2250 lines
85 KiB
HTML
2250 lines
85 KiB
HTML
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<meta charset="utf-8">
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<meta name="Author" content="M Mclaughlin">
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<title>bignumber.js API</title>
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</style>
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</head>
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<body>
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<div class="nav">
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<b>v9.0.2</b>
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<a class='nav-title' href="#">API</a>
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<b> CONSTRUCTOR </b>
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<ul>
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<li><a href="#bignumber">BigNumber</a></li>
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</ul>
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<a href="#methods">Methods</a>
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<ul>
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<li><a href="#clone">clone</a></li>
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<li><a href="#config" >config</a><span>set</span></li>
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<li>
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<ul class="inset">
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<li><a href="#decimal-places">DECIMAL_PLACES</a></li>
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<li><a href="#rounding-mode" >ROUNDING_MODE</a></li>
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<li><a href="#exponential-at">EXPONENTIAL_AT</a></li>
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<li><a href="#range" >RANGE</a></li>
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<li><a href="#crypto" >CRYPTO</a></li>
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<li><a href="#modulo-mode" >MODULO_MODE</a></li>
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<li><a href="#pow-precision" >POW_PRECISION</a></li>
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<li><a href="#format" >FORMAT</a></li>
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<li><a href="#alphabet" >ALPHABET</a></li>
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</ul>
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</li>
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<li><a href="#isBigNumber">isBigNumber</a></li>
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<li><a href="#max" >maximum</a><span>max</span></li>
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<li><a href="#min" >minimum</a><span>min</span></li>
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<li><a href="#random" >random</a></li>
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<li><a href="#sum" >sum</a></li>
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</ul>
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<a href="#constructor-properties">Properties</a>
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<ul>
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<li><a href="#round-up" >ROUND_UP</a></li>
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<li><a href="#round-down" >ROUND_DOWN</a></li>
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<li><a href="#round-ceil" >ROUND_CEIL</a></li>
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<li><a href="#round-floor" >ROUND_FLOOR</a></li>
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<li><a href="#round-half-up" >ROUND_HALF_UP</a></li>
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<li><a href="#round-half-down" >ROUND_HALF_DOWN</a></li>
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<li><a href="#round-half-even" >ROUND_HALF_EVEN</a></li>
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<li><a href="#round-half-ceil" >ROUND_HALF_CEIL</a></li>
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<li><a href="#round-half-floor">ROUND_HALF_FLOOR</a></li>
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<li><a href="#debug" >DEBUG</a></li>
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</ul>
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<b> INSTANCE </b>
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<a href="#prototype-methods">Methods</a>
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<ul>
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<li><a href="#abs" >absoluteValue </a><span>abs</span> </li>
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<li><a href="#cmp" >comparedTo </a> </li>
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<li><a href="#dp" >decimalPlaces </a><span>dp</span> </li>
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<li><a href="#div" >dividedBy </a><span>div</span> </li>
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<li><a href="#divInt" >dividedToIntegerBy </a><span>idiv</span> </li>
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<li><a href="#pow" >exponentiatedBy </a><span>pow</span> </li>
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<li><a href="#int" >integerValue </a> </li>
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<li><a href="#eq" >isEqualTo </a><span>eq</span> </li>
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<li><a href="#isF" >isFinite </a> </li>
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<li><a href="#gt" >isGreaterThan </a><span>gt</span> </li>
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<li><a href="#gte" >isGreaterThanOrEqualTo</a><span>gte</span> </li>
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<li><a href="#isInt" >isInteger </a> </li>
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<li><a href="#lt" >isLessThan </a><span>lt</span> </li>
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<li><a href="#lte" >isLessThanOrEqualTo </a><span>lte</span> </li>
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<li><a href="#isNaN" >isNaN </a> </li>
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<li><a href="#isNeg" >isNegative </a> </li>
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<li><a href="#isPos" >isPositive </a> </li>
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<li><a href="#isZ" >isZero </a> </li>
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<li><a href="#minus" >minus </a> </li>
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<li><a href="#mod" >modulo </a><span>mod</span> </li>
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<li><a href="#times" >multipliedBy </a><span>times</span></li>
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<li><a href="#neg" >negated </a> </li>
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<li><a href="#plus" >plus </a> </li>
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<li><a href="#sd" >precision </a><span>sd</span> </li>
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<li><a href="#shift" >shiftedBy </a> </li>
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<li><a href="#sqrt" >squareRoot </a><span>sqrt</span> </li>
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<li><a href="#toE" >toExponential </a> </li>
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<li><a href="#toFix" >toFixed </a> </li>
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<li><a href="#toFor" >toFormat </a> </li>
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<li><a href="#toFr" >toFraction </a> </li>
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<li><a href="#toJSON" >toJSON </a> </li>
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<li><a href="#toN" >toNumber </a> </li>
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<li><a href="#toP" >toPrecision </a> </li>
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<li><a href="#toS" >toString </a> </li>
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<li><a href="#valueOf">valueOf </a> </li>
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</ul>
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<a href="#instance-properties">Properties</a>
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<ul>
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<li><a href="#coefficient">c: coefficient</a></li>
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<li><a href="#exponent" >e: exponent</a></li>
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<li><a href="#sign" >s: sign</a></li>
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</ul>
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<a href="#zero-nan-infinity">Zero, NaN & Infinity</a>
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<a href="#Errors">Errors</a>
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<a href="#type-coercion">Type coercion</a>
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<a class='end' href="#faq">FAQ</a>
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</div>
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<div class="container">
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<h1>bignumber<span id='js'>.js</span></h1>
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<p>A JavaScript library for arbitrary-precision arithmetic.</p>
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<p><a href="https://github.com/MikeMcl/bignumber.js">Hosted on GitHub</a>. </p>
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<h2>API</h2>
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<p>
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See the <a href='https://github.com/MikeMcl/bignumber.js'>README</a> on GitHub for a
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quick-start introduction.
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</p>
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<p>
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In all examples below, <code>var</code> and semicolons are not shown, and if a commented-out
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value is in quotes it means <code>toString</code> has been called on the preceding expression.
