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  27.       <h1 class="title">std/math</h1>
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  40.         <li><a href="manual.html">Manual</a></li>
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  41.         <li><a href="lib.html">Standard library</a></li>
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  42.         <li> <a id="indexLink" href="theindex.html">Index</a></li>
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  54.   <li><a class="reference" id="see-also_toc" href="#see-also">See also</a></li>
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  55. <li>
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  56.   <a class="reference reference-toplevel" href="#6" id="56">Imports</a>
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  57. </li>
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  58. <li>
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  59.   <details open>
    60. 

  60.     <summary><a class="reference reference-toplevel" href="#7" id="57">Types</a></summary>
    61. 

  61.     <ul class="simple simple-toc-section">
    62. 

  62.       <li><a class="reference" href="#FloatClass" title="FloatClass = enum
    63. 

  63.   fcNormal,                 ## value is an ordinary nonzero floating point value
    64. 

  64.   fcSubnormal,              ## value is a subnormal (a very small) floating point value
    65. 

  65.   fcZero,                   ## value is zero
    66. 

  66.   fcNegZero,                ## value is the negative zero
    67. 

  67.   fcNan,                    ## value is Not a Number (NaN)
    68. 

  68.   fcInf,                    ## value is positive infinity
    69. 

  69.   fcNegInf                   ## value is negative infinity">FloatClass</a></li>
    70. 

  70. 

  71.     </ul>
    72. 

  72.   </details>
    73. 

  73. </li>
    74. 

  74. <li>
    75. 

  75.   <details open>
    76. 

  76.     <summary><a class="reference reference-toplevel" href="#10" id="60">Consts</a></summary>
    77. 

  77.     <ul class="simple simple-toc-section">
    78. 

  78.       <li><a class="reference" href="#E" title="E = 2.718281828459045">E</a></li>
    79. 

  79. <li><a class="reference" href="#MaxFloat32Precision" title="MaxFloat32Precision = 8">MaxFloat32Precision</a></li>
    80. 

  80. <li><a class="reference" href="#MaxFloat64Precision" title="MaxFloat64Precision = 16">MaxFloat64Precision</a></li>
    81. 

  81. <li><a class="reference" href="#MaxFloatPrecision" title="MaxFloatPrecision = 16">MaxFloatPrecision</a></li>
    82. 

  82. <li><a class="reference" href="#MinFloatNormal" title="MinFloatNormal = 2.225073858507201e-308">MinFloatNormal</a></li>
    83. 

  83. <li><a class="reference" href="#PI" title="PI = 3.141592653589793">PI</a></li>
    84. 

  84. <li><a class="reference" href="#TAU" title="TAU = 6.283185307179586">TAU</a></li>
    85. 

  85. 

  86.     </ul>
    87. 

  87.   </details>
    88. 

  88. </li>
    89. 

  89. <li>
    90. 

  90.   <details open>
    91. 

  91.     <summary><a class="reference reference-toplevel" href="#12" id="62">Procs</a></summary>
    92. 

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

  93.       <ul class="simple nested-toc-section">^
    94. 

  94.   <li><a class="reference" href="#%5E%2CT%2CU" title="`^`[T: SomeNumber; U: SomeFloat](x: T; y: U): float">`^`[T: SomeNumber; U: SomeFloat](x: T; y: U): float</a></li>
    95. 

  95. <li><a class="reference" href="#%5E%2CT%2CNatural" title="`^`[T: SomeNumber](x: T; y: Natural): T">`^`[T: SomeNumber](x: T; y: Natural): T</a></li>
    96. 

  96. 

  97. </ul>
    98. 

  98. <ul class="simple nested-toc-section">almostEqual
    99. 

  99.   <li><a class="reference" href="#almostEqual%2CT%2CT%2CNatural" title="almostEqual[T: SomeFloat](x, y: T; unitsInLastPlace: Natural = 4): bool">almostEqual[T: SomeFloat](x, y: T; unitsInLastPlace: Natural = 4): bool</a></li>
    100. 

  100. 

  101. </ul>
    102. 

  102. <ul class="simple nested-toc-section">arccos
    103. 

  103.   <li><a class="reference" href="#arccos%2Cfloat32" title="arccos(x: float32): float32">arccos(x: float32): float32</a></li>
    104. 

  104. <li><a class="reference" href="#arccos%2Cfloat64" title="arccos(x: float64): float64">arccos(x: float64): float64</a></li>
    105. 

  105. 

  106. </ul>
    107. 

  107. <ul class="simple nested-toc-section">arccosh
    108. 

  108.   <li><a class="reference" href="#arccosh%2Cfloat32" title="arccosh(x: float32): float32">arccosh(x: float32): float32</a></li>
    109. 

  109. <li><a class="reference" href="#arccosh%2Cfloat64" title="arccosh(x: float64): float64">arccosh(x: float64): float64</a></li>
    110. 

  110. 

  111. </ul>
    112. 

  112. <ul class="simple nested-toc-section">arccot
    113. 

  113.   <li><a class="reference" href="#arccot%2CT" title="arccot[T: float32 | float64](x: T): T">arccot[T: float32 | float64](x: T): T</a></li>
    114. 

  114. 

  115. </ul>
    116. 

  116. <ul class="simple nested-toc-section">arccoth
    117. 

  117.   <li><a class="reference" href="#arccoth%2CT" title="arccoth[T: float32 | float64](x: T): T">arccoth[T: float32 | float64](x: T): T</a></li>
    118. 

  118. 

  119. </ul>
    120. 

  120. <ul class="simple nested-toc-section">arccsc
    121. 

  121.   <li><a class="reference" href="#arccsc%2CT" title="arccsc[T: float32 | float64](x: T): T">arccsc[T: float32 | float64](x: T): T</a></li>
    122. 

  122. 

  123. </ul>
    124. 

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

  125.   <li><a class="reference" href="#arccsch%2CT" title="arccsch[T: float32 | float64](x: T): T">arccsch[T: float32 | float64](x: T): T</a></li>
    126. 

  126. 

  127. </ul>
    128. 

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

  129.   <li><a class="reference" href="#arcsec%2CT" title="arcsec[T: float32 | float64](x: T): T">arcsec[T: float32 | float64](x: T): T</a></li>
    130. 

  130. 

  131. </ul>
    132. 

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

  133.   <li><a class="reference" href="#arcsech%2CT" title="arcsech[T: float32 | float64](x: T): T">arcsech[T: float32 | float64](x: T): T</a></li>
    134. 

  134. 

  135. </ul>
    136. 

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

  137.   <li><a class="reference" href="#arcsin%2Cfloat32" title="arcsin(x: float32): float32">arcsin(x: float32): float32</a></li>
    138. 

  138. <li><a class="reference" href="#arcsin%2Cfloat64" title="arcsin(x: float64): float64">arcsin(x: float64): float64</a></li>
    139. 

  139. 

  140. </ul>
    141. 

  141. <ul class="simple nested-toc-section">arcsinh
    142. 

  142.   <li><a class="reference" href="#arcsinh%2Cfloat32" title="arcsinh(x: float32): float32">arcsinh(x: float32): float32</a></li>
    143. 

  143. <li><a class="reference" href="#arcsinh%2Cfloat64" title="arcsinh(x: float64): float64">arcsinh(x: float64): float64</a></li>
    144. 

  144. 

  145. </ul>
    146. 

  146. <ul class="simple nested-toc-section">arctan
    147. 

  147.   <li><a class="reference" href="#arctan%2Cfloat32" title="arctan(x: float32): float32">arctan(x: float32): float32</a></li>
    148. 

  148. <li><a class="reference" href="#arctan%2Cfloat64" title="arctan(x: float64): float64">arctan(x: float64): float64</a></li>
    149. 

  149. 

  150. </ul>
    151. 

  151. <ul class="simple nested-toc-section">arctan2
    152. 

  152.   <li><a class="reference" href="#arctan2%2Cfloat32%2Cfloat32" title="arctan2(y, x: float32): float32">arctan2(y, x: float32): float32</a></li>
    153. 

  153. <li><a class="reference" href="#arctan2%2Cfloat64%2Cfloat64" title="arctan2(y, x: float64): float64">arctan2(y, x: float64): float64</a></li>
    154. 

  154. 

  155. </ul>
    156. 

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

  157.   <li><a class="reference" href="#arctanh%2Cfloat32" title="arctanh(x: float32): float32">arctanh(x: float32): float32</a></li>
    158. 

  158. <li><a class="reference" href="#arctanh%2Cfloat64" title="arctanh(x: float64): float64">arctanh(x: float64): float64</a></li>
    159. 

  159. 

  160. </ul>
    161. 

  161. <ul class="simple nested-toc-section">binom
    162. 

  162.   <li><a class="reference" href="#binom%2Cint%2Cint" title="binom(n, k: int): int">binom(n, k: int): int</a></li>
    163. 

  163. 

  164. </ul>
    165. 

  165. <ul class="simple nested-toc-section">cbrt
    166. 

  166.   <li><a class="reference" href="#cbrt%2Cfloat32" title="cbrt(x: float32): float32">cbrt(x: float32): float32</a></li>
    167. 

  167. <li><a class="reference" href="#cbrt%2Cfloat64" title="cbrt(x: float64): float64">cbrt(x: float64): float64</a></li>
    168. 

  168. 

  169. </ul>
    170. 

  170. <ul class="simple nested-toc-section">ceil
    171. 

  171.   <li><a class="reference" href="#ceil%2Cfloat32" title="ceil(x: float32): float32">ceil(x: float32): float32</a></li>
    172. 

  172. <li><a class="reference" href="#ceil%2Cfloat64" title="ceil(x: float64): float64">ceil(x: float64): float64</a></li>
    173. 

  173. 

  174. </ul>
    175. 

  175. <ul class="simple nested-toc-section">ceilDiv
    176. 

  176.   <li><a class="reference" href="#ceilDiv%2CT%2CT" title="ceilDiv[T: SomeInteger](x, y: T): T">ceilDiv[T: SomeInteger](x, y: T): T</a></li>
    177. 

  177. 

  178. </ul>
    179. 

  179. <ul class="simple nested-toc-section">clamp
    180. 

  180.   <li><a class="reference" href="#clamp%2CT%2CSlice%5BT%5D" title="clamp[T](val: T; bounds: Slice[T]): T">clamp[T](val: T; bounds: Slice[T]): T</a></li>
    181. 

  181. 

  182. </ul>
    183. 

  183. <ul class="simple nested-toc-section">classify
    184. 

  184.   <li><a class="reference" href="#classify%2Cfloat" title="classify(x: float): FloatClass">classify(x: float): FloatClass</a></li>
    185. 

  185. 

  186. </ul>
    187. 

  187. <ul class="simple nested-toc-section">copySign
    188. 

  188.   <li><a class="reference" href="#copySign%2CT%2CT" title="copySign[T: SomeFloat](x, y: T): T">copySign[T: SomeFloat](x, y: T): T</a></li>
    189. 

  189. 

  190. </ul>
    191. 

  191. <ul class="simple nested-toc-section">cos
    192. 

  192.   <li><a class="reference" href="#cos%2Cfloat32" title="cos(x: float32): float32">cos(x: float32): float32</a></li>
    193. 

  193. <li><a class="reference" href="#cos%2Cfloat64" title="cos(x: float64): float64">cos(x: float64): float64</a></li>
    194. 

  194. 

  195. </ul>
    196. 

  196. <ul class="simple nested-toc-section">cosh
    197. 

  197.   <li><a class="reference" href="#cosh%2Cfloat32" title="cosh(x: float32): float32">cosh(x: float32): float32</a></li>
    198. 

  198. <li><a class="reference" href="#cosh%2Cfloat64" title="cosh(x: float64): float64">cosh(x: float64): float64</a></li>
    199. 

  199. 

  200. </ul>
    201. 

  201. <ul class="simple nested-toc-section">cot
    202. 

  202.   <li><a class="reference" href="#cot%2CT" title="cot[T: float32 | float64](x: T): T">cot[T: float32 | float64](x: T): T</a></li>
    203. 

  203. 

  204. </ul>
    205. 

  205. <ul class="simple nested-toc-section">coth
    206. 

  206.   <li><a class="reference" href="#coth%2CT" title="coth[T: float32 | float64](x: T): T">coth[T: float32 | float64](x: T): T</a></li>
    207. 

  207. 

  208. </ul>
    209. 

  209. <ul class="simple nested-toc-section">csc
    210. 

  210.   <li><a class="reference" href="#csc%2CT" title="csc[T: float32 | float64](x: T): T">csc[T: float32 | float64](x: T): T</a></li>
    211. 

  211. 

  212. </ul>
    213. 

  213. <ul class="simple nested-toc-section">csch
    214. 

  214.   <li><a class="reference" href="#csch%2CT" title="csch[T: float32 | float64](x: T): T">csch[T: float32 | float64](x: T): T</a></li>
    215. 

  215. 

  216. </ul>
    217. 

  217. <ul class="simple nested-toc-section">cumprod
    218. 

  218.   <li><a class="reference" href="#cumprod%2CopenArray%5BT%5D" title="cumprod[T](x: var openArray[T])">cumprod[T](x: var openArray[T])</a></li>
    219. 

  219. 

  220. </ul>
    221. 

  221. <ul class="simple nested-toc-section">cumproded
    222. 

  222.   <li><a class="reference" href="#cumproded%2CopenArray%5BT%5D" title="cumproded[T](x: openArray[T]): seq[T]">cumproded[T](x: openArray[T]): seq[T]</a></li>
    223. 

  223. 

  224. </ul>
    225. 

  225. <ul class="simple nested-toc-section">cumsum
    226. 

  226.   <li><a class="reference" href="#cumsum%2CopenArray%5BT%5D" title="cumsum[T](x: var openArray[T])">cumsum[T](x: var openArray[T])</a></li>
    227. 

  227. 

  228. </ul>
    229. 

  229. <ul class="simple nested-toc-section">cumsummed
    230. 

  230.   <li><a class="reference" href="#cumsummed%2CopenArray%5BT%5D" title="cumsummed[T](x: openArray[T]): seq[T]">cumsummed[T](x: openArray[T]): seq[T]</a></li>
    231. 

  231. 

  232. </ul>
    233. 

  233. <ul class="simple nested-toc-section">degToRad
    234. 

  234.   <li><a class="reference" href="#degToRad%2CT" title="degToRad[T: float32 | float64](d: T): T">degToRad[T: float32 | float64](d: T): T</a></li>
    235. 

  235. 

  236. </ul>
    237. 

  237. <ul class="simple nested-toc-section">divmod
    238. 

  238.   <li><a class="reference" href="#divmod%2CT%2CT" title="divmod[T: SomeInteger](x, y: T): (T, T)">divmod[T: SomeInteger](x, y: T): (T, T)</a></li>
    239. 

  239. 

  240. </ul>
    241. 

  241. <ul class="simple nested-toc-section">erf
    242. 

  242.   <li><a class="reference" href="#erf%2Cfloat32" title="erf(x: float32): float32">erf(x: float32): float32</a></li>
    243. 

  243. <li><a class="reference" href="#erf%2Cfloat64" title="erf(x: float64): float64">erf(x: float64): float64</a></li>
    244. 

  244. 

  245. </ul>
    246. 

  246. <ul class="simple nested-toc-section">erfc
    247. 

  247.   <li><a class="reference" href="#erfc%2Cfloat32" title="erfc(x: float32): float32">erfc(x: float32): float32</a></li>
    248. 

  248. <li><a class="reference" href="#erfc%2Cfloat64" title="erfc(x: float64): float64">erfc(x: float64): float64</a></li>
    249. 

  249. 

  250. </ul>
    251. 

  251. <ul class="simple nested-toc-section">euclDiv
    252. 

  252.   <li><a class="reference" href="#euclDiv%2CT%2CT" title="euclDiv[T: SomeInteger](x, y: T): T">euclDiv[T: SomeInteger](x, y: T): T</a></li>
    253. 

  253. 

  254. </ul>
    255. 

  255. <ul class="simple nested-toc-section">euclMod
    256. 

  256.   <li><a class="reference" href="#euclMod%2CT%2CT" title="euclMod[T: SomeNumber](x, y: T): T">euclMod[T: SomeNumber](x, y: T): T</a></li>
    257. 

  257. 

  258. </ul>
    259. 

  259. <ul class="simple nested-toc-section">exp
    260. 

  260.   <li><a class="reference" href="#exp%2Cfloat32" title="exp(x: float32): float32">exp(x: float32): float32</a></li>
    261. 

  261. <li><a class="reference" href="#exp%2Cfloat64" title="exp(x: float64): float64">exp(x: float64): float64</a></li>
    262. 

  262. 

  263. </ul>
    264. 

  264. <ul class="simple nested-toc-section">fac
    265. 

  265.   <li><a class="reference" href="#fac%2Cint" title="fac(n: int): int">fac(n: int): int</a></li>
    266. 

  266. 

  267. </ul>
    268. 

  268. <ul class="simple nested-toc-section">floor
    269. 

  269.   <li><a class="reference" href="#floor%2Cfloat32" title="floor(x: float32): float32">floor(x: float32): float32</a></li>
    270. 

  270. <li><a class="reference" href="#floor%2Cfloat64" title="floor(x: float64): float64">floor(x: float64): float64</a></li>
    271. 

  271. 

  272. </ul>
    273. 

  273. <ul class="simple nested-toc-section">floorDiv
    274. 

  274.   <li><a class="reference" href="#floorDiv%2CT%2CT" title="floorDiv[T: SomeInteger](x, y: T): T">floorDiv[T: SomeInteger](x, y: T): T</a></li>
    275. 

  275. 

  276. </ul>
    277. 

  277. <ul class="simple nested-toc-section">floorMod
    278. 

  278.   <li><a class="reference" href="#floorMod%2CT%2CT" title="floorMod[T: SomeNumber](x, y: T): T">floorMod[T: SomeNumber](x, y: T): T</a></li>
    279. 

  279. 

  280. </ul>
    281. 

  281. <ul class="simple nested-toc-section">frexp
    282. 

  282.   <li><a class="reference" href="#frexp%2CT" title="frexp[T: float32 | float64](x: T): tuple[frac: T, exp: int]">frexp[T: float32 | float64](x: T): tuple[frac: T, exp: int]</a></li>
    283. 

  283. <li><a class="reference" href="#frexp%2CT%2Cint" title="frexp[T: float32 | float64](x: T; exponent: var int): T">frexp[T: float32 | float64](x: T; exponent: var int): T</a></li>
    284. 

  284. 

  285. </ul>
    286. 

  286. <ul class="simple nested-toc-section">gamma
    287. 

  287.   <li><a class="reference" href="#gamma%2Cfloat32" title="gamma(x: float32): float32">gamma(x: float32): float32</a></li>
    288. 

  288. <li><a class="reference" href="#gamma%2Cfloat64" title="gamma(x: float64): float64">gamma(x: float64): float64</a></li>
    289. 

  289. 

  290. </ul>
    291. 

  291. <ul class="simple nested-toc-section">gcd
    292. 

  292.   <li><a class="reference" href="#gcd%2CSomeInteger%2CSomeInteger" title="gcd(x, y: SomeInteger): SomeInteger">gcd(x, y: SomeInteger): SomeInteger</a></li>
    293. 

  293. <li><a class="reference" href="#gcd%2CT%2CT" title="gcd[T](x, y: T): T">gcd[T](x, y: T): T</a></li>
    294. 

  294. <li><a class="reference" href="#gcd%2CopenArray%5BT%5D" title="gcd[T](x: openArray[T]): T">gcd[T](x: openArray[T]): T</a></li>
    295. 

  295. 

  296. </ul>
    297. 

  297. <ul class="simple nested-toc-section">hypot
    298. 

  298.   <li><a class="reference" href="#hypot%2Cfloat32%2Cfloat32" title="hypot(x, y: float32): float32">hypot(x, y: float32): float32</a></li>
    299. 

  299. <li><a class="reference" href="#hypot%2Cfloat64%2Cfloat64" title="hypot(x, y: float64): float64">hypot(x, y: float64): float64</a></li>
    300. 

  300. 

  301. </ul>
    302. 

  302. <ul class="simple nested-toc-section">isNaN
    303. 

  303.   <li><a class="reference" href="#isNaN%2CSomeFloat" title="isNaN(x: SomeFloat): bool">isNaN(x: SomeFloat): bool</a></li>
    304. 

  304. 

  305. </ul>
    306. 

  306. <ul class="simple nested-toc-section">isPowerOfTwo
    307. 

  307.   <li><a class="reference" href="#isPowerOfTwo%2Cint" title="isPowerOfTwo(x: int): bool">isPowerOfTwo(x: int): bool</a></li>
    308. 

  308. 

  309. </ul>
    310. 

  310. <ul class="simple nested-toc-section">lcm
    311. 

  311.   <li><a class="reference" href="#lcm%2CT%2CT" title="lcm[T](x, y: T): T">lcm[T](x, y: T): T</a></li>
    312. 

  312. <li><a class="reference" href="#lcm%2CopenArray%5BT%5D" title="lcm[T](x: openArray[T]): T">lcm[T](x: openArray[T]): T</a></li>
    313. 

  313. 

  314. </ul>
    315. 

  315. <ul class="simple nested-toc-section">lgamma
    316. 

  316.   <li><a class="reference" href="#lgamma%2Cfloat32" title="lgamma(x: float32): float32">lgamma(x: float32): float32</a></li>
    317. 

  317. <li><a class="reference" href="#lgamma%2Cfloat64" title="lgamma(x: float64): float64">lgamma(x: float64): float64</a></li>
    318. 

  318. 

  319. </ul>
    320. 

  320. <ul class="simple nested-toc-section">ln
    321. 

  321.   <li><a class="reference" href="#ln%2Cfloat32" title="ln(x: float32): float32">ln(x: float32): float32</a></li>
    322. 

  322. <li><a class="reference" href="#ln%2Cfloat64" title="ln(x: float64): float64">ln(x: float64): float64</a></li>
    323. 

  323. 

  324. </ul>
    325. 

  325. <ul class="simple nested-toc-section">log
    326. 

  326.   <li><a class="reference" href="#log%2CT%2CT" title="log[T: SomeFloat](x, base: T): T">log[T: SomeFloat](x, base: T): T</a></li>
    327. 

  327. 

  328. </ul>
    329. 

  329. <ul class="simple nested-toc-section">log2
    330. 

  330.   <li><a class="reference" href="#log2%2Cfloat32" title="log2(x: float32): float32">log2(x: float32): float32</a></li>
    331. 

  331. <li><a class="reference" href="#log2%2Cfloat64" title="log2(x: float64): float64">log2(x: float64): float64</a></li>
    332. 

  332. 

  333. </ul>
    334. 

  334. <ul class="simple nested-toc-section">log10
    335. 

  335.   <li><a class="reference" href="#log10%2Cfloat32" title="log10(x: float32): float32">log10(x: float32): float32</a></li>
    336. 

  336. <li><a class="reference" href="#log10%2Cfloat64" title="log10(x: float64): float64">log10(x: float64): float64</a></li>
    337. 

  337. 

  338. </ul>
    339. 

  339. <ul class="simple nested-toc-section">mod
    340. 

  340.   <li><a class="reference" href="#mod%2Cfloat32%2Cfloat32" title="`mod`(x, y: float32): float32">`mod`(x, y: float32): float32</a></li>
    341. 

  341. <li><a class="reference" href="#mod%2Cfloat64%2Cfloat64" title="`mod`(x, y: float64): float64">`mod`(x, y: float64): float64</a></li>
    342. 

  342. 

  343. </ul>
    344. 

  344. <ul class="simple nested-toc-section">nextPowerOfTwo
    345. 

  345.   <li><a class="reference" href="#nextPowerOfTwo%2Cint" title="nextPowerOfTwo(x: int): int">nextPowerOfTwo(x: int): int</a></li>
    346. 

  346. 

  347. </ul>
    348. 

  348. <ul class="simple nested-toc-section">pow
    349. 

  349.   <li><a class="reference" href="#pow%2Cfloat32%2Cfloat32" title="pow(x, y: float32): float32">pow(x, y: float32): float32</a></li>
    350. 

  350. <li><a class="reference" href="#pow%2Cfloat64%2Cfloat64" title="pow(x, y: float64): float64">pow(x, y: float64): float64</a></li>
    351. 

  351. 

  352. </ul>
    353. 

  353. <ul class="simple nested-toc-section">prod
    354. 

  354.   <li><a class="reference" href="#prod%2CopenArray%5BT%5D" title="prod[T](x: openArray[T]): T">prod[T](x: openArray[T]): T</a></li>
    355. 

  355. 

  356. </ul>
    357. 

  357. <ul class="simple nested-toc-section">radToDeg
    358. 

  358.   <li><a class="reference" href="#radToDeg%2CT" title="radToDeg[T: float32 | float64](d: T): T">radToDeg[T: float32 | float64](d: T): T</a></li>
    359. 

  359. 

  360. </ul>
    361. 

  361. <ul class="simple nested-toc-section">round
    362. 

