annotate scripts/general/nextpow2.m @ 33199:297fd823a953

nextpow2.m: Overhaul function for improved accuracy and Matlab compatibility (bug #65441) * nextpow2.m: Clarify documentation. Document return value of special input 0. Add input validation to exclude complex inputs. New algorithm for computing nextpow2 based on 2-output form of log2(). Use cast() to have output class match input class for Matlab compatibility. Add BIST tests. * NEWS.10.md: Announce changes to nextpow2 function.
author Rik <rik@octave.org>
date Tue, 12 Mar 2024 14:27:13 -0700
parents 2e484f9f1f18
children
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1 ########################################################################
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2 ##
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3 ## Copyright (C) 1995-2024 The Octave Project Developers
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4 ##
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5 ## See the file COPYRIGHT.md in the top-level directory of this
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6 ## distribution or <https://octave.org/copyright/>.
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7 ##
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8 ## This file is part of Octave.
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9 ##
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10 ## Octave is free software: you can redistribute it and/or modify it
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11 ## under the terms of the GNU General Public License as published by
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12 ## the Free Software Foundation, either version 3 of the License, or
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13 ## (at your option) any later version.
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14 ##
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15 ## Octave is distributed in the hope that it will be useful, but
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16 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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18 ## GNU General Public License for more details.
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19 ##
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20 ## You should have received a copy of the GNU General Public License
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21 ## along with Octave; see the file COPYING. If not, see
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22 ## <https://www.gnu.org/licenses/>.
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23 ##
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24 ########################################################################
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25
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26 ## -*- texinfo -*-
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27 ## @deftypefn {} {@var{n} =} nextpow2 (@var{x})
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28 ## Compute the exponent of the next power of two not smaller than the input.
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29 ##
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30 ## For each element in the input array @var{x}, return the smallest integer
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31 ## @var{n} such that
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32 ## @tex
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33 ## $2^n \ge |x|$.
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34 ## @end tex
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35 ## @ifnottex
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36 ## @code{2^@var{n} @geq{} abs (@var{x})}.
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37 ## @end ifnottex
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38 ## For input elements equal to zero, return zero.
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39 ##
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40 ## @seealso{pow2, log2}
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41 ## @end deftypefn
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42
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43 function n = nextpow2 (x)
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44
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45 if (nargin < 1)
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46 print_usage ();
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47 endif
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48
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49 if (! isnumeric (x))
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50 error ("nextpow2: X must be numeric");
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51 elseif (! isreal (x))
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52 error ("nextpow2: X must be real");
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53 endif
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54
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55 [f, n] = log2 (abs (x));
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56 n(f == 0.5)--;
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57
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58 if (isfloat (x))
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59 idx_nan = isnan (x);
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60 n(idx_nan) = x(idx_nan);
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61 n(isinf (x)) = Inf;
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62 else
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63 n = cast (n, class (x));
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64 if (intmax (x) > flintmax ())
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65 n((2 .^ n) < abs (x))++;
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66 endif
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67 endif
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68
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69 endfunction
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71
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72 %!assert (nextpow2 (16), 4)
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73 %!assert (nextpow2 (17), 5)
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74 %!assert (nextpow2 (31), 5)
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75 %!assert (nextpow2 (-16), 4)
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76 %!assert (nextpow2 (-17), 5)
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77 %!assert (nextpow2 (-31), 5)
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78 %!assert (nextpow2 (1:17), [0 1 2 2 3 3 3 3 4 4 4 4 4 4 4 4 5])
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79 %!assert <*62947> (nextpow2 (0.5), -1)
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80 %!assert <*62947> (nextpow2 (0.6), 0)
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81 ## Special cases
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82 %!assert (nextpow2 (0), 0)
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83 %!assert (nextpow2 (1), 0)
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84 %!assert (nextpow2 (Inf), Inf)
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85 %!assert (nextpow2 (-Inf), Inf)
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86 %!assert (nextpow2 (NaN), NaN)
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87 %!assert (nextpow2 (NA), NA)
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88 %!assert (nextpow2 ([1, Inf, 3, -Inf, 9, NaN, NA]), ...
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89 %! [0, Inf, 2, Inf, 4, NaN, NA])
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90
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91 %!test
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92 %! p = (-1074:1023).';
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93 %! x = 2 .^ p;
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94 %! x = [x, x + eps(x)];
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95 %! x = [x, -x];
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96 %! n = nextpow2 (x);
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97 %! assert (n(:, 1), p);
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98 %! assert (n(:, 3), p);
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99 %! assert (n(:, 2), p + 1);
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100 %! assert (n(:, 4), p + 1);
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101
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102 %!assert (nextpow2 (realmax ()), 1024)
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103 %!assert (nextpow2 (-realmax ()), 1024)
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104
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105 %!test
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106 %! p = single (-149:127).';
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107 %! x = 2 .^ p;
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108 %! x = [x, x + eps(x)];
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109 %! x = [x, -x];
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110 %! n = nextpow2 (x);
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111 %! assert (n(:, 1), p);
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112 %! assert (n(:, 3), p);
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113 %! assert (n(:, 2), p + 1);
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114 %! assert (n(:, 4), p + 1);
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115
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116 %!assert (nextpow2 (realmax ('single')), single (128))
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117 %!assert (nextpow2 (-realmax ('single')), single (128))
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118
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119 %!test
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120 %! p = int32 (0:30).';
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121 %! x = 2 .^ p;
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122 %! x = [x, x + 1];
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123 %! x = [x, -x];
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124 %! n = nextpow2 (x);
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125 %! assert (n(:, 1), p);
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126 %! assert (n(:, 3), p);
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127 %! assert (n(:, 2), p + 1);
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128 %! assert (n(:, 4), p + 1);
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129
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130 %!assert (nextpow2 (int32 (0)), int32 (0))
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131 %!assert (nextpow2 (intmin ('int32')), int32 (31))
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132 %!assert (nextpow2 (intmax ('int32')), int32 (31))
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133
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134 %!assert (nextpow2 (uint32 (0)), uint32 (0))
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135 %!assert (nextpow2 (intmax ('uint32')), uint32 (32))
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136
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137 %!test
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138 %! p = int64 (0:62).';
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139 %! x = 2 .^ p;
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140 %! x = [x, x + 1];
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141 %! x = [x, -x];
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142 %! n = nextpow2 (x);
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143 %! assert (n(:, 1), p);
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144 %! assert (n(:, 3), p);
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145 %! assert (n(:, 2), p + 1);
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146 %! assert (n(:, 4), p + 1);
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147
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148 %!assert (nextpow2 (int64 (0)), int64 (0))
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149 %!assert (nextpow2 (intmin ('int64')), int64 (63))
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150 %!assert (nextpow2 (intmax ('int64')), int64 (63))
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151
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152 %!assert (nextpow2 (uint64 (0)), uint64 (0))
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153 %!assert (nextpow2 (intmax ('uint64')), uint64 (64))
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154
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155 ## Test input validation
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156 %!error <Invalid call> nextpow2 ()
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157 %!error <X must be numeric> nextpow2 ("t")
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158 %!error <X must be real> nextpow2 (1 + 2i)