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  7. <title>bignumber.js API</title>

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  56. </head>

  57. <body>

  58. 

  59.   <div class="nav">

  60. 

  61.     <b>v9.0.2</b>

  62. 

  63. 	<a class='nav-title' href="#">API</a>

  64. 

  65.     <b> CONSTRUCTOR </b>

  66.     <ul>

  67.       <li><a href="#bignumber">BigNumber</a></li>

  68.     </ul>

  69. 

  70.     <a href="#methods">Methods</a>

  71.     <ul>

  72.       <li><a href="#clone">clone</a></li>

  73.       <li><a href="#config" >config</a><span>set</span></li>

  74.       <li>

  75.         <ul class="inset">

  76.           <li><a href="#decimal-places">DECIMAL_PLACES</a></li>

  77.           <li><a href="#rounding-mode" >ROUNDING_MODE</a></li>

  78.           <li><a href="#exponential-at">EXPONENTIAL_AT</a></li>

  79.           <li><a href="#range"         >RANGE</a></li>

  80.           <li><a href="#crypto"        >CRYPTO</a></li>

  81.           <li><a href="#modulo-mode"   >MODULO_MODE</a></li>

  82.           <li><a href="#pow-precision" >POW_PRECISION</a></li>

  83.           <li><a href="#format"        >FORMAT</a></li>

  84.           <li><a href="#alphabet"      >ALPHABET</a></li>

  85.         </ul>

  86.       </li>

  87.       <li><a href="#isBigNumber">isBigNumber</a></li>

  88.       <li><a href="#max"        >maximum</a><span>max</span></li>

  89.       <li><a href="#min"        >minimum</a><span>min</span></li>

  90.       <li><a href="#random"     >random</a></li>

  91.       <li><a href="#sum"        >sum</a></li>

  92.     </ul>

  93. 

  94.     <a href="#constructor-properties">Properties</a>

  95.     <ul>

  96.       <li><a href="#round-up"        >ROUND_UP</a></li>

  97.       <li><a href="#round-down"      >ROUND_DOWN</a></li>

  98.       <li><a href="#round-ceil"      >ROUND_CEIL</a></li>

  99.       <li><a href="#round-floor"     >ROUND_FLOOR</a></li>

  100.       <li><a href="#round-half-up"   >ROUND_HALF_UP</a></li>

  101.       <li><a href="#round-half-down" >ROUND_HALF_DOWN</a></li>

  102.       <li><a href="#round-half-even" >ROUND_HALF_EVEN</a></li>

  103.       <li><a href="#round-half-ceil" >ROUND_HALF_CEIL</a></li>

  104.       <li><a href="#round-half-floor">ROUND_HALF_FLOOR</a></li>

  105.       <li><a href="#debug"           >DEBUG</a></li>

  106.     </ul>

  107. 

  108.     <b> INSTANCE </b>

  109. 

  110.     <a href="#prototype-methods">Methods</a>

  111.     <ul>

  112.       <li><a href="#abs"    >absoluteValue         </a><span>abs</span>  </li>

  113.       <li><a href="#cmp"    >comparedTo            </a>                  </li>

  114.       <li><a href="#dp"     >decimalPlaces         </a><span>dp</span>   </li>

  115.       <li><a href="#div"    >dividedBy             </a><span>div</span>  </li>

  116.       <li><a href="#divInt" >dividedToIntegerBy    </a><span>idiv</span> </li>

  117.       <li><a href="#pow"    >exponentiatedBy       </a><span>pow</span>  </li>

  118.       <li><a href="#int"    >integerValue          </a>                  </li>

  119.       <li><a href="#eq"     >isEqualTo             </a><span>eq</span>   </li>

  120.       <li><a href="#isF"    >isFinite              </a>                  </li>

  121.       <li><a href="#gt"     >isGreaterThan         </a><span>gt</span>   </li>

  122.       <li><a href="#gte"    >isGreaterThanOrEqualTo</a><span>gte</span>  </li>

  123.       <li><a href="#isInt"  >isInteger             </a>                  </li>

  124.       <li><a href="#lt"     >isLessThan            </a><span>lt</span>   </li>

  125.       <li><a href="#lte"    >isLessThanOrEqualTo   </a><span>lte</span>  </li>

  126.       <li><a href="#isNaN"  >isNaN                 </a>                  </li>

  127.       <li><a href="#isNeg"  >isNegative            </a>                  </li>

  128.       <li><a href="#isPos"  >isPositive            </a>                  </li>

  129.       <li><a href="#isZ"    >isZero                </a>                  </li>

  130.       <li><a href="#minus"  >minus                 </a>                  </li>

  131.       <li><a href="#mod"    >modulo                </a><span>mod</span>  </li>

  132.       <li><a href="#times"  >multipliedBy          </a><span>times</span></li>

  133.       <li><a href="#neg"    >negated               </a>                  </li>

  134.       <li><a href="#plus"   >plus                  </a>                  </li>

  135.       <li><a href="#sd"     >precision             </a><span>sd</span>   </li>

  136.       <li><a href="#shift"  >shiftedBy             </a>                  </li>

  137.       <li><a href="#sqrt"   >squareRoot            </a><span>sqrt</span> </li>

  138.       <li><a href="#toE"    >toExponential         </a>                  </li>

  139.       <li><a href="#toFix"  >toFixed               </a>                  </li>

  140.       <li><a href="#toFor"  >toFormat              </a>                  </li>

  141.       <li><a href="#toFr"   >toFraction            </a>                  </li>

  142.       <li><a href="#toJSON" >toJSON                </a>                  </li>

  143.       <li><a href="#toN"    >toNumber              </a>                  </li>

  144.       <li><a href="#toP"    >toPrecision           </a>                  </li>

  145.       <li><a href="#toS"    >toString              </a>                  </li>

  146.       <li><a href="#valueOf">valueOf               </a>                  </li>

  147.     </ul>

  148. 

  149.     <a href="#instance-properties">Properties</a>

  150.     <ul>

  151.       <li><a href="#coefficient">c: coefficient</a></li>

  152.       <li><a href="#exponent"   >e: exponent</a></li>

  153.       <li><a href="#sign"       >s: sign</a></li>

  154.     </ul>

  155. 

  156.     <a href="#zero-nan-infinity">Zero, NaN &amp; Infinity</a>

  157.     <a href="#Errors">Errors</a>

  158.     <a href="#type-coercion">Type coercion</a>

  159.     <a class='end' href="#faq">FAQ</a>

  160. 

  161.   </div>

  162. 

  163.   <div class="container">

  164. 

  165.     <h1>bignumber<span id='js'>.js</span></h1>

  166. 

  167.     <p>A JavaScript library for arbitrary-precision arithmetic.</p>

  168.     <p><a href="https://github.com/MikeMcl/bignumber.js">Hosted on GitHub</a>. </p>

  169. 

  170.     <h2>API</h2>

  171. 

  172.     <p>

  173.       See the <a href='https://github.com/MikeMcl/bignumber.js'>README</a> on GitHub for a

  174.       quick-start introduction.

  175.     </p>

  176.     <p>

  177.       In all examples below, <code>var</code> and semicolons are not shown, and if a commented-out

  178.       value is in quotes it means <code>toString</code> has been called on the preceding expression.

  179.     </p>

  180. 

  181. 

  182.     <h3>CONSTRUCTOR</h3>

  183. 

  184. 

  185.     <h5 id="bignumber">

  186.       BigNumber<code class='inset'>BigNumber(n [, base]) <i>&rArr; BigNumber</i></code>

  187.     </h5>

  188.     <p>

  189.       <code>n</code>: <i>number|string|BigNumber</i><br />

  190.       <code>base</code>: <i>number</i>: integer, <code>2</code> to <code>36</code> inclusive. (See

  191.       <a href='#alphabet'><code>ALPHABET</code></a> to extend this range).

  192.     </p>

  193.     <p>

  194.       Returns a new instance of a BigNumber object with value <code>n</code>, where <code>n</code>

  195.       is a numeric value in the specified <code>base</code>, or base <code>10</code> if

  196.       <code>base</code> is omitted or is <code>null</code> or <code>undefined</code>.

  197.     </p>

  198.     <p>

  199.       Note that the BigNnumber constructor accepts an <code>n</code> of type <em>number</em> purely

  200.       as a convenience so that string quotes don't have to be typed when entering literal values,

  201.       and that it is the <code>toString</code> value of <code>n</code> that is used rather than its

  202.       underlying binary floating point value converted to decimal. 

  203.     </p>

  204.     <pre>

  205. x = new BigNumber(123.4567)                // '123.4567'

  206. // 'new' is optional

  207. y = BigNumber(x)                           // '123.4567'</pre>

  208.     <p>

  209.       If <code>n</code> is a base <code>10</code> value it can be in normal or exponential notation.

  210.       Values in other bases must be in normal notation. Values in any base can have fraction digits,

  211.       i.e. digits after the decimal point.

  212.     </p>

  213.     <pre>

  214. new BigNumber(43210)                       // '43210'

  215. new BigNumber('4.321e+4')                  // '43210'

  216. new BigNumber('-735.0918e-430')            // '-7.350918e-428'

  217. new BigNumber('123412421.234324', 5)       // '607236.557696'</pre>

  218.     <p>

  219.       Signed <code>0</code>, signed <code>Infinity</code> and <code>NaN</code> are supported.

  220.     </p>

  221.     <pre>

  222. new BigNumber('-Infinity')                 // '-Infinity'

  223. new BigNumber(NaN)                         // 'NaN'

  224. new BigNumber(-0)                          // '0'

  225. new BigNumber('.5')                        // '0.5'

  226. new BigNumber('+2')                        // '2'</pre>

  227.     <p>

  228.       String values in hexadecimal literal form, e.g. <code>'0xff'</code> or <code>'0xFF'</code>

  229.       (but not <code>'0xfF'</code>), are valid, as are string values with the octal and binary

  230.       prefixs <code>'0o'</code> and <code>'0b'</code>. String values in octal literal form without

  231.       the prefix will be interpreted as decimals, e.g. <code>'011'</code> is interpreted as 11, not 9.

  232.     </p>

  233.     <pre>

  234. new BigNumber(-10110100.1, 2)              // '-180.5'

  235. new BigNumber('-0b10110100.1')             // '-180.5'

  236. new BigNumber('ff.8', 16)                  // '255.5'

  237. new BigNumber('0xff.8')                    // '255.5'</pre>

  238.     <p>

  239.       If a base is specified, <code>n</code> is rounded according to the current

  240.       <a href='#decimal-places'><code>DECIMAL_PLACES</code></a> and

  241.       <a href='#rounding-mode'><code>ROUNDING_MODE</code></a> settings. <em>This includes base

  242.       <code>10</code> so don't include a <code>base</code> parameter for decimal values unless

  243.       this behaviour is wanted.</em>

  244.     </p>

  245.     <pre>BigNumber.config({ DECIMAL_PLACES: 5 })

  246. new BigNumber(1.23456789)                  // '1.23456789'

  247. new BigNumber(1.23456789, 10)              // '1.23457'</pre>

  248.     <p>An error is thrown if <code>base</code> is invalid. See <a href='#Errors'>Errors</a>.</p>

  249.     <p>

  250.       There is no limit to the number of digits of a value of type <em>string</em> (other than

  251.       that of JavaScript's maximum array size). See <a href='#range'><code>RANGE</code></a> to set

  252.       the maximum and minimum possible exponent value of a BigNumber.

  253.     </p>

  254.     <pre>

  255. new BigNumber('5032485723458348569331745.33434346346912144534543')

  256. new BigNumber('4.321e10000000')</pre>

  257.     <p>BigNumber <code>NaN</code> is returned if <code>n</code> is invalid

  258.     (unless <code>BigNumber.DEBUG</code> is <code>true</code>, see below).</p>

  259.     <pre>

  260. new BigNumber('.1*')                       // 'NaN'

  261. new BigNumber('blurgh')                    // 'NaN'

  262. new BigNumber(9, 2)                        // 'NaN'</pre>

  263.     <p>

  264.       To aid in debugging, if <code>BigNumber.DEBUG</code> is <code>true</code> then an error will

  265.       be thrown on an invalid <code>n</code>. An error will also be thrown if <code>n</code> is of

  266.       type <em>number</em> and has more than <code>15</code> significant digits, as calling

  267.       <code><a href='#toS'>toString</a></code> or <code><a href='#valueOf'>valueOf</a></code> on

  268.       these numbers may not result in the intended value.

  269.     </p>

  270.       <pre>

  271. console.log(823456789123456.3)            //  823456789123456.2

  272. new BigNumber(823456789123456.3)          // '823456789123456.2'

  273. BigNumber.DEBUG = true

  274. // '[BigNumber Error] Number primitive has more than 15 significant digits'

  275. new BigNumber(823456789123456.3)

  276. // '[BigNumber Error] Not a base 2 number'

  277. new BigNumber(9, 2)</pre>

  278.     <p>

  279.       A BigNumber can also be created from an object literal.

  280.       Use <code><a href='#isBigNumber'>isBigNumber</a></code> to check that it is well-formed.

  281.     </p>

  282.     <pre>new BigNumber({ s: 1, e: 2, c: [ 777, 12300000000000 ], _isBigNumber: true })    // '777.123'</pre>

  283. 

  284. 

  285. 

  286. 

