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<title>bignumber.js API</title>
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  <div class="nav">

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

    <b> CONSTRUCTOR </b>
    <ul>
      <li><a href="#bignumber">BigNumber</a></li>
    </ul>

    <a href="#methods">Methods</a>
    <ul>
      <li><a href="#another">another</a></li>
      <li><a href="#config" >config</a></li>
      <li>
        <ul class="inset">
          <li><a href="#decimal-places">DECIMAL_PLACES</a></li>
          <li><a href="#rounding-mode" >ROUNDING_MODE</a></li>
          <li><a href="#exponential-at">EXPONENTIAL_AT</a></li>
          <li><a href="#range"         >RANGE</a></li>
          <li><a href="#errors"        >ERRORS</a></li>
          <li><a href="#crypto"        >CRYPTO</a></li>
          <li><a href="#modulo-mode"   >MODULO_MODE</a></li>
          <li><a href="#pow-precision" >POW_PRECISION</a></li>
          <li><a href="#format"        >FORMAT</a></li>
        </ul>
      </li>
      <li><a href="#max"   >max</a></li>
      <li><a href="#min"   >min</a></li>
      <li><a href="#random">random</a></li>
    </ul>

    <a href="#constructor-properties">Properties</a>
    <ul>
      <li><a href="#round-up"        >ROUND_UP</a></li>
      <li><a href="#round-down"      >ROUND_DOWN</a></li>
      <li><a href="#round-ceil"      >ROUND_CEIL</a></li>
      <li><a href="#round-floor"     >ROUND_FLOOR</a></li>
      <li><a href="#round-half-up"   >ROUND_HALF_UP</a></li>
      <li><a href="#round-half-down" >ROUND_HALF_DOWN</a></li>
      <li><a href="#round-half-even" >ROUND_HALF_EVEN</a></li>
      <li><a href="#round-half-ceil" >ROUND_HALF_CEIL</a></li>
      <li><a href="#round-half-floor">ROUND_HALF_FLOOR</a></li>
    </ul>

    <b> INSTANCE </b>

    <a href="#prototype-methods">Methods</a>
    <ul>
      <li><a href="#abs"    >absoluteValue       </a><span>abs</span>     </li>
      <li><a href="#ceil"   >ceil                </a>                     </li>
      <li><a href="#cmp"    >comparedTo          </a><span>cmp</span>     </li>
      <li><a href="#dp"     >decimalPlaces       </a><span>dp</span>      </li>
      <li><a href="#div"    >dividedBy           </a><span>div</span>     </li>
      <li><a href="#divInt" >dividedToIntegerBy  </a><span>divToInt</span></li>
      <li><a href="#eq"     >equals              </a><span>eq</span>      </li>
      <li><a href="#floor"  >floor               </a>                     </li>
      <li><a href="#gt"     >greaterThan         </a><span>gt</span>      </li>
      <li><a href="#gte"    >greaterThanOrEqualTo</a><span>gte</span>     </li>
      <li><a href="#isF"    >isFinite            </a>                     </li>
      <li><a href="#isInt"  >isInteger           </a><span>isInt</span>   </li>
      <li><a href="#isNaN"  >isNaN               </a>                     </li>
      <li><a href="#isNeg"  >isNegative          </a><span>isNeg</span>   </li>
      <li><a href="#isZ"    >isZero              </a>                     </li>
      <li><a href="#lt"     >lessThan            </a><span>lt</span>      </li>
      <li><a href="#lte"    >lessThanOrEqualTo   </a><span>lte</span>     </li>
      <li><a href="#minus"  >minus               </a><span>sub</span>     </li>
      <li><a href="#mod"    >modulo              </a><span>mod</span>     </li>
      <li><a href="#neg"    >negated             </a><span>neg</span>     </li>
      <li><a href="#plus"   >plus                </a><span>add</span>     </li>
      <li><a href="#sd"     >precision           </a><span>sd</span>      </li>
      <li><a href="#round"  >round               </a>                     </li>
      <li><a href="#shift"  >shift               </a>                     </li>
      <li><a href="#sqrt"   >squareRoot          </a><span>sqrt</span>    </li>
      <li><a href="#times"  >times               </a><span>mul</span>     </li>
      <li><a href="#toD"    >toDigits            </a>                     </li>
      <li><a href="#toE"    >toExponential       </a>                     </li>
      <li><a href="#toFix"  >toFixed             </a>                     </li>
      <li><a href="#toFor"  >toFormat            </a>                     </li>
      <li><a href="#toFr"   >toFraction          </a>                     </li>
      <li><a href="#toJSON" >toJSON              </a>                     </li>
      <li><a href="#toN"    >toNumber            </a>                     </li>
      <li><a href="#pow"    >toPower             </a><span>pow</span>     </li>
      <li><a href="#toP"    >toPrecision         </a>                     </li>
      <li><a href="#toS"    >toString            </a>                     </li>
      <li><a href="#trunc"  >truncated           </a><span>trunc</span>   </li>
      <li><a href="#valueOf">valueOf             </a>                     </li>
    </ul>

    <a href="#instance-properties">Properties</a>
    <ul>
      <li><a href="#coefficient">c: coefficient</a></li>
      <li><a href="#exponent"   >e: exponent</a></li>
      <li><a href="#sign"       >s: sign</a></li>
      <li><a href="#isbig"      >isBigNumber</a></li>
    </ul>

    <a href="#zero-nan-infinity">Zero, NaN &amp; Infinity</a>
    <a href="#Errors">Errors</a>
    <a class='end' href="#faq">FAQ</a>

  </div>

  <div class="container">

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

    <p>A JavaScript library for arbitrary-precision arithmetic.</p>
    <p><a href="https://github.com/MikeMcl/bignumber.js">Hosted on GitHub</a>. </p>

    <h2>API</h2>

    <p>
      See the <a href='https://github.com/MikeMcl/bignumber.js'>README</a> on GitHub for a
      quick-start introduction.
    </p>
    <p>
      In all examples below, <code>var</code> and semicolons are not shown, and if a commented-out
      value is in quotes it means <code>toString</code> has been called on the preceding expression.
    </p>


    <h3>CONSTRUCTOR</h3>

    <h5 id="bignumber">
      BigNumber<code class='inset'>BigNumber(value [, base]) <i>&rArr; BigNumber</i></code>
    </h5>
    <dl>
      <dt><code>value</code></dt>
      <dd>
        <i>number|string|BigNumber</i>: see <a href='#range'>RANGE</a> for
        range.
      </dd>
      <dd>
        A numeric value.
      </dd>
      <dd>
        Legitimate values include &plusmn;<code>0</code>, &plusmn;<code>Infinity</code> and
        <code>NaN</code>.
      </dd>
      <dd>
        Values of type <em>number</em> with more than <code>15</code> significant digits are
        considered invalid (if <a href='#errors'><code>ERRORS</code></a> is true) as calling
        <code><a href='#toS'>toString</a></code> or <code><a href='#valueOf'>valueOf</a></code> on
        such numbers may not result in the intended value.
        <pre>console.log( 823456789123456.3 );    // 823456789123456.2</pre>
      </dd>
      <dd>
        There is no limit to the number of digits of a value of type <em>string</em> (other than
        that of JavaScript's maximum array size).
      </dd>
      <dd>
        Decimal string values may be in exponential, as well as normal (fixed-point) notation.
        Non-decimal values must be in normal notation.
      </dd>
      <dd>
        String values in hexadecimal literal form, e.g. <code>'0xff'</code>, are valid, as are
        string values with the octal and binary prefixs <code>'0o'</code> and <code>'0b'</code>.
        String values in octal literal form without the prefix will be interpreted as
        decimals, e.g. <code>'011'</code> is interpreted as 11, not 9.
      </dd>
      <dd>Values in any base may have fraction digits.</dd>
      <dd>
        For bases from <code>10</code> to <code>36</code>, lower and/or upper case letters can be
        used to represent values from <code>10</code> to <code>35</code>.
      </dd>
      <dd>
        For bases above 36, <code>a-z</code> represents values from <code>10</code> to
        <code>35</code>, <code>A-Z</code> from <code>36</code> to <code>61</code>, and
        <code>$</code> and <code>_</code> represent <code>62</code> and <code>63</code> respectively
        <i>(this can be changed by editing the <code>ALPHABET</code> variable near the top of the
        source file)</i>.
      </dd>
    </dl>
    <dl>
      <dt><code>base</code></dt>
      <dd>
        <i>number</i>: integer, <code>2</code> to <code>64</code> inclusive
      </dd>
      <dd>The base of <code>value</code>.</dd>
      <dd>
        If <code>base</code> is omitted, or is <code>null</code> or <code>undefined</code>, base
        <code>10</code> is assumed.
      </dd>
    </dl>
    <br />
    <p>Returns a new instance of a BigNumber object.</p>
    <p>
      If a base is specified, the value is rounded according to
      the current <a href='#decimal-places'><code>DECIMAL_PLACES</code></a> and
      <a href='#rounding-mode'><code>ROUNDING_MODE</code></a> configuration.
    </p>
    <p>
      See <a href='#Errors'>Errors</a> for the treatment of an invalid <code>value</code> or
      <code>base</code>.
    </p>
    <pre>
x = new BigNumber(9)                       // '9'
y = new BigNumber(x)                       // '9'

// 'new' is optional if ERRORS is false
BigNumber(435.345)                         // '435.345'

new BigNumber('5032485723458348569331745.33434346346912144534543')
new BigNumber('4.321e+4')                  // '43210'
new BigNumber('-735.0918e-430')            // '-7.350918e-428'
new BigNumber(Infinity)                    // 'Infinity'
new BigNumber(NaN)                         // 'NaN'
new BigNumber('.5')                        // '0.5'
new BigNumber('+2')                        // '2'
new BigNumber(-10110100.1, 2)              // '-180.5'
new BigNumber(-0b10110100.1)               // '-180.5'
new BigNumber('123412421.234324', 5)       // '607236.557696'
new BigNumber('ff.8', 16)                  // '255.5'
new BigNumber('0xff.8')                    // '255.5'</pre>
    <p>
      The following throws <code>'not a base 2 number'</code> if
      <a href='#errors'><code>ERRORS</code></a> is true, otherwise it returns a BigNumber with value
      <code>NaN</code>.
    </p>
    <pre>new BigNumber(9, 2)</pre>
    <p>
      The following throws <code>'number type has more than 15 significant digits'</code> if
      <a href='#errors'><code>ERRORS</code></a> is true, otherwise it returns a BigNumber with value
      <code>96517860459076820</code>.
    </p>
    <pre>new BigNumber(96517860459076817.4395)</pre>
    <p>
      The following throws <code>'not a number'</code> if <a href='#errors'><code>ERRORS</code></a>
      is true, otherwise it returns a BigNumber with value <code>NaN</code>.
    </p>
    <pre>new BigNumber('blurgh')</pre>
    <p>
      A value is only rounded by the constructor if a base is specified.
    </p>
    <pre>BigNumber.config({ DECIMAL_PLACES: 5 })
new BigNumber(1.23456789)                  // '1.23456789'
new BigNumber(1.23456789, 10)              // '1.23457'</pre>



