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<!DOCTYPE html><html lang='en'><head><title>[defs]</title><meta charset='UTF-8'/><link rel='stylesheet' type='text/css' href='14882.css'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Serif'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Sans'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Sans+Mono'/><link rel='icon' href='icon.png'/><link rel='stylesheet' type='text/css' href='expanded.css' title='Normal'/><link rel='alternate stylesheet' type='text/css' href='colored.css' title='Notes and examples colored'/><link rel='alternate stylesheet' type='text/css' href='normative-only.css' title='Notes and examples hidden'/></head><body><div class='wrapper'><h1 ><a class='secnum' style='min-width:50pt'>3</a> Terms and definitions <a class='abbr_ref' href='index.html#defs'>[defs]</a></h1><div class='para' id='1'><div class='marginalizedparent'><a class='marginalized' href='#1'>1</a></div><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-unitsdc6fb931ea342a21c76709e35f88b6d44ec9710d/source/intro.tex#L50'>#</a></div><div class='texpara'><div id='1.sentence-1' class='sentence'><a class='index' id=':definitions'></a>For the purposes of this document,
<!DOCTYPE html><html lang='en'><head><title>[defs]</title><meta charset='UTF-8'/><link rel='stylesheet' type='text/css' href='14882.css'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Serif'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Sans'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Sans+Mono'/><link rel='icon' href='icon.png'/><link rel='stylesheet' type='text/css' href='expanded.css' title='Normal'/><link rel='alternate stylesheet' type='text/css' href='colored.css' title='Notes and examples colored'/><link rel='alternate stylesheet' type='text/css' href='normative-only.css' title='Notes and examples hidden'/></head><body><div class='wrapper'><h1 ><a class='secnum' style='min-width:50pt'>3</a> Terms and definitions <a class='abbr_ref' href='index.html#defs'>[defs]</a></h1><div class='para' id='1'><div class='marginalizedparent'><a class='marginalized' href='#1'>1</a></div><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-units123b4c0f140a2d9b67d89230209e488889931198/source/intro.tex#L50'>#</a></div><div class='texpara'><div id='1.sentence-1' class='sentence'><a class='index' id=':definitions'></a>For the purposes of this document,
the terms and definitions given in
IEC 60050-102:2007/AMD3:2021,
IEC 60050-112:2010/AMD2:2020,
ISO 80000-2:2019,
and
N4971,
and the following apply<a class='hidden_link' href='#1.sentence-1'>.</a></div></div></div><div class='para' id='2'><div class='marginalizedparent'><a class='marginalized' href='#2'>2</a></div><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-unitsdc6fb931ea342a21c76709e35f88b6d44ec9710d/source/intro.tex#L61'>#</a></div><div class='texpara'><div id='2.sentence-1' class='sentence'>ISO and IEC maintain terminology databases
and the following apply<a class='hidden_link' href='#1.sentence-1'>.</a></div></div></div><div class='para' id='2'><div class='marginalizedparent'><a class='marginalized' href='#2'>2</a></div><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-units123b4c0f140a2d9b67d89230209e488889931198/source/intro.tex#L61'>#</a></div><div class='texpara'><div id='2.sentence-1' class='sentence'>ISO and IEC maintain terminology databases
for use in standardization
at the following addresses:
<ul class='itemize'><li id='2.1'><div class='marginalizedparent' style='left:-27mm'><a class='marginalized' href='#2.1'>(2.1)</a></div>ISO Online browsing platform: available at <a href='https://www.iso.org/obp'>https://www.iso.org/obp</a></li><li id='2.2'><div class='marginalizedparent' style='left:-27mm'><a class='marginalized' href='#2.2'>(2.2)</a></div>IEC Electropedia: available at <a href='http://www.electropedia.org'>http://www.electropedia.org</a></li></ul>

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<!DOCTYPE html><html lang='en'><head><title>[qty.helpers]</title><meta charset='UTF-8'/><link rel='stylesheet' type='text/css' href='14882.css'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Serif'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Sans'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Sans+Mono'/><link rel='icon' href='icon.png'/><link rel='stylesheet' type='text/css' href='expanded.css' title='Normal'/><link rel='alternate stylesheet' type='text/css' href='colored.css' title='Notes and examples colored'/><link rel='alternate stylesheet' type='text/css' href='normative-only.css' title='Notes and examples hidden'/></head><body><div class='wrapper'><h1 ><a class='secnum' style='min-width:50pt'>5</a> Quantities library <a class='abbr_ref' href='index.html#qties'>[qties]</a></h1><h2 ><a class='secnum' style='min-width:65pt'>5.5</a> Helpers <a class='abbr_ref'>[qty.helpers]</a></h2><div class='texpara'><div class='itemdecl' id='itemdecl:1'><div class='marginalizedparent'><a class='itemDeclLink' href='#itemdecl:1'>🔗</a></div><code class='itemdeclcode'><span class='keyword'>consteval</span> <span class='keyword'>bool</span> <span class='texttt'><i >converts-to-base-subobject-of</i></span><span class='parenthesis'>(</span>std<span class='operator'>::</span>meta type, std<span class='operator'>::</span>meta template_name<span class='parenthesis'>)</span>;
</code></div></div><div class='para' id='1'><div class='marginalizedparent'><a class='marginalized' href='#1'>1</a></div><div class='itemdescr'><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-unitsdc6fb931ea342a21c76709e35f88b6d44ec9710d/source/quantities.tex#L122'>#</a></div><div class='texpara'><div id='1.sentence-1' class='sentence'><i >Preconditions</i>: <span class='texttt'>is_<span class='shy'></span>type<span class='parenthesis'>(</span>type<span class='parenthesis'>)</span> <span class='operator'>&amp;</span><span class='operator'>&amp;</span> is_<span class='shy'></span>template<span class='parenthesis'>(</span>template_<span class='shy'></span>name<span class='parenthesis'>)</span></span> is <span class='texttt'><span class='literal'>true</span></span><a class='hidden_link' href='#1.sentence-1'>.</a></div></div></div></div><div class='para' id='2'><div class='marginalizedparent'><a class='marginalized' href='#2'>2</a></div><div class='itemdescr'><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-unitsdc6fb931ea342a21c76709e35f88b6d44ec9710d/source/quantities.tex#L126'>#</a></div><div class='texpara'><div id='2.sentence-1' class='sentence'><i >Returns</i>: <span class='texttt'><span class='literal'>true</span></span> if
</code></div></div><div class='para' id='1'><div class='marginalizedparent'><a class='marginalized' href='#1'>1</a></div><div class='itemdescr'><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-units123b4c0f140a2d9b67d89230209e488889931198/source/quantities.tex#L122'>#</a></div><div class='texpara'><div id='1.sentence-1' class='sentence'><i >Preconditions</i>: <span class='texttt'>is_<span class='shy'></span>type<span class='parenthesis'>(</span>type<span class='parenthesis'>)</span> <span class='operator'>&amp;</span><span class='operator'>&amp;</span> is_<span class='shy'></span>template<span class='parenthesis'>(</span>template_<span class='shy'></span>name<span class='parenthesis'>)</span></span> is <span class='texttt'><span class='literal'>true</span></span><a class='hidden_link' href='#1.sentence-1'>.</a></div></div></div></div><div class='para' id='2'><div class='marginalizedparent'><a class='marginalized' href='#2'>2</a></div><div class='itemdescr'><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-units123b4c0f140a2d9b67d89230209e488889931198/source/quantities.tex#L126'>#</a></div><div class='texpara'><div id='2.sentence-1' class='sentence'><i >Returns</i>: <span class='texttt'><span class='literal'>true</span></span> if
<span class='texttt'><span class='squarebracket'>[</span><span class='operator'>:</span>type<span class='operator'>:</span><span class='squarebracket'>]</span></span> has an unambiguous and accessible base
that is a specialization of <span class='texttt'><span class='squarebracket'>[</span><span class='operator'>:</span>template_<span class='shy'></span>name<span class='operator'>:</span><span class='squarebracket'>]</span></span>, and
<span class='texttt'><span class='literal'>false</span></span> otherwise<a class='hidden_link' href='#2.sentence-1'>.</a></div></div></div></div></div></body></html>

