1 | package Math::BigInt;
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2 |
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3 | #
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4 | # "Mike had an infinite amount to do and a negative amount of time in which
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5 | # to do it." - Before and After
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6 | #
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7 |
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8 | # The following hash values are used:
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9 | # value: unsigned int with actual value (as a Math::BigInt::Calc or similiar)
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10 | # sign : +,-,NaN,+inf,-inf
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11 | # _a : accuracy
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12 | # _p : precision
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13 | # _f : flags, used by MBF to flag parts of a float as untouchable
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14 |
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15 | # Remember not to take shortcuts ala $xs = $x->{value}; $CALC->foo($xs); since
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16 | # underlying lib might change the reference!
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17 |
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18 | my $class = "Math::BigInt";
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19 | require 5.005;
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20 |
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21 | $VERSION = '1.77';
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22 |
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23 | @ISA = qw(Exporter);
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24 | @EXPORT_OK = qw(objectify bgcd blcm);
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25 |
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26 | # _trap_inf and _trap_nan are internal and should never be accessed from the
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27 | # outside
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28 | use vars qw/$round_mode $accuracy $precision $div_scale $rnd_mode
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29 | $upgrade $downgrade $_trap_nan $_trap_inf/;
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30 | use strict;
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31 |
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32 | # Inside overload, the first arg is always an object. If the original code had
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33 | # it reversed (like $x = 2 * $y), then the third paramater is true.
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34 | # In some cases (like add, $x = $x + 2 is the same as $x = 2 + $x) this makes
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35 | # no difference, but in some cases it does.
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36 |
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37 | # For overloaded ops with only one argument we simple use $_[0]->copy() to
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38 | # preserve the argument.
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39 |
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40 | # Thus inheritance of overload operators becomes possible and transparent for
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41 | # our subclasses without the need to repeat the entire overload section there.
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42 |
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43 | use overload
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44 | '=' => sub { $_[0]->copy(); },
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45 |
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46 | # some shortcuts for speed (assumes that reversed order of arguments is routed
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47 | # to normal '+' and we thus can always modify first arg. If this is changed,
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48 | # this breaks and must be adjusted.)
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49 | '+=' => sub { $_[0]->badd($_[1]); },
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50 | '-=' => sub { $_[0]->bsub($_[1]); },
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51 | '*=' => sub { $_[0]->bmul($_[1]); },
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52 | '/=' => sub { scalar $_[0]->bdiv($_[1]); },
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53 | '%=' => sub { $_[0]->bmod($_[1]); },
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54 | '^=' => sub { $_[0]->bxor($_[1]); },
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55 | '&=' => sub { $_[0]->band($_[1]); },
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56 | '|=' => sub { $_[0]->bior($_[1]); },
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57 |
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58 | '**=' => sub { $_[0]->bpow($_[1]); },
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59 | '<<=' => sub { $_[0]->blsft($_[1]); },
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60 | '>>=' => sub { $_[0]->brsft($_[1]); },
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61 |
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62 | # not supported by Perl yet
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63 | '..' => \&_pointpoint,
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64 |
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65 | # we might need '==' and '!=' to get things like "NaN == NaN" right
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66 | '<=>' => sub { $_[2] ?
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67 | ref($_[0])->bcmp($_[1],$_[0]) :
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68 | $_[0]->bcmp($_[1]); },
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69 | 'cmp' => sub {
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70 | $_[2] ?
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71 | "$_[1]" cmp $_[0]->bstr() :
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72 | $_[0]->bstr() cmp "$_[1]" },
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73 |
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74 | # make cos()/sin()/exp() "work" with BigInt's or subclasses
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75 | 'cos' => sub { cos($_[0]->numify()) },
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76 | 'sin' => sub { sin($_[0]->numify()) },
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77 | 'exp' => sub { exp($_[0]->numify()) },
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78 | 'atan2' => sub { $_[2] ?
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79 | atan2($_[1],$_[0]->numify()) :
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80 | atan2($_[0]->numify(),$_[1]) },
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81 |
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82 | # are not yet overloadable
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83 | #'hex' => sub { print "hex"; $_[0]; },
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84 | #'oct' => sub { print "oct"; $_[0]; },
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85 |
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86 | 'log' => sub { $_[0]->copy()->blog($_[1]); },
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87 | 'int' => sub { $_[0]->copy(); },
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88 | 'neg' => sub { $_[0]->copy()->bneg(); },
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89 | 'abs' => sub { $_[0]->copy()->babs(); },
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90 | 'sqrt' => sub { $_[0]->copy()->bsqrt(); },
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91 | '~' => sub { $_[0]->copy()->bnot(); },
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92 |
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93 | # for subtract it's a bit tricky to not modify b: b-a => -a+b
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94 | '-' => sub { my $c = $_[0]->copy; $_[2] ?
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95 | $c->bneg()->badd( $_[1]) :
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96 | $c->bsub( $_[1]) },
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97 | '+' => sub { $_[0]->copy()->badd($_[1]); },
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98 | '*' => sub { $_[0]->copy()->bmul($_[1]); },
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99 |
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100 | '/' => sub {
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101 | $_[2] ? ref($_[0])->new($_[1])->bdiv($_[0]) : $_[0]->copy->bdiv($_[1]);
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102 | },
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103 | '%' => sub {
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104 | $_[2] ? ref($_[0])->new($_[1])->bmod($_[0]) : $_[0]->copy->bmod($_[1]);
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105 | },
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106 | '**' => sub {
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107 | $_[2] ? ref($_[0])->new($_[1])->bpow($_[0]) : $_[0]->copy->bpow($_[1]);
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108 | },
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109 | '<<' => sub {
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110 | $_[2] ? ref($_[0])->new($_[1])->blsft($_[0]) : $_[0]->copy->blsft($_[1]);
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111 | },
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112 | '>>' => sub {
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113 | $_[2] ? ref($_[0])->new($_[1])->brsft($_[0]) : $_[0]->copy->brsft($_[1]);
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114 | },
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115 | '&' => sub {
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116 | $_[2] ? ref($_[0])->new($_[1])->band($_[0]) : $_[0]->copy->band($_[1]);
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117 | },
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118 | '|' => sub {
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119 | $_[2] ? ref($_[0])->new($_[1])->bior($_[0]) : $_[0]->copy->bior($_[1]);
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120 | },
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121 | '^' => sub {
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122 | $_[2] ? ref($_[0])->new($_[1])->bxor($_[0]) : $_[0]->copy->bxor($_[1]);
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123 | },
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124 |
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125 | # can modify arg of ++ and --, so avoid a copy() for speed, but don't
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126 | # use $_[0]->bone(), it would modify $_[0] to be 1!
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127 | '++' => sub { $_[0]->binc() },
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128 | '--' => sub { $_[0]->bdec() },
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129 |
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130 | # if overloaded, O(1) instead of O(N) and twice as fast for small numbers
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131 | 'bool' => sub {
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132 | # this kludge is needed for perl prior 5.6.0 since returning 0 here fails :-/
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133 | # v5.6.1 dumps on this: return !$_[0]->is_zero() || undef; :-(
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134 | my $t = undef;
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135 | $t = 1 if !$_[0]->is_zero();
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136 | $t;
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137 | },
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138 |
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139 | # the original qw() does not work with the TIESCALAR below, why?
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140 | # Order of arguments unsignificant
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141 | '""' => sub { $_[0]->bstr(); },
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142 | '0+' => sub { $_[0]->numify(); }
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143 | ;
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144 |
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145 | ##############################################################################
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146 | # global constants, flags and accessory
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147 |
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148 | # These vars are public, but their direct usage is not recommended, use the
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149 | # accessor methods instead
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150 |
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151 | $round_mode = 'even'; # one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'
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152 | $accuracy = undef;
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153 | $precision = undef;
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154 | $div_scale = 40;
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155 |
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156 | $upgrade = undef; # default is no upgrade
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157 | $downgrade = undef; # default is no downgrade
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158 |
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159 | # These are internally, and not to be used from the outside at all
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160 |
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161 | $_trap_nan = 0; # are NaNs ok? set w/ config()
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162 | $_trap_inf = 0; # are infs ok? set w/ config()
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163 | my $nan = 'NaN'; # constants for easier life
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164 |
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165 | my $CALC = 'Math::BigInt::FastCalc'; # module to do the low level math
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166 | # default is FastCalc.pm
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167 | my $IMPORT = 0; # was import() called yet?
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168 | # used to make require work
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169 | my %WARN; # warn only once for low-level libs
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170 | my %CAN; # cache for $CALC->can(...)
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171 | my %CALLBACKS; # callbacks to notify on lib loads
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172 | my $EMU_LIB = 'Math/BigInt/CalcEmu.pm'; # emulate low-level math
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173 |
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174 | ##############################################################################
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175 | # the old code had $rnd_mode, so we need to support it, too
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176 |
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177 | $rnd_mode = 'even';
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178 | sub TIESCALAR { my ($class) = @_; bless \$round_mode, $class; }
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179 | sub FETCH { return $round_mode; }
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180 | sub STORE { $rnd_mode = $_[0]->round_mode($_[1]); }
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181 |
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182 | BEGIN
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183 | {
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184 | # tie to enable $rnd_mode to work transparently
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185 | tie $rnd_mode, 'Math::BigInt';
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186 |
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187 | # set up some handy alias names
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188 | *as_int = \&as_number;
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189 | *is_pos = \&is_positive;
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190 | *is_neg = \&is_negative;
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191 | }
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192 |
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193 | ##############################################################################
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194 |
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195 | sub round_mode
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196 | {
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197 | no strict 'refs';
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198 | # make Class->round_mode() work
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199 | my $self = shift;
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200 | my $class = ref($self) || $self || __PACKAGE__;
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201 | if (defined $_[0])
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202 | {
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203 | my $m = shift;
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204 | if ($m !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/)
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205 | {
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206 | require Carp; Carp::croak ("Unknown round mode '$m'");
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207 | }
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208 | return ${"${class}::round_mode"} = $m;
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209 | }
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210 | ${"${class}::round_mode"};
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211 | }
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212 |
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213 | sub upgrade
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214 | {
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215 | no strict 'refs';
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216 | # make Class->upgrade() work
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217 | my $self = shift;
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218 | my $class = ref($self) || $self || __PACKAGE__;
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219 | # need to set new value?
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220 | if (@_ > 0)
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221 | {
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222 | return ${"${class}::upgrade"} = $_[0];
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223 | }
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224 | ${"${class}::upgrade"};
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225 | }
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226 |
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227 | sub downgrade
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228 | {
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229 | no strict 'refs';
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230 | # make Class->downgrade() work
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231 | my $self = shift;
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232 | my $class = ref($self) || $self || __PACKAGE__;
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233 | # need to set new value?
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234 | if (@_ > 0)
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235 | {
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236 | return ${"${class}::downgrade"} = $_[0];
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237 | }
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238 | ${"${class}::downgrade"};
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239 | }
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240 |
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241 | sub div_scale
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242 | {
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243 | no strict 'refs';
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244 | # make Class->div_scale() work
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245 | my $self = shift;
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246 | my $class = ref($self) || $self || __PACKAGE__;
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247 | if (defined $_[0])
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248 | {
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249 | if ($_[0] < 0)
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250 | {
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251 | require Carp; Carp::croak ('div_scale must be greater than zero');
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252 | }
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253 | ${"${class}::div_scale"} = $_[0];
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254 | }
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255 | ${"${class}::div_scale"};
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256 | }
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257 |
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258 | sub accuracy
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259 | {
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260 | # $x->accuracy($a); ref($x) $a
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261 | # $x->accuracy(); ref($x)
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262 | # Class->accuracy(); class
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263 | # Class->accuracy($a); class $a
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264 |
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265 | my $x = shift;
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266 | my $class = ref($x) || $x || __PACKAGE__;
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267 |
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268 | no strict 'refs';
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269 | # need to set new value?
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270 | if (@_ > 0)
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271 | {
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272 | my $a = shift;
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273 | # convert objects to scalars to avoid deep recursion. If object doesn't
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274 | # have numify(), then hopefully it will have overloading for int() and
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275 | # boolean test without wandering into a deep recursion path...
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276 | $a = $a->numify() if ref($a) && $a->can('numify');
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277 |
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278 | if (defined $a)
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279 | {
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280 | # also croak on non-numerical
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281 | if (!$a || $a <= 0)
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282 | {
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283 | require Carp;
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284 | Carp::croak ('Argument to accuracy must be greater than zero');
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285 | }
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286 | if (int($a) != $a)
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287 | {
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288 | require Carp; Carp::croak ('Argument to accuracy must be an integer');
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289 | }
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290 | }
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291 | if (ref($x))
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292 | {
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293 | # $object->accuracy() or fallback to global
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294 | $x->bround($a) if $a; # not for undef, 0
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295 | $x->{_a} = $a; # set/overwrite, even if not rounded
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296 | delete $x->{_p}; # clear P
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297 | $a = ${"${class}::accuracy"} unless defined $a; # proper return value
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298 | }
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299 | else
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300 | {
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301 | ${"${class}::accuracy"} = $a; # set global A
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302 | ${"${class}::precision"} = undef; # clear global P
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303 | }
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304 | return $a; # shortcut
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305 | }
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306 |
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307 | my $a;
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308 | # $object->accuracy() or fallback to global
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309 | $a = $x->{_a} if ref($x);
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310 | # but don't return global undef, when $x's accuracy is 0!
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311 | $a = ${"${class}::accuracy"} if !defined $a;
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312 | $a;
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313 | }
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314 |
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315 | sub precision
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316 | {
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317 | # $x->precision($p); ref($x) $p
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318 | # $x->precision(); ref($x)
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319 | # Class->precision(); class
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320 | # Class->precision($p); class $p
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321 |
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322 | my $x = shift;
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323 | my $class = ref($x) || $x || __PACKAGE__;
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324 |
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325 | no strict 'refs';
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326 | if (@_ > 0)
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327 | {
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328 | my $p = shift;
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329 | # convert objects to scalars to avoid deep recursion. If object doesn't
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330 | # have numify(), then hopefully it will have overloading for int() and
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331 | # boolean test without wandering into a deep recursion path...
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332 | $p = $p->numify() if ref($p) && $p->can('numify');
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333 | if ((defined $p) && (int($p) != $p))
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334 | {
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335 | require Carp; Carp::croak ('Argument to precision must be an integer');
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336 | }
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337 | if (ref($x))
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338 | {
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339 | # $object->precision() or fallback to global
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340 | $x->bfround($p) if $p; # not for undef, 0
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341 | $x->{_p} = $p; # set/overwrite, even if not rounded
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342 | delete $x->{_a}; # clear A
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343 | $p = ${"${class}::precision"} unless defined $p; # proper return value
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344 | }
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345 | else
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346 | {
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347 | ${"${class}::precision"} = $p; # set global P
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348 | ${"${class}::accuracy"} = undef; # clear global A
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349 | }
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350 | return $p; # shortcut
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351 | }
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352 |
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353 | my $p;
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354 | # $object->precision() or fallback to global
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355 | $p = $x->{_p} if ref($x);
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356 | # but don't return global undef, when $x's precision is 0!
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357 | $p = ${"${class}::precision"} if !defined $p;
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358 | $p;
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359 | }
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360 |
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361 | sub config
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362 | {
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363 | # return (or set) configuration data as hash ref
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364 | my $class = shift || 'Math::BigInt';
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365 |
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366 | no strict 'refs';
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367 | if (@_ > 0)
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368 | {
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369 | # try to set given options as arguments from hash
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370 |
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371 | my $args = $_[0];
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372 | if (ref($args) ne 'HASH')
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373 | {
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374 | $args = { @_ };
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375 | }
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376 | # these values can be "set"
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377 | my $set_args = {};
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378 | foreach my $key (
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379 | qw/trap_inf trap_nan
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380 | upgrade downgrade precision accuracy round_mode div_scale/
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381 | )
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382 | {
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383 | $set_args->{$key} = $args->{$key} if exists $args->{$key};
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384 | delete $args->{$key};
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385 | }
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386 | if (keys %$args > 0)
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387 | {
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388 | require Carp;
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389 | Carp::croak ("Illegal key(s) '",
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390 | join("','",keys %$args),"' passed to $class\->config()");
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391 | }
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392 | foreach my $key (keys %$set_args)
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393 | {
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394 | if ($key =~ /^trap_(inf|nan)\z/)
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395 | {
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396 | ${"${class}::_trap_$1"} = ($set_args->{"trap_$1"} ? 1 : 0);
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397 | next;
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398 | }
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399 | # use a call instead of just setting the $variable to check argument
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400 | $class->$key($set_args->{$key});
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401 | }
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402 | }
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403 |
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404 | # now return actual configuration
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405 |
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406 | my $cfg = {
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407 | lib => $CALC,
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408 | lib_version => ${"${CALC}::VERSION"},
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409 | class => $class,
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410 | trap_nan => ${"${class}::_trap_nan"},
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411 | trap_inf => ${"${class}::_trap_inf"},
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412 | version => ${"${class}::VERSION"},
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413 | };
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414 | foreach my $key (qw/
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415 | upgrade downgrade precision accuracy round_mode div_scale
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416 | /)
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417 | {
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418 | $cfg->{$key} = ${"${class}::$key"};
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419 | };
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420 | $cfg;
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421 | }
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422 |
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423 | sub _scale_a
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424 | {
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425 | # select accuracy parameter based on precedence,
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426 | # used by bround() and bfround(), may return undef for scale (means no op)
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427 | my ($x,$scale,$mode) = @_;
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428 |
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429 | $scale = $x->{_a} unless defined $scale;
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430 |
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431 | no strict 'refs';
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432 | my $class = ref($x);
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433 |
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434 | $scale = ${ $class . '::accuracy' } unless defined $scale;
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435 | $mode = ${ $class . '::round_mode' } unless defined $mode;
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436 |
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437 | ($scale,$mode);
|
---|
438 | }
|
---|
439 |
|
---|
440 | sub _scale_p
|
---|
441 | {
|
---|
442 | # select precision parameter based on precedence,
|
---|
443 | # used by bround() and bfround(), may return undef for scale (means no op)
|
---|
444 | my ($x,$scale,$mode) = @_;
|
---|
445 |
|
---|
446 | $scale = $x->{_p} unless defined $scale;
|
---|
447 |
|
---|
448 | no strict 'refs';
|
---|
449 | my $class = ref($x);
|
---|
450 |
|
---|
451 | $scale = ${ $class . '::precision' } unless defined $scale;
|
---|
452 | $mode = ${ $class . '::round_mode' } unless defined $mode;
|
---|
453 |
|
---|
454 | ($scale,$mode);
|
---|
455 | }
|
---|
456 |
|
---|
457 | ##############################################################################
|
---|
458 | # constructors
|
---|
459 |
|
---|
460 | sub copy
|
---|
461 | {
|
---|
462 | my ($c,$x);
|
---|
463 | if (@_ > 1)
|
---|
464 | {
|
---|
465 | # if two arguments, the first one is the class to "swallow" subclasses
|
---|
466 | ($c,$x) = @_;
|
---|
467 | }
|
---|
468 | else
|
---|
469 | {
|
---|
470 | $x = shift;
|
---|
471 | $c = ref($x);
|
---|
472 | }
|
---|
473 | return unless ref($x); # only for objects
|
---|
474 |
|
---|
475 | my $self = bless {}, $c;
|
---|
476 |
|
---|
477 | $self->{sign} = $x->{sign};
|
---|
478 | $self->{value} = $CALC->_copy($x->{value});
|
---|
479 | $self->{_a} = $x->{_a} if defined $x->{_a};
|
---|
480 | $self->{_p} = $x->{_p} if defined $x->{_p};
|
---|
481 | $self;
|
---|
482 | }
|
---|
483 |
|
---|
484 | sub new
|
---|
485 | {
|
---|
486 | # create a new BigInt object from a string or another BigInt object.
|
---|
487 | # see hash keys documented at top
|
---|
488 |
|
---|
489 | # the argument could be an object, so avoid ||, && etc on it, this would
|
---|
490 | # cause costly overloaded code to be called. The only allowed ops are
|
---|
491 | # ref() and defined.
|
---|
492 |
|
---|
493 | my ($class,$wanted,$a,$p,$r) = @_;
|
---|
494 |
|
---|
495 | # avoid numify-calls by not using || on $wanted!
|
---|
496 | return $class->bzero($a,$p) if !defined $wanted; # default to 0
|
---|
497 | return $class->copy($wanted,$a,$p,$r)
|
---|
498 | if ref($wanted) && $wanted->isa($class); # MBI or subclass
|
---|
499 |
|
---|
500 | $class->import() if $IMPORT == 0; # make require work
|
---|
501 |
|
---|
502 | my $self = bless {}, $class;
|
---|
503 |
|
---|
504 | # shortcut for "normal" numbers
|
---|
505 | if ((!ref $wanted) && ($wanted =~ /^([+-]?)[1-9][0-9]*\z/))
|
---|
506 | {
|
---|
507 | $self->{sign} = $1 || '+';
|
---|
508 |
|
---|
509 | if ($wanted =~ /^[+-]/)
|
---|
510 | {
|
---|
511 | # remove sign without touching wanted to make it work with constants
|
---|
512 | my $t = $wanted; $t =~ s/^[+-]//;
|
---|
513 | $self->{value} = $CALC->_new($t);
|
---|
514 | }
|
---|
515 | else
|
---|
516 | {
|
---|
517 | $self->{value} = $CALC->_new($wanted);
|
---|
518 | }
|
---|
519 | no strict 'refs';
|
---|
520 | if ( (defined $a) || (defined $p)
|
---|
521 | || (defined ${"${class}::precision"})
|
---|
522 | || (defined ${"${class}::accuracy"})
|
---|
523 | )
|
---|
524 | {
|
---|
525 | $self->round($a,$p,$r) unless (@_ == 4 && !defined $a && !defined $p);
|
---|
526 | }
|
---|
527 | return $self;
|
---|
528 | }
|
---|
529 |
|
---|
530 | # handle '+inf', '-inf' first
|
---|
531 | if ($wanted =~ /^[+-]?inf\z/)
|
---|
532 | {
|
---|
533 | $self->{sign} = $wanted; # set a default sign for bstr()
|
---|
534 | return $self->binf($wanted);
|
---|
535 | }
|
---|
536 | # split str in m mantissa, e exponent, i integer, f fraction, v value, s sign
|
---|
537 | my ($mis,$miv,$mfv,$es,$ev) = _split($wanted);
|
---|
538 | if (!ref $mis)
|
---|
539 | {
|
---|
540 | if ($_trap_nan)
|
---|
541 | {
|
---|
542 | require Carp; Carp::croak("$wanted is not a number in $class");
|
---|
543 | }
|
---|
544 | $self->{value} = $CALC->_zero();
|
---|
545 | $self->{sign} = $nan;
|
---|
546 | return $self;
|
---|
547 | }
|
---|
548 | if (!ref $miv)
|
---|
549 | {
|
---|
550 | # _from_hex or _from_bin
|
---|
551 | $self->{value} = $mis->{value};
|
---|
552 | $self->{sign} = $mis->{sign};
|
---|
553 | return $self; # throw away $mis
|
---|
554 | }
|
---|
555 | # make integer from mantissa by adjusting exp, then convert to bigint
|
---|
556 | $self->{sign} = $$mis; # store sign
|
---|
557 | $self->{value} = $CALC->_zero(); # for all the NaN cases
|
---|
558 | my $e = int("$$es$$ev"); # exponent (avoid recursion)
|
---|
559 | if ($e > 0)
|
---|
560 | {
|
---|
561 | my $diff = $e - CORE::length($$mfv);
|
---|
562 | if ($diff < 0) # Not integer
|
---|
563 | {
|
---|
564 | if ($_trap_nan)
|
---|
565 | {
|
---|
566 | require Carp; Carp::croak("$wanted not an integer in $class");
|
---|
567 | }
|
---|
568 | #print "NOI 1\n";
|
---|
569 | return $upgrade->new($wanted,$a,$p,$r) if defined $upgrade;
|
---|
570 | $self->{sign} = $nan;
|
---|
571 | }
|
---|
572 | else # diff >= 0
|
---|
573 | {
|
---|
574 | # adjust fraction and add it to value
|
---|
575 | #print "diff > 0 $$miv\n";
|
---|
576 | $$miv = $$miv . ($$mfv . '0' x $diff);
|
---|
577 | }
|
---|
578 | }
|
---|
579 | else
|
---|
580 | {
|
---|
581 | if ($$mfv ne '') # e <= 0
|
---|
582 | {
|
---|
583 | # fraction and negative/zero E => NOI
|
---|
584 | if ($_trap_nan)
|
---|
585 | {
|
---|
586 | require Carp; Carp::croak("$wanted not an integer in $class");
|
---|
587 | }
|
---|
588 | #print "NOI 2 \$\$mfv '$$mfv'\n";
|
---|
589 | return $upgrade->new($wanted,$a,$p,$r) if defined $upgrade;
|
---|
590 | $self->{sign} = $nan;
|
---|
591 | }
|
---|
592 | elsif ($e < 0)
|
---|
593 | {
|
---|
594 | # xE-y, and empty mfv
|
---|
595 | #print "xE-y\n";
|
---|
596 | $e = abs($e);
|
---|
597 | if ($$miv !~ s/0{$e}$//) # can strip so many zero's?
