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  <div class="nav">

    <a class='nav-title' href="#">big.js</a>

    <b> CONSTRUCTOR </b>
    <ul>
      <li><a href="#big">Big</a></li>
    </ul>

    <a href="#constructor-properties">Properties</a>
    <ul>
      <li><a href="#dp"  >DP</a></li>
      <li><a href="#rm"  >RM</a></li>
      <li><a href="#eneg">E_NEG</a></li>
      <li><a href="#epos">E_POS</a></li>
    </ul>

    <b> INSTANCE </b>

    <a href="#prototype-methods">Methods</a>
    <ul>
      <li><a href="#abs"    >abs</a></li>
      <li><a href="#cmp"    >cmp</a></li>
      <li><a href="#div"    >div</a></li>
      <li><a href="#eq"     >eq</a></li>
      <li><a href="#gt"     >gt</a></li>
      <li><a href="#gte"    >gte</a></li>
      <li><a href="#lt"     >lt</a></li>
      <li><a href="#lte"    >lte</a></li>
      <li><a href="#minus"  >minus</a></li>
      <li><a href="#mod"    >mod</a></li>
      <li><a href="#plus"   >plus</a></li>
      <li><a href="#pow"    >pow</a></li>
      <li><a href="#round"  >round</a></li>
      <li><a href="#sqrt"   >sqrt</a></li>
      <li><a href="#times"  >times</a></li>
      <li><a href="#toE"    >toExponential</a></li>
      <li><a href="#toF"    >toFixed</a></li>
      <li><a href="#toP"    >toPrecision</a></li>
      <li><a href="#toS"    >toString</a></li>
      <li><a href="#valueOf">valueOf</a></li>
      <li><a href="#toJSON" >toJSON</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>
    </ul>

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

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

  </div>

  <div class="container">

    <h1>big.js</h1>

    <p>
      A small, fast, easy-to-use library for arbitrary-precision decimal
      arithmetic.
    </p>

    <p><a href="https://github.com/MikeMcl/big.js/">Hosted on GitHub</a>.</p>
     <p>
      <i>
        The library is incorporated into this page, so it should be available in
        the console now.
      </i>
    </p>


    <h2>API</h2>

    <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="big">
      Big<code class='inset'>Big( value ) &rArr; <i>Big</i></code>
    </h5>
    <dl>
      <dt><code>value</code></dt>
      <dd>
        <i>number|string|Big</i>
      </dd>
      <dd>
        A decimal value.
      </dd>
      <dd>
        String values may be in exponential, as well as normal (non-exponential)
        notation.
      </dd>
      <dd>
        There is no limit to the number of digits of a <em>string</em> value
        (other than that of Javascript's maximum array size), but the largest
        recommended exponent magnitude is 1e+6.
      </dd>
      <dd>
        <code>Infinity</code>, <code>NaN</code> and hexadecimal literal
        strings, e.g. '0xff', are <u>not</u> valid.<br>
        String values in octal literal form will be interpreted as decimals,
        e.g. '011' is 11, not 9.
      </dd>
    </dl>
    <p>Returns a new instance of a Big number object.</p>
    <p>
      Throws <code class='error'>NaN</code> on an invalid <code>value</code>.
    </p>
    <pre>
x = new Big(9)                       // '9'
y = new Big(x)                       // '9'
Big(435.345)                         // 'new' is optional
new Big('5032485723458348569331745.33434346346912144534543')
new Big('4.321e+4')                  // '43210'
new Big('-735.0918e-430')            // '-7.350918e-428'</pre>



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

    <h5 id="dp">DP</h5>
    <p>
      <i>number</i> : integer, 0 to 1e+6 inclusive<br />
      Default value: <code>20</code>
    </p>
    <p>
      The <u>maximum</u> number of decimal places of the results of operations
      involving division.<br />
      It is relevant only to the <code>div</code> and <code>sqrt</code> methods,
      and the <code>pow</code> method when the exponent is negative.
    </p>
    <p>
      The value will be checked for validity when one of the above methods is
      called.<br /> <code class='error'>!Big.DP!</code> will be thrown if the
      value is found to be invalid.
    </p>
    <pre>Big.DP = 40</pre>