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</p>
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<h3>CONSTRUCTOR</h3>
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<h5 id="bignumber">
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BigNumber<code class='inset'>BigNumber(n [, base]) <i>⇒ BigNumber</i></code>
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</h5>
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<p>
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<code>n</code>: <i>number|string|BigNumber</i><br />
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<code>base</code>: <i>number</i>: integer, <code>2</code> to <code>36</code> inclusive. (See
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<a href='#alphabet'><code>ALPHABET</code></a> to extend this range).
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</p>
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<p>
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Returns a new instance of a BigNumber object with value <code>n</code>, where <code>n</code>
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is a numeric value in the specified <code>base</code>, or base <code>10</code> if
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<code>base</code> is omitted or is <code>null</code> or <code>undefined</code>.
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</p>
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<p>
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Note that the BigNnumber constructor accepts an <code>n</code> of type <em>number</em> purely
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as a convenience so that string quotes don't have to be typed when entering literal values,
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and that it is the <code>toString</code> value of <code>n</code> that is used rather than its
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underlying binary floating point value converted to decimal.
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</p>
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<pre>
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x = new BigNumber(123.4567) // '123.4567'
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// 'new' is optional
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y = BigNumber(x) // '123.4567'</pre>
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<p>
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If <code>n</code> is a base <code>10</code> value it can be in normal or exponential notation.
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Values in other bases must be in normal notation. Values in any base can have fraction digits,
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i.e. digits after the decimal point.
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</p>
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<pre>
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new BigNumber(43210) // '43210'
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new BigNumber('4.321e+4') // '43210'
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new BigNumber('-735.0918e-430') // '-7.350918e-428'
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new BigNumber('123412421.234324', 5) // '607236.557696'</pre>
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<p>
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Signed <code>0</code>, signed <code>Infinity</code> and <code>NaN</code> are supported.
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</p>
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<pre>
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new BigNumber('-Infinity') // '-Infinity'
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new BigNumber(NaN) // 'NaN'
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new BigNumber(-0) // '0'
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new BigNumber('.5') // '0.5'
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new BigNumber('+2') // '2'</pre>
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<p>
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String values in hexadecimal literal form, e.g. <code>'0xff'</code> or <code>'0xFF'</code>
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(but not <code>'0xfF'</code>), are valid, as are string values with the octal and binary
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prefixs <code>'0o'</code> and <code>'0b'</code>. String values in octal literal form without
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the prefix will be interpreted as decimals, e.g. <code>'011'</code> is interpreted as 11, not 9.
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</p>
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<pre>
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new BigNumber(-10110100.1, 2) // '-180.5'
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new BigNumber('-0b10110100.1') // '-180.5'
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new BigNumber('ff.8', 16) // '255.5'
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new BigNumber('0xff.8') // '255.5'</pre>
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<p>
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If a base is specified, <code>n</code> is rounded according to the current
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<a href='#decimal-places'><code>DECIMAL_PLACES</code></a> and
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<a href='#rounding-mode'><code>ROUNDING_MODE</code></a> settings. <em>This includes base
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<code>10</code> so don't include a <code>base</code> parameter for decimal values unless
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this behaviour is wanted.</em>
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</p>
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<pre>BigNumber.config({ DECIMAL_PLACES: 5 })
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new BigNumber(1.23456789) // '1.23456789'
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new BigNumber(1.23456789, 10) // '1.23457'</pre>
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<p>An error is thrown if <code>base</code> is invalid. See <a href='#Errors'>Errors</a>.</p>
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<p>
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There is no limit to the number of digits of a value of type <em>string</em> (other than
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that of JavaScript's maximum array size). See <a href='#range'><code>RANGE</code></a> to set
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the maximum and minimum possible exponent value of a BigNumber.
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</p>
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<pre>
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new BigNumber('5032485723458348569331745.33434346346912144534543')
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new BigNumber('4.321e10000000')</pre>
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<p>BigNumber <code>NaN</code> is returned if <code>n</code> is invalid
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(unless <code>BigNumber.DEBUG</code> is <code>true</code>, see below).</p>
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<pre>
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new BigNumber('.1*') // 'NaN'
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new BigNumber('blurgh') // 'NaN'
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new BigNumber(9, 2) // 'NaN'</pre>
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<p>
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To aid in debugging, if <code>BigNumber.DEBUG</code> is <code>true</code> then an error will
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be thrown on an invalid <code>n</code>. An error will also be thrown if <code>n</code> is of
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type <em>number</em> and has more than <code>15</code> significant digits, as calling
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<code><a href='#toS'>toString</a></code> or <code><a href='#valueOf'>valueOf</a></code> on
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these numbers may not result in the intended value.
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</p>
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<pre>
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console.log(823456789123456.3) // 823456789123456.2
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new BigNumber(823456789123456.3) // '823456789123456.2'
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BigNumber.DEBUG = true
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// '[BigNumber Error] Number primitive has more than 15 significant digits'
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new BigNumber(823456789123456.3)
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// '[BigNumber Error] Not a base 2 number'
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new BigNumber(9, 2)</pre>
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<p>
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A BigNumber can also be created from an object literal.
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Use <code><a href='#isBigNumber'>isBigNumber</a></code> to check that it is well-formed.
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</p>
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<pre>new BigNumber({ s: 1, e: 2, c: [ 777, 12300000000000 ], _isBigNumber: true }) // '777.123'</pre>
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<h4 id="methods">Methods</h4>
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<p>The static methods of a BigNumber constructor.</p>
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<h5 id="clone">clone
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<code class='inset'>.clone([object]) <i>⇒ BigNumber constructor</i></code>
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</h5>
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<p><code>object</code>: <i>object</i></p>
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<p>
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Returns a new independent BigNumber constructor with configuration as described by
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<code>object</code> (see <a href='#config'><code>config</code></a>), or with the default
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configuration if <code>object</code> is <code>null</code> or <code>undefined</code>.
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</p>
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<p>
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Throws if <code>object</code> is not an object. See <a href='#Errors'>Errors</a>.
