
027dc388 |
112 | $self->{_e} = Math::BigInt->bzero(); |
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113 | $self->{_m}->babs(); |
114 | $self->{sign} = $wanted->sign(); |
0716bf9b |
115 | return $self->bnorm(); |
58cde26e |
116 | } |
117 | # got string |
118 | # handle '+inf', '-inf' first |
ee15d750 |
119 | if ($wanted =~ /^[+-]?inf$/) |
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120 | { |
027dc388 |
121 | $self->{_e} = Math::BigInt->bzero(); |
122 | $self->{_m} = Math::BigInt->bzero(); |
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123 | $self->{sign} = $wanted; |
ee15d750 |
124 | $self->{sign} = '+inf' if $self->{sign} eq 'inf'; |
0716bf9b |
125 | return $self->bnorm(); |
58cde26e |
126 | } |
127 | #print "new string '$wanted'\n"; |
128 | my ($mis,$miv,$mfv,$es,$ev) = Math::BigInt::_split(\$wanted); |
129 | if (!ref $mis) |
130 | { |
131 | die "$wanted is not a number initialized to $class" if !$NaNOK; |
027dc388 |
132 | $self->{_e} = Math::BigInt->bzero(); |
133 | $self->{_m} = Math::BigInt->bzero(); |
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134 | $self->{sign} = $nan; |
135 | } |
136 | else |
137 | { |
138 | # make integer from mantissa by adjusting exp, then convert to bigint |
139 | $self->{_e} = Math::BigInt->new("$$es$$ev"); # exponent |
027dc388 |
140 | $self->{_m} = Math::BigInt->new("$$miv$$mfv"); # create mantissa |
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141 | # 3.123E0 = 3123E-3, and 3.123E-2 => 3123E-5 |
027dc388 |
142 | $self->{_e} -= CORE::length($$mfv) if CORE::length($$mfv) != 0; |
143 | $self->{sign} = $$mis; |
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144 | } |
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145 | #print "$wanted => $self->{sign} $self->{value}\n"; |
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146 | $self->bnorm(); # first normalize |
147 | # if any of the globals is set, round to them and thus store them insid $self |
ee15d750 |
148 | $self->round($accuracy,$precision,$class->round_mode) |
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149 | if defined $accuracy || defined $precision; |
150 | return $self; |
151 | } |
a0d0e21e |
152 | |
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153 | sub bnan |
154 | { |
155 | # create a bigfloat 'NaN', if given a BigFloat, set it to 'NaN' |
156 | my $self = shift; |
157 | $self = $class if !defined $self; |
158 | if (!ref($self)) |
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159 | { |
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160 | my $c = $self; $self = {}; bless $self, $c; |
a0d0e21e |
161 | } |
574bacfe |
162 | $self->{_m} = Math::BigInt->bzero(); |
163 | $self->{_e} = Math::BigInt->bzero(); |
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164 | $self->{sign} = $nan; |
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165 | return $self; |
166 | } |
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167 | |
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168 | sub binf |
169 | { |
170 | # create a bigfloat '+-inf', if given a BigFloat, set it to '+-inf' |
171 | my $self = shift; |
172 | my $sign = shift; $sign = '+' if !defined $sign || $sign ne '-'; |
a0d0e21e |
173 | |
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174 | $self = $class if !defined $self; |
175 | if (!ref($self)) |
176 | { |
177 | my $c = $self; $self = {}; bless $self, $c; |
178 | } |
574bacfe |
179 | $self->{_m} = Math::BigInt->bzero(); |
180 | $self->{_e} = Math::BigInt->bzero(); |
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181 | $self->{sign} = $sign.'inf'; |
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182 | return $self; |
183 | } |
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184 | |
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185 | sub bone |
186 | { |
187 | # create a bigfloat '+-1', if given a BigFloat, set it to '+-1' |
188 | my $self = shift; |
189 | my $sign = shift; $sign = '+' if !defined $sign || $sign ne '-'; |
190 | |
191 | $self = $class if !defined $self; |
192 | if (!ref($self)) |
193 | { |
194 | my $c = $self; $self = {}; bless $self, $c; |
195 | } |
196 | $self->{_m} = Math::BigInt->bone(); |
197 | $self->{_e} = Math::BigInt->bzero(); |
198 | $self->{sign} = $sign; |
199 | return $self; |
200 | } |
201 | |
58cde26e |
202 | sub bzero |
203 | { |
204 | # create a bigfloat '+0', if given a BigFloat, set it to 0 |
205 | my $self = shift; |
206 | $self = $class if !defined $self; |
207 | if (!ref($self)) |
208 | { |
209 | my $c = $self; $self = {}; bless $self, $c; |
210 | } |
574bacfe |
211 | $self->{_m} = Math::BigInt->bzero(); |
212 | $self->{_e} = Math::BigInt->bone(); |
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213 | $self->{sign} = '+'; |
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214 | return $self; |
215 | } |
216 | |
217 | ############################################################################## |
218 | # string conversation |
219 | |
220 | sub bstr |
221 | { |
222 | # (ref to BFLOAT or num_str ) return num_str |
223 | # Convert number from internal format to (non-scientific) string format. |
224 | # internal format is always normalized (no leading zeros, "-0" => "+0") |
ee15d750 |
225 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
226 | #my $x = shift; my $class = ref($x) || $x; |
227 | #$x = $class->new(shift) unless ref($x); |
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228 | |
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229 | #die "Oups! e was $nan" if $x->{_e}->{sign} eq $nan; |
230 | #die "Oups! m was $nan" if $x->{_m}->{sign} eq $nan; |
231 | if ($x->{sign} !~ /^[+-]$/) |
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232 | { |
574bacfe |
233 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN |
234 | return 'inf'; # +inf |
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235 | } |
236 | |
574bacfe |
237 | my $es = '0'; my $len = 1; my $cad = 0; my $dot = '.'; |
238 | |
239 | my $not_zero = !$x->is_zero(); |
240 | if ($not_zero) |
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241 | { |
574bacfe |
242 | $es = $x->{_m}->bstr(); |
243 | $len = CORE::length($es); |
244 | if (!$x->{_e}->is_zero()) |
245 | # { |
246 | # $es = $x->{sign}.$es if $x->{sign} eq '-'; |
247 | # } |
248 | # else |
58cde26e |
249 | { |
574bacfe |
250 | if ($x->{_e}->sign() eq '-') |
251 | { |
252 | $dot = ''; |
253 | if ($x->{_e} <= -$len) |
254 | { |
255 | # print "style: 0.xxxx\n"; |
256 | my $r = $x->{_e}->copy(); $r->babs()->bsub( CORE::length($es) ); |
257 | $es = '0.'. ('0' x $r) . $es; $cad = -($len+$r); |
258 | } |
259 | else |
260 | { |
261 | # print "insert '.' at $x->{_e} in '$es'\n"; |
262 | substr($es,$x->{_e},0) = '.'; $cad = $x->{_e}; |
263 | } |
264 | } |
265 | else |
266 | { |
267 | # expand with zeros |
268 | $es .= '0' x $x->{_e}; $len += $x->{_e}; $cad = 0; |
269 | } |
82cf049f |
270 | } |
574bacfe |
271 | } # if not zero |
272 | $es = $x->{sign}.$es if $x->{sign} eq '-'; |
273 | # if set accuracy or precision, pad with zeros |
274 | if ((defined $x->{_a}) && ($not_zero)) |
275 | { |
276 | # 123400 => 6, 0.1234 => 4, 0.001234 => 4 |
277 | my $zeros = $x->{_a} - $cad; # cad == 0 => 12340 |
278 | $zeros = $x->{_a} - $len if $cad != $len; |
279 | #print "acc padd $x->{_a} $zeros (len $len cad $cad)\n"; |
280 | $es .= $dot.'0' x $zeros if $zeros > 0; |