  362.   <li><a class="reference" href="#round%2Cfloat32" title="round(x: float32): float32">round(x: float32): float32</a></li>
    363. 

  363. <li><a class="reference" href="#round%2Cfloat64" title="round(x: float64): float64">round(x: float64): float64</a></li>
    364. 

  364. <li><a class="reference" href="#round%2CT%2Cint" title="round[T: float32 | float64](x: T; places: int): T">round[T: float32 | float64](x: T; places: int): T</a></li>
    365. 

  365. 

  366. </ul>
    367. 

  367. <ul class="simple nested-toc-section">sec
    368. 

  368.   <li><a class="reference" href="#sec%2CT" title="sec[T: float32 | float64](x: T): T">sec[T: float32 | float64](x: T): T</a></li>
    369. 

  369. 

  370. </ul>
    371. 

  371. <ul class="simple nested-toc-section">sech
    372. 

  372.   <li><a class="reference" href="#sech%2CT" title="sech[T: float32 | float64](x: T): T">sech[T: float32 | float64](x: T): T</a></li>
    373. 

  373. 

  374. </ul>
    375. 

  375. <ul class="simple nested-toc-section">sgn
    376. 

  376.   <li><a class="reference" href="#sgn%2CT" title="sgn[T: SomeNumber](x: T): int">sgn[T: SomeNumber](x: T): int</a></li>
    377. 

  377. 

  378. </ul>
    379. 

  379. <ul class="simple nested-toc-section">signbit
    380. 

  380.   <li><a class="reference" href="#signbit%2CSomeFloat" title="signbit(x: SomeFloat): bool">signbit(x: SomeFloat): bool</a></li>
    381. 

  381. 

  382. </ul>
    383. 

  383. <ul class="simple nested-toc-section">sin
    384. 

  384.   <li><a class="reference" href="#sin%2Cfloat32" title="sin(x: float32): float32">sin(x: float32): float32</a></li>
    385. 

  385. <li><a class="reference" href="#sin%2Cfloat64" title="sin(x: float64): float64">sin(x: float64): float64</a></li>
    386. 

  386. 

  387. </ul>
    388. 

  388. <ul class="simple nested-toc-section">sinh
    389. 

  389.   <li><a class="reference" href="#sinh%2Cfloat32" title="sinh(x: float32): float32">sinh(x: float32): float32</a></li>
    390. 

  390. <li><a class="reference" href="#sinh%2Cfloat64" title="sinh(x: float64): float64">sinh(x: float64): float64</a></li>
    391. 

  391. 

  392. </ul>
    393. 

  393. <ul class="simple nested-toc-section">splitDecimal
    394. 

  394.   <li><a class="reference" href="#splitDecimal%2CT" title="splitDecimal[T: float32 | float64](x: T): tuple[intpart: T, floatpart: T]">splitDecimal[T: float32 | float64](x: T): tuple[intpart: T, floatpart: T]</a></li>
    395. 

  395. 

  396. </ul>
    397. 

  397. <ul class="simple nested-toc-section">sqrt
    398. 

  398.   <li><a class="reference" href="#sqrt%2Cfloat32" title="sqrt(x: float32): float32">sqrt(x: float32): float32</a></li>
    399. 

  399. <li><a class="reference" href="#sqrt%2Cfloat64" title="sqrt(x: float64): float64">sqrt(x: float64): float64</a></li>
    400. 

  400. 

  401. </ul>
    402. 

  402. <ul class="simple nested-toc-section">sum
    403. 

  403.   <li><a class="reference" href="#sum%2CopenArray%5BT%5D" title="sum[T](x: openArray[T]): T">sum[T](x: openArray[T]): T</a></li>
    404. 

  404. 

  405. </ul>
    406. 

  406. <ul class="simple nested-toc-section">tan
    407. 

  407.   <li><a class="reference" href="#tan%2Cfloat32" title="tan(x: float32): float32">tan(x: float32): float32</a></li>
    408. 

  408. <li><a class="reference" href="#tan%2Cfloat64" title="tan(x: float64): float64">tan(x: float64): float64</a></li>
    409. 

  409. 

  410. </ul>
    411. 

  411. <ul class="simple nested-toc-section">tanh
    412. 

  412.   <li><a class="reference" href="#tanh%2Cfloat32" title="tanh(x: float32): float32">tanh(x: float32): float32</a></li>
    413. 

  413. <li><a class="reference" href="#tanh%2Cfloat64" title="tanh(x: float64): float64">tanh(x: float64): float64</a></li>
    414. 

  414. 

  415. </ul>
    416. 

  416. <ul class="simple nested-toc-section">trunc
    417. 

  417.   <li><a class="reference" href="#trunc%2Cfloat32" title="trunc(x: float32): float32">trunc(x: float32): float32</a></li>
    418. 

  418. <li><a class="reference" href="#trunc%2Cfloat64" title="trunc(x: float64): float64">trunc(x: float64): float64</a></li>
    419. 

  419. 

  420. </ul>
    421. 

  421. 

  422.     </ul>
    423. 

  423.   </details>
    424. 

  424. </li>
    425. 

  425. 

  426. </ul>
    427. 

  427. 

  428.   </div>
    429. 

  429.   <div class="nine columns" id="content">
    430. 

  430.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L1" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    431. 

  431. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L1" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    432. 

  432. 

  433.     <div id="tocRoot"></div>
    434. 

  434.     
    435. 

  435.     <p class="module-desc"><p><em>Constructive mathematics is naturally typed.</em> -- Simon Thompson</p>
    436. 

  436. <p>Basic math routines for Nim.</p>
    437. 

  437. <p>Note that the trigonometric functions naturally operate on radians. The helper functions <a class="reference external" href="#degToRad,T">degToRad</a> and <a class="reference external" href="#radToDeg,T">radToDeg</a> provide conversion between radians and degrees.</p>
    438. 

  438. 

  439. <p><strong class="examples_text">Example:</strong></p>
    440. 

  440. <pre class="listing"><span class="Keyword">import</span> <span class="Identifier">std</span><span class="Operator">/</span><span class="Identifier">math</span>
    441. 

  441. <span class="Keyword">from</span> <span class="Identifier">std</span><span class="Operator">/</span><span class="Identifier">fenv</span> <span class="Keyword">import</span> <span class="Identifier">epsilon</span>
    442. 

  442. <span class="Keyword">from</span> <span class="Identifier">std</span><span class="Operator">/</span><span class="Identifier">random</span> <span class="Keyword">import</span> <span class="Identifier">rand</span>
    443. 

  443. 

  444. <span class="Keyword">proc</span> <span class="Identifier">generateGaussianNoise</span><span class="Punctuation">(</span><span class="Identifier">mu</span><span class="Punctuation">:</span> <span class="Identifier">float</span> <span class="Operator">=</span> <span class="FloatNumber">0.0</span><span class="Punctuation">,</span> <span class="Identifier">sigma</span><span class="Punctuation">:</span> <span class="Identifier">float</span> <span class="Operator">=</span> <span class="FloatNumber">1.0</span><span class="Punctuation">)</span><span class="Punctuation">:</span> <span class="Punctuation">(</span><span class="Identifier">float</span><span class="Punctuation">,</span> <span class="Identifier">float</span><span class="Punctuation">)</span> <span class="Operator">=</span>
    445. 

  445.   <span class="Comment"># Generates values from a normal distribution.</span>
    446. 

  446.   <span class="Comment"># Translated from https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform#Implementation.</span>
    447. 

  447.   <span class="Keyword">var</span> <span class="Identifier">u1</span><span class="Punctuation">:</span> <span class="Identifier">float</span>
    448. 

  448.   <span class="Keyword">var</span> <span class="Identifier">u2</span><span class="Punctuation">:</span> <span class="Identifier">float</span>
    449. 

  449.   <span class="Keyword">while</span> <span class="Identifier">true</span><span class="Punctuation">:</span>
    450. 

  450.     <span class="Identifier">u1</span> <span class="Operator">=</span> <span class="Identifier">rand</span><span class="Punctuation">(</span><span class="FloatNumber">1.0</span><span class="Punctuation">)</span>
    451. 

  451.     <span class="Identifier">u2</span> <span class="Operator">=</span> <span class="Identifier">rand</span><span class="Punctuation">(</span><span class="FloatNumber">1.0</span><span class="Punctuation">)</span>
    452. 

  452.     <span class="Keyword">if</span> <span class="Identifier">u1</span> <span class="Operator">&gt;</span> <span class="Identifier">epsilon</span><span class="Punctuation">(</span><span class="Identifier">float</span><span class="Punctuation">)</span><span class="Punctuation">:</span> <span class="Keyword">break</span>
    453. 

  453.   <span class="Keyword">let</span> <span class="Identifier">mag</span> <span class="Operator">=</span> <span class="Identifier">sigma</span> <span class="Operator">*</span> <span class="Identifier">sqrt</span><span class="Punctuation">(</span><span class="Operator">-</span><span class="DecNumber">2</span> <span class="Operator">*</span> <span class="Identifier">ln</span><span class="Punctuation">(</span><span class="Identifier">u1</span><span class="Punctuation">)</span><span class="Punctuation">)</span>
    454. 

  454.   <span class="Keyword">let</span> <span class="Identifier">z0</span> <span class="Operator">=</span> <span class="Identifier">mag</span> <span class="Operator">*</span> <span class="Identifier">cos</span><span class="Punctuation">(</span><span class="DecNumber">2</span> <span class="Operator">*</span> <span class="Identifier">PI</span> <span class="Operator">*</span> <span class="Identifier">u2</span><span class="Punctuation">)</span> <span class="Operator">+</span> <span class="Identifier">mu</span>
    455. 

  455.   <span class="Keyword">let</span> <span class="Identifier">z1</span> <span class="Operator">=</span> <span class="Identifier">mag</span> <span class="Operator">*</span> <span class="Identifier">sin</span><span class="Punctuation">(</span><span class="DecNumber">2</span> <span class="Operator">*</span> <span class="Identifier">PI</span> <span class="Operator">*</span> <span class="Identifier">u2</span><span class="Punctuation">)</span> <span class="Operator">+</span> <span class="Identifier">mu</span>
    456. 

  456.   <span class="Punctuation">(</span><span class="Identifier">z0</span><span class="Punctuation">,</span> <span class="Identifier">z1</span><span class="Punctuation">)</span>
    457. 

  457. 

  458. <span class="Identifier">echo</span> <span class="Identifier">generateGaussianNoise</span><span class="Punctuation">(</span><span class="Punctuation">)</span></pre>This module is available for the <a class="reference external" href="backends.html#backends-the-javascript-target">JavaScript target</a>.
    459. 

  459. <h1><a class="toc-backref" id="see-also" href="#see-also">See also</a></h1><ul class="simple"><li><a class="reference external" href="complex.html">complex module</a> for complex numbers and their mathematical operations</li>
    460. 

  460. <li><a class="reference external" href="rationals.html">rationals module</a> for rational numbers and their mathematical operations</li>
    461. 

  461. <li><a class="reference external" href="fenv.html">fenv module</a> for handling of floating-point rounding and exceptions (overflow, zero-divide, etc.)</li>
    462. 

  462. <li><a class="reference external" href="random.html">random module</a> for a fast and tiny random number generator</li>
    463. 

  463. <li><a class="reference external" href="stats.html">stats module</a> for statistical analysis</li>
    464. 

  464. <li><a class="reference external" href="strformat.html">strformat module</a> for formatting floats for printing</li>
    465. 

  465. <li><a class="reference external" href="system.html">system module</a> for some very basic and trivial math operators (<tt class="docutils literal"><span class="pre"><span class="Keyword">shr</span></span></tt>, <tt class="docutils literal"><span class="pre"><span class="Keyword">shl</span></span></tt>, <tt class="docutils literal"><span class="pre"><span class="Keyword">xor</span></span></tt>, <tt class="docutils literal"><span class="pre"><span class="Identifier">clamp</span></span></tt>, etc.)</li>
    466. 

  466. </ul>
    467. 

  467. this func uses bitwise comparisons from C compilers, which are not always available.</p>
    468. 

  468.     <div class="section" id="6">
    469. 

  469.   <h1><a class="toc-backref" href="#6">Imports</a></h1>
    470. 

  470.   <dl class="item">
    471. 

  471.     <a class="reference external" href="since.html">since</a>, <a class="reference external" href="bitops.html">bitops</a>, <a class="reference external" href="fenv.html">fenv</a>, <a class="reference external" href="countbits_impl.html">countbits_impl</a>, <a class="reference external" href="assertions.html">assertions</a>
    472. 

  472.   </dl>
    473. 

  473. </div>
    474. 

  474. <div class="section" id="7">
    475. 

  475.   <h1><a class="toc-backref" href="#7">Types</a></h1>
    476. 

  476.   <dl class="item">
    477. 

  477.     <div id="FloatClass">
    478. 

  478.   <dt><pre><a href="math.html#FloatClass"><span class="Identifier">FloatClass</span></a> <span class="Other">=</span> <span class="Keyword">enum</span>
    479. 

  479.   <span class="Identifier">fcNormal</span><span class="Other">,</span>                 <span class="Comment">## value is an ordinary nonzero floating point value</span>
    480. 

  480.   <span class="Identifier">fcSubnormal</span><span class="Other">,</span>              <span class="Comment">## value is a subnormal (a very small) floating point value</span>
    481. 

  481.   <span class="Identifier">fcZero</span><span class="Other">,</span>                   <span class="Comment">## value is zero</span>
    482. 

  482.   <span class="Identifier">fcNegZero</span><span class="Other">,</span>                <span class="Comment">## value is the negative zero</span>
    483. 

  483.   <span class="Identifier">fcNan</span><span class="Other">,</span>                    <span class="Comment">## value is Not a Number (NaN)</span>
    484. 

  484.   <span class="Identifier">fcInf</span><span class="Other">,</span>                    <span class="Comment">## value is positive infinity</span>
    485. 

  485.   <span class="Identifier">fcNegInf</span>                   <span class="Comment">## value is negative infinity</span></pre></dt>
    486. 

  486.   <dd>
    487. 

  487.     
    488. 

  488.     Describes the class a floating point value belongs to. This is the type that is returned by the <a class="reference external" href="#classify,float">classify func</a>.
    489. 

  489.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L182" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    490. 

  490. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L182" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    491. 

  491. 

  492.   </dd>
    493. 

  493. </div>
    494. 

  494. 

  495.   </dl>
    496. 

  496. </div>
    497. 

  497. <div class="section" id="10">
    498. 

  498.   <h1><a class="toc-backref" href="#10">Consts</a></h1>
    499. 

  499.   <dl class="item">
    500. 

  500.     <div id="E">
    501. 

  501.   <dt><pre><a href="math.html#E"><span class="Identifier">E</span></a> <span class="Other">=</span> <span class="FloatNumber">2.718281828459045</span></pre></dt>
    502. 

  502.   <dd>
    503. 

  503.     
    504. 

  504.     Euler's number.
    505. 

  505.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L165" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    506. 

  506. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L165" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    507. 

  507. 

  508.   </dd>
    509. 

  509. </div>
    510. 

  510. <div id="MaxFloat32Precision">
    511. 

  511.   <dt><pre><a href="math.html#MaxFloat32Precision"><span class="Identifier">MaxFloat32Precision</span></a> <span class="Other">=</span> <span class="DecNumber">8</span></pre></dt>
    512. 

  512.   <dd>
    513. 

  513.     
    514. 

  514.     Maximum number of meaningful digits after the decimal point for Nim's <tt class="docutils literal"><span class="pre"><span class="Identifier">float32</span></span></tt> type.
    515. 

  515.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L170" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    516. 

  516. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L170" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    517. 

  517. 

  518.   </dd>
    519. 

  519. </div>
    520. 

  520. <div id="MaxFloat64Precision">
    521. 

  521.   <dt><pre><a href="math.html#MaxFloat64Precision"><span class="Identifier">MaxFloat64Precision</span></a> <span class="Other">=</span> <span class="DecNumber">16</span></pre></dt>
    522. 

  522.   <dd>
    523. 

  523.     
    524. 

  524.     Maximum number of meaningful digits after the decimal point for Nim's <tt class="docutils literal"><span class="pre"><span class="Identifier">float64</span></span></tt> type.
    525. 

  525.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L167" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    526. 

  526. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L167" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    527. 

  527. 

  528.   </dd>
    529. 

  529. </div>
    530. 

  530. <div id="MaxFloatPrecision">
    531. 

  531.   <dt><pre><a href="math.html#MaxFloatPrecision"><span class="Identifier">MaxFloatPrecision</span></a> <span class="Other">=</span> <span class="DecNumber">16</span></pre></dt>
    532. 

  532.   <dd>
    533. 

  533.     
    534. 

  534.     Maximum number of meaningful digits after the decimal point for Nim's <tt class="docutils literal"><span class="pre"><span class="Identifier">float</span></span></tt> type.
    535. 

  535.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L173" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    536. 

  536. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L173" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    537. 

  537. 

  538.   </dd>
    539. 

  539. </div>
    540. 

  540. <div id="MinFloatNormal">
    541. 

  541.   <dt><pre><a href="math.html#MinFloatNormal"><span class="Identifier">MinFloatNormal</span></a> <span class="Other">=</span> <span class="FloatNumber">2.225073858507201e-308</span></pre></dt>
    542. 

  542.   <dd>
    543. 

  543.     
    544. 

  544.     Smallest normal number for Nim's <tt class="docutils literal"><span class="pre"><span class="Identifier">float</span></span></tt> type (= 2^-1022).
    545. 

  545.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L177" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    546. 

  546. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L177" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    547. 

  547. 

  548.   </dd>
    549. 

  549. </div>
    550. 

  550. <div id="PI">
    551. 

  551.   <dt><pre><a href="math.html#PI"><span class="Identifier">PI</span></a> <span class="Other">=</span> <span class="FloatNumber">3.141592653589793</span></pre></dt>
    552. 

  552.   <dd>
    553. 

  553.     
    554. 

  554.     The circle constant PI (Ludolph's number).
    555. 

  555.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L163" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    556. 

  556. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L163" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    557. 

  557. 

  558.   </dd>
    559. 

  559. </div>
    560. 

  560. <div id="TAU">
    561. 

  561.   <dt><pre><a href="math.html#TAU"><span class="Identifier">TAU</span></a> <span class="Other">=</span> <span class="FloatNumber">6.283185307179586</span></pre></dt>
    562. 

  562.   <dd>
    563. 

  563.     
    564. 

  564.     The circle constant TAU (= 2 * PI).
    565. 

  565.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L164" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    566. 

  566. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L164" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    567. 

  567. 

  568.   </dd>
    569. 

  569. </div>
    570. 

  570. 

  571.   </dl>
    572. 

  572. </div>
    573. 

  573. <div class="section" id="12">
    574. 

  574.   <h1><a class="toc-backref" href="#12">Procs</a></h1>
    575. 

  575.   <dl class="item">
    576. 

  576.     <div id="^-procs-all">
    577. 

  577.   <div id="^,T,U">
    578. 

  578.   <dt><pre><span class="Keyword">func</span> <a href="#%5E%2CT%2CU"><span class="Identifier">`^`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#SomeNumber"><span class="Identifier">SomeNumber</span></a><span class="Other">;</span> <span class="Identifier">U</span><span class="Other">:</span> <a href="system.html#SomeFloat"><span class="Identifier">SomeFloat</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="Identifier">y</span><span class="Other">:</span> <span class="Identifier">U</span><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float"><span class="Identifier">float</span></a></pre></dt>
    579. 

  579.   <dd>
    580. 

  580.     
    581. 

  581.     <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>
    582. 

  582. <p>Error handling follows the C++ specification even for the JS backend <a class="reference external" href="https://en.cppreference.com/w/cpp/numeric/math/pow">https://en.cppreference.com/w/cpp/numeric/math/pow</a></p>
    583. 

  583. <p><strong>See also:</strong></p>
    584. 

  584. <ul class="simple"><li><a class="reference external" href="#^,T,Natural">^ func</a></li>
    585. 

  585. <li><a class="reference external" href="#pow,float64,float64">pow func</a> for <tt class="docutils literal"><span class="pre"><span class="Identifier">float32</span></span></tt> or <tt class="docutils literal"><span class="pre"><span class="Identifier">float64</span></span></tt> output</li>
    586. 

  586. <li><a class="reference external" href="#sqrt,float64">sqrt func</a></li>
    587. 

  587. <li><a class="reference external" href="#cbrt,float64">cbrt func</a></li>
    588. 

  588. </ul>
    589. 

  589. 

  590. <p><strong class="examples_text">Example:</strong></p>
    591. 

  591. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="FloatNumber">5.5</span> <span class="Operator">^</span> <span class="FloatNumber">2.2</span><span class="Punctuation">,</span> <span class="FloatNumber">42.540042248725975</span><span class="Punctuation">)</span>
    592. 

  592. <span class="Identifier">doAssert</span> <span class="FloatNumber">1.0</span> <span class="Operator">^</span> <span class="Identifier">Inf</span> <span class="Operator">==</span> <span class="FloatNumber">1.0</span></pre>
    593. 

  593.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L1248" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    594. 

  594. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L1248" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    595. 

  595. 

  596.   </dd>
    597. 

  597. </div>
    598. 

  598. <div id="^,T,Natural">
    599. 

  599.   <dt><pre><span class="Keyword">func</span> <a href="#%5E%2CT%2CNatural"><span class="Identifier">`^`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#SomeNumber"><span class="Identifier">SomeNumber</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="Identifier">y</span><span class="Other">:</span> <a href="system.html#Natural"><span class="Identifier">Natural</span></a><span class="Other">)</span><span class="Other">:</span> <span class="Identifier">T</span></pre></dt>
    600. 

  600.   <dd>
    601. 

  601.     
    602. 

  602.     <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>
    603. 

  603. <p>The exponent <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt> must be non-negative, use <a class="reference external" href="#pow,float64,float64">pow</a> for negative exponents.</p>
    604. 

  604. <p><strong>See also:</strong></p>
    605. 

  605. <ul class="simple"><li><a class="reference external" href="#^,T,U">^ func</a> for negative exponent or floats</li>
    606. 

  606. <li><a class="reference external" href="#pow,float64,float64">pow func</a> for <tt class="docutils literal"><span class="pre"><span class="Identifier">float32</span></span></tt> or <tt class="docutils literal"><span class="pre"><span class="Identifier">float64</span></span></tt> output</li>
    607. 

  607. <li><a class="reference external" href="#sqrt,float64">sqrt func</a></li>
    608. 

  608. <li><a class="reference external" href="#cbrt,float64">cbrt func</a></li>
    609. 

  609. </ul>
    610. 

  610. 

  611. <p><strong class="examples_text">Example:</strong></p>
    612. 

  612. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Operator">-</span><span class="DecNumber">3</span> <span class="Operator">^</span> <span class="DecNumber">0</span> <span class="Operator">==</span> <span class="DecNumber">1</span>
    613. 

  613. <span class="Identifier">doAssert</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="Operator">-</span><span class="DecNumber">3</span>
    614. 

  614. <span class="Identifier">doAssert</span> <span class="Operator">-</span><span class="DecNumber">3</span> <span class="Operator">^</span> <span class="DecNumber">2</span> <span class="Operator">==</span> <span class="DecNumber">9</span></pre>
    615. 

  615.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L1212" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    616. 

  616. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L1212" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    617. 

  617. 

  618.   </dd>
    619. 

  619. </div>
    620. 

  620. 

  621. </div>
    622. 

  622. <div id="almostEqual-procs-all">
    623. 

  623.   <div id="almostEqual,T,T,Natural">
    624. 

  624.   <dt><pre><span class="Keyword">func</span> <a href="#almostEqual%2CT%2CT%2CNatural"><span class="Identifier">almostEqual</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#SomeFloat"><span class="Identifier">SomeFloat</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> <span class="Identifier">T</span><span class="Other">;</span> <span class="Identifier">unitsInLastPlace</span><span class="Other">:</span> <a href="system.html#Natural"><span class="Identifier">Natural</span></a> <span class="Other">=</span> <span class="DecNumber">4</span><span class="Other">)</span><span class="Other">:</span> <a href="system.html#bool"><span class="Identifier">bool</span></a> {.
    625. 

  625.     <span class="Identifier">inline</span>.}</pre></dt>
    626. 

  626.   <dd>
    627. 

  627.     
    628. 

  628.     <p>Checks if two float values are almost equal, using the <a class="reference external" href="https://en.wikipedia.org/wiki/Machine_epsilon">machine epsilon</a>.</p>
    629. 

  629. <p><tt class="docutils literal"><span class="pre"><span class="Identifier">unitsInLastPlace</span></span></tt> is the max number of <a class="reference external" href="https://en.wikipedia.org/wiki/Unit_in_the_last_place">units in the last place</a> difference tolerated when comparing two numbers. The larger the value, the more error is allowed. A <tt class="docutils literal"><span class="pre"><span class="DecNumber">0</span></span></tt> value means that two numbers must be exactly the same to be considered equal.</p>
    630. 

