Accueil Explorer Aide
Connexion
levovix
/
Nim
miroir de https://github.com/nim-lang/Nim
Suivre 1
Voter 0
Fork 1
Fichiers Tickets 0 Wiki
Branche: gh-pages
Branches Tags
Nim
/
rationals.html

rationals.html 79 KB
Lien permanent Historique Raw

123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300301302303304305306307308309310311312313314315316317318319320321322323324325326327328329330331332333334335336337338339340341342343344345346347348349350351352353354355356357358359360361362363364365366367368369370371372373374375376377378379380381382383384385386387388389390391392393394395396397398399400401402403404405406407408409410411412413414415416417418419420421422423424425426427428429430431432433434435436437438439440441442443444445446447448449450451452453454455456457458459460461462463464465466467468469470471472473474475476477478479480481482483484485486487488489490491492493494495496497498499500501502503504505506507508509510511512513514515516517518519520521522523524525526527528529530531532533534535536537538539540541542543544545546547548549550551552553554555556557558559560561562563564565566567568569570571572573574575576577578579580581582583584585586587588589590591592593594595596597598599600601602603604605606607608609610611612613614615616617618619620621622623624625626627628629630631632633634635636637638639640641642643644645646647648649650651652653654655656657658659660661662663664665666667668669670671672673674675676677678679680681682683684685686687688689690691692693694695696697698699700701702703704705706707708709710711712713714715716717718719720721722723724725726727728729730731732733734735736737738739740741742743744745746747748749750751752753754755756757758759760761762763764765766767768769770771772773774775776777778779780781782783784785786787788789790791792793 
  1. <?xml version="1.0" encoding="utf-8" ?>
    2. 

  2. <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
    3. 

  3. <!--  This file is generated by Nim. -->
    4. 

  4. <html xmlns="https://www.w3.org/1999/xhtml" xml:lang="en" lang="en" data-theme="auto">
    5. 

  5. <head>
    6. 

  6. <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
    7. 

  7. <meta name="viewport" content="width=device-width, initial-scale=1.0">
    8. 

  8. <title>std/rationals</title>
    9. 

  9. 

  10. <!-- Google fonts -->
    11. 

  11. <link href='https://fonts.googleapis.com/css?family=Lato:400,600,900' rel='stylesheet' type='text/css'/>
    12. 

  12. <link href='https://fonts.googleapis.com/css?family=Source+Code+Pro:400,500,600' rel='stylesheet' type='text/css'/>
    13. 

  13. 

  14. <!-- Favicon -->
    15. 

  15. <link rel="shortcut icon" href="data:image/x-icon;base64,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"/>
    16. 

  16. <link rel="icon" type="image/png" sizes="32x32" href="data:image/png;base64,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">
    17. 

  17. 

  18. <!-- CSS -->
    19. 

  19. <link rel="stylesheet" type="text/css" href="nimdoc.out.css?v=2.3.1">
    20. 

  20. 

  21. <!-- JS -->
    22. 

  22. <script type="text/javascript" src="dochack.js?v=2.3.1"></script>
    23. 

  23. </head>
    24. 

  24. <body>
    25. 

  25.   <div class="document" id="documentId">
    26. 

  26.     <div class="container">
    27. 

  27.       <h1 class="title">std/rationals</h1>
    28. 

  28.       <div class="row">
    29. 

  29.   <div class="three columns">
    30. 

  30.     <div class="theme-select-wrapper">
    31. 

  31.       <label for="theme-select">Theme:&nbsp;</label>
    32. 

  32.       <select id="theme-select" onchange="setTheme(this.value)">
    33. 

  33.         <option value="auto">🌗 Match OS</option>
    34. 

  34.         <option value="dark">🌑 Dark</option>
    35. 

  35.         <option value="light">🌕 Light</option>
    36. 

  36.       </select>
    37. 

  37.     </div>
    38. 

  38.     <div id="global-links">
    39. 

  39.       <ul class="simple-boot">
    40. 

  40.         <li><a href="manual.html">Manual</a></li>
    41. 

  41.         <li><a href="lib.html">Standard library</a></li>
    42. 

  42.         <li> <a id="indexLink" href="theindex.html">Index</a></li>
    43. 

  43.         <li><a href="compiler/theindex.html">Compiler docs</a></li>
    44. 

  44.         <li><a href="https://nim-lang.github.io/fusion/theindex.html">Fusion docs</a></li>
    45. 

  45.         <li><a href="https://nim-lang.github.io/Nim/">devel</a>, <a href="https://nim-lang.org/documentation.html">stable</a></li>
    46. 

  46.       </ul>
    47. 

  47.     </div>
    48. 

  48.     <div id="searchInputDiv">
    49. 

  49.       Search: <input type="search" id="searchInput"
    50. 

  50.         oninput="search()" />
    51. 

  51.     </div>
    52. 

  52.     
    53. 

  53.     <ul class="simple simple-toc" id="toc-list">
    54. 

  54.   <li>
    55. 

  55.   <a class="reference reference-toplevel" href="#6" id="56">Imports</a>
    56. 

  56. </li>
    57. 

  57. <li>
    58. 

  58.   <details open>
    59. 

  59.     <summary><a class="reference reference-toplevel" href="#7" id="57">Types</a></summary>
    60. 

  60.     <ul class="simple simple-toc-section">
    61. 

  61.       <li><a class="reference" href="#Rational" title="Rational[T] = object
    62. 

  62.   num*, den*: T">Rational</a></li>
    63. 

  63. 

  64.     </ul>
    65. 

  65.   </details>
    66. 

  66. </li>
    67. 

  67. <li>
    68. 

  68.   <details open>
    69. 

  69.     <summary><a class="reference reference-toplevel" href="#12" id="62">Procs</a></summary>
    70. 

  70.     <ul class="simple simple-toc-section">
    71. 

  71.       <ul class="simple nested-toc-section">$
    72. 

  72.   <li><a class="reference" href="#%24%2CRational%5BT%5D" title="`$`[T](x: Rational[T]): string">`$`[T](x: Rational[T]): string</a></li>
    73. 

  73. 

  74. </ul>
    75. 

  75. <ul class="simple nested-toc-section">*
    76. 

  76.   <li><a class="reference" href="#%2A%2CRational%5BT%5D%2CRational%5BT%5D" title="`*`[T](x, y: Rational[T]): Rational[T]">`*`[T](x, y: Rational[T]): Rational[T]</a></li>
    77. 

  77. <li><a class="reference" href="#%2A%2CRational%5BT%5D%2CT" title="`*`[T](x: Rational[T]; y: T): Rational[T]">`*`[T](x: Rational[T]; y: T): Rational[T]</a></li>
    78. 

  78. <li><a class="reference" href="#%2A%2CT%2CRational%5BT%5D" title="`*`[T](x: T; y: Rational[T]): Rational[T]">`*`[T](x: T; y: Rational[T]): Rational[T]</a></li>
    79. 

  79. 

  80. </ul>
    81. 

  81. <ul class="simple nested-toc-section">*=
    82. 

  82.   <li><a class="reference" href="#%2A%3D%2CRational%5BT%5D%2CRational%5BT%5D" title="`*=`[T](x: var Rational[T]; y: Rational[T])">`*=`[T](x: var Rational[T]; y: Rational[T])</a></li>
    83. 

  83. <li><a class="reference" href="#%2A%3D%2CRational%5BT%5D%2CT" title="`*=`[T](x: var Rational[T]; y: T)">`*=`[T](x: var Rational[T]; y: T)</a></li>
    84. 

