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2743 lines
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2743 lines
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<div class="nav">
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<a class='nav-title' href="#">API</a>
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<b>CONSTRUCTOR</b>
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<ul><li><a href="#decimal"><strong>Decimal</strong></a></li></ul>
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<a href="#methods">Methods</a>
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<ul>
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<li><a href="#Dabs" >abs</a></li>
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<li><a href="#Dacos" >acos</a></li>
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<li><a href="#Dacosh" >acosh</a></li>
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<li><a href="#Dadd" >add</a></li>
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<li><a href="#Dasin" >asin</a></li>
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<li><a href="#Dasinh" >asinh</a></li>
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<li><a href="#Datan" >atan</a></li>
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<li><a href="#Datanh" >atanh</a></li>
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<li><a href="#Datan2" >atan2</a></li>
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<li><a href="#Dcbrt" >cbrt</a></li>
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<li><a href="#Dceil" >ceil</a></li>
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<li><a href="#Dclamp" >clamp</a></li>
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<li><a href="#Dclone" >clone</a></li>
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<li><a href="#Dcos" >cos</a></li>
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<li><a href="#Dcosh" >cosh</a></li>
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<li><a href="#Ddiv" >div</a></li>
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<li><a href="#Dexp" >exp</a></li>
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<li><a href="#Dfloor" >floor</a></li>
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<li><a href="#Dhypot" >hypot</a></li>
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<li><a href="#DisDecimal" >isDecimal</a></li>
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<li><a href="#Dln" >ln</a></li>
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<li><a href="#Dlog" >log</a></li>
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<li><a href="#Dlog2" >log2</a></li>
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<li><a href="#Dlog10" >log10</a></li>
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<li><a href="#Dmax" >max</a></li>
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<li><a href="#Dmin" >min</a></li>
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<li><a href="#Dmod" >mod</a></li>
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<li><a href="#Dmul" >mul</a></li>
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<li><a href="#DnoConflict">noConflict</a></li>
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<li><a href="#Dpow" >pow</a></li>
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<li><a href="#Drandom" >random</a></li>
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<li><a href="#Dround" >round</a></li>
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<li><a href="#Dset" >set</a></li>
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<li><a href="#Dsign" >sign</a></li>
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<li><a href="#Dsin" >sin</a></li>
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<li><a href="#Dsinh" >sinh</a></li>
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<li><a href="#Dsqrt" >sqrt</a></li>
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<li><a href="#Dsub" >sub</a></li>
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<li><a href="#Dsum" >sum</a></li>
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<li><a href="#Dtan" >tan</a></li>
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<li><a href="#Dtanh" >tanh</a></li>
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<li><a href="#Dtrunc" >trunc</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="#precision">precision</a></li>
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<li><a href="#rounding" >rounding</a></li>
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<li><a href="#minE" >minE</a></li>
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<li><a href="#maxE" >maxE</a></li>
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<li><a href="#toExpNeg" >toExpNeg</a></li>
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<li><a href="#toExpPos" >toExpPos</a></li>
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<li><a href="#modulo" >modulo</a></li>
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<li><a href="#crypto" >crypto</a></li>
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<li class='spacer'> </li>
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<li><a href="#modes">ROUND_UP</a></li>
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<li><a href="#modes">ROUND_DOWN</a></li>
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<li><a href="#modes">ROUND_CEIL</a></li>
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<li><a href="#modes">ROUND_FLOOR</a></li>
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<li><a href="#modes">ROUND_HALF_UP</a></li>
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<li><a href="#modes">ROUND_HALF_DOWN</a></li>
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<li><a href="#modes">ROUND_HALF_EVEN</a></li>
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<li><a href="#modes">ROUND_HALF_CEIL</a></li>
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<li><a href="#modes">ROUND_HALF_FLOOR</a></li>
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<li><a href="#modes">EUCLID</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="#ceil" >ceil </a> </li>
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<li><a href="#cmp" >comparedTo </a><span>cmp</span> </li>
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<li><a href="#clamp" >clampedTo </a><span>clamp</span> </li>
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<li><a href="#cos" >cosine </a><span>cos</span> </li>
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<li><a href="#cbrt" >cubeRoot </a><span>cbrt</span> </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="#divToInt" >dividedToIntegerBy </a><span>divToInt</span></li>
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<li><a href="#eq" >equals </a><span>eq</span> </li>
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<li><a href="#floor" >floor </a> </li>
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<li><a href="#gt" >greaterThan </a><span>gt</span> </li>
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<li><a href="#gte" >greaterThanOrEqualTo </a><span>gte</span> </li>
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<li><a href="#cosh" >hyperbolicCosine </a><span>cosh</span> </li>
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<li><a href="#sinh" >hyperbolicSine </a><span>sinh</span> </li>
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<li><a href="#tanh" >hyperbolicTangent </a><span>tanh</span> </li>
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<li><a href="#acos" >inverseCosine </a><span>acos</span> </li>
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<li><a href="#acosh" >inverseHyperbolicCosine </a><span>acosh</span> </li>
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<li><a href="#asinh" >inverseHyperbolicSine </a><span>asinh</span> </li>
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<li><a href="#atanh" >inverseHyperbolicTangent</a><span>atanh</span> </li>
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<li><a href="#asin" >inverseSine </a><span>asin</span> </li>
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<li><a href="#atan" >inverseTangent </a><span>atan</span> </li>
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<li><a href="#isFinite" >isFinite </a> </li>
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<li><a href="#isInt" >isInteger </a><span>isInt</span> </li>
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<li><a href="#isNaN" >isNaN </a> </li>
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<li><a href="#isNeg" >isNegative </a><span>isNeg</span> </li>
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<li><a href="#isPos" >isPositive </a><span>isPos</span> </li>
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<li><a href="#isZero" >isZero </a> </li>
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<li><a href="#lt" >lessThan </a><span>lt</span> </li>
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<li><a href="#lte" >lessThanOrEqualTo </a><span>lte</span> </li>
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<li><a href="#log" >logarithm </a><span>log</span> </li>
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<li><a href="#sub" >minus </a><span>sub</span> </li>
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<li><a href="#mod" >modulo </a><span>mod</span> </li>
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<li><a href="#exp" >naturalExponential </a><span>exp</span> </li>
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<li><a href="#ln" >naturalLogarithm </a><span>ln</span> </li>
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<li><a href="#neg" >negated </a><span>neg</span> </li>
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<li><a href="#add" >plus </a><span>add</span> </li>
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<li><a href="#sd" >precision </a><span>sd</span> </li>
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<li><a href="#round" >round </a> </li>
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<li><a href="#sin" >sine </a><span>sin</span> </li>
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<li><a href="#sqrt" >squareRoot </a><span>sqrt</span> </li>
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<li><a href="#tan" >tangent </a><span>tan</span> </li>
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<li><a href="#mul" >times </a><span>mul</span> </li>
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<li><a href="#toBinary" >toBinary </a> </li>
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<li><a href="#toDP" >toDecimalPlaces </a><span>toDP</span> </li>
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<li><a href="#toExponential">toExponential </a> </li>
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<li><a href="#toFixed" >toFixed </a> </li>
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<li><a href="#toFraction" >toFraction </a> </li>
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<li><a href="#toHex" >toHexadecimal </a><span>toHex</span> </li>
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<li><a href="#toJSON" >toJSON </a> </li>
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<li><a href="#toNearest" >toNearest </a> </li>
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<li><a href="#toNumber" >toNumber </a> </li>
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<li><a href="#toOctal" >toOctal </a> </li>
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<li><a href="#pow" >toPower </a><span>pow</span> </li>
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<li><a href="#toPrecision" >toPrecision </a> </li>
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<li><a href="#toSD" >toSignificantDigits </a><span>toSD</span> </li>
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<li><a href="#toString" >toString </a> </li>
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<li><a href="#trunc" >truncated </a><span>trunc</span> </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="#digits" >d</a><span>digits</span></li>
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<li><a href="#exponent" >e</a><span>exponent</span></li>
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<li><a href="#sign" >s</a><span>sign</span></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="#Pi">Pi</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>decimal<span id='js'>.js</span></h1>
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<p>An arbitrary-precision Decimal type for JavaScript.</p>
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<p><a href='https://github.com/MikeMcl/decimal.js'>Hosted on GitHub</a>.</p>
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<p>
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<i>
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The library is incorporated into this page, so it should be available in the console now.
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</i>
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</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/decimal.js'>README</a> on GitHub for a quick-start
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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><br />
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<p>
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When the library is loaded, it defines a single function object,
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<a href='#decimal'><code>Decimal</code></a>, the constructor of Decimal instances.
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</p>
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<p>
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<i>
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If necessary, multiple Decimal constructors can be created, each with their own independent
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configuration, e.g. precision and range, which applies to all Decimal instances created from
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it.
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</i>
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</p>
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<p>
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<i>
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A new Decimal constructor is created by calling the <code><a href='#Dclone'>clone</a></code>
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method of an already existing Decimal constructor.
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</i>
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</p>
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<h3 class='end'>CONSTRUCTOR</h3>
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<h5 id="decimal">
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Decimal<code class='inset'>Decimal(value) <i>⇒ Decimal</i></code>
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</h5>
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<dl>
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<dt><code>value</code>: <i>number|string|Decimal</i></dt>
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<dd>
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A legitimate <code>value</code> is an integer or float, including <code>±0</code>, or
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is <code>±Infinity</code>, or <code>NaN</code>.
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</dd>
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<dd>
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The number of digits of <code>value</code> is not limited, except by JavaScript's maximum
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array size and, in practice, the processing time required.
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</dd>
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<dd>
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The allowable range of <code>value</code> is defined in terms of a maximum exponent, see
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<a href='#maxE'>maxE</a>, and a minimum exponent, see <a href='#minE'>minE</a>.
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</dd>
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<dd>
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As well as in decimal, a string <code>value</code> may be expressed in binary, hexadecimal
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or octal, if the appropriate prefix is included: <code>0x</code> or <code>0X</code> for
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hexadecimal, <code>0b</code> or <code>0B</code> for binary, and <code>0o</code> or
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<code>0O</code> for octal.
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</dd>
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<dd>
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Both decimal and non-decimal string values may use exponential (floating-point), as well as
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normal (fixed-point) notation.
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</dd>
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<dd>
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In exponential notation, <code>e</code> or <code>E</code> defines a power-of-ten exponent
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for decimal values, and <code>p</code> or <code>P</code> defines a power-of-two exponent for
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non-decimal values, i.e. binary, hexadecimal or octal.
