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pod |
time |
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package Math::BigInt::GMPz; |
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3
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7
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7
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313382
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use 5.006002; |
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7
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21
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4
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7
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7
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23
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use strict; |
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7
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11
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7
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810
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5
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7
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7
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24
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use warnings; |
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7
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8
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7
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191
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6
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7
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7
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7
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3272
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use Math::BigInt::Lib 1.999801; |
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32609
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7
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29
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8
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9
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our @ISA = qw< Math::BigInt::Lib >; |
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10
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11
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our $VERSION = '0.0001'; |
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13
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7
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7
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1571
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use Math::GMPz qw< :mpz >; |
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0
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0
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14
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15
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sub import { } |
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16
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17
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my $zero = Rmpz_init(); # for _is_zero |
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18
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my $one = Rmpz_init_set_str("1", 10); # for _is_one, _inc, and _dec |
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my $two = Rmpz_init_set_str("2", 10); # for _is_two |
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20
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my $ten = Rmpz_init_set_str("10", 10); # for _is_ten, _digit |
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21
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22
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sub api_version { 2; } |
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23
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24
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sub _new { |
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25
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Rmpz_init_set_str($_[1], 10); |
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} |
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27
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28
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sub _zero { |
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29
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Rmpz_init(); |
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30
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} |
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31
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32
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sub _one { |
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33
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Rmpz_init_set_str("1", 10); |
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34
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} |
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35
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36
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sub _two { |
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37
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Rmpz_init_set_str("2", 10); |
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38
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} |
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39
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40
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sub _ten { |
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41
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Rmpz_init_set_str("10", 10); |
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42
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} |
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43
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44
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sub _from_bin { |
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45
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my $str = $_[1]; |
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46
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$str =~ s/^0[Bb]//; # remove leading '0b' |
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47
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Rmpz_init_set_str($str, 2); |
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48
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} |
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49
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50
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sub _from_oct { |
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51
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Rmpz_init_set_str($_[1], 8); |
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52
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} |
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53
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54
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#sub _from_dec { |
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55
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# Rmpz_init_set_str($_[1], 10); |
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56
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#} |
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57
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58
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sub _from_hex { |
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59
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my $str = $_[1]; |
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60
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$str =~ s/^0[Xx]//; # remove leading '0x' |
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61
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Rmpz_init_set_str($str, 16); |
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62
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} |
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63
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64
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sub _from_bytes { |
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65
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my $rop = Rmpz_init(); |
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66
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my $bstr = $_[1]; |
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67
