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<!DOCTYPE html> < html lang = 'en' >< head >< title > [qties]</ 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 >< div id = 'summary' class = 'section' >< h2 >< a class = 'secnum' href = '#summary' style = 'min-width:65pt' > 5.1</ a > Summary < a class = 'abbr_ref' href = 'qties.summary.html' > [qties.summary]</ a ></ h2 >< div class = 'para' id = 'summary-1' >< div class = 'marginalizedparent' >< a class = 'marginalized' href = '#summary-1' > 1</ a ></ div >< div class = 'sourceLinkParent' >< a class = 'sourceLink' href = 'https://github.com/mpusz/mp-units6e06eddf205deaf6c2f2f63500c8c70ec220a99f/source/quantities.tex#L6' > #</ a ></ div >< div class = 'texpara' >< div id = 'summary-1.sentence-1' class = 'sentence' > This Clause describes components for dealing with quantities,
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as summarized in Table < a href = '#tab:qties.summary' title = 'Table 3: Quantities library summary' > 3</ a >< a class = 'hidden_link' href = '#summary-1.sentence-1' > .</ a ></ div ></ div >< div class = 'texpara' >< div class = 'numberedTable' id = 'tab:qties.summary' > Table < a href = '#tab:qties.summary' > 3</ a > : Quantities library summary  < a href = './tab:qties.summary.html' > [tab:qties.summary]</ a >< br >< table >< tr id = 'tab:qties.summary-row-1' class = 'rowsep' >< td class = 'hidden' >< div class = 'marginalizedparent' >< a class = 'itemDeclLink' href = '#tab:qties.summary-row-1' > 🔗</ a ></ div ></ td >< td class = 'empty left' ></ td >< td class = 'left' >< div class = 'texpara' >< div id = 'tab:qties.summary-row-1-column-2-sentence-1' class = 'sentence' >< b > Subclause</ b ></ div ></ div ></ td >< td class = 'left' >< div class = 'texpara' >< div id = 'tab:qties.summary-row-1-column-3-sentence-1' class = 'sentence' >< b > Module</ b ></ div ></ div ></ td ></ tr >< tr id = 'tab:qties.summary-row-2' class = 'capsep' >< td class = 'hidden' >< div class = 'marginalizedparent' >< a class = 'itemDeclLink' href = '#tab:qties.summary-row-2' > 🔗</ a ></ div ></ td >< td class = 'left' >< div class = 'texpara' >< div id = 'tab:qties.summary-row-2-column-1-sentence-1' class = 'sentence' >< a href = '#qty.helpers' title = '5.5 Helpers' > [qty.< span class = 'shy' ></ span > helpers]</ a ></ div ></ div ></ td >< td class = 'left' >< div class = 'texpara' >< div id = 'tab:qties.summary-row-2-column-2-sentence-1' class = 'sentence' > Helpers</ div ></ div ></ td >< td class = 'left' >< div class = 'texpara' >< div id = 'tab:qties.summary-row-2-column-3-sentence-1' class = 'sentence' >< span class = 'texttt' > mp_< span class = 'shy' ></ span > units< span class = 'operator' > .</ span > core</ span ></ div ></ div ></ td ></ tr >< tr id = 'tab:qties.summary-row-3' >< td class = 'hidden' >< div class = 'marginalizedparent' >< a class = 'itemDeclLink' href = '#tab:qties.summary-row-3' > 🔗</ a ></ div ></ td >< td class = 'left' >< div class = 'texpara' >< div id = 'tab:qties.summary-row-3-column-1-sentence-1' class = 'sentence' >< a href = '#qty.traits' title = '5.6 Traits' > [qty.< span class = 'shy' ></ span > traits]</ a ></ div ></ div ></ td >< td class = 'left' >< div class = 'texpara' >< div id = 'tab:qties.summary-row-3-column-2-sentence-1' class = 'sentence' > Traits</ div ></ div ></ td >< td class = 'empty left' ></ td ></ tr >< tr id = 'tab:qties.summary-row-4' >< td class = 'hidden' >< div class = 'marginalizedparent' >< a class = 'itemDeclLink' href = '#tab:qties.summary-row-4' > 🔗</ a ></ div ></ td >< td class = 'left' >< div class = 'texpara' >< div id = 'tab:qties.summary-row-4-column-1-sentence-1' class = 'sentence' >< a href = '#qty.concepts' title = '5.7 Concepts' > [qty.< span class = 'shy' ></ span > concepts]</ a ></ div ></ div ></ td >< td class = 'left' >< div class = 'texpara' >< div id = 'tab:qties.summary-row-4-column-2-sentence-1' class = 'sentence' > Concepts</ div ></ div ></ td >< td class = 'empty left' ></ td ></ tr >< tr id = 'tab:qties.summary-row-5' >< td class = 'hidden' >< div class = 'marginalizedparent' >< a class = 'itemDeclLink' href = '#tab:qties.summary-row-5' > 🔗</ a ></ div ></ td >< td class = 'left' >< div class = 'texpara' >< div id = 'tab:qties.summary-row-5-column-1-sentence-1' class = 'sentence' >< a href = '#qty.types' title = '5.8 Types' > [qty.< span class = 'shy' ></ span > types]</ a ></ div ></ div ></ td >< td class = 'left' >< div class = 'texpara' >< div id = 'tab:qties.summary-row-5-column-2-sentence-1' class = 'sentence' > Types</ div ></ div ></ td >< td class = 'empty left' ></ td ></ tr >< tr id = 'tab:qties.summary-row-6' >< td class = 'hidden' >< div class = 'marginalizedparent' >< a class = 'itemDeclLink' href = '#tab:qties.summary-row-6' > 🔗</ a ></ div ></ td >< td class = 'left' >< div class = 'texpara' >< div id = 'tab:qties.summary-row-6-column-1-sentence-1' class = 'sentence' >< a href = '#qty.compat' title = '5.9 Compatibility' > [qty.