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 |
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9 | # _f: flags, used to signal MBI not to touch our private parts |
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10 | |
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11 | package Math::BigFloat; |
12 | |
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13 | $VERSION = '1.27'; |
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14 | require 5.005; |
15 | use Exporter; |
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16 | use Math::BigInt qw/objectify/; |
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17 | @ISA = qw( Exporter Math::BigInt); |
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18 | |
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19 | use strict; |
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20 | use vars qw/$AUTOLOAD $accuracy $precision $div_scale $round_mode $rnd_mode/; |
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21 | my $class = "Math::BigFloat"; |
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22 | |
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23 | use overload |
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24 | '<=>' => sub { $_[2] ? |
25 | ref($_[0])->bcmp($_[1],$_[0]) : |
26 | ref($_[0])->bcmp($_[0],$_[1])}, |
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27 | 'int' => sub { $_[0]->as_number() }, # 'trunc' to bigint |
a5f75d66 |
28 | ; |
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29 | |
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30 | ############################################################################## |
31 | # global constants, flags and accessory |
32 | |
33 | use constant MB_NEVER_ROUND => 0x0001; |
34 | |
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35 | # are NaNs ok? |
36 | my $NaNOK=1; |
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37 | # constant for easier life |
38 | my $nan = 'NaN'; |
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39 | |
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40 | # class constants, use Class->constant_name() to access |
41 | $round_mode = 'even'; # one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc' |
42 | $accuracy = undef; |
43 | $precision = undef; |
44 | $div_scale = 40; |
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45 | |
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46 | ############################################################################## |
47 | # the old code had $rnd_mode, so we need to support it, too |
48 | |
49 | $rnd_mode = 'even'; |
50 | sub TIESCALAR { my ($class) = @_; bless \$round_mode, $class; } |
51 | sub FETCH { return $round_mode; } |
52 | sub STORE { $rnd_mode = $_[0]->round_mode($_[1]); } |
53 | |
54 | BEGIN { tie $rnd_mode, 'Math::BigFloat'; } |
55 | |
56 | ############################################################################## |
57 | |
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58 | # in case we call SUPER::->foo() and this wants to call modify() |
59 | # sub modify () { 0; } |
60 | |
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61 | { |
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62 | # valid method aliases for AUTOLOAD |
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63 | my %methods = map { $_ => 1 } |
64 | qw / fadd fsub fmul fdiv fround ffround fsqrt fmod fstr fsstr fpow fnorm |
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65 | fint facmp fcmp fzero fnan finf finc fdec flog |
66 | fceil ffloor frsft flsft fone flog |
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67 | /; |
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68 | # valid method's that can be hand-ed up (for AUTOLOAD) |
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69 | my %hand_ups = map { $_ => 1 } |
70 | qw / is_nan is_inf is_negative is_positive |
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71 | accuracy precision div_scale round_mode fneg fabs babs fnot |
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72 | /; |
73 | |
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74 | sub method_alias { return exists $methods{$_[0]||''}; } |
75 | sub method_hand_up { return exists $hand_ups{$_[0]||''}; } |
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76 | } |
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77 | |
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78 | ############################################################################## |
79 | # constructors |
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80 | |
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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" |
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87 | |
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88 | my ($class,$wanted,@r) = @_; |
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89 | |
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90 | # avoid numify-calls by not using || on $wanted! |
91 | return $class->bzero() if !defined $wanted; # default to 0 |
92 | return $wanted->copy() if UNIVERSAL::isa($wanted,'Math::BigFloat'); |
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93 | |
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94 | my $self = {}; bless $self, $class; |
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95 | # shortcut for bigints and its subclasses |
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96 | if ((ref($wanted)) && (ref($wanted) ne $class)) |
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97 | { |
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98 | $self->{_m} = $wanted->as_number(); # get us a bigint copy |
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99 | $self->{_e} = Math::BigInt->bzero(); |
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100 | $self->{_m}->babs(); |
101 | $self->{sign} = $wanted->sign(); |
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102 | return $self->bnorm(); |
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103 | } |
104 | # got string |
105 | # handle '+inf', '-inf' first |
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106 | if ($wanted =~ /^[+-]?inf$/) |
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107 | { |
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108 | $self->{_e} = Math::BigInt->bzero(); |
109 | $self->{_m} = Math::BigInt->bzero(); |
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110 | $self->{sign} = $wanted; |
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111 | $self->{sign} = '+inf' if $self->{sign} eq 'inf'; |
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112 | return $self->bnorm(); |
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113 | } |
114 | #print "new string '$wanted'\n"; |
115 | my ($mis,$miv,$mfv,$es,$ev) = Math::BigInt::_split(\$wanted); |
116 | if (!ref $mis) |
117 | { |
118 | die "$wanted is not a number initialized to $class" if !$NaNOK; |
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119 | $self->{_e} = Math::BigInt->bzero(); |
120 | $self->{_m} = Math::BigInt->bzero(); |
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121 | $self->{sign} = $nan; |
122 | } |
123 | else |
124 | { |
125 | # make integer from mantissa by adjusting exp, then convert to bigint |
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126 | # undef,undef to signal MBI that we don't need no bloody rounding |
127 | $self->{_e} = Math::BigInt->new("$$es$$ev",undef,undef); # exponent |
128 | $self->{_m} = Math::BigInt->new("$$miv$$mfv",undef,undef); # create mant. |
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129 | # 3.123E0 = 3123E-3, and 3.123E-2 => 3123E-5 |
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130 | $self->{_e} -= CORE::length($$mfv) if CORE::length($$mfv) != 0; |
131 | $self->{sign} = $$mis; |
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132 | } |
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133 | # print "mbf new ",join(' ',@r),"\n"; |
134 | $self->bnorm()->round(@r); # first normalize, then round |
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135 | } |
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136 | |
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137 | sub bnan |
138 | { |
139 | # create a bigfloat 'NaN', if given a BigFloat, set it to 'NaN' |
140 | my $self = shift; |
141 | $self = $class if !defined $self; |
142 | if (!ref($self)) |
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143 | { |
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144 | my $c = $self; $self = {}; bless $self, $c; |
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145 | } |
