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Minor doc clean-up. v1.0.1
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<title>decimal.js API</title>
v3.0.0
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<body>
v3.0.0
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<div class="nav">
<a class='nav-title' href="#">API</a>
<b>CONSTRUCTOR</b>
<ul><li><a href="#decimal">Decimal</a></li></ul>
<a href="#methods">Methods</a>
<ul>
<li><a href="#Dconfig">config</a></li>
<li><a href="#Dconstr">constructor</a></li>
<li><a href="#Dexp"> exp</a></li>
<li><a href="#Dln"> ln</a></li>
<li><a href="#Dlog"> log</a></li>
<li><a href="#Dmax"> max</a></li>
<li><a href="#Dmin"> min</a></li>
<li><a href="#DnoCon"> noConflict</a></li>
<li><a href="#Dpow"> pow</a></li>
<li><a href="#Drand"> random</a></li>
<li><a href="#Dsqrt"> sqrt</a></li>
</ul>
<a href="#constructor-properties">Properties</a>
<ul>
<li><a href="#one" >ONE</a></li>
<li class='spacer'>&nbsp;</li>
<li><a href="#precision">precision</a></li>
<li><a href="#rounding" >rounding</a></li>
<li><a href="#minE" >minE</a></li>
<li><a href="#maxE" >maxE</a></li>
<li><a href="#toExpNeg" >toExpNeg</a></li>
<li><a href="#toExpPos" >toExpPos</a></li>
<li><a href="#errors" >errors</a></li>
<li><a href="#modulo" >modulo</a></li>
<li><a href="#crypto" >crypto</a></li>
v4.0.0 Updated API doc and image re format
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<li><a href="#format" >format</a></li>
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<li class='spacer'>&nbsp;</li>
<li><a href="#modes">ROUND_UP</a></li>
<li><a href="#modes">ROUND_DOWN</a></li>
<li><a href="#modes">ROUND_CEIL</a></li>
<li><a href="#modes">ROUND_FLOOR</a></li>
<li><a href="#modes">ROUND_HALF_UP</a></li>
<li><a href="#modes">ROUND_HALF_DOWN</a></li>
<li><a href="#modes">ROUND_HALF_EVEN</a></li>
<li><a href="#modes">ROUND_HALF_CEIL</a></li>
<li><a href="#modes">ROUND_HALF_FLOOR</a></li>
<li><a href="#modes">EUCLID</a></li>
</ul>
<b> INSTANCE </b>
<a href="#prototype-methods">Methods</a>
<ul>
<li><a href="#abs" >absoluteValue </a><span>abs</span> </li>
<li><a href="#ceil" >ceil </a> </li>
<li><a href="#cmp" >comparedTo </a><span>cmp</span> </li>
<li><a href="#dp" >decimalPlaces </a><span>dp</span> </li>
<li><a href="#div" >dividedBy </a><span>div</span> </li>
<li><a href="#divInt" >dividedToIntegerBy </a><span>divToInt</span></li>
<li><a href="#eq" >equals </a><span>eq</span> </li>
<li><a href="#exp" >exponential </a><span>exp</span> </li>
<li><a href="#floor" >floor </a> </li>
<li><a href="#gt" >greaterThan </a><span>gt</span> </li>
<li><a href="#gte" >greaterThanOrEqualTo</a><span>gte</span> </li>
<li><a href="#isF" >isFinite </a> </li>
<li><a href="#isInt" >isInteger </a><span>isInt</span> </li>
<li><a href="#isNaN" >isNaN </a> </li>
<li><a href="#isNeg" >isNegative </a><span>isNeg</span> </li>
<li><a href="#isZ" >isZero </a> </li>
<li><a href="#lt" >lessThan </a><span>lt</span> </li>
<li><a href="#lte" >lessThanOrEqualTo </a><span>lte</span> </li>
<li><a href="#log" >logarithm </a><span>log</span> </li>
<li><a href="#minus" >minus </a> </li>
<li><a href="#mod" >modulo </a><span>mod</span> </li>
<li><a href="#ln" >naturalLogarithm </a><span>ln</span> </li>
<li><a href="#neg" >negated </a><span>neg</span> </li>
<li><a href="#plus" >plus </a> </li>
<li><a href="#sd" >precision </a><span>sd</span> </li>
<li><a href="#round" >round </a> </li>
<li><a href="#sqrt" >squareRoot </a><span>sqrt</span> </li>
<li><a href="#times" >times </a> </li>
<li><a href="#toDP" >toDecimalPlaces </a><span>toDP</span> </li>
<li><a href="#toE" >toExponential </a> </li>
<li><a href="#toFi" >toFixed </a> </li>
<li><a href="#toFo" >toFormat </a> </li>
<li><a href="#toFr" >toFraction </a> </li>
<li><a href="#toJSON" >toJSON </a> </li>
<li><a href="#toNear" >toNearest </a> </li>
<li><a href="#toNum" >toNumber </a> </li>
<li><a href="#pow" >toPower </a><span>pow</span> </li>
<li><a href="#toP" >toPrecision </a> </li>
<li><a href="#toSD" >toSignificantDigits </a><span>toSD</span> </li>
<li><a href="#toS" >toString </a> </li>
<li><a href="#trunc" >truncated </a><span>trunc</span> </li>
<li><a href="#valueOf">valueOf </a> </li>
</ul>
<a href="#instance-properties">Properties</a>
<ul>
<li><a href="#coefficient">c: coefficient</a></li>
<li><a href="#exponent" >e: exponent</a></li>
<li><a href="#sign" >s: sign</a></li>
</ul>
<a href="#zero-nan-infinity">Zero, NaN &amp; Infinity</a>
<a href="#Errors">Errors</a>
<a class='end' href="#faq">FAQ</a>
</div>
<div class="container">
<h1>decimal<span id='js'>.js</span></h1>
<p>An arbitrary-precision Decimal type for JavaScript.</p>
<p><a href='https://github.com/MikeMcl/decimal.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>
See the <a href='https://github.com/MikeMcl/decimal.js'>README</a> on GitHub for a quick-start
introduction.
</p>
<p>
In all examples below, <code>var</code> and semicolons are not shown, and if a commented-out
value is in quotes it means <code>toString</code> has been called on the preceding expression.
</p><br />
<p>
When the library is loaded, it defines a single function object,
<a href='#decimal'><code>Decimal</code></a>, the constructor of Decimal numbers.
</p>
<p>
Multiple Decimal constructors can be created, each with their own independent configuration,
e.g. precision and range, which applies to all Decimal numbers created from it.
</p>
<p>
A new Decimal constructor is created by calling the
<code><a href='#Dconstr'>constructor</a></code> method of an already existing Decimal
constructor - when the library is loaded this will be
<a href='#decimal'><code>Decimal</code></a>.
</p>
<h3 class='end'>CONSTRUCTOR</h3>
<h5 id="decimal">
Decimal<code class='inset'>Decimal(value [, base]) <i>&rArr; Decimal</i></code>
</h5>
<dl>
<dt><code>value</code></dt>
<dd><i>number|string|Decimal</i></dd>
<dd>A numeric value.</dd>
<dd>
Legitimate values include &plusmn;<code>0</code>, &plusmn;<code>Infinity</code> and
<code>NaN</code>.
</dd>
<dd>
Values of type <em>number</em> with more than 15 significant digits are considered invalid
(if <a href='#errors'><code>errors</code></a> is true) as calling
<code><a href='#toS'>toString</a></code> or <code><a href='#valueOf'>valueOf</a></code> on
such numbers may not result in the intended value.
<pre>console.log( 823456789123456.3 ); // 823456789123456.2</pre>
</dd>
<dd>
There is no limit to the number of digits of a value of type <em>string</em> (other than
that of JavaScript's maximum array size).
</dd>
<dd>
See <a href='#minE'>minE</a> and <a href='#maxE'>maxE</a> for the allowable range of a
Decimal in terms of exponent limits.
</dd>
<dd>
Decimal string values may be in exponential, as well as normal (fixed-point) notation.
Non-decimal values must be in normal notation.
</dd>
<dd>
String values in hexadecimal literal form, e.g. <code>'0xff'</code>, are invalid, and string
values in octal literal form will be interpreted as decimals, e.g. <code>'011'</code> is
interpreted as 11, not 9.
</dd>
<dd>Values in any base may have fraction digits.</dd>
<dd>
For bases from 10 to 36, lower and/or upper case letters can be used to represent values
from 10 to 35.
</dd>
<dd>
For bases above 36, <code>a-z</code> represents values from 10 to 35, <code>A-Z</code> from
36 to 61, and <code>$</code> and <code>_</code> represent 62 and 63 respectively.
</dd>
</dl>
<dl>
<dt><code>base</code></dt>
<dd>
<i>number</i>: integer, <code>2</code> to <code>64</code> inclusive
</dd>
<dd>The base of <code>value</code>.</dd>
<dd>
If <code>base</code> is omitted or is <code>null</code> or undefined, base 10 is assumed.
</dd>
</dl>
<p>Returns a new instance of a Decimal object.</p>
<p>
If a base is specified, <code>value</code> is rounded according to the current
<a href='#precision'><code>precision</code></a> and
<a href='#rounding'><code>rounding</code></a> settings.
</p>
<p>
See <a href='#Errors'>Errors</a> for the treatment of an invalid <code>value</code> or
<code>base</code>.
</p>
<pre>
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x = new Decimal(9) // '9'
y = new Decimal(x) // '9'
// 'new' is optional if errors is false
Decimal(435.345)
new Decimal('5032485723458348569331745.33434346346912144534543')
new Decimal('4.321e+4') // '43210'
new Decimal('-735.0918e-430') // '-7.350918e-428'
new Decimal('5.6700000') // '5.67'
new Decimal(Infinity) // 'Infinity'
new Decimal(NaN) // 'NaN'
new Decimal('.5') // '0.5'
new Decimal('+2') // '2'
new Decimal(-10110100.1, 2) // '-180.5'
new Decimal('123412421.234324', 5) // '607236.557696'
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new Decimal('ff.8', 16) // '255.5'</pre>
<p>
The following throws <code>'not a base 2 number'</code> if
<a href='#errors'><code>errors</code></a> is true, otherwise it returns a Decimal with value
<code>NaN</code>.
</p>
<pre>new Decimal(9, 2)</pre>
<p>
The following throws <code>'number type has more than 15 significant digits'</code> if
<a href='#errors'><code>errors</code></a> is true, otherwise it returns a Decimal with value
<code>96517860459076820</code>.
</p>
<pre>new Decimal(96517860459076817.4395)</pre>
<p>
The following throws <code>'not a number'</code> if <a href='#errors'><code>errors</code></a>
is true, otherwise it returns a Decimal with value <code>NaN</code>.