|
---|
598 | {
|
---|
599 | if ($_trap_nan)
|
---|
600 | {
|
---|
601 | require Carp; Carp::croak("$wanted not an integer in $class");
|
---|
602 | }
|
---|
603 | #print "NOI 3\n";
|
---|
604 | return $upgrade->new($wanted,$a,$p,$r) if defined $upgrade;
|
---|
605 | $self->{sign} = $nan;
|
---|
606 | }
|
---|
607 | }
|
---|
608 | }
|
---|
609 | $self->{sign} = '+' if $$miv eq '0'; # normalize -0 => +0
|
---|
610 | $self->{value} = $CALC->_new($$miv) if $self->{sign} =~ /^[+-]$/;
|
---|
611 | # if any of the globals is set, use them to round and store them inside $self
|
---|
612 | # do not round for new($x,undef,undef) since that is used by MBF to signal
|
---|
613 | # no rounding
|
---|
614 | $self->round($a,$p,$r) unless @_ == 4 && !defined $a && !defined $p;
|
---|
615 | $self;
|
---|
616 | }
|
---|
617 |
|
---|
618 | sub bnan
|
---|
619 | {
|
---|
620 | # create a bigint 'NaN', if given a BigInt, set it to 'NaN'
|
---|
621 | my $self = shift;
|
---|
622 | $self = $class if !defined $self;
|
---|
623 | if (!ref($self))
|
---|
624 | {
|
---|
625 | my $c = $self; $self = {}; bless $self, $c;
|
---|
626 | }
|
---|
627 | no strict 'refs';
|
---|
628 | if (${"${class}::_trap_nan"})
|
---|
629 | {
|
---|
630 | require Carp;
|
---|
631 | Carp::croak ("Tried to set $self to NaN in $class\::bnan()");
|
---|
632 | }
|
---|
633 | $self->import() if $IMPORT == 0; # make require work
|
---|
634 | return if $self->modify('bnan');
|
---|
635 | if ($self->can('_bnan'))
|
---|
636 | {
|
---|
637 | # use subclass to initialize
|
---|
638 | $self->_bnan();
|
---|
639 | }
|
---|
640 | else
|
---|
641 | {
|
---|
642 | # otherwise do our own thing
|
---|
643 | $self->{value} = $CALC->_zero();
|
---|
644 | }
|
---|
645 | $self->{sign} = $nan;
|
---|
646 | delete $self->{_a}; delete $self->{_p}; # rounding NaN is silly
|
---|
647 | $self;
|
---|
648 | }
|
---|
649 |
|
---|
650 | sub binf
|
---|
651 | {
|
---|
652 | # create a bigint '+-inf', if given a BigInt, set it to '+-inf'
|
---|
653 | # the sign is either '+', or if given, used from there
|
---|
654 | my $self = shift;
|
---|
655 | my $sign = shift; $sign = '+' if !defined $sign || $sign !~ /^-(inf)?$/;
|
---|
656 | $self = $class if !defined $self;
|
---|
657 | if (!ref($self))
|
---|
658 | {
|
---|
659 | my $c = $self; $self = {}; bless $self, $c;
|
---|
660 | }
|
---|
661 | no strict 'refs';
|
---|
662 | if (${"${class}::_trap_inf"})
|
---|
663 | {
|
---|
664 | require Carp;
|
---|
665 | Carp::croak ("Tried to set $self to +-inf in $class\::binf()");
|
---|
666 | }
|
---|
667 | $self->import() if $IMPORT == 0; # make require work
|
---|
668 | return if $self->modify('binf');
|
---|
669 | if ($self->can('_binf'))
|
---|
670 | {
|
---|
671 | # use subclass to initialize
|
---|
672 | $self->_binf();
|
---|
673 | }
|
---|
674 | else
|
---|
675 | {
|
---|
676 | # otherwise do our own thing
|
---|
677 | $self->{value} = $CALC->_zero();
|
---|
678 | }
|
---|
679 | $sign = $sign . 'inf' if $sign !~ /inf$/; # - => -inf
|
---|
680 | $self->{sign} = $sign;
|
---|
681 | ($self->{_a},$self->{_p}) = @_; # take over requested rounding
|
---|
682 | $self;
|
---|
683 | }
|
---|
684 |
|
---|
685 | sub bzero
|
---|
686 | {
|
---|
687 | # create a bigint '+0', if given a BigInt, set it to 0
|
---|
688 | my $self = shift;
|
---|
689 | $self = __PACKAGE__ if !defined $self;
|
---|
690 |
|
---|
691 | if (!ref($self))
|
---|
692 | {
|
---|
693 | my $c = $self; $self = {}; bless $self, $c;
|
---|
694 | }
|
---|
695 | $self->import() if $IMPORT == 0; # make require work
|
---|
696 | return if $self->modify('bzero');
|
---|
697 |
|
---|
698 | if ($self->can('_bzero'))
|
---|
699 | {
|
---|
700 | # use subclass to initialize
|
---|
701 | $self->_bzero();
|
---|
702 | }
|
---|
703 | else
|
---|
704 | {
|
---|
705 | # otherwise do our own thing
|
---|
706 | $self->{value} = $CALC->_zero();
|
---|
707 | }
|
---|
708 | $self->{sign} = '+';
|
---|
709 | if (@_ > 0)
|
---|
710 | {
|
---|
711 | if (@_ > 3)
|
---|
712 | {
|
---|
713 | # call like: $x->bzero($a,$p,$r,$y);
|
---|
714 | ($self,$self->{_a},$self->{_p}) = $self->_find_round_parameters(@_);
|
---|
715 | }
|
---|
716 | else
|
---|
717 | {
|
---|
718 | $self->{_a} = $_[0]
|
---|
719 | if ( (!defined $self->{_a}) || (defined $_[0] && $_[0] > $self->{_a}));
|
---|
720 | $self->{_p} = $_[1]
|
---|
721 | if ( (!defined $self->{_p}) || (defined $_[1] && $_[1] > $self->{_p}));
|
---|
722 | }
|
---|
723 | }
|
---|
724 | $self;
|
---|
725 | }
|
---|
726 |
|
---|
727 | sub bone
|
---|
728 | {
|
---|
729 | # create a bigint '+1' (or -1 if given sign '-'),
|
---|
730 | # if given a BigInt, set it to +1 or -1, respecively
|
---|
731 | my $self = shift;
|
---|
732 | my $sign = shift; $sign = '+' if !defined $sign || $sign ne '-';
|
---|
733 | $self = $class if !defined $self;
|
---|
734 |
|
---|
735 | if (!ref($self))
|
---|
736 | {
|
---|
737 | my $c = $self; $self = {}; bless $self, $c;
|
---|
738 | }
|
---|
739 | $self->import() if $IMPORT == 0; # make require work
|
---|
740 | return if $self->modify('bone');
|
---|
741 |
|
---|
742 | if ($self->can('_bone'))
|
---|
743 | {
|
---|
744 | # use subclass to initialize
|
---|
745 | $self->_bone();
|
---|
746 | }
|
---|
747 | else
|
---|
748 | {
|
---|
749 | # otherwise do our own thing
|
---|
750 | $self->{value} = $CALC->_one();
|
---|
751 | }
|
---|
752 | $self->{sign} = $sign;
|
---|
753 | if (@_ > 0)
|
---|
754 | {
|
---|
755 | if (@_ > 3)
|
---|
756 | {
|
---|
757 | # call like: $x->bone($sign,$a,$p,$r,$y);
|
---|
758 | ($self,$self->{_a},$self->{_p}) = $self->_find_round_parameters(@_);
|
---|
759 | }
|
---|
760 | else
|
---|
761 | {
|
---|
762 | # call like: $x->bone($sign,$a,$p,$r);
|
---|
763 | $self->{_a} = $_[0]
|
---|
764 | if ( (!defined $self->{_a}) || (defined $_[0] && $_[0] > $self->{_a}));
|
---|
765 | $self->{_p} = $_[1]
|
---|
766 | if ( (!defined $self->{_p}) || (defined $_[1] && $_[1] > $self->{_p}));
|
---|
767 | }
|
---|
768 | }
|
---|
769 | $self;
|
---|
770 | }
|
---|
771 |
|
---|
772 | ##############################################################################
|
---|
773 | # string conversation
|
---|
774 |
|
---|
775 | sub bsstr
|
---|
776 | {
|
---|
777 | # (ref to BFLOAT or num_str ) return num_str
|
---|
778 | # Convert number from internal format to scientific string format.
|
---|
779 | # internal format is always normalized (no leading zeros, "-0E0" => "+0E0")
|
---|
780 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
|
---|
781 |
|
---|
782 | if ($x->{sign} !~ /^[+-]$/)
|
---|
783 | {
|
---|
784 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN
|
---|
785 | return 'inf'; # +inf
|
---|
786 | }
|
---|
787 | my ($m,$e) = $x->parts();
|
---|
788 | #$m->bstr() . 'e+' . $e->bstr(); # e can only be positive in BigInt
|
---|
789 | # 'e+' because E can only be positive in BigInt
|
---|
790 | $m->bstr() . 'e+' . $CALC->_str($e->{value});
|
---|
791 | }
|
---|
792 |
|
---|
793 | sub bstr
|
---|
794 | {
|
---|
795 | # make a string from bigint object
|
---|
796 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
|
---|
797 |
|
---|
798 | if ($x->{sign} !~ /^[+-]$/)
|
---|
799 | {
|
---|
800 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN
|
---|
801 | return 'inf'; # +inf
|
---|
802 | }
|
---|
803 | my $es = ''; $es = $x->{sign} if $x->{sign} eq '-';
|
---|
804 | $es.$CALC->_str($x->{value});
|
---|
805 | }
|
---|
806 |
|
---|
807 | sub numify
|
---|
808 | {
|
---|
809 | # Make a "normal" scalar from a BigInt object
|
---|
810 | my $x = shift; $x = $class->new($x) unless ref $x;
|
---|
811 |
|
---|
812 | return $x->bstr() if $x->{sign} !~ /^[+-]$/;
|
---|
813 | my $num = $CALC->_num($x->{value});
|
---|
814 | return -$num if $x->{sign} eq '-';
|
---|
815 | $num;
|
---|
816 | }
|
---|
817 |
|
---|
818 | ##############################################################################
|
---|
819 | # public stuff (usually prefixed with "b")
|
---|
820 |
|
---|
821 | sub sign
|
---|
822 | {
|
---|
823 | # return the sign of the number: +/-/-inf/+inf/NaN
|
---|
824 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
|
---|
825 |
|
---|
826 | $x->{sign};
|
---|
827 | }
|
---|
828 |
|
---|
829 | sub _find_round_parameters
|
---|
830 | {
|
---|
831 | # After any operation or when calling round(), the result is rounded by
|
---|
832 | # regarding the A & P from arguments, local parameters, or globals.
|
---|
833 |
|
---|
834 | # !!!!!!! If you change this, remember to change round(), too! !!!!!!!!!!
|
---|
835 |
|
---|
836 | # This procedure finds the round parameters, but it is for speed reasons
|
---|
837 | # duplicated in round. Otherwise, it is tested by the testsuite and used
|
---|
838 | # by fdiv().
|
---|
839 |
|
---|
840 | # returns ($self) or ($self,$a,$p,$r) - sets $self to NaN of both A and P
|
---|
841 | # were requested/defined (locally or globally or both)
|
---|
842 |
|
---|
843 | my ($self,$a,$p,$r,@args) = @_;
|
---|
844 | # $a accuracy, if given by caller
|
---|
845 | # $p precision, if given by caller
|
---|
846 | # $r round_mode, if given by caller
|
---|
847 | # @args all 'other' arguments (0 for unary, 1 for binary ops)
|
---|
848 |
|
---|
849 | my $c = ref($self); # find out class of argument(s)
|
---|
850 | no strict 'refs';
|
---|
851 |
|
---|
852 | # now pick $a or $p, but only if we have got "arguments"
|
---|
853 | if (!defined $a)
|
---|
854 | {
|
---|
855 | foreach ($self,@args)
|
---|
856 | {
|
---|
857 | # take the defined one, or if both defined, the one that is smaller
|
---|
858 | $a = $_->{_a} if (defined $_->{_a}) && (!defined $a || $_->{_a} < $a);
|
---|
859 | }
|
---|
860 | }
|
---|
861 | if (!defined $p)
|
---|
862 | {
|
---|
863 | # even if $a is defined, take $p, to signal error for both defined
|
---|
864 | foreach ($self,@args)
|
---|
865 | {
|
---|
866 | # take the defined one, or if both defined, the one that is bigger
|
---|
867 | # -2 > -3, and 3 > 2
|
---|
868 | $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} > $p);
|
---|
869 | }
|
---|
870 | }
|
---|
871 | # if still none defined, use globals (#2)
|
---|
872 | $a = ${"$c\::accuracy"} unless defined $a;
|
---|
873 | $p = ${"$c\::precision"} unless defined $p;
|
---|
874 |
|
---|
875 | # A == 0 is useless, so undef it to signal no rounding
|
---|
876 | $a = undef if defined $a && $a == 0;
|
---|
877 |
|
---|
878 | # no rounding today?
|
---|
879 | return ($self) unless defined $a || defined $p; # early out
|
---|
880 |
|
---|
881 | # set A and set P is an fatal error
|
---|
882 | return ($self->bnan()) if defined $a && defined $p; # error
|
---|
883 |
|
---|
884 | $r = ${"$c\::round_mode"} unless defined $r;
|
---|
885 | if ($r !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/)
|
---|
886 | {
|
---|
887 | require Carp; Carp::croak ("Unknown round mode '$r'");
|
---|
888 | }
|
---|
889 |
|
---|
890 | ($self,$a,$p,$r);
|
---|
891 | }
|
---|
892 |
|
---|
893 | sub round
|
---|
894 | {
|
---|
895 | # Round $self according to given parameters, or given second argument's
|
---|
896 | # parameters or global defaults
|
---|
897 |
|
---|
898 | # for speed reasons, _find_round_parameters is embeded here:
|
---|
899 |
|
---|
900 | my ($self,$a,$p,$r,@args) = @_;
|
---|
901 | # $a accuracy, if given by caller
|
---|
902 | # $p precision, if given by caller
|
---|
903 | # $r round_mode, if given by caller
|
---|
904 | # @args all 'other' arguments (0 for unary, 1 for binary ops)
|
---|
905 |
|
---|
906 | my $c = ref($self); # find out class of argument(s)
|
---|
907 | no strict 'refs';
|
---|
908 |
|
---|
909 | # now pick $a or $p, but only if we have got "arguments"
|
---|
910 | if (!defined $a)
|
---|
911 | {
|
---|
912 | foreach ($self,@args)
|
---|
913 | {
|
---|
914 | # take the defined one, or if both defined, the one that is smaller
|
---|
915 | $a = $_->{_a} if (defined $_->{_a}) && (!defined $a || $_->{_a} < $a);
|
---|
916 | }
|
---|
917 | }
|
---|
918 | if (!defined $p)
|
---|
919 | {
|
---|
920 | # even if $a is defined, take $p, to signal error for both defined
|
---|
921 | foreach ($self,@args)
|
---|
922 | {
|
---|
923 | # take the defined one, or if both defined, the one that is bigger
|
---|
924 | # -2 > -3, and 3 > 2
|
---|
925 | $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} > $p);
|
---|
926 | }
|
---|
927 | }
|
---|
928 | # if still none defined, use globals (#2)
|
---|
929 | $a = ${"$c\::accuracy"} unless defined $a;
|
---|
930 | $p = ${"$c\::precision"} unless defined $p;
|
---|
931 |
|
---|
932 | # A == 0 is useless, so undef it to signal no rounding
|
---|
933 | $a = undef if defined $a && $a == 0;
|
---|
934 |
|
---|
935 | # no rounding today?
|
---|
936 | return $self unless defined $a || defined $p; # early out
|
---|
937 |
|
---|
938 | # set A and set P is an fatal error
|
---|
939 | return $self->bnan() if defined $a && defined $p;
|
---|
940 |
|
---|
941 | $r = ${"$c\::round_mode"} unless defined $r;
|
---|
942 | if ($r !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/)
|
---|
943 | {
|
---|
944 | require Carp; Carp::croak ("Unknown round mode '$r'");
|
---|
945 | }
|
---|
946 |
|
---|
947 | # now round, by calling either fround or ffround:
|
---|
948 | if (defined $a)
|
---|
949 | {
|
---|
950 | $self->bround($a,$r) if !defined $self->{_a} || $self->{_a} >= $a;
|
---|
951 | }
|
---|
952 | else # both can't be undefined due to early out
|
---|
953 | {
|
---|
954 | $self->bfround($p,$r) if !defined $self->{_p} || $self->{_p} <= $p;
|
---|
955 | }
|
---|
956 | # bround() or bfround() already callled bnorm() if necc.
|
---|
957 | $self;
|
---|
958 | }
|
---|
959 |
|
---|
960 | sub bnorm
|
---|
961 | {
|
---|
962 | # (numstr or BINT) return BINT
|
---|
963 | # Normalize number -- no-op here
|
---|
964 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
|
---|
965 | $x;
|
---|
966 | }
|
---|
967 |
|
---|
968 | sub babs
|
---|
969 | {
|
---|
970 | # (BINT or num_str) return BINT
|
---|
971 | # make number absolute, or return absolute BINT from string
|
---|
972 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
|
---|
973 |
|
---|
974 | return $x if $x->modify('babs');
|
---|
975 | # post-normalized abs for internal use (does nothing for NaN)
|
---|
976 | $x->{sign} =~ s/^-/+/;
|
---|
977 | $x;
|
---|
978 | }
|
---|
979 |
|
---|
980 | sub bneg
|
---|
981 | {
|
---|
982 | # (BINT or num_str) return BINT
|
---|
983 | # negate number or make a negated number from string
|
---|
984 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
|
---|
985 |
|
---|
986 | return $x if $x->modify('bneg');
|
---|
987 |
|
---|
988 | # for +0 dont negate (to have always normalized +0). Does nothing for 'NaN'
|
---|
989 | $x->{sign} =~ tr/+-/-+/ unless ($x->{sign} eq '+' && $CALC->_is_zero($x->{value}));
|
---|
990 | $x;
|
---|
991 | }
|
---|
992 |
|
---|
993 | sub bcmp
|
---|
994 | {
|
---|
995 | # Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort)
|
---|
996 | # (BINT or num_str, BINT or num_str) return cond_code
|
---|
997 |
|
---|
998 | # set up parameters
|
---|
999 | my ($self,$x,$y) = (ref($_[0]),@_);
|
---|
1000 |
|
---|
1001 | # objectify is costly, so avoid it
|
---|
1002 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
|
---|
1003 | {
|
---|
1004 | ($self,$x,$y) = objectify(2,@_);
|
---|
1005 | }
|
---|
1006 |
|
---|
1007 | return $upgrade->bcmp($x,$y) if defined $upgrade &&
|
---|
1008 | ((!$x->isa($self)) || (!$y->isa($self)));
|
---|
1009 |
|
---|
1010 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/))
|
---|
1011 | {
|
---|
1012 | # handle +-inf and NaN
|
---|
1013 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
|
---|
1014 | return 0 if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/;
|
---|
1015 | return +1 if $x->{sign} eq '+inf';
|
---|
1016 | return -1 if $x->{sign} eq '-inf';
|
---|
1017 | return -1 if $y->{sign} eq '+inf';
|
---|
1018 | return +1;
|
---|
1019 | }
|
---|
1020 | # check sign for speed first
|
---|
1021 | return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y
|
---|
1022 | return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0
|
---|
1023 |
|
---|
1024 | # have same sign, so compare absolute values. Don't make tests for zero here
|
---|
1025 | # because it's actually slower than testin in Calc (especially w/ Pari et al)
|
---|
1026 |
|
---|
1027 | # post-normalized compare for internal use (honors signs)
|
---|
1028 | if ($x->{sign} eq '+')
|
---|
1029 | {
|
---|
1030 | # $x and $y both > 0
|
---|
1031 | return $CALC->_acmp($x->{value},$y->{value});
|
---|
1032 | }
|
---|
1033 |
|
---|
1034 | # $x && $y both < 0
|
---|
1035 | $CALC->_acmp($y->{value},$x->{value}); # swaped acmp (lib returns 0,1,-1)
|
---|
1036 | }
|
---|
1037 |
|
---|
1038 | sub bacmp
|
---|
1039 | {
|
---|
1040 | # Compares 2 values, ignoring their signs.
|
---|
1041 | # Returns one of undef, <0, =0, >0. (suitable for sort)
|
---|
1042 | # (BINT, BINT) return cond_code
|
---|
1043 |
|
---|
1044 | # set up parameters
|
---|
1045 | my ($self,$x,$y) = (ref($_[0]),@_);
|
---|
1046 | # objectify is costly, so avoid it
|
---|
1047 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
|
---|
1048 | {
|
---|
1049 | ($self,$x,$y) = objectify(2,@_);
|
---|
1050 | }
|
---|
1051 |
|
---|
1052 | return $upgrade->bacmp($x,$y) if defined $upgrade &&
|
---|
1053 | ((!$x->isa($self)) || (!$y->isa($self)));
|
---|
1054 |
|
---|
1055 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/))
|
---|
1056 | {
|
---|
1057 | # handle +-inf and NaN
|
---|
1058 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
|
---|
1059 | return 0 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} =~ /^[+-]inf$/;
|
---|
1060 | return 1 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} !~ /^[+-]inf$/;
|
---|
1061 | return -1;
|
---|
1062 | }
|
---|
1063 | $CALC->_acmp($x->{value},$y->{value}); # lib does only 0,1,-1
|
---|
1064 | }
|
---|
1065 |
|
---|
1066 | sub badd
|
---|
1067 | {
|
---|
1068 | # add second arg (BINT or string) to first (BINT) (modifies first)
|
---|
1069 | # return result as BINT
|
---|
1070 |
|
---|
1071 | # set up parameters
|
---|
1072 | my ($self,$x,$y,@r) = (ref($_[0]),@_);
|
---|
1073 | # objectify is costly, so avoid it
|
---|
1074 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
|
---|
1075 | {
|
---|
1076 | ($self,$x,$y,@r) = objectify(2,@_);
|
---|
1077 | }
|
---|
1078 |
|
---|
1079 | return $x if $x->modify('badd');
|
---|
1080 | return $upgrade->badd($upgrade->new($x),$upgrade->new($y),@r) if defined $upgrade &&
|
---|
1081 | ((!$x->isa($self)) || (!$y->isa($self)));
|
---|
1082 |
|
---|
1083 | $r[3] = $y; # no push!
|
---|
1084 | # inf and NaN handling
|
---|
1085 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/))
|
---|
1086 | {
|
---|
1087 | # NaN first
|
---|
1088 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
|
---|
1089 | # inf handling
|
---|
1090 | if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/))
|
---|
1091 | {
|
---|
1092 | # +inf++inf or -inf+-inf => same, rest is NaN
|
---|
1093 | return $x if $x->{sign} eq $y->{sign};
|
---|
1094 | return $x->bnan();
|
---|
1095 | }
|
---|
1096 | # +-inf + something => +inf
|
---|
1097 | # something +-inf => +-inf
|
---|
1098 | $x->{sign} = $y->{sign}, return $x if $y->{sign} =~ /^[+-]inf$/;
|
---|
1099 | return $x;
|
---|
1100 | }
|
---|
1101 |
|
---|
1102 | my ($sx, $sy) = ( $x->{sign}, $y->{sign} ); # get signs
|
---|
1103 |
|
---|
1104 | if ($sx eq $sy)
|
---|
1105 | {
|
---|
1106 | $x->{value} = $CALC->_add($x->{value},$y->{value}); # same sign, abs add
|
---|
1107 | }
|
---|
1108 | else
|
---|
1109 | {
|
---|
1110 | my $a = $CALC->_acmp ($y->{value},$x->{value}); # absolute compare
|
---|
1111 | if ($a > 0)
|
---|
1112 | {
|
---|
1113 | $x->{value} = $CALC->_sub($y->{value},$x->{value},1); # abs sub w/ swap
|
---|
1114 | $x->{sign} = $sy;
|
---|
1115 | }
|
---|
1116 | elsif ($a == 0)
|
---|
1117 | {
|
---|
1118 | # speedup, if equal, set result to 0
|
---|
1119 | $x->{value} = $CALC->_zero();
|
---|
1120 | $x->{sign} = '+';
|
---|
1121 | }
|
---|
1122 | else # a < 0
|
---|
1123 | {
|
---|
1124 | $x->{value} = $CALC->_sub($x->{value}, $y->{value}); # abs sub
|
---|
1125 | }
|
---|
1126 | }
|
---|
1127 | $x->round(@r);
|
---|
1128 | }
|
---|
1129 |
|
---|
1130 | sub bsub
|
---|
1131 | {
|
---|
1132 | # (BINT or num_str, BINT or num_str) return BINT
|
---|
1133 | # subtract second arg from first, modify first
|
---|
1134 |
|
---|
1135 | # set up parameters
|
---|
1136 | my ($self,$x,$y,@r) = (ref($_[0]),@_);
|
---|
1137 | # objectify is costly, so avoid it
|
---|
1138 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
|
---|
1139 | {
|
---|
1140 | ($self,$x,$y,@r) = objectify(2,@_);
|
---|
1141 | }
|
---|
1142 |
|
---|
1143 | return $x if $x->modify('bsub');
|
---|
1144 |
|
---|
1145 | return $upgrade->new($x)->bsub($upgrade->new($y),@r) if defined $upgrade &&
|
---|
1146 | ((!$x->isa($self)) || (!$y->isa($self)));
|
---|
1147 |
|
---|
1148 | return $x->round(@r) if $y->is_zero();
|
---|
1149 |
|
---|
1150 | # To correctly handle the lone special case $x->bsub($x), we note the sign
|
---|
1151 | # of $x, then flip the sign from $y, and if the sign of $x did change, too,
|
---|
1152 | # then we caught the special case:
|
---|
1153 | my $xsign = $x->{sign};
|
---|
1154 | $y->{sign} =~ tr/+\-/-+/; # does nothing for NaN
|
---|
1155 | if ($xsign ne $x->{sign})
|
---|
1156 | {
|
---|
1157 | # special case of $x->bsub($x) results in 0
|
---|
1158 | return $x->bzero(@r) if $xsign =~ /^[+-]$/;
|
---|
1159 | return $x->bnan(); # NaN, -inf, +inf
|
---|
1160 | }
|
---|
1161 | $x->badd($y,@r); # badd does not leave internal zeros
|
---|
1162 | $y->{sign} =~ tr/+\-/-+/; # refix $y (does nothing for NaN)
|
---|
1163 | $x; # already rounded by badd() or no round necc.
|
---|
1164 | }
|
---|
1165 |
|
---|
1166 | sub binc
|
---|
1167 | {
|
---|
1168 | # increment arg by one
|
---|
1169 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
|
---|
1170 | return $x if $x->modify('binc');
|
---|
1171 |
|
---|
1172 | if ($x->{sign} eq '+')
|
---|
1173 | {
|
---|
1174 | $x->{value} = $CALC->_inc($x->{value});
|
---|
1175 | return $x->round($a,$p,$r);
|
---|
1176 | }
|
---|
1177 | elsif ($x->{sign} eq '-')
|
---|
1178 | {
|
---|
1179 | $x->{value} = $CALC->_dec($x->{value});
|
---|
1180 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # -1 +1 => -0 => +0
|
---|
1181 | return $x->round($a,$p,$r);
|
---|
1182 | }
|
---|
1183 | # inf, nan handling etc
|
---|
1184 | $x->badd($self->bone(),$a,$p,$r); # badd does round
|
---|
1185 | }
|
---|
1186 |
|
---|
1187 | sub bdec
|
---|
1188 | {
|
---|
1189 | # decrement arg by one
|
---|
1190 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
|
---|
1191 | return $x if $x->modify('bdec');
|
---|
1192 |
|
---|
1193 | if ($x->{sign} eq '-')
|
---|
1194 | {
|
---|
1195 | # x already < 0
|
---|
1196 | $x->{value} = $CALC->_inc($x->{value});
|
---|
1197 | }
|
---|
1198 | else
|
---|
1199 | {
|
---|
1200 | return $x->badd($self->bone('-'),@r) unless $x->{sign} eq '+'; # inf or NaN
|
---|
1201 | # >= 0
|
---|
1202 | if ($CALC->_is_zero($x->{value}))
|
---|
1203 | {
|
---|
1204 | # == 0
|
---|
1205 | $x->{value} = $CALC->_one(); $x->{sign} = '-'; # 0 => -1
|
---|
1206 | }
|
---|
1207 | else
|
---|
1208 | {
|
---|
1209 | # > 0
|
---|
1210 | $x->{value} = $CALC->_dec($x->{value});
|
---|
1211 | }
|
---|
1212 | }
|
---|
1213 | $x->round(@r);
|
---|
1214 | }
|
---|
1215 |
|
---|
1216 | sub blog
|
---|
1217 | {
|
---|
1218 | # calculate $x = $a ** $base + $b and return $a (e.g. the log() to base
|
---|
1219 | # $base of $x)
|
---|
1220 |
|
---|
1221 | # set up parameters
|
---|
1222 | my ($self,$x,$base,@r) = (undef,@_);
|
---|
1223 | # objectify is costly, so avoid it
|
---|
1224 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
|
---|
1225 | {
|
---|
1226 | ($self,$x,$base,@r) = objectify(1,ref($x),@_);
|
---|
1227 | }
|
---|
1228 |
|
---|
1229 | return $x if $x->modify('blog');
|
---|
1230 |
|
---|
1231 | # inf, -inf, NaN, <0 => NaN
|
---|
1232 | return $x->bnan()
|
---|
1233 | if $x->{sign} ne '+' || (defined $base && $base->{sign} ne '+');
|
---|
1234 |
|
---|
1235 | return $upgrade->blog($upgrade->new($x),$base,@r) if
|
---|
1236 | defined $upgrade;
|
---|
1237 |
|
---|
1238 | my ($rc,$exact) = $CALC->_log_int($x->{value},$base->{value});
|
---|
1239 | return $x->bnan() unless defined $rc; # not possible to take log?