    <h5 id="rm">RM</h5>
    <p>
      <i>number</i> : 0, 1, 2 or 3<br />
      Default value: <code>1</code>
    </p>
    <p>
      The rounding mode used in the above operations and by
      <a href='#round'><code>round</code></a>,
      <a href='#toE'><code>toExponential</code></a>,
      <a href='#toF'><code>toFixed</code></a> and
      <a href='#toP'><code>toPrecision</code></a>.
    </p>
    <table>
      <tr>
        <th>Value</th>
        <th>Description</th>
        <th>BigDecimal equivalent</th>
      </tr>
      <tr>
        <td class='centre'>0</td>
        <td>
          Rounds towards zero.<br />
          I.e. truncate, no rounding.
        </td>
        <td id="round-down">ROUND_DOWN</td>
      </tr>
      <tr>
        <td class='centre'>1</td>
        <td>
          Rounds towards nearest neighbour.<br />
          If equidistant, rounds away from zero.
        </td>
        <td id="round-half-up">ROUND_HALF_UP</td>
      </tr>
      <tr>
        <td class='centre'>2</td>
        <td>
          Rounds towards nearest neighbour.<br />
          If equidistant, rounds towards even neighbour.
        </td>
        <td id="round-half-even">ROUND_HALF_EVEN</td>
      </tr>
      <tr>
        <td class='centre'>3</td>
        <td>Rounds away from zero.</td>
        <td id="round-up">ROUND_UP</td>
      </tr>
    </table>
    <p>
      The value will be checked for validity when one of the above methods is
      called.<br /> <code class='error'>!Big.RM!</code> will be thrown if the
      value is found to be invalid.
    </p>
    <pre>Big.RM = 0</pre>



    <h5 id="eneg">E_NEG</h5>
    <p>
      <i>number</i> : integer, -1e+6 to 0 inclusive<br />
      Default value: <code>-7</code>
    </p>
    <p>
      The negative exponent value at and below which
      <a href='#toS'><code>toString</code></a> returns exponential notation.
    </p>
    <pre>
Big.E_NEG = -7
x = new Big(0.00000123)            // '0.00000123'       e is -6
x = new Big(0.000000123)           // '1.23e-7'</pre>
    <p>
      JavaScript numbers use exponential notation for negative exponents of
      <code>-7</code> and below.
    </p>
    <p>
      Regardless of the value of <code>Big.E_NEG</code>, the
      <a href='#toF'><code>toFixed</code></a> method will always return a value
      in normal notation and the <a href='#toE'><code>toExponential</code></a>
      method will always return a value in exponential form.
    </p>



    <h5 id="epos">E_POS</h5>
    <p>
      <i>number</i> : integer, 0 to 1e+6 inclusive<br />
      Default value: <code>21</code>
    </p>
    <p>
      The positive exponent value at and above which
      <a href='#toS'><code>toString</code></a> returns exponential notation.
    </p>
    <pre>
Big.E_POS = 2
x = new Big(12.3)                  // '12.3'        e is 1
x = new Big(123)                   // '1.23e+2'</pre>
    <p>
      JavaScript numbers use exponential notation for positive exponents of
      <code>21</code> and above.
    </p>
    <p>
      Regardless of the value of <code>Big.E_POS</code>, the
      <a href='#toF'><code>toFixed</code></a> method will always return a value
      in normal notation and the <a href='#toE'><code>toExponential</code></a>
      method will always return a value in exponential form.
    </p>



    <h3>INSTANCE</h3>

    <h4 id="prototype-methods">Methods</h4>
    <p>
      The methods inherited by a Big number instance from its constructor's
      prototype object.
    </p>
    <p>
      A Big number is immutable in the sense that it is not changed by its
      methods.
    </p>



    <h5 id="abs">abs<code class='inset'>.abs() &rArr; <i>Big</i></code></h5>
    <p>
      Returns a Big number whose value is the absolute value, i.e. the
      magnitude, of this Big number.
    </p>
    <pre>
x = new Big(-0.8)
x.abs()                     // '0.8'</pre>



    <h5 id="cmp">
      cmp<code class='inset'>.cmp( n ) &rArr; <i>number</i></code>
    </h5>
    <p><code>n</code> : <i>number|string|Big</i><br /></p>
    <table>
      <tr>
        <th>Returns</th>
        <th colspan=2>&nbsp;</th>
      </tr>
      <tr>
        <td class='centre'>1</td>
        <td>
          If the value of this Big number is greater than the value of
          <code>n</code>
        </td>
      </tr>
      <tr>
        <td class='centre'>-1</td>
        <td>
          If the value of this Big number is less than the value of
          <code>n</code>
        </td>
      </tr>
      <tr>
        <td class='centre'>0</td>
        <td>If this Big number and <code>n</code> have the same value</td>
      </tr>
    </table>
    <p>Throws <code class='error'>NaN</code> if <code>n</code> is invalid.</p>
    <pre>
x = new Big(6)
y = new Big(5)
x.cmp(y)                   // 1
y.cmp(x.minus(1))          // 0</pre>