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</p>
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<pre>BigNumber.config({ DECIMAL_PLACES: 5 })
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BN = BigNumber.clone({ DECIMAL_PLACES: 9 })
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x = new BigNumber(1)
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y = new BN(1)
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x.div(3) // 0.33333
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y.div(3) // 0.333333333
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// BN = BigNumber.clone({ DECIMAL_PLACES: 9 }) is equivalent to:
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BN = BigNumber.clone()
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BN.config({ DECIMAL_PLACES: 9 })</pre>
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<h5 id="config">config<code class='inset'>set([object]) <i>⇒ object</i></code></h5>
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<p>
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<code>object</code>: <i>object</i>: an object that contains some or all of the following
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properties.
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</p>
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<p>Configures the settings for this particular BigNumber constructor.</p>
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<dl class='inset'>
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<dt id="decimal-places"><code><b>DECIMAL_PLACES</b></code></dt>
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<dd>
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<i>number</i>: integer, <code>0</code> to <code>1e+9</code> inclusive<br />
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Default value: <code>20</code>
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</dd>
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<dd>
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The <em>maximum</em> number of decimal places of the results of operations involving
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division, i.e. division, square root and base conversion operations, and power operations
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with negative exponents.<br />
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</dd>
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<dd>
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<pre>BigNumber.config({ DECIMAL_PLACES: 5 })
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BigNumber.set({ DECIMAL_PLACES: 5 }) // equivalent</pre>
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</dd>
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<dt id="rounding-mode"><code><b>ROUNDING_MODE</b></code></dt>
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<dd>
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<i>number</i>: integer, <code>0</code> to <code>8</code> inclusive<br />
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Default value: <code>4</code> <a href="#round-half-up">(<code>ROUND_HALF_UP</code>)</a>
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</dd>
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<dd>
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The rounding mode used in the above operations and the default rounding mode of
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<a href='#dp'><code>decimalPlaces</code></a>,
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<a href='#sd'><code>precision</code></a>,
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<a href='#toE'><code>toExponential</code></a>,
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<a href='#toFix'><code>toFixed</code></a>,
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<a href='#toFor'><code>toFormat</code></a> and
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<a href='#toP'><code>toPrecision</code></a>.
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</dd>
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<dd>The modes are available as enumerated properties of the BigNumber constructor.</dd>
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<dd>
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<pre>BigNumber.config({ ROUNDING_MODE: 0 })
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BigNumber.set({ ROUNDING_MODE: BigNumber.ROUND_UP }) // equivalent</pre>
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</dd>
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<dt id="exponential-at"><code><b>EXPONENTIAL_AT</b></code></dt>
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<dd>
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<i>number</i>: integer, magnitude <code>0</code> to <code>1e+9</code> inclusive, or
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<br />
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<i>number</i>[]: [ integer <code>-1e+9</code> to <code>0</code> inclusive, integer
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<code>0</code> to <code>1e+9</code> inclusive ]<br />
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Default value: <code>[-7, 20]</code>
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</dd>
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<dd>
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The exponent value(s) at which <code>toString</code> returns exponential notation.
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</dd>
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<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="crypto"><code><b>CRYPTO</b></code></dt>
|
|
<dd>
|
|
<i>boolean</i>: <code>true</code> or <code>false</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 Node.js.
|
|
</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 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>
|
|
// Node.js
|
|
const crypto = require('crypto'); // CommonJS
|
|
import * as crypto from 'crypto'; // ES module
|
|
|
|
global.crypto = crypto;
|
|
|
|
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> precision, i.e. 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 significant digits will not be limited.</dd>
|
|
<dd>See <a href='#pow'><code>exponentiatedBy</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.
|
|
The object can include any number of the properties shown below.
|
|
</dd>
|
|
<dd>See <a href='#toFor'><code>toFormat</code></a> for examples of usage.</dd>
|
|
<dd>
|
|
<pre>
|
|
BigNumber.config({
|
|
FORMAT: {
|
|
// string to prepend
|
|
prefix: '',
|
|
// decimal separator
|
|
decimalSeparator: '.',
|
|
// grouping separator of the integer part
|
|
groupSeparator: ',',
|
|
// primary grouping size of the integer part
|
|
groupSize: 3,
|
|
// secondary grouping size of the integer part
|
|
secondaryGroupSize: 0,
|
|
// grouping separator of the fraction part
|
|
fractionGroupSeparator: ' ',
|
|
// grouping size of the fraction part
|
|
fractionGroupSize: 0,
|
|
// string to append
|
|
suffix: ''
|
|
}
|
|
});</pre>
|
|
</dd>
|
|
|
|
|
|
|
|
<dt id="alphabet"><code><b>ALPHABET</b></code></dt>
|
|
<dd>
|
|
<i>string</i><br />
|
|
Default value: <code>'0123456789abcdefghijklmnopqrstuvwxyz'</code>
|
|
</dd>
|
|
<dd>
|
|
The alphabet used for base conversion. The length of the alphabet corresponds to the
|
|
maximum value of the base argument that can be passed to the
|
|
<a href='#bignumber'><code>BigNumber</code></a> constructor or
|
|
<a href='#toS'><code>toString</code></a>.
|
|
</dd>
|
|
<dd>
|
|
There is no maximum length for the alphabet, but it must be at least 2 characters long, and
|
|
it must not contain whitespace or a repeated character, or the sign indicators
|
|
<code>'+'</code> and <code>'-'</code>, or the decimal separator <code>'.'</code>.
|
|
</dd>
|
|
<dd>
|
|
<pre>// duodecimal (base 12)
|
|
BigNumber.config({ ALPHABET: '0123456789TE' })
|
|
x = new BigNumber('T', 12)
|
|
x.toString() // '10'
|
|
x.toString(12) // 'T'</pre>
|
|
</dd>
|
|
|
|
|
|
|
|
</dl>
|
|
<br /><br />
|
|
<p>Returns an object with the above properties and their current values.</p>
|
|
<p>
|
|
Throws if <code>object</code> is not an object, or if an invalid value is assigned to
|
|
one or more of the above properties. See <a href='#Errors'>Errors</a>.