|
---|
1240 | $x->{value} = $rc;
|
---|
1241 | $x->round(@r);
|
---|
1242 | }
|
---|
1243 |
|
---|
1244 | sub blcm
|
---|
1245 | {
|
---|
1246 | # (BINT or num_str, BINT or num_str) return BINT
|
---|
1247 | # does not modify arguments, but returns new object
|
---|
1248 | # Lowest Common Multiplicator
|
---|
1249 |
|
---|
1250 | my $y = shift; my ($x);
|
---|
1251 | if (ref($y))
|
---|
1252 | {
|
---|
1253 | $x = $y->copy();
|
---|
1254 | }
|
---|
1255 | else
|
---|
1256 | {
|
---|
1257 | $x = $class->new($y);
|
---|
1258 | }
|
---|
1259 | my $self = ref($x);
|
---|
1260 | while (@_)
|
---|
1261 | {
|
---|
1262 | my $y = shift; $y = $self->new($y) if !ref ($y);
|
---|
1263 | $x = __lcm($x,$y);
|
---|
1264 | }
|
---|
1265 | $x;
|
---|
1266 | }
|
---|
1267 |
|
---|
1268 | sub bgcd
|
---|
1269 | {
|
---|
1270 | # (BINT or num_str, BINT or num_str) return BINT
|
---|
1271 | # does not modify arguments, but returns new object
|
---|
1272 | # GCD -- Euclids algorithm, variant C (Knuth Vol 3, pg 341 ff)
|
---|
1273 |
|
---|
1274 | my $y = shift;
|
---|
1275 | $y = $class->new($y) if !ref($y);
|
---|
1276 | my $self = ref($y);
|
---|
1277 | my $x = $y->copy()->babs(); # keep arguments
|
---|
1278 | return $x->bnan() if $x->{sign} !~ /^[+-]$/; # x NaN?
|
---|
1279 |
|
---|
1280 | while (@_)
|
---|
1281 | {
|
---|
1282 | $y = shift; $y = $self->new($y) if !ref($y);
|
---|
1283 | return $x->bnan() if $y->{sign} !~ /^[+-]$/; # y NaN?
|
---|
1284 | $x->{value} = $CALC->_gcd($x->{value},$y->{value});
|
---|
1285 | last if $CALC->_is_one($x->{value});
|
---|
1286 | }
|
---|
1287 | $x;
|
---|
1288 | }
|
---|
1289 |
|
---|
1290 | sub bnot
|
---|
1291 | {
|
---|
1292 | # (num_str or BINT) return BINT
|
---|
1293 | # represent ~x as twos-complement number
|
---|
1294 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster
|
---|
1295 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
|
---|
1296 |
|
---|
1297 | return $x if $x->modify('bnot');
|
---|
1298 | $x->binc()->bneg(); # binc already does round
|
---|
1299 | }
|
---|
1300 |
|
---|
1301 | ##############################################################################
|
---|
1302 | # is_foo test routines
|
---|
1303 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster
|
---|
1304 |
|
---|
1305 | sub is_zero
|
---|
1306 | {
|
---|
1307 | # return true if arg (BINT or num_str) is zero (array '+', '0')
|
---|
1308 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
|
---|
1309 |
|
---|
1310 | return 0 if $x->{sign} !~ /^\+$/; # -, NaN & +-inf aren't
|
---|
1311 | $CALC->_is_zero($x->{value});
|
---|
1312 | }
|
---|
1313 |
|
---|
1314 | sub is_nan
|
---|
1315 | {
|
---|
1316 | # return true if arg (BINT or num_str) is NaN
|
---|
1317 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
|
---|
1318 |
|
---|
1319 | $x->{sign} eq $nan ? 1 : 0;
|
---|
1320 | }
|
---|
1321 |
|
---|
1322 | sub is_inf
|
---|
1323 | {
|
---|
1324 | # return true if arg (BINT or num_str) is +-inf
|
---|
1325 | my ($self,$x,$sign) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
|
---|
1326 |
|
---|
1327 | if (defined $sign)
|
---|
1328 | {
|
---|
1329 | $sign = '[+-]inf' if $sign eq ''; # +- doesn't matter, only that's inf
|
---|
1330 | $sign = "[$1]inf" if $sign =~ /^([+-])(inf)?$/; # extract '+' or '-'
|
---|
1331 | return $x->{sign} =~ /^$sign$/ ? 1 : 0;
|
---|
1332 | }
|
---|
1333 | $x->{sign} =~ /^[+-]inf$/ ? 1 : 0; # only +-inf is infinity
|
---|
1334 | }
|
---|
1335 |
|
---|
1336 | sub is_one
|
---|
1337 | {
|
---|
1338 | # return true if arg (BINT or num_str) is +1, or -1 if sign is given
|
---|
1339 | my ($self,$x,$sign) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
|
---|
1340 |
|
---|
1341 | $sign = '+' if !defined $sign || $sign ne '-';
|
---|
1342 |
|
---|
1343 | return 0 if $x->{sign} ne $sign; # -1 != +1, NaN, +-inf aren't either
|
---|
1344 | $CALC->_is_one($x->{value});
|
---|
1345 | }
|
---|
1346 |
|
---|
1347 | sub is_odd
|
---|
1348 | {
|
---|
1349 | # return true when arg (BINT or num_str) is odd, false for even
|
---|
1350 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
|
---|
1351 |
|
---|
1352 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't
|
---|
1353 | $CALC->_is_odd($x->{value});
|
---|
1354 | }
|
---|
1355 |
|
---|
1356 | sub is_even
|
---|
1357 | {
|
---|
1358 | # return true when arg (BINT or num_str) is even, false for odd
|
---|
1359 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
|
---|
1360 |
|
---|
1361 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't
|
---|
1362 | $CALC->_is_even($x->{value});
|
---|
1363 | }
|
---|
1364 |
|
---|
1365 | sub is_positive
|
---|
1366 | {
|
---|
1367 | # return true when arg (BINT or num_str) is positive (>= 0)
|
---|
1368 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
|
---|
1369 |
|
---|
1370 | return 1 if $x->{sign} eq '+inf'; # +inf is positive
|
---|
1371 |
|
---|
1372 | # 0+ is neither positive nor negative
|
---|
1373 | ($x->{sign} eq '+' && !$x->is_zero()) ? 1 : 0;
|
---|
1374 | }
|
---|
1375 |
|
---|
1376 | sub is_negative
|
---|
1377 | {
|
---|
1378 | # return true when arg (BINT or num_str) is negative (< 0)
|
---|
1379 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
|
---|
1380 |
|
---|
1381 | $x->{sign} =~ /^-/ ? 1 : 0; # -inf is negative, but NaN is not
|
---|
1382 | }
|
---|
1383 |
|
---|
1384 | sub is_int
|
---|
1385 | {
|
---|
1386 | # return true when arg (BINT or num_str) is an integer
|
---|
1387 | # always true for BigInt, but different for BigFloats
|
---|
1388 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
|
---|
1389 |
|
---|
1390 | $x->{sign} =~ /^[+-]$/ ? 1 : 0; # inf/-inf/NaN aren't
|
---|
1391 | }
|
---|
1392 |
|
---|
1393 | ###############################################################################
|
---|
1394 |
|
---|
1395 | sub bmul
|
---|
1396 | {
|
---|
1397 | # multiply two numbers -- stolen from Knuth Vol 2 pg 233
|
---|
1398 | # (BINT or num_str, BINT or num_str) return BINT
|
---|
1399 |
|
---|
1400 | # set up parameters
|
---|
1401 | my ($self,$x,$y,@r) = (ref($_[0]),@_);
|
---|
1402 | # objectify is costly, so avoid it
|
---|
1403 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
|
---|
1404 | {
|
---|
1405 | ($self,$x,$y,@r) = objectify(2,@_);
|
---|
1406 | }
|
---|
1407 |
|
---|
1408 | return $x if $x->modify('bmul');
|
---|
1409 |
|
---|
1410 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
|
---|
1411 |
|
---|
1412 | # inf handling
|
---|
1413 | if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/))
|
---|
1414 | {
|
---|
1415 | return $x->bnan() if $x->is_zero() || $y->is_zero();
|
---|
1416 | # result will always be +-inf:
|
---|
1417 | # +inf * +/+inf => +inf, -inf * -/-inf => +inf
|
---|
1418 | # +inf * -/-inf => -inf, -inf * +/+inf => -inf
|
---|
1419 | return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/);
|
---|
1420 | return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/);
|
---|
1421 | return $x->binf('-');
|
---|
1422 | }
|
---|
1423 |
|
---|
1424 | return $upgrade->bmul($x,$upgrade->new($y),@r)
|
---|
1425 | if defined $upgrade && !$y->isa($self);
|
---|
1426 |
|
---|
1427 | $r[3] = $y; # no push here
|
---|
1428 |
|
---|
1429 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; # +1 * +1 or -1 * -1 => +
|
---|
1430 |
|
---|
1431 | $x->{value} = $CALC->_mul($x->{value},$y->{value}); # do actual math
|
---|
1432 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # no -0
|
---|
1433 |
|
---|
1434 | $x->round(@r);
|
---|
1435 | }
|
---|
1436 |
|
---|
1437 | sub _div_inf
|
---|
1438 | {
|
---|
1439 | # helper function that handles +-inf cases for bdiv()/bmod() to reuse code
|
---|
1440 | my ($self,$x,$y) = @_;
|
---|
1441 |
|
---|
1442 | # NaN if x == NaN or y == NaN or x==y==0
|
---|
1443 | return wantarray ? ($x->bnan(),$self->bnan()) : $x->bnan()
|
---|
1444 | if (($x->is_nan() || $y->is_nan()) ||
|
---|
1445 | ($x->is_zero() && $y->is_zero()));
|
---|
1446 |
|
---|
1447 | # +-inf / +-inf == NaN, reminder also NaN
|
---|
1448 | if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/))
|
---|
1449 | {
|
---|
1450 | return wantarray ? ($x->bnan(),$self->bnan()) : $x->bnan();
|
---|
1451 | }
|
---|
1452 | # x / +-inf => 0, remainder x (works even if x == 0)
|
---|
1453 | if ($y->{sign} =~ /^[+-]inf$/)
|
---|
1454 | {
|
---|
1455 | my $t = $x->copy(); # bzero clobbers up $x
|
---|
1456 | return wantarray ? ($x->bzero(),$t) : $x->bzero()
|
---|
1457 | }
|
---|
1458 |
|
---|
1459 | # 5 / 0 => +inf, -6 / 0 => -inf
|
---|
1460 | # +inf / 0 = inf, inf, and -inf / 0 => -inf, -inf
|
---|
1461 | # exception: -8 / 0 has remainder -8, not 8
|
---|
1462 | # exception: -inf / 0 has remainder -inf, not inf
|
---|
1463 | if ($y->is_zero())
|
---|
1464 | {
|
---|
1465 | # +-inf / 0 => special case for -inf
|
---|
1466 | return wantarray ? ($x,$x->copy()) : $x if $x->is_inf();
|
---|
1467 | if (!$x->is_zero() && !$x->is_inf())
|
---|
1468 | {
|
---|
1469 | my $t = $x->copy(); # binf clobbers up $x
|
---|
1470 | return wantarray ?
|
---|
1471 | ($x->binf($x->{sign}),$t) : $x->binf($x->{sign})
|
---|
1472 | }
|
---|
1473 | }
|
---|
1474 |
|
---|
1475 | # last case: +-inf / ordinary number
|
---|
1476 | my $sign = '+inf';
|
---|
1477 | $sign = '-inf' if substr($x->{sign},0,1) ne $y->{sign};
|
---|
1478 | $x->{sign} = $sign;
|
---|
1479 | return wantarray ? ($x,$self->bzero()) : $x;
|
---|
1480 | }
|
---|
1481 |
|
---|
1482 | sub bdiv
|
---|
1483 | {
|
---|
1484 | # (dividend: BINT or num_str, divisor: BINT or num_str) return
|
---|
1485 | # (BINT,BINT) (quo,rem) or BINT (only rem)
|
---|
1486 |
|
---|
1487 | # set up parameters
|
---|
1488 | my ($self,$x,$y,@r) = (ref($_[0]),@_);
|
---|
1489 | # objectify is costly, so avoid it
|
---|
1490 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
|
---|
1491 | {
|
---|
1492 | ($self,$x,$y,@r) = objectify(2,@_);
|
---|
1493 | }
|
---|
1494 |
|
---|
1495 | return $x if $x->modify('bdiv');
|
---|
1496 |
|
---|
1497 | return $self->_div_inf($x,$y)
|
---|
1498 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero());
|
---|
1499 |
|
---|
1500 | return $upgrade->bdiv($upgrade->new($x),$upgrade->new($y),@r)
|
---|
1501 | if defined $upgrade;
|
---|
1502 |
|
---|
1503 | $r[3] = $y; # no push!
|
---|
1504 |
|
---|
1505 | # calc new sign and in case $y == +/- 1, return $x
|
---|
1506 | my $xsign = $x->{sign}; # keep
|
---|
1507 | $x->{sign} = ($x->{sign} ne $y->{sign} ? '-' : '+');
|
---|
1508 |
|
---|
1509 | if (wantarray)
|
---|
1510 | {
|
---|
1511 | my $rem = $self->bzero();
|
---|
1512 | ($x->{value},$rem->{value}) = $CALC->_div($x->{value},$y->{value});
|
---|
1513 | $x->{sign} = '+' if $CALC->_is_zero($x->{value});
|
---|
1514 | $rem->{_a} = $x->{_a};
|
---|
1515 | $rem->{_p} = $x->{_p};
|
---|
1516 | $x->round(@r);
|
---|
1517 | if (! $CALC->_is_zero($rem->{value}))
|
---|
1518 | {
|
---|
1519 | $rem->{sign} = $y->{sign};
|
---|
1520 | $rem = $y->copy()->bsub($rem) if $xsign ne $y->{sign}; # one of them '-'
|
---|
1521 | }
|
---|
1522 | else
|
---|
1523 | {
|
---|
1524 | $rem->{sign} = '+'; # dont leave -0
|
---|
1525 | }
|
---|
1526 | $rem->round(@r);
|
---|
1527 | return ($x,$rem);
|
---|
1528 | }
|
---|
1529 |
|
---|
1530 | $x->{value} = $CALC->_div($x->{value},$y->{value});
|
---|
1531 | $x->{sign} = '+' if $CALC->_is_zero($x->{value});
|
---|
1532 |
|
---|
1533 | $x->round(@r);
|
---|
1534 | }
|
---|
1535 |
|
---|
1536 | ###############################################################################
|
---|
1537 | # modulus functions
|
---|
1538 |
|
---|
1539 | sub bmod
|
---|
1540 | {
|
---|
1541 | # modulus (or remainder)
|
---|
1542 | # (BINT or num_str, BINT or num_str) return BINT
|
---|
1543 |
|
---|
1544 | # set up parameters
|
---|
1545 | my ($self,$x,$y,@r) = (ref($_[0]),@_);
|
---|
1546 | # objectify is costly, so avoid it
|
---|
1547 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
|
---|
1548 | {
|
---|
1549 | ($self,$x,$y,@r) = objectify(2,@_);
|
---|
1550 | }
|
---|
1551 |
|
---|
1552 | return $x if $x->modify('bmod');
|
---|
1553 | $r[3] = $y; # no push!
|
---|
1554 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero())
|
---|
1555 | {
|
---|
1556 | my ($d,$r) = $self->_div_inf($x,$y);
|
---|
1557 | $x->{sign} = $r->{sign};
|
---|
1558 | $x->{value} = $r->{value};
|
---|
1559 | return $x->round(@r);
|
---|
1560 | }
|
---|
1561 |
|
---|
1562 | # calc new sign and in case $y == +/- 1, return $x
|
---|
1563 | $x->{value} = $CALC->_mod($x->{value},$y->{value});
|
---|
1564 | if (!$CALC->_is_zero($x->{value}))
|
---|
1565 | {
|
---|
1566 | $x->{value} = $CALC->_sub($y->{value},$x->{value},1) # $y-$x
|
---|
1567 | if ($x->{sign} ne $y->{sign});
|
---|
1568 | $x->{sign} = $y->{sign};
|
---|
1569 | }
|
---|
1570 | else
|
---|
1571 | {
|
---|
1572 | $x->{sign} = '+'; # dont leave -0
|
---|
1573 | }
|
---|
1574 | $x->round(@r);
|
---|
1575 | }
|
---|
1576 |
|
---|
1577 | sub bmodinv
|
---|
1578 | {
|
---|
1579 | # Modular inverse. given a number which is (hopefully) relatively
|
---|
1580 | # prime to the modulus, calculate its inverse using Euclid's
|
---|
1581 | # alogrithm. If the number is not relatively prime to the modulus
|
---|
1582 | # (i.e. their gcd is not one) then NaN is returned.
|
---|
1583 |
|
---|
1584 | # set up parameters
|
---|
1585 | my ($self,$x,$y,@r) = (undef,@_);
|
---|
1586 | # objectify is costly, so avoid it
|
---|
1587 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
|
---|
1588 | {
|
---|
1589 | ($self,$x,$y,@r) = objectify(2,@_);
|
---|
1590 | }
|
---|
1591 |
|
---|
1592 | return $x if $x->modify('bmodinv');
|
---|
1593 |
|
---|
1594 | return $x->bnan()
|
---|
1595 | if ($y->{sign} ne '+' # -, NaN, +inf, -inf
|
---|
1596 | || $x->is_zero() # or num == 0
|
---|
1597 | || $x->{sign} !~ /^[+-]$/ # or num NaN, inf, -inf
|
---|
1598 | );
|
---|
1599 |
|
---|
1600 | # put least residue into $x if $x was negative, and thus make it positive
|
---|
1601 | $x->bmod($y) if $x->{sign} eq '-';
|
---|
1602 |
|
---|
1603 | my $sign;
|
---|
1604 | ($x->{value},$sign) = $CALC->_modinv($x->{value},$y->{value});
|
---|
1605 | return $x->bnan() if !defined $x->{value}; # in case no GCD found
|
---|
1606 | return $x if !defined $sign; # already real result
|
---|
1607 | $x->{sign} = $sign; # flip/flop see below
|
---|
1608 | $x->bmod($y); # calc real result
|
---|
1609 | $x;
|
---|
1610 | }
|
---|
1611 |
|
---|
1612 | sub bmodpow
|
---|
1613 | {
|
---|
1614 | # takes a very large number to a very large exponent in a given very
|
---|
1615 | # large modulus, quickly, thanks to binary exponentation. supports
|
---|
1616 | # negative exponents.
|
---|
1617 | my ($self,$num,$exp,$mod,@r) = objectify(3,@_);
|
---|
1618 |
|
---|
1619 | return $num if $num->modify('bmodpow');
|
---|
1620 |
|
---|
1621 | # check modulus for valid values
|
---|
1622 | return $num->bnan() if ($mod->{sign} ne '+' # NaN, - , -inf, +inf
|
---|
1623 | || $mod->is_zero());
|
---|
1624 |
|
---|
1625 | # check exponent for valid values
|
---|
1626 | if ($exp->{sign} =~ /\w/)
|
---|
1627 | {
|
---|
1628 | # i.e., if it's NaN, +inf, or -inf...
|
---|
1629 | return $num->bnan();
|
---|
1630 | }
|
---|
1631 |
|
---|
1632 | $num->bmodinv ($mod) if ($exp->{sign} eq '-');
|
---|
1633 |
|
---|
1634 | # check num for valid values (also NaN if there was no inverse but $exp < 0)
|
---|
1635 | return $num->bnan() if $num->{sign} !~ /^[+-]$/;
|
---|
1636 |
|
---|
1637 | # $mod is positive, sign on $exp is ignored, result also positive
|
---|
1638 | $num->{value} = $CALC->_modpow($num->{value},$exp->{value},$mod->{value});
|
---|
1639 | $num;
|
---|
1640 | }
|
---|
1641 |
|
---|
1642 | ###############################################################################
|
---|
1643 |
|
---|
1644 | sub bfac
|
---|
1645 | {
|
---|
1646 | # (BINT or num_str, BINT or num_str) return BINT
|
---|
1647 | # compute factorial number from $x, modify $x in place
|
---|
1648 | my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
|
---|
1649 |
|
---|
1650 | return $x if $x->modify('bfac') || $x->{sign} eq '+inf'; # inf => inf
|
---|
1651 | return $x->bnan() if $x->{sign} ne '+'; # NaN, <0 etc => NaN
|
---|
1652 |
|
---|
1653 | $x->{value} = $CALC->_fac($x->{value});
|
---|
1654 | $x->round(@r);
|
---|
1655 | }
|
---|
1656 |
|
---|
1657 | sub bpow
|
---|
1658 | {
|
---|
1659 | # (BINT or num_str, BINT or num_str) return BINT
|
---|
1660 | # compute power of two numbers -- stolen from Knuth Vol 2 pg 233
|
---|
1661 | # modifies first argument
|
---|
1662 |
|
---|
1663 | # set up parameters
|
---|
1664 | my ($self,$x,$y,@r) = (ref($_[0]),@_);
|
---|
1665 | # objectify is costly, so avoid it
|
---|
1666 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
|
---|
1667 | {
|
---|
1668 | ($self,$x,$y,@r) = objectify(2,@_);
|
---|
1669 | }
|
---|
1670 |
|
---|
1671 | return $x if $x->modify('bpow');
|
---|
1672 |
|
---|
1673 | return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan;
|
---|
1674 |
|
---|
1675 | # inf handling
|
---|
1676 | if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/))
|
---|
1677 | {
|
---|
1678 | if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/))
|
---|
1679 | {
|
---|
1680 | # +-inf ** +-inf
|
---|
1681 | return $x->bnan();
|
---|
1682 | }
|
---|
1683 | # +-inf ** Y
|
---|
1684 | if ($x->{sign} =~ /^[+-]inf/)
|
---|
1685 | {
|
---|
1686 | # +inf ** 0 => NaN
|
---|
1687 | return $x->bnan() if $y->is_zero();
|
---|
1688 | # -inf ** -1 => 1/inf => 0
|
---|
1689 | return $x->bzero() if $y->is_one('-') && $x->is_negative();
|
---|
1690 |
|
---|
1691 | # +inf ** Y => inf
|
---|
1692 | return $x if $x->{sign} eq '+inf';
|
---|
1693 |
|
---|
1694 | # -inf ** Y => -inf if Y is odd
|
---|
1695 | return $x if $y->is_odd();
|
---|
1696 | return $x->babs();
|
---|
1697 | }
|
---|
1698 | # X ** +-inf
|
---|
1699 |
|
---|
1700 | # 1 ** +inf => 1
|
---|
1701 | return $x if $x->is_one();
|
---|
1702 |
|
---|
1703 | # 0 ** inf => 0
|
---|
1704 | return $x if $x->is_zero() && $y->{sign} =~ /^[+]/;
|
---|
1705 |
|
---|
1706 | # 0 ** -inf => inf
|
---|
1707 | return $x->binf() if $x->is_zero();
|
---|
1708 |
|
---|
1709 | # -1 ** -inf => NaN
|
---|
1710 | return $x->bnan() if $x->is_one('-') && $y->{sign} =~ /^[-]/;
|
---|
1711 |
|
---|
1712 | # -X ** -inf => 0
|
---|
1713 | return $x->bzero() if $x->{sign} eq '-' && $y->{sign} =~ /^[-]/;
|
---|
1714 |
|
---|
1715 | # -1 ** inf => NaN
|
---|
1716 | return $x->bnan() if $x->{sign} eq '-';
|
---|
1717 |
|
---|
1718 | # X ** inf => inf
|
---|
1719 | return $x->binf() if $y->{sign} =~ /^[+]/;
|
---|
1720 | # X ** -inf => 0
|
---|
1721 | return $x->bzero();
|
---|
1722 | }
|
---|
1723 |
|
---|
1724 | return $upgrade->bpow($upgrade->new($x),$y,@r)
|
---|
1725 | if defined $upgrade && !$y->isa($self);
|
---|
1726 |
|
---|
1727 | $r[3] = $y; # no push!
|
---|
1728 |
|
---|
1729 | # cases 0 ** Y, X ** 0, X ** 1, 1 ** Y are handled by Calc or Emu
|
---|
1730 |
|
---|
1731 | my $new_sign = '+';
|
---|
1732 | $new_sign = $y->is_odd() ? '-' : '+' if ($x->{sign} ne '+');
|
---|
1733 |
|
---|
1734 | # 0 ** -7 => ( 1 / (0 ** 7)) => 1 / 0 => +inf
|
---|
1735 | return $x->binf()
|
---|
1736 | if $y->{sign} eq '-' && $x->{sign} eq '+' && $CALC->_is_zero($x->{value});
|
---|
1737 | # 1 ** -y => 1 / (1 ** |y|)
|
---|
1738 | # so do test for negative $y after above's clause
|
---|
1739 | return $x->bnan() if $y->{sign} eq '-' && !$CALC->_is_one($x->{value});
|
---|
1740 |
|
---|
1741 | $x->{value} = $CALC->_pow($x->{value},$y->{value});
|
---|
1742 | $x->{sign} = $new_sign;
|
---|
1743 | $x->{sign} = '+' if $CALC->_is_zero($y->{value});
|
---|
1744 | $x->round(@r);
|
---|
1745 | }
|
---|
1746 |
|
---|
1747 | sub blsft
|
---|
1748 | {
|
---|
1749 | # (BINT or num_str, BINT or num_str) return BINT
|
---|
1750 | # compute x << y, base n, y >= 0
|
---|
1751 |
|
---|
1752 | # set up parameters
|
---|
1753 | my ($self,$x,$y,$n,@r) = (ref($_[0]),@_);
|
---|
1754 | # objectify is costly, so avoid it
|
---|
1755 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
|
---|
1756 | {
|
---|
1757 | ($self,$x,$y,$n,@r) = objectify(2,@_);
|
---|
1758 | }
|
---|
1759 |
|
---|
1760 | return $x if $x->modify('blsft');
|
---|
1761 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
|
---|
1762 | return $x->round(@r) if $y->is_zero();
|
---|
1763 |
|
---|
1764 | $n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-';
|
---|
1765 |
|
---|
1766 | $x->{value} = $CALC->_lsft($x->{value},$y->{value},$n);
|
---|
1767 | $x->round(@r);
|
---|
1768 | }
|
---|
1769 |
|
---|
1770 | sub brsft
|
---|
1771 | {
|
---|
1772 | # (BINT or num_str, BINT or num_str) return BINT
|
---|
1773 | # compute x >> y, base n, y >= 0
|
---|
1774 |
|
---|
1775 | # set up parameters
|
---|
1776 | my ($self,$x,$y,$n,@r) = (ref($_[0]),@_);
|
---|
1777 | # objectify is costly, so avoid it
|
---|
1778 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
|
---|
1779 | {
|
---|
1780 | ($self,$x,$y,$n,@r) = objectify(2,@_);
|
---|
1781 | }
|
---|
1782 |
|
---|
1783 | return $x if $x->modify('brsft');
|
---|
1784 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
|
---|
1785 | return $x->round(@r) if $y->is_zero();
|
---|
1786 | return $x->bzero(@r) if $x->is_zero(); # 0 => 0
|
---|
1787 |
|
---|
1788 | $n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-';
|
---|
1789 |
|
---|
1790 | # this only works for negative numbers when shifting in base 2
|
---|
1791 | if (($x->{sign} eq '-') && ($n == 2))
|
---|
1792 | {
|
---|
1793 | return $x->round(@r) if $x->is_one('-'); # -1 => -1
|
---|
1794 | if (!$y->is_one())
|
---|
1795 | {
|
---|
1796 | # although this is O(N*N) in calc (as_bin!) it is O(N) in Pari et al
|
---|
1797 | # but perhaps there is a better emulation for two's complement shift...
|
---|
1798 | # if $y != 1, we must simulate it by doing:
|
---|
1799 | # convert to bin, flip all bits, shift, and be done
|
---|
1800 | $x->binc(); # -3 => -2
|
---|
1801 | my $bin = $x->as_bin();
|
---|
1802 | $bin =~ s/^-0b//; # strip '-0b' prefix
|
---|
1803 | $bin =~ tr/10/01/; # flip bits
|
---|
1804 | # now shift
|
---|
1805 | if (CORE::length($bin) <= $y)
|
---|
1806 | {
|
---|
1807 | $bin = '0'; # shifting to far right creates -1
|
---|
1808 | # 0, because later increment makes
|
---|
1809 | # that 1, attached '-' makes it '-1'
|
---|
1810 | # because -1 >> x == -1 !
