From 5fd54409664d125e52a12dfcf74749f77c35bf57 Mon Sep 17 00:00:00 2001
From: hbk01 <3243430237@qq.com>
Date: Mon, 2 Jan 2023 20:52:03 +0800
Subject: [PATCH] =?UTF-8?q?+=20=E8=BF=9B=E6=A0=B7=E5=BA=8F=E5=88=97?=
 =?UTF-8?q?=E6=9B=B4=E5=90=8D=E4=B8=BA=E8=BF=9B=E6=A0=B7=E6=97=B6=E9=97=B4?=
 =?UTF-8?q?=20+=20=E8=BF=9B=E6=A0=B7=E6=97=B6=E9=97=B4=E5=8F=AF=E8=AE=A1?=
 =?UTF-8?q?=E7=AE=97=E5=85=A8=E5=BA=8F=E5=88=97=E7=9A=84=E5=BC=80=E5=A7=8B?=
 =?UTF-8?q?=E4=B8=8E=E7=BB=93=E6=9D=9F=E6=97=B6=E9=97=B4?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 index.html              |    2 +-
 injection-sequence.html |  145 +-
 modules/dayjs.min.js    |    1 +
 modules/decimal.mjs     | 4898 +++++++++++++++++++++++++++++++++++++++
 4 files changed, 4986 insertions(+), 60 deletions(-)
 create mode 100644 modules/dayjs.min.js
 create mode 100644 modules/decimal.mjs

diff --git a/index.html b/index.html
index ceae77d..2c9ca02 100644
--- a/index.html
+++ b/index.html
@@ -25,7 +25,7 @@
                 "location": "./roi.html"
             },
             {
-                "name": "进样序列",
+                "name": "进样时间",
                 "location": "./injection-sequence.html"
             },
             {
diff --git a/injection-sequence.html b/injection-sequence.html
index eaee322..e5980d8 100644
--- a/injection-sequence.html
+++ b/injection-sequence.html
@@ -5,50 +5,61 @@
     <meta charset="UTF-8">
     <meta http-equiv="X-UA-Compatible" content="IE=edge">
     <meta name="viewport" content="width=device-width, initial-scale=1.0, maximum-scale=1.0, user-scalable=no">
-    <title>进样序列</title>
+    <title>进样时间</title>
     <link rel="stylesheet" href="./github.css">
     <link rel="stylesheet" href="./theme.css">
-    <script src="./decimal.js"></script>
+    <script src="./modules/dayjs.min.js"></script>
     <script src="https://cdn.bootcdn.net/ajax/libs/jquery/3.6.0/jquery.min.js"></script>
-    <script>
-        let decimal = Decimal.set({
+    <script type="module">
+        import { Decimal } from "./modules/decimal.mjs"
+
+        const decimal = Decimal.set({
             rounding: Decimal.ROUND_HALF_EVEN,
             precision: 12
         })
+
         $(document).ready(() => {
             let tip = `
-            计算每一针走完的时间。<br>
-            设置时间提前量可以将每针的时间提前，用于给看样及配样等操作留时间。`
+            <p>此功能用于计算批处理中每一针样品运行的时间。</p>
+            <p>设置时间偏移量可以将每一针的结束时间提前，用于给查看样品图谱及现配现进等操作预留时间。</p>
+            <p>仪器进样需要一定的时间，该部分时间虽然短，积累起来却不可忽视。<br>
+                此功能以当前运行样品的时间为起点，再向前/向后计算其他针的时间。所以，越远离当前运行的样品，则误差越大。
+                </p>`
             $("#output").append(tip)
 
             $("#ok").click(() => {
-                let time = $("#time").val()
-                let num = $("#num").val()
-                let ptime = $("#ptime").val()
-                let stime = $("#stime").val()
+                let allId = new Decimal($("#allId").val()).toNumber()
+                let nowId = new Decimal($("#nowId").val()).toNumber()
+                let time = new Decimal($("#time").val()).toNumber()
+                let nowTime = new Decimal($("#nowTime").val()).toNumber()
+                let offset = new Decimal($("#offset").val()).toNumber()
                 let data = []
 
                 // 生成数据
-                for (let i = 1; i <= num; i++) {
-                    let t = injectionSequenceToDate(time, ptime, stime, i)
+                let array = genData(allId, nowId, time, nowTime, offset)
+                let formatString = 'YYYY-MM-DD HH:mm'
+                array.forEach((value, index) => {
                     data.push({
-                        "id": i,
-                        "time": t
+                        "id": index + 1,
+                        "startTime": value.format(formatString),
+                        "endTime": value.add(time, 'minute').format(formatString),
+                        "offsetTime": value.add(time - offset, 'minute').format(formatString)
                     })
-                }
+                })
 
                 // 未生成数据，不进行结果展示
                 if (data.length == 0) return
+
                 $("#output").empty()
                 $("#output").append(createTable(data))
             })
 
-
             $("#clear").click(() => {
+                $("#allId").val("")
+                $("#nowId").val("")
                 $("#time").val("")
-                $("#num").val("")
-                $("#ptime").val("")
-                $("#stime").val("")
+                $("#nowTime").val("")
+                $("#offset").val("")
                 $("#output").empty()
                 $("#output").append(tip)
             })
@@ -59,65 +70,80 @@
         })
 
         /**
-         * 计算进样时间，返回 yyyy-MM-dd hh:mm 格式的字符串
+         * 生成数据
