fish-shell/doc_src/cmds/math.rst

.. _cmd-math:

math - perform mathematics calculations
=======================================

Synopsis
--------

::

    math [-sN | --scale=N] [-bBASE | --base=BASE] [--] EXPRESSION


Description
-----------

``math`` performs mathematical calculations. It supports simple operations such as addition, subtraction, and so on, as well as functions like ``abs()``, ``sqrt()`` and ``ln()``.

By default, the output is a floating-point number with trailing zeroes trimmed. To get a fixed representation, the ``--scale`` option can be used, including ``--scale=0`` for integer output.

Keep in mind that parameter expansion happens before expressions are evaluated. This can be very useful in order to perform calculations involving shell variables or the output of command substitutions, but it also means that parenthesis (``()``) and the asterisk (``*``) glob character have to be escaped or quoted. ``x`` can also be used to denote multiplication, but it needs to be followed by whitespace to distinguish it from hexadecimal numbers.

``math`` ignores whitespace between arguments and takes its input as multiple arguments (internally joined with a space), so ``math 2 +2`` and ``math "2 +    2"`` work the same. ``math 2 2`` is an error.

The following options are available:

- ``-sN`` or ``--scale=N`` sets the scale of the result. ``N`` must be an integer or the word "max" for the maximum scale. A scale of zero causes results to be rounded down to the nearest integer. So ``3/2`` returns ``1`` rather than ``2`` which ``1.5`` would normally round to. This is for compatibility with ``bc`` which was the basis for this command prior to fish 3.0.0. Scale values greater than zero causes the result to be rounded using the usual rules to the specified number of decimal places.

- ``-b BASE`` or ``--base BASE`` sets the numeric base used for output (``math`` always understands hexadecimal numbers as input). It currently understands "hex" or "16" for hexadecimal and "octal" or "8" for octal and implies a scale of 0 (other scales cause an error), so it will truncate the result down to an integer. This might change in the future. Hex numbers will be printed with a ``0x`` prefix. Octal numbers will have a prefix of ``0`` and aren't understood by ``math`` as input.

Return Values
-------------

If the expression is successfully evaluated and doesn't over/underflow or return NaN the return ``status`` is zero (success) else one.

Syntax
------

``math`` knows some operators, constants, functions and can (obviously) read numbers.

For numbers, ``.`` is always the radix character regardless of locale - ``2.5``, not ``2,5``. Scientific notation (``10e5``) and hexadecimal (``0xFF``) are also available.

Operators
---------

``math`` knows the following operators:

- ``+`` for addition and ``-`` for subtraction.

- ``*`` or ``x`` for multiplication, ``/`` for division. (Note that ``*`` is the glob character and needs to be quoted or escaped, ``x`` needs to be followed by whitespace or it looks like ``0x`` hexadecimal notation.)

- ``^`` for exponentiation.

- ``%`` for modulo.

- ``(`` and ``)`` for grouping. (These need to be quoted or escaped because ``()`` denotes a command substitution.)

They are all used in an infix manner - ``5 + 2``, not ``+ 5 2``.

Constants
---------

``math`` knows the following constants:

- ``e`` - Euler's number.
- ``pi`` - π. You know this one. Half of Tau.
- ``tau``. Equivalent to 2π, or the number of radians in a circle.

Use them without a leading ``$`` - ``pi - 3`` should be about 0.

Functions
---------

``math`` supports the following functions:

- ``abs`` - the absolute value, with positive sign
- ``acos`` - arc cosine
- ``asin`` - arc sine
- ``atan`` - arc tangent
- ``atan2`` - arc tangent of two variables
- ``bitand``, ``bitor`` and ``bitxor`` to perform bitwise operations. These will throw away any non-integer parts and interpret the rest as an int.
- ``ceil`` - round number up to nearest integer
- ``cos`` - the cosine
- ``cosh`` - hyperbolic cosine
- ``exp`` - the base-e exponential function
- ``fac`` - factorial - also known as ``x!`` (``x * (x - 1) * (x - 2) * ... * 1``)
- ``floor`` - round number down to nearest integer
- ``ln`` - the base-e logarithm
- ``log`` or ``log10`` - the base-10 logarithm
- ``ncr`` - "from n choose r" combination function - how many subsets of size r can be taken from n (order doesn't matter)
- ``npr`` - the number of subsets of size r that can be taken from a set of n elements (including different order)
- ``pow(x,y)`` returns x to the y (and can be written as ``x ^ y``)
- ``round`` - rounds to the nearest integer, away from 0
- ``sin`` - the sine function
- ``sinh`` - the hyperbolic sine
- ``sqrt`` - the square root - (can also be written as ``x ^ 0.5``)
- ``tan`` - the tangent
- ``tanh`` - the hyperbolic tangent