< span class = 'shy' ></ span > compat]</ a ></ div ></ div ></ td >< td class = 'left' >< div class = 'texpara' >< div id = 'tab:qties.summary-row-6-column-2-sentence-1' class = 'sentence' > Compatibility</ div ></ div ></ td >< td class = 'empty left' ></ td ></ tr >< tr id = 'tab:qties.summary-row-7' >< td class = 'hidden' >< div class = 'marginalizedparent' >< a class = 'itemDeclLink' href = '#tab:qties.summary-row-7' > 🔗</ a ></ div ></ td >< td class = 'left' >< div class = 'texpara' >< div id = 'tab:qties.summary-row-7-column-1-sentence-1' class = 'sentence' >< a href = '#qty.one' title = '5.10 Di
<span class=' keyword ' > export</ span > < span class = 'keyword' > import</ span > mp_units< span class = 'operator' > .</ span > core;
< span class = 'keyword' > export</ span > < span class = 'keyword' > import</ span > mp_units< span class = 'operator' > .</ span > systems;
</ span ></ span ></ div ></ div >< div id = 'mp.units.core.syn' class = 'section' >< h2 >< a class = 'secnum' href = '#mp.units.core.syn' style = 'min-width:65pt' > 5.3</ a > Module < span class = 'texttt' > mp_< span class = 'shy' ></ span > units.core</ span > synopsis < a class = 'abbr_ref' href = 'mp.units.core.syn.html' > [mp.units.core.syn]</ a ></ h2 >< div class = 'texpara' >< span id = 'module:mp_units.core' >< div class = 'marginalizedparent' >< a class = 'itemDeclLink' href = '#module:mp_units.core' > 🔗</ a ></ div >< span class = 'codeblock' >< span class = 'keyword' > export</ span > < span class = 'keyword' > module</ span > mp_units< span class = 'operator' > .</ span > core;
< span class = 'keyword' > import</ span > std;
< span class = 'keyword' > export</ span > < span class = 'keyword' > namespace</ span > mp_units < span class = 'curlybracket' > {</ span >
< span class = 'keyword' > export</ span > < span class = 'keyword' > enum</ span > < span class = 'keyword' > class</ span > quantity_character < span class = 'curlybracket' > {</ span > scalar, vector, tensor < span class = 'curlybracket' > }</ span > ;
< span class = 'comment' > // < a href = '#qty.traits' title = '5.6 Traits' > [qty.< span class = 'shy' ></ span > traits]</ a > , traits</ span >
< span class = 'keyword' > template</ span >< span class = 'anglebracket' > < </ span >< span class = 'keyword' > typename</ span > Rep< span class = 'anglebracket' > > </ span >
< span class = 'keyword' > constexpr</ span > < span class = 'keyword' > bool</ span > treat_as_floating_point < span class = 'operator' > =</ span > std< span class = 'operator' > ::</ span > is_floating_point_v< span class = 'anglebracket' > < </ span > Rep< span class = 'anglebracket' > > </ span > ;
< span class = 'keyword' > template</ span >< span class = 'anglebracket' > < </ span >< span class = 'keyword' > typename</ span > Rep< span class = 'anglebracket' > > </ span >
< span class = 'keyword' > constexpr</ span > < span class = 'keyword' > bool</ span > is_scalar < span class = 'operator' > =</ span >
std< span class = 'operator' > ::</ span > is_floating_point_v< span class = 'anglebracket' > < </ span > Rep< span class = 'anglebracket' > > </ span > < span class = 'operator' > |</ span >< span class = 'operator' > |</ span > < span class = 'parenthesis' > (</ span > std< span class = 'operator' > ::</ span > is_integral_v< span class = 'anglebracket' > < </ span > Rep< span class = 'anglebracket' > > </ span > < span class = 'operator' > & </ span >< span class = 'operator' > & </ span > < span class = 'operator' > !</ span > is_same_v< span class = 'anglebracket' > < </ span > Rep, < span class = 'keyword' > bool</ span >< span class = 'anglebracket' > > </ span >< span class = 'parenthesis' > )</ span > ;
< span class = 'keyword' > template</ span >< span class = 'anglebracket' > < </ span >< span class = 'keyword' > typename</ span > Rep< span class = 'anglebracket' > > </ span >
< span class = 'keyword' > constexpr</ span > < span class = 'keyword' > bool</ span > is_vector < span class = 'operator' > =</ span > < span class = 'literal' > false</ span > ;
< span class = 'keyword' > template</ span >< span class = 'anglebracket' > < </ span >< span class = 'keyword' > typename</ span > Rep< span class = 'anglebracket' > > </ span >
< span class = 'keyword' > constexpr</ span > < span class = 'keyword' > bool</ span > is_tensor < span class = 'operator' > =</ span > < span class = 'literal' > false</ span > ;
< span class = 'keyword' > template</ span >< span class = 'anglebracket' > < </ span >< span class = 'keyword' > typename</ span > Rep< span class = 'anglebracket' > > </ span >