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</dd>
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</dl>
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<p>Returns a new Decimal object instance.</p>
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<p>Throws on an invalid <code>value</code>.</p>
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<pre>
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x = new Decimal(9) // '9'
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y = new Decimal(x) // '9'
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new Decimal('5032485723458348569331745.33434346346912144534543')
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new Decimal('4.321e+4') // '43210'
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new Decimal('-735.0918e-430') // '-7.350918e-428'
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new Decimal('5.6700000') // '5.67'
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new Decimal(Infinity) // 'Infinity'
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new Decimal(NaN) // 'NaN'
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new Decimal('.5') // '0.5'
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new Decimal('-0b10110100.1') // '-180.5'
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new Decimal('0xff.8') // '255.5'
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new Decimal(0.046875) // '0.046875'
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new Decimal('0.046875000000') // '0.046875'
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new Decimal('0.046_875_000_000') // '0.046875'
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new Decimal(4.6875e-2) // '0.046875'
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new Decimal('468.75e-4') // '0.046875'
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new Decimal('0b0.000011') // '0.046875'
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new Decimal('0o0.03') // '0.046875'
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new Decimal('0x0.0c') // '0.046875'
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new Decimal('0b1.1p-5') // '0.046875'
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new Decimal('0o1.4p-5') // '0.046875'
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new Decimal('0x1.8p-5') // '0.046875'</pre>
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<h4 id="methods">Methods</h4>
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<p>The methods of a Decimal constructor.</p>
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<h5 id="Dabs">abs<code class='inset'>.abs(x) <i>⇒ Decimal</i></code></h5>
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<p><code>x</code>: <i>number|string|Decimal</i></p>
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<p>See <code><a href='#abs'>absoluteValue</a></code>.</p>
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<pre>a = Decimal.abs(x)
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b = new Decimal(x).abs()
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a.equals(b) // true</pre>
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<h5 id="Dacos">acos<code class='inset'>.acos(x) <i>⇒ Decimal</i></code></h5>
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<p><code>x</code>: <i>number|string|Decimal</i></p>
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<p>See <code><a href='#acos'>inverseCosine</a></code>.</p>
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<pre>a = Decimal.acos(x)
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b = new Decimal(x).acos()
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a.equals(b) // true</pre>
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<h5 id="Dacosh">acosh<code class='inset'>.acosh(x) <i>⇒ Decimal</i></code></h5>
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<p><code>x</code>: <i>number|string|Decimal</i></p>
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<p>See <code><a href='#acos'>inverseHyperbolicCosine</a></code>.</p>
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<pre>a = Decimal.acosh(x)
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b = new Decimal(x).acosh()
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a.equals(b) // true</pre>
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<h5 id="Dadd">add<code class='inset'>.add(x, y) <i>⇒ Decimal</i></code></h5>
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<p>
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<code>x</code>: <i>number|string|Decimal</i><br />
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<code>y</code>: <i>number|string|Decimal</i>
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</p>
|
|
<p>See <code><a href='#add'>plus</a></code>.</p>
|
|
<pre>a = Decimal.add(x, y)
|
|
b = new Decimal(x).plus(y)
|
|
a.equals(b) // true</pre>
|
|
|
|
|
|
|
|
<h5 id="Dasin">asin<code class='inset'>.asin(x) <i>⇒ Decimal</i></code></h5>
|
|
<p><code>x</code>: <i>number|string|Decimal</i></p>
|
|
<p>See <code><a href='#asin'>inverseSine</a></code>.</p>
|
|
<pre>a = Decimal.asin(x)
|
|
b = new Decimal(x).asin()
|
|
a.equals(b) // true</pre>
|
|
|
|
|
|
|
|
<h5 id="Dasinh">asinh<code class='inset'>.asinh(x) <i>⇒ Decimal</i></code></h5>
|
|
<p><code>x</code>: <i>number|string|Decimal</i></p>
|
|
<p>See <code><a href='#asin'>inverseHyperbolicSine</a></code>.</p>
|
|
<pre>a = Decimal.asinh(x)
|
|
b = new Decimal(x).asinh()
|
|
a.equals(b) // true</pre>
|
|
|
|
|
|
|
|
<h5 id="Datan">atan<code class='inset'>.atan(x) <i>⇒ Decimal</i></code></h5>
|
|
<p><code>x</code>: <i>number|string|Decimal</i></p>
|
|
<p>See <code><a href='#atan'>inverseTangent</a></code>.</p>
|
|
<pre>a = Decimal.atan(x)
|
|
b = new Decimal(x).atan()
|
|
a.equals(b) // true</pre>
|
|
|
|
|
|
|
|
<h5 id="Datanh">atanh<code class='inset'>.atanh(x) <i>⇒ Decimal</i></code></h5>
|
|
<p><code>x</code>: <i>number|string|Decimal</i></p>
|
|
<p>See <code><a href='#atan'>inverseHyperbolicTangent</a></code>.</p>
|
|
<pre>a = Decimal.atanh(x)
|
|
b = new Decimal(x).atanh()
|
|
a.equals(b) // true</pre>
|
|
|
|
|
|
|
|
<h5 id="Datan2">atan2<code class='inset'>.atan2(y, x) <i>⇒ Decimal</i></code></h5>
|
|
<p>
|
|
<code>y</code>: <i>number|string|Decimal</i><br />
|
|
<code>x</code>: <i>number|string|Decimal</i>
|
|
</p>
|
|
<p>
|
|
Returns a new Decimal whose value is the inverse tangent in radians of the quotient of
|
|
<code>y</code> and <code>x</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 signs of <code>y</code> and <code>x</code> are used to determine the quadrant of the
|
|
result.
|
|
</p>
|
|
<p>
|
|
Domain: [<code>-Infinity, Infinity</code>]<br />
|
|
Range: [<code>-pi, pi</code>]
|
|
</p>
|
|
<p>
|
|
See <a href='#Pi'><code>Pi</code></a> and
|
|
<a href='https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Math/atan2'><code>Math.atan2()</code>.</a>
|
|
</p>
|
|
<pre>r = Decimal.atan2(y, x)</pre>
|
|
|
|
|
|
|
|
<h5 id="Dcbrt">cbrt<code class='inset'>.cbrt(x) <i>⇒ Decimal</i></code></h5>
|
|
<p><code>x</code>: <i>number|string|Decimal</i></p>
|
|
<p>See <code><a href='#cbrt'>cubeRoot</a></code>.</p>
|
|
<pre>a = Decimal.cbrt(x)
|
|
b = new Decimal(x).cbrt()
|
|
a.equals(b) // true</pre>
|
|
|
|
|
|
|
|
<h5 id="Dceil">ceil<code class='inset'>.ceil(x) <i>⇒ Decimal</i></code></h5>
|
|
<p><code>x</code>: <i>number|string|Decimal</i></p>
|
|
<p>See <code><a href='#ceil'>ceil</a></code>.</p>
|
|
<pre>a = Decimal.ceil(x)
|
|
b = new Decimal(x).ceil()
|
|
a.equals(b) // true</pre>
|
|
|
|
|
|
|
|
<h5 id="Dclamp">clamp<code class='inset'>.clamp(min, max) <i>⇒ Decimal</i></code></h5>
|
|
<p>
|
|
<code>min</code>: <i>number|string|Decimal</i><br />
|
|
<code>max</code>: <i>number|string|Decimal</i>
|
|
</p>
|
|
<p>See <code><a href='#clamp'>clampedTo</a></code>.</p>
|
|
<pre>Decimal.clamp(10.1, 0, 10) // '10'</pre>
|
|
|
|
|
|
|
|
<h5 id="Dclone">
|
|
clone
|
|
<code class='inset'>.clone([object]) <i>⇒ 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='#Dset'><code>set</code></a>), or with the same
|
|
settings as <code>this</code> Decimal constructor if <code>object</code> is omitted.
|
|
</p>
|
|
<pre>Decimal.set({ precision: 5 })
|
|
Decimal9 = Decimal.clone({ precision: 9 })
|
|
|
|
a = new Decimal(1)
|
|
b = new Decimal9(1)
|
|
|
|
a.div(3) // 0.33333
|
|
b.div(3) // 0.333333333
|
|
|
|
// Decimal9 = Decimal.clone({ precision: 9 }) is equivalent to:
|
|
Decimal9 = Decimal.clone()
|
|
Decimal9.set({ precision: 9 })</pre>
|
|
<p>
|
|
If <code>object</code> has a <code>'defaults'</code> property with value <code>true</code>
|
|
then the new constructor will use the default configuration.
|
|
</p>
|
|
<pre>
|
|
D1 = Decimal.clone({ defaults: true })
|
|
|
|
// Use the defaults except for precision
|
|
D2 = Decimal.clone({ defaults: true, precision: 50 })</pre>
|
|
<p>
|
|
It is not inefficient in terms of memory usage to use multiple Decimal constructors as
|
|
functions are shared between them.
|
|
</p>
|
|
|
|
|
|
<h5 id="Dcos">cos<code class='inset'>.cos(x) <i>⇒ Decimal</i></code></h5>
|
|
<p><code>x</code>: <i>number|string|Decimal</i></p>
|
|
<p>See <code><a href='#cos'>cosine</a></code>.</p>
|
|
<pre>a = Decimal.cos(x)
|
|
b = new Decimal(x).cos()
|
|
a.equals(b) // true</pre>
|
|
|
|
|
|
|
|
<h5 id="Dcosh">cosh<code class='inset'>.cosh(x) <i>⇒ Decimal</i></code></h5>
|
|
<p><code>x</code>: <i>number|string|Decimal</i></p>
|
|
<p>See <code><a href='#cos'>hyperbolicCosine</a></code>.</p>
|
|
<pre>a = Decimal.cosh(x)
|
|
b = new Decimal(x).cosh()
|
|
a.equals(b) // true</pre>
|
|
|
|
|
|
|
|
<h5 id="Ddiv">div<code class='inset'>.div(x, y) <i>⇒ Decimal</i></code></h5>
|
|
<p>
|
|
<code>x</code>: <i>number|string|Decimal</i><br />
|
|
<code>y</code>: <i>number|string|Decimal</i>
|
|
</p>
|
|
<p>See <code><a href='#div'>dividedBy</a></code>.</p>
|
|
<pre>a = Decimal.div(x, y)
|
|
b = new Decimal(x).div(y)
|
|
a.equals(b) // true</pre>
|
|
|
|
|
|
|
|
<h5 id="Dexp">exp<code class='inset'>.exp(x) <i>⇒ Decimal</i></code></h5>
|
|
<p><code>x</code>: <i>number|string|Decimal</i></p>
|
|
<p>See <code><a href='#exp'>naturalExponential</a></code>.</p>
|
|
<pre>a = Decimal.exp(x)
|
|
b = new Decimal(x).exp()
|
|
a.equals(b) // true</pre>
|
|
|
|
|
|
|
|
<h5 id="Dfloor">floor<code class='inset'>.floor(x) <i>⇒ Decimal</i></code></h5>
|
|
<p><code>x</code>: <i>number|string|Decimal</i></p>
|
|
<p>See <code><a href='#floor'>floor</a></code>.</p>
|
|
<pre>a = Decimal.floor(x)
|
|
b = new Decimal(x).floor()
|
|
a.equals(b) // true</pre>
|
|
|
|
|
|
|
|
<h5 id="Dhypot">
|
|
hypot<code class='inset'>.hypot([x [, y, ...]]) <i>⇒ Decimal</i></code>
|
|
</h5>
|
|
<p>
|
|
<code>x</code>: <i>number|string|Decimal</i><br />
|
|
<code>y</code>: <i>number|string|Decimal</i>
|
|
</p>
|
|
<p>
|
|
Returns a new Decimal whose value is the square root of the sum of the squares of the
|
|
arguments, rounded to <a href='#precision'><code>precision</code></a> significant digits using
|
|
rounding mode <a href='#rounding'><code>rounding</code></a>.