    <h4 id="methods">Methods</h4>
     <p>The static methods of a BigNumber constructor.</p>




    <h5 id="another">
       another<code class='inset'>.another([obj]) <i>&rArr; BigNumber constructor</i></code>
    </h5>
    <p><code>obj</code>: <i>object</i></p>
    <p>
      Returns a new independent BigNumber constructor with configuration as described by
      <code>obj</code> (see <a href='#config'><code>config</code></a>), or with the default
      configuration if <code>obj</code> is <code>null</code> or <code>undefined</code>.
    </p>
    <pre>BigNumber.config({ DECIMAL_PLACES: 5 })
BN = BigNumber.another({ DECIMAL_PLACES: 9 })

x = new BigNumber(1)
y = new BN(1)

x.div(3)                        // 0.33333
y.div(3)                        // 0.333333333

// BN = BigNumber.another({ DECIMAL_PLACES: 9 }) is equivalent to:
BN = BigNumber.another()
BN.config({ DECIMAL_PLACES: 9 })</pre>



    <h5 id="config">config<code class='inset'>set([obj]) <i>&rArr; object</i></code></h5>
    <p>
      <code>obj</code>: <i>object</i>: an object that contains some or all of the following
      properties.
    </p>
    <p>Configures the settings for this particular BigNumber constructor.</p>
    <p><i>Note: the configuration can also be supplied as an argument list, see below.</i></p>
    <dl class='inset'>
      <dt id="decimal-places"><code><b>DECIMAL_PLACES</b></code></dt>
      <dd>
        <i>number</i>: integer, <code>0</code> to <code>1e+9</code> inclusive<br />
        Default value: <code>20</code>
      </dd>
      <dd>
        The <u>maximum</u> number of decimal places of the results of operations involving
        division, i.e. division, square root and base conversion operations, and power
        operations with negative exponents.<br />
      </dd>
      <dd>
      <pre>BigNumber.config({ DECIMAL_PLACES: 5 })
BigNumber.set({ DECIMAL_PLACES: 5 })    // equivalent
BigNumber.config(5)    // equivalent</pre>
      </dd>



      <dt id="rounding-mode"><code><b>ROUNDING_MODE</b></code></dt>
      <dd>
        <i>number</i>: integer, <code>0</code> to <code>8</code> inclusive<br />
        Default value: <code>4</code> <a href="#round-half-up">(<code>ROUND_HALF_UP</code>)</a>
      </dd>
      <dd>
        The rounding mode used in the above operations and the default rounding mode of
        <a href='#round'><code>round</code></a>,
        <a href='#toE'><code>toExponential</code></a>,
        <a href='#toFix'><code>toFixed</code></a>,
        <a href='#toFor'><code>toFormat</code></a> and
        <a href='#toP'><code>toPrecision</code></a>.
      </dd>
      <dd>The modes are available as enumerated properties of the BigNumber constructor.</dd>
       <dd>
      <pre>BigNumber.config({ ROUNDING_MODE: 0 })
BigNumber.config(null, BigNumber.ROUND_UP)    // equivalent</pre>
        </dd>



      <dt id="exponential-at"><code><b>EXPONENTIAL_AT</b></code></dt>
      <dd>
        <i>number</i>: integer, magnitude <code>0</code> to <code>1e+9</code> inclusive, or
        <br />
        <i>number</i>[]: [ integer <code>-1e+9</code> to <code>0</code> inclusive, integer
        <code>0</code> to <code>1e+9</code> inclusive ]<br />
        Default value: <code>[-7, 20]</code>
      </dd>
      <dd>
        The exponent value(s) at which <code>toString</code> returns exponential notation.
      </dd>
      <dd>
        If a single number is assigned, the value is the exponent magnitude.<br />
        If an array of two numbers is assigned then the first number is the negative exponent
        value at and beneath which exponential notation is used, and the second number is the
        positive exponent value at and above which the same.
      </dd>
      <dd>
        For example, to emulate JavaScript numbers in terms of the exponent values at which they
        begin to use exponential notation, use <code>[-7, 20]</code>.
      </dd>
      <dd>
      <pre>BigNumber.config({ EXPONENTIAL_AT: 2 })
new BigNumber(12.3)         // '12.3'        e is only 1
new BigNumber(123)          // '1.23e+2'
new BigNumber(0.123)        // '0.123'       e is only -1
new BigNumber(0.0123)       // '1.23e-2'

BigNumber.config({ EXPONENTIAL_AT: [-7, 20] })
new BigNumber(123456789)    // '123456789'   e is only 8
new BigNumber(0.000000123)  // '1.23e-7'

// Almost never return exponential notation:
BigNumber.config({ EXPONENTIAL_AT: 1e+9 })

// Always return exponential notation:
BigNumber.config({ EXPONENTIAL_AT: 0 })</pre>
      </dd>
      <dd>
        Regardless of the value of <code>EXPONENTIAL_AT</code>, the <code>toFixed</code> method
        will always return a value in normal notation and the <code>toExponential</code> method
        will always return a value in exponential form.
      </dd>
      <dd>
        Calling <code>toString</code> with a base argument, e.g. <code>toString(10)</code>, will
        also always return normal notation.
      </dd>



      <dt id="range"><code><b>RANGE</b></code></dt>
      <dd>
        <i>number</i>: integer, magnitude <code>1</code> to <code>1e+9</code> inclusive, or
        <br />
        <i>number</i>[]: [ integer <code>-1e+9</code> to <code>-1</code> inclusive, integer
        <code>1</code> to <code>1e+9</code> inclusive ]<br />
        Default value: <code>[-1e+9, 1e+9]</code>
      </dd>
      <dd>
        The exponent value(s) beyond which overflow to <code>Infinity</code> and underflow to
        zero occurs.
      </dd>
      <dd>
        If a single number is assigned, it is the maximum exponent magnitude: values wth a
        positive exponent of greater magnitude become <code>Infinity</code> and those with a
        negative exponent of greater magnitude become zero.
      <dd>
        If an array of two numbers is assigned then the first number is the negative exponent
        limit and the second number is the positive exponent limit.
      </dd>
      <dd>
        For example, to emulate JavaScript numbers in terms of the exponent values at which they
        become zero and <code>Infinity</code>, use <code>[-324, 308]</code>.
      </dd>
      <dd>
      <pre>BigNumber.config({ RANGE: 500 })
BigNumber.config().RANGE     // [ -500, 500 ]
new BigNumber('9.999e499')   // '9.999e+499'
new BigNumber('1e500')       // 'Infinity'
new BigNumber('1e-499')      // '1e-499'
new BigNumber('1e-500')      // '0'

BigNumber.config({ RANGE: [-3, 4] })
new BigNumber(99999)         // '99999'      e is only 4
new BigNumber(100000)        // 'Infinity'   e is 5
new BigNumber(0.001)         // '0.01'       e is only -3
new BigNumber(0.0001)        // '0'          e is -4</pre>
      </dd>
      <dd>
        The largest possible magnitude of a finite BigNumber is
        <code>9.999...e+1000000000</code>.<br />
        The smallest possible magnitude of a non-zero BigNumber is <code>1e-1000000000</code>.
      </dd>



      <dt id="errors"><code><b>ERRORS</b></code></dt>
      <dd>
        <i>boolean|number</i>: <code>true</code>, <code>false</code>, <code>0</code> or
        <code>1</code>.<br />
        Default value: <code>true</code>
      </dd>
      <dd>
        The value that determines whether BigNumber Errors are thrown.<br />
        If <code>ERRORS</code> is false, no errors will be thrown.
      </dd>
      <dd>See <a href='#Errors'>Errors</a>.</dd>
      <dd><pre>BigNumber.config({ ERRORS: false })</pre></dd>



      <dt id="crypto"><code><b>CRYPTO</b></code></dt>
      <dd>
        <i>boolean|number</i>: <code>true</code>, <code>false</code>, <code>0</code> or
        <code>1</code>.<br />
        Default value: <code>false</code>
      </dd>
      <dd>
        The value that determines whether cryptographically-secure pseudo-random number
        generation is used.
      </dd>
      <dd>
        If <code>CRYPTO</code> is set to <code>true</code> then the
        <a href='#random'><code>random</code></a> method will generate random digits using
        <code>crypto.getRandomValues</code> in browsers that support it, or
        <code>crypto.randomBytes</code> if using a version of Node.js that supports it.
      </dd>
      <dd>
        If neither function is supported by the host environment then attempting to set
        <code>CRYPTO</code> to <code>true</code> will fail, and if <code>ERRORS</code>
        is <code>true</code> an exception will be thrown.
      </dd>
      <dd>
        If <code>CRYPTO</code> is <code>false</code> then the source of randomness used will be
        <code>Math.random</code> (which is assumed to generate at least <code>30</code> bits of
        randomness).
      </dd>
      <dd>See <a href='#random'><code>random</code></a>.</dd>
      <dd>
      <pre>BigNumber.config({ CRYPTO: true })
BigNumber.config().CRYPTO       // true
BigNumber.random()              // 0.54340758610486147524</pre>
      </dd>



