Mercurial > octave
annotate doc/interpreter/numbers.txi @ 31069:43974344fe19 stable
doc: Expand documentation about type promotion and demotion (bug #62283)
| author | Arun Giridhar <arungiridhar@gmail.com> |
|---|---|
| date | Sat, 04 Jun 2022 17:13:38 -0400 |
| parents | 796f54d4ddbf |
| children | 2dee06f4635c |
| rev | line source |
|---|---|
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update Octave Project Developers copyright for the new year
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1 @c Copyright (C) 1996-2022 The Octave Project Developers |
| 7018 | 2 @c |
| 3 @c This file is part of Octave. | |
| 4 @c | |
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5 @c Octave is free software: you can redistribute it and/or modify it |
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6 @c under the terms of the GNU General Public License as published by |
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7 @c the Free Software Foundation, either version 3 of the License, or |
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8 @c (at your option) any later version. |
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9 @c |
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10 @c Octave is distributed in the hope that it will be useful, but |
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11 @c WITHOUT ANY WARRANTY; without even the implied warranty of |
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12 @c MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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13 @c GNU General Public License for more details. |
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14 @c |
| 7018 | 15 @c You should have received a copy of the GNU General Public License |
| 16 @c along with Octave; see the file COPYING. If not, see | |
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17 @c <https://www.gnu.org/licenses/>. |
| 3294 | 18 |
| 4167 | 19 @node Numeric Data Types |
| 3294 | 20 @chapter Numeric Data Types |
| 21 @cindex numeric constant | |
| 22 @cindex numeric value | |
| 23 | |
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24 A @dfn{numeric constant} may be a scalar, a vector, or a matrix, and it may |
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25 contain complex values. |
| 3294 | 26 |
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27 The simplest form of a numeric constant, a scalar, is a single number. Note |
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28 that by default numeric constants are represented within Octave by IEEE 754 |
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29 double precision (binary64) floating-point format (complex constants are |
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30 stored as pairs of binary64 values). It is, however, possible to represent |
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31 real integers as described in @ref{Integer Data Types}. |
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32 |
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33 If the numeric constant is a real integer, it can be defined in decimal, |
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34 hexadecimal, or binary notation. Hexadecimal notation starts with @samp{0x} or |
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35 @samp{0X}, binary notation starts with @samp{0b} or @samp{0B}, otherwise |
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36 decimal notation is assumed. As a consequence, @samp{0b} is not a hexadecimal |
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37 number, in fact, it is not a valid number at all. |
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38 |
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39 For better readability, digits may be partitioned by the underscore separator |
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40 @samp{_}, which is ignored by the Octave interpreter. Here are some examples |
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41 of real-valued integer constants, which all represent the same value and are |
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42 internally stored as binary64: |
| 3294 | 43 |
| 44 @example | |
| 45 @group | |
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46 42 # decimal notation |
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47 0x2A # hexadecimal notation |
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48 0b101010 # binary notation |
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49 0b10_1010 # underscore notation |
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50 round (42.1) # also binary64 |
| 3294 | 51 @end group |
| 52 @end example | |
| 53 | |
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54 In decimal notation, the numeric constant may be denoted as decimal fraction |
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55 or even in scientific (exponential) notation. Note that this is not possible |
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56 for hexadecimal or binary notation. Again, in the following example all |
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57 numeric constants represent the same value: |
| 3294 | 58 |
| 59 @example | |
| 60 @group | |
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61 .105 |
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62 1.05e-1 |
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63 .00105e+2 |
| 3294 | 64 @end group |
| 65 @end example | |
| 66 | |
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67 Unlike most programming languages, complex numeric constants are denoted as |
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68 the sum of real and imaginary parts. The imaginary part is denoted by a |
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69 real-valued numeric constant followed immediately by a complex value indicator |
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70 (@samp{i}, @samp{j}, @samp{I}, or @samp{J} which represents |
| 3294 | 71 @tex |
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72 $\sqrt{-1}$). |
| 3294 | 73 @end tex |
| 6620 | 74 @ifnottex |
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75 @code{sqrt (-1)}). |
| 6620 | 76 @end ifnottex |
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77 No spaces are allowed between the numeric constant and the complex value |
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78 indicator. Some examples of complex numeric constants that all represent the |
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79 same value: |
| 3294 | 80 |
| 81 @example | |
| 82 @group | |
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83 3 + 42i |
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84 3 + 42j |
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85 3 + 42I |
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86 3 + 42J |
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87 3.0 + 42.0i |
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88 3.0 + 0x2Ai |
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89 3.0 + 0b10_1010i |
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90 0.3e1 + 420e-1i |
| 3294 | 91 @end group |
| 92 @end example | |
| 93 | |
| 6549 | 94 @DOCSTRING(double) |
| 95 | |
| 96 @DOCSTRING(complex) | |
| 97 | |
| 3294 | 98 @menu |