All of the trigonometric functions use radians (the pi-based scale, not 360°).

Examples
--------

``math 1+1`` outputs 2.

``math $status - 128`` outputs the numerical exit status of the last command minus 128.

``math 10 / 6`` outputs ``1.666667``.

``math -s0 10.0 / 6.0`` outputs ``1``.

``math -s3 10 / 6`` outputs ``1.666``.

``math "sin(pi)"`` outputs ``0``.

``math 5 \* 2`` or ``math "5 * 2"`` or ``math 5 "*" 2`` all output ``10``.

``math 0xFF`` outputs 255, ``math 0 x 3`` outputs 0 (because it computes 0 multiplied by 3).

``math "bitand(0xFE, 0x2e)"`` outputs 46.

``math "bitor(9,2)"`` outputs 11.

``math --base=hex 192`` prints ``0xc0``.

``math 'ncr(49,6)'`` prints 13983816 - that's the number of possible picks in 6-from-49 lotto.

Compatibility notes
-------------------

Fish 1.x and 2.x releases relied on the ``bc`` command for handling ``math`` expressions. Starting with fish 3.0.0 fish uses the tinyexpr library and evaluates the expression without the involvement of any external commands.

You don't need to use ``--`` before the expression, even if it begins with a minus sign which might otherwise be interpreted as an invalid option. If you do insert ``--`` before the expression, it will cause option scanning to stop just like for every other command and it won't be part of the expression.
docs: Add labels to all commands This allows us to use :ref: references, which don't require hardcoding it as html [ci skip] 2019-03-31 17:05:09 +08:00			`.. _cmd-math:`

doc: homogenize commands titles 2020-03-31 23:37:38 +08:00			`math - perform mathematics calculations`
Fix command section separator line lengths 2019-01-03 12:10:47 +08:00			`=======================================`
Switch command docs from \section to reStructuredText 2018-12-17 09:39:33 +08:00
Migrate the 'synopsis' sections to .rst format 2018-12-18 09:58:24 +08:00			`Synopsis`
			`--------`
Copy doc_src to sphinx_doc_src and add a TOC 2018-12-17 05:08:41 +08:00
docs: update all command synopsis formatting Adds synopses for those commands missing them. Moves all synopsis sections to code blocks. This improves the appearance, although highlighting as fish code may not be the ideal appearance. 2019-09-17 17:59:04 +08:00			`::`