      <dt id="modulo-mode"><code><b>MODULO_MODE</b></code></dt>
      <dd>
        <i>number</i>: integer, <code>0</code> to <code>9</code> inclusive<br />
        Default value: <code>1</code> (<a href="#round-down"><code>ROUND_DOWN</code></a>)
      </dd>
      <dd>The modulo mode used when calculating the modulus: <code>a mod n</code>.</dd>
      <dd>
        The quotient, <code>q = a / n</code>, is calculated according to the
        <a href='#rounding-mode'><code>ROUNDING_MODE</code></a> that corresponds to the chosen
        <code>MODULO_MODE</code>.
      </dd>
      <dd>The remainder, <code>r</code>, is calculated as: <code>r = a - n * q</code>.</dd>
      <dd>
        The modes that are most commonly used for the modulus/remainder operation are shown in
        the following table. Although the other rounding modes can be used, they may not give
        useful results.
      </dd>
      <dd>
        <table>
          <tr><th>Property</th><th>Value</th><th>Description</th></tr>
          <tr>
            <td><b>ROUND_UP</b></td><td class='centre'>0</td>
            <td>
              The remainder is positive if the dividend is negative, otherwise it is negative.
            </td>
          </tr>
          <tr>
            <td><b>ROUND_DOWN</b></td><td class='centre'>1</td>
            <td>
              The remainder has the same sign as the dividend.<br />
              This uses 'truncating division' and matches the behaviour of JavaScript's
              remainder operator <code>%</code>.
            </td>
          </tr>
          <tr>
            <td><b>ROUND_FLOOR</b></td><td class='centre'>3</td>
            <td>
              The remainder has the same sign as the divisor.<br />
              This matches Python's <code>%</code> operator.
            </td>
          </tr>
          <tr>
            <td><b>ROUND_HALF_EVEN</b></td><td class='centre'>6</td>
            <td>The <i>IEEE 754</i> remainder function.</td>
          </tr>
           <tr>
             <td><b>EUCLID</b></td><td class='centre'>9</td>
             <td>
               The remainder is always positive. Euclidian division: <br />
               <code>q = sign(n) * floor(a / abs(n))</code>
             </td>
           </tr>
        </table>
      </dd>
      <dd>
        The rounding/modulo modes are available as enumerated properties of the BigNumber
        constructor.
      </dd>
      <dd>See <a href='#mod'><code>modulo</code></a>.</dd>
      <dd>
        <pre>BigNumber.config({ MODULO_MODE: BigNumber.EUCLID })
BigNumber.config({ MODULO_MODE: 9 })          // equivalent</pre>
      </dd>



      <dt id="pow-precision"><code><b>POW_PRECISION</b></code></dt>
      <dd>
        <i>number</i>: integer, <code>0</code> to <code>1e+9</code> inclusive.<br />
        Default value: <code>0</code>
      </dd>
      <dd>
        The <i>maximum</i> number of significant digits of the result of the power operation
        (unless a modulus is specified).
      </dd>
      <dd>If set to <code>0</code>, the number of signifcant digits will not be limited.</dd>
      <dd>See <a href='#pow'><code>toPower</code></a>.</dd>
      <dd><pre>BigNumber.config({ POW_PRECISION: 100 })</pre></dd>



      <dt id="format"><code><b>FORMAT</b></code></dt>
      <dd><i>object</i></dd>
      <dd>
        The <code>FORMAT</code> object configures the format of the string returned by the
        <a href='#toFor'><code>toFormat</code></a> method.
      </dd>
      <dd>
        The example below shows the properties of the <code>FORMAT</code> object that are
        recognised, and their default values.
      </dd>
      <dd>
         Unlike the other configuration properties, the values of the properties of the
         <code>FORMAT</code> object will not be checked for validity. The existing
         <code>FORMAT</code> object will simply be replaced by the object that is passed in.
         Note that all the properties shown below do not have to be included.
      </dd>
      <dd>See <a href='#toFor'><code>toFormat</code></a> for examples of usage.</dd>
      <dd>
      <pre>
BigNumber.config({
    FORMAT: {
        // the decimal separator
        decimalSeparator: '.',
        // the grouping separator of the integer part
        groupSeparator: ',',
        // the primary grouping size of the integer part
        groupSize: 3,
        // the secondary grouping size of the integer part
        secondaryGroupSize: 0,
        // the grouping separator of the fraction part
        fractionGroupSeparator: ' ',
        // the grouping size of the fraction part
        fractionGroupSize: 0
    }
});</pre>
      </dd>
    </dl>
    <br />
    <p>Returns an object with the above properties and their current values.</p>
    <p>
      If the value to be assigned to any of the above properties is <code>null</code> or
      <code>undefined</code> it is ignored.
    </p>
    <p>See <a href='#Errors'>Errors</a> for the treatment of invalid values.</p>
    <pre>
BigNumber.config({
    DECIMAL_PLACES: 40,
    ROUNDING_MODE: BigNumber.ROUND_HALF_CEIL,
    EXPONENTIAL_AT: [-10, 20],
    RANGE: [-500, 500],
    ERRORS: true,
    CRYPTO: true,
    MODULO_MODE: BigNumber.ROUND_FLOOR,
    POW_PRECISION: 80,
    FORMAT: {
        groupSize: 3,
        groupSeparator: ' ',
        decimalSeparator: ','
    }
});

// Alternatively but equivalently (excluding FORMAT):
BigNumber.config( 40, 7, [-10, 20], 500, 1, 1, 3, 80 )

obj = BigNumber.config();
obj.ERRORS       // true
obj.RANGE        // [-500, 500]</pre>



    <h5 id="max">
      max<code class='inset'>.max([arg1 [, arg2, ...]]) <i>&rArr; BigNumber</i></code>
    </h5>
    <p>
      <code>arg1</code>, <code>arg2</code>, ...: <i>number|string|BigNumber</i><br />
      <i>See <code><a href="#bignumber">BigNumber</a></code> for further parameter details.</i>
    </p>
    <p>
      Returns a BigNumber whose value is the maximum of <code>arg1</code>,
      <code>arg2</code>,... .
    </p>
    <p>The argument to this method can also be an array of values.</p>
    <p>The return value is always exact and unrounded.</p>
    <pre>x = new BigNumber('3257869345.0378653')
BigNumber.max(4e9, x, '123456789.9')          // '4000000000'

arr = [12, '13', new BigNumber(14)]
BigNumber.max(arr)                            // '14'</pre>



    <h5 id="min">
      min<code class='inset'>.min([arg1 [, arg2, ...]]) <i>&rArr; BigNumber</i></code>
    </h5>
    <p>
      <code>arg1</code>, <code>arg2</code>, ...: <i>number|string|BigNumber</i><br />
      <i>See <code><a href="#bignumber">BigNumber</a></code> for further parameter details.</i>
    </p>
    <p>
      Returns a BigNumber whose value is the minimum of <code>arg1</code>,
      <code>arg2</code>,... .
    </p>
    <p>The argument to this method can also be an array of values.</p>
    <p>The return value is always exact and unrounded.</p>
    <pre>x = new BigNumber('3257869345.0378653')
BigNumber.min(4e9, x, '123456789.9')          // '123456789.9'

arr = [2, new BigNumber(-14), '-15.9999', -12]
BigNumber.min(arr)                            // '-15.9999'</pre>



    <h5 id="random">
      random<code class='inset'>.random([dp]) <i>&rArr; BigNumber</i></code>
    </h5>
    <p><code>dp</code>: <i>number</i>: integer, <code>0</code> to <code>1e+9</code> inclusive</p>
    <p>
      Returns a new BigNumber with a pseudo-random value equal to or greater than <code>0</code> and
      less than <code>1</code>.
    </p>
    <p>
      The return value will have <code>dp</code> decimal places (or less if trailing zeros are
      produced).<br />
      If <code>dp</code> is omitted then the number of decimal places will default to the current
      <a href='#decimal-places'><code>DECIMAL_PLACES</code></a> setting.
    </p>
    <p>
      Depending on the value of this BigNumber constructor's
      <a href='#crypto'><code>CRYPTO</code></a> setting and the support for the
      <code>crypto</code> object in the host environment, the random digits of the return value are
      generated by either <code>Math.random</code> (fastest), <code>crypto.getRandomValues</code>
      (Web Cryptography API in recent browsers) or <code>crypto.randomBytes</code> (Node.js).
    </p>
    <p>
      If <a href='#crypto'><code>CRYPTO</code></a> is <code>true</code>, i.e. one of the
      <code>crypto</code> methods is to be used, the value of a returned BigNumber should be
      cryptographically-secure and statistically indistinguishable from a random value.
    </p>
    <pre>BigNumber.config({ DECIMAL_PLACES: 10 })
BigNumber.random()              // '0.4117936847'
BigNumber.random(20)            // '0.78193327636914089009'</pre>



    <h4 id="constructor-properties">Properties</h4>
    <p>
      The library's enumerated rounding modes are stored as properties of the constructor.<br />
      (They are not referenced internally by the library itself.)
    </p>
    <p>
      Rounding modes <code>0</code> to <code>6</code> (inclusive) are the same as those of Java's
      BigDecimal class.
    </p>
    <table>
      <tr>
        <th>Property</th>
        <th>Value</th>
        <th>Description</th>
      </tr>
      <tr>
        <td id="round-up"><b>ROUND_UP</b></td>
        <td class='centre'>0</td>
        <td>Rounds away from zero</td>
      </tr>
      <tr>
        <td id="round-down"><b>ROUND_DOWN</b></td>
        <td class='centre'>1</td>
        <td>Rounds towards zero</td>
      </tr>
      <tr>
        <td id="round-ceil"><b>ROUND_CEIL</b></td>
        <td class='centre'>2</td>
        <td>Rounds towards <code>Infinity</code></td>
      </tr>
      <tr>
        <td id="round-floor"><b>ROUND_FLOOR</b></td>
        <td class='centre'>3</td>
        <td>Rounds towards <code>-Infinity</code></td>
      </tr>
      <tr>
        <td id="round-half-up"><b>ROUND_HALF_UP</b></td>
        <td class='centre'>4</td>
        <td>
          Rounds towards nearest neighbour.<br />
          If equidistant, rounds away from zero
        </td>
      </tr>
      <tr>
        <td id="round-half-down"><b>ROUND_HALF_DOWN</b></td>
        <td class='centre'>5</td>
        <td>
          Rounds towards nearest neighbour.<br />
          If equidistant, rounds towards zero
        </td>
      </tr>
      <tr>
        <td id="round-half-even"><b>ROUND_HALF_EVEN</b></td>
        <td class='centre'>6</td>
        <td>
          Rounds towards nearest neighbour.<br />
          If equidistant, rounds towards even neighbour
        </td>
      </tr>
      <tr>
        <td id="round-half-ceil"><b>ROUND_HALF_CEIL</b></td>
        <td class='centre'>7</td>
        <td>
          Rounds towards nearest neighbour.<br />
          If equidistant, rounds towards <code>Infinity</code>
        </td>
      </tr>
      <tr>
        <td id="round-half-floor"><b>ROUND_HALF_FLOOR</b></td>
        <td class='centre'>8</td>
        <td>
          Rounds towards nearest neighbour.<br />
          If equidistant, rounds towards <code>-Infinity</code>
        </td>
      </tr>
    </table>
    <pre>
BigNumber.config({ ROUNDING_MODE: BigNumber.ROUND_CEIL })
BigNumber.config({ ROUNDING_MODE: 2 })     // equivalent</pre>