  630. <p>The machine epsilon has to be scaled to the magnitude of the values used and multiplied by the desired precision in ULPs unless the difference is subnormal. </p>
    631. 

  631. 

  632. <p><strong class="examples_text">Example:</strong></p>
    633. 

  633. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">PI</span><span class="Punctuation">,</span> <span class="FloatNumber">3.14159265358979</span><span class="Punctuation">)</span>
    634. 

  634. <span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">Inf</span><span class="Punctuation">,</span> <span class="Identifier">Inf</span><span class="Punctuation">)</span>
    635. 

  635. <span class="Identifier">doAssert</span> <span class="Keyword">not</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">NaN</span><span class="Punctuation">,</span> <span class="Identifier">NaN</span><span class="Punctuation">)</span></pre>
    636. 

  636.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L295" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    637. 

  637. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L295" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    638. 

  638. 

  639.   </dd>
    640. 

  640. </div>
    641. 

  641. 

  642. </div>
    643. 

  643. <div id="arccos-procs-all">
    644. 

  644.   <div id="arccos,float32">
    645. 

  645.   <dt><pre><span class="Keyword">func</span> <a href="#arccos%2Cfloat32"><span class="Identifier">arccos</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;acosf&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    646. 

  646.                                    <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>
    647. 

  647.   <dd>
    648. 

  648.     
    649. 

  649.     
    650. 

  650.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L513" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    651. 

  651. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L513" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    652. 

  652. 

  653.   </dd>
    654. 

  654. </div>
    655. 

  655. <div id="arccos,float64">
    656. 

  656.   <dt><pre><span class="Keyword">func</span> <a href="#arccos%2Cfloat64"><span class="Identifier">arccos</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;acos&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    657. 

  657.                                    <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>
    658. 

  658.   <dd>
    659. 

  659.     
    660. 

  660.     <p>Computes the arc cosine of <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>.</p>
    661. 

  661. <p><strong>See also:</strong></p>
    662. 

  662. <ul class="simple"><li><a class="reference external" href="#cos,float64">cos func</a></li>
    663. 

  663. </ul>
    664. 

  664. 

  665. <p><strong class="examples_text">Example:</strong></p>
    666. 

  666. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">radToDeg</span><span class="Punctuation">(</span><span class="Identifier">arccos</span><span class="Punctuation">(</span><span class="FloatNumber">0.0</span><span class="Punctuation">)</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="FloatNumber">90.0</span><span class="Punctuation">)</span>
    667. 

  667. <span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">radToDeg</span><span class="Punctuation">(</span><span class="Identifier">arccos</span><span class="Punctuation">(</span><span class="FloatNumber">1.0</span><span class="Punctuation">)</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="FloatNumber">0.0</span><span class="Punctuation">)</span></pre>
    668. 

  668.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L514" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    669. 

  669. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L514" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    670. 

  670. 

  671.   </dd>
    672. 

  672. </div>
    673. 

  673. 

  674. </div>
    675. 

  675. <div id="arccosh-procs-all">
    676. 

  676.   <div id="arccosh,float32">
    677. 

  677.   <dt><pre><span class="Keyword">func</span> <a href="#arccosh%2Cfloat32"><span class="Identifier">arccosh</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;acoshf&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    678. 

  678.                                     <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>
    679. 

  679.   <dd>
    680. 

  680.     
    681. 

  681.     
    682. 

  682.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L550" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    683. 

  683. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L550" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    684. 

  684. 

  685.   </dd>
    686. 

  686. </div>
    687. 

  687. <div id="arccosh,float64">
    688. 

  688.   <dt><pre><span class="Keyword">func</span> <a href="#arccosh%2Cfloat64"><span class="Identifier">arccosh</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;acosh&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    689. 

  689.                                     <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>
    690. 

  690.   <dd>
    691. 

  691.     
    692. 

  692.     <p>Computes the inverse hyperbolic cosine of <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>.</p>
    693. 

  693. <p><strong>See also:</strong></p>
    694. 

  694. <ul class="simple"><li><a class="reference external" href="#cosh,float64">cosh func</a></li>
    695. 

  695. </ul>
    696. 

  696. 

  697.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L551" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    698. 

  698. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L551" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    699. 

  699. 

  700.   </dd>
    701. 

  701. </div>
    702. 

  702. 

  703. </div>
    704. 

  704. <div id="arccot-procs-all">
    705. 

  705.   <div id="arccot,T">
    706. 

  706.   <dt><pre><span class="Keyword">func</span> <a href="#arccot%2CT"><span class="Identifier">arccot</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> <span class="Operator">|</span> <a href="system.html#float64"><span class="Identifier">float64</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> <span class="Identifier">T</span></pre></dt>
    707. 

  707.   <dd>
    708. 

  708.     
    709. 

  709.     Computes the inverse cotangent of <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> (<tt class="docutils literal"><span class="pre"><span class="Identifier">arctan</span><span class="Punctuation">(</span><span class="DecNumber">1</span><span class="Operator">/</span><span class="Identifier">x</span><span class="Punctuation">)</span></span></tt>).
    710. 

  710.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L604" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    711. 

  711. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L604" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    712. 

  712. 

  713.   </dd>
    714. 

  714. </div>
    715. 

  715. 

  716. </div>
    717. 

  717. <div id="arccoth-procs-all">
    718. 

  718.   <div id="arccoth,T">
    719. 

  719.   <dt><pre><span class="Keyword">func</span> <a href="#arccoth%2CT"><span class="Identifier">arccoth</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> <span class="Operator">|</span> <a href="system.html#float64"><span class="Identifier">float64</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> <span class="Identifier">T</span></pre></dt>
    720. 

  720.   <dd>
    721. 

  721.     
    722. 

  722.     Computes the inverse hyperbolic cotangent of <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> (<tt class="docutils literal"><span class="pre"><span class="Identifier">arctanh</span><span class="Punctuation">(</span><span class="DecNumber">1</span><span class="Operator">/</span><span class="Identifier">x</span><span class="Punctuation">)</span></span></tt>).
    723. 

  723.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L611" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    724. 

  724. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L611" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    725. 

  725. 

  726.   </dd>
    727. 

  727. </div>
    728. 

  728. 

  729. </div>
    730. 

  730. <div id="arccsc-procs-all">
    731. 

  731.   <div id="arccsc,T">
    732. 

  732.   <dt><pre><span class="Keyword">func</span> <a href="#arccsc%2CT"><span class="Identifier">arccsc</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> <span class="Operator">|</span> <a href="system.html#float64"><span class="Identifier">float64</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> <span class="Identifier">T</span></pre></dt>
    733. 

  733.   <dd>
    734. 

  734.     
    735. 

  735.     Computes the inverse cosecant of <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> (<tt class="docutils literal"><span class="pre"><span class="Identifier">arcsin</span><span class="Punctuation">(</span><span class="DecNumber">1</span><span class="Operator">/</span><span class="Identifier">x</span><span class="Punctuation">)</span></span></tt>).
    736. 

  736.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L608" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    737. 

  737. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L608" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    738. 

  738. 

  739.   </dd>
    740. 

  740. </div>
    741. 

  741. 

  742. </div>
    743. 

  743. <div id="arccsch-procs-all">
    744. 

  744.   <div id="arccsch,T">
    745. 

  745.   <dt><pre><span class="Keyword">func</span> <a href="#arccsch%2CT"><span class="Identifier">arccsch</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> <span class="Operator">|</span> <a href="system.html#float64"><span class="Identifier">float64</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> <span class="Identifier">T</span></pre></dt>
    746. 

  746.   <dd>
    747. 

  747.     
    748. 

  748.     Computes the inverse hyperbolic cosecant of <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> (<tt class="docutils literal"><span class="pre"><span class="Identifier">arcsinh</span><span class="Punctuation">(</span><span class="DecNumber">1</span><span class="Operator">/</span><span class="Identifier">x</span><span class="Punctuation">)</span></span></tt>).
    749. 

  749.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L615" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    750. 

  750. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L615" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    751. 

  751. 

  752.   </dd>
    753. 

  753. </div>
    754. 

  754. 

  755. </div>
    756. 

  756. <div id="arcsec-procs-all">
    757. 

  757.   <div id="arcsec,T">
    758. 

  758.   <dt><pre><span class="Keyword">func</span> <a href="#arcsec%2CT"><span class="Identifier">arcsec</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> <span class="Operator">|</span> <a href="system.html#float64"><span class="Identifier">float64</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> <span class="Identifier">T</span></pre></dt>
    759. 

  759.   <dd>
    760. 

  760.     
    761. 

  761.     Computes the inverse secant of <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> (<tt class="docutils literal"><span class="pre"><span class="Identifier">arccos</span><span class="Punctuation">(</span><span class="DecNumber">1</span><span class="Operator">/</span><span class="Identifier">x</span><span class="Punctuation">)</span></span></tt>).
    762. 

  762.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L606" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    763. 

  763. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L606" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    764. 

  764. 

  765.   </dd>
    766. 

  766. </div>
    767. 

  767. 

  768. </div>
    769. 

  769. <div id="arcsech-procs-all">
    770. 

  770.   <div id="arcsech,T">
    771. 

  771.   <dt><pre><span class="Keyword">func</span> <a href="#arcsech%2CT"><span class="Identifier">arcsech</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> <span class="Operator">|</span> <a href="system.html#float64"><span class="Identifier">float64</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> <span class="Identifier">T</span></pre></dt>
    772. 

  772.   <dd>
    773. 

  773.     
    774. 

  774.     Computes the inverse hyperbolic secant of <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> (<tt class="docutils literal"><span class="pre"><span class="Identifier">arccosh</span><span class="Punctuation">(</span><span class="DecNumber">1</span><span class="Operator">/</span><span class="Identifier">x</span><span class="Punctuation">)</span></span></tt>).
    775. 

  775.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L613" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    776. 

  776. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L613" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    777. 

  777. 

  778.   </dd>
    779. 

  779. </div>
    780. 

  780. 

  781. </div>
    782. 

  782. <div id="arcsin-procs-all">
    783. 

  783.   <div id="arcsin,float32">
    784. 

  784.   <dt><pre><span class="Keyword">func</span> <a href="#arcsin%2Cfloat32"><span class="Identifier">arcsin</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;asinf&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    785. 

  785.                                    <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>
    786. 

  786.   <dd>
    787. 

  787.     
    788. 

  788.     
    789. 

  789.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L504" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    790. 

  790. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L504" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    791. 

  791. 

  792.   </dd>
    793. 

  793. </div>
    794. 

  794. <div id="arcsin,float64">
    795. 

  795.   <dt><pre><span class="Keyword">func</span> <a href="#arcsin%2Cfloat64"><span class="Identifier">arcsin</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;asin&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    796. 

  796.                                    <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>
    797. 

  797.   <dd>
    798. 

  798.     
    799. 

  799.     <p>Computes the arc sine of <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>.</p>
    800. 

  800. <p><strong>See also:</strong></p>
    801. 

  801. <ul class="simple"><li><a class="reference external" href="#sin,float64">sin func</a></li>
    802. 

  802. </ul>
    803. 

  803. 

  804. <p><strong class="examples_text">Example:</strong></p>
    805. 

  805. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">radToDeg</span><span class="Punctuation">(</span><span class="Identifier">arcsin</span><span class="Punctuation">(</span><span class="FloatNumber">0.0</span><span class="Punctuation">)</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="FloatNumber">0.0</span><span class="Punctuation">)</span>
    806. 

  806. <span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">radToDeg</span><span class="Punctuation">(</span><span class="Identifier">arcsin</span><span class="Punctuation">(</span><span class="FloatNumber">1.0</span><span class="Punctuation">)</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="FloatNumber">90.0</span><span class="Punctuation">)</span></pre>
    807. 

  807.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L505" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    808. 

  808. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L505" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    809. 

  809. 

  810.   </dd>
    811. 

  811. </div>
    812. 

  812. 

  813. </div>
    814. 

  814. <div id="arcsinh-procs-all">
    815. 

  815.   <div id="arcsinh,float32">
    816. 

  816.   <dt><pre><span class="Keyword">func</span> <a href="#arcsinh%2Cfloat32"><span class="Identifier">arcsinh</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;asinhf&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    817. 

  817.                                     <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>
    818. 

  818.   <dd>
    819. 

  819.     
    820. 

  820.     
    821. 

  821.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L544" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    822. 

  822. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L544" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    823. 

  823. 

  824.   </dd>
    825. 

  825. </div>
    826. 

  826. <div id="arcsinh,float64">
    827. 

  827.   <dt><pre><span class="Keyword">func</span> <a href="#arcsinh%2Cfloat64"><span class="Identifier">arcsinh</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;asinh&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    828. 

  828.                                     <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>
    829. 

  829.   <dd>
    830. 

  830.     
    831. 

  831.     <p>Computes the inverse hyperbolic sine of <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>.</p>
    832. 

  832. <p><strong>See also:</strong></p>
    833. 

  833. <ul class="simple"><li><a class="reference external" href="#sinh,float64">sinh func</a></li>
    834. 

  834. </ul>
    835. 

  835. 

  836.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L545" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    837. 

  837. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L545" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    838. 

  838. 

  839.   </dd>
    840. 

  840. </div>
    841. 

  841. 

  842. </div>
    843. 

  843. <div id="arctan-procs-all">
    844. 

  844.   <div id="arctan,float32">
    845. 

  845.   <dt><pre><span class="Keyword">func</span> <a href="#arctan%2Cfloat32"><span class="Identifier">arctan</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;atanf&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    846. 

  846.                                    <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>
    847. 

  847.   <dd>
    848. 

  848.     
    849. 

  849.     
    850. 

  850.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L522" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    851. 

  851. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L522" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    852. 

  852. 

  853.   </dd>
    854. 

  854. </div>
    855. 

  855. <div id="arctan,float64">
    856. 

  856.   <dt><pre><span class="Keyword">func</span> <a href="#arctan%2Cfloat64"><span class="Identifier">arctan</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;atan&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    857. 

  857.                                    <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>
    858. 

  858.   <dd>
    859. 

  859.     
    860. 

  860.     <p>Calculate the arc tangent of <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>.</p>
    861. 

  861. <p><strong>See also:</strong></p>
    862. 

  862. <ul class="simple"><li><a class="reference external" href="#arctan2,float64,float64">arctan2 func</a></li>
    863. 

  863. <li><a class="reference external" href="#tan,float64">tan func</a></li>
    864. 

  864. </ul>
    865. 

  865. 

  866. <p><strong class="examples_text">Example:</strong></p>
    867. 

  867. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">arctan</span><span class="Punctuation">(</span><span class="FloatNumber">1.0</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="FloatNumber">0.7853981633974483</span><span class="Punctuation">)</span>
    868. 

  868. <span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">radToDeg</span><span class="Punctuation">(</span><span class="Identifier">arctan</span><span class="Punctuation">(</span><span class="FloatNumber">1.0</span><span class="Punctuation">)</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="FloatNumber">45.0</span><span class="Punctuation">)</span></pre>
    869. 

  869.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L523" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    870. 

  870. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L523" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    871. 

  871. 

  872.   </dd>
    873. 

  873. </div>
    874. 

  874. 

  875. </div>
    876. 

  876. <div id="arctan2-procs-all">
    877. 

  877.   <div id="arctan2,float32,float32">
    878. 

  878.   <dt><pre><span class="Keyword">func</span> <a href="#arctan2%2Cfloat32%2Cfloat32"><span class="Identifier">arctan2</span></a><span class="Other">(</span><span class="Identifier">y</span><span class="Other">,</span> <span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;atan2f&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    879. 

  879.                                        <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>
    880. 

  880.   <dd>
    881. 

  881.     
    882. 

  882.     
    883. 

  883.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L532" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    884. 

  884. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L532" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    885. 

  885. 

  886.   </dd>
    887. 

  887. </div>
    888. 

  888. <div id="arctan2,float64,float64">
    889. 

  889.   <dt><pre><span class="Keyword">func</span> <a href="#arctan2%2Cfloat64%2Cfloat64"><span class="Identifier">arctan2</span></a><span class="Other">(</span><span class="Identifier">y</span><span class="Other">,</span> <span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;atan2&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    890. 

  890.                                        <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>
    891. 

  891.   <dd>
    892. 

  892.     
    893. 

  893.     <p>Calculate the arc tangent of <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span><span class="Operator">/</span><span class="Identifier">x</span></span></tt>.</p>
    894. 

  894. <p>It produces correct results even when the resulting angle is near <tt class="docutils literal"><span class="pre"><span class="Identifier">PI</span><span class="Operator">/</span><span class="DecNumber">2</span></span></tt> or <tt class="docutils literal"><span class="pre"><span class="Operator">-</span><span class="Identifier">PI</span><span class="Operator">/</span><span class="DecNumber">2</span></span></tt> (<tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> near 0).</p>
    895. 

  895. <p><strong>See also:</strong></p>
    896. 

  896. <ul class="simple"><li><a class="reference external" href="#arctan,float64">arctan func</a></li>
    897. 

  897. </ul>
    898. 

  898. 

  899. <p><strong class="examples_text">Example:</strong></p>
    900. 

  900. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">arctan2</span><span class="Punctuation">(</span><span class="FloatNumber">1.0</span><span class="Punctuation">,</span> <span class="FloatNumber">0.0</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="Identifier">PI</span> <span class="Operator">/</span> <span class="FloatNumber">2.0</span><span class="Punctuation">)</span>
    901. 

  901. <span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">radToDeg</span><span class="Punctuation">(</span><span class="Identifier">arctan2</span><span class="Punctuation">(</span><span class="FloatNumber">1.0</span><span class="Punctuation">,</span> <span class="FloatNumber">0.0</span><span class="Punctuation">)</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="FloatNumber">90.0</span><span class="Punctuation">)</span></pre>
    902. 

  902.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L533" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    903. 

  903. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L533" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    904. 

  904. 

  905.   </dd>
    906. 

  906. </div>
    907. 

  907. 

  908. </div>
    909. 

  909. <div id="arctanh-procs-all">
    910. 

  910.   <div id="arctanh,float32">
    911. 

  911.   <dt><pre><span class="Keyword">func</span> <a href="#arctanh%2Cfloat32"><span class="Identifier">arctanh</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;atanhf&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    912. 

  912.                                     <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>
    913. 

  913.   <dd>
    914. 

  914.     
    915. 

  915.     
    916. 

  916.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L556" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    917. 

  917. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L556" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    918. 

  918. 

  919.   </dd>
    920. 

  920. </div>
    921. 

  921. <div id="arctanh,float64">
    922. 

  922.   <dt><pre><span class="Keyword">func</span> <a href="#arctanh%2Cfloat64"><span class="Identifier">arctanh</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;atanh&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    923. 

  923.                                     <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>
    924. 

  924.   <dd>
    925. 

  925.     
    926. 

  926.     <p>Computes the inverse hyperbolic tangent of <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>.</p>
    927. 

  927. <p><strong>See also:</strong></p>
    928. 

  928. <ul class="simple"><li><a class="reference external" href="#tanh,float64">tanh func</a></li>
    929. 

  929. </ul>
    930. 

  930. 

  931.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L557" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    932. 

  932. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L557" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    933. 

  933. 

  934.   </dd>
    935. 

  935. </div>
    936. 

  936. 

  937. </div>
    938. 

  938. <div id="binom-procs-all">
    939. 

  939.   <div id="binom,int,int">
    940. 

  940.   <dt><pre><span class="Keyword">func</span> <a href="#binom%2Cint%2Cint"><span class="Identifier">binom</span></a><span class="Other">(</span><span class="Identifier">n</span><span class="Other">,</span> <span class="Identifier">k</span><span class="Other">:</span> <a href="system.html#int"><span class="Identifier">int</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#int"><span class="Identifier">int</span></a> {.<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>
    941. 

  941.   <dd>
    942. 

  942.     
    943. 

  943.     Computes the <a class="reference external" href="https://en.wikipedia.org/wiki/Binomial_coefficient">binomial coefficient</a>.
    944. 

  944. <p><strong class="examples_text">Example:</strong></p>
    945. 

  945. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">binom</span><span class="Punctuation">(</span><span class="DecNumber">6</span><span class="Punctuation">,</span> <span class="DecNumber">2</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="DecNumber">15</span>
    946. 

  946. <span class="Identifier">doAssert</span> <span class="Identifier">binom</span><span class="Punctuation">(</span><span class="Operator">-</span><span class="DecNumber">6</span><span class="Punctuation">,</span> <span class="DecNumber">2</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="DecNumber">1</span>
    947. 

  947. <span class="Identifier">doAssert</span> <span class="Identifier">binom</span><span class="Punctuation">(</span><span class="DecNumber">6</span><span class="Punctuation">,</span> <span class="DecNumber">0</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="DecNumber">1</span></pre>
    948. 

  948.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L117" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    949. 

  949. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L117" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    950. 

  950. 

  951.   </dd>
    952. 

  952. </div>
    953. 

  953. 

  954. </div>
    955. 

  955. <div id="cbrt-procs-all">
    956. 

  956.   <div id="cbrt,float32">
    957. 

  957.   <dt><pre><span class="Keyword">func</span> <a href="#cbrt%2Cfloat32"><span class="Identifier">cbrt</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;cbrtf&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    958. 

  958.                                  <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>
    959. 

  959.   <dd>
    960. 

  960.     
    961. 

  961.     
    962. 

  962.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L377" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    963. 

  963. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L377" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    964. 

  964. 

  965.   </dd>
    966. 

  966. </div>
    967. 

  967. <div id="cbrt,float64">
    968. 

  968.   <dt><pre><span class="Keyword">func</span> <a href="#cbrt%2Cfloat64"><span class="Identifier">cbrt</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;cbrt&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    969. 

  969.                                  <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>
    970. 

  970.   <dd>
    971. 

  971.     
    972. 

  972.     <p>Computes the cube root of <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>.</p>
    973. 

  973. <p><strong>See also:</strong></p>
    974. 

  974. <ul class="simple"><li><a class="reference external" href="#sqrt,float64">sqrt func</a> for the square root</li>
    975. 

  975. </ul>
    976. 

  976. 

  977. <p><strong class="examples_text">Example:</strong></p>
    978. 

  978. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">cbrt</span><span class="Punctuation">(</span><span class="FloatNumber">8.0</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="FloatNumber">2.0</span><span class="Punctuation">)</span>
    979. 

  979. <span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">cbrt</span><span class="Punctuation">(</span><span class="FloatNumber">2.197</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="FloatNumber">1.3</span><span class="Punctuation">)</span>
    980. 

  980. <span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">cbrt</span><span class="Punctuation">(</span><span class="Operator">-</span><span class="FloatNumber">27.0</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="Operator">-</span><span class="FloatNumber">3.0</span><span class="Punctuation">)</span></pre>
    981. 

  981.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L378" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    982. 

  982. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L378" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    983. 

  983. 

  984.   </dd>
    985. 

  985. </div>
    986. 

  986. 

  987. </div>
    988. 

  988. <div id="ceil-procs-all">
    989. 

  989.   <div id="ceil,float32">
    990. 

  990.   <dt><pre><span class="Keyword">func</span> <a href="#ceil%2Cfloat32"><span class="Identifier">ceil</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;ceilf&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    991. 

  991.                                  <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>
    992. 

  992.   <dd>
    993. 

  993.     
    994. 

  994.     
    995. 

  995.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L688" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    996. 

  996. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L688" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    997. 

  997. 

  998.   </dd>
    999. 

  999. </div>
    1000. 

  1000. <div id="ceil,float64">
    1001. 

  1001.   <dt><pre><span class="Keyword">func</span> <a href="#ceil%2Cfloat64"><span class="Identifier">ceil</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;ceil&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    1002. 

  1002.                                  <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>
    1003. 

  1003.   <dd>
    1004. 

  1004.     
    1005. 

  1005.     <p>Computes the ceiling function (i.e. the smallest integer not smaller than <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>).</p>
    1006. 

  1006. <p><strong>See also:</strong></p>
    1007. 

  1007. <ul class="simple"><li><a class="reference external" href="#floor,float64">floor func</a></li>
    1008. 

  1008. <li><a class="reference external" href="#round,float64">round func</a></li>
    1009. 

  1009. <li><a class="reference external" href="#trunc,float64">trunc func</a></li>
    1010. 

  1010. </ul>
    1011. 

  1011. 

  1012. <p><strong class="examples_text">Example:</strong></p>
    1013. 

  1013. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">ceil</span><span class="Punctuation">(</span><span class="FloatNumber">2.1</span><span class="Punctuation">)</span>  <span class="Operator">==</span> <span class="FloatNumber">3.0</span>
    1014. 

  1014. <span class="Identifier">doAssert</span> <span class="Identifier">ceil</span><span class="Punctuation">(</span><span class="FloatNumber">2.9</span><span class="Punctuation">)</span>  <span class="Operator">==</span> <span class="FloatNumber">3.0</span>
    1015. 

  1015. <span class="Identifier">doAssert</span> <span class="Identifier">ceil</span><span class="Punctuation">(</span><span class="Operator">-</span><span class="FloatNumber">2.1</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="Operator">-</span><span class="FloatNumber">2.0</span></pre>
    1016. 