< span class = 'keyword' > struct</ span > quantity_values;
< span class = 'keyword' > template</ span >< span class = 'anglebracket' > < </ span >< span class = 'keyword' > typename</ span > T< span class = 'anglebracket' > > </ span >
< span class = 'keyword' > struct</ span > quantity_like_traits;
< span class = 'keyword' > template</ span >< span class = 'anglebracket' > < </ span >< span class = 'keyword' > typename</ span > T< span class = 'anglebracket' > > </ span >
< span class = 'keyword' > struct</ span > quantity_point_like_traits;
< span class = 'comment' > // < a href = '#qty.concepts' title = '5.7 Concepts' > [qty.< span class = 'shy' ></ span > concepts]</ a > , concepts</ span >
< span class = 'keyword' > template</ span >< span class = 'anglebracket' > < </ span >< span class = 'keyword' > typename</ span > T< span class = 'anglebracket' > > </ span >
< span class = 'keyword' > concept</ span > < a class = 'hidden_link' href = '#concept:some_reference' title = '5.3 Module mp_­units.core synopsis [mp.units.core.syn]' >< span id = 'concept:some_reference' >< span id = 'lib:some_reference' >< span class = 'tcode_in_codeblock' > some_< span class = 'shy' ></ span > reference</ span ></ span ></ span ></ a > < span class = 'operator' > =</ span > template_of< span class = 'parenthesis' > (</ span >< span class = 'operator' > ^</ span > std< span class = 'operator' > ::</ span > remove_cvref_t< span class = 'anglebracket' > < </ span > T< span class = 'anglebracket' > > </ span >< span class = 'parenthesis' > )</ span > < span class = 'operator' > =</ span >< span class = 'operator' > =</ span > < span class = 'operator' > ^</ span > reference;
< span class = 'keyword' > template</ span >< span class = 'anglebracket' > < </ span >< span class = 'keyword' > typename</ span > T< span class = 'anglebracket' > > </ span >
< span class = 'keyword' > concept</ span > representation < span class = 'operator' > =</ span > < i >< span class = 'texttt' > see below</ span ></ i > ;
< span class = 'keyword' > template</ span >< span class = 'anglebracket' > < </ span >< span class = 'keyword' > typename</ span > T, quantity_character Ch< span class = 'anglebracket' > > </ span >
< span class = 'keyword' > concept</ span > representation_of < span class = 'operator' > =</ span > < i >< span class = 'texttt' > see below</ span ></ i > ;
< span class = 'keyword' > template</ span >< span class = 'anglebracket' > < </ span >< span class = 'keyword' > typename</ span > T< span class = 'anglebracket' > > </ span >
< span class = 'keyword' > concept</ span > some_quantity_spec < span class = 'operator' > =</ span > < i >< span class = 'texttt' > see below</ span ></ i > ;
< span class = 'comment' > // < a href = '#qty.types' title = '5.8 Types' > [qty.< span class = 'shy' ></ span > types]</ a > , types</ span >
< span class = 'keyword' > template</ span >< span class = 'anglebracket' > < </ span >< span class = 'keyword' > auto</ span >< span class = 'operator' > .</ span >< span class = 'operator' > .</ span >< span class = 'operator' > .</ span >< span class = 'anglebracket' > > </ span >
< span class = 'keyword' > struct</ span > quantity_spec; < span class = 'comment' > // < i > not defined</ i ></ span >
< span class = 'keyword' > template</ span >< span class = 'anglebracket' > < </ span >< span class = 'keyword' > auto</ span > Q< span class = 'anglebracket' > > </ span >
< span class = 'keyword' > struct</ span > kind_of_; < span class = 'comment' > // < i > not defined</ i ></ span >
< span class = 'keyword' > template</ span >< span class = 'anglebracket' > < </ span >< i >< span class = 'texttt' > unspecified</ span ></ i >< span class = 'operator' > .</ span >< span class = 'operator' > .</ span >< span class = 'operator' > .</ span > Expr< span class = 'anglebracket' > > </ span >
< span class = 'keyword' > struct</ span > derived_quantity_spec;
< span class = 'comment' > // < a href = '#qty.type' title = '5.8.2 Class template quantity' > [qty.< span class = 'shy' ></ span > type]</ a > , class template < span class = 'tcode_in_codeblock' > quantity</ span ></ span >
< span class = 'keyword' > export</ span > < span class = 'keyword' > template</ span >< span class = 'anglebracket' > < </ span >< a href = '#concept:some_reference' title = '5.3 Module mp_­units.core synopsis [mp.units.core.syn]' >< span id = 'conceptref:some_reference' >< span class = 'tcode_in_codeblock' > some_< span class = 'shy' ></ span > reference</ span ></ span ></ a > < span class = 'keyword' > auto</ span > R,