|
|
</p>
|
|
<pre>
|
|
BigNumber.config({
|
|
DECIMAL_PLACES: 40,
|
|
ROUNDING_MODE: BigNumber.ROUND_HALF_CEIL,
|
|
EXPONENTIAL_AT: [-10, 20],
|
|
RANGE: [-500, 500],
|
|
CRYPTO: true,
|
|
MODULO_MODE: BigNumber.ROUND_FLOOR,
|
|
POW_PRECISION: 80,
|
|
FORMAT: {
|
|
groupSize: 3,
|
|
groupSeparator: ' ',
|
|
decimalSeparator: ','
|
|
},
|
|
ALPHABET: '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ$_'
|
|
});
|
|
|
|
obj = BigNumber.config();
|
|
obj.DECIMAL_PLACES // 40
|
|
obj.RANGE // [-500, 500]</pre>
|
|
|
|
|
|
|
|
<h5 id="isBigNumber">
|
|
isBigNumber<code class='inset'>.isBigNumber(value) <i>⇒ boolean</i></code>
|
|
</h5>
|
|
<p><code>value</code>: <i>any</i><br /></p>
|
|
<p>
|
|
Returns <code>true</code> if <code>value</code> is a BigNumber instance, otherwise returns
|
|
<code>false</code>.
|
|
</p>
|
|
<pre>x = 42
|
|
y = new BigNumber(x)
|
|
|
|
BigNumber.isBigNumber(x) // false
|
|
y instanceof BigNumber // true
|
|
BigNumber.isBigNumber(y) // true
|
|
|
|
BN = BigNumber.clone();
|
|
z = new BN(x)
|
|
z instanceof BigNumber // false
|
|
BigNumber.isBigNumber(z) // true</pre>
|
|
<p>
|
|
If <code>value</code> is a BigNumber instance and <code>BigNumber.DEBUG</code> is <code>true</code>,
|
|
then this method will also check if <code>value</code> is well-formed, and throw if it is not.
|
|
See <a href='#Errors'>Errors</a>.
|
|
</p>
|
|
<p>
|
|
The check can be useful if creating a BigNumber from an object literal.
|
|
See <a href='#bignumber'>BigNumber</a>.
|
|
</p>
|
|
<pre>
|
|
x = new BigNumber(10)
|
|
|
|
// Change x.c to an illegitimate value.
|
|
x.c = NaN
|
|
|
|
BigNumber.DEBUG = false
|
|
|
|
// No error.
|
|
BigNumber.isBigNumber(x) // true
|
|
|
|
BigNumber.DEBUG = true
|
|
|
|
// Error.
|
|
BigNumber.isBigNumber(x) // '[BigNumber Error] Invalid BigNumber'</pre>
|
|
|
|
|
|
|
|
<h5 id="max">maximum<code class='inset'>.max(n...) <i>⇒ BigNumber</i></code></h5>
|
|
<p>
|
|
<code>n</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 the arguments.
|
|
</p>
|
|
<p>The return value is always exact and unrounded.</p>
|
|
<pre>x = new BigNumber('3257869345.0378653')
|
|
BigNumber.maximum(4e9, x, '123456789.9') // '4000000000'
|
|
|
|
arr = [12, '13', new BigNumber(14)]
|
|
BigNumber.max.apply(null, arr) // '14'</pre>
|
|
|
|
|
|
|
|
<h5 id="min">minimum<code class='inset'>.min(n...) <i>⇒ BigNumber</i></code></h5>
|
|
<p>
|
|
<code>n</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 the arguments.
|
|
</p>
|
|
<p>The return value is always exact and unrounded.</p>
|
|
<pre>x = new BigNumber('3257869345.0378653')
|
|
BigNumber.minimum(4e9, x, '123456789.9') // '123456789.9'
|
|
|
|
arr = [2, new BigNumber(-14), '-15.9999', -12]
|
|
BigNumber.min.apply(null, arr) // '-15.9999'</pre>
|
|
|
|
|
|
|
|
<h5 id="random">
|
|
random<code class='inset'>.random([dp]) <i>⇒ 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>
|
|
To be able to set <a href='#crypto'><code>CRYPTO</code></a> to <code>true</code> when using
|
|
Node.js, the <code>crypto</code> object must be available globally:
|
|
</p>
|
|
<pre>// Node.js
|
|
const crypto = require('crypto'); // CommonJS
|
|
import * as crypto from 'crypto'; // ES module
|
|
global.crypto = crypto;</pre>
|
|
<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>
|
|
<p>
|
|
Throws if <code>dp</code> is invalid. See <a href='#Errors'>Errors</a>.
|
|
</p>
|
|
<pre>BigNumber.config({ DECIMAL_PLACES: 10 })
|
|
BigNumber.random() // '0.4117936847'
|
|
BigNumber.random(20) // '0.78193327636914089009'</pre>
|
|
|
|
|
|
|
|
<h5 id="sum">sum<code class='inset'>.sum(n...) <i>⇒ BigNumber</i></code></h5>
|
|
<p>
|
|
<code>n</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 sum of the arguments.</p>
|
|
<p>The return value is always exact and unrounded.</p>
|
|
<pre>x = new BigNumber('3257869345.0378653')
|
|
BigNumber.sum(4e9, x, '123456789.9') // '7381326134.9378653'
|
|
|
|
arr = [2, new BigNumber(14), '15.9999', 12]
|
|
BigNumber.sum.apply(null, arr) // '43.9999'</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>
|
|
|
|
<h5 id="debug">DEBUG</h5>
|
|
<p><i>undefined|false|true</i></p>
|
|
<p>
|
|
If <code>BigNumber.DEBUG</code> is set <code>true</code> then an error will be thrown
|
|
if this <a href='#bignumber'>BigNumber</a> constructor receives an invalid value, such as
|
|
a value of type <em>number</em> with more than <code>15</code> significant digits.
|
|
See <a href='#bignumber'>BigNumber</a>.
|
|
</p>
|
|
<p>
|
|
An error will also be thrown if the <code><a href='#isBigNumber'>isBigNumber</a></code>
|
|
method receives a BigNumber that is not well-formed.
|
|
See <code><a href='#isBigNumber'>isBigNumber</a></code>.
|
|
</p>
|
|
<pre>BigNumber.DEBUG = true</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 ±<code>0</code>, ±<code>Infinity</code> and <code>NaN</code> is
|
|
consistent with how JavaScript treats these values.
