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<li><a class="reference internal" href="#">math - perform mathematics calculations</a><ul>
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<section id="math-perform-mathematics-calculations">
<h1>math - perform mathematics calculations<a class="headerlink" href="#math-perform-mathematics-calculations" title="Link to this heading">¶</a></h1>
<section id="synopsis">
<h2>Synopsis<a class="headerlink" href="#synopsis" title="Link to this heading">¶</a></h2>
<div class="highlight-fish-synopsis notranslate"><div class="highlight"><pre><span></span><span class="nf">math</span><span class="w"> </span><span class="g g-Other">[(</span><span class="no">-s</span><span class="w"> </span><span class="g g-Other">|</span><span class="w"> </span><span class="no">--scale</span><span class="g g-Other">)</span><span class="w"> </span><span class="no">N</span><span class="g g-Other">]</span><span class="w"> </span><span class="g g-Other">[(</span><span class="no">-b</span><span class="w"> </span><span class="g g-Other">|</span><span class="w"> </span><span class="no">--base</span><span class="g g-Other">)</span><span class="w"> </span><span class="no">BASE</span><span class="g g-Other">]</span><span class="w"> </span><span class="g g-Other">[(</span><span class="no">-m</span><span class="w"> </span><span class="g g-Other">|</span><span class="w"> </span><span class="no">--scale-mode</span><span class="g g-Other">)</span><span class="w"> </span><span class="no">MODE</span><span class="g g-Other">]</span><span class="w"> </span><span class="no">EXPRESSION</span><span class="w"> </span><span class="g g-Other">...</span>
</pre></div>
</div>
</section>
<section id="description">
<h2>Description<a class="headerlink" href="#description" title="Link to this heading">¶</a></h2>
<p><code class="docutils literal notranslate"><span class="pre">math</span></code> performs mathematical calculations.
It supports simple operations such as addition, subtraction, and so on, as well as functions like <code class="docutils literal notranslate"><span class="pre">abs()</span></code>, <code class="docutils literal notranslate"><span class="pre">sqrt()</span></code> and <code class="docutils literal notranslate"><span class="pre">ln()</span></code>.</p>
<p>By default, the output shows up to 6 decimal places.
To change the number of decimal places, use the <code class="docutils literal notranslate"><span class="pre">--scale</span></code> option, including <code class="docutils literal notranslate"><span class="pre">--scale=0</span></code> for integer output.</p>
<p>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 (<code class="docutils literal notranslate"><span class="pre">()</span></code>) and the asterisk (<code class="docutils literal notranslate"><span class="pre">*</span></code>) glob character have to be escaped or quoted.
<code class="docutils literal notranslate"><span class="pre">x</span></code> can also be used to denote multiplication, but it needs to be followed by whitespace to distinguish it from hexadecimal numbers.</p>
<p>Parentheses for functions are optional - <code class="docutils literal notranslate"><span class="pre">math</span> <span class="pre">sin</span> <span class="pre">pi</span></code> prints <code class="docutils literal notranslate"><span class="pre">0</span></code>.
However, a comma will bind to the inner function, so <code class="docutils literal notranslate"><span class="pre">math</span> <span class="pre">pow</span> <span class="pre">sin</span> <span class="pre">3,</span> <span class="pre">5</span></code> is an error because it tries to give <code class="docutils literal notranslate"><span class="pre">sin</span></code> the arguments <code class="docutils literal notranslate"><span class="pre">3</span></code> and <code class="docutils literal notranslate"><span class="pre">5</span></code>.
When in doubt, use parentheses.</p>
<p><code class="docutils literal notranslate"><span class="pre">math</span></code> ignores whitespace between arguments and takes its input as multiple arguments (internally joined with a space), so <code class="docutils literal notranslate"><span class="pre">math</span> <span class="pre">2</span> <span class="pre">+2</span></code> and <code class="docutils literal notranslate"><span class="pre">math</span> <span class="pre">"2</span> <span class="pre">+</span>    <span class="pre">2"</span></code> work the same.
<code class="docutils literal notranslate"><span class="pre">math</span> <span class="pre">2</span> <span class="pre">2</span></code> is an error.</p>
<p>The following options are available:</p>
<dl class="simple">
<dt><strong>-s</strong> <em>N</em> or <strong>--scale</strong> <em>N</em></dt><dd><p>Sets the scale of the result.