</p>
<pre>new Decimal('blurgh')</pre>
<p>
A value is rounded only if a base is specified.
</p>
<pre>Decimal.config({ precision: 5 })
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new Decimal(1.23456789) // '1.23456789'
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new Decimal(1.23456789, 10) // '1.2346'</pre>
<h4 id="methods">Methods</h4>
<p>The static methods of a Decimal constructor.</p>
<h5 id="Dconfig">
config<code class='inset'>.config(object) <i>&rArr; Decimal constructor</i></code>
</h5>
<p><code>object</code>: <i>object</i></p>
<p>Configures the 'global' settings for this particular Decimal constructor.</p>
<p>Returns this Decimal constructor.</p>
<p>
The configuration object, <code>object</code>, can contain some or all of the properties
described in detail at <a href="#constructor-properties">Properties</a> and shown in the
example below.
</p>
<p>
The values of the configuration object properties are checked for validity and then stored as
equivalently-named properties of this Decimal constructor.
</p>
<p>
If the value to be assigned to any of the properties is <code>null</code> or undefined
it is ignored.<br />See <a href='#Errors'>Errors</a> for the treatment of invalid values.
</p>
<pre>
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// Defaults
Decimal.config({
precision: 20,
rounding: 4,
toExpNeg: -7,
toExpPos: 21,
minE: -9e15,
maxE: 9e15,
errors: true,
crypto: false,
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modulo: 1,
format: {
decimalSeparator : '.',
groupSeparator : ',',
groupSize : 3,
secondaryGroupSize : 0,
fractionGroupSeparator : '\xA0', // non-breaking space
fractionGroupSize : 0
}
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})</pre>
<p>
The properties of a Decimal constructor can also be set by direct assignment, but that will
obviously by-pass the validity checking that this method performs.
</p>
<h5 id="Dconstr">
constructor
<code class='inset'>.constructor([object]) <i>&rArr; Decimal constructor</i></code>
</h5>
<p><code>object</code>: <i>object</i></p>
<p>
Returns a new independent Decimal constructor with configuration settings as described by
<code>object</code> (see <a href='#Dconfig'><code>config</code></a>).
</p>
<pre>Decimal.config({ precision: 5 })
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D9 = Decimal.constructor({ precision: 9 })
x = new Decimal(1)
y = new D9(1)
x.div(3) // 0.33333
y.div(3) // 0.333333333
// D9 = Decimal.constructor({ precision: 9 }) is equivalent to:
D9 = Decimal.constructor()
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D9.config({ precision: 9 })</pre>
<p>
It is not inefficient in terms of memory usage to use multiple Decimal constructors as
functions are shared between them.
</p>
<p>
<code>constructor</code> is a factory method so it is not necessary or desirable to use
<code>new</code> but it will do no harm.
</p>
<pre>D = new Decimal.constructor()</pre>
<h5 id="Dexp">exp<code class='inset'>.exp() <i>&rArr; Decimal</i></code></h5>
<p>See <code><a href='#exp'>exponential</a></code>.</p>
<pre>x = Decimal.exp(3)
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y = new Decimal(3).exp()
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x.equals(y) // true</pre>
<h5 id="Dln">ln<code class='inset'>.ln() <i>&rArr; Decimal</i></code></h5>
<p>See <code><a href='#ln'>naturalLogarithm</a></code>.</p>
<pre>x = Decimal.ln(4.321)
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y = new Decimal(4.321).ln()
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x.equals(y) // true</pre>
<h5 id="Dlog">log<code class='inset'>.log(arg [, base]) <i>&rArr; Decimal</i></code></h5>
<p>
<code>arg</code>: <i>number|string|Decimal</i><br />
<code>base</code>: <i>number|string|Decimal</i><br />
<i>See <code><a href="#decimal">Decimal</a></code> for further parameter details.</i>
</p>
<p>See <code><a href='#log'>logarithm</a></code>.</p>
<pre>x = Decimal.log(100, 2.5)
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y = new Decimal(100).log(2.5)
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x.equals(y) // true</pre>
<h5 id="Dmax">
max<code class='inset'>.max([arg1 [, arg2, ...]]) <i>&rArr; Decimal</i></code>
</h5>
<p>
<code>arg1</code>, <code>arg2</code>, ... : <i>number|string|Decimal</i><br />
<i>See <code><a href="#decimal">Decimal</a></code> for further parameter details.</i>
</p>
<p>
Returns a new Decimal whose value is the maximum of <code>arg1</code>, <code>arg2</code>,... .
</p>
<p>Alternatively, the argument to this method can be an array of values.</p>
<pre>x = new Decimal('3257869345.0378653')
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Decimal.max(4e9, x, '123456789.9') // '4000000000'
arr = [12, '13', new Decimal(14)]
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Decimal.max(arr) // '14'</pre>
<h5 id="Dmin">
min<code class='inset'>.min([arg1 [, arg2, ...]]) <i>&rArr; Decimal</i></code>
</h5>
<p>
<code>arg1</code>, <code>arg2</code>, ... : <i>number|string|Decimal</i><br />
<i>See <code><a href="#decimal">Decimal</a></code> for further parameter details.</i>
</p>
<p>
Returns a new Decimal whose value is the minimum of <code>arg1</code>, <code>arg2</code>,... .
</p>
<p>Alternatively, the argument to this method can be an array of values.</p>
<pre>x = new Decimal('3257869345.0378653')
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Decimal.min(4e9, x, '123456789.9') // '123456789.9'
arr = [2, new Decimal(-14), '-15.9999', -12]
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Decimal.min(arr) // '-15.9999'</pre>
<h5 id="DnoCon">
noConflict<code class='inset'>.noConflict() <i>&rArr; Decimal constructor</i></code>
</h5>
<p><i>Browsers only.</i></p>
<p>
Reverts the <code>Decimal</code> variable to the value it had before this library
was loaded and returns a reference to the original Decimal constructor so it can be assigned
to a variable with a different name.
</p>
<pre>
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&lt;script&gt; Decimal = 1 &lt;/script&gt;
&lt;script src='/path/to/decimal.js'&gt;&lt;/script&gt;
&lt;script&gt;
x = new Decimal(2) // '2'
D = Decimal.noConflict()
Decimal // 1
y = new D(3) // '3'
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&lt;/script&gt;</pre>
<h5 id="Dpow">pow<code class='inset'>.pow(base, exponent) <i>&rArr; Decimal</i></code></h5>
<p>
<code>base</code>: <i>number|string|Decimal</i><br />
<code>exponent</code>: <i>number|string|Decimal</i><br />
<i>See <code><a href="#decimal">Decimal</a></code> for further parameter details.</i>
</p>
<p>See <code><a href="#pow">toPower</a></code>.</p>
<pre>x = Decimal.pow(3257.4, 17.01)
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y = new Decimal(3257.4).pow(17.01)
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x.equals(y) // true</pre>
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v3.0.0
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<h5 id="Drand">
random<code class='inset'>.random([dp]) <i>&rArr; Decimal</i></code>
</h5>
<p><code>dp</code>: <i>number</i>: integer, 0 to 1e+9 inclusive</p>
<p>
Returns a new Decimal 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></a> decimal places (or less if trailing zeros are
produced). If <code>dp</code> is omitted then the number of decimal places will
default to the current <a href='#precision'><code>precision</code></a> setting.
</p>
<p>
Depending on the value of a Decimal constructor's <a href='#crypto'><code>crypto</code></a>
property and the support for the <code>crypto</code> object in the host environment, the
random digits of the return value are generated by either <code>Math.random</code> (fastest),
<code>crypto.getRandomValues</code> (Web Cryptography API in recent browsers) or
<code>crypto.randomBytes</code> (Node.js).
</p>
<p>
If <a href='#crypto'><code>crypto</code></a> is <code>true</code>, i.e. one of the
<code>crypto</code> methods is to be used, the value of a returned Decimal should be
cryptographically-secure and statistically indistinguishable from a random value.
</p>
<pre>Decimal.config({ precision: 10 })
Decimal.random() // '0.4117936847'
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Decimal.random(20) // '0.78193327636914089009'</pre>
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<h5 id="Dsqrt">sqrt<code class='inset'>.sqrt() <i>&rArr; Decimal</i></code></h5>
<p>See <a href='#sqrt'>squareRoot</a>.</p>
<pre>x = Decimal.sqrt('987654321.123456789')
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y = new Decimal('987654321.123456789').sqrt()
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x.equals(y) // true</pre>
<h4 id="constructor-properties">Properties</h4>
<p>
The static properties of a Decimal constructor.
</p>
<h5 id="one">ONE</h5>
<p>A Decimal instance with value one.</p>
<pre>new Decimal(3).times(Decimal.ONE) // '3'</pre>
<h6 id='configProps'>Configuration properties</h6>
<p>
The values of the configuration properties <a href='#precision'><code>precision</code></a>,
<a href='#rounding'><code>rounding</code></a>, <a href='#minE'><code>minE</code></a>,
<a href='#maxE'><code>maxE</code></a>, <a href='#toExpNeg'><code>toExpNeg</code></a>,
<a href='#toExpPos'><code>toExpPos</code></a>, <a href='#errors'><code>errors</code></a>,
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<a href='#modulo'><code>modulo</code></a>, <a href='#crypto'><code>crypto</code></a> and
<a href='#format'><code>format</code></a> are set using the
<a href='#Dconfig'><code>config</code></a> method.
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</p>
<p>
As simple object properties they can be set directly without using
<a href='#Dconfig'><code>config</code></a>, and it is fine to do so, but the values assigned
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will not then be checked for validity (the properties of the
<a href='#Dconfig'><code>format</code></a> object are not checked by
<code>config</code>). For example:
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</p>
<pre>Decimal.config({ precision: 0 })
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// 'Decimal Error: config() precision out of range: 0'
Decimal.precision = 0
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// No error is thrown and the results of calculations are unpredictable</pre>
<h5 id="precision">precision</h5>
<p>
<i>number</i>: integer, <code>1</code> to <code>1e+9</code> inclusive<br />
Default value: <code>20</code>
</p>
<p>
The <i>maximum</i> number of significant digits of the result of a calculation or base
conversion.
</p>
<p>
All methods which return a Decimal will round the return value to <code>precision</code>
significant digits except <a href='#abs'><code>absoluteValue</code></a>,
<a href='#ceil'><code>ceil</code></a>, <a href='#floor'><code>floor</code></a>,
<a href='#neg'><code>negated</code></a>, <a href='#round'><code>round</code></a>,
<a href='#toDP'><code>toDecimalPlaces</code></a>, <a href='#toNear'><code>toNearest</code></a>
and <a href='#trunc'><code>truncated</code></a>.