math: Add --base option Currently a bit limited, unfortunately printf's `%a` specifier is absolutely unreadable. So we add `hex` and `octal` with `0x` and `0` prefixes respectively, and also take a number but currently only allow 16 and 8. The output is truncated to integer, so scale values other than 0 are invalid and 0 is implied. The docs mention this may change. 2020-10-08 01:03:19 +08:00			`math [-sN \| --scale=N] [-bBASE \| --base=BASE] [--] EXPRESSION`
Migrate the 'synopsis' sections to .rst format 2018-12-18 09:58:24 +08:00
Copy doc_src to sphinx_doc_src and add a TOC 2018-12-17 05:08:41 +08:00
Convert \\subsection sections into rst format 2018-12-19 10:44:30 +08:00			`Description`
Fix command section separator line lengths 2019-01-03 12:10:47 +08:00			`-----------`
Copy doc_src to sphinx_doc_src and add a TOC 2018-12-17 05:08:41 +08:00
docs: minor updates to math documentation Closes #7734. 2021-02-21 21:34:15 +08:00			``math`` performs mathematical calculations. It supports simple operations such as addition, subtraction, and so on, as well as functions like ``abs()``, ``sqrt()`` and ``ln()``.
Copy doc_src to sphinx_doc_src and add a TOC 2018-12-17 05:08:41 +08:00
docs: minor updates to math documentation Closes #7734. 2021-02-21 21:34:15 +08:00			By default, the output is a floating-point number with trailing zeroes trimmed. To get a fixed representation, the ``--scale`` option can be used, including ``--scale=0`` for integer output.
Copy doc_src to sphinx_doc_src and add a TOC 2018-12-17 05:08:41 +08:00
Fix typo (verb clarification) in math.rst Was: "parameter expansion takes before expressions are evaluated." Now: "parameter expansion happens before expressions are evaluated." I suspect the original intent was to use "takes place," but I see "happens" as less idiomatic and therefore may benefit non-English-native users. 2020-08-19 07:56:57 +08:00			Keep in mind that parameter expansion happens before expressions are evaluated. This can be very useful in order to perform calculations involving shell variables or the output of command substitutions, but it also means that parenthesis (``()``) and the asterisk (``*``) glob character have to be escaped or quoted. ``x`` can also be used to denote multiplication, but it needs to be followed by whitespace to distinguish it from hexadecimal numbers.
Copy doc_src to sphinx_doc_src and add a TOC 2018-12-17 05:08:41 +08:00
Switch backticks to double backticks for rst compatibility 2018-12-20 04:02:45 +08:00			``math`` ignores whitespace between arguments and takes its input as multiple arguments (internally joined with a space), so ``math 2 +2`` and ``math "2 + 2"`` work the same. ``math 2 2`` is an error.
Copy doc_src to sphinx_doc_src and add a TOC 2018-12-17 05:08:41 +08:00
			`The following options are available:`

Incorporate most new doc changes since branch Adds most documentation changes since 72c0213d42b77b2f01223b5515669840110ea9b9 2019-02-25 07:01:16 +08:00			- ``-sN`` or ``--scale=N`` sets the scale of the result. ``N`` must be an integer or the word "max" for the maximum scale. A scale of zero causes results to be rounded down to the nearest integer. So ``3/2`` returns ``1`` rather than ``2`` which ``1.5`` would normally round to. This is for compatibility with ``bc`` which was the basis for this command prior to fish 3.0.0. Scale values greater than zero causes the result to be rounded using the usual rules to the specified number of decimal places.
Copy doc_src to sphinx_doc_src and add a TOC 2018-12-17 05:08:41 +08:00
math: Add --base option Currently a bit limited, unfortunately printf's `%a` specifier is absolutely unreadable. So we add `hex` and `octal` with `0x` and `0` prefixes respectively, and also take a number but currently only allow 16 and 8. The output is truncated to integer, so scale values other than 0 are invalid and 0 is implied. The docs mention this may change. 2020-10-08 01:03:19 +08:00			- ``-b BASE`` or ``--base BASE`` sets the numeric base used for output (``math`` always understands hexadecimal numbers as input). It currently understands "hex" or "16" for hexadecimal and "octal" or "8" for octal and implies a scale of 0 (other scales cause an error), so it will truncate the result down to an integer. This might change in the future. Hex numbers will be printed with a ``0x`` prefix. Octal numbers will have a prefix of ``0`` and aren't understood by ``math`` as input.