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146 | $self->{_m} = Math::BigInt->bzero(); |
147 | $self->{_e} = Math::BigInt->bzero(); |
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148 | $self->{sign} = $nan; |
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149 | $self->{_a} = undef; $self->{_p} = undef; |
150 | $self; |
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151 | } |
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152 | |
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153 | sub binf |
154 | { |
155 | # create a bigfloat '+-inf', if given a BigFloat, set it to '+-inf' |
156 | my $self = shift; |
157 | my $sign = shift; $sign = '+' if !defined $sign || $sign ne '-'; |
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158 | |
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159 | $self = $class if !defined $self; |
160 | if (!ref($self)) |
161 | { |
162 | my $c = $self; $self = {}; bless $self, $c; |
163 | } |
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164 | $self->{_m} = Math::BigInt->bzero(); |
165 | $self->{_e} = Math::BigInt->bzero(); |
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166 | $self->{sign} = $sign.'inf'; |
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167 | $self->{_a} = undef; $self->{_p} = undef; |
168 | $self; |
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169 | } |
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170 | |
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171 | sub bone |
172 | { |
173 | # create a bigfloat '+-1', if given a BigFloat, set it to '+-1' |
174 | my $self = shift; |
175 | my $sign = shift; $sign = '+' if !defined $sign || $sign ne '-'; |
176 | |
177 | $self = $class if !defined $self; |
178 | if (!ref($self)) |
179 | { |
180 | my $c = $self; $self = {}; bless $self, $c; |
181 | } |
182 | $self->{_m} = Math::BigInt->bone(); |
183 | $self->{_e} = Math::BigInt->bzero(); |
184 | $self->{sign} = $sign; |
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185 | if (@_ > 0) |
186 | { |
187 | $self->{_a} = $_[0] |
188 | if (defined $self->{_a} && defined $_[0] && $_[0] > $self->{_a}); |
189 | $self->{_p} = $_[1] |
190 | if (defined $self->{_p} && defined $_[1] && $_[1] < $self->{_p}); |
191 | } |
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192 | return $self; |
193 | } |
194 | |
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195 | sub bzero |
196 | { |
197 | # create a bigfloat '+0', if given a BigFloat, set it to 0 |
198 | my $self = shift; |
199 | $self = $class if !defined $self; |
200 | if (!ref($self)) |
201 | { |
202 | my $c = $self; $self = {}; bless $self, $c; |
203 | } |
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204 | $self->{_m} = Math::BigInt->bzero(); |
205 | $self->{_e} = Math::BigInt->bone(); |
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206 | $self->{sign} = '+'; |
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207 | if (@_ > 0) |
208 | { |
209 | $self->{_a} = $_[0] |
210 | if (defined $self->{_a} && defined $_[0] && $_[0] > $self->{_a}); |
211 | $self->{_p} = $_[1] |
212 | if (defined $self->{_p} && defined $_[1] && $_[1] < $self->{_p}); |
213 | } |
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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 | { |
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233 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN |
234 | return 'inf'; # +inf |
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235 | } |
236 | |
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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 | { |
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242 | $es = $x->{_m}->bstr(); |
243 | $len = CORE::length($es); |
244 | if (!$x->{_e}->is_zero()) |
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245 | { |
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246 | if ($x->{_e}->sign() eq '-') |
247 | { |
248 | $dot = ''; |
249 | if ($x->{_e} <= -$len) |
250 | { |
251 | # print "style: 0.xxxx\n"; |
252 | my $r = $x->{_e}->copy(); $r->babs()->bsub( CORE::length($es) ); |
253 | $es = '0.'. ('0' x $r) . $es; $cad = -($len+$r); |
254 | } |
255 | else |
256 | { |
257 | # print "insert '.' at $x->{_e} in '$es'\n"; |
258 | substr($es,$x->{_e},0) = '.'; $cad = $x->{_e}; |
259 | } |
260 | } |
261 | else |
262 | { |
263 | # expand with zeros |
264 | $es .= '0' x $x->{_e}; $len += $x->{_e}; $cad = 0; |
265 | } |
82cf049f |
266 | } |
574bacfe |
267 | } # if not zero |
268 | $es = $x->{sign}.$es if $x->{sign} eq '-'; |
269 | # if set accuracy or precision, pad with zeros |
270 | if ((defined $x->{_a}) && ($not_zero)) |
271 | { |
272 | # 123400 => 6, 0.1234 => 4, 0.001234 => 4 |
273 | my $zeros = $x->{_a} - $cad; # cad == 0 => 12340 |
274 | $zeros = $x->{_a} - $len if $cad != $len; |
574bacfe |
275 | $es .= $dot.'0' x $zeros if $zeros > 0; |
82cf049f |
276 | } |
574bacfe |
277 | elsif ($x->{_p} || 0 < 0) |
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278 | { |
574bacfe |
279 | # 123400 => 6, 0.1234 => 4, 0.001234 => 6 |
280 | my $zeros = -$x->{_p} + $cad; |
574bacfe |
281 | $es .= $dot.'0' x $zeros if $zeros > 0; |
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282 | } |
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283 | return $es; |
82cf049f |
284 | } |
f216259d |
285 | |
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286 | sub bsstr |
287 | { |
288 | # (ref to BFLOAT or num_str ) return num_str |
289 | # Convert number from internal format to scientific string format. |
290 | # internal format is always normalized (no leading zeros, "-0E0" => "+0E0") |
ee15d750 |
291 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
292 | #my $x = shift; my $class = ref($x) || $x; |
293 | #$x = $class->new(shift) unless ref($x); |
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294 | |
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295 | #die "Oups! e was $nan" if $x->{_e}->{sign} eq $nan; |
296 | #die "Oups! m was $nan" if $x->{_m}->{sign} eq $nan; |
297 | if ($x->{sign} !~ /^[+-]$/) |
298 | { |
299 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN |
300 | return 'inf'; # +inf |
301 | } |
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302 | my $sign = $x->{_e}->{sign}; $sign = '' if $sign eq '-'; |
303 | my $sep = 'e'.$sign; |
304 | return $x->{_m}->bstr().$sep.$x->{_e}->bstr(); |
305 | } |
306 | |
307 | sub numify |
308 | { |
309 | # Make a number from a BigFloat object |
574bacfe |
310 | # simple return string and let Perl's atoi()/atof() handle the rest |
ee15d750 |
311 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
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312 | return $x->bsstr(); |
313 | } |
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314 | |
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315 | ############################################################################## |
316 | # public stuff (usually prefixed with "b") |
317 | |
574bacfe |
318 | # tels 2001-08-04 |
319 | # todo: this must be overwritten and return NaN for non-integer values |
320 | # band(), bior(), bxor(), too |
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321 | #sub bnot |
322 | # { |
323 | # $class->SUPER::bnot($class,@_); |
324 | # } |
325 | |
326 | sub bcmp |
327 | { |
328 | # Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort) |
329 | # (BFLOAT or num_str, BFLOAT or num_str) return cond_code |
330 | my ($self,$x,$y) = objectify(2,@_); |
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331 | |
0716bf9b |
332 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
333 | { |
334 | # handle +-inf and NaN |
335 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
336 | return 0 if ($x->{sign} eq $y->{sign}) && ($x->{sign} =~ /^[+-]inf$/); |
337 | return +1 if $x->{sign} eq '+inf'; |
338 | return -1 if $x->{sign} eq '-inf'; |
339 | return -1 if $y->{sign} eq '+inf'; |
340 | return +1 if $y->{sign} eq '-inf'; |
341 | } |
342 | |
343 | # check sign for speed first |
574bacfe |
344 | return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y |
58cde26e |
345 | return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0 |
346 | |
574bacfe |
347 | # shortcut |
348 | my $xz = $x->is_zero(); |
349 | my $yz = $y->is_zero(); |
350 | return 0 if $xz && $yz; # 0 <=> 0 |
351 | return -1 if $xz && $y->{sign} eq '+'; # 0 <=> +y |
352 | return 1 if $yz && $x->{sign} eq '+'; # +x <=> 0 |
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353 | |
354 | # adjust so that exponents are equal |
bd05a461 |
355 | my $lxm = $x->{_m}->length(); |
356 | my $lym = $y->{_m}->length(); |
357 | my $lx = $lxm + $x->{_e}; |
358 | my $ly = $lym + $y->{_e}; |
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359 | # print "x $x y $y lx $lx ly $ly\n"; |