+         * @author <a href="mailto:3243430237@qq.com" target="_blank">hbk01</a>
+         * @param {Number} allId 总针数（即需要计算多少条数据）
+         * @param {Number} nowId 当前针数（当前仪器运行到第几针）
+         * @param {Number} time 一针有多少分钟（包括后运行）
+         * @param {Number} nowTime 当前这针已经运行了多少分钟
+         * @param {Number} offset 每一针需偏移多少分钟
+         * @return {Array} dayjs
          */
-        function injectionSequenceToDate(time, ptime, stime, num) {
-            let t = injectionSequence(time, ptime, stime, num)
-            let t_hour = Math.floor(Math.abs(t) / 60)
-            let t_min = t % 60
-            let date = new Date()
-            let dateAfter = new Date(date.getFullYear(), date.getMonth(), date.getDate(),
-                date.getHours() + t_hour, date.getMinutes() + t_min).format("yyyy-MM-dd hh:mm")
-            return dateAfter
+        function genData(allId, nowId, time, nowTime, offset) {
+            let array = new Array(allId)
+            let now = new dayjs()
+            // 将当前这针的开始时间先设置好
+            array[nowId - 1] = now.subtract(nowTime, 'minute')
+            // 计算当前这针前面的时间
+            for (let index = nowId - 2; index >= 0; index--) {
+                array[index] = array[index + 1].subtract(time, 'minute')
+            }
+            // 计算当前这针后面的时间
+            for (let index = nowId; index < allId; index++) {
+                array[index] = array[index - 1].add(time, 'minute')
+            }
+            return array
         }
 
         /**
          * 创建表格元素并将数据填入其中。
          */
         function createTable(data) {
+            let nowId = new Decimal($("#nowId").val()).toNumber()
+
             let table = document.createElement("table")
-            table.setAttribute("style", "width: 100%; text-align: center;")
+            table.setAttribute("style", "width: 100%; text-align: center; font-size: smaller;")
             table.setAttribute("class", "pure-table")
 
             let row = document.createElement("tr")
-            let th1 = document.createElement("th")
-            let th2 = document.createElement("th")
-            th1.innerText = "第几针"
-            th2.innerText = "进样时间"
-            row.appendChild(th1)
-            row.appendChild(th2)
+            let lineNum = document.createElement("th")
+            let startTime = document.createElement("th")
+            let endTime = document.createElement("th")
+            let offset = document.createElement("th")
+            lineNum.innerText = "序号"
+            startTime.innerText = "开始时间"
+            endTime.innerText = "结束时间"
+            offset.innerText = "偏移后"
+            row.appendChild(lineNum)
+            row.appendChild(startTime)
+            row.appendChild(endTime)
+            // row.appendChild(offset)
             table.appendChild(row)
+            let highlight = 'background-color: #ffffcc;'
             data.forEach(element => {
                 let tr = document.createElement("tr")
                 let td_id = document.createElement("td")
-                let td_time = document.createElement("td")
+                let td_start_time = document.createElement("td")
+                let td_end_time = document.createElement("td")
+                let td_offset_time = document.createElement("td")
 
                 td_id.innerText = element.id
-                td_time.innerText = element.time
+                td_start_time.innerText = element.startTime
+                // td_end_time.innerText = element.endTime
+                td_end_time.innerText = element.offsetTime
+                td_offset_time.innerText = element.offsetTime
+
+                if (element.id == nowId) tr.style = highlight
 
                 tr.appendChild(td_id)
-                tr.appendChild(td_time)
+                tr.appendChild(td_start_time)
+                tr.appendChild(td_end_time)
+                // tr.appendChild(td_offset_time)
                 table.appendChild(tr)
             })
             return table
         }
 
-        /**
-         * 计算总共的进样时间
-         * @param time 多少分钟一针
-         * @param ptime 时间需要提前多少分钟
-         * @param stime 现在这针运行多少分钟
-         * @param num 计算第n针后的时间
-         */
-        function injectionSequence(time, ptime, stime, num) {
-            // formal: InjectionSequence = time * num - ptime - stime
-            let t = new Decimal(time)
-            let p = new Decimal(ptime)
-            let s = new Decimal(stime)
-            let n = new Decimal(num)
-            return decimal.mul(t, n).sub(p).sub(s).toString()
-        }
-
         // 为 Date 创建日期格式化方法
         Date.prototype.format = function (fmt) {
             let o = {
@@ -144,13 +170,14 @@
 </head>
 
 <body>
-    <h3>进样序列</h3>
+    <h3>进样时间</h3>
