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11 Arithmetic Evaluation
The shell can perform integer and floating point arithmetic, either
using the builtin let, or via a substitution of the form $((...
)). For
integers, the shell is usually compiled to use 8byte precision where
this is available, otherwise precision is 4 bytes. This can be tested,
for example, by giving the command ‘print  $(( 12345678901 ))’; if the
number appears unchanged, the precision is at least 8 bytes. Floating
point arithmetic always uses the ‘double’ type with whatever
corresponding precision is provided by the compiler and the library.
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 ‘((’, all the characters until a matching
‘))’ are treated as a doublequoted expression and arithmetic expansion
performed as for an argument of let. More precisely, ‘((...
))’ is
equivalent to ‘let "...
"’. The return status is 0 if the arithmetic
value of the expression is nonzero, 1 if it is zero, and 2 if an error
occurred.
For example, the following statement
(( val = 2 + 1 ))
is equivalent to
let "val = 2 + 1"
both assigning the value 3 to the shell variable val and returning a zero status.
Integers can be in bases other than 10. A leading ‘0x’ or ‘0X’ denotes
hexadecimal and a leading ‘0b’ or ‘0B’ binary. Integers may also be of
the form ‘base
#n
’, where base
is a decimal number between two and
thirtysix representing the arithmetic base and n
is a number in that
base (for example, ‘16#ff’ is 255 in hexadecimal). The base
# may also
be omitted, in which case base 10 is used. For backwards compatibility
the form ‘[base
]n
’ is also accepted.
An integer expression or a base given in the form ‘base
#n
’ may
contain underscores (‘_’) after the leading digit for visual guidance;
these are ignored in computation. Examples are 1_000_000 or 0xffff_ffff
which are equivalent to 1000000 and 0xffffffff respectively.
It is also possible to specify a base to be used for output in the form
‘[#base
]’, for example ‘[#16]’. This is used when outputting
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’s
output arithmetic base as if the option ‘i base
’ to the typeset
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:
typeset i 16 y
print $(( [#8] x = 32, y = 32 ))
print $x $y
outputs first ‘8#40’, the rightmost value in the given output base, and then ‘8#40 16#20’, because y has been explicitly declared to have output base 16, while x (assuming it does not already exist) is implicitly typed by the arithmetic evaluation, where it acquires the output base 8.
The base
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:
setopt cbases
print $(( [#16_4] 65536 ** 2 ))
outputs ‘0x1_0000_0000’.
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,
zmodload zsh/mathfunc
print $(( [#_] sqrt(1e7) ))
outputs ‘3_162.277_660_168_379_5’ (the number of decimal places shown may vary).
If the C_BASES option is set, hexadecimal numbers are output in the standard C format, for example ‘0xFF’ instead of the usual ‘16#FF’. If the option OCTAL_ZEROES is also set (it is not by default), octal numbers will be treated similarly and hence appear as ‘077’ instead of ‘8#77’. This option has no effect on the output of bases other than hexadecimal and octal, and these formats are always understood on input.
When an output base is specified using the ‘[#base
]’ syntax, an
appropriate base prefix will be output if necessary, so that the value
output is valid syntax for input. If the # is doubled, for example
‘[##16]’, then no base prefix is output.
Floating point constants are recognized by the presence of a decimal point or an exponent. The decimal point may be the first character of 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.
An arithmetic expression uses nearly the same syntax and associativity of expressions as in C.
In the native mode of operation, the following operators are supported (listed in decreasing order of precedence):
+  ! ~ ++ –
unary plus/minus, logical NOT, complement, {pre,post}{in,de}crement
<< >>
bitwise shift left, right
&
bitwise AND
^
bitwise XOR

bitwise OR
**
exponentiation
* / %
multiplication, division, modulus (remainder)
+ 
addition, subtraction
< > <= >=
comparison
== !=
equality and inequality
&&
logical AND
 ^^
logical OR, XOR
? :
ternary operator
= += = *= /= %= &= ^= = <<= >>= &&= = ^^= **=
assignment
,
comma operator
The operators ‘&&’, ‘’, ‘&&=’, and ‘=’ are shortcircuiting, 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.
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:
+  ! ~ ++ –
unary plus/minus, logical NOT, complement, {pre,post}{in,de}crement
**
exponentiation
* / %
multiplication, division, modulus (remainder)
+ 
addition, subtraction
<< >>
bitwise shift left, right
< > <= >=
comparison
== !=
equality and inequality
&
bitwise AND
^
bitwise XOR

bitwise OR
&&
logical AND
^^
logical XOR

logical OR
? :
ternary operator
= += = *= /= %= &= ^= = <<= >>= &&= = ^^= **=
assignment
,
comma operator
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.
Mathematical functions can be called with the syntax ‘func
(args
)’,
where the function decides if the args
is used as a string or a
commaseparated 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.
An expression of the form ‘##x
’ where x
is any character sequence
such as ‘a’, ‘^A’, or ‘\M\Cx’ gives the value of this character and
an expression of the form ‘#name
’ gives the value of the first
character of the contents of the parameter name
. 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 ‘$#name
’, a standard parameter substitution which
gives the length of the parameter name
. ‘#\’ is accepted instead of
‘##’, but its use is deprecated.
Named parameters and subscripted arrays can be referenced by name within an arithmetic expression without using the parameter expansion syntax. For example,
((val2 = val1 * 2))
assigns twice the value of $val1 to the parameter named val2.
An internal integer representation of a named parameter can be specified with the integer builtin. Arithmetic evaluation is performed on the value of each assignment to a named parameter declared integer in this manner. Assigning a floating point number to an integer results in rounding towards zero.
Likewise, floating point numbers can be declared with the float builtin;
there are two types, differing only in their output format, as described
for the typeset builtin. The output format can be bypassed by using
arithmetic substitution instead of the parameter substitution, i.e.
‘${float
}’ uses the defined format, but ‘$((float
))’ uses a generic
floating point format.
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.
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.
Scalar variables can hold integer or floating point values at different times; there is no memory of the numeric type in this case.
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
for (( f = 0; f < 1; f += 0.1 )); do
# use $f
done
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.
This document was generated on May 14, 2022 using texi2html
5.0.
Zsh version 5.9, released on May 14, 2022.