360 | my $l = $lx - $ly; $l = -$l if $x->{sign} eq '-'; |
361 | # print "$l $x->{sign}\n"; |
bd05a461 |
362 | return $l <=> 0 if $l != 0; |
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363 | |
bd05a461 |
364 | # lengths (corrected by exponent) are equal |
365 | # so make mantissa euqal length by padding with zero (shift left) |
366 | my $diff = $lxm - $lym; |
367 | my $xm = $x->{_m}; # not yet copy it |
368 | my $ym = $y->{_m}; |
369 | if ($diff > 0) |
370 | { |
371 | $ym = $y->{_m}->copy()->blsft($diff,10); |
372 | } |
373 | elsif ($diff < 0) |
374 | { |
375 | $xm = $x->{_m}->copy()->blsft(-$diff,10); |
376 | } |
377 | my $rc = $xm->bcmp($ym); |
58cde26e |
378 | $rc = -$rc if $x->{sign} eq '-'; # -124 < -123 |
bd05a461 |
379 | return $rc <=> 0; |
58cde26e |
380 | } |
381 | |
382 | sub bacmp |
383 | { |
384 | # Compares 2 values, ignoring their signs. |
385 | # Returns one of undef, <0, =0, >0. (suitable for sort) |
386 | # (BFLOAT or num_str, BFLOAT or num_str) return cond_code |
387 | my ($self,$x,$y) = objectify(2,@_); |
ee15d750 |
388 | |
389 | # handle +-inf and NaN's |
abcfbf51 |
390 | if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/) |
ee15d750 |
391 | { |
392 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
393 | return 0 if ($x->is_inf() && $y->is_inf()); |
394 | return 1 if ($x->is_inf() && !$y->is_inf()); |
395 | return -1 if (!$x->is_inf() && $y->is_inf()); |
396 | } |
397 | |
398 | # shortcut |
399 | my $xz = $x->is_zero(); |
400 | my $yz = $y->is_zero(); |
401 | return 0 if $xz && $yz; # 0 <=> 0 |
402 | return -1 if $xz && !$yz; # 0 <=> +y |
403 | return 1 if $yz && !$xz; # +x <=> 0 |
404 | |
405 | # adjust so that exponents are equal |
406 | my $lxm = $x->{_m}->length(); |
407 | my $lym = $y->{_m}->length(); |
408 | my $lx = $lxm + $x->{_e}; |
409 | my $ly = $lym + $y->{_e}; |
410 | # print "x $x y $y lx $lx ly $ly\n"; |
394e6ffb |
411 | my $l = $lx - $ly; |
ee15d750 |
412 | # print "$l $x->{sign}\n"; |
413 | return $l <=> 0 if $l != 0; |
58cde26e |
414 | |
ee15d750 |
415 | # lengths (corrected by exponent) are equal |
394e6ffb |
416 | # so make mantissa equal-length by padding with zero (shift left) |
ee15d750 |
417 | my $diff = $lxm - $lym; |
418 | my $xm = $x->{_m}; # not yet copy it |
419 | my $ym = $y->{_m}; |
420 | if ($diff > 0) |
421 | { |
422 | $ym = $y->{_m}->copy()->blsft($diff,10); |
423 | } |
424 | elsif ($diff < 0) |
425 | { |
426 | $xm = $x->{_m}->copy()->blsft(-$diff,10); |
427 | } |
428 | my $rc = $xm->bcmp($ym); |
ee15d750 |
429 | return $rc <=> 0; |
58cde26e |
430 | } |
a0d0e21e |
431 | |
58cde26e |
432 | sub badd |
433 | { |
434 | # add second arg (BFLOAT or string) to first (BFLOAT) (modifies first) |
435 | # return result as BFLOAT |
58cde26e |
436 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
437 | |
574bacfe |
438 | # inf and NaN handling |
439 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
440 | { |
441 | # NaN first |
442 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
443 | # inf handline |
444 | if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) |
445 | { |
446 | # + and + => +, - and - => -, + and - => 0, - and + => 0 |
447 | return $x->bzero() if $x->{sign} ne $y->{sign}; |
448 | return $x; |
449 | } |
450 | # +-inf + something => +inf |
451 | # something +-inf => +-inf |
452 | $x->{sign} = $y->{sign}, return $x if $y->{sign} =~ /^[+-]inf$/; |
453 | return $x; |
454 | } |
455 | |
58cde26e |
456 | # speed: no add for 0+y or x+0 |
457 | return $x if $y->is_zero(); # x+0 |
458 | if ($x->is_zero()) # 0+y |
459 | { |
460 | # make copy, clobbering up x (modify in place!) |
461 | $x->{_e} = $y->{_e}->copy(); |
462 | $x->{_m} = $y->{_m}->copy(); |
463 | $x->{sign} = $y->{sign} || $nan; |
464 | return $x->round($a,$p,$r,$y); |
a0d0e21e |
465 | } |
58cde26e |
466 | |
467 | # take lower of the two e's and adapt m1 to it to match m2 |
468 | my $e = $y->{_e}; $e = Math::BigInt::bzero() if !defined $e; # if no BFLOAT |
469 | $e = $e - $x->{_e}; |
470 | my $add = $y->{_m}->copy(); |
471 | if ($e < 0) |
472 | { |
58cde26e |
473 | my $e1 = $e->copy()->babs(); |
474 | $x->{_m} *= (10 ** $e1); |
475 | $x->{_e} += $e; # need the sign of e |
58cde26e |
476 | } |
477 | elsif ($e > 0) |
478 | { |
58cde26e |
479 | $add *= (10 ** $e); |
58cde26e |
480 | } |
61f5c3f5 |
481 | # else: both e are the same, so just leave them |
482 | $x->{_m}->{sign} = $x->{sign}; # fiddle with signs |
58cde26e |
483 | $add->{sign} = $y->{sign}; |
61f5c3f5 |
484 | $x->{_m} += $add; # finally do add/sub |
485 | $x->{sign} = $x->{_m}->{sign}; # re-adjust signs |
486 | $x->{_m}->{sign} = '+'; # mantissa always positiv |
487 | # delete trailing zeros, then round |
488 | return $x->bnorm()->round($a,$p,$r,$y); |
58cde26e |
489 | } |
490 | |
491 | sub bsub |
492 | { |
0716bf9b |
493 | # (BigFloat or num_str, BigFloat or num_str) return BigFloat |
58cde26e |
494 | # subtract second arg from first, modify first |
e745a66c |
495 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
a0d0e21e |
496 | |
e745a66c |
497 | if (!$y->is_zero()) # don't need to do anything if $y is 0 |
498 | { |
499 | $y->{sign} =~ tr/+\-/-+/; # does nothing for NaN |
500 | $x->badd($y,$a,$p,$r); # badd does not leave internal zeros |
501 | $y->{sign} =~ tr/+\-/-+/; # refix $y (does nothing for NaN) |
502 | } |
503 | $x; # already rounded by badd() |
58cde26e |
504 | } |
505 | |
506 | sub binc |
507 | { |
508 | # increment arg by one |
ee15d750 |
509 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
e745a66c |
510 | |
511 | if ($x->{_e}->sign() eq '-') |
512 | { |
513 | return $x->badd($self->bone(),$a,$p,$r); # digits after dot |
514 | } |
515 | |
516 | if (!$x->{_e}->is_zero()) |
517 | { |
518 | $x->{_m}->blsft($x->{_e},10); # 1e2 => 100 |
519 | $x->{_e}->bzero(); |
520 | } |
521 | # now $x->{_e} == 0 |
522 | if ($x->{sign} eq '+') |
523 | { |
524 | $x->{_m}->binc(); |
525 | return $x->bnorm()->bround($a,$p,$r); |
526 | } |
527 | elsif ($x->{sign} eq '-') |
528 | { |
529 | $x->{_m}->bdec(); |
530 | $x->{sign} = '+' if $x->{_m}->is_zero(); # -1 +1 => -0 => +0 |
531 | return $x->bnorm()->bround($a,$p,$r); |
532 | } |
533 | # inf, nan handling etc |
534 | $x->badd($self->__one(),$a,$p,$r); # does round |
58cde26e |
535 | } |
536 | |
537 | sub bdec |
538 | { |
539 | # decrement arg by one |
ee15d750 |
540 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
e745a66c |
541 | |
542 | if ($x->{_e}->sign() eq '-') |
543 | { |
544 | return $x->badd($self->bone('-'),$a,$p,$r); # digits after dot |
545 | } |
546 | |
547 | if (!$x->{_e}->is_zero()) |
548 | { |
549 | $x->{_m}->blsft($x->{_e},10); # 1e2 => 100 |
550 | $x->{_e}->bzero(); |
551 | } |
552 | # now $x->{_e} == 0 |
553 | my $zero = $x->is_zero(); |
554 | # <= 0 |
555 | if (($x->{sign} eq '-') || $zero) |
556 | { |
557 | $x->{_m}->binc(); |
558 | $x->{sign} = '-' if $zero; # 0 => 1 => -1 |
559 | $x->{sign} = '+' if $x->{_m}->is_zero(); # -1 +1 => -0 => +0 |
560 | return $x->bnorm()->round($a,$p,$r); |
561 | } |
562 | # > 0 |
563 | elsif ($x->{sign} eq '+') |
564 | { |
565 | $x->{_m}->bdec(); |
566 | return $x->bnorm()->round($a,$p,$r); |
567 | } |
568 | # inf, nan handling etc |
569 | $x->badd($self->bone('-'),$a,$p,$r); # does round |
58cde26e |
570 | } |
571 | |
61f5c3f5 |
572 | sub blog |
573 | { |
574 | my ($self,$x,$base,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(2,@_); |
575 | |
576 | # http://www.efunda.com/math/taylor_series/logarithmic.cfm?search_string=log |
577 | |
578 | # u = x-1, v = x +1 |
579 | # _ _ |
580 | # taylor: | u 1 u^3 1 u^5 | |
581 | # ln (x) = 2 | --- + - * --- + - * --- + ... | x > 0 |
582 | # |_ v 3 v 5 v _| |
583 | |
584 | return $x->bzero(@r) if $x->is_one(); |
585 | return $x->bone(@r) if $x->bcmp($base) == 0; |
586 | |
587 | my $d = $r[0] || $self->accuracy() || 40; |
588 | $d += 2; # 2 more for rounding |
589 | |
590 | my $u = $x->copy(); $u->bdec(); |
591 | my $v = $x->copy(); $v->binc(); |
592 | |
593 | $x->bdec()->bdiv($v,$d); # first term: u/v |
594 | |
595 | $u *= $u; $v *= $v; |
596 | my $below = $v->copy()->bmul($v); |
597 | my $over = $u->copy()->bmul($u); |
598 | my $factor = $self->new(3); my $two = $self->new(2); |
599 | |
600 | my $diff = $self->bone(); |
601 | my $limit = $self->new("1E-". ($d-1)); my $last; |
602 | # print "diff $diff limit $limit\n"; |
603 | while ($diff > $limit) |
604 | { |
605 | print "$x $over $below $factor\n"; |
606 | $diff = $x->copy()->bsub($last)->babs(); |
607 | print "diff $diff $limit\n"; |
608 | $last = $x->copy(); |
609 | $x += $over->copy()->bdiv($below->copy()->bmul($factor),$d); |
610 | $over *= $u; $below *= $v; $factor->badd($two); |
611 | } |
612 | $x->bmul($two); |
613 | return $x->round(@r); |
614 | } |
615 | |
58cde26e |
616 | sub blcm |
617 | { |
ee15d750 |