< a href = '#concept:representation_of' title = '5.7 Concepts [qty.concepts]' >< span id = 'conceptref:representation_of' >< span class = 'tcode_in_codeblock' > representation_< span class = 'shy' ></ span > of</ span ></ span ></ a >< span class = 'anglebracket' > < </ span > get_quantity_spec< span class = 'parenthesis' > (</ span > R< span class = 'parenthesis' > )</ span >< span class = 'operator' > .</ span > character< span class = 'anglebracket' > > </ span > Rep < span class = 'operator' > =</ span > < span class = 'keyword' > double</ span >< span class = 'anglebracket' > > </ span >
< span class = 'keyword' > class</ span > quantity;
< span class = 'comment' > // < a href = '#qty.point.type' title = '5.8.3 Class template quantity_­point' > [qty.< span class = 'shy' ></ span > point.< span class = 'shy' ></ span > type]</ a > , class template < span class = 'tcode_in_codeblock' > quantity_< span class = 'shy' ></ span > point</ span ></ span >
< span class = 'keyword' > template</ span >< span class = 'anglebracket' > < </ span >< i >< span class = 'texttt' > unspecified</ span ></ i >< span class = 'anglebracket' > > </ span >
< span class = 'keyword' > class</ span > quantity_point;
< span class = 'curlybracket' > }</ span >
</ span ></ span ></ div ></ div >< div id = 'mp.units.systems.syn' class = 'section' >< h2 >< a class = 'secnum' href = '#mp.units.systems.syn' style = 'min-width:65pt' > 5.4</ a > Module < span class = 'texttt' > mp_< span class = 'shy' ></ span > units.systems</ span > synopsis < a class = 'abbr_ref' href = 'mp.units.systems.syn.html' > [mp.units.systems.syn]</ a ></ h2 >< div class = 'texpara' >< span id = 'module:mp_units.systems' >< div class = 'marginalizedparent' >< a class = 'itemDeclLink' href = '#module:mp_units.systems' > 🔗</ a ></ div >< span class = 'codeblock' >< span class = 'keyword' > export</ span > < span class = 'keyword' > module</ span > mp_units< span class = 'operator' > .</ span > systems;
< span class = 'keyword' > export</ span > < span class = 'keyword' > import</ span > mp_units< span class = 'operator' > .</ span > core;
< span class = 'keyword' > import</ span > std;
< span class = 'keyword' > export</ span > < span class = 'keyword' > namespace</ span > mp_units < span class = 'curlybracket' > {</ span >
< span class = 'curlybracket' > }</ span >
</ span ></ span ></ div ></ div >< div id = 'qty.helpers' class = 'section' >< h2 >< a class = 'secnum' href = '#qty.helpers' style = 'min-width:65pt' > 5.5</ a > Helpers < a class = 'abbr_ref' href = 'qty.helpers.html' > [qty.helpers]</ a ></ h2 >< div class = 'texpara' >< div class = 'itemdecl' id = 'qty.helpers-itemdecl:1' >< div class = 'marginalizedparent' >< a class = 'itemDeclLink' href = '#qty.helpers-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 > ;
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</ code ></ div ></ div >< div class = 'para' id = 'qty.helpers-1' >< div class = 'marginalizedparent' >< a class = 'marginalized' href = '#qty.helpers-1' > 1</ a ></ div >< div class = 'itemdescr' >< div class = 'sourceLinkParent' >< a class = 'sourceLink' href = 'https://github.com/mpusz/mp-units6e06eddf205deaf6c2f2f63500c8c70ec220a99f/source/quantities.tex#L122' > #</ a ></ div >< div class = 'texpara' >< div id = 'qty.helpers-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' > & </ span >< span class = 'operator' > & </ 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 = '#qty.helpers-1.sentence-1' > .</ a ></ div ></ div ></ div ></ div >< div class = 'para' id = 'qty.helpers-2' >< div class = 'marginalizedparent' >< a class = 'marginalized' href = '#qty.helpers-2' > 2</ a ></ div >< div class = 'itemdescr' >< div class = 'sourceLinkParent' >< a class = 'sourceLink' href = 'https://github.com/mpusz/mp-units6e06eddf205deaf6c2f2f63500c8c70ec220a99f/source/quantities.tex#L126' > #</ a ></ div >< div class = 'texpara' >< div id = 'qty.helpers-2.sentence-1' class = 'sentence' >< i > Returns</ i > : < span class = 'texttt' >< span class = 'literal' > true</ span ></ span > if
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< 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 = '#qty.helpers-2.sentence-1' > .</ a ></ div ></ div ></ div ></ div ></ div >< div id = 'qty.traits' class = 'section' >< h2 >< a class = 'secnum' href = '#qty.traits' style = 'min-width:65pt' > 5.6</ a > Traits < a class = 'abbr_ref' href = 'qty.traits.html' > [qty.traits]</ a ></ h2 >< div class = 'texpara' >< div class = 'itemdecl' id = 'qty.traits-itemdecl:1' >< div class = 'marginalizedparent' >< a class = 'itemDeclLink' href = '#qty.traits-itemdecl:1' > 🔗</ a ></ div >< code class = 'itemdeclcode' >< span class = 'keyword' > template</ span >< span class = 'anglebracket' > < </ span >< span class = 'keyword' > typename</ span > Rep< span class = 'anglebracket' > > </ span >
< span class = 'keyword' > constexpr</ span > < span class = 'keyword' > bool</ span > < span id = 'lib:is_scalar' >< a class = 'hidden_link' href = '#lib:is_scalar' title = '5.6 Traits [qty.traits]' > is_scalar</ a ></ span > < span class = 'operator' > =</ span >