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<span class='keyword'>template</span><span class='anglebracket'>&lt;</span><span class='keyword'>typename</span> Rep<span class='anglebracket'>&gt;</span>
<span class='keyword'>constexpr</span> <span class='keyword'>bool</span> <span id='lib:is_tensor'><a class='hidden_link' href='#lib:is_tensor' title='5.6&emsp;Traits&emsp;[qty.traits]'>is_tensor</a></span> <span class='operator'>=</span> <span class='literal'>false</span>;
</code></div></div><div class='para' id='1'><div class='marginalizedparent'><a class='marginalized' href='#1'>1</a></div><div class='itemdescr'><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-unitsdc6fb931ea342a21c76709e35f88b6d44ec9710d/source/quantities.tex#L149'>#</a></div><div class='texpara'><div id='1.sentence-1' class='sentence'><i >Remarks</i>: Pursuant to <a href="https://wg21.link/namespace.std">N4971, [namespace.std]</a> (<a href='spec.ext.html' title='4.1&emsp;External'>[spec.<span class='shy'></span>ext]</a>),
</code></div></div><div class='para' id='1'><div class='marginalizedparent'><a class='marginalized' href='#1'>1</a></div><div class='itemdescr'><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-units123b4c0f140a2d9b67d89230209e488889931198/source/quantities.tex#L149'>#</a></div><div class='texpara'><div id='1.sentence-1' class='sentence'><i >Remarks</i>: Pursuant to <a href="https://wg21.link/namespace.std">N4971, [namespace.std]</a> (<a href='spec.ext.html' title='4.1&emsp;External'>[spec.<span class='shy'></span>ext]</a>),
users may specialize <span class='texttt'>is_<span class='shy'></span>scalar</span>, <span class='texttt'>is_<span class='shy'></span>vector</span>, and <span class='texttt'>is_<span class='shy'></span>tensor</span> to <span class='texttt'><span class='literal'>true</span></span>
for cv-unqualified program-defined types
which respectively represent

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<!DOCTYPE html><html lang='en'><head><title>[qty.types.general]</title><meta charset='UTF-8'/><link rel='stylesheet' type='text/css' href='14882.css'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Serif'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Sans'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Sans+Mono'/><link rel='icon' href='icon.png'/><link rel='stylesheet' type='text/css' href='expanded.css' title='Normal'/><link rel='alternate stylesheet' type='text/css' href='colored.css' title='Notes and examples colored'/><link rel='alternate stylesheet' type='text/css' href='normative-only.css' title='Notes and examples hidden'/></head><body><div class='wrapper'><h1 ><a class='secnum' style='min-width:50pt'>5</a> Quantities library <a class='abbr_ref' href='index.html#qties'>[qties]</a></h1><h2 ><a class='secnum' style='min-width:65pt'>5.8</a> Types <a class='abbr_ref' href='qty.types.html#general'>[qty.types]</a></h2><h3 ><a class='secnum' style='min-width:80pt'>5.8.1</a> General <a class='abbr_ref'>[qty.types.general]</a></h3><div class='para' id='1'><div class='marginalizedparent'><a class='marginalized' href='#1'>1</a></div><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-unitsdc6fb931ea342a21c76709e35f88b6d44ec9710d/source/quantities.tex#L196'>#</a></div><div class='texpara'><div id='1.sentence-1' class='sentence'>A <a class='hidden_link' href='#def:type,quantity' title='5.8.1&emsp;General&emsp;[qty.types.general]'><span id='def:type,quantity'><i >quantity type</i></span></a>
<!DOCTYPE html><html lang='en'><head><title>[qty.types.general]</title><meta charset='UTF-8'/><link rel='stylesheet' type='text/css' href='14882.css'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Serif'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Sans'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Sans+Mono'/><link rel='icon' href='icon.png'/><link rel='stylesheet' type='text/css' href='expanded.css' title='Normal'/><link rel='alternate stylesheet' type='text/css' href='colored.css' title='Notes and examples colored'/><link rel='alternate stylesheet' type='text/css' href='normative-only.css' title='Notes and examples hidden'/></head><body><div class='wrapper'><h1 ><a class='secnum' style='min-width:50pt'>5</a> Quantities library <a class='abbr_ref' href='index.html#qties'>[qties]</a></h1><h2 ><a class='secnum' style='min-width:65pt'>5.8</a> Types <a class='abbr_ref' href='qty.types.html#general'>[qty.types]</a></h2><h3 ><a class='secnum' style='min-width:80pt'>5.8.1</a> General <a class='abbr_ref'>[qty.types.general]</a></h3><div class='para' id='1'><div class='marginalizedparent'><a class='marginalized' href='#1'>1</a></div><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-units123b4c0f140a2d9b67d89230209e488889931198/source/quantities.tex#L196'>#</a></div><div class='texpara'><div id='1.sentence-1' class='sentence'>A <a class='hidden_link' href='#def:type,quantity' title='5.8.1&emsp;General&emsp;[qty.types.general]'><span id='def:type,quantity'><i >quantity type</i></span></a>
is a type <span class='texttt'><i >Q</i></span>
that is a specialization of <span class='texttt'>quantity</span> or <span class='texttt'>quantity_<span class='shy'></span>point</span><a class='hidden_link' href='#1.sentence-1'>.</a></div> <div id='1.sentence-2' class='sentence'><span class='texttt'><i >Q</i></span> represents a quantity (<a href="https://www.electropedia.org/iev/iev.nsf/display?openform&ievref=112-01-01">IEC 60050, 112-01-01</a>)
with <span class='texttt'><i >Q</i><span class='operator'>&#x200b;::&#x200b;</span>rep</span> as its number
and <span class='texttt'><i >Q</i><span class='operator'>&#x200b;::&#x200b;</span>reference</span> as its reference<a class='hidden_link' href='#1.sentence-2'>.</a></div> <div id='1.sentence-3' class='sentence'><span class='texttt'><i >Q</i></span> is a structural type (<a href="https://wg21.link/temp.paramterm.structural.type">N4971, [temp.param]</a>)
if <span class='texttt'><i >Q</i><span class='operator'>&#x200b;::&#x200b;</span>rep</span> is a structural type<a class='hidden_link' href='#1.sentence-3'>.</a></div></div></div><div class='para' id='2'><div class='marginalizedparent'><a class='marginalized' href='#2'>2</a></div><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-unitsdc6fb931ea342a21c76709e35f88b6d44ec9710d/source/quantities.tex#L206'>#</a></div><div class='texpara'><div id='2.sentence-1' class='sentence'>Each class template defined in subclause <a href='qty.types.html' title='5.8&emsp;Types'>[qty.<span class='shy'></span>types]</a>
if <span class='texttt'><i >Q</i><span class='operator'>&#x200b;::&#x200b;</span>rep</span> is a structural type<a class='hidden_link' href='#1.sentence-3'>.</a></div></div></div><div class='para' id='2'><div class='marginalizedparent'><a class='marginalized' href='#2'>2</a></div><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-units123b4c0f140a2d9b67d89230209e488889931198/source/quantities.tex#L206'>#</a></div><div class='texpara'><div id='2.sentence-1' class='sentence'>Each class template defined in subclause <a href='qty.types.html' title='5.8&emsp;Types'>[qty.<span class='shy'></span>types]</a>
has data members and special members specified below, and
has no base classes or members other than those specified<a class='hidden_link' href='#2.sentence-1'>.</a></div></div></div></div></body></html>

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<!DOCTYPE html><html lang='en'><head><title>[qty.types]</title><meta charset='UTF-8'/><link rel='stylesheet' type='text/css' href='14882.css'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Serif'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Sans'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Sans+Mono'/><link rel='icon' href='icon.png'/><link rel='stylesheet' type='text/css' href='expanded.css' title='Normal'/><link rel='alternate stylesheet' type='text/css' href='colored.css' title='Notes and examples colored'/><link rel='alternate stylesheet' type='text/css' href='normative-only.css' title='Notes and examples hidden'/></head><body><div class='wrapper'><h1 ><a class='secnum' style='min-width:50pt'>5</a> Quantities library <a class='abbr_ref' href='index.html#qties'>[qties]</a></h1><h2 ><a class='secnum' style='min-width:65pt'>5.8</a> Types <a class='abbr_ref'>[qty.types]</a></h2><div id='general' class='section'><h3 ><a class='secnum' href='#general' style='min-width:80pt'>5.8.1</a> General <a class='abbr_ref' href='qty.types.general.html'>[qty.types.general]</a></h3><div class='para' id='general-1'><div class='marginalizedparent'><a class='marginalized' href='#general-1'>1</a></div><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-unitsdc6fb931ea342a21c76709e35f88b6d44ec9710d/source/quantities.tex#L196'>#</a></div><div class='texpara'><div id='general-1.sentence-1' class='sentence'>A <a class='hidden_link' href='#def:type,quantity' title='5.8.1&emsp;General&emsp;[qty.types.general]'><span id='def:type,quantity'><i >quantity type</i></span></a>