<code class="docutils literal notranslate"><span class="pre">N</span></code> must be an integer or the word “max” for the maximum scale.
A scale of zero causes results to be truncated by default. Any non-integer component is thrown away.
So <code class="docutils literal notranslate"><span class="pre">3/2</span></code> returns <code class="docutils literal notranslate"><span class="pre">1</span></code> by default, rather than <code class="docutils literal notranslate"><span class="pre">2</span></code> which <code class="docutils literal notranslate"><span class="pre">1.5</span></code> would normally round to.
This is for compatibility with <code class="docutils literal notranslate"><span class="pre">bc</span></code> 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.</p>
</dd>
<dt><strong>-b</strong> <em>BASE</em> or <strong>--base</strong> <em>BASE</em></dt><dd><p>Sets the numeric base used for output (<code class="docutils literal notranslate"><span class="pre">math</span></code> 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 <code class="docutils literal notranslate"><span class="pre">0x</span></code> prefix.
Octal numbers will have a prefix of <code class="docutils literal notranslate"><span class="pre">0</span></code> but aren’t understood by <code class="docutils literal notranslate"><span class="pre">math</span></code> as input.</p>
</dd>
<dt><strong>-m</strong> <em>MODE</em> or <strong>--scale-mode</strong> <em>MODE</em></dt><dd><p>Sets scale behavior.
The <code class="docutils literal notranslate"><span class="pre">MODE</span></code> can be <code class="docutils literal notranslate"><span class="pre">truncate</span></code>, <code class="docutils literal notranslate"><span class="pre">round</span></code>, <code class="docutils literal notranslate"><span class="pre">floor</span></code>, <code class="docutils literal notranslate"><span class="pre">ceiling</span></code>.
The default value of scale mode is <code class="docutils literal notranslate"><span class="pre">round</span></code> with non zero scale and <code class="docutils literal notranslate"><span class="pre">truncate</span></code> with zero scale.</p>
</dd>
<dt><strong>-h</strong> or <strong>--help</strong></dt><dd><p>Displays help about using this command.</p>
</dd>
</dl>
</section>
<section id="return-values">
<h2>Return Values<a class="headerlink" href="#return-values" title="Link to this heading">¶</a></h2>
<p>If the expression is successfully evaluated and doesn’t over/underflow or return NaN the return <code class="docutils literal notranslate"><span class="pre">status</span></code> is zero (success) else one.</p>
</section>
<section id="syntax">
<h2>Syntax<a class="headerlink" href="#syntax" title="Link to this heading">¶</a></h2>
<p><code class="docutils literal notranslate"><span class="pre">math</span></code> knows some operators, constants, functions and can (obviously) read numbers.</p>
<p>For numbers, <code class="docutils literal notranslate"><span class="pre">.</span></code> is always the radix character regardless of locale - <code class="docutils literal notranslate"><span class="pre">2.5</span></code>, not <code class="docutils literal notranslate"><span class="pre">2,5</span></code>.
Scientific notation (<code class="docutils literal notranslate"><span class="pre">10e5</span></code>) and hexadecimal (<code class="docutils literal notranslate"><span class="pre">0xFF</span></code>) are also available.</p>
<p><code class="docutils literal notranslate"><span class="pre">math</span></code> allows you to use underscores as visual separators for digit grouping. For example, you can write <code class="docutils literal notranslate"><span class="pre">1_000_000</span></code>, <code class="docutils literal notranslate"><span class="pre">0x_89_AB_CD_EF</span></code>, and <code class="docutils literal notranslate"><span class="pre">1.234_567_e89</span></code>.</p>
</section>
<section id="operators">
<h2>Operators<a class="headerlink" href="#operators" title="Link to this heading">¶</a></h2>
