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<ol class="chapter"><li class="chapter-item expanded "><a href="The-Z-Shell-Manual.html"><strong aria-hidden="true">1.</strong> The Z Shell Manual</a></li><li class="chapter-item expanded "><a href="Introduction.html"><strong aria-hidden="true">2.</strong> Introduction</a></li><li class="chapter-item expanded "><a href="Roadmap.html"><strong aria-hidden="true">3.</strong> Roadmap</a></li><li class="chapter-item expanded "><a href="Invocation.html"><strong aria-hidden="true">4.</strong> Invocation</a></li><li class="chapter-item expanded "><a href="Files.html"><strong aria-hidden="true">5.</strong> Files</a></li><li class="chapter-item expanded "><a href="Shell-Grammar.html"><strong aria-hidden="true">6.</strong> Shell Grammar</a></li><li class="chapter-item expanded "><a href="Redirection.html"><strong aria-hidden="true">7.</strong> Redirection</a></li><li class="chapter-item expanded "><a href="Command-Execution.html"><strong aria-hidden="true">8.</strong> Command Execution</a></li><li class="chapter-item expanded "><a href="Functions.html"><strong aria-hidden="true">9.</strong> Functions</a></li><li class="chapter-item expanded "><a href="Jobs-&-Signals.html"><strong aria-hidden="true">10.</strong> Jobs & Signals</a></li><li class="chapter-item expanded "><a href="Arithmetic-Evaluation.html" class="active"><strong aria-hidden="true">11.</strong> Arithmetic Evaluation</a></li><li class="chapter-item expanded "><a href="Conditional-Expressions.html"><strong aria-hidden="true">12.</strong> Conditional Expressions</a></li><li class="chapter-item expanded "><a href="Prompt-Expansion.html"><strong aria-hidden="true">13.</strong> Prompt Expansion</a></li><li class="chapter-item expanded "><a href="Expansion.html"><strong aria-hidden="true">14.</strong> Expansion</a></li><li class="chapter-item expanded "><a href="Parameters.html"><strong aria-hidden="true">15.</strong> Parameters</a></li><li class="chapter-item expanded "><a href="Options.html"><strong aria-hidden="true">16.</strong> Options</a></li><li class="chapter-item expanded "><a href="Shell-Builtin-Commands.html"><strong aria-hidden="true">17.</strong> Shell Builtin Commands</a></li><li class="chapter-item expanded "><a href="Zsh-Line-Editor.html"><strong aria-hidden="true">18.</strong> Zsh Line Editor</a></li><li class="chapter-item expanded "><a href="Completion-Widgets.html"><strong aria-hidden="true">19.</strong> Completion Widgets</a></li><li class="chapter-item expanded "><a href="Completion-System.html"><strong aria-hidden="true">20.</strong> Completion System</a></li><li class="chapter-item expanded "><a href="Completion-Using-compctl.html"><strong aria-hidden="true">21.</strong> Completion Using compctl</a></li><li class="chapter-item expanded "><a href="Zsh-Modules.html"><strong aria-hidden="true">22.</strong> Zsh Modules</a></li><li class="chapter-item expanded "><a href="Calendar-Function-System.html"><strong aria-hidden="true">23.</strong> Calendar Function System</a></li><li class="chapter-item expanded "><a href="TCP-Function-System.html"><strong aria-hidden="true">24.</strong> TCP Function System</a></li><li class="chapter-item expanded "><a href="Zftp-Function-System.html"><strong aria-hidden="true">25.</strong> Zftp Function System</a></li><li class="chapter-item expanded "><a href="User-Contributions.html"><strong aria-hidden="true">26.</strong> User Contributions</a></li></ol>
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<!-- START doctoc generated TOC please keep comment here to allow auto update -->
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<p><strong>Table of Contents</strong> <em>generated with <a href="https://github.com/thlorenz/doctoc">DocToc</a></em></p>
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<ul>
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<li><a href="#11-arithmetic-evaluation">11 Arithmetic Evaluation</a></li>
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</ul>
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<!-- END doctoc generated TOC please keep comment here to allow auto update -->
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<p><span id="Arithmetic-Evaluation"></span> <span
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id="Arithmetic-Evaluation-1"></span></p>
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<h1 id="11-arithmetic-evaluation"><a class="header" href="#11-arithmetic-evaluation">11 Arithmetic Evaluation</a></h1>
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<p><span id="index-arithmetic-evaluation"></span> <span
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id="index-evaluation_002c-arithmetic"></span> <span
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id="index-let_002c-use-of"></span></p>
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<p>The shell can perform integer and floating point arithmetic, either
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using the builtin let, or via a substitution of the form $((<code>...</code>)). For
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integers, the shell is usually compiled to use 8-byte precision where
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this is available, otherwise precision is 4 bytes. This can be tested,
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for example, by giving the command ‘print - $(( 12345678901 ))’; if the
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number appears unchanged, the precision is at least 8 bytes. Floating
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point arithmetic always uses the ‘double’ type with whatever
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corresponding precision is provided by the compiler and the library.</p>
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<p>The let builtin command takes arithmetic expressions as arguments; each
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is evaluated separately. Since many of the arithmetic operators, as well
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as spaces, require quoting, an alternative form is provided: for any
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command which begins with a ‘((’, all the characters until a matching
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‘))’ are treated as a double-quoted expression and arithmetic expansion
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performed as for an argument of let. More precisely, ‘((<code>...</code>))’ is
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equivalent to ‘let "<code>...</code>"’. The return status is 0 if the arithmetic
