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1 ## Copyright (C) 2000, 2001, 2002, 2003, 2005, 2006, 2007 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{n}, @var{b}, @var{len}) |
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21 ## Return a string of symbols in base @var{b} corresponding to |
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22 ## the nonnegative integer @var{n}. |
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23 ## |
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24 ## @example |
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25 ## dec2base (123, 3) |
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26 ## @result{} "11120" |
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27 ## @end example |
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28 ## |
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29 ## If @var{n} is a vector, return a string matrix with one row per value, |
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30 ## padded with leading zeros to the width of the largest value. |
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31 ## |
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32 ## If @var{b} is a string then the characters of @var{b} are used as |
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33 ## the symbols for the digits of @var{n}. Space (' ') may not be used |
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34 ## as a symbol. |
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35 ## |
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36 ## @example |
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37 ## dec2base (123, "aei") |
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38 ## @result{} "eeeia" |
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39 ## @end example |
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40 ## |
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41 ## The optional third argument, @var{len}, specifies the minimum |
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42 ## number of digits in the result. |
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43 ## @seealso{base2dec, dec2bin, bin2dec, hex2dec, dec2hex} |
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44 ## @end deftypefn |
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45 |
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46 ## Author: Daniel Calvelo <dcalvelo@yahoo.com> |
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47 ## Adapted-by: Paul Kienzle <pkienzle@kienzle.powernet.co.uk> |
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48 |
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49 function retval = dec2base (n, base, len) |
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50 |
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51 if (nargin < 2 || nargin > 3) |
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52 print_usage (); |
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53 endif |
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54 |
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55 if (numel (n) != length (n)) |
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56 n = n(:); |
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57 elseif (any (n < 0 | n != fix (n))) |
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58 error ("dec2base: can only convert non-negative integers") |
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59 endif |
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60 |
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61 symbols = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"; |
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62 if (ischar (base)) |
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63 symbols = base; |
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64 base = length (symbols); |
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65 if any (diff (sort (toascii (symbols))) == 0) |
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66 error ("dec2base: symbols representing digits must be unique"); |
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67 endif |
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68 elseif (! isscalar (base)) |
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69 error ("dec2base: cannot convert from several bases at once"); |
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70 elseif (base < 2 || base > length (symbols)) |
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71 error ("dec2base: base must be between 2 and 36 or a string of symbols"); |
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72 endif |
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73 |
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74 ## determine number of digits required to handle all numbers, can overflow |
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75 ## by 1 digit |
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76 max_len = round (log (max (max (n), 1)) ./ log (base)) + 1; |
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77 |
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78 if (nargin == 3) |
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79 max_len = max (max_len, len); |
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80 endif |
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81 |
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82 ## determine digits for each number |
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83 power = ones (length (n), 1) * (base .^ (max_len-1 : -1 : 0)); |
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84 n = n(:) * ones (1, max_len); |
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85 digits = floor (rem (n, base*power) ./ power); |
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86 |
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87 ## convert digits to symbols |
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88 retval = reshape (symbols (digits+1), size (digits)); |
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89 |
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90 ## Check if the first element is the zero symbol. It seems possible |
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91 ## that LEN is provided, and is less than the computed MAX_LEN and |
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92 ## MAX_LEN is computed to be one larger than necessary, so we would |
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93 ## have a leading zero to remove. But if LEN >= MAX_LEN, we should |
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94 ## not remove any leading zeros. |
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95 if ((nargin == 2 || (nargin == 3 && max_len > len)) |
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96 && all (retval(:,1) == symbols(1)) && length (retval) != 1) |
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97 retval = retval(:,2:end); |
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98 endif |
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99 |
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100 endfunction |
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101 |
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102 %!test |
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103 %! s0=''; |
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104 %! for n=1:13 |
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105 %! for b=2:16 |
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106 %! pp=dec2base(b^n+1,b); |
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107 %! assert(dec2base(b^n,b),['1',s0,'0']); |
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108 %! assert(dec2base(b^n+1,b),['1',s0,'1']); |
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109 %! end |
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110 %! s0=[s0,'0']; |
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111 %! end |
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112 |
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113 %!test |
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114 %! digits='0123456789ABCDEF'; |
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115 %! for n=1:13 |
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116 %! for b=2:16 |
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117 %! pm=dec2base(b^n-1,b); |
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118 %! assert(length(pm),n); |
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119 %! assert(all(pm==digits(b))); |
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120 %! end |
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121 %! end |
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122 |
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123 %!test |
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124 %! for b=2:16 |
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125 %! assert(dec2base(0,b),'0'); |
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126 %! end |
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127 |
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128 %!test |
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129 %! assert(dec2base(2^51-1,2), |
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130 %! '111111111111111111111111111111111111111111111111111'); |
