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< main >
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< p > < strong > Table of Contents< / strong > < em > generated with < a href = "https://github.com/thlorenz/doctoc" > DocToc< / a > < / em > < / p >
< ul >
< li > < a href = "#11-arithmetic-evaluation" > 11 Arithmetic Evaluation< / a > < / li >
< / ul >
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< p > < span id = "Arithmetic-Evaluation" > < / span > < span
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
id="index-evaluation_002c-arithmetic">< / span > < span
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
integers, the shell is usually compiled to use 8-byte precision where
this is available, otherwise precision is 4 bytes. This can be tested,
for example, by giving the command ‘ ’
number appears unchanged, the precision is at least 8 bytes. Floating
point arithmetic always uses the ‘ ’
corresponding precision is provided by the compiler and the library.< / p >
< p > The let builtin command takes arithmetic expressions as arguments; each
is evaluated separately. Since many of the arithmetic operators, as well
as spaces, require quoting, an alternative form is provided: for any
command which begins with a ‘ ’
‘ ’
performed as for an argument of let. More precisely, ‘ < code > ...< / code > ))’
equivalent to ‘ " < code > ...< / code > " ’
value of the expression is non-zero, 1 if it is zero, and 2 if an error
occurred.< / p >
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< p > For example, the following statement< / p >
< div class = "example" >
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< pre > < code class = "language-zsh" > (( val = 2 + 1 ))
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< / code > < / pre >
< / div >
< p > is equivalent to< / p >
< div class = "example" >
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< pre > < code class = "language-zsh" > let " val = 2 + 1"
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< / code > < / pre >
< / 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
id="index-bases_002c-in-arithmetic">< / span > < / p >
< p > Integers can be in bases other than 10. A leading ‘ ’ ‘ ’
hexadecimal and a leading ‘ ’ ‘ ’
the form ‘ < code > base< / code > #< code > n< / code > ’ < code > base< / code > is a decimal number between two and
thirty-six representing the arithmetic base and < code > n< / code > is a number in that
base (for example, ‘ ’ < code > base< / code > # may also
be omitted, in which case base 10 is used. For backwards compatibility
the form ‘ < code > base< / code > ]< code > n< / code > ’ < / p >
< p > An integer expression or a base given in the form ‘ < code > base< / code > #< code > n< / code > ’
contain underscores (‘ ’
these are ignored in computation. Examples are 1_000_000 or 0xffff_ffff
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 > ]’ ‘ ’
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arithmetical substitutions or when assigning to scalar parameters, but
an explicitly defined integer or floating point parameter will not be
affected. If an integer variable is implicitly defined by an arithmetic
expression, any base specified in this way will be set as the variable’
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output arithmetic base as if the option ‘ < code > base< / code > ’
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builtin had been used. The expression has no precedence and if it occurs
more than once in a mathematical expression, the last encountered is
used. For clarity it is recommended that it appear at the beginning of
an expression. As an example:< / p >
< 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 ))
print $x $y
< / code > < / pre >
< / div >
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< p > outputs first ‘ ’
then ‘ ’
base 16, while x (assuming it does not already exist) is implicitly
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
itself be followed by a positive integer (if it is missing the value 3
is used). This indicates that underscores should be inserted into the
output string, grouping the number for visual clarity. The following
integer specifies the number of digits to group together. For example:< / p >
< div class = "example" >
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< pre > < code class = "language-zsh" > setopt cbases
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print $(( [#16_4] 65536 ** 2 ))
< / code > < / pre >
< / div >
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< p > outputs ‘ ’ < / p >
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< p > The feature can be used with floating point numbers, in which case the
base must be omitted; grouping is away from the decimal point. For
example,< / p >
< div class = "example" >
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< pre > < code class = "language-zsh" > zmodload zsh/mathfunc
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print $(( [#_] sqrt(1e7) ))
< / code > < / pre >
< / div >
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< p > outputs ‘ ’
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may vary).< / p >
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< p > < span id = "index-C_005fBASES_002c-use-of" > < / span > < span
id="index-OCTAL_005fZEROES_002c-use-of">< / span > < / p >
< p > If the C_BASES option is set, hexadecimal numbers are output in the
standard C format, for example ‘ ’ ‘ ’
the option OCTAL_ZEROES is also set (it is not by default), octal
numbers will be treated similarly and hence appear as ‘ ’
‘ ’
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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 > ]’
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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
‘ ’ < / p >
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< p > Floating point constants are recognized by the presence of a decimal
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
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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 >
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< p > + - ! ~ ++ – < br / >
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unary plus/minus, logical NOT, complement, {pre,post}{in,de}crement< / p >
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< p > < < > > < br / >
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bitwise shift left, right< / p >
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< p > & < br / >
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bitwise AND< / p >
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< p > ^< br / >
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bitwise XOR< / p >
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< p > |< br / >
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bitwise OR< / p >
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< p > **< br / >
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exponentiation< / p >
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< p > * / %< br / >
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multiplication, division, modulus (remainder)< / p >
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< p > + -< br / >
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addition, subtraction< / p >
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< p > < > < = > =< br / >
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comparison< / p >