    <h3>INSTANCE</h3>

    <h4 id="prototype-methods">Methods</h4>
    <p>The methods inherited by a BigNumber instance from its constructor's prototype object.</p>
    <p>A BigNumber is immutable in the sense that it is not changed by its methods. </p>
    <p>
      The treatment of &plusmn;<code>0</code>, &plusmn;<code>Infinity</code> and <code>NaN</code> is
      consistent with how JavaScript treats these values.
    </p>
    <p>
      Many method names have a shorter alias.<br />
      (Internally, the library always uses the shorter method names.)
    </p>



    <h5 id="abs">absoluteValue<code class='inset'>.abs() <i>&rArr; BigNumber</i></code></h5>
    <p>
      Returns a BigNumber whose value is the absolute value, i.e. the magnitude, of the value of
      this BigNumber.
    </p>
    <p>The return value is always exact and unrounded.</p>
    <pre>
x = new BigNumber(-0.8)
y = x.absoluteValue()           // '0.8'
z = y.abs()                     // '0.8'</pre>



    <h5 id="ceil">ceil<code class='inset'>.ceil() <i>&rArr; BigNumber</i></code></h5>
    <p>
      Returns a BigNumber whose value is the value of this BigNumber rounded to
      a whole number in the direction of positive <code>Infinity</code>.
    </p>
    <pre>
x = new BigNumber(1.3)
x.ceil()                        // '2'
y = new BigNumber(-1.8)
y.ceil()                        // '-1'</pre>



    <h5 id="cmp">comparedTo<code class='inset'>.cmp(n [, base]) <i>&rArr; number</i></code></h5>
    <p>
      <code>n</code>: <i>number|string|BigNumber</i><br />
      <code>base</code>: <i>number</i><br />
      <i>See <a href="#bignumber">BigNumber</a> for further parameter details.</i>
    </p>
    <table>
      <tr><th>Returns</th><th>&nbsp;</th></tr>
      <tr>
        <td class='centre'><code>1</code></td>
        <td>If the value of this BigNumber is greater than the value of <code>n</code></td>
      </tr>
      <tr>
        <td class='centre'><code>-1</code></td>
        <td>If the value of this BigNumber is less than the value of <code>n</code></td>
      </tr>
      <tr>
        <td class='centre'><code>0</code></td>
        <td>If this BigNumber and <code>n</code> have the same value</td>
      </tr>
       <tr>
        <td class='centre'><code>null</code></td>
        <td>If the value of either this BigNumber or <code>n</code> is <code>NaN</code></td>
      </tr>
    </table>
    <pre>
x = new BigNumber(Infinity)
y = new BigNumber(5)
x.comparedTo(y)                 // 1
x.comparedTo(x.minus(1))        // 0
y.cmp(NaN)                      // null
y.cmp('110', 2)                 // -1</pre>



    <h5 id="dp">decimalPlaces<code class='inset'>.dp() <i>&rArr; number</i></code></h5>
    <p>
      Return the number of decimal places of the value of this BigNumber, or <code>null</code> if
      the value of this BigNumber is &plusmn;<code>Infinity</code> or <code>NaN</code>.
    </p>
    <pre>
x = new BigNumber(123.45)
x.decimalPlaces()               // 2
y = new BigNumber('9.9e-101')
y.dp()                          // 102</pre>



    <h5 id="div">dividedBy<code class='inset'>.div(n [, base]) <i>&rArr; BigNumber</i></code>
    </h5>
    <p>
      <code>n</code>: <i>number|string|BigNumber</i><br />
      <code>base</code>: <i>number</i><br />
      <i>See <a href="#bignumber">BigNumber</a> for further parameter details.</i>
    </p>
    <p>
      Returns a BigNumber whose value is the value of this BigNumber divided by
      <code>n</code>, rounded according to the current
      <a href='#decimal-places'><code>DECIMAL_PLACES</code></a> and
      <a href='#rounding-mode'><code>ROUNDING_MODE</code></a> configuration.
    </p>
    <pre>
x = new BigNumber(355)
y = new BigNumber(113)
x.dividedBy(y)                  // '3.14159292035398230088'
x.div(5)                        // '71'
x.div(47, 16)                   // '5'</pre>



    <h5 id="divInt">
      dividedToIntegerBy<code class='inset'>.divToInt(n [, base]) &rArr;
      <i>BigNumber</i></code>
    </h5>
    <p>
      <code>n</code>: <i>number|string|BigNumber</i><br />
      <code>base</code>: <i>number</i><br />
      <i>See <a href="#bignumber">BigNumber</a> for further parameter details.</i>
    </p>
    <p>
      Return a BigNumber whose value is the integer part of dividing the value of this BigNumber by
      <code>n</code>.
    </p>
    <pre>
x = new BigNumber(5)
y = new BigNumber(3)
x.dividedToIntegerBy(y)         // '1'
x.divToInt(0.7)                 // '7'
x.divToInt('0.f', 16)           // '5'</pre>



    <h5 id="eq">equals<code class='inset'>.eq(n [, base]) <i>&rArr; boolean</i></code></h5>
    <p>
      <code>n</code>: <i>number|string|BigNumber</i><br />
      <code>base</code>: <i>number</i><br />
      <i>See <a href="#bignumber">BigNumber</a> for further parameter details.</i>
    </p>
    <p>
      Returns <code>true</code> if the value of this BigNumber equals the value of <code>n</code>,
      otherwise returns <code>false</code>.<br />
      As with JavaScript, <code>NaN</code> does not equal <code>NaN</code>.
    </p>
    <p>Note: This method uses the <a href='#cmp'><code>comparedTo</code></a> method internally.</p>
    <pre>
0 === 1e-324                    // true
x = new BigNumber(0)
x.equals('1e-324')              // false
BigNumber(-0).eq(x)             // true  ( -0 === 0 )
BigNumber(255).eq('ff', 16)     // true

y = new BigNumber(NaN)
y.equals(NaN)                   // false</pre>



    <h5 id="floor">floor<code class='inset'>.floor() <i>&rArr; BigNumber</i></code></h5>
    <p>
      Returns a BigNumber whose value is the value of this BigNumber rounded to a whole number in
      the direction of negative <code>Infinity</code>.
    </p>
    <pre>
x = new BigNumber(1.8)
x.floor()                       // '1'
y = new BigNumber(-1.3)
y.floor()                       // '-2'</pre>



    <h5 id="gt">greaterThan<code class='inset'>.gt(n [, base]) <i>&rArr; boolean</i></code></h5>
    <p>
      <code>n</code>: <i>number|string|BigNumber</i><br />
      <code>base</code>: <i>number</i><br />
      <i>See <a href="#bignumber">BigNumber</a> for further parameter details.</i>
    </p>
    <p>
      Returns <code>true</code> if the value of this BigNumber is greater than the value of
      <code>n</code>, otherwise returns <code>false</code>.
    </p>
    <p>Note: This method uses the <a href='#cmp'><code>comparedTo</code></a> method internally.</p>
    <pre>
0.1 &gt; (0.3 - 0.2)                           // true
x = new BigNumber(0.1)
x.greaterThan(BigNumber(0.3).minus(0.2))    // false
BigNumber(0).gt(x)                          // false
BigNumber(11, 3).gt(11.1, 2)                // true</pre>



    <h5 id="gte">
      greaterThanOrEqualTo<code class='inset'>.gte(n [, base]) <i>&rArr; boolean</i></code>
    </h5>
    <p>
      <code>n</code>: <i>number|string|BigNumber</i><br />
      <code>base</code>: <i>number</i><br />
      <i>See <a href="#bignumber">BigNumber</a> for further parameter details.</i>
    </p>
    <p>
      Returns <code>true</code> if the value of this BigNumber is greater than or equal to the value
      of <code>n</code>, otherwise returns <code>false</code>.
    </p>
    <p>Note: This method uses the <a href='#cmp'><code>comparedTo</code></a> method internally.</p>
    <pre>
(0.3 - 0.2) &gt;= 0.1                   // false
x = new BigNumber(0.3).minus(0.2)
x.greaterThanOrEqualTo(0.1)          // true
BigNumber(1).gte(x)                  // true
BigNumber(10, 18).gte('i', 36)       // true</pre>



    <h5 id="isF">isFinite<code class='inset'>.isFinite() <i>&rArr; boolean</i></code></h5>
    <p>
      Returns <code>true</code> if the value of this BigNumber is a finite number, otherwise
      returns <code>false</code>.
    </p>
    <p>
      The only possible non-finite values of a BigNumber are <code>NaN</code>, <code>Infinity</code>
      and <code>-Infinity</code>.
    </p>
    <pre>
x = new BigNumber(1)
x.isFinite()                    // true
y = new BigNumber(Infinity)
y.isFinite()                    // false</pre>
    <p>
      Note: The native method <code>isFinite()</code> can be used if
      <code>n &lt;= Number.MAX_VALUE</code>.
    </p>



    <h5 id="isInt">isInteger<code class='inset'>.isInt() <i>&rArr; boolean</i></code></h5>
    <p>
      Returns <code>true</code> if the value of this BigNumber is a whole number, otherwise returns
      <code>false</code>.
    </p>
    <pre>
x = new BigNumber(1)
x.isInteger()                   // true
y = new BigNumber(123.456)
y.isInt()                       // false</pre>



    <h5 id="isNaN">isNaN<code class='inset'>.isNaN() <i>&rArr; boolean</i></code></h5>
    <p>
      Returns <code>true</code> if the value of this BigNumber is <code>NaN</code>, otherwise
      returns <code>false</code>.
    </p>
    <pre>
x = new BigNumber(NaN)
x.isNaN()                       // true
y = new BigNumber('Infinity')
y.isNaN()                       // false</pre>
    <p>Note: The native method <code>isNaN()</code> can also be used.</p>



    <h5 id="isNeg">isNegative<code class='inset'>.isNeg() <i>&rArr; boolean</i></code></h5>
    <p>
      Returns <code>true</code> if the value of this BigNumber is negative, otherwise returns
      <code>false</code>.
    </p>
    <pre>
x = new BigNumber(-0)
x.isNegative()                  // true
y = new BigNumber(2)
y.isNeg()                       // false</pre>
    <p>Note: <code>n &lt; 0</code> can be used if <code>n &lt;= -Number.MIN_VALUE</code>.</p>