std< span class = 'operator' > ::</ span > is_floating_point_v< span class = 'anglebracket' > < </ span > Rep< span class = 'anglebracket' > > </ span > < span class = 'operator' > |</ span >< span class = 'operator' > |</ span > < span class = 'parenthesis' > (</ span > std< span class = 'operator' > ::</ span > is_integral_v< span class = 'anglebracket' > < </ span > Rep< span class = 'anglebracket' > > </ span > < span class = 'operator' > & </ span >< span class = 'operator' > & </ span > < span class = 'operator' > !</ span > is_same_v< span class = 'anglebracket' > < </ span > Rep, < span class = 'keyword' > bool</ span >< span class = 'anglebracket' > > </ span >< span class = 'parenthesis' > )</ span > ;
< span class = 'keyword' > template</ span >< span class = 'anglebracket' > < </ span >< span class = 'keyword' > typename</ span > Rep< span class = 'anglebracket' > > </ span >
< span class = 'keyword' > constexpr</ span > < span class = 'keyword' > bool</ span > < span id = 'lib:is_vector' >< a class = 'hidden_link' href = '#lib:is_vector' title = '5.6 Traits [qty.traits]' > is_vector</ a ></ span > < span class = 'operator' > =</ span > < span class = 'literal' > false</ span > ;
< span class = 'keyword' > template</ span >< span class = 'anglebracket' > < </ span >< span class = 'keyword' > typename</ span > Rep< span class = 'anglebracket' > > </ 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 Traits [qty.traits]' > is_tensor</ a ></ span > < span class = 'operator' > =</ span > < span class = 'literal' > false</ span > ;
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</ code ></ div ></ div >< div class = 'para' id = 'qty.traits-1' >< div class = 'marginalizedparent' >< a class = 'marginalized' href = '#qty.traits-1' > 1</ a ></ div >< div class = 'itemdescr' >< div class = 'sourceLinkParent' >< a class = 'sourceLink' href = 'https://github.com/mpusz/mp-units6e06eddf205deaf6c2f2f63500c8c70ec220a99f/source/quantities.tex#L149' > #</ a ></ div >< div class = 'texpara' >< div id = 'qty.traits-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 External' > [spec.< span class = 'shy' ></ span > ext]</ a > ),
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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
a scalar (< a href = "https://www.electropedia.org/iev/iev.nsf/display?openform&ievref=102-02-18" > IEC 60050, 102-02-18</ a > ),
a vector (< a href = "https://www.electropedia.org/iev/iev.nsf/display?openform&ievref=102-03-04" > IEC 60050, 102-03-04</ a > ), and
a tensor,
and < span class = 'texttt' >< span class = 'literal' > false</ span ></ span > for types which respectively do not< a class = 'hidden_link' href = '#qty.traits-1.sentence-1' > .</ a ></ div ></ div ></ div ></ div ></ div >< div id = 'qty.concepts' class = 'section' >< h2 >< a class = 'secnum' href = '#qty.concepts' style = 'min-width:65pt' > 5.7</ a > Concepts < a class = 'abbr_ref' href = 'qty.concepts.html' > [qty.concepts]</ a ></ h2 >< div class = 'texpara' >< div class = 'itemdecl' id = 'concept:representation' >< div class = 'marginalizedparent' >< a class = 'itemDeclLink' href = '#concept:representation' > 🔗</ a ></ div >< code class = 'itemdeclcode' >< span class = 'keyword' > export</ span > < span class = 'keyword' > template</ span >< span class = 'anglebracket' > < </ span >< span class = 'keyword' > typename</ span > T< span class = 'anglebracket' > > </ span >
< span class = 'keyword' > concept</ span > < a class = 'hidden_link' href = '#concept:representation' title = '5.7 Concepts [qty.concepts]' >< span id = 'concept:representation' >< span id = 'lib:representation' >< span class = 'texttt' > representation</ span ></ span ></ span ></ a > < span class = 'operator' > =</ span >
< span class = 'parenthesis' > (</ span > is_scalar< span class = 'anglebracket' > < </ span > T< span class = 'anglebracket' > > </ span > < span class = 'operator' > |</ span >< span class = 'operator' > |</ span > is_vector< span class = 'anglebracket' > < </ span > T< span class = 'anglebracket' > > </ span > < span class = 'operator' > |</ span >< span class = 'operator' > |</ span > is_tensor< span class = 'anglebracket' > < </ span > T< span class = 'anglebracket' > > </ span >< span class = 'parenthesis' > )</ span >< span class = 'operator' > & </ span >< span class = 'operator' > & </ span > std< span class = 'operator' > ::</ span > regular< span class = 'anglebracket' > < </ span > T< span class = 'anglebracket' > > </ span > < span class = 'operator' > & </ span >< span class = 'operator' > & </ span > < span class = 'texttt' >< i > scalable</ i ></ span >< span class = 'anglebracket' > < </ span > T< span class = 'anglebracket' > > </ span > ;