82cf049f |
281 | } |
574bacfe |
282 | elsif ($x->{_p} || 0 < 0) |
58cde26e |
283 | { |
574bacfe |
284 | # 123400 => 6, 0.1234 => 4, 0.001234 => 6 |
285 | my $zeros = -$x->{_p} + $cad; |
286 | #print "pre padd $x->{_p} $zeros (len $len cad $cad)\n"; |
287 | $es .= $dot.'0' x $zeros if $zeros > 0; |
58cde26e |
288 | } |
58cde26e |
289 | return $es; |
82cf049f |
290 | } |
f216259d |
291 | |
58cde26e |
292 | sub bsstr |
293 | { |
294 | # (ref to BFLOAT or num_str ) return num_str |
295 | # Convert number from internal format to scientific string format. |
296 | # internal format is always normalized (no leading zeros, "-0E0" => "+0E0") |
ee15d750 |
297 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
298 | #my $x = shift; my $class = ref($x) || $x; |
299 | #$x = $class->new(shift) unless ref($x); |
a0d0e21e |
300 | |
574bacfe |
301 | #die "Oups! e was $nan" if $x->{_e}->{sign} eq $nan; |
302 | #die "Oups! m was $nan" if $x->{_m}->{sign} eq $nan; |
303 | if ($x->{sign} !~ /^[+-]$/) |
304 | { |
305 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN |
306 | return 'inf'; # +inf |
307 | } |
58cde26e |
308 | my $sign = $x->{_e}->{sign}; $sign = '' if $sign eq '-'; |
309 | my $sep = 'e'.$sign; |
310 | return $x->{_m}->bstr().$sep.$x->{_e}->bstr(); |
311 | } |
312 | |
313 | sub numify |
314 | { |
315 | # Make a number from a BigFloat object |
574bacfe |
316 | # simple return string and let Perl's atoi()/atof() handle the rest |
ee15d750 |
317 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
318 | return $x->bsstr(); |
319 | } |
a0d0e21e |
320 | |
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321 | ############################################################################## |
322 | # public stuff (usually prefixed with "b") |
323 | |
324 | # really? Just for exporting them is not what I had in mind |
325 | #sub babs |
326 | # { |
327 | # $class->SUPER::babs($class,@_); |
328 | # } |
329 | #sub bneg |
330 | # { |
331 | # $class->SUPER::bneg($class,@_); |
332 | # } |
574bacfe |
333 | |
334 | # tels 2001-08-04 |
335 | # todo: this must be overwritten and return NaN for non-integer values |
336 | # band(), bior(), bxor(), too |
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337 | #sub bnot |
338 | # { |
339 | # $class->SUPER::bnot($class,@_); |
340 | # } |
341 | |
342 | sub bcmp |
343 | { |
344 | # Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort) |
345 | # (BFLOAT or num_str, BFLOAT or num_str) return cond_code |
346 | my ($self,$x,$y) = objectify(2,@_); |
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347 | |
0716bf9b |
348 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
349 | { |
350 | # handle +-inf and NaN |
351 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
352 | return 0 if ($x->{sign} eq $y->{sign}) && ($x->{sign} =~ /^[+-]inf$/); |
353 | return +1 if $x->{sign} eq '+inf'; |
354 | return -1 if $x->{sign} eq '-inf'; |
355 | return -1 if $y->{sign} eq '+inf'; |
356 | return +1 if $y->{sign} eq '-inf'; |
357 | } |
358 | |
359 | # check sign for speed first |
574bacfe |
360 | return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y |
58cde26e |
361 | return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0 |
362 | |
574bacfe |
363 | # shortcut |
364 | my $xz = $x->is_zero(); |
365 | my $yz = $y->is_zero(); |
366 | return 0 if $xz && $yz; # 0 <=> 0 |
367 | return -1 if $xz && $y->{sign} eq '+'; # 0 <=> +y |
368 | return 1 if $yz && $x->{sign} eq '+'; # +x <=> 0 |
58cde26e |
369 | |
370 | # adjust so that exponents are equal |
bd05a461 |
371 | my $lxm = $x->{_m}->length(); |
372 | my $lym = $y->{_m}->length(); |
373 | my $lx = $lxm + $x->{_e}; |
374 | my $ly = $lym + $y->{_e}; |
58cde26e |
375 | # print "x $x y $y lx $lx ly $ly\n"; |
376 | my $l = $lx - $ly; $l = -$l if $x->{sign} eq '-'; |
377 | # print "$l $x->{sign}\n"; |
bd05a461 |
378 | return $l <=> 0 if $l != 0; |
58cde26e |
379 | |
bd05a461 |
380 | # lengths (corrected by exponent) are equal |
381 | # so make mantissa euqal length by padding with zero (shift left) |
382 | my $diff = $lxm - $lym; |
383 | my $xm = $x->{_m}; # not yet copy it |
384 | my $ym = $y->{_m}; |
385 | if ($diff > 0) |
386 | { |
387 | $ym = $y->{_m}->copy()->blsft($diff,10); |
388 | } |
389 | elsif ($diff < 0) |
390 | { |
391 | $xm = $x->{_m}->copy()->blsft(-$diff,10); |
392 | } |
393 | my $rc = $xm->bcmp($ym); |
58cde26e |
394 | $rc = -$rc if $x->{sign} eq '-'; # -124 < -123 |
bd05a461 |
395 | return $rc <=> 0; |
58cde26e |
396 | } |
397 | |
398 | sub bacmp |
399 | { |
400 | # Compares 2 values, ignoring their signs. |
401 | # Returns one of undef, <0, =0, >0. (suitable for sort) |
402 | # (BFLOAT or num_str, BFLOAT or num_str) return cond_code |
403 | my ($self,$x,$y) = objectify(2,@_); |
ee15d750 |
404 | |
405 | # handle +-inf and NaN's |
abcfbf51 |
406 | if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/) |
ee15d750 |
407 | { |
408 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
409 | return 0 if ($x->is_inf() && $y->is_inf()); |
410 | return 1 if ($x->is_inf() && !$y->is_inf()); |
411 | return -1 if (!$x->is_inf() && $y->is_inf()); |
412 | } |
413 | |
414 | # shortcut |
415 | my $xz = $x->is_zero(); |
416 | my $yz = $y->is_zero(); |
417 | return 0 if $xz && $yz; # 0 <=> 0 |
418 | return -1 if $xz && !$yz; # 0 <=> +y |
419 | return 1 if $yz && !$xz; # +x <=> 0 |
420 | |
421 | # adjust so that exponents are equal |
422 | my $lxm = $x->{_m}->length(); |
423 | my $lym = $y->{_m}->length(); |
424 | my $lx = $lxm + $x->{_e}; |
425 | my $ly = $lym + $y->{_e}; |
426 | # print "x $x y $y lx $lx ly $ly\n"; |
427 | my $l = $lx - $ly; # $l = -$l if $x->{sign} eq '-'; |
428 | # print "$l $x->{sign}\n"; |
429 | return $l <=> 0 if $l != 0; |
58cde26e |
430 | |
ee15d750 |
431 | # lengths (corrected by exponent) are equal |
432 | # so make mantissa euqal length by padding with zero (shift left) |
433 | my $diff = $lxm - $lym; |
434 | my $xm = $x->{_m}; # not yet copy it |
435 | my $ym = $y->{_m}; |
436 | if ($diff > 0) |
437 | { |
438 | $ym = $y->{_m}->copy()->blsft($diff,10); |
439 | } |
440 | elsif ($diff < 0) |
441 | { |
442 | $xm = $x->{_m}->copy()->blsft(-$diff,10); |
443 | } |
444 | my $rc = $xm->bcmp($ym); |
445 | # $rc = -$rc if $x->{sign} eq '-'; # -124 < -123 |
446 | return $rc <=> 0; |
447 | |
448 | # # signs are ignored, so check length |
449 | # # length(x) is length(m)+e aka length of non-fraction part |
450 | # # the longer one is bigger |
451 | # my $l = $x->length() - $y->length(); |
452 | # #print "$l\n"; |
453 | # return $l if $l != 0; |
454 | # #print "equal lengths\n"; |
455 | # |
456 | # # if both are equal long, make full compare |
457 | # # first compare only the mantissa |
458 | # # if mantissa are equal, compare fractions |
459 | # |
460 | # return $x->{_m} <=> $y->{_m} || $x->{_e} <=> $y->{_e}; |
58cde26e |
461 | } |
a0d0e21e |
462 | |
58cde26e |
463 | sub badd |
464 | { |
465 | # add second arg (BFLOAT or string) to first (BFLOAT) (modifies first) |
466 | # return result as BFLOAT |
58cde26e |
467 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
468 | |
574bacfe |
469 | # inf and NaN handling |
470 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
471 | { |
472 | # NaN first |
473 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
474 | # inf handline |
475 | if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) |