|
---|
1811 | }
|
---|
1812 | else
|
---|
1813 | {
|
---|
1814 | $bin =~ s/.{$y}$//; # cut off at the right side
|
---|
1815 | $bin = '1' . $bin; # extend left side by one dummy '1'
|
---|
1816 | $bin =~ tr/10/01/; # flip bits back
|
---|
1817 | }
|
---|
1818 | my $res = $self->new('0b'.$bin); # add prefix and convert back
|
---|
1819 | $res->binc(); # remember to increment
|
---|
1820 | $x->{value} = $res->{value}; # take over value
|
---|
1821 | return $x->round(@r); # we are done now, magic, isn't?
|
---|
1822 | }
|
---|
1823 | # x < 0, n == 2, y == 1
|
---|
1824 | $x->bdec(); # n == 2, but $y == 1: this fixes it
|
---|
1825 | }
|
---|
1826 |
|
---|
1827 | $x->{value} = $CALC->_rsft($x->{value},$y->{value},$n);
|
---|
1828 | $x->round(@r);
|
---|
1829 | }
|
---|
1830 |
|
---|
1831 | sub band
|
---|
1832 | {
|
---|
1833 | #(BINT or num_str, BINT or num_str) return BINT
|
---|
1834 | # compute x & y
|
---|
1835 |
|
---|
1836 | # set up parameters
|
---|
1837 | my ($self,$x,$y,@r) = (ref($_[0]),@_);
|
---|
1838 | # objectify is costly, so avoid it
|
---|
1839 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
|
---|
1840 | {
|
---|
1841 | ($self,$x,$y,@r) = objectify(2,@_);
|
---|
1842 | }
|
---|
1843 |
|
---|
1844 | return $x if $x->modify('band');
|
---|
1845 |
|
---|
1846 | $r[3] = $y; # no push!
|
---|
1847 |
|
---|
1848 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
|
---|
1849 |
|
---|
1850 | my $sx = $x->{sign} eq '+' ? 1 : -1;
|
---|
1851 | my $sy = $y->{sign} eq '+' ? 1 : -1;
|
---|
1852 |
|
---|
1853 | if ($sx == 1 && $sy == 1)
|
---|
1854 | {
|
---|
1855 | $x->{value} = $CALC->_and($x->{value},$y->{value});
|
---|
1856 | return $x->round(@r);
|
---|
1857 | }
|
---|
1858 |
|
---|
1859 | if ($CAN{signed_and})
|
---|
1860 | {
|
---|
1861 | $x->{value} = $CALC->_signed_and($x->{value},$y->{value},$sx,$sy);
|
---|
1862 | return $x->round(@r);
|
---|
1863 | }
|
---|
1864 |
|
---|
1865 | require $EMU_LIB;
|
---|
1866 | __emu_band($self,$x,$y,$sx,$sy,@r);
|
---|
1867 | }
|
---|
1868 |
|
---|
1869 | sub bior
|
---|
1870 | {
|
---|
1871 | #(BINT or num_str, BINT or num_str) return BINT
|
---|
1872 | # compute x | y
|
---|
1873 |
|
---|
1874 | # set up parameters
|
---|
1875 | my ($self,$x,$y,@r) = (ref($_[0]),@_);
|
---|
1876 | # objectify is costly, so avoid it
|
---|
1877 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
|
---|
1878 | {
|
---|
1879 | ($self,$x,$y,@r) = objectify(2,@_);
|
---|
1880 | }
|
---|
1881 |
|
---|
1882 | return $x if $x->modify('bior');
|
---|
1883 | $r[3] = $y; # no push!
|
---|
1884 |
|
---|
1885 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
|
---|
1886 |
|
---|
1887 | my $sx = $x->{sign} eq '+' ? 1 : -1;
|
---|
1888 | my $sy = $y->{sign} eq '+' ? 1 : -1;
|
---|
1889 |
|
---|
1890 | # the sign of X follows the sign of X, e.g. sign of Y irrelevant for bior()
|
---|
1891 |
|
---|
1892 | # don't use lib for negative values
|
---|
1893 | if ($sx == 1 && $sy == 1)
|
---|
1894 | {
|
---|
1895 | $x->{value} = $CALC->_or($x->{value},$y->{value});
|
---|
1896 | return $x->round(@r);
|
---|
1897 | }
|
---|
1898 |
|
---|
1899 | # if lib can do negative values, let it handle this
|
---|
1900 | if ($CAN{signed_or})
|
---|
1901 | {
|
---|
1902 | $x->{value} = $CALC->_signed_or($x->{value},$y->{value},$sx,$sy);
|
---|
1903 | return $x->round(@r);
|
---|
1904 | }
|
---|
1905 |
|
---|
1906 | require $EMU_LIB;
|
---|
1907 | __emu_bior($self,$x,$y,$sx,$sy,@r);
|
---|
1908 | }
|
---|
1909 |
|
---|
1910 | sub bxor
|
---|
1911 | {
|
---|
1912 | #(BINT or num_str, BINT or num_str) return BINT
|
---|
1913 | # compute x ^ y
|
---|
1914 |
|
---|
1915 | # set up parameters
|
---|
1916 | my ($self,$x,$y,@r) = (ref($_[0]),@_);
|
---|
1917 | # objectify is costly, so avoid it
|
---|
1918 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
|
---|
1919 | {
|
---|
1920 | ($self,$x,$y,@r) = objectify(2,@_);
|
---|
1921 | }
|
---|
1922 |
|
---|
1923 | return $x if $x->modify('bxor');
|
---|
1924 | $r[3] = $y; # no push!
|
---|
1925 |
|
---|
1926 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
|
---|
1927 |
|
---|
1928 | my $sx = $x->{sign} eq '+' ? 1 : -1;
|
---|
1929 | my $sy = $y->{sign} eq '+' ? 1 : -1;
|
---|
1930 |
|
---|
1931 | # don't use lib for negative values
|
---|
1932 | if ($sx == 1 && $sy == 1)
|
---|
1933 | {
|
---|
1934 | $x->{value} = $CALC->_xor($x->{value},$y->{value});
|
---|
1935 | return $x->round(@r);
|
---|
1936 | }
|
---|
1937 |
|
---|
1938 | # if lib can do negative values, let it handle this
|
---|
1939 | if ($CAN{signed_xor})
|
---|
1940 | {
|
---|
1941 | $x->{value} = $CALC->_signed_xor($x->{value},$y->{value},$sx,$sy);
|
---|
1942 | return $x->round(@r);
|
---|
1943 | }
|
---|
1944 |
|
---|
1945 | require $EMU_LIB;
|
---|
1946 | __emu_bxor($self,$x,$y,$sx,$sy,@r);
|
---|
1947 | }
|
---|
1948 |
|
---|
1949 | sub length
|
---|
1950 | {
|
---|
1951 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
|
---|
1952 |
|
---|
1953 | my $e = $CALC->_len($x->{value});
|
---|
1954 | wantarray ? ($e,0) : $e;
|
---|
1955 | }
|
---|
1956 |
|
---|
1957 | sub digit
|
---|
1958 | {
|
---|
1959 | # return the nth decimal digit, negative values count backward, 0 is right
|
---|
1960 | my ($self,$x,$n) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
|
---|
1961 |
|
---|
1962 | $n = $n->numify() if ref($n);
|
---|
1963 | $CALC->_digit($x->{value},$n||0);
|
---|
1964 | }
|
---|
1965 |
|
---|
1966 | sub _trailing_zeros
|
---|
1967 | {
|
---|
1968 | # return the amount of trailing zeros in $x (as scalar)
|
---|
1969 | my $x = shift;
|
---|
1970 | $x = $class->new($x) unless ref $x;
|
---|
1971 |
|
---|
1972 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN, inf, -inf etc
|
---|
1973 |
|
---|
1974 | $CALC->_zeros($x->{value}); # must handle odd values, 0 etc
|
---|
1975 | }
|
---|
1976 |
|
---|
1977 | sub bsqrt
|
---|
1978 | {
|
---|
1979 | # calculate square root of $x
|
---|
1980 | my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
|
---|
1981 |
|
---|
1982 | return $x if $x->modify('bsqrt');
|
---|
1983 |
|
---|
1984 | return $x->bnan() if $x->{sign} !~ /^\+/; # -x or -inf or NaN => NaN
|
---|
1985 | return $x if $x->{sign} eq '+inf'; # sqrt(+inf) == inf
|
---|
1986 |
|
---|
1987 | return $upgrade->bsqrt($x,@r) if defined $upgrade;
|
---|
1988 |
|
---|
1989 | $x->{value} = $CALC->_sqrt($x->{value});
|
---|
1990 | $x->round(@r);
|
---|
1991 | }
|
---|
1992 |
|
---|
1993 | sub broot
|
---|
1994 | {
|
---|
1995 | # calculate $y'th root of $x
|
---|
1996 |
|
---|
1997 | # set up parameters
|
---|
1998 | my ($self,$x,$y,@r) = (ref($_[0]),@_);
|
---|
1999 |
|
---|
2000 | $y = $self->new(2) unless defined $y;
|
---|
2001 |
|
---|
2002 | # objectify is costly, so avoid it
|
---|
2003 | if ((!ref($x)) || (ref($x) ne ref($y)))
|
---|
2004 | {
|
---|
2005 | ($self,$x,$y,@r) = objectify(2,$self || $class,@_);
|
---|
2006 | }
|
---|
2007 |
|
---|
2008 | return $x if $x->modify('broot');
|
---|
2009 |
|
---|
2010 | # NaN handling: $x ** 1/0, x or y NaN, or y inf/-inf or y == 0
|
---|
2011 | return $x->bnan() if $x->{sign} !~ /^\+/ || $y->is_zero() ||
|
---|
2012 | $y->{sign} !~ /^\+$/;
|
---|
2013 |
|
---|
2014 | return $x->round(@r)
|
---|
2015 | if $x->is_zero() || $x->is_one() || $x->is_inf() || $y->is_one();
|
---|
2016 |
|
---|
2017 | return $upgrade->new($x)->broot($upgrade->new($y),@r) if defined $upgrade;
|
---|
2018 |
|
---|
2019 | $x->{value} = $CALC->_root($x->{value},$y->{value});
|
---|
2020 | $x->round(@r);
|
---|
2021 | }
|
---|
2022 |
|
---|
2023 | sub exponent
|
---|
2024 | {
|
---|
2025 | # return a copy of the exponent (here always 0, NaN or 1 for $m == 0)
|
---|
2026 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
|
---|
2027 |
|
---|
2028 | if ($x->{sign} !~ /^[+-]$/)
|
---|
2029 | {
|
---|
2030 | my $s = $x->{sign}; $s =~ s/^[+-]//; # NaN, -inf,+inf => NaN or inf
|
---|
2031 | return $self->new($s);
|
---|
2032 | }
|
---|
2033 | return $self->bone() if $x->is_zero();
|
---|
2034 |
|
---|
2035 | $self->new($x->_trailing_zeros());
|
---|
2036 | }
|
---|
2037 |
|
---|
2038 | sub mantissa
|
---|
2039 | {
|
---|
2040 | # return the mantissa (compatible to Math::BigFloat, e.g. reduced)
|
---|
2041 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
|
---|
2042 |
|
---|
2043 | if ($x->{sign} !~ /^[+-]$/)
|
---|
2044 | {
|
---|
2045 | # for NaN, +inf, -inf: keep the sign
|
---|
2046 | return $self->new($x->{sign});
|
---|
2047 | }
|
---|
2048 | my $m = $x->copy(); delete $m->{_p}; delete $m->{_a};
|
---|
2049 | # that's a bit inefficient:
|
---|
2050 | my $zeros = $m->_trailing_zeros();
|
---|
2051 | $m->brsft($zeros,10) if $zeros != 0;
|
---|
2052 | $m;
|
---|
2053 | }
|
---|
2054 |
|
---|
2055 | sub parts
|
---|
2056 | {
|
---|
2057 | # return a copy of both the exponent and the mantissa
|
---|
2058 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
|
---|
2059 |
|
---|
2060 | ($x->mantissa(),$x->exponent());
|
---|
2061 | }
|
---|
2062 |
|
---|
2063 | ##############################################################################
|
---|
2064 | # rounding functions
|
---|
2065 |
|
---|
2066 | sub bfround
|
---|
2067 | {
|
---|
2068 | # precision: round to the $Nth digit left (+$n) or right (-$n) from the '.'
|
---|
2069 | # $n == 0 || $n == 1 => round to integer
|
---|
2070 | my $x = shift; my $self = ref($x) || $x; $x = $self->new($x) unless ref $x;
|
---|
2071 |
|
---|
2072 | my ($scale,$mode) = $x->_scale_p(@_);
|
---|
2073 |
|
---|
2074 | return $x if !defined $scale || $x->modify('bfround'); # no-op
|
---|
2075 |
|
---|
2076 | # no-op for BigInts if $n <= 0
|
---|
2077 | $x->bround( $x->length()-$scale, $mode) if $scale > 0;
|
---|
2078 |
|
---|
2079 | delete $x->{_a}; # delete to save memory
|
---|
2080 | $x->{_p} = $scale; # store new _p
|
---|
2081 | $x;
|
---|
2082 | }
|
---|
2083 |
|
---|
2084 | sub _scan_for_nonzero
|
---|
2085 | {
|
---|
2086 | # internal, used by bround() to scan for non-zeros after a '5'
|
---|
2087 | my ($x,$pad,$xs,$len) = @_;
|
---|
2088 |
|
---|
2089 | return 0 if $len == 1; # "5" is trailed by invisible zeros
|
---|
2090 | my $follow = $pad - 1;
|
---|
2091 | return 0 if $follow > $len || $follow < 1;
|
---|
2092 |
|
---|
2093 | # use the string form to check whether only '0's follow or not
|
---|
2094 | substr ($xs,-$follow) =~ /[^0]/ ? 1 : 0;
|
---|
2095 | }
|
---|
2096 |
|
---|
2097 | sub fround
|
---|
2098 | {
|
---|
2099 | # Exists to make life easier for switch between MBF and MBI (should we
|
---|
2100 | # autoload fxxx() like MBF does for bxxx()?)
|
---|
2101 | my $x = shift; $x = $class->new($x) unless ref $x;
|
---|
2102 | $x->bround(@_);
|
---|
2103 | }
|
---|
2104 |
|
---|
2105 | sub bround
|
---|
2106 | {
|
---|
2107 | # accuracy: +$n preserve $n digits from left,
|
---|
2108 | # -$n preserve $n digits from right (f.i. for 0.1234 style in MBF)
|
---|
2109 | # no-op for $n == 0
|
---|
2110 | # and overwrite the rest with 0's, return normalized number
|
---|
2111 | # do not return $x->bnorm(), but $x
|
---|
2112 |
|
---|
2113 | my $x = shift; $x = $class->new($x) unless ref $x;
|
---|
2114 | my ($scale,$mode) = $x->_scale_a(@_);
|
---|
2115 | return $x if !defined $scale || $x->modify('bround'); # no-op
|
---|
2116 |
|
---|
2117 | if ($x->is_zero() || $scale == 0)
|
---|
2118 | {
|
---|
2119 | $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; # 3 > 2
|
---|
2120 | return $x;
|
---|
2121 | }
|
---|
2122 | return $x if $x->{sign} !~ /^[+-]$/; # inf, NaN
|
---|
2123 |
|
---|
2124 | # we have fewer digits than we want to scale to
|
---|
2125 | my $len = $x->length();
|
---|
2126 | # convert $scale to a scalar in case it is an object (put's a limit on the
|
---|
2127 | # number length, but this would already limited by memory constraints), makes
|
---|
2128 | # it faster
|
---|
2129 | $scale = $scale->numify() if ref ($scale);
|
---|
2130 |
|
---|
2131 | # scale < 0, but > -len (not >=!)
|
---|
2132 | if (($scale < 0 && $scale < -$len-1) || ($scale >= $len))
|
---|
2133 | {
|
---|
2134 | $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; # 3 > 2
|
---|
2135 | return $x;
|
---|
2136 | }
|
---|
2137 |
|
---|
2138 | # count of 0's to pad, from left (+) or right (-): 9 - +6 => 3, or |-6| => 6
|
---|
2139 | my ($pad,$digit_round,$digit_after);
|
---|
2140 | $pad = $len - $scale;
|
---|
2141 | $pad = abs($scale-1) if $scale < 0;
|
---|
2142 |
|
---|
2143 | # do not use digit(), it is very costly for binary => decimal
|
---|
2144 | # getting the entire string is also costly, but we need to do it only once
|
---|
2145 | my $xs = $CALC->_str($x->{value});
|
---|
2146 | my $pl = -$pad-1;
|
---|
2147 |
|
---|
2148 | # pad: 123: 0 => -1, at 1 => -2, at 2 => -3, at 3 => -4
|
---|
2149 | # pad+1: 123: 0 => 0, at 1 => -1, at 2 => -2, at 3 => -3
|
---|
2150 | $digit_round = '0'; $digit_round = substr($xs,$pl,1) if $pad <= $len;
|
---|
2151 | $pl++; $pl ++ if $pad >= $len;
|
---|
2152 | $digit_after = '0'; $digit_after = substr($xs,$pl,1) if $pad > 0;
|
---|
2153 |
|
---|
2154 | # in case of 01234 we round down, for 6789 up, and only in case 5 we look
|
---|
2155 | # closer at the remaining digits of the original $x, remember decision
|
---|
2156 | my $round_up = 1; # default round up
|
---|
2157 | $round_up -- if
|
---|
2158 | ($mode eq 'trunc') || # trunc by round down
|
---|
2159 | ($digit_after =~ /[01234]/) || # round down anyway,
|
---|
2160 | # 6789 => round up
|
---|
2161 | ($digit_after eq '5') && # not 5000...0000
|
---|
2162 | ($x->_scan_for_nonzero($pad,$xs,$len) == 0) &&
|
---|
2163 | (
|
---|
2164 | ($mode eq 'even') && ($digit_round =~ /[24680]/) ||
|
---|
2165 | ($mode eq 'odd') && ($digit_round =~ /[13579]/) ||
|
---|
2166 | ($mode eq '+inf') && ($x->{sign} eq '-') ||
|
---|
2167 | ($mode eq '-inf') && ($x->{sign} eq '+') ||
|
---|
2168 | ($mode eq 'zero') # round down if zero, sign adjusted below
|
---|
2169 | );
|
---|
2170 | my $put_back = 0; # not yet modified
|
---|
2171 |
|
---|
2172 | if (($pad > 0) && ($pad <= $len))
|
---|
2173 | {
|
---|
2174 | substr($xs,-$pad,$pad) = '0' x $pad; # replace with '00...'
|
---|
2175 | $put_back = 1; # need to put back
|
---|
2176 | }
|
---|
2177 | elsif ($pad > $len)
|
---|
2178 | {
|
---|
2179 | $x->bzero(); # round to '0'
|
---|
2180 | }
|
---|
2181 |
|
---|
2182 | if ($round_up) # what gave test above?
|
---|
2183 | {
|
---|
2184 | $put_back = 1; # need to put back
|
---|
2185 | $pad = $len, $xs = '0' x $pad if $scale < 0; # tlr: whack 0.51=>1.0
|
---|
2186 |
|
---|
2187 | # we modify directly the string variant instead of creating a number and
|
---|
2188 | # adding it, since that is faster (we already have the string)
|
---|
2189 | my $c = 0; $pad ++; # for $pad == $len case
|
---|
2190 | while ($pad <= $len)
|
---|
2191 | {
|
---|
2192 | $c = substr($xs,-$pad,1) + 1; $c = '0' if $c eq '10';
|
---|
2193 | substr($xs,-$pad,1) = $c; $pad++;
|
---|
2194 | last if $c != 0; # no overflow => early out
|
---|
2195 | }
|
---|
2196 | $xs = '1'.$xs if $c == 0;
|
---|
2197 |
|
---|
2198 | }
|
---|
2199 | $x->{value} = $CALC->_new($xs) if $put_back == 1; # put back, if needed
|
---|
2200 |
|
---|
2201 | $x->{_a} = $scale if $scale >= 0;
|
---|
2202 | if ($scale < 0)
|
---|
2203 | {
|
---|
2204 | $x->{_a} = $len+$scale;
|
---|
2205 | $x->{_a} = 0 if $scale < -$len;
|
---|
2206 | }
|
---|
2207 | $x;
|
---|
2208 | }
|
---|
2209 |
|
---|
2210 | sub bfloor
|
---|
2211 | {
|
---|
2212 | # return integer less or equal then number; no-op since it's already integer
|
---|
2213 | my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
|
---|
2214 |
|
---|
2215 | $x->round(@r);
|
---|
2216 | }
|
---|
2217 |
|
---|
2218 | sub bceil
|
---|
2219 | {
|
---|
2220 | # return integer greater or equal then number; no-op since it's already int
|
---|
2221 | my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
|
---|
2222 |
|
---|
2223 | $x->round(@r);
|
---|
2224 | }
|
---|
2225 |
|
---|
2226 | sub as_number
|
---|
2227 | {
|
---|
2228 | # An object might be asked to return itself as bigint on certain overloaded
|
---|
2229 | # operations, this does exactly this, so that sub classes can simple inherit
|
---|
2230 | # it or override with their own integer conversion routine.
|
---|
2231 | $_[0]->copy();
|
---|
2232 | }
|
---|
2233 |
|
---|
2234 | sub as_hex
|
---|
2235 | {
|
---|
2236 | # return as hex string, with prefixed 0x
|
---|
2237 | my $x = shift; $x = $class->new($x) if !ref($x);
|
---|
2238 |
|
---|
2239 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc
|
---|
2240 |
|
---|
2241 | my $s = '';
|
---|
2242 | $s = $x->{sign} if $x->{sign} eq '-';
|
---|
2243 | $s . $CALC->_as_hex($x->{value});
|
---|
2244 | }
|
---|
2245 |
|
---|
2246 | sub as_bin
|
---|
2247 | {
|
---|
2248 | # return as binary string, with prefixed 0b
|
---|
2249 | my $x = shift; $x = $class->new($x) if !ref($x);
|
---|
2250 |
|
---|
2251 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc
|
---|
2252 |
|
---|
2253 | my $s = ''; $s = $x->{sign} if $x->{sign} eq '-';
|
---|
2254 | return $s . $CALC->_as_bin($x->{value});
|
---|
2255 | }
|
---|
2256 |
|
---|
2257 | ##############################################################################
|
---|
2258 | # private stuff (internal use only)
|
---|
2259 |
|
---|
2260 | sub objectify
|
---|
2261 | {
|
---|
2262 | # check for strings, if yes, return objects instead
|
---|
2263 |
|
---|
2264 | # the first argument is number of args objectify() should look at it will
|
---|
2265 | # return $count+1 elements, the first will be a classname. This is because
|
---|
2266 | # overloaded '""' calls bstr($object,undef,undef) and this would result in
|
---|
2267 | # useless objects beeing created and thrown away. So we cannot simple loop
|
---|
2268 | # over @_. If the given count is 0, all arguments will be used.
|
---|
2269 |
|
---|
2270 | # If the second arg is a ref, use it as class.
|
---|
2271 | # If not, try to use it as classname, unless undef, then use $class
|
---|
2272 | # (aka Math::BigInt). The latter shouldn't happen,though.
|
---|
2273 |
|
---|
2274 | # caller: gives us:
|
---|
2275 | # $x->badd(1); => ref x, scalar y
|
---|
2276 | # Class->badd(1,2); => classname x (scalar), scalar x, scalar y
|
---|
2277 | # Class->badd( Class->(1),2); => classname x (scalar), ref x, scalar y
|
---|
2278 | # Math::BigInt::badd(1,2); => scalar x, scalar y
|
---|
2279 | # In the last case we check number of arguments to turn it silently into
|
---|
2280 | # $class,1,2. (We can not take '1' as class ;o)
|
---|
2281 | # badd($class,1) is not supported (it should, eventually, try to add undef)
|
---|
2282 | # currently it tries 'Math::BigInt' + 1, which will not work.
|
---|
2283 |
|
---|
2284 | # some shortcut for the common cases
|
---|
2285 | # $x->unary_op();
|
---|
2286 | return (ref($_[1]),$_[1]) if (@_ == 2) && ($_[0]||0 == 1) && ref($_[1]);
|
---|
2287 |
|
---|
2288 | my $count = abs(shift || 0);
|
---|
2289 |
|
---|
2290 | my (@a,$k,$d); # resulting array, temp, and downgrade
|
---|
2291 | if (ref $_[0])
|
---|
2292 | {
|
---|
2293 | # okay, got object as first
|
---|
2294 | $a[0] = ref $_[0];
|
---|
2295 | }
|
---|
2296 | else
|
---|
2297 | {
|
---|
2298 | # nope, got 1,2 (Class->xxx(1) => Class,1 and not supported)
|
---|
2299 | $a[0] = $class;
|
---|
2300 | $a[0] = shift if $_[0] =~ /^[A-Z].*::/; # classname as first?
|
---|
2301 | }
|
---|
2302 |
|
---|
2303 | no strict 'refs';
|
---|
2304 | # disable downgrading, because Math::BigFLoat->foo('1.0','2.0') needs floats
|
---|
2305 | if (defined ${"$a[0]::downgrade"})
|
---|
2306 | {
|
---|
2307 | $d = ${"$a[0]::downgrade"};
|
---|
2308 | ${"$a[0]::downgrade"} = undef;
|
---|
2309 | }
|
---|
2310 |
|
---|
2311 | my $up = ${"$a[0]::upgrade"};
|
---|
2312 | #print "Now in objectify, my class is today $a[0], count = $count\n";
|
---|
2313 | if ($count == 0)
|
---|
2314 | {
|
---|
2315 | while (@_)
|
---|
2316 | {
|
---|
2317 | $k = shift;
|
---|
2318 | if (!ref($k))
|
---|
2319 | {
|
---|
2320 | $k = $a[0]->new($k);
|
---|
2321 | }
|
---|
2322 | elsif (!defined $up && ref($k) ne $a[0])
|
---|
2323 | {
|
---|
2324 | # foreign object, try to convert to integer
|
---|
2325 | $k->can('as_number') ? $k = $k->as_number() : $k = $a[0]->new($k);
|
---|
2326 | }
|
---|
2327 | push @a,$k;
|
---|
2328 | }
|
---|
2329 | }
|
---|
2330 | else
|
---|
2331 | {
|
---|
2332 | while ($count > 0)
|
---|
2333 | {
|
---|
2334 | $count--;
|
---|
2335 | $k = shift;
|
---|
2336 | if (!ref($k))
|
---|
2337 | {
|
---|
2338 | $k = $a[0]->new($k);
|
---|
2339 | }
|
---|
2340 | elsif (!defined $up && ref($k) ne $a[0])
|
---|
2341 | {
|
---|
2342 | # foreign object, try to convert to integer
|
---|
2343 | $k->can('as_number') ? $k = $k->as_number() : $k = $a[0]->new($k);
|
---|
2344 | }
|
---|
2345 | push @a,$k;
|
---|
2346 | }
|
---|
2347 | push @a,@_; # return other params, too
|
---|
2348 | }
|
---|
2349 | if (! wantarray)
|
---|
2350 | {
|
---|
2351 | require Carp; Carp::croak ("$class objectify needs list context");
|
---|
2352 | }
|
---|
2353 | ${"$a[0]::downgrade"} = $d;
|
---|
2354 | @a;
|
---|
2355 | }
|
---|
2356 |
|
---|
2357 | sub _register_callback
|
---|
2358 | {
|
---|
2359 | my ($class,$callback) = @_;
|
---|
2360 |
|
---|
2361 | if (ref($callback) ne 'CODE')
|
---|
2362 | {
|
---|
2363 | require Carp;
|
---|
2364 | Carp::croak ("$callback is not a coderef");
|
---|
2365 | }
|
---|
2366 | $CALLBACKS{$class} = $callback;
|
---|
2367 | }
|
---|
2368 |
|
---|
2369 | sub import
|
---|
2370 | {
|
---|
2371 | my $self = shift;
|
---|
2372 |
|
---|
2373 | $IMPORT++; # remember we did import()
|
---|
2374 | my @a; my $l = scalar @_;
|
---|
2375 | for ( my $i = 0; $i < $l ; $i++ )
|
---|
2376 | {
|
---|
2377 | if ($_[$i] eq ':constant')
|
---|
2378 | {
|
---|
2379 | # this causes overlord er load to step in
|
---|
2380 | overload::constant
|
---|
2381 | integer => sub { $self->new(shift) },
|
---|
2382 | binary => sub { $self->new(shift) };
|
---|
2383 | }
|
---|
2384 | elsif ($_[$i] eq 'upgrade')
|
---|
2385 | {
|
---|
2386 | # this causes upgrading
|
---|
2387 | $upgrade = $_[$i+1]; # or undef to disable
|
---|
2388 | $i++;
|
---|
2389 | }
|
---|
2390 | elsif ($_[$i] =~ /^lib$/i)
|
---|
2391 | {
|
---|
2392 | # this causes a different low lib to take care...