</p>
<p>
A Decimal constructor will also not round to <code>precision</code> unless a base is
specified.
</p>
<pre>Decimal.config({ precision: 5 })
Decimal.precision // 5</pre>
<h5 id="rounding">rounding</h5>
<p>
<i>number</i>: integer, <code>0</code> to <code>8</code> inclusive<br />
Default value: <code>4</code> <a href="#h-up">(<code>ROUND_HALF_UP</code>)</a>
</p>
<p>
The default rounding mode used when rounding the result of a calculation or base conversion to
<code><a href='#precision'>precision</a></code> significant digits, and when rounding the
return value of the <a href='#round'><code>round</code></a>,
<a href='#toDP'><code>toDecimalPlaces</code></a>,
<a href='#toE'><code>toExponential</code></a>, <a href='#toFi'><code>toFixed</code></a>,
<a href='#toFo'><code>toFormat</code></a>, <a href='#toNear'><code>toNearest</code></a>,
<a href='#toP'><code>toPrecision</code></a> and
<a href='#toSD'><code>toSignificantDigits</code></a> methods.
</p>
<p>
The <a href='#modes'>rounding modes</a> are available as enumerated properties of the
constructor.
</p>
<pre>Decimal.config({ rounding: Decimal.ROUND_UP })
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Decimal.config({ rounding: 0 }) // equivalent
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Decimal.rounding // 0</pre>
<h5 id="minE">minE</h5>
<p>
<i>number</i>: integer, <code>-9e15</code> to <code>0</code> inclusive<br />
Default value: <code>-9e15</code>
</p>
<p>
The negative exponent limit, i.e. the exponent value below which underflow to zero occurs.
</p>
<p>
If the <code>Decimal</code> to be returned by a calculation would have an exponent lower than
<code>minE</code> then its value becomes zero.
<p>
JavaScript numbers underflow to zero for exponents below <code>-324</code>.
</p>
<pre>Decimal.config({ minE: -500 })
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Decimal.minE // -500
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new Decimal('1e-500') // '1e-500'
new Decimal('9.9e-501') // '0'
Decimal.config({ minE: -3 })
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new Decimal(0.001) // '0.01' e is -3
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new Decimal(0.0001) // '0' e is -4</pre>
<p>
The smallest possible magnitude of a non-zero Decimal is <code>1e-9000000000000000</code>
</p>
<h5 id="maxE">maxE</h5>
<p>
<i>number</i>: integer, <code>0</code> to <code>9e15</code> inclusive<br />
Default value: <code>9e15</code>
</p>
<p>
The positive exponent limit, i.e. the exponent value above which overflow to
<code>Infinity</code> occurs.
</p>
<p>
If the <code>Decimal</code> to be returned by a calculation would have an exponent higher than
<code>maxE</code> then its value becomes <code>Infinity</code>.
<p>
JavaScript numbers overflow to <code>Infinity</code> for exponents above <code>308</code>.
</p>
<pre>Decimal.config({ maxE: 500 })
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Decimal.maxE // 500
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new Decimal('9.999e500') // '9.999e+500'
new Decimal('1e501') // 'Infinity'
Decimal.config({ maxE: 4 })
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new Decimal(99999) // '99999' e is 4
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new Decimal(100000) // 'Infinity'</pre>
<p>
The largest possible magnitude of a finite Decimal is <code>9.999...e+9000000000000000</code>
</p>
<h5 id="toExpNeg">toExpNeg</h5>
<p>
<i>number</i>: integer, <code>-9e15</code> to <code>0</code> 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>Decimal.config({ toExpNeg: -7 })
Decimal.toExpNeg // -7
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new Decimal(0.00000123) // '0.00000123' e is -6
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new Decimal(0.000000123) // '1.23e-7'
// Always return exponential notation:
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Decimal.config({ toExpNeg: 0 })</pre>
<p>
JavaScript numbers use exponential notation for negative exponents of <code>-7</code> and
below.
</p>
<p>
Regardless of the value of <code>toExpNeg</code>, the
<a href='#toFi'><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>
<p>
Calling <a href='#toS'><code>toString</code></a> with a base argument, e.g.
<code>toString(10)</code>, will also always return normal notation.
</p>
<h5 id="toExpPos">toExpPos</h5>
<p>
<i>number</i>: integer, <code>0</code> to <code>9e15</code> inclusive<br />
Default value: <code>20</code>
</p>
<p>
The positive exponent value at and above which <a href='#toS'><code>toString</code></a>
returns exponential notation.
</p>
<pre>Decimal.config({ toExpPos: 2 })
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Decimal.toExpPos // 2
new Decimal(12.3) // '12.3' e is 1
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new Decimal(123) // '1.23e+2'
// Always return exponential notation:
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Decimal.config({ toExpPos: 0 })</pre>
<p>
JavaScript numbers use exponential notation for positive exponents of <code>20</code> and
above.
</p>
<p>
Regardless of the value of <code>toExpPos</code>, the
<a href='#toFi'><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>
<p>
Calling <a href='#toS'><code>toString</code></a> with a base argument, e.g.
<code>toString(10)</code>, will also always return normal notation.
</p>
<h5 id="errors">errors</h5>
<p>
<i>boolean/number</i>: <code>true, false, 1 or 0</code><br /> Default value: <code>true</code>
</p>
<p>
The value that determines whether Decimal Errors are thrown.<br />
If <code>errors</code> is false, this library will not throw errors.
</p>
<p>See <a href='#Errors'>Errors</a>.</p>
<pre>Decimal.config({ errors: false })
Decimal.errors // false</pre>
<h5 id="modulo">modulo</h5>
<p>
<i>number</i>: integer, <code>0</code> to <code>9</code> inclusive<br />
Default value: <code>1</code> (<code>ROUND_DOWN</code>)
</p>
<p>The modulo mode used when calculating the modulus: <code>a mod n</code>.</p>
<p>
The quotient, <code>q = a / n</code>, is calculated according to the
<a href='#rounding'><code>rounding</code></a> mode that corresponds to the chosen
<code>modulo</code> mode.
</p>
<p>The remainder, <code>r</code>, is calculated as: <code>r = a - n * q</code>.</p>
<p>
The modes that are most commonly used for the modulus/remainder operation are shown in the
following table. Although the other <a href='#rounding'><code>rounding</code></a> modes can
be used, they may not give useful results.
</p>
<table>
<tr><th>Property</th><th>Value</th><th>Description</th></tr>
<tr>
<td>ROUND_UP</td><td class='centre'>0</td>
<td>The remainder is positive if the dividend is negative, else is negative</td>
</tr>
<tr>
<td>ROUND_DOWN</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>ROUND_FLOOR</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>ROUND_HALF_EVEN</td><td class='centre'>6</td>
<td>The <i>IEEE 754</i> remainder function</td>
</tr>
<tr>
<td>EUCLID</td><td class='centre'>9</td>
<td>
The remainder is always positive.<br />
Euclidian division: <code>q = sign(n) * floor(a / abs(n))</code>.
</td>
</tr>
</table>
<p>
The rounding/modulo modes are available as enumerated properties of the Decimal
constructor.
</p>
<pre>Decimal.config({ modulo: Decimal.EUCLID })
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Decimal.config({ modulo: 9 }) // equivalent
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Decimal.modulo // 9</pre>
<h5 id="crypto">crypto</h5>
<p>
<i>boolean/number</i>: <code>true, false, 1 or 0</code><br /> Default value:
<code>false</code>
</p>
<p>
The value that determines whether cryptographically-secure pseudo-random number generation
is used.
</p>
<p>
If <code>crypto</code> is truthy then the <a href='#Drand'><code>random</code></a> method will
generate random digits using <code>crypto.getRandomValues</code> in browsers that support it,
or <code>crypto.randomBytes</code> if using a version of Node.js that supports it.
</p>
<p>
If neither function is supported by the host environment or if <code>crypto</code> is falsey
then the source of randomness will be <code>Math.random</code>. If the <code>crypto</code>
property is set directly (i.e. without using <code>config</code>) to <code>true</code>, then
at the time the <code>random</code> method is called, if
<a href='#errors'><code>errors</code></a> is <code>true</code>, an error will be thrown if the
<code>crypto</code> methods are unavailable.
</p>
</p>
<pre>
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Decimal.crypto // false
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Decimal.config({ crypto: true })</pre>
<p>
If <code>crypto.getRandomValues</code> and <code>crypto.randomBytes</code> are undefined, the
crypto property will remain <code>false</code>.
</p>
<pre>Decimal.crypto // false</pre>
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<h5 id="format">format</h5>
<p><i>object</i>
<p>
The <code>format</code> object configures the format of the string returned by the
<a href='#toFo'><code>toFormat</code></a> method.
</p>
<p>
The example below shows the properties of the <code>format</code> object
that are recognised, and their default values.
</p>
<p>
Unlike setting other properties using <code>config</code>, 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. Only the
<a href='#toFo'><code>toFormat</code></a> method ever references a Decimal constructor's
<code>format</code> object property.
</p>
<p>
See <a href='#toFo'><code>toFormat</code></a> for examples of usage, and of setting
<code>format</code> properties individually and directly without using <code>config</code>.
</p>
<pre>
Decimal.config({
format : {
// the decimal separator
decimalSeparator : '.',
// the grouping separator of the integer part of the number
groupSeparator : ',',
// the primary grouping size of the integer part of the number
groupSize : 3,
// the secondary grouping size of the integer part of the number
secondaryGroupSize : 0,
// the grouping separator of the fraction part of the number
fractionGroupSeparator : ' ',
// the grouping size of the fraction part of the number
fractionGroupSize : 0
}
});</pre>
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<h6 id="modes">Rounding modes</h6>
<p>
The library's enumerated rounding modes are stored as properties of a Decimal constructor.
<br />They are not referenced internally by the library itself.
