46 lines
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46 lines
16 KiB
HTML
<!DOCTYPE html><html lang='en'><head><title>[qty.ratio]</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 and units library <a class='abbr_ref' href='index.html#quantities'>[quantities]</a></h1><h2 ><a class='secnum' style='min-width:65pt'>5.3</a> Utilities <a class='abbr_ref' href='qty.utils.html#qty.ratio'>[qty.utils]</a></h2><h3 ><a class='secnum' style='min-width:80pt'>5.3.2</a> Ratio <a class='abbr_ref'>[qty.ratio]</a></h3><div class='texpara'><span id='lib:ratio,is-integral'><span id='lib:is-integral,ratio'><span id='lib:ratio,operator/'><span id='lib:operator/,ratio'><span id='lib:ratio,operator+'><span id='lib:operator+,ratio'><span id='lib:ratio,operator-'><span id='lib:operator-,ratio'><span id='lib:ratio,operator<=>'><span id='lib:operator<=>,ratio'><span id='lib:ratio,operator=='><span id='lib:operator==,ratio'><span id='lib:ratio'><div class='marginalizedparent'><a class='itemDeclLink' href='#lib:ratio'>🔗</a></div><span class='codeblock'><span class='keyword'>namespace</span> mp_units <span class='curlybracket'>{</span>
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<span class='keyword'>struct</span> <i >ratio</i> <span class='curlybracket'>{</span> <span class='comment'>// <i >exposition only</i></span>
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std<span class='operator'>::</span>intmax_t num;
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std<span class='operator'>::</span>intmax_t den;
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<span class='keyword'>consteval</span> <i >ratio</i><span class='parenthesis'>(</span>std<span class='operator'>::</span>intmax_t n, std<span class='operator'>::</span>intmax_t d <span class='operator'>=</span> <span class='literal'>1</span><span class='parenthesis'>)</span>;
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<span class='keyword'>friend</span> <span class='keyword'>consteval</span> <span class='keyword'>bool</span> <span class='keyword'>operator</span><span class='operator'>=</span><span class='operator'>=</span><span class='parenthesis'>(</span><i >ratio</i>, <i >ratio</i><span class='parenthesis'>)</span> <span class='operator'>=</span> <span class='keyword'>default</span>;
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<span class='keyword'>friend</span> <span class='keyword'>consteval</span> <span class='keyword'>auto</span> <span class='keyword'>operator</span><span class='anglebracket'><</span><span class='operator'>=</span><span class='anglebracket'>></span><span class='parenthesis'>(</span><i >ratio</i> lhs, <i >ratio</i> rhs<span class='parenthesis'>)</span> <span class='curlybracket'>{</span> <span class='keyword'>return</span> <span class='parenthesis'>(</span>lhs <span class='operator'>-</span> rhs<span class='parenthesis'>)</span><span class='operator'>.</span>num <span class='anglebracket'><</span><span class='operator'>=</span><span class='anglebracket'>></span> <span class='literal'>0</span>; <span class='curlybracket'>}</span>
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<span class='keyword'>friend</span> <span class='keyword'>consteval</span> <i >ratio</i> <span class='keyword'>operator</span><span class='operator'>-</span><span class='parenthesis'>(</span><i >ratio</i> r<span class='parenthesis'>)</span> <span class='curlybracket'>{</span> <span class='keyword'>return</span> <span class='curlybracket'>{</span><span class='operator'>-</span>r<span class='operator'>.</span>num, r<span class='operator'>.</span>den<span class='curlybracket'>}</span>; <span class='curlybracket'>}</span>
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<span class='keyword'>friend</span> <span class='keyword'>consteval</span> <i >ratio</i> <span class='keyword'>operator</span><span class='operator'>+</span><span class='parenthesis'>(</span><i >ratio</i> lhs, <i >ratio</i> rhs<span class='parenthesis'>)</span>
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<span class='curlybracket'>{</span>
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<span class='keyword'>return</span> <span class='curlybracket'>{</span>lhs<span class='operator'>.</span>num <span class='operator'>*</span> rhs<span class='operator'>.</span>den <span class='operator'>+</span> lhs<span class='operator'>.</span>den <span class='operator'>*</span> rhs<span class='operator'>.</span>num, lhs<span class='operator'>.</span>den <span class='operator'>*</span> rhs<span class='operator'>.</span>den<span class='curlybracket'>}</span>;
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<span class='curlybracket'>}</span>
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<span class='keyword'>friend</span> <span class='keyword'>consteval</span> <i >ratio</i> <span class='keyword'>operator</span><span class='operator'>-</span><span class='parenthesis'>(</span><i >ratio</i> lhs, <i >ratio</i> rhs<span class='parenthesis'>)</span> <span class='curlybracket'>{</span> <span class='keyword'>return</span> lhs <span class='operator'>+</span> <span class='parenthesis'>(</span><span class='operator'>-</span>rhs<span class='parenthesis'>)</span>; <span class='curlybracket'>}</span>
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<span class='keyword'>friend</span> <span class='keyword'>consteval</span> <i >ratio</i> <span class='keyword'>operator</span><span class='operator'>*</span><span class='parenthesis'>(</span><i >ratio</i> lhs, <i >ratio</i> rhs<span class='parenthesis'>)</span>;