|
---|
2393 | $CALC = $_[$i+1] || '';
|
---|
2394 | $i++;
|
---|
2395 | }
|
---|
2396 | else
|
---|
2397 | {
|
---|
2398 | push @a, $_[$i];
|
---|
2399 | }
|
---|
2400 | }
|
---|
2401 | # any non :constant stuff is handled by our parent, Exporter
|
---|
2402 | if (@a > 0)
|
---|
2403 | {
|
---|
2404 | require Exporter;
|
---|
2405 |
|
---|
2406 | $self->SUPER::import(@a); # need it for subclasses
|
---|
2407 | $self->export_to_level(1,$self,@a); # need it for MBF
|
---|
2408 | }
|
---|
2409 |
|
---|
2410 | # try to load core math lib
|
---|
2411 | my @c = split /\s*,\s*/,$CALC;
|
---|
2412 | foreach (@c)
|
---|
2413 | {
|
---|
2414 | $_ =~ tr/a-zA-Z0-9://cd; # limit to sane characters
|
---|
2415 | }
|
---|
2416 | push @c, 'FastCalc', 'Calc'; # if all fail, try these
|
---|
2417 | $CALC = ''; # signal error
|
---|
2418 | foreach my $lib (@c)
|
---|
2419 | {
|
---|
2420 | next if ($lib || '') eq '';
|
---|
2421 | $lib = 'Math::BigInt::'.$lib if $lib !~ /^Math::BigInt/i;
|
---|
2422 | $lib =~ s/\.pm$//;
|
---|
2423 | if ($] < 5.006)
|
---|
2424 | {
|
---|
2425 | # Perl < 5.6.0 dies with "out of memory!" when eval("") and ':constant' is
|
---|
2426 | # used in the same script, or eval("") inside import().
|
---|
2427 | my @parts = split /::/, $lib; # Math::BigInt => Math BigInt
|
---|
2428 | my $file = pop @parts; $file .= '.pm'; # BigInt => BigInt.pm
|
---|
2429 | require File::Spec;
|
---|
2430 | $file = File::Spec->catfile (@parts, $file);
|
---|
2431 | eval { require "$file"; $lib->import( @c ); }
|
---|
2432 | }
|
---|
2433 | else
|
---|
2434 | {
|
---|
2435 | eval "use $lib qw/@c/;";
|
---|
2436 | }
|
---|
2437 | if ($@ eq '')
|
---|
2438 | {
|
---|
2439 | my $ok = 1;
|
---|
2440 | # loaded it ok, see if the api_version() is high enough
|
---|
2441 | if ($lib->can('api_version') && $lib->api_version() >= 1.0)
|
---|
2442 | {
|
---|
2443 | $ok = 0;
|
---|
2444 | # api_version matches, check if it really provides anything we need
|
---|
2445 | for my $method (qw/
|
---|
2446 | one two ten
|
---|
2447 | str num
|
---|
2448 | add mul div sub dec inc
|
---|
2449 | acmp len digit is_one is_zero is_even is_odd
|
---|
2450 | is_two is_ten
|
---|
2451 | new copy check from_hex from_bin as_hex as_bin zeros
|
---|
2452 | rsft lsft xor and or
|
---|
2453 | mod sqrt root fac pow modinv modpow log_int gcd
|
---|
2454 | /)
|
---|
2455 | {
|
---|
2456 | if (!$lib->can("_$method"))
|
---|
2457 | {
|
---|
2458 | if (($WARN{$lib}||0) < 2)
|
---|
2459 | {
|
---|
2460 | require Carp;
|
---|
2461 | Carp::carp ("$lib is missing method '_$method'");
|
---|
2462 | $WARN{$lib} = 1; # still warn about the lib
|
---|
2463 | }
|
---|
2464 | $ok++; last;
|
---|
2465 | }
|
---|
2466 | }
|
---|
2467 | }
|
---|
2468 | if ($ok == 0)
|
---|
2469 | {
|
---|
2470 | $CALC = $lib;
|
---|
2471 | last; # found a usable one, break
|
---|
2472 | }
|
---|
2473 | else
|
---|
2474 | {
|
---|
2475 | if (($WARN{$lib}||0) < 2)
|
---|
2476 | {
|
---|
2477 | my $ver = eval "\$$lib\::VERSION" || 'unknown';
|
---|
2478 | require Carp;
|
---|
2479 | Carp::carp ("Cannot load outdated $lib v$ver, please upgrade");
|
---|
2480 | $WARN{$lib} = 2; # never warn again
|
---|
2481 | }
|
---|
2482 | }
|
---|
2483 | }
|
---|
2484 | }
|
---|
2485 | if ($CALC eq '')
|
---|
2486 | {
|
---|
2487 | require Carp;
|
---|
2488 | Carp::croak ("Couldn't load any math lib, not even 'Calc.pm'");
|
---|
2489 | }
|
---|
2490 |
|
---|
2491 | # notify callbacks
|
---|
2492 | foreach my $class (keys %CALLBACKS)
|
---|
2493 | {
|
---|
2494 | &{$CALLBACKS{$class}}($CALC);
|
---|
2495 | }
|
---|
2496 |
|
---|
2497 | # Fill $CAN with the results of $CALC->can(...) for emulating lower math lib
|
---|
2498 | # functions
|
---|
2499 |
|
---|
2500 | %CAN = ();
|
---|
2501 | for my $method (qw/ signed_and signed_or signed_xor /)
|
---|
2502 | {
|
---|
2503 | $CAN{$method} = $CALC->can("_$method") ? 1 : 0;
|
---|
2504 | }
|
---|
2505 |
|
---|
2506 | # import done
|
---|
2507 | }
|
---|
2508 |
|
---|
2509 | sub __from_hex
|
---|
2510 | {
|
---|
2511 | # internal
|
---|
2512 | # convert a (ref to) big hex string to BigInt, return undef for error
|
---|
2513 | my $hs = shift;
|
---|
2514 |
|
---|
2515 | my $x = Math::BigInt->bzero();
|
---|
2516 |
|
---|
2517 | # strip underscores
|
---|
2518 | $hs =~ s/([0-9a-fA-F])_([0-9a-fA-F])/$1$2/g;
|
---|
2519 | $hs =~ s/([0-9a-fA-F])_([0-9a-fA-F])/$1$2/g;
|
---|
2520 |
|
---|
2521 | return $x->bnan() if $hs !~ /^[\-\+]?0x[0-9A-Fa-f]+$/;
|
---|
2522 |
|
---|
2523 | my $sign = '+'; $sign = '-' if $hs =~ /^-/;
|
---|
2524 |
|
---|
2525 | $hs =~ s/^[+-]//; # strip sign
|
---|
2526 | $x->{value} = $CALC->_from_hex($hs);
|
---|
2527 | $x->{sign} = $sign unless $CALC->_is_zero($x->{value}); # no '-0'
|
---|
2528 | $x;
|
---|
2529 | }
|
---|
2530 |
|
---|
2531 | sub __from_bin
|
---|
2532 | {
|
---|
2533 | # internal
|
---|
2534 | # convert a (ref to) big binary string to BigInt, return undef for error
|
---|
2535 | my $bs = shift;
|
---|
2536 |
|
---|
2537 | my $x = Math::BigInt->bzero();
|
---|
2538 | # strip underscores
|
---|
2539 | $bs =~ s/([01])_([01])/$1$2/g;
|
---|
2540 | $bs =~ s/([01])_([01])/$1$2/g;
|
---|
2541 | return $x->bnan() if $bs !~ /^[+-]?0b[01]+$/;
|
---|
2542 |
|
---|
2543 | my $sign = '+'; $sign = '-' if $bs =~ /^\-/;
|
---|
2544 | $bs =~ s/^[+-]//; # strip sign
|
---|
2545 |
|
---|
2546 | $x->{value} = $CALC->_from_bin($bs);
|
---|
2547 | $x->{sign} = $sign unless $CALC->_is_zero($x->{value}); # no '-0'
|
---|
2548 | $x;
|
---|
2549 | }
|
---|
2550 |
|
---|
2551 | sub _split
|
---|
2552 | {
|
---|
2553 | # input: num_str; output: undef for invalid or
|
---|
2554 | # (\$mantissa_sign,\$mantissa_value,\$mantissa_fraction,\$exp_sign,\$exp_value)
|
---|
2555 | # Internal, take apart a string and return the pieces.
|
---|
2556 | # Strip leading/trailing whitespace, leading zeros, underscore and reject
|
---|
2557 | # invalid input.
|
---|
2558 | my $x = shift;
|
---|
2559 |
|
---|
2560 | # strip white space at front, also extranous leading zeros
|
---|
2561 | $x =~ s/^\s*([-]?)0*([0-9])/$1$2/g; # will not strip ' .2'
|
---|
2562 | $x =~ s/^\s+//; # but this will
|
---|
2563 | $x =~ s/\s+$//g; # strip white space at end
|
---|
2564 |
|
---|
2565 | # shortcut, if nothing to split, return early
|
---|
2566 | if ($x =~ /^[+-]?\d+\z/)
|
---|
2567 | {
|
---|
2568 | $x =~ s/^([+-])0*([0-9])/$2/; my $sign = $1 || '+';
|
---|
2569 | return (\$sign, \$x, \'', \'', \0);
|
---|
2570 | }
|
---|
2571 |
|
---|
2572 | # invalid starting char?
|
---|
2573 | return if $x !~ /^[+-]?(\.?[0-9]|0b[0-1]|0x[0-9a-fA-F])/;
|
---|
2574 |
|
---|
2575 | return __from_hex($x) if $x =~ /^[\-\+]?0x/; # hex string
|
---|
2576 | return __from_bin($x) if $x =~ /^[\-\+]?0b/; # binary string
|
---|
2577 |
|
---|
2578 | # strip underscores between digits
|
---|
2579 | $x =~ s/(\d)_(\d)/$1$2/g;
|
---|
2580 | $x =~ s/(\d)_(\d)/$1$2/g; # do twice for 1_2_3
|
---|
2581 |
|
---|
2582 | # some possible inputs:
|
---|
2583 | # 2.1234 # 0.12 # 1 # 1E1 # 2.134E1 # 434E-10 # 1.02009E-2
|
---|
2584 | # .2 # 1_2_3.4_5_6 # 1.4E1_2_3 # 1e3 # +.2 # 0e999
|
---|
2585 |
|
---|
2586 | my ($m,$e,$last) = split /[Ee]/,$x;
|
---|
2587 | return if defined $last; # last defined => 1e2E3 or others
|
---|
2588 | $e = '0' if !defined $e || $e eq "";
|
---|
2589 |
|
---|
2590 | # sign,value for exponent,mantint,mantfrac
|
---|
2591 | my ($es,$ev,$mis,$miv,$mfv);
|
---|
2592 | # valid exponent?
|
---|
2593 | if ($e =~ /^([+-]?)0*(\d+)$/) # strip leading zeros
|
---|
2594 | {
|
---|
2595 | $es = $1; $ev = $2;
|
---|
2596 | # valid mantissa?
|
---|
2597 | return if $m eq '.' || $m eq '';
|
---|
2598 | my ($mi,$mf,$lastf) = split /\./,$m;
|
---|
2599 | return if defined $lastf; # lastf defined => 1.2.3 or others
|
---|
2600 | $mi = '0' if !defined $mi;
|
---|
2601 | $mi .= '0' if $mi =~ /^[\-\+]?$/;
|
---|
2602 | $mf = '0' if !defined $mf || $mf eq '';
|
---|
2603 | if ($mi =~ /^([+-]?)0*(\d+)$/) # strip leading zeros
|
---|
2604 | {
|
---|
2605 | $mis = $1||'+'; $miv = $2;
|
---|
2606 | return unless ($mf =~ /^(\d*?)0*$/); # strip trailing zeros
|
---|
2607 | $mfv = $1;
|
---|
2608 | # handle the 0e999 case here
|
---|
2609 | $ev = 0 if $miv eq '0' && $mfv eq '';
|
---|
2610 | return (\$mis,\$miv,\$mfv,\$es,\$ev);
|
---|
2611 | }
|
---|
2612 | }
|
---|
2613 | return; # NaN, not a number
|
---|
2614 | }
|
---|
2615 |
|
---|
2616 | ##############################################################################
|
---|
2617 | # internal calculation routines (others are in Math::BigInt::Calc etc)
|
---|
2618 |
|
---|
2619 | sub __lcm
|
---|
2620 | {
|
---|
2621 | # (BINT or num_str, BINT or num_str) return BINT
|
---|
2622 | # does modify first argument
|
---|
2623 | # LCM
|
---|
2624 |
|
---|
2625 | my ($x,$ty) = @_;
|
---|
2626 | return $x->bnan() if ($x->{sign} eq $nan) || ($ty->{sign} eq $nan);
|
---|
2627 | my $method = ref($x) . '::bgcd';
|
---|
2628 | no strict 'refs';
|
---|
2629 | $x * $ty / &$method($x,$ty);
|
---|
2630 | }
|
---|
2631 |
|
---|
2632 | ###############################################################################
|
---|
2633 | # this method returns 0 if the object can be modified, or 1 if not.
|
---|
2634 | # We use a fast constant sub() here, to avoid costly calls. Subclasses
|
---|
2635 | # may override it with special code (f.i. Math::BigInt::Constant does so)
|
---|
2636 |
|
---|
2637 | sub modify () { 0; }
|
---|
2638 |
|
---|
2639 | 1;
|
---|
2640 | __END__
|
---|
2641 |
|
---|
2642 | =pod
|
---|
2643 |
|
---|
2644 | =head1 NAME
|
---|
2645 |
|
---|
2646 | Math::BigInt - Arbitrary size integer/float math package
|
---|
2647 |
|
---|
2648 | =head1 SYNOPSIS
|
---|
2649 |
|
---|
2650 | use Math::BigInt;
|
---|
2651 |
|
---|
2652 | # or make it faster: install (optional) Math::BigInt::GMP
|
---|
2653 | # and always use (it will fall back to pure Perl if the
|
---|
2654 | # GMP library is not installed):
|
---|
2655 |
|
---|
2656 | use Math::BigInt lib => 'GMP';
|
---|
2657 |
|
---|
2658 | my $str = '1234567890';
|
---|
2659 | my @values = (64,74,18);
|
---|
2660 | my $n = 1; my $sign = '-';
|
---|
2661 |
|
---|
2662 | # Number creation
|
---|
2663 | $x = Math::BigInt->new($str); # defaults to 0
|
---|
2664 | $y = $x->copy(); # make a true copy
|
---|
2665 | $nan = Math::BigInt->bnan(); # create a NotANumber
|
---|
2666 | $zero = Math::BigInt->bzero(); # create a +0
|
---|
2667 | $inf = Math::BigInt->binf(); # create a +inf
|
---|
2668 | $inf = Math::BigInt->binf('-'); # create a -inf
|
---|
2669 | $one = Math::BigInt->bone(); # create a +1
|
---|
2670 | $one = Math::BigInt->bone('-'); # create a -1
|
---|
2671 |
|
---|
2672 | # Testing (don't modify their arguments)
|
---|
2673 | # (return true if the condition is met, otherwise false)
|
---|
2674 |
|
---|
2675 | $x->is_zero(); # if $x is +0
|
---|
2676 | $x->is_nan(); # if $x is NaN
|
---|
2677 | $x->is_one(); # if $x is +1
|
---|
2678 | $x->is_one('-'); # if $x is -1
|
---|
2679 | $x->is_odd(); # if $x is odd
|
---|
2680 | $x->is_even(); # if $x is even
|
---|
2681 | $x->is_pos(); # if $x >= 0
|
---|
2682 | $x->is_neg(); # if $x < 0
|
---|
2683 | $x->is_inf($sign); # if $x is +inf, or -inf (sign is default '+')
|
---|
2684 | $x->is_int(); # if $x is an integer (not a float)
|
---|
2685 |
|
---|
2686 | # comparing and digit/sign extration
|
---|
2687 | $x->bcmp($y); # compare numbers (undef,<0,=0,>0)
|
---|
2688 | $x->bacmp($y); # compare absolutely (undef,<0,=0,>0)
|
---|
2689 | $x->sign(); # return the sign, either +,- or NaN
|
---|
2690 | $x->digit($n); # return the nth digit, counting from right
|
---|
2691 | $x->digit(-$n); # return the nth digit, counting from left
|
---|
2692 |
|
---|
2693 | # The following all modify their first argument. If you want to preserve
|
---|
2694 | # $x, use $z = $x->copy()->bXXX($y); See under L<CAVEATS> for why this is
|
---|
2695 | # neccessary when mixing $a = $b assigments with non-overloaded math.
|
---|
2696 |
|
---|
2697 | $x->bzero(); # set $x to 0
|
---|
2698 | $x->bnan(); # set $x to NaN
|
---|
2699 | $x->bone(); # set $x to +1
|
---|
2700 | $x->bone('-'); # set $x to -1
|
---|
2701 | $x->binf(); # set $x to inf
|
---|
2702 | $x->binf('-'); # set $x to -inf
|
---|
2703 |
|
---|
2704 | $x->bneg(); # negation
|
---|
2705 | $x->babs(); # absolute value
|
---|
2706 | $x->bnorm(); # normalize (no-op in BigInt)
|
---|
2707 | $x->bnot(); # two's complement (bit wise not)
|
---|
2708 | $x->binc(); # increment $x by 1
|
---|
2709 | $x->bdec(); # decrement $x by 1
|
---|
2710 |
|
---|
2711 | $x->badd($y); # addition (add $y to $x)
|
---|
2712 | $x->bsub($y); # subtraction (subtract $y from $x)
|
---|
2713 | $x->bmul($y); # multiplication (multiply $x by $y)
|
---|
2714 | $x->bdiv($y); # divide, set $x to quotient
|
---|
2715 | # return (quo,rem) or quo if scalar
|
---|
2716 |
|
---|
2717 | $x->bmod($y); # modulus (x % y)
|
---|
2718 | $x->bmodpow($exp,$mod); # modular exponentation (($num**$exp) % $mod))
|
---|
2719 | $x->bmodinv($mod); # the inverse of $x in the given modulus $mod
|
---|
2720 |
|
---|
2721 | $x->bpow($y); # power of arguments (x ** y)
|
---|
2722 | $x->blsft($y); # left shift
|
---|
2723 | $x->brsft($y); # right shift
|
---|
2724 | $x->blsft($y,$n); # left shift, by base $n (like 10)
|
---|
2725 | $x->brsft($y,$n); # right shift, by base $n (like 10)
|
---|
2726 |
|
---|
2727 | $x->band($y); # bitwise and
|
---|
2728 | $x->bior($y); # bitwise inclusive or
|
---|
2729 | $x->bxor($y); # bitwise exclusive or
|
---|
2730 | $x->bnot(); # bitwise not (two's complement)
|
---|
2731 |
|
---|
2732 | $x->bsqrt(); # calculate square-root
|
---|
2733 | $x->broot($y); # $y'th root of $x (e.g. $y == 3 => cubic root)
|
---|
2734 | $x->bfac(); # factorial of $x (1*2*3*4*..$x)
|
---|
2735 |
|
---|
2736 | $x->round($A,$P,$mode); # round to accuracy or precision using mode $mode
|
---|
2737 | $x->bround($n); # accuracy: preserve $n digits
|
---|
2738 | $x->bfround($n); # round to $nth digit, no-op for BigInts
|
---|
2739 |
|
---|
2740 | # The following do not modify their arguments in BigInt (are no-ops),
|
---|
2741 | # but do so in BigFloat:
|
---|
2742 |
|
---|
2743 | $x->bfloor(); # return integer less or equal than $x
|
---|
2744 | $x->bceil(); # return integer greater or equal than $x
|
---|
2745 |
|
---|
2746 | # The following do not modify their arguments:
|
---|
2747 |
|
---|
2748 | # greatest common divisor (no OO style)
|
---|
2749 | my $gcd = Math::BigInt::bgcd(@values);
|
---|
2750 | # lowest common multiplicator (no OO style)
|
---|
2751 | my $lcm = Math::BigInt::blcm(@values);
|
---|
2752 |
|
---|
2753 | $x->length(); # return number of digits in number
|
---|
2754 | ($xl,$f) = $x->length(); # length of number and length of fraction part,
|
---|
2755 | # latter is always 0 digits long for BigInts
|
---|
2756 |
|
---|
2757 | $x->exponent(); # return exponent as BigInt
|
---|
2758 | $x->mantissa(); # return (signed) mantissa as BigInt
|
---|
2759 | $x->parts(); # return (mantissa,exponent) as BigInt
|
---|
2760 | $x->copy(); # make a true copy of $x (unlike $y = $x;)
|
---|
2761 | $x->as_int(); # return as BigInt (in BigInt: same as copy())
|
---|
2762 | $x->numify(); # return as scalar (might overflow!)
|
---|
2763 |
|
---|
2764 | # conversation to string (do not modify their argument)
|
---|
2765 | $x->bstr(); # normalized string (e.g. '3')
|
---|
2766 | $x->bsstr(); # norm. string in scientific notation (e.g. '3E0')
|
---|
2767 | $x->as_hex(); # as signed hexadecimal string with prefixed 0x
|
---|
2768 | $x->as_bin(); # as signed binary string with prefixed 0b
|
---|
2769 |
|
---|
2770 |
|
---|
2771 | # precision and accuracy (see section about rounding for more)
|
---|
2772 | $x->precision(); # return P of $x (or global, if P of $x undef)
|
---|
2773 | $x->precision($n); # set P of $x to $n
|
---|
2774 | $x->accuracy(); # return A of $x (or global, if A of $x undef)
|
---|
2775 | $x->accuracy($n); # set A $x to $n
|
---|
2776 |
|
---|
2777 | # Global methods
|
---|
2778 | Math::BigInt->precision(); # get/set global P for all BigInt objects
|
---|
2779 | Math::BigInt->accuracy(); # get/set global A for all BigInt objects
|
---|
2780 | Math::BigInt->round_mode(); # get/set global round mode, one of
|
---|
2781 | # 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'
|
---|
2782 | Math::BigInt->config(); # return hash containing configuration
|
---|
2783 |
|
---|
2784 | =head1 DESCRIPTION
|
---|
2785 |
|
---|
2786 | All operators (inlcuding basic math operations) are overloaded if you
|
---|
2787 | declare your big integers as
|
---|
2788 |
|
---|
2789 | $i = new Math::BigInt '123_456_789_123_456_789';
|
---|
2790 |
|
---|
2791 | Operations with overloaded operators preserve the arguments which is
|
---|
2792 | exactly what you expect.
|
---|
2793 |
|
---|
2794 | =over 2
|
---|
2795 |
|
---|
2796 | =item Input
|
---|
2797 |
|
---|
2798 | Input values to these routines may be any string, that looks like a number
|
---|
2799 | and results in an integer, including hexadecimal and binary numbers.
|
---|
2800 |
|
---|
2801 | Scalars holding numbers may also be passed, but note that non-integer numbers
|
---|
2802 | may already have lost precision due to the conversation to float. Quote
|
---|
2803 | your input if you want BigInt to see all the digits:
|
---|
2804 |
|
---|
2805 | $x = Math::BigInt->new(12345678890123456789); # bad
|
---|
2806 | $x = Math::BigInt->new('12345678901234567890'); # good
|
---|
2807 |
|
---|
2808 | You can include one underscore between any two digits.
|
---|
2809 |
|
---|
2810 | This means integer values like 1.01E2 or even 1000E-2 are also accepted.
|
---|
2811 | Non-integer values result in NaN.
|
---|
2812 |
|
---|
2813 | Currently, Math::BigInt::new() defaults to 0, while Math::BigInt::new('')
|
---|
2814 | results in 'NaN'. This might change in the future, so use always the following
|
---|
2815 | explicit forms to get a zero or NaN:
|
---|
2816 |
|
---|
2817 | $zero = Math::BigInt->bzero();
|
---|
2818 | $nan = Math::BigInt->bnan();
|
---|
2819 |
|
---|
2820 | C<bnorm()> on a BigInt object is now effectively a no-op, since the numbers
|
---|
2821 | are always stored in normalized form. If passed a string, creates a BigInt
|
---|
2822 | object from the input.
|
---|
2823 |
|
---|
2824 | =item Output
|
---|
2825 |
|
---|
2826 | Output values are BigInt objects (normalized), except for the methods which
|
---|
2827 | return a string (see L<SYNOPSIS>).
|
---|
2828 |
|
---|
2829 | Some routines (C<is_odd()>, C<is_even()>, C<is_zero()>, C<is_one()>,
|
---|
2830 | C<is_nan()>, etc.) return true or false, while others (C<bcmp()>, C<bacmp()>)
|
---|
2831 | return either undef (if NaN is involved), <0, 0 or >0 and are suited for sort.
|
---|
2832 |
|
---|
2833 | =back
|
---|
2834 |
|
---|
2835 | =head1 METHODS
|
---|
2836 |
|
---|
2837 | Each of the methods below (except config(), accuracy() and precision())
|
---|
2838 | accepts three additional parameters. These arguments C<$A>, C<$P> and C<$R>
|
---|
2839 | are C<accuracy>, C<precision> and C<round_mode>. Please see the section about
|
---|
2840 | L<ACCURACY and PRECISION> for more information.
|
---|
2841 |
|
---|
2842 | =head2 config
|
---|
2843 |
|
---|
2844 | use Data::Dumper;
|
---|
2845 |
|
---|
2846 | print Dumper ( Math::BigInt->config() );
|
---|
2847 | print Math::BigInt->config()->{lib},"\n";
|
---|
2848 |
|
---|
2849 | Returns a hash containing the configuration, e.g. the version number, lib
|
---|
2850 | loaded etc. The following hash keys are currently filled in with the
|
---|
2851 | appropriate information.
|
---|
2852 |
|
---|
2853 | key Description
|
---|
2854 | Example
|
---|
2855 | ============================================================
|
---|
2856 | lib Name of the low-level math library
|
---|
2857 | Math::BigInt::Calc
|
---|
2858 | lib_version Version of low-level math library (see 'lib')
|
---|
2859 | 0.30
|
---|
2860 | class The class name of config() you just called
|
---|
2861 | Math::BigInt
|
---|
2862 | upgrade To which class math operations might be upgraded
|
---|
2863 | Math::BigFloat
|
---|
2864 | downgrade To which class math operations might be downgraded
|
---|
2865 | undef
|
---|
2866 | precision Global precision
|
---|
2867 | undef
|
---|
2868 | accuracy Global accuracy
|
---|
2869 | undef
|
---|
2870 | round_mode Global round mode
|
---|
2871 | even
|
---|
2872 | version version number of the class you used
|
---|
2873 | 1.61
|
---|
2874 | div_scale Fallback acccuracy for div
|
---|
2875 | 40
|
---|
2876 | trap_nan If true, traps creation of NaN via croak()
|
---|
2877 | 1
|
---|
2878 | trap_inf If true, traps creation of +inf/-inf via croak()
|
---|
2879 | 1
|
---|
2880 |
|
---|
2881 | The following values can be set by passing C<config()> a reference to a hash:
|
---|
2882 |
|
---|
2883 | trap_inf trap_nan
|
---|
2884 | upgrade downgrade precision accuracy round_mode div_scale
|
---|
2885 |
|
---|
2886 | Example:
|
---|
2887 |
|
---|
2888 | $new_cfg = Math::BigInt->config( { trap_inf => 1, precision => 5 } );
|
---|
2889 |
|
---|
2890 | =head2 accuracy
|
---|
2891 |
|
---|
2892 | $x->accuracy(5); # local for $x
|
---|
2893 | CLASS->accuracy(5); # global for all members of CLASS
|
---|
2894 | # Note: This also applies to new()!