    <h5 id="isZ">isZero<code class='inset'>.isZero() <i>&rArr; boolean</i></code></h5>
    <p>
      Returns <code>true</code> if the value of this BigNumber is zero or minus zero, otherwise
      returns <code>false</code>.
    </p>
    <pre>
x = new BigNumber(-0)
x.isZero() && x.isNeg()         // true
y = new BigNumber(Infinity)
y.isZero()                      // false</pre>
    <p>Note: <code>n == 0</code> can be used if <code>n &gt;= Number.MIN_VALUE</code>.</p>



    <h5 id="lt">lessThan<code class='inset'>.lt(n [, base]) <i>&rArr; boolean</i></code></h5>
    <p>
      <code>n</code>: <i>number|string|BigNumber</i><br />
      <code>base</code>: <i>number</i><br />
      <i>See <a href="#bignumber">BigNumber</a> for further parameter details.</i>
    </p>
    <p>
      Returns <code>true</code> if the value of this BigNumber is less than the value of
      <code>n</code>, otherwise returns <code>false</code>.
    </p>
     <p>Note: This method uses the <a href='#cmp'><code>comparedTo</code></a> method internally.</p>
    <pre>
(0.3 - 0.2) &lt; 0.1                     // true
x = new BigNumber(0.3).minus(0.2)
x.lessThan(0.1)                       // false
BigNumber(0).lt(x)                    // true
BigNumber(11.1, 2).lt(11, 3)          // true</pre>



    <h5 id="lte">
      lessThanOrEqualTo<code class='inset'>.lte(n [, base]) <i>&rArr; boolean</i></code>
    </h5>
    <p>
      <code>n</code>: <i>number|string|BigNumber</i><br />
      <code>base</code>: <i>number</i><br />
      <i>See <a href="#bignumber">BigNumber</a> for further parameter details.</i>
    </p>
    <p>
      Returns <code>true</code> if the value of this BigNumber is less than or equal to the value of
      <code>n</code>, otherwise returns <code>false</code>.
    </p>
    <p>Note: This method uses the <a href='#cmp'><code>comparedTo</code></a> method internally.</p>
    <pre>
0.1 &lt;= (0.3 - 0.2)                                // false
x = new BigNumber(0.1)
x.lessThanOrEqualTo(BigNumber(0.3).minus(0.2))    // true
BigNumber(-1).lte(x)                              // true
BigNumber(10, 18).lte('i', 36)                    // true</pre>



    <h5 id="minus">
      minus<code class='inset'>.minus(n [, base]) <i>&rArr; BigNumber</i></code>
    </h5>
    <p>
      <code>n</code>: <i>number|string|BigNumber</i><br />
      <code>base</code>: <i>number</i><br />
      <i>See <a href="#bignumber">BigNumber</a> for further parameter details.</i>
    </p>
    <p>Returns a BigNumber whose value is the value of this BigNumber minus <code>n</code>.</p>
    <p>The return value is always exact and unrounded.</p>
    <pre>
0.3 - 0.1                       // 0.19999999999999998
x = new BigNumber(0.3)
x.minus(0.1)                    // '0.2'
x.minus(0.6, 20)                // '0'</pre>



    <h5 id="mod">modulo<code class='inset'>.mod(n [, base]) <i>&rArr; BigNumber</i></code></h5>
    <p>
      <code>n</code>: <i>number|string|BigNumber</i><br />
      <code>base</code>: <i>number</i><br />
      <i>See <a href="#bignumber">BigNumber</a> for further parameter details.</i>
    </p>
    <p>
      Returns a BigNumber whose value is the value of this BigNumber modulo <code>n</code>, i.e.
      the integer remainder of dividing this BigNumber by <code>n</code>.
    </p>
    <p>
      The value returned, and in particular its sign, is dependent on the value of the
      <a href='#modulo-mode'><code>MODULO_MODE</code></a> setting of this BigNumber constructor.
      If it is <code>1</code> (default value), the result will have the same sign as this BigNumber,
      and it will match that of Javascript's <code>%</code> operator (within the limits of double
      precision) and BigDecimal's <code>remainder</code> method.
    </p>
    <p>The return value is always exact and unrounded.</p>
    <p>
      See <a href='#modulo-mode'><code>MODULO_MODE</code></a> for a description of the other
      modulo modes.
    </p>
    <pre>
1 % 0.9                         // 0.09999999999999998
x = new BigNumber(1)
x.modulo(0.9)                   // '0.1'
y = new BigNumber(33)
y.mod('a', 33)                  // '3'</pre>



    <h5 id="neg">negated<code class='inset'>.neg() <i>&rArr; BigNumber</i></code></h5>
    <p>
      Returns a BigNumber whose value is the value of this BigNumber negated, i.e. multiplied by
      <code>-1</code>.
    </p>
    <pre>
x = new BigNumber(1.8)
x.negated()                     // '-1.8'
y = new BigNumber(-1.3)
y.neg()                         // '1.3'</pre>



    <h5 id="plus">plus<code class='inset'>.plus(n [, base]) <i>&rArr; BigNumber</i></code></h5>
    <p>
      <code>n</code>: <i>number|string|BigNumber</i><br />
      <code>base</code>: <i>number</i><br />
      <i>See <a href="#bignumber">BigNumber</a> for further parameter details.</i>
    </p>
    <p>Returns a BigNumber whose value is the value of this BigNumber plus <code>n</code>.</p>
    <p>The return value is always exact and unrounded.</p>
    <pre>
0.1 + 0.2                       // 0.30000000000000004
x = new BigNumber(0.1)
y = x.plus(0.2)                 // '0.3'
BigNumber(0.7).plus(x).plus(y)  // '1'
x.plus('0.1', 8)                // '0.225'</pre>



    <h5 id="sd">precision<code class='inset'>.sd([z]) <i>&rArr; number</i></code></h5>
    <p>
      <code>z</code>: <i>boolean|number</i>: <code>true</code>, <code>false</code>, <code>0</code>
      or <code>1</code>
    </p>
    <p>Returns the number of significant digits of the value of this BigNumber.</p>
    <p>
      If <code>z</code> is <code>true</code> or <code>1</code> then any trailing zeros of the
      integer part of a number are counted as significant digits, otherwise they are not.
    </p>
    <pre>
x = new BigNumber(1.234)
x.precision()                   // 4
y = new BigNumber(987000)
y.sd()                          // 3
y.sd(true)                      // 6</pre>



    <h5 id="round">round<code class='inset'>.round([dp [, rm]]) <i>&rArr; BigNumber</i></code></h5>
    <p>
      <code>dp</code>: <i>number</i>: integer, <code>0</code> to <code>1e+9</code> inclusive<br />
      <code>rm</code>: <i>number</i>: integer, <code>0</code> to <code>8</code> inclusive
    </p>
    <p>
      Returns a BigNumber whose value is the value of this BigNumber rounded by rounding mode
      <code>rm</code> to a maximum of <code>dp</code> decimal places.
    </p>
    <p>
      if <code>dp</code> is omitted, or is <code>null</code> or <code>undefined</code>, the
      return value is <code>n</code> rounded to a whole number.<br />
      if <code>rm</code> is omitted, or is <code>null</code> or <code>undefined</code>,
      <a href='#rounding-mode'><code>ROUNDING_MODE</code></a> is used.
    </p>
    <p>
      See <a href='#Errors'>Errors</a> for the treatment of other non-integer or out of range
      <code>dp</code> or <code>rm</code> values.
    </p>
    <pre>
x = 1234.56
Math.round(x)                             // 1235

y = new BigNumber(x)
y.round()                                 // '1235'
y.round(1)                                // '1234.6'
y.round(2)                                // '1234.56'
y.round(10)                               // '1234.56'
y.round(0, 1)                             // '1234'
y.round(0, 6)                             // '1235'
y.round(1, 1)                             // '1234.5'
y.round(1, BigNumber.ROUND_HALF_EVEN)     // '1234.6'
y                                         // '1234.56'</pre>



    <h5 id="shift">shift<code class='inset'>.shift(n) <i>&rArr; BigNumber</i></code></h5>
    <p>
      <code>n</code>: <i>number</i>: integer,
      <code>-9007199254740991</code> to <code>9007199254740991</code> inclusive
    </p>
    <p>
      Returns a BigNumber whose value is the value of this BigNumber shifted <code>n</code> places.
    <p>
      The shift is of the decimal point, i.e. of powers of ten, and is to the left if <code>n</code>
      is negative or to the right if <code>n</code> is positive.
    </p>
    <p>The return value is always exact and unrounded.</p>
    <pre>
x = new BigNumber(1.23)
x.shift(3)                      // '1230'
x.shift(-3)                     // '0.00123'</pre>



    <h5 id="sqrt">squareRoot<code class='inset'>.sqrt() <i>&rArr; BigNumber</i></code></h5>
    <p>
      Returns a BigNumber whose value is the square root of the value of this BigNumber,
      rounded according to the current
      <a href='#decimal-places'><code>DECIMAL_PLACES</code></a> and
      <a href='#rounding-mode'><code>ROUNDING_MODE</code></a> configuration.
    </p>
    <p>
      The return value will be correctly rounded, i.e. rounded as if the result was first calculated
      to an infinite number of correct digits before rounding.
    </p>
    <pre>
x = new BigNumber(16)
x.squareRoot()                  // '4'
y = new BigNumber(3)
y.sqrt()                        // '1.73205080756887729353'</pre>



    <h5 id="times">times<code class='inset'>.times(n [, base]) <i>&rArr; BigNumber</i></code></h5>
    <p>
      <code>n</code>: <i>number|string|BigNumber</i><br />
      <code>base</code>: <i>number</i><br />
      <i>See <a href="#bignumber">BigNumber</a> for further parameter details.</i>
    </p>
    <p>Returns a BigNumber whose value is the value of this BigNumber times <code>n</code>.</p>
    <p>The return value is always exact and unrounded.</p>
    <pre>
0.6 * 3                         // 1.7999999999999998
x = new BigNumber(0.6)
y = x.times(3)                  // '1.8'
BigNumber('7e+500').times(y)    // '1.26e+501'
x.times('-a', 16)               // '-6'</pre>