618 | # (BFLOAT or num_str, BFLOAT or num_str) return BFLOAT |
58cde26e |
619 | # does not modify arguments, but returns new object |
620 | # Lowest Common Multiplicator |
58cde26e |
621 | |
622 | my ($self,@arg) = objectify(0,@_); |
623 | my $x = $self->new(shift @arg); |
624 | while (@arg) { $x = _lcm($x,shift @arg); } |
625 | $x; |
626 | } |
627 | |
628 | sub bgcd |
629 | { |
ee15d750 |
630 | # (BFLOAT or num_str, BFLOAT or num_str) return BINT |
58cde26e |
631 | # does not modify arguments, but returns new object |
632 | # GCD -- Euclids algorithm Knuth Vol 2 pg 296 |
58cde26e |
633 | |
634 | my ($self,@arg) = objectify(0,@_); |
635 | my $x = $self->new(shift @arg); |
636 | while (@arg) { $x = _gcd($x,shift @arg); } |
637 | $x; |
638 | } |
639 | |
640 | sub is_zero |
641 | { |
ee15d750 |
642 | # return true if arg (BFLOAT or num_str) is zero (array '+', '0') |
643 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
574bacfe |
644 | |
645 | return 1 if $x->{sign} eq '+' && $x->{_m}->is_zero(); |
646 | return 0; |
58cde26e |
647 | } |
648 | |
649 | sub is_one |
650 | { |
ee15d750 |
651 | # return true if arg (BFLOAT or num_str) is +1 (array '+', '1') |
58cde26e |
652 | # or -1 if signis given |
ee15d750 |
653 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
654 | |
655 | my $sign = shift || ''; $sign = '+' if $sign ne '-'; |
656 | return 1 |
657 | if ($x->{sign} eq $sign && $x->{_e}->is_zero() && $x->{_m}->is_one()); |
658 | return 0; |
58cde26e |
659 | } |
660 | |
661 | sub is_odd |
662 | { |
ee15d750 |
663 | # return true if arg (BFLOAT or num_str) is odd or false if even |
664 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
0716bf9b |
665 | |
666 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
ee15d750 |
667 | return 1 if ($x->{_e}->is_zero() && $x->{_m}->is_odd()); |
668 | return 0; |
58cde26e |
669 | } |
670 | |
671 | sub is_even |
672 | { |
b22b3e31 |
673 | # return true if arg (BINT or num_str) is even or false if odd |
ee15d750 |
674 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
0716bf9b |
675 | |
676 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
677 | return 1 if $x->{_m}->is_zero(); # 0e1 is even |
ee15d750 |
678 | return 1 if ($x->{_e}->is_zero() && $x->{_m}->is_even()); # 123.45 is never |
679 | return 0; |
58cde26e |
680 | } |
681 | |
682 | sub bmul |
683 | { |
684 | # multiply two numbers -- stolen from Knuth Vol 2 pg 233 |
685 | # (BINT or num_str, BINT or num_str) return BINT |
686 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
58cde26e |
687 | |
0716bf9b |
688 | # print "mbf bmul $x->{_m}e$x->{_e} $y->{_m}e$y->{_e}\n"; |
58cde26e |
689 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
690 | |
574bacfe |
691 | # handle result = 0 |
692 | return $x->bzero() if $x->is_zero() || $y->is_zero(); |
693 | # inf handling |
694 | if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) |
695 | { |
696 | # result will always be +-inf: |
697 | # +inf * +/+inf => +inf, -inf * -/-inf => +inf |
698 | # +inf * -/-inf => -inf, -inf * +/+inf => -inf |
699 | return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); |
700 | return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); |
701 | return $x->binf('-'); |
702 | } |
703 | |
58cde26e |
704 | # aEb * cEd = (a*c)E(b+d) |
394e6ffb |
705 | $x->{_m}->bmul($y->{_m}); |
706 | $x->{_e}->badd($y->{_e}); |
58cde26e |
707 | # adjust sign: |
708 | $x->{sign} = $x->{sign} ne $y->{sign} ? '-' : '+'; |
394e6ffb |
709 | return $x->bnorm()->round($a,$p,$r,$y); |
58cde26e |
710 | } |
711 | |
712 | sub bdiv |
713 | { |
714 | # (dividend: BFLOAT or num_str, divisor: BFLOAT or num_str) return |
715 | # (BFLOAT,BFLOAT) (quo,rem) or BINT (only rem) |
716 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
717 | |
574bacfe |
718 | # x / +-inf => 0, reminder x |
719 | return wantarray ? ($x->bzero(),$x->copy()) : $x->bzero() |
720 | if $y->{sign} =~ /^[+-]inf$/; |
721 | |
722 | # NaN if x == NaN or y == NaN or x==y==0 |
58cde26e |
723 | return wantarray ? ($x->bnan(),bnan()) : $x->bnan() |
574bacfe |
724 | if (($x->is_nan() || $y->is_nan()) || |
725 | ($x->is_zero() && $y->is_zero())); |
726 | |
727 | # 5 / 0 => +inf, -6 / 0 => -inf |
728 | return wantarray |
729 | ? ($x->binf($x->{sign}),$self->bnan()) : $x->binf($x->{sign}) |
730 | if ($x->{sign} =~ /^[+-]$/ && $y->is_zero()); |
0716bf9b |
731 | |
394e6ffb |
732 | # x== 0 or y == 1 or y == -1 |
733 | return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero(); |
0716bf9b |
734 | |
58cde26e |
735 | # we need to limit the accuracy to protect against overflow |
574bacfe |
736 | my $fallback = 0; |
ee15d750 |
737 | my $scale = 0; |
ee15d750 |
738 | my @params = $x->_find_round_parameters($a,$p,$r,$y); |
739 | |
740 | # no rounding at all, so must use fallback |
741 | if (scalar @params == 1) |
58cde26e |
742 | { |
0716bf9b |
743 | # simulate old behaviour |
ee15d750 |
744 | $params[1] = $self->div_scale(); # and round to it as accuracy |
61f5c3f5 |
745 | $scale = $params[1]+4; # at least four more for proper round |
ee15d750 |
746 | $params[3] = $r; # round mode by caller or undef |
747 | $fallback = 1; # to clear a/p afterwards |
748 | } |
749 | else |
750 | { |
751 | # the 4 below is empirical, and there might be cases where it is not |
752 | # enough... |
753 | $scale = abs($params[1] || $params[2]) + 4; # take whatever is defined |
a0d0e21e |
754 | } |
0716bf9b |
755 | my $lx = $x->{_m}->length(); my $ly = $y->{_m}->length(); |
58cde26e |
756 | $scale = $lx if $lx > $scale; |
58cde26e |
757 | $scale = $ly if $ly > $scale; |
0716bf9b |
758 | my $diff = $ly - $lx; |
759 | $scale += $diff if $diff > 0; # if lx << ly, but not if ly << lx! |
a0d0e21e |
760 | |
58cde26e |
761 | $x->{sign} = $x->{sign} ne $y->sign() ? '-' : '+'; |
a0d0e21e |
762 | |
58cde26e |
763 | # check for / +-1 ( +/- 1E0) |
394e6ffb |
764 | if (!$y->is_one()) |
58cde26e |
765 | { |
394e6ffb |
766 | # promote BigInts and it's subclasses (except when already a BigFloat) |
767 | $y = $self->new($y) unless $y->isa('Math::BigFloat'); |
768 | |
769 | # calculate the result to $scale digits and then round it |
770 | # a * 10 ** b / c * 10 ** d => a/c * 10 ** (b-d) |
771 | $x->{_m}->blsft($scale,10); |
772 | $x->{_m}->bdiv( $y->{_m} ); # a/c |
773 | $x->{_e}->bsub( $y->{_e} ); # b-d |
774 | $x->{_e}->bsub($scale); # correct for 10**scale |
775 | $x->bnorm(); # remove trailing 0's |
a0d0e21e |
776 | } |
a5f75d66 |
777 | |
ee15d750 |
778 | # shortcut to not run trough _find_round_parameters again |
779 | if (defined $params[1]) |
780 | { |
61f5c3f5 |
781 | $x->bround($params[1],$params[3]); # then round accordingly |
ee15d750 |
782 | } |
783 | else |
784 | { |
785 | $x->bfround($params[2],$params[3]); # then round accordingly |
786 | } |
574bacfe |
787 | if ($fallback) |
788 | { |
789 | # clear a/p after round, since user did not request it |
ee15d750 |
790 | $x->{_a} = undef; $x->{_p} = undef; |
574bacfe |
791 | } |
0716bf9b |
792 | |
58cde26e |
793 | if (wantarray) |
794 | { |
394e6ffb |
795 | my $rem; |
796 | if (!$y->is_one()) |
797 | { |
798 | $rem = $x->copy(); |
799 | $rem->bmod($y,$params[1],$params[2],$params[3]); |
800 | } |
801 | else |
802 | { |
803 | $rem = $self->bzero(); |
804 | } |
574bacfe |
805 | if ($fallback) |
806 | { |
807 | # clear a/p after round, since user did not request it |
ee15d750 |
808 | $rem->{_a} = undef; $rem->{_p} = undef; |
574bacfe |
809 | } |
0716bf9b |
810 | return ($x,$rem); |
58cde26e |
811 | } |
812 | return $x; |
813 | } |
a0d0e21e |
814 | |
58cde26e |
815 | sub bmod |
816 | { |
817 | # (dividend: BFLOAT or num_str, divisor: BFLOAT or num_str) return reminder |
818 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
a0d0e21e |
819 | |
61f5c3f5 |
820 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
821 | { |
822 | my ($d,$re) = $self->SUPER::_div_inf($x,$y); |
823 | return $re->round($a,$p,$r,$y); |
824 | } |
825 | return $x->bnan() if $x->is_zero() && $y->is_zero(); |
826 | return $x if $y->is_zero(); |
827 | return $x->bnan() if $x->is_nan() || $y->is_nan(); |
828 | return $x->bzero() if $y->is_one() || $x->is_zero(); |
58cde26e |
829 | |
61f5c3f5 |
830 | # inf handling is missing here |
831 | |
832 | my $cmp = $x->bacmp($y); # equal or $x < $y? |
833 | return $x->bzero($a,$p) if $cmp == 0; # $x == $y => result 0 |
834 | |
835 | # only $y of the operands negative? |
836 | my $neg = 0; $neg = 1 if $x->{sign} ne $y->{sign}; |
837 | |
838 | $x->{sign} = $y->{sign}; # calc sign first |
839 | return $x->round($a,$p,$r) if $cmp < 0 && $neg == 0; # $x < $y => result $x |
840 | |
841 | my $ym = $y->{_m}->copy(); |
842 | |
843 | # 2e1 => 20 |
844 | $ym->blsft($y->{_e},10) if $y->{_e}->{sign} eq '+' && !$y->{_e}->is_zero(); |
845 | |
846 | # if $y has digits after dot |
847 | my $shifty = 0; # correct _e of $x by this |