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99 * Matrices:: |
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100 * Ranges:: |
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101 * Single Precision Data Types:: |
| 6549 | 102 * Integer Data Types:: |
| 6781 | 103 * Bit Manipulations:: |
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104 * Logical Values:: |
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105 * Promotion and Demotion of Data Types:: |
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106 * Predicates for Numeric Objects:: |
| 3294 | 107 @end menu |
| 108 | |
| 4167 | 109 @node Matrices |
| 3294 | 110 @section Matrices |
| 111 @cindex matrices | |
| 112 | |
| 113 @opindex [ | |
| 114 @opindex ] | |
| 115 @opindex ; | |
| 116 @opindex , | |
| 117 | |
| 118 It is easy to define a matrix of values in Octave. The size of the | |
| 119 matrix is determined automatically, so it is not necessary to explicitly | |
| 120 state the dimensions. The expression | |
| 121 | |
| 122 @example | |
| 123 a = [1, 2; 3, 4] | |
| 124 @end example | |
| 125 | |
| 126 @noindent | |
| 127 results in the matrix | |
| 128 @tex | |
| 129 $$ a = \left[ \matrix{ 1 & 2 \cr 3 & 4 } \right] $$ | |
| 130 @end tex | |
| 6620 | 131 @ifnottex |
| 3294 | 132 |
| 133 @example | |
| 134 @group | |
| 135 | |
| 136 / \ | |
| 137 | 1 2 | | |
| 138 a = | | | |
| 139 | 3 4 | | |
| 140 \ / | |
| 141 | |
| 142 @end group | |
| 143 @end example | |
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144 |
| 6620 | 145 @end ifnottex |
| 3294 | 146 |
| 147 Elements of a matrix may be arbitrary expressions, provided that the | |
| 148 dimensions all make sense when combining the various pieces. For | |
| 149 example, given the above matrix, the expression | |
| 150 | |
| 151 @example | |
| 152 [ a, a ] | |
| 153 @end example | |
| 154 | |
| 155 @noindent | |
| 156 produces the matrix | |
| 157 | |
| 158 @example | |
| 159 @group | |
| 160 ans = | |
| 161 | |
| 162 1 2 1 2 | |
| 163 3 4 3 4 | |
| 164 @end group | |
| 165 @end example | |
| 166 | |
| 167 @noindent | |
| 168 but the expression | |
| 169 | |
| 170 @example | |
| 171 [ a, 1 ] | |
| 172 @end example | |
| 173 | |
| 174 @noindent | |
| 175 produces the error | |
| 176 | |
| 177 @example | |
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178 error: number of rows must match (1 != 2) near line 13, column 6 |
| 3294 | 179 @end example |
| 180 | |
| 181 @noindent | |
| 182 (assuming that this expression was entered as the first thing on line | |
| 183 13, of course). | |
| 184 | |
| 185 Inside the square brackets that delimit a matrix expression, Octave | |
| 186 looks at the surrounding context to determine whether spaces and newline | |
| 187 characters should be converted into element and row separators, or | |
| 4476 | 188 simply ignored, so an expression like |
| 3294 | 189 |
| 190 @example | |
| 191 @group | |
| 192 a = [ 1 2 | |
| 193 3 4 ] | |
| 194 @end group | |
| 195 @end example | |
| 196 | |
| 197 @noindent | |
| 198 will work. However, some possible sources of confusion remain. For | |
| 199 example, in the expression | |
| 200 | |
| 201 @example | |
| 202 [ 1 - 1 ] | |
| 203 @end example | |
| 204 | |
| 205 @noindent | |
| 206 the @samp{-} is treated as a binary operator and the result is the | |
| 207 scalar 0, but in the expression | |
| 208 | |
| 209 @example | |
| 210 [ 1 -1 ] | |
| 211 @end example | |
| 212 | |
| 213 @noindent | |
| 214 the @samp{-} is treated as a unary operator and the result is the | |
| 4476 | 215 vector @code{[ 1, -1 ]}. Similarly, the expression |
| 216 | |
| 217 @example | |
| 218 [ sin (pi) ] | |
| 219 @end example | |
| 220 | |
| 221 @noindent | |
| 222 will be parsed as | |
| 223 | |
| 224 @example | |
| 225 [ sin, (pi) ] | |
| 226 @end example | |
| 3294 | 227 |
| 4476 | 228 @noindent |
| 229 and will result in an error since the @code{sin} function will be | |
| 230 called with no arguments. To get around this, you must omit the space | |
| 231 between @code{sin} and the opening parenthesis, or enclose the | |
| 232 expression in a set of parentheses: | |
| 233 | |
| 234 @example | |
| 235 [ (sin (pi)) ] | |
| 236 @end example | |
| 237 | |
| 238 Whitespace surrounding the single quote character (@samp{'}, used as a | |
| 239 transpose operator and for delimiting character strings) can also cause | |
| 240 confusion. Given @code{a = 1}, the expression | |
| 3294 | 241 |
| 242 @example | |
| 243 [ 1 a' ] | |
| 244 @end example | |
| 245 | |
| 246 @noindent | |
| 4476 | 247 results in the single quote character being treated as a |
| 3294 | 248 transpose operator and the result is the vector @code{[ 1, 1 ]}, but the |
| 249 expression | |
| 250 | |
| 251 @example | |
| 252 [ 1 a ' ] | |
| 253 @end example | |
| 254 | |
| 255 @noindent | |
| 256 produces the error message | |
| 257 | |
| 258 @example | |
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259 @group |
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260 parse error: |
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261 |
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262 syntax error |
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263 |
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264 >>> [ 1 a ' ] |
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265 ^ |
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266 @end group |
| 3294 | 267 @end example |
| 268 | |
| 269 @noindent | |
| 6620 | 270 because not doing so would cause trouble when parsing the valid expression |
| 3294 | 271 |
| 272 @example | |
| 273 [ a 'foo' ] | |
| 274 @end example | |
| 275 | |
| 276 For clarity, it is probably best to always use commas and semicolons to | |
| 4476 | 277 separate matrix elements and rows. |
| 3294 | 278 |
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279 The maximum number of elements in a matrix is fixed when Octave is compiled. |
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280 The allowable number can be queried with the function @code{sizemax}. Note |
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281 that other factors, such as the amount of memory available on your machine, |
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282 may limit the maximum size of matrices to something smaller. |
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283 |
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284 @DOCSTRING(sizemax) |
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285 |
| 3294 | 286 When you type a matrix or the name of a variable whose value is a |
| 287 matrix, Octave responds by printing the matrix in with neatly aligned | |
| 288 rows and columns. If the rows of the matrix are too large to fit on the | |
| 289 screen, Octave splits the matrix and displays a header before each | |
| 290 section to indicate which columns are being displayed. You can use the | |
| 291 following variables to control the format of the output. | |
| 292 | |
| 3321 | 293 @DOCSTRING(output_precision) |
| 3294 | 294 |
| 295 It is possible to achieve a wide range of output styles by using | |
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296 different values of @code{output_precision}. Reasonable combinations can be |
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297 set using the @code{format} function. @xref{Basic Input and Output}. |
| 3294 | 298 |
| 3321 | 299 @DOCSTRING(split_long_rows) |