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my $len = length $bstr; |
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68
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my ($order, $size, $endian, $nails) = (1, 1, 0, 0); |
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69
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Rmpz_import($rop, $len, $order, $size, $endian, $nails, $bstr); |
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70
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return $rop; |
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71
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} |
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72
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73
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sub _1ex { |
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74
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Rmpz_init_set_str("1" . ("0" x $_[1])); |
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75
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} |
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76
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77
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sub _add { |
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78
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Rmpz_add($_[1], $_[1], $_[2]); |
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79
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return $_[1]; |
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80
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} |
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81
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82
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sub _mul { |
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83
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Rmpz_mul($_[1], $_[1], $_[2]); |
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84
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return $_[1]; |
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85
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} |
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86
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87
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sub _div { |
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88
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if (wantarray) { |
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89
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my $r = Rmpz_init(); |
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90
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Rmpz_fdiv_qr($_[1], $r, $_[1], $_[2]); |
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91
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return ($_[1], $r); |
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92
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} |
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93
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Rmpz_fdiv_q($_[1], $_[1], $_[2]); |
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94
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return $_[1]; |
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95
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} |
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96
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97
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sub _sub { |
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98
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if ($_[3]) { |
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99
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$_[2] = $_[1] - $_[2]; |
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100
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return $_[2]; |
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101
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} |
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102
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Rmpz_sub($_[1], $_[1], $_[2]); |
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103
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return $_[1]; |
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104
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} |
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105
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106
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sub _dec { |
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107
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Rmpz_sub_ui($_[1], $_[1], 1); |
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108
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return $_[1]; |
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109
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} |
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110
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111
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sub _inc { |
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112
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Rmpz_add_ui($_[1], $_[1], 1); |
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113
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return $_[1]; |
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114
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} |
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115
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116
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sub _mod { |
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117
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Rmpz_fdiv_r($_[1], $_[1], $_[2]); |
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118
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return $_[1]; |
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119
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}; |
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120
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121
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sub _sqrt { |
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122
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Rmpz_sqrt($_[1], $_[1]); |
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123
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return $_[1]; |
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124
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} |
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125
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126
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sub _root { |
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127
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Rmpz_root($_[1], $_[1], $_[2]); |
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128
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return $_[1]; |
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129
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} |
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130
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131
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sub _fac { |
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132
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Rmpz_fac_ui($_[1], $_[1]); |
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133
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return $_[1]; |
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134
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} |
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135
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136
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sub _dfac { |
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137
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Rmpz_2fac_ui($_[1], $_[1]); |
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138
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return $_[1]; |
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139
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} |
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140
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141
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sub _pow { |
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142
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Rmpz_pow_ui($_[1], $_[1], $_[2]); |
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143
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return $_[1]; |
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144