|
|
</p>
|
|
<pre>r = Decimal.hypot(x, y)</pre>
|
|
|
|
|
|
|
|
<h5 id="Dln">ln<code class='inset'>.ln(x) <i>⇒ Decimal</i></code></h5>
|
|
<p><code>x</code>: <i>number|string|Decimal</i></p>
|
|
<p>See <code><a href='#ln'>naturalLogarithm</a></code>.</p>
|
|
<pre>a = Decimal.ln(x)
|
|
b = new Decimal(x).ln()
|
|
a.equals(b) // true</pre>
|
|
|
|
|
|
|
|
<h5 id="DisDecimal">
|
|
isDecimal<code class='inset'>.isDecimal(object) <i>⇒ boolean</i></code>
|
|
</h5>
|
|
<p><code>object</code>: <i>any</i></p>
|
|
<p>
|
|
Returns <code>true</code> if <code>object</code> is a Decimal instance (where Decimal is any
|
|
Decimal constructor), or <code>false</code> if it is not.
|
|
</p>
|
|
<pre>a = new Decimal(1)
|
|
b = {}
|
|
a instanceof Decimal // true
|
|
Decimal.isDecimal(a) // true
|
|
Decimal.isDecimal(b) // false</pre>
|
|
|
|
|
|
|
|
<h5 id="Dlog">log<code class='inset'>.log(x [, base]) <i>⇒ Decimal</i></code></h5>
|
|
<p>
|
|
<code>x</code>: <i>number|string|Decimal</i><br />
|
|
<code>base</code>: <i>number|string|Decimal</i>
|
|
</p>
|
|
<p>See <code><a href='#log'>logarithm</a></code>.</p>
|
|
<p>
|
|
The default base is <code>10</code>, which is not the same as JavaScript's
|
|
<code>Math.log()</code>, which returns the natural logarithm (base <code>e</code>).
|
|
</p>
|
|
<pre>a = Decimal.log(x, y)
|
|
b = new Decimal(x).log(y)
|
|
a.equals(b) // true</pre>
|
|
|
|
|
|
|
|
<h5 id="Dlog2">log2<code class='inset'>.log2(x) <i>⇒ Decimal</i></code></h5>
|
|
<p><code>x</code>: <i>number|string|Decimal</i></p>
|
|
<p>
|
|
Returns a new Decimal whose value is the base <code>2</code> logarithm of <code>x</code>,
|
|
rounded to <a href='#precision'><code>precision</code></a> significant digits using rounding
|
|
mode <a href='#rounding'><code>rounding</code></a>.
|
|
</p>
|
|
<pre>r = Decimal.log2(x)</pre>
|
|
|
|
|
|
|
|
<h5 id="Dlog10">log10<code class='inset'>.log10(x) <i>⇒ Decimal</i></code></h5>
|
|
<p><code>x</code>: <i>number|string|Decimal</i></p>
|
|
<p>
|
|
Returns a new Decimal whose value is the base <code>10</code> logarithm of <code>x</code>,
|
|
rounded to <a href='#precision'><code>precision</code></a> significant digits using rounding
|
|
mode <a href='#rounding'><code>rounding</code></a>.
|
|
</p>
|
|
<pre>r = Decimal.log10(x)</pre>
|
|
|
|
|
|
|
|
<h5 id="Dmax">
|
|
max<code class='inset'>.max(x [, y, ...]) <i>⇒ Decimal</i></code>
|
|
</h5>
|
|
<p>
|
|
<code>x</code>: <i>number|string|Decimal</i><br />
|
|
<code>y</code>: <i>number|string|Decimal</i>
|
|
</p>
|
|
<p>Returns a new Decimal whose value is the maximum of the <code>arguments</code>.</p>
|
|
<pre>r = Decimal.max(x, y, z)</pre>
|
|
|
|
|
|
|
|
<h5 id="Dmin">
|
|
min<code class='inset'>.min(x [, y, ...]) <i>⇒ Decimal</i></code>
|
|
</h5>
|
|
<p>
|
|
<code>x</code>: <i>number|string|Decimal</i><br />
|
|
<code>y</code>: <i>number|string|Decimal</i>
|
|
</p>
|
|
<p>Returns a new Decimal whose value is the minimum of the <code>arguments</code>.</p>
|
|
<pre>r = Decimal.min(x, y, z)</pre>
|
|
|
|
|
|
|
|
<h5 id="Dmod">mod<code class='inset'>.mod(x, y) <i>⇒ Decimal</i></code></h5>
|
|
<p>
|
|
<code>x</code>: <i>number|string|Decimal</i><br />
|
|
<code>y</code>: <i>number|string|Decimal</i>
|
|
</p>
|
|
<p>See <code><a href='#mod'>modulo</a></code>.</p>
|
|
<pre>a = Decimal.mod(x, y)
|
|
b = new Decimal(x).mod(y)
|
|
a.equals(b) // true</pre>
|
|
|
|
|
|
|
|
<h5 id="Dmul">mul<code class='inset'>.mul(x, y) <i>⇒ Decimal</i></code></h5>
|
|
<p>
|
|
<code>x</code>: <i>number|string|Decimal</i><br />
|
|
<code>y</code>: <i>number|string|Decimal</i>
|
|
</p>
|
|
<p>See <code><a href='#mul'>times</a></code>.</p>
|
|
<pre>a = Decimal.mul(x, y)
|
|
b = new Decimal(x).mul(y)
|
|
a.equals(b) // true</pre>
|
|
|
|
|
|
|
|
<h5 id="DnoConflict">
|
|
noConflict<code class='inset'>.noConflict() <i>⇒ 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>
|
|
<script> Decimal = 1 </script>
|
|
<script src='/path/to/decimal.js'></script>
|
|
<script>
|
|
a = new Decimal(2) // '2'
|
|
D = Decimal.noConflict()
|
|
Decimal // 1
|
|
b = new D(3) // '3'
|
|
</script></pre>
|
|
|
|
|
|
|
|
<h5 id="Dpow">pow<code class='inset'>.pow(base, exponent) <i>⇒ Decimal</i></code></h5>
|
|
<p>
|
|
<code>base</code>: <i>number|string|Decimal</i><br />
|
|
<code>exponent</code>: <i>number|string|Decimal</i>
|
|
</p>
|
|
<p>See <code><a href="#pow">toPower</a></code>.</p>
|
|
<pre>a = Decimal.pow(x, y)
|
|
b = new Decimal(x).pow(y)
|
|
a.equals(b) // true</pre>
|
|
|
|
|
|
|
|
<h5 id="Drandom">
|
|
random<code class='inset'>.random([dp]) <i>⇒ Decimal</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 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> 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>
|
|
If the value of <code>this</code> Decimal constructor's
|
|
<a href='#crypto'><code>crypto</code></a> property is <code>true</code>, and the
|
|
<code>crypto</code> object is available globally in the host environment, the random digits of
|
|
the return value are generated by either <code>crypto.getRandomValues</code> (Web Cryptography
|
|
API in modern browsers) or <code>crypto.randomBytes</code> (Node.js), otherwise, if the the
|
|
value of the property is <code>false</code> the return value is generated by
|
|
<code>Math.random</code> (fastest).
|
|
</p>
|
|
<p>To make the <code>crypto</code> object available globally in Node.js use</p>
|
|
<pre>global.crypto = require('crypto')</pre>
|
|
<p>
|
|
If the value of <code>this</code> Decimal constructor's
|
|
<a href='#crypto'><code>crypto</code></a> property is set <code>true</code> and the
|
|
<code>crypto</code> object and associated method are not available, an exception will be
|
|
thrown.
|
|
</p>
|
|
<p>
|
|
If one of the <code>crypto</code> methods is used, the value of the returned Decimal should be
|
|
cryptographically-secure and statistically indistinguishable from a random value.
|
|
</p>
|
|
<pre>Decimal.set({ precision: 10 })
|
|
Decimal.random() // '0.4117936847'
|
|
Decimal.random(20) // '0.78193327636914089009'</pre>
|
|
|
|
|
|
<h5 id="Dround">round<code class='inset'>.round(x) <i>⇒ Decimal</i></code></h5>
|
|
<p><code>x</code>: <i>number|string|Decimal</i></p>
|
|
<p>See <code><a href='#round'>round</a></code>.</p>
|
|
<pre>a = Decimal.round(x)
|
|
b = new Decimal(x).round()
|
|
a.equals(b) // true</pre>
|
|
|
|
|
|
|
|
<h5 id="Dset">set<code class='inset'>.set(object) <i>⇒ Decimal constructor</i></code></h5>
|
|
<p><code>object</code>: <i>object</i></p>
|
|
<p>
|
|
Configures the 'global' settings for <code>this</code> particular Decimal constructor, i.e.
|
|
the settings which apply to operations performed on the Decimal instances created by it.
|
|
</p>
|
|
<p>Returns <code>this</code> 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 <code>this</code> Decimal constructor.
|
|
</p>
|
|
<p>
|
|
If <code>object</code> has a <code>'defaults'</code> property with value <code>true</code>
|
|
then any unspecified properties will be reset to their default values.
|
|
</p>
|
|
<p>Throws on an invalid <code>object</code> or configuration property value.</p>
|
|
<pre>
|
|
// Defaults
|
|
Decimal.set({
|
|
precision: 20,
|
|
rounding: 4,
|
|
toExpNeg: -7,
|
|
toExpPos: 21,
|
|
maxE: 9e15,
|
|
minE: -9e15,
|
|
modulo: 1,
|
|
crypto: false
|
|
})
|
|
|
|
// Reset all properties to their default values
|
|
Decimal.set({ defaults: true })
|
|
|
|
// Set precision to 50 and all other properties to their default values
|
|
Decimal.set({ precision: 50, defaults: true })</pre>
|
|
<p>
|
|
The properties of a Decimal constructor can also be set by direct assignment, but that will
|
|
by-pass the validity checking that this method performs - this is not a problem if the user
|
|
knows that the assignment is valid.