| 3294 | 300 |
| 301 Octave automatically switches to scientific notation when values become | |
| 302 very large or very small. This guarantees that you will see several | |
| 303 significant figures for every value in a matrix. If you would prefer to | |
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304 see all values in a matrix printed in a fixed point format, you can use |
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305 the function @code{fixed_point_format}. But doing so is not |
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306 recommended, because it can produce output that can easily be |
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307 misinterpreted. |
| 3294 | 308 |
| 3321 | 309 @DOCSTRING(fixed_point_format) |
| 3294 | 310 |
| 311 @menu | |
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312 * Empty Matrices:: |
| 3294 | 313 @end menu |
| 314 | |
| 4167 | 315 @node Empty Matrices |
| 3294 | 316 @subsection Empty Matrices |
| 317 | |
| 318 A matrix may have one or both dimensions zero, and operations on empty | |
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319 matrices are handled as described by @nospell{Carl de Boor} in |
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320 @cite{An Empty Exercise}, SIGNUM, Volume 25, pages 2--6, 1990 and |
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321 @nospell{C. N. Nett and W. M. Haddad}, in |
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322 @cite{A System-Theoretic Appropriate Realization of the Empty Matrix Concept}, |
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323 IEEE Transactions on Automatic Control, Volume 38, Number 5, May 1993. |
| 3294 | 324 @tex |
| 325 Briefly, given a scalar $s$, an $m\times n$ matrix $M_{m\times n}$, | |
| 326 and an $m\times n$ empty matrix $[\,]_{m\times n}$ (with either one or | |
| 327 both dimensions equal to zero), the following are true: | |
| 328 $$ | |
| 329 \eqalign{% | |
| 330 s \cdot [\,]_{m\times n} = [\,]_{m\times n} \cdot s &= [\,]_{m\times n}\cr | |
| 331 [\,]_{m\times n} + [\,]_{m\times n} &= [\,]_{m\times n}\cr | |
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332 [\,]_{0\times m} \cdot M_{m\times n} &= [\,]_{0\times n}\cr |
| 3294 | 333 M_{m\times n} \cdot [\,]_{n\times 0} &= [\,]_{m\times 0}\cr |
| 334 [\,]_{m\times 0} \cdot [\,]_{0\times n} &= 0_{m\times n}} | |
| 335 $$ | |
| 336 @end tex | |
| 6620 | 337 @ifnottex |
| 3294 | 338 Briefly, given a scalar @var{s}, an @var{m} by |
| 339 @var{n} matrix @code{M(mxn)}, and an @var{m} by @var{n} empty matrix | |
| 340 @code{[](mxn)} (with either one or both dimensions equal to zero), the | |
| 341 following are true: | |
| 342 | |
| 343 @example | |
| 344 @group | |
| 345 s * [](mxn) = [](mxn) * s = [](mxn) | |
| 346 | |
| 347 [](mxn) + [](mxn) = [](mxn) | |
| 348 | |
| 349 [](0xm) * M(mxn) = [](0xn) | |
| 350 | |
| 351 M(mxn) * [](nx0) = [](mx0) | |
| 352 | |
| 353 [](mx0) * [](0xn) = 0(mxn) | |
| 354 @end group | |
| 355 @end example | |
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356 |
| 6620 | 357 @end ifnottex |
| 3294 | 358 |
| 359 By default, dimensions of the empty matrix are printed along with the | |
| 360 empty matrix symbol, @samp{[]}. The built-in variable | |
| 361 @code{print_empty_dimensions} controls this behavior. | |
| 362 | |
| 3321 | 363 @DOCSTRING(print_empty_dimensions) |
| 3294 | 364 |
| 365 Empty matrices may also be used in assignment statements as a convenient | |
| 366 way to delete rows or columns of matrices. | |
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367 @xref{Assignment Ops,,Assignment Expressions}. |
| 3294 | 368 |
| 369 When Octave parses a matrix expression, it examines the elements of the | |
| 370 list to determine whether they are all constants. If they are, it | |
| 371 replaces the list with a single matrix constant. | |
| 372 | |
| 4167 | 373 @node Ranges |
| 3294 | 374 @section Ranges |
| 375 @cindex range expressions | |
| 376 @cindex expression, range | |
| 377 | |
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378 @opindex :, range expressions |
| 3294 | 379 |
| 380 A @dfn{range} is a convenient way to write a row vector with evenly | |
| 381 spaced elements. A range expression is defined by the value of the first | |
| 382 element in the range, an optional value for the increment between | |
| 383 elements, and a maximum value which the elements of the range will not | |
| 384 exceed. The base, increment, and limit are separated by colons (the | |
| 385 @samp{:} character) and may contain any arithmetic expressions and | |
| 386 function calls. If the increment is omitted, it is assumed to be 1. | |
| 387 For example, the range | |
| 388 | |
| 389 @example | |
| 390 1 : 5 | |
| 391 @end example | |
| 392 | |
| 393 @noindent | |
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394 defines the set of values @code{[ 1, 2, 3, 4, 5 ]}, and the range |
| 3294 | 395 |
| 396 @example | |
| 397 1 : 3 : 5 | |
| 398 @end example | |
| 399 | |
| 400 @noindent | |
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401 defines the set of values @code{[ 1, 4 ]}. |
| 3294 | 402 |
| 403 Although a range constant specifies a row vector, Octave does @emph{not} | |
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404 normally convert range constants to vectors unless it is necessary to do so. |
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405 This allows you to write a constant like @code{1 : 10000} without using |
| 3294 | 406 80,000 bytes of storage on a typical 32-bit workstation. |
| 407 | |
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408 A common example of when it does become necessary to convert ranges into |
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409 vectors occurs when they appear within a vector (i.e., inside square |
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410 brackets). For instance, whereas |
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411 |
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412 @example |
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413 x = 0 : 0.1 : 1; |
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414 @end example |
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415 |
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416 @noindent |
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417 defines @var{x} to be a variable of type @code{range} and occupies 24 |
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418 bytes of memory, the expression |
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419 |
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420 @example |
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421 y = [ 0 : 0.1 : 1]; |
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422 @end example |
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423 |
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424 @noindent |
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425 defines @var{y} to be of type @code{matrix} and occupies 88 bytes of |
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426 memory. |
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427 |
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428 This space saving optimization may be disabled using the function |
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429 @dfn{optimize_range}. |