<!DOCTYPE html><html lang='en'><head><title>[qty.types]</title><meta charset='UTF-8'/><link rel='stylesheet' type='text/css' href='14882.css'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Serif'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Sans'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Sans+Mono'/><link rel='icon' href='icon.png'/><link rel='stylesheet' type='text/css' href='expanded.css' title='Normal'/><link rel='alternate stylesheet' type='text/css' href='colored.css' title='Notes and examples colored'/><link rel='alternate stylesheet' type='text/css' href='normative-only.css' title='Notes and examples hidden'/></head><body><div class='wrapper'><h1 ><a class='secnum' style='min-width:50pt'>5</a> Quantities library <a class='abbr_ref' href='index.html#qties'>[qties]</a></h1><h2 ><a class='secnum' style='min-width:65pt'>5.8</a> Types <a class='abbr_ref'>[qty.types]</a></h2><div id='general' class='section'><h3 ><a class='secnum' href='#general' style='min-width:80pt'>5.8.1</a> General <a class='abbr_ref' href='qty.types.general.html'>[qty.types.general]</a></h3><div class='para' id='general-1'><div class='marginalizedparent'><a class='marginalized' href='#general-1'>1</a></div><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-units123b4c0f140a2d9b67d89230209e488889931198/source/quantities.tex#L196'>#</a></div><div class='texpara'><div id='general-1.sentence-1' class='sentence'>A <a class='hidden_link' href='#def:type,quantity' title='5.8.1&emsp;General&emsp;[qty.types.general]'><span id='def:type,quantity'><i >quantity type</i></span></a>
is a type <span class='texttt'><i >Q</i></span>
that is a specialization of <span class='texttt'>quantity</span> or <span class='texttt'>quantity_<span class='shy'></span>point</span><a class='hidden_link' href='#general-1.sentence-1'>.</a></div> <div id='general-1.sentence-2' class='sentence'><span class='texttt'><i >Q</i></span> represents a quantity (<a href="https://www.electropedia.org/iev/iev.nsf/display?openform&ievref=112-01-01">IEC 60050, 112-01-01</a>)
with <span class='texttt'><i >Q</i><span class='operator'>&#x200b;::&#x200b;</span>rep</span> as its number
and <span class='texttt'><i >Q</i><span class='operator'>&#x200b;::&#x200b;</span>reference</span> as its reference<a class='hidden_link' href='#general-1.sentence-2'>.</a></div> <div id='general-1.sentence-3' class='sentence'><span class='texttt'><i >Q</i></span> is a structural type (<a href="https://wg21.link/temp.paramterm.structural.type">N4971, [temp.param]</a>)
if <span class='texttt'><i >Q</i><span class='operator'>&#x200b;::&#x200b;</span>rep</span> is a structural type<a class='hidden_link' href='#general-1.sentence-3'>.</a></div></div></div><div class='para' id='general-2'><div class='marginalizedparent'><a class='marginalized' href='#general-2'>2</a></div><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-unitsdc6fb931ea342a21c76709e35f88b6d44ec9710d/source/quantities.tex#L206'>#</a></div><div class='texpara'><div id='general-2.sentence-1' class='sentence'>Each class template defined in subclause [qty.<span class='shy'></span>types]
if <span class='texttt'><i >Q</i><span class='operator'>&#x200b;::&#x200b;</span>rep</span> is a structural type<a class='hidden_link' href='#general-1.sentence-3'>.</a></div></div></div><div class='para' id='general-2'><div class='marginalizedparent'><a class='marginalized' href='#general-2'>2</a></div><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-units123b4c0f140a2d9b67d89230209e488889931198/source/quantities.tex#L206'>#</a></div><div class='texpara'><div id='general-2.sentence-1' class='sentence'>Each class template defined in subclause [qty.<span class='shy'></span>types]
has data members and special members specified below, and
has no base classes or members other than those specified<a class='hidden_link' href='#general-2.sentence-1'>.</a></div></div></div></div><div id='qty.type' class='section'><h3 ><a class='secnum' href='#qty.type' style='min-width:80pt'>5.8.2</a> Class template <span class='texttt'>quantity</span> <a class='abbr_ref' href='qty.type.html'>[qty.type]</a></h3><div class='texpara'><span class='codeblock'><span class='keyword'>namespace</span> mp_units <span class='curlybracket'>{</span>

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<!DOCTYPE html><html lang='en'><head><title>[refs]</title><meta charset='UTF-8'/><link rel='stylesheet' type='text/css' href='14882.css'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Serif'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Sans'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Sans+Mono'/><link rel='icon' href='icon.png'/><link rel='stylesheet' type='text/css' href='expanded.css' title='Normal'/><link rel='alternate stylesheet' type='text/css' href='colored.css' title='Notes and examples colored'/><link rel='alternate stylesheet' type='text/css' href='normative-only.css' title='Notes and examples hidden'/></head><body><div class='wrapper'><h1 ><a class='secnum' style='min-width:50pt'>2</a> References <a class='abbr_ref' href='index.html#refs'>[refs]</a></h1><div class='para' id='1'><div class='marginalizedparent'><a class='marginalized' href='#1'>1</a></div><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-unitsdc6fb931ea342a21c76709e35f88b6d44ec9710d/source/intro.tex#L14'>#</a></div><div class='texpara'><div id='1.sentence-1' class='sentence'><a class='index' id=':references'></a>The following documents are referred to in the text
<!DOCTYPE html><html lang='en'><head><title>[refs]</title><meta charset='UTF-8'/><link rel='stylesheet' type='text/css' href='14882.css'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Serif'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Sans'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Sans+Mono'/><link rel='icon' href='icon.png'/><link rel='stylesheet' type='text/css' href='expanded.css' title='Normal'/><link rel='alternate stylesheet' type='text/css' href='colored.css' title='Notes and examples colored'/><link rel='alternate stylesheet' type='text/css' href='normative-only.css' title='Notes and examples hidden'/></head><body><div class='wrapper'><h1 ><a class='secnum' style='min-width:50pt'>2</a> References <a class='abbr_ref' href='index.html#refs'>[refs]</a></h1><div class='para' id='1'><div class='marginalizedparent'><a class='marginalized' href='#1'>1</a></div><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-units123b4c0f140a2d9b67d89230209e488889931198/source/intro.tex#L14'>#</a></div><div class='texpara'><div id='1.sentence-1' class='sentence'><a class='index' id=':references'></a>The following documents are referred to in the text
in such a way that some or all of their content
constitutes requirements of this document<a class='hidden_link' href='#1.sentence-1'>.</a></div> <div id='1.sentence-2' class='sentence'>For dated references, only the edition cited applies<a class='hidden_link' href='#1.sentence-2'>.</a></div> <div id='1.sentence-3' class='sentence'>For undated references,
the latest edition of the referenced document

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<!DOCTYPE html><html lang='en'><head><title>[scope]</title><meta charset='UTF-8'/><link rel='stylesheet' type='text/css' href='14882.css'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Serif'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Sans'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Sans+Mono'/><link rel='icon' href='icon.png'/><link rel='stylesheet' type='text/css' href='expanded.css' title='Normal'/><link rel='alternate stylesheet' type='text/css' href='colored.css' title='Notes and examples colored'/><link rel='alternate stylesheet' type='text/css' href='normative-only.css' title='Notes and examples hidden'/></head><body><div class='wrapper'><h1 ><a class='secnum' style='min-width:50pt'>1</a> Scope <a class='abbr_ref' href='index.html#scope'>[scope]</a></h1><div class='para' id='1'><div class='marginalizedparent'><a class='marginalized' href='#1'>1</a></div><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-unitsdc6fb931ea342a21c76709e35f88b6d44ec9710d/source/intro.tex#L6'>#</a></div><div class='texpara'><div id='1.sentence-1' class='sentence'><a class='index' id=':scope'></a>This document describes the contents of the <a class='hidden_link' href='#def:mp-units_library' title='1&emsp;Scope&emsp;[scope]'><span id='def:mp-units_library'><i >mp-units library</i></span></a><a class='hidden_link' href='#1.sentence-1'>.</a></div> </div></div></div></body></html>