</p>
<p>Rounding modes 0 to 6 (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><b>ROUND_UP</b></td><td class='centre'>0</td><td>Rounds away from zero</td></tr>
<tr><td><b>ROUND_DOWN</b></td><td class='centre'>1</td><td>Rounds towards zero</td></tr>
<tr><td><b>ROUND_CEIL</b></td><td class='centre'>2</td><td>Rounds towards Infinity</td></tr>
<tr><td><b>ROUND_FLOOR</b></td><td class='centre'>3</td><td>Rounds towards -Infinity</td></tr>
<tr>
<td><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><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><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><b>ROUND_HALF_CEIL</b></td><td class='centre'>7</td>
<td>Rounds towards nearest neighbour.<br />If equidistant, rounds towards Infinity</td>
</tr>
<tr>
<td><b>ROUND_HALF_FLOOR</b></td><td class='centre'>8</td>
<td>Rounds towards nearest neighbour.<br />If equidistant, rounds towards -Infinity</td>
</tr>
<tr>
<td><b>EUCLID</b></td><td class='centre'>9</td>
<td>Not a rounding mode, see <a href='#modulo'>modulo</a></td>
</tr>
</table>
<pre>Decimal.config({ rounding: Decimal.ROUND_CEIL })
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Decimal.config({ rounding: 2 }) // equivalent
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Decimal.rounding // 2</pre>
<h3>INSTANCE</h3>
<h4 id="prototype-methods">Methods</h4>
<p>The methods inherited by a Decimal instance from its constructor's prototype object.</p>
<p>A Decimal is immutable in the sense that it is not changed by its methods.</p>
<p>Methods that return a Decimal can be chained:</p>
<pre>x = new Decimal(2).times('999.999999999999999').dividedBy(4).ceil()</pre>
<p>Methods do not round their arguments before execution.</p>
<p>
The treatment of &plusmn;<code>0</code>, &plusmn;<code>Infinity</code> and <code>NaN</code>
is consistent with how JavaScript treats these values.
</p>
<p>
Some method names have a shorter alias. (Internally, the library always uses the shorter method
names.)
</p>
<h5 id="abs">absoluteValue<code class='inset'>.abs() <i>&rArr; Decimal</i></code></h5>
<p>
Returns a new Decimal whose value is the absolute value, i.e. the magnitude, of the value of
this Decimal.
</p>
<p>The return value is not rounded.</p>
<pre>
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x = new Decimal(-0.8)
y = x.absoluteValue() // '0.8'
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z = y.abs() // '0.8'</pre>
<h5 id="ceil">ceil<code class='inset'>.ceil() <i>&rArr; Decimal</i></code></h5>
<p>
Returns a new Decimal whose value is the value of this Decimal rounded to a whole number in
the direction of positive <code>Infinity</code>.
</p>
<p>The return value is not rounded to <a href='#precision'><code>precision</code></a>.</p>
<pre>
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x = new Decimal(1.3)
x.ceil() // '2'
y = new Decimal(-1.8)
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y.ceil() // '-1'</pre>
<h5 id="cmp">comparedTo<code class='inset'>.cmp(n [, base]) <i>&rArr; number</i></code></h5>
<p>
<code>n</code>: <i>number|string|Decimal</i><br />
<code>base</code>: <i>number</i><br />
<i>See <code><a href="#decimal">Decimal</a></code> for further parameter details.</i>
</p>
<table>
<tr><th>Returns</th><th>&nbsp;</th></tr>
<tr>
<td class='centre'><code>1</code></td>
<td>If the value of this Decimal 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 Decimal is less than the value of <code>n</code></td>
</tr>
<tr>
<td class='centre'><code>0</code></td>
<td>If this Decimal 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 Decimal or <code>n</code> is <code>NaN</code> </td>
</tr>
</table>
<pre>
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x = new Decimal(Infinity)
y = new Decimal(5)
x.comparedTo(y) // 1
x.comparedTo(x.minus(1)) // 0
y.cmp(NaN) // null
v3.0.0
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y.cmp('110', 2) // -1</pre>
<h5 id="dp">decimalPlaces<code class='inset'>.dp() <i>&rArr; number</i></code></h5>
<p>
Returns the number of decimal places, i.e. the number of digits after the decimal point, of
the value of this Decimal.
</p>
<pre>
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x = new Decimal(1.234)
x.decimalPlaces() // '3'
y = new Decimal(987.654321)
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y.dp() // '6'</pre>
<h5 id="div">dividedBy<code class='inset'>.div(n [, base]) <i>&rArr; Decimal</i></code></h5>
<p>
<code>n</code>: <i>number|string|Decimal</i><br /><code>base</code>: <i>number</i><br />
<i>See <code><a href="#decimal">Decimal</a></code> for further parameter details.</i>
</p>
<p>
Returns a new Decimal whose value is the value of this Decimal divided by <code>n</code>,
rounded to <a href='#precision'><code>precision</code></a> significant digits using rounding
mode <a href='#rounding'><code>rounding</code></a>.
</p>
<pre>
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x = new Decimal(355)
y = new Decimal(113)
x.dividedBy(y) // '3.14159292035398230088'
x.div(5) // '71'
v3.0.0
2014-06-04 23:08:09 +00:00
x.div(47, 16) // '5'</pre>
<h5 id="divInt">
dividedToIntegerBy<code class='inset'>.divToInt(n [, base]) <i>&rArr; Decimal</i></code>
</h5>
<p>
<code>n</code>: <i>number|string|Decimal</i><br /><code>base</code>: <i>number</i><br />
<i>See <code><a href="#decimal">Decimal</a></code> for further parameter details.</i>
</p>
<p>
Return a new Decimal whose value is the integer part of dividing this Decimal by
<code>n</code>, rounded to <code><a href='#precision'>precision</a></code> significant digits
using rounding mode <a href='#rounding'><code>rounding</code></a>.
</p>
<pre>
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x = new Decimal(5)
y = new Decimal(3)
x.dividedToIntegerBy(y) // '1'
x.divToInt(0.7) // '7'
v3.0.0
2014-06-04 23:08:09 +00:00
x.divToInt('0.f', 16) // '5'</pre>
<h5 id="eq">equals<code class='inset'>.eq(n [, base]) <i>&rArr; boolean</i></code></h5>
<p>
<code>n</code>: <i>number|string|Decimal</i><br /><code>base</code>: <i>number</i><br />
<i>See <code><a href="#decimal">Decimal</a></code> for further parameter details.</i>
</p>
<p>
Returns <code>true</code> if the value of this Decimal equals the value of <code>n</code>,
otherwise returns <code>false</code>.<br /> As with JavaScript, <code>NaN</code> does not
equal <code>NaN</code>.
</p>
<p>Note: This method uses the <code>cmp</code> method internally.</p>
<pre>
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0 === 1e-324 // true
x = new Decimal(0)
x.equals('1e-324') // false
new Decimal(-0).eq(x) // true ( -0 === 0 )
new Decimal(255).eq('ff', 16) // true
y = new Decimal(NaN)
v3.0.0
2014-06-04 23:08:09 +00:00
y.equals(NaN) // false</pre>
<h5 id="exp">exponential<code class='inset'>.exp() <i>&rArr; Decimal</i></code></h5>
<p>
Returns a new Decimal whose value is the base <code>e</code> (Euler's number, the base of the
natural logarithm) exponential of the value of this Decimal, rounded to
<a href='#precision'><code>precision</code></a> significant digits using rounding mode
<a href='#rounding'><code>rounding</code></a>.
</p>
<p>
The <code><a href='#ln'>naturalLogarithm</a></code> function is the inverse of this function.
</p>
<pre>
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x = new Decimal(1)
x.exponential() // '2.7182818284590452354'
y = new Decimal(2)
v3.0.0
2014-06-04 23:08:09 +00:00
y.exp() // '7.3890560989306502272'</pre>
<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. (The mathematical result of the
exponential function is non-terminating, unless its argument is <code>0</code>).
</p>
<p>The performance of this method degrades exponentially with increasing digits.</p>
<h5 id="floor">floor<code class='inset'>.floor() <i>&rArr; Decimal</i></code></h5>
<p>
Returns a new Decimal whose value is the value of this Decimal rounded to a whole number in
the direction of negative <code>Infinity</code>.
</p>
<p>The return value is not rounded to <a href='#precision'><code>precision</code></a>.</p>
<pre>
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x = new Decimal(1.8)
x.floor() // '1'
y = new Decimal(-1.3)
v3.0.0
2014-06-04 23:08:09 +00:00
y.floor() // '-2'</pre>
<h5 id="gt">greaterThan<code class='inset'>.gt(n [, base]) <i>&rArr; boolean</i></code></h5>
<p>
<code>n</code>: <i>number|string|Decimal</i><br />
<code>base</code>: <i>number</i><br />
<i>See <code><a href="#decimal">Decimal</a></code> for further parameter details.</i>
</p>
<p>
Returns <code>true</code> if the value of this Decimal is greater than the value of
<code>n</code>, otherwise returns <code>false</code>.
</p>
<p>Note: This method uses the <code>cmp</code> method internally.</p>
<pre>
Minor doc clean-up. v1.0.1
2014-04-07 16:15:36 +00:00
0.1 &gt; (0.3 - 0.2) // true
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x = new Decimal(0.1)
x.greaterThan(Decimal(0.3).minus(0.2)) // false
new Decimal(0).gt(x) // false
v3.0.0
2014-06-04 23:08:09 +00:00
new Decimal(11, 3).gt(11.1, 2) // true</pre>
<h5 id="gte">
greaterThanOrEqualTo<code class='inset'>.gte(n [, base]) <i>&rArr; boolean</i></code>
</h5>
<p>
<code>n</code>: <i>number|string|Decimal</i><br />
<code>base</code>: <i>number</i><br />
<i>See <code><a href="#decimal">Decimal</a></code> for further parameter details.</i>
</p>
<p>
Returns <code>true</code> if the value of this Decimal is greater than or equal to the value
of <code>n</code>, otherwise returns <code>false</code>.
</p>
<p>Note: This method uses the <code>cmp</code> method internally.</p>
<pre>
Minor doc clean-up. v1.0.1
2014-04-07 16:15:36 +00:00
(0.3 - 0.2) &gt;= 0.1 // false
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x = new Decimal(0.3).minus(0.2)
x.greaterThanOrEqualTo(0.1) // true
new Decimal(1).gte(x) // true
v3.0.0
2014-06-04 23:08:09 +00:00
new Decimal(10, 18).gte('i', 36) // true</pre>
<h5 id="isF">isFinite<code class='inset'>.isFinite() <i>&rArr; boolean</i></code></h5>
<p>
Returns <code>true</code> if the value of this Decimal is a finite number, otherwise returns
<code>false</code>.<br />
The only possible non-finite values of a Decimal are <code>NaN</code>, <code>Infinity</code>
and <code>-Infinity</code>.
</p>
<pre>
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x = new Decimal(1)
x.isFinite() // true
y = new Decimal(Infinity)
v3.0.0
2014-06-04 23:08:09 +00:00
y.isFinite() // false</pre>
<p>
Note: The native method <code>isFinite()</code> can be used if
<code>n &lt;= Number.MAX_VALUE</code>.
</p>
<h5 id="isInt">isInteger<code class='inset'>.isInt() <i>&rArr; boolean</i></code></h5>
<p>
Returns <code>true</code> if the value of this Decimal is a whole number, otherwise returns
<code>false</code>.