848 | if ($y->{_e}->{sign} eq '-') # has digits after dot |
849 | { |
850 | # 123 % 2.5 => 1230 % 25 => 5 => 0.5 |
851 | $shifty = $y->{_e}->copy()->babs(); # no more digits after dot |
852 | $x->blsft($shifty,10); # 123 => 1230, $y->{_m} is already 25 |
853 | } |
854 | # $ym is now mantissa of $y based on exponent 0 |
855 | |
856 | my $shiftx = 0; # correct _e of $x by this |
857 | if ($x->{_e}->{sign} eq '-') # has digits after dot |
858 | { |
859 | # 123.4 % 20 => 1234 % 200 |
860 | $shiftx = $x->{_e}->copy()->babs(); # no more digits after dot |
861 | $ym->blsft($shiftx,10); |
862 | } |
863 | # 123e1 % 20 => 1230 % 20 |
864 | if ($x->{_e}->{sign} eq '+' && !$x->{_e}->is_zero()) |
865 | { |
866 | $x->{_m}->blsft($x->{_e},10); |
867 | } |
868 | $x->{_e} = Math::BigInt->bzero() unless $x->{_e}->is_zero(); |
869 | |
870 | $x->{_e}->bsub($shiftx) if $shiftx != 0; |
871 | $x->{_e}->bsub($shifty) if $shifty != 0; |
872 | |
873 | # now mantissas are equalized, exponent of $x is adjusted, so calc result |
874 | $x->{_m}->bmod($ym); |
875 | |
876 | $x->{sign} = '+' if $x->{_m}->is_zero(); # fix sign for -0 |
877 | $x->bnorm(); |
878 | |
879 | if ($neg != 0) # one of them negative => correct in place |
880 | { |
881 | my $r = $y - $x; |
882 | $x->{_m} = $r->{_m}; |
883 | $x->{_e} = $r->{_e}; |
884 | $x->{sign} = '+' if $x->{_m}->is_zero(); # fix sign for -0 |
885 | $x->bnorm(); |
886 | } |
887 | |
888 | $x->round($a,$p,$r,$y); # round and return |
58cde26e |
889 | } |
890 | |
891 | sub bsqrt |
892 | { |
0716bf9b |
893 | # calculate square root; this should probably |
894 | # use a different test to see whether the accuracy we want is... |
ee15d750 |
895 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e |
896 | |
0716bf9b |
897 | return $x->bnan() if $x->{sign} eq 'NaN' || $x->{sign} =~ /^-/; # <0, NaN |
898 | return $x if $x->{sign} eq '+inf'; # +inf |
394e6ffb |
899 | return $x if $x->is_zero() || $x->is_one(); |
58cde26e |
900 | |
61f5c3f5 |
901 | # we need to limit the accuracy to protect against overflow |
574bacfe |
902 | my $fallback = 0; |
61f5c3f5 |
903 | my $scale = 0; |
904 | my @params = $x->_find_round_parameters($a,$p,$r); |
905 | |
906 | # no rounding at all, so must use fallback |
907 | if (scalar @params == 1) |
0716bf9b |
908 | { |
909 | # simulate old behaviour |
61f5c3f5 |
910 | $params[1] = $self->div_scale(); # and round to it as accuracy |
911 | $scale = $params[1]+4; # at least four more for proper round |
912 | $params[3] = $r; # round mode by caller or undef |
ee15d750 |
913 | $fallback = 1; # to clear a/p afterwards |
0716bf9b |
914 | } |
61f5c3f5 |
915 | else |
916 | { |
917 | # the 4 below is empirical, and there might be cases where it is not |
918 | # enough... |
919 | $scale = abs($params[1] || $params[2]) + 4; # take whatever is defined |
920 | } |
921 | |
922 | # when user set globals, they would interfere with our calculation, so |
923 | # disable then and later re-enable them |
924 | no strict 'refs'; |
925 | my $abr = "$self\::accuracy"; my $ab = $$abr; $$abr = undef; |
926 | $abr = "$self\::precision"; my $pb = $$abr; $$abr = undef; |
927 | # we also need to disable any set A or P on $x (_find_round_parameters took |
928 | # them already into account), since these would interfere, too |
929 | delete $x->{_a}; delete $x->{_p}; |
930 | |
394e6ffb |
931 | my $xas = $x->as_number(); |
932 | my $gs = $xas->copy()->bsqrt(); # some guess |
933 | if (($x->{_e}->{sign} ne '-') # guess can't be accurate if there are |
934 | # digits after the dot |
935 | && ($xas->bcmp($gs * $gs) == 0)) # guess hit the nail on the head? |
936 | { |
937 | # exact result |
61f5c3f5 |
938 | $x->{_m} = $gs; $x->{_e} = Math::BigInt->bzero(); $x->bnorm(); |
939 | # shortcut to not run trough _find_round_parameters again |
940 | if (defined $params[1]) |
941 | { |
942 | $x->bround($params[1],$params[3]); # then round accordingly |
943 | } |
944 | else |
945 | { |
946 | $x->bfround($params[2],$params[3]); # then round accordingly |
947 | } |
948 | if ($fallback) |
949 | { |
950 | # clear a/p after round, since user did not request it |
951 | $x->{_a} = undef; $x->{_p} = undef; |
952 | } |
953 | return $x; |
394e6ffb |
954 | } |
61f5c3f5 |
955 | $gs = $self->new( $gs ); # BigInt to BigFloat |
394e6ffb |
956 | |
0716bf9b |
957 | my $lx = $x->{_m}->length(); |
958 | $scale = $lx if $scale < $lx; |
394e6ffb |
959 | my $e = $self->new("1E-$scale"); # make test variable |
58cde26e |
960 | return $x->bnan() if $e->sign() eq 'NaN'; |
961 | |
58cde26e |
962 | my $y = $x->copy(); |
394e6ffb |
963 | my $two = $self->new(2); |
61f5c3f5 |
964 | my $diff = $e; |
ee15d750 |
965 | # promote BigInts and it's subclasses (except when already a BigFloat) |
966 | $y = $self->new($y) unless $y->isa('Math::BigFloat'); |
61f5c3f5 |
967 | |
ee15d750 |
968 | my $rem; |
394e6ffb |
969 | # my $steps = 0; |
58cde26e |
970 | while ($diff >= $e) |
971 | { |
61f5c3f5 |
972 | # return $x->bnan() if $gs->is_zero(); |
394e6ffb |
973 | |
61f5c3f5 |
974 | $rem = $y->copy()->bdiv($gs,$scale)->badd($gs)->bdiv($two,$scale); |
975 | $diff = $rem->copy()->bsub($gs)->babs(); |
976 | $gs = $rem->copy(); |
394e6ffb |
977 | # $steps++; |
a0d0e21e |
978 | } |
394e6ffb |
979 | # print "steps $steps\n"; |
61f5c3f5 |
980 | # copy over to modify $x |
981 | $x->{_m} = $rem->{_m}; $x->{_e} = $rem->{_e}; |
982 | |
983 | # shortcut to not run trough _find_round_parameters again |
984 | if (defined $params[1]) |
985 | { |
986 | $x->bround($params[1],$params[3]); # then round accordingly |
987 | } |
988 | else |
989 | { |
990 | $x->bfround($params[2],$params[3]); # then round accordingly |
991 | } |
574bacfe |
992 | if ($fallback) |
993 | { |
994 | # clear a/p after round, since user did not request it |
ee15d750 |
995 | $x->{_a} = undef; $x->{_p} = undef; |
574bacfe |
996 | } |
61f5c3f5 |
997 | # restore globals |
998 | ${"$self\::accuracy"} = $ab; ${"$self\::precision"} = $pb; |
574bacfe |
999 | $x; |
58cde26e |
1000 | } |
1001 | |
1002 | sub bpow |
1003 | { |
1004 | # (BFLOAT or num_str, BFLOAT or num_str) return BFLOAT |
1005 | # compute power of two numbers, second arg is used as integer |
1006 | # modifies first argument |
1007 | |
1008 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
1009 | |
0716bf9b |
1010 | return $x if $x->{sign} =~ /^[+-]inf$/; |
58cde26e |
1011 | return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan; |
574bacfe |
1012 | return $x->bone() if $y->is_zero(); |
58cde26e |
1013 | return $x if $x->is_one() || $y->is_one(); |
ee15d750 |
1014 | my $y1 = $y->as_number(); # make bigint (trunc) |
394e6ffb |
1015 | # if ($x == -1) |
1016 | if ($x->{sign} eq '-' && $x->{_m}->is_one() && $x->{_e}->is_zero()) |
58cde26e |
1017 | { |
1018 | # if $x == -1 and odd/even y => +1/-1 because +-1 ^ (+-1) => +-1 |
0716bf9b |
1019 | return $y1->is_odd() ? $x : $x->babs(1); |
288d023a |
1020 | } |
58cde26e |
1021 | return $x if $x->is_zero() && $y->{sign} eq '+'; # 0**y => 0 (if not y <= 0) |
574bacfe |
1022 | # 0 ** -y => 1 / (0 ** y) => / 0! (1 / 0 => +inf) |
1023 | return $x->binf() if $x->is_zero() && $y->{sign} eq '-'; |
58cde26e |
1024 | |
1025 | # calculate $x->{_m} ** $y and $x->{_e} * $y separately (faster) |
1026 | $y1->babs(); |
1027 | $x->{_m}->bpow($y1); |
1028 | $x->{_e}->bmul($y1); |
1029 | $x->{sign} = $nan if $x->{_m}->{sign} eq $nan || $x->{_e}->{sign} eq $nan; |
1030 | $x->bnorm(); |
1031 | if ($y->{sign} eq '-') |
1032 | { |
1033 | # modify $x in place! |
0716bf9b |
1034 | my $z = $x->copy(); $x->bzero()->binc(); |
58cde26e |
1035 | return $x->bdiv($z,$a,$p,$r); # round in one go (might ignore y's A!) |
a0d0e21e |
1036 | } |
58cde26e |
1037 | return $x->round($a,$p,$r,$y); |
1038 | } |
1039 | |
1040 | ############################################################################### |
1041 | # rounding functions |
1042 | |
1043 | sub bfround |
1044 | { |
1045 | # precision: round to the $Nth digit left (+$n) or right (-$n) from the '.' |
1046 | # $n == 0 means round to integer |
1047 | # expects and returns normalized numbers! |
ee15d750 |
1048 | my $x = shift; my $self = ref($x) || $x; $x = $self->new(shift) if !ref($x); |
a0d0e21e |
1049 | |
58cde26e |
1050 | return $x if $x->modify('bfround'); |
1051 | |
ee15d750 |
1052 | my ($scale,$mode) = $x->_scale_p($self->precision(),$self->round_mode(),@_); |
58cde26e |
1053 | return $x if !defined $scale; # no-op |
1054 | |
574bacfe |
1055 | # never round a 0, +-inf, NaN |
61f5c3f5 |
1056 | if ($x->is_zero()) |
1057 | { |
1058 | $x->{_p} = $scale if !defined $x->{_p} || $x->{_p} < $scale; # -3 < -2 |
1059 | return $x; |
1060 | } |
1061 | return $x if $x->{sign} !~ /^[+-]$/; |
58cde26e |
1062 | # print "MBF bfround $x to scale $scale mode $mode\n"; |
58cde26e |
1063 | |
ee15d750 |