<!DOCTYPE html><html lang='en'><head><title>[scope]</title><meta charset='UTF-8'/><link rel='stylesheet' type='text/css' href='14882.css'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Serif'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Sans'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Sans+Mono'/><link rel='icon' href='icon.png'/><link rel='stylesheet' type='text/css' href='expanded.css' title='Normal'/><link rel='alternate stylesheet' type='text/css' href='colored.css' title='Notes and examples colored'/><link rel='alternate stylesheet' type='text/css' href='normative-only.css' title='Notes and examples hidden'/></head><body><div class='wrapper'><h1 ><a class='secnum' style='min-width:50pt'>1</a> Scope <a class='abbr_ref' href='index.html#scope'>[scope]</a></h1><div class='para' id='1'><div class='marginalizedparent'><a class='marginalized' href='#1'>1</a></div><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-units123b4c0f140a2d9b67d89230209e488889931198/source/intro.tex#L6'>#</a></div><div class='texpara'><div id='1.sentence-1' class='sentence'><a class='index' id=':scope'></a>This document describes the contents of the <a class='hidden_link' href='#def:mp-units_library' title='1&emsp;Scope&emsp;[scope]'><span id='def:mp-units_library'><i >mp-units library</i></span></a><a class='hidden_link' href='#1.sentence-1'>.</a></div> </div></div></div></body></html>

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<!DOCTYPE html><html lang='en'><head><title>[spec.cats]</title><meta charset='UTF-8'/><link rel='stylesheet' type='text/css' href='14882.css'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Serif'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Sans'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Sans+Mono'/><link rel='icon' href='icon.png'/><link rel='stylesheet' type='text/css' href='expanded.css' title='Normal'/><link rel='alternate stylesheet' type='text/css' href='colored.css' title='Notes and examples colored'/><link rel='alternate stylesheet' type='text/css' href='normative-only.css' title='Notes and examples hidden'/></head><body><div class='wrapper'><h1 ><a class='secnum' style='min-width:50pt'>4</a> Specification <a class='abbr_ref' href='index.html#spec'>[spec]</a></h1><h2 ><a class='secnum' style='min-width:65pt'>4.2</a> Categories <a class='abbr_ref'>[spec.cats]</a></h2><div class='para' id='1'><div class='marginalizedparent'><a class='marginalized' href='#1'>1</a></div><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-unitsdc6fb931ea342a21c76709e35f88b6d44ec9710d/source/intro.tex#L96'>#</a></div><div class='texpara'><div id='1.sentence-1' class='sentence'>Detailed specifications for each of the components in the library are in
<!DOCTYPE html><html lang='en'><head><title>[spec.cats]</title><meta charset='UTF-8'/><link rel='stylesheet' type='text/css' href='14882.css'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Serif'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Sans'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Sans+Mono'/><link rel='icon' href='icon.png'/><link rel='stylesheet' type='text/css' href='expanded.css' title='Normal'/><link rel='alternate stylesheet' type='text/css' href='colored.css' title='Notes and examples colored'/><link rel='alternate stylesheet' type='text/css' href='normative-only.css' title='Notes and examples hidden'/></head><body><div class='wrapper'><h1 ><a class='secnum' style='min-width:50pt'>4</a> Specification <a class='abbr_ref' href='index.html#spec'>[spec]</a></h1><h2 ><a class='secnum' style='min-width:65pt'>4.2</a> Categories <a class='abbr_ref'>[spec.cats]</a></h2><div class='para' id='1'><div class='marginalizedparent'><a class='marginalized' href='#1'>1</a></div><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-units123b4c0f140a2d9b67d89230209e488889931198/source/intro.tex#L96'>#</a></div><div class='texpara'><div id='1.sentence-1' class='sentence'>Detailed specifications for each of the components in the library are in
<a href='qties.html' title='5&emsp;Quantities library'>[qties]</a>–<a href='qties.html' title='5&emsp;Quantities library'>[qties]</a>,
as shown in Table <a href='#tab:lib.cats' title='Table 1: Library categories'>1</a><a class='hidden_link' href='#1.sentence-1'>.</a></div></div><div class='texpara'><div class='numberedTable' id='tab:lib.cats'>Table <a href='#tab:lib.cats'>1</a>: Library categories&emsp;<a href='./tab:lib.cats.html'>[tab:lib.cats]</a><br><table ><tr id='tab:lib.cats-row-1' class='rowsep'><td class='hidden'><div class='marginalizedparent'><a class='itemDeclLink' href='#tab:lib.cats-row-1'>🔗</a></div></td><td class='left'><div class='texpara'><div id='tab:lib.cats-row-1-column-1-sentence-1' class='sentence'><b>Clause</b></div></div></td><td class='left'><div class='texpara'><div id='tab:lib.cats-row-1-column-2-sentence-1' class='sentence'><b>Category</b></div></div></td></tr><tr id='tab:lib.cats-row-2' class='capsep'><td class='hidden'><div class='marginalizedparent'><a class='itemDeclLink' href='#tab:lib.cats-row-2'>🔗</a></div></td><td class='left'><div class='texpara'><div id='tab:lib.cats-row-2-column-1-sentence-1' class='sentence'><a href='qties.html' title='5&emsp;Quantities library'>[qties]</a></div></div></td><td class='left'><div class='texpara'><div id='tab:lib.cats-row-2-column-2-sentence-1' class='sentence'>Quantities library</div></div></td></tr></table></div></div></div><div class='para' id='2'><div class='marginalizedparent'><a class='marginalized' href='#2'>2</a></div><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-unitsdc6fb931ea342a21c76709e35f88b6d44ec9710d/source/intro.tex#L108'>#</a></div><div class='texpara'><div id='2.sentence-1' class='sentence'>The quantities library (<a href='qties.html' title='5&emsp;Quantities library'>[qties]</a>)
as shown in Table <a href='#tab:lib.cats' title='Table 1: Library categories'>1</a><a class='hidden_link' href='#1.sentence-1'>.</a></div></div><div class='texpara'><div class='numberedTable' id='tab:lib.cats'>Table <a href='#tab:lib.cats'>1</a>: Library categories&emsp;<a href='./tab:lib.cats.html'>[tab:lib.cats]</a><br><table ><tr id='tab:lib.cats-row-1' class='rowsep'><td class='hidden'><div class='marginalizedparent'><a class='itemDeclLink' href='#tab:lib.cats-row-1'>🔗</a></div></td><td class='left'><div class='texpara'><div id='tab:lib.cats-row-1-column-1-sentence-1' class='sentence'><b>Clause</b></div></div></td><td class='left'><div class='texpara'><div id='tab:lib.cats-row-1-column-2-sentence-1' class='sentence'><b>Category</b></div></div></td></tr><tr id='tab:lib.cats-row-2' class='capsep'><td class='hidden'><div class='marginalizedparent'><a class='itemDeclLink' href='#tab:lib.cats-row-2'>🔗</a></div></td><td class='left'><div class='texpara'><div id='tab:lib.cats-row-2-column-1-sentence-1' class='sentence'><a href='qties.html' title='5&emsp;Quantities library'>[qties]</a></div></div></td><td class='left'><div class='texpara'><div id='tab:lib.cats-row-2-column-2-sentence-1' class='sentence'>Quantities library</div></div></td></tr></table></div></div></div><div class='para' id='2'><div class='marginalizedparent'><a class='marginalized' href='#2'>2</a></div><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-units123b4c0f140a2d9b67d89230209e488889931198/source/intro.tex#L108'>#</a></div><div class='texpara'><div id='2.sentence-1' class='sentence'>The quantities library (<a href='qties.html' title='5&emsp;Quantities library'>[qties]</a>)
describes components for dealing with quantities<a class='hidden_link' href='#2.sentence-1'>.</a></div></div></div></div></body></html>

