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annotate scripts/strings/dec2base.m @ 11169:51beeeff9027

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Update dec2base to handle numbers up to 2^64-1.
author Rik <octave@nomad.inbox5.com>
date Sat, 30 Oct 2010 12:14:27 -0700
parents edf065b51fa9
children 7e8ce65f73cf
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John W. Eaton <jwe@octave.org>
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1 ## Copyright (C) 2000, 2001, 2002, 2003, 2005, 2006, 2007, 2009 Daniel Calvelo
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {} dec2base (@var{d}, @var{b})
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21 ## @deftypefnx {Function File} {} dec2base (@var{d}, @var{b}, @var{len})
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22 ## Return a string of symbols in base @var{b} corresponding to
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23 ## the non-negative integer @var{d}.
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24 ##
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25 ## @example
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26 ## @group
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27 ## dec2base (123, 3)
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28 ## @result{} "11120"
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29 ## @end group
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30 ## @end example
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31 ##
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32 ## If @var{d} is a vector, return a string matrix with one row per value,
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33 ## padded with leading zeros to the width of the largest value.
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34 ##
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35 ## If @var{b} is a string then the characters of @var{b} are used as
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36 ## the symbols for the digits of @var{d}. Space (' ') may not be used
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37 ## as a symbol.
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38 ##
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39 ## @example
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40 ## @group
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41 ## dec2base (123, "aei")
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42 ## @result{} "eeeia"
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43 ## @end group
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44 ## @end example
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45 ##
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46 ## The optional third argument, @var{len}, specifies the minimum
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47 ## number of digits in the result.
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48 ## @seealso{base2dec, dec2bin, bin2dec, hex2dec, dec2hex}
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49 ## @end deftypefn
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50
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51 ## Author: Daniel Calvelo <dcalvelo@yahoo.com>
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52 ## Adapted-by: Paul Kienzle <pkienzle@kienzle.powernet.co.uk>
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53
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54 function retval = dec2base (d, base, len)
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55
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56 if (nargin < 2 || nargin > 3)
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57 print_usage ();
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58 endif
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59
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60 # Create column vector for algorithm
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61 if (columns (d) > 1 || !isvector (d))
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62 d = d(:);
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63 endif
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64
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65 if (any (d < 0 | d != fix (d)))
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66 error ("dec2base: input must be non-negative integers");
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67 endif
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68
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69 symbols = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";
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70 if (ischar (base))
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71 symbols = base;
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72 base = length (symbols);
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73 if (length (unique (symbols)) != base)
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74 error ("dec2base: symbols representing digits must be unique");
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75 endif
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76 elseif (! isscalar (base))
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77 error ("dec2base: cannot convert from several bases at once");
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78 elseif (base < 2 || base > length (symbols))
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79 error ("dec2base: BASE must be between 2 and 36, or a string of symbols");
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80 endif
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81
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82 ## determine number of digits required to handle all numbers, can overflow
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83 ## by 1 digit
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84 max_len = round (log (max (max (d), 1)) ./ log (base)) + 1;
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85
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86 if (nargin == 3)
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87 max_len = max (max_len, len);
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88 endif
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89
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90 ## determine digits for each number
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91 digits = zeros (length (d), max_len);
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92 for k = max_len:-1:1
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93 digits(:,k) = mod(d, base);
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94 d = round ((d - digits(:,k)) / base);
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95 endfor
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96
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97 ## convert digits to symbols
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98 retval = reshape (symbols (digits+1), size (digits));
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99
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100 ## Check if the first element is the zero symbol. It seems possible
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101 ## that LEN is provided, and is less than the computed MAX_LEN and
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102 ## MAX_LEN is computed to be one larger than necessary, so we would
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103 ## have a leading zero to remove. But if LEN >= MAX_LEN, we should
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104 ## not remove any leading zeros.
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105 if ((nargin == 2 || (nargin == 3 && max_len > len))
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106 && all (retval(:,1) == symbols(1)) && length (retval) != 1)
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107 retval = retval(:,2:end);
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108 endif
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109
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110 endfunction
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111
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112 %!test
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113 %! s0='';
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114 %! for n=1:13
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115 %! for b=2:16
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116 %! pp=dec2base(b^n+1,b);
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117 %! assert(dec2base(b^n,b),['1',s0,'0']);
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118 %! assert(dec2base(b^n+1,b),['1',s0,'1']);
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119 %! end
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120 %! s0=[s0,'0'];
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121 %! end
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122
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123 %!test
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124 %! digits='0123456789ABCDEF';
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125 %! for n=1:13
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126 %! for b=2:16
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127 %! pm=dec2base(b^n-1,b);
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128 %! assert(length(pm),n);
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129 %! assert(all(pm==digits(b)));
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130 %! end
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131 %! end
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132
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133 %!test
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134 %! for b=2:16
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135 %! assert(dec2base(0,b),'0');
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136 %! end
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137
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138 %!assert(dec2base(0,2,4), "0000");
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139 %!assert(dec2base(2^51-1,2), ...
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140 %! '111111111111111111111111111111111111111111111111111');
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141 %!assert(dec2base(uint64(2)^63-1,16), '7FFFFFFFFFFFFFFF');
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142
51beeeff9027 Update dec2base to handle numbers up to 2^64-1.
Rik <octave@nomad.inbox5.com>
parents: 9844
diff changeset
143 %!Test input validation
51beeeff9027 Update dec2base to handle numbers up to 2^64-1.
Rik <octave@nomad.inbox5.com>
parents: 9844
diff changeset
144 %!error dec2base ()
51beeeff9027 Update dec2base to handle numbers up to 2^64-1.
Rik <octave@nomad.inbox5.com>
parents: 9844
diff changeset
145 %!error dec2base (1)
51beeeff9027 Update dec2base to handle numbers up to 2^64-1.
Rik <octave@nomad.inbox5.com>
parents: 9844
diff changeset
146 %!error dec2base (1, 2, 3, 4)
51beeeff9027 Update dec2base to handle numbers up to 2^64-1.
Rik <octave@nomad.inbox5.com>
parents: 9844
diff changeset
147 %!error dec2base (-1)
51beeeff9027 Update dec2base to handle numbers up to 2^64-1.
Rik <octave@nomad.inbox5.com>
parents: 9844
diff changeset
148 %!error dec2base (1.1)
51beeeff9027 Update dec2base to handle numbers up to 2^64-1.
Rik <octave@nomad.inbox5.com>
parents: 9844
diff changeset
149 %!error dec2base (1,"ABA")
51beeeff9027 Update dec2base to handle numbers up to 2^64-1.
Rik <octave@nomad.inbox5.com>
parents: 9844
diff changeset
150 %!error dec2base (1, ones(2))
51beeeff9027 Update dec2base to handle numbers up to 2^64-1.
Rik <octave@nomad.inbox5.com>
parents: 9844
diff changeset
151 %!error dec2base (1, 1)
51beeeff9027 Update dec2base to handle numbers up to 2^64-1.
Rik <octave@nomad.inbox5.com>
parents: 9844
diff changeset
152 %!error dec2base (1, 37)
51beeeff9027 Update dec2base to handle numbers up to 2^64-1.
Rik <octave@nomad.inbox5.com>
parents: 9844
diff changeset
153