</ code ></ div ></ div >< div class = 'texpara' >< div class = 'itemdecl' id = 'concept:representation_of' >< div class = 'marginalizedparent' >< a class = 'itemDeclLink' href = '#concept:representation_of' > 🔗</ a ></ div >< code class = 'itemdeclcode' >< span class = 'keyword' > export</ span > < span class = 'keyword' > template</ span >< span class = 'anglebracket' > < </ span >< span class = 'keyword' > typename</ span > T, quantity_character Ch< span class = 'anglebracket' > > </ span >
< span class = 'keyword' > concept</ span > < a class = 'hidden_link' href = '#concept:representation_of' title = '5.7 Concepts [qty.concepts]' >< span id = 'concept:representation_of' >< span id = 'lib:representation_of' >< span class = 'texttt' > representation_< span class = 'shy' ></ span > of</ span ></ span ></ span ></ a > < span class = 'operator' > =</ span >
< a href = '#concept:representation' title = '5.7 Concepts [qty.concepts]' >< span id = 'conceptref:representation' >< span class = 'texttt' > representation</ span ></ span ></ a >< span class = 'anglebracket' > < </ span > T< span class = 'anglebracket' > > </ span > < span class = 'operator' > & </ span >< span class = 'operator' > & </ span > < span class = 'parenthesis' > (</ span >< span class = 'parenthesis' > (</ span > Ch < span class = 'operator' > =</ span >< span class = 'operator' > =</ span > quantity_character< span class = 'operator' > ::</ span > scalar < span class = 'operator' > & </ span >< span class = 'operator' > & </ span > is_scalar< span class = 'anglebracket' > < </ span > T< span class = 'anglebracket' > > </ span >< span class = 'parenthesis' > )</ span > < span class = 'operator' > |</ span >< span class = 'operator' > |</ span >
< span class = 'parenthesis' > (</ span > Ch < span class = 'operator' > =</ span >< span class = 'operator' > =</ span > quantity_character< span class = 'operator' > ::</ span > vector < span class = 'operator' > & </ span >< span class = 'operator' > & </ span > is_vector< span class = 'anglebracket' > < </ span > T< span class = 'anglebracket' > > </ span >< span class = 'parenthesis' > )</ span > < span class = 'operator' > |</ span >< span class = 'operator' > |</ span >
< span class = 'parenthesis' > (</ span > Ch < span class = 'operator' > =</ span >< span class = 'operator' > =</ span > quantity_character< span class = 'operator' > ::</ span > tensor < span class = 'operator' > & </ span >< span class = 'operator' > & </ span > is_tensor< span class = 'anglebracket' > < </ span > T< span class = 'anglebracket' > > </ span >< span class = 'parenthesis' > )</ span >< span class = 'parenthesis' > )</ span > ;
</ code ></ div ></ div >< div class = 'texpara' >< div class = 'itemdecl' id = 'qty.concepts-itemdecl:3' >< div class = 'marginalizedparent' >< a class = 'itemDeclLink' href = '#qty.concepts-itemdecl:3' > 🔗</ a ></ div >< code class = 'itemdeclcode' >< span class = 'keyword' > template</ span >< span class = 'anglebracket' > < </ span >< span class = 'keyword' > typename</ span > T< span class = 'anglebracket' > > </ span >
< span class = 'keyword' > concept</ span > < span class = 'texttt' >< i > named-quantity-spec</ i ></ span >< a class = 'index' id = 'concept:named-quantity-spec' ></ a > < span class = 'operator' > =</ span >
< span class = 'parenthesis' > (</ span >< span class = 'texttt' >< i > converts-to-base-subobject-of</ i ></ span >< span class = 'parenthesis' > (</ span >< span class = 'operator' > ^</ span > T, < span class = 'operator' > ^</ span > quantity_spec< span class = 'parenthesis' > )</ span > < span class = 'operator' > & </ span >< span class = 'operator' > & </ span > template_of< span class = 'parenthesis' > (</ span >< span class = 'operator' > ^</ span > T< span class = 'parenthesis' > )</ span > < span class = 'operator' > !</ span >< span class = 'operator' > =</ span > < span class = 'operator' > ^</ span > kind_of_< span class = 'parenthesis' > )</ span > ;
< span class = 'keyword' > template</ span >< span class = 'anglebracket' > < </ span >< span class = 'keyword' > typename</ span > T< span class = 'anglebracket' > > </ span >
< span class = 'keyword' > concept</ span > < a class = 'hidden_link' href = '#concept:some_quantity_spec' title = '5.7 Concepts [qty.concepts]' >< span id = 'concept:some_quantity_spec' >< span id = 'lib:some_quantity_spec' >< span class = 'texttt' > some_< span class = 'shy' ></ span > quantity_< span class = 'shy' ></ span > spec</ span ></ span ></ span ></ a > < span class = 'operator' > =</ span >
< a class = 'index' id = 'conceptref:named-quantity-spec' ></ a >< span class = 'texttt' >< i > named-quantity-spec</ i ></ span >< span class = 'anglebracket' > < </ span > T< span class = 'anglebracket' > > </ span > < span class = 'operator' > |</ span >< span class = 'operator' > |</ span >