Convert \\subsection sections into rst format 2018-12-19 10:44:30 +08:00			`Return Values`
Fix command section separator line lengths 2019-01-03 12:10:47 +08:00			`-------------`
Copy doc_src to sphinx_doc_src and add a TOC 2018-12-17 05:08:41 +08:00
Switch backticks to double backticks for rst compatibility 2018-12-20 04:02:45 +08:00			If the expression is successfully evaluated and doesn't over/underflow or return NaN the return ``status`` is zero (success) else one.
Copy doc_src to sphinx_doc_src and add a TOC 2018-12-17 05:08:41 +08:00
Convert \\subsection sections into rst format 2018-12-19 10:44:30 +08:00			`Syntax`
Fix command section separator line lengths 2019-01-03 12:10:47 +08:00			`------`
Copy doc_src to sphinx_doc_src and add a TOC 2018-12-17 05:08:41 +08:00
Switch backticks to double backticks for rst compatibility 2018-12-20 04:02:45 +08:00			``math`` knows some operators, constants, functions and can (obviously) read numbers.
Copy doc_src to sphinx_doc_src and add a TOC 2018-12-17 05:08:41 +08:00
math: Document hex numbers 2020-08-26 23:29:46 +08:00			For numbers, ``.`` is always the radix character regardless of locale - ``2.5``, not ``2,5``. Scientific notation (``10e5``) and hexadecimal (``0xFF``) are also available.
Copy doc_src to sphinx_doc_src and add a TOC 2018-12-17 05:08:41 +08:00
Convert \\subsection sections into rst format 2018-12-19 10:44:30 +08:00			`Operators`
Fix command section separator line lengths 2019-01-03 12:10:47 +08:00			`---------`
Copy doc_src to sphinx_doc_src and add a TOC 2018-12-17 05:08:41 +08:00
Switch backticks to double backticks for rst compatibility 2018-12-20 04:02:45 +08:00			``math`` knows the following operators:
Copy doc_src to sphinx_doc_src and add a TOC 2018-12-17 05:08:41 +08:00
Switch backticks to double backticks for rst compatibility 2018-12-20 04:02:45 +08:00			- ``+`` for addition and ``-`` for subtraction.
Copy doc_src to sphinx_doc_src and add a TOC 2018-12-17 05:08:41 +08:00
math: Allow "x" for multiplication It's always a bit annoying that `*` requires quoting. So we allow "x" as an alternative, only it needs to be followed by whitespace to distinguish it from "0x" hexadecimal notation. 2019-05-30 22:00:45 +08:00			- ```` or ``x`` for multiplication, ``/`` for division. (Note that ```` is the glob character and needs to be quoted or escaped, ``x`` needs to be followed by whitespace or it looks like ``0x`` hexadecimal notation.)
Copy doc_src to sphinx_doc_src and add a TOC 2018-12-17 05:08:41 +08:00
Switch backticks to double backticks for rst compatibility 2018-12-20 04:02:45 +08:00			- ``^`` for exponentiation.
Copy doc_src to sphinx_doc_src and add a TOC 2018-12-17 05:08:41 +08:00
Switch backticks to double backticks for rst compatibility 2018-12-20 04:02:45 +08:00			- ``%`` for modulo.
Copy doc_src to sphinx_doc_src and add a TOC 2018-12-17 05:08:41 +08:00
Incorporate most new doc changes since branch Adds most documentation changes since 72c0213d42b77b2f01223b5515669840110ea9b9 2019-02-25 07:01:16 +08:00			- ``(`` and ``)`` for grouping. (These need to be quoted or escaped because ``()`` denotes a command substitution.)
Copy doc_src to sphinx_doc_src and add a TOC 2018-12-17 05:08:41 +08:00
Switch backticks to double backticks for rst compatibility 2018-12-20 04:02:45 +08:00			They are all used in an infix manner - ``5 + 2``, not ``+ 5 2``.
Copy doc_src to sphinx_doc_src and add a TOC 2018-12-17 05:08:41 +08:00
Convert \\subsection sections into rst format 2018-12-19 10:44:30 +08:00			`Constants`
Fix command section separator line lengths 2019-01-03 12:10:47 +08:00			`---------`
Copy doc_src to sphinx_doc_src and add a TOC 2018-12-17 05:08:41 +08:00
Switch backticks to double backticks for rst compatibility 2018-12-20 04:02:45 +08:00			``math`` knows the following constants:
Copy doc_src to sphinx_doc_src and add a TOC 2018-12-17 05:08:41 +08:00
Switch backticks to double backticks for rst compatibility 2018-12-20 04:02:45 +08:00			- ``e`` - Euler's number.
docs: minor updates to math documentation Closes #7734. 2021-02-21 21:34:15 +08:00			- ``pi`` - π. You know this one. Half of Tau.
			- ``tau``. Equivalent to 2π, or the number of radians in a circle.
Copy doc_src to sphinx_doc_src and add a TOC 2018-12-17 05:08:41 +08:00
Switch backticks to double backticks for rst compatibility 2018-12-20 04:02:45 +08:00			Use them without a leading ``$`` - ``pi - 3`` should be about 0.
Copy doc_src to sphinx_doc_src and add a TOC 2018-12-17 05:08:41 +08:00
Convert \\subsection sections into rst format 2018-12-19 10:44:30 +08:00			`Functions`
Fix command section separator line lengths 2019-01-03 12:10:47 +08:00			`---------`
Copy doc_src to sphinx_doc_src and add a TOC 2018-12-17 05:08:41 +08:00
Switch backticks to double backticks for rst compatibility 2018-12-20 04:02:45 +08:00			``math`` supports the following functions:

