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<!doctype html><html lang=en class=no-js> <head><meta charset=utf-8><meta name=viewport content="width=device-width,initial-scale=1"><link href=https://flokoe.github.io/bash-hackers-wiki/syntax/arith_expr/ rel=canonical><link href=../../snipplets/xclip/ rel=prev><link href=../arrays/ rel=next><link rel=icon href=../../assets/images/favicon.png><meta name=generator content="mkdocs-1.6.1, mkdocs-material-9.5.44"><title>Arithmetic expressions - The Bash Hackers Wiki</title><link rel=stylesheet href=../../assets/stylesheets/main.0253249f.min.css><link rel=stylesheet href=../../assets/stylesheets/palette.06af60db.min.css><link rel=preconnect href=https://fonts.gstatic.com crossorigin><link rel=stylesheet href="https://fonts.googleapis.com/css?family=Roboto:300,300i,400,400i,700,700i%7CRoboto+Mono:400,400i,700,700i&display=fallback"><style>:root{--md-text-font:"Roboto";--md-code-font:"Roboto Mono"}</style><script>__md_scope=new URL("../..",location),__md_hash=e=>[...e].reduce(((e,_)=>(e<<5)-e+_.charCodeAt(0)),0),__md_get=(e,_=localStorage,t=__md_scope)=>JSON.parse(_.getItem(t.pathname+"."+e)),__md_set=(e,_,t=localStorage,a=__md_scope)=>{try{t.setItem(a.pathname+"."+e,JSON.stringify(_))}catch(e){}}</script></head> <body dir=ltr data-md-color-scheme=default data-md-color-primary=indigo data-md-color-accent=indigo> <input class=md-toggle data-md-toggle=drawer type=checkbox id=__drawer autocomplete=off> <input class=md-toggle data-md-toggle=search type=checkbox id=__search autocomplete=off> <label class=md-overlay for=__drawer></label> <div data-md-component=skip> <a href=#arithmetic-expressions class=md-skip> Skip to content </a> </div> <div data-md-component=announce> </div> <header class=md-header data-md-component=header> <nav class="md-header__inner md-grid" aria-label=Header> <a href=../.. title="The Bash Hackers Wiki" class="md-header__button md-logo" aria-label="The Bash Hackers Wiki" data-md-component=logo> <svg xmlns=http://www.w3.org/2000/svg viewbox="0 0 24 24"><path d="M12 8a3 3 0 0 0 3-3 3 3 0 0 0-3-3 3 3 0 0 0-3 3 3 3 0 0 0 3 3m0 3.54C9.64 9.35 6.5 8 3 8v11c3.5 0 6.64 1.35 9 3.54 2.36-2.19 5.5-3.54 9-3.54V8c-3.5 0-6.64 1.35-9 3.54"/></svg> </a> <label class="md-header__button md-icon" for=__drawer> <svg xmlns=http://www.w3.org/2000/svg viewbox="0 0 24 24"><path d="M3 6h18v2H3zm0 5h18v2H3zm0 5h18v2H3z"/></svg> </label> <div class=md-header__title data-md-component=header-title> <div class=md-header__ellipsis> <div class=md-header__topic> <span class=md-ellipsis> The Bash Hackers Wiki </span> </div> <div class=md-header__topic data-md-component=header-topic> <span class=md-ellipsis> Arithmetic expressions </span> </div> </div> </div> <form class=md-header__option data-md-component=palette> <input class=md-option data-md-color-media data-md-color-scheme=default data-md-color-primary=indigo data-md-color-accent=indigo aria-label="Switch to dark mode" type=radio name=__palette id=__palette_0> <label class="md-header__button md-icon" title="Switch to dark mode" for=__palette_1 hidden> <svg xmlns=http://www.w3.org/2000/svg viewbox="0 0 24 24"><path d="M12 8a4 4 0 0 0-4 4 4 4 0 0 0 4 4 4 4 0 0 0 4-4 4 4 0 0 0-4-4m0 10a6 6 0 0 1-6-6 6 6 0 0 1 6-6 6 6 0 0 1 6 6 6 6 0 0 1-6 6m8-9.31V4h-4.69L12 .69 8.69 4H4v4.69L.69 12 4 15.31V20h4.69L12 23.31 15.31 20H20v-4.69L23.31 12z"/></svg> </label> <input class=md-option data-md-color-media data-md-color-scheme=slate data-md-color-primary=indigo data-md-color-accent=indigo aria-label="Switch to light mode" type=radio name=__palette id=__palette_1> <label class="md-header__button md-icon" title="Switch to light mode" for=__palette_0 hidden> <svg xmlns=http://www.w3.org/2000/svg viewbox="0 0 24 24"><path d="M12 18c-.89 0-1.74-.2-2.5-.55C11.56 16.5 13 14.42 13 12s-1.44-4.5-3.5-5.45C10.26 6.2 11.11 6 12 6a6 6 0 0 1 6 6 6 6 0 0 1-6 6m8-9.31V4h-4.69L12 .69 8.69 4H4v4.69L.69 12 4 15.31V20h4.69L12 23.31 15.31 20H20v-4.69L23.31 12z"/></svg> </label> </form> <script>var palette=__md_get("__palette");if(palette&&palette.color){if("(prefers-color-scheme)"===palette.color.media){var media=matchMedia