     <div class="input">
         <div class="inputbox">
-            <input type="number" id="time" placeholder="多少分钟一针" inputmode="decimal" autocomplete="off">
-            <input type="number" id="num" placeholder="一共有多少针（包括正在运行的）" inputmode="decimal" autocomplete="off">
-            <input type="number" id="stime" placeholder="现在这针运行多少分钟" inputmode="decimal" autocomplete="off">
-            <input type="number" id="ptime" placeholder="时间提前量（分钟）" inputmode="decimal" autocomplete="off">
+            <input type="number" id="allId" placeholder="批处理中样品的总数" inputmode="decimal" autocomplete="off">
+            <input type="number" id="time" placeholder="每一针的运行时间" inputmode="decimal" autocomplete="off">
+            <input type="number" id="nowId" placeholder="当前运行到第几针" inputmode="decimal" autocomplete="off">
+            <input type="number" id="nowTime" placeholder="现在这针运行多少分钟" inputmode="decimal" autocomplete="off">
+            <input type="number" id="offset" placeholder="时间偏移量" inputmode="decimal" autocomplete="off">
         </div>
         <br>
         <div class="buttons">
diff --git a/modules/dayjs.min.js b/modules/dayjs.min.js
new file mode 100644
index 0000000..af2b347
--- /dev/null
+++ b/modules/dayjs.min.js
@@ -0,0 +1 @@
+!function (t, e) { "object" == typeof exports && "undefined" != typeof module ? module.exports = e() : "function" == typeof define && define.amd ? define(e) : (t = "undefined" != typeof globalThis ? globalThis : t || self).dayjs = e() }(this, (function () { "use strict"; var t = 1e3, e = 6e4, n = 36e5, r = "millisecond", i = "second", s = "minute", u = "hour", a = "day", o = "week", f = "month", h = "quarter", c = "year", d = "date", $ = "Invalid Date", l = /^(\d{4})[-/]?(\d{1,2})?[-/]?(\d{0,2})[Tt\s]*(\d{1,2})?:?(\d{1,2})?:?(\d{1,2})?[.:]?(\d+)?$/, y = /\[([^\]]+)]|Y{1,4}|M{1,4}|D{1,2}|d{1,4}|H{1,2}|h{1,2}|a|A|m{1,2}|s{1,2}|Z{1,2}|SSS/g, M = { name: "en", weekdays: "Sunday_Monday_Tuesday_Wednesday_Thursday_Friday_Saturday".split("_"), months: "January_February_March_April_May_June_July_August_September_October_November_December".split("_") }, m = function (t, e, n) { var r = String(t); return !r || r.length >= e ? t : "" + Array(e + 1 - r.length).join(n) + t }, g = { s: m, z: function (t) { var e = -t.utcOffset(), n = Math.abs(e), r = Math.floor(n / 60), i = n % 60; return (e <= 0 ? "+" : "-") + m(r, 2, "0") + ":" + m(i, 2, "0") }, m: function t(e, n) { if (e.date() < n.date()) return -t(n, e); var r = 12 * (n.year() - e.year()) + (n.month() - e.month()), i = e.clone().add(r, f), s = n - i < 0, u = e.clone().add(r + (s ? -1 : 1), f); return +(-(r + (n - i) / (s ? i - u : u - i)) || 0) }, a: function (t) { return t < 0 ? Math.ceil(t) || 0 : Math.floor(t) }, p: function (t) { return { M: f, y: c, w: o, d: a, D: d, h: u, m: s, s: i, ms: r, Q: h }[t] || String(t || "").toLowerCase().replace(/s$/, "") }, u: function (t) { return void 0 === t } }, v = "en", D = {}; D[v] = M; var p = function (t) { return t instanceof _ }, S = function t(e, n, r) { var i; if (!e) return v; if ("string" == typeof e) { var s = e.toLowerCase(); D[s] && (i = s), n && (D[s] = n, i = s); var u = e.split("-"); if (!i && u.length > 1) return t(u[0]) } else { var a = e.name; D[a] = e, i = a } return !r && i && (v = i), i || !r && v }, w = function (t, e) { if (p(t)) return t.clone(); var n = "object" == typeof e ? e : {}; return n.date = t, n.args = arguments, new _(n) }, O = g; O.l = S, O.i = p, O.w = function (t, e) { return w(t, { locale: e.$L, utc: e.$u, x: e.$x, $offset: e.$offset }) }; var _ = function () { function M(t) { this.$L = S(t.locale, null, !0), this.parse(t) } var m = M.prototype; return m.parse = function (t) { this.$d = function (t) { var e = t.date, n = t.utc; if (null === e) return new Date(NaN); if (O.u(e)) return new Date; if (e instanceof Date) return new Date(e); if ("string" == typeof e && !/Z$/i.test(e)) { var r = e.match(l); if (r) { var i = r[2] - 1 || 0, s = (r[7] || "0").substring(0, 3); return n ? new Date(Date.UTC(r[1], i, r[3] || 1, r[4] || 0, r[5] || 0, r[6] || 0, s)) : new Date(r[1], i, r[3] || 1, r[4] || 0, r[5] || 0, r[6] || 0, s) } } return new Date(e) }(t), this.$x = t.x || {}, this.init() }, m.init = function () { var t = this.$d; this.$y = t.getFullYear(), this.$M = t.getMonth(), this.$D = t.getDate(), this.$W = t.getDay(), this.$H = t.getHours(), this.$m = t.getMinutes(), this.$s = t.getSeconds(), this.$ms = t.getMilliseconds() }, m.$utils = function () { return O }, m.isValid = function () { return !(this.$d.toString() === $) }, m.isSame = function (t, e) { var n = w(t); return this.startOf(e) <= n && n <= this.endOf(e) }, m.isAfter = function (t, e) { return w(t) < this.startOf(e) }, m.isBefore = function (t, e) { return this.endOf(e) < w(t) }, m.