</p>
<pre>
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x = new Decimal(1)
x.isInteger() // true
y = new Decimal(123.456)
v3.0.0
2014-06-04 23:08:09 +00:00
y.isInt() // false</pre>
<h5 id="isNaN">isNaN<code class='inset'>.isNaN() <i>&rArr; boolean</i></code></h5>
<p>
Returns <code>true</code> if the value of this Decimal is <code>NaN</code>, otherwise returns
<code>false</code>.
</p>
<pre>
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x = new Decimal(NaN)
x.isNaN() // true
y = new Decimal('Infinity')
v3.0.0
2014-06-04 23:08:09 +00:00
y.isNaN() // false</pre>
<p>Note: The native method <code>isNaN()</code> can also be used.</p>
<h5 id="isNeg">isNegative<code class='inset'>.isNeg() <i>&rArr; boolean</i></code></h5>
<p>
Returns <code>true</code> if the value of this Decimal is negative, otherwise returns
<code>false</code>.
</p>
<pre>
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x = new Decimal(-0)
x.isNegative() // true
y = new Decimal(2)
v3.0.0
2014-06-04 23:08:09 +00:00
y.isNeg // false</pre>
<p>Note: <code>n &lt; 0</code> can be used if <code>n &lt;= -Number.MIN_VALUE</code>.</p>
<h5 id="isZ">isZero<code class='inset'>.isZero() <i>&rArr; boolean</i></code></h5>
<p>
Returns <code>true</code> if the value of this Decimal is zero or minus zero, otherwise
returns <code>false</code>.
</p>
<pre>
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x = new Decimal(-0)
x.isZero() && x.isNeg() // true
y = new Decimal(Infinity)
v3.0.0
2014-06-04 23:08:09 +00:00
y.isZero() // false</pre>
<p>Note: <code>n == 0</code> can be used if <code>n &gt;= Number.MIN_VALUE</code>.</p>
<h5 id="lt">lessThan<code class='inset'>.lt(n [, base]) <i>&rArr; boolean</i></code></h5>
<p>
<code>n</code>: <i>number|string|Decimal</i><br /><code>base</code>: <i>number</i><br />
<i>See <code><a href="#decimal">Decimal</a></code> for further parameter details.</i>
</p>
<p>
Returns <code>true</code> if the value of this Decimal is less than the value of
<code>n</code>, otherwise returns <code>false</code>.
</p>
<p>Note: This method uses the <code>cmp</code> method internally.</p>
<pre>
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(0.3 - 0.2) &lt; 0.1 // true
x = new Decimal(0.3).minus(0.2)
x.lessThan(0.1) // false
new Decimal(0).lt(x) // true
v3.0.0
2014-06-04 23:08:09 +00:00
new Decimal(11.1, 2).lt(11, 3) // true</pre>
<h5 id="lte">
lessThanOrEqualTo<code class='inset'>.lte(n [, base]) <i>&rArr; boolean</i></code>
</h5>
<p>
<code>n</code>: <i>number|string|Decimal</i><br /><code>base</code>: <i>number</i><br />
<i>See <code><a href="#decimal">Decimal</a></code> for further parameter details. </i>
</p>
<p>
Returns <code>true</code> if the value of this Decimal is less than or equal to the value of
<code>n</code>, otherwise returns <code>false</code>.
</p>
<p>Note: This method uses the <code>cmp</code> method internally.</p>
<pre>
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0.1 &lt;= (0.3 - 0.2) // false
x = new Decimal(0.1)
x.lessThanOrEqualTo(Decimal(0.3).minus(0.2)) // true
new Decimal(-1).lte(x) // true
v3.0.0
2014-06-04 23:08:09 +00:00
new Decimal(10, 18).lte('i', 36) // true</pre>
<h5 id="log">logarithm<code class='inset'>.log([n [, base]]) <i>&rArr; Decimal</i></code></h5>
<p>
<code>n</code>: <i>number|string|Decimal</i><br />
<code>base</code>: <i>number</i> <i>(This is not the base of the logarithm but the base of
<code>n</code>)</i><br />
<i>See <code><a href="#decimal">Decimal</a></code> for further parameter details. </i>
</p>
<p>
Returns a new Decimal whose value is the base <code>n</code> logarithm of the value of this
Decimal, rounded to <a href='#precision'><code>precision</code></a> significant digits using
rounding mode <a href='#rounding'><code>rounding</code></a>.
</p>
<p>
If <code>n</code> is <code>null</code> or undefined, then the base 10 logarithm of the
value of this Decimal will be returned.
</p>
<pre>
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x = new Decimal(1000)
x.logarithm() // '3'
y = new Decimal(256)
v3.0.0
2014-06-04 23:08:09 +00:00
y.log(2) // '8'</pre>
<p>
The return value will <i>almost always</i> be correctly rounded, i.e. rounded as if the result
was first calculated to an infinite number of correct digits before rounding. If a result is
incorrectly rounded the maximum error will be <code>1</code> <i>ulp</i> (unit in the last
place).
</p>
<p>Logarithms to base <code>2</code> or <code>10</code> will always be correctly rounded.</p>
<p>
See <a href='#pow'><code>toPower</code></a> for the circumstances in which this method may
return an incorrectly rounded result.
</p>
<p>The performance of this method degrades exponentially with increasing digits.</p>
<h5 id="minus">minus<code class='inset'>.minus(n [, base]) <i>&rArr; Decimal</i></code></h5>
<p>
<code>n</code>: <i>number|string|Decimal</i><br />
<code>base</code>: <i>number</i><br />
<i>See <code><a href="#decimal">Decimal</a></code> for further parameter details.</i>
</p>
<p>
Returns a new Decimal whose value is the value of this Decimal minus <code>n</code>, rounded
to <a href='#precision'><code>precision</code></a> significant digits using rounding mode
<a href='#rounding'><code>rounding</code></a>.
</p>
<pre>
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0.3 - 0.1 // 0.19999999999999998
x = new Decimal(0.3)
x.minus(0.1) // '0.2'
v3.0.0
2014-06-04 23:08:09 +00:00
x.minus(0.6, 20) // '0'</pre>
<h5 id="mod">modulo<code class='inset'>.mod(n [, base]) <i>&rArr; Decimal</i></code></h5>
<p>
<code>n</code>: <i>number|string|Decimal</i><br />
<code>base</code>: <i>number</i><br />
<i>See <code><a href="#decimal">Decimal</a></code> for further parameter details.</i>
</p>
<p>
Returns a new Decimal whose value is the value of this Decimal modulo <code>n</code>,
rounded to <a href='#precision'><code>precision</code></a> significant digits using rounding
mode <a href='#rounding'><code>rounding</code></a>.
</p>
<p>
The value returned, and in particular its sign, is dependent on the value of the
<a href='#modulo'><code>modulo</code></a> property of this Decimal's constructor. If it is
<code>1</code> (default value), the result will have the same sign as this Decimal, 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>
See <a href='#modulo'><code>modulo</code></a> for a description of the other modulo modes.
</p>
<pre>
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1 % 0.9 // 0.09999999999999998
x = new Decimal(1)
x.modulo(0.9) // '0.1'
Correct links
2014-04-30 16:24:46 +00:00
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2014-04-02 15:31:40 +00:00
y = new Decimal(33)
Correct links
2014-04-30 16:24:46 +00:00
y.mod('a', 33) // '3'
x = new Decimal(8)
y = new Decimal(-3)
Decimal.modulo = 1
x.mod(y) // '2'
Decimal.modulo = 3
v3.0.0
2014-06-04 23:08:09 +00:00
x.mod(y) // '-1'</pre>
<h5 id="ln">naturalLogarithm<code class='inset'>.ln() <i>&rArr; Decimal</i></code></h5>
<p>
Returns a new Decimal whose value is the natural logarithm of the value of this Decimal,
rounded to <a href='#precision'><code>precision</code></a> significant digits using rounding
mode <a href='#rounding'><code>rounding</code></a>.
</p>
<p>
The natual logarithm is the inverse of the <code><a href='#exp'>exponential</a></code>
function.
</p>
<pre>
Added index.html and images to gh-pages
2014-04-02 15:31:40 +00:00
x = new Decimal(10)
x.naturalLogarithm() // '2.3026'
y = new Decimal('1.23e+30')
v3.0.0
2014-06-04 23:08:09 +00:00
y.ln() // '69.28'</pre>
<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. (The mathematical result of the
natural logarithm function is non-terminating, unless its argument is <code>1</code>).
</p>
<p>
Internally, this method is dependent on a constant whose value is the natural logarithm of
<code>10</code>. This <code>LN10</code> variable in the source code currently has a precision
of <code>1025</code> digits, meaning that this method can accurately calculate up to
<code>1000</code> digits.
</p>
<p>
If more than <code>1000</code> digits is required then the precision of <code>LN10</code>
will need to be increased to <code>25</code> digits more than is required - though, as the
time-taken by this method increases exponentially with increasing digits, it is unlikely to be
viable to calculate over <code>1000</code> digits anyway.
</p>
<h5 id="neg">negated<code class='inset'>.neg() <i>&rArr; Decimal</i></code></h5>
<p>
Returns a new Decimal whose value is the value of this Decimal negated, i.e. multiplied by
<code>-1</code>.
</p>
<p>The return value is not rounded.</p>
<pre>
Added index.html and images to gh-pages
2014-04-02 15:31:40 +00:00
x = new Decimal(1.8)
x.negated() // '-1.8'
y = new Decimal(-1.3)
v3.0.0
2014-06-04 23:08:09 +00:00
y.neg() // '1.3'</pre>
<h5 id="plus">plus<code class='inset'>.plus(n [, base]) <i>&rArr; Decimal</i></code></h5>
<p>
<code>n</code>: <i>number|string|Decimal</i><br />
<code>base</code>: <i>number</i><br />
<i>See <code><a href="#decimal">Decimal</a></code> for further parameter details.</i>
</p>
<p>
Returns a new Decimal whose value is the value of this Decimal plus <code>n</code>, rounded to
<a href='#precision'><code>precision</code></a> significant digits using rounding mode
<a href='#rounding'><code>rounding</code></a>.
</p>
<pre>
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0.1 + 0.2 // 0.30000000000000004
x = new Decimal(0.1)
y = x.plus(0.2) // '0.3'
new Decimal(0.7).plus(x).plus(y) // '1.1'
v3.0.0
2014-06-04 23:08:09 +00:00
x.plus('0.1', 8) // '0.225'</pre>
<h5 id="sd">precision<code class='inset'>.sd([include_zeros]) <i>&rArr; number</i></code></h5>
<p>Returns the number of significant digits of the value of this Decimal.</p>
<p>
If <code>include_zeros</code> is <code>true</code> or <code>1</code> then any trailing zeros
of the integer part of a number are counted as significant digits, otherwise they are not.