    <h5 id="div">div<code class='inset'>.div(n) &rArr; <i>Big</i></code></h5>
    <p><code>n</code> : <i>number|string|Big</i><br /></p>
    <p>
      Returns a Big number whose value is the value of this Big number divided
      by <code>n</code>.
    </p>
    <p>
      If the result has more fraction digits than is specified by
      <a href='#dp'><code>Big.DP</code></a>, it will be rounded to
      <a href='#dp'><code>Big.DP</code></a> decimal places using rounding mode
      <a href='#rm'><code>Big.RM</code></a>.
    </p>
    <p>
      Throws <code class='error'>NaN</code> if <code>n</code> is invalid.<br />
      Throws <code class='error'>&plusmn;Infinity</code> on division by zero.<br />
      Throws <code class='error'>NaN</code> on division of zero by zero.
    </p>
    <pre>
x = new Big(355)
y = new Big(113)
x.div(y)                   // '3.14159292035398230088'
Big.DP = 2
x.div(y)                   // '3.14'
x.div(5)                   // '71'</pre>






    <h5 id="eq">eq<code class='inset'>.eq(n) &rArr; <i>boolean</i></code></h5>
    <p><code>n</code> : <i>number|string|Big</i></p>
    <p>
      Returns <code>true</code> if the value of this Big equals the value
      of <code>n</code>, otherwise returns <code>false</code>.
    </p>
    <p>Throws <code class='error'>NaN</code> if <code>n</code> is invalid.</p>
    <pre>
0 === 1e-324               // true
x = new Big(0)
x.eq('1e-324')             // false
Big(-0).eq(x)              // true  ( -0 === 0 )</pre>



    <h5 id="gt">
      gt<code class='inset'>.gt(n) &rArr; <i>boolean</i></code>
    </h5>
    <p><code>n</code> : <i>number|string|Big</i></p>
    <p>
      Returns <code>true</code> if the value of this Big is greater than
      the value of <code>n</code>, otherwise returns <code>false</code>.
    </p>
    <p>Throws <code class='error'>NaN</code> if <code>n</code> is invalid.</p>
    <pre>
0.1 &gt; 0.3 - 0.2              // true
x = new Big(0.1)
x.gt(Big(0.3).minus(0.2))    // false
Big(0).gt(x)                 // false</pre>



    <h5 id="gte">
      gte<code class='inset'>.gte(n) &rArr; <i>boolean</i></code>
    </h5>
    <p><code>n</code> : <i>number|string|Big</i></p>
    <p>
      Returns <code>true</code> if the value of this Big is greater than
      or equal to the value of <code>n</code>, otherwise returns
      <code>false</code>.
    </p>
    <p>Throws <code class='error'>NaN</code> if <code>n</code> is invalid.</p>
    <pre>
0.3 - 0.2 &gt;= 0.1               // false
x = new Big(0.3).minus(0.2)
x.gte(0.1)                     // true
Big(1).gte(x)                  // true</pre>



    <h5 id="lt">
      lt<code class='inset'>.lt(n) &rArr; <i>boolean</i></code>
    </h5>
    <p><code>n</code> : <i>number|string|Big</i></p>
    <p>
      Returns <code>true</code> if the value of this Big is less than the
      value of <code>n</code>, otherwise returns <code>false</code>.
    </p>
    <p>Throws <code class='error'>NaN</code> if <code>n</code> is invalid.</p>
    <pre>
0.3 - 0.2 &lt; 0.1                // true
x = new Big(0.3).minus(0.2)
x.lt(0.1)                      // false
Big(0).lt(x)                   // true</pre>



    <h5 id="lte">
      lte<code class='inset'>.lte(n) &rArr; <i>boolean</i></code>
    </h5>
    <p><code>n</code> : <i>number|string|Big</i></p>
    <p>
      Returns <code>true</code> if the value of this Big is less than or
      equal to the value of <code>n</code>, otherwise returns
      <code>false</code>.
    </p>
    <p>Throws <code class='error'>NaN</code> if <code>n</code> is invalid.</p>
    <pre>
0.1 &lt;= 0.3 - 0.2               // false
x = new Big(0.1)
x.lte(Big(0.3).minus(0.2))     // true
Big(-1).lte(x)                 // true</pre>



    <h5 id="minus">
      minus<code class='inset'>.minus(n) &rArr; <i>Big</i></code>
    </h5>
    <p><code>n</code> : <i>number|string|Big</i></p>
    <p>
      Returns a Big number whose value is the value of this Big number minus
      <code>n</code>.
    </p>
    <p>Throws <code class='error'>NaN</code> if <code>n</code> is invalid.</p>
    <pre>
0.3 - 0.1                  // 0.19999999999999998
x = new Big(0.3)
x.minus(0.1)               // '0.2'</pre>