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} |
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145
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146
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sub _modinv { |
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147
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my $bool = Rmpz_invert($_[1], $_[1], $_[2]); |
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148
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return $bool ? ($_[1], '+') : (undef, undef); |
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149
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} |
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150
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151
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sub _modpow { |
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152
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Rmpz_powm($_[1], $_[1], $_[2], $_[3]); |
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153
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return $_[1]; |
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154
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} |
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155
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156
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sub _rsft { |
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157
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# (X, Y, N) = @_; means X >> Y in base N |
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158
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if ($_[3] == 2) { |
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159
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Rmpz_div_2exp($_[1], $_[1], $_[2]); |
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160
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} else { |
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161
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# N must be an unsigned integer |
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162
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my $n = Rmpz_init_set_ui($_[3]); |
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163
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# Y must be a Math::GMPz |
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164
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my $y = Rmpz_get_ui($_[2]); |
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165
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Rmpz_pow_ui($n, $n, $y); |
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166
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Rmpz_div($_[1], $_[1], $n); |
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167
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} |
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168
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return $_[1]; |
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169
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} |
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170
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171
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sub _lsft { |
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172
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# (X, Y, N) = @_; means X << Y in base N (= X * N^Y) |
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173
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if ($_[3] == 2) { |
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174
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Rmpz_mul_2exp($_[1], $_[1], $_[2]); |
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175
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} else { |
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176
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# N must be an unsigned integer |
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177
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my $n = Rmpz_init_set_ui($_[3]); |
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178
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# Y must be a Math::GMPz |
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179
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my $y = Rmpz_get_ui($_[2]); |
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180
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#$_[1] = $_[1] * $n ** $y; |
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181
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Rmpz_pow_ui($n, $n, $y); |
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182
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Rmpz_mul($_[1], $_[1], $n); |
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183
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} |
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184
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return $_[1]; |
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185
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} |
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186
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187
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#sub _log_int { } |
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188
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189
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sub _gcd { |
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190
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Rmpz_gcd($_[1], $_[1], $_[2]); |
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191
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return $_[1]; |
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192
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} |
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193
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194
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sub _lcm { |
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195
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Rmpz_lcm($_[1], $_[1], $_[2]); |
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196
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return $_[1]; |
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197
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} |
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198
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199
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sub _and { |
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200
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Rmpz_and($_[1], $_[1], $_[2]); |
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201
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return $_[1]; |
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202
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} |
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203
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204
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sub _or { |
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205
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Rmpz_ior($_[1], $_[1], $_[2]); |
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206
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return $_[1]; |
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207
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} |
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208
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209
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sub _xor { |
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210
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Rmpz_xor($_[1], $_[1], $_[2]); |
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211
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return $_[1]; |
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212
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} |
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213
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214
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sub _is_zero { |
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215
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!Rmpz_cmp($_[1], $zero); |
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216
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} |
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217
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218
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sub _is_one { |