    <h5 id="toD">
      toDigits<code class='inset'>.toDigits([sd [, rm]]) <i>&rArr; BigNumber</i></code>
    </h5>
    <p>
      <code>sd</code>: <i>number</i>: integer, <code>1</code> to <code>1e+9</code> inclusive.<br />
      <code>rm</code>: <i>number</i>: integer, <code>0</code> to <code>8</code> inclusive.
    </p>
    <p>
      Returns a BigNumber whose value is the value of this BigNumber rounded to <code>sd</code>
      significant digits using rounding mode <code>rm</code>.
    </p>
    <p>
      If <code>sd</code> is omitted or is <code>null</code> or <code>undefined</code>, the return
      value will not be rounded.<br />
      If <code>rm</code> is omitted or is <code>null</code> or <code>undefined</code>,
      <a href='#rounding-mode'><code>ROUNDING_MODE</code></a> will be used.
    </p>
    <p>
      See <a href='#Errors'>Errors</a> for the treatment of other non-integer or out of range
      <code>sd</code> or <code>rm</code> values.
    </p>
    <pre>
BigNumber.config({ precision: 5, rounding: 4 })
x = new BigNumber(9876.54321)

x.toDigits()                          // '9876.5'
x.toDigits(6)                         // '9876.54'
x.toDigits(6, BigNumber.ROUND_UP)     // '9876.55'
x.toDigits(2)                         // '9900'
x.toDigits(2, 1)                      // '9800'
x                                     // '9876.54321'</pre>



    <h5 id="toE">
      toExponential<code class='inset'>.toExponential([dp [, rm]]) <i>&rArr; string</i></code>
    </h5>
    <p>
      <code>dp</code>: <i>number</i>: integer, <code>0</code> to <code>1e+9</code> inclusive<br />
      <code>rm</code>: <i>number</i>: integer, <code>0</code> to <code>8</code> inclusive
    </p>
    <p>
      Returns a string representing the value of this BigNumber in exponential notation rounded
      using rounding mode <code>rm</code> to <code>dp</code> decimal places, i.e with one digit
      before the decimal point and <code>dp</code> digits after it.
    </p>
    <p>
      If the value of this BigNumber in exponential notation has fewer than <code>dp</code> fraction
      digits, the return value will be appended with zeros accordingly.
    </p>
    <p>
      If <code>dp</code> is omitted, or is <code>null</code> or <code>undefined</code>, the number
      of digits after the decimal point defaults to the minimum number of digits necessary to
      represent the value exactly.<br />
      If <code>rm</code> is omitted or is <code>null</code> or <code>undefined</code>,
      <a href='#rounding-mode'><code>ROUNDING_MODE</code></a> is used.
    </p>
    <p>
      See <a href='#Errors'>Errors</a> for the treatment of other non-integer or out of range
      <code>dp</code> or <code>rm</code> values.
    </p>
     <pre>
x = 45.6
y = new BigNumber(x)
x.toExponential()               // '4.56e+1'
y.toExponential()               // '4.56e+1'
x.toExponential(0)              // '5e+1'
y.toExponential(0)              // '5e+1'
x.toExponential(1)              // '4.6e+1'
y.toExponential(1)              // '4.6e+1'
y.toExponential(1, 1)           // '4.5e+1'  (ROUND_DOWN)
x.toExponential(3)              // '4.560e+1'
y.toExponential(3)              // '4.560e+1'</pre>



    <h5 id="toFix">
      toFixed<code class='inset'>.toFixed([dp [, rm]]) <i>&rArr; string</i></code>
    </h5>
    <p>
      <code>dp</code>: <i>number</i>: integer, <code>0</code> to <code>1e+9</code> inclusive<br />
      <code>rm</code>: <i>number</i>: integer, <code>0</code> to <code>8</code> inclusive
    </p>
    <p>
      Returns a string representing the value of this BigNumber in normal (fixed-point) notation
      rounded to <code>dp</code> decimal places using rounding mode <code>rm</code>.
    </p>
    <p>
      If the value of this BigNumber in normal notation has fewer than <code>dp</code> fraction
      digits, the return value will be appended with zeros accordingly.
    </p>
   <p>
      Unlike <code>Number.prototype.toFixed</code>, which returns exponential notation if a number
      is greater or equal to <code>10<sup>21</sup></code>, this method will always return normal
      notation.
    </p>
    <p>
      If <code>dp</code> is omitted or is <code>null</code> or <code>undefined</code>, the return
      value will be unrounded and in normal notation. This is also unlike
      <code>Number.prototype.toFixed</code>, which returns the value to zero decimal places.<br />
      It is useful when fixed-point notation is required and the current
      <a href="#exponential-at"><code>EXPONENTIAL_AT</code></a> setting causes
      <code><a href='#toS'>toString</a></code> to return exponential notation.<br />
      If <code>rm</code> is omitted or is <code>null</code> or <code>undefined</code>,
      <a href='#rounding-mode'><code>ROUNDING_MODE</code></a> is used.
    </p>
    <p>
      See <a href='#Errors'>Errors</a> for the treatment of other non-integer or out of range
      <code>dp</code> or <code>rm</code> values.
    </p>
    <pre>
x = 3.456
y = new BigNumber(x)
x.toFixed()                     // '3'
y.toFixed()                     // '3.456'
y.toFixed(0)                    // '3'
x.toFixed(2)                    // '3.46'
y.toFixed(2)                    // '3.46'
y.toFixed(2, 1)                 // '3.45'  (ROUND_DOWN)
x.toFixed(5)                    // '3.45600'
y.toFixed(5)                    // '3.45600'</pre>



    <h5 id="toFor">
      toFormat<code class='inset'>.toFormat([dp [, rm]]) <i>&rArr; string</i></code>
    </h5>
    <p>
      <code>dp</code>: <i>number</i>: integer, <code>0</code> to <code>1e+9</code> inclusive<br />
      <code>rm</code>: <i>number</i>: integer, <code>0</code> to <code>8</code> inclusive
    </p>
    <p>
      <p>
      Returns a string representing the value of this BigNumber in normal (fixed-point) notation
      rounded to <code>dp</code> decimal places using rounding mode <code>rm</code>, and formatted
      according to the properties of the <a href='#format'><code>FORMAT</code></a> object.
    </p>
    <p>
      See the examples below for the properties of the
      <a href='#format'><code>FORMAT</code></a> object, their types and their usage.
    </p>
    <p>
      If <code>dp</code> is omitted or is <code>null</code> or <code>undefined</code>, then the
      return value is not rounded to a fixed number of decimal places.<br />
      If <code>rm</code> is omitted or is <code>null</code> or <code>undefined</code>,
      <a href='#rounding-mode'><code>ROUNDING_MODE</code></a> is used.
    </p>
    <p>
      See <a href='#Errors'>Errors</a> for the treatment of other non-integer or out of range
      <code>dp</code> or <code>rm</code> values.
    </p>
    <pre>
format = {
    decimalSeparator: '.',
    groupSeparator: ',',
    groupSize: 3,
    secondaryGroupSize: 0,
    fractionGroupSeparator: ' ',
    fractionGroupSize: 0
}
BigNumber.config({ FORMAT: format })

x = new BigNumber('123456789.123456789')
x.toFormat()                    // '123,456,789.123456789'
x.toFormat(1)                   // '123,456,789.1'

// If a reference to the object assigned to FORMAT has been retained,
// the format properties can be changed directly
format.groupSeparator = ' '
format.fractionGroupSize = 5
x.toFormat()                    // '123 456 789.12345 6789'

BigNumber.config({
    FORMAT: {
        decimalSeparator: ',',
        groupSeparator: '.',
        groupSize: 3,
        secondaryGroupSize: 2
    }
})

x.toFormat(6)                   // '12.34.56.789,123'</pre>



    <h5 id="toFr">
      toFraction<code class='inset'>.toFraction([max]) <i>&rArr; [string, string]</i></code>
    </h5>
    <p>
      <code>max</code>: <i>number|string|BigNumber</i>: integer &gt;= <code>1</code> and &lt;
      <code>Infinity</code>
    </p>
    <p>
      Returns a string array representing the value of this BigNumber as a simple fraction with an
      integer numerator and an integer denominator. The denominator will be a positive non-zero
      value less than or equal to <code>max</code>.
    </p>
    <p>
      If a maximum denominator, <code>max</code>, is not specified, or is <code>null</code> or
      <code>undefined</code>, the denominator will be the lowest value necessary to represent the
      number exactly.
    </p>
    <p>
      See <a href='#Errors'>Errors</a> for the treatment of other non-integer or out of range
      <code>max</code> values.
    </p>
    <pre>
x = new BigNumber(1.75)
x.toFraction()                  // '7, 4'

pi = new BigNumber('3.14159265358')
pi.toFraction()                 // '157079632679,50000000000'
pi.toFraction(100000)           // '312689, 99532'
pi.toFraction(10000)            // '355, 113'
pi.toFraction(100)              // '311, 99'
pi.toFraction(10)               // '22, 7'
pi.toFraction(1)                // '3, 1'</pre>



    <h5 id="toJSON">toJSON<code class='inset'>.toJSON() <i>&rArr; string</i></code></h5>
    <p>As <code>valueOf</code>.</p>
    <pre>
x = new BigNumber('177.7e+457')
y = new BigNumber(235.4325)
z = new BigNumber('0.0098074')

// Serialize an array of three BigNumbers
str = JSON.stringify( [x, y, z] )
// "["1.777e+459","235.4325","0.0098074"]"

// Return an array of three BigNumbers
JSON.parse(str, function (key, val) {
    return key === '' ? val : new BigNumber(val)
})</pre>



    <h5 id="toN">toNumber<code class='inset'>.toNumber() <i>&rArr; number</i></code></h5>
    <p>Returns the value of this BigNumber as a JavaScript number primitive.</p>
    <p>
      Type coercion with, for example, the unary plus operator will also work, except that a
      BigNumber with the value minus zero will be converted to positive zero.
    </p>
    <pre>
x = new BigNumber(456.789)
x.toNumber()                    // 456.789
+x                              // 456.789

y = new BigNumber('45987349857634085409857349856430985')
y.toNumber()                    // 4.598734985763409e+34

z = new BigNumber(-0)
1 / +z                          // Infinity
1 / z.toNumber()                // -Infinity</pre>