    <h5 id="mod">mod<code class='inset'>.mod(n) &rArr; <i>Big</i></code></h5>
    <p><code>n</code> : <i>number|string|Big</i></p>
    <p>
      Returns a Big number whose value is the value of this Big number modulo
      <code>n</code>, i.e. the integer remainder of dividing this Big number by
      <code>n</code>.
    </p>
    <p>
      The result will have the same sign as this Big number, and it will match
      that of Javascript's % operator (within the limits of its precision) and
      BigDecimal's remainder method.
    </p>
     <p>
       Throws <code class='error'>NaN</code> if <code>n</code> is negative or
       otherwise invalid.
     </p>
    <pre>
1 % 0.9                    // 0.09999999999999998
x = new Big(1)
x.mod(0.9)                 // '0.1'</pre>



    <h5 id="plus">
      plus<code class='inset'>.plus(n) &rArr; <i>Big</i></code>
    </h5>
    <p><code>n</code> : <i>number|string|Big</i></p>
    <p>
      Returns a Big number whose value is the value of this Big number plus
      <code>n</code>.
    </p>
    <p>Throws <code class='error'>NaN</code> if <code>n</code> is invalid.</p>
    <pre>
0.1 + 0.2                  // 0.30000000000000004
x = new Big(0.1)
y = x.plus(0.2)            // '0.3'
Big(0.7).plus(x).plus(y)   // '1'</pre>



     <h5 id="pow">pow<code class='inset'>.pow( exp ) &rArr; <i>Big</i></code>
    </h5>
    <p>
      <code>exp</code> : <i>number</i> : integer, -1e+6 to 1e+6 inclusive
    </p>
    <p>
      Returns a Big number whose value is the value of this Big number raised to
      the power <code>exp</code>.
    </p>
    <p>
      If <code>exp</code> is negative and the result has more fraction digits
      than is specified by <a href='#dp'><code>Big.DP</code></a>, it will be
      rounded to <a href='#dp'><code>Big.DP</code></a> decimal places using
      rounding mode <a href='#rm'><code>Big.RM</code></a>.
    </p>
    <p>
      Throws <code class='error'>!pow!</code> if <code>exp</code> is invalid.
    </p>
    <p>
      Note: High value exponents may cause this method to be slow to return.
    </p>
    <pre>
Math.pow(0.7, 2)           // 0.48999999999999994
x = new Big(0.7)
x.pow(2)                   // '0.49'
Big.DP = 20
Big(3).pow(-2)             // '0.11111111111111111111'

new Big(123.456).pow(1000).toString().length     // 5099
new Big(2).pow(1e+6)       // Time taken (Node.js): 9 minutes 34 secs.</pre>



    <h5 id="round">
      round<code class='inset'>.round( [dp [, rm]] )
      &rArr; <i>Big</i></code>
    </h5>
    <p>
      <code>dp</code> : <i>number</i> : integer, 0 to 1e+6 inclusive
      <br />
      <code>rm</code> : <i>number</i> : 0, 1, 2 or 3
    </p>
    <p>
      Returns a Big number whose value is the value of this Big number rounded
      using 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 undefined, 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
      undefined, the current <a href='#rm'><code>Big.RM</code></a> setting is
      used.
    </p>
    <p>
      Throws <code class='error'>!round!</code> if <code>dp</code> is invalid.
      <br />
      Throws <code class='error'>!Big.RM!</code> if <code>rm</code> is invalid.
    </p>
    <pre>
x = 123.45
Math.round(x)              // 123
y = new Big(x)
y.round()                  // '123'
y.round(2)                 // '123.45'
y.round(10)                // '123.45'
y.round(1, 0)              // '123.4'
y.round(1, 1)              // '123.5'
y.round(1, 2)              // '123.4'
y.round(1, 3)              // '123.5'
y                          // '123.45'</pre>



    <h5 id="sqrt">sqrt<code class='inset'>.sqrt() &rArr; <i>Big</i></code></h5>
    <p>
      Returns a Big number whose value is the square root of this Big number.
    </p>
    <p>
      If the result has more fraction digits than is specified by
      <a href='#dp'><code>Big.DP</code></a>, it will be rounded to
      <a href='#dp'><code>Big.DP</code></a> decimal places using rounding mode
      <a href='#rm'><code>Big.RM</code></a>.
    </p>
    <p>Throws <code class='error'>NaN</code> if this Big number is negative.</p>
    <pre>
x = new Big(16)
x.sqrt()                   // '4'
y = new Big(3)
y.sqrt()                   // '1.73205080756887729353'</pre>