</p>
<pre>
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x = new Decimal(1.234)
x.precision() // '4'
y = new Decimal(987000)
y.sd() // '3'
v3.0.0
2014-06-04 23:08:09 +00:00
y.sd(true) // '6'</pre>
<h5 id="round">round<code class='inset'>.round() <i>&rArr; Decimal</i></code></h5>
<p>
Returns a new Decimal whose value is the value of this Decimal rounded to a whole number using
rounding mode <a href='#rounding'><code>rounding</code></a>.
</p>
<p>
To emulate <code>Math.round</code>, set <a href='#rounding'><code>rounding</code></a> to
<code>7</code>, i.e. <a href='#modes'><code>ROUND_HALF_CEIL</code></a>.
</p>
<pre>
v2.0.0
2014-04-10 18:46:16 +00:00
Decimal.config({ rounding: 4 })
x = 1234.5
x.round() // '1235'
Minor doc clean-up. v1.0.1
2014-04-07 16:15:36 +00:00
v2.0.0
2014-04-10 18:46:16 +00:00
Decimal.rounding = Decimal.ROUND_DOWN
x.round() // '1234'
v3.0.0
2014-06-04 23:08:09 +00:00
x // '1234.5'</pre>
<h5 id="sqrt">squareRoot<code class='inset'>.sqrt() <i>&rArr; Decimal</i></code></h5>
<p>
Returns a new Decimal whose value is the square root of this Decimal, rounded to
<a href='#precision'><code>precision</code></a> significant digits using rounding mode
<a href='#rounding'><code>rounding</code></a>.
</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>
<p>
This method is much faster than using the <a href='#pow'><code>toPower</code></a> method with
an exponent of <code>0.5</code>.
</p>
<pre>
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x = new Decimal(16)
x.squareRoot() // '4'
y = new Decimal(3)
y.sqrt() // '1.73205080756887729353'
v3.0.0
2014-06-04 23:08:09 +00:00
y.sqrt().eq( y.pow(0.5) ) // true</pre>
<h5 id="times">times<code class='inset'>.times(n [, base]) <i>&rArr; Decimal</i></code></h5>
<p>
<code>n</code>: <i>number|string|Decimal</i><br />
<code>base</code>: <i>number</i><br />
<i>See <code><a href="#decimal">Decimal</a></code> for further parameter details.</i>
</p>
<p>
Returns a new Decimal whose value is the value of this Decimal times <code>n</code>,
rounded to <a href='#precision'><code>precision</code></a> significant digits using rounding
mode <a href='#rounding'><code>rounding</code></a>.
</p>
<pre>
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0.6 * 3 // 1.7999999999999998
x = new Decimal(0.6)
y = x.times(3) // '1.8'
new Decimal('7e+500').times(y) // '1.26e+501'
v3.0.0
2014-06-04 23:08:09 +00:00
x.times('-a', 16) // '-6'</pre>
<h5 id="toDP">
toDecimalPlaces<code class='inset'>.toDP([dp [, rm]]) <i>&rArr; Decimal</i></code>
</h5>
<p>
<code>dp</code>: <i>number</i>: integer, 0 to 1e+9 inclusive<br />
<code>rm</code>: <i>number</i>: integer, 0 to 8 inclusive.
</p>
<p>
Returns a new Decimal whose value is the value of this Decimal rounded to <code>dp</code>
decimal places using rounding mode <code>rm</code>.
</p>
<p>
If <code>dp</code> is omitted or is <code>null</code> or undefined, the return value will
have the same value as this Decimal.
</p>
<p>
if <code>rm</code> is omitted or is <code>null</code> or undefined, rounding mode
<a href='#rounding'><code>rounding</code></a> is used.
</p>
<p>
See <a href='#Errors'>Errors</a> for the treatment of other non-integer or out of range
<code>dp</code> values.
</p>
<pre>
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2014-04-02 15:31:40 +00:00
x = new Decimal(12.24567)
v2.0.0
2014-04-10 18:46:16 +00:00
x.toDecimalPlaces(0) // '12'
x.toDecimalPlaces(1, 0) // '12.3'
Minor doc clean-up. v1.0.1
2014-04-07 16:15:36 +00:00
v2.0.0
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y = new Decimal(9876.54321)
y.toDP(3) // '9876.543'
y.toDP(1, 0) // '9876.6'
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y.toDP(1, Decimal.ROUND_DOWN) // '9876.5'</pre>
<h5 id="toE">
toExponential<code class='inset'>.toExponential([dp [, rm]]) <i>&rArr; string</i></code>
</h5>
<p>
<code>dp</code>: <i>number</i>: integer, 0 to 1e+9 inclusive<br />
<code>rm</code>: <i>number</i>: integer, 0 to 8 inclusive
</p>
<p>
Returns a string representing the value of this Decimal 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 Decimal 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 undefined, the number of digits
after the decimal point defaults to the minimum number of digits necessary to represent the
value exactly.
</p>
<p>
If <code>rm</code> is omitted or is <code>null</code> or undefined, rounding mode
<a href='#rounding'><code>rounding</code></a> is used.
</p>
<p>
See <a href='#Errors'>Errors</a> for the treatment of other non-integer or out of range
<code>decimal_places</code> values.
</p>
<pre>
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x = 45.6
y = new Decimal(x)
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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'
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y.toExponential(3) // '4.560e+1'</pre>
<h5 id="toFi">toFixed<code class='inset'>.toFixed([dp [, rm]]) <i>&rArr; string</i></code></h5>
<p>
<code>dp</code>: <i>number</i>: integer, 0 to 1e+9 inclusive<br />
<code>rm</code>: <i>number</i>: integer, 0 to 8 inclusive
</p>
<p>
Returns a string representing the value of this Decimal 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 Decimal 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 undefined, then the return value will
be unrounded and in normal notation. This is unlike <code>Number.prototype.toFixed</code>,
which returns the value to zero decimal places, but is useful when because of the current
<a href="#toExpNeg"><code>toExpNeg</code></a> or
<a href="#toExpPos"><code>toExpNeg</code></a> values, <code><a href='#toS'>toString</a></code>
returns exponential notation.
</p>
<p>
if <code>rm</code> is omitted or is <code>null</code> or undefined, rounding mode
<a href='#rounding'><code>rounding</code></a> is used.
</p>
<p>
See <a href='#Errors'>Errors</a> for the treatment of other non-integer or out of range
<code>dp</code> values.
</p>
<pre>
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x = 3.456
y = new Decimal(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'
v3.0.0
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y.toFixed(5) // '3.45600'</pre>
<h5 id="toFo">
v4.0.0 Updated API doc and image re format
2014-11-10 15:55:57 +00:00
toFormat<code class='inset'>.toFormat([dp [, rm]]) <i>&rArr; string</i></code>
v3.0.0
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</h5>
<p>
v4.0.0 Updated API doc and image re format
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<code>dp</code>: <i>number</i>: integer, 0 to 1e+9 inclusive<br />
<code>rm</code>: <i>number</i>: integer, 0 to 8 inclusive
v3.0.0
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</p>
<p>
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Returns a string representing the value of this Decimal in fixed-point notation rounded to
<code>dp</code> decimal places using rounding mode <code>rm</code> (as
<a href='#toFi'><code>toFixed</code></a>), and formatted according to the properties of this
Decimal's constructor's <a href='#format'><code>format</code></a> object property.
v3.0.0
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</p>
<p>
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See the examples below for the properties of the <a href='#format'><code>format</code></a>
object, their types and their usage.
v3.0.0
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</p>
<p>
If <code>dp</code> is omitted or is <code>null</code> or undefined, then the return value is
not rounded to a fixed number of decimal places.
</p>
v4.0.0 Updated API doc and image re format
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<p>
if <code>rm</code> is omitted or is <code>null</code> or undefined, rounding mode
<a href='#rounding'><code>rounding</code></a> is used.
</p>
v3.0.0
2014-06-04 23:08:09 +00:00
<pre>
v4.0.0 Updated API doc and image re format
2014-11-10 15:55:57 +00:00
// Using config to assign values to the format object
Decimal.config({
format : {
decimalSeparator : '.',
groupSeparator : ',',
groupSize : 3,
secondaryGroupSize : 0,
fractionGroupSeparator : ' ',
fractionGroupSize : 0
}
});
x = new Decimal('123456789.123456789')
x.toFormat() // '123,456,789.123456789'
x.toFormat(1) // '123,456,789.1'
// Assigning the format properties directly
Decimal.format.groupSeparator = ' ';
Decimal.format.fractionGroupSize = 5;
x.toFormat() // '123 456 789.12345 6789'
// Assigning the format object directly
Decimal.format = {
decimalSeparator = ',',
groupSeparator = '.',
groupSize = 3,
secondaryGroupSize = 2
}
x.toFormat() // '12.34.56.789,123456789'</pre>
v3.0.0
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<h5 id="toFr">
toFraction
<code class='inset'>.toFraction([max_denominator]) <i>&rArr; [string, string]</i></code>
</h5>
<p>
<code>max_denominator</code>: <i>number|string|Decimal</i>: <code>1</code> &gt;= integer &lt;
<code>Infinity</code>
</p>
<p>
Returns a string array representing the value of this Decimal as a simple fraction with an
integer numerator and an integer denominator. The denominator will be a positive non-zero
value less than or equal to <code>max_denominator</code>.
</p>
<p>
If a maximum denominator is not specified, or is <code>null</code> or undefined, the
denominator will be the lowest value necessary to represent the number exactly.
</p>
<p>
See <a href='#Errors'>Errors</a> for the treatment of other non-integer or out of range
<code>max_denominator</code> values.