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430 |
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431 @DOCSTRING(optimize_range) |
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432 |
| 3294 | 433 Note that the upper (or lower, if the increment is negative) bound on |
| 434 the range is not always included in the set of values, and that ranges | |
| 435 defined by floating point values can produce surprising results because | |
| 436 Octave uses floating point arithmetic to compute the values in the | |
| 437 range. If it is important to include the endpoints of a range and the | |
| 438 number of elements is known, you should use the @code{linspace} function | |
| 439 instead (@pxref{Special Utility Matrices}). | |
| 440 | |
| 9158 | 441 When adding a scalar to a range, subtracting a scalar from it (or subtracting a |
| 442 range from a scalar) and multiplying by scalar, Octave will attempt to avoid | |
| 443 unpacking the range and keep the result as a range, too, if it can determine | |
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444 that it is safe to do so. For instance, doing |
| 9158 | 445 |
| 446 @example | |
| 447 a = 2*(1:1e7) - 1; | |
| 448 @end example | |
| 449 | |
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450 @noindent |
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451 will produce the same result as @code{1:2:2e7-1}, but without ever forming a |
| 9158 | 452 vector with ten million elements. |
| 453 | |
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454 Using zero as an increment in the colon notation, as @code{1:0:1} is not |
| 9158 | 455 allowed, because a division by zero would occur in determining the number of |
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456 range elements. However, ranges with zero increment (i.e., all elements equal) |
| 9158 | 457 are useful, especially in indexing, and Octave allows them to be constructed |
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458 using the built-in function @code{ones}. Note that because a range must be a |
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459 row vector, @code{ones (1, 10)} produces a range, while @code{ones (10, 1)} |
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460 does not. |
| 9158 | 461 |
| 3294 | 462 When Octave parses a range expression, it examines the elements of the |
| 463 expression to determine whether they are all constants. If they are, it | |
| 464 replaces the range expression with a single range constant. | |
| 465 | |
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466 @node Single Precision Data Types |
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467 @section Single Precision Data Types |
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468 |
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469 Octave includes support for single precision data types, and most of the |
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470 functions in Octave accept single precision values and return single |
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471 precision answers. A single precision variable is created with the |
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472 @code{single} function. |
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473 |
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474 @DOCSTRING(single) |
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475 |
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476 for example: |
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477 |
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478 @example |
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479 @group |
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480 sngl = single (rand (2, 2)) |
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481 @result{} sngl = |
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482 0.37569 0.92982 |
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483 0.11962 0.50876 |
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484 class (sngl) |
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485 @result{} single |
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486 @end group |
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487 @end example |
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488 |
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489 Many functions can also return single precision values directly. For |
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490 example |
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491 |
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492 @example |
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493 @group |
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494 ones (2, 2, "single") |
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495 zeros (2, 2, "single") |
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496 eye (2, 2, "single") |
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497 rand (2, 2, "single") |
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498 NaN (2, 2, "single") |
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499 NA (2, 2, "single") |
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500 Inf (2, 2, "single") |
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501 @end group |
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502 @end example |
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503 |
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504 @noindent |
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505 will all return single precision matrices. |
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506 |
| 6549 | 507 @node Integer Data Types |
| 508 @section Integer Data Types | |
| 509 | |
| 6620 | 510 Octave supports integer matrices as an alternative to using double |
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511 precision. It is possible to use both signed and unsigned integers |
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512 represented by 8, 16, 32, or 64 bits. It should be noted that most |
| 6620 | 513 computations require floating point data, meaning that integers will |
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514 often change type when involved in numeric computations. For this |
| 6620 | 515 reason integers are most often used to store data, and not for |
| 516 calculations. | |
| 517 | |
| 518 In general most integer matrices are created by casting | |
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519 existing matrices to integers. The following example shows how to cast |
| 6620 | 520 a matrix into 32 bit integers. |
| 521 | |
| 522 @example | |
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523 @group |
| 6620 | 524 float = rand (2, 2) |
| 525 @result{} float = 0.37569 0.92982 | |
| 526 0.11962 0.50876 | |
| 527 integer = int32 (float) | |
| 528 @result{} integer = 0 1 | |
| 529 0 1 | |
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530 @end group |
| 6620 | 531 @end example |
| 532 | |
| 533 @noindent | |
| 534 As can be seen, floating point values are rounded to the nearest integer | |
| 535 when converted. | |
| 536 | |
| 6549 | 537 @DOCSTRING(isinteger) |
| 538 | |
| 539 @DOCSTRING(int8) | |
| 540 | |
| 541 @DOCSTRING(uint8) | |
| 542 | |
| 543 @DOCSTRING(int16) | |