  84. 

  85. </ul>
    86. 

  86. <ul class="simple nested-toc-section">+
    87. 

  87.   <li><a class="reference" href="#%2B%2CRational%5BT%5D%2CRational%5BT%5D" title="`+`[T](x, y: Rational[T]): Rational[T]">`+`[T](x, y: Rational[T]): Rational[T]</a></li>
    88. 

  88. <li><a class="reference" href="#%2B%2CRational%5BT%5D%2CT" title="`+`[T](x: Rational[T]; y: T): Rational[T]">`+`[T](x: Rational[T]; y: T): Rational[T]</a></li>
    89. 

  89. <li><a class="reference" href="#%2B%2CT%2CRational%5BT%5D" title="`+`[T](x: T; y: Rational[T]): Rational[T]">`+`[T](x: T; y: Rational[T]): Rational[T]</a></li>
    90. 

  90. 

  91. </ul>
    92. 

  92. <ul class="simple nested-toc-section">+=
    93. 

  93.   <li><a class="reference" href="#%2B%3D%2CRational%5BT%5D%2CRational%5BT%5D" title="`+=`[T](x: var Rational[T]; y: Rational[T])">`+=`[T](x: var Rational[T]; y: Rational[T])</a></li>
    94. 

  94. <li><a class="reference" href="#%2B%3D%2CRational%5BT%5D%2CT" title="`+=`[T](x: var Rational[T]; y: T)">`+=`[T](x: var Rational[T]; y: T)</a></li>
    95. 

  95. 

  96. </ul>
    97. 

  97. <ul class="simple nested-toc-section">-
    98. 

  98.   <li><a class="reference" href="#-%2CRational%5BT%5D%2CRational%5BT%5D" title="`-`[T](x, y: Rational[T]): Rational[T]">`-`[T](x, y: Rational[T]): Rational[T]</a></li>
    99. 

  99. <li><a class="reference" href="#-%2CRational%5BT%5D" title="`-`[T](x: Rational[T]): Rational[T]">`-`[T](x: Rational[T]): Rational[T]</a></li>
    100. 

  100. <li><a class="reference" href="#-%2CRational%5BT%5D%2CT" title="`-`[T](x: Rational[T]; y: T): Rational[T]">`-`[T](x: Rational[T]; y: T): Rational[T]</a></li>
    101. 

  101. <li><a class="reference" href="#-%2CT%2CRational%5BT%5D" title="`-`[T](x: T; y: Rational[T]): Rational[T]">`-`[T](x: T; y: Rational[T]): Rational[T]</a></li>
    102. 

  102. 

  103. </ul>
    104. 

  104. <ul class="simple nested-toc-section">-=
    105. 

  105.   <li><a class="reference" href="#-%3D%2CRational%5BT%5D%2CRational%5BT%5D" title="`-=`[T](x: var Rational[T]; y: Rational[T])">`-=`[T](x: var Rational[T]; y: Rational[T])</a></li>
    106. 

  106. <li><a class="reference" href="#-%3D%2CRational%5BT%5D%2CT" title="`-=`[T](x: var Rational[T]; y: T)">`-=`[T](x: var Rational[T]; y: T)</a></li>
    107. 

  107. 

  108. </ul>
    109. 

  109. <ul class="simple nested-toc-section">/
    110. 

  110.   <li><a class="reference" href="#%2F%2CRational%5BT%5D%2CRational%5BT%5D" title="`/`[T](x, y: Rational[T]): Rational[T]">`/`[T](x, y: Rational[T]): Rational[T]</a></li>
    111. 

  111. <li><a class="reference" href="#%2F%2CRational%5BT%5D%2CT" title="`/`[T](x: Rational[T]; y: T): Rational[T]">`/`[T](x: Rational[T]; y: T): Rational[T]</a></li>
    112. 

  112. <li><a class="reference" href="#%2F%2CT%2CRational%5BT%5D" title="`/`[T](x: T; y: Rational[T]): Rational[T]">`/`[T](x: T; y: Rational[T]): Rational[T]</a></li>
    113. 

  113. 

  114. </ul>
    115. 

  115. <ul class="simple nested-toc-section">//
    116. 

  116.   <li><a class="reference" href="#%2F%2F%2CT%2CT" title="`//`[T](num, den: T): Rational[T]">`//`[T](num, den: T): Rational[T]</a></li>
    117. 

  117. 

  118. </ul>
    119. 

  119. <ul class="simple nested-toc-section">/=
    120. 

  120.   <li><a class="reference" href="#%2F%3D%2CRational%5BT%5D%2CRational%5BT%5D" title="`/=`[T](x: var Rational[T]; y: Rational[T])">`/=`[T](x: var Rational[T]; y: Rational[T])</a></li>
    121. 

  121. <li><a class="reference" href="#%2F%3D%2CRational%5BT%5D%2CT" title="`/=`[T](x: var Rational[T]; y: T)">`/=`[T](x: var Rational[T]; y: T)</a></li>
    122. 

  122. 

  123. </ul>
    124. 

  124. <ul class="simple nested-toc-section"><
    125. 

  125.   <li><a class="reference" href="#%3C%2CRational%2CRational" title="`&lt;`(x, y: Rational): bool">`&lt;`(x, y: Rational): bool</a></li>
    126. 

  126. 

  127. </ul>
    128. 

  128. <ul class="simple nested-toc-section"><=
    129. 

  129.   <li><a class="reference" href="#%3C%3D%2CRational%2CRational" title="`&lt;=`(x, y: Rational): bool">`&lt;=`(x, y: Rational): bool</a></li>
    130. 

  130. 

  131. </ul>
    132. 

  132. <ul class="simple nested-toc-section">==
    133. 

  133.   <li><a class="reference" href="#%3D%3D%2CRational%2CRational" title="`==`(x, y: Rational): bool">`==`(x, y: Rational): bool</a></li>
    134. 

  134. 

  135. </ul>
    136. 

  136. <ul class="simple nested-toc-section">^
    137. 

  137.   <li><a class="reference" href="#%5E%2CRational%5BT%3A%20SomeInteger%5D%2CT" title="`^`[T: SomeInteger](x: Rational[T]; y: T): Rational[T]">`^`[T: SomeInteger](x: Rational[T]; y: T): Rational[T]</a></li>
    138. 

  138. 

  139. </ul>
    140. 

  140. <ul class="simple nested-toc-section">abs
    141. 

  141.   <li><a class="reference" href="#abs%2CRational%5BT%5D" title="abs[T](x: Rational[T]): Rational[T]">abs[T](x: Rational[T]): Rational[T]</a></li>
    142. 

  142. 

  143. </ul>
    144. 

  144. <ul class="simple nested-toc-section">cmp
    145. 

  145.   <li><a class="reference" href="#cmp%2CRational%2CRational" title="cmp(x, y: Rational): int">cmp(x, y: Rational): int</a></li>
    146. 

  146. 

  147. </ul>
    148. 

  148. <ul class="simple nested-toc-section">div
    149. 

  149.   <li><a class="reference" href="#div%2CRational%5BT%3A%20SomeInteger%5D%2CRational%5BT%3A%20SomeInteger%5D" title="`div`[T: SomeInteger](x, y: Rational[T]): T">`div`[T: SomeInteger](x, y: Rational[T]): T</a></li>
    150. 

  150. 

  151. </ul>
    152. 

  152. <ul class="simple nested-toc-section">floorDiv
    153. 