|
|
</p>
|
|
<pre>Decimal.precision = 40</pre>
|
|
|
|
|
|
|
|
<h5 id="Dsign">sign<code class='inset'>.sign(x) <i>⇒ number</i></code></h5>
|
|
<p><code>x</code>: <i>number|string|Decimal</i></p>
|
|
<table>
|
|
<tr><th>Returns</th><th> </th></tr>
|
|
<tr>
|
|
<td class='centre'><code>1</code></td>
|
|
<td>if the value of <code>x</code> is non-zero and its sign is positive</td>
|
|
</tr>
|
|
<tr>
|
|
<td class='centre'><code>-1</code></td>
|
|
<td>if the value of <code>x</code> is non-zero and its sign is negative</td>
|
|
</tr>
|
|
<tr>
|
|
<td class='centre'><code>0</code></td>
|
|
<td>if the value of <code>x</code> is positive zero</td>
|
|
</tr>
|
|
<tr>
|
|
<td class='centre'><code>-0</code></td>
|
|
<td>if the value of <code>x</code> is negative zero</td>
|
|
</tr>
|
|
<tr>
|
|
<td class='centre'><code>NaN</code></td>
|
|
<td>if the value of <code>x</code> is <code>NaN</code></td>
|
|
</tr>
|
|
</table>
|
|
<pre>r = Decimal.sign(x)</pre>
|
|
|
|
|
|
|
|
<h5 id="Dsin">sin<code class='inset'>.sin(x) <i>⇒ Decimal</i></code></h5>
|
|
<p><code>x</code>: <i>number|string|Decimal</i></p>
|
|
<p>See <code><a href='#sin'>sine</a></code>.</p>
|
|
<pre>a = Decimal.sin(x)
|
|
b = new Decimal(x).sin()
|
|
a.equals(b) // true</pre>
|
|
|
|
|
|
|
|
<h5 id="Dsinh">sinh<code class='inset'>.sinh(x) <i>⇒ Decimal</i></code></h5>
|
|
<p><code>x</code>: <i>number|string|Decimal</i></p>
|
|
<p>See <code><a href='#sin'>hyperbolicSine</a></code>.</p>
|
|
<pre>a = Decimal.sinh(x)
|
|
b = new Decimal(x).sinh()
|
|
a.equals(b) // true</pre>
|
|
|
|
|
|
|
|
<h5 id="Dsqrt">sqrt<code class='inset'>.sqrt(x) <i>⇒ Decimal</i></code></h5>
|
|
<p><code>x</code>: <i>number|string|Decimal</i></p>
|
|
<p>See <a href='#sqrt'>squareRoot</a>.</p>
|
|
<pre>a = Decimal.sqrt(x)
|
|
b = new Decimal(x).sqrt()
|
|
a.equals(b) // true</pre>
|
|
|
|
|
|
|
|
<h5 id="Dsub">sub<code class='inset'>.sub(x, y) <i>⇒ Decimal</i></code></h5>
|
|
<p>
|
|
<code>x</code>: <i>number|string|Decimal</i><br />
|
|
<code>y</code>: <i>number|string|Decimal</i>
|
|
</p>
|
|
<p>See <code><a href='#sub'>minus</a></code>.</p>
|
|
<pre>a = Decimal.sub(x, y)
|
|
b = new Decimal(x).sub(y)
|
|
a.equals(b) // true</pre>
|
|
|
|
|
|
|
|
<h5 id="Dsum">sum<code class='inset'>.sum(x [, y, ...]) <i>⇒ Decimal</i></code></h5>
|
|
<p>
|
|
<code>x</code>: <i>number|string|Decimal</i><br />
|
|
<code>y</code>: <i>number|string|Decimal</i>
|
|
</p>
|
|
<p>
|
|
Returns a new Decimal whose value is the sum of the <code>arguments</code>,
|
|
rounded to <a href='#precision'><code>precision</code></a> significant digits using
|
|
rounding mode <a href='#rounding'><code>rounding</code></a>.<br />
|
|
Only the result is rounded, not the intermediate summations.
|
|
</p>
|
|
<pre>
|
|
x = 5
|
|
y = '16'
|
|
z = new Decimal(-11)
|
|
Decimal.sum(x, y, z) // '10'</pre>
|
|
|
|
|
|
|
|
<h5 id="Dtan">tan<code class='inset'>.tan(x) <i>⇒ Decimal</i></code></h5>
|
|
<p><code>x</code>: <i>number|string|Decimal</i></p>
|
|
<p>See <code><a href='#tan'>tangent</a></code>.</p>
|
|
<pre>a = Decimal.tan(x)
|
|
b = new Decimal(x).tan()
|
|
a.equals(b) // true</pre>
|
|
|
|
|
|
|
|
<h5 id="Dtanh">tanh<code class='inset'>.tanh(x) <i>⇒ Decimal</i></code></h5>
|
|
<p><code>x</code>: <i>number|string|Decimal</i></p>
|
|
<p>See <code><a href='#tan'>hyperbolicTangent</a></code>.</p>
|
|
<pre>a = Decimal.tanh(x)
|
|
b = new Decimal(x).tanh()
|
|
a.equals(b) // true</pre>
|
|
|
|
|
|
|
|
<h5 id="Dtrunc">trunc<code class='inset'>.trunc(x) <i>⇒ Decimal</i></code></h5>
|
|
<p><code>x</code>: <i>number|string|Decimal</i></p>
|
|
<p>See <code><a href='#trunc'>truncated</a></code>.</p>
|
|
<pre>a = Decimal.trunc(x)
|
|
b = new Decimal(x).trunc()
|
|
a.equals(b) // true</pre>
|
|
|
|
|
|
|
|
|
|
<h4 id="constructor-properties">Properties</h4>
|
|
<p>The properties of a Decimal constructor.</p>
|
|
|
|
|
|
|
|
<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='#modulo'><code>modulo</code></a>, and
|
|
<a href='#crypto'><code>crypto</code></a> are set using the
|
|
<a href='#Dset'><code>set</code></a> method.
|
|
</p>
|
|
<p>
|
|
As simple object properties they can be set directly without using
|
|
<a href='#Dset'><code>set</code></a>, and it is fine to do so, but the values assigned
|
|
will not then be checked for validity. For example:
|
|
</p>
|
|
<pre>Decimal.set({ precision: 0 })
|
|
// '[DecimalError] Invalid argument: precision: 0'
|
|
|
|
Decimal.precision = 0
|
|
// No error is thrown and the results of calculations are unreliable</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 an operation.</p>
|
|
<p>
|
|
All functions which return a Decimal will round the return value to <code>precision</code>
|
|
significant digits except <a href='#decimal'><code>Decimal</code></a>,
|
|
<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='#toNearest'><code>toNearest</code></a> and
|
|
<a href='#trunc'><code>truncated</code></a>.
|
|
</p>
|
|
<p>
|
|
See <code><a href='#Pi'>Pi</a></code> for the precision limit of the trigonometric methods.
|
|
</p>
|
|
<pre>Decimal.set({ 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="#modes">(<code>ROUND_HALF_UP</code>)</a>
|
|
</p>
|
|
<p>
|
|
The default rounding mode used when rounding the result of an operation 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='#toBinary'><code>toBinary</code></a>,
|
|
<a href='#toDP'><code>toDecimalPlaces</code></a>,
|
|
<a href='#toExponential'><code>toExponential</code></a>,
|
|
<a href='#toFixed'><code>toFixed</code></a>,
|
|
<a href='#toHexadecimal'><code>toHexadecimal</code></a>,
|
|
<a href='#toNearest'><code>toNearest</code></a>,
|
|
<a href='#toOctal'><code>toOctal</code></a>,
|
|
<a href='#toPrecision'><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.set({ rounding: Decimal.ROUND_UP })
|
|
Decimal.set({ rounding: 0 }) // equivalent
|
|
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 the value of that <code>Decimal</code> becomes zero.
|
|
<p>
|
|
JavaScript numbers underflow to zero for exponents below <code>-324</code>.
|
|
</p>
|
|
<pre>Decimal.set({ minE: -500 })
|
|
Decimal.minE // -500
|
|
new Decimal('1e-500') // '1e-500'
|
|
new Decimal('9.9e-501') // '0'
|
|
|
|
Decimal.set({ minE: -3 })
|
|
new Decimal(0.001) // '0.01' e is -3
|
|
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 the value of that <code>Decimal</code> becomes <code>Infinity</code>.
|
|
<p>
|
|
JavaScript numbers overflow to <code>Infinity</code> for exponents above <code>308</code>.
|
|
</p>
|
|
<pre>Decimal.set({ maxE: 500 })
|
|
Decimal.maxE // 500
|
|
new Decimal('9.999e500') // '9.999e+500'
|
|
new Decimal('1e501') // 'Infinity'
|
|
|
|
Decimal.set({ maxE: 4 })
|
|
new Decimal(99999) // '99999' e is 4
|
|
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='#toString'><code>toString</code></a>
|
|
returns exponential notation.
|
|
</p>
|
|
<pre>Decimal.set({ toExpNeg: -7 })
|
|
Decimal.toExpNeg // -7
|
|
new Decimal(0.00000123) // '0.00000123' e is -6
|
|
new Decimal(0.000000123) // '1.23e-7'
|
|
|
|
// Always return exponential notation:
|
|
Decimal.set({ 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='#toFixed'><code>toFixed</code></a> method will always return a value in normal
|
|
notation and the <a href='#toExponential'><code>toExponential</code></a> method will always
|
|
return a value in exponential form.
|
|
</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='#toString'><code>toString</code></a>
|
|
returns exponential notation.
|
|
</p>
|
|
<pre>Decimal.set({ toExpPos: 2 })
|
|
Decimal.toExpPos // 2
|
|
new Decimal(12.3) // '12.3' e is 1
|
|
new Decimal(123) // '1.23e+2'
|
|
|
|
// Always return exponential notation:
|
|
Decimal.set({ 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='#toFixed'><code>toFixed</code></a> method will always return a value in normal
|
|
notation and the <a href='#toExponential'><code>toExponential</code></a> method will always
|
|
return a value in exponential form.
|
|
</p>
|
|
|
|
|
|
|
|
<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(x) * floor(a / abs(x))</code>.
|
|
</td>
|
|
</tr>
|
|
</table>
|
|
<p>
|
|
The rounding/modulo modes are available as enumerated properties of the Decimal constructor.
|
|
</p>
|
|
<pre>Decimal.set({ modulo: Decimal.EUCLID })
|
|
Decimal.set({ modulo: 9 }) // equivalent
|
|
Decimal.modulo // 9</pre>
|
|
|
|
|
|
|
|
<h5 id="crypto">crypto</h5>
|
|
<p>
|
|
<i>boolean</i>: <code>true/false</code><br /> Default value: <code>false</code>
|
|
</p>
|
|
<p>
|
|
The value that determines whether cryptographically-secure pseudo-random number generation is
|
|
used.
|
|
</p>
|
|
<p>See <a href='#Drandom'><code>random</code></a>.</p>
|
|
<pre>
|
|
// Node.js
|
|
global.crypto = require('crypto')
|
|
|
|
Decimal.crypto // false
|
|
Decimal.set({ crypto: true })
|
|
Decimal.crypto // true</pre>
|
|
|
|
|
|
|
|
<h6 id="modes">Rounding modes</h6>
|
|
<p>
|
|
The library's enumerated rounding modes are stored as properties of the 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.set({ rounding: Decimal.ROUND_CEIL })
|
|
Decimal.set({ rounding: 2 }) // equivalent
|
|
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 instance 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 <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. (Internally, the library always uses the shorter
|
|
method names.)
|
|
</p>
|
|
|
|
|
|
|
|
<h5 id="abs">absoluteValue<code class='inset'>.abs() <i>⇒ 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 affected by the value of the
|
|
<a href='#precision'><code>precision</code></a> setting.
|
|
</p>
|
|
<pre>
|
|
x = new Decimal(-0.8)
|
|
y = x.absoluteValue() // '0.8'
|
|
z = y.abs() // '0.8'</pre>
|
|
|
|
|
|
|
|
<h5 id="ceil">ceil<code class='inset'>.ceil() <i>⇒ 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 affected by the value of the
|
|
<a href='#precision'><code>precision</code></a> setting.