$g = function (t, e, n) { return O.u(t) ? this[e] : this.set(n, t) }, m.unix = function () { return Math.floor(this.valueOf() / 1e3) }, m.valueOf = function () { return this.$d.getTime() }, m.startOf = function (t, e) { var n = this, r = !!O.u(e) || e, h = O.p(t), $ = function (t, e) { var i = O.w(n.$u ? Date.UTC(n.$y, e, t) : new Date(n.$y, e, t), n); return r ? i : i.endOf(a) }, l = function (t, e) { return O.w(n.toDate()[t].apply(n.toDate("s"), (r ? [0, 0, 0, 0] : [23, 59, 59, 999]).slice(e)), n) }, y = this.$W, M = this.$M, m = this.$D, g = "set" + (this.$u ? "UTC" : ""); switch (h) { case c: return r ? $(1, 0) : $(31, 11); case f: return r ? $(1, M) : $(0, M + 1); case o: var v = this.$locale().weekStart || 0, D = (y < v ? y + 7 : y) - v; return $(r ? m - D : m + (6 - D), M); case a: case d: return l(g + "Hours", 0); case u: return l(g + "Minutes", 1); case s: return l(g + "Seconds", 2); case i: return l(g + "Milliseconds", 3); default: return this.clone() } }, m.endOf = function (t) { return this.startOf(t, !1) }, m.$set = function (t, e) { var n, o = O.p(t), h = "set" + (this.$u ? "UTC" : ""), $ = (n = {}, n[a] = h + "Date", n[d] = h + "Date", n[f] = h + "Month", n[c] = h + "FullYear", n[u] = h + "Hours", n[s] = h + "Minutes", n[i] = h + "Seconds", n[r] = h + "Milliseconds", n)[o], l = o === a ? this.$D + (e - this.$W) : e; if (o === f || o === c) { var y = this.clone().set(d, 1); y.$d[$](l), y.init(), this.$d = y.set(d, Math.min(this.$D, y.daysInMonth())).$d } else $ && this.$d[$](l); return this.init(), this }, m.set = function (t, e) { return this.clone().$set(t, e) }, m.get = function (t) { return this[O.p(t)]() }, m.add = function (r, h) { var d, $ = this; r = Number(r); var l = O.p(h), y = function (t) { var e = w($); return O.w(e.date(e.date() + Math.round(t * r)), $) }; if (l === f) return this.set(f, this.$M + r); if (l === c) return this.set(c, this.$y + r); if (l === a) return y(1); if (l === o) return y(7); var M = (d = {}, d[s] = e, d[u] = n, d[i] = t, d)[l] || 1, m = this.$d.getTime() + r * M; return O.w(m, this) }, m.subtract = function (t, e) { return this.add(-1 * t, e) }, m.format = function (t) { var e = this, n = this.$locale(); if (!this.isValid()) return n.invalidDate || $; var r = t || "YYYY-MM-DDTHH:mm:ssZ", i = O.z(this), s = this.$H, u = this.$m, a = this.$M, o = n.weekdays, f = n.months, h = function (t, n, i, s) { return t && (t[n] || t(e, r)) || i[n].slice(0, s) }, c = function (t) { return O.s(s % 12 || 12, t, "0") }, d = n.meridiem || function (t, e, n) { var r = t < 12 ? "AM" : "PM"; return n ? r.toLowerCase() : r }, l = { YY: String(this.$y).slice(-2), YYYY: this.$y, M: a + 1, MM: O.s(a + 1, 2, "0"), MMM: h(n.monthsShort, a, f, 3), MMMM: h(f, a), D: this.$D, DD: O.s(this.$D, 2, "0"), d: String(this.$W), dd: h(n.weekdaysMin, this.$W, o, 2), ddd: h(n.weekdaysShort, this.$W, o, 3), dddd: o[this.$W], H: String(s), HH: O.s(s, 2, "0"), h: c(1), hh: c(2), a: d(s, u, !0), A: d(s, u, !1), m: String(u), mm: O.s(u, 2, "0"), s: String(this.$s), ss: O.s(this.$s, 2, "0"), SSS: O.s(this.$ms, 3, "0"), Z: i }; return r.replace(y, (function (t, e) { return e || l[t] || i.replace(":", "") })) }, m.utcOffset = function () { return 15 * -Math.round(this.$d.getTimezoneOffset() / 15) }, m.diff = function (r, d, $) { var l, y = O.p(d), M = w(r), m = (M.utcOffset() - this.utcOffset()) * e, g = this - M, v = O.m(this, M); return v = (l = {}, l[c] = v / 12, l[f] = v, l[h] = v / 3, l[o] = (g - m) / 6048e5, l[a] = (g - m) / 864e5, l[u] = g / n, l[s] = g / e, l[i] = g / t, l)[y] || g, $ ? v : O.a(v) }, m.daysInMonth = function () { return this.endOf(f).$D }, m.$locale = function () { return D[this.$L] }, m.locale = function (t, e) { if (!t) return this.$L; var n = this.clone(), r = S(t, e, !0); return r && (n.$L = r), n }, m.clone = function () { return O.w(this.$d, this) }, m.toDate = function () { return new Date(this.valueOf()) }, m.toJSON = function () { return this.isValid() ? this.toISOString() : null }, m.toISOString = function () { return this.$d.toISOString() }, m.toString = function () { return this.$d.toUTCString() }, M }(), T = _.prototype; return w.prototype = T, [["$ms", r], ["$s", i], ["$m", s], ["$H", u], ["$W", a], ["$M", f], ["$y", c], ["$D", d]].forEach((function (t) { T[t[1]] = function (e) { return this.$g(e, t[0], t[1]) } })), w.extend = function (t, e) { return t.$i || (t(e, _, w), t.$i = !0), w }, w.locale = S, w.isDayjs = p, w.unix = function (t) { return w(1e3 * t) }, w.en = D[v], w.Ls = D, w.p = {}, w }));
diff --git a/modules/decimal.mjs b/modules/decimal.mjs
new file mode 100644
index 0000000..9124f59
--- /dev/null
+++ b/modules/decimal.mjs
@@ -0,0 +1,4898 @@
+/*!