  1016.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L689" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1017. 

  1017. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L689" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1018. 

  1018. 

  1019.   </dd>
    1020. 

  1020. </div>
    1021. 

  1021. 

  1022. </div>
    1023. 

  1023. <div id="ceilDiv-procs-all">
    1024. 

  1024.   <div id="ceilDiv,T,T">
    1025. 

  1025.   <dt><pre><span class="Keyword">func</span> <a href="#ceilDiv%2CT%2CT"><span class="Identifier">ceilDiv</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> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <span class="Identifier">T</span> {.<span class="Identifier">inline</span>.}</pre></dt>
    1026. 

  1026.   <dd>
    1027. 

  1027.     
    1028. 

  1028.     <p>Ceil division is conceptually defined as <tt class="docutils literal"><span class="pre"><span class="Identifier">ceil</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>.</p>
    1029. 

  1029. <p>Assumes <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span> <span class="Operator">&gt;=</span> <span class="DecNumber">0</span></span></tt> and <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span> <span class="Operator">&gt;</span> <span class="DecNumber">0</span></span></tt> (and <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span> <span class="Operator">+</span> <span class="Identifier">y</span> <span class="Operator">-</span> <span class="DecNumber">1</span> <span class="Operator">&lt;=</span> <span class="Identifier">high</span><span class="Punctuation">(</span><span class="Identifier">T</span><span class="Punctuation">)</span></span></tt> if T is SomeUnsignedInt).</p>
    1030. 

  1030. <p>This is different from the <a class="reference external" href="system.html#div,int,int">system.div</a> operator, which works like <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 <tt class="docutils literal"><span class="pre"><span class="DecNumber">0</span></span></tt> and <tt class="docutils literal"><span class="pre"><span class="Identifier">ceilDiv</span></span></tt> rounds up.</p>
    1031. 

  1031. <p>This function has the above input limitation, because that allows the compiler to generate faster code and it is rarely used with negative values or unsigned integers close to <tt class="docutils literal"><span class="pre"><span class="Identifier">high</span><span class="Punctuation">(</span><span class="Identifier">T</span><span class="Punctuation">)</span><span class="Operator">/</span><span class="DecNumber">2</span></span></tt>. If you need a <tt class="docutils literal"><span class="pre"><span class="Identifier">ceilDiv</span></span></tt> that works with any input, see: <a class="reference external" href="https://github.com/demotomohiro/divmath">https://github.com/demotomohiro/divmath</a>.</p>
    1032. 

  1032. <p><strong>See also:</strong></p>
    1033. 

  1033. <ul class="simple"><li><a class="reference external" href="system.html#div,int,int">system.div proc</a> for integer division</li>
    1034. 

  1034. <li><a class="reference external" href="#floorDiv,T,T">floorDiv func</a> for integer division which rounds down.</li>
    1035. 

  1035. </ul>
    1036. 

  1036. 

  1037. <p><strong class="examples_text">Example:</strong></p>
    1038. 

  1038. <pre class="listing"><span class="Identifier">assert</span> <span class="Identifier">ceilDiv</span><span class="Punctuation">(</span><span class="DecNumber">12</span><span class="Punctuation">,</span> <span class="DecNumber">3</span><span class="Punctuation">)</span> <span class="Operator">==</span>  <span class="DecNumber">4</span>
    1039. 

  1039. <span class="Identifier">assert</span> <span class="Identifier">ceilDiv</span><span class="Punctuation">(</span><span class="DecNumber">13</span><span class="Punctuation">,</span> <span class="DecNumber">3</span><span class="Punctuation">)</span> <span class="Operator">==</span>  <span class="DecNumber">5</span></pre>
    1040. 

  1040.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L925" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1041. 

  1041. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L925" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1042. 

  1042. 

  1043.   </dd>
    1044. 

  1044. </div>
    1045. 

  1045. 

  1046. </div>
    1047. 

  1047. <div id="clamp-procs-all">
    1048. 

  1048.   <div id="clamp,T,Slice[T]">
    1049. 

  1049.   <dt><pre><span class="Keyword">func</span> <a href="#clamp%2CT%2CSlice%5BT%5D"><span class="Identifier">clamp</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">val</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">;</span> <span class="Identifier">bounds</span><span class="Other">:</span> <a href="system.html#Slice"><span class="Identifier">Slice</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> {.<span class="Identifier">inline</span>.}</pre></dt>
    1050. 

  1050.   <dd>
    1051. 

  1051.     
    1052. 

  1052.     Like <tt class="docutils literal"><span class="pre"><span class="Identifier">system</span><span class="Operator">.</span><span class="Identifier">clamp</span></span></tt>, but takes a slice, so you can easily clamp within a range.
    1053. 

  1053. <p><strong class="examples_text">Example:</strong></p>
    1054. 

  1054. <pre class="listing"><span class="Identifier">assert</span> <span class="Identifier">clamp</span><span class="Punctuation">(</span><span class="DecNumber">10</span><span class="Punctuation">,</span> <span class="DecNumber">1</span> <span class="Operator">..</span> <span class="DecNumber">5</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="DecNumber">5</span>
    1055. 

  1055. <span class="Identifier">assert</span> <span class="Identifier">clamp</span><span class="Punctuation">(</span><span class="DecNumber">1</span><span class="Punctuation">,</span> <span class="DecNumber">1</span> <span class="Operator">..</span> <span class="DecNumber">3</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="DecNumber">1</span>
    1056. 

  1056. <span class="Keyword">type</span> <span class="Identifier">A</span> <span class="Operator">=</span> <span class="Keyword">enum</span> <span class="Identifier">a0</span><span class="Punctuation">,</span> <span class="Identifier">a1</span><span class="Punctuation">,</span> <span class="Identifier">a2</span><span class="Punctuation">,</span> <span class="Identifier">a3</span><span class="Punctuation">,</span> <span class="Identifier">a4</span><span class="Punctuation">,</span> <span class="Identifier">a5</span>
    1057. 

  1057. <span class="Identifier">assert</span> <span class="Identifier">a1</span><span class="Operator">.</span><span class="Identifier">clamp</span><span class="Punctuation">(</span><span class="Identifier">a2</span><span class="Operator">..</span><span class="Identifier">a4</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="Identifier">a2</span>
    1058. 

  1058. <span class="Identifier">assert</span> <span class="Identifier">clamp</span><span class="Punctuation">(</span><span class="Punctuation">(</span><span class="DecNumber">3</span><span class="Punctuation">,</span> <span class="DecNumber">0</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="Punctuation">(</span><span class="DecNumber">1</span><span class="Punctuation">,</span> <span class="DecNumber">0</span><span class="Punctuation">)</span> <span class="Operator">..</span> <span class="Punctuation">(</span><span class="DecNumber">2</span><span class="Punctuation">,</span> <span class="DecNumber">9</span><span class="Punctuation">)</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="Punctuation">(</span><span class="DecNumber">2</span><span class="Punctuation">,</span> <span class="DecNumber">9</span><span class="Punctuation">)</span>
    1059. 

  1059. <span class="Identifier">doAssertRaises</span><span class="Punctuation">(</span><span class="Identifier">AssertionDefect</span><span class="Punctuation">)</span><span class="Punctuation">:</span> <span class="Keyword">discard</span> <span class="Identifier">clamp</span><span class="Punctuation">(</span><span class="DecNumber">1</span><span class="Punctuation">,</span> <span class="FloatNumber">3.</span><span class="Operator">.</span><span class="DecNumber">2</span><span class="Punctuation">)</span> <span class="Comment"># invalid bounds</span></pre>
    1060. 

  1060.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L1364" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1061. 

  1061. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L1364" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1062. 

  1062. 

  1063.   </dd>
    1064. 

  1064. </div>
    1065. 

  1065. 

  1066. </div>
    1067. 

  1067. <div id="classify-procs-all">
    1068. 

  1068.   <div id="classify,float">
    1069. 

  1069.   <dt><pre><span class="Keyword">func</span> <a href="#classify%2Cfloat"><span class="Identifier">classify</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="Other">:</span> <a href="math.html#FloatClass"><span class="Identifier">FloatClass</span></a> {.<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>
    1070. 

  1070.   <dd>
    1071. 

  1071.     
    1072. 

  1072.     <p>Classifies a floating point value.</p>
    1073. 

  1073. <p>Returns <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>'s class as specified by the <a class="reference external" href="#FloatClass">FloatClass enum</a>.</p>
    1074. 

  1074. 

  1075. <p><strong class="examples_text">Example:</strong></p>
    1076. 

  1076. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">classify</span><span class="Punctuation">(</span><span class="FloatNumber">0.3</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="Identifier">fcNormal</span>
    1077. 

  1077. <span class="Identifier">doAssert</span> <span class="Identifier">classify</span><span class="Punctuation">(</span><span class="FloatNumber">0.0</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="Identifier">fcZero</span>
    1078. 

  1078. <span class="Identifier">doAssert</span> <span class="Identifier">classify</span><span class="Punctuation">(</span><span class="FloatNumber">0.3</span> <span class="Operator">/</span> <span class="FloatNumber">0.0</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="Identifier">fcInf</span>
    1079. 

  1079. <span class="Identifier">doAssert</span> <span class="Identifier">classify</span><span class="Punctuation">(</span><span class="Operator">-</span><span class="FloatNumber">0.3</span> <span class="Operator">/</span> <span class="FloatNumber">0.0</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="Identifier">fcNegInf</span>
    1080. 

  1080. <span class="Identifier">doAssert</span> <span class="Identifier">classify</span><span class="Punctuation">(</span><span class="FloatNumber">5.0e-324</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="Identifier">fcSubnormal</span></pre>
    1081. 

  1081.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L270" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1082. 

  1082. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L270" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1083. 

  1083. 

  1084.   </dd>
    1085. 

  1085. </div>
    1086. 

  1086. 

  1087. </div>
    1088. 

  1088. <div id="copySign-procs-all">
    1089. 

  1089.   <div id="copySign,T,T">
    1090. 

  1090.   <dt><pre><span class="Keyword">func</span> <a href="#copySign%2CT%2CT"><span class="Identifier">copySign</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#SomeFloat"><span class="Identifier">SomeFloat</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> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <span class="Identifier">T</span> {.<span class="Identifier">inline</span>.}</pre></dt>
    1091. 

  1091.   <dd>
    1092. 

  1092.     
    1093. 

  1093.     Returns a value with the magnitude of <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> and the sign of <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt>; this works even if x or y are NaN, infinity or zero, all of which can carry a sign.
    1094. 

  1094. <p><strong class="examples_text">Example:</strong></p>
    1095. 

  1095. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">copySign</span><span class="Punctuation">(</span><span class="FloatNumber">10.0</span><span class="Punctuation">,</span> <span class="FloatNumber">1.0</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="FloatNumber">10.0</span>
    1096. 

  1096. <span class="Identifier">doAssert</span> <span class="Identifier">copySign</span><span class="Punctuation">(</span><span class="FloatNumber">10.0</span><span class="Punctuation">,</span> <span class="Operator">-</span><span class="FloatNumber">1.0</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="Operator">-</span><span class="FloatNumber">10.0</span>
    1097. 

  1097. <span class="Identifier">doAssert</span> <span class="Identifier">copySign</span><span class="Punctuation">(</span><span class="Operator">-</span><span class="Identifier">Inf</span><span class="Punctuation">,</span> <span class="Operator">-</span><span class="FloatNumber">0.0</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="Operator">-</span><span class="Identifier">Inf</span>
    1098. 

  1098. <span class="Identifier">doAssert</span> <span class="Identifier">copySign</span><span class="Punctuation">(</span><span class="Identifier">NaN</span><span class="Punctuation">,</span> <span class="FloatNumber">1.0</span><span class="Punctuation">)</span><span class="Operator">.</span><span class="Identifier">isNaN</span>
    1099. 

  1099. <span class="Identifier">doAssert</span> <span class="Identifier">copySign</span><span class="Punctuation">(</span><span class="FloatNumber">1.0</span><span class="Punctuation">,</span> <span class="Identifier">copySign</span><span class="Punctuation">(</span><span class="Identifier">NaN</span><span class="Punctuation">,</span> <span class="Operator">-</span><span class="FloatNumber">1.0</span><span class="Punctuation">)</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="Operator">-</span><span class="FloatNumber">1.0</span></pre>
    1100. 

  1100.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L245" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1101. 

  1101. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L245" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1102. 

  1102. 

  1103.   </dd>
    1104. 

  1104. </div>
    1105. 

  1105. 

  1106. </div>
    1107. 

  1107. <div id="cos-procs-all">
    1108. 

  1108.   <div id="cos,float32">
    1109. 

  1109.   <dt><pre><span class="Keyword">func</span> <a href="#cos%2Cfloat32"><span class="Identifier">cos</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;cosf&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span> <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>
    1110. 

  1110.                                 <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>
    1111. 

  1111.   <dd>
    1112. 

  1112.     
    1113. 

  1113.     
    1114. 

  1114.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L459" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1115. 

  1115. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L459" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1116. 

  1116. 

  1117.   </dd>
    1118. 

  1118. </div>
    1119. 

  1119. <div id="cos,float64">
    1120. 

  1120.   <dt><pre><span class="Keyword">func</span> <a href="#cos%2Cfloat64"><span class="Identifier">cos</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;cos&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span> <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>
    1121. 

  1121.                                 <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>
    1122. 

  1122.   <dd>
    1123. 

  1123.     
    1124. 

  1124.     <p>Computes the cosine of <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>.</p>
    1125. 

  1125. <p><strong>See also:</strong></p>
    1126. 

  1126. <ul class="simple"><li><a class="reference external" href="#arccos,float64">arccos func</a></li>
    1127. 

  1127. </ul>
    1128. 

  1128. 

  1129. <p><strong class="examples_text">Example:</strong></p>
    1130. 

  1130. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">cos</span><span class="Punctuation">(</span><span class="DecNumber">2</span> <span class="Operator">*</span> <span class="Identifier">PI</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="FloatNumber">1.0</span><span class="Punctuation">)</span>
    1131. 

  1131. <span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">cos</span><span class="Punctuation">(</span><span class="Identifier">degToRad</span><span class="Punctuation">(</span><span class="FloatNumber">60.0</span><span class="Punctuation">)</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="FloatNumber">0.5</span><span class="Punctuation">)</span></pre>
    1132. 

  1132.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L460" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1133. 

  1133. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L460" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1134. 

  1134. 

  1135.   </dd>
    1136. 

  1136. </div>
    1137. 

  1137. 

  1138. </div>
    1139. 

  1139. <div id="cosh-procs-all">
    1140. 

  1140.   <div id="cosh,float32">
    1141. 

  1141.   <dt><pre><span class="Keyword">func</span> <a href="#cosh%2Cfloat32"><span class="Identifier">cosh</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;coshf&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    1142. 

  1142.                                  <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>
    1143. 

  1143.   <dd>
    1144. 

  1144.     
    1145. 

  1145.     
    1146. 

  1146.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L486" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1147. 

  1147. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L486" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1148. 

  1148. 

  1149.   </dd>
    1150. 

  1150. </div>
    1151. 

  1151. <div id="cosh,float64">
    1152. 

  1152.   <dt><pre><span class="Keyword">func</span> <a href="#cosh%2Cfloat64"><span class="Identifier">cosh</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;cosh&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    1153. 

  1153.                                  <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>
    1154. 

  1154.   <dd>
    1155. 

  1155.     
    1156. 

  1156.     <p>Computes the <a class="reference external" href="https://en.wikipedia.org/wiki/Hyperbolic_function#Definitions">hyperbolic cosine</a> of <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>.</p>
    1157. 

  1157. <p><strong>See also:</strong></p>
    1158. 

  1158. <ul class="simple"><li><a class="reference external" href="#arccosh,float64">arccosh func</a></li>
    1159. 

  1159. </ul>
    1160. 

  1160. 

  1161. <p><strong class="examples_text">Example:</strong></p>
    1162. 

  1162. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">cosh</span><span class="Punctuation">(</span><span class="FloatNumber">0.0</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="FloatNumber">1.0</span><span class="Punctuation">)</span>
    1163. 

  1163. <span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">cosh</span><span class="Punctuation">(</span><span class="FloatNumber">1.0</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="FloatNumber">1.543080634815244</span><span class="Punctuation">)</span></pre>
    1164. 

  1164.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L487" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1165. 

  1165. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L487" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1166. 

  1166. 

  1167.   </dd>
    1168. 

  1168. </div>
    1169. 

  1169. 

  1170. </div>
    1171. 

  1171. <div id="cot-procs-all">
    1172. 

  1172.   <div id="cot,T">
    1173. 

  1173.   <dt><pre><span class="Keyword">func</span> <a href="#cot%2CT"><span class="Identifier">cot</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> <span class="Operator">|</span> <a href="system.html#float64"><span class="Identifier">float64</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> <span class="Identifier">T</span></pre></dt>
    1174. 

  1174.   <dd>
    1175. 

  1175.     
    1176. 

  1176.     Computes the cotangent 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">tan</span><span class="Punctuation">(</span><span class="Identifier">x</span><span class="Punctuation">)</span></span></tt>).
    1177. 

  1177.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L590" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1178. 

  1178. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L590" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1179. 

  1179. 

  1180.   </dd>
    1181. 

  1181. </div>
    1182. 

  1182. 

  1183. </div>
    1184. 

  1184. <div id="coth-procs-all">
    1185. 

  1185.   <div id="coth,T">
    1186. 

  1186.   <dt><pre><span class="Keyword">func</span> <a href="#coth%2CT"><span class="Identifier">coth</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> <span class="Operator">|</span> <a href="system.html#float64"><span class="Identifier">float64</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> <span class="Identifier">T</span></pre></dt>
    1187. 

  1187.   <dd>
    1188. 

  1188.     
    1189. 

  1189.     Computes the hyperbolic cotangent 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">tanh</span><span class="Punctuation">(</span><span class="Identifier">x</span><span class="Punctuation">)</span></span></tt>).
    1190. 

  1190.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L597" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1191. 

  1191. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L597" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1192. 

  1192. 

  1193.   </dd>
    1194. 

  1194. </div>
    1195. 

  1195. 

  1196. </div>
    1197. 

  1197. <div id="csc-procs-all">
    1198. 

  1198.   <div id="csc,T">
    1199. 

  1199.   <dt><pre><span class="Keyword">func</span> <a href="#csc%2CT"><span class="Identifier">csc</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> <span class="Operator">|</span> <a href="system.html#float64"><span class="Identifier">float64</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> <span class="Identifier">T</span></pre></dt>
    1200. 

  1200.   <dd>
    1201. 

  1201.     
    1202. 

  1202.     Computes the cosecant 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">sin</span><span class="Punctuation">(</span><span class="Identifier">x</span><span class="Punctuation">)</span></span></tt>).
    1203. 

  1203.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L594" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1204. 

  1204. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L594" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1205. 

  1205. 

  1206.   </dd>
    1207. 

  1207. </div>
    1208. 

  1208. 

  1209. </div>
    1210. 

  1210. <div id="csch-procs-all">
    1211. 

  1211.   <div id="csch,T">
    1212. 

  1212.   <dt><pre><span class="Keyword">func</span> <a href="#csch%2CT"><span class="Identifier">csch</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> <span class="Operator">|</span> <a href="system.html#float64"><span class="Identifier">float64</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> <span class="Identifier">T</span></pre></dt>
    1213. 

  1213.   <dd>
    1214. 

  1214.     
    1215. 

  1215.     Computes the hyperbolic cosecant 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">sinh</span><span class="Punctuation">(</span><span class="Identifier">x</span><span class="Punctuation">)</span></span></tt>).
    1216. 

  1216.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L601" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1217. 

  1217. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L601" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1218. 

  1218. 

  1219.   </dd>
    1220. 

  1220. </div>
    1221. 

  1221. 

  1222. </div>
    1223. 

  1223. <div id="cumprod-procs-all">
    1224. 

  1224.   <div id="cumprod,openArray[T]">
    1225. 

  1225.   <dt><pre><span class="Keyword">func</span> <a href="#cumprod%2CopenArray%5BT%5D"><span class="Identifier">cumprod</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="system.html#openArray"><span class="Identifier">openArray</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span></pre></dt>
    1226. 

  1226.   <dd>
    1227. 

  1227.     
    1228. 

  1228.     <p>Transforms <tt class="docutils literal"><span class="pre">x</span></tt> in-place (must be declared as <tt class="docutils literal"><span class="pre"><span class="Keyword">var</span></span></tt>) into its product.</p>
    1229. 

  1229. <p>See also:</p>
    1230. 

  1230. <ul class="simple"><li><a class="reference external" href="#sum,openArray[T]">prod proc</a></li>
    1231. 

  1231. <li><a class="reference external" href="#cumproded,openArray[T]">cumproded proc</a> for a version which returns cumproded sequence</li>
    1232. 

  1232. </ul>
    1233. 

  1233. 

  1234. <p><strong class="examples_text">Example:</strong></p>
    1235. 

  1235. <pre class="listing"><span class="Keyword">var</span> <span class="Identifier">a</span> <span class="Operator">=</span> <span class="Punctuation">[</span><span class="DecNumber">1</span><span class="Punctuation">,</span> <span class="DecNumber">2</span><span class="Punctuation">,</span> <span class="DecNumber">3</span><span class="Punctuation">,</span> <span class="DecNumber">4</span><span class="Punctuation">]</span>
    1236. 

  1236. <span class="Identifier">cumprod</span><span class="Punctuation">(</span><span class="Identifier">a</span><span class="Punctuation">)</span>
    1237. 

  1237. <span class="Identifier">doAssert</span> <span class="Identifier">a</span> <span class="Operator">==</span> <span class="Operator">@</span><span class="Punctuation">[</span><span class="DecNumber">1</span><span class="Punctuation">,</span> <span class="DecNumber">2</span><span class="Punctuation">,</span> <span class="DecNumber">6</span><span class="Punctuation">,</span> <span class="DecNumber">24</span><span class="Punctuation">]</span></pre>
    1238. 

  1238.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L1148" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1239. 

  1239. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L1148" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1240. 

  1240. 

  1241.   </dd>
    1242. 

  1242. </div>
    1243. 

  1243. 

  1244. </div>
    1245. 

  1245. <div id="cumproded-procs-all">
    1246. 

  1246.   <div id="cumproded,openArray[T]">
    1247. 

  1247.   <dt><pre><span class="Keyword">func</span> <a href="#cumproded%2CopenArray%5BT%5D"><span class="Identifier">cumproded</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="system.html#openArray"><span class="Identifier">openArray</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#seq"><span class="Identifier">seq</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    1248. 

  1248.   <dd>
    1249. 

  1249.     
    1250. 

  1250.     <p>Return cumulative (aka prefix) product of <tt class="docutils literal"><span class="pre">x</span></tt>.</p>
    1251. 

  1251. <p>See also:</p>
    1252. 

  1252. <ul class="simple"><li><a class="reference external" href="#prod,openArray[T]">prod proc</a></li>
    1253. 

  1253. <li><a class="reference external" href="#cumprod,openArray[T]">cumprod proc</a> for the in-place version</li>
    1254. 

  1254. </ul>
    1255. 

  1255. 

  1256. <p><strong class="examples_text">Example:</strong></p>
    1257. 

  1257. <pre class="listing"><span class="Keyword">let</span> <span class="Identifier">a</span> <span class="Operator">=</span> <span class="Punctuation">[</span><span class="DecNumber">1</span><span class="Punctuation">,</span> <span class="DecNumber">2</span><span class="Punctuation">,</span> <span class="DecNumber">3</span><span class="Punctuation">,</span> <span class="DecNumber">4</span><span class="Punctuation">]</span>
    1258. 

  1258. <span class="Identifier">doAssert</span> <span class="Identifier">cumproded</span><span class="Punctuation">(</span><span class="Identifier">a</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="Operator">@</span><span class="Punctuation">[</span><span class="DecNumber">1</span><span class="Punctuation">,</span> <span class="DecNumber">2</span><span class="Punctuation">,</span> <span class="DecNumber">6</span><span class="Punctuation">,</span> <span class="DecNumber">24</span><span class="Punctuation">]</span></pre>
    1259. 

  1259.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L1162" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1260. 

  1260. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L1162" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1261. 

  1261. 

  1262.   </dd>
    1263. 

  1263. </div>
    1264. 

  1264. 

  1265. </div>
    1266. 

  1266. <div id="cumsum-procs-all">
    1267. 

  1267.   <div id="cumsum,openArray[T]">
    1268. 

  1268.   <dt><pre><span class="Keyword">func</span> <a href="#cumsum%2CopenArray%5BT%5D"><span class="Identifier">cumsum</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="system.html#openArray"><span class="Identifier">openArray</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span></pre></dt>
    1269. 

  1269.   <dd>
    1270. 

  1270.     
    1271. 

  1271.     <p>Transforms <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> in-place (must be declared as <tt class="docutils literal"><span class="pre"><span class="Keyword">var</span></span></tt>) into its cumulative (aka prefix) summation.</p>
    1272. 