|
|
</p>
|
|
<pre>
|
|
x = new Decimal(1.3)
|
|
x.ceil() // '2'
|
|
y = new Decimal(-1.8)
|
|
y.ceil() // '-1'</pre>
|
|
|
|
|
|
|
|
<h5 id="clamp">clampedTo<code class='inset'>.clamp(min, max) <i>⇒ Decimal</i></code></h5>
|
|
<p>
|
|
<code>min</code>: <i>number|string|Decimal</i><br />
|
|
<code>max</code>: <i>number|string|Decimal</i>
|
|
</p>
|
|
<p>
|
|
Returns a new Decimal whose value is the value of this Decimal clamped to the range
|
|
delineated by <code>min</code> and <code>max</code>.
|
|
</p>
|
|
<p>
|
|
The return value is not affected by the value of the
|
|
<a href='#precision'><code>precision</code></a> setting.
|
|
</p>
|
|
<pre>
|
|
x = new Decimal(5)
|
|
min = new Decimal(100)
|
|
max = new Decimal(Infinity)
|
|
x.clampedTo(min, max) // '100'
|
|
x.clamp(-10, -0.1) // '-0.1'</pre>
|
|
|
|
|
|
|
|
<h5 id="cmp">comparedTo<code class='inset'>.cmp(x) <i>⇒ number</i></code></h5>
|
|
<p><code>x</code>: <i>number|string|Decimal</i></p>
|
|
<table>
|
|
<tr><th>Returns</th><th> </th></tr>
|
|
<tr>
|
|
<td class='centre'><code>1</code></td>
|
|
<td>if the value of this Decimal is greater than the value of <code>x</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>x</code></td>
|
|
</tr>
|
|
<tr>
|
|
<td class='centre'><code>0</code></td>
|
|
<td>if this Decimal and <code>x</code> have the same value</td>
|
|
</tr>
|
|
<tr>
|
|
<td class='centre'><code>NaN</code></td>
|
|
<td>if the value of either this Decimal or <code>x</code> is <code>NaN</code> </td>
|
|
</tr>
|
|
</table>
|
|
<pre>
|
|
x = new Decimal(Infinity)
|
|
y = new Decimal(5)
|
|
x.comparedTo(y) // 1
|
|
x.comparedTo(x.minus(1)) // 0
|
|
y.cmp(NaN) // NaN</pre>
|
|
|
|
|
|
|
|
<h5 id="cos">cosine<code class='inset'>.cos() <i>⇒ Decimal</i></code></h5>
|
|
<p>
|
|
Returns a new Decimal whose value is the cosine of the value in radians 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>
|
|
Domain: [<code>-Infinity, Infinity</code>]<br />
|
|
Range: [<code>-1, 1</code>]
|
|
</p>
|
|
<p>See <a href='#Pi'><code>Pi</code></a> for the precision limit of this method.</p>
|
|
<pre>
|
|
x = new Decimal(0.25)
|
|
x.cosine() // '0.96891242171064478414'
|
|
y = new Decimal(-0.25)
|
|
y.cos() // '0.96891242171064478414'</pre>
|
|
|
|
|
|
|
|
<h5 id="cbrt">cubeRoot<code class='inset'>.cbrt() <i>⇒ Decimal</i></code></h5>
|
|
<p>
|
|
Returns a new Decimal whose value is the cube 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>
|
|
<pre>
|
|
x = new Decimal(125)
|
|
x.cubeRoot() // '5'
|
|
y = new Decimal(3)
|
|
y.cbrt() // '1.4422495703074083823'</pre>
|
|
|
|
|
|
|
|
<h5 id="dp">decimalPlaces<code class='inset'>.dp() <i>⇒ 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>
|
|
x = new Decimal(1.234)
|
|
x.decimalPlaces() // '3'
|
|
y = new Decimal(987.654321)
|
|
y.dp() // '6'</pre>
|
|
|
|
|
|
|
|
<h5 id="div">dividedBy<code class='inset'>.div(x) <i>⇒ Decimal</i></code></h5>
|
|
<p><code>x</code>: <i>number|string|Decimal</i></p>
|
|
<p>
|
|
Returns a new Decimal whose value is the value of this Decimal divided by <code>x</code>,
|
|
rounded to <a href='#precision'><code>precision</code></a> significant digits using rounding
|
|
mode <a href='#rounding'><code>rounding</code></a>.
|
|
</p>
|
|
<pre>
|
|
x = new Decimal(355)
|
|
y = new Decimal(113)
|
|
x.dividedBy(y) // '3.14159292035398230088'
|
|
x.div(5) // '71'</pre>
|
|
|
|
|
|
|
|
<h5 id="divToInt">
|
|
dividedToIntegerBy<code class='inset'>.divToInt(x) <i>⇒ Decimal</i></code>
|
|
</h5>
|
|
<p><code>x</code>: <i>number|string|Decimal</i></p>
|
|
<p>
|
|
Return a new Decimal whose value is the integer part of dividing this Decimal by
|
|
<code>x</code>, rounded to <code><a href='#precision'>precision</a></code> significant digits
|
|
using rounding mode <a href='#rounding'><code>rounding</code></a>.
|
|
</p>
|
|
<pre>
|
|
x = new Decimal(5)
|
|
y = new Decimal(3)
|
|
x.dividedToIntegerBy(y) // '1'
|
|
x.divToInt(0.7) // '7'</pre>
|
|
|
|
|
|
|
|
<h5 id="eq">equals<code class='inset'>.eq(x) <i>⇒ boolean</i></code></h5>
|
|
<p><code>x</code>: <i>number|string|Decimal</i></p>
|
|
<p>
|
|
Returns <code>true</code> if the value of this Decimal equals the value of <code>x</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>
|
|
0 === 1e-324 // true
|
|
x = new Decimal(0)
|
|
x.equals('1e-324') // false
|
|
new Decimal(-0).eq(x) // true ( -0 === 0 )
|
|
|
|
y = new Decimal(NaN)
|
|
y.equals(NaN) // false</pre>
|
|
|
|
|
|
|
|
<h5 id="floor">floor<code class='inset'>.floor() <i>⇒ 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 affected by the value of the
|
|
<a href='#precision'><code>precision</code></a> setting.
|
|
</p>
|
|
<pre>
|
|
x = new Decimal(1.8)
|
|
x.floor() // '1'
|
|
y = new Decimal(-1.3)
|
|
y.floor() // '-2'</pre>
|
|
|
|
|
|
|
|
<h5 id="gt">greaterThan<code class='inset'>.gt(x) <i>⇒ boolean</i></code></h5>
|
|
<p><code>x</code>: <i>number|string|Decimal</i></p>
|
|
<p>
|
|
Returns <code>true</code> if the value of this Decimal is greater than the value of
|
|
<code>x</code>, otherwise returns <code>false</code>.
|
|
</p>
|
|
<p>Note: This method uses the <code>cmp</code> method internally.</p>
|
|
<pre>
|
|
0.1 > (0.3 - 0.2) // true
|
|
x = new Decimal(0.1)
|
|
x.greaterThan(Decimal(0.3).minus(0.2)) // false
|
|
new Decimal(0).gt(x) // false</pre>
|
|
|
|
|
|
|
|
<h5 id="gte">
|
|
greaterThanOrEqualTo<code class='inset'>.gte(x) <i>⇒ boolean</i></code>
|
|
</h5>
|
|
<p><code>x</code>: <i>number|string|Decimal</i></p>
|
|
<p>
|
|
Returns <code>true</code> if the value of this Decimal is greater than or equal to the value
|
|
of <code>x</code>, otherwise returns <code>false</code>.
|
|
</p>
|
|
<p>Note: This method uses the <code>cmp</code> method internally.</p>
|
|
<pre>
|
|
(0.3 - 0.2) >= 0.1 // false
|
|
x = new Decimal(0.3).minus(0.2)
|
|
x.greaterThanOrEqualTo(0.1) // true
|
|
new Decimal(1).gte(x) // true</pre>
|
|
|
|
|
|
|
|
<h5 id="cosh">hyperbolicCosine<code class='inset'>.cosh() <i>⇒ Decimal</i></code></h5>
|
|
<p>
|
|
Returns a new Decimal whose value is the hyperbolic cosine of the value in radians 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>
|
|
Domain: [<code>-Infinity, Infinity</code>]<br />
|
|
Range: [<code>1, Infinity</code>]
|
|
</p>
|
|
<p>See <a href='#Pi'><code>Pi</code></a> for the precision limit of this method.</p>
|
|
<pre>
|
|
x = new Decimal(1)
|
|
x.hyperbolicCosine() // '1.5430806348152437785'
|
|
y = new Decimal(0.5)
|
|
y.cosh() // '1.1276259652063807852'</pre>
|
|
|
|
|
|
|
|
<h5 id="sinh">hyperbolicSine<code class='inset'>.sinh() <i>⇒ Decimal</i></code></h5>
|
|
<p>
|
|
Returns a new Decimal whose value is the hyperbolic sine of the value in radians 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>
|
|
Domain: [<code>-Infinity, Infinity</code>]<br />
|
|
Range: [<code>-Infinity, Infinity</code>]
|
|
</p>
|
|
<p>See <a href='#Pi'><code>Pi</code></a> for the precision limit of this method.</p>
|
|
<pre>
|
|
x = new Decimal(1)
|
|
x.hyperbolicSine() // '1.1752011936438014569'
|
|
y = new Decimal(0.5)
|
|
y.sinh() // '0.52109530549374736162'</pre>
|
|
|
|
|
|
|
|
<h5 id="tanh">hyperbolicTangent<code class='inset'>.tanh() <i>⇒ Decimal</i></code></h5>
|
|
<p>
|
|
Returns a new Decimal whose value is the hyperbolic tangent of the value in radians 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>
|
|
Domain: [<code>-Infinity, Infinity</code>]<br />
|
|
Range: [<code>-1, 1</code>]
|
|
</p>
|
|
<p>See <a href='#Pi'><code>Pi</code></a> for the precision limit of this method.</p>
|
|
<pre>
|
|
x = new Decimal(1)
|
|
x.hyperbolicTangent() // '0.76159415595576488812'
|
|
y = new Decimal(0.5)
|
|
y.tanh() // '0.4621171572600097585'</pre>
|
|
|
|
|
|
|
|
<h5 id="acos">inverseCosine<code class='inset'>.acos() <i>⇒ Decimal</i></code></h5>
|
|
<p>
|
|
Returns a new Decimal whose value is the inverse cosine in radians 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>
|
|
Domain: [<code>-1, 1</code>]<br />
|
|
Range: [<code>0, pi</code>]
|
|
</p>
|
|
<p>See <a href='#Pi'><code>Pi</code></a> for the precision limit of this method.</p>
|
|
<pre>
|
|
x = new Decimal(0)
|
|
x.inverseCosine() // '1.5707963267948966192'
|
|
y = new Decimal(0.5)
|
|
y.acos() // '1.0471975511965977462'</pre>
|
|
|
|
|
|
|
|
<h5 id="acosh">
|
|
inverseHyperbolicCosine<code class='inset'>.acosh() <i>⇒ Decimal</i></code>
|
|
</h5>
|
|
<p>
|
|
Returns a new Decimal whose value is the inverse hyperbolic cosine in radians 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>
|
|
Domain: [<code>1, Infinity</code>]<br />
|
|
Range: [<code>0, Infinity</code>]
|
|
</p>
|
|