  287.     <h4 id="methods">Methods</h4>

  288.      <p>The static methods of a BigNumber constructor.</p>

  289. 

  290. 

  291. 

  292. 

  293.     <h5 id="clone">clone

  294.       <code class='inset'>.clone([object]) <i>&rArr; BigNumber constructor</i></code>

  295.     </h5>

  296.     <p><code>object</code>: <i>object</i></p>

  297.     <p>

  298.       Returns a new independent BigNumber constructor with configuration as described by

  299.       <code>object</code> (see <a href='#config'><code>config</code></a>), or with the default

  300.       configuration if <code>object</code> is <code>null</code> or <code>undefined</code>.

  301.     </p>

  302.     <p>

  303.       Throws if <code>object</code> is not an object. See <a href='#Errors'>Errors</a>.

  304.     </p>

  305.     <pre>BigNumber.config({ DECIMAL_PLACES: 5 })

  306. BN = BigNumber.clone({ DECIMAL_PLACES: 9 })

  307. 

  308. x = new BigNumber(1)

  309. y = new BN(1)

  310. 

  311. x.div(3)                        // 0.33333

  312. y.div(3)                        // 0.333333333

  313. 

  314. // BN = BigNumber.clone({ DECIMAL_PLACES: 9 }) is equivalent to:

  315. BN = BigNumber.clone()

  316. BN.config({ DECIMAL_PLACES: 9 })</pre>

  317. 

  318. 

  319. 

  320.     <h5 id="config">config<code class='inset'>set([object]) <i>&rArr; object</i></code></h5>

  321.     <p>

  322.       <code>object</code>: <i>object</i>: an object that contains some or all of the following

  323.       properties.

  324.     </p>

  325.     <p>Configures the settings for this particular BigNumber constructor.</p>

  326. 

  327.     <dl class='inset'>

  328.       <dt id="decimal-places"><code><b>DECIMAL_PLACES</b></code></dt>

  329.       <dd>

  330.         <i>number</i>: integer, <code>0</code> to <code>1e+9</code> inclusive<br />

  331.         Default value: <code>20</code>

  332.       </dd>

  333.       <dd>

  334.         The <em>maximum</em> number of decimal places of the results of operations involving

  335.         division, i.e. division, square root and base conversion operations, and power operations

  336.         with negative exponents.<br />

  337.       </dd>

  338.       <dd>

  339.       <pre>BigNumber.config({ DECIMAL_PLACES: 5 })

  340. BigNumber.set({ DECIMAL_PLACES: 5 })    // equivalent</pre>

  341.       </dd>

  342. 

  343. 

  344. 

  345.       <dt id="rounding-mode"><code><b>ROUNDING_MODE</b></code></dt>

  346.       <dd>

  347.         <i>number</i>: integer, <code>0</code> to <code>8</code> inclusive<br />

  348.         Default value: <code>4</code> <a href="#round-half-up">(<code>ROUND_HALF_UP</code>)</a>

  349.       </dd>

  350.       <dd>

  351.         The rounding mode used in the above operations and the default rounding mode of

  352.         <a href='#dp'><code>decimalPlaces</code></a>,

  353.         <a href='#sd'><code>precision</code></a>,

  354.         <a href='#toE'><code>toExponential</code></a>,

  355.         <a href='#toFix'><code>toFixed</code></a>,

  356.         <a href='#toFor'><code>toFormat</code></a> and

  357.         <a href='#toP'><code>toPrecision</code></a>.

  358.       </dd>

  359.       <dd>The modes are available as enumerated properties of the BigNumber constructor.</dd>

  360.        <dd>

  361.       <pre>BigNumber.config({ ROUNDING_MODE: 0 })

  362. BigNumber.set({ ROUNDING_MODE: BigNumber.ROUND_UP })    // equivalent</pre>

  363.         </dd>

  364. 

  365. 

  366. 

  367.       <dt id="exponential-at"><code><b>EXPONENTIAL_AT</b></code></dt>

  368.       <dd>

  369.         <i>number</i>: integer, magnitude <code>0</code> to <code>1e+9</code> inclusive, or

  370.         <br />

  371.         <i>number</i>[]: [ integer <code>-1e+9</code> to <code>0</code> inclusive, integer

  372.         <code>0</code> to <code>1e+9</code> inclusive ]<br />

  373.         Default value: <code>[-7, 20]</code>

  374.       </dd>

  375.       <dd>

  376.         The exponent value(s) at which <code>toString</code> returns exponential notation.

  377.       </dd>

  378.       <dd>

  379.         If a single number is assigned, the value is the exponent magnitude.<br />

  380.         If an array of two numbers is assigned then the first number is the negative exponent

  381.         value at and beneath which exponential notation is used, and the second number is the

  382.         positive exponent value at and above which the same.

  383.       </dd>

  384.       <dd>

  385.         For example, to emulate JavaScript numbers in terms of the exponent values at which they

  386.         begin to use exponential notation, use <code>[-7, 20]</code>.

  387.       </dd>

  388.       <dd>

  389.       <pre>BigNumber.config({ EXPONENTIAL_AT: 2 })

  390. new BigNumber(12.3)         // '12.3'        e is only 1

  391. new BigNumber(123)          // '1.23e+2'

  392. new BigNumber(0.123)        // '0.123'       e is only -1

  393. new BigNumber(0.0123)       // '1.23e-2'

  394. 

  395. BigNumber.config({ EXPONENTIAL_AT: [-7, 20] })

  396. new BigNumber(123456789)    // '123456789'   e is only 8

  397. new BigNumber(0.000000123)  // '1.23e-7'

  398. 

  399. // Almost never return exponential notation:

  400. BigNumber.config({ EXPONENTIAL_AT: 1e+9 })

  401. 

  402. // Always return exponential notation:

  403. BigNumber.config({ EXPONENTIAL_AT: 0 })</pre>

  404.       </dd>

  405.       <dd>

  406.         Regardless of the value of <code>EXPONENTIAL_AT</code>, the <code>toFixed</code> method

  407.         will always return a value in normal notation and the <code>toExponential</code> method

  408.         will always return a value in exponential form.

  409.       </dd>

  410.       <dd>

  411.         Calling <code>toString</code> with a base argument, e.g. <code>toString(10)</code>, will

  412.         also always return normal notation.

  413.       </dd>

  414. 

  415. 

  416. 

  417.       <dt id="range"><code><b>RANGE</b></code></dt>

  418.       <dd>

  419.         <i>number</i>: integer, magnitude <code>1</code> to <code>1e+9</code> inclusive, or

  420.         <br />

  421.         <i>number</i>[]: [ integer <code>-1e+9</code> to <code>-1</code> inclusive, integer

  422.         <code>1</code> to <code>1e+9</code> inclusive ]<br />

  423.         Default value: <code>[-1e+9, 1e+9]</code>

  424.       </dd>

  425.       <dd>

  426.         The exponent value(s) beyond which overflow to <code>Infinity</code> and underflow to

  427.         zero occurs.

  428.       </dd>

  429.       <dd>

  430.         If a single number is assigned, it is the maximum exponent magnitude: values wth a

  431.         positive exponent of greater magnitude become <code>Infinity</code> and those with a

  432.         negative exponent of greater magnitude become zero.

  433.       <dd>

  434.         If an array of two numbers is assigned then the first number is the negative exponent

  435.         limit and the second number is the positive exponent limit.

  436.       </dd>

  437.       <dd>

  438.         For example, to emulate JavaScript numbers in terms of the exponent values at which they

  439.         become zero and <code>Infinity</code>, use <code>[-324, 308]</code>.

  440.       </dd>

  441.       <dd>

  442.       <pre>BigNumber.config({ RANGE: 500 })

  443. BigNumber.config().RANGE     // [ -500, 500 ]

  444. new BigNumber('9.999e499')   // '9.999e+499'

  445. new BigNumber('1e500')       // 'Infinity'

  446. new BigNumber('1e-499')      // '1e-499'

  447. new BigNumber('1e-500')      // '0'

  448. 

  449. BigNumber.config({ RANGE: [-3, 4] })

  450. new BigNumber(99999)         // '99999'      e is only 4

  451. new BigNumber(100000)        // 'Infinity'   e is 5

  452. new BigNumber(0.001)         // '0.01'       e is only -3

  453. new BigNumber(0.0001)        // '0'          e is -4</pre>

  454.       </dd>

  455.       <dd>

  456.         The largest possible magnitude of a finite BigNumber is

  457.         <code>9.999...e+1000000000</code>.<br />

  458.         The smallest possible magnitude of a non-zero BigNumber is <code>1e-1000000000</code>.

  459.       </dd>

  460. 

  461. 

  462. 

  463.       <dt id="crypto"><code><b>CRYPTO</b></code></dt>

  464.       <dd>

  465.         <i>boolean</i>: <code>true</code> or <code>false</code>.<br />

  466.         Default value: <code>false</code>

  467.       </dd>

  468.       <dd>

  469.         The value that determines whether cryptographically-secure pseudo-random number

  470.         generation is used.

  471.       </dd>

  472.       <dd>

  473.         If <code>CRYPTO</code> is set to <code>true</code> then the

  474.         <a href='#random'><code>random</code></a> method will generate random digits using

  475.         <code>crypto.getRandomValues</code> in browsers that support it, or

  476.         <code>crypto.randomBytes</code> if using Node.js.

  477.       </dd>

  478.       <dd>

  479.         If neither function is supported by the host environment then attempting to set

  480.         <code>CRYPTO</code> to <code>true</code> will fail and an exception will be thrown.

  481.       </dd>

  482.       <dd>

  483.         If <code>CRYPTO</code> is <code>false</code> then the source of randomness used will be

  484.         <code>Math.random</code> (which is assumed to generate at least <code>30</code> bits of

  485.         randomness).

  486.       </dd>

  487.       <dd>See <a href='#random'><code>random</code></a>.</dd>

  488.       <dd>

  489.       <pre>

  490. // Node.js

  491. const crypto = require('crypto');   // CommonJS

  492. import * as crypto from 'crypto';   // ES module

  493. 

  494. global.crypto = crypto;

  495. 

  496. BigNumber.config({ CRYPTO: true })

  497. BigNumber.config().CRYPTO       // true

  498. BigNumber.random()              // 0.54340758610486147524</pre>

  499.       </dd>

  500. 

  501. 

  502. 

  503.       <dt id="modulo-mode"><code><b>MODULO_MODE</b></code></dt>

  504.       <dd>

  505.         <i>number</i>: integer, <code>0</code> to <code>9</code> inclusive<br />

  506.         Default value: <code>1</code> (<a href="#round-down"><code>ROUND_DOWN</code></a>)

  507.       </dd>

  508.       <dd>The modulo mode used when calculating the modulus: <code>a mod n</code>.</dd>

  509.       <dd>

  510.         The quotient, <code>q = a / n</code>, is calculated according to the

  511.         <a href='#rounding-mode'><code>ROUNDING_MODE</code></a> that corresponds to the chosen

  512.         <code>MODULO_MODE</code>.

  513.       </dd>

  514.       <dd>The remainder, <code>r</code>, is calculated as: <code>r = a - n * q</code>.</dd>

  515.       <dd>

  516.         The modes that are most commonly used for the modulus/remainder operation are shown in

  517.         the following table. Although the other rounding modes can be used, they may not give

  518.         useful results.

  519.       </dd>

  520.       <dd>

  521.         <table>

  522.           <tr><th>Property</th><th>Value</th><th>Description</th></tr>

  523.           <tr>

  524.             <td><b>ROUND_UP</b></td><td class='centre'>0</td>

  525.             <td>

  526.               The remainder is positive if the dividend is negative, otherwise it is negative.

  527.             </td>

  528.           </tr>

  529.           <tr>

  530.             <td><b>ROUND_DOWN</b></td><td class='centre'>1</td>

  531.             <td>

  532.               The remainder has the same sign as the dividend.<br />

  533.               This uses 'truncating division' and matches the behaviour of JavaScript's

  534.               remainder operator <code>%</code>.

  535.             </td>

  536.           </tr>

  537.           <tr>

  538.             <td><b>ROUND_FLOOR</b></td><td class='centre'>3</td>

  539.             <td>

  540.               The remainder has the same sign as the divisor.<br />

  541.               This matches Python's <code>%</code> operator.

  542.             </td>

  543.           </tr>

  544.           <tr>

  545.             <td><b>ROUND_HALF_EVEN</b></td><td class='centre'>6</td>

  546.             <td>The <i>IEEE 754</i> remainder function.</td>

  547.           </tr>

  548.            <tr>

  549.              <td><b>EUCLID</b></td><td class='centre'>9</td>

  550.              <td>

  551.                The remainder is always positive. Euclidian division: <br />

  552.                <code>q = sign(n) * floor(a / abs(n))</code>

  553.              </td>

  554.            </tr>

  555.         </table>

  556.       </dd>

  557.       <dd>

  558.         The rounding/modulo modes are available as enumerated properties of the BigNumber

  559.         constructor.

  560.       </dd>

  561.       <dd>See <a href='#mod'><code>modulo</code></a>.</dd>

  562.       <dd>

  563.         <pre>BigNumber.config({ MODULO_MODE: BigNumber.EUCLID })

  564. BigNumber.config({ MODULO_MODE: 9 })          // equivalent</pre>

  565.       </dd>

  566. 

  567. 

  568. 