docs: Document the math functions better 2021-03-12 02:46:02 +08:00			- ``abs`` - the absolute value, with positive sign
			- ``acos`` - arc cosine
			- ``asin`` - arc sine
			- ``atan`` - arc tangent
			- ``atan2`` - arc tangent of two variables
math: Add bitwise and/or functions Just as `math "bitand(5,3)"` and `math "bitor(6,2)"`. These cast to long long before doing their thing, so they truncate to an integer, producing weird results with floats. That's to be expected because float representation is very different, and performing bitwise operations on floats feels quite useless. Fixes #7281. 2020-08-25 22:45:31 +08:00			- ``bitand``, ``bitor`` and ``bitxor`` to perform bitwise operations. These will throw away any non-integer parts and interpret the rest as an int.
docs: Document the math functions better 2021-03-12 02:46:02 +08:00			- ``ceil`` - round number up to nearest integer
			- ``cos`` - the cosine
			- ``cosh`` - hyperbolic cosine
Switch backticks to double backticks for rst compatibility 2018-12-20 04:02:45 +08:00			- ``exp`` - the base-e exponential function
docs: Document the math functions better 2021-03-12 02:46:02 +08:00			- ``fac`` - factorial - also known as ``x!`` (``x * (x - 1) * (x - 2) * ... * 1``)
			- ``floor`` - round number down to nearest integer
docs: minor updates to math documentation Closes #7734. 2021-02-21 21:34:15 +08:00			- ``ln`` - the base-e logarithm
Switch backticks to double backticks for rst compatibility 2018-12-20 04:02:45 +08:00			- ``log`` or ``log10`` - the base-10 logarithm
docs: Document the math functions better 2021-03-12 02:46:02 +08:00			- ``ncr`` - "from n choose r" combination function - how many subsets of size r can be taken from n (order doesn't matter)
			- ``npr`` - the number of subsets of size r that can be taken from a set of n elements (including different order)
Switch backticks to double backticks for rst compatibility 2018-12-20 04:02:45 +08:00			- ``pow(x,y)`` returns x to the y (and can be written as ``x ^ y``)
			- ``round`` - rounds to the nearest integer, away from 0
docs: Document the math functions better 2021-03-12 02:46:02 +08:00			- ``sin`` - the sine function
			- ``sinh`` - the hyperbolic sine
			- ``sqrt`` - the square root - (can also be written as ``x ^ 0.5``)
			- ``tan`` - the tangent
			- ``tanh`` - the hyperbolic tangent
Copy doc_src to sphinx_doc_src and add a TOC 2018-12-17 05:08:41 +08:00
docs: Document the math functions better 2021-03-12 02:46:02 +08:00			`All of the trigonometric functions use radians (the pi-based scale, not 360°).`
Copy doc_src to sphinx_doc_src and add a TOC 2018-12-17 05:08:41 +08:00
Convert \\subsection sections into rst format 2018-12-19 10:44:30 +08:00			`Examples`
Fix command section separator line lengths 2019-01-03 12:10:47 +08:00			`--------`
Copy doc_src to sphinx_doc_src and add a TOC 2018-12-17 05:08:41 +08:00
Switch backticks to double backticks for rst compatibility 2018-12-20 04:02:45 +08:00			``math 1+1`` outputs 2.
Copy doc_src to sphinx_doc_src and add a TOC 2018-12-17 05:08:41 +08:00
Switch backticks to double backticks for rst compatibility 2018-12-20 04:02:45 +08:00			``math $status - 128`` outputs the numerical exit status of the last command minus 128.
Copy doc_src to sphinx_doc_src and add a TOC 2018-12-17 05:08:41 +08:00
Switch backticks to double backticks for rst compatibility 2018-12-20 04:02:45 +08:00			``math 10 / 6`` outputs ``1.666667``.
Copy doc_src to sphinx_doc_src and add a TOC 2018-12-17 05:08:41 +08:00
Switch backticks to double backticks for rst compatibility 2018-12-20 04:02:45 +08:00			``math -s0 10.0 / 6.0`` outputs ``1``.
Copy doc_src to sphinx_doc_src and add a TOC 2018-12-17 05:08:41 +08:00
Switch backticks to double backticks for rst compatibility 2018-12-20 04:02:45 +08:00			``math -s3 10 / 6`` outputs ``1.666``.
Copy doc_src to sphinx_doc_src and add a TOC 2018-12-17 05:08:41 +08:00
Switch backticks to double backticks for rst compatibility 2018-12-20 04:02:45 +08:00			``math "sin(pi)"`` outputs ``0``.
Copy doc_src to sphinx_doc_src and add a TOC 2018-12-17 05:08:41 +08:00
Incorporate most new doc changes since branch Adds most documentation changes since 72c0213d42b77b2f01223b5515669840110ea9b9 2019-02-25 07:01:16 +08:00			``math 5 \* 2`` or ``math "5 * 2"`` or ``math 5 "*" 2`` all output ``10``.