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</code></pre></div> <p>this is interpreted as an octal value. If you want it to be interpreted as a decimal value, you need to expand the parameter and specify base 10:</p> <div class=highlight><pre><span></span><code># this is interpreted as a decimal:
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echo $(( 10#$x ))
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# this is interpreted as an octal:
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echo $(( x ))
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# this is an invalid digit for base 10 (the "x")...:
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echo $(( 10#x ))
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</code></pre></div> <h2 id=different-bases>Different bases<a class=headerlink href=#different-bases title="Permanent link">¶</a></h2> <p>For a constant, the base can be specified using the form</p> <div class=highlight><pre><span></span><code><BASE>#<DIGITS...>
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</code></pre></div> <p>Regardless of the specified base, the arithmetic expressions will, if ever displayed, be <strong>displayed in decimal</strong>!</p> <p>When no base is specified, the base 10 (decimal) is assumed, except when the prefixes as mentioned above (octals, hexadecimals) are present. The specified base can range from 2 to 64. To represent digits in a specified base greater than 10, characters other than 0 to 9 are needed (in this order, low => high):</p> <ul> <li><code>0 ... 9</code></li> <li><code>a ... z</code></li> <li><code>A ... Z</code></li> <li><code>@</code></li> <li><code>_</code></li> </ul> <p>Let's quickly invent a new number system with base 43 to show what I mean:</p> <div class=highlight><pre><span></span><code>$ echo $((43#1))
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1
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$ echo $((43#a))
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10
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$echo $((43#A))
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36
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$ echo $((43#G))
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42
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$ echo $((43#H))
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bash: 43#H: value too great for base (error token is "43#H")
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</code></pre></div> <p>If you have no clue what a base is and why there might be other bases, and what numbers are and how they are built, then you don't need different bases.</p> <p>If you want to convert between the usual bases (octal, decimal, hex), use <a href=../../commands/builtin/printf/ >the printf command</a> and its format strings.</p> <h2 id=shell-variables>Shell variables<a class=headerlink href=#shell-variables title="Permanent link">¶</a></h2> <p>Shell variables can of course be used as operands, even when the integer attribute is not turned on (by <code>declare -i <NAME></code>). If the variable is empty (null) or unset, its reference evaluates to 0. If the variable doesn't hold a value that looks like a valid expression (numbers or operations), the expression is re-used to reference, for example, the named parameters, e.g.:</p> <div class=highlight><pre><span></span><code>test=string
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string=3
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echo $((test))
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# will output "3"!