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< p > == !=< br / >
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equality and inequality< / p >
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< p > & & < br / >
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logical AND< / p >
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< p > || ^^< br / >
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logical OR, XOR< / p >
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< p > ? :< br / >
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ternary operator< / p >
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< p > = += -= *= /= %= & = ^= |= < < = > > = & & = ||= ^^= **=< br / >
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assignment< / p >
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< p > ,< br / >
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comma operator< / p >
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< p > The operators ‘ & & ’ ‘ ’ ‘ & & =’ ‘ ’
only one of the latter two expressions in a ternary operator is
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evaluated. Note the precedence of the bitwise AND, OR, and XOR
operators.< / p >
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< 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 / >
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unary plus/minus, logical NOT, complement, {pre,post}{in,de}crement< / p >
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< p > **< br / >
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exponentiation< / p >
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< p > * / %< br / >
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multiplication, division, modulus (remainder)< / p >
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< p > + -< br / >
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addition, subtraction< / p >
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< p > < < > > < br / >
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bitwise shift left, right< / p >
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< p > < > < = > =< br / >
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comparison< / p >
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< p > == !=< br / >
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equality and inequality< / p >
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< p > & < br / >
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bitwise AND< / p >
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< p > ^< br / >
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bitwise XOR< / p >
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< p > |< br / >
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bitwise OR< / p >
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< p > & & < br / >
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logical AND< / p >
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< p > ^^< br / >
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logical XOR< / p >
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< p > ||< br / >
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logical OR< / p >
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< p > ? :< br / >
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ternary operator< / p >
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< p > = += -= *= /= %= & = ^= |= < < = > > = & & = ||= ^^= **=< br / >
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assignment< / p >
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< p > ,< br / >
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comma operator< / p >
< p > Note the precedence of exponentiation in both cases is below that of
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unary operators, hence ‘ ’ ‘ ’ ‘ ’
parentheses where necessary: ‘ ’
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other shells.< / p >
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< 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 > ’ < code > x< / code > is any character sequence
such as ‘ ’ ‘ ’ ‘ ’
an expression of the form ‘ < code > name< / code > ’
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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
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character handling the option MULTIBYTE must be set. Note that this form
is different from ‘ < code > name< / code > ’
gives the length of the parameter < code > name< / code > . ‘ ’
‘ ’ < / p >
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< 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" >
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< pre > < code class = "language-zsh" > ((val2 = val1 * 2))
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< / code > < / pre >
< / div >
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< p > assigns twice the value of $val1 to the parameter named val2.< / p >
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< p > An internal integer representation of a named parameter can be specified
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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
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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 >
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< 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 > }’ ‘ < code > float< / code > ))’
floating point format.< / p >
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< p > Promotion of integer to floating point values is performed where
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necessary. In addition, if any operator which requires an integer (‘ & ’
‘ ’ ‘ ’ ‘ < < ’ ‘ > > ’
a floating point argument, it will be silently rounded towards zero
except for ‘ ’ < / p >
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< 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
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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
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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
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being declared, it will be implicitly typed as integer or float and
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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" >
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< pre > < code class = "language-zsh" > for (( f = 0; f < 1; f += 0.1 )); do
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# use $f
done
< / code > < / pre >
< / div >
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< p > if f has not already been declared, the first assignment will cause it
to be created as an integer, and consequently the operation ‘ ’
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will always cause the result to be truncated to zero, so that the loop
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will fail. A simple fix would be to turn the initialization into ‘
0.0’
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types.< / p >
< hr / >
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< 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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< / main >
< nav class = "nav-wrapper" aria-label = "Page navigation" >
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