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219
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!Rmpz_cmp($_[1], $one); |
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220
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} |
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221
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222
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sub _is_two { |
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223
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!Rmpz_cmp($_[1], $two); |
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224
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} |
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225
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226
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sub _is_ten { |
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227
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!Rmpz_cmp($_[1], $ten); |
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228
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} |
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229
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230
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sub _is_even { |
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231
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Rmpz_even_p($_[1]); |
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232
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} |
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233
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234
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sub _is_odd { |
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235
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Rmpz_odd_p($_[1]); |
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236
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} |
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237
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238
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sub _acmp { |
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239
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Rmpz_cmp($_[1], $_[2]); |
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240
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} |
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241
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242
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sub _str { |
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243
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Rmpz_get_str($_[1], 10); |
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244
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} |
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245
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246
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sub _as_bin { |
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247
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'0b' . Rmpz_get_str($_[1], 2); |
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248
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} |
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249
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250
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sub _as_oct { |
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251
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'0' . Rmpz_get_str($_[1], 8); |
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252
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} |
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253
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254
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sub _as_hex { |
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255
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'0x' . Rmpz_get_str($_[1], 16); |
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256
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} |
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257
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258
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sub _to_bin { |
|
259
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Rmpz_get_str($_[1], 2); |
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260
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} |
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261
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262
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sub _to_oct { |
|
263
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Rmpz_get_str($_[1], 8); |
|
264
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} |
|
265
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266
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#sub _to_dec { |
|
267
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# Rmpz_get_str($_[1], 10); |
|
268
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#} |
|
269
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|
270
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sub _to_hex { |
|
271
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|
Rmpz_get_str($_[1], 16); |
|
272
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|
} |
|
273
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|
274
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|
|
sub _to_bytes { |
|
275
|
|
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|
|
my ($class, $x) = @_; |
|
276
|
|
|
|
|
|
|
return "\x00" if $class -> _is_zero($x); |
|
277
|
|
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|
|
my ($order, $size, $endian, $nails) = (1, 1, 0, 0); |
|
278
|
|
|
|
|
|
|
Rmpz_export($order, $size, $endian, $nails, $x); |
|
279
|
|
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|
|
} |
|
280
|
|
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|
|
281
|
|
|
|
|
|
|
*_as_bytes = \&_to_bytes; |
|
282
|
|
|
|
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|
283
|
|
|
|
|
|
|
sub _num { |
|
284
|
|
|
|
|
|
|
0 + Rmpz_get_str($_[1], 10); |
|
285
|
|
|
|
|
|
|
} |
|
286
|
|
|
|
|
|
|
|
|
287
|
|
|
|
|
|
|
sub _copy { Rmpz_init_set($_[1]); } |
|
288
|
|
|
|
|
|
|
|
|
289
|
|
|
|
|
|
|
sub _len { |
|
290
|
|
|
|
|
|
|
length Rmpz_get_str($_[1], 10); |
|
291
|
|
|
|
|
|
|
} |
|
292
|
|
|
|
|
|
|
|
|
293
|
|
|
|
|
|
|
sub _zeros { |
|
294
|
|
|
|
|
|
|
return 0 unless Rmpz_cmp($_[1], $zero); # 0 has no trailing zeros |
|
295
|
|
|
|
|
|
|
my $str = Rmpz_get_str($_[1], 10); |
|
296
|
|
|
|
|
|
|
$str =~ /(0*)\z/; |
|
297
|
|
|
|
|
|
|
return length($1); |
|
298
|
|
|
|
|
|
|
} |
|
299
|
|
|
|
|
|
|
|
|
300
|
|
|
|
|
|
|
sub _digit { |
|
301
|
|
|
|
|
|
|
substr(Rmpz_get_str($_[1], 10), -($_[2]+1), 1); |
|
302
|
|
|
|
|
|
|
#if ($_[2] >= 0) { |
|
303
|
|
|
|
|
|
|
# return( ($_[1] / (10 ** $_[2])) % 10); |
|
304
|
|
|
|
|
|
|
#} else { |
|
305
|
|
|
|
|
|
|
# substr(Rmpz_get_str($_[1], 10), -($_[2]+1), 1); |
|
306
|
|
|
|
|
|
|
#} |
|
307
|
|
|
|
|
|
|
} |
|
308
|
|
|
|
|
|
|
|
|
309
|
|
|
|
|
|
|
sub _check { |
|
310
|
|
|
|
|
|
|
my ($class, $x) = @_; |
|
311
|
|
|
|
|
|
|
return "Undefined" unless defined $x; |
|
312
|
|
|
|
|
|
|
return "$x is not a reference to Math::GMPz" |
|
313
|
|
|
|
|
|
|
unless ref($x) eq 'Math::GMPz'; |
|
314
|
|
|
|
|
|
|
return 0; |
|
315
|
|
|
|
|
|
|
} |
|
316
|
|
|
|
|
|
|
|
|
317
|
|
|
|
|
|
|
sub _nok { |
|
318
|
|
|
|
|
|
|
my ($class, $n, $k) = @_; |
|
319
|
|
|
|
|
|
|
|
|
320
|
|
|
|
|
|
|
# If k > n/2, use the fact that binomial(n, k) = binomial(n, n-k). To avoid |
|
321
|
|
|
|
|
|
|
# division, don't test k > n/2, but rather 2*k > n. |
|
322
|
|
|
|
|
|
|
|
|
323
|
|
|
|
|
|
|
{ |
|
324
|
|
|
|
|
|
|
my $twok = Rmpz_init(); # |
|
325
|
|
|
|
|
|
|
Rmpz_mul_2exp($twok, $k, 1); # $twok = 2 * $k |
|
326
|
|
|
|
|
|
|
if (Rmpz_cmp($twok, $n) > 0) { # if 2*k > n |
|
327
|
|
|
|
|
|
|
$k = Rmpz_init_set($k); # copy k |
|
328
|
|
|
|
|
|
|
Rmpz_sub($k, $n, $k); # k = n - k |
|
329
|
|
|
|
|
|
|
} |
|
330
|
|
|
|
|
|
|
} |
|
331
|
|
|
|
|
|
|
|
|
332
|
|
|
|
|
|
|
Rmpz_bin_ui($n, $n, $k); |
|
333
|
|
|
|
|
|
|
return $n; |
|
334
|
|
|
|
|
|
|
} |
|
335
|
|
|
|
|
|
|
|
|
336
|
|
|
|
|
|
|
# XXX TODO: calc len in base 2 then appr. in base 10 |
|
337
|
|
|
|
|
|
|
sub _alen { |
|
338
|
|
|
|
|
|
|
Rmpz_sizeinbase($_[1], 10); |
|
339
|
|
|
|
|
|
|
} |
|
340
|
|
|
|
|
|
|
|
|
341
|
|
|
|
|
|
|
# _set() - set an already existing object to the given scalar value |
|
342
|
|
|
|
|
|
|
|
|
343
|
|
|
|
|
|
|
sub _set { |
|
344
|
|
|
|
|
|
|
Rmpz_set($_[1], $_[2]); |
|
345
|
|
|
|
|
|
|
return $_[1]; |
|
346
|
|
|
|
|
|
|
} |
|
347
|
|
|
|
|
|
|
|
|
348
|
|
|
|
|
|
|
1; |
|
349
|
|
|
|
|
|
|
|
|
350
|
|
|
|
|
|
|
__END__ |