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value of the expression is non-zero, 1 if it is zero, and 2 if an error
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occurred.</p>
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<p>For example, the following statement</p>
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<div class="example">
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<pre><code class="language-zsh">(( val = 2 + 1 ))
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</code></pre>
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</div>
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<p>is equivalent to</p>
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<div class="example">
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<pre><code class="language-zsh">let "val = 2 + 1"
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</code></pre>
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</div>
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<p>both assigning the value 3 to the shell variable val and returning a
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zero status.</p>
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<p><span id="index-arithmetic-base"></span> <span
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id="index-bases_002c-in-arithmetic"></span></p>
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<p>Integers can be in bases other than 10. A leading ‘0x’ or ‘0X’ denotes
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hexadecimal and a leading ‘0b’ or ‘0B’ binary. Integers may also be of
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the form ‘<code>base</code>#<code>n</code>’, where <code>base</code> is a decimal number between two and
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thirty-six representing the arithmetic base and <code>n</code> is a number in that
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base (for example, ‘16#ff’ is 255 in hexadecimal). The <code>base</code># may also
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be omitted, in which case base 10 is used. For backwards compatibility
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the form ‘[<code>base</code>]<code>n</code>’ is also accepted.</p>
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<p>An integer expression or a base given in the form ‘<code>base</code>#<code>n</code>’ may
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contain underscores (‘_’) after the leading digit for visual guidance;
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these are ignored in computation. Examples are 1_000_000 or 0xffff_ffff
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which are equivalent to 1000000 and 0xffffffff respectively.</p>
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<p>It is also possible to specify a base to be used for output in the form
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‘[#<code>base</code>]’, for example ‘[#16]’. This is used when outputting
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arithmetical substitutions or when assigning to scalar parameters, but
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an explicitly defined integer or floating point parameter will not be
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affected. If an integer variable is implicitly defined by an arithmetic
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expression, any base specified in this way will be set as the variable’s
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output arithmetic base as if the option ‘-i <code>base</code>’ to the typeset
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builtin had been used. The expression has no precedence and if it occurs
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more than once in a mathematical expression, the last encountered is
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used. For clarity it is recommended that it appear at the beginning of
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an expression. As an example:</p>
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<div class="example">
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<pre><code class="language-zsh">typeset -i 16 y
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print $(( [#8] x = 32, y = 32 ))
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print $x $y
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</code></pre>
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</div>
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<p>outputs first ‘8#40’, the rightmost value in the given output base, and
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then ‘8#40 16#20’, because y has been explicitly declared to have output
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base 16, while x (assuming it does not already exist) is implicitly
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typed by the arithmetic evaluation, where it acquires the output base 8.</p>
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<p>The <code>base</code> may be replaced or followed by an underscore, which may
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itself be followed by a positive integer (if it is missing the value 3
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is used). This indicates that underscores should be inserted into the
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output string, grouping the number for visual clarity. The following
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integer specifies the number of digits to group together. For example:</p>
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<div class="example">
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<pre><code class="language-zsh">setopt cbases
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print $(( [#16_4] 65536 ** 2 ))
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</code></pre>
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</div>
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<p>outputs ‘0x1_0000_0000’.</p>
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<p>The feature can be used with floating point numbers, in which case the
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base must be omitted; grouping is away from the decimal point. For
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example,</p>
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<div class="example">
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<pre><code class="language-zsh">zmodload zsh/mathfunc