|
---|
2895 |
|
---|
2896 | $A = $x->accuracy(); # read out accuracy that affects $x
|
---|
2897 | $A = CLASS->accuracy(); # read out global accuracy
|
---|
2898 |
|
---|
2899 | Set or get the global or local accuracy, aka how many significant digits the
|
---|
2900 | results have. If you set a global accuracy, then this also applies to new()!
|
---|
2901 |
|
---|
2902 | Warning! The accuracy I<sticks>, e.g. once you created a number under the
|
---|
2903 | influence of C<< CLASS->accuracy($A) >>, all results from math operations with
|
---|
2904 | that number will also be rounded.
|
---|
2905 |
|
---|
2906 | In most cases, you should probably round the results explicitely using one of
|
---|
2907 | L<round()>, L<bround()> or L<bfround()> or by passing the desired accuracy
|
---|
2908 | to the math operation as additional parameter:
|
---|
2909 |
|
---|
2910 | my $x = Math::BigInt->new(30000);
|
---|
2911 | my $y = Math::BigInt->new(7);
|
---|
2912 | print scalar $x->copy()->bdiv($y, 2); # print 4300
|
---|
2913 | print scalar $x->copy()->bdiv($y)->bround(2); # print 4300
|
---|
2914 |
|
---|
2915 | Please see the section about L<ACCURACY AND PRECISION> for further details.
|
---|
2916 |
|
---|
2917 | Value must be greater than zero. Pass an undef value to disable it:
|
---|
2918 |
|
---|
2919 | $x->accuracy(undef);
|
---|
2920 | Math::BigInt->accuracy(undef);
|
---|
2921 |
|
---|
2922 | Returns the current accuracy. For C<$x->accuracy()> it will return either the
|
---|
2923 | local accuracy, or if not defined, the global. This means the return value
|
---|
2924 | represents the accuracy that will be in effect for $x:
|
---|
2925 |
|
---|
2926 | $y = Math::BigInt->new(1234567); # unrounded
|
---|
2927 | print Math::BigInt->accuracy(4),"\n"; # set 4, print 4
|
---|
2928 | $x = Math::BigInt->new(123456); # $x will be automatically rounded!
|
---|
2929 | print "$x $y\n"; # '123500 1234567'
|
---|
2930 | print $x->accuracy(),"\n"; # will be 4
|
---|
2931 | print $y->accuracy(),"\n"; # also 4, since global is 4
|
---|
2932 | print Math::BigInt->accuracy(5),"\n"; # set to 5, print 5
|
---|
2933 | print $x->accuracy(),"\n"; # still 4
|
---|
2934 | print $y->accuracy(),"\n"; # 5, since global is 5
|
---|
2935 |
|
---|
2936 | Note: Works also for subclasses like Math::BigFloat. Each class has it's own
|
---|
2937 | globals separated from Math::BigInt, but it is possible to subclass
|
---|
2938 | Math::BigInt and make the globals of the subclass aliases to the ones from
|
---|
2939 | Math::BigInt.
|
---|
2940 |
|
---|
2941 | =head2 precision
|
---|
2942 |
|
---|
2943 | $x->precision(-2); # local for $x, round at the second digit right of the dot
|
---|
2944 | $x->precision(2); # ditto, round at the second digit left of the dot
|
---|
2945 |
|
---|
2946 | CLASS->precision(5); # Global for all members of CLASS
|
---|
2947 | # This also applies to new()!
|
---|
2948 | CLASS->precision(-5); # ditto
|
---|
2949 |
|
---|
2950 | $P = CLASS->precision(); # read out global precision
|
---|
2951 | $P = $x->precision(); # read out precision that affects $x
|
---|
2952 |
|
---|
2953 | Note: You probably want to use L<accuracy()> instead. With L<accuracy> you
|
---|
2954 | set the number of digits each result should have, with L<precision> you
|
---|
2955 | set the place where to round!
|
---|
2956 |
|
---|
2957 | C<precision()> sets or gets the global or local precision, aka at which digit
|
---|
2958 | before or after the dot to round all results. A set global precision also
|
---|
2959 | applies to all newly created numbers!
|
---|
2960 |
|
---|
2961 | In Math::BigInt, passing a negative number precision has no effect since no
|
---|
2962 | numbers have digits after the dot. In L<Math::BigFloat>, it will round all
|
---|
2963 | results to P digits after the dot.
|
---|
2964 |
|
---|
2965 | Please see the section about L<ACCURACY AND PRECISION> for further details.
|
---|
2966 |
|
---|
2967 | Pass an undef value to disable it:
|
---|
2968 |
|
---|
2969 | $x->precision(undef);
|
---|
2970 | Math::BigInt->precision(undef);
|
---|
2971 |
|
---|
2972 | Returns the current precision. For C<$x->precision()> it will return either the
|
---|
2973 | local precision of $x, or if not defined, the global. This means the return
|
---|
2974 | value represents the prevision that will be in effect for $x:
|
---|
2975 |
|
---|
2976 | $y = Math::BigInt->new(1234567); # unrounded
|
---|
2977 | print Math::BigInt->precision(4),"\n"; # set 4, print 4
|
---|
2978 | $x = Math::BigInt->new(123456); # will be automatically rounded
|
---|
2979 | print $x; # print "120000"!
|
---|
2980 |
|
---|
2981 | Note: Works also for subclasses like L<Math::BigFloat>. Each class has its
|
---|
2982 | own globals separated from Math::BigInt, but it is possible to subclass
|
---|
2983 | Math::BigInt and make the globals of the subclass aliases to the ones from
|
---|
2984 | Math::BigInt.
|
---|
2985 |
|
---|
2986 | =head2 brsft
|
---|
2987 |
|
---|
2988 | $x->brsft($y,$n);
|
---|
2989 |
|
---|
2990 | Shifts $x right by $y in base $n. Default is base 2, used are usually 10 and
|
---|
2991 | 2, but others work, too.
|
---|
2992 |
|
---|
2993 | Right shifting usually amounts to dividing $x by $n ** $y and truncating the
|
---|
2994 | result:
|
---|
2995 |
|
---|
2996 |
|
---|
2997 | $x = Math::BigInt->new(10);
|
---|
2998 | $x->brsft(1); # same as $x >> 1: 5
|
---|
2999 | $x = Math::BigInt->new(1234);
|
---|
3000 | $x->brsft(2,10); # result 12
|
---|
3001 |
|
---|
3002 | There is one exception, and that is base 2 with negative $x:
|
---|
3003 |
|
---|
3004 |
|
---|
3005 | $x = Math::BigInt->new(-5);
|
---|
3006 | print $x->brsft(1);
|
---|
3007 |
|
---|
3008 | This will print -3, not -2 (as it would if you divide -5 by 2 and truncate the
|
---|
3009 | result).
|
---|
3010 |
|
---|
3011 | =head2 new
|
---|
3012 |
|
---|
3013 | $x = Math::BigInt->new($str,$A,$P,$R);
|
---|
3014 |
|
---|
3015 | Creates a new BigInt object from a scalar or another BigInt object. The
|
---|
3016 | input is accepted as decimal, hex (with leading '0x') or binary (with leading
|
---|
3017 | '0b').
|
---|
3018 |
|
---|
3019 | See L<Input> for more info on accepted input formats.
|
---|
3020 |
|
---|
3021 | =head2 bnan
|
---|
3022 |
|
---|
3023 | $x = Math::BigInt->bnan();
|
---|
3024 |
|
---|
3025 | Creates a new BigInt object representing NaN (Not A Number).
|
---|
3026 | If used on an object, it will set it to NaN:
|
---|
3027 |
|
---|
3028 | $x->bnan();
|
---|
3029 |
|
---|
3030 | =head2 bzero
|
---|
3031 |
|
---|
3032 | $x = Math::BigInt->bzero();
|
---|
3033 |
|
---|
3034 | Creates a new BigInt object representing zero.
|
---|
3035 | If used on an object, it will set it to zero:
|
---|
3036 |
|
---|
3037 | $x->bzero();
|
---|
3038 |
|
---|
3039 | =head2 binf
|
---|
3040 |
|
---|
3041 | $x = Math::BigInt->binf($sign);
|
---|
3042 |
|
---|
3043 | Creates a new BigInt object representing infinity. The optional argument is
|
---|
3044 | either '-' or '+', indicating whether you want infinity or minus infinity.
|
---|
3045 | If used on an object, it will set it to infinity:
|
---|
3046 |
|
---|
3047 | $x->binf();
|
---|
3048 | $x->binf('-');
|
---|
3049 |
|
---|
3050 | =head2 bone
|
---|
3051 |
|
---|
3052 | $x = Math::BigInt->binf($sign);
|
---|
3053 |
|
---|
3054 | Creates a new BigInt object representing one. The optional argument is
|
---|
3055 | either '-' or '+', indicating whether you want one or minus one.
|
---|
3056 | If used on an object, it will set it to one:
|
---|
3057 |
|
---|
3058 | $x->bone(); # +1
|
---|
3059 | $x->bone('-'); # -1
|
---|
3060 |
|
---|
3061 | =head2 is_one()/is_zero()/is_nan()/is_inf()
|
---|
3062 |
|
---|
3063 |
|
---|
3064 | $x->is_zero(); # true if arg is +0
|
---|
3065 | $x->is_nan(); # true if arg is NaN
|
---|
3066 | $x->is_one(); # true if arg is +1
|
---|
3067 | $x->is_one('-'); # true if arg is -1
|
---|
3068 | $x->is_inf(); # true if +inf
|
---|
3069 | $x->is_inf('-'); # true if -inf (sign is default '+')
|
---|
3070 |
|
---|
3071 | These methods all test the BigInt for beeing one specific value and return
|
---|
3072 | true or false depending on the input. These are faster than doing something
|
---|
3073 | like:
|
---|
3074 |
|
---|
3075 | if ($x == 0)
|
---|
3076 |
|
---|
3077 | =head2 is_pos()/is_neg()
|
---|
3078 |
|
---|
3079 | $x->is_pos(); # true if > 0
|
---|
3080 | $x->is_neg(); # true if < 0
|
---|
3081 |
|
---|
3082 | The methods return true if the argument is positive or negative, respectively.
|
---|
3083 | C<NaN> is neither positive nor negative, while C<+inf> counts as positive, and
|
---|
3084 | C<-inf> is negative. A C<zero> is neither positive nor negative.
|
---|
3085 |
|
---|
3086 | These methods are only testing the sign, and not the value.
|
---|
3087 |
|
---|
3088 | C<is_positive()> and C<is_negative()> are aliase to C<is_pos()> and
|
---|
3089 | C<is_neg()>, respectively. C<is_positive()> and C<is_negative()> were
|
---|
3090 | introduced in v1.36, while C<is_pos()> and C<is_neg()> were only introduced
|
---|
3091 | in v1.68.
|
---|
3092 |
|
---|
3093 | =head2 is_odd()/is_even()/is_int()
|
---|
3094 |
|
---|
3095 | $x->is_odd(); # true if odd, false for even
|
---|
3096 | $x->is_even(); # true if even, false for odd
|
---|
3097 | $x->is_int(); # true if $x is an integer
|
---|
3098 |
|
---|
3099 | The return true when the argument satisfies the condition. C<NaN>, C<+inf>,
|
---|
3100 | C<-inf> are not integers and are neither odd nor even.
|
---|
3101 |
|
---|
3102 | In BigInt, all numbers except C<NaN>, C<+inf> and C<-inf> are integers.
|
---|
3103 |
|
---|
3104 | =head2 bcmp
|
---|
3105 |
|
---|
3106 | $x->bcmp($y);
|
---|
3107 |
|
---|
3108 | Compares $x with $y and takes the sign into account.
|
---|
3109 | Returns -1, 0, 1 or undef.
|
---|
3110 |
|
---|
3111 | =head2 bacmp
|
---|
3112 |
|
---|
3113 | $x->bacmp($y);
|
---|
3114 |
|
---|
3115 | Compares $x with $y while ignoring their. Returns -1, 0, 1 or undef.
|
---|
3116 |
|
---|
3117 | =head2 sign
|
---|
3118 |
|
---|
3119 | $x->sign();
|
---|
3120 |
|
---|
3121 | Return the sign, of $x, meaning either C<+>, C<->, C<-inf>, C<+inf> or NaN.
|
---|
3122 |
|
---|
3123 | If you want $x to have a certain sign, use one of the following methods:
|
---|
3124 |
|
---|
3125 | $x->babs(); # '+'
|
---|
3126 | $x->babs()->bneg(); # '-'
|
---|
3127 | $x->bnan(); # 'NaN'
|
---|
3128 | $x->binf(); # '+inf'
|
---|
3129 | $x->binf('-'); # '-inf'
|
---|
3130 |
|
---|
3131 | =head2 digit
|
---|
3132 |
|
---|
3133 | $x->digit($n); # return the nth digit, counting from right
|
---|
3134 |
|
---|
3135 | If C<$n> is negative, returns the digit counting from left.
|
---|
3136 |
|
---|
3137 | =head2 bneg
|
---|
3138 |
|
---|
3139 | $x->bneg();
|
---|
3140 |
|
---|
3141 | Negate the number, e.g. change the sign between '+' and '-', or between '+inf'
|
---|
3142 | and '-inf', respectively. Does nothing for NaN or zero.
|
---|
3143 |
|
---|
3144 | =head2 babs
|
---|
3145 |
|
---|
3146 | $x->babs();
|
---|
3147 |
|
---|
3148 | Set the number to it's absolute value, e.g. change the sign from '-' to '+'
|
---|
3149 | and from '-inf' to '+inf', respectively. Does nothing for NaN or positive
|
---|
3150 | numbers.
|
---|
3151 |
|
---|
3152 | =head2 bnorm
|
---|
3153 |
|
---|
3154 | $x->bnorm(); # normalize (no-op)
|
---|
3155 |
|
---|
3156 | =head2 bnot
|
---|
3157 |
|
---|
3158 | $x->bnot();
|
---|
3159 |
|
---|
3160 | Two's complement (bit wise not). This is equivalent to
|
---|
3161 |
|
---|
3162 | $x->binc()->bneg();
|
---|
3163 |
|
---|
3164 | but faster.
|
---|
3165 |
|
---|
3166 | =head2 binc
|
---|
3167 |
|
---|
3168 | $x->binc(); # increment x by 1
|
---|
3169 |
|
---|
3170 | =head2 bdec
|
---|
3171 |
|
---|
3172 | $x->bdec(); # decrement x by 1
|
---|
3173 |
|
---|
3174 | =head2 badd
|
---|
3175 |
|
---|
3176 | $x->badd($y); # addition (add $y to $x)
|
---|
3177 |
|
---|
3178 | =head2 bsub
|
---|
3179 |
|
---|
3180 | $x->bsub($y); # subtraction (subtract $y from $x)
|
---|
3181 |
|
---|
3182 | =head2 bmul
|
---|
3183 |
|
---|
3184 | $x->bmul($y); # multiplication (multiply $x by $y)
|
---|
3185 |
|
---|
3186 | =head2 bdiv
|
---|
3187 |
|
---|
3188 | $x->bdiv($y); # divide, set $x to quotient
|
---|
3189 | # return (quo,rem) or quo if scalar
|
---|
3190 |
|
---|
3191 | =head2 bmod
|
---|
3192 |
|
---|
3193 | $x->bmod($y); # modulus (x % y)
|
---|
3194 |
|
---|
3195 | =head2 bmodinv
|
---|
3196 |
|
---|
3197 | num->bmodinv($mod); # modular inverse
|
---|
3198 |
|
---|
3199 | Returns the inverse of C<$num> in the given modulus C<$mod>. 'C<NaN>' is
|
---|
3200 | returned unless C<$num> is relatively prime to C<$mod>, i.e. unless
|
---|
3201 | C<bgcd($num, $mod)==1>.
|
---|
3202 |
|
---|
3203 | =head2 bmodpow
|
---|
3204 |
|
---|
3205 | $num->bmodpow($exp,$mod); # modular exponentation
|
---|
3206 | # ($num**$exp % $mod)
|
---|
3207 |
|
---|
3208 | Returns the value of C<$num> taken to the power C<$exp> in the modulus
|
---|
3209 | C<$mod> using binary exponentation. C<bmodpow> is far superior to
|
---|
3210 | writing
|
---|
3211 |
|
---|
3212 | $num ** $exp % $mod
|
---|
3213 |
|
---|
3214 | because it is much faster - it reduces internal variables into
|
---|
3215 | the modulus whenever possible, so it operates on smaller numbers.
|
---|
3216 |
|
---|
3217 | C<bmodpow> also supports negative exponents.
|
---|
3218 |
|
---|
3219 | bmodpow($num, -1, $mod)
|
---|
3220 |
|
---|
3221 | is exactly equivalent to
|
---|
3222 |
|
---|
3223 | bmodinv($num, $mod)
|
---|
3224 |
|
---|
3225 | =head2 bpow
|
---|
3226 |
|
---|
3227 | $x->bpow($y); # power of arguments (x ** y)
|
---|
3228 |
|
---|
3229 | =head2 blsft
|
---|
3230 |
|
---|
3231 | $x->blsft($y); # left shift
|
---|
3232 | $x->blsft($y,$n); # left shift, in base $n (like 10)
|
---|
3233 |
|
---|
3234 | =head2 brsft
|
---|
3235 |
|
---|
3236 | $x->brsft($y); # right shift
|
---|
3237 | $x->brsft($y,$n); # right shift, in base $n (like 10)
|
---|
3238 |
|
---|
3239 | =head2 band
|
---|
3240 |
|
---|
3241 | $x->band($y); # bitwise and
|
---|
3242 |
|
---|
3243 | =head2 bior
|
---|
3244 |
|
---|
3245 | $x->bior($y); # bitwise inclusive or
|
---|
3246 |
|
---|
3247 | =head2 bxor
|
---|
3248 |
|
---|
3249 | $x->bxor($y); # bitwise exclusive or
|
---|
3250 |
|
---|
3251 | =head2 bnot
|
---|
3252 |
|
---|
3253 | $x->bnot(); # bitwise not (two's complement)
|
---|
3254 |
|
---|
3255 | =head2 bsqrt
|
---|
3256 |
|
---|
3257 | $x->bsqrt(); # calculate square-root
|
---|
3258 |
|
---|
3259 | =head2 bfac
|
---|
3260 |
|
---|
3261 | $x->bfac(); # factorial of $x (1*2*3*4*..$x)
|
---|
3262 |
|
---|
3263 | =head2 round
|
---|
3264 |
|
---|
3265 | $x->round($A,$P,$round_mode);
|
---|
3266 |
|
---|
3267 | Round $x to accuracy C<$A> or precision C<$P> using the round mode
|
---|
3268 | C<$round_mode>.
|
---|
3269 |
|
---|
3270 | =head2 bround
|
---|
3271 |
|
---|
3272 | $x->bround($N); # accuracy: preserve $N digits
|
---|
3273 |
|
---|
3274 | =head2 bfround
|
---|
3275 |
|
---|
3276 | $x->bfround($N); # round to $Nth digit, no-op for BigInts
|
---|
3277 |
|
---|
3278 | =head2 bfloor
|
---|
3279 |
|
---|
3280 | $x->bfloor();
|
---|
3281 |
|
---|
3282 | Set $x to the integer less or equal than $x. This is a no-op in BigInt, but
|
---|
3283 | does change $x in BigFloat.
|
---|
3284 |
|
---|
3285 | =head2 bceil
|
---|
3286 |
|
---|
3287 | $x->bceil();
|
---|
3288 |
|
---|
3289 | Set $x to the integer greater or equal than $x. This is a no-op in BigInt, but
|
---|
3290 | does change $x in BigFloat.
|
---|
3291 |
|
---|
3292 | =head2 bgcd
|
---|
3293 |
|
---|
3294 | bgcd(@values); # greatest common divisor (no OO style)
|
---|
3295 |
|
---|
3296 | =head2 blcm
|
---|
3297 |
|
---|
3298 | blcm(@values); # lowest common multiplicator (no OO style)
|
---|
3299 |
|
---|
3300 | head2 length
|
---|
3301 |
|
---|
3302 | $x->length();
|
---|
3303 | ($xl,$fl) = $x->length();
|
---|
3304 |
|
---|
3305 | Returns the number of digits in the decimal representation of the number.
|
---|
3306 | In list context, returns the length of the integer and fraction part. For
|
---|
3307 | BigInt's, the length of the fraction part will always be 0.
|
---|
3308 |
|
---|
3309 | =head2 exponent
|
---|
3310 |
|
---|
3311 | $x->exponent();
|
---|
3312 |
|
---|
3313 | Return the exponent of $x as BigInt.
|
---|
3314 |
|
---|
3315 | =head2 mantissa
|
---|
3316 |
|
---|
3317 | $x->mantissa();
|
---|
3318 |
|
---|
3319 | Return the signed mantissa of $x as BigInt.
|
---|
3320 |
|
---|
3321 | =head2 parts
|
---|
3322 |
|
---|
3323 | $x->parts(); # return (mantissa,exponent) as BigInt
|
---|
3324 |
|
---|
3325 | =head2 copy
|
---|
3326 |
|
---|
3327 | $x->copy(); # make a true copy of $x (unlike $y = $x;)
|
---|
3328 |
|
---|
3329 | =head2 as_int
|
---|
3330 |
|
---|
3331 | $x->as_int();
|
---|
3332 |
|
---|
3333 | Returns $x as a BigInt (truncated towards zero). In BigInt this is the same as
|
---|
3334 | C<copy()>.
|
---|
3335 |
|
---|
3336 | C<as_number()> is an alias to this method. C<as_number> was introduced in
|
---|
3337 | v1.22, while C<as_int()> was only introduced in v1.68.
|
---|
3338 |
|
---|
3339 | =head2 bstr
|
---|
3340 |
|
---|
3341 | $x->bstr();
|
---|
3342 |
|
---|
3343 | Returns a normalized string represantation of C<$x>.
|
---|
3344 |
|
---|
3345 | =head2 bsstr
|
---|
3346 |
|
---|
3347 | $x->bsstr(); # normalized string in scientific notation
|
---|
3348 |
|
---|
3349 | =head2 as_hex
|
---|
3350 |
|
---|
3351 | $x->as_hex(); # as signed hexadecimal string with prefixed 0x
|
---|
3352 |
|
---|
3353 | =head2 as_bin
|
---|
3354 |
|
---|
3355 | $x->as_bin(); # as signed binary string with prefixed 0b
|
---|
3356 |
|
---|
3357 | =head1 ACCURACY and PRECISION
|
---|
3358 |
|
---|
3359 | Since version v1.33, Math::BigInt and Math::BigFloat have full support for
|
---|
3360 | accuracy and precision based rounding, both automatically after every
|
---|
3361 | operation, as well as manually.
|
---|
3362 |
|
---|
3363 | This section describes the accuracy/precision handling in Math::Big* as it
|
---|
3364 | used to be and as it is now, complete with an explanation of all terms and
|
---|
3365 | abbreviations.
|
---|
3366 |
|
---|
3367 | Not yet implemented things (but with correct description) are marked with '!',
|
---|
3368 | things that need to be answered are marked with '?'.
|
---|
3369 |
|
---|
3370 | In the next paragraph follows a short description of terms used here (because
|
---|
3371 | these may differ from terms used by others people or documentation).
|
---|
3372 |
|
---|
3373 | During the rest of this document, the shortcuts A (for accuracy), P (for
|
---|
3374 | precision), F (fallback) and R (rounding mode) will be used.
|
---|
3375 |
|
---|
3376 | =head2 Precision P
|
---|
3377 |
|
---|
3378 | A fixed number of digits before (positive) or after (negative)
|
---|
3379 | the decimal point. For example, 123.45 has a precision of -2. 0 means an
|
---|
3380 | integer like 123 (or 120). A precision of 2 means two digits to the left
|
---|
3381 | of the decimal point are zero, so 123 with P = 1 becomes 120. Note that
|
---|
3382 | numbers with zeros before the decimal point may have different precisions,
|
---|
3383 | because 1200 can have p = 0, 1 or 2 (depending on what the inital value
|
---|
3384 | was). It could also have p < 0, when the digits after the decimal point
|
---|
3385 | are zero.
|
---|
3386 |
|
---|
3387 | The string output (of floating point numbers) will be padded with zeros:
|
---|
3388 |
|
---|
3389 | Initial value P A Result String
|
---|
3390 | ------------------------------------------------------------
|
---|
3391 | 1234.01 -3 1000 1000
|
---|
3392 | 1234 -2 1200 1200
|
---|
3393 | 1234.5 -1 1230 1230
|
---|
3394 | 1234.001 1 1234 1234.0
|
---|
3395 | 1234.01 0 1234 1234
|
---|
3396 | 1234.01 2 1234.01 1234.01
|
---|
3397 | 1234.01 5 1234.01 1234.01000
|
---|
3398 |
|
---|
3399 | For BigInts, no padding occurs.
|
---|
3400 |
|
---|
3401 | =head2 Accuracy A
|
---|
3402 |
|
---|
3403 | Number of significant digits. Leading zeros are not counted. A
|
---|
3404 | number may have an accuracy greater than the non-zero digits
|
---|
3405 | when there are zeros in it or trailing zeros. For example, 123.456 has
|
---|
3406 | A of 6, 10203 has 5, 123.0506 has 7, 123.450000 has 8 and 0.000123 has 3.
|
---|
3407 |
|
---|
3408 | The string output (of floating point numbers) will be padded with zeros:
|
---|
3409 |
|
---|
3410 | Initial value P A Result String
|
---|
3411 | ------------------------------------------------------------
|
---|
3412 | 1234.01 3 1230 1230
|
---|
3413 | 1234.01 6 1234.01 1234.01
|
---|
3414 | 1234.1 8 1234.1 1234.1000
|
---|
3415 |
|
---|
3416 | For BigInts, no padding occurs.
|
---|
3417 |
|
---|
3418 | =head2 Fallback F
|
---|
3419 |
|
---|
3420 | When both A and P are undefined, this is used as a fallback accuracy when
|
---|
3421 | dividing numbers.
|
---|
3422 |
|
---|
3423 | =head2 Rounding mode R
|
---|
3424 |
|
---|
3425 | When rounding a number, different 'styles' or 'kinds'
|
---|
3426 | of rounding are possible. (Note that random rounding, as in
|
---|
3427 | Math::Round, is not implemented.)
|
---|
3428 |
|
---|
3429 | =over 2
|
---|
3430 |
|
---|
3431 | =item 'trunc'
|
---|
3432 |
|
---|
3433 | truncation invariably removes all digits following the
|
---|
3434 | rounding place, replacing them with zeros. Thus, 987.65 rounded
|
---|
3435 | to tens (P=1) becomes 980, and rounded to the fourth sigdig
|
---|
3436 | becomes 987.6 (A=4). 123.456 rounded to the second place after the
|
---|
3437 | decimal point (P=-2) becomes 123.46.
|
---|
3438 |
|
---|
3439 | All other implemented styles of rounding attempt to round to the
|
---|
3440 | "nearest digit." If the digit D immediately to the right of the
|
---|
3441 | rounding place (skipping the decimal point) is greater than 5, the
|
---|
3442 | number is incremented at the rounding place (possibly causing a
|
---|
3443 | cascade of incrementation): e.g. when rounding to units, 0.9 rounds
|
---|
3444 | to 1, and -19.9 rounds to -20. If D < 5, the number is similarly
|
---|
3445 | truncated at the rounding place: e.g. when rounding to units, 0.4
|
---|
3446 | rounds to 0, and -19.4 rounds to -19.