  1272. <p><strong>See also:</strong></p>
    1273. 

  1273. <ul class="simple"><li><a class="reference external" href="#sum,openArray[T]">sum func</a></li>
    1274. 

  1274. <li><a class="reference external" href="#cumsummed,openArray[T]">cumsummed func</a> for a version which returns a cumsummed sequence</li>
    1275. 

  1275. </ul>
    1276. 

  1276. 

  1277. <p><strong class="examples_text">Example:</strong></p>
    1278. 

  1278. <pre class="listing"><span class="Keyword">var</span> <span class="Identifier">a</span> <span class="Operator">=</span> <span class="Punctuation">[</span><span class="DecNumber">1</span><span class="Punctuation">,</span> <span class="DecNumber">2</span><span class="Punctuation">,</span> <span class="DecNumber">3</span><span class="Punctuation">,</span> <span class="DecNumber">4</span><span class="Punctuation">]</span>
    1279. 

  1279. <span class="Identifier">cumsum</span><span class="Punctuation">(</span><span class="Identifier">a</span><span class="Punctuation">)</span>
    1280. 

  1280. <span class="Identifier">doAssert</span> <span class="Identifier">a</span> <span class="Operator">==</span> <span class="Operator">@</span><span class="Punctuation">[</span><span class="DecNumber">1</span><span class="Punctuation">,</span> <span class="DecNumber">3</span><span class="Punctuation">,</span> <span class="DecNumber">6</span><span class="Punctuation">,</span> <span class="DecNumber">10</span><span class="Punctuation">]</span></pre>
    1281. 

  1281.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L1197" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1282. 

  1282. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L1197" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1283. 

  1283. 

  1284.   </dd>
    1285. 

  1285. </div>
    1286. 

  1286. 

  1287. </div>
    1288. 

  1288. <div id="cumsummed-procs-all">
    1289. 

  1289.   <div id="cumsummed,openArray[T]">
    1290. 

  1290.   <dt><pre><span class="Keyword">func</span> <a href="#cumsummed%2CopenArray%5BT%5D"><span class="Identifier">cumsummed</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="system.html#openArray"><span class="Identifier">openArray</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#seq"><span class="Identifier">seq</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    1291. 

  1291.   <dd>
    1292. 

  1292.     
    1293. 

  1293.     <p>Returns the cumulative (aka prefix) summation of <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>.</p>
    1294. 

  1294. <p>If <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> is empty, <tt class="docutils literal"><span class="pre"><span class="Operator">@</span><span class="Punctuation">[</span><span class="Punctuation">]</span></span></tt> is returned.</p>
    1295. 

  1295. <p><strong>See also:</strong></p>
    1296. 

  1296. <ul class="simple"><li><a class="reference external" href="#sum,openArray[T]">sum func</a></li>
    1297. 

  1297. <li><a class="reference external" href="#cumsum,openArray[T]">cumsum func</a> for the in-place version</li>
    1298. 

  1298. </ul>
    1299. 

  1299. 

  1300. <p><strong class="examples_text">Example:</strong></p>
    1301. 

  1301. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">cumsummed</span><span class="Punctuation">(</span><span class="Punctuation">[</span><span class="DecNumber">1</span><span class="Punctuation">,</span> <span class="DecNumber">2</span><span class="Punctuation">,</span> <span class="DecNumber">3</span><span class="Punctuation">,</span> <span class="DecNumber">4</span><span class="Punctuation">]</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="Operator">@</span><span class="Punctuation">[</span><span class="DecNumber">1</span><span class="Punctuation">,</span> <span class="DecNumber">3</span><span class="Punctuation">,</span> <span class="DecNumber">6</span><span class="Punctuation">,</span> <span class="DecNumber">10</span><span class="Punctuation">]</span></pre>
    1302. 

  1302.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L1179" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1303. 

  1303. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L1179" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1304. 

  1304. 

  1305.   </dd>
    1306. 

  1306. </div>
    1307. 

  1307. 

  1308. </div>
    1309. 

  1309. <div id="degToRad-procs-all">
    1310. 

  1310.   <div id="degToRad,T">
    1311. 

  1311.   <dt><pre><span class="Keyword">func</span> <a href="#degToRad%2CT"><span class="Identifier">degToRad</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> <span class="Operator">|</span> <a href="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">]</span><span class="Other">(</span><span class="Identifier">d</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <span class="Identifier">T</span> {.<span class="Identifier">inline</span>.}</pre></dt>
    1312. 

  1312.   <dd>
    1313. 

  1313.     
    1314. 

  1314.     <p>Converts from degrees to radians.</p>
    1315. 

  1315. <p><strong>See also:</strong></p>
    1316. 

  1316. <ul class="simple"><li><a class="reference external" href="#radToDeg,T">radToDeg func</a></li>
    1317. 

  1317. </ul>
    1318. 

  1318. 

  1319. <p><strong class="examples_text">Example:</strong></p>
    1320. 

  1320. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">degToRad</span><span class="Punctuation">(</span><span class="FloatNumber">180.0</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="Identifier">PI</span><span class="Punctuation">)</span></pre>
    1321. 

  1321.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L1081" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1322. 

  1322. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L1081" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1323. 

  1323. 

  1324.   </dd>
    1325. 

  1325. </div>
    1326. 

  1326. 

  1327. </div>
    1328. 

  1328. <div id="divmod-procs-all">
    1329. 

  1329.   <div id="divmod,T,T">
    1330. 

  1330.   <dt><pre><span class="Keyword">func</span> <a href="#divmod%2CT%2CT"><span class="Identifier">divmod</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> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <span class="Other">(</span><span class="Identifier">T</span><span class="Other">,</span> <span class="Identifier">T</span><span class="Other">)</span> {.<span class="Identifier">inline</span>.}</pre></dt>
    1331. 

  1331.   <dd>
    1332. 

  1332.     
    1333. 

  1333.     Specialized instructions for computing both division and modulus. Return structure is: (quotient, remainder)
    1334. 

  1334. <p><strong class="examples_text">Example:</strong></p>
    1335. 

  1335. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">divmod</span><span class="Punctuation">(</span><span class="DecNumber">5</span><span class="Punctuation">,</span> <span class="DecNumber">2</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="Punctuation">(</span><span class="DecNumber">2</span><span class="Punctuation">,</span> <span class="DecNumber">1</span><span class="Punctuation">)</span>
    1336. 

  1336. <span class="Identifier">doAssert</span> <span class="Identifier">divmod</span><span class="Punctuation">(</span><span class="DecNumber">5</span><span class="Punctuation">,</span> <span class="Operator">-</span><span class="DecNumber">3</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="Punctuation">(</span><span class="Operator">-</span><span class="DecNumber">1</span><span class="Punctuation">,</span> <span class="DecNumber">2</span><span class="Punctuation">)</span></pre>
    1337. 

  1337.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L98" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1338. 

  1338. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L98" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1339. 

  1339. 

  1340.   </dd>
    1341. 

  1341. </div>
    1342. 

  1342. 

  1343. </div>
    1344. 

  1344. <div id="erf-procs-all">
    1345. 

  1345.   <div id="erf,float32">
    1346. 

  1346.   <dt><pre><span class="Keyword">func</span> <a href="#erf%2Cfloat32"><span class="Identifier">erf</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;erff&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span> <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>
    1347. 

  1347.                                 <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>
    1348. 

  1348.   <dd>
    1349. 

  1349.     
    1350. 

  1350.     
    1351. 

  1351.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L644" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1352. 

  1352. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L644" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1353. 

  1353. 

  1354.   </dd>
    1355. 

  1355. </div>
    1356. 

  1356. <div id="erf,float64">
    1357. 

  1357.   <dt><pre><span class="Keyword">func</span> <a href="#erf%2Cfloat64"><span class="Identifier">erf</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;erf&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span> <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>
    1358. 

  1358.                                 <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>
    1359. 

  1359.   <dd>
    1360. 

  1360.     
    1361. 

  1361.     <p>Computes the <a class="reference external" href="https://en.wikipedia.org/wiki/Error_function">error function</a> for <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>.</p>
    1362. 

  1362. <p><strong>Note:</strong> Not available for the JS backend.</p>
    1363. 

  1363. 

  1364.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L645" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1365. 

  1365. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L645" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1366. 

  1366. 

  1367.   </dd>
    1368. 

  1368. </div>
    1369. 

  1369. 

  1370. </div>
    1371. 

  1371. <div id="erfc-procs-all">
    1372. 

  1372.   <div id="erfc,float32">
    1373. 

  1373.   <dt><pre><span class="Keyword">func</span> <a href="#erfc%2Cfloat32"><span class="Identifier">erfc</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;erfcf&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    1374. 

  1374.                                  <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>
    1375. 

  1375.   <dd>
    1376. 

  1376.     
    1377. 

  1377.     
    1378. 

  1378.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L649" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1379. 

  1379. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L649" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1380. 

  1380. 

  1381.   </dd>
    1382. 

  1382. </div>
    1383. 

  1383. <div id="erfc,float64">
    1384. 

  1384.   <dt><pre><span class="Keyword">func</span> <a href="#erfc%2Cfloat64"><span class="Identifier">erfc</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;erfc&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    1385. 

  1385.                                  <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>
    1386. 

  1386.   <dd>
    1387. 

  1387.     
    1388. 

  1388.     <p>Computes the <a class="reference external" href="https://en.wikipedia.org/wiki/Error_function#Complementary_error_function">complementary error function</a> for <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>.</p>
    1389. 

  1389. <p><strong>Note:</strong> Not available for the JS backend.</p>
    1390. 

  1390. 

  1391.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L650" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1392. 

  1392. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L650" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1393. 

  1393. 

  1394.   </dd>
    1395. 

  1395. </div>
    1396. 

  1396. 

  1397. </div>
    1398. 

  1398. <div id="euclDiv-procs-all">
    1399. 

  1399.   <div id="euclDiv,T,T">
    1400. 

  1400.   <dt><pre><span class="Keyword">func</span> <a href="#euclDiv%2CT%2CT"><span class="Identifier">euclDiv</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> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <span class="Identifier">T</span></pre></dt>
    1401. 

  1401.   <dd>
    1402. 

  1402.     
    1403. 

  1403.     Returns euclidean division of <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>.
    1404. 

  1404. <p><strong class="examples_text">Example:</strong></p>
    1405. 

  1405. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">euclDiv</span><span class="Punctuation">(</span><span class="DecNumber">13</span><span class="Punctuation">,</span> <span class="DecNumber">3</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="DecNumber">4</span>
    1406. 

  1406. <span class="Identifier">doAssert</span> <span class="Identifier">euclDiv</span><span class="Punctuation">(</span><span class="Operator">-</span><span class="DecNumber">13</span><span class="Punctuation">,</span> <span class="DecNumber">3</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="Operator">-</span><span class="DecNumber">5</span>
    1407. 

  1407. <span class="Identifier">doAssert</span> <span class="Identifier">euclDiv</span><span class="Punctuation">(</span><span class="DecNumber">13</span><span class="Punctuation">,</span> <span class="Operator">-</span><span class="DecNumber">3</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="Operator">-</span><span class="DecNumber">4</span>
    1408. 

  1408. <span class="Identifier">doAssert</span> <span class="Identifier">euclDiv</span><span class="Punctuation">(</span><span class="Operator">-</span><span class="DecNumber">13</span><span class="Punctuation">,</span> <span class="Operator">-</span><span class="DecNumber">3</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="DecNumber">5</span></pre>
    1409. 

  1409.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L897" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1410. 

  1410. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L897" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1411. 

  1411. 

  1412.   </dd>
    1413. 

  1413. </div>
    1414. 

  1414. 

  1415. </div>
    1416. 

  1416. <div id="euclMod-procs-all">
    1417. 

  1417.   <div id="euclMod,T,T">
    1418. 

  1418.   <dt><pre><span class="Keyword">func</span> <a href="#euclMod%2CT%2CT"><span class="Identifier">euclMod</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#SomeNumber"><span class="Identifier">SomeNumber</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> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <span class="Identifier">T</span></pre></dt>
    1419. 

  1419.   <dd>
    1420. 

  1420.     
    1421. 

  1421.     Returns euclidean modulo of <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>. <tt class="docutils literal"><span class="pre"><span class="Identifier">euclMod</span><span class="Punctuation">(</span><span class="Identifier">x</span><span class="Punctuation">,</span> <span class="Identifier">y</span><span class="Punctuation">)</span></span></tt> is non-negative.
    1422. 

  1422. <p><strong class="examples_text">Example:</strong></p>
    1423. 

  1423. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">euclMod</span><span class="Punctuation">(</span><span class="DecNumber">13</span><span class="Punctuation">,</span> <span class="DecNumber">3</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="DecNumber">1</span>
    1424. 

  1424. <span class="Identifier">doAssert</span> <span class="Identifier">euclMod</span><span class="Punctuation">(</span><span class="Operator">-</span><span class="DecNumber">13</span><span class="Punctuation">,</span> <span class="DecNumber">3</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="DecNumber">2</span>
    1425. 

  1425. <span class="Identifier">doAssert</span> <span class="Identifier">euclMod</span><span class="Punctuation">(</span><span class="DecNumber">13</span><span class="Punctuation">,</span> <span class="Operator">-</span><span class="DecNumber">3</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="DecNumber">1</span>
    1426. 

  1426. <span class="Identifier">doAssert</span> <span class="Identifier">euclMod</span><span class="Punctuation">(</span><span class="Operator">-</span><span class="DecNumber">13</span><span class="Punctuation">,</span> <span class="Operator">-</span><span class="DecNumber">3</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="DecNumber">2</span></pre>
    1427. 

  1427.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L912" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1428. 

  1428. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L912" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1429. 

  1429. 

  1430.   </dd>
    1431. 

  1431. </div>
    1432. 

  1432. 

  1433. </div>
    1434. 

  1434. <div id="exp-procs-all">
    1435. 

  1435.   <div id="exp,float32">
    1436. 

  1436.   <dt><pre><span class="Keyword">func</span> <a href="#exp%2Cfloat32"><span class="Identifier">exp</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;expf&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span> <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>
    1437. 

  1437.                                 <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>
    1438. 

  1438.   <dd>
    1439. 

  1439.     
    1440. 

  1440.     
    1441. 

  1441.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L440" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1442. 

  1442. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L440" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1443. 

  1443. 

  1444.   </dd>
    1445. 

  1445. </div>
    1446. 

  1446. <div id="exp,float64">
    1447. 

  1447.   <dt><pre><span class="Keyword">func</span> <a href="#exp%2Cfloat64"><span class="Identifier">exp</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;exp&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span> <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>
    1448. 

  1448.                                 <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>
    1449. 

  1449.   <dd>
    1450. 

  1450.     
    1451. 

  1451.     <p>Computes the exponential function of <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> (<tt class="docutils literal"><span class="pre"><span class="Identifier">e</span><span class="Operator">^</span><span class="Identifier">x</span></span></tt>).</p>
    1452. 

  1452. <p><strong>See also:</strong></p>
    1453. 

  1453. <ul class="simple"><li><a class="reference external" href="#ln,float64">ln func</a></li>
    1454. 

  1454. </ul>
    1455. 

  1455. 

  1456. <p><strong class="examples_text">Example:</strong></p>
    1457. 

  1457. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">exp</span><span class="Punctuation">(</span><span class="FloatNumber">1.0</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="Identifier">E</span><span class="Punctuation">)</span>
    1458. 

  1458. <span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">ln</span><span class="Punctuation">(</span><span class="Identifier">exp</span><span class="Punctuation">(</span><span class="FloatNumber">4.0</span><span class="Punctuation">)</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="FloatNumber">4.0</span><span class="Punctuation">)</span>
    1459. 

  1459. <span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">exp</span><span class="Punctuation">(</span><span class="FloatNumber">0.0</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="FloatNumber">1.0</span><span class="Punctuation">)</span></pre>
    1460. 

  1460.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L441" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1461. 

  1461. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L441" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1462. 

  1462. 

  1463.   </dd>
    1464. 

  1464. </div>
    1465. 

  1465. 

  1466. </div>
    1467. 

  1467. <div id="fac-procs-all">
    1468. 

  1468.   <div id="fac,int">
    1469. 

  1469.   <dt><pre><span class="Keyword">func</span> <a href="#fac%2Cint"><span class="Identifier">fac</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="Other">:</span> <a href="system.html#int"><span class="Identifier">int</span></a> {.<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>
    1470. 

  1470.   <dd>
    1471. 

  1471.     
    1472. 

  1472.     <p>Computes the <a class="reference external" href="https://en.wikipedia.org/wiki/Factorial">factorial</a> of a non-negative integer <tt class="docutils literal"><span class="pre"><span class="Identifier">n</span></span></tt>.</p>
    1473. 

  1473. <p><strong>See also:</strong></p>
    1474. 

  1474. <ul class="simple"><li><a class="reference external" href="#prod,openArray[T]">prod func</a></li>
    1475. 

  1475. </ul>
    1476. 

  1476. 

  1477. <p><strong class="examples_text">Example:</strong></p>
    1478. 

  1478. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">fac</span><span class="Punctuation">(</span><span class="DecNumber">0</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="DecNumber">1</span>
    1479. 

  1479. <span class="Identifier">doAssert</span> <span class="Identifier">fac</span><span class="Punctuation">(</span><span class="DecNumber">4</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="DecNumber">24</span>
    1480. 

  1480. <span class="Identifier">doAssert</span> <span class="Identifier">fac</span><span class="Punctuation">(</span><span class="DecNumber">10</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="DecNumber">3628800</span></pre>
    1481. 

  1481.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L135" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1482. 

  1482. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L135" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1483. 

  1483. 

  1484.   </dd>
    1485. 

  1485. </div>
    1486. 

  1486. 

  1487. </div>
    1488. 

  1488. <div id="floor-procs-all">
    1489. 

  1489.   <div id="floor,float32">
    1490. 

  1490.   <dt><pre><span class="Keyword">func</span> <a href="#floor%2Cfloat32"><span class="Identifier">floor</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;floorf&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    1491. 

  1491.                                   <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>
    1492. 

  1492.   <dd>
    1493. 

  1493.     
    1494. 

  1494.     
    1495. 

  1495.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L675" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1496. 

  1496. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L675" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1497. 

  1497. 

  1498.   </dd>
    1499. 

  1499. </div>
    1500. 

  1500. <div id="floor,float64">
    1501. 

  1501.   <dt><pre><span class="Keyword">func</span> <a href="#floor%2Cfloat64"><span class="Identifier">floor</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;floor&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    1502. 

  1502.                                   <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>
    1503. 

  1503.   <dd>
    1504. 

  1504.     
    1505. 

  1505.     <p>Computes the floor function (i.e. the largest integer not greater than <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>).</p>
    1506. 

  1506. <p><strong>See also:</strong></p>
    1507. 

  1507. <ul class="simple"><li><a class="reference external" href="#ceil,float64">ceil func</a></li>
    1508. 

  1508. <li><a class="reference external" href="#round,float64">round func</a></li>
    1509. 

  1509. <li><a class="reference external" href="#trunc,float64">trunc func</a></li>
    1510. 

  1510. </ul>
    1511. 

  1511. 

  1512. <p><strong class="examples_text">Example:</strong></p>
    1513. 

  1513. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">floor</span><span class="Punctuation">(</span><span class="FloatNumber">2.1</span><span class="Punctuation">)</span>  <span class="Operator">==</span> <span class="FloatNumber">2.0</span>
    1514. 

  1514. <span class="Identifier">doAssert</span> <span class="Identifier">floor</span><span class="Punctuation">(</span><span class="FloatNumber">2.9</span><span class="Punctuation">)</span>  <span class="Operator">==</span> <span class="FloatNumber">2.0</span>
    1515. 

  1515. <span class="Identifier">doAssert</span> <span class="Identifier">floor</span><span class="Punctuation">(</span><span class="Operator">-</span><span class="FloatNumber">3.5</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="Operator">-</span><span class="FloatNumber">4.0</span></pre>
    1516. 

  1516.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L676" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1517. 

  1517. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L676" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1518. 

  1518. 

  1519.   </dd>
    1520. 

  1520. </div>
    1521. 

  1521. 

  1522. </div>
    1523. 

  1523. <div id="floorDiv-procs-all">
    1524. 

  1524.   <div id="floorDiv,T,T">
    1525. 

  1525.   <dt><pre><span class="Keyword">func</span> <a href="#floorDiv%2CT%2CT"><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> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <span class="Identifier">T</span></pre></dt>
    1526. 

  1526.   <dd>
    1527. 

  1527.     
    1528. 

  1528.     <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>.</p>
    1529. 

  1529. <p>This is different from the <a class="reference external" href="system.html#div,int,int">system.div</a> 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 <tt class="docutils literal"><span class="pre"><span class="DecNumber">0</span></span></tt> and <tt class="docutils literal"><span class="pre"><span class="Identifier">floorDiv</span></span></tt> rounds down.</p>
    1530. 

  1530. <p><strong>See also:</strong></p>
    1531. 

  1531. <ul class="simple"><li><a class="reference external" href="system.html#div,int,int">system.div proc</a> for integer division</li>
    1532. 

  1532. <li><a class="reference external" href="#floorMod,T,T">floorMod func</a> for Python-like (<tt class="docutils literal"><span class="pre"><span class="Operator">%</span></span></tt> operator) behavior</li>
    1533. 

  1533. </ul>
    1534. 

  1534. 

  1535. <p><strong class="examples_text">Example:</strong></p>
    1536. 

  1536. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">floorDiv</span><span class="Punctuation">(</span> <span class="DecNumber">13</span><span class="Punctuation">,</span>  <span class="DecNumber">3</span><span class="Punctuation">)</span> <span class="Operator">==</span>  <span class="DecNumber">4</span>
    1537. 

  1537. <span class="Identifier">doAssert</span> <span class="Identifier">floorDiv</span><span class="Punctuation">(</span><span class="Operator">-</span><span class="DecNumber">13</span><span class="Punctuation">,</span>  <span class="DecNumber">3</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="Operator">-</span><span class="DecNumber">5</span>
    1538. 

  1538. <span class="Identifier">doAssert</span> <span class="Identifier">floorDiv</span><span class="Punctuation">(</span> <span class="DecNumber">13</span><span class="Punctuation">,</span> <span class="Operator">-</span><span class="DecNumber">3</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="Operator">-</span><span class="DecNumber">5</span>
    1539. 

  1539. <span class="Identifier">doAssert</span> <span class="Identifier">floorDiv</span><span class="Punctuation">(</span><span class="Operator">-</span><span class="DecNumber">13</span><span class="Punctuation">,</span> <span class="Operator">-</span><span class="DecNumber">3</span><span class="Punctuation">)</span> <span class="Operator">==</span>  <span class="DecNumber">4</span></pre>
    1540. 

  1540.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L860" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1541. 

  1541. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L860" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1542. 

  1542. 

  1543.   </dd>
    1544. 

  1544. </div>
    1545. 

  1545. 

  1546. </div>
    1547. 

  1547. <div id="floorMod-procs-all">
    1548. 

  1548.   <div id="floorMod,T,T">
    1549. 

  1549.   <dt><pre><span class="Keyword">func</span> <a href="#floorMod%2CT%2CT"><span class="Identifier">floorMod</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#SomeNumber"><span class="Identifier">SomeNumber</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> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <span class="Identifier">T</span></pre></dt>
    1550. 

  1550.   <dd>
    1551. 

  1551.     
    1552. 

  1552.     <p>Floor modulo is conceptually defined as <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span> <span class="Operator">-</span> <span class="Punctuation">(</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 class="Punctuation">)</span></span></tt>.</p>
    1553. 

  1553. <p>This func behaves the same as the <tt class="docutils literal"><span class="pre"><span class="Operator">%</span></span></tt> operator in Python.</p>
    1554. 

  1554. <p><strong>See also:</strong></p>
    1555. 

  1555. <ul class="simple"><li><a class="reference external" href="#mod,float64,float64">mod func</a></li>
    1556. 

  1556. <li><a class="reference external" href="#floorDiv,T,T">floorDiv func</a></li>
    1557. 

  1557. </ul>
    1558. 

  1558. 

  1559. <p><strong class="examples_text">Example:</strong></p>
    1560. 

  1560. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">floorMod</span><span class="Punctuation">(</span> <span class="DecNumber">13</span><span class="Punctuation">,</span>  <span class="DecNumber">3</span><span class="Punctuation">)</span> <span class="Operator">==</span>  <span class="DecNumber">1</span>
    1561. 

  1561. <span class="Identifier">doAssert</span> <span class="Identifier">floorMod</span><span class="Punctuation">(</span><span class="Operator">-</span><span class="DecNumber">13</span><span class="Punctuation">,</span>  <span class="DecNumber">3</span><span class="Punctuation">)</span> <span class="Operator">==</span>  <span class="DecNumber">2</span>
    1562. 

  1562. <span class="Identifier">doAssert</span> <span class="Identifier">floorMod</span><span class="Punctuation">(</span> <span class="DecNumber">13</span><span class="Punctuation">,</span> <span class="Operator">-</span><span class="DecNumber">3</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="Operator">-</span><span class="DecNumber">2</span>
    1563. 