</p>
<pre>
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x = new Decimal(1.75)
x.toFraction() // '7, 4'
pi = new Decimal('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'
v3.0.0
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pi.toFraction(1) // '3, 1'</pre>
<h5 id="toJSON">toJSON<code class='inset'>.toJSON() <i>&rArr; string</i></code></h5>
<p>As <code>valueOf</code>.</p>
<pre>
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x = new Decimal('177.7e+457')
y = new Decimal(235.4325)
z = new Decimal('0.0098074')
// Serialize an array of three Decimals
str = JSON.stringify( [x, y, z] )
// "["1.777e+459","235.4325","0.0098074"]"
// Return an array of three Decimals
JSON.parse(str, function (key, val) {
return key === '' ? val : new Decimal(val)
v3.0.0
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})</pre>
<p>If the <code>toJSON</code> method was not present, the objects (Decimal instances) themselves
would be serialized, rather then the string returned by <code>valueOf</code>:</p>
<pre>JSON.stringify( [x, y, z] )
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/*
v3.0.0
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"[{"s":1,"e":459,"c":[17770]},
{"s":1,"e":2,"c":[235,4325000]},
{"s":1,"e":-3,"c":[98074]}]"
*/</pre>
<h5 id="toNear">
toNearest<code class='inset'>.toNearest(n [, rm]) <i>&rArr; Decimal</i></code>
</h5>
<p>
<code>n</code>: <i>number|string|Decimal</i><br />
<code>rm</code>: <i>number</i>: integer, 0 to 8 inclusive<br />
<i>See <code><a href="#decimal">Decimal</a></code> for further parameter details.</i>
</p>
<p>
Returns a new Decimal whose value is the nearest multiple of <code>n</code> to the value of
this Decimal.
</p>
<p>
If the value of this Decimal is equidistant from two multiples of <code>n</code>, the rounding
mode <code>rm</code>, or <a href='#rounding'><code>rounding</code></a> if <code>rm</code> is
omitted or is <code>null</code> or undefined, determines the direction of the nearest.
</p>
<p>
In this context, rounding mode <a href='#rounding'><code>ROUND_HALF_UP</code></a> is
interpreted the same as rounding mode <a href='#rounding'><code>ROUND_UP</code></a>, and so
on. I.e. the rounding is either up, down, to ceil, to floor or to even.
</p>
<p>
The return value will always have the same sign as this Decimal, unless either this Decimal
or <code>n</code> is <code>NaN</code>, in which case the return value will be also be
<code>NaN</code>.
</p>
<p>The return value is not rounded to <a href='#precision'><code>precision</code></a>.</p>
<pre>
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x = new Decimal(1.39)
x.toNearest(0.25) // '1.5'
y = new Decimal(0.75) // equidistant from 0.5 and 1
y.toNearest(0.5, 0) // '1' (ROUND_UP)
v3.0.0
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y.toNearest(0.5, 1) // '0.5' (ROUND_DOWN)</pre>
<h5 id="toNum">toNumber<code class='inset'>.toNumber() <i>&rArr; number</i></code></h5>
<p>Returns the value of this Decimal converted to a number primitive.</p>
<p>
Type coercion with, for example, JavaScript's unary plus operator will also work, except that
a Decimal with the value minus zero will convert to positive zero.
</p>
<pre>
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x = new Decimal(456.789)
Minor doc clean-up. v1.0.1
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x.toNumber() // 456.789
+x // 456.789
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y = new Decimal('45987349857634085409857349856430985')
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y.toNumber() // 4.598734985763409e+34
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z = new Decimal(-0)
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1 / +z // Infinity
v3.0.0
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1 / z.toNumber() // -Infinity</pre>
<h5 id="pow">toPower<code class='inset'>.pow(n [, base]) <i>&rArr; Decimal</i></code></h5>
<p>
<code>n</code>: <i>number|string|Decimal</i>: integer or non-integer<br />
<code>base</code>: <i>number</i><br />
<i>See <code><a href="#decimal">Decimal</a></code> for further parameter details.</i>
</p>
<p>
Returns a new Decimal whose value is the value of this Decimal raised to the power
<code>n</code>, rounded to <a href='#precision'><code>precision</code></a> significant digits
using rounding mode <a href='#rounding'><code>rounding</code></a>.
</p>
<p>
The performance of this method degrades exponentially with increasing digits. For
non-integer exponents in particular, the performance of this method may not be adequate.
</p>
<pre>
Minor doc clean-up. v1.0.1
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Math.pow(0.7, 2) // 0.48999999999999994
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x = new Decimal(0.7)
Minor doc clean-up. v1.0.1
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x.toPower(2) // '0.49'
new Decimal(3).pow(-2) // '0.11111111111111111111'
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new Decimal(1217652.23).pow('98765.489305603941')
v3.0.0
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// '4.8227010515242461181e+601039'</pre>
<p><i>Is the pow function guaranteed to be correctly rounded?</i></p>
<p>
The return value will <i>almost always</i> be correctly rounded, i.e. rounded as if the result
was first calculated to an infinite number of correct digits before rounding. If a result is
incorrectly rounded the maximum error will be <code>1</code> <i>ulp</i> (unit in the last
place).
</p>
<p>For non-integer and larger exponents this method uses the formula</p>
<blockquote><code>x<sup>y</sup> = exp(y*ln(x))</code></blockquote>
<p>
As the mathematical return values of the <code>exp</code> and <code>ln</code> functions are
both non-terminating (excluding arguments of <code>0</code> or <code>1</code>), the Decimal
return values of the functions as implemented by this library will be rounded approximations,
which means that there can be no guarantee of correct rounding when they are combined in the
above formula.
</p>
<p>
The return value may, depending on the rounding mode, be incorrectly rounded only if the first
<code>15</code> rounding digits are <code>15</code> zeros (and there are non-zero digits
following at some point) or <code>15</code> nines (the first rounding digit may also be
<code>5</code> or <code>4</code> respectively).
</p>
<p>
Therefore, assuming the first <code>15</code> rounding digits are each equally likely to be
any digit, <code>0-9</code>, the probability of an incorrectly rounded result is less than
<code>1</code> in <code>250,000,000,000,000</code>.
</p>
<p>
An example of incorrect rounding:
</p>
<pre>
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Decimal.config({ precision: 20, rounding: 1 })
new Decimal(28).pow('6.166675020000903537297764507632802193308677149')
v3.0.0
2014-06-04 23:08:09 +00:00
// 839756321.64088511</pre>
<p>As the exact mathematical result begins</p>
<pre>839756321.6408851099999999999999999999999999998969466049426031167...</pre>
<p>
and the rounding mode is set to <code><a href='#modes'>ROUND_DOWN</a></code>, the correct
return value should be
</p>
<pre>839756321.64088510999</pre>
<h5 id="toP">
toPrecision<code class='inset'>.toPrecision([sd [, rm]]) <i>&rArr; string</i></code>
</h5>
<p>
<code>sd</code>: <i>number</i>: integer, 1 to 1e+9 inclusive<br />
<code>rm</code>: <i>number</i>: integer, 0 to 8 inclusive
</p>
<p>
Returns a string representing the value of this Decimal 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 undefined, then the return value is
the same as <code><a href='#toS'>toString</a></code>.
</p>
<p>
if <code>rm</code> is omitted or is <code>null</code> or undefined, rounding mode
<a href='#rounding'><code>rounding</code></a> is used.
</p>
<p>
See <a href='#Errors'>Errors</a> for the treatment of other non-integer or out of range
<code>sd</code> values.
</p>
<pre>
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x = 45.6
y = new Decimal(x)
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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'
v3.0.0
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y.toPrecision(5) // '45.600'</pre>
<h5 id="toSD">
toSignificantDigits<code class='inset'>.toSD([sd [, rm]]) <i>&rArr; Decimal</i></code>
</h5>
<p>
<code>sd</code>: <i>number</i>: integer, 1 to 1e+9 inclusive.<br />
<code>rm</code>: <i>number</i>: integer, 0 to 8 inclusive.
</p>
<p>
Returns a new Decimal whose value is the value of this Decimal rounded to <code>sd</code>
significant digits using rounding mode <code>rm</code>.
</p>
<p>
If <code>sd</code> is omitted or is <code>null</code> or undefined, the return value will
be rounded to <a href='#precision'><code>precision</code></a> significant digits.
</p>
<p>
if <code>rm</code> is omitted or is <code>null</code> or undefined, rounding mode
<a href='#rounding'><code>rounding</code></a> will be used.
</p>
<p>
See <a href='#Errors'>Errors</a> for the treatment of other non-integer or out of range
<code>sd</code> or <code>rm</code> values.
</p>
<pre>
v2.0.0
2014-04-10 18:46:16 +00:00
Decimal.config({ precision: 5, rounding: 4 })
x = new Decimal(9876.54321)
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v2.0.0
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x.toSignificantDigits() // '9876.5'
x.toSignificantDigits(6) // '9876.54'
x.toSignificantDigits(6, Decimal.ROUND_UP) // '9876.55'
x.toSD(2) // '9900'
x.toSD(2, 1) // '9800'
v3.0.0
2014-06-04 23:08:09 +00:00
x // '9876.54321'</pre>
<h5 id="toS">toString<code class='inset'>.toString([base]) <i>&rArr; string</i></code></h5>
<p><code>base</code>: <i>number</i>: integer, 2 to 64 inclusive</p>
<p>
Returns a string representing the value of this Decimal in the specified base, or base 10 if
<code>base</code> is omitted or is <code>null</code> or undefined.
</p>
<p>
For bases above 10, values from 10 to 35 are represented by <code>a-z</code> (as with
<code>Number.prototype.toString</code>), 36 to 61 by <code>A-Z</code>, and 62 and 63 by
<code>$</code> and <code>_</code> respectively.
</p>
<p>
If a base is specified the value is rounded to <a href='#precision'><code>precision</code></a>
significant digits using rounding mode <a href='#rounding'><code>rounding</code></a>.
</p>
<p>
If a base is not specified and this Decimal has a positive exponent that is equal to or
greater than <a href="#toExpPos"><code>toExpPos</code></a>, or a negative exponent equal to
or less than <a href="#toExpPos"><code>toExpNeg</code></a>, then exponential notation is
returned.
</p>
<p>If <code>base</code> is <code>null</code> or undefined it is ignored.</p>
<p>
See <a href='#Errors'>Errors</a> for the treatment of other non-integer or out of range
<code>base</code> values.
</p>
<pre>
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x = new Decimal(750000)
x.toString() // '750000'
Decimal.config({ toExpPos: 5 })
x.toString() // '7.5e+5'
y = new Decimal(362.875)
y.toString(2) // '101101010.111'
y.toString(9) // '442.77777777777777777778'
y.toString(32) // 'ba.s'
Decimal.config({ precision: 4 });
z = new Decimal('1.23456789')
z.toString() // '1.23456789'
v3.0.0
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z.toString(10) // '1.2346'</pre>
<h5 id="trunc">truncated<code class='inset'>.trunc() <i>&rArr; Decimal</i></code></h5>
<p>
Returns a new Decimal whose value is the value of this Decimal truncated to a whole number.