    <h5 id="times">
      times<code class='inset'>.times(n) &rArr; <i>Big</i></code>
    </h5>
    <p><code>n</code> : <i>number|string|Big</i><br /></p>
    <p>
      Returns a Big number whose value is the value of this Big number times
      <code>n</code>.
    </p>
    <p>Throws <code class='error'>NaN</code> if <code>n</code> is invalid.</p>
    <pre>
0.6 * 3                    // 1.7999999999999998
x = new Big(0.6)
y = x.times(3)             // '1.8'
Big('7e+500').times(y)     // '1.26e+501'</pre>



    <h5 id="toE">
      toExponential<code class='inset'>.toExponential( [dp] ) &rArr;
      <i>string</i></code>
    </h5>
    <p><code>dp</code> : <i>number</i> : integer, 0 to 1e+6 inclusive</p>
    <p>
      Returns a string representing the value of this Big number in exponential
      notation to a fixed number of decimal places <code>dp</code>.
    </p>
    <p>
      If the value of this Big number in exponential notation has more digits to
      the right of the decimal point than is specified by <code>dp</code>, the
      return value will be rounded to <code>dp</code> decimal places using
      rounding mode <a href='#rm'><code>Big.RM</code></a>.
    </p>
    <p>
      If the value of this Big number in exponential notation has fewer digits
      to the right of the decimal point than is specified by <code>dp</code>,
      the return value will be appended with zeros accordingly.
    </p>
    <p>
      If <code>dp</code> is omitted, or is <code>null</code> or undefined, the
      number of digits after the decimal point defaults to the minimum number of
      digits necessary to represent the value exactly.
    </p>
    <p>
      Throws <code class='error'>!toExp!</code> if <code>dp</code> is invalid.
    </p>
    <pre>
x = 45.6
y = new Big(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'
x.toExponential(3)         // '4.560e+1'
y.toExponential(3)         // '4.560e+1'</pre>



    <h5 id="toF">
      toFixed<code class='inset'>.toFixed( [dp] ) &rArr;
      <i>string</i></code>
    </h5>
    <p>
      <code>dp</code> : <i>number</i> : integer, 0 to 1e+6 inclusive
    </p>
    <p>
      Returns a string representing the value of this Big number in normal
      notation to a fixed number of decimal places <code>dp</code>.
    </p>
    <p>
      If the value of this Big number in normal notation has more digits to the
      right of the decimal point than is specified by <code>dp</code>, the
      return value will be rounded to <code>dp</code> decimal places using
      rounding mode <a href='#rm'><code>Big.RM</code></a>.
    </p>
    <p>
      If the value of this Big number in normal notation has fewer fraction
      digits then is specified by <code>dp</code>, 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 10<sup>21</sup>,
      this method will always return normal notation.
    </p>
    <p>
      If <code>dp</code> is omitted, or is <code>null</code> or
      undefined, then the return value is simply the value in normal notation.
      This is  also unlike <code>Number.prototype.toFixed</code>, which returns
      the value to zero decimal places.
    </p>
    <p>
      Throws <code class='error'>!toFix!</code> if <code>dp</code> is invalid.
    </p>
    <pre>
x = 45.6
y = new Big(x)
x.toFixed()                // '46'
y.toFixed()                // '45.6'
y.toFixed(0)               // '46'
x.toFixed(3)               // '45.600'
y.toFixed(3)               // '45.600'</pre>



    <h5 id="toP">
      toPrecision<code class='inset'>.toPrecision( [sd] ) &rArr;
      <i>string</i></code>
    </h5>
    <p><code>sd</code> : <i>number</i> : integer, 1 to 1e+6 inclusive</p>
    <p>
      Returns a string representing the value of this Big number to the
      specified number of significant digits <code>sd</code>.
    </p>
    <p>
      If the value of this Big number has more digits than is specified by
      <code>sd</code>, the return value will be rounded to <code>sd</code>
      significant digits using rounding mode
      <a href='#rm'><code>Big.RM</code></a>.
    </p>
    <p>
      If the value of this Big number has fewer digits than is specified by
      <code>sd</code>, the return value will be appended with zeros accordingly.
    </p>
    <p>
      If <code>sd</code> is less than the number of digits necessary to
      represent the integer part of the value in normal notation, then
      exponential notation is used.
    </p>
    <p>
      If <code>sd</code> is omitted, or is <code>null</code> or undefined, then
      the return value is the same as <code>.toString()</code>.
    </p>
    <p>
      Throws <code class='error'>!toPre!</code> if <code>sd</code> is invalid.
    </p>
    <pre>
x = 45.6
y = new Big(x)
x.toPrecision()            // '45.6'
y.toPrecision()            // '45.6'
x.toPrecision(1)           // '5e+1'
y.toPrecision(1)           // '5e+1'
x.toPrecision(5)           // '45.600'
y.toPrecision(5)           // '45.600'</pre>