  1563. <span class="Identifier">doAssert</span> <span class="Identifier">floorMod</span><span class="Punctuation">(</span><span class="Operator">-</span><span class="DecNumber">13</span><span class="Punctuation">,</span> <span class="Operator">-</span><span class="DecNumber">3</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="Operator">-</span><span class="DecNumber">1</span></pre>
    1564. 

  1564.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L880" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1565. 

  1565. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L880" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1566. 

  1566. 

  1567.   </dd>
    1568. 

  1568. </div>
    1569. 

  1569. 

  1570. </div>
    1571. 

  1571. <div id="frexp-procs-all">
    1572. 

  1572.   <div id="frexp,T">
    1573. 

  1573.   <dt><pre><span class="Keyword">func</span> <a href="#frexp%2CT"><span class="Identifier">frexp</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> <span class="Operator">|</span> <a href="system.html#float64"><span class="Identifier">float64</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> <span class="Keyword">tuple</span><span class="Other">[</span><span class="Identifier">frac</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">,</span> <span class="Identifier">exp</span><span class="Other">:</span> <a href="system.html#int"><span class="Identifier">int</span></a><span class="Other">]</span> {.<span class="Identifier">inline</span>.}</pre></dt>
    1574. 

  1574.   <dd>
    1575. 

  1575.     
    1576. 

  1576.     Splits <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> into a normalized fraction <tt class="docutils literal"><span class="pre"><span class="Identifier">frac</span></span></tt> and an integral power of 2 <tt class="docutils literal"><span class="pre"><span class="Identifier">exp</span></span></tt>, such that <tt class="docutils literal"><span class="pre"><span class="Identifier">abs</span><span class="Punctuation">(</span><span class="Identifier">frac</span><span class="Punctuation">)</span> <span class="Keyword">in</span> <span class="FloatNumber">0.5</span><span class="Operator">..&lt;</span><span class="DecNumber">1</span></span></tt> and <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span> <span class="Operator">==</span> <span class="Identifier">frac</span> <span class="Operator">*</span> <span class="DecNumber">2</span> <span class="Operator">^</span> <span class="Identifier">exp</span></span></tt>, except for special cases shown below.
    1577. 

  1577. <p><strong class="examples_text">Example:</strong></p>
    1578. 

  1578. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">frexp</span><span class="Punctuation">(</span><span class="FloatNumber">8.0</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="Punctuation">(</span><span class="FloatNumber">0.5</span><span class="Punctuation">,</span> <span class="DecNumber">4</span><span class="Punctuation">)</span>
    1579. 

  1579. <span class="Identifier">doAssert</span> <span class="Identifier">frexp</span><span class="Punctuation">(</span><span class="Operator">-</span><span class="FloatNumber">8.0</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="Punctuation">(</span><span class="Operator">-</span><span class="FloatNumber">0.5</span><span class="Punctuation">,</span> <span class="DecNumber">4</span><span class="Punctuation">)</span>
    1580. 

  1580. <span class="Identifier">doAssert</span> <span class="Identifier">frexp</span><span class="Punctuation">(</span><span class="FloatNumber">0.0</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="Punctuation">(</span><span class="FloatNumber">0.0</span><span class="Punctuation">,</span> <span class="DecNumber">0</span><span class="Punctuation">)</span>
    1581. 

  1581. 

  1582. <span class="Comment"># special cases:</span>
    1583. 

  1583. <span class="Keyword">when</span> <span class="Identifier">sizeof</span><span class="Punctuation">(</span><span class="Identifier">int</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="DecNumber">8</span><span class="Punctuation">:</span>
    1584. 

  1584.   <span class="Identifier">doAssert</span> <span class="Identifier">frexp</span><span class="Punctuation">(</span><span class="Operator">-</span><span class="FloatNumber">0.0</span><span class="Punctuation">)</span><span class="Operator">.</span><span class="Identifier">frac</span><span class="Operator">.</span><span class="Identifier">signbit</span> <span class="Comment"># signbit preserved for +-0</span>
    1585. 

  1585.   <span class="Identifier">doAssert</span> <span class="Identifier">frexp</span><span class="Punctuation">(</span><span class="Identifier">Inf</span><span class="Punctuation">)</span><span class="Operator">.</span><span class="Identifier">frac</span> <span class="Operator">==</span> <span class="Identifier">Inf</span> <span class="Comment"># +- Inf preserved</span>
    1586. 

  1586.   <span class="Identifier">doAssert</span> <span class="Identifier">frexp</span><span class="Punctuation">(</span><span class="Identifier">NaN</span><span class="Punctuation">)</span><span class="Operator">.</span><span class="Identifier">frac</span><span class="Operator">.</span><span class="Identifier">isNaN</span></pre>
    1587. 

  1587.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L977" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1588. 

  1588. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L977" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1589. 

  1589. 

  1590.   </dd>
    1591. 

  1591. </div>
    1592. 

  1592. <div id="frexp,T,int">
    1593. 

  1593.   <dt><pre><span class="Keyword">func</span> <a href="#frexp%2CT%2Cint"><span class="Identifier">frexp</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> <span class="Operator">|</span> <a href="system.html#float64"><span class="Identifier">float64</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="Identifier">exponent</span><span class="Other">:</span> <span class="Keyword">var</span> <a href="system.html#int"><span class="Identifier">int</span></a><span class="Other">)</span><span class="Other">:</span> <span class="Identifier">T</span> {.<span class="Identifier">inline</span>.}</pre></dt>
    1594. 

  1594.   <dd>
    1595. 

  1595.     
    1596. 

  1596.     Overload of <tt class="docutils literal"><span class="pre"><span class="Identifier">frexp</span></span></tt> that calls <tt class="docutils literal"><span class="pre"><span class="Punctuation">(</span><span class="Identifier">result</span><span class="Punctuation">,</span> <span class="Identifier">exponent</span><span class="Punctuation">)</span> <span class="Operator">=</span> <span class="Identifier">frexp</span><span class="Punctuation">(</span><span class="Identifier">x</span><span class="Punctuation">)</span></span></tt>.
    1597. 

  1597. <p><strong class="examples_text">Example:</strong></p>
    1598. 

  1598. <pre class="listing"><span class="Keyword">var</span> <span class="Identifier">x</span><span class="Punctuation">:</span> <span class="Identifier">int</span>
    1599. 

  1599. <span class="Identifier">doAssert</span> <span class="Identifier">frexp</span><span class="Punctuation">(</span><span class="FloatNumber">5.0</span><span class="Punctuation">,</span> <span class="Identifier">x</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="FloatNumber">0.625</span>
    1600. 

  1600. <span class="Identifier">doAssert</span> <span class="Identifier">x</span> <span class="Operator">==</span> <span class="DecNumber">3</span></pre>
    1601. 

  1601.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L1019" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1602. 

  1602. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L1019" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1603. 

  1603. 

  1604.   </dd>
    1605. 

  1605. </div>
    1606. 

  1606. 

  1607. </div>
    1608. 

  1608. <div id="gamma-procs-all">
    1609. 

  1609.   <div id="gamma,float32">
    1610. 

  1610.   <dt><pre><span class="Keyword">func</span> <a href="#gamma%2Cfloat32"><span class="Identifier">gamma</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;tgammaf&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    1611. 

  1611.                                   <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>
    1612. 

  1612.   <dd>
    1613. 

  1613.     
    1614. 

  1614.     
    1615. 

  1615.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L654" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1616. 

  1616. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L654" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1617. 

  1617. 

  1618.   </dd>
    1619. 

  1619. </div>
    1620. 

  1620. <div id="gamma,float64">
    1621. 

  1621.   <dt><pre><span class="Keyword">func</span> <a href="#gamma%2Cfloat64"><span class="Identifier">gamma</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;tgamma&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    1622. 

  1622.                                   <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>
    1623. 

  1623.   <dd>
    1624. 

  1624.     
    1625. 

  1625.     <p>Computes the <a class="reference external" href="https://en.wikipedia.org/wiki/Gamma_function">gamma function</a> for <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>.</p>
    1626. 

  1626. <p><strong>Note:</strong> Not available for the JS backend.</p>
    1627. 

  1627. <p><strong>See also:</strong></p>
    1628. 

  1628. <ul class="simple"><li><a class="reference external" href="#lgamma,float64">lgamma func</a> for the natural logarithm of the gamma function</li>
    1629. 

  1629. </ul>
    1630. 

  1630. 

  1631. <p><strong class="examples_text">Example:</strong></p>
    1632. 

  1632. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">gamma</span><span class="Punctuation">(</span><span class="FloatNumber">1.0</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="FloatNumber">1.0</span><span class="Punctuation">)</span>
    1633. 

  1633. <span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">gamma</span><span class="Punctuation">(</span><span class="FloatNumber">4.0</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="FloatNumber">6.0</span><span class="Punctuation">)</span>
    1634. 

  1634. <span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">gamma</span><span class="Punctuation">(</span><span class="FloatNumber">11.0</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="FloatNumber">3628800.0</span><span class="Punctuation">)</span></pre>
    1635. 

  1635.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L655" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1636. 

  1636. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L655" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1637. 

  1637. 

  1638.   </dd>
    1639. 

  1639. </div>
    1640. 

  1640. 

  1641. </div>
    1642. 

  1642. <div id="gcd-procs-all">
    1643. 

  1643.   <div id="gcd,SomeInteger,SomeInteger">
    1644. 

  1644.   <dt><pre><span class="Keyword">func</span> <a href="#gcd%2CSomeInteger%2CSomeInteger"><span class="Identifier">gcd</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="system.html#SomeInteger"><span class="Identifier">SomeInteger</span></a><span class="Other">)</span><span class="Other">:</span> <span class="Identifier">SomeInteger</span></pre></dt>
    1645. 

  1645.   <dd>
    1646. 

  1646.     
    1647. 

  1647.     <p>Computes the greatest common (positive) divisor of <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> and <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt>, using the binary GCD (aka Stein's) algorithm.</p>
    1648. 

  1648. <p><strong>See also:</strong></p>
    1649. 

  1649. <ul class="simple"><li><a class="reference external" href="#gcd,T,T">gcd func</a> for a float version</li>
    1650. 

  1650. <li><a class="reference external" href="#lcm,T,T">lcm func</a></li>
    1651. 

  1651. </ul>
    1652. 

  1652. 

  1653. <p><strong class="examples_text">Example:</strong></p>
    1654. 

  1654. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">gcd</span><span class="Punctuation">(</span><span class="DecNumber">12</span><span class="Punctuation">,</span> <span class="DecNumber">8</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="DecNumber">4</span>
    1655. 

  1655. <span class="Identifier">doAssert</span> <span class="Identifier">gcd</span><span class="Punctuation">(</span><span class="DecNumber">17</span><span class="Punctuation">,</span> <span class="DecNumber">63</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="DecNumber">1</span></pre>
    1656. 

  1656.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L1307" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1657. 

  1657. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L1307" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1658. 

  1658. 

  1659.   </dd>
    1660. 

  1660. </div>
    1661. 

  1661. <div id="gcd,T,T">
    1662. 

  1662.   <dt><pre><span class="Keyword">func</span> <a href="#gcd%2CT%2CT"><span class="Identifier">gcd</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> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <span class="Identifier">T</span></pre></dt>
    1663. 

  1663.   <dd>
    1664. 

  1664.     
    1665. 

  1665.     <p>Computes the greatest common (positive) divisor of <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> and <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt>.</p>
    1666. 

  1666. <p>Note that for floats, the result cannot always be interpreted as &quot;greatest decimal <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt> such that <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span><span class="Operator">*</span><span class="Identifier">N</span> <span class="Operator">==</span> <span class="Identifier">x</span> <span class="Keyword">and</span> <span class="Identifier">z</span><span class="Operator">*</span><span class="Identifier">M</span> <span class="Operator">==</span> <span class="Identifier">y</span></span></tt> where N and M are positive integers&quot;.</p>
    1667. 

  1667. <p><strong>See also:</strong></p>
    1668. 

  1668. <ul class="simple"><li><a class="reference external" href="#gcd,SomeInteger,SomeInteger">gcd func</a> for an integer version</li>
    1669. 

  1669. <li><a class="reference external" href="#lcm,T,T">lcm func</a></li>
    1670. 

  1670. </ul>
    1671. 

  1671. 

  1672. <p><strong class="examples_text">Example:</strong></p>
    1673. 

  1673. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">gcd</span><span class="Punctuation">(</span><span class="FloatNumber">13.5</span><span class="Punctuation">,</span> <span class="FloatNumber">9.0</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="FloatNumber">4.5</span></pre>
    1674. 

  1674.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L1286" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1675. 

  1675. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L1286" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1676. 

  1676. 

  1677.   </dd>
    1678. 

  1678. </div>
    1679. 

  1679. <div id="gcd,openArray[T]">
    1680. 

  1680.   <dt><pre><span class="Keyword">func</span> <a href="#gcd%2CopenArray%5BT%5D"><span class="Identifier">gcd</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="system.html#openArray"><span class="Identifier">openArray</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>
    1681. 

  1681.   <dd>
    1682. 

  1682.     
    1683. 

  1683.     <p>Computes the greatest common (positive) divisor of the elements of <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>.</p>
    1684. 

  1684. <p><strong>See also:</strong></p>
    1685. 

  1685. <ul class="simple"><li><a class="reference external" href="#gcd,T,T">gcd func</a> for a version with two arguments</li>
    1686. 

  1686. </ul>
    1687. 

  1687. 

  1688. <p><strong class="examples_text">Example:</strong></p>
    1689. 

  1689. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">gcd</span><span class="Punctuation">(</span><span class="Operator">@</span><span class="Punctuation">[</span><span class="FloatNumber">13.5</span><span class="Punctuation">,</span> <span class="FloatNumber">9.0</span><span class="Punctuation">]</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="FloatNumber">4.5</span></pre>
    1690. 

  1690.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L1341" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1691. 

  1691. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L1341" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1692. 

  1692. 

  1693.   </dd>
    1694. 

  1694. </div>
    1695. 

  1695. 

  1696. </div>
    1697. 

  1697. <div id="hypot-procs-all">
    1698. 

  1698.   <div id="hypot,float32,float32">
    1699. 

  1699.   <dt><pre><span class="Keyword">func</span> <a href="#hypot%2Cfloat32%2Cfloat32"><span class="Identifier">hypot</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="system.html#float32"><span class="Identifier">float32</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;hypotf&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    1700. 

  1700.                                      <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>
    1701. 

  1701.   <dd>
    1702. 

  1702.     
    1703. 

  1703.     
    1704. 

  1704.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L621" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1705. 

  1705. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L621" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1706. 

  1706. 

  1707.   </dd>
    1708. 

  1708. </div>
    1709. 

  1709. <div id="hypot,float64,float64">
    1710. 

  1710.   <dt><pre><span class="Keyword">func</span> <a href="#hypot%2Cfloat64%2Cfloat64"><span class="Identifier">hypot</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="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;hypot&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    1711. 

  1711.                                      <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>
    1712. 

  1712.   <dd>
    1713. 

  1713.     
    1714. 

  1714.     Computes the length of the hypotenuse of a right-angle triangle with <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> as its base and <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt> as its height. Equivalent to <tt class="docutils literal"><span class="pre"><span class="Identifier">sqrt</span><span class="Punctuation">(</span><span class="Identifier">x</span><span class="Operator">*</span><span class="Identifier">x</span> <span class="Operator">+</span> <span class="Identifier">y</span><span class="Operator">*</span><span class="Identifier">y</span><span class="Punctuation">)</span></span></tt>.
    1715. 

  1715. <p><strong class="examples_text">Example:</strong></p>
    1716. 

  1716. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">hypot</span><span class="Punctuation">(</span><span class="FloatNumber">3.0</span><span class="Punctuation">,</span> <span class="FloatNumber">4.0</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="FloatNumber">5.0</span><span class="Punctuation">)</span></pre>
    1717. 

  1717.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L622" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1718. 

  1718. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L622" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1719. 

  1719. 

  1720.   </dd>
    1721. 

  1721. </div>
    1722. 

  1722. 

  1723. </div>
    1724. 

  1724. <div id="isNaN-procs-all">
    1725. 

  1725.   <div id="isNaN,SomeFloat">
    1726. 

  1726.   <dt><pre><span class="Keyword">func</span> <a href="#isNaN%2CSomeFloat"><span class="Identifier">isNaN</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#SomeFloat"><span class="Identifier">SomeFloat</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#bool"><span class="Identifier">bool</span></a> {.<span class="Identifier">inline</span>.}</pre></dt>
    1727. 

  1727.   <dd>
    1728. 

  1728.     
    1729. 

  1729.     Returns whether <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> is a <tt class="docutils literal"><span class="pre"><span class="Identifier">NaN</span></span></tt>, more efficiently than via <tt class="docutils literal"><span class="pre"><span class="Identifier">classify</span><span class="Punctuation">(</span><span class="Identifier">x</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="Identifier">fcNan</span></span></tt>. Works even with <tt class="docutils literal"><span class="pre"><span class="Operator">--</span><span class="Identifier">passc</span><span class="Punctuation">:</span><span class="Operator">-</span><span class="Identifier">ffast</span><span class="Operator">-</span><span class="Identifier">math</span></span></tt>.
    1730. 

  1730. <p><strong class="examples_text">Example:</strong></p>
    1731. 

  1731. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">NaN</span><span class="Operator">.</span><span class="Identifier">isNaN</span>
    1732. 

  1732. <span class="Identifier">doAssert</span> <span class="Keyword">not</span> <span class="Identifier">Inf</span><span class="Operator">.</span><span class="Identifier">isNaN</span>
    1733. 

  1733. <span class="Identifier">doAssert</span> <span class="Keyword">not</span> <span class="Identifier">isNaN</span><span class="Punctuation">(</span><span class="FloatNumber">3.1415926</span><span class="Punctuation">)</span></pre>
    1734. 

  1734.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L193" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1735. 

  1735. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L193" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1736. 

  1736. 

  1737.   </dd>
    1738. 

  1738. </div>
    1739. 

  1739. 

  1740. </div>
    1741. 

  1741. <div id="isPowerOfTwo-procs-all">
    1742. 

  1742.   <div id="isPowerOfTwo,int">
    1743. 

  1743.   <dt><pre><span class="Keyword">func</span> <a href="#isPowerOfTwo%2Cint"><span class="Identifier">isPowerOfTwo</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#int"><span class="Identifier">int</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#bool"><span class="Identifier">bool</span></a> {.<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>
    1744. 

  1744.   <dd>
    1745. 

  1745.     
    1746. 

  1746.     <p>Returns <tt class="docutils literal"><span class="pre"><span class="Identifier">true</span></span></tt>, if <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> is a power of two, <tt class="docutils literal"><span class="pre"><span class="Identifier">false</span></span></tt> otherwise.</p>
    1747. 

  1747. <p>Zero and negative numbers are not a power of two.</p>
    1748. 

  1748. <p><strong>See also:</strong></p>
    1749. 

  1749. <ul class="simple"><li><a class="reference external" href="#nextPowerOfTwo,int">nextPowerOfTwo func</a></li>
    1750. 

  1750. </ul>
    1751. 

  1751. 

  1752. <p><strong class="examples_text">Example:</strong></p>
    1753. 

  1753. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">isPowerOfTwo</span><span class="Punctuation">(</span><span class="DecNumber">16</span><span class="Punctuation">)</span>
    1754. 

  1754. <span class="Identifier">doAssert</span> <span class="Keyword">not</span> <span class="Identifier">isPowerOfTwo</span><span class="Punctuation">(</span><span class="DecNumber">5</span><span class="Punctuation">)</span>
    1755. 

  1755. <span class="Identifier">doAssert</span> <span class="Keyword">not</span> <span class="Identifier">isPowerOfTwo</span><span class="Punctuation">(</span><span class="DecNumber">0</span><span class="Punctuation">)</span>
    1756. 

  1756. <span class="Identifier">doAssert</span> <span class="Keyword">not</span> <span class="Identifier">isPowerOfTwo</span><span class="Punctuation">(</span><span class="Operator">-</span><span class="DecNumber">16</span><span class="Punctuation">)</span></pre>
    1757. 

  1757.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L324" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1758. 

  1758. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L324" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1759. 

  1759. 

  1760.   </dd>
    1761. 

  1761. </div>
    1762. 

  1762. 

  1763. </div>
    1764. 

  1764. <div id="lcm-procs-all">
    1765. 

  1765.   <div id="lcm,T,T">
    1766. 

  1766.   <dt><pre><span class="Keyword">func</span> <a href="#lcm%2CT%2CT"><span class="Identifier">lcm</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> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <span class="Identifier">T</span></pre></dt>
    1767. 

  1767.   <dd>
    1768. 

  1768.     
    1769. 

  1769.     <p>Computes the least common multiple of <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> and <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt>.</p>
    1770. 

  1770. <p><strong>See also:</strong></p>
    1771. 

  1771. <ul class="simple"><li><a class="reference external" href="#gcd,T,T">gcd func</a></li>
    1772. 

  1772. </ul>
    1773. 

  1773. 

  1774. <p><strong class="examples_text">Example:</strong></p>
    1775. 

  1775. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">lcm</span><span class="Punctuation">(</span><span class="DecNumber">24</span><span class="Punctuation">,</span> <span class="DecNumber">30</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="DecNumber">120</span>
    1776. 

  1776. <span class="Identifier">doAssert</span> <span class="Identifier">lcm</span><span class="Punctuation">(</span><span class="DecNumber">13</span><span class="Punctuation">,</span> <span class="DecNumber">39</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="DecNumber">39</span></pre>
    1777. 

  1777.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L1353" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1778. 

  1778. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L1353" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1779. 

  1779. 

  1780.   </dd>
    1781. 

  1781. </div>
    1782. 

  1782. <div id="lcm,openArray[T]">
    1783. 

  1783.   <dt><pre><span class="Keyword">func</span> <a href="#lcm%2CopenArray%5BT%5D"><span class="Identifier">lcm</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="system.html#openArray"><span class="Identifier">openArray</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>
    1784. 

  1784.   <dd>
    1785. 

  1785.     
    1786. 

  1786.     <p>Computes the least common multiple of the elements of <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>.</p>
    1787. 

  1787. <p><strong>See also:</strong></p>
    1788. 

  1788. <ul class="simple"><li><a class="reference external" href="#lcm,T,T">lcm func</a> for a version with two arguments</li>
    1789. 

  1789. </ul>
    1790. 

  1790. 

  1791. <p><strong class="examples_text">Example:</strong></p>
    1792. 

  1792. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">lcm</span><span class="Punctuation">(</span><span class="Operator">@</span><span class="Punctuation">[</span><span class="DecNumber">24</span><span class="Punctuation">,</span> <span class="DecNumber">30</span><span class="Punctuation">]</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="DecNumber">120</span></pre>
    1793. 

  1793.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L1376" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1794. 

  1794. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L1376" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1795. 

  1795. 

  1796.   </dd>
    1797. 

  1797. </div>
    1798. 

  1798. 

  1799. </div>
    1800. 

  1800. <div id="lgamma-procs-all">
    1801. 

  1801.   <div id="lgamma,float32">
    1802. 

  1802.   <dt><pre><span class="Keyword">func</span> <a href="#lgamma%2Cfloat32"><span class="Identifier">lgamma</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;lgammaf&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    1803. 

  1803.                                    <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>
    1804. 

  1804.   <dd>
    1805. 

  1805.     
    1806. 

  1806.     
    1807. 

  1807.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L666" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1808. 

  1808. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L666" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1809. 

  1809. 

  1810.   </dd>
    1811. 

  1811. </div>
    1812. 

  1812. <div id="lgamma,float64">
    1813. 

  1813.   <dt><pre><span class="Keyword">func</span> <a href="#lgamma%2Cfloat64"><span class="Identifier">lgamma</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;lgamma&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    1814. 

  1814.                                    <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>
    1815. 

  1815.   <dd>
    1816. 

  1816.     
    1817. 

  1817.     <p>Computes the natural logarithm of the gamma function for <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>.</p>
    1818. 

  1818. <p><strong>Note:</strong> Not available for the JS backend.</p>
    1819. 

  1819. <p><strong>See also:</strong></p>
    1820. 

  1820. <ul class="simple"><li><a class="reference external" href="#gamma,float64">gamma func</a> for gamma function</li>
    1821. 

  1821. </ul>
    1822. 

  1822. 

  1823.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L667" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1824. 

  1824. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L667" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1825. 

  1825. 

  1826.   </dd>
    1827. 

  1827. </div>
    1828. 

  1828. 

  1829. </div>
    1830. 

  1830. <div id="ln-procs-all">
    1831. 

  1831.   <div id="ln,float32">
    1832. 

  1832.   <dt><pre><span class="Keyword">func</span> <a href="#ln%2Cfloat32"><span class="Identifier">ln</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;logf&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span> <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>
    1833. 

  1833.                                <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>
    1834. 

  1834.   <dd>
    1835. 

  1835.     
    1836. 