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<!DOCTYPE html><html lang='en'><head><title>[spec.ext]</title><meta charset='UTF-8'/><link rel='stylesheet' type='text/css' href='14882.css'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Serif'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Sans'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Sans+Mono'/><link rel='icon' href='icon.png'/><link rel='stylesheet' type='text/css' href='expanded.css' title='Normal'/><link rel='alternate stylesheet' type='text/css' href='colored.css' title='Notes and examples colored'/><link rel='alternate stylesheet' type='text/css' href='normative-only.css' title='Notes and examples hidden'/></head><body><div class='wrapper'><h1 ><a class='secnum' style='min-width:50pt'>4</a> Specification <a class='abbr_ref' href='index.html#spec'>[spec]</a></h1><h2 ><a class='secnum' style='min-width:65pt'>4.1</a> External <a class='abbr_ref'>[spec.ext]</a></h2><div class='para' id='1'><div class='marginalizedparent'><a class='marginalized' href='#1'>1</a></div><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-unitsdc6fb931ea342a21c76709e35f88b6d44ec9710d/source/intro.tex#L76'>#</a></div><div class='texpara'><div id='1.sentence-1' class='sentence'>The specification of the mp-units library subsumes
<!DOCTYPE html><html lang='en'><head><title>[spec.ext]</title><meta charset='UTF-8'/><link rel='stylesheet' type='text/css' href='14882.css'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Serif'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Sans'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Sans+Mono'/><link rel='icon' href='icon.png'/><link rel='stylesheet' type='text/css' href='expanded.css' title='Normal'/><link rel='alternate stylesheet' type='text/css' href='colored.css' title='Notes and examples colored'/><link rel='alternate stylesheet' type='text/css' href='normative-only.css' title='Notes and examples hidden'/></head><body><div class='wrapper'><h1 ><a class='secnum' style='min-width:50pt'>4</a> Specification <a class='abbr_ref' href='index.html#spec'>[spec]</a></h1><h2 ><a class='secnum' style='min-width:65pt'>4.1</a> External <a class='abbr_ref'>[spec.ext]</a></h2><div class='para' id='1'><div class='marginalizedparent'><a class='marginalized' href='#1'>1</a></div><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-units123b4c0f140a2d9b67d89230209e488889931198/source/intro.tex#L76'>#</a></div><div class='texpara'><div id='1.sentence-1' class='sentence'>The specification of the mp-units library subsumes
<a href="https://wg21.link/description">N4971, [description]</a>, <a href="https://wg21.link/requirements">N4971, [requirements]</a>, <a href="https://wg21.link/concepts.equality">N4971, [concepts.equality]</a>, and SD-8,
all assumingly amended for the context of this library<a class='hidden_link' href='#1.sentence-1'>.</a></div> <div id='note-1' class='note'><div class='texpara'>[<i>Note&nbsp;<a href='#note-1'>1</a></i>:&ensp;<div id='1.sentence-2' class='sentence'>This means that, non exhaustively,
<ul class='itemize'><li id='1.1'><div class='marginalizedparent' style='left:-27mm'><a class='marginalized' href='#1.1'>(1.1)</a></div><span class='texttt'><span class='operator'>&#x200b;::&#x200b;</span>mp_<span class='shy'></span>units2</span> is a reserved namespace, and</li><li id='1.2'><div class='marginalizedparent' style='left:-27mm'><a class='marginalized' href='#1.2'>(1.2)</a></div><span class='texttt'>std<span class='operator'>&#x200b;::&#x200b;</span>vector<span class='anglebracket'>&lt;</span>mp_<span class='shy'></span>units<span class='operator'>&#x200b;::&#x200b;</span><i >type</i><span class='anglebracket'>&gt;</span></span>
is a program-defined specialization and a library-defined specialization
from the point of view of the C++ standard library and the mp-units library, respectively<a class='hidden_link' href='#1.sentence-2'>.</a></li></ul></div> —&nbsp;<i>end note</i>]</div></div></div></div><div class='para' id='2'><div class='marginalizedparent'><a class='marginalized' href='#2'>2</a></div><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-unitsdc6fb931ea342a21c76709e35f88b6d44ec9710d/source/intro.tex#L91'>#</a></div><div class='texpara'><div id='2.sentence-1' class='sentence'>The mp-units library is not part of the C++ implementation<a class='hidden_link' href='#2.sentence-1'>.</a></div></div></div></div></body></html>
from the point of view of the C++ standard library and the mp-units library, respectively<a class='hidden_link' href='#1.sentence-2'>.</a></li></ul></div> —&nbsp;<i>end note</i>]</div></div></div></div><div class='para' id='2'><div class='marginalizedparent'><a class='marginalized' href='#2'>2</a></div><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-units123b4c0f140a2d9b67d89230209e488889931198/source/intro.tex#L91'>#</a></div><div class='texpara'><div id='2.sentence-1' class='sentence'>The mp-units library is not part of the C++ implementation<a class='hidden_link' href='#2.sentence-1'>.</a></div></div></div></div></body></html>

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<!DOCTYPE html><html lang='en'><head><title>[spec]</title><meta charset='UTF-8'/><link rel='stylesheet' type='text/css' href='14882.css'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Serif'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Sans'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Sans+Mono'/><link rel='icon' href='icon.png'/><link rel='stylesheet' type='text/css' href='expanded.css' title='Normal'/><link rel='alternate stylesheet' type='text/css' href='colored.css' title='Notes and examples colored'/><link rel='alternate stylesheet' type='text/css' href='normative-only.css' title='Notes and examples hidden'/></head><body><div class='wrapper'><h1 ><a class='secnum' style='min-width:50pt'>4</a> Specification <a class='abbr_ref' href='index.html#spec'>[spec]</a></h1><div id='ext' class='section'><h2 ><a class='secnum' href='#ext' style='min-width:65pt'>4.1</a> External <a class='abbr_ref' href='spec.ext.html'>[spec.ext]</a></h2><div class='para' id='ext-1'><div class='marginalizedparent'><a class='marginalized' href='#ext-1'>1</a></div><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-unitsdc6fb931ea342a21c76709e35f88b6d44ec9710d/source/intro.tex#L76'>#</a></div><div class='texpara'><div id='ext-1.sentence-1' class='sentence'>The specification of the mp-units library subsumes
<!DOCTYPE html><html lang='en'><head><title>[spec]</title><meta charset='UTF-8'/><link rel='stylesheet' type='text/css' href='14882.css'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Serif'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Sans'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Sans+Mono'/><link rel='icon' href='icon.png'/><link rel='stylesheet' type='text/css' href='expanded.css' title='Normal'/><link rel='alternate stylesheet' type='text/css' href='colored.css' title='Notes and examples colored'/><link rel='alternate stylesheet' type='text/css' href='normative-only.css' title='Notes and examples hidden'/></head><body><div class='wrapper'><h1 ><a class='secnum' style='min-width:50pt'>4</a> Specification <a class='abbr_ref' href='index.html#spec'>[spec]</a></h1><div id='ext' class='section'><h2 ><a class='secnum' href='#ext' style='min-width:65pt'>4.1</a> External <a class='abbr_ref' href='spec.ext.html'>[spec.ext]</a></h2><div class='para' id='ext-1'><div class='marginalizedparent'><a class='marginalized' href='#ext-1'>1</a></div><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-units123b4c0f140a2d9b67d89230209e488889931198/source/intro.tex#L76'>#</a></div><div class='texpara'><div id='ext-1.sentence-1' class='sentence'>The specification of the mp-units library subsumes
<a href="https://wg21.link/description">N4971, [description]</a>, <a href="https://wg21.link/requirements">N4971, [requirements]</a>, <a href="https://wg21.link/concepts.equality">N4971, [concepts.equality]</a>, and SD-8,
all assumingly amended for the context of this library<a class='hidden_link' href='#ext-1.sentence-1'>.</a></div> <div id='ext-note-1' class='note'><div class='texpara'>[<i>Note&nbsp;<a href='#ext-note-1'>1</a></i>:&ensp;<div id='ext-1.sentence-2' class='sentence'>This means that, non exhaustively,
<ul class='itemize'><li id='ext-1.1'><div class='marginalizedparent' style='left:-27mm'><a class='marginalized' href='#ext-1.1'>(1.1)</a></div><span class='texttt'><span class='operator'>&#x200b;::&#x200b;</span>mp_<span class='shy'></span>units2</span> is a reserved namespace, and</li><li id='ext-1.2'><div class='marginalizedparent' style='left:-27mm'><a class='marginalized' href='#ext-1.2'>(1.2)</a></div><span class='texttt'>std<span class='operator'>&#x200b;::&#x200b;</span>vector<span class='anglebracket'>&lt;</span>mp_<span class='shy'></span>units<span class='operator'>&#x200b;::&#x200b;</span><i >type</i><span class='anglebracket'>&gt;</span></span>