476 | { |
477 | # + and + => +, - and - => -, + and - => 0, - and + => 0 |
478 | return $x->bzero() if $x->{sign} ne $y->{sign}; |
479 | return $x; |
480 | } |
481 | # +-inf + something => +inf |
482 | # something +-inf => +-inf |
483 | $x->{sign} = $y->{sign}, return $x if $y->{sign} =~ /^[+-]inf$/; |
484 | return $x; |
485 | } |
486 | |
58cde26e |
487 | # speed: no add for 0+y or x+0 |
488 | return $x if $y->is_zero(); # x+0 |
489 | if ($x->is_zero()) # 0+y |
490 | { |
491 | # make copy, clobbering up x (modify in place!) |
492 | $x->{_e} = $y->{_e}->copy(); |
493 | $x->{_m} = $y->{_m}->copy(); |
494 | $x->{sign} = $y->{sign} || $nan; |
495 | return $x->round($a,$p,$r,$y); |
a0d0e21e |
496 | } |
58cde26e |
497 | |
498 | # take lower of the two e's and adapt m1 to it to match m2 |
499 | my $e = $y->{_e}; $e = Math::BigInt::bzero() if !defined $e; # if no BFLOAT |
500 | $e = $e - $x->{_e}; |
501 | my $add = $y->{_m}->copy(); |
502 | if ($e < 0) |
503 | { |
0716bf9b |
504 | # print "e < 0\n"; |
58cde26e |
505 | #print "\$x->{_m}: $x->{_m} "; |
506 | #print "\$x->{_e}: $x->{_e}\n"; |
507 | my $e1 = $e->copy()->babs(); |
508 | $x->{_m} *= (10 ** $e1); |
509 | $x->{_e} += $e; # need the sign of e |
510 | #$x->{_m} += $y->{_m}; |
511 | #print "\$x->{_m}: $x->{_m} "; |
512 | #print "\$x->{_e}: $x->{_e}\n"; |
513 | } |
514 | elsif ($e > 0) |
515 | { |
0716bf9b |
516 | # print "e > 0\n"; |
58cde26e |
517 | #print "\$x->{_m}: $x->{_m} \$y->{_m}: $y->{_m} \$e: $e ",ref($e),"\n"; |
518 | $add *= (10 ** $e); |
519 | #$x->{_m} += $y->{_m} * (10 ** $e); |
520 | #print "\$x->{_m}: $x->{_m}\n"; |
521 | } |
522 | # else: both e are same, so leave them |
523 | #print "badd $x->{sign}$x->{_m} + $y->{sign}$add\n"; |
524 | # fiddle with signs |
525 | $x->{_m}->{sign} = $x->{sign}; |
526 | $add->{sign} = $y->{sign}; |
527 | # finally do add/sub |
528 | $x->{_m} += $add; |
529 | # re-adjust signs |
530 | $x->{sign} = $x->{_m}->{sign}; |
531 | $x->{_m}->{sign} = '+'; |
0716bf9b |
532 | #$x->bnorm(); # delete trailing zeros |
58cde26e |
533 | return $x->round($a,$p,$r,$y); |
534 | } |
535 | |
536 | sub bsub |
537 | { |
0716bf9b |
538 | # (BigFloat or num_str, BigFloat or num_str) return BigFloat |
58cde26e |
539 | # subtract second arg from first, modify first |
e745a66c |
540 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
a0d0e21e |
541 | |
e745a66c |
542 | if (!$y->is_zero()) # don't need to do anything if $y is 0 |
543 | { |
544 | $y->{sign} =~ tr/+\-/-+/; # does nothing for NaN |
545 | $x->badd($y,$a,$p,$r); # badd does not leave internal zeros |
546 | $y->{sign} =~ tr/+\-/-+/; # refix $y (does nothing for NaN) |
547 | } |
548 | $x; # already rounded by badd() |
58cde26e |
549 | } |
550 | |
551 | sub binc |
552 | { |
553 | # increment arg by one |
ee15d750 |
554 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
e745a66c |
555 | |
556 | if ($x->{_e}->sign() eq '-') |
557 | { |
558 | return $x->badd($self->bone(),$a,$p,$r); # digits after dot |
559 | } |
560 | |
561 | if (!$x->{_e}->is_zero()) |
562 | { |
563 | $x->{_m}->blsft($x->{_e},10); # 1e2 => 100 |
564 | $x->{_e}->bzero(); |
565 | } |
566 | # now $x->{_e} == 0 |
567 | if ($x->{sign} eq '+') |
568 | { |
569 | $x->{_m}->binc(); |
570 | return $x->bnorm()->bround($a,$p,$r); |
571 | } |
572 | elsif ($x->{sign} eq '-') |
573 | { |
574 | $x->{_m}->bdec(); |
575 | $x->{sign} = '+' if $x->{_m}->is_zero(); # -1 +1 => -0 => +0 |
576 | return $x->bnorm()->bround($a,$p,$r); |
577 | } |
578 | # inf, nan handling etc |
579 | $x->badd($self->__one(),$a,$p,$r); # does round |
58cde26e |
580 | } |
581 | |
582 | sub bdec |
583 | { |
584 | # decrement arg by one |
ee15d750 |
585 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
e745a66c |
586 | |
587 | if ($x->{_e}->sign() eq '-') |
588 | { |
589 | return $x->badd($self->bone('-'),$a,$p,$r); # digits after dot |
590 | } |
591 | |
592 | if (!$x->{_e}->is_zero()) |
593 | { |
594 | $x->{_m}->blsft($x->{_e},10); # 1e2 => 100 |
595 | $x->{_e}->bzero(); |
596 | } |
597 | # now $x->{_e} == 0 |
598 | my $zero = $x->is_zero(); |
599 | # <= 0 |
600 | if (($x->{sign} eq '-') || $zero) |
601 | { |
602 | $x->{_m}->binc(); |
603 | $x->{sign} = '-' if $zero; # 0 => 1 => -1 |
604 | $x->{sign} = '+' if $x->{_m}->is_zero(); # -1 +1 => -0 => +0 |
605 | return $x->bnorm()->round($a,$p,$r); |
606 | } |
607 | # > 0 |
608 | elsif ($x->{sign} eq '+') |
609 | { |
610 | $x->{_m}->bdec(); |
611 | return $x->bnorm()->round($a,$p,$r); |
612 | } |
613 | # inf, nan handling etc |
614 | $x->badd($self->bone('-'),$a,$p,$r); # does round |
58cde26e |
615 | } |
616 | |
617 | sub blcm |
618 | { |
ee15d750 |
619 | # (BFLOAT or num_str, BFLOAT or num_str) return BFLOAT |
58cde26e |
620 | # does not modify arguments, but returns new object |
621 | # Lowest Common Multiplicator |
58cde26e |
622 | |
623 | my ($self,@arg) = objectify(0,@_); |
624 | my $x = $self->new(shift @arg); |
625 | while (@arg) { $x = _lcm($x,shift @arg); } |
626 | $x; |
627 | } |
628 | |
629 | sub bgcd |
630 | { |
ee15d750 |
631 | # (BFLOAT or num_str, BFLOAT or num_str) return BINT |
58cde26e |
632 | # does not modify arguments, but returns new object |
633 | # GCD -- Euclids algorithm Knuth Vol 2 pg 296 |
58cde26e |
634 | |
635 | my ($self,@arg) = objectify(0,@_); |
636 | my $x = $self->new(shift @arg); |
637 | while (@arg) { $x = _gcd($x,shift @arg); } |
638 | $x; |
639 | } |
640 | |
641 | sub is_zero |
642 | { |
ee15d750 |
643 | # return true if arg (BFLOAT or num_str) is zero (array '+', '0') |
644 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
574bacfe |
645 | |
646 | return 1 if $x->{sign} eq '+' && $x->{_m}->is_zero(); |
647 | return 0; |
58cde26e |
648 | } |
649 | |
650 | sub is_one |
651 | { |
ee15d750 |
652 | # return true if arg (BFLOAT or num_str) is +1 (array '+', '1') |
58cde26e |
653 | # or -1 if signis given |
ee15d750 |
654 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
655 | |
656 | my $sign = shift || ''; $sign = '+' if $sign ne '-'; |
657 | return 1 |
658 | if ($x->{sign} eq $sign && $x->{_e}->is_zero() && $x->{_m}->is_one()); |
659 | return 0; |
58cde26e |
660 | } |
661 | |
662 | sub is_odd |
663 | { |
ee15d750 |
664 | # return true if arg (BFLOAT or num_str) is odd or false if even |
665 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
0716bf9b |
666 | |
667 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
ee15d750 |
668 | return 1 if ($x->{_e}->is_zero() && $x->{_m}->is_odd()); |
669 | return 0; |
58cde26e |
670 | } |
671 | |
672 | sub is_even |
673 | { |
b22b3e31 |
674 | # return true if arg (BINT or num_str) is even or false if odd |
ee15d750 |
675 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
0716bf9b |
676 | |
677 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
678 | return 1 if $x->{_m}->is_zero(); # 0e1 is even |
ee15d750 |
679 | return 1 if ($x->{_e}->is_zero() && $x->{_m}->is_even()); # 123.45 is never |
680 | return 0; |
58cde26e |
681 | } |
682 | |
683 | sub bmul |
684 | { |
685 | # multiply two numbers -- stolen from Knuth Vol 2 pg 233 |
686 | # (BINT or num_str, BINT or num_str) return BINT |
687 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
58cde26e |
688 | |
0716bf9b |
689 | # print "mbf bmul $x->{_m}e$x->{_e} $y->{_m}e$y->{_e}\n"; |
58cde26e |
690 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
691 | |
574bacfe |
692 | # handle result = 0 |