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</code></pre></div> <p>Of course, in the end, when it finally evaluates to something that is <strong>not</strong> a valid arithmetic expression (newlines, ordinary text, ...) then you'll get an error.</p> <p>When variables are referenced, the notation <code>1 + $X</code> is equivalent to the notation <code>1 + X</code>, both are allowed.</p> <p>When variables are referenced like <code>$X</code>, the rules of <a href=../pe/ >parameter expansion</a> apply and are performed <strong>before</strong> the expression is evaluated. Thus, a construct like <code>${MYSTRING:4:3}</code> is valid inside an arithmetic expression.</p> <h2 id=truth>Truth<a class=headerlink href=#truth title="Permanent link">¶</a></h2> <p>Unlike command exit and return codes, arithmetic expressions evaluate to logical "true" when they are not 0. When they are 0, they evaluate to "false". The <a href=../ccmd/arithmetic_eval/ >arithmetic evaluation compound command</a> reverses the "truth" of an arithmetic expression to match the "truth" of command exit codes:</p> <ul> <li>if the arithmetic expression brings up a value not 0 (arithmetic true), it returns 0 (shell true)</li> <li>if the arithmetic expression evaluates to 0 (arithmetic false), it returns 1 (shell false)</li> </ul> <p>That means, the following <code>if</code>-clause will execute the <code>else</code>-thread:</p> <div class=highlight><pre><span></span><code>if ((0)); then
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echo "true"
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else
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echo "false"
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fi
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</code></pre></div> <h2 id=operators>Operators<a class=headerlink href=#operators title="Permanent link">¶</a></h2> <h3 id=assignment>Assignment<a class=headerlink href=#assignment title="Permanent link">¶</a></h3> <table> <thead> <tr> <th>Operator</th> <th>Description</th> </tr> </thead> <tbody> <tr> <td><code><ID> = <EXPR></code></td> <td>normal assignment</td> </tr> <tr> <td><code><ID> *= <EXPR></code></td> <td>equivalent to <code><ID> = <ID> * <EXPR></code>, see <a href=./#calculations>calculation operators</a></td> </tr> <tr> <td><code><ID> /= <EXPR></code></td> <td>equivalent to <code><ID> = <ID> / <EXPR></code>, see <a href=./#calculations>calculation operators</a></td> </tr> <tr> <td><code><ID> %= <EXPR></code></td> <td>equivalent to <code><ID> = <ID> % <EXPR></code>, see <a href=./#calculations>calculation operators</a></td> </tr> <tr> <td><code><ID> += <EXPR></code></td> <td>equivalent to <code><ID> = <ID> + <EXPR></code>, see <a href=./#calculations>calculation operators</a></td> </tr> <tr> <td><code><ID> -= <EXPR></code></td> <td>equivalent to <code><ID> = <ID> - <EXPR></code>, see <a href=./#calculations>calculation operators</a></td> </tr> <tr> <td><code><ID> <<= <NUMBER></code></td> <td>equivalent to <code><ID> = <ID> << <NUMBER></code>, see <a href=./#bit_operations>bit operations</a></td> </tr> <tr> <td><code><ID> >>= <NUMBER></code></td> <td>equivalent to <code><ID> = <ID> >> <NUMBER></code>, see <a href=./#bit_operations>bit operations</a></td> </tr> <tr> <td><code><ID> &= <EXPR></code></td> <td>equivalent to <code><ID> = <ID> & <EXPR></code>, see <a href=./#bit_operations>bit operations</a></td> </tr> <tr> <td><code><ID> ^= <EXPR></code></td> <td>equivalent to <code><ID> = <ID> ^ <EXPR></code>, see <a href=./#bit_operations>bit operations</a></td> </tr> <tr> <td><code><ID>|= <EXPR></code></td> <td>equivalent to <code><ID> = <ID>|<EXPR></code>, see <a href=./#bit_operations>bit operations</a></td> </tr> </tbody> </table> <h3 id=calculations>Calculations<a