<p><code class="docutils literal notranslate"><span class="pre">math</span></code> knows the following operators:</p>
<dl class="simple">
<dt><code class="docutils literal notranslate"><span class="pre">+</span></code></dt><dd><p>for addition</p>
</dd>
<dt><code class="docutils literal notranslate"><span class="pre">-</span></code></dt><dd><p>for subtraction</p>
</dd>
<dt><code class="docutils literal notranslate"><span class="pre">*</span></code> or <code class="docutils literal notranslate"><span class="pre">x</span></code></dt><dd><p>for multiplication. <code class="docutils literal notranslate"><span class="pre">*</span></code> is the glob character and needs to be quoted or escaped, <code class="docutils literal notranslate"><span class="pre">x</span></code> needs to be followed by whitespace or it looks like <code class="docutils literal notranslate"><span class="pre">0x</span></code> hexadecimal notation.</p>
</dd>
<dt><code class="docutils literal notranslate"><span class="pre">/</span></code></dt><dd><p>for division</p>
</dd>
<dt><code class="docutils literal notranslate"><span class="pre">^</span></code></dt><dd><p>for exponentiation</p>
</dd>
<dt><code class="docutils literal notranslate"><span class="pre">%</span></code></dt><dd><p>for modulo</p>
</dd>
<dt><code class="docutils literal notranslate"><span class="pre">(</span></code> or <code class="docutils literal notranslate"><span class="pre">)</span></code></dt><dd><p>for grouping. These need to be quoted or escaped because <code class="docutils literal notranslate"><span class="pre">()</span></code> denotes a command substitution.</p>
</dd>
</dl>
<p>They are all used in an infix manner - <code class="docutils literal notranslate"><span class="pre">5</span> <span class="pre">+</span> <span class="pre">2</span></code>, not <code class="docutils literal notranslate"><span class="pre">+</span> <span class="pre">5</span> <span class="pre">2</span></code>.</p>
</section>
<section id="constants">
<h2>Constants<a class="headerlink" href="#constants" title="Link to this heading">¶</a></h2>
<p><code class="docutils literal notranslate"><span class="pre">math</span></code> knows the following constants:</p>
<dl class="simple">
<dt><code class="docutils literal notranslate"><span class="pre">e</span></code></dt><dd><p>Euler’s number</p>
</dd>
<dt><code class="docutils literal notranslate"><span class="pre">pi</span></code></dt><dd><p>π, you know this one.
Half of Tau</p>
</dd>
<dt><code class="docutils literal notranslate"><span class="pre">tau</span></code></dt><dd><p>Equivalent to 2π, or the number of radians in a circle</p>
</dd>
</dl>
<p>Use them without a leading <code class="docutils literal notranslate"><span class="pre">$</span></code> - <code class="docutils literal notranslate"><span class="pre">pi</span> <span class="pre">-</span> <span class="pre">3</span></code> should be about 0.</p>
</section>
<section id="functions">
<h2>Functions<a class="headerlink" href="#functions" title="Link to this heading">¶</a></h2>
<p><code class="docutils literal notranslate"><span class="pre">math</span></code> supports the following functions:</p>
<dl>
<dt><code class="docutils literal notranslate"><span class="pre">abs</span></code></dt><dd><p>the absolute value, with positive sign</p>
</dd>
<dt><code class="docutils literal notranslate"><span class="pre">acos</span></code></dt><dd><p>arc cosine</p>
</dd>
<dt><code class="docutils literal notranslate"><span class="pre">asin</span></code></dt><dd><p>arc sine</p>
</dd>
<dt><code class="docutils literal notranslate"><span class="pre">atan</span></code></dt><dd><p>arc tangent</p>
</dd>
<dt><code class="docutils literal notranslate"><span class="pre">atan2</span></code></dt><dd><p>arc tangent of two variables</p>
</dd>
<dt><code class="docutils literal notranslate"><span class="pre">bitand</span></code>, <code class="docutils literal notranslate"><span class="pre">bitor</span></code> and <code class="docutils literal notranslate"><span class="pre">bitxor</span></code></dt><dd><p>perform bitwise operations.