693 | return $x->bzero() if $x->is_zero() || $y->is_zero(); |
694 | # inf handling |
695 | if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) |
696 | { |
697 | # result will always be +-inf: |
698 | # +inf * +/+inf => +inf, -inf * -/-inf => +inf |
699 | # +inf * -/-inf => -inf, -inf * +/+inf => -inf |
700 | return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); |
701 | return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); |
702 | return $x->binf('-'); |
703 | } |
704 | |
58cde26e |
705 | # aEb * cEd = (a*c)E(b+d) |
706 | $x->{_m} = $x->{_m} * $y->{_m}; |
707 | #print "m: $x->{_m}\n"; |
708 | $x->{_e} = $x->{_e} + $y->{_e}; |
709 | #print "e: $x->{_m}\n"; |
710 | # adjust sign: |
711 | $x->{sign} = $x->{sign} ne $y->{sign} ? '-' : '+'; |
712 | #print "s: $x->{sign}\n"; |
0716bf9b |
713 | $x->bnorm(); |
58cde26e |
714 | return $x->round($a,$p,$r,$y); |
715 | } |
716 | |
717 | sub bdiv |
718 | { |
719 | # (dividend: BFLOAT or num_str, divisor: BFLOAT or num_str) return |
720 | # (BFLOAT,BFLOAT) (quo,rem) or BINT (only rem) |
721 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
722 | |
ee15d750 |
723 | |
574bacfe |
724 | # x / +-inf => 0, reminder x |
725 | return wantarray ? ($x->bzero(),$x->copy()) : $x->bzero() |
726 | if $y->{sign} =~ /^[+-]inf$/; |
727 | |
728 | # NaN if x == NaN or y == NaN or x==y==0 |
58cde26e |
729 | return wantarray ? ($x->bnan(),bnan()) : $x->bnan() |
574bacfe |
730 | if (($x->is_nan() || $y->is_nan()) || |
731 | ($x->is_zero() && $y->is_zero())); |
732 | |
733 | # 5 / 0 => +inf, -6 / 0 => -inf |
734 | return wantarray |
735 | ? ($x->binf($x->{sign}),$self->bnan()) : $x->binf($x->{sign}) |
736 | if ($x->{sign} =~ /^[+-]$/ && $y->is_zero()); |
0716bf9b |
737 | |
ee15d750 |
738 | # promote BigInts and it's subclasses (except when already a BigFloat) |
739 | $y = $self->new($y) unless $y->isa('Math::BigFloat'); |
740 | |
741 | # old, broken way |
742 | # $y = $class->new($y) if ref($y) ne $self; # promote bigints |
0716bf9b |
743 | |
744 | # print "mbf bdiv $x ",ref($x)," ",$y," ",ref($y),"\n"; |
58cde26e |
745 | # we need to limit the accuracy to protect against overflow |
ee15d750 |
746 | |
574bacfe |
747 | my $fallback = 0; |
ee15d750 |
748 | my $scale = 0; |
749 | # print "s=$scale a=",$a||'undef'," p=",$p||'undef'," r=",$r||'undef',"\n"; |
750 | my @params = $x->_find_round_parameters($a,$p,$r,$y); |
751 | |
752 | # no rounding at all, so must use fallback |
753 | if (scalar @params == 1) |
58cde26e |
754 | { |
0716bf9b |
755 | # simulate old behaviour |
ee15d750 |
756 | $scale = $self->div_scale()+1; # at least one more for proper round |
757 | $params[1] = $self->div_scale(); # and round to it as accuracy |
758 | $params[3] = $r; # round mode by caller or undef |
759 | $fallback = 1; # to clear a/p afterwards |
760 | } |
761 | else |
762 | { |
763 | # the 4 below is empirical, and there might be cases where it is not |
764 | # enough... |
765 | $scale = abs($params[1] || $params[2]) + 4; # take whatever is defined |
a0d0e21e |
766 | } |
ee15d750 |
767 | # print "s=$scale a=",$params[1]||'undef'," p=",$params[2]||'undef'," f=$fallback\n"; |
0716bf9b |
768 | my $lx = $x->{_m}->length(); my $ly = $y->{_m}->length(); |
58cde26e |
769 | $scale = $lx if $lx > $scale; |
58cde26e |
770 | $scale = $ly if $ly > $scale; |
ee15d750 |
771 | # print "scale $scale $lx $ly\n"; |
0716bf9b |
772 | my $diff = $ly - $lx; |
773 | $scale += $diff if $diff > 0; # if lx << ly, but not if ly << lx! |
a0d0e21e |
774 | |
58cde26e |
775 | return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero(); |
776 | |
777 | $x->{sign} = $x->{sign} ne $y->sign() ? '-' : '+'; |
a0d0e21e |
778 | |
58cde26e |
779 | # check for / +-1 ( +/- 1E0) |
780 | if ($y->is_one()) |
781 | { |
ee15d750 |
782 | return wantarray ? ($x,$self->bzero()) : $x; |
a0d0e21e |
783 | } |
a5f75d66 |
784 | |
ee15d750 |
785 | # calculate the result to $scale digits and then round it |
58cde26e |
786 | # a * 10 ** b / c * 10 ** d => a/c * 10 ** (b-d) |
ee15d750 |
787 | #$scale = 82; |
58cde26e |
788 | #print "self: $self x: $x ref(x) ", ref($x)," m: $x->{_m}\n"; |
58cde26e |
789 | $x->{_m}->blsft($scale,10); |
0716bf9b |
790 | #print "m: $x->{_m} $y->{_m}\n"; |
58cde26e |
791 | $x->{_m}->bdiv( $y->{_m} ); # a/c |
792 | #print "m: $x->{_m}\n"; |
ee15d750 |
793 | #print "e: $x->{_e} $y->{_e} ",$scale,"\n"; |
58cde26e |
794 | $x->{_e}->bsub($y->{_e}); # b-d |
795 | #print "e: $x->{_e}\n"; |
796 | $x->{_e}->bsub($scale); # correct for 10**scale |
0716bf9b |
797 | #print "after div: m: $x->{_m} e: $x->{_e}\n"; |
798 | $x->bnorm(); # remove trailing 0's |
ee15d750 |
799 | #print "after norm: m: $x->{_m} e: $x->{_e}\n"; |
800 | |
801 | # shortcut to not run trough _find_round_parameters again |
802 | if (defined $params[1]) |
803 | { |
804 | $x->bround($params[1],undef,$params[3]); # then round accordingly |
805 | } |
806 | else |
807 | { |
808 | $x->bfround($params[2],$params[3]); # then round accordingly |
809 | } |
574bacfe |
810 | if ($fallback) |
811 | { |
812 | # clear a/p after round, since user did not request it |
ee15d750 |
813 | $x->{_a} = undef; $x->{_p} = undef; |
574bacfe |
814 | } |
0716bf9b |
815 | |
58cde26e |
816 | if (wantarray) |
817 | { |
818 | my $rem = $x->copy(); |
ee15d750 |
819 | $rem->bmod($y,$params[1],$params[2],$params[3]); |
574bacfe |
820 | if ($fallback) |
821 | { |
822 | # clear a/p after round, since user did not request it |
ee15d750 |
823 | $rem->{_a} = undef; $rem->{_p} = undef; |
574bacfe |
824 | } |
0716bf9b |
825 | return ($x,$rem); |
58cde26e |
826 | } |
827 | return $x; |
828 | } |
a0d0e21e |
829 | |
58cde26e |
830 | sub bmod |
831 | { |
832 | # (dividend: BFLOAT or num_str, divisor: BFLOAT or num_str) return reminder |
833 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
a0d0e21e |
834 | |
abcfbf51 |
835 | return $x->bnan() if ($x->is_nan() || $y->is_nan() || $y->is_zero()); |
58cde26e |
836 | return $x->bzero() if $y->is_one(); |
837 | |
838 | # XXX tels: not done yet |
839 | return $x->round($a,$p,$r,$y); |
840 | } |
841 | |
842 | sub bsqrt |
843 | { |
0716bf9b |
844 | # calculate square root; this should probably |
845 | # use a different test to see whether the accuracy we want is... |
ee15d750 |
846 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e |
847 | |
0716bf9b |
848 | return $x->bnan() if $x->{sign} eq 'NaN' || $x->{sign} =~ /^-/; # <0, NaN |
849 | return $x if $x->{sign} eq '+inf'; # +inf |
58cde26e |
850 | return $x if $x->is_zero() || $x == 1; |
851 | |
ee15d750 |
852 | # we need to limit the accuracy to protect against overflow (ignore $p) |
853 | my ($scale) = $x->_scale_a($self->accuracy(),$self->round_mode,$a,$r); |
574bacfe |
854 | my $fallback = 0; |
0716bf9b |
855 | if (!defined $scale) |
856 | { |
857 | # simulate old behaviour |
ee15d750 |
858 | $scale = $self->div_scale()+1; # one more for proper riund |
859 | $a = $self->div_scale(); # and round to it |
860 | $fallback = 1; # to clear a/p afterwards |
0716bf9b |
861 | } |
862 | my $lx = $x->{_m}->length(); |
863 | $scale = $lx if $scale < $lx; |
58cde26e |
864 | my $e = Math::BigFloat->new("1E-$scale"); # make test variable |
865 | return $x->bnan() if $e->sign() eq 'NaN'; |
866 | |
58cde26e |
867 | # start with some reasonable guess |
0716bf9b |
868 | #$x *= 10 ** ($len - $org->{_e}); $x /= 2; # !?!? |
574bacfe |