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<span class='keyword'>friend</span> <span class='keyword'>consteval</span> <i >ratio</i> <span class='keyword'>operator</span><span class='operator'>/</span><span class='parenthesis'>(</span><i >ratio</i> lhs, <i >ratio</i> rhs<span class='parenthesis'>)</span>
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<span class='curlybracket'>{</span>
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<span class='keyword'>return</span> lhs <span class='operator'>*</span> <i >ratio</i><span class='curlybracket'>{</span>rhs<span class='operator'>.</span>den, rhs<span class='operator'>.</span>num<span class='curlybracket'>}</span>;
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<span class='curlybracket'>}</span>
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<span class='curlybracket'>}</span>;
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<span class='keyword'>consteval</span> <span class='keyword'>bool</span> <i >is-integral</i><span class='parenthesis'>(</span><i >ratio</i> r<span class='parenthesis'>)</span> <span class='curlybracket'>{</span> <span class='keyword'>return</span> r<span class='operator'>.</span>num <span class='operator'>%</span> r<span class='operator'>.</span>den <span class='operator'>=</span><span class='operator'>=</span> <span class='literal'>0</span>; <span class='curlybracket'>}</span>
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<span class='keyword'>consteval</span> <i >ratio</i> <i >common-ratio</i><span class='parenthesis'>(</span><i >ratio</i> r1, <i >ratio</i> r2<span class='parenthesis'>)</span>;
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<span class='curlybracket'>}</span>
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</span></span></span></span></span></span></span></span></span></span></span></span></span></span></div><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-units94d7b2bb104446bf4399cd3942b7c74dff32c269/source/quantities.tex#L775'>#</a></div><div class='texpara'><div id='1.sentence-1' class='sentence'><span class='texttt'><i >ratio</i></span> represents the rational number <span class="mjx-chtml"><span class="mjx-math"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">num</span></span></span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">/</span></span></span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">den</span></span></span></span></span></span></span><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-units94d7b2bb104446bf4399cd3942b7c74dff32c269/source/quantities.tex#L778'>#</a></div><div class='texpara'><div id='2.sentence-1' class='sentence'>Unless otherwise specified,
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in the following descriptions,
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let <span class='texttt'>R<span class='parenthesis'>(</span>r<span class='parenthesis'>)</span></span> be <span class='texttt'>std<span class='operator'>​::​</span>ratio<span class='anglebracket'><</span>N, D<span class='anglebracket'>></span></span>,
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where <span class='texttt'>N</span> and <span class='texttt'>D</span> are the values of <span class='texttt'>r<span class='operator'>.</span>num</span> and <span class='texttt'>r<span class='operator'>.</span>den</span><a class='hidden_link' href='#2.sentence-1'>.</a></div></div></div><div class='texpara'><div id='lib:ratio,constructor'><div class='itemdecl'><div class='marginalizedparent'><a class='itemDeclLink' href='#lib:ratio,constructor'>🔗</a></div><code class='itemdeclcode'><span class='keyword'>consteval</span> <span class='texttt'><i >ratio</i></span><span class='parenthesis'>(</span>std<span class='operator'>::</span>intmax_t n, std<span class='operator'>::</span>intmax_t d <span class='operator'>=</span> <span class='literal'>1</span><span class='parenthesis'>)</span>;
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</code></div></div></div><div class='para' id='3'><div class='marginalizedparent'><a class='marginalized' href='#3'>3</a></div><div class='itemdescr'><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-units94d7b2bb104446bf4399cd3942b7c74dff32c269/source/quantities.tex#L790'>#</a></div><div class='texpara'><div id='3.sentence-1' class='sentence'>Let <span class='texttt'>N</span> and <span class='texttt'>D</span> be the values of <span class='texttt'>n</span> and <span class='texttt'>d</span><a class='hidden_link' href='#3.sentence-1'>.</a></div> <div id='3.sentence-2' class='sentence'>Let <span class='texttt'>R</span> be <span class='texttt'>std<span class='operator'>​::​</span>ratio<span class='anglebracket'><</span>N, D<span class='anglebracket'>></span></span><a class='hidden_link' href='#3.sentence-2'>.</a></div></div></div></div><div class='para' id='4'><div class='marginalizedparent'><a class='marginalized' href='#4'>4</a></div><div class='itemdescr'><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-units94d7b2bb104446bf4399cd3942b7c74dff32c269/source/quantities.tex#L794'>#</a></div><div class='texpara'><div id='4.sentence-1' class='sentence'><i >Effects</i>: Equivalent to
