Mercurial > octave
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> |
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date | Tue, 12 Mar 2024 14:27:13 -0700 |
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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/>. |
3426 | 7 ## |
3922 | 8 ## This file is part of Octave. |
9 ## | |
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10 ## Octave is free software: you can redistribute it and/or modify it |
3922 | 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. |
3426 | 14 ## |
3922 | 15 ## Octave is distributed in the hope that it will be useful, but |
2539 | 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. |
3426 | 19 ## |
2539 | 20 ## You should have received a copy of the GNU General Public License |
7016 | 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 ######################################################################## |
2539 | 25 |
3321 | 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 |
3321 | 32 ## @tex |
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33 ## $2^n \ge |x|$. |
3321 | 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. |
3426 | 39 ## |
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40 ## @seealso{pow2, log2} |
3321 | 41 ## @end deftypefn |
2539 | 42 |
43 function n = nextpow2 (x) | |
3426 | 44 |
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45 if (nargin < 1) |
6046 | 46 print_usage (); |
2539 | 47 endif |
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"); |
2816 | 53 endif |
3426 | 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 |
3426 | 68 |
2539 | 69 endfunction |
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70 |
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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) |