  153.   <li><a class="reference" href="#floorDiv%2CRational%5BT%3A%20SomeInteger%5D%2CRational%5BT%3A%20SomeInteger%5D" title="floorDiv[T: SomeInteger](x, y: Rational[T]): T">floorDiv[T: SomeInteger](x, y: Rational[T]): T</a></li>
    154. 

  154. 

  155. </ul>
    156. 

  156. <ul class="simple nested-toc-section">floorMod
    157. 

  157.   <li><a class="reference" href="#floorMod%2CRational%5BT%3A%20SomeInteger%5D%2CRational%5BT%3A%20SomeInteger%5D" title="floorMod[T: SomeInteger](x, y: Rational[T]): Rational[T]">floorMod[T: SomeInteger](x, y: Rational[T]): Rational[T]</a></li>
    158. 

  158. 

  159. </ul>
    160. 

  160. <ul class="simple nested-toc-section">hash
    161. 

  161.   <li><a class="reference" href="#hash%2CRational%5BT%5D" title="hash[T](x: Rational[T]): Hash">hash[T](x: Rational[T]): Hash</a></li>
    162. 

  162. 

  163. </ul>
    164. 

  164. <ul class="simple nested-toc-section">initRational
    165. 

  165.   <li><a class="reference" href="#initRational%2CT%2CT" title="initRational[T: SomeInteger](num, den: T): Rational[T]">initRational[T: SomeInteger](num, den: T): Rational[T]</a></li>
    166. 

  166. 

  167. </ul>
    168. 

  168. <ul class="simple nested-toc-section">mod
    169. 

  169.   <li><a class="reference" href="#mod%2CRational%5BT%3A%20SomeInteger%5D%2CRational%5BT%3A%20SomeInteger%5D" title="`mod`[T: SomeInteger](x, y: Rational[T]): Rational[T]">`mod`[T: SomeInteger](x, y: Rational[T]): Rational[T]</a></li>
    170. 

  170. 

  171. </ul>
    172. 

  172. <ul class="simple nested-toc-section">reciprocal
    173. 

  173.   <li><a class="reference" href="#reciprocal%2CRational%5BT%5D" title="reciprocal[T](x: Rational[T]): Rational[T]">reciprocal[T](x: Rational[T]): Rational[T]</a></li>
    174. 

  174. 

  175. </ul>
    176. 

  176. <ul class="simple nested-toc-section">reduce
    177. 

  177.   <li><a class="reference" href="#reduce%2CRational%5BT%3A%20SomeInteger%5D" title="reduce[T: SomeInteger](x: var Rational[T])">reduce[T: SomeInteger](x: var Rational[T])</a></li>
    178. 

  178. 

  179. </ul>
    180. 

  180. <ul class="simple nested-toc-section">toFloat
    181. 

  181.   <li><a class="reference" href="#toFloat%2CRational%5BT%5D" title="toFloat[T](x: Rational[T]): float">toFloat[T](x: Rational[T]): float</a></li>
    182. 

  182. 

  183. </ul>
    184. 

  184. <ul class="simple nested-toc-section">toInt
    185. 

  185.   <li><a class="reference" href="#toInt%2CRational%5BT%5D" title="toInt[T](x: Rational[T]): int">toInt[T](x: Rational[T]): int</a></li>
    186. 

  186. 

  187. </ul>
    188. 

  188. <ul class="simple nested-toc-section">toRational
    189. 

  189.   <li><a class="reference" href="#toRational%2Cfloat%2Cint" title="toRational(x: float; n: int = high(int) shr 32): Rational[int]">toRational(x: float; n: int = high(int) shr 32): Rational[int]</a></li>
    190. 

  190. <li><a class="reference" href="#toRational%2CT" title="toRational[T: SomeInteger](x: T): Rational[T]">toRational[T: SomeInteger](x: T): Rational[T]</a></li>
    191. 

  191. 

  192. </ul>
    193. 

  193. 

  194.     </ul>
    195. 

  195.   </details>
    196. 

  196. </li>
    197. 

  197. 

  198. </ul>
    199. 

  199. 

  200.   </div>
    201. 

  201.   <div class="nine columns" id="content">
    202. 

  202.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L1" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    203. 

  203. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L1" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    204. 

  204. 

  205.     <div id="tocRoot"></div>
    206. 

  206.     
    207. 

  207.     <p class="module-desc">This module implements rational numbers, consisting of a numerator and a denominator. The denominator can not be 0.
    208. 

  208. <p><strong class="examples_text">Example:</strong></p>
    209. 

  209. <pre class="listing"><span class="Keyword">import</span> <span class="Identifier">std</span><span class="Operator">/</span><span class="Identifier">rationals</span>
    210. 

  210. <span class="Keyword">let</span>
    211. 

  211.   <span class="Identifier">r1</span> <span class="Operator">=</span> <span class="DecNumber">1</span> <span class="Operator">//</span> <span class="DecNumber">2</span>
    212. 

  212.   <span class="Identifier">r2</span> <span class="Operator">=</span> <span class="Operator">-</span><span class="DecNumber">3</span> <span class="Operator">//</span> <span class="DecNumber">4</span>
    213. 

  213. 

  214. <span class="Identifier">doAssert</span> <span class="Identifier">r1</span> <span class="Operator">+</span> <span class="Identifier">r2</span> <span class="Operator">==</span> <span class="Operator">-</span><span class="DecNumber">1</span> <span class="Operator">//</span> <span class="DecNumber">4</span>
    215. 

  215. <span class="Identifier">doAssert</span> <span class="Identifier">r1</span> <span class="Operator">-</span> <span class="Identifier">r2</span> <span class="Operator">==</span>  <span class="DecNumber">5</span> <span class="Operator">//</span> <span class="DecNumber">4</span>
    216. 

  216. <span class="Identifier">doAssert</span> <span class="Identifier">r1</span> <span class="Operator">*</span> <span class="Identifier">r2</span> <span class="Operator">==</span> <span class="Operator">-</span><span class="DecNumber">3</span> <span class="Operator">//</span> <span class="DecNumber">8</span>
    217. 

  217. <span class="Identifier">doAssert</span> <span class="Identifier">r1</span> <span class="Operator">/</span> <span class="Identifier">r2</span> <span class="Operator">==</span> <span class="Operator">-</span><span class="DecNumber">2</span> <span class="Operator">//</span> <span class="DecNumber">3</span></pre></p>
    218. 

  218.     <div class="section" id="6">
    219. 

  219.   <h1><a class="toc-backref" href="#6">Imports</a></h1>
    220. 

  220.   <dl class="item">
    221. 

  221.     <a class="reference external" href="math.html">math</a>, <a class="reference external" href="hashes.html">hashes</a>, <a class="reference external" href="assertions.html">assertions</a>
    222. 

  222.   </dl>
    223. 

  223. </div>
    224. 

  224. <div class="section" id="7">
    225. 

  225.   <h1><a class="toc-backref" href="#7">Types</a></h1>
    226. 

  226.   <dl class="item">
    227. 

  227.     <div id="Rational">
    228. 

  228.   <dt><pre><a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span> <span class="Other">=</span> <span class="Keyword">object</span>
    229. 

  229.   <span class="Identifier">num</span><span class="Operator">*</span><span class="Other">,</span> <span class="Identifier">den</span><span class="Operator">*</span><span class="Other">:</span> <span class="Identifier">T</span></pre></dt>
    230. 

  230.   <dd>
    231. 

  231.     
    232. 

  232.     A rational number, consisting of a numerator <tt class="docutils literal"><span class="pre"><span class="Identifier">num</span></span></tt> and a denominator <tt class="docutils literal"><span class="pre"><span class="Identifier">den</span></span></tt>.
    233. 