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print $(( [#_] sqrt(1e7) ))
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</code></pre>
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</div>
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<p>outputs ‘3_162.277_660_168_379_5’ (the number of decimal places shown
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may vary).</p>
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<p><span id="index-C_005fBASES_002c-use-of"></span> <span
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id="index-OCTAL_005fZEROES_002c-use-of"></span></p>
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<p>If the C_BASES option is set, hexadecimal numbers are output in the
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standard C format, for example ‘0xFF’ instead of the usual ‘16#FF’. If
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the option OCTAL_ZEROES is also set (it is not by default), octal
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numbers will be treated similarly and hence appear as ‘077’ instead of
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‘8#77’. This option has no effect on the output of bases other than
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hexadecimal and octal, and these formats are always understood on input.</p>
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<p>When an output base is specified using the ‘[#<code>base</code>]’ syntax, an
|
||
appropriate base prefix will be output if necessary, so that the value
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||
output is valid syntax for input. If the # is doubled, for example
|
||
‘[##16]’, then no base prefix is output.</p>
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||
<p>Floating point constants are recognized by the presence of a decimal
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||
point or an exponent. The decimal point may be the first character of
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the constant, but the exponent character e or E may not, as it will be
|
||
taken for a parameter name. All numeric parts (before and after the
|
||
decimal point and in the exponent) may contain underscores after the
|
||
leading digit for visual guidance; these are ignored in computation.</p>
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||
<p><span id="index-arithmetic-operators"></span> <span
|
||
id="index-operators_002c-arithmetic"></span></p>
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||
<p>An arithmetic expression uses nearly the same syntax and associativity
|
||
of expressions as in C.</p>
|
||
<p>In the native mode of operation, the following operators are supported
|
||
(listed in decreasing order of precedence):</p>
|
||
<p>+ - ! ~ ++ –<br />
|
||
unary plus/minus, logical NOT, complement, {pre,post}{in,de}crement</p>
|
||
<p><< >><br />
|
||
bitwise shift left, right</p>
|
||
<p>&<br />
|
||
bitwise AND</p>
|
||
<p>^<br />
|
||
bitwise XOR</p>
|
||
<p>|<br />
|
||
bitwise OR</p>
|
||
<p>**<br />
|
||
exponentiation</p>
|
||
<p>* / %<br />
|
||
multiplication, division, modulus (remainder)</p>
|
||
<p>+ -<br />
|
||
addition, subtraction</p>
|
||
<p>< > <= >=<br />
|
||
comparison</p>
|
||
<p>== !=<br />
|
||
equality and inequality</p>
|
||
<p>&&<br />
|
||
logical AND</p>
|
||
<p>|| ^^<br />
|
||
logical OR, XOR</p>
|
||
<p>? :<br />
|
||
ternary operator</p>
|
||
<p>= += -= *= /= %= &= ^= |= <<= >>= &&= ||= ^^= **=<br />
|
||
assignment</p>
|
||
<p>,<br />
|
||
comma operator</p>
|
||
<p>The operators ‘&&’, ‘||’, ‘&&=’, and ‘||=’ are short-circuiting, and
|
||
only one of the latter two expressions in a ternary operator is
|
||
evaluated. Note the precedence of the bitwise AND, OR, and XOR
|
||
operators.</p>
|
||
<p>With the option C_PRECEDENCES the precedences (but no other properties)
|
||
of the operators are altered to be the same as those in most other
|
||
languages that support the relevant operators:</p>
|
||
<p>+ - ! ~ ++ –<br />
|
||
unary plus/minus, logical NOT, complement, {pre,post}{in,de}crement</p>
|
||
<p>**<br />
|
||
exponentiation</p>
|
||
<p>* / %<br />
|
||
multiplication, division, modulus (remainder)</p>
|
||
<p>+ -<br />
|
||
addition, subtraction</p>
|
||
<p><< >><br />
|
||
bitwise shift left, right</p>
|
||
<p>< > <= >=<br />
|
||
comparison</p>
|
||
<p>== !=<br />
|
||
equality and inequality</p>
|
||
<p>&<br />
|
||
bitwise AND</p>
|
||
<p>^<br />
|
||
bitwise XOR</p>
|
||
<p>|<br />
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||
bitwise OR</p>
|
||
<p>&&<br />
|
||
logical AND</p>
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||
<p>^^<br />
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||
logical XOR</p>
|
||
<p>||<br />
|
||
logical OR</p>
|
||
<p>? :<br />
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||
ternary operator</p>
|
||
<p>= += -= *= /= %= &= ^= |= <<= >>= &&= ||= ^^= **=<br />
|
||
assignment</p>
|
||
<p>,<br />
|
||
comma operator</p>
|
||
<p>Note the precedence of exponentiation in both cases is below that of
|
||
unary operators, hence ‘-3**2’ evaluates as ‘9’, not ‘-9’. Use
|
||
parentheses where necessary: ‘-(3**2)’. This is for compatibility with
|
||
other shells.</p>
|
||
<p><span id="index-mathematical-functions_002c-use-of"></span> <span
|
||
id="index-functions_002c-math_002c-use-of"></span></p>
|
||
<p>Mathematical functions can be called with the syntax ‘<code>func</code>(<code>args</code>)’,
|
||
where the function decides if the <code>args</code> is used as a string or a
|
||
comma-separated list of arithmetic expressions. The shell currently
|
||
defines no mathematical functions by default, but the module
|
||
zsh/mathfunc may be loaded with the zmodload builtin to provide standard
|
||
floating point mathematical functions.</p>
|
||
<p>An expression of the form ‘##<code>x</code>’ where <code>x</code> is any character sequence
|
||
such as ‘a’, ‘^A’, or ‘\M-\C-x’ gives the value of this character and
|
||
an expression of the form ‘#<code>name</code>’ gives the value of the first
|
||
character of the contents of the parameter <code>name</code>. Character values are
|
||
according to the character set used in the current locale; for multibyte
|
||
character handling the option MULTIBYTE must be set. Note that this form
|
||
is different from ‘$#<code>name</code>’, a standard parameter substitution which
|
||
gives the length of the parameter <code>name</code>. ‘#\’ is accepted instead of
|
||
‘##’, but its use is deprecated.</p>
|
||
<p>Named parameters and subscripted arrays can be referenced by name within
|
||
an arithmetic expression without using the parameter expansion syntax.