|
|
</p>
|
|
<p>Many method names have a shorter alias.</p>
|
|
|
|
|
|
|
|
<h5 id="abs">absoluteValue<code class='inset'>.abs() <i>⇒ 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="cmp">
|
|
comparedTo<code class='inset'>.comparedTo(n [, base]) <i>⇒ 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> </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.comparedTo(NaN) // null
|
|
y.comparedTo('110', 2) // -1</pre>
|
|
|
|
|
|
|
|
<h5 id="dp">
|
|
decimalPlaces<code class='inset'>.dp([dp [, rm]]) <i>⇒ BigNumber|number</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>
|
|
If <code>dp</code> is a number, 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 the number of decimal places of the value of this BigNumber, or <code>null</code> if
|
|
the value of this BigNumber is ±<code>Infinity</code> or <code>NaN</code>.
|
|
</p>
|
|
<p>
|
|
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>
|
|
Throws if <code>dp</code> or <code>rm</code> is invalid. See <a href='#Errors'>Errors</a>.
|
|
</p>
|
|
<pre>
|
|
x = new BigNumber(1234.56)
|
|
x.decimalPlaces(1) // '1234.6'
|
|
x.dp() // 2
|
|
x.decimalPlaces(2) // '1234.56'
|
|
x.dp(10) // '1234.56'
|
|
x.decimalPlaces(0, 1) // '1234'
|
|
x.dp(0, 6) // '1235'
|
|
x.decimalPlaces(1, 1) // '1234.5'
|
|
x.dp(1, BigNumber.ROUND_HALF_EVEN) // '1234.6'
|
|
x // '1234.56'
|
|
y = new BigNumber('9.9e-101')
|
|
y.dp() // 102</pre>
|
|
|
|
|
|
|
|
<h5 id="div">dividedBy<code class='inset'>.div(n [, base]) <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>
|
|
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> settings.
|
|
</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'>.idiv(n [, base]) ⇒
|
|
<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>
|
|
Returns 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.idiv(0.7) // '7'
|
|
x.idiv('0.f', 16) // '5'</pre>
|
|
|
|
|
|
|
|
<h5 id="pow">
|
|
exponentiatedBy<code class='inset'>.pow(n [, m]) <i>⇒ BigNumber</i></code>
|
|
</h5>
|
|
<p>
|
|
<code>n</code>: <i>number|string|BigNumber</i>: integer<br />
|
|
<code>m</code>: <i>number|string|BigNumber</i>
|
|
</p>
|
|
<p>
|
|
Returns a BigNumber whose value is the value of this BigNumber exponentiated by
|
|
<code>n</code>, i.e. raised to the power <code>n</code>, and optionally modulo a modulus
|
|
<code>m</code>.
|
|
</p>
|
|
<p>
|
|
Throws if <code>n</code> is not an integer. See <a href='#Errors'>Errors</a>.
|
|
</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> settings.
|
|
</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>
|
|
If <code>m</code> is specified and the value of <code>m</code>, <code>n</code> and this
|
|
BigNumber are integers, and <code>n</code> is positive, then a fast modular exponentiation
|
|
algorithm is used, otherwise the operation will be performed as
|
|
<code>x.exponentiatedBy(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.exponentiatedBy(2) // '0.49'
|
|
BigNumber(3).pow(-2) // '0.11111111111111111111'</pre>
|
|
|
|
|
|
|
|
<h5 id="int">
|
|
integerValue<code class='inset'>.integerValue([rm]) <i>⇒ BigNumber</i></code>
|
|
</h5>
|
|
<p>
|
|
<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 an integer using
|
|
rounding mode <code>rm</code>.
|
|
</p>
|
|
<p>
|
|
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>
|
|
Throws if <code>rm</code> is invalid. See <a href='#Errors'>Errors</a>.
|
|
</p>
|
|
<pre>
|
|
x = new BigNumber(123.456)
|
|
x.integerValue() // '123'
|
|
x.integerValue(BigNumber.ROUND_CEIL) // '124'
|
|
y = new BigNumber(-12.7)
|
|
y.integerValue() // '-13'
|
|
y.integerValue(BigNumber.ROUND_DOWN) // '-12'</pre>
|
|
<p>
|
|
The following is an example of how to add a prototype method that emulates JavaScript's
|
|
<code>Math.round</code> function. <code>Math.ceil</code>, <code>Math.floor</code> and
|
|
<code>Math.trunc</code> can be emulated in the same way with
|
|
<code>BigNumber.ROUND_CEIL</code>, <code>BigNumber.ROUND_FLOOR</code> and
|
|
<code> BigNumber.ROUND_DOWN</code> respectively.
|
|
</p>
|
|
<pre>
|
|
BigNumber.prototype.round = function () {
|
|
return this.integerValue(BigNumber.ROUND_HALF_CEIL);
|
|
};
|
|
x.round() // '123'</pre>
|
|
|
|
|
|
|
|
<h5 id="eq">isEqualTo<code class='inset'>.eq(n [, base]) <i>⇒ 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 equal to 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.isEqualTo('1e-324') // false
|
|
BigNumber(-0).eq(x) // true ( -0 === 0 )
|
|
BigNumber(255).eq('ff', 16) // true
|
|
|
|
y = new BigNumber(NaN)
|
|
y.isEqualTo(NaN) // false</pre>
|
|
|
|
|
|
|
|
<h5 id="isF">isFinite<code class='inset'>.isFinite() <i>⇒ 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 <= Number.MAX_VALUE</code>.
|
|
</p>
|
|
|
|
|
|
|
|
<h5 id="gt">isGreaterThan<code class='inset'>.gt(n [, base]) <i>⇒ 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 > (0.3 - 0.2) // true
|
|
x = new BigNumber(0.1)
|
|
x.isGreaterThan(BigNumber(0.3).minus(0.2)) // false
|
|
BigNumber(0).gt(x) // false
|
|
BigNumber(11, 3).gt(11.1, 2) // true</pre>
|
|
|
|
|
|
|
|
<h5 id="gte">
|
|
isGreaterThanOrEqualTo<code class='inset'>.gte(n [, base]) <i>⇒ 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) >= 0.1 // false
|
|
x = new BigNumber(0.3).minus(0.2)
|
|
x.isGreaterThanOrEqualTo(0.1) // true
|
|
BigNumber(1).gte(x) // true
|
|
BigNumber(10, 18).gte('i', 36) // true</pre>
|
|
|
|
|
|
|
|
<h5 id="isInt">isInteger<code class='inset'>.isInteger() <i>⇒ boolean</i></code></h5>
|
|
<p>
|
|
Returns <code>true</code> if the value of this BigNumber is an integer, otherwise returns
|
|
<code>false</code>.