| 544 | |
| 545 @DOCSTRING(uint16) | |
| 546 | |
| 547 @DOCSTRING(int32) | |
| 548 | |
| 549 @DOCSTRING(uint32) | |
| 550 | |
| 551 @DOCSTRING(int64) | |
| 552 | |
| 553 @DOCSTRING(uint64) | |
| 554 | |
| 555 @DOCSTRING(intmax) | |
| 556 | |
| 557 @DOCSTRING(intmin) | |
| 558 | |
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559 @DOCSTRING(flintmax) |
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560 |
| 6624 | 561 @menu |
| 562 * Integer Arithmetic:: | |
| 563 @end menu | |
| 564 | |
| 6620 | 565 @node Integer Arithmetic |
| 566 @subsection Integer Arithmetic | |
| 567 | |
| 568 While many numerical computations can't be carried out in integers, | |
| 569 Octave does support basic operations like addition and multiplication | |
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570 on integers. The operators @code{+}, @code{-}, @code{.*}, and @code{./} |
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571 work on integers of the same type. So, it is possible to add two 32 bit |
| 6620 | 572 integers, but not to add a 32 bit integer and a 16 bit integer. |
| 573 | |
| 574 When doing integer arithmetic one should consider the possibility of | |
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575 underflow and overflow. This happens when the result of the computation |
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576 can't be represented using the chosen integer type. As an example it is |
| 6620 | 577 not possible to represent the result of @math{10 - 20} when using |
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578 unsigned integers. Octave makes sure that the result of integer |
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579 computations is the integer that is closest to the true result. So, the |
| 6620 | 580 result of @math{10 - 20} when using unsigned integers is zero. |
| 581 | |
| 582 When doing integer division Octave will round the result to the nearest | |
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583 integer. This is different from most programming languages, where the |
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584 result is often floored to the nearest integer. So, the result of |
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585 @code{int32 (5) ./ int32 (8)} is @code{1}. |
| 6620 | 586 |
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587 @DOCSTRING(idivide) |
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588 |
| 6781 | 589 @node Bit Manipulations |
| 590 @section Bit Manipulations | |
| 591 | |
| 592 Octave provides a number of functions for the manipulation of numeric | |
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593 values on a bit by bit basis. The basic functions to set and obtain the |
| 6781 | 594 values of individual bits are @code{bitset} and @code{bitget}. |
| 595 | |
| 596 @DOCSTRING(bitset) | |
| 597 | |
| 598 @DOCSTRING(bitget) | |
| 599 | |
| 600 The arguments to all of Octave's bitwise operations can be scalar or | |
| 601 arrays, except for @code{bitcmp}, whose @var{k} argument must a | |
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602 scalar. In the case where more than one argument is an array, then all |
| 6781 | 603 arguments must have the same shape, and the bitwise operator is applied |
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604 to each of the elements of the argument individually. If at least one |
| 6781 | 605 argument is a scalar and one an array, then the scalar argument is |
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606 duplicated. Therefore |
| 6781 | 607 |
| 608 @example | |
| 609 bitget (100, 8:-1:1) | |
| 610 @end example | |
| 611 | |
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612 @noindent |
| 6781 | 613 is the same as |
| 614 | |
| 615 @example | |
| 616 bitget (100 * ones (1, 8), 8:-1:1) | |
| 617 @end example | |
| 618 | |
| 619 It should be noted that all values passed to the bit manipulation | |
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620 functions of Octave are treated as integers. Therefore, even though the |
| 6781 | 621 example for @code{bitset} above passes the floating point value |
| 622 @code{10}, it is treated as the bits @code{[1, 0, 1, 0]} rather than the | |
| 623 bits of the native floating point format representation of @code{10}. | |
| 624 | |
| 8828 | 625 As the maximum value that can be represented by a number is important |
| 6781 | 626 for bit manipulation, particularly when forming masks, Octave supplies |
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627 two utility functions: @code{flintmax} for floating point integers, and |
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628 @code{intmax} for integer objects (@code{uint8}, @code{int64}, etc.). |
| 6781 | 629 |
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630 Octave also includes the basic bitwise 'and', 'or', and 'exclusive or' |
| 6781 | 631 operators. |
| 632 | |
| 633 @DOCSTRING(bitand) | |
| 634 | |
| 635 @DOCSTRING(bitor) | |
| 636 | |
| 637 @DOCSTRING(bitxor) | |
| 638 | |
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639 The bitwise 'not' operator is a unary operator that performs a logical |
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640 negation of each of the bits of the value. For this to make sense, the |
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641 mask against which the value is negated must be defined. Octave's |
| 6781 | 642 bitwise 'not' operator is @code{bitcmp}. |
| 643 | |
| 644 @DOCSTRING(bitcmp) | |
| 645 | |
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646 Octave also includes the ability to left-shift and right-shift values bitwise. |
| 6781 | 647 |
| 648 @DOCSTRING(bitshift) | |
| 649 | |
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650 Bits that are shifted out of either end of the value are lost. Octave |
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651 also uses arithmetic shifts, where the sign bit of the value is kept |
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652 during a right shift. For example: |
| 6781 | 653 |
| 654 @example | |
| 655 @group | |
| 656 bitshift (-10, -1) | |
| 657 @result{} -5 | |
| 658 bitshift (int8 (-1), -1) | |
| 659 @result{} -1 | |
| 660 @end group | |
| 661 @end example | |
| 662 | |
| 663 Note that @code{bitshift (int8 (-1), -1)} is @code{-1} since the bit | |
| 664 representation of @code{-1} in the @code{int8} data type is @code{[1, 1, | |
| 665 1, 1, 1, 1, 1, 1]}. | |
| 666 | |
| 4167 | 667 @node Logical Values |
| 3428 | 668 @section Logical Values |
| 669 | |
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670 Octave has built-in support for logical values, i.e., variables that |
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671 are either @code{true} or @code{false}. When comparing two variables, |
| 6620 | 672 the result will be a logical value whose value depends on whether or |
| 673 not the comparison is true. | |
| 674 | |
| 675 The basic logical operations are @code{&}, @code{|}, and @code{!}, | |
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676 which correspond to ``Logical And'', ``Logical Or'', and ``Logical |
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677 Negation''. These operations all follow the usual rules of logic. |
| 6620 | 678 |
| 679 It is also possible to use logical values as part of standard numerical | |