    <h5 id="pow">toPower<code class='inset'>.pow(n [, m]) <i>&rArr; BigNumber</i></code></h5>
    <p>
      <code>n</code>: <i>number</i>: integer,
      <code>-9007199254740991</code> to <code>9007199254740991</code> inclusive<br />
      <code>m</code>: <i>number|string|BigNumber</i>
    </p>
    <p>
      Returns a BigNumber whose value is the value of this BigNumber raised to the power
      <code>n</code>, and optionally modulo a modulus <code>m</code>.
    </p>
    <p>
      If <code>n</code> is negative the result is rounded according to the current
      <a href='#decimal-places'><code>DECIMAL_PLACES</code></a> and
      <a href='#rounding-mode'><code>ROUNDING_MODE</code></a> configuration.
    </p>
    <p>
      If <code>n</code> is not an integer or is out of range:
    </p>
    <p class='inset'>
      If <code>ERRORS</code> is <code>true</code> a BigNumber Error is thrown,<br />
      else if <code>n</code> is greater than <code>9007199254740991</code>, it is interpreted as
      <code>Infinity</code>;<br />
      else if <code>n</code> is less than <code>-9007199254740991</code>, it is interpreted as
      <code>-Infinity</code>;<br />
      else if <code>n</code> is otherwise a number, it is truncated to an integer;<br />
      else it is interpreted as <code>NaN</code>.
    </p>
    <p>
      As the number of digits of the result of the power operation can grow so large so quickly,
      e.g. 123.456<sup>10000</sup> has over <code>50000</code> digits, the number of significant
      digits calculated is limited to the value of the
      <a href='#pow-precision'><code>POW_PRECISION</code></a> setting (unless a modulus
      <code>m</code> is specified).
    </p>
    <p>
      By default <a href='#pow-precision'><code>POW_PRECISION</code></a> is set to <code>0</code>.
      This means that an unlimited number of significant digits will be calculated, and that the
      method's performance will decrease dramatically for larger exponents.
    </p>
    <p>
      Negative exponents will be calculated to the number of decimal places specified by
      <a href='#decimal-places'><code>DECIMAL_PLACES</code></a> (but not to more than
      <a href='#pow-precision'><code>POW_PRECISION</code></a> significant digits).
    </p>
    <p>
      If <code>m</code> is specified and the value of <code>m</code>, <code>n</code> and this
      BigNumber are positive integers, then a fast modular exponentiation algorithm is used,
      otherwise if any of the values is not a positive integer the operation will simply be
      performed as <code>x.toPower(n).modulo(m)</code> with a
      <a href='#pow-precision'><code>POW_PRECISION</code></a> of <code>0</code>.
    </p>
    <pre>
Math.pow(0.7, 2)                // 0.48999999999999994
x = new BigNumber(0.7)
x.toPower(2)                    // '0.49'
BigNumber(3).pow(-2)            // '0.11111111111111111111'</pre>



    <h5 id="toP">
      toPrecision<code class='inset'>.toPrecision([sd [, rm]]) <i>&rArr; string</i></code>
    </h5>
    <p>
      <code>sd</code>: <i>number</i>: integer, <code>1</code> to <code>1e+9</code> inclusive<br />
      <code>rm</code>: <i>number</i>: integer, <code>0</code> to <code>8</code> inclusive
    </p>
    <p>
      Returns a string representing the value of this BigNumber rounded to <code>sd</code>
      significant digits using rounding mode <code>rm</code>.
    </p>
    <p>
      If <code>sd</code> is less than the number of digits necessary to represent the integer part
      of the value in normal (fixed-point) notation, then exponential notation is used.
    </p>
    <p>
      If <code>sd</code> is omitted, or is <code>null</code> or <code>undefined</code>, then the
      return value is the same as <code>n.toString()</code>.<br />
      If <code>rm</code> is omitted or is <code>null</code> or <code>undefined</code>,
      <a href='#rounding-mode'><code>ROUNDING_MODE</code></a> is used.
    </p>
    <p>
      See <a href='#Errors'>Errors</a> for the treatment of other non-integer or out of range
      <code>sd</code> or <code>rm</code> values.
    </p>
     <pre>
x = 45.6
y = new BigNumber(x)
x.toPrecision()                 // '45.6'
y.toPrecision()                 // '45.6'
x.toPrecision(1)                // '5e+1'
y.toPrecision(1)                // '5e+1'
y.toPrecision(2, 0)             // '4.6e+1'  (ROUND_UP)
y.toPrecision(2, 1)             // '4.5e+1'  (ROUND_DOWN)
x.toPrecision(5)                // '45.600'
y.toPrecision(5)                // '45.600'</pre>



    <h5 id="toS">toString<code class='inset'>.toString([base]) <i>&rArr; string</i></code></h5>
    <p><code>base</code>: <i>number</i>: integer, <code>2</code> to <code>64</code> inclusive</p>
    <p>
      Returns a string representing the value of this BigNumber in the specified base, or base
      <code>10</code> if <code>base</code> is omitted or is <code>null</code> or
      <code>undefined</code>.
    </p>
    <p>
      For bases above <code>10</code>, values from <code>10</code> to <code>35</code> are
      represented by <code>a-z</code> (as with <code>Number.prototype.toString</code>),
      <code>36</code> to <code>61</code> by <code>A-Z</code>, and <code>62</code> and
      <code>63</code> by <code>$</code> and <code>_</code> respectively.
    </p>
    <p>
      If a base is specified the value is rounded according to the current
      <a href='#decimal-places'><code>DECIMAL_PLACES</code></a>
      and <a href='#rounding-mode'><code>ROUNDING_MODE</code></a> configuration.
    </p>
    <p>
      If a base is not specified, and this BigNumber has a positive
      exponent that is equal to or greater than the positive component of the
      current <a href="#exponential-at"><code>EXPONENTIAL_AT</code></a> setting,
      or a negative exponent equal to or less than the negative component of the
      setting, then exponential notation is returned.
    </p>
    <p>If <code>base</code> is <code>null</code> or <code>undefined</code> it is ignored.</p>
    <p>
      See <a href='#Errors'>Errors</a> for the treatment of other non-integer or out of range
      <code>base</code> values.
    </p>
    <pre>
x = new BigNumber(750000)
x.toString()                    // '750000'
BigNumber.config({ EXPONENTIAL_AT: 5 })
x.toString()                    // '7.5e+5'

y = new BigNumber(362.875)
y.toString(2)                   // '101101010.111'
y.toString(9)                   // '442.77777777777777777778'
y.toString(32)                  // 'ba.s'

BigNumber.config({ DECIMAL_PLACES: 4 });
z = new BigNumber('1.23456789')
z.toString()                    // '1.23456789'
z.toString(10)                  // '1.2346'</pre>



    <h5 id="trunc">truncated<code class='inset'>.trunc() <i>&rArr; BigNumber</i></code></h5>
    <p>
      Returns a BigNumber whose value is the value of this BigNumber truncated to a whole number.
    </p>
    <pre>
x = new BigNumber(123.456)
x.truncated()                   // '123'
y = new BigNumber(-12.3)
y.trunc()                       // '-12'</pre>



    <h5 id="valueOf">valueOf<code class='inset'>.valueOf() <i>&rArr; string</i></code></h5>
    <p>
      As <code>toString</code>, but does not accept a base argument and includes the minus sign
      for negative zero.
    </p>
    <pre>
x = new BigNumber('-0')
x.toString()                    // '0'
x.valueOf()                     // '-0'
y = new BigNumber('1.777e+457')
y.valueOf()                     // '1.777e+457'</pre>



    <h4 id="instance-properties">Properties</h4>
    <p>The properties of a BigNumber instance:</p>
    <table>
      <tr>
        <th>Property</th>
        <th>Description</th>
        <th>Type</th>
        <th>Value</th>
      </tr>
      <tr>
        <td class='centre' id='coefficient'><b>c</b></td>
        <td>coefficient<sup>*</sup></td>
        <td><i>number</i><code>[]</code></td>
        <td> Array of base <code>1e14</code> numbers</td>
      </tr>
      <tr>
        <td class='centre' id='exponent'><b>e</b></td>
        <td>exponent</td>
        <td><i>number</i></td>
        <td>Integer, <code>-1000000000</code> to <code>1000000000</code> inclusive</td>
      </tr>
      <tr>
        <td class='centre' id='sign'><b>s</b></td>
        <td>sign</td>
        <td><i>number</i></td>
        <td><code>-1</code> or <code>1</code></td>
      </tr>
      <tr>
        <td class='centre' id='isbig'><b>isBigNumber</b></td>
        <td>type identifier</td>
        <td><i>boolean</i></td>
        <td><code>true</code></td>
      </tr>
    </table>
    <p><sup>*</sup>significand</p>
    <p>
      The value of any of the <code>c</code>, <code>e</code> and <code>s</code> properties may also
      be <code>null</code>.
    </p>
    <p>
      From v2.0.0 of this library, the value of the coefficient of a BigNumber is stored in a
      normalised base <code>100000000000000</code> floating point format, as opposed to the base
      <code>10</code> format used in v1.x.x
    </p>
    <p>
      This change means the properties of a BigNumber are now best considered to be read-only.
      Previously it was acceptable to change the exponent of a BigNumber by writing to its exponent
      property directly, but this is no longer recommended as the number of digits in the first
      element of the coefficient array is dependent on the exponent, so the coefficient would also
      need to be altered.
    </p>
    <p>
      Note that, as with JavaScript numbers, the original exponent and fractional trailing zeros are
      not necessarily preserved.
    </p>
    <pre>x = new BigNumber(0.123)              // '0.123'
x.toExponential()                     // '1.23e-1'
x.c                                   // '1,2,3'
x.e                                   // -1
x.s                                   // 1

y = new Number(-123.4567000e+2)       // '-12345.67'
y.toExponential()                     // '-1.234567e+4'
z = new BigNumber('-123.4567000e+2')  // '-12345.67'
z.toExponential()                     // '-1.234567e+4'
z.c                                   // '1,2,3,4,5,6,7'
z.e                                   // 4
z.s                                   // -1</pre>
    <p>Checking if a value is a BigNumber instance:</p>
    <pre>
x = new BigNumber(3)
x instanceof BigNumber     // true
x.isBigNumber              // true

BN = BigNumber.another();

y = new BN(3)
y instanceof BigNumber     // false
y.isBigNumber              // true</pre>
    



    <h4 id="zero-nan-infinity">Zero, NaN and Infinity</h4>
    <p>
      The table below shows how &plusmn;<code>0</code>, <code>NaN</code> and
      &plusmn;<code>Infinity</code> are stored.
    </p>
    <table>
      <tr>
        <th> </th>
        <th class='centre'>c</th>
        <th class='centre'>e</th>
        <th class='centre'>s</th>
      </tr>
      <tr>
        <td>&plusmn;0</td>
        <td><code>[0]</code></td>
        <td><code>0</code></td>
        <td><code>&plusmn;1</code></td>
      </tr>
      <tr>
        <td>NaN</td>
        <td><code>null</code></td>
        <td><code>null</code></td>
        <td><code>null</code></td>
      </tr>
      <tr>
        <td>&plusmn;Infinity</td>
        <td><code>null</code></td>
        <td><code>null</code></td>
        <td><code>&plusmn;1</code></td>
      </tr>
    </table>
    <pre>
x = new Number(-0)              // 0
1 / x == -Infinity              // true

y = new BigNumber(-0)           // '0'
y.c                             // '0' ( [0].toString() )
y.e                             // 0
y.s                             // -1</pre>