|
||
For example,</p>
|
||
<div class="example">
|
||
<pre><code class="language-zsh">((val2 = val1 * 2))
|
||
</code></pre>
|
||
</div>
|
||
<p>assigns twice the value of $val1 to the parameter named val2.</p>
|
||
<p>An internal integer representation of a named parameter can be specified
|
||
with the integer builtin. <span
|
||
id="index-parameters_002c-integer"></span> <span
|
||
id="index-integer-parameters"></span> <span
|
||
id="index-integer_002c-use-of"></span> Arithmetic evaluation is
|
||
performed on the value of each assignment to a named parameter declared
|
||
integer in this manner. Assigning a floating point number to an integer
|
||
results in rounding towards zero.</p>
|
||
<p><span id="index-parameters_002c-floating-point"></span> <span
|
||
id="index-floating-point-parameters"></span> <span
|
||
id="index-float_002c-use-of"></span></p>
|
||
<p>Likewise, floating point numbers can be declared with the float builtin;
|
||
there are two types, differing only in their output format, as described
|
||
for the typeset builtin. The output format can be bypassed by using
|
||
arithmetic substitution instead of the parameter substitution, i.e.
|
||
‘${<code>float</code>}’ uses the defined format, but ‘$((<code>float</code>))’ uses a generic
|
||
floating point format.</p>
|
||
<p>Promotion of integer to floating point values is performed where
|
||
necessary. In addition, if any operator which requires an integer (‘&’,
|
||
‘|’, ‘^’, ‘<<’, ‘>>’ and their equivalents with assignment) is given
|
||
a floating point argument, it will be silently rounded towards zero
|
||
except for ‘~’ which rounds down.</p>
|
||
<p>Users should beware that, in common with many other programming
|
||
languages but not software designed for calculation, the evaluation of
|
||
an expression in zsh is taken a term at a time and promotion of integers
|
||
to floating point does not occur in terms only containing integers. A
|
||
typical result of this is that a division such as 6/8 is truncated, in
|
||
this being rounded towards 0. The FORCE_FLOAT shell option can be used
|
||
in scripts or functions where floating point evaluation is required
|
||
throughout.</p>
|
||
<p>Scalar variables can hold integer or floating point values at different
|
||
times; there is no memory of the numeric type in this case.</p>
|
||
<p>If a variable is first assigned in a numeric context without previously
|
||
being declared, it will be implicitly typed as integer or float and
|
||
retain that type either until the type is explicitly changed or until
|
||
the end of the scope. This can have unforeseen consequences. For
|
||
example, in the loop</p>
|
||
<div class="example">
|
||
<pre><code class="language-zsh">for (( f = 0; f < 1; f += 0.1 )); do
|
||
# use $f
|
||
done
|
||
</code></pre>
|
||
</div>
|
||
<p>if f has not already been declared, the first assignment will cause it
|
||
to be created as an integer, and consequently the operation ‘f += 0.1’
|
||
will always cause the result to be truncated to zero, so that the loop
|
||
will fail. A simple fix would be to turn the initialization into ‘f =
|
||
0.0’. It is therefore best to declare numeric variables with explicit
|
||
types.</p>
|
||
<hr />
|
||
<p>This document was generated on <em>May 14, 2022</em> using <a href="http://www.nongnu.org/texi2html/"><em>texi2html
|
||
5.0</em></a>.<br />
|
||
Zsh version 5.9, released on May 14, 2022.</p>
|
||
|
||
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