<p>See <a href='#Pi'><code>Pi</code></a> for the precision limit of this method.</p>
|
|
<pre>
|
|
x = new Decimal(5)
|
|
x.inverseHyperbolicCosine() // '2.2924316695611776878'
|
|
y = new Decimal(50)
|
|
y.acosh() // '4.6050701709847571595'</pre>
|
|
|
|
|
|
|
|
<h5 id="asinh">
|
|
inverseHyperbolicSine<code class='inset'>.asinh() <i>⇒ Decimal</i></code>
|
|
</h5>
|
|
<p>
|
|
Returns a new Decimal whose value is the inverse hyperbolic sine in radians 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>
|
|
Domain: [<code>-Infinity, Infinity</code>]<br />
|
|
Range: [<code>-Infinity, Infinity</code>]
|
|
</p>
|
|
<p>See <a href='#Pi'><code>Pi</code></a> for the precision limit of this method.</p>
|
|
<pre>
|
|
x = new Decimal(5)
|
|
x.inverseHyperbolicSine() // '2.3124383412727526203'
|
|
y = new Decimal(50)
|
|
y.asinh() // '4.6052701709914238266'</pre>
|
|
|
|
|
|
|
|
<h5 id="atanh">
|
|
inverseHyperbolicTangent<code class='inset'>.atanh() <i>⇒ Decimal</i></code>
|
|
</h5>
|
|
<p>
|
|
Returns a new Decimal whose value is the inverse hyperbolic tangent in radians 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>
|
|
Domain: [<code>-1, 1</code>]<br />
|
|
Range: [<code>-Infinity, Infinity</code>]
|
|
</p>
|
|
<p>See <a href='#Pi'><code>Pi</code></a> for the precision limit of this method.</p>
|
|
<pre>
|
|
x = new Decimal(0.5)
|
|
x.inverseHyperbolicTangent() // '0.5493061443340548457'
|
|
y = new Decimal(0.75)
|
|
y.atanh() // '0.97295507452765665255'</pre>
|
|
|
|
|
|
|
|
<h5 id="asin">inverseSine<code class='inset'>.asin() <i>⇒ Decimal</i></code></h5>
|
|
<p>
|
|
Returns a new Decimal whose value is the inverse sine in radians 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>
|
|
Domain: [<code>-1, 1</code>]<br />
|
|
Range: [<code>-pi/2, pi/2</code>]
|
|
</p>
|
|
<p>See <a href='#Pi'><code>Pi</code></a> for the precision limit of this method.</p>
|
|
<pre>
|
|
x = new Decimal(0.5)
|
|
x.inverseSine() // '0.52359877559829887308'
|
|
y = new Decimal(0.75)
|
|
y.asin() // '0.84806207898148100805'</pre>
|
|
|
|
|
|
|
|
<h5 id="atan">inverseTangent<code class='inset'>.atan() <i>⇒ Decimal</i></code></h5>
|
|
<p>
|
|
Returns a new Decimal whose value is the inverse tangent in radians 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>
|
|
Domain: [<code>-Infinity, Infinity</code>]<br />
|
|
Range: [<code>-pi/2, pi/2</code>]
|
|
</p>
|
|
<p>See <a href='#Pi'><code>Pi</code></a> for the precision limit of this method.</p>
|
|
<pre>
|
|
x = new Decimal(0.5)
|
|
x.inverseTangent() // '0.46364760900080611621'
|
|
y = new Decimal(0.75)
|
|
y.atan() // '0.6435011087932843868'</pre>
|
|
|
|
|
|
|
|
<h5 id="isFinite">isFinite<code class='inset'>.isFinite() <i>⇒ 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>
|
|
x = new Decimal(1)
|
|
x.isFinite() // true
|
|
y = new Decimal(Infinity)
|
|
y.isFinite() // false</pre>
|
|
|
|
|
|
|
|
<h5 id="isInt">isInteger<code class='inset'>.isInt() <i>⇒ 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>
|
|
x = new Decimal(1)
|
|
x.isInteger() // true
|
|
y = new Decimal(123.456)
|
|
y.isInt() // false</pre>
|
|
|
|
|
|
|
|
<h5 id="isNaN">isNaN<code class='inset'>.isNaN() <i>⇒ 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>
|
|
x = new Decimal(NaN)
|
|
x.isNaN() // true
|
|
y = new Decimal('Infinity')
|
|
y.isNaN() // false</pre>
|
|
|
|
|
|
|
|
<h5 id="isNeg">isNegative<code class='inset'>.isNeg() <i>⇒ boolean</i></code></h5>
|
|
<p>
|
|
Returns <code>true</code> if the value of this Decimal is negative, otherwise returns
|
|
<code>false</code>.
|
|
</p>
|
|
<pre>
|
|
x = new Decimal(-0)
|
|
x.isNegative() // true
|
|
y = new Decimal(2)
|
|
y.isNeg // false</pre>
|
|
<p>Note that zero is signed.</p>
|
|
<pre>
|
|
new Decimal(0).valueOf() // '0'
|
|
new Decimal(0).isNegative() // false
|
|
new Decimal(0).negated().valueOf() // '-0'
|
|
new Decimal(0).negated().isNegative() // true
|
|
new Decimal(-0).isNegative() // true
|
|
</pre>
|
|
|
|
|
|
|
|
<h5 id="isPos">isPositive<code class='inset'>.isPos() <i>⇒ boolean</i></code></h5>
|
|
<p>
|
|
Returns <code>true</code> if the value of this Decimal is positive, otherwise returns
|
|
<code>false</code>.
|
|
</p>
|
|
<pre>
|
|
x = new Decimal(0)
|
|
x.isPositive() // true
|
|
y = new Decimal(-2)
|
|
y.isPos // false</pre>
|
|
|
|
|
|
|
|
<h5 id="isZero">isZero<code class='inset'>.isZero() <i>⇒ 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>
|
|
x = new Decimal(-0)
|
|
x.isZero() && x.isNeg() // true
|
|
y = new Decimal(Infinity)
|
|
y.isZero() // false</pre>
|
|
|
|
|
|
|
|
<h5 id="lt">lessThan<code class='inset'>.lt(x) <i>⇒ boolean</i></code></h5>
|
|
<p><code>x</code>: <i>number|string|Decimal</i></p>
|
|
<p>
|
|
Returns <code>true</code> if the value of this Decimal is less than the value of
|
|
<code>x</code>, otherwise returns <code>false</code>.
|
|
</p>
|
|
<p>Note: This method uses the <code>cmp</code> method internally.</p>
|
|
<pre>
|
|
(0.3 - 0.2) < 0.1 // true
|
|
x = new Decimal(0.3).minus(0.2)
|
|
x.lessThan(0.1) // false
|
|
new Decimal(0).lt(x) // true</pre>
|
|
|
|
|
|
|
|
<h5 id="lte">lessThanOrEqualTo<code class='inset'>.lte(x) <i>⇒ boolean</i></code></h5>
|
|
<p><code>x</code>: <i>number|string|Decimal</i></p>
|
|
<p>
|
|
Returns <code>true</code> if the value of this Decimal is less than or equal to the value of
|
|
<code>x</code>, otherwise returns <code>false</code>.
|
|
</p>
|
|
<p>Note: This method uses the <code>cmp</code> method internally.</p>
|
|
<pre>
|
|
0.1 <= (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</pre>
|
|
|
|
|
|
|
|
<h5 id="log">logarithm<code class='inset'>.log(x) <i>⇒ Decimal</i></code></h5>
|
|
<p><code>x</code>: <i>number|string|Decimal</i></p>
|
|
<p>
|
|
Returns a new Decimal whose value is the base <code>x</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>x</code> is omitted, the base 10 logarithm of the value of this Decimal will be
|
|
returned.
|
|
</p>
|
|
<pre>
|
|
x = new Decimal(1000)
|
|
x.logarithm() // '3'
|
|
y = new Decimal(256)
|
|
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, and see <a href='#ln'><code>naturalLogarithm</code></a>
|
|
for the precision limit.
|
|
</p>
|
|
<p>The performance of this method degrades exponentially with increasing digits.</p>
|
|
|
|
|
|
|
|
<h5 id="sub">minus<code class='inset'>.minus(x) <i>⇒ Decimal</i></code></h5>
|
|
<p><code>x</code>: <i>number|string|Decimal</i></p>
|
|
<p>
|
|
Returns a new Decimal whose value is the value of this Decimal minus <code>x</code>, rounded
|
|
to <a href='#precision'><code>precision</code></a> significant digits using rounding mode
|
|
<a href='#rounding'><code>rounding</code></a>.
|
|
</p>
|
|
<pre>
|
|
0.3 - 0.1 // 0.19999999999999998
|
|
x = new Decimal(0.3)
|
|
x.minus(0.1) // '0.2'</pre>
|
|
|
|
|
|
|
|
<h5 id="mod">modulo<code class='inset'>.mod(x) <i>⇒ Decimal</i></code></h5>
|
|
<p><code>x</code>: <i>number|string|Decimal</i></p>
|
|
<p>
|
|
Returns a new Decimal whose value is the value of this Decimal modulo <code>x</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>
|
|
1 % 0.9 // 0.09999999999999998
|
|
x = new Decimal(1)
|
|
x.modulo(0.9) // '0.1'
|
|
|
|
y = new Decimal(8)
|
|
z = new Decimal(-3)
|
|
Decimal.modulo = 1
|
|
y.mod(z) // '2'
|
|
Decimal.modulo = 3
|
|
y.mod(z) // '-1'</pre>
|
|
|
|
|
|
|
|
<h5 id="exp">naturalExponential<code class='inset'>.exp() <i>⇒ 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>
|
|
x = new Decimal(1)
|
|
x.naturalExponential() // '2.7182818284590452354'
|
|
y = new Decimal(2)
|
|
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="ln">naturalLogarithm<code class='inset'>.ln() <i>⇒ 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 natural logarithm is the inverse of the <code><a href='#exp'>naturalExponential</a></code>
|
|
function.
|
|
</p>
|
|
<pre>
|
|
x = new Decimal(10)
|
|
x.naturalLogarithm() // '2.3026'
|
|
y = new Decimal('1.23e+30')
|
|
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>⇒ 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 affected by the value of the
|
|
<a href='#precision'><code>precision</code></a> setting.
|
|
</p>
|
|
<pre>
|
|
x = new Decimal(1.8)
|
|
x.negated() // '-1.8'
|
|
y = new Decimal(-1.3)
|
|
y.neg() // '1.3'</pre>
|
|
|
|
|
|
|
|
<h5 id="add">plus<code class='inset'>.plus(x) <i>⇒ Decimal</i></code></h5>
|
|
<p><code>x</code>: <i>number|string|Decimal</i></p>
|
|
<p>
|
|
Returns a new Decimal whose value is the value of this Decimal plus <code>x</code>, rounded to
|
|
<a href='#precision'><code>precision</code></a> significant digits using rounding mode
|
|
<a href='#rounding'><code>rounding</code></a>.