869 | $lx = $lx+$x->{_e}; |
0716bf9b |
870 | $lx = 1 if $lx < 1; |
871 | my $gs = Math::BigFloat->new('1'. ('0' x $lx)); |
872 | |
ee15d750 |
873 | # print "first guess: $gs (x $x) scale $scale\n"; |
58cde26e |
874 | |
875 | my $diff = $e; |
876 | my $y = $x->copy(); |
877 | my $two = Math::BigFloat->new(2); |
ee15d750 |
878 | # promote BigInts and it's subclasses (except when already a BigFloat) |
879 | $y = $self->new($y) unless $y->isa('Math::BigFloat'); |
880 | # old, broken way |
881 | # $x = Math::BigFloat->new($x) if ref($x) ne $class; # promote BigInts |
882 | my $rem; |
58cde26e |
883 | # $scale = 2; |
884 | while ($diff >= $e) |
885 | { |
58cde26e |
886 | return $x->bnan() if $gs->is_zero(); |
ee15d750 |
887 | $rem = $y->copy(); $rem->bdiv($gs,$scale); |
888 | #print "y $y gs $gs ($gs->{_a}) rem (y/gs)\n $rem\n"; |
889 | $x = ($rem + $gs); |
890 | #print "x $x rem $rem gs $gs gsa: $gs->{_a}\n"; |
891 | $x->bdiv($two,$scale); |
892 | #print "x $x (/2)\n"; |
58cde26e |
893 | $diff = $x->copy()->bsub($gs)->babs(); |
58cde26e |
894 | $gs = $x->copy(); |
a0d0e21e |
895 | } |
ee15d750 |
896 | # print "before $x $x->{_a} ",$a||'a undef'," ",$p||'p undef',"\n"; |
0716bf9b |
897 | $x->round($a,$p,$r); |
ee15d750 |
898 | # print "after $x $x->{_a} ",$a||'a undef'," ",$p||'p undef',"\n"; |
574bacfe |
899 | if ($fallback) |
900 | { |
901 | # clear a/p after round, since user did not request it |
ee15d750 |
902 | $x->{_a} = undef; $x->{_p} = undef; |
574bacfe |
903 | } |
904 | $x; |
58cde26e |
905 | } |
906 | |
907 | sub bpow |
908 | { |
909 | # (BFLOAT or num_str, BFLOAT or num_str) return BFLOAT |
910 | # compute power of two numbers, second arg is used as integer |
911 | # modifies first argument |
912 | |
913 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
914 | |
0716bf9b |
915 | return $x if $x->{sign} =~ /^[+-]inf$/; |
58cde26e |
916 | return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan; |
574bacfe |
917 | return $x->bone() if $y->is_zero(); |
58cde26e |
918 | return $x if $x->is_one() || $y->is_one(); |
ee15d750 |
919 | my $y1 = $y->as_number(); # make bigint (trunc) |
58cde26e |
920 | if ($x == -1) |
921 | { |
922 | # if $x == -1 and odd/even y => +1/-1 because +-1 ^ (+-1) => +-1 |
0716bf9b |
923 | return $y1->is_odd() ? $x : $x->babs(1); |
288d023a |
924 | } |
58cde26e |
925 | return $x if $x->is_zero() && $y->{sign} eq '+'; # 0**y => 0 (if not y <= 0) |
574bacfe |
926 | # 0 ** -y => 1 / (0 ** y) => / 0! (1 / 0 => +inf) |
927 | return $x->binf() if $x->is_zero() && $y->{sign} eq '-'; |
58cde26e |
928 | |
929 | # calculate $x->{_m} ** $y and $x->{_e} * $y separately (faster) |
930 | $y1->babs(); |
931 | $x->{_m}->bpow($y1); |
932 | $x->{_e}->bmul($y1); |
933 | $x->{sign} = $nan if $x->{_m}->{sign} eq $nan || $x->{_e}->{sign} eq $nan; |
934 | $x->bnorm(); |
935 | if ($y->{sign} eq '-') |
936 | { |
937 | # modify $x in place! |
0716bf9b |
938 | my $z = $x->copy(); $x->bzero()->binc(); |
58cde26e |
939 | return $x->bdiv($z,$a,$p,$r); # round in one go (might ignore y's A!) |
a0d0e21e |
940 | } |
58cde26e |
941 | return $x->round($a,$p,$r,$y); |
942 | } |
943 | |
944 | ############################################################################### |
945 | # rounding functions |
946 | |
947 | sub bfround |
948 | { |
949 | # precision: round to the $Nth digit left (+$n) or right (-$n) from the '.' |
950 | # $n == 0 means round to integer |
951 | # expects and returns normalized numbers! |
ee15d750 |
952 | my $x = shift; my $self = ref($x) || $x; $x = $self->new(shift) if !ref($x); |
a0d0e21e |
953 | |
58cde26e |
954 | return $x if $x->modify('bfround'); |
955 | |
ee15d750 |
956 | my ($scale,$mode) = $x->_scale_p($self->precision(),$self->round_mode(),@_); |
58cde26e |
957 | return $x if !defined $scale; # no-op |
958 | |
574bacfe |
959 | # never round a 0, +-inf, NaN |
960 | return $x if $x->{sign} !~ /^[+-]$/ || $x->is_zero(); |
58cde26e |
961 | # print "MBF bfround $x to scale $scale mode $mode\n"; |
58cde26e |
962 | |
ee15d750 |
963 | # don't round if x already has lower precision |
964 | return $x if (defined $x->{_p} && $x->{_p} < 0 && $scale < $x->{_p}); |
965 | |
966 | $x->{_p} = $scale; # remember round in any case |
967 | $x->{_a} = undef; # and clear A |
58cde26e |
968 | if ($scale < 0) |
969 | { |
970 | # print "bfround scale $scale e $x->{_e}\n"; |
971 | # round right from the '.' |
972 | return $x if $x->{_e} >= 0; # nothing to round |
973 | $scale = -$scale; # positive for simplicity |
974 | my $len = $x->{_m}->length(); # length of mantissa |
975 | my $dad = -$x->{_e}; # digits after dot |
976 | my $zad = 0; # zeros after dot |
977 | $zad = -$len-$x->{_e} if ($x->{_e} < -$len);# for 0.00..00xxx style |
ee15d750 |
978 | #print "scale $scale dad $dad zad $zad len $len\n"; |
58cde26e |
979 | |
980 | # number bsstr len zad dad |
981 | # 0.123 123e-3 3 0 3 |
982 | # 0.0123 123e-4 3 1 4 |
983 | # 0.001 1e-3 1 2 3 |
984 | # 1.23 123e-2 3 0 2 |
985 | # 1.2345 12345e-4 5 0 4 |
986 | |
987 | # do not round after/right of the $dad |
988 | return $x if $scale > $dad; # 0.123, scale >= 3 => exit |
989 | |
ee15d750 |
990 | # round to zero if rounding inside the $zad, but not for last zero like: |
991 | # 0.0065, scale -2, round last '0' with following '65' (scale == zad case) |
992 | return $x->bzero() if $scale < $zad; |
993 | if ($scale == $zad) # for 0.006, scale -3 and trunc |
58cde26e |
994 | { |
ee15d750 |
995 | $scale = -$len-1; |
58cde26e |
996 | } |
997 | else |
998 | { |
999 | # adjust round-point to be inside mantissa |
1000 | if ($zad != 0) |
1001 | { |
1002 | $scale = $scale-$zad; |
1003 | } |
1004 | else |
1005 | { |
1006 | my $dbd = $len - $dad; $dbd = 0 if $dbd < 0; # digits before dot |
1007 | $scale = $dbd+$scale; |
1008 | } |
1009 | } |
1010 | # print "round to $x->{_m} to $scale\n"; |
a0d0e21e |
1011 | } |
58cde26e |
1012 | else |
1013 | { |
1014 | # 123 => 100 means length(123) = 3 - $scale (2) => 1 |
a5f75d66 |
1015 | |
58cde26e |
1016 | # calculate digits before dot |
1017 | my $dbt = $x->{_m}->length(); $dbt += $x->{_e} if $x->{_e}->sign() eq '-'; |
ee15d750 |
1018 | # if not enough digits before dot, round to zero |
1019 | return $x->bzero() if ($scale > $dbt) && ($dbt < 0); |
1020 | # scale always >= 0 here |
1021 | if ($dbt == 0) |
58cde26e |
1022 | { |
1023 | # 0.49->bfround(1): scale == 1, dbt == 0: => 0.0 |
1024 | # 0.51->bfround(0): scale == 0, dbt == 0: => 1.0 |
1025 | # 0.5->bfround(0): scale == 0, dbt == 0: => 0 |
1026 | # 0.05->bfround(0): scale == 0, dbt == 0: => 0 |
1027 | # print "$scale $dbt $x->{_m}\n"; |
1028 | $scale = -$x->{_m}->length(); |
1029 | } |
1030 | elsif ($dbt > 0) |
1031 | { |
1032 | # correct by subtracting scale |
1033 | $scale = $dbt - $scale; |
1034 | } |
1035 | else |
1036 | { |
1037 | $scale = $x->{_m}->length() - $scale; |
1038 | } |
a0d0e21e |
1039 | } |
574bacfe |
1040 | # print "using $scale for $x->{_m} with '$mode'\n"; |
1041 | # pass sign to bround for rounding modes '+inf' and '-inf' |
58cde26e |
1042 | $x->{_m}->{sign} = $x->{sign}; |
1043 | $x->{_m}->bround($scale,$mode); |
1044 | $x->{_m}->{sign} = '+'; # fix sign back |
1045 | $x->bnorm(); |
1046 | } |
1047 | |
1048 | sub bround |
1049 | { |
1050 | # accuracy: preserve $N digits, and overwrite the rest with 0's |
ee15d750 |
1051 | my $x = shift; my $self = ref($x) || $x; $x = $self->new(shift) if !ref($x); |