class=headerlink href=#calculations title="Permanent link">¶</a></h3> <table> <thead> <tr> <th>Operator</th> <th>Description</th> </tr> </thead> <tbody> <tr> <td><code>*</code></td> <td>multiplication</td> </tr> <tr> <td><code>/</code></td> <td>division</td> </tr> <tr> <td><code>%</code></td> <td>remainder (modulo)</td> </tr> <tr> <td><code>+</code></td> <td>addition</td> </tr> <tr> <td><code>-</code></td> <td>subtraction</td> </tr> <tr> <td><code>**</code></td> <td>exponentiation</td> </tr> </tbody> </table> <h3 id=comparisons>Comparisons<a class=headerlink href=#comparisons title="Permanent link">¶</a></h3> <table> <thead> <tr> <th>Operator</th> <th>Description</th> </tr> </thead> <tbody> <tr> <td><code><</code></td> <td>comparison: less than</td> </tr> <tr> <td><code>></code></td> <td>comparison: greater than</td> </tr> <tr> <td><code><=</code></td> <td>comparison: less than or equal</td> </tr> <tr> <td><code>>=</code></td> <td>comparison: greater than or equal</td> </tr> <tr> <td><code>==</code></td> <td>equality</td> </tr> <tr> <td><code>!=</code></td> <td>inequality</td> </tr> </tbody> </table> <h3 id=bit-operations>Bit operations<a class=headerlink href=#bit-operations title="Permanent link">¶</a></h3> <table> <thead> <tr> <th>Operator</th> <th>Description</th> </tr> </thead> <tbody> <tr> <td><code>~</code></td> <td>bitwise negation</td> </tr> <tr> <td><code><<</code></td> <td>bitwise shifting (left)</td> </tr> <tr> <td><code>>></code></td> <td>bitwise shifting (right)</td> </tr> <tr> <td><code>&</code></td> <td>bitwise AND</td> </tr> <tr> <td><code>^</code></td> <td>bitwise exclusive OR (XOR)</td> </tr> <tr> <td><code>|</code></td> <td>bitwise OR</td> <
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<a id=__codelineno-0-2 name=__codelineno-0-2 href=#__codelineno-0-2></a>
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<a id=__codelineno-0-3 name=__codelineno-0-3 href=#__codelineno-0-3></a><span class=k>if</span><span class=w> </span><span class=o>((</span>MY_TEST_FLAG<span class=o>))</span><span class=p>;</span><span class=w> </span><span class=k>then</span>
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<a id=__codelineno-0-4 name=__codelineno-0-4 href=#__codelineno-0-4></a><span class=w> </span><span class=nb>echo</span><span class=w> </span><span class=s2>"MY_TEST_FLAG is ON"</span>
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<a id=__codelineno-0-5 name=__codelineno-0-5 href=#__codelineno-0-5></a><span class=k>else</span>
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<a id=__codelineno-0-6 name=__codelineno-0-6 href=#__codelineno-0-6></a><span class=w> </span><span class=nb>echo</span><span class=w> </span><span class=s2>"MY_TEST_FLAG is OFF"</span>
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<a id=__codelineno-0-7 name=__codelineno-0-7 href=#__codelineno-0-7></a><span class=k>fi</span>
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</code></pre></div> <div class="admonition warning"> <p class=admonition-title>Beware that <code>set -e</code> can change the runtime behavior of scripts.</p> <p>For example,</p> <p>This non-equivalence of code behavior deserves some attention. Consider what happens if v happens to be zero in the expression below:</p> <div class=highlight><pre><span></span><code><a id=__codelineno-1-1 name=__codelineno-1-1 href=#__codelineno-1-1></a><span class=o>((</span><span class=nv>v</span><span class=w> </span><span class=o>+=</span><span class=w> </span><span class=m>0</span><span class=o>))</span>
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<a id=__codelineno-1-2 name=__codelineno-1-2 href=#__codelineno-1-2></a><span class=nb>echo</span><span class=w> </span><span class=nv>$?</span>