|
|
</p>
|
|
<pre>
|
|
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'</pre>
|
|
|
|
|
|
|
|
<h5 id="sd">precision<code class='inset'>.sd([include_zeros]) <i>⇒ 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>
|
|
x = new Decimal(1.234)
|
|
x.precision() // '4'
|
|
y = new Decimal(987000)
|
|
y.sd() // '3'
|
|
y.sd(true) // '6'</pre>
|
|
|
|
|
|
|
|
<h5 id="round">round<code class='inset'>.round() <i>⇒ 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>
|
|
Decimal.set({ rounding: 4 })
|
|
x = 1234.5
|
|
x.round() // '1235'
|
|
|
|
Decimal.rounding = Decimal.ROUND_DOWN
|
|
x.round() // '1234'
|
|
x // '1234.5'</pre>
|
|
|
|
|
|
|
|
<h5 id="sin">sine<code class='inset'>.sin() <i>⇒ Decimal</i></code></h5>
|
|
<p>
|
|
Returns a new Decimal whose value is the sine of the value in radians 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>
|
|
Domain: [<code>-Infinity, Infinity</code>]<br />
|
|
Range: [<code>-1, 1</code>]
|
|
</p>
|
|
<p>See <a href='#Pi'><code>Pi</code></a> for the precision limit of this method.</p>
|
|
<pre>
|
|
x = new Decimal(0.5)
|
|
x.sine() // '0.47942553860420300027'
|
|
y = new Decimal(0.75)
|
|
y.sin() // '0.68163876002333416673'</pre>
|
|
|
|
|
|
|
|
<h5 id="sqrt">squareRoot<code class='inset'>.sqrt() <i>⇒ 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>
|
|
x = new Decimal(16)
|
|
x.squareRoot() // '4'
|
|
y = new Decimal(3)
|
|
y.sqrt() // '1.73205080756887729353'
|
|
y.sqrt().eq( y.pow(0.5) ) // true</pre>
|
|
|
|
|
|
|
|
<h5 id="tan">tangent<code class='inset'>.tan() <i>⇒ Decimal</i></code></h5>
|
|
<p>
|
|
Returns a new Decimal whose value is the tangent of the value in radians 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>
|
|
Domain: [<code>-Infinity, Infinity</code>]<br />
|
|
Range: [<code>-Infinity, Infinity</code>]
|
|
</p>
|
|
<p>See <a href='#Pi'><code>Pi</code></a> for the precision limit of this method.</p>
|
|
<pre>
|
|
x = new Decimal(0.5)
|
|
x.tangent() // '0.54630248984379051326'
|
|
y = new Decimal(0.75)
|
|
y.tan() // '0.93159645994407246117'</pre>
|
|
|
|
|
|
|
|
<h5 id="mul">times<code class='inset'>.times(x) <i>⇒ Decimal</i></code></h5>
|
|
<p><code>x</code>: <i>number|string|Decimal</i></p>
|
|
<p>
|
|
Returns a new Decimal whose value is the value of this Decimal times <code>x</code>,
|
|
rounded to <a href='#precision'><code>precision</code></a> significant digits using rounding
|
|
mode <a href='#rounding'><code>rounding</code></a>.
|
|
</p>
|
|
<pre>
|
|
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'</pre>
|
|
|
|
|
|
|
|
<h5 id="toBinary">
|
|
toBinary<code class='inset'>.toBinary([sd [, rm]]) <i>⇒ string</i></code>
|
|
</h5>
|
|
<p>
|
|
<code>sd</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 Decimal in binary, rounded to <code>sd</code>
|
|
significant digits using rounding mode <code>rm</code>.
|
|
</p>
|
|
<p>
|
|
If <code>sd</code> is defined, the return value will use binary exponential notation.
|
|
</p>
|
|
<p>
|
|
If <code>sd</code> is omitted, the return value will be rounded to
|
|
<a href='#precision'><code>precision</code></a> significant digits.
|
|
</p>
|
|
<p>
|
|
If <code>rm</code> is omitted, rounding mode <a href='#rounding'><code>rounding</code></a>
|
|
will be used.
|
|
</p>
|
|
<p>Throws on an invalid <code>sd</code> or <code>rm</code> value.</p>
|
|
<pre>
|
|
x = new Decimal(256)
|
|
x.toBinary() // '0b100000000'
|
|
x.toBinary(1) // '0b1p+8'</pre>
|
|
|
|
|
|
|
|
<h5 id="toDP">
|
|
toDecimalPlaces<code class='inset'>.toDP([dp [, rm]]) <i>⇒ Decimal</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 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, the return value will have the same value as this Decimal.
|
|
</p>
|
|
<p>
|
|
If <code>rm</code> is omitted, rounding mode <a href='#rounding'><code>rounding</code></a>
|
|
is used.
|
|
</p>
|
|
<p>Throws on an invalid <code>dp</code> or <code>rm</code> value.</p>
|
|
<pre>
|
|
x = new Decimal(12.34567)
|
|
x.toDecimalPlaces(0) // '12'
|
|
x.toDecimalPlaces(1, Decimal.ROUND_UP) // '12.4'
|
|
|
|
y = new Decimal(9876.54321)
|
|
y.toDP(3) // '9876.543'
|
|
y.toDP(1, 0) // '9876.6'
|
|
y.toDP(1, Decimal.ROUND_DOWN) // '9876.5'</pre>
|
|
|
|
|
|
|
|
<h5 id="toExponential">
|
|
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 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, 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, rounding mode <a href='#rounding'><code>rounding</code></a> is
|
|
used.
|
|
</p>
|
|
<p>Throws on an invalid <code>dp</code> or <code>rm</code> value.</p>
|
|
<pre>
|
|
x = 45.6
|
|
y = new Decimal(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, Decimal.ROUND_DOWN) // '4.5e+1'
|
|
x.toExponential(3) // '4.560e+1'
|
|
y.toExponential(3) // '4.560e+1'</pre>
|
|
|
|
|
|
|
|
<h5 id="toFixed">
|
|
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 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, 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='#toString'>toString</a></code> returns exponential notation.
|
|
</p>
|
|
<p>
|
|
If <code>rm</code> is omitted, rounding mode <a href='#rounding'><code>rounding</code></a> is
|
|
used.
|
|
</p>
|
|
<p>Throws on an invalid <code>dp</code> or <code>rm</code> value.</p>
|
|
<pre>
|
|
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, Decimal.ROUND_DOWN) // '3.45'
|
|
x.toFixed(5) // '3.45600'
|
|
y.toFixed(5) // '3.45600'</pre>
|
|
|
|
|
|
|
|
<h5 id="toFraction">
|
|
toFraction
|
|
<code class='inset'>.toFraction([max_denominator]) <i>⇒ [Decimal, Decimal]</i></code>
|
|
</h5>
|
|
<p>
|
|
<code>max_denominator</code>: <i>number|string|Decimal</i>: <code>1</code> >= integer <
|
|
<code>Infinity</code>
|
|
</p>
|
|
<p>
|
|
Returns an array of two Decimals 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 omitted, the denominator will be the lowest value necessary to
|
|
represent the number exactly.
|
|
</p>
|
|
<p>Throws on an invalid <code>max_denominator</code> value.</p>
|
|
<pre>
|
|
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'
|
|
pi.toFraction(1) // '3, 1'</pre>
|
|
|
|
|
|
|
|
<h5 id="toHex">
|
|
toHexadecimal<code class='inset'>.toHex([sd [, rm]]) <i>⇒ string</i></code>
|
|
</h5>
|
|
<p>
|
|
<code>sd</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 Decimal in hexadecimal, rounded to
|
|
<code>sd</code> significant digits using rounding mode <code>rm</code>.
|
|
</p>
|
|
<p>
|
|
If <code>sd</code> is defined, the return value will use binary exponential notation.
|
|
</p>
|
|
<p>
|
|
If <code>sd</code> is omitted, the return value will be rounded to
|
|
<a href='#precision'><code>precision</code></a> significant digits.
|
|
</p>
|
|
<p>
|
|
If <code>rm</code> is omitted, rounding mode <a href='#rounding'><code>rounding</code></a>
|
|
will be used.
|
|
</p>
|
|
<p>Throws on an invalid <code>sd</code> or <code>rm</code> value.</p>
|
|
<pre>
|
|
x = new Decimal(256)
|
|
x.toHexadecimal() // '0x100'
|
|
x.toHex(1) // '0x1p+8'</pre>
|
|
|
|
|
|
|
|
<h5 id="toJSON">toJSON<code class='inset'>.toJSON() <i>⇒ string</i></code></h5>
|
|
<p>As <a href='#valueOf'><code>valueOf</code></a>.</p>
|
|
|
|
|
|
|
|
<h5 id="toNearest">
|
|
toNearest<code class='inset'>.toNearest(x [, rm]) <i>⇒ Decimal</i></code>
|
|
</h5>
|
|
<p>
|
|
<code>x</code>: <i>number|string|Decimal</i><br />
|
|
<code>rm</code>: <i>number</i>: integer, <code>0</code> to <code>8</code> inclusive
|
|
</p>
|
|
<p>
|
|
Returns a new Decimal whose value is the nearest multiple of <code>x</code> in the direction
|
|
of rounding mode <code>rm</code>, or <a href='#rounding'><code>rounding</code></a> if
|
|
<code>rm</code> is omitted, to the value of this Decimal.
|
|
</p>
|
|
<p>
|
|
The return value will always have the same sign as this Decimal, unless either this Decimal
|
|
or <code>x</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 affected by the value of the
|
|
<a href='#precision'><code>precision</code></a> setting.
|
|
</p>
|
|
<pre>
|
|
x = new Decimal(1.39)
|
|
x.toNearest(0.25) // '1.5'
|
|
|
|
y = new Decimal(9.499)
|
|
y.toNearest(0.5, Decimal.ROUND_UP) // '9.5'
|
|
y.toNearest(0.5, Decimal.ROUND_DOWN) // '9'</pre>
|
|
|
|
|
|
|
|
<h5 id="toNumber">toNumber<code class='inset'>.toNumber() <i>⇒ number</i></code></h5>
|
|
<p>Returns the value of this Decimal converted to a primitive number.</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>
|
|
x = new Decimal(456.789)
|
|
x.toNumber() // 456.789
|
|
+x // 456.789
|
|
|
|
y = new Decimal('45987349857634085409857349856430985')
|
|
y.toNumber() // 4.598734985763409e+34
|
|
|
|
z = new Decimal(-0)
|
|
1 / +z // Infinity
|
|
1 / z.toNumber() // -Infinity</pre>
|
|
|
|
|
|
|
|
<h5 id="toOctal">
|
|
toOctal<code class='inset'>.toOctal([sd [, rm]]) <i>⇒ string</i></code>
|
|
</h5>
|
|
<p>
|
|
<code>sd</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 Decimal in octal, rounded to <code>sd</code>
|
|
significant digits using rounding mode <code>rm</code>.
|
|
</p>
|
|
<p>
|
|
If <code>sd</code> is defined, the return value will use binary exponential notation.