1064 | # don't round if x already has lower precision |
1065 | return $x if (defined $x->{_p} && $x->{_p} < 0 && $scale < $x->{_p}); |
1066 | |
1067 | $x->{_p} = $scale; # remember round in any case |
1068 | $x->{_a} = undef; # and clear A |
58cde26e |
1069 | if ($scale < 0) |
1070 | { |
1071 | # print "bfround scale $scale e $x->{_e}\n"; |
1072 | # round right from the '.' |
1073 | return $x if $x->{_e} >= 0; # nothing to round |
1074 | $scale = -$scale; # positive for simplicity |
1075 | my $len = $x->{_m}->length(); # length of mantissa |
1076 | my $dad = -$x->{_e}; # digits after dot |
1077 | my $zad = 0; # zeros after dot |
1078 | $zad = -$len-$x->{_e} if ($x->{_e} < -$len);# for 0.00..00xxx style |
ee15d750 |
1079 | #print "scale $scale dad $dad zad $zad len $len\n"; |
58cde26e |
1080 | |
1081 | # number bsstr len zad dad |
1082 | # 0.123 123e-3 3 0 3 |
1083 | # 0.0123 123e-4 3 1 4 |
1084 | # 0.001 1e-3 1 2 3 |
1085 | # 1.23 123e-2 3 0 2 |
1086 | # 1.2345 12345e-4 5 0 4 |
1087 | |
1088 | # do not round after/right of the $dad |
1089 | return $x if $scale > $dad; # 0.123, scale >= 3 => exit |
1090 | |
ee15d750 |
1091 | # round to zero if rounding inside the $zad, but not for last zero like: |
1092 | # 0.0065, scale -2, round last '0' with following '65' (scale == zad case) |
1093 | return $x->bzero() if $scale < $zad; |
1094 | if ($scale == $zad) # for 0.006, scale -3 and trunc |
58cde26e |
1095 | { |
ee15d750 |
1096 | $scale = -$len-1; |
58cde26e |
1097 | } |
1098 | else |
1099 | { |
1100 | # adjust round-point to be inside mantissa |
1101 | if ($zad != 0) |
1102 | { |
1103 | $scale = $scale-$zad; |
1104 | } |
1105 | else |
1106 | { |
1107 | my $dbd = $len - $dad; $dbd = 0 if $dbd < 0; # digits before dot |
1108 | $scale = $dbd+$scale; |
1109 | } |
1110 | } |
1111 | # print "round to $x->{_m} to $scale\n"; |
a0d0e21e |
1112 | } |
58cde26e |
1113 | else |
1114 | { |
1115 | # 123 => 100 means length(123) = 3 - $scale (2) => 1 |
a5f75d66 |
1116 | |
58cde26e |
1117 | # calculate digits before dot |
1118 | my $dbt = $x->{_m}->length(); $dbt += $x->{_e} if $x->{_e}->sign() eq '-'; |
ee15d750 |
1119 | # if not enough digits before dot, round to zero |
1120 | return $x->bzero() if ($scale > $dbt) && ($dbt < 0); |
1121 | # scale always >= 0 here |
1122 | if ($dbt == 0) |
58cde26e |
1123 | { |
1124 | # 0.49->bfround(1): scale == 1, dbt == 0: => 0.0 |
1125 | # 0.51->bfround(0): scale == 0, dbt == 0: => 1.0 |
1126 | # 0.5->bfround(0): scale == 0, dbt == 0: => 0 |
1127 | # 0.05->bfround(0): scale == 0, dbt == 0: => 0 |
1128 | # print "$scale $dbt $x->{_m}\n"; |
1129 | $scale = -$x->{_m}->length(); |
1130 | } |
1131 | elsif ($dbt > 0) |
1132 | { |
1133 | # correct by subtracting scale |
1134 | $scale = $dbt - $scale; |
1135 | } |
1136 | else |
1137 | { |
1138 | $scale = $x->{_m}->length() - $scale; |
1139 | } |
a0d0e21e |
1140 | } |
574bacfe |
1141 | # print "using $scale for $x->{_m} with '$mode'\n"; |
1142 | # pass sign to bround for rounding modes '+inf' and '-inf' |
58cde26e |
1143 | $x->{_m}->{sign} = $x->{sign}; |
1144 | $x->{_m}->bround($scale,$mode); |
1145 | $x->{_m}->{sign} = '+'; # fix sign back |
1146 | $x->bnorm(); |
1147 | } |
1148 | |
1149 | sub bround |
1150 | { |
1151 | # accuracy: preserve $N digits, and overwrite the rest with 0's |
ee15d750 |
1152 | my $x = shift; my $self = ref($x) || $x; $x = $self->new(shift) if !ref($x); |
1153 | |
1154 | die ('bround() needs positive accuracy') if ($_[0] || 0) < 0; |
58cde26e |
1155 | |
ee15d750 |
1156 | my ($scale,$mode) = $x->_scale_a($self->accuracy(),$self->round_mode(),@_); |
1157 | return $x if !defined $scale; # no-op |
61f5c3f5 |
1158 | |
58cde26e |
1159 | return $x if $x->modify('bround'); |
61f5c3f5 |
1160 | |
ee15d750 |
1161 | # scale is now either $x->{_a}, $accuracy, or the user parameter |
1162 | # test whether $x already has lower accuracy, do nothing in this case |
1163 | # but do round if the accuracy is the same, since a math operation might |
1164 | # want to round a number with A=5 to 5 digits afterwards again |
1165 | return $x if defined $_[0] && defined $x->{_a} && $x->{_a} < $_[0]; |
58cde26e |
1166 | |
61f5c3f5 |
1167 | # scale < 0 makes no sense |
1168 | # never round a +-inf, NaN |
1169 | return $x if ($scale < 0) || $x->{sign} !~ /^[+-]$/; |
58cde26e |
1170 | |
61f5c3f5 |
1171 | # 1: $scale == 0 => keep all digits |
1172 | # 2: never round a 0 |
1173 | # 3: if we should keep more digits than the mantissa has, do nothing |
1174 | if ($scale == 0 || $x->is_zero() || $x->{_m}->length() <= $scale) |
1175 | { |
1176 | $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; |
1177 | return $x; |
1178 | } |
f216259d |
1179 | |
58cde26e |
1180 | # pass sign to bround for '+inf' and '-inf' rounding modes |
1181 | $x->{_m}->{sign} = $x->{sign}; |
1182 | $x->{_m}->bround($scale,$mode); # round mantissa |
1183 | $x->{_m}->{sign} = '+'; # fix sign back |
61f5c3f5 |
1184 | # $x->{_m}->{_a} = undef; $x->{_m}->{_p} = undef; |
ee15d750 |
1185 | $x->{_a} = $scale; # remember rounding |
1186 | $x->{_p} = undef; # and clear P |
574bacfe |
1187 | $x->bnorm(); # del trailing zeros gen. by bround() |
58cde26e |
1188 | } |
1189 | |
1190 | sub bfloor |
1191 | { |
1192 | # return integer less or equal then $x |
ee15d750 |
1193 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e |
1194 | |
1195 | return $x if $x->modify('bfloor'); |
1196 | |
1197 | return $x if $x->{sign} !~ /^[+-]$/; # nan, +inf, -inf |
1198 | |
1199 | # if $x has digits after dot |
1200 | if ($x->{_e}->{sign} eq '-') |
1201 | { |
1202 | $x->{_m}->brsft(-$x->{_e},10); |
1203 | $x->{_e}->bzero(); |
1204 | $x-- if $x->{sign} eq '-'; |
f216259d |
1205 | } |
61f5c3f5 |
1206 | $x->round($a,$p,$r); |
58cde26e |
1207 | } |
288d023a |
1208 | |
58cde26e |
1209 | sub bceil |
1210 | { |
1211 | # return integer greater or equal then $x |
ee15d750 |
1212 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e |
1213 | |
1214 | return $x if $x->modify('bceil'); |
1215 | return $x if $x->{sign} !~ /^[+-]$/; # nan, +inf, -inf |
1216 | |
1217 | # if $x has digits after dot |
1218 | if ($x->{_e}->{sign} eq '-') |
1219 | { |
1220 | $x->{_m}->brsft(-$x->{_e},10); |
1221 | $x->{_e}->bzero(); |
1222 | $x++ if $x->{sign} eq '+'; |
a0d0e21e |
1223 | } |
61f5c3f5 |
1224 | $x->round($a,$p,$r); |
58cde26e |
1225 | } |
1226 | |
394e6ffb |
1227 | sub brsft |
1228 | { |
1229 | # shift right by $y (divide by power of 2) |
1230 | my ($self,$x,$y,$n,$a,$p,$r) = objectify(2,@_); |
1231 | |
1232 | return $x if $x->modify('brsft'); |
1233 | return $x if $x->{sign} !~ /^[+-]$/; # nan, +inf, -inf |
1234 | |
1235 | $n = 2 if !defined $n; $n = Math::BigFloat->new($n); |
1236 | $x->bdiv($n ** $y,$a,$p,$r,$y); |
1237 | } |
1238 | |
1239 | sub blsft |
1240 | { |
1241 | # shift right by $y (divide by power of 2) |
1242 | my ($self,$x,$y,$n,$a,$p,$r) = objectify(2,@_); |
1243 | |
1244 | return $x if $x->modify('brsft'); |
1245 | return $x if $x->{sign} !~ /^[+-]$/; # nan, +inf, -inf |
1246 | |
1247 | $n = 2 if !defined $n; $n = Math::BigFloat->new($n); |
1248 | $x->bmul($n ** $y,$a,$p,$r,$y); |
1249 | } |
1250 | |
58cde26e |
1251 | ############################################################################### |
a5f75d66 |
1252 | |
58cde26e |
1253 | sub DESTROY |
1254 | { |
ee15d750 |
1255 | # going through AUTOLOAD for every DESTROY is costly, so avoid it by empty sub |
58cde26e |
1256 | } |
1257 | |
1258 | sub AUTOLOAD |
1259 | { |
1260 | # make fxxx and bxxx work |
1261 | # my $self = $_[0]; |
1262 | my $name = $AUTOLOAD; |
1263 | |
1264 | $name =~ s/.*:://; # split package |
1265 | #print "$name\n"; |
ee15d750 |
1266 | no strict 'refs'; |
1267 | if (!method_alias($name)) |
58cde26e |
1268 | { |
ee15d750 |
1269 | if (!defined $name) |
1270 | { |
1271 | # delayed load of Carp and avoid recursion |
1272 | require Carp; |
1273 | Carp::croak ("Can't call a method without name"); |
1274 | } |
ee15d750 |
1275 | if (!method_hand_up($name)) |
1276 | { |
1277 | # delayed load of Carp and avoid recursion |
1278 | require Carp; |
1279 | Carp::croak ("Can't call $class\-\>$name, not a valid method"); |
1280 | } |
1281 | # try one level up, but subst. bxxx() for fxxx() since MBI only got bxxx() |
1282 | $name =~ s/^f/b/; |
1283 | return &{'Math::BigInt'."::$name"}(@_); |
a0d0e21e |
1284 | } |
58cde26e |
1285 | my $bname = $name; $bname =~ s/^f/b/; |
1286 | *{$class."\:\:$name"} = \&$bname; |
1287 | &$bname; # uses @_ |
1288 | } |
1289 | |
1290 | sub exponent |
1291 | { |
1292 | # return a copy of the exponent |
ee15d750 |
1293 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
1294 | |
ee15d750 |
1295 | if ($x->{sign} !~ /^[+-]$/) |
1296 | { |
1297 | my $s = $x->{sign}; $s =~ s/^[+-]//; |
1298 | return $self->new($s); # -inf, +inf => +inf |
1299 | } |