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680 calculations. In this case @code{true} is converted to @code{1}, and |
| 6620 | 681 @code{false} to 0, both represented using double precision floating |
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682 point numbers. So, the result of @code{true*22 - false/6} is @code{22}. |
| 6620 | 683 |
| 684 Logical values can also be used to index matrices and cell arrays. | |
| 685 When indexing with a logical array the result will be a vector containing | |
| 686 the values corresponding to @code{true} parts of the logical array. | |
| 687 The following example illustrates this. | |
| 688 | |
| 689 @example | |
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690 @group |
| 6620 | 691 data = [ 1, 2; 3, 4 ]; |
| 692 idx = (data <= 2); | |
| 693 data(idx) | |
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694 @result{} ans = [ 1; 2 ] |
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695 @end group |
| 6620 | 696 @end example |
| 697 | |
| 698 @noindent | |
| 699 Instead of creating the @code{idx} array it is possible to replace | |
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700 @code{data(idx)} with @w{@code{data( data <= 2 )}} in the above code. |
| 6620 | 701 |
| 8828 | 702 Logical values can also be constructed by |
| 6620 | 703 casting numeric objects to logical values, or by using the @code{true} |
| 704 or @code{false} functions. | |
| 705 | |
| 6549 | 706 @DOCSTRING(logical) |
| 707 | |
| 3428 | 708 @DOCSTRING(true) |
| 709 | |
| 710 @DOCSTRING(false) | |
| 711 | |
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712 @node Promotion and Demotion of Data Types |
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713 @section Promotion and Demotion of Data Types |
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714 |
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715 Many operators and functions can work with mixed data types. For example, |
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716 |
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717 @example |
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718 @group |
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719 uint8 (1) + 1 |
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720 @result{} 2 |
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721 @end group |
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722 @end example |
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723 |
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724 @noindent |
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725 where the above operator works with an 8-bit integer and a double precision |
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726 value and returns an 8-bit integer value. Note that the type is demoted |
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727 to an 8-bit integer, rather than promoted to a double precision value as |
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728 might be expected. The reason is that if Octave promoted values in |
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729 expressions like the above with all numerical constants would need to be |
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730 explicitly cast to the appropriate data type like |
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731 |
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732 @example |
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733 @group |
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734 uint8 (1) + uint8 (1) |
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735 @result{} 2 |
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736 @end group |
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737 @end example |
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738 |
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739 @noindent |
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740 which becomes difficult for the user to apply uniformly and might allow |
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741 hard to find bugs to be introduced. The same applies to single precision |
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742 values where a mixed operation such as |
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743 |
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744 @example |
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745 @group |
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746 single (1) + 1 |
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747 @result{} 2 |
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748 @end group |
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749 @end example |
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750 |
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751 @noindent |
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752 returns a single precision value. The mixed operations that are valid |
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753 and their returned data types are |
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754 |
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755 @multitable @columnfractions .2 .3 .3 .2 |
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756 @headitem @tab Mixed Operation @tab Result @tab |
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757 @item @tab double OP single @tab single @tab |
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758 @item @tab double OP integer @tab integer @tab |
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759 @item @tab double OP char @tab double @tab |
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760 @item @tab double OP logical @tab double @tab |
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761 @item @tab single OP integer @tab integer @tab |
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762 @item @tab single OP char @tab single @tab |
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763 @item @tab single OP logical @tab single @tab |
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764 @end multitable |
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765 |
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766 The same logic applies to functions with mixed arguments such as |
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767 |
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768 @example |
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769 @group |
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770 min (single (1), 0) |
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771 @result{} 0 |
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772 @end group |
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773 @end example |
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774 |
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775 @noindent |
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776 where the returned value is single precision. |
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777 |
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778 Many functions and operators will also promote integer or logical types to |
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779 double, or single to double, especially if they take only one argument. |