1052 | |
1053 | die ('bround() needs positive accuracy') if ($_[0] || 0) < 0; |
58cde26e |
1054 | |
ee15d750 |
1055 | my ($scale,$mode) = $x->_scale_a($self->accuracy(),$self->round_mode(),@_); |
1056 | return $x if !defined $scale; # no-op |
1057 | |
58cde26e |
1058 | return $x if $x->modify('bround'); |
ee15d750 |
1059 | |
1060 | # scale is now either $x->{_a}, $accuracy, or the user parameter |
1061 | # test whether $x already has lower accuracy, do nothing in this case |
1062 | # but do round if the accuracy is the same, since a math operation might |
1063 | # want to round a number with A=5 to 5 digits afterwards again |
1064 | return $x if defined $_[0] && defined $x->{_a} && $x->{_a} < $_[0]; |
58cde26e |
1065 | |
1066 | # print "bround $scale $mode\n"; |
1067 | # 0 => return all digits, scale < 0 makes no sense |
1068 | return $x if ($scale <= 0); |
574bacfe |
1069 | # never round a 0, +-inf, NaN |
1070 | return $x if $x->{sign} !~ /^[+-]$/ || $x->is_zero(); |
58cde26e |
1071 | |
1072 | # if $e longer than $m, we have 0.0000xxxyyy style number, and must |
1073 | # subtract the delta from scale, to simulate keeping the zeros |
1074 | # -5 +5 => 1; -10 +5 => -4 |
1075 | my $delta = $x->{_e} + $x->{_m}->length() + 1; |
58cde26e |
1076 | |
1077 | # if we should keep more digits than the mantissa has, do nothing |
1078 | return $x if $x->{_m}->length() <= $scale; |
f216259d |
1079 | |
58cde26e |
1080 | # pass sign to bround for '+inf' and '-inf' rounding modes |
1081 | $x->{_m}->{sign} = $x->{sign}; |
1082 | $x->{_m}->bround($scale,$mode); # round mantissa |
1083 | $x->{_m}->{sign} = '+'; # fix sign back |
ee15d750 |
1084 | $x->{_a} = $scale; # remember rounding |
1085 | $x->{_p} = undef; # and clear P |
574bacfe |
1086 | $x->bnorm(); # del trailing zeros gen. by bround() |
58cde26e |
1087 | } |
1088 | |
1089 | sub bfloor |
1090 | { |
1091 | # return integer less or equal then $x |
ee15d750 |
1092 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e |
1093 | |
1094 | return $x if $x->modify('bfloor'); |
1095 | |
1096 | return $x if $x->{sign} !~ /^[+-]$/; # nan, +inf, -inf |
1097 | |
1098 | # if $x has digits after dot |
1099 | if ($x->{_e}->{sign} eq '-') |
1100 | { |
1101 | $x->{_m}->brsft(-$x->{_e},10); |
1102 | $x->{_e}->bzero(); |
1103 | $x-- if $x->{sign} eq '-'; |
f216259d |
1104 | } |
58cde26e |
1105 | return $x->round($a,$p,$r); |
1106 | } |
288d023a |
1107 | |
58cde26e |
1108 | sub bceil |
1109 | { |
1110 | # return integer greater or equal then $x |
ee15d750 |
1111 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e |
1112 | |
1113 | return $x if $x->modify('bceil'); |
1114 | return $x if $x->{sign} !~ /^[+-]$/; # nan, +inf, -inf |
1115 | |
1116 | # if $x has digits after dot |
1117 | if ($x->{_e}->{sign} eq '-') |
1118 | { |
1119 | $x->{_m}->brsft(-$x->{_e},10); |
1120 | $x->{_e}->bzero(); |
1121 | $x++ if $x->{sign} eq '+'; |
a0d0e21e |
1122 | } |
58cde26e |
1123 | return $x->round($a,$p,$r); |
1124 | } |
1125 | |
1126 | ############################################################################### |
a5f75d66 |
1127 | |
58cde26e |
1128 | sub DESTROY |
1129 | { |
ee15d750 |
1130 | # going through AUTOLOAD for every DESTROY is costly, so avoid it by empty sub |
58cde26e |
1131 | } |
1132 | |
1133 | sub AUTOLOAD |
1134 | { |
1135 | # make fxxx and bxxx work |
1136 | # my $self = $_[0]; |
1137 | my $name = $AUTOLOAD; |
1138 | |
1139 | $name =~ s/.*:://; # split package |
1140 | #print "$name\n"; |
ee15d750 |
1141 | no strict 'refs'; |
1142 | if (!method_alias($name)) |
58cde26e |
1143 | { |
ee15d750 |
1144 | if (!defined $name) |
1145 | { |
1146 | # delayed load of Carp and avoid recursion |
1147 | require Carp; |
1148 | Carp::croak ("Can't call a method without name"); |
1149 | } |
1150 | # try one level up, but subst. bxxx() for fxxx() since MBI only got bxxx() |
1151 | if (!method_hand_up($name)) |
1152 | { |
1153 | # delayed load of Carp and avoid recursion |
1154 | require Carp; |
1155 | Carp::croak ("Can't call $class\-\>$name, not a valid method"); |
1156 | } |
1157 | # try one level up, but subst. bxxx() for fxxx() since MBI only got bxxx() |
1158 | $name =~ s/^f/b/; |
1159 | return &{'Math::BigInt'."::$name"}(@_); |
a0d0e21e |
1160 | } |
58cde26e |
1161 | my $bname = $name; $bname =~ s/^f/b/; |
1162 | *{$class."\:\:$name"} = \&$bname; |
1163 | &$bname; # uses @_ |
1164 | } |
1165 | |
1166 | sub exponent |
1167 | { |
1168 | # return a copy of the exponent |
ee15d750 |
1169 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
1170 | |
ee15d750 |
1171 | if ($x->{sign} !~ /^[+-]$/) |
1172 | { |
1173 | my $s = $x->{sign}; $s =~ s/^[+-]//; |
1174 | return $self->new($s); # -inf, +inf => +inf |
1175 | } |
1176 | return $x->{_e}->copy(); |
58cde26e |
1177 | } |
1178 | |
1179 | sub mantissa |
1180 | { |
1181 | # return a copy of the mantissa |
ee15d750 |
1182 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
1183 | |
ee15d750 |
1184 | if ($x->{sign} !~ /^[+-]$/) |
1185 | { |
1186 | my $s = $x->{sign}; $s =~ s/^[+]//; |
1187 | return $self->new($s); # -inf, +inf => +inf |
1188 | } |
1189 | my $m = $x->{_m}->copy(); # faster than going via bstr() |
1190 | $m->bneg() if $x->{sign} eq '-'; |
58cde26e |
1191 | |
1192 | return $m; |
1193 | } |
1194 | |
1195 | sub parts |
1196 | { |
1197 | # return a copy of both the exponent and the mantissa |
ee15d750 |
1198 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
1199 | |
ee15d750 |
1200 | if ($x->{sign} !~ /^[+-]$/) |
1201 | { |
1202 | my $s = $x->{sign}; $s =~ s/^[+]//; my $se = $s; $se =~ s/^[-]//; |
1203 | return ($self->new($s),$self->new($se)); # +inf => inf and -inf,+inf => inf |
1204 | } |
1205 | my $m = $x->{_m}->copy(); # faster than going via bstr() |
1206 | $m->bneg() if $x->{sign} eq '-'; |
1207 | return ($m,$x->{_e}->copy()); |
58cde26e |
1208 | } |
1209 | |
1210 | ############################################################################## |
1211 | # private stuff (internal use only) |
1212 | |
58cde26e |
1213 | sub import |
1214 | { |
1215 | my $self = shift; |
58cde26e |
1216 | for ( my $i = 0; $i < @_ ; $i++ ) |
1217 | { |
1218 | if ( $_[$i] eq ':constant' ) |
1219 | { |
1220 | # this rest causes overlord er load to step in |
1221 | # print "overload @_\n"; |
1222 | overload::constant float => sub { $self->new(shift); }; |
1223 | splice @_, $i, 1; last; |
1224 | } |
1225 | } |
1226 | # any non :constant stuff is handled by our parent, Exporter |
1227 | # even if @_ is empty, to give it a chance |
abcfbf51 |
1228 | $self->SUPER::import(@_); # for subclasses |
1229 | $self->export_to_level(1,$self,@_); # need this, too |
58cde26e |
1230 | } |
1231 | |
1232 | sub bnorm |
1233 | { |
1234 | # adjust m and e so that m is smallest possible |
1235 | # round number according to accuracy and precision settings |
ee15d750 |
1236 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
1237 | |
0716bf9b |
1238 | return $x if $x->{sign} !~ /^[+-]$/; # inf, nan etc |
58cde26e |
1239 | |
1240 | my $zeros = $x->{_m}->_trailing_zeros(); # correct for trailing zeros |
1241 | if ($zeros != 0) |
1242 | { |
1243 | $x->{_m}->brsft($zeros,10); $x->{_e} += $zeros; |
1244 | } |
ee15d750 |
1245 | # for something like 0Ey, set y to 1, and -0 => +0 |
1246 | $x->{sign} = '+', $x->{_e}->bone() if $x->{_m}->is_zero(); |
1247 | # this is to prevent automatically rounding when MBI's globals are set |