1300 | return $x->{_e}->copy(); |
58cde26e |
1301 | } |
1302 | |
1303 | sub mantissa |
1304 | { |
1305 | # return a copy of the mantissa |
ee15d750 |
1306 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
1307 | |
ee15d750 |
1308 | if ($x->{sign} !~ /^[+-]$/) |
1309 | { |
1310 | my $s = $x->{sign}; $s =~ s/^[+]//; |
1311 | return $self->new($s); # -inf, +inf => +inf |
1312 | } |
1313 | my $m = $x->{_m}->copy(); # faster than going via bstr() |
1314 | $m->bneg() if $x->{sign} eq '-'; |
58cde26e |
1315 | |
61f5c3f5 |
1316 | $m; |
58cde26e |
1317 | } |
1318 | |
1319 | sub parts |
1320 | { |
1321 | # return a copy of both the exponent and the mantissa |
ee15d750 |
1322 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
1323 | |
ee15d750 |
1324 | if ($x->{sign} !~ /^[+-]$/) |
1325 | { |
1326 | my $s = $x->{sign}; $s =~ s/^[+]//; my $se = $s; $se =~ s/^[-]//; |
1327 | return ($self->new($s),$self->new($se)); # +inf => inf and -inf,+inf => inf |
1328 | } |
1329 | my $m = $x->{_m}->copy(); # faster than going via bstr() |
1330 | $m->bneg() if $x->{sign} eq '-'; |
1331 | return ($m,$x->{_e}->copy()); |
58cde26e |
1332 | } |
1333 | |
1334 | ############################################################################## |
1335 | # private stuff (internal use only) |
1336 | |
58cde26e |
1337 | sub import |
1338 | { |
1339 | my $self = shift; |
58cde26e |
1340 | for ( my $i = 0; $i < @_ ; $i++ ) |
1341 | { |
1342 | if ( $_[$i] eq ':constant' ) |
1343 | { |
1344 | # this rest causes overlord er load to step in |
1345 | # print "overload @_\n"; |
1346 | overload::constant float => sub { $self->new(shift); }; |
1347 | splice @_, $i, 1; last; |
1348 | } |
1349 | } |
1350 | # any non :constant stuff is handled by our parent, Exporter |
1351 | # even if @_ is empty, to give it a chance |
abcfbf51 |
1352 | $self->SUPER::import(@_); # for subclasses |
1353 | $self->export_to_level(1,$self,@_); # need this, too |
58cde26e |
1354 | } |
1355 | |
1356 | sub bnorm |
1357 | { |
1358 | # adjust m and e so that m is smallest possible |
1359 | # round number according to accuracy and precision settings |
ee15d750 |
1360 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
1361 | |
0716bf9b |
1362 | return $x if $x->{sign} !~ /^[+-]$/; # inf, nan etc |
58cde26e |
1363 | |
1364 | my $zeros = $x->{_m}->_trailing_zeros(); # correct for trailing zeros |
1365 | if ($zeros != 0) |
1366 | { |
1367 | $x->{_m}->brsft($zeros,10); $x->{_e} += $zeros; |
1368 | } |
ee15d750 |
1369 | # for something like 0Ey, set y to 1, and -0 => +0 |
1370 | $x->{sign} = '+', $x->{_e}->bone() if $x->{_m}->is_zero(); |
1371 | # this is to prevent automatically rounding when MBI's globals are set |
0716bf9b |
1372 | $x->{_m}->{_f} = MB_NEVER_ROUND; |
1373 | $x->{_e}->{_f} = MB_NEVER_ROUND; |
ee15d750 |
1374 | # 'forget' that mantissa was rounded via MBI::bround() in MBF's bfround() |
1375 | $x->{_m}->{_a} = undef; $x->{_e}->{_a} = undef; |
1376 | $x->{_m}->{_p} = undef; $x->{_e}->{_p} = undef; |
61f5c3f5 |
1377 | $x; # MBI bnorm is no-op, so dont call it |
1378 | } |
58cde26e |
1379 | |
1380 | ############################################################################## |
1381 | # internal calculation routines |
1382 | |
1383 | sub as_number |
1384 | { |
394e6ffb |
1385 | # return copy as a bigint representation of this BigFloat number |
1386 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
1387 | |
1388 | my $z; |
1389 | if ($x->{_e}->is_zero()) |
1390 | { |
1391 | $z = $x->{_m}->copy(); |
1392 | $z->{sign} = $x->{sign}; |
1393 | return $z; |
1394 | } |
0716bf9b |
1395 | $z = $x->{_m}->copy(); |
58cde26e |
1396 | if ($x->{_e} < 0) |
1397 | { |
0716bf9b |
1398 | $z->brsft(-$x->{_e},10); |
1399 | } |
1400 | else |
1401 | { |
1402 | $z->blsft($x->{_e},10); |
58cde26e |
1403 | } |
58cde26e |
1404 | $z->{sign} = $x->{sign}; |
61f5c3f5 |
1405 | $z; |
58cde26e |
1406 | } |
1407 | |
1408 | sub length |
1409 | { |
ee15d750 |
1410 | my $x = shift; |
1411 | my $class = ref($x) || $x; |
1412 | $x = $class->new(shift) unless ref($x); |
58cde26e |
1413 | |
ee15d750 |
1414 | return 1 if $x->{_m}->is_zero(); |
58cde26e |
1415 | my $len = $x->{_m}->length(); |
1416 | $len += $x->{_e} if $x->{_e}->sign() eq '+'; |
1417 | if (wantarray()) |
1418 | { |
1419 | my $t = Math::BigInt::bzero(); |
1420 | $t = $x->{_e}->copy()->babs() if $x->{_e}->sign() eq '-'; |
1421 | return ($len,$t); |
1422 | } |
61f5c3f5 |
1423 | $len; |
58cde26e |
1424 | } |
a0d0e21e |
1425 | |
1426 | 1; |
a5f75d66 |
1427 | __END__ |
1428 | |
1429 | =head1 NAME |
1430 | |
58cde26e |
1431 | Math::BigFloat - Arbitrary size floating point math package |
a5f75d66 |
1432 | |
1433 | =head1 SYNOPSIS |
1434 | |
a2008d6d |
1435 | use Math::BigFloat; |
58cde26e |
1436 | |
1437 | # Number creation |
1438 | $x = Math::BigInt->new($str); # defaults to 0 |
1439 | $nan = Math::BigInt->bnan(); # create a NotANumber |
1440 | $zero = Math::BigInt->bzero();# create a "+0" |
1441 | |
1442 | # Testing |
1443 | $x->is_zero(); # return whether arg is zero or not |
0716bf9b |
1444 | $x->is_nan(); # return whether arg is NaN or not |
1445 | $x->is_one(); # true if arg is +1 |
1446 | $x->is_one('-'); # true if arg is -1 |
1447 | $x->is_odd(); # true if odd, false for even |
1448 | $x->is_even(); # true if even, false for odd |
1449 | $x->is_positive(); # true if >= 0 |
1450 | $x->is_negative(); # true if < 0 |
1451 | $x->is_inf(sign) # true if +inf or -inf (sign default '+') |
58cde26e |
1452 | $x->bcmp($y); # compare numbers (undef,<0,=0,>0) |
1453 | $x->bacmp($y); # compare absolutely (undef,<0,=0,>0) |
1454 | $x->sign(); # return the sign, either +,- or NaN |
1455 | |
1456 | # The following all modify their first argument: |
1457 | |
1458 | # set |
1459 | $x->bzero(); # set $i to 0 |
1460 | $x->bnan(); # set $i to NaN |
1461 | |
1462 | $x->bneg(); # negation |
1463 | $x->babs(); # absolute value |
1464 | $x->bnorm(); # normalize (no-op) |
1465 | $x->bnot(); # two's complement (bit wise not) |
1466 | $x->binc(); # increment x by 1 |
1467 | $x->bdec(); # decrement x by 1 |
1468 | |
1469 | $x->badd($y); # addition (add $y to $x) |
1470 | $x->bsub($y); # subtraction (subtract $y from $x) |
1471 | $x->bmul($y); # multiplication (multiply $x by $y) |
1472 | $x->bdiv($y); # divide, set $i to quotient |
1473 | # return (quo,rem) or quo if scalar |
1474 | |
1475 | $x->bmod($y); # modulus |
1476 | $x->bpow($y); # power of arguments (a**b) |
1477 | $x->blsft($y); # left shift |
1478 | $x->brsft($y); # right shift |
1479 | # return (quo,rem) or quo if scalar |
1480 | |
61f5c3f5 |
1481 | $x->blog($base); # logarithm of $x, base defaults to e |
1482 | # (other bases than e not supported yet) |
1483 | |
58cde26e |
1484 | $x->band($y); # bit-wise and |
1485 | $x->bior($y); # bit-wise inclusive or |
1486 | $x->bxor($y); # bit-wise exclusive or |
1487 | $x->bnot(); # bit-wise not (two's complement) |
1488 | |
1489 | $x->bround($N); # accuracy: preserver $N digits |
1490 | $x->bfround($N); # precision: round to the $Nth digit |
1491 | |
1492 | # The following do not modify their arguments: |
1493 | |
1494 | bgcd(@values); # greatest common divisor |
1495 | blcm(@values); # lowest common multiplicator |
1496 | |
1497 | $x->bstr(); # return string |
1498 | $x->bsstr(); # return string in scientific notation |
1499 | |
1500 | $x->exponent(); # return exponent as BigInt |
1501 | $x->mantissa(); # return mantissa as BigInt |
1502 | $x->parts(); # return (mantissa,exponent) as BigInt |
1503 | |
1504 | $x->length(); # number of digits (w/o sign and '.') |
1505 | ($l,$f) = $x->length(); # number of digits, and length of fraction |
a5f75d66 |
1506 | |
1507 | =head1 DESCRIPTION |
1508 | |
58cde26e |
1509 | All operators (inlcuding basic math operations) are overloaded if you |
1510 | declare your big floating point numbers as |
a5f75d66 |
1511 | |
58cde26e |
1512 | $i = new Math::BigFloat '12_3.456_789_123_456_789E-2'; |
1513 | |
1514 | Operations with overloaded operators preserve the arguments, which is |
1515 | exactly what you expect. |
1516 | |
1517 | =head2 Canonical notation |
1518 | |
1519 | Input to these routines are either BigFloat objects, or strings of the |
1520 | following four forms: |
a5f75d66 |
1521 | |
1522 | =over 2 |
1523 | |
58cde26e |
1524 | =item * |
1525 | |
1526 | C</^[+-]\d+$/> |
a5f75d66 |
1527 | |
58cde26e |
1528 | =item * |
a5f75d66 |
1529 | |
58cde26e |
1530 | C</^[+-]\d+\.\d*$/> |
a5f75d66 |
1531 | |
58cde26e |
1532 | =item * |
a5f75d66 |
1533 | |
58cde26e |
1534 | C</^[+-]\d+E[+-]?\d+$/> |
a5f75d66 |
1535 | |
58cde26e |
1536 | =item * |
a5f75d66 |
1537 | |
58cde26e |
1538 | C</^[+-]\d*\.\d+E[+-]?\d+$/> |
5d7098d5 |
1539 | |
58cde26e |
1540 | =back |
1541 | |
1542 | all with optional leading and trailing zeros and/or spaces. Additonally, |