  233.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L28" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    234. 

  234. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L28" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    235. 

  235. 

  236.   </dd>
    237. 

  237. </div>
    238. 

  238. 

  239.   </dl>
    240. 

  240. </div>
    241. 

  241. <div class="section" id="12">
    242. 

  242.   <h1><a class="toc-backref" href="#12">Procs</a></h1>
    243. 

  243.   <dl class="item">
    244. 

  244.     <div id="$-procs-all">
    245. 

  245.   <div id="$,Rational[T]">
    246. 

  246.   <dt><pre><span class="Keyword">func</span> <a href="#%24%2CRational%5BT%5D"><span class="Identifier">`$`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="system.html#string"><span class="Identifier">string</span></a></pre></dt>
    247. 

  247.   <dd>
    248. 

  248.     
    249. 

  249.     Turns a rational number into a string.
    250. 

  250. <p><strong class="examples_text">Example:</strong></p>
    251. 

  251. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Operator">$</span><span class="Punctuation">(</span><span class="DecNumber">1</span> <span class="Operator">//</span> <span class="DecNumber">2</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="StringLit">&quot;1/2&quot;</span></pre>
    252. 

  252.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L71" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    253. 

  253. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L71" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    254. 

  254. 

  255.   </dd>
    256. 

  256. </div>
    257. 

  257. 

  258. </div>
    259. 

  259. <div id="*-procs-all">
    260. 

  260.   <div id="*,Rational[T],Rational[T]">
    261. 

  261.   <dt><pre><span class="Keyword">func</span> <a href="#%2A%2CRational%5BT%5D%2CRational%5BT%5D"><span class="Identifier">`*`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">,</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    262. 

  262.   <dd>
    263. 

  263.     
    264. 

  264.     Multiplies two rational numbers.
    265. 

  265.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L180" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    266. 

  266. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L180" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    267. 

  267. 

  268.   </dd>
    269. 

  269. </div>
    270. 

  270. <div id="*,Rational[T],T">
    271. 

  271.   <dt><pre><span class="Keyword">func</span> <a href="#%2A%2CRational%5BT%5D%2CT"><span class="Identifier">`*`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    272. 

  272.   <dd>
    273. 

  273.     
    274. 

  274.     Multiplies the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> with the int <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt>.
    275. 

  275.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L185" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    276. 

  276. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L185" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    277. 

  277. 

  278.   </dd>
    279. 

  279. </div>
    280. 

  280. <div id="*,T,Rational[T]">
    281. 

  281.   <dt><pre><span class="Keyword">func</span> <a href="#%2A%2CT%2CRational%5BT%5D"><span class="Identifier">`*`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    282. 

  282.   <dd>
    283. 

  283.     
    284. 

  284.     Multiplies the int <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> with the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt>.
    285. 

  285.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L190" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    286. 

  286. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L190" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    287. 

  287. 

  288.   </dd>
    289. 

  289. </div>
    290. 

  290. 

  291. </div>
    292. 

  292. <div id="*=-procs-all">
    293. 

  293.   <div id="*=,Rational[T],Rational[T]">
    294. 

  294.   <dt><pre><span class="Keyword">func</span> <a href="#%2A%3D%2CRational%5BT%5D%2CRational%5BT%5D"><span class="Identifier">`*=`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Keyword">var</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span></pre></dt>
    295. 

  295.   <dd>
    296. 

  296.     
    297. 

  297.     Multiplies the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> by <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt> in-place.
    298. 

  298.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L195" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    299. 

  299. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L195" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    300. 

  300. 

  301.   </dd>
    302. 

  302. </div>
    303. 

  303. <div id="*=,Rational[T],T">
    304. 

  304.   <dt><pre><span class="Keyword">func</span> <a href="#%2A%3D%2CRational%5BT%5D%2CT"><span class="Identifier">`*=`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Keyword">var</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">)</span></pre></dt>
    305. 

  305.   <dd>
    306. 

  306.     
    307. 

  307.     Multiplies the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> by the int <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt> in-place.
    308. 

  308.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L201" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    309. 

  309. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L201" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    310. 

  310. 

  311.   </dd>
    312. 

  312. </div>
    313. 

  313. 

  314. </div>
    315. 

  315. <div id="+-procs-all">
    316. 

  316.   <div id="+,Rational[T],Rational[T]">
    317. 

  317.   <dt><pre><span class="Keyword">func</span> <a href="#%2B%2CRational%5BT%5D%2CRational%5BT%5D"><span class="Identifier">`+`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">,</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    318. 

  318.   <dd>
    319. 

  319.     
    320. 

  320.     Adds two rational numbers.
    321. 

  321.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L122" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    322. 

  322. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L122" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    323. 

  323. 

  324.   </dd>
    325. 

  325. </div>
    326. 

  326. <div id="+,Rational[T],T">
    327. 

  327.   <dt><pre><span class="Keyword">func</span> <a href="#%2B%2CRational%5BT%5D%2CT"><span class="Identifier">`+`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    328. 

  328.   <dd>
    329. 

  329.     
    330. 

  330.     Adds the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> to the int <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt>.
    331. 

  331.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L130" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    332. 

  332. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L130" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    333. 

  333. 

  334.   </dd>
    335. 

  335. </div>
    336. 

  336. <div id="+,T,Rational[T]">
    337. 

  337.   <dt><pre><span class="Keyword">func</span> <a href="#%2B%2CT%2CRational%5BT%5D"><span class="Identifier">`+`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    338. 

  338.   <dd>
    339. 

  339.     
    340. 

  340.     Adds the int <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> to the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt>.
    341. 

  341.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L134" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    342. 

  342. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L134" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    343. 

  343. 

  344.   </dd>
    345. 

  345. </div>
    346. 

  346. 

  347. </div>
    348. 

  348. <div id="+=-procs-all">
    349. 

  349.   <div id="+=,Rational[T],Rational[T]">
    350. 

  350.   <dt><pre><span class="Keyword">func</span> <a href="#%2B%3D%2CRational%5BT%5D%2CRational%5BT%5D"><span class="Identifier">`+=`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Keyword">var</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span></pre></dt>
    351. 

  351.   <dd>
    352. 

  352.     
    353. 

  353.     Adds the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt> to the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> in-place.
    354. 

  354.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L138" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    355. 

  355. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L138" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    356. 

  356. 

  357.   </dd>
    358. 

  358. </div>
    359. 

  359. <div id="+=,Rational[T],T">
    360. 

  360.   <dt><pre><span class="Keyword">func</span> <a href="#%2B%3D%2CRational%5BT%5D%2CT"><span class="Identifier">`+=`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Keyword">var</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">)</span></pre></dt>
    361. 

  361.   <dd>
    362. 

  362.     
    363. 

  363.     Adds the int <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt> to the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> in-place.
    364. 

  364.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L145" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    365. 

  365. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L145" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    366. 

  366. 

  367.   </dd>
    368. 

  368. </div>
    369. 

  369. 

  370. </div>
    371. 

  371. <div id="--procs-all">
    372. 

  372.   <div id="-,Rational[T],Rational[T]">
    373. 

  373.   <dt><pre><span class="Keyword">func</span> <a href="#-%2CRational%5BT%5D%2CRational%5BT%5D"><span class="Identifier">`-`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">,</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    374. 

  374.   <dd>
    375. 

  375.     
    376. 

  376.     Subtracts two rational numbers.
    377. 

  377.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L153" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    378. 

  378. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L153" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    379. 