+ *  decimal.js v10.4.2
+ *  An arbitrary-precision Decimal type for JavaScript.
+ *  https://github.com/MikeMcl/decimal.js
+ *  Copyright (c) 2022 Michael Mclaughlin <M8ch88l@gmail.com>
+ *  MIT Licence
+ */
+
+
+// -----------------------------------  EDITABLE DEFAULTS  ------------------------------------ //
+
+
+  // The maximum exponent magnitude.
+  // The limit on the value of `toExpNeg`, `toExpPos`, `minE` and `maxE`.
+var EXP_LIMIT = 9e15,                      // 0 to 9e15
+
+  // The limit on the value of `precision`, and on the value of the first argument to
+  // `toDecimalPlaces`, `toExponential`, `toFixed`, `toPrecision` and `toSignificantDigits`.
+  MAX_DIGITS = 1e9,                        // 0 to 1e9
+
+  // Base conversion alphabet.
+  NUMERALS = '0123456789abcdef',
+
+  // The natural logarithm of 10 (1025 digits).
+  LN10 = '2.3025850929940456840179914546843642076011014886287729760333279009675726096773524802359972050895982983419677840422862486334095254650828067566662873690987816894829072083255546808437998948262331985283935053089653777326288461633662222876982198867465436674744042432743651550489343149393914796194044002221051017141748003688084012647080685567743216228355220114804663715659121373450747856947683463616792101806445070648000277502684916746550586856935673420670581136429224554405758925724208241314695689016758940256776311356919292033376587141660230105703089634572075440370847469940168269282808481184289314848524948644871927809676271275775397027668605952496716674183485704422507197965004714951050492214776567636938662976979522110718264549734772662425709429322582798502585509785265383207606726317164309505995087807523710333101197857547331541421808427543863591778117054309827482385045648019095610299291824318237525357709750539565187697510374970888692180205189339507238539205144634197265287286965110862571492198849978748873771345686209167058',
+
+  // Pi (1025 digits).
+  PI = '3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632789',
+
+
+  // The initial configuration properties of the Decimal constructor.
+  DEFAULTS = {
+
+    // These values must be integers within the stated ranges (inclusive).
+    // Most of these values can be changed at run-time using the `Decimal.config` method.
+
+    // The maximum number of significant digits of the result of a calculation or base conversion.
+    // E.g. `Decimal.config({ precision: 20 });`
+    precision: 20,                         // 1 to MAX_DIGITS
+
+    // The rounding mode used when rounding to `precision`.
+    //
+    // ROUND_UP         0 Away from zero.
+    // ROUND_DOWN       1 Towards zero.
+    // ROUND_CEIL       2 Towards +Infinity.
+    // ROUND_FLOOR      3 Towards -Infinity.
+    // ROUND_HALF_UP    4 Towards nearest neighbour. If equidistant, up.
+    // ROUND_HALF_DOWN  5 Towards nearest neighbour. If equidistant, down.
+    // ROUND_HALF_EVEN  6 Towards nearest neighbour. If equidistant, towards even neighbour.
+    // ROUND_HALF_CEIL  7 Towards nearest neighbour. If equidistant, towards +Infinity.
+    // ROUND_HALF_FLOOR 8 Towards nearest neighbour. If equidistant, towards -Infinity.
+    //
+    // E.g.
+    // `Decimal.rounding = 4;`
+    // `Decimal.rounding = Decimal.ROUND_HALF_UP;`
+    rounding: 4,                           // 0 to 8
+
+    // The modulo mode used when calculating the modulus: a mod n.
+    // The quotient (q = a / n) is calculated according to the corresponding rounding mode.
+    // The remainder (r) is calculated as: r = a - n * q.
+    //
+    // UP         0 The remainder is positive if the dividend is negative, else is negative.