  569.       <dt id="pow-precision"><code><b>POW_PRECISION</b></code></dt>

  570.       <dd>

  571.         <i>number</i>: integer, <code>0</code> to <code>1e+9</code> inclusive.<br />

  572.         Default value: <code>0</code>

  573.       </dd>

  574.       <dd>

  575.         The <i>maximum</i> precision, i.e. number of significant digits, of the result of the power

  576.         operation (unless a modulus is specified).

  577.       </dd>

  578.       <dd>If set to <code>0</code>, the number of significant digits will not be limited.</dd>

  579.       <dd>See <a href='#pow'><code>exponentiatedBy</code></a>.</dd>

  580.       <dd><pre>BigNumber.config({ POW_PRECISION: 100 })</pre></dd>

  581. 

  582. 

  583. 

  584.       <dt id="format"><code><b>FORMAT</b></code></dt>

  585.       <dd><i>object</i></dd>

  586.       <dd>

  587.         The <code>FORMAT</code> object configures the format of the string returned by the

  588.         <a href='#toFor'><code>toFormat</code></a> method.

  589.       </dd>

  590.       <dd>

  591.         The example below shows the properties of the <code>FORMAT</code> object that are

  592.         recognised, and their default values.

  593.       </dd>

  594.       <dd>

  595.          Unlike the other configuration properties, the values of the properties of the

  596.          <code>FORMAT</code> object will not be checked for validity. The existing

  597.          <code>FORMAT</code> object will simply be replaced by the object that is passed in.

  598.          The object can include any number of the properties shown below.

  599.       </dd>

  600.       <dd>See <a href='#toFor'><code>toFormat</code></a> for examples of usage.</dd>

  601.       <dd>

  602.       <pre>

  603. BigNumber.config({

  604.   FORMAT: {

  605.     // string to prepend

  606.     prefix: '',

  607.     // decimal separator

  608.     decimalSeparator: '.',

  609.     // grouping separator of the integer part

  610.     groupSeparator: ',',

  611.     // primary grouping size of the integer part

  612.     groupSize: 3,

  613.     // secondary grouping size of the integer part

  614.     secondaryGroupSize: 0,

  615.     // grouping separator of the fraction part

  616.     fractionGroupSeparator: ' ',

  617.     // grouping size of the fraction part

  618.     fractionGroupSize: 0,

  619.     // string to append

  620.     suffix: ''

  621.   }

  622. });</pre>

  623.       </dd>

  624. 

  625. 

  626. 

  627.       <dt id="alphabet"><code><b>ALPHABET</b></code></dt>

  628.       <dd>

  629.         <i>string</i><br />

  630.         Default value: <code>'0123456789abcdefghijklmnopqrstuvwxyz'</code>

  631.       </dd>

  632.       <dd>

  633.         The alphabet used for base conversion. The length of the alphabet corresponds to the

  634.         maximum value of the base argument that can be passed to the

  635.         <a href='#bignumber'><code>BigNumber</code></a> constructor or

  636.         <a href='#toS'><code>toString</code></a>.

  637.       </dd>

  638.       <dd>

  639.         There is no maximum length for the alphabet, but it must be at least 2 characters long, and

  640.         it must not contain whitespace or a repeated character, or the sign indicators

  641.         <code>'+'</code> and <code>'-'</code>, or the decimal separator <code>'.'</code>.

  642.       </dd>

  643.       <dd>

  644.         <pre>// duodecimal (base 12)

  645. BigNumber.config({ ALPHABET: '0123456789TE' })

  646. x = new BigNumber('T', 12)

  647. x.toString()                // '10'

  648. x.toString(12)              // 'T'</pre>

  649.       </dd>

  650. 

  651. 

  652. 

  653.     </dl>

  654.     <br /><br />

  655.     <p>Returns an object with the above properties and their current values.</p>

  656.     <p>

  657.       Throws if <code>object</code> is not an object, or if an invalid value is assigned to

  658.       one or more of the above properties. See <a href='#Errors'>Errors</a>.

  659.     </p>

  660.     <pre>

  661. BigNumber.config({

  662.   DECIMAL_PLACES: 40,

  663.   ROUNDING_MODE: BigNumber.ROUND_HALF_CEIL,

  664.   EXPONENTIAL_AT: [-10, 20],

  665.   RANGE: [-500, 500],

  666.   CRYPTO: true,

  667.   MODULO_MODE: BigNumber.ROUND_FLOOR,

  668.   POW_PRECISION: 80,

  669.   FORMAT: {

  670.     groupSize: 3,

  671.     groupSeparator: ' ',

  672.     decimalSeparator: ','

  673.   },

  674.   ALPHABET: '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ$_'

  675. });

  676. 

  677. obj = BigNumber.config();

  678. obj.DECIMAL_PLACES        // 40

  679. obj.RANGE                 // [-500, 500]</pre>

  680. 

  681. 

  682. 

  683.     <h5 id="isBigNumber">

  684.       isBigNumber<code class='inset'>.isBigNumber(value) <i>&rArr; boolean</i></code>

  685.     </h5>

  686.     <p><code>value</code>: <i>any</i><br /></p>

  687.     <p>

  688.       Returns <code>true</code> if <code>value</code> is a BigNumber instance, otherwise returns

  689.       <code>false</code>.

  690.     </p>

  691.     <pre>x = 42

  692. y = new BigNumber(x)

  693. 

  694. BigNumber.isBigNumber(x)             // false

  695. y instanceof BigNumber               // true

  696. BigNumber.isBigNumber(y)             // true

  697. 

  698. BN = BigNumber.clone();

  699. z = new BN(x)

  700. z instanceof BigNumber               // false

  701. BigNumber.isBigNumber(z)             // true</pre>

  702.     <p>

  703.       If <code>value</code> is a BigNumber instance and <code>BigNumber.DEBUG</code> is <code>true</code>,

  704.       then this method will also check if <code>value</code> is well-formed, and throw if it is not.

  705.       See <a href='#Errors'>Errors</a>.

  706.     </p>

  707.     <p>

  708.       The check can be useful if creating a BigNumber from an object literal.

  709.       See <a href='#bignumber'>BigNumber</a>.

  710.     </p>

  711.     <pre>

  712. x = new BigNumber(10)

  713. 

  714. // Change x.c to an illegitimate value.

  715. x.c = NaN

  716. 

  717. BigNumber.DEBUG = false

  718. 

  719. // No error.

  720. BigNumber.isBigNumber(x)    // true

  721. 

  722. BigNumber.DEBUG = true

  723. 

  724. // Error.

  725. BigNumber.isBigNumber(x)    // '[BigNumber Error] Invalid BigNumber'</pre>

  726. 

  727. 

  728. 

  729.     <h5 id="max">maximum<code class='inset'>.max(n...) <i>&rArr; BigNumber</i></code></h5>

  730.     <p>

  731.       <code>n</code>: <i>number|string|BigNumber</i><br />

  732.       <i>See <code><a href="#bignumber">BigNumber</a></code> for further parameter details.</i>

  733.     </p>

  734.     <p>

  735.       Returns a BigNumber whose value is the maximum of the arguments.

  736.     </p>

  737.     <p>The return value is always exact and unrounded.</p>

  738.     <pre>x = new BigNumber('3257869345.0378653')

  739. BigNumber.maximum(4e9, x, '123456789.9')      // '4000000000'

  740. 

  741. arr = [12, '13', new BigNumber(14)]

  742. BigNumber.max.apply(null, arr)                // '14'</pre>

  743. 

  744. 

  745. 

  746.     <h5 id="min">minimum<code class='inset'>.min(n...) <i>&rArr; BigNumber</i></code></h5>

  747.     <p>

  748.       <code>n</code>: <i>number|string|BigNumber</i><br />

  749.       <i>See <code><a href="#bignumber">BigNumber</a></code> for further parameter details.</i>

  750.     </p>

  751.     <p>

  752.       Returns a BigNumber whose value is the minimum of the arguments.

  753.     </p>

  754.     <p>The return value is always exact and unrounded.</p>

  755.     <pre>x = new BigNumber('3257869345.0378653')

  756. BigNumber.minimum(4e9, x, '123456789.9')      // '123456789.9'

  757. 

  758. arr = [2, new BigNumber(-14), '-15.9999', -12]

  759. BigNumber.min.apply(null, arr)                // '-15.9999'</pre>

  760. 

  761. 

  762. 

  763.     <h5 id="random">

  764.       random<code class='inset'>.random([dp]) <i>&rArr; BigNumber</i></code>

  765.     </h5>

  766.     <p><code>dp</code>: <i>number</i>: integer, <code>0</code> to <code>1e+9</code> inclusive</p>

  767.     <p>

  768.       Returns a new BigNumber with a pseudo-random value equal to or greater than <code>0</code> and

  769.       less than <code>1</code>.

  770.     </p>

  771.     <p>

  772.       The return value will have <code>dp</code> decimal places (or less if trailing zeros are

  773.       produced).<br />

  774.       If <code>dp</code> is omitted then the number of decimal places will default to the current

  775.       <a href='#decimal-places'><code>DECIMAL_PLACES</code></a> setting.

  776.     </p>

  777.     <p>

  778.       Depending on the value of this BigNumber constructor's

  779.       <a href='#crypto'><code>CRYPTO</code></a> setting and the support for the

  780.       <code>crypto</code> object in the host environment, the random digits of the return value are

  781.       generated by either <code>Math.random</code> (fastest), <code>crypto.getRandomValues</code>

  782.       (Web Cryptography API in recent browsers) or <code>crypto.randomBytes</code> (Node.js).

  783.     </p>

  784.     <p>

  785.       To be able to set <a href='#crypto'><code>CRYPTO</code></a> to <code>true</code> when using

  786.       Node.js, the <code>crypto</code> object must be available globally:

  787.     </p>

  788.     <pre>// Node.js

  789. const crypto = require('crypto');   // CommonJS

  790. import * as crypto from 'crypto';   // ES module

  791. global.crypto = crypto;</pre>

  792.     <p>

  793.       If <a href='#crypto'><code>CRYPTO</code></a> is <code>true</code>, i.e. one of the

  794.       <code>crypto</code> methods is to be used, the value of a returned BigNumber should be

  795.       cryptographically-secure and statistically indistinguishable from a random value.

  796.     </p>

  797.     <p>

  798.       Throws if <code>dp</code> is invalid. See <a href='#Errors'>Errors</a>.

  799.     </p>

  800.     <pre>BigNumber.config({ DECIMAL_PLACES: 10 })

  801. BigNumber.random()              // '0.4117936847'

  802. BigNumber.random(20)            // '0.78193327636914089009'</pre>

  803. 

  804. 

  805. 

  806.     <h5 id="sum">sum<code class='inset'>.sum(n...) <i>&rArr; BigNumber</i></code></h5>

  807.     <p>

  808.       <code>n</code>: <i>number|string|BigNumber</i><br />

  809.       <i>See <code><a href="#bignumber">BigNumber</a></code> for further parameter details.</i>

  810.     </p>

  811.     <p>Returns a BigNumber whose value is the sum of the arguments.</p>

  812.     <p>The return value is always exact and unrounded.</p>

  813.     <pre>x = new BigNumber('3257869345.0378653')

  814. BigNumber.sum(4e9, x, '123456789.9')      // '7381326134.9378653'

  815. 

  816. arr = [2, new BigNumber(14), '15.9999', 12]

  817. BigNumber.sum.apply(null, arr)            // '43.9999'</pre>

  818. 

  819. 

  820. 

  821.     <h4 id="constructor-properties">Properties</h4>

  822.     <p>

  823.       The library's enumerated rounding modes are stored as properties of the constructor.<br />

  824.       (They are not referenced internally by the library itself.)

  825.     </p>

  826.     <p>

  827.       Rounding modes <code>0</code> to <code>6</code> (inclusive) are the same as those of Java's

  828.       BigDecimal class.

  829.     </p>

  830.     <table>

  831.       <tr>

  832.         <th>Property</th>

  833.         <th>Value</th>

  834.         <th>Description</th>

  835.       </tr>

  836.       <tr>

  837.         <td id="round-up"><b>ROUND_UP</b></td>

  838.         <td class='centre'>0</td>

  839.         <td>Rounds away from zero</td>

  840.       </tr>

  841.       <tr>

  842.         <td id="round-down"><b>ROUND_DOWN</b></td>

  843.         <td class='centre'>1</td>

  844.         <td>Rounds towards zero</td>

  845.       </tr>

  846.       <tr>

  847.         <td id="round-ceil"><b>ROUND_CEIL</b></td>

  848.         <td class='centre'>2</td>

  849.         <td>Rounds towards <code>Infinity</code></td>

  850.       </tr>

  851.       <tr>

  852.         <td id="round-floor"><b>ROUND_FLOOR</b></td>

  853.         <td class='centre'>3</td>

  854.         <td>Rounds towards <code>-Infinity</code></td>

  855.       </tr>

  856.       <tr>

  857.         <td id="round-half-up"><b>ROUND_HALF_UP</b></td>

  858.         <td class='centre'>4</td>

  859.         <td>

  860.           Rounds towards nearest neighbour.<br />

  861.           If equidistant, rounds away from zero

  862.         </td>

  863.       </tr>

  864.       <tr>

  865.         <td id="round-half-down"><b>ROUND_HALF_DOWN</b></td>

  866.         <td class='centre'>5</td>

  867.         <td>

  868.           Rounds towards nearest neighbour.<br />

  869.           If equidistant, rounds towards zero

  870.         </td>

  871.       </tr>

  872.       <tr>

  873.         <td id="round-half-even"><b>ROUND_HALF_EVEN</b></td>

  874.         <td class='centre'>6</td>

  875.         <td>

  876.           Rounds towards nearest neighbour.<br />

  877.           If equidistant, rounds towards even neighbour

  878.         </td>

  879.       </tr>

  880.       <tr>

  881.         <td id="round-half-ceil"><b>ROUND_HALF_CEIL</b></td>

  882.         <td class='centre'>7</td>

  883.         <td>

  884.           Rounds towards nearest neighbour.<br />

  885.           If equidistant, rounds towards <code>Infinity</code>

  886.         </td>

  887.       </tr>

  888.       <tr>

  889.         <td id="round-half-floor"><b>ROUND_HALF_FLOOR</b></td>

  890.         <td class='centre'>8</td>

  891.         <td>

  892.           Rounds towards nearest neighbour.<br />

  893.           If equidistant, rounds towards <code>-Infinity</code>

  894.         </td>

  895.       </tr>

  896.     </table>

  897.     <pre>

  898. BigNumber.config({ ROUNDING_MODE: BigNumber.ROUND_CEIL })

  899. BigNumber.config({ ROUNDING_MODE: 2 })     // equivalent</pre>

  900. 