detail< span class = 'operator' > ::</ span > IntermediateDerivedQuantitySpec< span class = 'anglebracket' > < </ span > T< span class = 'anglebracket' > > </ span > < span class = 'operator' > |</ span >< span class = 'operator' > |</ span >
template_of< span class = 'parenthesis' > (</ span >< span class = 'operator' > ^</ span > T< span class = 'parenthesis' > )</ span > < span class = 'operator' > =</ span >< span class = 'operator' > =</ span > < span class = 'operator' > ^</ span > kind_of;
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</ code ></ div ></ div ></ div >< div id = 'qty.types' class = 'section' >< h2 >< a class = 'secnum' href = '#qty.types' style = 'min-width:65pt' > 5.8</ a > Types < a class = 'abbr_ref' href = 'qty.types.html' > [qty.types]</ a ></ h2 >< div id = 'qty.types.general' class = 'section' >< h3 >< a class = 'secnum' href = '#qty.types.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 = 'qty.types.general-1' >< div class = 'marginalizedparent' >< a class = 'marginalized' href = '#qty.types.general-1' > 1</ a ></ div >< div class = 'sourceLinkParent' >< a class = 'sourceLink' href = 'https://github.com/mpusz/mp-units6e06eddf205deaf6c2f2f63500c8c70ec220a99f/source/quantities.tex#L196' > #</ a ></ div >< div class = 'texpara' >< div id = 'qty.types.general-1.sentence-1' class = 'sentence' > A < a class = 'hidden_link' href = '#def:type,quantity' title = '5.8.1 General [qty.types.general]' >< span id = 'def:type,quantity' >< i > quantity type</ i ></ span ></ a >
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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 = '#qty.types.general-1.sentence-1' > .</ a ></ div > < div id = 'qty.types.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' > ​ ::​ </ span > rep</ span > as its number
and < span class = 'texttt' >< i > Q</ i >< span class = 'operator' > ​ ::​ </ span > reference</ span > as its reference< a class = 'hidden_link' href = '#qty.types.general-1.sentence-2' > .</ a ></ div > < div id = 'qty.types.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 > )
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if < span class = 'texttt' >< i > Q</ i >< span class = 'operator' > ​ ::​ </ span > rep</ span > is a structural type< a class = 'hidden_link' href = '#qty.types.general-1.sentence-3' > .</ a ></ div ></ div ></ div >< div class = 'para' id = 'qty.types.general-2' >< div class = 'marginalizedparent' >< a class = 'marginalized' href = '#qty.types.general-2' > 2</ a ></ div >< div class = 'sourceLinkParent' >< a class = 'sourceLink' href = 'https://github.com/mpusz/mp-units6e06eddf205deaf6c2f2f63500c8c70ec220a99f/source/quantities.tex#L206' > #</ a ></ div >< div class = 'texpara' >< div id = 'qty.types.general-2.sentence-1' class = 'sentence' > Each class template defined in subclause < a href = '#qty.types' title = '5.8 Types' > [qty.< span class = 'shy' ></ span > types]</ a >
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has data members and special members specified below, and
has no base classes or members other than those specified< a class = 'hidden_link' href = '#qty.types.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 >
< span class = 'keyword' > export</ span > < span class = 'keyword' > template</ span >< span class = 'anglebracket' > < </ span >< a href = '#concept:some_reference' title = '5.3 Module mp_­units.core synopsis [mp.units.core.syn]' >< span id = 'conceptref:some_reference_' >< span class = 'tcode_in_codeblock' > some_< span class = 'shy' ></ span > reference</ span ></ span ></ a > < span class = 'keyword' > auto</ span > R,
< a href = '#concept:representation_of' title = '5.7 Concepts [qty.concepts]' >< span id = 'conceptref:representation_of_' >< span class = 'tcode_in_codeblock' > representation_< span class = 'shy' ></ span > of</ span ></ span ></ a >< span class = 'anglebracket' > < </ span > get_quantity_spec< span class = 'parenthesis' > (</ span > R< span class = 'parenthesis' > )</ span >< span class = 'operator' > .</ span > character< span class = 'anglebracket' > > </ span > Rep < span class = 'operator' > =</ span > < span class = 'keyword' > double</ span >< span class = 'anglebracket' > > </ span >
< span class = 'keyword' > class</ span > quantity < span class = 'curlybracket' > {</ span > < i >< span class = 'texttt' > unspecified</ span ></ i > < span class = 'curlybracket' > }</ span > ;
< span class = 'curlybracket' > }</ span >
</ span ></ div >< div class = 'texpara' >< div id = 'qty.type-sentence-1' class = 'sentence' > Let < span class = 'texttt' >< i > Q</ i ></ span > be a specialization of < span class = 'texttt' > quantity</ span >< a class = 'hidden_link' href = '#qty.type-sentence-1' > .</ a ></ div > < ul class = 'itemize' >< li >< div class = 'texpara' >< div id = 'qty.type-sentence-1' class = 'sentence' > If < span class = 'texttt' > Rep</ span > is a scalar,