|
|
</p>
|
|
<pre>
|
|
x = new BigNumber(1)
|
|
x.isInteger() // true
|
|
y = new BigNumber(123.456)
|
|
y.isInteger() // false</pre>
|
|
|
|
|
|
|
|
<h5 id="lt">isLessThan<code class='inset'>.lt(n [, base]) <i>⇒ 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) < 0.1 // true
|
|
x = new BigNumber(0.3).minus(0.2)
|
|
x.isLessThan(0.1) // false
|
|
BigNumber(0).lt(x) // true
|
|
BigNumber(11.1, 2).lt(11, 3) // true</pre>
|
|
|
|
|
|
|
|
<h5 id="lte">
|
|
isLessThanOrEqualTo<code class='inset'>.lte(n [, base]) <i>⇒ 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 <= (0.3 - 0.2) // false
|
|
x = new BigNumber(0.1)
|
|
x.isLessThanOrEqualTo(BigNumber(0.3).minus(0.2)) // true
|
|
BigNumber(-1).lte(x) // true
|
|
BigNumber(10, 18).lte('i', 36) // true</pre>
|
|
|
|
|
|
|
|
<h5 id="isNaN">isNaN<code class='inset'>.isNaN() <i>⇒ 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'>.isNegative() <i>⇒ boolean</i></code></h5>
|
|
<p>
|
|
Returns <code>true</code> if the sign of this BigNumber is negative, otherwise returns
|
|
<code>false</code>.
|
|
</p>
|
|
<pre>
|
|
x = new BigNumber(-0)
|
|
x.isNegative() // true
|
|
y = new BigNumber(2)
|
|
y.isNegative() // false</pre>
|
|
<p>Note: <code>n < 0</code> can be used if <code>n <= -Number.MIN_VALUE</code>.</p>
|
|
|
|
|
|
|
|
<h5 id="isPos">isPositive<code class='inset'>.isPositive() <i>⇒ boolean</i></code></h5>
|
|
<p>
|
|
Returns <code>true</code> if the sign of this BigNumber is positive, otherwise returns
|
|
<code>false</code>.
|
|
</p>
|
|
<pre>
|
|
x = new BigNumber(-0)
|
|
x.isPositive() // false
|
|
y = new BigNumber(2)
|
|
y.isPositive() // true</pre>
|
|
|
|
|
|
|
|
<h5 id="isZ">isZero<code class='inset'>.isZero() <i>⇒ 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.isNegative() // true
|
|
y = new BigNumber(Infinity)
|
|
y.isZero() // false</pre>
|
|
<p>Note: <code>n == 0</code> can be used if <code>n >= Number.MIN_VALUE</code>.</p>
|
|
|
|
|
|
|
|
<h5 id="minus">
|
|
minus<code class='inset'>.minus(n [, base]) <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>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>⇒ 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="times">
|
|
multipliedBy<code class='inset'>.times(n [, base]) <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>
|
|
Returns a BigNumber whose value is the value of this BigNumber multiplied by <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.multipliedBy(3) // '1.8'
|
|
BigNumber('7e+500').times(y) // '1.26e+501'
|
|
x.multipliedBy('-a', 16) // '-6'</pre>
|
|
|
|
|
|
|
|
<h5 id="neg">negated<code class='inset'>.negated() <i>⇒ 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.negated() // '1.3'</pre>
|
|
|
|
|
|
|
|
<h5 id="plus">plus<code class='inset'>.plus(n [, base]) <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>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) // '1.1'
|
|
x.plus('0.1', 8) // '0.225'</pre>
|
|
|
|
|
|
|
|
<h5 id="sd">
|
|
precision<code class='inset'>.sd([d [, rm]]) <i>⇒ BigNumber|number</i></code>
|
|
</h5>
|
|
<p>
|
|
<code>d</code>: <i>number|boolean</i>: integer, <code>1</code> to <code>1e+9</code>
|
|
inclusive, or <code>true</code> or <code>false</code><br />
|
|
<code>rm</code>: <i>number</i>: integer, <code>0</code> to <code>8</code> inclusive.
|
|
</p>
|
|
<p>
|
|
If <code>d</code> is a number, returns a BigNumber whose value is the value of this BigNumber
|
|
rounded to a precision of <code>d</code> significant digits using rounding mode
|
|
<code>rm</code>.
|
|
</p>
|
|
<p>
|
|
If <code>d</code> is omitted or is <code>null</code> or <code>undefined</code>, the return
|
|
value is the number of significant digits of the value of this BigNumber, or <code>null</code>
|
|
if the value of this BigNumber is ±<code>Infinity</code> or <code>NaN</code>.
|
|
</p>
|
|
<p>
|
|
If <code>d</code> is <code>true</code> then any trailing zeros of the integer
|
|
part of a number are counted as significant digits, otherwise they are not.
|
|
</p>
|
|
<p>
|
|
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>
|
|
Throws if <code>d</code> or <code>rm</code> is invalid. See <a href='#Errors'>Errors</a>.
|
|
</p>
|
|
<pre>
|
|
x = new BigNumber(9876.54321)
|
|
x.precision(6) // '9876.54'
|
|
x.sd() // 9
|
|
x.precision(6, BigNumber.ROUND_UP) // '9876.55'
|
|
x.sd(2) // '9900'
|
|
x.precision(2, 1) // '9800'
|
|
x // '9876.54321'
|
|
y = new BigNumber(987000)
|
|
y.precision() // 3
|
|
y.sd(true) // 6</pre>
|
|
|
|
|
|
|
|
<h5 id="shift">shiftedBy<code class='inset'>.shiftedBy(n) <i>⇒ 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 by <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>
|
|
<p>
|
|
Throws if <code>n</code> is invalid. See <a href='#Errors'>Errors</a>.