  1836.     
    1837. 

  1837.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L387" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1838. 

  1838. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L387" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1839. 

  1839. 

  1840.   </dd>
    1841. 

  1841. </div>
    1842. 

  1842. <div id="ln,float64">
    1843. 

  1843.   <dt><pre><span class="Keyword">func</span> <a href="#ln%2Cfloat64"><span class="Identifier">ln</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;log&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span> <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>
    1844. 

  1844.                                <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>
    1845. 

  1845.   <dd>
    1846. 

  1846.     
    1847. 

  1847.     <p>Computes the <a class="reference external" href="https://en.wikipedia.org/wiki/Natural_logarithm">natural logarithm</a> of <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>.</p>
    1848. 

  1848. <p><strong>See also:</strong></p>
    1849. 

  1849. <ul class="simple"><li><a class="reference external" href="#log,T,T">log func</a></li>
    1850. 

  1850. <li><a class="reference external" href="#log10,float64">log10 func</a></li>
    1851. 

  1851. <li><a class="reference external" href="#log2,float64">log2 func</a></li>
    1852. 

  1852. <li><a class="reference external" href="#exp,float64">exp func</a></li>
    1853. 

  1853. </ul>
    1854. 

  1854. 

  1855. <p><strong class="examples_text">Example:</strong></p>
    1856. 

  1856. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">ln</span><span class="Punctuation">(</span><span class="Identifier">exp</span><span class="Punctuation">(</span><span class="FloatNumber">4.0</span><span class="Punctuation">)</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="FloatNumber">4.0</span><span class="Punctuation">)</span>
    1857. 

  1857. <span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">ln</span><span class="Punctuation">(</span><span class="FloatNumber">1.0</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="FloatNumber">0.0</span><span class="Punctuation">)</span>
    1858. 

  1858. <span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">ln</span><span class="Punctuation">(</span><span class="FloatNumber">0.0</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="Operator">-</span><span class="Identifier">Inf</span><span class="Punctuation">)</span>
    1859. 

  1859. <span class="Identifier">doAssert</span> <span class="Identifier">ln</span><span class="Punctuation">(</span><span class="Operator">-</span><span class="FloatNumber">7.0</span><span class="Punctuation">)</span><span class="Operator">.</span><span class="Identifier">isNaN</span></pre>
    1860. 

  1860.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L388" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1861. 

  1861. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L388" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1862. 

  1862. 

  1863.   </dd>
    1864. 

  1864. </div>
    1865. 

  1865. 

  1866. </div>
    1867. 

  1867. <div id="log-procs-all">
    1868. 

  1868.   <div id="log,T,T">
    1869. 

  1869.   <dt><pre><span class="Keyword">func</span> <a href="#log%2CT%2CT"><span class="Identifier">log</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#SomeFloat"><span class="Identifier">SomeFloat</span></a><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">,</span> <span class="Identifier">base</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <span class="Identifier">T</span></pre></dt>
    1870. 

  1870.   <dd>
    1871. 

  1871.     
    1872. 

  1872.     <p>Computes the logarithm of <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> to base <tt class="docutils literal"><span class="pre"><span class="Identifier">base</span></span></tt>.</p>
    1873. 

  1873. <p><strong>See also:</strong></p>
    1874. 

  1874. <ul class="simple"><li><a class="reference external" href="#ln,float64">ln func</a></li>
    1875. 

  1875. <li><a class="reference external" href="#log10,float64">log10 func</a></li>
    1876. 

  1876. <li><a class="reference external" href="#log2,float64">log2 func</a></li>
    1877. 

  1877. </ul>
    1878. 

  1878. 

  1879. <p><strong class="examples_text">Example:</strong></p>
    1880. 

  1880. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">log</span><span class="Punctuation">(</span><span class="FloatNumber">9.0</span><span class="Punctuation">,</span> <span class="FloatNumber">3.0</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="FloatNumber">2.0</span><span class="Punctuation">)</span>
    1881. 

  1881. <span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">log</span><span class="Punctuation">(</span><span class="FloatNumber">0.0</span><span class="Punctuation">,</span> <span class="FloatNumber">2.0</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="Operator">-</span><span class="Identifier">Inf</span><span class="Punctuation">)</span>
    1882. 

  1882. <span class="Identifier">doAssert</span> <span class="Identifier">log</span><span class="Punctuation">(</span><span class="Operator">-</span><span class="FloatNumber">7.0</span><span class="Punctuation">,</span> <span class="FloatNumber">4.0</span><span class="Punctuation">)</span><span class="Operator">.</span><span class="Identifier">isNaN</span>
    1883. 

  1883. <span class="Identifier">doAssert</span> <span class="Identifier">log</span><span class="Punctuation">(</span><span class="FloatNumber">8.0</span><span class="Punctuation">,</span> <span class="Operator">-</span><span class="FloatNumber">2.0</span><span class="Punctuation">)</span><span class="Operator">.</span><span class="Identifier">isNaN</span></pre>
    1884. 

  1884.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L412" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1885. 

  1885. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L412" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1886. 

  1886. 

  1887.   </dd>
    1888. 

  1888. </div>
    1889. 

  1889. 

  1890. </div>
    1891. 

  1891. <div id="log2-procs-all">
    1892. 

  1892.   <div id="log2,float32">
    1893. 

  1893.   <dt><pre><span class="Keyword">func</span> <a href="#log2%2Cfloat32"><span class="Identifier">log2</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;log2f&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    1894. 

  1894.                                  <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>
    1895. 

  1895.   <dd>
    1896. 

  1896.     
    1897. 

  1897.     
    1898. 

  1898.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L1047" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1899. 

  1899. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L1047" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1900. 

  1900. 

  1901.   </dd>
    1902. 

  1902. </div>
    1903. 

  1903. <div id="log2,float64">
    1904. 

  1904.   <dt><pre><span class="Keyword">func</span> <a href="#log2%2Cfloat64"><span class="Identifier">log2</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;log2&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    1905. 

  1905.                                  <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>
    1906. 

  1906.   <dd>
    1907. 

  1907.     
    1908. 

  1908.     <p>Computes the binary logarithm (base 2) of <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>.</p>
    1909. 

  1909. <p><strong>See also:</strong></p>
    1910. 

  1910. <ul class="simple"><li><a class="reference external" href="#log,T,T">log func</a></li>
    1911. 

  1911. <li><a class="reference external" href="#log10,float64">log10 func</a></li>
    1912. 

  1912. <li><a class="reference external" href="#ln,float64">ln func</a></li>
    1913. 

  1913. </ul>
    1914. 

  1914. 

  1915. <p><strong class="examples_text">Example:</strong></p>
    1916. 

  1916. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">log2</span><span class="Punctuation">(</span><span class="FloatNumber">8.0</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="FloatNumber">3.0</span><span class="Punctuation">)</span>
    1917. 

  1917. <span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">log2</span><span class="Punctuation">(</span><span class="FloatNumber">1.0</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="FloatNumber">0.0</span><span class="Punctuation">)</span>
    1918. 

  1918. <span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">log2</span><span class="Punctuation">(</span><span class="FloatNumber">0.0</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="Operator">-</span><span class="Identifier">Inf</span><span class="Punctuation">)</span>
    1919. 

  1919. <span class="Identifier">doAssert</span> <span class="Identifier">log2</span><span class="Punctuation">(</span><span class="Operator">-</span><span class="FloatNumber">2.0</span><span class="Punctuation">)</span><span class="Operator">.</span><span class="Identifier">isNaN</span></pre>
    1920. 

  1920.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L1048" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1921. 

  1921. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L1048" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1922. 

  1922. 

  1923.   </dd>
    1924. 

  1924. </div>
    1925. 

  1925. 

  1926. </div>
    1927. 

  1927. <div id="log10-procs-all">
    1928. 

  1928.   <div id="log10,float32">
    1929. 

  1929.   <dt><pre><span class="Keyword">func</span> <a href="#log10%2Cfloat32"><span class="Identifier">log10</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;log10f&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    1930. 

  1930.                                   <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>
    1931. 

  1931.   <dd>
    1932. 

  1932.     
    1933. 

  1933.     
    1934. 

  1934.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L428" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1935. 

  1935. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L428" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1936. 

  1936. 

  1937.   </dd>
    1938. 

  1938. </div>
    1939. 

  1939. <div id="log10,float64">
    1940. 

  1940.   <dt><pre><span class="Keyword">func</span> <a href="#log10%2Cfloat64"><span class="Identifier">log10</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;log10&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    1941. 

  1941.                                   <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>
    1942. 

  1942.   <dd>
    1943. 

  1943.     
    1944. 

  1944.     <p>Computes the common logarithm (base 10) of <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>.</p>
    1945. 

  1945. <p><strong>See also:</strong></p>
    1946. 

  1946. <ul class="simple"><li><a class="reference external" href="#ln,float64">ln func</a></li>
    1947. 

  1947. <li><a class="reference external" href="#log,T,T">log func</a></li>
    1948. 

  1948. <li><a class="reference external" href="#log2,float64">log2 func</a></li>
    1949. 

  1949. </ul>
    1950. 

  1950. 

  1951. <p><strong class="examples_text">Example:</strong></p>
    1952. 

  1952. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">log10</span><span class="Punctuation">(</span><span class="FloatNumber">100.0</span><span class="Punctuation">)</span> <span class="Punctuation">,</span> <span class="FloatNumber">2.0</span><span class="Punctuation">)</span>
    1953. 

  1953. <span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">log10</span><span class="Punctuation">(</span><span class="FloatNumber">0.0</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="Operator">-</span><span class="Identifier">Inf</span><span class="Punctuation">)</span>
    1954. 

  1954. <span class="Identifier">doAssert</span> <span class="Identifier">log10</span><span class="Punctuation">(</span><span class="Operator">-</span><span class="FloatNumber">100.0</span><span class="Punctuation">)</span><span class="Operator">.</span><span class="Identifier">isNaN</span></pre>
    1955. 

  1955.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L429" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1956. 

  1956. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L429" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1957. 

  1957. 

  1958.   </dd>
    1959. 

  1959. </div>
    1960. 

  1960. 

  1961. </div>
    1962. 

  1962. <div id="mod-procs-all">
    1963. 

  1963.   <div id="mod,float32,float32">
    1964. 

  1964.   <dt><pre><span class="Keyword">func</span> <a href="#mod%2Cfloat32%2Cfloat32"><span class="Identifier">`mod`</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="system.html#float32"><span class="Identifier">float32</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;fmodf&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    1965. 

  1965.                                      <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>
    1966. 

  1966.   <dd>
    1967. 

  1967.     
    1968. 

  1968.     
    1969. 

  1969.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L788" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1970. 

  1970. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L788" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1971. 

  1971. 

  1972.   </dd>
    1973. 

  1973. </div>
    1974. 

  1974. <div id="mod,float64,float64">
    1975. 

  1975.   <dt><pre><span class="Keyword">func</span> <a href="#mod%2Cfloat64%2Cfloat64"><span class="Identifier">`mod`</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="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;fmod&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    1976. 

  1976.                                      <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>
    1977. 

  1977.   <dd>
    1978. 

  1978.     
    1979. 

  1979.     <p>Computes the modulo operation for float values (the remainder of <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> divided by <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt>).</p>
    1980. 

  1980. <p><strong>See also:</strong></p>
    1981. 

  1981. <ul class="simple"><li><a class="reference external" href="#floorMod,T,T">floorMod func</a> for Python-like (<tt class="docutils literal"><span class="pre"><span class="Operator">%</span></span></tt> operator) behavior</li>
    1982. 

  1982. </ul>
    1983. 

  1983. 

  1984. <p><strong class="examples_text">Example:</strong></p>
    1985. 

  1985. <pre class="listing"><span class="Identifier">doAssert</span>  <span class="FloatNumber">6.5</span> <span class="Keyword">mod</span>  <span class="FloatNumber">2.5</span> <span class="Operator">==</span>  <span class="FloatNumber">1.5</span>
    1986. 

  1986. <span class="Identifier">doAssert</span> <span class="Operator">-</span><span class="FloatNumber">6.5</span> <span class="Keyword">mod</span>  <span class="FloatNumber">2.5</span> <span class="Operator">==</span> <span class="Operator">-</span><span class="FloatNumber">1.5</span>
    1987. 

  1987. <span class="Identifier">doAssert</span>  <span class="FloatNumber">6.5</span> <span class="Keyword">mod</span> <span class="Operator">-</span><span class="FloatNumber">2.5</span> <span class="Operator">==</span>  <span class="FloatNumber">1.5</span>
    1988. 

  1988. <span class="Identifier">doAssert</span> <span class="Operator">-</span><span class="FloatNumber">6.5</span> <span class="Keyword">mod</span> <span class="Operator">-</span><span class="FloatNumber">2.5</span> <span class="Operator">==</span> <span class="Operator">-</span><span class="FloatNumber">1.5</span></pre>
    1989. 

  1989.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L789" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1990. 

  1990. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L789" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1991. 

  1991. 

  1992.   </dd>
    1993. 

  1993. </div>
    1994. 

  1994. 

  1995. </div>
    1996. 

  1996. <div id="nextPowerOfTwo-procs-all">
    1997. 

  1997.   <div id="nextPowerOfTwo,int">
    1998. 

  1998.   <dt><pre><span class="Keyword">func</span> <a href="#nextPowerOfTwo%2Cint"><span class="Identifier">nextPowerOfTwo</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#int"><span class="Identifier">int</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#int"><span class="Identifier">int</span></a> {.<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>
    1999. 

  1999.   <dd>
    2000. 

  2000.     
    2001. 

  2001.     <p>Returns <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> rounded up to the nearest power of two.</p>
    2002. 

  2002. <p>Zero and negative numbers get rounded up to 1.</p>
    2003. 

  2003. <p><strong>See also:</strong></p>
    2004. 

  2004. <ul class="simple"><li><a class="reference external" href="#isPowerOfTwo,int">isPowerOfTwo func</a></li>
    2005. 

  2005. </ul>
    2006. 

  2006. 

  2007. <p><strong class="examples_text">Example:</strong></p>
    2008. 

  2008. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">nextPowerOfTwo</span><span class="Punctuation">(</span><span class="DecNumber">16</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="DecNumber">16</span>
    2009. 

  2009. <span class="Identifier">doAssert</span> <span class="Identifier">nextPowerOfTwo</span><span class="Punctuation">(</span><span class="DecNumber">5</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="DecNumber">8</span>
    2010. 

  2010. <span class="Identifier">doAssert</span> <span class="Identifier">nextPowerOfTwo</span><span class="Punctuation">(</span><span class="DecNumber">0</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="DecNumber">1</span>
    2011. 

  2011. <span class="Identifier">doAssert</span> <span class="Identifier">nextPowerOfTwo</span><span class="Punctuation">(</span><span class="Operator">-</span><span class="DecNumber">16</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="DecNumber">1</span></pre>
    2012. 

  2012.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L339" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    2013. 

  2013. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L339" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    2014. 

  2014. 

  2015.   </dd>
    2016. 

  2016. </div>
    2017. 

  2017. 

  2018. </div>
    2019. 

  2019. <div id="pow-procs-all">
    2020. 

  2020.   <div id="pow,float32,float32">
    2021. 

  2021.   <dt><pre><span class="Keyword">func</span> <a href="#pow%2Cfloat32%2Cfloat32"><span class="Identifier">pow</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="system.html#float32"><span class="Identifier">float32</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;powf&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    2022. 

  2022.                                    <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>
    2023. 

  2023.   <dd>
    2024. 

  2024.     
    2025. 

  2025.     
    2026. 

  2026.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L627" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    2027. 

  2027. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L627" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    2028. 

  2028. 

  2029.   </dd>
    2030. 

  2030. </div>
    2031. 

  2031. <div id="pow,float64,float64">
    2032. 

  2032.   <dt><pre><span class="Keyword">func</span> <a href="#pow%2Cfloat64%2Cfloat64"><span class="Identifier">pow</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="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;pow&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    2033. 

  2033.                                    <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>
    2034. 

  2034.   <dd>
    2035. 

  2035.     
    2036. 

  2036.     <p>Computes <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> raised to the power of <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt>.</p>
    2037. 

  2037. <p>You may use the <a class="reference external" href="#^, T, U">^ func</a> instead.</p>
    2038. 

  2038. <p><strong>See also:</strong></p>
    2039. 

  2039. <ul class="simple"><li><a class="reference external" href="#^,T,Natural">^ (SomeNumber, Natural) func</a></li>
    2040. 

  2040. <li><a class="reference external" href="#^,T,U">^ (SomeNumber, SomeFloat) func</a></li>
    2041. 

  2041. <li><a class="reference external" href="#sqrt,float64">sqrt func</a></li>
    2042. 

  2042. <li><a class="reference external" href="#cbrt,float64">cbrt func</a></li>
    2043. 

  2043. </ul>
    2044. 

  2044. 

  2045. <p><strong class="examples_text">Example:</strong></p>
    2046. 

  2046. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">pow</span><span class="Punctuation">(</span><span class="DecNumber">100</span><span class="Punctuation">,</span> <span class="FloatNumber">1.5</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="FloatNumber">1000.0</span><span class="Punctuation">)</span>
    2047. 

  2047. <span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">pow</span><span class="Punctuation">(</span><span class="FloatNumber">16.0</span><span class="Punctuation">,</span> <span class="FloatNumber">0.5</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="FloatNumber">4.0</span><span class="Punctuation">)</span></pre>
    2048. 

  2048.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L628" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    2049. 

  2049. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L628" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    2050. 

  2050. 

  2051.   </dd>
    2052. 

  2052. </div>
    2053. 

  2053. 

  2054. </div>
    2055. 

  2055. <div id="prod-procs-all">
    2056. 

  2056.   <div id="prod,openArray[T]">
    2057. 

  2057.   <dt><pre><span class="Keyword">func</span> <a href="#prod%2CopenArray%5BT%5D"><span class="Identifier">prod</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="system.html#openArray"><span class="Identifier">openArray</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>
    2058. 

  2058.   <dd>
    2059. 

  2059.     
    2060. 

  2060.     <p>Computes the product of the elements in <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>.</p>
    2061. 

  2061. <p>If <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> is empty, 1 is returned.</p>
    2062. 

  2062. <p><strong>See also:</strong></p>
    2063. 

  2063. <ul class="simple"><li><a class="reference external" href="#sum,openArray[T]">sum func</a></li>
    2064. 

  2064. <li><a class="reference external" href="#fac,int">fac func</a></li>
    2065. 

  2065. </ul>
    2066. 

  2066. 

  2067. <p><strong class="examples_text">Example:</strong></p>
    2068. 

  2068. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">prod</span><span class="Punctuation">(</span><span class="Punctuation">[</span><span class="DecNumber">1</span><span class="Punctuation">,</span> <span class="DecNumber">2</span><span class="Punctuation">,</span> <span class="DecNumber">3</span><span class="Punctuation">,</span> <span class="DecNumber">4</span><span class="Punctuation">]</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="DecNumber">24</span>
    2069. 

  2069. <span class="Identifier">doAssert</span> <span class="Identifier">prod</span><span class="Punctuation">(</span><span class="Punctuation">[</span><span class="Operator">-</span><span class="DecNumber">4</span><span class="Punctuation">,</span> <span class="DecNumber">3</span><span class="Punctuation">,</span> <span class="DecNumber">5</span><span class="Punctuation">]</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="Operator">-</span><span class="DecNumber">60</span></pre>
    2070. 

  2070.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L1133" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    2071. 

  2071. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L1133" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    2072. 

  2072. 

  2073.   </dd>
    2074. 

  2074. </div>
    2075. 

  2075. 

  2076. </div>
    2077. 

  2077. <div id="radToDeg-procs-all">
    2078. 

  2078.   <div id="radToDeg,T">
    2079. 

  2079.   <dt><pre><span class="Keyword">func</span> <a href="#radToDeg%2CT"><span class="Identifier">radToDeg</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> <span class="Operator">|</span> <a href="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">]</span><span class="Other">(</span><span class="Identifier">d</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <span class="Identifier">T</span> {.<span class="Identifier">inline</span>.}</pre></dt>
    2080. 

  2080.   <dd>
    2081. 

  2081.     
    2082. 

  2082.     <p>Converts from radians to degrees.</p>
    2083. 

  2083. <p><strong>See also:</strong></p>
    2084. 

  2084. <ul class="simple"><li><a class="reference external" href="#degToRad,T">degToRad func</a></li>
    2085. 

  2085. </ul>
    2086. 

  2086. 

  2087. <p><strong class="examples_text">Example:</strong></p>
    2088. 

  2088. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">radToDeg</span><span class="Punctuation">(</span><span class="DecNumber">2</span> <span class="Operator">*</span> <span class="Identifier">PI</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="FloatNumber">360.0</span><span class="Punctuation">)</span></pre>
    2089. 

  2089.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L1091" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    2090. 

  2090. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L1091" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    2091. 

  2091. 

  2092.   </dd>
    2093. 

  2093. </div>
    2094. 

  2094. 

  2095. </div>
    2096. 

  2096. <div id="round-procs-all">
    2097. 

  2097.   <div id="round,float32">
    2098. 

  2098.   <dt><pre><span class="Keyword">func</span> <a href="#round%2Cfloat32"><span class="Identifier">round</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;roundf&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    2099. 

  2099.                                   <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>
    2100. 

  2100.   <dd>
    2101. 

  2101.     
    2102. 

  2102.     
    2103. 

  2103.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L758" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    2104. 

  2104. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L758" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    2105. 

  2105. 

  2106.   </dd>
    2107. 

  2107. </div>
    2108. 

  2108. <div id="round,float64">
    2109. 

  2109.   <dt><pre><span class="Keyword">func</span> <a href="#round%2Cfloat64"><span class="Identifier">round</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;round&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    2110. 

  2110.                                   <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>
    2111. 

  2111.   <dd>
    2112. 

  2112.     
    2113. 

  2113.     <p>Rounds a float to zero decimal places.</p>
    2114. 

  2114. <p>Used internally by the <a class="reference external" href="#round,T,int">round func</a> when the specified number of places is 0.</p>
    2115. 

  2115. <p><strong>See also:</strong></p>
    2116. 

  2116. <ul class="simple"><li><a class="reference external" href="#round,T,int">round func</a> for rounding to the specific number of decimal places</li>
    2117. 

  2117. <li><a class="reference external" href="#floor,float64">floor func</a></li>
    2118. 

  2118. <li><a class="reference external" href="#ceil,float64">ceil func</a></li>
    2119. 

  2119. <li><a class="reference external" href="#trunc,float64">trunc func</a></li>
    2120. 

  2120. </ul>
    2121. 

  2121. 

  2122. <p><strong class="examples_text">Example:</strong></p>
    2123. 

  2123. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">round</span><span class="Punctuation">(</span><span class="FloatNumber">3.4</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="FloatNumber">3.0</span>
    2124. 

  2124. <span class="Identifier">doAssert</span> <span class="Identifier">round</span><span class="Punctuation">(</span><span class="FloatNumber">3.5</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="FloatNumber">4.0</span>
    2125. 

  2125. <span class="Identifier">doAssert</span> <span class="Identifier">round</span><span class="Punctuation">(</span><span class="FloatNumber">4.5</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="FloatNumber">5.0</span></pre>
    2126. 

  2126.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L759" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    2127. 

  2127. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L759" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    2128. 

  2128. 

  2129.   </dd>
    2130. 

  2130. </div>
    2131. 

  2131. <div id="round,T,int">
    2132. 

  2132.   <dt><pre><span class="Keyword">func</span> <a href="#round%2CT%2Cint"><span class="Identifier">round</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> <span class="Operator">|</span> <a href="system.html#float64"><span class="Identifier">float64</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="Identifier">places</span><span class="Other">:</span> <a href="system.html#int"><span class="Identifier">int</span></a><span class="Other">)</span><span class="Other">:</span> <span class="Identifier">T</span></pre></dt>
    2133. 

  2133.   <dd>
    2134. 

  2134.     
    2135. 

  2135.     <p>Decimal rounding on a binary floating point number.</p>
    2136. 

  2136. <p>This function is NOT reliable. Floating point numbers cannot hold non integer decimals precisely. If <tt class="docutils literal"><span class="pre"><span class="Identifier">places</span></span></tt> is 0 (or omitted), round to the nearest integral value following normal mathematical rounding rules (e.g.  <tt class="docutils literal"><span class="pre"><span class="Identifier">round</span><span class="Punctuation">(</span><span class="FloatNumber">54.5</span><span class="Punctuation">)</span> <span class="Operator">-&gt;</span> <span class="FloatNumber">55.0</span></span></tt>). If <tt class="docutils literal"><span class="pre"><span class="Identifier">places</span></span></tt> is greater than 0, round to the given number of decimal places, e.g. <tt class="docutils literal"><span class="pre"><span class="Identifier">round</span><span class="Punctuation">(</span><span class="FloatNumber">54.346</span><span class="Punctuation">,</span> <span class="DecNumber">2</span><span class="Punctuation">)</span> <span class="Operator">-&gt;</span> <span class="FloatNumber">54.350000000000001421</span><span class="Identifier">…</span></span></tt>. If <tt class="docutils literal"><span class="pre"><span class="Identifier">places</span></span></tt> is negative, round to the left of the decimal place, e.g. <tt class="docutils literal"><span class="pre"><span class="Identifier">round</span><span class="Punctuation">(</span><span class="FloatNumber">537.345</span><span class="Punctuation">,</span> <span class="Operator">-</span><span class="DecNumber">1</span><span class="Punctuation">)</span> <span class="Operator">-&gt;</span> <span class="FloatNumber">540.0</span></span></tt>.</p>
    2137. 