  379. 

  380.   </dd>
    381. 

  381. </div>
    382. 

  382. <div id="-,Rational[T]">
    383. 

  383.   <dt><pre><span class="Keyword">func</span> <a href="#-%2CRational%5BT%5D"><span class="Identifier">`-`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    384. 

  384.   <dd>
    385. 

  385.     
    386. 

  386.     Unary minus for rational numbers.
    387. 

  387.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L149" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    388. 

  388. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L149" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    389. 

  389. 

  390.   </dd>
    391. 

  391. </div>
    392. 

  392. <div id="-,Rational[T],T">
    393. 

  393.   <dt><pre><span class="Keyword">func</span> <a href="#-%2CRational%5BT%5D%2CT"><span class="Identifier">`-`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    394. 

  394.   <dd>
    395. 

  395.     
    396. 

  396.     Subtracts the int <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt> from the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>.
    397. 

  397.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L161" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    398. 

  398. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L161" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    399. 

  399. 

  400.   </dd>
    401. 

  401. </div>
    402. 

  402. <div id="-,T,Rational[T]">
    403. 

  403.   <dt><pre><span class="Keyword">func</span> <a href="#-%2CT%2CRational%5BT%5D"><span class="Identifier">`-`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    404. 

  404.   <dd>
    405. 

  405.     
    406. 

  406.     Subtracts the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt> from the int <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>.
    407. 

  407.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L165" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    408. 

  408. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L165" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    409. 

  409. 

  410.   </dd>
    411. 

  411. </div>
    412. 

  412. 

  413. </div>
    414. 

  414. <div id="-=-procs-all">
    415. 

  415.   <div id="-=,Rational[T],Rational[T]">
    416. 

  416.   <dt><pre><span class="Keyword">func</span> <a href="#-%3D%2CRational%5BT%5D%2CRational%5BT%5D"><span class="Identifier">`-=`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Keyword">var</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span></pre></dt>
    417. 

  417.   <dd>
    418. 

  418.     
    419. 

  419.     Subtracts the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt> from the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> in-place.
    420. 

  420.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L169" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    421. 

  421. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L169" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    422. 

  422. 

  423.   </dd>
    424. 

  424. </div>
    425. 

  425. <div id="-=,Rational[T],T">
    426. 

  426.   <dt><pre><span class="Keyword">func</span> <a href="#-%3D%2CRational%5BT%5D%2CT"><span class="Identifier">`-=`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Keyword">var</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">)</span></pre></dt>
    427. 

  427.   <dd>
    428. 

  428.     
    429. 

  429.     Subtracts the int <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt> from the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> in-place.
    430. 

  430.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L176" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    431. 

  431. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L176" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    432. 

  432. 

  433.   </dd>
    434. 

  434. </div>
    435. 

  435. 

  436. </div>
    437. 

  437. <div id="/-procs-all">
    438. 

  438.   <div id="/,Rational[T],Rational[T]">
    439. 

  439.   <dt><pre><span class="Keyword">func</span> <a href="#%2F%2CRational%5BT%5D%2CRational%5BT%5D"><span class="Identifier">`/`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">,</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    440. 

  440.   <dd>
    441. 

  441.     
    442. 

  442.     Divides the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> by the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt>.
    443. 

  443.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L216" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    444. 

  444. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L216" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    445. 

  445. 

  446.   </dd>
    447. 

  447. </div>
    448. 

  448. <div id="/,Rational[T],T">
    449. 

  449.   <dt><pre><span class="Keyword">func</span> <a href="#%2F%2CRational%5BT%5D%2CT"><span class="Identifier">`/`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    450. 

  450.   <dd>
    451. 

  451.     
    452. 

  452.     Divides the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> by the int <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt>.
    453. 

  453.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L221" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    454. 

  454. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L221" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    455. 

  455. 

  456.   </dd>
    457. 

  457. </div>
    458. 

  458. <div id="/,T,Rational[T]">
    459. 

  459.   <dt><pre><span class="Keyword">func</span> <a href="#%2F%2CT%2CRational%5BT%5D"><span class="Identifier">`/`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    460. 

  460.   <dd>
    461. 

  461.     
    462. 

  462.     Divides the int <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> by the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt>.
    463. 

  463.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L226" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    464. 

  464. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L226" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    465. 

  465. 

  466.   </dd>
    467. 

  467. </div>
    468. 

  468. 

  469. </div>
    470. 

  470. <div id="//-procs-all">
    471. 

  471.   <div id="//,T,T">
    472. 

  472.   <dt><pre><span class="Keyword">func</span> <a href="#%2F%2F%2CT%2CT"><span class="Identifier">`//`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">num</span><span class="Other">,</span> <span class="Identifier">den</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    473. 

  473.   <dd>
    474. 

  474.     
    475. 

  475.     A friendlier version of <a class="reference external" href="#initRational,T,T">initRational</a>.
    476. 

  476. <p><strong class="examples_text">Example:</strong></p>
    477. 

  477. <pre class="listing"><span class="Keyword">let</span> <span class="Identifier">x</span> <span class="Operator">=</span> <span class="DecNumber">1</span> <span class="Operator">//</span> <span class="DecNumber">3</span> <span class="Operator">+</span> <span class="DecNumber">1</span> <span class="Operator">//</span> <span class="DecNumber">5</span>
    478. 

  478. <span class="Identifier">doAssert</span> <span class="Identifier">x</span> <span class="Operator">==</span> <span class="DecNumber">8</span> <span class="Operator">//</span> <span class="DecNumber">15</span></pre>
    479. 

  479.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L63" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    480. 

  480. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L63" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    481. 

  481. 

  482.   </dd>
    483. 

  483. </div>
    484. 

  484. 

  485. </div>
    486. 

  486. <div id="/=-procs-all">
    487. 

  487.   <div id="/=,Rational[T],Rational[T]">
    488. 

  488.   <dt><pre><span class="Keyword">func</span> <a href="#%2F%3D%2CRational%5BT%5D%2CRational%5BT%5D"><span class="Identifier">`/=`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Keyword">var</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span></pre></dt>
    489. 

  489.   <dd>
    490. 

  490.     
    491. 

  491.     Divides the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> by the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt> in-place.
    492. 

  492.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L231" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    493. 

  493. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L231" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    494. 

  494. 

  495.   </dd>
    496. 

  496. </div>
    497. 

  497. <div id="/=,Rational[T],T">
    498. 

  498.   <dt><pre><span class="Keyword">func</span> <a href="#%2F%3D%2CRational%5BT%5D%2CT"><span class="Identifier">`/=`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Keyword">var</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">)</span></pre></dt>
    499. 

  499.   <dd>
    500. 

  500.     
    501. 

  501.     Divides the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> by the int <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt> in-place.
    502. 

  502.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L237" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    503. 

  503. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L237" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    504. 

  504. 

  505.   </dd>
    506. 

  506. </div>
    507. 

  507. 

  508. </div>
    509. 

  509. <div id="&lt;-procs-all">
    510. 

  510.   <div id="<,Rational,Rational">
    511. 

  511.   <dt><pre><span class="Keyword">func</span> <a href="#%3C%2CRational%2CRational"><span class="Identifier">`&lt;`</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">,</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#bool"><span class="Identifier">bool</span></a></pre></dt>
    512. 

  512.   <dd>
    513. 

  513.     
    514. 

  514.     Returns true if <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> is less than <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt>.
    515. 

  515.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L249" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    516. 

  516. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L249" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    517. 

  517. 

  518.   </dd>
    519. 