|
|
</p>
|
|
<pre>
|
|
x = new BigNumber(1.23)
|
|
x.shiftedBy(3) // '1230'
|
|
x.shiftedBy(-3) // '0.00123'</pre>
|
|
|
|
|
|
|
|
<h5 id="sqrt">squareRoot<code class='inset'>.sqrt() <i>⇒ 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> settings.
|
|
</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="toE">
|
|
toExponential<code class='inset'>.toExponential([dp [, rm]]) <i>⇒ 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>
|
|
Throws if <code>dp</code> or <code>rm</code> is invalid. See <a href='#Errors'>Errors</a>.
|
|
</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>⇒ 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>
|
|
Throws if <code>dp</code> or <code>rm</code> is invalid. See <a href='#Errors'>Errors</a>.
|
|
</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[, format]]]) <i>⇒ 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<br />
|
|
<code>format</code>: <i>object</i>: see <a href='#format'><code>FORMAT</code></a>
|
|
</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 <code>format</code> object.
|
|
</p>
|
|
<p>
|
|
See <a href='#format'><code>FORMAT</code></a> and the examples below for the properties of the
|
|
<code>format</code> object, their types, and their usage. A formatting object may contain
|
|
some or all of the recognised properties.
|
|
</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.<br />
|
|
If <code>format</code> is omitted or is <code>null</code> or <code>undefined</code>, the
|
|
<a href='#format'><code>FORMAT</code></a> object is used.
|
|
</p>
|
|
<p>
|
|
Throws if <code>dp</code>, <code>rm</code> or <code>format</code> is invalid. See
|
|
<a href='#Errors'>Errors</a>.
|
|
</p>
|
|
<pre>
|
|
fmt = {
|
|
prefix: '',
|
|
decimalSeparator: '.',
|
|
groupSeparator: ',',
|
|
groupSize: 3,
|
|
secondaryGroupSize: 0,
|
|
fractionGroupSeparator: ' ',
|
|
fractionGroupSize: 0,
|
|
suffix: ''
|
|
}
|
|
|
|
x = new BigNumber('123456789.123456789')
|
|
|
|
// Set the global formatting options
|
|
BigNumber.config({ FORMAT: fmt })
|
|
|
|
x.toFormat() // '123,456,789.123456789'
|
|
x.toFormat(3) // '123,456,789.123'
|
|
|
|
// If a reference to the object assigned to FORMAT has been retained,
|
|
// the format properties can be changed directly
|
|
fmt.groupSeparator = ' '
|
|
fmt.fractionGroupSize = 5
|
|
x.toFormat() // '123 456 789.12345 6789'
|
|
|
|
// Alternatively, pass the formatting options as an argument
|
|
fmt = {
|
|
prefix: '=> ',
|
|
decimalSeparator: ',',
|
|
groupSeparator: '.',
|
|
groupSize: 3,
|
|
secondaryGroupSize: 2
|
|
}
|
|
|
|
x.toFormat() // '123 456 789.12345 6789'
|
|
x.toFormat(fmt) // '=> 12.34.56.789,123456789'
|
|
x.toFormat(2, fmt) // '=> 12.34.56.789,12'
|
|
x.toFormat(3, BigNumber.ROUND_UP, fmt) // '=> 12.34.56.789,124'</pre>
|
|
|
|
|
|
|
|
<h5 id="toFr">
|
|
toFraction<code class='inset'>.toFraction([maximum_denominator])
|
|
<i>⇒ [BigNumber, BigNumber]</i></code>
|
|
</h5>
|
|
<p>
|
|
<code>maximum_denominator</code>:
|
|
<i>number|string|BigNumber</i>: integer >= <code>1</code> and <=
|
|
<code>Infinity</code>
|
|
</p>
|
|
<p>
|
|
Returns an array of two BigNumbers 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>maximum_denominator</code>.
|
|
</p>
|
|
<p>
|
|
If a <code>maximum_denominator</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>
|
|
Throws if <code>maximum_denominator</code> is invalid. See <a href='#Errors'>Errors</a>.
|
|
</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>⇒ string</i></code></h5>
|
|
<p>As <a href='#valueOf'><code>valueOf</code></a>.</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>⇒ number</i></code></h5>
|
|
<p>Returns the value of this BigNumber as a JavaScript number primitive.</p>
|
|
<p>
|
|
This method is identical to using type coercion with the unary plus operator.
|
|
</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.toNumber() // -Infinity
|
|
1 / +z // -Infinity</pre>
|
|
|
|
|
|
|
|
<h5 id="toP">
|
|
toPrecision<code class='inset'>.toPrecision([sd [, rm]]) <i>⇒ 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>
|
|
Throws if <code>sd</code> or <code>rm</code> is invalid. See <a href='#Errors'>Errors</a>.
|
|
</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>⇒ string</i></code></h5>
|
|
<p>
|
|
<code>base</code>: <i>number</i>: integer, <code>2</code> to <code>ALPHABET.length</code>
|
|
inclusive (see <a href='#alphabet'><code>ALPHABET</code></a>).
|
|
</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>, and using the default base conversion alphabet
|
|
(see <a href='#alphabet'><code>ALPHABET</code></a>), values from <code>10</code> to
|
|
<code>35</code> are represented by <code>a-z</code>
|
|
(as with <code>Number.prototype.toString</code>).
|
|
</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> settings.
|
|
</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>
|
|
Throws if <code>base</code> is invalid. See <a href='#Errors'>Errors</a>.
|
|
</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="valueOf">valueOf<code class='inset'>.valueOf() <i>⇒ string</i></code></h5>
|
|
<p>
|
|
As <a href='#toS'><code>toString</code></a>, 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>
|
|
</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>
|
|
The above properties are best considered to be read-only. In early versions of this library it
|
|
was okay to change the exponent of a BigNumber by writing to its exponent property directly,
|
|
but this is no longer reliable as the value of the first element of the coefficient array is
|
|
now dependent on the exponent.