These will throw away any non-integer parts and interpret the rest as an int.</p>
<p>Note: <code class="docutils literal notranslate"><span class="pre">bitnot</span></code> and <code class="docutils literal notranslate"><span class="pre">bitnand</span></code> don’t exist. This is because numbers in math don’t really have a <em>width</em> in terms of bits,
and these operations necessarily care about leading zeroes.</p>
<p>If you need to negate a specific number you can do it with an xor with a mask, e.g.:</p>
<div class="highlight-fish-docs-samples notranslate"><div class="highlight"><pre><span></span><span class="gp">> </span><span class="nf">math</span><span class="w"> </span><span class="no">--base=hex</span><span class="w"> </span><span class="no">bitxor</span><span class="w"> </span><span class="no">0x0F,</span><span class="w"> </span><span class="no">0xFF</span>
<span class="go">0xF0</span>
<span class="gp">> </span><span class="nf">math</span><span class="w"> </span><span class="no">--base=hex</span><span class="w"> </span><span class="no">bitxor</span><span class="w"> </span><span class="no">0x2,</span><span class="w"> </span><span class="no">0x3</span>
<span class="go"># Here we mask with 0x3 == 0b111, so our number is 3 bits wide</span>
<span class="go"># Only the 1 bit isn't set.</span>
<span class="go">0x1</span>
</pre></div>
</div>
</dd>
<dt><code class="docutils literal notranslate"><span class="pre">ceil</span></code></dt><dd><p>round number up to the nearest integer</p>
</dd>
<dt><code class="docutils literal notranslate"><span class="pre">cos</span></code></dt><dd><p>the cosine</p>
</dd>
<dt><code class="docutils literal notranslate"><span class="pre">cosh</span></code></dt><dd><p>hyperbolic cosine</p>
</dd>
<dt><code class="docutils literal notranslate"><span class="pre">exp</span></code></dt><dd><p>the base-e exponential function</p>
</dd>
<dt><code class="docutils literal notranslate"><span class="pre">fac</span></code></dt><dd><p>factorial - also known as <code class="docutils literal notranslate"><span class="pre">x!</span></code> (<code class="docutils literal notranslate"><span class="pre">x</span> <span class="pre">*</span> <span class="pre">(x</span> <span class="pre">-</span> <span class="pre">1)</span> <span class="pre">*</span> <span class="pre">(x</span> <span class="pre">-</span> <span class="pre">2)</span> <span class="pre">*</span> <span class="pre">...</span> <span class="pre">*</span> <span class="pre">1</span></code>)</p>
</dd>
<dt><code class="docutils literal notranslate"><span class="pre">floor</span></code></dt><dd><p>round number down to the nearest integer</p>
</dd>
<dt><code class="docutils literal notranslate"><span class="pre">ln</span></code></dt><dd><p>the base-e logarithm</p>
</dd>
<dt><code class="docutils literal notranslate"><span class="pre">log</span></code> or <code class="docutils literal notranslate"><span class="pre">log10</span></code></dt><dd><p>the base-10 logarithm</p>
</dd>
<dt><code class="docutils literal notranslate"><span class="pre">log2</span></code></dt><dd><p>the base-2 logarithm</p>
</dd>
<dt><code class="docutils literal notranslate"><span class="pre">max</span></code></dt><dd><p>returns the largest of the given numbers - this takes an arbitrary number of arguments (but at least one)</p>
</dd>
<dt><code class="docutils literal notranslate"><span class="pre">min</span></code></dt><dd><p>returns the smallest of the given numbers - this takes an arbitrary number of arguments (but at least one)</p>
</dd>
<dt><code class="docutils literal notranslate"><span class="pre">ncr</span></code></dt><dd><p>“from n choose r” combination function - how many subsets of size r can be taken from n (order doesn’t matter)</p>
</dd>
<dt><code class="docutils literal notranslate"><span class="pre">npr</span></code></dt><dd><p>the number of subsets of size r that can be taken from a set of n elements (including different order)</p>
</dd>
<dt><code class="docutils literal notranslate"><span class="pre">pow(x,y)</span></code></dt><dd><p>returns x to the y (and can be written as <code class="docutils literal notranslate"><span class="pre">x</span> <span class="pre">^</span> <span class="pre">y</span></code>)</p>
</dd>
<dt><code class="docutils literal notranslate"><span class="pre">round</span></code></dt><dd><p>rounds to the nearest integer, away from 0</p>
</dd>
<dt><code class="docutils literal notranslate"><span class="pre">sin</span></code></dt><dd><p>the sine function</p>
</dd>
<dt><code class="docutils literal notranslate"><span class="pre">sinh</span></code></dt><dd><p>the hyperbolic sine</p>
</dd>
<dt><code class="docutils literal notranslate"><span class="pre">sqrt</span></code></dt><dd><p>the square root - (can also be written as <code class="docutils literal notranslate"><span class="pre">x</span> <span class="pre">^</span> <span class="pre">0.5</span></code>)</p>