is a program-defined specialization and a library-defined specialization
from the point of view of the C++ standard library and the mp-units library, respectively<a class='hidden_link' href='#ext-1.sentence-2'>.</a></li></ul></div> —&nbsp;<i>end note</i>]</div></div></div></div><div class='para' id='ext-2'><div class='marginalizedparent'><a class='marginalized' href='#ext-2'>2</a></div><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-unitsdc6fb931ea342a21c76709e35f88b6d44ec9710d/source/intro.tex#L91'>#</a></div><div class='texpara'><div id='ext-2.sentence-1' class='sentence'>The mp-units library is not part of the C++ implementation<a class='hidden_link' href='#ext-2.sentence-1'>.</a></div></div></div></div><div id='cats' class='section'><h2 ><a class='secnum' href='#cats' style='min-width:65pt'>4.2</a> Categories <a class='abbr_ref' href='spec.cats.html'>[spec.cats]</a></h2><div class='para' id='cats-1'><div class='marginalizedparent'><a class='marginalized' href='#cats-1'>1</a></div><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-unitsdc6fb931ea342a21c76709e35f88b6d44ec9710d/source/intro.tex#L96'>#</a></div><div class='texpara'><div id='cats-1.sentence-1' class='sentence'>Detailed specifications for each of the components in the library are in
from the point of view of the C++ standard library and the mp-units library, respectively<a class='hidden_link' href='#ext-1.sentence-2'>.</a></li></ul></div> —&nbsp;<i>end note</i>]</div></div></div></div><div class='para' id='ext-2'><div class='marginalizedparent'><a class='marginalized' href='#ext-2'>2</a></div><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-units123b4c0f140a2d9b67d89230209e488889931198/source/intro.tex#L91'>#</a></div><div class='texpara'><div id='ext-2.sentence-1' class='sentence'>The mp-units library is not part of the C++ implementation<a class='hidden_link' href='#ext-2.sentence-1'>.</a></div></div></div></div><div id='cats' class='section'><h2 ><a class='secnum' href='#cats' style='min-width:65pt'>4.2</a> Categories <a class='abbr_ref' href='spec.cats.html'>[spec.cats]</a></h2><div class='para' id='cats-1'><div class='marginalizedparent'><a class='marginalized' href='#cats-1'>1</a></div><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-units123b4c0f140a2d9b67d89230209e488889931198/source/intro.tex#L96'>#</a></div><div class='texpara'><div id='cats-1.sentence-1' class='sentence'>Detailed specifications for each of the components in the library are in
<a href='qties.html' title='5&emsp;Quantities library'>[qties]</a>–<a href='qties.html' title='5&emsp;Quantities library'>[qties]</a>,
as shown in Table <a href='#tab:lib.cats' title='Table 1: Library categories'>1</a><a class='hidden_link' href='#cats-1.sentence-1'>.</a></div></div><div class='texpara'><div class='numberedTable' id='tab:lib.cats'>Table <a href='#tab:lib.cats'>1</a>: Library categories&emsp;<a href='./tab:lib.cats.html'>[tab:lib.cats]</a><br><table ><tr id='tab:lib.cats-row-1' class='rowsep'><td class='hidden'><div class='marginalizedparent'><a class='itemDeclLink' href='#tab:lib.cats-row-1'>🔗</a></div></td><td class='left'><div class='texpara'><div id='tab:lib.cats-row-1-column-1-sentence-1' class='sentence'><b>Clause</b></div></div></td><td class='left'><div class='texpara'><div id='tab:lib.cats-row-1-column-2-sentence-1' class='sentence'><b>Category</b></div></div></td></tr><tr id='tab:lib.cats-row-2' class='capsep'><td class='hidden'><div class='marginalizedparent'><a class='itemDeclLink' href='#tab:lib.cats-row-2'>🔗</a></div></td><td class='left'><div class='texpara'><div id='tab:lib.cats-row-2-column-1-sentence-1' class='sentence'><a href='qties.html' title='5&emsp;Quantities library'>[qties]</a></div></div></td><td class='left'><div class='texpara'><div id='tab:lib.cats-row-2-column-2-sentence-1' class='sentence'>Quantities library</div></div></td></tr></table></div></div></div><div class='para' id='cats-2'><div class='marginalizedparent'><a class='marginalized' href='#cats-2'>2</a></div><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-unitsdc6fb931ea342a21c76709e35f88b6d44ec9710d/source/intro.tex#L108'>#</a></div><div class='texpara'><div id='cats-2.sentence-1' class='sentence'>The quantities library (<a href='qties.html' title='5&emsp;Quantities library'>[qties]</a>)
describes components for dealing with quantities<a class='hidden_link' href='#cats-2.sentence-1'>.</a></div></div></div></div><div id='mods' class='section'><h2 ><a class='secnum' href='#mods' style='min-width:65pt'>4.3</a> Modules <a class='abbr_ref' href='spec.mods.html'>[spec.mods]</a></h2><div class='para' id='mods-1'><div class='marginalizedparent'><a class='marginalized' href='#mods-1'>1</a></div><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-unitsdc6fb931ea342a21c76709e35f88b6d44ec9710d/source/intro.tex#L114'>#</a></div><div class='texpara'><div id='mods-1.sentence-1' class='sentence'>The mp-units library provides the
as shown in Table <a href='#tab:lib.cats' title='Table 1: Library categories'>1</a><a class='hidden_link' href='#cats-1.sentence-1'>.</a></div></div><div class='texpara'><div class='numberedTable' id='tab:lib.cats'>Table <a href='#tab:lib.cats'>1</a>: Library categories&emsp;<a href='./tab:lib.cats.html'>[tab:lib.cats]</a><br><table ><tr id='tab:lib.cats-row-1' class='rowsep'><td class='hidden'><div class='marginalizedparent'><a class='itemDeclLink' href='#tab:lib.cats-row-1'>🔗</a></div></td><td class='left'><div class='texpara'><div id='tab:lib.cats-row-1-column-1-sentence-1' class='sentence'><b>Clause</b></div></div></td><td class='left'><div class='texpara'><div id='tab:lib.cats-row-1-column-2-sentence-1' class='sentence'><b>Category</b></div></div></td></tr><tr id='tab:lib.cats-row-2' class='capsep'><td class='hidden'><div class='marginalizedparent'><a class='itemDeclLink' href='#tab:lib.cats-row-2'>🔗</a></div></td><td class='left'><div class='texpara'><div id='tab:lib.cats-row-2-column-1-sentence-1' class='sentence'><a href='qties.html' title='5&emsp;Quantities library'>[qties]</a></div></div></td><td class='left'><div class='texpara'><div id='tab:lib.cats-row-2-column-2-sentence-1' class='sentence'>Quantities library</div></div></td></tr></table></div></div></div><div class='para' id='cats-2'><div class='marginalizedparent'><a class='marginalized' href='#cats-2'>2</a></div><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-units123b4c0f140a2d9b67d89230209e488889931198/source/intro.tex#L108'>#</a></div><div class='texpara'><div id='cats-2.sentence-1' class='sentence'>The quantities library (<a href='qties.html' title='5&emsp;Quantities library'>[qties]</a>)
describes components for dealing with quantities<a class='hidden_link' href='#cats-2.sentence-1'>.</a></div></div></div></div><div id='mods' class='section'><h2 ><a class='secnum' href='#mods' style='min-width:65pt'>4.3</a> Modules <a class='abbr_ref' href='spec.mods.html'>[spec.mods]</a></h2><div class='para' id='mods-1'><div class='marginalizedparent'><a class='marginalized' href='#mods-1'>1</a></div><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-units123b4c0f140a2d9b67d89230209e488889931198/source/intro.tex#L114'>#</a></div><div class='texpara'><div id='mods-1.sentence-1' class='sentence'>The mp-units library provides the
<a class='hidden_link' href='#def:module,mp-units' title='4.3&emsp;Modules&emsp;[spec.mods]'><span id='def:module,mp-units'><i >mp-units modules</i></span></a>,