  519. </div>
    520. 

  520. 

  521. </div>
    522. 

  522. <div id="&lt;=-procs-all">
    523. 

  523.   <div id="<=,Rational,Rational">
    524. 

  524.   <dt><pre><span class="Keyword">func</span> <a href="#%3C%3D%2CRational%2CRational"><span class="Identifier">`&lt;=`</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">,</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#bool"><span class="Identifier">bool</span></a></pre></dt>
    525. 

  525.   <dd>
    526. 

  526.     
    527. 

  527.     Returns tue if <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> is less than or equal to <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt>.
    528. 

  528.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L253" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    529. 

  529. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L253" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    530. 

  530. 

  531.   </dd>
    532. 

  532. </div>
    533. 

  533. 

  534. </div>
    535. 

  535. <div id="==-procs-all">
    536. 

  536.   <div id="==,Rational,Rational">
    537. 

  537.   <dt><pre><span class="Keyword">func</span> <a href="#%3D%3D%2CRational%2CRational"><span class="Identifier">`==`</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">,</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#bool"><span class="Identifier">bool</span></a></pre></dt>
    538. 

  538.   <dd>
    539. 

  539.     
    540. 

  540.     Compares two rationals for equality.
    541. 

  541.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L257" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    542. 

  542. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L257" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    543. 

  543. 

  544.   </dd>
    545. 

  545. </div>
    546. 

  546. 

  547. </div>
    548. 

  548. <div id="^-procs-all">
    549. 

  549.   <div id="^,Rational[T: SomeInteger],T">
    550. 

  550.   <dt><pre><span class="Keyword">func</span> <a href="#%5E%2CRational%5BT%3A%20SomeInteger%5D%2CT"><span class="Identifier">`^`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#SomeInteger"><span class="Identifier">SomeInteger</span></a><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    551. 

  551.   <dd>
    552. 

  552.     
    553. 

  553.     <p>Computes <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> to the power of <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt>.</p>
    554. 

  554. <p>The exponent <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt> must be an integer. Negative exponents are supported but floating point exponents are not.</p>
    555. 

  555. 

  556. <p><strong class="examples_text">Example:</strong></p>
    557. 

  557. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Punctuation">(</span><span class="Operator">-</span><span class="DecNumber">3</span> <span class="Operator">//</span> <span class="DecNumber">5</span><span class="Punctuation">)</span> <span class="Operator">^</span> <span class="DecNumber">0</span> <span class="Operator">==</span> <span class="Punctuation">(</span><span class="DecNumber">1</span> <span class="Operator">//</span> <span class="DecNumber">1</span><span class="Punctuation">)</span>
    558. 

  558. <span class="Identifier">doAssert</span> <span class="Punctuation">(</span><span class="Operator">-</span><span class="DecNumber">3</span> <span class="Operator">//</span> <span class="DecNumber">5</span><span class="Punctuation">)</span> <span class="Operator">^</span> <span class="DecNumber">1</span> <span class="Operator">==</span> <span class="Punctuation">(</span><span class="Operator">-</span><span class="DecNumber">3</span> <span class="Operator">//</span> <span class="DecNumber">5</span><span class="Punctuation">)</span>
    559. 

  559. <span class="Identifier">doAssert</span> <span class="Punctuation">(</span><span class="Operator">-</span><span class="DecNumber">3</span> <span class="Operator">//</span> <span class="DecNumber">5</span><span class="Punctuation">)</span> <span class="Operator">^</span> <span class="DecNumber">2</span> <span class="Operator">==</span> <span class="Punctuation">(</span><span class="DecNumber">9</span> <span class="Operator">//</span> <span class="DecNumber">25</span><span class="Punctuation">)</span>
    560. 

  560. <span class="Identifier">doAssert</span> <span class="Punctuation">(</span><span class="Operator">-</span><span class="DecNumber">3</span> <span class="Operator">//</span> <span class="DecNumber">5</span><span class="Punctuation">)</span> <span class="Operator">^</span> <span class="Operator">-</span><span class="DecNumber">2</span> <span class="Operator">==</span> <span class="Punctuation">(</span><span class="DecNumber">25</span> <span class="Operator">//</span> <span class="DecNumber">9</span><span class="Punctuation">)</span></pre>
    561. 

  561.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L307" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    562. 

  562. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L307" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    563. 

  563. 

  564.   </dd>
    565. 

  565. </div>
    566. 

  566. 

  567. </div>
    568. 

  568. <div id="abs-procs-all">
    569. 

  569.   <div id="abs,Rational[T]">
    570. 

  570.   <dt><pre><span class="Keyword">func</span> <a href="#abs%2CRational%5BT%5D"><span class="Identifier">abs</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    571. 

  571.   <dd>
    572. 

  572.     
    573. 

  573.     Returns the absolute value of <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>.
    574. 

  574. <p><strong class="examples_text">Example:</strong></p>
    575. 

  575. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">abs</span><span class="Punctuation">(</span><span class="DecNumber">1</span> <span class="Operator">//</span> <span class="DecNumber">2</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="DecNumber">1</span> <span class="Operator">//</span> <span class="DecNumber">2</span>
    576. 

  576. <span class="Identifier">doAssert</span> <span class="Identifier">abs</span><span class="Punctuation">(</span><span class="Operator">-</span><span class="DecNumber">1</span> <span class="Operator">//</span> <span class="DecNumber">2</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="DecNumber">1</span> <span class="Operator">//</span> <span class="DecNumber">2</span></pre>
    577. 

  577.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L261" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    578. 

  578. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L261" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    579. 

  579. 

  580.   </dd>
    581. 

  581. </div>
    582. 

  582. 

  583. </div>
    584. 

  584. <div id="cmp-procs-all">
    585. 

  585.   <div id="cmp,Rational,Rational">
    586. 

  586.   <dt><pre><span class="Keyword">func</span> <a href="#cmp%2CRational%2CRational"><span class="Identifier">cmp</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">,</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#int"><span class="Identifier">int</span></a></pre></dt>
    587. 

  587.   <dd>
    588. 

  588.     
    589. 

  589.     Compares two rationals. Returns<ul class="simple"><li>a value less than zero, if <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span> <span class="Operator">&lt;</span> <span class="Identifier">y</span></span></tt></li>
    590. 

  590. <li>a value greater than zero, if <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span> <span class="Operator">&gt;</span> <span class="Identifier">y</span></span></tt></li>
    591. 

  591. <li>zero, if <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span> <span class="Operator">==</span> <span class="Identifier">y</span></span></tt></li>
    592. 

  592. </ul>
    593. 

  593. 

  594.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L242" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    595. 

  595. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L242" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    596. 

  596. 

  597.   </dd>
    598. 

  598. </div>
    599. 

  599. 

  600. </div>
    601. 

  601. <div id="div-procs-all">
    602. 

  602.   <div id="div,Rational[T: SomeInteger],Rational[T: SomeInteger]">
    603. 

  603.   <dt><pre><span class="Keyword">func</span> <a href="#div%2CRational%5BT%3A%20SomeInteger%5D%2CRational%5BT%3A%20SomeInteger%5D"><span class="Identifier">`div`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#SomeInteger"><span class="Identifier">SomeInteger</span></a><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">,</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <span class="Identifier">T</span></pre></dt>
    604. 

  604.   <dd>
    605. 

  605.     
    606. 

  606.     Computes the rational truncated division.
    607. 

  607.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L268" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    608. 

  608. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L268" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    609. 

  609. 

  610.   </dd>
    611. 

  611. </div>
    612. 

  612. 