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</code></pre></div> <p>1</p> <p>("FAILURE")</p> <div class=highlight><pre><span></span><code><a id=__codelineno-2-1 name=__codelineno-2-1 href=#__codelineno-2-1></a><span class=nv>v</span><span class=o>=</span><span class=k>$((</span><span class=nv>v</span><span class=w> </span><span class=o>+</span><span class=w> </span><span class=m>0</span><span class=k>))</span>
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<a id=__codelineno-2-2 name=__codelineno-2-2 href=#__codelineno-2-2></a><span class=nb>echo</span><span class=w> </span><span class=nv>$?</span>
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</code></pre></div> <p>0</p> <p>("SUCCESS")</p> <p>The return code behavior is not equivalent to the arithmetic behavior, as has been noted.</p> <p>A workaround is to use a list operation that returns True, or use the second assignment style.</p> <div class=highlight><pre><span></span><code><a id=__codelineno-3-1 name=__codelineno-3-1 href=#__codelineno-3-1></a><span class=o>((</span><span class=nv>v</span><span class=w> </span><span class=o>+=</span><span class=w> </span><span class=m>0</span><span class=o>))</span><span class=w> </span><span class=o>||</span><span class=w> </span>:
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<a id=__codelineno-3-2 name=__codelineno-3-2 href=#__codelineno-3-2></a><span class=nb>echo</span><span class=w> </span><span class=nv>$?</span>
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</code></pre></div> <p>0</p> <p>("SUCCESS")</p> <p>This change in code behavior was discovered once the script was run under set -e.</p> </div> <h2 id=arithmetic-expressions-in-bash>Arithmetic expressions in Bash<a class=headerlink href=#arithmetic-expressions-in-bash title="Permanent link">¶</a></h2> <ul> <li><a href=../ccmd/c_for/ >The C-style for-loop</a></li> <li><a href=../expansion/arith/ >Arithmetic expansion</a></li> <li><a href=../ccmd/arithmetic_eval/ >Arithmetic evaluation compound command</a></li> <li><a href=../../commands/builtin/let/ >The "let" builtin command</a></li> </ul> <aside class=md-source-file> <span class=md-source-file__fact> <span class=md-icon title="Last update"> <svg xmlns=http://www.w3.org/2000/svg viewbox="0 0 24 24"><path d="M21 13.1c-.1 0-.3.1-.4.2l-1 1 2.1 2.1 1-1c.2-.2.2-.6 0-.8l-1.3-1.3c-.1-.1-.2-.2-.4-.2m-1.9 1.8-6.1 6V23h2.1l6.1-6.1zM12.5 7v5.2l4 2.4-1 1L11 13V7zM11 21.9c-5.1-.5-9-4.8-9-9.9C2 6.5 6.5 2 12 2c5.3 0 9.6 4.1 10 9.3-.3-.1-.6-.2-1-.2s-.7.1-1 .2C19.6 7.2 16.2 4 12 4c-4.4 0-8 3.6-8 8 0 4.1 3.1 7.5 7.1 7.9l-.1.2z"/></svg> </span> <span class="git-revision-date-localized-plugin git-revision-date-localized-plugin-date">November 13, 2024</span> </span> <span class=md-source-file__fact> <span class=md-icon title=Created> <svg xmlns=http://www.w3.org/2000/svg viewbox="0 0 24 24"><path d="M14.47 15.08 11 13V7h1.5v5.25l3.08 1.83c-.41.28-.79.62-1.11 1m-1.39 4.84c-.36.05-.71.08-1.08.08-4.42 0-8-3.58-8-8s3.58-8 8-8 8 3.58 8 8c0 .37-.03.72-.08 1.08.69.1 1.33.32 1.92.64.1-.56.16-1.13.16-1.72 0-5.5-4.5-10-10-10S2 6.5 2 12s4.47 10 10 10c.59 0 1.16-.06 1.72-.16-.32-.59-.54-1.23-.64-1.92M18 15v3h-3v2h3v3h2v-3h3v-2h-3v-3z"/></svg> </span> <span class="git-revision-date-localized-plugin git-revision-date-localized-plugin-date">November 13, 2024</span> </span> </aside> <h2 id=__comments>Comments</h2> <script src=https://giscus.app/client.js data-repo=flokoe/bash-hackers-wiki data-repo-id=R_kgDOJ3Nr6Q data-category="Giscus Page Comments" data-category-id=DIC_kwDOJ3Nr6c4CXq9t data-mapping=pathname data-strict=1 data-reactions-enabled=1 data-emit-metadata=0 data-input-position=top data-theme=preferred_color_scheme data-lang=en data-loading=lazy crossorigin=anonymous async>
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