  901.     <h5 id="debug">DEBUG</h5>

  902.     <p><i>undefined|false|true</i></p>

  903.     <p>

  904.       If <code>BigNumber.DEBUG</code> is set <code>true</code> then an error will be thrown

  905.       if this <a href='#bignumber'>BigNumber</a> constructor receives an invalid value, such as

  906.       a value of type <em>number</em> with more than <code>15</code> significant digits.

  907.       See <a href='#bignumber'>BigNumber</a>.

  908.     </p>

  909.     <p>

  910.       An error will also be thrown if the <code><a href='#isBigNumber'>isBigNumber</a></code>

  911.       method receives a BigNumber that is not well-formed.

  912.       See <code><a href='#isBigNumber'>isBigNumber</a></code>.

  913.     </p>

  914.     <pre>BigNumber.DEBUG = true</pre>

  915. 

  916. 

  917.     <h3>INSTANCE</h3>

  918. 

  919. 

  920.     <h4 id="prototype-methods">Methods</h4>

  921.     <p>The methods inherited by a BigNumber instance from its constructor's prototype object.</p>

  922.     <p>A BigNumber is immutable in the sense that it is not changed by its methods. </p>

  923.     <p>

  924.       The treatment of &plusmn;<code>0</code>, &plusmn;<code>Infinity</code> and <code>NaN</code> is

  925.       consistent with how JavaScript treats these values.

  926.     </p>

  927.     <p>Many method names have a shorter alias.</p>

  928. 

  929. 

  930. 

  931.     <h5 id="abs">absoluteValue<code class='inset'>.abs() <i>&rArr; BigNumber</i></code></h5>

  932.     <p>

  933.       Returns a BigNumber whose value is the absolute value, i.e. the magnitude, of the value of

  934.       this BigNumber.

  935.     </p>

  936.     <p>The return value is always exact and unrounded.</p>

  937.     <pre>

  938. x = new BigNumber(-0.8)

  939. y = x.absoluteValue()           // '0.8'

  940. z = y.abs()                     // '0.8'</pre>

  941. 

  942. 

  943. 

  944.     <h5 id="cmp">

  945.       comparedTo<code class='inset'>.comparedTo(n [, base]) <i>&rArr; number</i></code>

  946.     </h5>

  947.     <p>

  948.       <code>n</code>: <i>number|string|BigNumber</i><br />

  949.       <code>base</code>: <i>number</i><br />

  950.       <i>See <a href="#bignumber">BigNumber</a> for further parameter details.</i>

  951.     </p>

  952.     <table>

  953.       <tr><th>Returns</th><th>&nbsp;</th></tr>

  954.       <tr>

  955.         <td class='centre'><code>1</code></td>

  956.         <td>If the value of this BigNumber is greater than the value of <code>n</code></td>

  957.       </tr>

  958.       <tr>

  959.         <td class='centre'><code>-1</code></td>

  960.         <td>If the value of this BigNumber is less than the value of <code>n</code></td>

  961.       </tr>

  962.       <tr>

  963.         <td class='centre'><code>0</code></td>

  964.         <td>If this BigNumber and <code>n</code> have the same value</td>

  965.       </tr>

  966.        <tr>

  967.         <td class='centre'><code>null</code></td>

  968.         <td>If the value of either this BigNumber or <code>n</code> is <code>NaN</code></td>

  969.       </tr>

  970.     </table>

  971.     <pre>

  972. x = new BigNumber(Infinity)

  973. y = new BigNumber(5)

  974. x.comparedTo(y)                 // 1

  975. x.comparedTo(x.minus(1))        // 0

  976. y.comparedTo(NaN)               // null

  977. y.comparedTo('110', 2)          // -1</pre>

  978. 

  979. 

  980. 

  981.     <h5 id="dp">

  982.       decimalPlaces<code class='inset'>.dp([dp [, rm]]) <i>&rArr; BigNumber|number</i></code>

  983.     </h5>

  984.     <p>

  985.       <code>dp</code>: <i>number</i>: integer, <code>0</code> to <code>1e+9</code> inclusive<br />

  986.       <code>rm</code>: <i>number</i>: integer, <code>0</code> to <code>8</code> inclusive

  987.     </p>

  988.     <p>

  989.       If <code>dp</code> is a number, returns a BigNumber whose value is the value of this BigNumber

  990.       rounded by rounding mode <code>rm</code> to a maximum of <code>dp</code> decimal places.

  991.     </p>

  992.     <p>

  993.       If <code>dp</code> is omitted, or is <code>null</code> or <code>undefined</code>, the return

  994.       value is the number of decimal places of the value of this BigNumber, or <code>null</code> if

  995.       the value of this BigNumber is &plusmn;<code>Infinity</code> or <code>NaN</code>.

  996.     </p>

  997.     <p>

  998.       If <code>rm</code> is omitted, or is <code>null</code> or <code>undefined</code>,

  999.       <a href='#rounding-mode'><code>ROUNDING_MODE</code></a> is used.

  1000.     </p>

  1001.     <p>

  1002.       Throws if <code>dp</code> or <code>rm</code> is invalid. See <a href='#Errors'>Errors</a>.

  1003.     </p>

  1004.     <pre>

  1005. x = new BigNumber(1234.56)

  1006. x.decimalPlaces(1)                     // '1234.6'

  1007. x.dp()                                 // 2

  1008. x.decimalPlaces(2)                     // '1234.56'

  1009. x.dp(10)                               // '1234.56'

  1010. x.decimalPlaces(0, 1)                  // '1234'

  1011. x.dp(0, 6)                             // '1235'

  1012. x.decimalPlaces(1, 1)                  // '1234.5'

  1013. x.dp(1, BigNumber.ROUND_HALF_EVEN)     // '1234.6'

  1014. x                                      // '1234.56'

  1015. y = new BigNumber('9.9e-101')

  1016. y.dp()                                 // 102</pre>

  1017. 

  1018. 

  1019. 

  1020.     <h5 id="div">dividedBy<code class='inset'>.div(n [, base]) <i>&rArr; BigNumber</i></code>

  1021.     </h5>

  1022.     <p>

  1023.       <code>n</code>: <i>number|string|BigNumber</i><br />

  1024.       <code>base</code>: <i>number</i><br />

  1025.       <i>See <a href="#bignumber">BigNumber</a> for further parameter details.</i>

  1026.     </p>

  1027.     <p>

  1028.       Returns a BigNumber whose value is the value of this BigNumber divided by

  1029.       <code>n</code>, rounded according to the current

  1030.       <a href='#decimal-places'><code>DECIMAL_PLACES</code></a> and

  1031.       <a href='#rounding-mode'><code>ROUNDING_MODE</code></a> settings.

  1032.     </p>

  1033.     <pre>

  1034. x = new BigNumber(355)

  1035. y = new BigNumber(113)

  1036. x.dividedBy(y)                  // '3.14159292035398230088'

  1037. x.div(5)                        // '71'

  1038. x.div(47, 16)                   // '5'</pre>

  1039. 

  1040. 

  1041. 

  1042.     <h5 id="divInt">

  1043.       dividedToIntegerBy<code class='inset'>.idiv(n [, base]) &rArr;

  1044.       <i>BigNumber</i></code>

  1045.     </h5>

  1046.     <p>

  1047.       <code>n</code>: <i>number|string|BigNumber</i><br />

  1048.       <code>base</code>: <i>number</i><br />

  1049.       <i>See <a href="#bignumber">BigNumber</a> for further parameter details.</i>

  1050.     </p>

  1051.     <p>

  1052.       Returns a BigNumber whose value is the integer part of dividing the value of this BigNumber by

  1053.       <code>n</code>.

  1054.     </p>

  1055.     <pre>

  1056. x = new BigNumber(5)

  1057. y = new BigNumber(3)

  1058. x.dividedToIntegerBy(y)         // '1'

  1059. x.idiv(0.7)                     // '7'

  1060. x.idiv('0.f', 16)               // '5'</pre>

  1061. 

  1062. 

  1063. 

  1064.     <h5 id="pow">

  1065.       exponentiatedBy<code class='inset'>.pow(n [, m]) <i>&rArr; BigNumber</i></code>

  1066.     </h5>

  1067.     <p>

  1068.       <code>n</code>: <i>number|string|BigNumber</i>: integer<br />

  1069.       <code>m</code>: <i>number|string|BigNumber</i>

  1070.     </p>

  1071.     <p>

  1072.       Returns a BigNumber whose value is the value of this BigNumber exponentiated by

  1073.       <code>n</code>, i.e. raised to the power <code>n</code>, and optionally modulo a modulus

  1074.       <code>m</code>.

  1075.     </p>

  1076.     <p>

  1077.       Throws if <code>n</code> is not an integer. See <a href='#Errors'>Errors</a>.

  1078.     </p>

  1079.     <p>

  1080.       If <code>n</code> is negative the result is rounded according to the current

  1081.       <a href='#decimal-places'><code>DECIMAL_PLACES</code></a> and

  1082.       <a href='#rounding-mode'><code>ROUNDING_MODE</code></a> settings.

  1083.     </p>

  1084.     <p>

  1085.       As the number of digits of the result of the power operation can grow so large so quickly,

  1086.       e.g. 123.456<sup>10000</sup> has over <code>50000</code> digits, the number of significant

  1087.       digits calculated is limited to the value of the

  1088.       <a href='#pow-precision'><code>POW_PRECISION</code></a> setting (unless a modulus

  1089.       <code>m</code> is specified).

  1090.     </p>

  1091.     <p>

  1092.       By default <a href='#pow-precision'><code>POW_PRECISION</code></a> is set to <code>0</code>.

  1093.       This means that an unlimited number of significant digits will be calculated, and that the

  1094.       method's performance will decrease dramatically for larger exponents.

  1095.     </p>

  1096.     <p>

  1097.       If <code>m</code> is specified and the value of <code>m</code>, <code>n</code> and this

  1098.       BigNumber are integers, and <code>n</code> is positive, then a fast modular exponentiation

  1099.       algorithm is used, otherwise the operation will be performed as

  1100.       <code>x.exponentiatedBy(n).modulo(m)</code> with a

  1101.       <a href='#pow-precision'><code>POW_PRECISION</code></a> of <code>0</code>.

  1102.     </p>

  1103.     <pre>

  1104. Math.pow(0.7, 2)                // 0.48999999999999994

  1105. x = new BigNumber(0.7)

  1106. x.exponentiatedBy(2)            // '0.49'

  1107. BigNumber(3).pow(-2)            // '0.11111111111111111111'</pre>

  1108. 

  1109. 

  1110. 

  1111.     <h5 id="int">

  1112.       integerValue<code class='inset'>.integerValue([rm]) <i>&rArr; BigNumber</i></code>

  1113.     </h5>

  1114.     <p>

  1115.       <code>rm</code>: <i>number</i>: integer, <code>0</code> to <code>8</code> inclusive

  1116.     </p>

  1117.    <p>

  1118.       Returns a BigNumber whose value is the value of this BigNumber rounded to an integer using

  1119.       rounding mode <code>rm</code>.

  1120.     </p>

  1121.     <p>

  1122.       If <code>rm</code> is omitted, or is <code>null</code> or <code>undefined</code>,

  1123.       <a href='#rounding-mode'><code>ROUNDING_MODE</code></a> is used.

  1124.     </p>

  1125.     <p>

  1126.       Throws if <code>rm</code> is invalid. See <a href='#Errors'>Errors</a>.

  1127.     </p>

  1128.     <pre>

  1129. x = new BigNumber(123.456)

  1130. x.integerValue()                        // '123'

  1131. x.integerValue(BigNumber.ROUND_CEIL)    // '124'

  1132. y = new BigNumber(-12.7)

  1133. y.integerValue()                        // '-13'

  1134. y.integerValue(BigNumber.ROUND_DOWN)    // '-12'</pre>

  1135.     <p>

  1136.       The following is an example of how to add a prototype method that emulates JavaScript's

  1137.       <code>Math.round</code> function. <code>Math.ceil</code>, <code>Math.floor</code> and

  1138.       <code>Math.trunc</code> can be emulated in the same way with

  1139.       <code>BigNumber.ROUND_CEIL</code>, <code>BigNumber.ROUND_FLOOR</code> and

  1140.       <code> BigNumber.ROUND_DOWN</code> respectively.