  613. </div>
    614. 

  614. <div id="floorDiv-procs-all">
    615. 

  615.   <div id="floorDiv,Rational[T: SomeInteger],Rational[T: SomeInteger]">
    616. 

  616.   <dt><pre><span class="Keyword">func</span> <a href="#floorDiv%2CRational%5BT%3A%20SomeInteger%5D%2CRational%5BT%3A%20SomeInteger%5D"><span class="Identifier">floorDiv</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#SomeInteger"><span class="Identifier">SomeInteger</span></a><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">,</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <span class="Identifier">T</span></pre></dt>
    617. 

  617.   <dd>
    618. 

  618.     
    619. 

  619.     <p>Computes the rational floor division.</p>
    620. 

  620. <p>Floor division is conceptually defined as <tt class="docutils literal"><span class="pre"><span class="Identifier">floor</span><span class="Punctuation">(</span><span class="Identifier">x</span> <span class="Operator">/</span> <span class="Identifier">y</span><span class="Punctuation">)</span></span></tt>. This is different from the <tt class="docutils literal"><span class="pre"><span class="Keyword">div</span></span></tt> operator, which is defined as <tt class="docutils literal"><span class="pre"><span class="Identifier">trunc</span><span class="Punctuation">(</span><span class="Identifier">x</span> <span class="Operator">/</span> <span class="Identifier">y</span><span class="Punctuation">)</span></span></tt>. That is, <tt class="docutils literal"><span class="pre"><span class="Keyword">div</span></span></tt> rounds towards 0 and <tt class="docutils literal"><span class="pre"><span class="Identifier">floorDiv</span></span></tt> rounds down.</p>
    621. 

  621. 

  622.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L278" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    623. 

  623. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L278" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    624. 

  624. 

  625.   </dd>
    626. 

  626. </div>
    627. 

  627. 

  628. </div>
    629. 

  629. <div id="floorMod-procs-all">
    630. 

  630.   <div id="floorMod,Rational[T: SomeInteger],Rational[T: SomeInteger]">
    631. 

  631.   <dt><pre><span class="Keyword">func</span> <a href="#floorMod%2CRational%5BT%3A%20SomeInteger%5D%2CRational%5BT%3A%20SomeInteger%5D"><span class="Identifier">floorMod</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#SomeInteger"><span class="Identifier">SomeInteger</span></a><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">,</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    632. 

  632.   <dd>
    633. 

  633.     
    634. 

  634.     <p>Computes the rational modulo by floor division (modulo).</p>
    635. 

  635. <p>This is same as <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span> <span class="Operator">-</span> <span class="Identifier">floorDiv</span><span class="Punctuation">(</span><span class="Identifier">x</span><span class="Punctuation">,</span> <span class="Identifier">y</span><span class="Punctuation">)</span> <span class="Operator">*</span> <span class="Identifier">y</span></span></tt>. This func behaves the same as the <tt class="docutils literal"><span class="pre"><span class="Operator">%</span></span></tt> operator in Python.</p>
    636. 

  636. 

  637.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L287" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    638. 

  638. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L287" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    639. 

  639. 

  640.   </dd>
    641. 

  641. </div>
    642. 

  642. 

  643. </div>
    644. 

  644. <div id="hash-procs-all">
    645. 

  645.   <div id="hash,Rational[T]">
    646. 

  646.   <dt><pre><span class="Keyword">func</span> <a href="#hash%2CRational%5BT%5D"><span class="Identifier">hash</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="hashes.html#Hash"><span class="Identifier">Hash</span></a></pre></dt>
    647. 

  647.   <dd>
    648. 

  648.     
    649. 

  649.     Computes the hash for the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>.
    650. 

  650.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L295" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    651. 

  651. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L295" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    652. 

  652. 

  653.   </dd>
    654. 

  654. </div>
    655. 

  655. 

  656. </div>
    657. 

  657. <div id="initRational-procs-all">
    658. 

  658.   <div id="initRational,T,T">
    659. 

  659.   <dt><pre><span class="Keyword">func</span> <a href="#initRational%2CT%2CT"><span class="Identifier">initRational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#SomeInteger"><span class="Identifier">SomeInteger</span></a><span class="Other">]</span><span class="Other">(</span><span class="Identifier">num</span><span class="Other">,</span> <span class="Identifier">den</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    660. 

  660.   <dd>
    661. 

  661.     
    662. 

  662.     <p>Creates a new rational number with numerator <tt class="docutils literal"><span class="pre"><span class="Identifier">num</span></span></tt> and denominator <tt class="docutils literal"><span class="pre"><span class="Identifier">den</span></span></tt>. <tt class="docutils literal"><span class="pre"><span class="Identifier">den</span></span></tt> must not be 0.</p>
    663. 

  663. <p><strong>Note:</strong> <tt class="docutils literal"><span class="pre"><span class="Identifier">den</span> <span class="Operator">!=</span> <span class="DecNumber">0</span></span></tt> is not checked when assertions are turned off.</p>
    664. 

  664. 

  665.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L54" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    666. 

  666. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L54" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    667. 

  667. 

  668.   </dd>
    669. 

  669. </div>
    670. 

  670. 

  671. </div>
    672. 

  672. <div id="mod-procs-all">
    673. 

  673.   <div id="mod,Rational[T: SomeInteger],Rational[T: SomeInteger]">
    674. 

  674.   <dt><pre><span class="Keyword">func</span> <a href="#mod%2CRational%5BT%3A%20SomeInteger%5D%2CRational%5BT%3A%20SomeInteger%5D"><span class="Identifier">`mod`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#SomeInteger"><span class="Identifier">SomeInteger</span></a><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">,</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    675. 

  675.   <dd>
    676. 

  676.     
    677. 

  677.     Computes the rational modulo by truncated division (remainder). This is same as <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span> <span class="Operator">-</span> <span class="Punctuation">(</span><span class="Identifier">x</span> <span class="Keyword">div</span> <span class="Identifier">y</span><span class="Punctuation">)</span> <span class="Operator">*</span> <span class="Identifier">y</span></span></tt>.
    678. 

  678.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L272" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    679. 

  679. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L272" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    680. 

  680. 

  681.   </dd>
    682. 

  682. </div>
    683. 

  683. 

  684. </div>
    685. 

  685. <div id="reciprocal-procs-all">
    686. 

  686.   <div id="reciprocal,Rational[T]">
    687. 

  687.   <dt><pre><span class="Keyword">func</span> <a href="#reciprocal%2CRational%5BT%5D"><span class="Identifier">reciprocal</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    688. 

  688.   <dd>
    689. 

  689.     
    690. 

  690.     Calculates the reciprocal of <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> (<tt class="docutils literal"><span class="pre"><span class="DecNumber">1</span><span class="Operator">/</span><span class="Identifier">x</span></span></tt>). If <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> is 0, raises <tt class="docutils literal"><span class="pre"><span class="Identifier">DivByZeroDefect</span></span></tt>.
    691. 

  691.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L206" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    692. 

  692. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L206" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    693. 

  693. 

  694.   </dd>
    695. 

  695. </div>
    696. 

  696. 

  697. </div>
    698. 

  698. <div id="reduce-procs-all">
    699. 

  699.   <div id="reduce,Rational[T: SomeInteger]">
    700. 

  700.   <dt><pre><span class="Keyword">func</span> <a href="#reduce%2CRational%5BT%3A%20SomeInteger%5D"><span class="Identifier">reduce</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#SomeInteger"><span class="Identifier">SomeInteger</span></a><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Keyword">var</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span></pre></dt>
    701. 