    <h5 id="toS">
      toString<code class='inset'>.toString() &rArr; <i>string</i></code>
    </h5>
    <p>
      Returns a string representing the value of this Big number.
    </p>
     <p>
      If this Big number has a positive exponent that is equal to or greater
      than 21, or a negative exponent equal to or less than -7, then exponential
      notation is returned.
    </p>
    <p>
      The point at which <code>toString</code> returns exponential rather than
      normal notation can be adjusted by changing the value of
      <a href='#epos'><code>Big.E_POS</code></a> and
      <a href='#eneg'><code>Big.E_NEG</code></a>. By default, Big numbers
      correspond to Javascript's number type in this regard.
    </p>
    <pre>
x = new Big('9.99e+20')
x.toString()               // '999000000000000000000'
y = new Big('1E21')
y.toString()               // '1e+21'
</pre>



    <h5 id="valueOf">
      valueOf<code class='inset'>.valueOf() &rArr; <i>string</i></code>
    </h5>
    <p>
      As <code>toString</code>.
    </p>
    <pre>
x = new Big('177.7e+457')
x.valueOf()                // '1.777e+459'</pre>



    <h5 id="toJSON">
      toJSON<code class='inset'>.toJSON() &rArr; <i>string</i></code>
    </h5>
    <p>
      As <code>toString</code>.
    </p>
    <pre>
x = new Big('177.7e+457')
y = new Big(235.4325)
z = new Big('0.0098074')
str = JSON.stringify( [x, y, z] )

JSON.parse( str, function ( k, v ) { return k === '' ? v : new Big(v) } )
// Returns an array of three Big numbers.</pre>



    <h4 id="instance-properties">Properties</h4>
    <p>
      A Big number is an object with three properties:
    </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 single digits</td>
      </tr>
      <tr>
        <td class='centre' id='exponent'><b>e</b></td>
        <td>exponent</td>
        <td><i>number</i></td>
        <td>Integer, -1e+6 to 1e+6 inclusive</td>
      </tr>
      <tr>
        <td class='centre' id='sign'><b>s</b></td>
        <td>sign</td>
        <td><i>number</i></td>
        <td>-1 or 1</td>
      </tr>
    </table>
    <p><sup>*</sup>significand</p>
    <p>
      The value of a Big number is stored in a normalised decimal floating point
      format which corresponds to the value's <code>toExponential</code> form,
      with the decimal point to be positioned after the most significant
      (left-most) digit of the coefficient.
    </p>
    <p>
      Note that, as with Javascript numbers, the original exponent and
      fractional trailing zeros are not preserved.
    </p>
    <pre>x = new Big(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 Big('-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>
      A Big number is mutable in the sense that the value of its properties can
      be changed.<br />
      For example, to rapidly shift a value by a power of 10:
    </p>
    <pre>
x = new Big('1234.000')    // '1234'
x.toExponential()          // '1.234e+3'
x.c                        // '1,2,3,4'
x.e                        // 3

x.e = -5
x                          // '0.00001234'</pre>
    <p>
      If changing the coefficient array directly, which is not recommended, be
      careful to avoid leading or trailing zeros (unless zero itself is being
      represented).
    </p>
    <p>
      Minus zero is a valid Big number value, but like Javascript numbers the
      minus sign is not shown.
    </p>
    <pre>
x = new Number(-0)         // 0
1 / x == -Infinity         // true