shown in Table <a href='#tab:modules' title='Table 2: mp-units modules'>2</a><a class='hidden_link' href='#mods-1.sentence-1'>.</a></div></div><div class='texpara'><div class='numberedTable' id='tab:modules'>Table <a href='#tab:modules'>2</a>: mp-units modules&emsp;<a href='./tab:modules.html'>[tab:modules]</a><br><table ><tr id='tab:modules-row-1'><td class='hidden'><div class='marginalizedparent'><a class='itemDeclLink' href='#tab:modules-row-1'>🔗</a></div></td><td class='left'><div class='texpara'><div id='tab:modules-row-1-column-1-sentence-1' class='sentence'><span class='texttt'>mp_<span class='shy'></span>units</span></div></div></td><td class='left'><div class='texpara'><div id='tab:modules-row-1-column-2-sentence-1' class='sentence'><span class='texttt'>mp_<span class='shy'></span>units<span class='operator'>.</span>core</span></div></div></td><td class='left'><div class='texpara'><div id='tab:modules-row-1-column-3-sentence-1' class='sentence'><span class='texttt'>mp_<span class='shy'></span>units<span class='operator'>.</span>systems</span></div></div></td></tr></table></div></div></div></div><div id='reqs' class='section'><h2 ><a class='secnum' href='#reqs' style='min-width:65pt'>4.4</a> Library-wide requirements <a class='abbr_ref' href='spec.reqs.html'>[spec.reqs]</a></h2><div id='res.names' class='section'><h3 ><a class='secnum' href='#res.names' style='min-width:80pt'>4.4.1</a> Reserved names <a class='abbr_ref' href='spec.res.names.html'>[spec.res.names]</a></h3><div class='para' id='res.names-1'><div class='marginalizedparent'><a class='marginalized' href='#res.names-1'>1</a></div><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-unitsdc6fb931ea342a21c76709e35f88b6d44ec9710d/source/intro.tex#L132'>#</a></div><div class='texpara'><div id='res.names-1.sentence-1' class='sentence'>The mp-units library reserves macro names that start with
shown in Table <a href='#tab:modules' title='Table 2: mp-units modules'>2</a><a class='hidden_link' href='#mods-1.sentence-1'>.</a></div></div><div class='texpara'><div class='numberedTable' id='tab:modules'>Table <a href='#tab:modules'>2</a>: mp-units modules&emsp;<a href='./tab:modules.html'>[tab:modules]</a><br><table ><tr id='tab:modules-row-1'><td class='hidden'><div class='marginalizedparent'><a class='itemDeclLink' href='#tab:modules-row-1'>🔗</a></div></td><td class='left'><div class='texpara'><div id='tab:modules-row-1-column-1-sentence-1' class='sentence'><span class='texttt'>mp_<span class='shy'></span>units</span></div></div></td><td class='left'><div class='texpara'><div id='tab:modules-row-1-column-2-sentence-1' class='sentence'><span class='texttt'>mp_<span class='shy'></span>units<span class='operator'>.</span>core</span></div></div></td><td class='left'><div class='texpara'><div id='tab:modules-row-1-column-3-sentence-1' class='sentence'><span class='texttt'>mp_<span class='shy'></span>units<span class='operator'>.</span>systems</span></div></div></td></tr></table></div></div></div></div><div id='reqs' class='section'><h2 ><a class='secnum' href='#reqs' style='min-width:65pt'>4.4</a> Library-wide requirements <a class='abbr_ref' href='spec.reqs.html'>[spec.reqs]</a></h2><div id='res.names' class='section'><h3 ><a class='secnum' href='#res.names' style='min-width:80pt'>4.4.1</a> Reserved names <a class='abbr_ref' href='spec.res.names.html'>[spec.res.names]</a></h3><div class='para' id='res.names-1'><div class='marginalizedparent'><a class='marginalized' href='#res.names-1'>1</a></div><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-units123b4c0f140a2d9b67d89230209e488889931198/source/intro.tex#L132'>#</a></div><div class='texpara'><div id='res.names-1.sentence-1' class='sentence'>The mp-units library reserves macro names that start with
<span class='texttt'>MP_<span class='shy'></span>UNITS<span class='textsf'><i >digit-sequence</i></span><span class="mjx-chtml"><span class="mjx-math"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char"></span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mstyle" style="font-size: 113.1%; color: black;"><span class="mjx-mrow" style="font-size: 88.4%;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">o</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-I" style="padding-top: 0.225em; padding-bottom: 0.446em;">p</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span></span></span></span></span></span>_<span class='shy'></span></span><a class='hidden_link' href='#res.names-1.sentence-1'>.</a></div></div></div></div></div></div></body></html>

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<!DOCTYPE html><html lang='en'><head><title>[spec.mods]</title><meta charset='UTF-8'/><link rel='stylesheet' type='text/css' href='14882.css'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Serif'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Sans'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Sans+Mono'/><link rel='icon' href='icon.png'/><link rel='stylesheet' type='text/css' href='expanded.css' title='Normal'/><link rel='alternate stylesheet' type='text/css' href='colored.css' title='Notes and examples colored'/><link rel='alternate stylesheet' type='text/css' href='normative-only.css' title='Notes and examples hidden'/></head><body><div class='wrapper'><h1 ><a class='secnum' style='min-width:50pt'>4</a> Specification <a class='abbr_ref' href='index.html#spec'>[spec]</a></h1><h2 ><a class='secnum' style='min-width:65pt'>4.3</a> Modules <a class='abbr_ref'>[spec.mods]</a></h2><div class='para' id='1'><div class='marginalizedparent'><a class='marginalized' href='#1'>1</a></div><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-unitsdc6fb931ea342a21c76709e35f88b6d44ec9710d/source/intro.tex#L114'>#</a></div><div class='texpara'><div id='1.sentence-1' class='sentence'>The mp-units library provides the
<!DOCTYPE html><html lang='en'><head><title>[spec.mods]</title><meta charset='UTF-8'/><link rel='stylesheet' type='text/css' href='14882.css'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Serif'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Sans'/><link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css2?family=Noto+Sans+Mono'/><link rel='icon' href='icon.png'/><link rel='stylesheet' type='text/css' href='expanded.css' title='Normal'/><link rel='alternate stylesheet' type='text/css' href='colored.css' title='Notes and examples colored'/><link rel='alternate stylesheet' type='text/css' href='normative-only.css' title='Notes and examples hidden'/></head><body><div class='wrapper'><h1 ><a class='secnum' style='min-width:50pt'>4</a> Specification <a class='abbr_ref' href='index.html#spec'>[spec]</a></h1><h2 ><a class='secnum' style='min-width:65pt'>4.3</a> Modules <a class='abbr_ref'>[spec.mods]</a></h2><div class='para' id='1'><div class='marginalizedparent'><a class='marginalized' href='#1'>1</a></div><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-units123b4c0f140a2d9b67d89230209e488889931198/source/intro.tex#L114'>#</a></div><div class='texpara'><div id='1.sentence-1' class='sentence'>The mp-units library provides the
<a class='hidden_link' href='#def:module,mp-units' title='4.3&emsp;Modules&emsp;[spec.mods]'><span id='def:module,mp-units'><i >mp-units modules</i></span></a>,
shown in Table <a href='#tab:modules' title='Table 2: mp-units modules'>2</a><a class='hidden_link' href='#1.sentence-1'>.</a></div></div><div class='texpara'><div class='numberedTable' id='tab:modules'>Table <a href='#tab:modules'>2</a>: mp-units modules&emsp;<a href='./tab:modules.html'>[tab:modules]</a><br><table ><tr id='tab:modules-row-1'><td class='hidden'><div class='marginalizedparent'><a class='itemDeclLink' href='#tab:modules-row-1'>🔗</a></div></td><td class='left'><div class='texpara'><div id='tab:modules-row-1-column-1-sentence-1' class='sentence'><span class='texttt'>mp_<span class='shy'></span>units</span></div></div></td><td class='left'><div class='texpara'><div id='tab:modules-row-1-column-2-sentence-1' class='sentence'><span class='texttt'>mp_<span class='shy'></span>units<span class='operator'>.</span>core</span></div></div></td><td class='left'><div class='texpara'><div id='tab:modules-row-1-column-3-sentence-1' class='sentence'><span class='texttt'>mp_<span class='shy'></span>units<span class='operator'>.</span>systems</span></div></div></td></tr></table></div></div></div></div></body></html>

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<span class='texttt'>MP_<span class='shy'></span>UNITS<span class='textsf'><i >digit-sequence</i></span><span class="mjx-chtml"><span class="mjx-math"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char"></span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mstyle" style="font-size: 113.1%; color: black;"><span class="mjx-mrow" style="font-size: 88.4%;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">o</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-I" style="padding-top: 0.225em; padding-bottom: 0.446em;">p</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span></span></span></span></span></span>_<span class='shy'></span></span><a class='hidden_link' href='#spec.res.names-1.sentence-1'>.</a></div></div></div></div></div></body></html>

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@ -2728,20 +2728,45 @@ and then verify that everything works as expected.</p>
</li>
<li>complex quantities expressed in VA (volt-ampere) (e.g., <em>complex power</em>).</li>