  701.   <dd>
    702. 

  702.     
    703. 

  703.     <p>Reduces the rational number <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>, so that the numerator and denominator have no common divisors other than 1 (and -1). If <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> is 0, raises <tt class="docutils literal"><span class="pre"><span class="Identifier">DivByZeroDefect</span></span></tt>.</p>
    704. 

  704. <p><strong>Note:</strong> This is called automatically by the various operations on rationals.</p>
    705. 

  705. 

  706. <p><strong class="examples_text">Example:</strong></p>
    707. 

  707. <pre class="listing"><span class="Keyword">var</span> <span class="Identifier">r</span> <span class="Operator">=</span> <span class="Identifier">Rational</span><span class="Punctuation">[</span><span class="Identifier">int</span><span class="Punctuation">]</span><span class="Punctuation">(</span><span class="Identifier">num</span><span class="Punctuation">:</span> <span class="DecNumber">2</span><span class="Punctuation">,</span> <span class="Identifier">den</span><span class="Punctuation">:</span> <span class="DecNumber">4</span><span class="Punctuation">)</span> <span class="Comment"># 1/2</span>
    708. 

  708. <span class="Identifier">reduce</span><span class="Punctuation">(</span><span class="Identifier">r</span><span class="Punctuation">)</span>
    709. 

  709. <span class="Identifier">doAssert</span> <span class="Identifier">r</span><span class="Operator">.</span><span class="Identifier">num</span> <span class="Operator">==</span> <span class="DecNumber">1</span>
    710. 

  710. <span class="Identifier">doAssert</span> <span class="Identifier">r</span><span class="Operator">.</span><span class="Identifier">den</span> <span class="Operator">==</span> <span class="DecNumber">2</span></pre>
    711. 

  711.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L32" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    712. 

  712. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L32" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    713. 

  713. 

  714.   </dd>
    715. 

  715. </div>
    716. 

  716. 

  717. </div>
    718. 

  718. <div id="toFloat-procs-all">
    719. 

  719.   <div id="toFloat,Rational[T]">
    720. 

  720.   <dt><pre><span class="Keyword">func</span> <a href="#toFloat%2CRational%5BT%5D"><span class="Identifier">toFloat</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float"><span class="Identifier">float</span></a></pre></dt>
    721. 

  721.   <dd>
    722. 

  722.     
    723. 

  723.     Converts a rational number <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> to a <tt class="docutils literal"><span class="pre"><span class="Identifier">float</span></span></tt>.
    724. 

  724.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L113" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    725. 

  725. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L113" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    726. 

  726. 

  727.   </dd>
    728. 

  728. </div>
    729. 

  729. 

  730. </div>
    731. 

  731. <div id="toInt-procs-all">
    732. 

  732.   <div id="toInt,Rational[T]">
    733. 

  733.   <dt><pre><span class="Keyword">func</span> <a href="#toInt%2CRational%5BT%5D"><span class="Identifier">toInt</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="system.html#int"><span class="Identifier">int</span></a></pre></dt>
    734. 

  734.   <dd>
    735. 

  735.     
    736. 

  736.     Converts a rational number <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> to an <tt class="docutils literal"><span class="pre"><span class="Identifier">int</span></span></tt>. Conversion rounds towards 0 if <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> does not contain an integer value.
    737. 

  737.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L117" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    738. 

  738. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L117" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    739. 

  739. 

  740.   </dd>
    741. 

  741. </div>
    742. 

  742. 

  743. </div>
    744. 

  744. <div id="toRational-procs-all">
    745. 

  745.   <div id="toRational,float,int">
    746. 

  746.   <dt><pre><span class="Keyword">func</span> <a href="#toRational%2Cfloat%2Cint"><span class="Identifier">toRational</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float"><span class="Identifier">float</span></a><span class="Other">;</span> <span class="Identifier">n</span><span class="Other">:</span> <a href="system.html#int"><span class="Identifier">int</span></a> <span class="Other">=</span> <span class="Identifier">high</span><span class="Other">(</span><a href="system.html#int"><span class="Identifier">int</span></a><span class="Other">)</span> <span class="Keyword">shr</span> <span class="DecNumber">32</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><a href="system.html#int"><span class="Identifier">int</span></a><span class="Other">]</span> {.
    747. 

  747.     <span><span class="Other pragmadots">...</span></span><span class="pragmawrap"><span class="Identifier">raises</span><span class="Other">:</span> <span class="Other">[</span><span class="Other">]</span><span class="Other">,</span> <span class="Identifier">tags</span><span class="Other">:</span> <span class="Other">[</span><span class="Other">]</span><span class="Other">,</span> <span class="Identifier">forbids</span><span class="Other">:</span> <span class="Other">[</span><span class="Other">]</span></span>.}</pre></dt>
    748. 

  748.   <dd>
    749. 

  749.     
    750. 

  750.     <p>Calculates the best rational approximation of <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>, where the denominator is smaller than <tt class="docutils literal"><span class="pre"><span class="Identifier">n</span></span></tt> (default is the largest possible <tt class="docutils literal"><span class="pre"><span class="Identifier">int</span></span></tt> for maximal resolution).</p>
    751. 

  751. <p>The algorithm is based on the theory of continued fractions.</p>
    752. 

  752. 

  753. <p><strong class="examples_text">Example:</strong></p>
    754. 

  754. <pre class="listing"><span class="Keyword">let</span> <span class="Identifier">x</span> <span class="Operator">=</span> <span class="FloatNumber">1.2</span>
    755. 

  755. <span class="Identifier">doAssert</span> <span class="Identifier">x</span><span class="Operator">.</span><span class="Identifier">toRational</span><span class="Operator">.</span><span class="Identifier">toFloat</span> <span class="Operator">==</span> <span class="Identifier">x</span></pre>
    756. 

  756.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L84" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    757. 

  757. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L84" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    758. 

  758. 

  759.   </dd>
    760. 

  760. </div>
    761. 

  761. <div id="toRational,T">
    762. 

  762.   <dt><pre><span class="Keyword">func</span> <a href="#toRational%2CT"><span class="Identifier">toRational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#SomeInteger"><span class="Identifier">SomeInteger</span></a><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    763. 

  763.   <dd>
    764. 

  764.     
    765. 

  765.     Converts some integer <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> to a rational number.
    766. 

  766. <p><strong class="examples_text">Example:</strong></p>
    767. 

  767. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">toRational</span><span class="Punctuation">(</span><span class="DecNumber">42</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="DecNumber">42</span> <span class="Operator">//</span> <span class="DecNumber">1</span></pre>
    768. 

  768.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L78" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    769. 

  769. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L78" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    770. 

  770. 

  771.   </dd>
    772. 

  772. </div>
    773. 

  773. 

  774. </div>
    775. 

  775. 

  776.   </dl>
    777. 

  777. </div>
    778. 

  778. 

  779.   </div>
    780. 

  780. </div>
    781. 

  781. 

  782.       <div class="twelve-columns footer">
    783. 

  783.         <span class="nim-sprite"></span>
    784. 

  784.         <br>
    785. 

  785.         <small style="color: var(--hint);">Made with Nim. Generated: 2025-01-09 12:00:03 UTC</small>
    786. 

  786.       </div>
    787. 

  787.     </div>
    788. 

  788.   </div>
    789. 

  789.       <script defer data-domain="nim-lang.org" src="https://plausible.io/js/plausible.js"></script>
    790. 

  790.     
    791. 

  791. </body>
    792. 

  792. </html>
    793. 

  793.