y = new Big(-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 instances of <code>Error</code> with
      <code>name</code> <code class='error'>BigError</code> and message as
      shown in the table below.
    </p>
    <table>
      <tr>
        <th>Method(s)</th>
        <th>Error message</th>
        <th>Thrown on</th>
      </tr>
      <tr>
        <td>
          <code>
            Big<br />cmp<br />div<br />eq gt gte lt lte<br />minus<br />mod
            <br />plus<br />times
          </code>
        </td>
        <td><code>NaN</code></td>
        <td>Invalid number</td>
      </tr>
      <tr>
        <td rowspan=4><code>div</code></td>
        <td><code>&plusmn;Infinity</code></td>
        <td>Division by zero</td>
      </tr>
      <tr>
        <td><code>NaN</code></td>
        <td>Division of zero by zero</td>
      </tr>
      <tr>
        <td>!Big.DP!</td>
        <td>Invalid Big.DP</td>
      </tr>
      <tr>
        <td>!Big.RM!</td>
        <td>Invalid Big.RM</td>
      </tr>
      <tr>
        <td><code>mod</code></td>
        <td><code>NaN</code></td>
        <td>Modulo zero</td>
      </tr>
      <tr>
        <td rowspan=3><code>pow</code></td>
        <td>!pow!</td>
        <td>Invalid exponent</td>
      </tr>
      <tr>
        <td>!Big.DP!</td>
        <td>Invalid Big.DP</td>
      </tr>
      <tr>
        <td>!Big.RM!</td>
        <td>Invalid Big.RM</td>
      </tr>
      <tr>
        <td rowspan=2><code>round</code></td>
        <td>!round!</td>
        <td>Invalid dp</td>
      </tr>
      <tr>
        <td>!Big.RM!</td>
        <td>Invalid rm/Big.RM</td>
      </tr>
      <tr>
        <td rowspan=3><code>sqrt</code></td>
        <td><code>NaN</code></td>
        <td>Negative number</td>
      </tr>
      <tr>
        <td>!Big.DP!</td>
        <td>Invalid Big.DP</td>
      </tr>
      <tr>
        <td>!Big.RM!</td>
        <td>Invalid Big.RM</td>
      </tr>
      <tr>
        <td rowspan=2><code>toExponential</code></td>
        <td>!toExp!</td>
        <td>Invalid dp</td>
      </tr>
      <tr>
        <td>!Big.RM!</td>
        <td>Invalid Big.RM</td>
      </tr>
      <tr>
        <td rowspan=2><code>toFixed</code></td>
        <td>!toFix!</td>
        <td>Invalid dp</td>
      </tr>
      <tr>
        <td>!Big.RM!</td>
        <td>Invalid Big.RM</td>
      </tr>
      <tr>
        <td rowspan=2><code>toPrecision</code></td>
        <td>!toPre!</td>
        <td>Invalid sd</td>
      </tr>
      <tr>
        <td>!Big.RM!</td>
        <td>Invalid Big.RM</td>
      </tr>
    </table>



     <h4 id='faq'>FAQ</h4>
    <h6>How can I convert a Big number to a primitive JavaScript number?</h6>
    <p>
      To convert a Big number to a primitive number, <code>parseFloat</code> or
      any of the other methods for converting a string to a number can be used.
    </p>
    <pre>
x = new Big('12345.6789')
parseFloat(x)             // 12345.6789
Number(x)                 // 12345.6789
+x                        // 12345.6789
x * 1                     // 12345.6789
x / 1                     // 12345.6789
x - 0                     // 12345.6789
x + 0                     // '12345.67890' (string concatenation, do not use!)
</pre>
    <p>
      If converting to an integer be aware that <code>parseInt</code> doees not
      handle exponential notation.
    <p>
    <pre>
x = new Big('9.87654e+32')
parseInt(x)               // 9
parseInt(+x)              // 9
parseInt(x.toFixed())     // 9.87654e+32 
parseInt(x.round())       // 9.87654e+32 
</pre>
    <p>
      The <code>Math</code> methods can also be used.
    <p>
    <pre>
x = new Big('1234.56')
Math.floor(x)             // 1234
Math.round(x)             // 1235 
</pre>
    <br />
    
     <h6>
      How can I round a Big number to a specified number of significant digits?
    </h6>
    <p>
      <a href='#toP'><code>toPrecision</code></a> returns a string representing
      the value of a Big number rounded to a specified number of significant
      digits. Or, the number of significant digits of a Big number can be set by
      truncating the array that stores its coefficient. For example, using the
      array's length property:
    </p>
    <pre>
x = new Big('987.654321')
len = x.c.length          // 9
if (len > 6) x.c.length = 6            
x                         // 987.654  
</pre>
    <br />
    
    <h6>
      How can I set the decimal places and/or rounding mode for just one
      operation?
    </h6>
    <p>
      This library uses a global configuration for the decimal places and
      rounding mode used by division operations, so it is just a matter of
      altering this as required.
    </p>
    <pre>
Big.DP = 10
y = x.sqrt()
Big.DP = 0
Big.RM = 1
z = x.div(3)
</pre>
    <p>
      There is also the ability to create separate Big number constructors each
      with their own particular <code>DP</code> and <code>RM</code> settings.
      See below.
    </p>
    <p>
      Finally, there is the option of redefining the relevant prototype method
      as required. For example, the following would enable a decimal
      places and rounding mode to be passed to the <code>div</code> method.
    </p>
    <pre>
Big.prototype.div = (function () {
  var div = Big.prototype.div;
  return function (n, dp, rm) {
    var result,
      Big = this.constructor,
      _dp = Big.DP,
      _rm = Big.RM;
    if (dp != null) Big.DP = dp;
    if (rm != null) Big.RM = rm;
    result = div.call(this, n);
    Big.DP = _dp;
    Big.RM = _rm;
    return result;    
  }
})();