|
|
</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>
|
|
|
|
|
|
|
|
<h4 id="zero-nan-infinity">Zero, NaN and Infinity</h4>
|
|
<p>
|
|
The table below shows how ±<code>0</code>, <code>NaN</code> and
|
|
±<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>±0</td>
|
|
<td><code>[0]</code></td>
|
|
<td><code>0</code></td>
|
|
<td><code>±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>±Infinity</td>
|
|
<td><code>null</code></td>
|
|
<td><code>null</code></td>
|
|
<td><code>±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 table below shows the errors that are thrown.</p>
|
|
<p>
|
|
The errors are generic <code>Error</code> objects whose message begins
|
|
<code>'[BigNumber Error]'</code>.
|
|
</p>
|
|
<table class='error-table'>
|
|
<tr>
|
|
<th>Method</th>
|
|
<th>Throws</th>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan=6>
|
|
<code>BigNumber</code><br />
|
|
<code>comparedTo</code><br />
|
|
<code>dividedBy</code><br />
|
|
<code>dividedToIntegerBy</code><br />
|
|
<code>isEqualTo</code><br />
|
|
<code>isGreaterThan</code><br />
|
|
<code>isGreaterThanOrEqualTo</code><br />
|
|
<code>isLessThan</code><br />
|
|
<code>isLessThanOrEqualTo</code><br />
|
|
<code>minus</code><br />
|
|
<code>modulo</code><br />
|
|
<code>plus</code><br />
|
|
<code>multipliedBy</code>
|
|
</td>
|
|
<td>Base not a primitive number</td>
|
|
</tr>
|
|
<tr>
|
|
<td>Base not an integer</td>
|
|
</tr>
|
|
<tr>
|
|
<td>Base out of range</td>
|
|
</tr>
|
|
<tr>
|
|
<td>Number primitive has more than 15 significant digits<sup>*</sup></td>
|
|
</tr>
|
|
<tr>
|
|
<td>Not a base... number<sup>*</sup></td>
|
|
</tr>
|
|
<tr>
|
|
<td>Not a number<sup>*</sup></td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>clone</code></td>
|
|
<td>Object expected</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan=24><code>config</code></td>
|
|
<td>Object expected</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>DECIMAL_PLACES</code> not a primitive number</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>DECIMAL_PLACES</code> not an integer</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>DECIMAL_PLACES</code> out of range</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>ROUNDING_MODE</code> not a primitive number</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>ROUNDING_MODE</code> not an integer</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>ROUNDING_MODE</code> out of range</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>EXPONENTIAL_AT</code> not a primitive number</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>EXPONENTIAL_AT</code> not an integer</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>EXPONENTIAL_AT</code> out of range</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>RANGE</code> not a primitive number</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>RANGE</code> not an integer</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>RANGE</code> cannot be zero</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>RANGE</code> cannot be zero</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>CRYPTO</code> not true or false</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>crypto</code> unavailable</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>MODULO_MODE</code> not a primitive number</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>MODULO_MODE</code> not an integer</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>MODULO_MODE</code> out of range</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>POW_PRECISION</code> not a primitive number</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>POW_PRECISION</code> not an integer</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>POW_PRECISION</code> out of range</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>FORMAT</code> not an object</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>ALPHABET</code> invalid</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan=3>
|
|
<code>decimalPlaces</code><br />
|
|
<code>precision</code><br />
|
|
<code>random</code><br />
|
|
<code>shiftedBy</code><br />
|
|
<code>toExponential</code><br />
|
|
<code>toFixed</code><br />
|
|
<code>toFormat</code><br />
|
|
<code>toPrecision</code>
|
|
</td>
|
|
<td>Argument not a primitive number</td>
|
|
</tr>
|
|
<tr>
|
|
<td>Argument not an integer</td>
|
|
</tr>
|
|
<tr>
|
|
<td>Argument out of range</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<code>decimalPlaces</code><br />
|
|
<code>precision</code>
|
|
</td>
|
|
<td>Argument not true or false</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>exponentiatedBy</code></td>
|
|
<td>Argument not an integer</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>isBigNumber</code></td>
|
|
<td>Invalid BigNumber<sup>*</sup></td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<code>minimum</code><br />
|
|
<code>maximum</code>
|
|
</td>
|
|
<td>Not a number<sup>*</sup></td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<code>random</code>
|
|
</td>
|
|
<td>crypto unavailable</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<code>toFormat</code>
|
|
</td>
|
|
<td>Argument not an object</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan=2><code>toFraction</code></td>
|
|
<td>Argument not an integer</td>
|
|
</tr>
|
|
<tr>
|
|
<td>Argument out of range</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan=3><code>toString</code></td>
|
|
<td>Base not a primitive number</td>
|
|
</tr>
|
|
<tr>
|
|
<td>Base not an integer</td>
|
|
</tr>
|
|
<tr>
|
|
<td>Base out of range</td>
|
|
</tr>
|
|
</table>
|
|
<p><sup>*</sup>Only thrown if <code>BigNumber.DEBUG</code> is <code>true</code>.</p>
|
|
<p>To determine if an exception is a BigNumber Error:</p>
|
|
<pre>
|
|
try {
|
|
// ...
|
|
} catch (e) {
|
|
if (e instanceof Error && e.message.indexOf('[BigNumber Error]') === 0) {
|
|
// ...
|
|
}
|
|
}</pre>
|
|
|
|
|
|
|
|
<h4 id="type-coercion">Type coercion</h4>
|
|
<p>
|
|
To prevent the accidental use of a BigNumber in primitive number operations, or the
|
|
accidental addition of a BigNumber to a string, the <code>valueOf</code> method can be safely
|
|
overwritten as shown below.
|
|
</p>
|
|
<p>
|
|
The <a href='#valueOf'><code>valueOf</code></a> method is the same as the
|
|
<a href='#toJSON'><code>toJSON</code></a> method, and both are the same as the
|
|
<a href='#toS'><code>toString</code></a> method except they do not take a <code>base</code>
|
|
argument and they include the minus sign for negative zero.
|
|
</p>
|
|
<pre>
|
|
BigNumber.prototype.valueOf = function () {
|
|
throw Error('valueOf called!')
|
|
}
|
|
|
|
x = new BigNumber(1)
|
|
x / 2 // '[BigNumber Error] valueOf called!'
|
|
x + 'abc' // '[BigNumber Error] valueOf called!'
|
|
</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>
|
|
|
|
</body>
|
|
</html>
|