  1141.     </p>

  1142.     <pre>

  1143. BigNumber.prototype.round = function () {

  1144.   return this.integerValue(BigNumber.ROUND_HALF_CEIL);

  1145. };

  1146. x.round()                               // '123'</pre>

  1147. 

  1148. 

  1149. 

  1150.     <h5 id="eq">isEqualTo<code class='inset'>.eq(n [, base]) <i>&rArr; boolean</i></code></h5>

  1151.     <p>

  1152.       <code>n</code>: <i>number|string|BigNumber</i><br />

  1153.       <code>base</code>: <i>number</i><br />

  1154.       <i>See <a href="#bignumber">BigNumber</a> for further parameter details.</i>

  1155.     </p>

  1156.     <p>

  1157.       Returns <code>true</code> if the value of this BigNumber is equal to the value of

  1158.       <code>n</code>, otherwise returns <code>false</code>.<br />

  1159.       As with JavaScript, <code>NaN</code> does not equal <code>NaN</code>.

  1160.     </p>

  1161.     <p>Note: This method uses the <a href='#cmp'><code>comparedTo</code></a> method internally.</p>

  1162.     <pre>

  1163. 0 === 1e-324                    // true

  1164. x = new BigNumber(0)

  1165. x.isEqualTo('1e-324')           // false

  1166. BigNumber(-0).eq(x)             // true  ( -0 === 0 )

  1167. BigNumber(255).eq('ff', 16)     // true

  1168. 

  1169. y = new BigNumber(NaN)

  1170. y.isEqualTo(NaN)                // false</pre>

  1171. 

  1172. 

  1173. 

  1174.     <h5 id="isF">isFinite<code class='inset'>.isFinite() <i>&rArr; boolean</i></code></h5>

  1175.     <p>

  1176.       Returns <code>true</code> if the value of this BigNumber is a finite number, otherwise

  1177.       returns <code>false</code>.

  1178.     </p>

  1179.     <p>

  1180.       The only possible non-finite values of a BigNumber are <code>NaN</code>, <code>Infinity</code>

  1181.       and <code>-Infinity</code>.

  1182.     </p>

  1183.     <pre>

  1184. x = new BigNumber(1)

  1185. x.isFinite()                    // true

  1186. y = new BigNumber(Infinity)

  1187. y.isFinite()                    // false</pre>

  1188.     <p>

  1189.       Note: The native method <code>isFinite()</code> can be used if

  1190.       <code>n &lt;= Number.MAX_VALUE</code>.

  1191.     </p>

  1192. 

  1193. 

  1194. 

  1195.     <h5 id="gt">isGreaterThan<code class='inset'>.gt(n [, base]) <i>&rArr; boolean</i></code></h5>

  1196.     <p>

  1197.       <code>n</code>: <i>number|string|BigNumber</i><br />

  1198.       <code>base</code>: <i>number</i><br />

  1199.       <i>See <a href="#bignumber">BigNumber</a> for further parameter details.</i>

  1200.     </p>

  1201.     <p>

  1202.       Returns <code>true</code> if the value of this BigNumber is greater than the value of

  1203.       <code>n</code>, otherwise returns <code>false</code>.

  1204.     </p>

  1205.     <p>Note: This method uses the <a href='#cmp'><code>comparedTo</code></a> method internally.</p>

  1206.     <pre>

  1207. 0.1 &gt; (0.3 - 0.2)                             // true

  1208. x = new BigNumber(0.1)

  1209. x.isGreaterThan(BigNumber(0.3).minus(0.2))    // false

  1210. BigNumber(0).gt(x)                            // false

  1211. BigNumber(11, 3).gt(11.1, 2)                  // true</pre>

  1212. 

  1213. 

  1214. 

  1215.     <h5 id="gte">

  1216.       isGreaterThanOrEqualTo<code class='inset'>.gte(n [, base]) <i>&rArr; boolean</i></code>

  1217.     </h5>

  1218.     <p>

  1219.       <code>n</code>: <i>number|string|BigNumber</i><br />

  1220.       <code>base</code>: <i>number</i><br />

  1221.       <i>See <a href="#bignumber">BigNumber</a> for further parameter details.</i>

  1222.     </p>

  1223.     <p>

  1224.       Returns <code>true</code> if the value of this BigNumber is greater than or equal to the value

  1225.       of <code>n</code>, otherwise returns <code>false</code>.

  1226.     </p>

  1227.     <p>Note: This method uses the <a href='#cmp'><code>comparedTo</code></a> method internally.</p>

  1228.     <pre>

  1229. (0.3 - 0.2) &gt;= 0.1                     // false

  1230. x = new BigNumber(0.3).minus(0.2)

  1231. x.isGreaterThanOrEqualTo(0.1)          // true

  1232. BigNumber(1).gte(x)                    // true

  1233. BigNumber(10, 18).gte('i', 36)         // true</pre>

  1234. 

  1235. 

  1236. 

  1237.     <h5 id="isInt">isInteger<code class='inset'>.isInteger() <i>&rArr; boolean</i></code></h5>

  1238.     <p>

  1239.       Returns <code>true</code> if the value of this BigNumber is an integer, otherwise returns

  1240.       <code>false</code>.

  1241.     </p>

  1242.     <pre>

  1243. x = new BigNumber(1)

  1244. x.isInteger()                   // true

  1245. y = new BigNumber(123.456)

  1246. y.isInteger()                   // false</pre>

  1247. 

  1248. 

  1249. 

  1250.     <h5 id="lt">isLessThan<code class='inset'>.lt(n [, base]) <i>&rArr; boolean</i></code></h5>

  1251.     <p>

  1252.       <code>n</code>: <i>number|string|BigNumber</i><br />

  1253.       <code>base</code>: <i>number</i><br />

  1254.       <i>See <a href="#bignumber">BigNumber</a> for further parameter details.</i>

  1255.     </p>

  1256.     <p>

  1257.       Returns <code>true</code> if the value of this BigNumber is less than the value of

  1258.       <code>n</code>, otherwise returns <code>false</code>.

  1259.     </p>

  1260.      <p>Note: This method uses the <a href='#cmp'><code>comparedTo</code></a> method internally.</p>

  1261.     <pre>

  1262. (0.3 - 0.2) &lt; 0.1                       // true

  1263. x = new BigNumber(0.3).minus(0.2)

  1264. x.isLessThan(0.1)                       // false

  1265. BigNumber(0).lt(x)                      // true

  1266. BigNumber(11.1, 2).lt(11, 3)            // true</pre>

  1267. 

  1268. 

  1269. 

  1270.     <h5 id="lte">

  1271.       isLessThanOrEqualTo<code class='inset'>.lte(n [, base]) <i>&rArr; boolean</i></code>

  1272.     </h5>

  1273.     <p>

  1274.       <code>n</code>: <i>number|string|BigNumber</i><br />

  1275.       <code>base</code>: <i>number</i><br />

  1276.       <i>See <a href="#bignumber">BigNumber</a> for further parameter details.</i>

  1277.     </p>

  1278.     <p>

  1279.       Returns <code>true</code> if the value of this BigNumber is less than or equal to the value of

  1280.       <code>n</code>, otherwise returns <code>false</code>.

  1281.     </p>

  1282.     <p>Note: This method uses the <a href='#cmp'><code>comparedTo</code></a> method internally.</p>

  1283.     <pre>

  1284. 0.1 &lt;= (0.3 - 0.2)                                // false

  1285. x = new BigNumber(0.1)

  1286. x.isLessThanOrEqualTo(BigNumber(0.3).minus(0.2))  // true

  1287. BigNumber(-1).lte(x)                              // true

  1288. BigNumber(10, 18).lte('i', 36)                    // true</pre>

  1289. 

  1290. 

  1291. 

  1292.     <h5 id="isNaN">isNaN<code class='inset'>.isNaN() <i>&rArr; boolean</i></code></h5>

  1293.     <p>

  1294.       Returns <code>true</code> if the value of this BigNumber is <code>NaN</code>, otherwise

  1295.       returns <code>false</code>.

  1296.     </p>

  1297.     <pre>

  1298. x = new BigNumber(NaN)

  1299. x.isNaN()                       // true

  1300. y = new BigNumber('Infinity')

  1301. y.isNaN()                       // false</pre>

  1302.     <p>Note: The native method <code>isNaN()</code> can also be used.</p>

  1303. 

  1304. 

  1305. 

  1306.     <h5 id="isNeg">isNegative<code class='inset'>.isNegative() <i>&rArr; boolean</i></code></h5>

  1307.     <p>

  1308.       Returns <code>true</code> if the sign of this BigNumber is negative, otherwise returns

  1309.       <code>false</code>.

  1310.     </p>

  1311.     <pre>

  1312. x = new BigNumber(-0)

  1313. x.isNegative()                  // true

  1314. y = new BigNumber(2)

  1315. y.isNegative()                  // false</pre>

  1316.     <p>Note: <code>n &lt; 0</code> can be used if <code>n &lt;= -Number.MIN_VALUE</code>.</p>

  1317. 

  1318. 

  1319. 

  1320.     <h5 id="isPos">isPositive<code class='inset'>.isPositive() <i>&rArr; boolean</i></code></h5>

  1321.     <p>

  1322.       Returns <code>true</code> if the sign of this BigNumber is positive, otherwise returns

  1323.       <code>false</code>.

  1324.     </p>

  1325.     <pre>

  1326. x = new BigNumber(-0)

  1327. x.isPositive()                  // false

  1328. y = new BigNumber(2)

  1329. y.isPositive()                  // true</pre>

  1330. 

  1331. 

  1332. 

  1333.     <h5 id="isZ">isZero<code class='inset'>.isZero() <i>&rArr; boolean</i></code></h5>

  1334.     <p>

  1335.       Returns <code>true</code> if the value of this BigNumber is zero or minus zero, otherwise

  1336.       returns <code>false</code>.

  1337.     </p>

  1338.     <pre>

  1339. x = new BigNumber(-0)

  1340. x.isZero() &amp;&amp; x.isNegative()         // true

  1341. y = new BigNumber(Infinity)

  1342. y.isZero()                      // false</pre>

  1343.     <p>Note: <code>n == 0</code> can be used if <code>n &gt;= Number.MIN_VALUE</code>.</p>

  1344. 

  1345. 

  1346. 

  1347.     <h5 id="minus">

  1348.       minus<code class='inset'>.minus(n [, base]) <i>&rArr; BigNumber</i></code>

  1349.     </h5>

  1350.     <p>

  1351.       <code>n</code>: <i>number|string|BigNumber</i><br />

  1352.       <code>base</code>: <i>number</i><br />

  1353.       <i>See <a href="#bignumber">BigNumber</a> for further parameter details.</i>

  1354.     </p>

  1355.     <p>Returns a BigNumber whose value is the value of this BigNumber minus <code>n</code>.</p>

  1356.     <p>The return value is always exact and unrounded.</p>

  1357.     <pre>

  1358. 0.3 - 0.1                       // 0.19999999999999998

  1359. x = new BigNumber(0.3)

  1360. x.minus(0.1)                    // '0.2'

  1361. x.minus(0.6, 20)                // '0'</pre>

  1362. 

  1363. 

  1364. 

  1365.     <h5 id="mod">modulo<code class='inset'>.mod(n [, base]) <i>&rArr; BigNumber</i></code></h5>

  1366.     <p>

  1367.       <code>n</code>: <i>number|string|BigNumber</i><br />

  1368.       <code>base</code>: <i>number</i><br />

  1369.       <i>See <a href="#bignumber">BigNumber</a> for further parameter details.</i>

  1370.     </p>

  1371.     <p>

  1372.       Returns a BigNumber whose value is the value of this BigNumber modulo <code>n</code>, i.e.

  1373.       the integer remainder of dividing this BigNumber by <code>n</code>.

  1374.     </p>

  1375.     <p>

  1376.       The value returned, and in particular its sign, is dependent on the value of the

  1377.       <a href='#modulo-mode'><code>MODULO_MODE</code></a> setting of this BigNumber constructor.

  1378.       If it is <code>1</code> (default value), the result will have the same sign as this BigNumber,

  1379.       and it will match that of Javascript's <code>%</code> operator (within the limits of double

  1380.       precision) and BigDecimal's <code>remainder</code> method.

  1381.     </p>

  1382.     <p>The return value is always exact and unrounded.</p>

  1383.     <p>

  1384.       See <a href='#modulo-mode'><code>MODULO_MODE</code></a> for a description of the other

  1385.       modulo modes.

  1386.     </p>

  1387.     <pre>

  1388. 1 % 0.9                         // 0.09999999999999998

  1389. x = new BigNumber(1)

  1390. x.modulo(0.9)                   // '0.1'

  1391. y = new BigNumber(33)

  1392. y.mod('a', 33)                  // '3'</pre>

  1393. 

  1394. 

  1395. 