var dp = 10;
var round_up = 2;
x = x.div(y, dp, round_up);
</pre>
    <br />

    <h6>
      How can I simultaneously use different decimal places and/or rounding mode
      settings for different Big numbers?
    </h6>
    <p>
      From <i>v3.0.0</i>, it is possible to have multiple Big number
      constructors each with their own particular <code>DP</code> and
      <code>RM</code> settings which apply to all Big numbers created from it.
    </p>
    <pre>
/*
Create an additional Big number constructor by calling the original Big
number constructor without using new and without any argument.
*/
Big10 = Big();

// Set the decimal places of division operations for each constructor.
Big.DP = 3;
Big10.DP = 10;

x = Big(5);
y = Big10(5);

x.div(3)     // 1.667
y.div(3)     // 1.6666666667
</pre>
    <p>
      Big numbers created by different constructors can be used together in
      operations, and it is the <code>DP</code> and <code>RM</code> setting of
      the Big number that an operation is called upon that will apply.
    </p>
    <p>
      In the interest of memory efficiency, all Big number constructors share
      the same <code>prototype</code> object, so while the <code>DP</code> and
      <code>RM</code> (and any other <i>own</i> properties) of a constructor are
      isolated and untouchable by another, its prototype methods are not.
    </p>
    <br />
        
    <h6>Why are trailing fractional zeros removed from Big numbers?</h6>
    <p>
      Many 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 imply that the value lies
      within a certain range.
    </p>
    <p>
      In the first example, <code>x</code> has a value of 1.0. The trailing zero
      shows the precision of the value, implying that the value is in the range
      0.95 to 1.05. Similarly, the precision indicated by the trailing zeros of
      <code>y</code> indicates that the value is in the range 1.09995 to
      1.10005. If we add the two lowest values in the ranges we get 0.95 +
      1.09995 = 2.04995 and if we add the two highest values we get 1.05 +
      1.10005 = 2.15005, so the range of the result of the addition implied by
      the precision of its operands is 2.04995 to 2.15005. The result given by
      BigDecimal of 2.1000 however, indicates that the value is in the range
      2.09995 to 2.10005 and therefore the precision implied by its trailing
      zeros is misleading.
    </p>
    <p>
      In the second example, the true range is 4.122744 to 4.157256 yet the
      BigDecimal answer of 4.1400000 indicates a range of 4.13999995 to
      4.14000005. Again, the precision implied by the trailing zeros is
      misleading.
    </p>
    <p>
      This library, like binary floating-point and most calculators, does not
      retain trailing fractional zeros.<br />
      Instead, the <code>toExponential</code>, <code>toFixed</code> and
      <code>toPrecision</code> methods enable trailing zeros to be added if and
      when required.
    </p>    
    <br />

  </div>
   <script>
   /* big.js v3.1.1 https://github.com/MikeMcl/big.js/LICENCE */
   (function(global){"use strict";var DP=20,RM=1,MAX_DP=1e6,MAX_POWER=1e6,E_NEG=-7,E_POS=21,P={},isValid=/^-?(\d+(\.\d*)?|\.\d+)(e[+-]?\d+)?$/i,Big;function bigFactory(){function Big(n){var x=this;if(!(x instanceof Big)){return n===void 0?bigFactory():new Big(n)}if(n instanceof Big){x.s=n.s;x.e=n.e;x.c=n.c.slice()}else{parse(x,n)}x.constructor=Big}Big.prototype=P;Big.DP=DP;Big.RM=RM;Big.E_NEG=E_NEG;Big.E_POS=E_POS;return Big}function format(x,dp,toE){var Big=x.constructor,i=dp-(x=new Big(x)).e,c=x.c;if(c.length>++dp){rnd(x,i,Big.RM)}if(!c[0]){++i}else if(toE){i=dp}else{c=x.c;i=x.e+i+1}for(;c.length<i;c.push(0)){}i=x.e;return toE===1||toE&&(dp<=i||i<=Big.E_NEG)?(x.s<0&&c[0]?"-":"")+(c.length>1?c[0]+"."+c.join("").slice(1):c[0])+(i<0?"e":"e+")+i:x.toString()}function parse(x,n){var e,i,nL;if(n===0&&1/n<0){n="-0"}else 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