1543 | numbers are allowed to have an underscore between any two digits. |
1544 | |
1545 | Empty strings as well as other illegal numbers results in 'NaN'. |
1546 | |
1547 | bnorm() on a BigFloat object is now effectively a no-op, since the numbers |
1548 | are always stored in normalized form. On a string, it creates a BigFloat |
1549 | object. |
1550 | |
1551 | =head2 Output |
1552 | |
1553 | Output values are BigFloat objects (normalized), except for bstr() and bsstr(). |
1554 | |
1555 | The string output will always have leading and trailing zeros stripped and drop |
1556 | a plus sign. C<bstr()> will give you always the form with a decimal point, |
1557 | while C<bsstr()> (for scientific) gives you the scientific notation. |
1558 | |
1559 | Input bstr() bsstr() |
1560 | '-0' '0' '0E1' |
1561 | ' -123 123 123' '-123123123' '-123123123E0' |
1562 | '00.0123' '0.0123' '123E-4' |
1563 | '123.45E-2' '1.2345' '12345E-4' |
1564 | '10E+3' '10000' '1E4' |
1565 | |
1566 | Some routines (C<is_odd()>, C<is_even()>, C<is_zero()>, C<is_one()>, |
1567 | C<is_nan()>) return true or false, while others (C<bcmp()>, C<bacmp()>) |
1568 | return either undef, <0, 0 or >0 and are suited for sort. |
1569 | |
1570 | Actual math is done by using BigInts to represent the mantissa and exponent. |
1571 | The sign C</^[+-]$/> is stored separately. The string 'NaN' is used to |
1572 | represent the result when input arguments are not numbers, as well as |
1573 | the result of dividing by zero. |
1574 | |
1575 | =head2 C<mantissa()>, C<exponent()> and C<parts()> |
1576 | |
1577 | C<mantissa()> and C<exponent()> return the said parts of the BigFloat |
1578 | as BigInts such that: |
1579 | |
1580 | $m = $x->mantissa(); |
1581 | $e = $x->exponent(); |
1582 | $y = $m * ( 10 ** $e ); |
1583 | print "ok\n" if $x == $y; |
1584 | |
1585 | C<< ($m,$e) = $x->parts(); >> is just a shortcut giving you both of them. |
1586 | |
1587 | A zero is represented and returned as C<0E1>, B<not> C<0E0> (after Knuth). |
1588 | |
1589 | Currently the mantissa is reduced as much as possible, favouring higher |
1590 | exponents over lower ones (e.g. returning 1e7 instead of 10e6 or 10000000e0). |
1591 | This might change in the future, so do not depend on it. |
1592 | |
1593 | =head2 Accuracy vs. Precision |
1594 | |
1595 | See also: L<Rounding|Rounding>. |
1596 | |
027dc388 |
1597 | Math::BigFloat supports both precision and accuracy. For a full documentation, |
1598 | examples and tips on these topics please see the large section in |
1599 | L<Math::BigInt>. |
5d7098d5 |
1600 | |
58cde26e |
1601 | Since things like sqrt(2) or 1/3 must presented with a limited precision lest |
1602 | a operation consumes all resources, each operation produces no more than |
1603 | C<Math::BigFloat::precision()> digits. |
1604 | |
1605 | In case the result of one operation has more precision than specified, |
1606 | it is rounded. The rounding mode taken is either the default mode, or the one |
1607 | supplied to the operation after the I<scale>: |
1608 | |
1609 | $x = Math::BigFloat->new(2); |
1610 | Math::BigFloat::precision(5); # 5 digits max |
1611 | $y = $x->copy()->bdiv(3); # will give 0.66666 |
1612 | $y = $x->copy()->bdiv(3,6); # will give 0.666666 |
1613 | $y = $x->copy()->bdiv(3,6,'odd'); # will give 0.666667 |
1614 | Math::BigFloat::round_mode('zero'); |
1615 | $y = $x->copy()->bdiv(3,6); # will give 0.666666 |
1616 | |
1617 | =head2 Rounding |
1618 | |
1619 | =over 2 |
1620 | |
5dc6f178 |
1621 | =item ffround ( +$scale ) |
58cde26e |
1622 | |
0716bf9b |
1623 | Rounds to the $scale'th place left from the '.', counting from the dot. |
1624 | The first digit is numbered 1. |
58cde26e |
1625 | |
5dc6f178 |
1626 | =item ffround ( -$scale ) |
58cde26e |
1627 | |
0716bf9b |
1628 | Rounds to the $scale'th place right from the '.', counting from the dot. |
58cde26e |
1629 | |
5dc6f178 |
1630 | =item ffround ( 0 ) |
1631 | |
0716bf9b |
1632 | Rounds to an integer. |
5dc6f178 |
1633 | |
1634 | =item fround ( +$scale ) |
1635 | |
0716bf9b |
1636 | Preserves accuracy to $scale digits from the left (aka significant digits) |
1637 | and pads the rest with zeros. If the number is between 1 and -1, the |
1638 | significant digits count from the first non-zero after the '.' |
5dc6f178 |
1639 | |
1640 | =item fround ( -$scale ) and fround ( 0 ) |
1641 | |
0716bf9b |
1642 | These are effetively no-ops. |
5d7098d5 |
1643 | |
a5f75d66 |
1644 | =back |
1645 | |
0716bf9b |
1646 | All rounding functions take as a second parameter a rounding mode from one of |
1647 | the following: 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'. |
58cde26e |
1648 | |
1649 | The default rounding mode is 'even'. By using |
ee15d750 |
1650 | C<< Math::BigFloat::round_mode($round_mode); >> you can get and set the default |
1651 | mode for subsequent rounding. The usage of C<$Math::BigFloat::$round_mode> is |
0716bf9b |
1652 | no longer supported. |
b22b3e31 |
1653 | The second parameter to the round functions then overrides the default |
0716bf9b |
1654 | temporarily. |
58cde26e |
1655 | |
1656 | The C<< as_number() >> function returns a BigInt from a Math::BigFloat. It uses |
1657 | 'trunc' as rounding mode to make it equivalent to: |
1658 | |
1659 | $x = 2.5; |
1660 | $y = int($x) + 2; |
1661 | |
1662 | You can override this by passing the desired rounding mode as parameter to |
1663 | C<as_number()>: |
1664 | |
1665 | $x = Math::BigFloat->new(2.5); |
1666 | $y = $x->as_number('odd'); # $y = 3 |
1667 | |
1668 | =head1 EXAMPLES |
1669 | |
58cde26e |
1670 | # not ready yet |
58cde26e |
1671 | |
1672 | =head1 Autocreating constants |
1673 | |
1674 | After C<use Math::BigFloat ':constant'> all the floating point constants |
1675 | in the given scope are converted to C<Math::BigFloat>. This conversion |
1676 | happens at compile time. |
1677 | |
1678 | In particular |
1679 | |
1680 | perl -MMath::BigFloat=:constant -e 'print 2E-100,"\n"' |
1681 | |
1682 | prints the value of C<2E-100>. Note that without conversion of |
1683 | constants the expression 2E-100 will be calculated as normal floating point |
1684 | number. |
1685 | |
a5f75d66 |
1686 | =head1 BUGS |
1687 | |
58cde26e |
1688 | =over 2 |
1689 | |
1690 | =item * |
1691 | |
1692 | The following does not work yet: |
1693 | |
1694 | $m = $x->mantissa(); |
1695 | $e = $x->exponent(); |
1696 | $y = $m * ( 10 ** $e ); |
1697 | print "ok\n" if $x == $y; |
1698 | |
1699 | =item * |
1700 | |
1701 | There is no fmod() function yet. |
1702 | |
1703 | =back |
1704 | |
1705 | =head1 CAVEAT |
1706 | |
1707 | =over 1 |
1708 | |
1709 | =item stringify, bstr() |
1710 | |
1711 | Both stringify and bstr() now drop the leading '+'. The old code would return |
1712 | '+1.23', the new returns '1.23'. See the documentation in L<Math::BigInt> for |
1713 | reasoning and details. |
1714 | |
1715 | =item bdiv |
1716 | |
1717 | The following will probably not do what you expect: |
1718 | |
1719 | print $c->bdiv(123.456),"\n"; |
1720 | |
1721 | It prints both quotient and reminder since print works in list context. Also, |
1722 | bdiv() will modify $c, so be carefull. You probably want to use |
1723 | |
1724 | print $c / 123.456,"\n"; |
1725 | print scalar $c->bdiv(123.456),"\n"; # or if you want to modify $c |
1726 | |
1727 | instead. |
1728 | |
1729 | =item Modifying and = |
1730 | |
1731 | Beware of: |
1732 | |
1733 | $x = Math::BigFloat->new(5); |
1734 | $y = $x; |
1735 | |
1736 | It will not do what you think, e.g. making a copy of $x. Instead it just makes |
1737 | a second reference to the B<same> object and stores it in $y. Thus anything |
1738 | that modifies $x will modify $y, and vice versa. |
1739 | |
1740 | $x->bmul(2); |
1741 | print "$x, $y\n"; # prints '10, 10' |
1742 | |
1743 | If you want a true copy of $x, use: |
1744 | |
1745 | $y = $x->copy(); |
1746 | |
1747 | See also the documentation in L<overload> regarding C<=>. |
1748 | |
1749 | =item bpow |
1750 | |
1751 | C<bpow()> now modifies the first argument, unlike the old code which left |
1752 | it alone and only returned the result. This is to be consistent with |
1753 | C<badd()> etc. The first will modify $x, the second one won't: |
1754 | |
1755 | print bpow($x,$i),"\n"; # modify $x |
1756 | print $x->bpow($i),"\n"; # ditto |
1757 | print $x ** $i,"\n"; # leave $x alone |
1758 | |
1759 | =back |
1760 | |
1761 | =head1 LICENSE |
a5f75d66 |
1762 | |
58cde26e |
1763 | This program is free software; you may redistribute it and/or modify it under |
1764 | the same terms as Perl itself. |
5d7098d5 |
1765 | |
58cde26e |
1766 | =head1 AUTHORS |
5d7098d5 |
1767 | |
58cde26e |
1768 | Mark Biggar, overloaded interface by Ilya Zakharevich. |
1769 | Completely rewritten by Tels http://bloodgate.com in 2001. |
a5f75d66 |
1770 | |
a5f75d66 |
1771 | =cut |