  1396.     <h5 id="times">

  1397.       multipliedBy<code class='inset'>.times(n [, base]) <i>&rArr; BigNumber</i></code>

  1398.     </h5>

  1399.     <p>

  1400.       <code>n</code>: <i>number|string|BigNumber</i><br />

  1401.       <code>base</code>: <i>number</i><br />

  1402.       <i>See <a href="#bignumber">BigNumber</a> for further parameter details.</i>

  1403.     </p>

  1404.     <p>

  1405.       Returns a BigNumber whose value is the value of this BigNumber multiplied by <code>n</code>.

  1406.     </p>

  1407.     <p>The return value is always exact and unrounded.</p>

  1408.     <pre>

  1409. 0.6 * 3                         // 1.7999999999999998

  1410. x = new BigNumber(0.6)

  1411. y = x.multipliedBy(3)           // '1.8'

  1412. BigNumber('7e+500').times(y)    // '1.26e+501'

  1413. x.multipliedBy('-a', 16)        // '-6'</pre>

  1414. 

  1415. 

  1416. 

  1417.     <h5 id="neg">negated<code class='inset'>.negated() <i>&rArr; BigNumber</i></code></h5>

  1418.     <p>

  1419.       Returns a BigNumber whose value is the value of this BigNumber negated, i.e. multiplied by

  1420.       <code>-1</code>.

  1421.     </p>

  1422.     <pre>

  1423. x = new BigNumber(1.8)

  1424. x.negated()                     // '-1.8'

  1425. y = new BigNumber(-1.3)

  1426. y.negated()                     // '1.3'</pre>

  1427. 

  1428. 

  1429. 

  1430.     <h5 id="plus">plus<code class='inset'>.plus(n [, base]) <i>&rArr; BigNumber</i></code></h5>

  1431.     <p>

  1432.       <code>n</code>: <i>number|string|BigNumber</i><br />

  1433.       <code>base</code>: <i>number</i><br />

  1434.       <i>See <a href="#bignumber">BigNumber</a> for further parameter details.</i>

  1435.     </p>

  1436.     <p>Returns a BigNumber whose value is the value of this BigNumber plus <code>n</code>.</p>

  1437.     <p>The return value is always exact and unrounded.</p>

  1438.     <pre>

  1439. 0.1 + 0.2                       // 0.30000000000000004

  1440. x = new BigNumber(0.1)

  1441. y = x.plus(0.2)                 // '0.3'

  1442. BigNumber(0.7).plus(x).plus(y)  // '1.1'

  1443. x.plus('0.1', 8)                // '0.225'</pre>

  1444. 

  1445. 

  1446. 

  1447.     <h5 id="sd">

  1448.       precision<code class='inset'>.sd([d [, rm]]) <i>&rArr; BigNumber|number</i></code>

  1449.     </h5>

  1450.     <p>

  1451.       <code>d</code>: <i>number|boolean</i>: integer, <code>1</code> to <code>1e+9</code>

  1452.       inclusive, or <code>true</code> or <code>false</code><br />

  1453.       <code>rm</code>: <i>number</i>: integer, <code>0</code> to <code>8</code> inclusive.

  1454.     </p>

  1455.     <p>

  1456.       If <code>d</code> is a number, returns a BigNumber whose value is the value of this BigNumber

  1457.       rounded to a precision of <code>d</code> significant digits using rounding mode

  1458.       <code>rm</code>.

  1459.     </p>

  1460.     <p>

  1461.       If <code>d</code> is omitted or is <code>null</code> or <code>undefined</code>, the return

  1462.       value is the number of significant digits of the value of this BigNumber, or <code>null</code>

  1463.       if the value of this BigNumber is &plusmn;<code>Infinity</code> or <code>NaN</code>.

  1464.     </p>

  1465.     <p>

  1466.       If <code>d</code> is <code>true</code> then any trailing zeros of the integer

  1467.       part of a number are counted as significant digits, otherwise they are not.

  1468.     </p>

  1469.     <p>

  1470.       If <code>rm</code> is omitted or is <code>null</code> or <code>undefined</code>,

  1471.       <a href='#rounding-mode'><code>ROUNDING_MODE</code></a> will be used.

  1472.     </p>

  1473.     <p>

  1474.       Throws if <code>d</code> or <code>rm</code> is invalid. See <a href='#Errors'>Errors</a>.

  1475.     </p>

  1476.     <pre>

  1477. x = new BigNumber(9876.54321)

  1478. x.precision(6)                         // '9876.54'

  1479. x.sd()                                 // 9

  1480. x.precision(6, BigNumber.ROUND_UP)     // '9876.55'

  1481. x.sd(2)                                // '9900'

  1482. x.precision(2, 1)                      // '9800'

  1483. x                                      // '9876.54321'

  1484. y = new BigNumber(987000)

  1485. y.precision()                          // 3

  1486. y.sd(true)                             // 6</pre>

  1487. 

  1488. 

  1489. 

  1490. <h5 id="shift">shiftedBy<code class='inset'>.shiftedBy(n) <i>&rArr; BigNumber</i></code></h5>

  1491.     <p>

  1492.       <code>n</code>: <i>number</i>: integer,

  1493.       <code>-9007199254740991</code> to <code>9007199254740991</code> inclusive

  1494.     </p>

  1495.     <p>

  1496.       Returns a BigNumber whose value is the value of this BigNumber shifted by <code>n</code>

  1497.       places.

  1498.     <p>

  1499.       The shift is of the decimal point, i.e. of powers of ten, and is to the left if <code>n</code>

  1500.       is negative or to the right if <code>n</code> is positive.

  1501.     </p>

  1502.     <p>The return value is always exact and unrounded.</p>

  1503.     <p>

  1504.       Throws if <code>n</code> is invalid. See <a href='#Errors'>Errors</a>.

  1505.     </p>

  1506.     <pre>

  1507. x = new BigNumber(1.23)

  1508. x.shiftedBy(3)                      // '1230'

  1509. x.shiftedBy(-3)                     // '0.00123'</pre>

  1510. 

  1511. 

  1512. 

  1513.     <h5 id="sqrt">squareRoot<code class='inset'>.sqrt() <i>&rArr; BigNumber</i></code></h5>

  1514.     <p>

  1515.       Returns a BigNumber whose value is the square root of the value of this BigNumber,

  1516.       rounded according to the current

  1517.       <a href='#decimal-places'><code>DECIMAL_PLACES</code></a> and

  1518.       <a href='#rounding-mode'><code>ROUNDING_MODE</code></a> settings.

  1519.     </p>

  1520.     <p>

  1521.       The return value will be correctly rounded, i.e. rounded as if the result was first calculated

  1522.       to an infinite number of correct digits before rounding.

  1523.     </p>

  1524.     <pre>

  1525. x = new BigNumber(16)

  1526. x.squareRoot()                  // '4'

  1527. y = new BigNumber(3)

  1528. y.sqrt()                        // '1.73205080756887729353'</pre>

  1529. 

  1530. 

  1531. 

  1532.     <h5 id="toE">

  1533.       toExponential<code class='inset'>.toExponential([dp [, rm]]) <i>&rArr; string</i></code>

  1534.     </h5>

  1535.     <p>

  1536.       <code>dp</code>: <i>number</i>: integer, <code>0</code> to <code>1e+9</code> inclusive<br />

  1537.       <code>rm</code>: <i>number</i>: integer, <code>0</code> to <code>8</code> inclusive

  1538.     </p>

  1539.     <p>

  1540.       Returns a string representing the value of this BigNumber in exponential notation rounded

  1541.       using rounding mode <code>rm</code> to <code>dp</code> decimal places, i.e with one digit

  1542.       before the decimal point and <code>dp</code> digits after it.

  1543.     </p>

  1544.     <p>

  1545.       If the value of this BigNumber in exponential notation has fewer than <code>dp</code> fraction

  1546.       digits, the return value will be appended with zeros accordingly.

  1547.     </p>

  1548.     <p>

  1549.       If <code>dp</code> is omitted, or is <code>null</code> or <code>undefined</code>, the number

  1550.       of digits after the decimal point defaults to the minimum number of digits necessary to

  1551.       represent the value exactly.<br />

  1552.       If <code>rm</code> is omitted or is <code>null</code> or <code>undefined</code>,

  1553.       <a href='#rounding-mode'><code>ROUNDING_MODE</code></a> is used.

  1554.     </p>

  1555.     <p>

  1556.       Throws if <code>dp</code> or <code>rm</code> is invalid. See <a href='#Errors'>Errors</a>.

  1557.     </p>

  1558.      <pre>

  1559. x = 45.6

  1560. y = new BigNumber(x)

  1561. x.toExponential()               // '4.56e+1'

  1562. y.toExponential()               // '4.56e+1'

  1563. x.toExponential(0)              // '5e+1'

  1564. y.toExponential(0)              // '5e+1'

  1565. x.toExponential(1)              // '4.6e+1'

  1566. y.toExponential(1)              // '4.6e+1'

  1567. y.toExponential(1, 1)           // '4.5e+1'  (ROUND_DOWN)

  1568. x.toExponential(3)              // '4.560e+1'

  1569. y.toExponential(3)              // '4.560e+1'</pre>

  1570. 

  1571. 

  1572. 

  1573.     <h5 id="toFix">

  1574.       toFixed<code class='inset'>.toFixed([dp [, rm]]) <i>&rArr; string</i></code>

  1575.     </h5>

  1576.     <p>

  1577.       <code>dp</code>: <i>number</i>: integer, <code>0</code> to <code>1e+9</code> inclusive<br />

  1578.       <code>rm</code>: <i>number</i>: integer, <code>0</code> to <code>8</code> inclusive

  1579.     </p>

  1580.     <p>

  1581.       Returns a string representing the value of this BigNumber in normal (fixed-point) notation

  1582.       rounded to <code>dp</code> decimal places using rounding mode <code>rm</code>.

  1583.     </p>

  1584.     <p>

  1585.       If the value of this BigNumber in normal notation has fewer than <code>dp</code> fraction

  1586.       digits, the return value will be appended with zeros accordingly.

  1587.     </p>

  1588.    <p>

  1589.       Unlike <code>Number.prototype.toFixed</code>, which returns exponential notation if a number

  1590.       is greater or equal to <code>10<sup>21</sup></code>, this method will always return normal

  1591.       notation.

  1592.     </p>

  1593.     <p>

  1594.       If <code>dp</code> is omitted or is <code>null</code> or <code>undefined</code>, the return

  1595.       value will be unrounded and in normal notation. This is also unlike

  1596.       <code>Number.prototype.toFixed</code>, which returns the value to zero decimal places.<br />

  1597.       It is useful when fixed-point notation is required and the current

  1598.       <a href="#exponential-at"><code>EXPONENTIAL_AT</code></a> setting causes

  1599.       <code><a href='#toS'>toString</a></code> to return exponential notation.<br />

  1600.       If <code>rm</code> is omitted or is <code>null</code> or <code>undefined</code>,

  1601.       <a href='#rounding-mode'><code>ROUNDING_MODE</code></a> is used.

  1602.     </p>

  1603.     <p>

  1604.       Throws if <code>dp</code> or <code>rm</code> is invalid. See <a href='#Errors'>Errors</a>.

  1605.     </p>

  1606.     <pre>

  1607. x = 3.456

  1608. y = new BigNumber(x)

  1609. x.toFixed()                     // '3'

  1610. y.toFixed()                     // '3.456'

  1611. y.toFixed(0)                    // '3'

  1612. x.toFixed(2)                    // '3.46'

  1613. y.toFixed(2)                    // '3.46'

  1614. y.toFixed(2, 1)                 // '3.45'  (ROUND_DOWN)

  1615. x.toFixed(5)                    // '3.45600'

  1616. y.toFixed(5)                    // '3.45600'</pre>

  1617. 

  1618. 

  1619. 

  1620.     <h5 id="toFor">

  1621.       toFormat<code class='inset'>.toFormat([dp [, rm[, format]]]) <i>&rArr; string</i></code>

  1622.     </h5>

  1623.     <p>

  1624.       <code>dp</code>: <i>number</i>: integer, <code>0</code> to <code>1e+9</code> inclusive<br />

  1625.       <code>rm</code>: <i>number</i>: integer, <code>0</code> to <code>8</code> inclusive<br />

  1626.       <code>format</code>: <i>object</i>: see <a href='#format'><code>FORMAT</code></a>

  1627.     </p>

  1628.     <p>

  1629.       <p>

  1630.       Returns a string representing the value of this BigNumber in normal (fixed-point) notation

  1631.       rounded to <code>dp</code> decimal places using rounding mode <code>rm</code>, and formatted

  1632.       according to the properties of the <code>format</code> object.

  1633.     </p>

  1634.     <p>

  1635.       See <a href='#format'><code>FORMAT</code></a> and the examples below for the properties of the

  1636.       <code>format</code> object, their types, and their usage. A formatting object may contain

  1637.       some or all of the recognised properties.

  1638.     </p>

  1639.     <p>

  1640.       If <code>dp</code> is omitted or is <code>null</code> or <code>undefined</code>, then the

  1641.       return value is not rounded to a fixed number of decimal places.<br />

  1642.       If <code>rm</code> is omitted or is <code>null</code> or <code>undefined</code>,

  1643.       <a href='#rounding-mode'><code>ROUNDING_MODE</code></a> is used.<br />

  1644.       If <code>format</code> is omitted or is <code>null</code> or <code>undefined</code>, the

  1645.       <a href='#format'><code>FORMAT</code></a> object is used.