+    // DOWN       1 The remainder has the same sign as the dividend (JavaScript %).
+    // FLOOR      3 The remainder has the same sign as the divisor (Python %).
+    // HALF_EVEN  6 The IEEE 754 remainder function.
+    // EUCLID     9 Euclidian division. q = sign(n) * floor(a / abs(n)). Always positive.
+    //
+    // Truncated division (1), floored division (3), the IEEE 754 remainder (6), and Euclidian
+    // division (9) are commonly used for the modulus operation. The other rounding modes can also
+    // be used, but they may not give useful results.
+    modulo: 1,                             // 0 to 9
+
+    // The exponent value at and beneath which `toString` returns exponential notation.
+    // JavaScript numbers: -7
+    toExpNeg: -7,                          // 0 to -EXP_LIMIT
+
+    // The exponent value at and above which `toString` returns exponential notation.
+    // JavaScript numbers: 21
+    toExpPos:  21,                         // 0 to EXP_LIMIT
+
+    // The minimum exponent value, beneath which underflow to zero occurs.
+    // JavaScript numbers: -324  (5e-324)
+    minE: -EXP_LIMIT,                      // -1 to -EXP_LIMIT
+
+    // The maximum exponent value, above which overflow to Infinity occurs.
+    // JavaScript numbers: 308  (1.7976931348623157e+308)
+    maxE: EXP_LIMIT,                       // 1 to EXP_LIMIT
+
+    // Whether to use cryptographically-secure random number generation, if available.
+    crypto: false                          // true/false
+  },
+
+
+// ----------------------------------- END OF EDITABLE DEFAULTS ------------------------------- //
+
+
+  inexact, quadrant,
+  external = true,
+
+  decimalError = '[DecimalError] ',
+  invalidArgument = decimalError + 'Invalid argument: ',
+  precisionLimitExceeded = decimalError + 'Precision limit exceeded',
+  cryptoUnavailable = decimalError + 'crypto unavailable',
+  tag = '[object Decimal]',
+
+  mathfloor = Math.floor,
+  mathpow = Math.pow,
+
+  isBinary = /^0b([01]+(\.[01]*)?|\.[01]+)(p[+-]?\d+)?$/i,
+  isHex = /^0x([0-9a-f]+(\.[0-9a-f]*)?|\.[0-9a-f]+)(p[+-]?\d+)?$/i,
+  isOctal = /^0o([0-7]+(\.[0-7]*)?|\.[0-7]+)(p[+-]?\d+)?$/i,
+  isDecimal = /^(\d+(\.\d*)?|\.\d+)(e[+-]?\d+)?$/i,
+
+  BASE = 1e7,
+  LOG_BASE = 7,
+  MAX_SAFE_INTEGER = 9007199254740991,
+
+  LN10_PRECISION = LN10.length - 1,
+  PI_PRECISION = PI.length - 1,
+
+  // Decimal.prototype object
+  P = { toStringTag: tag };
+
+
+// Decimal prototype methods
+
+
+/*
+ *  absoluteValue             abs
+ *  ceil
+ *  clampedTo                 clamp
+ *  comparedTo                cmp
+ *  cosine                    cos
+ *  cubeRoot                  cbrt
+ *  decimalPlaces             dp
+ *  dividedBy                 div
+ *  dividedToIntegerBy        divToInt
+ *  equals                    eq
+ *  floor
+ *  greaterThan               gt
+ *  greaterThanOrEqualTo      gte
+ *  hyperbolicCosine          cosh
+ *  hyperbolicSine            sinh
+ *  hyperbolicTangent         tanh
+ *  inverseCosine             acos
+ *  inverseHyperbolicCosine   acosh
+ *  inverseHyperbolicSine     asinh
+ *  inverseHyperbolicTangent  atanh
+ *  inverseSine               asin
+ *  inverseTangent            atan
+ *  isFinite
+ *  isInteger                 isInt
+ *  isNaN
+ *  isNegative                isNeg
+ *  isPositive                isPos
+ *  isZero
+ *  lessThan                  lt
+ *  lessThanOrEqualTo         lte
+ *  logarithm                 log
+ *  [maximum]                 [max]
+ *  [minimum]                 [min]
+ *  minus                     sub
+ *  modulo                    mod
+ *  naturalExponential        exp
+ *  naturalLogarithm          ln
+ *  negated                   neg
+ *  plus                      add
+ *  precision                 sd
+ *  round
+ *  sine                      sin
+ *  squareRoot                sqrt
+ *  tangent                   tan
+ *  times                     mul
+ *  toBinary
+ *  toDecimalPlaces           toDP
+ *  toExponential
+ *  toFixed
+ *  toFraction
+ *  toHexadecimal             toHex
+ *  toNearest
+ *  toNumber
+ *  toOctal
+ *  toPower                   pow
+ *  toPrecision
+ *  toSignificantDigits       toSD
+ *  toString
+ *  truncated                 trunc
+ *  valueOf                   toJSON
+ */
+
+
+/*
+ * Return a new Decimal whose value is the absolute value of this Decimal.