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780 |
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781 @example |
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782 @group |
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783 a = det (int8 ([1 2; 3 4])) |
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784 @result{} a = -2 |
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785 class (a) |
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786 @result{} double |
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787 @end group |
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788 @end example |
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789 |
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790 But there are also exceptions for promoting to double, especially if the |
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791 function or operator in question can take multiple arguments. |
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|
792 |
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793 @example |
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794 @group |
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795 a = eig (int8 ([1 2; 3 4])) |
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796 @result{} error: eig: wrong type argument 'int8 matrix' |
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797 @end group |
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798 @end example |
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799 |
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800 When the two operands are both integers but of different widths, then the |
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801 behavior depends on the operator or the function in question. For some |
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802 operators and functions, narrow-bitwidth operands are promoted to a wider |
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803 bitwidth: |
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804 |
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805 @example |
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806 @group |
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807 a = min (int8 (100), int16 (200)) |
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808 @result{} 100 |
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809 class (a) |
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810 @result{} int16 |
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811 @end group |
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812 @end example |
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813 |
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814 However, not all functions or operators will accept integer operands of |
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815 differing types: |
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816 |
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817 @example |
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818 @group |
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819 int8 (100) + int16 (200) |
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820 @result{} error: binary operator '+' not implemented |
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821 for 'int8 scalar' by 'int16 scalar' operations |
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822 @end group |
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823 @end example |
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824 |
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825 Further, in most cases, both operands need to be signed or both need to be |
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826 unsigned. Mixing signed and unsigned usually causes an error, even if they |
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827 are of the same bitwidth. |
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828 |
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829 @example |
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830 @group |
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831 min (int8 (100), uint16 (200)) |
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832 @result{} error: min: cannot compute min (int8 scalar, uint16 scalar) |
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833 @end group |
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834 @end example |
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835 |
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836 In the case of mixed type indexed assignments, the type is not |
|
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837 changed. For example, |
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838 |
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839 @example |
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840 @group |
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841 x = ones (2, 2); |
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842 x(1, 1) = single (2) |
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843 @result{} x = 2 1 |
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844 1 1 |
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845 @end group |
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846 @end example |
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847 |
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848 @noindent |
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849 where @code{x} remains of the double precision type. |
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850 |
| 4167 | 851 @node Predicates for Numeric Objects |
| 3294 | 852 @section Predicates for Numeric Objects |
| 853 | |
| 6620 | 854 Since the type of a variable may change during the execution of a |
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855 program, it can be necessary to do type checking at run-time. Doing this |
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856 also allows you to change the behavior of a function depending on the |
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857 type of the input. As an example, this naive implementation of @code{abs} |
| 7001 | 858 returns the absolute value of the input if it is a real number, and the |
| 6620 | 859 length of the input if it is a complex number. |
| 860 | |
| 861 @example | |
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9158
diff
changeset
|
862 @group |
| 6620 | 863 function a = abs (x) |
| 864 if (isreal (x)) | |
| 865 a = sign (x) .* x; | |
| 866 elseif (iscomplex (x)) | |
| 867 a = sqrt (real(x).^2 + imag(x).^2); | |
| 868 endif | |
| 869 endfunction | |
|
9209
923c7cb7f13f
Simplify TeXinfo files by eliminating redundant @iftex followed by @tex construction.
Rik <rdrider0-list@yahoo.com>
parents:
9158
diff
changeset
|
870 @end group |
| 6620 | 871 @end example |
| 872 | |
| 873 The following functions are available for determining the type of a | |
| 874 variable. | |
| 875 | |
| 3428 | 876 @DOCSTRING(isnumeric) |
| 877 | |
|
18900
49961d67e4b9
Add new matrix functions (isdiag, isbanded, istril, istriu) (bug #42688).
Massimiliano Fasi <massimiliano.fasi@gmail.com>
parents:
17744
diff
changeset
|
878 @DOCSTRING(islogical) |
|
49961d67e4b9
Add new matrix functions (isdiag, isbanded, istril, istriu) (bug #42688).