0716bf9b |
1248 | $x->{_m}->{_f} = MB_NEVER_ROUND; |
1249 | $x->{_e}->{_f} = MB_NEVER_ROUND; |
ee15d750 |
1250 | # 'forget' that mantissa was rounded via MBI::bround() in MBF's bfround() |
1251 | $x->{_m}->{_a} = undef; $x->{_e}->{_a} = undef; |
1252 | $x->{_m}->{_p} = undef; $x->{_e}->{_p} = undef; |
0716bf9b |
1253 | return $x; # MBI bnorm is no-op |
58cde26e |
1254 | } |
1255 | |
1256 | ############################################################################## |
1257 | # internal calculation routines |
1258 | |
1259 | sub as_number |
1260 | { |
1261 | # return a bigint representation of this BigFloat number |
ee15d750 |
1262 | my $x = shift; my $class = ref($x) || $x; $x = $class->new(shift) unless ref($x); |
58cde26e |
1263 | |
1264 | my $z; |
1265 | if ($x->{_e}->is_zero()) |
1266 | { |
1267 | $z = $x->{_m}->copy(); |
1268 | $z->{sign} = $x->{sign}; |
1269 | return $z; |
1270 | } |
0716bf9b |
1271 | $z = $x->{_m}->copy(); |
58cde26e |
1272 | if ($x->{_e} < 0) |
1273 | { |
0716bf9b |
1274 | $z->brsft(-$x->{_e},10); |
1275 | } |
1276 | else |
1277 | { |
1278 | $z->blsft($x->{_e},10); |
58cde26e |
1279 | } |
58cde26e |
1280 | $z->{sign} = $x->{sign}; |
1281 | return $z; |
1282 | } |
1283 | |
1284 | sub length |
1285 | { |
ee15d750 |
1286 | my $x = shift; |
1287 | my $class = ref($x) || $x; |
1288 | $x = $class->new(shift) unless ref($x); |
58cde26e |
1289 | |
ee15d750 |
1290 | return 1 if $x->{_m}->is_zero(); |
58cde26e |
1291 | my $len = $x->{_m}->length(); |
1292 | $len += $x->{_e} if $x->{_e}->sign() eq '+'; |
1293 | if (wantarray()) |
1294 | { |
1295 | my $t = Math::BigInt::bzero(); |
1296 | $t = $x->{_e}->copy()->babs() if $x->{_e}->sign() eq '-'; |
1297 | return ($len,$t); |
1298 | } |
1299 | return $len; |
1300 | } |
a0d0e21e |
1301 | |
1302 | 1; |
a5f75d66 |
1303 | __END__ |
1304 | |
1305 | =head1 NAME |
1306 | |
58cde26e |
1307 | Math::BigFloat - Arbitrary size floating point math package |
a5f75d66 |
1308 | |
1309 | =head1 SYNOPSIS |
1310 | |
a2008d6d |
1311 | use Math::BigFloat; |
58cde26e |
1312 | |
1313 | # Number creation |
1314 | $x = Math::BigInt->new($str); # defaults to 0 |
1315 | $nan = Math::BigInt->bnan(); # create a NotANumber |
1316 | $zero = Math::BigInt->bzero();# create a "+0" |
1317 | |
1318 | # Testing |
1319 | $x->is_zero(); # return whether arg is zero or not |
0716bf9b |
1320 | $x->is_nan(); # return whether arg is NaN or not |
1321 | $x->is_one(); # true if arg is +1 |
1322 | $x->is_one('-'); # true if arg is -1 |
1323 | $x->is_odd(); # true if odd, false for even |
1324 | $x->is_even(); # true if even, false for odd |
1325 | $x->is_positive(); # true if >= 0 |
1326 | $x->is_negative(); # true if < 0 |
1327 | $x->is_inf(sign) # true if +inf or -inf (sign default '+') |
58cde26e |
1328 | $x->bcmp($y); # compare numbers (undef,<0,=0,>0) |
1329 | $x->bacmp($y); # compare absolutely (undef,<0,=0,>0) |
1330 | $x->sign(); # return the sign, either +,- or NaN |
1331 | |
1332 | # The following all modify their first argument: |
1333 | |
1334 | # set |
1335 | $x->bzero(); # set $i to 0 |
1336 | $x->bnan(); # set $i to NaN |
1337 | |
1338 | $x->bneg(); # negation |
1339 | $x->babs(); # absolute value |
1340 | $x->bnorm(); # normalize (no-op) |
1341 | $x->bnot(); # two's complement (bit wise not) |
1342 | $x->binc(); # increment x by 1 |
1343 | $x->bdec(); # decrement x by 1 |
1344 | |
1345 | $x->badd($y); # addition (add $y to $x) |
1346 | $x->bsub($y); # subtraction (subtract $y from $x) |
1347 | $x->bmul($y); # multiplication (multiply $x by $y) |
1348 | $x->bdiv($y); # divide, set $i to quotient |
1349 | # return (quo,rem) or quo if scalar |
1350 | |
1351 | $x->bmod($y); # modulus |
1352 | $x->bpow($y); # power of arguments (a**b) |
1353 | $x->blsft($y); # left shift |
1354 | $x->brsft($y); # right shift |
1355 | # return (quo,rem) or quo if scalar |
1356 | |
1357 | $x->band($y); # bit-wise and |
1358 | $x->bior($y); # bit-wise inclusive or |
1359 | $x->bxor($y); # bit-wise exclusive or |
1360 | $x->bnot(); # bit-wise not (two's complement) |
1361 | |
1362 | $x->bround($N); # accuracy: preserver $N digits |
1363 | $x->bfround($N); # precision: round to the $Nth digit |
1364 | |
1365 | # The following do not modify their arguments: |
1366 | |
1367 | bgcd(@values); # greatest common divisor |
1368 | blcm(@values); # lowest common multiplicator |
1369 | |
1370 | $x->bstr(); # return string |
1371 | $x->bsstr(); # return string in scientific notation |
1372 | |
1373 | $x->exponent(); # return exponent as BigInt |
1374 | $x->mantissa(); # return mantissa as BigInt |
1375 | $x->parts(); # return (mantissa,exponent) as BigInt |
1376 | |
1377 | $x->length(); # number of digits (w/o sign and '.') |
1378 | ($l,$f) = $x->length(); # number of digits, and length of fraction |
a5f75d66 |
1379 | |
1380 | =head1 DESCRIPTION |
1381 | |
58cde26e |
1382 | All operators (inlcuding basic math operations) are overloaded if you |
1383 | declare your big floating point numbers as |
a5f75d66 |
1384 | |
58cde26e |
1385 | $i = new Math::BigFloat '12_3.456_789_123_456_789E-2'; |
1386 | |
1387 | Operations with overloaded operators preserve the arguments, which is |
1388 | exactly what you expect. |
1389 | |
1390 | =head2 Canonical notation |
1391 | |
1392 | Input to these routines are either BigFloat objects, or strings of the |
1393 | following four forms: |
a5f75d66 |
1394 | |
1395 | =over 2 |
1396 | |
58cde26e |
1397 | =item * |
1398 | |
1399 | C</^[+-]\d+$/> |
a5f75d66 |
1400 | |
58cde26e |
1401 | =item * |
a5f75d66 |
1402 | |
58cde26e |
1403 | C</^[+-]\d+\.\d*$/> |
a5f75d66 |
1404 | |
58cde26e |
1405 | =item * |
a5f75d66 |
1406 | |
58cde26e |
1407 | C</^[+-]\d+E[+-]?\d+$/> |
a5f75d66 |
1408 | |
58cde26e |
1409 | =item * |
a5f75d66 |
1410 | |
58cde26e |
1411 | C</^[+-]\d*\.\d+E[+-]?\d+$/> |
5d7098d5 |
1412 | |
58cde26e |
1413 | =back |
1414 | |
1415 | all with optional leading and trailing zeros and/or spaces. Additonally, |
1416 | numbers are allowed to have an underscore between any two digits. |
1417 | |
1418 | Empty strings as well as other illegal numbers results in 'NaN'. |
1419 | |
1420 | bnorm() on a BigFloat object is now effectively a no-op, since the numbers |
1421 | are always stored in normalized form. On a string, it creates a BigFloat |
1422 | object. |
1423 | |
1424 | =head2 Output |
1425 | |
1426 | Output values are BigFloat objects (normalized), except for bstr() and bsstr(). |
1427 | |
1428 | The string output will always have leading and trailing zeros stripped and drop |
1429 | a plus sign. C<bstr()> will give you always the form with a decimal point, |
1430 | while C<bsstr()> (for scientific) gives you the scientific notation. |
1431 | |
1432 | Input bstr() bsstr() |
1433 | '-0' '0' '0E1' |
1434 | ' -123 123 123' '-123123123' '-123123123E0' |
1435 | '00.0123' '0.0123' '123E-4' |
1436 | '123.45E-2' '1.2345' '12345E-4' |
1437 | '10E+3' '10000' '1E4' |
1438 | |
1439 | Some routines (C<is_odd()>, C<is_even()>, C<is_zero()>, C<is_one()>, |
1440 | C<is_nan()>) return true or false, while others (C<bcmp()>, C<bacmp()>) |
1441 | return either undef, <0, 0 or >0 and are suited for sort. |
1442 | |
1443 | Actual math is done by using BigInts to represent the mantissa and exponent. |
1444 | The sign C</^[+-]$/> is stored separately. The string 'NaN' is used to |
1445 | represent the result when input arguments are not numbers, as well as |