+ *
+ */
+P.absoluteValue = P.abs = function () {
+  var x = new this.constructor(this);
+  if (x.s < 0) x.s = 1;
+  return finalise(x);
+};
+
+
+/*
+ * Return a new Decimal whose value is the value of this Decimal rounded to a whole number in the
+ * direction of positive Infinity.
+ *
+ */
+P.ceil = function () {
+  return finalise(new this.constructor(this), this.e + 1, 2);
+};
+
+
+/*
+ * Return a new Decimal whose value is the value of this Decimal clamped to the range
+ * delineated by `min` and `max`.
+ *
+ * min {number|string|Decimal}
+ * max {number|string|Decimal}
+ *
+ */
+P.clampedTo = P.clamp = function (min, max) {
+  var k,
+    x = this,
+    Ctor = x.constructor;
+  min = new Ctor(min);
+  max = new Ctor(max);
+  if (!min.s || !max.s) return new Ctor(NaN);
+  if (min.gt(max)) throw Error(invalidArgument + max);
+  k = x.cmp(min);
+  return k < 0 ? min : x.cmp(max) > 0 ? max : new Ctor(x);
+};
+
+
+/*
+ * Return
+ *   1    if the value of this Decimal is greater than the value of `y`,
+ *  -1    if the value of this Decimal is less than the value of `y`,
+ *   0    if they have the same value,
+ *   NaN  if the value of either Decimal is NaN.
+ *
+ */
+P.comparedTo = P.cmp = function (y) {
+  var i, j, xdL, ydL,
+    x = this,
+    xd = x.d,
+    yd = (y = new x.constructor(y)).d,
+    xs = x.s,
+    ys = y.s;
+
+  // Either NaN or ±Infinity?
+  if (!xd || !yd) {
+    return !xs || !ys ? NaN : xs !== ys ? xs : xd === yd ? 0 : !xd ^ xs < 0 ? 1 : -1;
+  }
+
+  // Either zero?
+  if (!xd[0] || !yd[0]) return xd[0] ? xs : yd[0] ? -ys : 0;
+
+  // Signs differ?
+  if (xs !== ys) return xs;
+
+  // Compare exponents.
+  if (x.e !== y.e) return x.e > y.e ^ xs < 0 ? 1 : -1;
+
+  xdL = xd.length;
+  ydL = yd.length;
+
+  // Compare digit by digit.
+  for (i = 0, j = xdL < ydL ? xdL : ydL; i < j; ++i) {
+    if (xd[i] !== yd[i]) return xd[i] > yd[i] ^ xs < 0 ? 1 : -1;
+  }
+
+  // Compare lengths.
+  return xdL === ydL ? 0 : xdL > ydL ^ xs < 0 ? 1 : -1;
+};
+
+
+/*
+ * Return a new Decimal whose value is the cosine of the value in radians of this Decimal.
+ *
+ * Domain: [-Infinity, Infinity]
+ * Range: [-1, 1]
+ *
+ * cos(0)         = 1
+ * cos(-0)        = 1
+ * cos(Infinity)  = NaN
+ * cos(-Infinity) = NaN
+ * cos(NaN)       = NaN
+ *
+ */
+P.cosine = P.cos = function () {
+  var pr, rm,
+    x = this,
+    Ctor = x.constructor;
+
+  if (!x.d) return new Ctor(NaN);
+
+  // cos(0) = cos(-0) = 1
+  if (!x.d[0]) return new Ctor(1);
+
+  pr = Ctor.precision;
+  rm = Ctor.rounding;
+  Ctor.precision = pr + Math.max(x.e, x.sd()) + LOG_BASE;
+  Ctor.rounding = 1;
+
+  x = cosine(Ctor, toLessThanHalfPi(Ctor, x));
+
+  Ctor.precision = pr;
+  Ctor.rounding = rm;
+
+  return finalise(quadrant == 2 || quadrant == 3 ? x.neg() : x, pr, rm, true);
+};
+
+
+/*
+ *
+ * Return a new Decimal whose value is the cube root of the value of this Decimal, rounded to
+ * `precision` significant digits using rounding mode `rounding`.
+ *
+ *  cbrt(0)  =  0
+ *  cbrt(-0) = -0
+ *  cbrt(1)  =  1
+ *  cbrt(-1) = -1
+ *  cbrt(N)  =  N
+ *  cbrt(-I) = -I
+ *  cbrt(I)  =  I
+ *
+ * Math.cbrt(x) = (x < 0 ? -Math.pow(-x, 1/3) : Math.pow(x, 1/3))
+ *
+ */
+P.cubeRoot = P.cbrt = function () {
+  var e, m, n, r, rep, s, sd, t, t3, t3plusx,
+    x = this,
+    Ctor = x.constructor;
+
+  if (!x.isFinite() || x.isZero()) return new Ctor(x);
+  external = false;
+
+  // Initial estimate.
+  s = x.s * mathpow(x.s * x, 1 / 3);
+
+   // Math.cbrt underflow/overflow?
+   // Pass x to Math.pow as integer, then adjust the exponent of the result.
+  if (!s || Math.abs(s) == 1 / 0) {
+    n = digitsToString(x.d);
+    e = x.e;
+
+    // Adjust n exponent so it is a multiple of 3 away from x exponent.