Massimiliano Fasi <massimiliano.fasi@gmail.com>
parents:
17744
diff
changeset
|
879 |
|
12581
c8be316f9543
Group commonly used isXXX functions together in documentation.
Rik <octave@nomad.inbox5.com>
parents:
12488
diff
changeset
|
880 @DOCSTRING(isfloat) |
| 3428 | 881 |
|
12581
c8be316f9543
Group commonly used isXXX functions together in documentation.
Rik <octave@nomad.inbox5.com>
parents:
12488
diff
changeset
|
882 @DOCSTRING(isreal) |
|
7638
2df457529cfa
implement expm1 and log1p functions
Jaroslav Hajek <highegg@gmail.com>
parents:
7018
diff
changeset
|
883 |
| 4029 | 884 @DOCSTRING(iscomplex) |
| 3428 | 885 |
| 4029 | 886 @DOCSTRING(ismatrix) |
| 3294 | 887 |
| 4029 | 888 @DOCSTRING(isvector) |
| 3294 | 889 |
|
12488
bea828c03969
Add new isrow, iscolumn functions.
Rik <octave@nomad.inbox5.com>
parents:
12190
diff
changeset
|
890 @DOCSTRING(isrow) |
|
bea828c03969
Add new isrow, iscolumn functions.
Rik <octave@nomad.inbox5.com>
parents:
12190
diff
changeset
|
891 |
|
bea828c03969
Add new isrow, iscolumn functions.
Rik <octave@nomad.inbox5.com>
parents:
12190
diff
changeset
|
892 @DOCSTRING(iscolumn) |
|
bea828c03969
Add new isrow, iscolumn functions.
Rik <octave@nomad.inbox5.com>
parents:
12190
diff
changeset
|
893 |
| 4029 | 894 @DOCSTRING(isscalar) |
| 3294 | 895 |
| 4029 | 896 @DOCSTRING(issquare) |
| 3294 | 897 |
| 4029 | 898 @DOCSTRING(issymmetric) |
| 3428 | 899 |
|
11431
0d9640d755b1
Improve docstrings for all isXXX functions.
Rik <octave@nomad.inbox5.com>
parents:
11403
diff
changeset
|
900 @DOCSTRING(ishermitian) |
|
0d9640d755b1
Improve docstrings for all isXXX functions.
Rik <octave@nomad.inbox5.com>
parents:
11403
diff
changeset
|
901 |
| 6550 | 902 @DOCSTRING(isdefinite) |
| 903 | |
|
18900
49961d67e4b9
Add new matrix functions (isdiag, isbanded, istril, istriu) (bug #42688).
Massimiliano Fasi <massimiliano.fasi@gmail.com>
parents:
17744
diff
changeset
|
904 @DOCSTRING(isbanded) |
|
49961d67e4b9
Add new matrix functions (isdiag, isbanded, istril, istriu) (bug #42688).
Massimiliano Fasi <massimiliano.fasi@gmail.com>
parents:
17744
diff
changeset
|
905 |
|
49961d67e4b9
Add new matrix functions (isdiag, isbanded, istril, istriu) (bug #42688).
Massimiliano Fasi <massimiliano.fasi@gmail.com>
parents:
17744
diff
changeset
|
906 @DOCSTRING(isdiag) |
|
49961d67e4b9
Add new matrix functions (isdiag, isbanded, istril, istriu) (bug #42688).
Massimiliano Fasi <massimiliano.fasi@gmail.com>
parents:
17744
diff
changeset
|
907 |
|
49961d67e4b9
Add new matrix functions (isdiag, isbanded, istril, istriu) (bug #42688).
Massimiliano Fasi <massimiliano.fasi@gmail.com>
parents:
17744
diff
changeset
|
908 @DOCSTRING(istril) |
|
49961d67e4b9
Add new matrix functions (isdiag, isbanded, istril, istriu) (bug #42688).
Massimiliano Fasi <massimiliano.fasi@gmail.com>
parents:
17744
diff
changeset
|
909 |
|
49961d67e4b9
Add new matrix functions (isdiag, isbanded, istril, istriu) (bug #42688).
Massimiliano Fasi <massimiliano.fasi@gmail.com>
parents:
17744
diff
changeset
|
910 @DOCSTRING(istriu) |
| 6550 | 911 |
| 912 @DOCSTRING(isprime) | |
|
13017
aaf6fbb2512f
doc: Add cross references to "status of variables" in sections for predicates
Jordi Gutiérrez Hermoso <jordigh@gmail.com>
parents:
12581
diff
changeset
|
913 |
|
aaf6fbb2512f
doc: Add cross references to "status of variables" in sections for predicates
Jordi Gutiérrez Hermoso <jordigh@gmail.com>
parents:
12581
diff
changeset
|
914 If instead of knowing properties of variables, you wish to know which |
|
aaf6fbb2512f
doc: Add cross references to "status of variables" in sections for predicates
Jordi Gutiérrez Hermoso <jordigh@gmail.com>
parents:
12581
diff
changeset
|
915 variables are defined and to gather other information about the |
|
17097
e7a059a9a644
doc: Use XREF as anchor prefix in documentation for clearer results in Info viewer.
Rik <rik@octave.org>
parents:
16939
diff
changeset
|
916 workspace itself, @pxref{Status of Variables}. |