math: Allow "x" for multiplication It's always a bit annoying that `*` requires quoting. So we allow "x" as an alternative, only it needs to be followed by whitespace to distinguish it from "0x" hexadecimal notation. 2019-05-30 22:00:45 +08:00			``math 0xFF`` outputs 255, ``math 0 x 3`` outputs 0 (because it computes 0 multiplied by 3).

math: Add bitwise and/or functions Just as `math "bitand(5,3)"` and `math "bitor(6,2)"`. These cast to long long before doing their thing, so they truncate to an integer, producing weird results with floats. That's to be expected because float representation is very different, and performing bitwise operations on floats feels quite useless. Fixes #7281. 2020-08-25 22:45:31 +08:00			``math "bitand(0xFE, 0x2e)"`` outputs 46.

			``math "bitor(9,2)"`` outputs 11.

math: Add --base option Currently a bit limited, unfortunately printf's `%a` specifier is absolutely unreadable. So we add `hex` and `octal` with `0x` and `0` prefixes respectively, and also take a number but currently only allow 16 and 8. The output is truncated to integer, so scale values other than 0 are invalid and 0 is implied. The docs mention this may change. 2020-10-08 01:03:19 +08:00			``math --base=hex 192`` prints ``0xc0``.

docs: Document the math functions better 2021-03-12 02:46:02 +08:00			``math 'ncr(49,6)'`` prints 13983816 - that's the number of possible picks in 6-from-49 lotto.

Convert \\subsection sections into rst format 2018-12-19 10:44:30 +08:00			`Compatibility notes`
Fix command section separator line lengths 2019-01-03 12:10:47 +08:00			`-------------------`
Copy doc_src to sphinx_doc_src and add a TOC 2018-12-17 05:08:41 +08:00
Switch backticks to double backticks for rst compatibility 2018-12-20 04:02:45 +08:00			Fish 1.x and 2.x releases relied on the ``bc`` command for handling ``math`` expressions. Starting with fish 3.0.0 fish uses the tinyexpr library and evaluates the expression without the involvement of any external commands.
Copy doc_src to sphinx_doc_src and add a TOC 2018-12-17 05:08:41 +08:00
docs: minor updates to math documentation Closes #7734. 2021-02-21 21:34:15 +08:00			You don't need to use ``--`` before the expression, even if it begins with a minus sign which might otherwise be interpreted as an invalid option. If you do insert ``--`` before the expression, it will cause option scanning to stop just like for every other command and it won't be part of the expression.