</ul>
<p>How should we model this? Maybe those should be two independent trees of quantities, each having
a different unit?</p>
<p>How should we model this? Maybe those should be two or three independent trees of quantities, each
having its own unit?</p>
<pre class="mermaid"><code>flowchart TD
power["&lt;b&gt;power&lt;/b&gt;&lt;br&gt;&lt;i&gt;(mass * length&lt;sup&gt;2&lt;/sup&gt; / time&lt;sup&gt;3&lt;/sup&gt;)&lt;/i&gt;&lt;br&gt;[W]"]
power --- mechanical_power["&lt;b&gt;mechanical_power&lt;/b&gt;&lt;br&gt;&lt;i&gt;(scalar_product(force, velocity))&lt;/i&gt;"]
power --- electromagnetism_power["&lt;b&gt;electromagnetism_power&lt;/b&gt; | &lt;b&gt;instantaneous_power&lt;/b&gt;&lt;br&gt;&lt;i&gt;(instantaneous_voltage * instantaneous_electric_current)&lt;/i&gt;"]
power --- active_power["&lt;b&gt;active_power&lt;/b&gt;&lt;br&gt;&lt;i&gt;(1 / period * instantaneous_power * time)&lt;br&gt;(re(complex_power))&lt;/i&gt;"]
apparent_power["&lt;b&gt;apparent_power&lt;/b&gt;&lt;br&gt;&lt;i&gt;(voltage * electric_current)&lt;br&gt;(mod(complex_power))&lt;/i&gt;&lt;br&gt;[VA]"]
nonactive_power["&lt;b&gt;nonactive_power&lt;/b&gt;&lt;br&gt;&lt;i&gt;(mass * length&lt;sup&gt;2&lt;/sup&gt; / time&lt;sup&gt;3&lt;/sup&gt;)&lt;/i&gt;&lt;br&gt;[VA]"]
nonactive_power --- reactive_power["&lt;b&gt;reactive_power&lt;/b&gt;&lt;br&gt;&lt;i&gt;(im(complex_power))&lt;/i&gt;&lt;br&gt;[var]"]
complex_power["&lt;b&gt;complex_power&lt;/b&gt;&lt;br&gt;{complex}&lt;br&gt;&lt;i&gt;(voltage_phasor * electric_current_phasor)&lt;br&gt;(active_power + j * reactive_power)&lt;/i&gt;&lt;br&gt;[VA]"]
complex_power --- apparent_power["&lt;b&gt;apparent_power&lt;/b&gt;&lt;br&gt;&lt;i&gt;(voltage * electric_current)&lt;br&gt;(mod(complex_power))&lt;/i&gt;"]</code></pre>
<p>This will mean that we will not be able to add or compare <em>active power</em>, <em>reactive power</em>, and
<em>apparent power</em>, which probably makes a lot of sense. However, it also means that the following
will fail to compile:</p>
<div class="language-cpp highlight"><pre><span></span><code><span id="__span-8-1"><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="n">quantity</span><span class="w"> </span><span class="n">apparent</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">isq</span><span class="o">::</span><span class="n">apparent_power</span><span class="p">(</span><span class="mi">100</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">VA</span><span class="p">);</span>
</span><span id="__span-8-2"><a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="n">quantity</span><span class="w"> </span><span class="n">active</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">isq</span><span class="o">::</span><span class="n">active_power</span><span class="p">(</span><span class="mi">60</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">W</span><span class="p">);</span>
</span><span id="__span-8-3"><a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="n">quantity</span><span class="o">&lt;</span><span class="n">isq</span><span class="o">::</span><span class="n">nonactive_power</span><span class="p">[</span><span class="n">VA</span><span class="p">]</span><span class="o">&gt;</span><span class="w"> </span><span class="n">q</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">sqrt</span><span class="p">(</span><span class="n">pow</span><span class="o">&lt;</span><span class="mi">2</span><span class="o">&gt;</span><span class="p">(</span><span class="n">apparent</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">pow</span><span class="o">&lt;</span><span class="mi">2</span><span class="o">&gt;</span><span class="p">(</span><span class="n">active</span><span class="p">));</span><span class="w"> </span><span class="c1">// Compile-time error</span>
</span></code></pre></div>
<p>Also the following will not work:</p>
<div class="language-cpp highlight"><pre><span></span><code><span id="__span-9-1"><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="n">quantity</span><span class="w"> </span><span class="n">active</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">isq</span><span class="o">::</span><span class="n">active_power</span><span class="p">(</span><span class="mi">60</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">W</span><span class="p">);</span>
</span><span id="__span-9-2"><a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="n">quantity</span><span class="w"> </span><span class="n">reactive</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">isq</span><span class="o">::</span><span class="n">reactive_power</span><span class="p">(</span><span class="mi">40</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">var</span><span class="p">);</span>
</span><span id="__span-9-3"><a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="n">quantity</span><span class="o">&lt;</span><span class="n">isq</span><span class="o">::</span><span class="n">apparent_power</span><span class="p">[</span><span class="n">VA</span><span class="p">]</span><span class="o">&gt;</span><span class="w"> </span><span class="n">q</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">sqrt</span><span class="p">(</span><span class="n">pow</span><span class="o">&lt;</span><span class="mi">2</span><span class="o">&gt;</span><span class="p">(</span><span class="n">active</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">pow</span><span class="o">&lt;</span><span class="mi">2</span><span class="o">&gt;</span><span class="p">(</span><span class="n">reactive</span><span class="p">));</span><span class="w"> </span><span class="c1">// Compile-time error</span>
</span></code></pre></div>
<p>If we want the above to work maybe we need to implement the tree as follows?</p>
<pre class="mermaid"><code>flowchart TD
power["&lt;b&gt;power&lt;/b&gt;&lt;br&gt;&lt;i&gt;(mass * length&lt;sup&gt;2&lt;/sup&gt; / time&lt;sup&gt;3&lt;/sup&gt;)&lt;/i&gt;&lt;br&gt;[W]"]
power --- mechanical_power["&lt;b&gt;mechanical_power&lt;/b&gt;&lt;br&gt;&lt;i&gt;(scalar_product(force, velocity))&lt;/i&gt;"]
power --- electromagnetism_power["&lt;b&gt;electromagnetism_power&lt;/b&gt; | &lt;b&gt;instantaneous_power&lt;/b&gt;&lt;br&gt;&lt;i&gt;(instantaneous_voltage * instantaneous_electric_current)&lt;/i&gt;"]
power --- apparent_power["&lt;b&gt;apparent_power&lt;/b&gt;&lt;br&gt;&lt;i&gt;(voltage * electric_current)&lt;br&gt;(mod(complex_power))&lt;/i&gt;&lt;br&gt;[VA]"]
apparent_power --- active_power["&lt;b&gt;active_power&lt;/b&gt;&lt;br&gt;&lt;i&gt;(1 / period * instantaneous_power * time)&lt;br&gt;(re(complex_power))&lt;/i&gt;"]
apparent_power --- nonactive_power["&lt;b&gt;nonactive_power&lt;/b&gt;&lt;br&gt;&lt;i&gt;(sqrt(apparent_power&lt;sup&gt;2&lt;/sup&gt; - active_power&lt;sup&gt;2&lt;/sup&gt;))&lt;/i&gt;&lt;br&gt;"]
nonactive_power --- reactive_power["&lt;b&gt;reactive_power&lt;/b&gt;&lt;br&gt;&lt;i&gt;(im(complex_power))&lt;/i&gt;&lt;br&gt;[var]"]
apparent_power --- complex_power["&lt;b&gt;complex_power&lt;/b&gt;&lt;br&gt;{complex}&lt;br&gt;&lt;i&gt;(voltage_phasor * electric_current_phasor)&lt;br&gt;(active_power + j * reactive_power)&lt;/i&gt;"]</code></pre>
<p>This will mean that we will not be able to add or compare <em>active power</em> with <em>apparent power</em>,
which probably makes a lot of sense. Again, ISQ does not provide a direct answer here.</p>
<p>However, the above allows direct addition and comparison of <em>active power</em> and <em>nonactive power</em>,
and also will not complain if someone will try to use watt (W) as a unit of <em>apparent power</em> or
<em>reactive power</em>.</p>
<p>Again, ISQ does not provide a direct answer here.</p>
<h2 id="more-base-quantities">More base quantities?<a class="headerlink" href="#more-base-quantities" title="Permanent link">&para;</a></h2>
<p>Is ISQ really based on only seven base quantities? Let's look at the definition of
<em>traffic intensity</em> in IEC 80000-13 "Information science and technology":</p>
@ -2799,7 +2824,7 @@ important problems to solve to allow this:</p>
a daily basis.</p>
<p>I hope you enjoyed following this series and learned more about the International System
of Quantities. Please try it out in your domain and share feedback with us. We always love to
hear about the projects in which our library is being used and about use cases it helps
hear about the projects in which our library is being used and about use cases it helps
address.</p>

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