  1646.     </p>

  1647.     <p>

  1648.       Throws if <code>dp</code>, <code>rm</code> or <code>format</code> is invalid. See

  1649.       <a href='#Errors'>Errors</a>.

  1650.     </p>

  1651.     <pre>

  1652. fmt = {

  1653.   prefix: '',

  1654.   decimalSeparator: '.',

  1655.   groupSeparator: ',',

  1656.   groupSize: 3,

  1657.   secondaryGroupSize: 0,

  1658.   fractionGroupSeparator: ' ',

  1659.   fractionGroupSize: 0,

  1660.   suffix: ''

  1661. }

  1662. 

  1663. x = new BigNumber('123456789.123456789')

  1664. 

  1665. // Set the global formatting options

  1666. BigNumber.config({ FORMAT: fmt })

  1667. 

  1668. x.toFormat()                              // '123,456,789.123456789'

  1669. x.toFormat(3)                             // '123,456,789.123'

  1670. 

  1671. // If a reference to the object assigned to FORMAT has been retained,

  1672. // the format properties can be changed directly

  1673. fmt.groupSeparator = ' '

  1674. fmt.fractionGroupSize = 5

  1675. x.toFormat()                              // '123 456 789.12345 6789'

  1676. 

  1677. // Alternatively, pass the formatting options as an argument

  1678. fmt = {

  1679.   prefix: '=> ',

  1680.   decimalSeparator: ',',

  1681.   groupSeparator: '.',

  1682.   groupSize: 3,

  1683.   secondaryGroupSize: 2

  1684. }

  1685. 

  1686. x.toFormat()                              // '123 456 789.12345 6789'

  1687. x.toFormat(fmt)                           // '=> 12.34.56.789,123456789'

  1688. x.toFormat(2, fmt)                        // '=> 12.34.56.789,12'

  1689. x.toFormat(3, BigNumber.ROUND_UP, fmt)    // '=> 12.34.56.789,124'</pre>

  1690. 

  1691. 

  1692. 

  1693.     <h5 id="toFr">

  1694.       toFraction<code class='inset'>.toFraction([maximum_denominator])

  1695.       <i>&rArr; [BigNumber, BigNumber]</i></code>

  1696.     </h5>

  1697.     <p>

  1698.       <code>maximum_denominator</code>:

  1699.       <i>number|string|BigNumber</i>: integer &gt;= <code>1</code> and &lt;=

  1700.       <code>Infinity</code>

  1701.     </p>

  1702.     <p>

  1703.       Returns an array of two BigNumbers representing the value of this BigNumber as a simple

  1704.       fraction with an integer numerator and an integer denominator. The denominator will be a

  1705.       positive non-zero value less than or equal to <code>maximum_denominator</code>.

  1706.     </p>

  1707.     <p>

  1708.       If a <code>maximum_denominator</code> is not specified, or is <code>null</code> or

  1709.       <code>undefined</code>, the denominator will be the lowest value necessary to represent the

  1710.       number exactly.

  1711.     </p>

  1712.     <p>

  1713.       Throws if <code>maximum_denominator</code> is invalid. See <a href='#Errors'>Errors</a>.

  1714.     </p>

  1715.     <pre>

  1716. x = new BigNumber(1.75)

  1717. x.toFraction()                  // '7, 4'

  1718. 

  1719. pi = new BigNumber('3.14159265358')

  1720. pi.toFraction()                 // '157079632679,50000000000'

  1721. pi.toFraction(100000)           // '312689, 99532'

  1722. pi.toFraction(10000)            // '355, 113'

  1723. pi.toFraction(100)              // '311, 99'

  1724. pi.toFraction(10)               // '22, 7'

  1725. pi.toFraction(1)                // '3, 1'</pre>

  1726. 

  1727. 

  1728. 

  1729.     <h5 id="toJSON">toJSON<code class='inset'>.toJSON() <i>&rArr; string</i></code></h5>

  1730.     <p>As <a href='#valueOf'><code>valueOf</code></a>.</p>

  1731.     <pre>

  1732. x = new BigNumber('177.7e+457')

  1733. y = new BigNumber(235.4325)

  1734. z = new BigNumber('0.0098074')

  1735. 

  1736. // Serialize an array of three BigNumbers

  1737. str = JSON.stringify( [x, y, z] )

  1738. // "["1.777e+459","235.4325","0.0098074"]"

  1739. 

  1740. // Return an array of three BigNumbers

  1741. JSON.parse(str, function (key, val) {

  1742.     return key === '' ? val : new BigNumber(val)

  1743. })</pre>

  1744. 

  1745. 

  1746. 

  1747.     <h5 id="toN">toNumber<code class='inset'>.toNumber() <i>&rArr; number</i></code></h5>

  1748.     <p>Returns the value of this BigNumber as a JavaScript number primitive.</p>

  1749.     <p>

  1750.       This method is identical to using type coercion with the unary plus operator.

  1751.     </p>

  1752.     <pre>

  1753. x = new BigNumber(456.789)

  1754. x.toNumber()                    // 456.789

  1755. +x                              // 456.789

  1756. 

  1757. y = new BigNumber('45987349857634085409857349856430985')

  1758. y.toNumber()                    // 4.598734985763409e+34

  1759. 

  1760. z = new BigNumber(-0)

  1761. 1 / z.toNumber()                // -Infinity

  1762. 1 / +z                          // -Infinity</pre>

  1763. 

  1764. 

  1765. 

  1766.     <h5 id="toP">

  1767.       toPrecision<code class='inset'>.toPrecision([sd [, rm]]) <i>&rArr; string</i></code>

  1768.     </h5>

  1769.     <p>

  1770.       <code>sd</code>: <i>number</i>: integer, <code>1</code> to <code>1e+9</code> inclusive<br />

  1771.       <code>rm</code>: <i>number</i>: integer, <code>0</code> to <code>8</code> inclusive

  1772.     </p>

  1773.     <p>

  1774.       Returns a string representing the value of this BigNumber rounded to <code>sd</code>

  1775.       significant digits using rounding mode <code>rm</code>.

  1776.     </p>

  1777.     <p>

  1778.       If <code>sd</code> is less than the number of digits necessary to represent the integer part

  1779.       of the value in normal (fixed-point) notation, then exponential notation is used.

  1780.     </p>

  1781.     <p>

  1782.       If <code>sd</code> is omitted, or is <code>null</code> or <code>undefined</code>, then the

  1783.       return value is the same as <code>n.toString()</code>.<br />

  1784.       If <code>rm</code> is omitted or is <code>null</code> or <code>undefined</code>,

  1785.       <a href='#rounding-mode'><code>ROUNDING_MODE</code></a> is used.

  1786.     </p>

  1787.     <p>

  1788.       Throws if <code>sd</code> or <code>rm</code> is invalid. See <a href='#Errors'>Errors</a>.

  1789.     </p>

  1790.      <pre>

  1791. x = 45.6

  1792. y = new BigNumber(x)

  1793. x.toPrecision()                 // '45.6'

  1794. y.toPrecision()                 // '45.6'

  1795. x.toPrecision(1)                // '5e+1'

  1796. y.toPrecision(1)                // '5e+1'

  1797. y.toPrecision(2, 0)             // '4.6e+1'  (ROUND_UP)

  1798. y.toPrecision(2, 1)             // '4.5e+1'  (ROUND_DOWN)

  1799. x.toPrecision(5)                // '45.600'

  1800. y.toPrecision(5)                // '45.600'</pre>

  1801. 

  1802. 

  1803. 

  1804.     <h5 id="toS">toString<code class='inset'>.toString([base]) <i>&rArr; string</i></code></h5>

  1805.     <p>

  1806.       <code>base</code>: <i>number</i>: integer, <code>2</code> to <code>ALPHABET.length</code>

  1807.       inclusive (see <a href='#alphabet'><code>ALPHABET</code></a>).

  1808.     </p>

  1809.     <p>

  1810.       Returns a string representing the value of this BigNumber in the specified base, or base

  1811.       <code>10</code> if <code>base</code> is omitted or is <code>null</code> or

  1812.       <code>undefined</code>.

  1813.     </p>

  1814.     <p>

  1815.       For bases above <code>10</code>, and using the default base conversion alphabet

  1816.       (see <a href='#alphabet'><code>ALPHABET</code></a>), values from <code>10</code> to

  1817.       <code>35</code> are represented by <code>a-z</code>

  1818.       (as with <code>Number.prototype.toString</code>).

  1819.     </p>

  1820.     <p>

  1821.       If a base is specified the value is rounded according to the current

  1822.       <a href='#decimal-places'><code>DECIMAL_PLACES</code></a>

  1823.       and <a href='#rounding-mode'><code>ROUNDING_MODE</code></a> settings.

  1824.     </p>

  1825.     <p>

  1826.       If a base is not specified, and this BigNumber has a positive

  1827.       exponent that is equal to or greater than the positive component of the

  1828.       current <a href="#exponential-at"><code>EXPONENTIAL_AT</code></a> setting,

  1829.       or a negative exponent equal to or less than the negative component of the

  1830.       setting, then exponential notation is returned.

  1831.     </p>

  1832.     <p>If <code>base</code> is <code>null</code> or <code>undefined</code> it is ignored.</p>

  1833.     <p>

  1834.       Throws if <code>base</code> is invalid. See <a href='#Errors'>Errors</a>.

  1835.     </p>

  1836.     <pre>

  1837. x = new BigNumber(750000)

  1838. x.toString()                    // '750000'

  1839. BigNumber.config({ EXPONENTIAL_AT: 5 })

  1840. x.toString()                    // '7.5e+5'

  1841. 

  1842. y = new BigNumber(362.875)

  1843. y.toString(2)                   // '101101010.111'

  1844. y.toString(9)                   // '442.77777777777777777778'

  1845. y.toString(32)                  // 'ba.s'

  1846. 

  1847. BigNumber.config({ DECIMAL_PLACES: 4 });

  1848. z = new BigNumber('1.23456789')

  1849. z.toString()                    // '1.23456789'

  1850. z.toString(10)                  // '1.2346'</pre>

  1851. 

  1852. 

  1853. 

  1854.     <h5 id="valueOf">valueOf<code class='inset'>.valueOf() <i>&rArr; string</i></code></h5>

  1855.     <p>

  1856.       As <a href='#toS'><code>toString</code></a>, but does not accept a base argument and includes

  1857.       the minus sign for negative zero.

  1858.     </p>

  1859.     <pre>

  1860. x = new BigNumber('-0')

  1861. x.toString()                    // '0'

  1862. x.valueOf()                     // '-0'

  1863. y = new BigNumber('1.777e+457')

  1864. y.valueOf()                     // '1.777e+457'</pre>

  1865. 

  1866. 

  1867. 

  1868.     <h4 id="instance-properties">Properties</h4>

  1869.     <p>The properties of a BigNumber instance:</p>

  1870.     <table>

  1871.       <tr>

  1872.         <th>Property</th>

  1873.         <th>Description</th>

  1874.         <th>Type</th>

  1875.         <th>Value</th>

  1876.       </tr>

  1877.       <tr>

  1878.         <td class='centre' id='coefficient'><b>c</b></td>

  1879.         <td>coefficient<sup>*</sup></td>

  1880.         <td><i>number</i><code>[]</code></td>

  1881.         <td> Array of base <code>1e14</code> numbers</td>

  1882.       </tr>

  1883.       <tr>

  1884.         <td class='centre' id='exponent'><b>e</b></td>

  1885.         <td>exponent</td>

  1886.         <td><i>number</i></td>

  1887.         <td>Integer, <code>-1000000000</code> to <code>1000000000</code> inclusive</td>

  1888.       </tr>

  1889.       <tr>

  1890.         <td class='centre' id='sign'><b>s</b></td>

  1891.         <td>sign</td>

  1892.         <td><i>number</i></td>

  1893.         <td><code>-1</code> or <code>1</code></td>

  1894.       </tr>

  1895.     </table>

  1896.     <p><sup>*</sup>significand</p>

  1897.     <p>

  1898.       The value of any of the <code>c</code>, <code>e</code> and <code>s</code> properties may also

  1899.       be <code>null</code>.

  1900.     </p>

  1901.     <p>

  1902.       The above properties are best considered to be read-only. In early versions of this library it

  1903.       was okay to change the exponent of a BigNumber by writing to its exponent property directly,

  1904.       but this is no longer reliable as the value of the first element of the coefficient array is

  1905.       now dependent on the exponent.

  1906.     </p>

  1907.     <p>

  1908.       Note that, as with JavaScript numbers, the original exponent and fractional trailing zeros are

  1909.       not necessarily preserved.

  1910.     </p>

  1911.     <pre>x = new BigNumber(0.123)              // '0.123'

  1912. x.toExponential()                     // '1.23e-1'

  1913. x.c                                   // '1,2,3'

  1914. x.e                                   // -1

  1915. x.s                                   // 1

  1916. 

  1917. y = new Number(-123.4567000e+2)       // '-12345.67'

  1918. y.toExponential()                     // '-1.234567e+4'

  1919. z = new BigNumber('-123.4567000e+2')  // '-12345.67'

  1920. z.toExponential()                     // '-1.234567e+4'

  1921. z.c                                   // '1,2,3,4,5,6,7'

  1922. z.e                                   // 4

  1923. z.s                                   // -1</pre>

  1924. 