  2137. 

  2138. <p><strong class="examples_text">Example:</strong></p>
    2139. 

  2139. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">round</span><span class="Punctuation">(</span><span class="Identifier">PI</span><span class="Punctuation">,</span> <span class="DecNumber">2</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="FloatNumber">3.14</span>
    2140. 

  2140. <span class="Identifier">doAssert</span> <span class="Identifier">round</span><span class="Punctuation">(</span><span class="Identifier">PI</span><span class="Punctuation">,</span> <span class="DecNumber">4</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="FloatNumber">3.1416</span></pre>
    2141. 

  2141.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L840" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    2142. 

  2142. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L840" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    2143. 

  2143. 

  2144.   </dd>
    2145. 

  2145. </div>
    2146. 

  2146. 

  2147. </div>
    2148. 

  2148. <div id="sec-procs-all">
    2149. 

  2149.   <div id="sec,T">
    2150. 

  2150.   <dt><pre><span class="Keyword">func</span> <a href="#sec%2CT"><span class="Identifier">sec</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> <span class="Operator">|</span> <a href="system.html#float64"><span class="Identifier">float64</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> <span class="Identifier">T</span></pre></dt>
    2151. 

  2151.   <dd>
    2152. 

  2152.     
    2153. 

  2153.     Computes the secant 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">cos</span><span class="Punctuation">(</span><span class="Identifier">x</span><span class="Punctuation">)</span></span></tt>).
    2154. 

  2154.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L592" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    2155. 

  2155. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L592" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    2156. 

  2156. 

  2157.   </dd>
    2158. 

  2158. </div>
    2159. 

  2159. 

  2160. </div>
    2161. 

  2161. <div id="sech-procs-all">
    2162. 

  2162.   <div id="sech,T">
    2163. 

  2163.   <dt><pre><span class="Keyword">func</span> <a href="#sech%2CT"><span class="Identifier">sech</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> <span class="Operator">|</span> <a href="system.html#float64"><span class="Identifier">float64</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> <span class="Identifier">T</span></pre></dt>
    2164. 

  2164.   <dd>
    2165. 

  2165.     
    2166. 

  2166.     Computes the hyperbolic secant 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">cosh</span><span class="Punctuation">(</span><span class="Identifier">x</span><span class="Punctuation">)</span></span></tt>).
    2167. 

  2167.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L599" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    2168. 

  2168. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L599" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    2169. 

  2169. 

  2170.   </dd>
    2171. 

  2171. </div>
    2172. 

  2172. 

  2173. </div>
    2174. 

  2174. <div id="sgn-procs-all">
    2175. 

  2175.   <div id="sgn,T">
    2176. 

  2176.   <dt><pre><span class="Keyword">func</span> <a href="#sgn%2CT"><span class="Identifier">sgn</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#SomeNumber"><span class="Identifier">SomeNumber</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="system.html#int"><span class="Identifier">int</span></a> {.<span class="Identifier">inline</span>.}</pre></dt>
    2177. 

  2177.   <dd>
    2178. 

  2178.     
    2179. 

  2179.     <p>Sign function.</p>
    2180. 

  2180. <p>Returns:</p>
    2181. 

  2181. <ul class="simple"><li><tt class="docutils literal"><span class="pre"><span class="Operator">-</span><span class="DecNumber">1</span></span></tt> for negative numbers and <tt class="docutils literal"><span class="pre"><span class="Identifier">NegInf</span></span></tt>,</li>
    2182. 

  2182. <li><tt class="docutils literal"><span class="pre"><span class="DecNumber">1</span></span></tt> for positive numbers and <tt class="docutils literal"><span class="pre"><span class="Identifier">Inf</span></span></tt>,</li>
    2183. 

  2183. <li><tt class="docutils literal"><span class="pre"><span class="DecNumber">0</span></span></tt> for positive zero, negative zero and <tt class="docutils literal"><span class="pre"><span class="Identifier">NaN</span></span></tt></li>
    2184. 

  2184. </ul>
    2185. 

  2185. 

  2186. <p><strong class="examples_text">Example:</strong></p>
    2187. 

  2187. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">sgn</span><span class="Punctuation">(</span><span class="DecNumber">5</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="DecNumber">1</span>
    2188. 

  2188. <span class="Identifier">doAssert</span> <span class="Identifier">sgn</span><span class="Punctuation">(</span><span class="DecNumber">0</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="DecNumber">0</span>
    2189. 

  2189. <span class="Identifier">doAssert</span> <span class="Identifier">sgn</span><span class="Punctuation">(</span><span class="Operator">-</span><span class="FloatNumber">4.1</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="Operator">-</span><span class="DecNumber">1</span></pre>
    2190. 

  2190.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L1101" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    2191. 

  2191. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L1101" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    2192. 

  2192. 

  2193.   </dd>
    2194. 

  2194. </div>
    2195. 

  2195. 

  2196. </div>
    2197. 

  2197. <div id="signbit-procs-all">
    2198. 

  2198.   <div id="signbit,SomeFloat">
    2199. 

  2199.   <dt><pre><span class="Keyword">proc</span> <a href="#signbit%2CSomeFloat"><span class="Identifier">signbit</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#SomeFloat"><span class="Identifier">SomeFloat</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#bool"><span class="Identifier">bool</span></a> {.<span class="Identifier">inline</span>.}</pre></dt>
    2200. 

  2200.   <dd>
    2201. 

  2201.     
    2202. 

  2202.     Returns true if <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> is negative, false otherwise.
    2203. 

  2203. <p><strong class="examples_text">Example:</strong></p>
    2204. 

  2204. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Keyword">not</span> <span class="Identifier">signbit</span><span class="Punctuation">(</span><span class="FloatNumber">0.0</span><span class="Punctuation">)</span>
    2205. 

  2205. <span class="Identifier">doAssert</span> <span class="Identifier">signbit</span><span class="Punctuation">(</span><span class="Operator">-</span><span class="FloatNumber">0.0</span><span class="Punctuation">)</span>
    2206. 

  2206. <span class="Identifier">doAssert</span> <span class="Identifier">signbit</span><span class="Punctuation">(</span><span class="Operator">-</span><span class="FloatNumber">0.1</span><span class="Punctuation">)</span>
    2207. 

  2207. <span class="Identifier">doAssert</span> <span class="Keyword">not</span> <span class="Identifier">signbit</span><span class="Punctuation">(</span><span class="FloatNumber">0.1</span><span class="Punctuation">)</span></pre>
    2208. 

  2208.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L231" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    2209. 

  2209. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L231" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    2210. 

  2210. 

  2211.   </dd>
    2212. 

  2212. </div>
    2213. 

  2213. 

  2214. </div>
    2215. 

  2215. <div id="sin-procs-all">
    2216. 

  2216.   <div id="sin,float32">
    2217. 

  2217.   <dt><pre><span class="Keyword">func</span> <a href="#sin%2Cfloat32"><span class="Identifier">sin</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;sinf&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span> <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>
    2218. 

  2218.                                 <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>
    2219. 

  2219.   <dd>
    2220. 

  2220.     
    2221. 

  2221.     
    2222. 

  2222.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L450" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    2223. 

  2223. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L450" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    2224. 

  2224. 

  2225.   </dd>
    2226. 

  2226. </div>
    2227. 

  2227. <div id="sin,float64">
    2228. 

  2228.   <dt><pre><span class="Keyword">func</span> <a href="#sin%2Cfloat64"><span class="Identifier">sin</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;sin&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span> <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>
    2229. 

  2229.                                 <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>
    2230. 

  2230.   <dd>
    2231. 

  2231.     
    2232. 

  2232.     <p>Computes the sine of <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>.</p>
    2233. 

  2233. <p><strong>See also:</strong></p>
    2234. 

  2234. <ul class="simple"><li><a class="reference external" href="#arcsin,float64">arcsin func</a></li>
    2235. 

  2235. </ul>
    2236. 

  2236. 

  2237. <p><strong class="examples_text">Example:</strong></p>
    2238. 

  2238. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">sin</span><span class="Punctuation">(</span><span class="Identifier">PI</span> <span class="Operator">/</span> <span class="DecNumber">6</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="FloatNumber">0.5</span><span class="Punctuation">)</span>
    2239. 

  2239. <span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">sin</span><span class="Punctuation">(</span><span class="Identifier">degToRad</span><span class="Punctuation">(</span><span class="FloatNumber">90.0</span><span class="Punctuation">)</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="FloatNumber">1.0</span><span class="Punctuation">)</span></pre>
    2240. 

  2240.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L451" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    2241. 

  2241. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L451" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    2242. 

  2242. 

  2243.   </dd>
    2244. 

  2244. </div>
    2245. 

  2245. 

  2246. </div>
    2247. 

  2247. <div id="sinh-procs-all">
    2248. 

  2248.   <div id="sinh,float32">
    2249. 

  2249.   <dt><pre><span class="Keyword">func</span> <a href="#sinh%2Cfloat32"><span class="Identifier">sinh</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;sinhf&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    2250. 

  2250.                                  <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>
    2251. 

  2251.   <dd>
    2252. 

  2252.     
    2253. 

  2253.     
    2254. 

  2254.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L477" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    2255. 

  2255. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L477" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    2256. 

  2256. 

  2257.   </dd>
    2258. 

  2258. </div>
    2259. 

  2259. <div id="sinh,float64">
    2260. 

  2260.   <dt><pre><span class="Keyword">func</span> <a href="#sinh%2Cfloat64"><span class="Identifier">sinh</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;sinh&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    2261. 

  2261.                                  <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>
    2262. 

  2262.   <dd>
    2263. 

  2263.     
    2264. 

  2264.     <p>Computes the <a class="reference external" href="https://en.wikipedia.org/wiki/Hyperbolic_function#Definitions">hyperbolic sine</a> of <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>.</p>
    2265. 

  2265. <p><strong>See also:</strong></p>
    2266. 

  2266. <ul class="simple"><li><a class="reference external" href="#arcsinh,float64">arcsinh func</a></li>
    2267. 

  2267. </ul>
    2268. 

  2268. 

  2269. <p><strong class="examples_text">Example:</strong></p>
    2270. 

  2270. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">sinh</span><span class="Punctuation">(</span><span class="FloatNumber">0.0</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="FloatNumber">0.0</span><span class="Punctuation">)</span>
    2271. 

  2271. <span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">sinh</span><span class="Punctuation">(</span><span class="FloatNumber">1.0</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="FloatNumber">1.175201193643801</span><span class="Punctuation">)</span></pre>
    2272. 

  2272.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L478" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    2273. 

  2273. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L478" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    2274. 

  2274. 

  2275.   </dd>
    2276. 

  2276. </div>
    2277. 

  2277. 

  2278. </div>
    2279. 

  2279. <div id="splitDecimal-procs-all">
    2280. 

  2280.   <div id="splitDecimal,T">
    2281. 

  2281.   <dt><pre><span class="Keyword">func</span> <a href="#splitDecimal%2CT"><span class="Identifier">splitDecimal</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> <span class="Operator">|</span> <a href="system.html#float64"><span class="Identifier">float64</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> <span class="Keyword">tuple</span><span class="Other">[</span><span class="Identifier">intpart</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">,</span> <span class="Identifier">floatpart</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    2282. 

  2282.   <dd>
    2283. 

  2283.     
    2284. 

  2284.     <p>Breaks <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> into an integer and a fractional part.</p>
    2285. 

  2285. <p>Returns a tuple containing <tt class="docutils literal"><span class="pre"><span class="Identifier">intpart</span></span></tt> and <tt class="docutils literal"><span class="pre"><span class="Identifier">floatpart</span></span></tt>, representing the integer part and the fractional part, respectively.</p>
    2286. 

  2286. <p>Both parts have the same sign as <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>.  Analogous to the <tt class="docutils literal"><span class="pre"><span class="Identifier">modf</span></span></tt> function in C.</p>
    2287. 

  2287. 

  2288. <p><strong class="examples_text">Example:</strong></p>
    2289. 

  2289. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">splitDecimal</span><span class="Punctuation">(</span><span class="FloatNumber">5.25</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="Punctuation">(</span><span class="Identifier">intpart</span><span class="Punctuation">:</span> <span class="FloatNumber">5.0</span><span class="Punctuation">,</span> <span class="Identifier">floatpart</span><span class="Punctuation">:</span> <span class="FloatNumber">0.25</span><span class="Punctuation">)</span>
    2290. 

  2290. <span class="Identifier">doAssert</span> <span class="Identifier">splitDecimal</span><span class="Punctuation">(</span><span class="Operator">-</span><span class="FloatNumber">2.73</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="Punctuation">(</span><span class="Identifier">intpart</span><span class="Punctuation">:</span> <span class="Operator">-</span><span class="FloatNumber">2.0</span><span class="Punctuation">,</span> <span class="Identifier">floatpart</span><span class="Punctuation">:</span> <span class="Operator">-</span><span class="FloatNumber">0.73</span><span class="Punctuation">)</span></pre>
    2291. 

  2291.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L1061" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    2292. 

  2292. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L1061" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    2293. 

  2293. 

  2294.   </dd>
    2295. 

  2295. </div>
    2296. 

  2296. 

  2297. </div>
    2298. 

  2298. <div id="sqrt-procs-all">
    2299. 

  2299.   <div id="sqrt,float32">
    2300. 

  2300.   <dt><pre><span class="Keyword">func</span> <a href="#sqrt%2Cfloat32"><span class="Identifier">sqrt</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;sqrtf&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    2301. 

  2301.                                  <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>
    2302. 

  2302.   <dd>
    2303. 

  2303.     
    2304. 

  2304.     
    2305. 

  2305.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L368" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    2306. 

  2306. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L368" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    2307. 

  2307. 

  2308.   </dd>
    2309. 

  2309. </div>
    2310. 

  2310. <div id="sqrt,float64">
    2311. 

  2311.   <dt><pre><span class="Keyword">func</span> <a href="#sqrt%2Cfloat64"><span class="Identifier">sqrt</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;sqrt&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    2312. 

  2312.                                  <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>
    2313. 

  2313.   <dd>
    2314. 

  2314.     
    2315. 

  2315.     <p>Computes the square root of <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>.</p>
    2316. 

  2316. <p><strong>See also:</strong></p>
    2317. 

  2317. <ul class="simple"><li><a class="reference external" href="#cbrt,float64">cbrt func</a> for the cube root</li>
    2318. 

  2318. </ul>
    2319. 

  2319. 

  2320. <p><strong class="examples_text">Example:</strong></p>
    2321. 

  2321. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">sqrt</span><span class="Punctuation">(</span><span class="FloatNumber">4.0</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="FloatNumber">2.0</span><span class="Punctuation">)</span>
    2322. 

  2322. <span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">sqrt</span><span class="Punctuation">(</span><span class="FloatNumber">1.44</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="FloatNumber">1.2</span><span class="Punctuation">)</span></pre>
    2323. 

  2323.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L369" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    2324. 

  2324. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L369" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    2325. 

  2325. 

  2326.   </dd>
    2327. 

  2327. </div>
    2328. 

  2328. 

  2329. </div>
    2330. 

  2330. <div id="sum-procs-all">
    2331. 

  2331.   <div id="sum,openArray[T]">
    2332. 

  2332.   <dt><pre><span class="Keyword">func</span> <a href="#sum%2CopenArray%5BT%5D"><span class="Identifier">sum</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="system.html#openArray"><span class="Identifier">openArray</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>
    2333. 

  2333.   <dd>
    2334. 

  2334.     
    2335. 

  2335.     <p>Computes the sum of the elements in <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>.</p>
    2336. 

  2336. <p>If <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> is empty, 0 is returned.</p>
    2337. 

  2337. <p><strong>See also:</strong></p>
    2338. 

  2338. <ul class="simple"><li><a class="reference external" href="#prod,openArray[T]">prod func</a></li>
    2339. 

  2339. <li><a class="reference external" href="#cumsum,openArray[T]">cumsum func</a></li>
    2340. 

  2340. <li><a class="reference external" href="#cumsummed,openArray[T]">cumsummed func</a></li>
    2341. 

  2341. </ul>
    2342. 

  2342. 

  2343. <p><strong class="examples_text">Example:</strong></p>
    2344. 

  2344. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">sum</span><span class="Punctuation">(</span><span class="Punctuation">[</span><span class="DecNumber">1</span><span class="Punctuation">,</span> <span class="DecNumber">2</span><span class="Punctuation">,</span> <span class="DecNumber">3</span><span class="Punctuation">,</span> <span class="DecNumber">4</span><span class="Punctuation">]</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="DecNumber">10</span>
    2345. 

  2345. <span class="Identifier">doAssert</span> <span class="Identifier">sum</span><span class="Punctuation">(</span><span class="Punctuation">[</span><span class="Operator">-</span><span class="DecNumber">4</span><span class="Punctuation">,</span> <span class="DecNumber">3</span><span class="Punctuation">,</span> <span class="DecNumber">5</span><span class="Punctuation">]</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="DecNumber">4</span></pre>
    2346. 

  2346.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L1118" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    2347. 

  2347. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L1118" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    2348. 

  2348. 

  2349.   </dd>
    2350. 

  2350. </div>
    2351. 

  2351. 

  2352. </div>
    2353. 

  2353. <div id="tan-procs-all">
    2354. 

  2354.   <div id="tan,float32">
    2355. 

  2355.   <dt><pre><span class="Keyword">func</span> <a href="#tan%2Cfloat32"><span class="Identifier">tan</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;tanf&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span> <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>
    2356. 

  2356.                                 <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>
    2357. 

  2357.   <dd>
    2358. 

  2358.     
    2359. 

  2359.     
    2360. 

  2360.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L468" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    2361. 

  2361. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L468" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    2362. 

  2362. 

  2363.   </dd>
    2364. 

  2364. </div>
    2365. 

  2365. <div id="tan,float64">
    2366. 

  2366.   <dt><pre><span class="Keyword">func</span> <a href="#tan%2Cfloat64"><span class="Identifier">tan</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;tan&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span> <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>
    2367. 

  2367.                                 <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>
    2368. 

  2368.   <dd>
    2369. 

  2369.     
    2370. 

  2370.     <p>Computes the tangent of <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>.</p>
    2371. 

  2371. <p><strong>See also:</strong></p>
    2372. 

  2372. <ul class="simple"><li><a class="reference external" href="#arctan,float64">arctan func</a></li>
    2373. 

  2373. </ul>
    2374. 

  2374. 

  2375. <p><strong class="examples_text">Example:</strong></p>
    2376. 

  2376. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">tan</span><span class="Punctuation">(</span><span class="Identifier">degToRad</span><span class="Punctuation">(</span><span class="FloatNumber">45.0</span><span class="Punctuation">)</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="FloatNumber">1.0</span><span class="Punctuation">)</span>
    2377. 

  2377. <span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">tan</span><span class="Punctuation">(</span><span class="Identifier">PI</span> <span class="Operator">/</span> <span class="DecNumber">4</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="FloatNumber">1.0</span><span class="Punctuation">)</span></pre>
    2378. 

  2378.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L469" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    2379. 

  2379. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L469" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    2380. 

  2380. 

  2381.   </dd>
    2382. 

  2382. </div>
    2383. 

  2383. 

  2384. </div>
    2385. 

  2385. <div id="tanh-procs-all">
    2386. 

  2386.   <div id="tanh,float32">
    2387. 

  2387.   <dt><pre><span class="Keyword">func</span> <a href="#tanh%2Cfloat32"><span class="Identifier">tanh</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;tanhf&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    2388. 

  2388.                                  <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>
    2389. 

  2389.   <dd>
    2390. 

  2390.     
    2391. 

  2391.     
    2392. 

  2392.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L495" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    2393. 

  2393. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L495" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    2394. 

  2394. 

  2395.   </dd>
    2396. 

  2396. </div>
    2397. 

  2397. <div id="tanh,float64">
    2398. 

  2398.   <dt><pre><span class="Keyword">func</span> <a href="#tanh%2Cfloat64"><span class="Identifier">tanh</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;tanh&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    2399. 

  2399.                                  <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>
    2400. 

  2400.   <dd>
    2401. 

  2401.     
    2402. 

  2402.     <p>Computes the <a class="reference external" href="https://en.wikipedia.org/wiki/Hyperbolic_function#Definitions">hyperbolic tangent</a> of <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>.</p>
    2403. 

  2403. <p><strong>See also:</strong></p>
    2404. 

  2404. <ul class="simple"><li><a class="reference external" href="#arctanh,float64">arctanh func</a></li>
    2405. 

  2405. </ul>
    2406. 

  2406. 

  2407. <p><strong class="examples_text">Example:</strong></p>
    2408. 

  2408. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">tanh</span><span class="Punctuation">(</span><span class="FloatNumber">0.0</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="FloatNumber">0.0</span><span class="Punctuation">)</span>
    2409. 

  2409. <span class="Identifier">doAssert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">tanh</span><span class="Punctuation">(</span><span class="FloatNumber">1.0</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="FloatNumber">0.7615941559557649</span><span class="Punctuation">)</span></pre>
    2410. 

  2410.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L496" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    2411. 

  2411. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L496" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    2412. 

  2412. 

  2413.   </dd>
    2414. 

  2414. </div>
    2415. 

  2415. 

  2416. </div>
    2417. 

  2417. <div id="trunc-procs-all">
    2418. 

  2418.   <div id="trunc,float32">
    2419. 

  2419.   <dt><pre><span class="Keyword">func</span> <a href="#trunc%2Cfloat32"><span class="Identifier">trunc</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;truncf&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    2420. 

  2420.                                   <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>
    2421. 

  2421.   <dd>
    2422. 

  2422.     
    2423. 

  2423.     
    2424. 

  2424.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L776" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    2425. 

  2425. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L776" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    2426. 

  2426. 

  2427.   </dd>
    2428. 

  2428. </div>
    2429. 

  2429. <div id="trunc,float64">
    2430. 

  2430.   <dt><pre><span class="Keyword">func</span> <a href="#trunc%2Cfloat64"><span class="Identifier">trunc</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a> {.<span class="Identifier">importc</span><span class="Other">:</span> <span class="StringLit">&quot;trunc&quot;</span><span class="Other">,</span> <span class="Identifier">header</span><span class="Other">:</span> <span class="StringLit">&quot;&lt;math.h&gt;&quot;</span><span class="Other">,</span>
    2431. 

  2431.                                   <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>
    2432. 

  2432.   <dd>
    2433. 

  2433.     
    2434. 

  2434.     <p>Truncates <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> to the decimal point.</p>
    2435. 

  2435. <p><strong>See also:</strong></p>
    2436. 

  2436. <ul class="simple"><li><a class="reference external" href="#floor,float64">floor func</a></li>
    2437. 

  2437. <li><a class="reference external" href="#ceil,float64">ceil func</a></li>
    2438. 

  2438. <li><a class="reference external" href="#round,float64">round func</a></li>
    2439. 

  2439. </ul>
    2440. 

  2440. 

  2441. <p><strong class="examples_text">Example:</strong></p>
    2442. 

  2442. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">trunc</span><span class="Punctuation">(</span><span class="Identifier">PI</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="FloatNumber">3.0</span>
    2443. 

  2443. <span class="Identifier">doAssert</span> <span class="Identifier">trunc</span><span class="Punctuation">(</span><span class="Operator">-</span><span class="FloatNumber">1.85</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="Operator">-</span><span class="FloatNumber">1.0</span></pre>
    2444. 

  2444.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/math.nim#L777" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    2445. 

  2445. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/math.nim#L777" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    2446. 

  2446. 

  2447.   </dd>
    2448. 

  2448. </div>
    2449. 

  2449. 

  2450. </div>
    2451. 

  2451. 

  2452.   </dl>
    2453. 

  2453. </div>
    2454. 

  2454. 

  2455.   </div>
    2456. 

  2456. </div>
    2457. 

  2457. 

  2458.       <div class="twelve-columns footer">
    2459. 

  2459.         <span class="nim-sprite"></span>
    2460. 

  2460.         <br>
    2461. 

  2461.         <small style="color: var(--hint);">Made with Nim. Generated: 2025-02-06 22:27:50 UTC</small>
    2462. 

  2462.       </div>
    2463. 

  2463.     </div>
    2464. 

  2464.   </div>
    2465. 

  2465.       <script defer data-domain="nim-lang.org" src="https://plausible.io/js/plausible.js"></script>
    2466. 

  2466.     
    2467. 

  2467. </body>
    2468. 

  2468. </html>
    2469. 

  2469.