1446 | the result of dividing by zero. |
1447 | |
1448 | =head2 C<mantissa()>, C<exponent()> and C<parts()> |
1449 | |
1450 | C<mantissa()> and C<exponent()> return the said parts of the BigFloat |
1451 | as BigInts such that: |
1452 | |
1453 | $m = $x->mantissa(); |
1454 | $e = $x->exponent(); |
1455 | $y = $m * ( 10 ** $e ); |
1456 | print "ok\n" if $x == $y; |
1457 | |
1458 | C<< ($m,$e) = $x->parts(); >> is just a shortcut giving you both of them. |
1459 | |
1460 | A zero is represented and returned as C<0E1>, B<not> C<0E0> (after Knuth). |
1461 | |
1462 | Currently the mantissa is reduced as much as possible, favouring higher |
1463 | exponents over lower ones (e.g. returning 1e7 instead of 10e6 or 10000000e0). |
1464 | This might change in the future, so do not depend on it. |
1465 | |
1466 | =head2 Accuracy vs. Precision |
1467 | |
1468 | See also: L<Rounding|Rounding>. |
1469 | |
027dc388 |
1470 | Math::BigFloat supports both precision and accuracy. For a full documentation, |
1471 | examples and tips on these topics please see the large section in |
1472 | L<Math::BigInt>. |
5d7098d5 |
1473 | |
58cde26e |
1474 | Since things like sqrt(2) or 1/3 must presented with a limited precision lest |
1475 | a operation consumes all resources, each operation produces no more than |
1476 | C<Math::BigFloat::precision()> digits. |
1477 | |
1478 | In case the result of one operation has more precision than specified, |
1479 | it is rounded. The rounding mode taken is either the default mode, or the one |
1480 | supplied to the operation after the I<scale>: |
1481 | |
1482 | $x = Math::BigFloat->new(2); |
1483 | Math::BigFloat::precision(5); # 5 digits max |
1484 | $y = $x->copy()->bdiv(3); # will give 0.66666 |
1485 | $y = $x->copy()->bdiv(3,6); # will give 0.666666 |
1486 | $y = $x->copy()->bdiv(3,6,'odd'); # will give 0.666667 |
1487 | Math::BigFloat::round_mode('zero'); |
1488 | $y = $x->copy()->bdiv(3,6); # will give 0.666666 |
1489 | |
1490 | =head2 Rounding |
1491 | |
1492 | =over 2 |
1493 | |
5dc6f178 |
1494 | =item ffround ( +$scale ) |
58cde26e |
1495 | |
0716bf9b |
1496 | Rounds to the $scale'th place left from the '.', counting from the dot. |
1497 | The first digit is numbered 1. |
58cde26e |
1498 | |
5dc6f178 |
1499 | =item ffround ( -$scale ) |
58cde26e |
1500 | |
0716bf9b |
1501 | Rounds to the $scale'th place right from the '.', counting from the dot. |
58cde26e |
1502 | |
5dc6f178 |
1503 | =item ffround ( 0 ) |
1504 | |
0716bf9b |
1505 | Rounds to an integer. |
5dc6f178 |
1506 | |
1507 | =item fround ( +$scale ) |
1508 | |
0716bf9b |
1509 | Preserves accuracy to $scale digits from the left (aka significant digits) |
1510 | and pads the rest with zeros. If the number is between 1 and -1, the |
1511 | significant digits count from the first non-zero after the '.' |
5dc6f178 |
1512 | |
1513 | =item fround ( -$scale ) and fround ( 0 ) |
1514 | |
0716bf9b |
1515 | These are effetively no-ops. |
5d7098d5 |
1516 | |
a5f75d66 |
1517 | =back |
1518 | |
0716bf9b |
1519 | All rounding functions take as a second parameter a rounding mode from one of |
1520 | the following: 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'. |
58cde26e |
1521 | |
1522 | The default rounding mode is 'even'. By using |
ee15d750 |
1523 | C<< Math::BigFloat::round_mode($round_mode); >> you can get and set the default |
1524 | mode for subsequent rounding. The usage of C<$Math::BigFloat::$round_mode> is |
0716bf9b |
1525 | no longer supported. |
b22b3e31 |
1526 | The second parameter to the round functions then overrides the default |
0716bf9b |
1527 | temporarily. |
58cde26e |
1528 | |
1529 | The C<< as_number() >> function returns a BigInt from a Math::BigFloat. It uses |
1530 | 'trunc' as rounding mode to make it equivalent to: |
1531 | |
1532 | $x = 2.5; |
1533 | $y = int($x) + 2; |
1534 | |
1535 | You can override this by passing the desired rounding mode as parameter to |
1536 | C<as_number()>: |
1537 | |
1538 | $x = Math::BigFloat->new(2.5); |
1539 | $y = $x->as_number('odd'); # $y = 3 |
1540 | |
1541 | =head1 EXAMPLES |
1542 | |
58cde26e |
1543 | # not ready yet |
58cde26e |
1544 | |
1545 | =head1 Autocreating constants |
1546 | |
1547 | After C<use Math::BigFloat ':constant'> all the floating point constants |
1548 | in the given scope are converted to C<Math::BigFloat>. This conversion |
1549 | happens at compile time. |
1550 | |
1551 | In particular |
1552 | |
1553 | perl -MMath::BigFloat=:constant -e 'print 2E-100,"\n"' |
1554 | |
1555 | prints the value of C<2E-100>. Note that without conversion of |
1556 | constants the expression 2E-100 will be calculated as normal floating point |
1557 | number. |
1558 | |
a5f75d66 |
1559 | =head1 BUGS |
1560 | |
58cde26e |
1561 | =over 2 |
1562 | |
1563 | =item * |
1564 | |
1565 | The following does not work yet: |
1566 | |
1567 | $m = $x->mantissa(); |
1568 | $e = $x->exponent(); |
1569 | $y = $m * ( 10 ** $e ); |
1570 | print "ok\n" if $x == $y; |
1571 | |
1572 | =item * |
1573 | |
1574 | There is no fmod() function yet. |
1575 | |
1576 | =back |
1577 | |
1578 | =head1 CAVEAT |
1579 | |
1580 | =over 1 |
1581 | |
1582 | =item stringify, bstr() |
1583 | |
1584 | Both stringify and bstr() now drop the leading '+'. The old code would return |
1585 | '+1.23', the new returns '1.23'. See the documentation in L<Math::BigInt> for |
1586 | reasoning and details. |
1587 | |
1588 | =item bdiv |
1589 | |
1590 | The following will probably not do what you expect: |
1591 | |
1592 | print $c->bdiv(123.456),"\n"; |
1593 | |
1594 | It prints both quotient and reminder since print works in list context. Also, |
1595 | bdiv() will modify $c, so be carefull. You probably want to use |
1596 | |
1597 | print $c / 123.456,"\n"; |
1598 | print scalar $c->bdiv(123.456),"\n"; # or if you want to modify $c |
1599 | |
1600 | instead. |
1601 | |
1602 | =item Modifying and = |
1603 | |
1604 | Beware of: |
1605 | |
1606 | $x = Math::BigFloat->new(5); |
1607 | $y = $x; |
1608 | |
1609 | It will not do what you think, e.g. making a copy of $x. Instead it just makes |
1610 | a second reference to the B<same> object and stores it in $y. Thus anything |
1611 | that modifies $x will modify $y, and vice versa. |
1612 | |
1613 | $x->bmul(2); |
1614 | print "$x, $y\n"; # prints '10, 10' |
1615 | |
1616 | If you want a true copy of $x, use: |
1617 | |
1618 | $y = $x->copy(); |
1619 | |
1620 | See also the documentation in L<overload> regarding C<=>. |
1621 | |
1622 | =item bpow |
1623 | |
1624 | C<bpow()> now modifies the first argument, unlike the old code which left |
1625 | it alone and only returned the result. This is to be consistent with |
1626 | C<badd()> etc. The first will modify $x, the second one won't: |
1627 | |
1628 | print bpow($x,$i),"\n"; # modify $x |
1629 | print $x->bpow($i),"\n"; # ditto |
1630 | print $x ** $i,"\n"; # leave $x alone |
1631 | |
1632 | =back |
1633 | |
1634 | =head1 LICENSE |
a5f75d66 |
1635 | |
58cde26e |
1636 | This program is free software; you may redistribute it and/or modify it under |
1637 | the same terms as Perl itself. |
5d7098d5 |
1638 | |
58cde26e |
1639 | =head1 AUTHORS |
5d7098d5 |
1640 | |
58cde26e |
1641 | Mark Biggar, overloaded interface by Ilya Zakharevich. |
1642 | Completely rewritten by Tels http://bloodgate.com in 2001. |
a5f75d66 |
1643 | |
a5f75d66 |
1644 | =cut |