    <h4 id='Errors'>Errors</h4>
    <p>
      The errors that are thrown are generic <code>Error</code> objects with <code>name</code>
      <i>BigNumber Error</i>.
    </p>
    <p>
      The table below shows the errors that may be thrown if <code>ERRORS</code> is
      <code>true</code>, and the action taken if <code>ERRORS</code> is <code>false</code>.
    </p>
    <table class='error-table'>
      <tr>
        <th>Method(s)</th>
        <th>ERRORS: true<br />Throw BigNumber Error</th>
        <th>ERRORS: false<br />Action on invalid argument</th>
      </tr>
      <tr>
        <td rowspan=5>
          <code>
            BigNumber<br />
            comparedTo<br />
            dividedBy<br />
            dividedToIntegerBy<br />
            equals<br />
            greaterThan<br />
            greaterThanOrEqualTo<br />
            lessThan<br />
            lessThanOrEqualTo<br />
            minus<br />
            modulo<br />
            plus<br />
            times
          </code></td>
        <td>number type has more than<br />15 significant digits</td>
        <td>Accept.</td>
      </tr>
      <tr>
        <td>not a base... number</td>
        <td>Substitute <code>NaN</code>.</td>
      </tr>
      <tr>
        <td>base not an integer</td>
        <td>Truncate to integer.<br />Ignore if not a number.</td>
      </tr>
      <tr>
        <td>base out of range</td>
        <td>Ignore.</td>
      </tr>
      <tr>
        <td>not a number<sup>*</sup></td>
        <td>Substitute <code>NaN</code>.</td>
      </tr>
      <tr>
        <td><code>another</code></td>
        <td>not an object</td>
        <td>Ignore.</td>
      </tr>
      <tr>
        <td rowspan=17><code>config</code></td>
        <td><code>DECIMAL_PLACES</code> not an integer</td>
        <td>Truncate to integer.<br />Ignore if not a number.</td>
      </tr>
      <tr>
        <td><code>DECIMAL_PLACES</code> out of range</td>
        <td>Ignore.</td>
      </tr>
      <tr>
        <td><code>ROUNDING_MODE</code> not an integer</td>
        <td>Truncate to integer.<br />Ignore if not a number.</td>
      </tr>
      <tr>
        <td><code>ROUNDING_MODE</code> out of range</td>
        <td>Ignore.</td>
      </tr>
      <tr>
        <td><code>EXPONENTIAL_AT</code> not an integer<br />or not [integer, integer]</td>
        <td>Truncate to integer(s).<br />Ignore if not number(s).</td>
      </tr>
      <tr>
        <td><code>EXPONENTIAL_AT</code> out of range<br />or not [negative, positive]</td>
        <td>Ignore.</td>
      </tr>
      <tr>
        <td><code>RANGE</code> not an integer<br />or not [integer, integer]</td>
        <td> Truncate to integer(s).<br />Ignore if not number(s).</td>
      </tr>
      <tr>
        <td><code>RANGE</code> cannot be zero</td>
        <td>Ignore.</td>
      </tr>
      <tr>
        <td><code>RANGE</code> out of range<br />or not [negative, positive]</td>
        <td>Ignore.</td>
      </tr>
      <tr>
        <td><code>ERRORS</code> not a boolean<br />or binary digit</td>
        <td>Ignore.</td>
      </tr>
      <tr>
        <td><code>CRYPTO</code> not a boolean<br />or binary digit</td>
        <td>Ignore.</td>
      </tr>
      <tr>
        <td><code>CRYPTO</code> crypto unavailable</td>
        <td>Ignore.</td>
      </tr>
      <tr>
        <td><code>MODULO_MODE</code> not an integer</td>
        <td>Truncate to integer.<br />Ignore if not a number.</td>
      </tr>
      <tr>
        <td><code>MODULO_MODE</code> out of range</td>
        <td>Ignore.</td>
      </tr>
      <tr>
        <td><code>POW_PRECISION</code> not an integer</td>
        <td>Truncate to integer.<br />Ignore if not a number.</td>
      </tr>
      <tr>
        <td><code>POW_PRECISION</code> out of range</td>
        <td>Ignore.</td>
      </tr>
      <tr>
        <td><code>FORMAT</code> not an object</td>
        <td>Ignore.</td>
      </tr>
      <tr>
        <td><code>precision</code></td>
        <td>argument not a boolean<br />or binary digit</td>
        <td>Ignore.</td>
      </tr>
      <tr>
        <td rowspan=4><code>round</code></td>
        <td>decimal places not an integer</td>
        <td>Truncate to integer.<br />Ignore if not a number.</td>
      </tr>
      <tr>
        <td>decimal places out of range</td>
        <td>Ignore.</td>
      </tr>
      <tr>
        <td>rounding mode not an integer</td>
        <td>Truncate to integer.<br />Ignore if not a number.</td>
      </tr>
      <tr>
        <td>rounding mode out of range</td>
        <td>Ignore.</td>
      </tr>
      <tr>
        <td rowspan=2><code>shift</code></td>
        <td>argument not an integer</td>
        <td>Truncate to integer.<br />Ignore if not a number.</td>
      </tr>
      <tr>
        <td>argument out of range</td>
        <td>Substitute &plusmn;<code>Infinity</code>.
      </tr>
      <tr>
        <td rowspan=4>
          <code>toExponential</code><br />
          <code>toFixed</code><br />
          <code>toFormat</code>
        </td>
        <td>decimal places not an integer</td>
        <td>Truncate to integer.<br />Ignore if not a number.</td>
      </tr>
      <tr>
        <td>decimal places out of range</td>
        <td>Ignore.</td>
      </tr>
      <tr>
        <td>rounding mode not an integer</td>
        <td>Truncate to integer.<br />Ignore if not a number.</td>
      </tr>
      <tr>
        <td>rounding mode out of range</td>
        <td>Ignore.</td>
      </tr>
      <tr>
        <td rowspan=2><code>toFraction</code></td>
        <td>max denominator not an integer</td>
        <td>Truncate to integer.<br />Ignore if not a number.</td>
      </tr>
      <tr>
        <td>max denominator out of range</td>
        <td>Ignore.</td>
      </tr>
      <tr>
        <td rowspan=4>
          <code>toDigits</code><br />
          <code>toPrecision</code>
        </td>
        <td>precision not an integer</td>
        <td>Truncate to integer.<br />Ignore if not a number.</td>
      </tr>
      <tr>
        <td>precision out of range</td>
        <td>Ignore.</td>
      </tr>
      <tr>
        <td>rounding mode not an integer</td>
        <td>Truncate to integer.<br />Ignore if not a number.</td>
      </tr>
      <tr>
        <td>rounding mode out of range</td>
        <td>Ignore.</td>
      </tr>
      <tr>
        <td rowspan=2><code>toPower</code></td>
        <td>exponent not an integer</td>
        <td>Truncate to integer.<br />Substitute <code>NaN</code> if not a number.</td>
      </tr>
       <tr>
        <td>exponent out of range</td>
        <td>Substitute &plusmn;<code>Infinity</code>.
        </td>
      </tr>
      <tr>
        <td rowspan=2><code>toString</code></td>
        <td>base not an integer</td>
        <td>Truncate to integer.<br />Ignore if not a number.</td>
      </tr>
      <tr>
        <td>base out of range</td>
        <td>Ignore.</td>
      </tr>
    </table>
    <p><sup>*</sup>No error is thrown if the value is <code>NaN</code> or 'NaN'.</p>
    <p>
      The message of a <i>BigNumber Error</i> will also contain the name of the method from which
      the error originated.
    </p>
    <p>To determine if an exception is a <i>BigNumber Error</i>:</p>
    <pre>
try {
    // ...
} catch (e) {
    if ( e instanceof Error && e.name == 'BigNumber Error' ) {
        // ...
    }
}</pre>



    <h4 id='faq'>FAQ</h4>

    <h6>Why are trailing fractional zeros removed from BigNumbers?</h6>
    <p>
      Some arbitrary-precision libraries retain trailing fractional zeros as they can indicate the
      precision of a value. This can be useful but the results of arithmetic operations can be
      misleading.
    </p>
    <pre>
x = new BigDecimal("1.0")
y = new BigDecimal("1.1000")
z = x.add(y)                      // 2.1000

x = new BigDecimal("1.20")
y = new BigDecimal("3.45000")
z = x.multiply(y)                 // 4.1400000</pre>
    <p>
      To specify the precision of a value is to specify that the value lies
      within a certain range.
    </p>
    <p>
      In the first example, <code>x</code> has a value of <code>1.0</code>. The trailing zero shows
      the precision of the value, implying that it is in the range <code>0.95</code> to
      <code>1.05</code>. Similarly, the precision indicated by the trailing zeros of <code>y</code>
      indicates that the value is in the range <code>1.09995</code> to <code>1.10005</code>.
    </p>
    <p>
      If we  add the two lowest values in the ranges we have, <code>0.95 + 1.09995 = 2.04995</code>,
      and if we add the two highest values we have, <code>1.05 + 1.10005 = 2.15005</code>, so the
      range of the result of the addition implied by the precision of its operands is
      <code>2.04995</code> to <code>2.15005</code>.
    </p>
    <p>
      The result given by BigDecimal of <code>2.1000</code> however, indicates that the value is in
      the range <code>2.09995</code> to <code>2.10005</code> and therefore the precision implied by
      its trailing zeros may be misleading.
    </p>
    <p>
      In the second example, the true range is <code>4.122744</code> to <code>4.157256</code> yet
      the BigDecimal answer of <code>4.1400000</code> indicates a range of <code>4.13999995</code>
      to  <code>4.14000005</code>. Again, the precision implied by the trailing zeros may be
      misleading.
    </p>
    <p>
      This library, like binary floating point and most calculators, does not retain trailing
      fractional zeros. Instead, the <code>toExponential</code>, <code>toFixed</code> and
      <code>toPrecision</code> methods enable trailing zeros to be added if and when required.<br />
    </p>
  </div>

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