  1925. 

  1926. 

  1927.     <h4 id="zero-nan-infinity">Zero, NaN and Infinity</h4>

  1928.     <p>

  1929.       The table below shows how &plusmn;<code>0</code>, <code>NaN</code> and

  1930.       &plusmn;<code>Infinity</code> are stored.

  1931.     </p>

  1932.     <table>

  1933.       <tr>

  1934.         <th> </th>

  1935.         <th class='centre'>c</th>

  1936.         <th class='centre'>e</th>

  1937.         <th class='centre'>s</th>

  1938.       </tr>

  1939.       <tr>

  1940.         <td>&plusmn;0</td>

  1941.         <td><code>[0]</code></td>

  1942.         <td><code>0</code></td>

  1943.         <td><code>&plusmn;1</code></td>

  1944.       </tr>

  1945.       <tr>

  1946.         <td>NaN</td>

  1947.         <td><code>null</code></td>

  1948.         <td><code>null</code></td>

  1949.         <td><code>null</code></td>

  1950.       </tr>

  1951.       <tr>

  1952.         <td>&plusmn;Infinity</td>

  1953.         <td><code>null</code></td>

  1954.         <td><code>null</code></td>

  1955.         <td><code>&plusmn;1</code></td>

  1956.       </tr>

  1957.     </table>

  1958.     <pre>

  1959. x = new Number(-0)              // 0

  1960. 1 / x == -Infinity              // true

  1961. 

  1962. y = new BigNumber(-0)           // '0'

  1963. y.c                             // '0' ( [0].toString() )

  1964. y.e                             // 0

  1965. y.s                             // -1</pre>

  1966. 

  1967. 

  1968. 

  1969.     <h4 id='Errors'>Errors</h4>

  1970.     <p>The table below shows the errors that are thrown.</p>

  1971.     <p>

  1972.       The errors are generic <code>Error</code> objects whose message begins

  1973.       <code>'[BigNumber Error]'</code>.

  1974.     </p>

  1975.     <table class='error-table'>

  1976.       <tr>

  1977.         <th>Method</th>

  1978.         <th>Throws</th>

  1979.       </tr>

  1980.       <tr>

  1981.         <td rowspan=6>

  1982.           <code>BigNumber</code><br />

  1983.           <code>comparedTo</code><br />

  1984.           <code>dividedBy</code><br />

  1985.           <code>dividedToIntegerBy</code><br />

  1986.           <code>isEqualTo</code><br />

  1987.           <code>isGreaterThan</code><br />

  1988.           <code>isGreaterThanOrEqualTo</code><br />

  1989.           <code>isLessThan</code><br />

  1990.           <code>isLessThanOrEqualTo</code><br />

  1991.           <code>minus</code><br />

  1992.           <code>modulo</code><br />

  1993.           <code>plus</code><br />

  1994.           <code>multipliedBy</code>

  1995.         </td>

  1996.         <td>Base not a primitive number</td>

  1997.       </tr>

  1998.       <tr>

  1999.         <td>Base not an integer</td>

  2000.       </tr>

  2001.       <tr>

  2002.         <td>Base out of range</td>

  2003.       </tr>

  2004.        <tr>

  2005.         <td>Number primitive has more than 15 significant digits<sup>*</sup></td>

  2006.       </tr>

  2007.       <tr>

  2008.         <td>Not a base... number<sup>*</sup></td>

  2009.       </tr>

  2010.       <tr>

  2011.         <td>Not a number<sup>*</sup></td>

  2012.       </tr>

  2013.       <tr>

  2014.         <td><code>clone</code></td>

  2015.         <td>Object expected</td>

  2016.       </tr>

  2017.       <tr>

  2018.         <td rowspan=24><code>config</code></td>

  2019.         <td>Object expected</td>

  2020.       </tr>

  2021.       <tr>

  2022.         <td><code>DECIMAL_PLACES</code> not a primitive number</td>

  2023.       </tr>

  2024.       <tr>

  2025.         <td><code>DECIMAL_PLACES</code> not an integer</td>

  2026.       </tr>

  2027.       <tr>

  2028.         <td><code>DECIMAL_PLACES</code> out of range</td>

  2029.       </tr>

  2030.       <tr>

  2031.         <td><code>ROUNDING_MODE</code> not a primitive number</td>

  2032.       </tr>

  2033.       <tr>

  2034.         <td><code>ROUNDING_MODE</code> not an integer</td>

  2035.       </tr>

  2036.       <tr>

  2037.         <td><code>ROUNDING_MODE</code> out of range</td>

  2038.       </tr>

  2039.       <tr>

  2040.         <td><code>EXPONENTIAL_AT</code> not a primitive number</td>

  2041.       </tr>

  2042.       <tr>

  2043.         <td><code>EXPONENTIAL_AT</code> not an integer</td>

  2044.       </tr>

  2045.       <tr>

  2046.         <td><code>EXPONENTIAL_AT</code> out of range</td>

  2047.       </tr>

  2048.       <tr>

  2049.         <td><code>RANGE</code> not a primitive number</td>

  2050.       </tr>

  2051.       <tr>

  2052.         <td><code>RANGE</code> not an integer</td>

  2053.       </tr>

  2054.       <tr>

  2055.         <td><code>RANGE</code> cannot be zero</td>

  2056.       </tr>

  2057.       <tr>

  2058.         <td><code>RANGE</code> cannot be zero</td>

  2059.       </tr>

  2060.       <tr>

  2061.         <td><code>CRYPTO</code> not true or false</td>

  2062.       </tr>

  2063.       <tr>

  2064.         <td><code>crypto</code> unavailable</td>

  2065.       </tr>

  2066.       <tr>

  2067.         <td><code>MODULO_MODE</code> not a primitive number</td>

  2068.       </tr>

  2069.       <tr>

  2070.         <td><code>MODULO_MODE</code> not an integer</td>

  2071.       </tr>

  2072.       <tr>

  2073.         <td><code>MODULO_MODE</code> out of range</td>

  2074.       </tr>

  2075.       <tr>

  2076.         <td><code>POW_PRECISION</code> not a primitive number</td>

  2077.       </tr>

  2078.       <tr>

  2079.         <td><code>POW_PRECISION</code> not an integer</td>

  2080.       </tr>

  2081.       <tr>

  2082.         <td><code>POW_PRECISION</code> out of range</td>

  2083.       </tr>

  2084.       <tr>

  2085.         <td><code>FORMAT</code> not an object</td>

  2086.       </tr>

  2087.       <tr>

  2088.         <td><code>ALPHABET</code> invalid</td>

  2089.       </tr>

  2090.       <tr>

  2091.         <td rowspan=3>

  2092.           <code>decimalPlaces</code><br />

  2093.           <code>precision</code><br />

  2094.           <code>random</code><br />

  2095.           <code>shiftedBy</code><br />

  2096.           <code>toExponential</code><br />

  2097.           <code>toFixed</code><br />

  2098.           <code>toFormat</code><br />

  2099.           <code>toPrecision</code>

  2100.         </td>

  2101.         <td>Argument not a primitive number</td>

  2102.       </tr>

  2103.       <tr>

  2104.         <td>Argument not an integer</td>

  2105.       </tr>

  2106.       <tr>

  2107.         <td>Argument out of range</td>

  2108.       </tr>

  2109.       <tr>

  2110.         <td>

  2111.           <code>decimalPlaces</code><br />

  2112.           <code>precision</code>

  2113.         </td>

  2114.         <td>Argument not true or false</td>

  2115.       </tr>

  2116.       <tr>

  2117.         <td><code>exponentiatedBy</code></td>

  2118.         <td>Argument not an integer</td>

  2119.       </tr>

  2120.       <tr>

  2121.         <td><code>isBigNumber</code></td>

  2122.         <td>Invalid BigNumber<sup>*</sup></td>

  2123.       </tr>

  2124.       <tr>

  2125.         <td>

  2126.           <code>minimum</code><br />

  2127.           <code>maximum</code>

  2128.         </td>

  2129.         <td>Not a number<sup>*</sup></td>

  2130.       </tr>

  2131.       <tr>

  2132.         <td>

  2133.           <code>random</code>

  2134.         </td>

  2135.         <td>crypto unavailable</td>

  2136.       </tr>

  2137.       <tr>

  2138.         <td>

  2139.           <code>toFormat</code>

  2140.         </td>

  2141.         <td>Argument not an object</td>

  2142.       </tr>

  2143.       <tr>

  2144.         <td rowspan=2><code>toFraction</code></td>

  2145.         <td>Argument not an integer</td>

  2146.       </tr>

  2147.       <tr>

  2148.         <td>Argument out of range</td>

  2149.       </tr>

  2150.       <tr>

  2151.         <td rowspan=3><code>toString</code></td>

  2152.         <td>Base not a primitive number</td>

  2153.       </tr>

  2154.       <tr>

  2155.         <td>Base not an integer</td>

  2156.       </tr>

  2157.       <tr>

  2158.         <td>Base out of range</td>

  2159.       </tr>

  2160.     </table>

  2161.     <p><sup>*</sup>Only thrown if <code>BigNumber.DEBUG</code> is <code>true</code>.</p>

  2162.     <p>To determine if an exception is a BigNumber Error:</p>

  2163.     <pre>

  2164. try {

  2165.   // ...

  2166. } catch (e) {

  2167.   if (e instanceof Error &amp;&amp; e.message.indexOf('[BigNumber Error]') === 0) {

  2168.       // ...

  2169.   }

  2170. }</pre>

  2171. 

  2172. 

  2173. 

  2174.     <h4 id="type-coercion">Type coercion</h4>

  2175.     <p>

  2176.       To prevent the accidental use of a BigNumber in primitive number operations, or the

  2177.       accidental addition of a BigNumber to a string, the <code>valueOf</code> method can be safely

  2178.       overwritten as shown below.

  2179.     </p>

  2180.     <p>

  2181.       The <a href='#valueOf'><code>valueOf</code></a> method is the same as the

  2182.       <a href='#toJSON'><code>toJSON</code></a> method, and both are the same as the

  2183.       <a href='#toS'><code>toString</code></a> method except they do not take a <code>base</code>

  2184.       argument and they include the minus sign for negative zero.

  2185.     </p>

  2186.     <pre>

  2187. BigNumber.prototype.valueOf = function () {

  2188.   throw Error('valueOf called!')

  2189. }

  2190. 

  2191. x = new BigNumber(1)

  2192. x / 2                    // '[BigNumber Error] valueOf called!'

  2193. x + 'abc'                // '[BigNumber Error] valueOf called!'

  2194. </pre>

  2195. 

  2196. 

  2197. 

  2198.     <h4 id='faq'>FAQ</h4>

  2199. 

  2200.     <h6>Why are trailing fractional zeros removed from BigNumbers?</h6>

  2201.     <p>

  2202.       Some arbitrary-precision libraries retain trailing fractional zeros as they can indicate the

  2203.       precision of a value. This can be useful but the results of arithmetic operations can be

  2204.       misleading.

  2205.     </p>

  2206.     <pre>

  2207. x = new BigDecimal("1.0")

  2208. y = new BigDecimal("1.1000")

  2209. z = x.add(y)                      // 2.1000

  2210. 

  2211. x = new BigDecimal("1.20")

  2212. y = new BigDecimal("3.45000")

  2213. z = x.multiply(y)                 // 4.1400000</pre>

  2214.     <p>

  2215.       To specify the precision of a value is to specify that the value lies

  2216.       within a certain range.

  2217.     </p>

  2218.     <p>

  2219.       In the first example, <code>x</code> has a value of <code>1.0</code>. The trailing zero shows

  2220.       the precision of the value, implying that it is in the range <code>0.95</code> to

  2221.       <code>1.05</code>. Similarly, the precision indicated by the trailing zeros of <code>y</code>

  2222.       indicates that the value is in the range <code>1.09995</code> to <code>1.10005</code>.

  2223.     </p>

  2224.     <p>

  2225.       If we  add the two lowest values in the ranges we have, <code>0.95 + 1.09995 = 2.04995</code>,

  2226.       and if we add the two highest values we have, <code>1.05 + 1.10005 = 2.15005</code>, so the

  2227.       range of the result of the addition implied by the precision of its operands is

  2228.       <code>2.04995</code> to <code>2.15005</code>.

  2229.     </p>

  2230.     <p>

  2231.       The result given by BigDecimal of <code>2.1000</code> however, indicates that the value is in

  2232.       the range <code>2.09995</code> to <code>2.10005</code> and therefore the precision implied by

  2233.       its trailing zeros may be misleading.

  2234.     </p>

  2235.     <p>

  2236.       In the second example, the true range is <code>4.122744</code> to <code>4.157256</code> yet

  2237.       the BigDecimal answer of <code>4.1400000</code> indicates a range of <code>4.13999995</code>

  2238.       to  <code>4.14000005</code>. Again, the precision implied by the trailing zeros may be

  2239.       misleading.

  2240.     </p>

  2241.     <p>

  2242.       This library, like binary floating point and most calculators, does not retain trailing

  2243.       fractional zeros. Instead, the <code>toExponential</code>, <code>toFixed</code> and

  2244.       <code>toPrecision</code> methods enable trailing zeros to be added if and when required.<br />

  2245.     </p>

  2246.   </div>

  2247. 

  2248. </body>

  2249. </html>