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<span class='texttt'>R</span><a class='hidden_link' href='#4.sentence-1'>.</a></div></div></div></div><div class='para' id='5'><div class='marginalizedparent'><a class='marginalized' href='#5'>5</a></div><div class='itemdescr'><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-units94d7b2bb104446bf4399cd3942b7c74dff32c269/source/quantities.tex#L799'>#</a></div><div class='texpara'><div id='5.sentence-1' class='sentence'><i >Postconditions</i>: <span class='texttt'>num <span class='operator'>=</span><span class='operator'>=</span> R<span class='operator'>​::​</span>num <span class='operator'>&</span><span class='operator'>&</span> den <span class='operator'>=</span><span class='operator'>=</span> R<span class='operator'>​::​</span>den</span> is <span class='texttt'><span class='literal'>true</span></span><a class='hidden_link' href='#5.sentence-1'>.</a></div></div></div></div><div class='texpara'><div id='lib:ratio,operator*'><div id='lib:operator*,ratio'><div class='itemdecl'><div class='marginalizedparent'><a class='itemDeclLink' href='#lib:operator*,ratio'>🔗</a></div><code class='itemdeclcode'><span class='keyword'>friend</span> <span class='keyword'>consteval</span> <span class='texttt'><i >ratio</i></span> <span class='keyword'>operator</span><span class='operator'>*</span><span class='parenthesis'>(</span><span class='texttt'><i >ratio</i></span> lhs, <span class='texttt'><i >ratio</i></span> rhs<span class='parenthesis'>)</span>;
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</code></div></div></div></div><div class='para' id='6'><div class='marginalizedparent'><a class='marginalized' href='#6'>6</a></div><div class='itemdescr'><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-units94d7b2bb104446bf4399cd3942b7c74dff32c269/source/quantities.tex#L810'>#</a></div><div class='texpara'><div id='6.sentence-1' class='sentence'>Let <span class='texttt'>Res</span> be <span class='texttt'>std<span class='operator'>​::​</span>ratio_<span class='shy'></span>multiply<span class='anglebracket'><</span>R<span class='parenthesis'>(</span>lhs<span class='parenthesis'>)</span>, R<span class='parenthesis'>(</span>rhs<span class='parenthesis'>)</span><span class='anglebracket'>></span></span><a class='hidden_link' href='#6.sentence-1'>.</a></div></div></div></div><div class='para' id='7'><div class='marginalizedparent'><a class='marginalized' href='#7'>7</a></div><div class='itemdescr'><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-units94d7b2bb104446bf4399cd3942b7c74dff32c269/source/quantities.tex#L813'>#</a></div><div class='texpara'><div id='7.sentence-1' class='sentence'><i >Effects</i>: Equivalent to:
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<span class='texttt'><span class='keyword'>return</span> <span class='curlybracket'>{</span>Res<span class='operator'>​::​</span>num, Res<span class='operator'>​::​</span>den<span class='curlybracket'>}</span>;</span></div></div></div></div><div class='texpara'><div id='lib:ratio,common-ratio'><div id='lib:common-ratio,ratio'><div class='itemdecl'><div class='marginalizedparent'><a class='itemDeclLink' href='#lib:common-ratio,ratio'>🔗</a></div><code class='itemdeclcode'><span class='keyword'>consteval</span> <span class='texttt'><i >ratio</i></span> <span class='texttt'><i >common-ratio</i></span><span class='parenthesis'>(</span><span class='texttt'><i >ratio</i></span> r1, <span class='texttt'><i >ratio</i></span> r2<span class='parenthesis'>)</span>;
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</code></div></div></div></div><div class='para' id='8'><div class='marginalizedparent'><a class='marginalized' href='#8'>8</a></div><div class='itemdescr'><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-units94d7b2bb104446bf4399cd3942b7c74dff32c269/source/quantities.tex#L825'>#</a></div><div class='texpara'><div id='8.sentence-1' class='sentence'>Let <span class='texttt'>Res</span> be equal to
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<span class='codeblock'>std<span class='operator'>::</span>common_type<span class='anglebracket'><</span>std<span class='operator'>::</span>chrono<span class='operator'>::</span>duration<span class='anglebracket'><</span><span class='keyword'>int</span>, R<span class='parenthesis'>(</span>r1<span class='parenthesis'>)</span><span class='anglebracket'>></span>,
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std<span class='operator'>::</span>chrono<span class='operator'>::</span>duration<span class='anglebracket'><</span><span class='keyword'>int</span>, R<span class='parenthesis'>(</span>r2<span class='parenthesis'>)</span><span class='anglebracket'>></span><span class='anglebracket'>></span><span class='operator'>::</span>type<span class='operator'>::</span>period
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</span></div></div></div></div><div class='para' id='9'><div class='marginalizedparent'><a class='marginalized' href='#9'>9</a></div><div class='itemdescr'><div class='sourceLinkParent'><a class='sourceLink' href='https://github.com/mpusz/mp-units94d7b2bb104446bf4399cd3942b7c74dff32c269/source/quantities.tex#L832'>#</a></div><div class='texpara'><div id='9.sentence-1' class='sentence'><i >Effects</i>: Equivalent to:
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<span class='texttt'><span class='keyword'>return</span> <span class='curlybracket'>{</span>Res<span class='operator'>​::​</span>num, Res<span class='operator'>​::​</span>den<span class='curlybracket'>}</span>;</span></div></div></div></div></div></body></html> |