< span class = 'texttt' >< i > Q</ i ></ span > represents a scalar quantity (< a href = "https://www.electropedia.org/iev/iev.nsf/display?openform&ievref=102-02-19" > IEC 60050, 102-02-19</ a > )< a class = 'hidden_link' href = '#qty.type-sentence-1' > .</ a ></ div ></ div ></ li >< li >< div class = 'texpara' >< div id = 'qty.type-sentence-1' class = 'sentence' > If < span class = 'texttt' > Rep</ span > is a vector,
< span class = 'texttt' >< i > Q</ i ></ span > represents a vector (< a href = "https://www.electropedia.org/iev/iev.nsf/display?openform&ievref=102-03-04" > IEC 60050, 102-03-04</ a > )< a class = 'hidden_link' href = '#qty.type-sentence-1' > .</ a ></ div ></ div ></ li ></ ul ></ div ></ div >< div id = 'qty.point.type' class = 'section' >< h3 >< a class = 'secnum' href = '#qty.point.type' style = 'min-width:80pt' > 5.8.3</ a > Class template < span class = 'texttt' > quantity_< span class = 'shy' ></ span > point</ span > < a class = 'abbr_ref' href = 'qty.point.type.html' > [qty.point.type]</ a ></ h3 >< div class = 'texpara' >< span class = 'codeblock' >< span class = 'keyword' > namespace</ span > mp_units < span class = 'curlybracket' > {</ span >
< span class = 'keyword' > export</ span > < span class = 'keyword' > template</ span >< span class = 'anglebracket' > < </ span >< i >< span class = 'texttt' > unspecified</ span ></ i >< span class = 'anglebracket' > > </ span >
< span class = 'keyword' > class</ span > quantity_point < span class = 'curlybracket' > {</ span > < i >< span class = 'texttt' > unspecified</ span ></ i > < span class = 'curlybracket' > }</ span > ;
< span class = 'curlybracket' > }</ span >
</ span ></ div >< div class = 'texpara' >< div id = 'qty.point.type-sentence-1' class = 'sentence' > A < a class = 'hidden_link' href = '#def:type,quantity_point' title = '5.8.3 Class template quantity_­point [qty.point.type]' >< span id = 'def:type,quantity_point' >< i > quantity point type</ i ></ span ></ a > is a specialization of < span class = 'texttt' > quantity_< span class = 'shy' ></ span > point</ span >< a class = 'hidden_link' href = '#qty.point.type-sentence-1' > .</ a ></ div > < div id = 'qty.point.type-sentence-2' class = 'sentence' > Let < span class = 'texttt' >< i > Q</ i ></ span > be a quantity point type< a class = 'hidden_link' href = '#qty.point.type-sentence-2' > .</ a ></ div > < div id = 'qty.point.type-sentence-3' class = 'sentence' >< span class = 'texttt' >< i > Q</ i >< span class = 'operator' > ​ ::​ </ span > point_< span class = 'shy' ></ span > origin</ span > represents
the origin point of a position vector (< a href = "https://www.electropedia.org/iev/iev.nsf/display?openform&ievref=102-03-15" > IEC 60050, 102-03-15</ a > )< a class = 'hidden_link' href = '#qty.point.type-sentence-3' > .</ a ></ div > < ul class = 'itemize' >< li >< div class = 'texpara' >< div id = 'qty.point.type-sentence-1' class = 'sentence' > If < span class = 'texttt' > Rep</ span > is a scalar,
< span class = 'texttt' >< i > Q</ i ></ span > represents the scalar quantity (< a href = "https://www.electropedia.org/iev/iev.nsf/display?openform&ievref=102-02-19" > IEC 60050, 102-02-19</ a > )
of a position vector< a class = 'hidden_link' href = '#qty.point.type-sentence-1' > .</ a ></ div ></ div ></ li >< li >< div class = 'texpara' >< div id = 'qty.point.type-sentence-1' class = 'sentence' > If < span class = 'texttt' > Rep</ span > is a vector,
< span class = 'texttt' >< i > Q</ i ></ span > represents a position vector< a class = 'hidden_link' href = '#qty.point.type-sentence-1' > .</ a ></ div ></ div ></ li ></ ul ></ div ></ div ></ div >< div id = 'qty.compat' class = 'section' >< h2 >< a class = 'secnum' href = '#qty.compat' style = 'min-width:65pt' > 5.9</ a > Compatibility < a class = 'abbr_ref' href = 'qty.compat.html' > [qty.compat]</ a ></ h2 ></ div >< div id = 'qty.one' class = 'section' >< h2 >< a class = 'secnum' href = '#qty.one' style = 'min-width:65pt' > 5.10</ a > Dimension one < a class = 'abbr_ref' href = 'qty.one.html' > [qty.one]</ a ></ h2 ></ div >< div id = 'qty.systems' class = 'section' >< h2 >< a class = 'secnum' href = '#qty.systems' style = 'min-width:65pt' > 5.11</ a > Systems < a class = 'abbr_ref' href = 'qty.systems.html' > [qty.systems]</ a ></ h2 ></ div >< div id = 'qty.chrono' class = 'section' >< h2 >< a class = 'secnum' href = '#qty.chrono' style = 'min-width:65pt' > 5.12</ a > < span class = 'texttt' > std​ ::​ chrono</ span > compatibility < a class = 'abbr_ref' href = 'qty.chrono.html' > [qty.chrono]</ a ></ h2 ></ div ></ div ></ body ></ html >