|
---|
3447 |
|
---|
3448 | However the results of other styles of rounding differ if the
|
---|
3449 | digit immediately to the right of the rounding place (skipping the
|
---|
3450 | decimal point) is 5 and if there are no digits, or no digits other
|
---|
3451 | than 0, after that 5. In such cases:
|
---|
3452 |
|
---|
3453 | =item 'even'
|
---|
3454 |
|
---|
3455 | rounds the digit at the rounding place to 0, 2, 4, 6, or 8
|
---|
3456 | if it is not already. E.g., when rounding to the first sigdig, 0.45
|
---|
3457 | becomes 0.4, -0.55 becomes -0.6, but 0.4501 becomes 0.5.
|
---|
3458 |
|
---|
3459 | =item 'odd'
|
---|
3460 |
|
---|
3461 | rounds the digit at the rounding place to 1, 3, 5, 7, or 9 if
|
---|
3462 | it is not already. E.g., when rounding to the first sigdig, 0.45
|
---|
3463 | becomes 0.5, -0.55 becomes -0.5, but 0.5501 becomes 0.6.
|
---|
3464 |
|
---|
3465 | =item '+inf'
|
---|
3466 |
|
---|
3467 | round to plus infinity, i.e. always round up. E.g., when
|
---|
3468 | rounding to the first sigdig, 0.45 becomes 0.5, -0.55 becomes -0.5,
|
---|
3469 | and 0.4501 also becomes 0.5.
|
---|
3470 |
|
---|
3471 | =item '-inf'
|
---|
3472 |
|
---|
3473 | round to minus infinity, i.e. always round down. E.g., when
|
---|
3474 | rounding to the first sigdig, 0.45 becomes 0.4, -0.55 becomes -0.6,
|
---|
3475 | but 0.4501 becomes 0.5.
|
---|
3476 |
|
---|
3477 | =item 'zero'
|
---|
3478 |
|
---|
3479 | round to zero, i.e. positive numbers down, negative ones up.
|
---|
3480 | E.g., when rounding to the first sigdig, 0.45 becomes 0.4, -0.55
|
---|
3481 | becomes -0.5, but 0.4501 becomes 0.5.
|
---|
3482 |
|
---|
3483 | =back
|
---|
3484 |
|
---|
3485 | The handling of A & P in MBI/MBF (the old core code shipped with Perl
|
---|
3486 | versions <= 5.7.2) is like this:
|
---|
3487 |
|
---|
3488 | =over 2
|
---|
3489 |
|
---|
3490 | =item Precision
|
---|
3491 |
|
---|
3492 | * ffround($p) is able to round to $p number of digits after the decimal
|
---|
3493 | point
|
---|
3494 | * otherwise P is unused
|
---|
3495 |
|
---|
3496 | =item Accuracy (significant digits)
|
---|
3497 |
|
---|
3498 | * fround($a) rounds to $a significant digits
|
---|
3499 | * only fdiv() and fsqrt() take A as (optional) paramater
|
---|
3500 | + other operations simply create the same number (fneg etc), or more (fmul)
|
---|
3501 | of digits
|
---|
3502 | + rounding/truncating is only done when explicitly calling one of fround
|
---|
3503 | or ffround, and never for BigInt (not implemented)
|
---|
3504 | * fsqrt() simply hands its accuracy argument over to fdiv.
|
---|
3505 | * the documentation and the comment in the code indicate two different ways
|
---|
3506 | on how fdiv() determines the maximum number of digits it should calculate,
|
---|
3507 | and the actual code does yet another thing
|
---|
3508 | POD:
|
---|
3509 | max($Math::BigFloat::div_scale,length(dividend)+length(divisor))
|
---|
3510 | Comment:
|
---|
3511 | result has at most max(scale, length(dividend), length(divisor)) digits
|
---|
3512 | Actual code:
|
---|
3513 | scale = max(scale, length(dividend)-1,length(divisor)-1);
|
---|
3514 | scale += length(divisior) - length(dividend);
|
---|
3515 | So for lx = 3, ly = 9, scale = 10, scale will actually be 16 (10+9-3).
|
---|
3516 | Actually, the 'difference' added to the scale is calculated from the
|
---|
3517 | number of "significant digits" in dividend and divisor, which is derived
|
---|
3518 | by looking at the length of the mantissa. Which is wrong, since it includes
|
---|
3519 | the + sign (oops) and actually gets 2 for '+100' and 4 for '+101'. Oops
|
---|
3520 | again. Thus 124/3 with div_scale=1 will get you '41.3' based on the strange
|
---|
3521 | assumption that 124 has 3 significant digits, while 120/7 will get you
|
---|
3522 | '17', not '17.1' since 120 is thought to have 2 significant digits.
|
---|
3523 | The rounding after the division then uses the remainder and $y to determine
|
---|
3524 | wether it must round up or down.
|
---|
3525 | ? I have no idea which is the right way. That's why I used a slightly more
|
---|
3526 | ? simple scheme and tweaked the few failing testcases to match it.
|
---|
3527 |
|
---|
3528 | =back
|
---|
3529 |
|
---|
3530 | This is how it works now:
|
---|
3531 |
|
---|
3532 | =over 2
|
---|
3533 |
|
---|
3534 | =item Setting/Accessing
|
---|
3535 |
|
---|
3536 | * You can set the A global via C<< Math::BigInt->accuracy() >> or
|
---|
3537 | C<< Math::BigFloat->accuracy() >> or whatever class you are using.
|
---|
3538 | * You can also set P globally by using C<< Math::SomeClass->precision() >>
|
---|
3539 | likewise.
|
---|
3540 | * Globals are classwide, and not inherited by subclasses.
|
---|
3541 | * to undefine A, use C<< Math::SomeCLass->accuracy(undef); >>
|
---|
3542 | * to undefine P, use C<< Math::SomeClass->precision(undef); >>
|
---|
3543 | * Setting C<< Math::SomeClass->accuracy() >> clears automatically
|
---|
3544 | C<< Math::SomeClass->precision() >>, and vice versa.
|
---|
3545 | * To be valid, A must be > 0, P can have any value.
|
---|
3546 | * If P is negative, this means round to the P'th place to the right of the
|
---|
3547 | decimal point; positive values mean to the left of the decimal point.
|
---|
3548 | P of 0 means round to integer.
|
---|
3549 | * to find out the current global A, use C<< Math::SomeClass->accuracy() >>
|
---|
3550 | * to find out the current global P, use C<< Math::SomeClass->precision() >>
|
---|
3551 | * use C<< $x->accuracy() >> respective C<< $x->precision() >> for the local
|
---|
3552 | setting of C<< $x >>.
|
---|
3553 | * Please note that C<< $x->accuracy() >> respecive C<< $x->precision() >>
|
---|
3554 | return eventually defined global A or P, when C<< $x >>'s A or P is not
|
---|
3555 | set.
|
---|
3556 |
|
---|
3557 | =item Creating numbers
|
---|
3558 |
|
---|
3559 | * When you create a number, you can give it's desired A or P via:
|
---|
3560 | $x = Math::BigInt->new($number,$A,$P);
|
---|
3561 | * Only one of A or P can be defined, otherwise the result is NaN
|
---|
3562 | * If no A or P is give ($x = Math::BigInt->new($number) form), then the
|
---|
3563 | globals (if set) will be used. Thus changing the global defaults later on
|
---|
3564 | will not change the A or P of previously created numbers (i.e., A and P of
|
---|
3565 | $x will be what was in effect when $x was created)
|
---|
3566 | * If given undef for A and P, B<no> rounding will occur, and the globals will
|
---|
3567 | B<not> be used. This is used by subclasses to create numbers without
|
---|
3568 | suffering rounding in the parent. Thus a subclass is able to have it's own
|
---|
3569 | globals enforced upon creation of a number by using
|
---|
3570 | C<< $x = Math::BigInt->new($number,undef,undef) >>:
|
---|
3571 |
|
---|
3572 | use Math::BigInt::SomeSubclass;
|
---|
3573 | use Math::BigInt;
|
---|
3574 |
|
---|
3575 | Math::BigInt->accuracy(2);
|
---|
3576 | Math::BigInt::SomeSubClass->accuracy(3);
|
---|
3577 | $x = Math::BigInt::SomeSubClass->new(1234);
|
---|
3578 |
|
---|
3579 | $x is now 1230, and not 1200. A subclass might choose to implement
|
---|
3580 | this otherwise, e.g. falling back to the parent's A and P.
|
---|
3581 |
|
---|
3582 | =item Usage
|
---|
3583 |
|
---|
3584 | * If A or P are enabled/defined, they are used to round the result of each
|
---|
3585 | operation according to the rules below
|
---|
3586 | * Negative P is ignored in Math::BigInt, since BigInts never have digits
|
---|
3587 | after the decimal point
|
---|
3588 | * Math::BigFloat uses Math::BigInt internally, but setting A or P inside
|
---|
3589 | Math::BigInt as globals does not tamper with the parts of a BigFloat.
|
---|
3590 | A flag is used to mark all Math::BigFloat numbers as 'never round'.
|
---|
3591 |
|
---|
3592 | =item Precedence
|
---|
3593 |
|
---|
3594 | * It only makes sense that a number has only one of A or P at a time.
|
---|
3595 | If you set either A or P on one object, or globally, the other one will
|
---|
3596 | be automatically cleared.
|
---|
3597 | * If two objects are involved in an operation, and one of them has A in
|
---|
3598 | effect, and the other P, this results in an error (NaN).
|
---|
3599 | * A takes precendence over P (Hint: A comes before P).
|
---|
3600 | If neither of them is defined, nothing is used, i.e. the result will have
|
---|
3601 | as many digits as it can (with an exception for fdiv/fsqrt) and will not
|
---|
3602 | be rounded.
|
---|
3603 | * There is another setting for fdiv() (and thus for fsqrt()). If neither of
|
---|
3604 | A or P is defined, fdiv() will use a fallback (F) of $div_scale digits.
|
---|
3605 | If either the dividend's or the divisor's mantissa has more digits than
|
---|
3606 | the value of F, the higher value will be used instead of F.
|
---|
3607 | This is to limit the digits (A) of the result (just consider what would
|
---|
3608 | happen with unlimited A and P in the case of 1/3 :-)
|
---|
3609 | * fdiv will calculate (at least) 4 more digits than required (determined by
|
---|
3610 | A, P or F), and, if F is not used, round the result
|
---|
3611 | (this will still fail in the case of a result like 0.12345000000001 with A
|
---|
3612 | or P of 5, but this can not be helped - or can it?)
|
---|
3613 | * Thus you can have the math done by on Math::Big* class in two modi:
|
---|
3614 | + never round (this is the default):
|
---|
3615 | This is done by setting A and P to undef. No math operation
|
---|
3616 | will round the result, with fdiv() and fsqrt() as exceptions to guard
|
---|
3617 | against overflows. You must explicitely call bround(), bfround() or
|
---|
3618 | round() (the latter with parameters).
|
---|
3619 | Note: Once you have rounded a number, the settings will 'stick' on it
|
---|
3620 | and 'infect' all other numbers engaged in math operations with it, since
|
---|
3621 | local settings have the highest precedence. So, to get SaferRound[tm],
|
---|
3622 | use a copy() before rounding like this:
|
---|
3623 |
|
---|
3624 | $x = Math::BigFloat->new(12.34);
|
---|
3625 | $y = Math::BigFloat->new(98.76);
|
---|
3626 | $z = $x * $y; # 1218.6984
|
---|
3627 | print $x->copy()->fround(3); # 12.3 (but A is now 3!)
|
---|
3628 | $z = $x * $y; # still 1218.6984, without
|
---|
3629 | # copy would have been 1210!
|
---|
3630 |
|
---|
3631 | + round after each op:
|
---|
3632 | After each single operation (except for testing like is_zero()), the
|
---|
3633 | method round() is called and the result is rounded appropriately. By
|
---|
3634 | setting proper values for A and P, you can have all-the-same-A or
|
---|
3635 | all-the-same-P modes. For example, Math::Currency might set A to undef,
|
---|
3636 | and P to -2, globally.
|
---|
3637 |
|
---|
3638 | ?Maybe an extra option that forbids local A & P settings would be in order,
|
---|
3639 | ?so that intermediate rounding does not 'poison' further math?
|
---|
3640 |
|
---|
3641 | =item Overriding globals
|
---|
3642 |
|
---|
3643 | * you will be able to give A, P and R as an argument to all the calculation
|
---|
3644 | routines; the second parameter is A, the third one is P, and the fourth is
|
---|
3645 | R (shift right by one for binary operations like badd). P is used only if
|
---|
3646 | the first parameter (A) is undefined. These three parameters override the
|
---|
3647 | globals in the order detailed as follows, i.e. the first defined value
|
---|
3648 | wins:
|
---|
3649 | (local: per object, global: global default, parameter: argument to sub)
|
---|
3650 | + parameter A
|
---|
3651 | + parameter P
|
---|
3652 | + local A (if defined on both of the operands: smaller one is taken)
|
---|
3653 | + local P (if defined on both of the operands: bigger one is taken)
|
---|
3654 | + global A
|
---|
3655 | + global P
|
---|
3656 | + global F
|
---|
3657 | * fsqrt() will hand its arguments to fdiv(), as it used to, only now for two
|
---|
3658 | arguments (A and P) instead of one
|
---|
3659 |
|
---|
3660 | =item Local settings
|
---|
3661 |
|
---|
3662 | * You can set A or P locally by using C<< $x->accuracy() >> or
|
---|
3663 | C<< $x->precision() >>
|
---|
3664 | and thus force different A and P for different objects/numbers.
|
---|
3665 | * Setting A or P this way immediately rounds $x to the new value.
|
---|
3666 | * C<< $x->accuracy() >> clears C<< $x->precision() >>, and vice versa.
|
---|
3667 |
|
---|
3668 | =item Rounding
|
---|
3669 |
|
---|
3670 | * the rounding routines will use the respective global or local settings.
|
---|
3671 | fround()/bround() is for accuracy rounding, while ffround()/bfround()
|
---|
3672 | is for precision
|
---|
3673 | * the two rounding functions take as the second parameter one of the
|
---|
3674 | following rounding modes (R):
|
---|
3675 | 'even', 'odd', '+inf', '-inf', 'zero', 'trunc'
|
---|
3676 | * you can set/get the global R by using C<< Math::SomeClass->round_mode() >>
|
---|
3677 | or by setting C<< $Math::SomeClass::round_mode >>
|
---|
3678 | * after each operation, C<< $result->round() >> is called, and the result may
|
---|
3679 | eventually be rounded (that is, if A or P were set either locally,
|
---|
3680 | globally or as parameter to the operation)
|
---|
3681 | * to manually round a number, call C<< $x->round($A,$P,$round_mode); >>
|
---|
3682 | this will round the number by using the appropriate rounding function
|
---|
3683 | and then normalize it.
|
---|
3684 | * rounding modifies the local settings of the number:
|
---|
3685 |
|
---|
3686 | $x = Math::BigFloat->new(123.456);
|
---|
3687 | $x->accuracy(5);
|
---|
3688 | $x->bround(4);
|
---|
3689 |
|
---|
3690 | Here 4 takes precedence over 5, so 123.5 is the result and $x->accuracy()
|
---|
3691 | will be 4 from now on.
|
---|
3692 |
|
---|
3693 | =item Default values
|
---|
3694 |
|
---|
3695 | * R: 'even'
|
---|
3696 | * F: 40
|
---|
3697 | * A: undef
|
---|
3698 | * P: undef
|
---|
3699 |
|
---|
3700 | =item Remarks
|
---|
3701 |
|
---|
3702 | * The defaults are set up so that the new code gives the same results as
|
---|
3703 | the old code (except in a few cases on fdiv):
|
---|
3704 | + Both A and P are undefined and thus will not be used for rounding
|
---|
3705 | after each operation.
|
---|
3706 | + round() is thus a no-op, unless given extra parameters A and P
|
---|
3707 |
|
---|
3708 | =back
|
---|
3709 |
|
---|
3710 | =head1 Infinity and Not a Number
|
---|
3711 |
|
---|
3712 | While BigInt has extensive handling of inf and NaN, certain quirks remain.
|
---|
3713 |
|
---|
3714 | =over 2
|
---|
3715 |
|
---|
3716 | =item oct()/hex()
|
---|
3717 |
|
---|
3718 | These perl routines currently (as of Perl v.5.8.6) cannot handle passed
|
---|
3719 | inf.
|
---|
3720 |
|
---|
3721 | te@linux:~> perl -wle 'print 2 ** 3333'
|
---|
3722 | inf
|
---|
3723 | te@linux:~> perl -wle 'print 2 ** 3333 == 2 ** 3333'
|
---|
3724 | 1
|
---|
3725 | te@linux:~> perl -wle 'print oct(2 ** 3333)'
|
---|
3726 | 0
|
---|
3727 | te@linux:~> perl -wle 'print hex(2 ** 3333)'
|
---|
3728 | Illegal hexadecimal digit 'i' ignored at -e line 1.
|
---|
3729 | 0
|
---|
3730 |
|
---|
3731 | The same problems occur if you pass them Math::BigInt->binf() objects. Since
|
---|
3732 | overloading these routines is not possible, this cannot be fixed from BigInt.
|
---|
3733 |
|
---|
3734 | =item ==, !=, <, >, <=, >= with NaNs
|
---|
3735 |
|
---|
3736 | BigInt's bcmp() routine currently returns undef to signal that a NaN was
|
---|
3737 | involved in a comparisation. However, the overload code turns that into
|
---|
3738 | either 1 or '' and thus operations like C<< NaN != NaN >> might return
|
---|
3739 | wrong values.
|
---|
3740 |
|
---|
3741 | =item log(-inf)
|
---|
3742 |
|
---|
3743 | C<< log(-inf) >> is highly weird. Since log(-x)=pi*i+log(x), then
|
---|
3744 | log(-inf)=pi*i+inf. However, since the imaginary part is finite, the real
|
---|
3745 | infinity "overshadows" it, so the number might as well just be infinity.
|
---|
3746 | However, the result is a complex number, and since BigInt/BigFloat can only
|
---|
3747 | have real numbers as results, the result is NaN.
|
---|
3748 |
|
---|
3749 | =item exp(), cos(), sin(), atan2()
|
---|
3750 |
|
---|
3751 | These all might have problems handling infinity right.
|
---|
3752 |
|
---|
3753 | =back
|
---|
3754 |
|
---|
3755 | =head1 INTERNALS
|
---|
3756 |
|
---|
3757 | The actual numbers are stored as unsigned big integers (with seperate sign).
|
---|
3758 |
|
---|
3759 | You should neither care about nor depend on the internal representation; it
|
---|
3760 | might change without notice. Use B<ONLY> method calls like C<< $x->sign(); >>
|
---|
3761 | instead relying on the internal representation.
|
---|
3762 |
|
---|
3763 | =head2 MATH LIBRARY
|
---|
3764 |
|
---|
3765 | Math with the numbers is done (by default) by a module called
|
---|
3766 | C<Math::BigInt::Calc>. This is equivalent to saying:
|
---|
3767 |
|
---|
3768 | use Math::BigInt lib => 'Calc';
|
---|
3769 |
|
---|
3770 | You can change this by using:
|
---|
3771 |
|
---|
3772 | use Math::BigInt lib => 'BitVect';
|
---|
3773 |
|
---|
3774 | The following would first try to find Math::BigInt::Foo, then
|
---|
3775 | Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc:
|
---|
3776 |
|
---|
3777 | use Math::BigInt lib => 'Foo,Math::BigInt::Bar';
|
---|
3778 |
|
---|
3779 | Since Math::BigInt::GMP is in almost all cases faster than Calc (especially in
|
---|
3780 | math involving really big numbers, where it is B<much> faster), and there is
|
---|
3781 | no penalty if Math::BigInt::GMP is not installed, it is a good idea to always
|
---|
3782 | use the following:
|
---|
3783 |
|
---|
3784 | use Math::BigInt lib => 'GMP';
|
---|
3785 |
|
---|
3786 | Different low-level libraries use different formats to store the
|
---|
3787 | numbers. You should B<NOT> depend on the number having a specific format
|
---|
3788 | internally.
|
---|
3789 |
|
---|
3790 | See the respective math library module documentation for further details.
|
---|
3791 |
|
---|
3792 | =head2 SIGN
|
---|
3793 |
|
---|
3794 | The sign is either '+', '-', 'NaN', '+inf' or '-inf'.
|
---|
3795 |
|
---|
3796 | A sign of 'NaN' is used to represent the result when input arguments are not
|
---|
3797 | numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively
|
---|
3798 | minus infinity. You will get '+inf' when dividing a positive number by 0, and
|
---|
3799 | '-inf' when dividing any negative number by 0.
|
---|
3800 |
|
---|
3801 | =head2 mantissa(), exponent() and parts()
|
---|
3802 |
|
---|
3803 | C<mantissa()> and C<exponent()> return the said parts of the BigInt such
|
---|
3804 | that:
|
---|
3805 |
|
---|
3806 | $m = $x->mantissa();
|
---|
3807 | $e = $x->exponent();
|
---|
3808 | $y = $m * ( 10 ** $e );
|
---|
3809 | print "ok\n" if $x == $y;
|
---|
3810 |
|
---|
3811 | C<< ($m,$e) = $x->parts() >> is just a shortcut that gives you both of them
|
---|
3812 | in one go. Both the returned mantissa and exponent have a sign.
|
---|
3813 |
|
---|
3814 | Currently, for BigInts C<$e> is always 0, except for NaN, +inf and -inf,
|
---|
3815 | where it is C<NaN>; and for C<$x == 0>, where it is C<1> (to be compatible
|
---|
3816 | with Math::BigFloat's internal representation of a zero as C<0E1>).
|
---|
3817 |
|
---|
3818 | C<$m> is currently just a copy of the original number. The relation between
|
---|
3819 | C<$e> and C<$m> will stay always the same, though their real values might
|
---|
3820 | change.
|
---|
3821 |
|
---|
3822 | =head1 EXAMPLES
|
---|
3823 |
|
---|
3824 | use Math::BigInt;
|
---|
3825 |
|
---|
3826 | sub bint { Math::BigInt->new(shift); }
|
---|
3827 |
|
---|
3828 | $x = Math::BigInt->bstr("1234") # string "1234"
|
---|
3829 | $x = "$x"; # same as bstr()
|
---|
3830 | $x = Math::BigInt->bneg("1234"); # BigInt "-1234"
|
---|
3831 | $x = Math::BigInt->babs("-12345"); # BigInt "12345"
|
---|
3832 | $x = Math::BigInt->bnorm("-0 00"); # BigInt "0"
|
---|
3833 | $x = bint(1) + bint(2); # BigInt "3"
|
---|
3834 | $x = bint(1) + "2"; # ditto (auto-BigIntify of "2")
|
---|
3835 | $x = bint(1); # BigInt "1"
|
---|
3836 | $x = $x + 5 / 2; # BigInt "3"
|
---|
3837 | $x = $x ** 3; # BigInt "27"
|
---|
3838 | $x *= 2; # BigInt "54"
|
---|
3839 | $x = Math::BigInt->new(0); # BigInt "0"
|
---|
3840 | $x--; # BigInt "-1"
|
---|
3841 | $x = Math::BigInt->badd(4,5) # BigInt "9"
|
---|
3842 | print $x->bsstr(); # 9e+0
|
---|
3843 |
|
---|
3844 | Examples for rounding:
|
---|
3845 |
|
---|
3846 | use Math::BigFloat;
|
---|
3847 | use Test;
|
---|
3848 |
|
---|
3849 | $x = Math::BigFloat->new(123.4567);
|
---|
3850 | $y = Math::BigFloat->new(123.456789);
|
---|
3851 | Math::BigFloat->accuracy(4); # no more A than 4
|
---|
3852 |
|
---|
3853 | ok ($x->copy()->fround(),123.4); # even rounding
|
---|
3854 | print $x->copy()->fround(),"\n"; # 123.4
|
---|
3855 | Math::BigFloat->round_mode('odd'); # round to odd
|
---|
3856 | print $x->copy()->fround(),"\n"; # 123.5
|
---|
3857 | Math::BigFloat->accuracy(5); # no more A than 5
|
---|
3858 | Math::BigFloat->round_mode('odd'); # round to odd
|
---|
3859 | print $x->copy()->fround(),"\n"; # 123.46
|
---|
3860 | $y = $x->copy()->fround(4),"\n"; # A = 4: 123.4
|
---|
3861 | print "$y, ",$y->accuracy(),"\n"; # 123.4, 4
|
---|
3862 |
|
---|
3863 | Math::BigFloat->accuracy(undef); # A not important now
|
---|
3864 | Math::BigFloat->precision(2); # P important
|
---|
3865 | print $x->copy()->bnorm(),"\n"; # 123.46
|
---|
3866 | print $x->copy()->fround(),"\n"; # 123.46
|
---|
3867 |
|
---|
3868 | Examples for converting:
|
---|
3869 |
|
---|
3870 | my $x = Math::BigInt->new('0b1'.'01' x 123);
|
---|
3871 | print "bin: ",$x->as_bin()," hex:",$x->as_hex()," dec: ",$x,"\n";
|
---|
3872 |
|
---|
3873 | =head1 Autocreating constants
|
---|
3874 |
|
---|
3875 | After C<use Math::BigInt ':constant'> all the B<integer> decimal, hexadecimal
|
---|
3876 | and binary constants in the given scope are converted to C<Math::BigInt>.
|
---|
3877 | This conversion happens at compile time.
|
---|
3878 |
|
---|
3879 | In particular,
|
---|
3880 |
|
---|
3881 | perl -MMath::BigInt=:constant -e 'print 2**100,"\n"'
|
---|
3882 |
|
---|
3883 | prints the integer value of C<2**100>. Note that without conversion of
|
---|
3884 | constants the expression 2**100 will be calculated as perl scalar.
|
---|
3885 |
|
---|
3886 | Please note that strings and floating point constants are not affected,
|
---|
3887 | so that
|
---|
3888 |
|
---|
3889 | use Math::BigInt qw/:constant/;
|
---|
3890 |
|
---|
3891 | $x = 1234567890123456789012345678901234567890
|
---|
3892 | + 123456789123456789;
|
---|
3893 | $y = '1234567890123456789012345678901234567890'
|
---|
3894 | + '123456789123456789';
|
---|
3895 |
|
---|
3896 | do not work. You need an explicit Math::BigInt->new() around one of the
|
---|
3897 | operands. You should also quote large constants to protect loss of precision:
|
---|
3898 |
|
---|
3899 | use Math::BigInt;
|
---|
3900 |
|
---|
3901 | $x = Math::BigInt->new('1234567889123456789123456789123456789');
|
---|
3902 |
|
---|
3903 | Without the quotes Perl would convert the large number to a floating point
|
---|
3904 | constant at compile time and then hand the result to BigInt, which results in
|
---|
3905 | an truncated result or a NaN.
|
---|
3906 |
|
---|
3907 | This also applies to integers that look like floating point constants:
|
---|
3908 |
|
---|
3909 | use Math::BigInt ':constant';
|
---|
3910 |
|
---|
3911 | print ref(123e2),"\n";
|
---|
3912 | print ref(123.2e2),"\n";
|
---|
3913 |
|
---|
3914 | will print nothing but newlines. Use either L<bignum> or L<Math::BigFloat>
|
---|
3915 | to get this to work.
|
---|
3916 |
|
---|
3917 | =head1 PERFORMANCE
|
---|
3918 |
|
---|
3919 | Using the form $x += $y; etc over $x = $x + $y is faster, since a copy of $x
|
---|
3920 | must be made in the second case. For long numbers, the copy can eat up to 20%
|
---|
3921 | of the work (in the case of addition/subtraction, less for
|
---|
3922 | multiplication/division). If $y is very small compared to $x, the form
|
---|
3923 | $x += $y is MUCH faster than $x = $x + $y since making the copy of $x takes
|
---|
3924 | more time then the actual addition.