</dd>
<dt><code class="docutils literal notranslate"><span class="pre">tan</span></code></dt><dd><p>the tangent</p>
</dd>
<dt><code class="docutils literal notranslate"><span class="pre">tanh</span></code></dt><dd><p>the hyperbolic tangent</p>
</dd>
</dl>
<p>All of the trigonometric functions use radians (the pi-based scale, not 360°).</p>
</section>
<section id="examples">
<h2>Examples<a class="headerlink" href="#examples" title="Link to this heading">¶</a></h2>
<p><code class="docutils literal notranslate"><span class="pre">math</span> <span class="pre">1+1</span></code> outputs 2.</p>
<p><code class="docutils literal notranslate"><span class="pre">math</span> <span class="pre">$status</span> <span class="pre">-</span> <span class="pre">128</span></code> outputs the numerical exit status of the last command minus 128.</p>
<p><code class="docutils literal notranslate"><span class="pre">math</span> <span class="pre">10</span> <span class="pre">/</span> <span class="pre">6</span></code> outputs <code class="docutils literal notranslate"><span class="pre">1.666667</span></code>.</p>
<p><code class="docutils literal notranslate"><span class="pre">math</span> <span class="pre">-s0</span> <span class="pre">10.0</span> <span class="pre">/</span> <span class="pre">6.0</span></code> outputs <code class="docutils literal notranslate"><span class="pre">1</span></code>.</p>
<p><code class="docutils literal notranslate"><span class="pre">math</span> <span class="pre">-s3</span> <span class="pre">10</span> <span class="pre">/</span> <span class="pre">6</span></code> outputs <code class="docutils literal notranslate"><span class="pre">1.667</span></code>.</p>
<p><code class="docutils literal notranslate"><span class="pre">math</span> <span class="pre">"sin(pi)"</span></code> outputs <code class="docutils literal notranslate"><span class="pre">0</span></code>.</p>
<p><code class="docutils literal notranslate"><span class="pre">math</span> <span class="pre">5</span> <span class="pre">\*</span> <span class="pre">2</span></code> or <code class="docutils literal notranslate"><span class="pre">math</span> <span class="pre">"5</span> <span class="pre">*</span> <span class="pre">2"</span></code> or <code class="docutils literal notranslate"><span class="pre">math</span> <span class="pre">5</span> <span class="pre">"*"</span> <span class="pre">2</span></code> all output <code class="docutils literal notranslate"><span class="pre">10</span></code>.</p>
<p><code class="docutils literal notranslate"><span class="pre">math</span> <span class="pre">0xFF</span></code> outputs 255, <code class="docutils literal notranslate"><span class="pre">math</span> <span class="pre">0</span> <span class="pre">x</span> <span class="pre">3</span></code> outputs 0 (because it computes 0 multiplied by 3).</p>
<p><code class="docutils literal notranslate"><span class="pre">math</span> <span class="pre">bitand</span> <span class="pre">0xFE,</span> <span class="pre">0x2e</span></code> outputs 46.</p>
<p><code class="docutils literal notranslate"><span class="pre">math</span> <span class="pre">"bitor(9,2)"</span></code> outputs 11.</p>
<p><code class="docutils literal notranslate"><span class="pre">math</span> <span class="pre">--base=hex</span> <span class="pre">192</span></code> prints <code class="docutils literal notranslate"><span class="pre">0xc0</span></code>.</p>
<p><code class="docutils literal notranslate"><span class="pre">math</span> <span class="pre">'ncr(49,6)'</span></code> prints 13983816 - that’s the number of possible picks in 6-from-49 lotto.</p>
<p><code class="docutils literal notranslate"><span class="pre">math</span> <span class="pre">max</span> <span class="pre">5,2,3,1</span></code> prints 5.</p>
</section>
<section id="compatibility-notes">
<h2>Compatibility notes<a class="headerlink" href="#compatibility-notes" title="Link to this heading">¶</a></h2>
<p>Fish 1.x and 2.x releases relied on the <code class="docutils literal notranslate"><span class="pre">bc</span></code> command for handling <code class="docutils literal notranslate"><span class="pre">math</span></code> expressions. Starting with fish 3.0.0 fish uses the tinyexpr library and evaluates the expression without the involvement of any external commands.</p>
<p>You don’t need to use <code class="docutils literal notranslate"><span class="pre">--</span></code> before the expression, even if it begins with a minus sign which might otherwise be interpreted as an invalid option. If you do insert <code class="docutils literal notranslate"><span class="pre">--</span></code> 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.</p>
</section>
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