|
|
</p>
|
|
<p>
|
|
If <code>sd</code> is omitted, the return value will be rounded to
|
|
<a href='#precision'><code>precision</code></a> significant digits.
|
|
</p>
|
|
<p>
|
|
If <code>rm</code> is omitted, rounding mode <a href='#rounding'><code>rounding</code></a>
|
|
will be used.
|
|
</p>
|
|
<p>Throws on an invalid <code>sd</code> or <code>rm</code> value.</p>
|
|
<pre>
|
|
x = new Decimal(256)
|
|
x.toOctal() // '0o400'
|
|
x.toOctal(1) // '0o1p+8'</pre>
|
|
|
|
|
|
|
|
<h5 id="pow">toPower<code class='inset'>.pow(x) <i>⇒ Decimal</i></code></h5>
|
|
<p><code>x</code>: <i>number|string|Decimal</i>: integer or non-integer</p>
|
|
<p>
|
|
Returns a new Decimal whose value is the value of this Decimal raised to the power
|
|
<code>x</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>
|
|
Math.pow(0.7, 2) // 0.48999999999999994
|
|
x = new Decimal(0.7)
|
|
x.toPower(2) // '0.49'
|
|
new Decimal(3).pow(-2) // '0.11111111111111111111'
|
|
|
|
new Decimal(1217652.23).pow('98765.489305603941')
|
|
// '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 <a href='#exp'><code>exp</code></a> and
|
|
<a href='#ln'><code>ln</code></a> functions are both non-terminating (excluding arguments of
|
|
<code>0</code> or <code>1</code>), the values of the Decimals returned by the functions as
|
|
implemented by this library will necessarily 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, or a <code>5</code> or <code>4</code>
|
|
followed by <code>14</code> nines.
|
|
</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>
|
|
Decimal.set({ precision: 20, rounding: 1 })
|
|
new Decimal(28).pow('6.166675020000903537297764507632802193308677149')
|
|
// 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="toPrecision">
|
|
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 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, the return value is the same as
|
|
<code><a href='#toString'>toString</a></code>.
|
|
</p>
|
|
<p>
|
|
If <code>rm</code> is omitted, rounding mode <a href='#rounding'><code>rounding</code></a> is
|
|
used.
|
|
</p>
|
|
<p>Throws on an invalid <code>sd</code> or <code>rm</code> value.</p>
|
|
<pre>
|
|
x = 45.6
|
|
y = new Decimal(x)
|
|
x.toPrecision() // '45.6'
|
|
y.toPrecision() // '45.6'
|
|
x.toPrecision(1) // '5e+1'
|
|
y.toPrecision(1) // '5e+1'
|
|
y.toPrecision(2, Decimal.ROUND_UP) // '46'
|
|
y.toPrecision(2, Decimal.ROUND_DOWN) // '45'
|
|
x.toPrecision(5) // '45.600'
|
|
y.toPrecision(5) // '45.600'</pre>
|
|
|
|
|
|
|
|
<h5 id="toSD">
|
|
toSignificantDigits<code class='inset'>.toSD([sd [, rm]]) <i>⇒ Decimal</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 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, the return value will be rounded to
|
|
<a href='#precision'><code>precision</code></a> significant digits.
|
|
</p>
|
|
<p>
|
|
If <code>rm</code> is omitted, rounding mode <a href='#rounding'><code>rounding</code></a>
|
|
will be used.
|
|
</p>
|
|
<p>Throws on an invalid <code>sd</code> or <code>rm</code> value.</p>
|
|
<pre>
|
|
Decimal.set({ precision: 5, rounding: 4 })
|
|
x = new Decimal(9876.54321)
|
|
|
|
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'
|
|
x // '9876.54321'</pre>
|
|
|
|
|
|
|
|
<h5 id="toString">toString<code class='inset'>.toString() <i>⇒ string</i></code></h5>
|
|
<p>Returns a string representing the value of this Decimal.</p>
|
|
<p>
|
|
If 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 will be returned.
|
|
</p>
|
|
<pre>
|
|
x = new Decimal(750000)
|
|
x.toString() // '750000'
|
|
Decimal.set({ toExpPos: 5 })
|
|
x.toString() // '7.5e+5'
|
|
|
|
Decimal.set({ precision: 4 })
|
|
y = new Decimal('1.23456789')
|
|
y.toString() // '1.23456789'</pre>
|
|
|
|
|
|
|
|
<h5 id="trunc">truncated<code class='inset'>.trunc() <i>⇒ 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 affected by the value of the
|
|
<a href='#precision'><code>precision</code></a> setting.
|
|
</p>
|
|
<pre>
|
|
x = new Decimal(123.456)
|
|
x.truncated() // '123'
|
|
y = new Decimal(-12.3)
|
|
y.trunc() // '-12'</pre>
|
|
|
|
|
|
|
|
<h5 id="valueOf">valueOf<code class='inset'>.valueOf() <i>⇒ string</i></code></h5>
|
|
<p>As <a href='#toString'><code>toString</code></a>, but zero is signed.</p>
|
|
<pre>
|
|
x = new Decimal(-0)
|
|
x.valueOf() // '-0'</pre>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<h4 id="instance-properties">Properties</h4>
|
|
<p>
|
|
The value of a Decimal is stored in a normalised base <code>10000000</code> floating point
|
|
format.
|
|
</p>
|
|
<p>
|
|
A Decimal instance 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='digits'><b>d</b></td>
|
|
<td>digits</td>
|
|
<td><i>number</i><code style='color:#000'>[]</code></td>
|
|
<td> Array of integers, each <code>0</code> - <code>1e7</code>, or <code>null</code></td>
|
|
</tr>
|
|
<tr>
|
|
<td class='centre' id='exponent'><b>e</b></td>
|
|
<td>exponent</td>
|
|
<td><i>number</i></td>
|
|
<td>Integer, <code>-9e15</code> to <code>9e15</code> inclusive, or <code>NaN</code></td>
|
|
</tr>
|
|
<tr>
|
|
<td class='centre' id='sign'><b>s</b></td>
|
|
<td>sign</td>
|
|
<td><i>number</i></td>
|
|
<td><code>-1</code>, <code>1</code>, or <code>NaN</code></td>
|
|
</tr>
|
|
</table>
|
|
<p>All the properties are best considered to be read-only.</p>
|
|
<p>
|
|
As with JavaScript numbers, the original exponent and fractional trailing zeros of a value
|
|
are not preserved.
|
|
</p>
|
|
<pre>
|
|
x = new Decimal(0.123) // '0.123'
|
|
x.toExponential() // '1.23e-1'
|
|
x.d // [ 1230000 ]
|
|
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'
|
|
z.d // [ 12345, 6700000 ]
|
|
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>±0</th>
|
|
<th>NaN</th>
|
|
<th>±Infinity</th>
|
|
</tr>
|
|
<tr>
|
|
<td><b> d </b></td>
|
|
<td><code>[0]</code></td>
|
|
<td><code>null</code></td>
|
|
<td><code>null</code></td>
|
|
</tr>
|
|
<tr>
|
|
<td><b> e </b></td>
|
|
<td><code>0</code></td>
|
|
<td><code>NaN</code></td>
|
|
<td><code>NaN</code></td>
|
|
</tr>
|
|
<tr>
|
|
<td><b> s </b></td>
|
|
<td><code>±1</code></td>
|
|
<td><code>NaN</code></td>
|
|
<td><code>±1</code></td>
|
|
</tr>
|
|
</table>
|
|
<pre>
|
|
x = new Number(-0) // 0
|
|
1 / x == -Infinity // true
|
|
|
|
y = new Decimal(-0)
|
|
y.d // '0' ( [0].toString() )
|
|
y.e // 0
|
|
y.s // -1
|
|
y.toString() // '0'
|
|
y.valueOf() // '-0'</pre>
|
|
|
|
|
|
|
|
<h4 id='Errors'>Errors</h4>
|
|
<p>
|
|
The errors that are thrown are generic <code>Error</code> objects whose <code>message</code>
|
|
property begins with <code>"[DecimalError]"</code>.
|
|
</p>
|
|
<p>To determine if an exception is a Decimal Error:</p>
|
|
<pre>
|
|
try {
|
|
// ...
|
|
} catch (e) {
|
|
if ( e instanceof Error && /DecimalError/.test(e.message) ) {
|
|
// ...
|
|
}
|
|
}</pre>
|
|
|
|
|
|
|
|
<h4 id='Pi'>Pi</h4>
|
|
<p>
|
|
The maximum precision of the trigonometric methods is dependent on the internal value of the
|
|
constant pi, which is defined as the string <code>PI</code> near the top of the source file.
|
|
</p>
|
|
<p>
|
|
It has a precision of <code>1025</code> digits, meaning that the trigonometric methods
|
|
can calculate up to just over <code>1000</code> digits, but the actual figure depends on the
|
|
precision of the argument passed to them. To calculate the actual figure use:
|
|
</p>
|
|
<p><b>maximum_result_precision = 1000 - argument_precision</b></p>
|
|
For example, the following both work fine:
|
|
<pre>
|
|
Decimal.set({precision: 991}).tan(123456789)
|
|
Decimal.set({precision: 9}).tan(991_digit_number)</pre>
|
|
<p>
|
|
as, for each, the result precision plus the argument precision, i.e. <code>991 + 9</code> and
|
|
<code>9 + 991</code>, is less than or equal to <code>1000</code>.
|
|
</p>
|
|
<p>
|
|
If greater precision is required then the value of <code>PI</code> will need to be extended to
|
|
about <code>25</code> digits more than the precision required. The time taken by the methods
|
|
will then be the limiting factor.
|
|
</p>
|
|
<p>
|
|
The value can also be shortened to reduce the size of the source file if such high precision
|
|
is not required.
|
|
</p>
|
|
<p>To get the value of pi:</p>
|
|
<pre>
|
|
pi = Decimal.acos(-1)</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>
|
|
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>
|
|
|
|
<script>
|
|
/* decimal.js v10.5.0 https://github.com/MikeMcl/decimal.js/LICENCE */
|
|
!function(n){"use strict";var e,i,t,r,s=9e15,o=1e9,u="0123456789abcdef",c="2.3025850929940456840179914546843642076011014886287729760333279009675726096773524802359972050895982983419677840422862486334095254650828067566662873690987816894829072083255546808437998948262331985283935053089653777326288461633662222876982198867465436674744042432743651550489343149393914796194044002221051017141748003688084012647080685567743216228355220114804663715659121373450747856947683463616792101806445070648000277502684916746550586856935673420670581136429224554405758925724208241314695689016758940256776311356919292033376587141660230105703089634572075440370847469940168269282808481184289314848524948644871927809676271275775397027668605952496716674183485704422507197965004714951050492214776567636938662976979522110718264549734772662425709429322582798502585509785265383207606726317164309505995087807523710333101197857547331541421808427543863591778117054309827482385045648019095610299291824318237525357709750539565187697510374970888692180205189339507238539205144634197265287286965110862571492198849978748873771345686209167058",f="3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632789",a={precision:20,rounding:4,modulo:1,toExpNeg:-7,toExpPos:21,minE:-s,maxE:s,crypto:!1},l=!0,d="[DecimalError] 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