|
---|
3925 |
|
---|
3926 | With a technique called copy-on-write, the cost of copying with overload could
|
---|
3927 | be minimized or even completely avoided. A test implementation of COW did show
|
---|
3928 | performance gains for overloaded math, but introduced a performance loss due
|
---|
3929 | to a constant overhead for all other operatons. So Math::BigInt does currently
|
---|
3930 | not COW.
|
---|
3931 |
|
---|
3932 | The rewritten version of this module (vs. v0.01) is slower on certain
|
---|
3933 | operations, like C<new()>, C<bstr()> and C<numify()>. The reason are that it
|
---|
3934 | does now more work and handles much more cases. The time spent in these
|
---|
3935 | operations is usually gained in the other math operations so that code on
|
---|
3936 | the average should get (much) faster. If they don't, please contact the author.
|
---|
3937 |
|
---|
3938 | Some operations may be slower for small numbers, but are significantly faster
|
---|
3939 | for big numbers. Other operations are now constant (O(1), like C<bneg()>,
|
---|
3940 | C<babs()> etc), instead of O(N) and thus nearly always take much less time.
|
---|
3941 | These optimizations were done on purpose.
|
---|
3942 |
|
---|
3943 | If you find the Calc module to slow, try to install any of the replacement
|
---|
3944 | modules and see if they help you.
|
---|
3945 |
|
---|
3946 | =head2 Alternative math libraries
|
---|
3947 |
|
---|
3948 | You can use an alternative library to drive Math::BigInt via:
|
---|
3949 |
|
---|
3950 | use Math::BigInt lib => 'Module';
|
---|
3951 |
|
---|
3952 | See L<MATH LIBRARY> for more information.
|
---|
3953 |
|
---|
3954 | For more benchmark results see L<http://bloodgate.com/perl/benchmarks.html>.
|
---|
3955 |
|
---|
3956 | =head2 SUBCLASSING
|
---|
3957 |
|
---|
3958 | =head1 Subclassing Math::BigInt
|
---|
3959 |
|
---|
3960 | The basic design of Math::BigInt allows simple subclasses with very little
|
---|
3961 | work, as long as a few simple rules are followed:
|
---|
3962 |
|
---|
3963 | =over 2
|
---|
3964 |
|
---|
3965 | =item *
|
---|
3966 |
|
---|
3967 | The public API must remain consistent, i.e. if a sub-class is overloading
|
---|
3968 | addition, the sub-class must use the same name, in this case badd(). The
|
---|
3969 | reason for this is that Math::BigInt is optimized to call the object methods
|
---|
3970 | directly.
|
---|
3971 |
|
---|
3972 | =item *
|
---|
3973 |
|
---|
3974 | The private object hash keys like C<$x->{sign}> may not be changed, but
|
---|
3975 | additional keys can be added, like C<$x->{_custom}>.
|
---|
3976 |
|
---|
3977 | =item *
|
---|
3978 |
|
---|
3979 | Accessor functions are available for all existing object hash keys and should
|
---|
3980 | be used instead of directly accessing the internal hash keys. The reason for
|
---|
3981 | this is that Math::BigInt itself has a pluggable interface which permits it
|
---|
3982 | to support different storage methods.
|
---|
3983 |
|
---|
3984 | =back
|
---|
3985 |
|
---|
3986 | More complex sub-classes may have to replicate more of the logic internal of
|
---|
3987 | Math::BigInt if they need to change more basic behaviors. A subclass that
|
---|
3988 | needs to merely change the output only needs to overload C<bstr()>.
|
---|
3989 |
|
---|
3990 | All other object methods and overloaded functions can be directly inherited
|
---|
3991 | from the parent class.
|
---|
3992 |
|
---|
3993 | At the very minimum, any subclass will need to provide it's own C<new()> and can
|
---|
3994 | store additional hash keys in the object. There are also some package globals
|
---|
3995 | that must be defined, e.g.:
|
---|
3996 |
|
---|
3997 | # Globals
|
---|
3998 | $accuracy = undef;
|
---|
3999 | $precision = -2; # round to 2 decimal places
|
---|
4000 | $round_mode = 'even';
|
---|
4001 | $div_scale = 40;
|
---|
4002 |
|
---|
4003 | Additionally, you might want to provide the following two globals to allow
|
---|
4004 | auto-upgrading and auto-downgrading to work correctly:
|
---|
4005 |
|
---|
4006 | $upgrade = undef;
|
---|
4007 | $downgrade = undef;
|
---|
4008 |
|
---|
4009 | This allows Math::BigInt to correctly retrieve package globals from the
|
---|
4010 | subclass, like C<$SubClass::precision>. See t/Math/BigInt/Subclass.pm or
|
---|
4011 | t/Math/BigFloat/SubClass.pm completely functional subclass examples.
|
---|
4012 |
|
---|
4013 | Don't forget to
|
---|
4014 |
|
---|
4015 | use overload;
|
---|
4016 |
|
---|
4017 | in your subclass to automatically inherit the overloading from the parent. If
|
---|
4018 | you like, you can change part of the overloading, look at Math::String for an
|
---|
4019 | example.
|
---|
4020 |
|
---|
4021 | =head1 UPGRADING
|
---|
4022 |
|
---|
4023 | When used like this:
|
---|
4024 |
|
---|
4025 | use Math::BigInt upgrade => 'Foo::Bar';
|
---|
4026 |
|
---|
4027 | certain operations will 'upgrade' their calculation and thus the result to
|
---|
4028 | the class Foo::Bar. Usually this is used in conjunction with Math::BigFloat:
|
---|
4029 |
|
---|
4030 | use Math::BigInt upgrade => 'Math::BigFloat';
|
---|
4031 |
|
---|
4032 | As a shortcut, you can use the module C<bignum>:
|
---|
4033 |
|
---|
4034 | use bignum;
|
---|
4035 |
|
---|
4036 | Also good for oneliners:
|
---|
4037 |
|
---|
4038 | perl -Mbignum -le 'print 2 ** 255'
|
---|
4039 |
|
---|
4040 | This makes it possible to mix arguments of different classes (as in 2.5 + 2)
|
---|
4041 | as well es preserve accuracy (as in sqrt(3)).
|
---|
4042 |
|
---|
4043 | Beware: This feature is not fully implemented yet.
|
---|
4044 |
|
---|
4045 | =head2 Auto-upgrade
|
---|
4046 |
|
---|
4047 | The following methods upgrade themselves unconditionally; that is if upgrade
|
---|
4048 | is in effect, they will always hand up their work:
|
---|
4049 |
|
---|
4050 | =over 2
|
---|
4051 |
|
---|
4052 | =item bsqrt()
|
---|
4053 |
|
---|
4054 | =item div()
|
---|
4055 |
|
---|
4056 | =item blog()
|
---|
4057 |
|
---|
4058 | =back
|
---|
4059 |
|
---|
4060 | Beware: This list is not complete.
|
---|
4061 |
|
---|
4062 | All other methods upgrade themselves only when one (or all) of their
|
---|
4063 | arguments are of the class mentioned in $upgrade (This might change in later
|
---|
4064 | versions to a more sophisticated scheme):
|
---|
4065 |
|
---|
4066 | =head1 BUGS
|
---|
4067 |
|
---|
4068 | =over 2
|
---|
4069 |
|
---|
4070 | =item broot() does not work
|
---|
4071 |
|
---|
4072 | The broot() function in BigInt may only work for small values. This will be
|
---|
4073 | fixed in a later version.
|
---|
4074 |
|
---|
4075 | =item Out of Memory!
|
---|
4076 |
|
---|
4077 | Under Perl prior to 5.6.0 having an C<use Math::BigInt ':constant';> and
|
---|
4078 | C<eval()> in your code will crash with "Out of memory". This is probably an
|
---|
4079 | overload/exporter bug. You can workaround by not having C<eval()>
|
---|
4080 | and ':constant' at the same time or upgrade your Perl to a newer version.
|
---|
4081 |
|
---|
4082 | =item Fails to load Calc on Perl prior 5.6.0
|
---|
4083 |
|
---|
4084 | Since eval(' use ...') can not be used in conjunction with ':constant', BigInt
|
---|
4085 | will fall back to eval { require ... } when loading the math lib on Perls
|
---|
4086 | prior to 5.6.0. This simple replaces '::' with '/' and thus might fail on
|
---|
4087 | filesystems using a different seperator.
|
---|
4088 |
|
---|
4089 | =back
|
---|
4090 |
|
---|
4091 | =head1 CAVEATS
|
---|
4092 |
|
---|
4093 | Some things might not work as you expect them. Below is documented what is
|
---|
4094 | known to be troublesome:
|
---|
4095 |
|
---|
4096 | =over 1
|
---|
4097 |
|
---|
4098 | =item bstr(), bsstr() and 'cmp'
|
---|
4099 |
|
---|
4100 | Both C<bstr()> and C<bsstr()> as well as automated stringify via overload now
|
---|
4101 | drop the leading '+'. The old code would return '+3', the new returns '3'.
|
---|
4102 | This is to be consistent with Perl and to make C<cmp> (especially with
|
---|
4103 | overloading) to work as you expect. It also solves problems with C<Test.pm>,
|
---|
4104 | because it's C<ok()> uses 'eq' internally.
|
---|
4105 |
|
---|
4106 | Mark Biggar said, when asked about to drop the '+' altogether, or make only
|
---|
4107 | C<cmp> work:
|
---|
4108 |
|
---|
4109 | I agree (with the first alternative), don't add the '+' on positive
|
---|
4110 | numbers. It's not as important anymore with the new internal
|
---|
4111 | form for numbers. It made doing things like abs and neg easier,
|
---|
4112 | but those have to be done differently now anyway.
|
---|
4113 |
|
---|
4114 | So, the following examples will now work all as expected:
|
---|
4115 |
|
---|
4116 | use Test;
|
---|
4117 | BEGIN { plan tests => 1 }
|
---|
4118 | use Math::BigInt;
|
---|
4119 |
|
---|
4120 | my $x = new Math::BigInt 3*3;
|
---|
4121 | my $y = new Math::BigInt 3*3;
|
---|
4122 |
|
---|
4123 | ok ($x,3*3);
|
---|
4124 | print "$x eq 9" if $x eq $y;
|
---|
4125 | print "$x eq 9" if $x eq '9';
|
---|
4126 | print "$x eq 9" if $x eq 3*3;
|
---|
4127 |
|
---|
4128 | Additionally, the following still works:
|
---|
4129 |
|
---|
4130 | print "$x == 9" if $x == $y;
|
---|
4131 | print "$x == 9" if $x == 9;
|
---|
4132 | print "$x == 9" if $x == 3*3;
|
---|
4133 |
|
---|
4134 | There is now a C<bsstr()> method to get the string in scientific notation aka
|
---|
4135 | C<1e+2> instead of C<100>. Be advised that overloaded 'eq' always uses bstr()
|
---|
4136 | for comparisation, but Perl will represent some numbers as 100 and others
|
---|
4137 | as 1e+308. If in doubt, convert both arguments to Math::BigInt before
|
---|
4138 | comparing them as strings:
|
---|
4139 |
|
---|
4140 | use Test;
|
---|
4141 | BEGIN { plan tests => 3 }
|
---|
4142 | use Math::BigInt;
|
---|
4143 |
|
---|
4144 | $x = Math::BigInt->new('1e56'); $y = 1e56;
|
---|
4145 | ok ($x,$y); # will fail
|
---|
4146 | ok ($x->bsstr(),$y); # okay
|
---|
4147 | $y = Math::BigInt->new($y);
|
---|
4148 | ok ($x,$y); # okay
|
---|
4149 |
|
---|
4150 | Alternatively, simple use C<< <=> >> for comparisations, this will get it
|
---|
4151 | always right. There is not yet a way to get a number automatically represented
|
---|
4152 | as a string that matches exactly the way Perl represents it.
|
---|
4153 |
|
---|
4154 | See also the section about L<Infinity and Not a Number> for problems in
|
---|
4155 | comparing NaNs.
|
---|
4156 |
|
---|
4157 | =item int()
|
---|
4158 |
|
---|
4159 | C<int()> will return (at least for Perl v5.7.1 and up) another BigInt, not a
|
---|
4160 | Perl scalar:
|
---|
4161 |
|
---|
4162 | $x = Math::BigInt->new(123);
|
---|
4163 | $y = int($x); # BigInt 123
|
---|
4164 | $x = Math::BigFloat->new(123.45);
|
---|
4165 | $y = int($x); # BigInt 123
|
---|
4166 |
|
---|
4167 | In all Perl versions you can use C<as_number()> or C<as_int> for the same
|
---|
4168 | effect:
|
---|
4169 |
|
---|
4170 | $x = Math::BigFloat->new(123.45);
|
---|
4171 | $y = $x->as_number(); # BigInt 123
|
---|
4172 | $y = $x->as_int(); # ditto
|
---|
4173 |
|
---|
4174 | This also works for other subclasses, like Math::String.
|
---|
4175 |
|
---|
4176 | It is yet unlcear whether overloaded int() should return a scalar or a BigInt.
|
---|
4177 |
|
---|
4178 | If you want a real Perl scalar, use C<numify()>:
|
---|
4179 |
|
---|
4180 | $y = $x->numify(); # 123 as scalar
|
---|
4181 |
|
---|
4182 | This is seldom necessary, though, because this is done automatically, like
|
---|
4183 | when you access an array:
|
---|
4184 |
|
---|
4185 | $z = $array[$x]; # does work automatically
|
---|
4186 |
|
---|
4187 | =item length
|
---|
4188 |
|
---|
4189 | The following will probably not do what you expect:
|
---|
4190 |
|
---|
4191 | $c = Math::BigInt->new(123);
|
---|
4192 | print $c->length(),"\n"; # prints 30
|
---|
4193 |
|
---|
4194 | It prints both the number of digits in the number and in the fraction part
|
---|
4195 | since print calls C<length()> in list context. Use something like:
|
---|
4196 |
|
---|
4197 | print scalar $c->length(),"\n"; # prints 3
|
---|
4198 |
|
---|
4199 | =item bdiv
|
---|
4200 |
|
---|
4201 | The following will probably not do what you expect:
|
---|
4202 |
|
---|
4203 | print $c->bdiv(10000),"\n";
|
---|
4204 |
|
---|
4205 | It prints both quotient and remainder since print calls C<bdiv()> in list
|
---|
4206 | context. Also, C<bdiv()> will modify $c, so be carefull. You probably want
|
---|
4207 | to use
|
---|
4208 |
|
---|
4209 | print $c / 10000,"\n";
|
---|
4210 | print scalar $c->bdiv(10000),"\n"; # or if you want to modify $c
|
---|
4211 |
|
---|
4212 | instead.
|
---|
4213 |
|
---|
4214 | The quotient is always the greatest integer less than or equal to the
|
---|
4215 | real-valued quotient of the two operands, and the remainder (when it is
|
---|
4216 | nonzero) always has the same sign as the second operand; so, for
|
---|
4217 | example,
|
---|
4218 |
|
---|
4219 | 1 / 4 => ( 0, 1)
|
---|
4220 | 1 / -4 => (-1,-3)
|
---|
4221 | -3 / 4 => (-1, 1)
|
---|
4222 | -3 / -4 => ( 0,-3)
|
---|
4223 | -11 / 2 => (-5,1)
|
---|
4224 | 11 /-2 => (-5,-1)
|
---|
4225 |
|
---|
4226 | As a consequence, the behavior of the operator % agrees with the
|
---|
4227 | behavior of Perl's built-in % operator (as documented in the perlop
|
---|
4228 | manpage), and the equation
|
---|
4229 |
|
---|
4230 | $x == ($x / $y) * $y + ($x % $y)
|
---|
4231 |
|
---|
4232 | holds true for any $x and $y, which justifies calling the two return
|
---|
4233 | values of bdiv() the quotient and remainder. The only exception to this rule
|
---|
4234 | are when $y == 0 and $x is negative, then the remainder will also be
|
---|
4235 | negative. See below under "infinity handling" for the reasoning behing this.
|
---|
4236 |
|
---|
4237 | Perl's 'use integer;' changes the behaviour of % and / for scalars, but will
|
---|
4238 | not change BigInt's way to do things. This is because under 'use integer' Perl
|
---|
4239 | will do what the underlying C thinks is right and this is different for each
|
---|
4240 | system. If you need BigInt's behaving exactly like Perl's 'use integer', bug
|
---|
4241 | the author to implement it ;)
|
---|
4242 |
|
---|
4243 | =item infinity handling
|
---|
4244 |
|
---|
4245 | Here are some examples that explain the reasons why certain results occur while
|
---|
4246 | handling infinity:
|
---|
4247 |
|
---|
4248 | The following table shows the result of the division and the remainder, so that
|
---|
4249 | the equation above holds true. Some "ordinary" cases are strewn in to show more
|
---|
4250 | clearly the reasoning:
|
---|
4251 |
|
---|
4252 | A / B = C, R so that C * B + R = A
|
---|
4253 | =========================================================
|
---|
4254 | 5 / 8 = 0, 5 0 * 8 + 5 = 5
|
---|
4255 | 0 / 8 = 0, 0 0 * 8 + 0 = 0
|
---|
4256 | 0 / inf = 0, 0 0 * inf + 0 = 0
|
---|
4257 | 0 /-inf = 0, 0 0 * -inf + 0 = 0
|
---|
4258 | 5 / inf = 0, 5 0 * inf + 5 = 5
|
---|
4259 | 5 /-inf = 0, 5 0 * -inf + 5 = 5
|
---|
4260 | -5/ inf = 0, -5 0 * inf + -5 = -5
|
---|
4261 | -5/-inf = 0, -5 0 * -inf + -5 = -5
|
---|
4262 | inf/ 5 = inf, 0 inf * 5 + 0 = inf
|
---|
4263 | -inf/ 5 = -inf, 0 -inf * 5 + 0 = -inf
|
---|
4264 | inf/ -5 = -inf, 0 -inf * -5 + 0 = inf
|
---|
4265 | -inf/ -5 = inf, 0 inf * -5 + 0 = -inf
|
---|
4266 | 5/ 5 = 1, 0 1 * 5 + 0 = 5
|
---|
4267 | -5/ -5 = 1, 0 1 * -5 + 0 = -5
|
---|
4268 | inf/ inf = 1, 0 1 * inf + 0 = inf
|
---|
4269 | -inf/-inf = 1, 0 1 * -inf + 0 = -inf
|
---|
4270 | inf/-inf = -1, 0 -1 * -inf + 0 = inf
|
---|
4271 | -inf/ inf = -1, 0 1 * -inf + 0 = -inf
|
---|
4272 | 8/ 0 = inf, 8 inf * 0 + 8 = 8
|
---|
4273 | inf/ 0 = inf, inf inf * 0 + inf = inf
|
---|
4274 | 0/ 0 = NaN
|
---|
4275 |
|
---|
4276 | These cases below violate the "remainder has the sign of the second of the two
|
---|
4277 | arguments", since they wouldn't match up otherwise.
|
---|
4278 |
|
---|
4279 | A / B = C, R so that C * B + R = A
|
---|
4280 | ========================================================
|
---|
4281 | -inf/ 0 = -inf, -inf -inf * 0 + inf = -inf
|
---|
4282 | -8/ 0 = -inf, -8 -inf * 0 + 8 = -8
|
---|
4283 |
|
---|
4284 | =item Modifying and =
|
---|
4285 |
|
---|
4286 | Beware of:
|
---|
4287 |
|
---|
4288 | $x = Math::BigFloat->new(5);
|
---|
4289 | $y = $x;
|
---|
4290 |
|
---|
4291 | It will not do what you think, e.g. making a copy of $x. Instead it just makes
|
---|
4292 | a second reference to the B<same> object and stores it in $y. Thus anything
|
---|
4293 | that modifies $x (except overloaded operators) will modify $y, and vice versa.
|
---|
4294 | Or in other words, C<=> is only safe if you modify your BigInts only via
|
---|
4295 | overloaded math. As soon as you use a method call it breaks:
|
---|
4296 |
|
---|
4297 | $x->bmul(2);
|
---|
4298 | print "$x, $y\n"; # prints '10, 10'
|
---|
4299 |
|
---|
4300 | If you want a true copy of $x, use:
|
---|
4301 |
|
---|
4302 | $y = $x->copy();
|
---|
4303 |
|
---|
4304 | You can also chain the calls like this, this will make first a copy and then
|
---|
4305 | multiply it by 2:
|
---|
4306 |
|
---|
4307 | $y = $x->copy()->bmul(2);
|
---|
4308 |
|
---|
4309 | See also the documentation for overload.pm regarding C<=>.
|
---|
4310 |
|
---|
4311 | =item bpow
|
---|
4312 |
|
---|
4313 | C<bpow()> (and the rounding functions) now modifies the first argument and
|
---|
4314 | returns it, unlike the old code which left it alone and only returned the
|
---|
4315 | result. This is to be consistent with C<badd()> etc. The first three will
|
---|
4316 | modify $x, the last one won't:
|
---|
4317 |
|
---|
4318 | print bpow($x,$i),"\n"; # modify $x
|
---|
4319 | print $x->bpow($i),"\n"; # ditto
|
---|
4320 | print $x **= $i,"\n"; # the same
|
---|
4321 | print $x ** $i,"\n"; # leave $x alone
|
---|
4322 |
|
---|
4323 | The form C<$x **= $y> is faster than C<$x = $x ** $y;>, though.
|
---|
4324 |
|
---|
4325 | =item Overloading -$x
|
---|
4326 |
|
---|
4327 | The following:
|
---|
4328 |
|
---|
4329 | $x = -$x;
|
---|
4330 |
|
---|
4331 | is slower than
|
---|
4332 |
|
---|
4333 | $x->bneg();
|
---|
4334 |
|
---|
4335 | since overload calls C<sub($x,0,1);> instead of C<neg($x)>. The first variant
|
---|
4336 | needs to preserve $x since it does not know that it later will get overwritten.
|
---|
4337 | This makes a copy of $x and takes O(N), but $x->bneg() is O(1).
|
---|
4338 |
|
---|
4339 | =item Mixing different object types
|
---|
4340 |
|
---|
4341 | In Perl you will get a floating point value if you do one of the following:
|
---|
4342 |
|
---|
4343 | $float = 5.0 + 2;
|
---|
4344 | $float = 2 + 5.0;
|
---|
4345 | $float = 5 / 2;
|
---|
4346 |
|
---|
4347 | With overloaded math, only the first two variants will result in a BigFloat:
|
---|
4348 |
|
---|
4349 | use Math::BigInt;
|
---|
4350 | use Math::BigFloat;
|
---|
4351 |
|
---|
4352 | $mbf = Math::BigFloat->new(5);
|
---|
4353 | $mbi2 = Math::BigInteger->new(5);
|
---|
4354 | $mbi = Math::BigInteger->new(2);
|
---|
4355 |
|
---|
4356 | # what actually gets called:
|
---|
4357 | $float = $mbf + $mbi; # $mbf->badd()
|
---|
4358 | $float = $mbf / $mbi; # $mbf->bdiv()
|
---|
4359 | $integer = $mbi + $mbf; # $mbi->badd()
|
---|
4360 | $integer = $mbi2 / $mbi; # $mbi2->bdiv()
|
---|
4361 | $integer = $mbi2 / $mbf; # $mbi2->bdiv()
|
---|
4362 |
|
---|
4363 | This is because math with overloaded operators follows the first (dominating)
|
---|
4364 | operand, and the operation of that is called and returns thus the result. So,
|
---|
4365 | Math::BigInt::bdiv() will always return a Math::BigInt, regardless whether
|
---|
4366 | the result should be a Math::BigFloat or the second operant is one.
|
---|
4367 |
|
---|
4368 | To get a Math::BigFloat you either need to call the operation manually,
|
---|
4369 | make sure the operands are already of the proper type or casted to that type
|
---|
4370 | via Math::BigFloat->new():
|
---|
4371 |
|
---|
4372 | $float = Math::BigFloat->new($mbi2) / $mbi; # = 2.5
|
---|
4373 |
|
---|
4374 | Beware of simple "casting" the entire expression, this would only convert
|
---|
4375 | the already computed result:
|
---|
4376 |
|
---|
4377 | $float = Math::BigFloat->new($mbi2 / $mbi); # = 2.0 thus wrong!
|
---|
4378 |
|
---|
4379 | Beware also of the order of more complicated expressions like:
|
---|
4380 |
|
---|
4381 | $integer = ($mbi2 + $mbi) / $mbf; # int / float => int
|
---|
4382 | $integer = $mbi2 / Math::BigFloat->new($mbi); # ditto
|
---|
4383 |
|
---|
4384 | If in doubt, break the expression into simpler terms, or cast all operands
|
---|
4385 | to the desired resulting type.
|
---|
4386 |
|
---|
4387 | Scalar values are a bit different, since:
|
---|
4388 |
|
---|
4389 | $float = 2 + $mbf;
|
---|
4390 | $float = $mbf + 2;
|
---|
4391 |
|
---|
4392 | will both result in the proper type due to the way the overloaded math works.
|
---|
4393 |
|
---|
4394 | This section also applies to other overloaded math packages, like Math::String.
|
---|
4395 |
|
---|
4396 | One solution to you problem might be autoupgrading|upgrading. See the
|
---|
4397 | pragmas L<bignum>, L<bigint> and L<bigrat> for an easy way to do this.
|
---|
4398 |
|
---|
4399 | =item bsqrt()
|
---|
4400 |
|
---|
4401 | C<bsqrt()> works only good if the result is a big integer, e.g. the square
|
---|
4402 | root of 144 is 12, but from 12 the square root is 3, regardless of rounding
|
---|
4403 | mode. The reason is that the result is always truncated to an integer.
|
---|
4404 |
|
---|
4405 | If you want a better approximation of the square root, then use:
|
---|
4406 |
|
---|
4407 | $x = Math::BigFloat->new(12);
|
---|
4408 | Math::BigFloat->precision(0);
|
---|
4409 | Math::BigFloat->round_mode('even');
|
---|
4410 | print $x->copy->bsqrt(),"\n"; # 4
|
---|
4411 |
|
---|
4412 | Math::BigFloat->precision(2);
|
---|
4413 | print $x->bsqrt(),"\n"; # 3.46
|
---|
4414 | print $x->bsqrt(3),"\n"; # 3.464
|
---|
4415 |
|
---|
4416 | =item brsft()
|
---|
4417 |
|
---|
4418 | For negative numbers in base see also L<brsft|brsft>.
|
---|
4419 |
|
---|
4420 | =back
|
---|
4421 |
|
---|
4422 | =head1 LICENSE
|
---|
4423 |
|
---|
4424 | This program is free software; you may redistribute it and/or modify it under
|
---|
4425 | the same terms as Perl itself.
|
---|
4426 |
|
---|
4427 | =head1 SEE ALSO
|
---|
4428 |
|
---|
4429 | L<Math::BigFloat>, L<Math::BigRat> and L<Math::Big> as well as
|
---|
4430 | L<Math::BigInt::BitVect>, L<Math::BigInt::Pari> and L<Math::BigInt::GMP>.
|
---|
4431 |
|
---|
4432 | The pragmas L<bignum>, L<bigint> and L<bigrat> also might be of interest
|
---|
4433 | because they solve the autoupgrading/downgrading issue, at least partly.
|
---|
4434 |
|
---|
4435 | The package at
|
---|
4436 | L<http://search.cpan.org/search?mode=module&query=Math%3A%3ABigInt> contains
|
---|
4437 | more documentation including a full version history, testcases, empty
|
---|
4438 | subclass files and benchmarks.
|
---|
4439 |
|
---|
4440 | =head1 AUTHORS
|
---|
4441 |
|
---|
4442 | Original code by Mark Biggar, overloaded interface by Ilya Zakharevich.
|
---|
4443 | Completely rewritten by Tels http://bloodgate.com in late 2000, 2001 - 2004
|
---|
4444 | and still at it in 2005.
|
---|
4445 |
|
---|
4446 | Many people contributed in one or more ways to the final beast, see the file
|
---|
4447 | CREDITS for an (uncomplete) list. If you miss your name, please drop me a
|
---|
4448 | mail. Thank you!
|
---|
4449 |
|
---|
4450 | =cut
|
---|