</p>
<p>The return value is not rounded to <a href='#precision'><code>precision</code></a>.</p>
<pre>
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x = new Decimal(123.456)
x.truncated() // '123'
y = new Decimal(-12.3)
v3.0.0
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y.trunc() // '-12'</pre>
<h5 id="valueOf">valueOf<code class='inset'>.valueOf() <i>&rArr; string</i></code></h5>
<p>As <code>toString</code>, but does not accept a base argument.</p>
<pre>
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x = new Decimal('1.777e+457')
v3.0.0
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x.valueOf() // '1.777e+457'</pre>
<h4 id="instance-properties">Properties</h4>
<p>
A Decimal 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 style='color:#000'>[]</code></td>
<td> Array of integers, each 0 - 1e7</td>
</tr>
<tr>
<td class='centre' id='exponent'><b>e</b></td>
<td>exponent</td>
<td><i>number</i></td>
<td>Integer, -9e15 to 9e15 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 any of the three properties may also be <code>null</code>.
</p>
<p>
The properties are best considered to be read-only.
</p>
<p>
From version 3 of this library, the value of a Decimal is stored in a normalised base
<code>10000</code> floating point format. While previously it was acceptable to change the
exponent of a Decimal by writing to its exponent property directly, this is no longer
recommended (as the number of digits in the first element of the coefficient array is
dependent on the exponent, so the coefficient would also need to be altered).
</p>
<p>
As with JavaScript numbers, the original exponent and fractional trailing zeros of a number
are not preserved.
</p>
<pre>
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x = new Decimal(0.123) // '0.123'
x.toExponential() // '1.23e-1'
v3.0.0
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x.c // [ 1230000 ]
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x.e // -1
x.s // 1
y = new Number(-123.4567000e+2) // '-12345.67'
y.toExponential() // '-1.234567e+4'
z = new Decimal('-123.4567000e+2') // '-12345.67'
z.toExponential() // '-1.234567e+4'
v3.0.0
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z.c // [ 12345, 6700000 ]
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z.e // 4
v3.0.0
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z.s // -1</pre>
<h4 id="zero-nan-infinity">Zero, NaN and Infinity</h4>
<p>
The table below shows how &plusmn;<code>0</code>, <code>NaN</code> and
&plusmn;<code>Infinity</code> are stored.
</p>
<table>
<tr>
<th> </th>
<th class='centre'>c</th>
<th class='centre'>e</th>
<th class='centre'>s</th>
</tr>
<tr>
<td>&plusmn;0</td>
<td><code>[0]</code></td>
<td><code>0</code></td>
<td><code>&plusmn;1</code></td>
</tr>
<tr>
<td>NaN</td>
<td><code>null</code></td>
<td><code>null</code></td>
<td><code>null</code></td>
</tr>
<tr>
<td>&plusmn;Infinity</td>
<td><code>null</code></td>
<td><code>null</code></td>
<td><code>&plusmn;1</code></td>
</tr>
</table>
<pre>
Minor doc clean-up. v1.0.1
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x = new Number(-0) // 0
1 / x == -Infinity // true
y = new Decimal(-0) // '0'
y.c // '0' ( [0].toString() )
y.e // 0
v3.0.0
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y.s // -1</pre>
<h4 id='Errors'>Errors</h4>
<p>
The errors that are thrown are generic <code>Error</code> objects with <code>name</code>
<i>Decimal Error</i>.
</p>
<p>
The table below shows the errors that may be thrown if <code>errors</code> is
<code>true</code>, and the action taken if <code>errors</code> is <code>false</code>.
</p>
<table class='error-table'>
<tr>
<th>Method(s)</th>
<th>errors: true<br />Throw Decimal Error</th>
<th>errors: false<br />Action on invalid argument</th>
</tr>
<tr>
<td rowspan=5>
<code>
comparedTo<br />
Decimal<br />
dividedBy<br />
dividedToIntegerBy<br />
equals<br />
greaterThan<br />
greaterThanOrEqualTo<br />
lessThan<br />
lessThanOrEqualTo<br />
logarithm <br />
minus<br />
modulo<br />
naturalLogarithm<br />
plus<br />
times<br />
toPower
</code>
</td>
<td>number type has more than<br />15 significant digits</td>
<td>Accept.</td>
</tr>
<tr>
<td>not a base... number</td>
<td>Substitute <code>NaN</code></td>
</tr>
<tr>
<td>base not an integer</td>
<td>Truncate to integer.<br />Ignore if not a number</td>
</tr>
<tr>
<td>base out of range</td>
<td>Ignore</td>
</tr>
<tr>
<td>not a number<sup>*</sup></td>
<td>Substitute <code>NaN</code></td>
</tr>
<tr>
<td rowspan=16><code>config</code></td>
<td><code>precision</code> not an integer</td>
<td>Truncate to integer.<br />Ignore if not a number</td>
</tr>
<tr>
<td><code>precision</code> out of range</td>
<td>Ignore</td>
</tr>
<tr>
<td><code>rounding</code> not an integer</td>
<td>Truncate to integer.<br />Ignore if not a number</td>
</tr>
<tr>
<td><code>rounding</code> out of range</td>
<td>Ignore</td>
</tr>
<tr>
<td><code>toExpNeg</code> not an integer</td>
<td>Truncate to integer.<br />Ignore if not a number</td>
</tr>
<tr>
<td><code>toExpNeg</code> out of range</td>
<td>Ignore</td>
</tr>
<tr>
<td><code>toExpPos</code> not an integer</td>
<td>Truncate to integer.<br />Ignore if not a number</td>
</tr>
<tr>
<td><code>toExpPos</code> out of range</td>
<td>Ignore</td>
</tr>
<tr>
<td><code>minE</code> not an integer</td>
<td> Truncate to integer.<br />Ignore if not a number</td>
</tr>
<tr>
<td><code>minE</code> out of range</td>
<td>Ignore</td>
</tr>
<tr>
<td><code>maxE</code> not an integer</td>
<td> Truncate to integer.<br />Ignore if not a number</td>
</tr>
<tr>
<td><code>maxE</code> out of range</td>
<td>Ignore</td>
</tr>
<tr>
<td><code>errors</code> not a boolean or binary digit</td>
<td>Ignore</td>
</tr>
<tr>
<td><code>crypto</code> not a boolean or binary digit</td>
<td>Ignore</td>
</tr>
<tr>
<td><code>modulo</code> not an integer</td>
<td> Truncate to integer.<br />Ignore if not a number</td>
</tr>
<tr>
<td><code>modulo</code> out of range</td>
<td>Ignore</td>
</tr>
<tr>
<td><code>logarithm<br />naturalLogarithm</code></td>
<td>LN10 out of digits</td>
<td>Ignore</td>
</tr>
<tr>
<td><code>precision</code></td>
<td>argument not a boolean or binary digit</td>
<td>Ignore</td>
</tr>
<tr>
<td><code>random</code></td>
<td><code>crypto</code> unavailable</td>
<td>Use <code>Math.random</code></td>
</tr>
<tr>
<td rowspan=4>
<code>
toDecimalPlaces<br />
toExponential<br />
toFixed<br />
toPrecision<br />
toSignificantDigits
</code>
</td>
<td>argument not an integer</td>
<td>Truncate to integer.<br />Ignore if not a number</td>
</tr>
<tr>
<td>argument out of range</td>
<td>Ignore</td>
</tr>
<tr>
<td>rounding mode not an integer</td>
<td>Truncate to integer.<br />Ignore if not a number</td>
</tr>
<tr>
<td>rounding mode out of range</td>
<td>Ignore</td>
</tr>
<tr>
<td rowspan=3><code>toFraction</code></td>
<td>number type has more than<br />15 significant digits</td>
<td>Accept.</td>
</tr>
<tr>
<td>max denominator not an integer</td>
<td>Truncate to integer.<br />Ignore if not a number</td>
</tr>
<tr>
<td>max denominator out of range</td>
<td>Ignore</td>
</tr>
<tr>
<td rowspan=2><code>toNearest</code></td>
<td>number type has more than<br />15 significant digits</td>
<td>Accept.</td>
</tr>
<tr>
<td>rounding mode out of range</td>
<td>Ignore</td>
</tr>
<tr>
<td rowspan=2><code>toString</code></td>
<td>base not an integer</td>
<td>Truncate to integer.<br />Ignore if not a number</td>
</tr>
<tr>
<td>base out of range</td>
<td>Ignore</td>
</tr>
</table>
<p><sup>*</sup>No error is thrown if the value is <code>NaN</code> or 'NaN'.</p>
<p>
The message of a <i>Decimal Error</i> will also contain the name of the method from which the
error originated.
</p>
<p>To determine if an exception is a <i>Decimal Error</i>:</p>
<pre>
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try {
// ...
} catch (e) {
if ( e instanceof Error && e.name == 'Decimal Error' ) {
// ...
}
v3.0.0
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}</pre>
<h2 id='faq'>FAQ</h2>
<h6>Why are trailing fractional zeros removed from Decimals?</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>
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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")
v3.0.0
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z = x.multiply(y) // 4.1400000</pre>
<p>
To specify the precision of a value is to specify that the value lies
within a certain range.
</p>
<p>
In the first example, <code>x</code> has a value of <code>1.0</code>. The trailing zero shows
the precision of the value, implying that it is in the range <code>0.95</code> to
<code>1.05</code>. Similarly, the precision indicated by the trailing zeros of <code>y</code>
indicates that the value is in the range <code>1.09995</code> to <code>1.10005</code>.
</p>
<p>
If we add the two lowest values in the ranges we have, <code>0.95 + 1.09995 = 2.04995</code>,
and if we add the two highest values we have, <code>1.05 + 1.10005 = 2.15005</code>, so the
range of the result of the addition implied by the precision of its operands is
<code>2.04995</code> to <code>2.15005</code>.
</p>
<p>
The result given by BigDecimal of <code>2.1000</code> however, indicates that the value is in
the range <code>2.09995</code> to <code>2.10005</code> and therefore the precision implied by
its trailing zeros may be misleading.
</p>
<p>
In the second example, the true range is <code>4.122744</code> to <code>4.157256</code> yet
the BigDecimal answer of <code>4.1400000</code> indicates a range of <code>4.13999995</code>
to <code>4.14000005</code>. Again, the precision implied by the trailing zeros may be
misleading.
</p>
<p>
This library, like binary floating point and most calculators, does not retain trailing
fractional zeros. Instead, the <code>toExponential</code>, <code>toFixed</code> and
<code>toPrecision</code> methods enable trailing zeros to be added if and when required.<br />
</p>
</div>
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<script>
v4.0.0 Updated API doc and image re format
2014-11-10 15:55:57 +00:00
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Added index.html and images to gh-pages
2014-04-02 15:31:40 +00:00
</script>
</body>
Minor doc clean-up. v1.0.1
2014-04-07 16:15:36 +00:00
</html>
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