+    if (s = (e - n.length + 1) % 3) n += (s == 1 || s == -2 ? '0' : '00');
+    s = mathpow(n, 1 / 3);
+
+    // Rarely, e may be one less than the result exponent value.
+    e = mathfloor((e + 1) / 3) - (e % 3 == (e < 0 ? -1 : 2));
+
+    if (s == 1 / 0) {
+      n = '5e' + e;
+    } else {
+      n = s.toExponential();
+      n = n.slice(0, n.indexOf('e') + 1) + e;
+    }
+
+    r = new Ctor(n);
+    r.s = x.s;
+  } else {
+    r = new Ctor(s.toString());
+  }
+
+  sd = (e = Ctor.precision) + 3;
+
+  // Halley's method.
+  // TODO? Compare Newton's method.
+  for (;;) {
+    t = r;
+    t3 = t.times(t).times(t);
+    t3plusx = t3.plus(x);
+    r = divide(t3plusx.plus(x).times(t), t3plusx.plus(t3), sd + 2, 1);
+
+    // TODO? Replace with for-loop and checkRoundingDigits.
+    if (digitsToString(t.d).slice(0, sd) === (n = digitsToString(r.d)).slice(0, sd)) {
+      n = n.slice(sd - 3, sd + 1);
+
+      // The 4th rounding digit may be in error by -1 so if the 4 rounding digits are 9999 or 4999
+      // , i.e. approaching a rounding boundary, continue the iteration.
+      if (n == '9999' || !rep && n == '4999') {
+
+        // On the first iteration only, check to see if rounding up gives the exact result as the
+        // nines may infinitely repeat.
+        if (!rep) {
+          finalise(t, e + 1, 0);
+
+          if (t.times(t).times(t).eq(x)) {
+            r = t;
+            break;
+          }
+        }
+
+        sd += 4;
+        rep = 1;
+      } else {
+
+        // If the rounding digits are null, 0{0,4} or 50{0,3}, check for an exact result.
+        // If not, then there are further digits and m will be truthy.
+        if (!+n || !+n.slice(1) && n.charAt(0) == '5') {
+
+          // Truncate to the first rounding digit.
+          finalise(r, e + 1, 1);
+          m = !r.times(r).times(r).eq(x);
+        }
+
+        break;
+      }
+    }
+  }
+
+  external = true;
+
+  return finalise(r, e, Ctor.rounding, m);
+};
+
+
+/*
+ * Return the number of decimal places of the value of this Decimal.
+ *
+ */
+P.decimalPlaces = P.dp = function () {
+  var w,
+    d = this.d,
+    n = NaN;
+
+  if (d) {
+    w = d.length - 1;
+    n = (w - mathfloor(this.e / LOG_BASE)) * LOG_BASE;
+
+    // Subtract the number of trailing zeros of the last word.
+    w = d[w];
+    if (w) for (; w % 10 == 0; w /= 10) n--;
+    if (n < 0) n = 0;
+  }
+
+  return n;
+};
+
+
+/*
+ *  n / 0 = I
+ *  n / N = N
+ *  n / I = 0
+ *  0 / n = 0
+ *  0 / 0 = N
+ *  0 / N = N
+ *  0 / I = 0
+ *  N / n = N
+ *  N / 0 = N
+ *  N / N = N
+ *  N / I = N
+ *  I / n = I
+ *  I / 0 = I
+ *  I / N = N
+ *  I / I = N
+ *
+ * Return a new Decimal whose value is the value of this Decimal divided by `y`, rounded to
+ * `precision` significant digits using rounding mode `rounding`.
+ *
+ */
+P.dividedBy = P.div = function (y) {
+  return divide(this, new this.constructor(y));
+};
+
+
+/*
+ * Return a new Decimal whose value is the integer part of dividing the value of this Decimal
+ * by the value of `y`, rounded to `precision` significant digits using rounding mode `rounding`.
+ *
+ */
+P.dividedToIntegerBy = P.divToInt = function (y) {
+  var x = this,
+    Ctor = x.constructor;
+  return finalise(divide(x, new Ctor(y), 0, 1, 1), Ctor.precision, Ctor.rounding);
+};
+
+
+/*
+ * Return true if the value of this Decimal is equal to the value of `y`, otherwise return false.
+ *
+ */
+P.equals = P.eq = function (y) {
+  return this.cmp(y) === 0;
+};
+
+
+/*
+ * Return a new Decimal whose value is the value of this Decimal rounded to a whole number in the
+ * direction of negative Infinity.
+ *
+ */
+P.floor = function () {
+  return finalise(new this.constructor(this), this.e + 1, 3);
+};
+
+
+/*
+ * Return true if the value of this Decimal is greater than the value of `y`, otherwise return
+ * false.
+ *
+ */
+P.greaterThan = P.gt = function (y) {
+  return this.cmp(y) > 0;
+};
+
+
+/*
+ * Return true if the value of this Decimal is greater than or equal to the value of `y`,
+ * otherwise return false.
+ *
+ */
+P.greaterThanOrEqualTo = P.gte = function (y) {
+  var k = this.cmp(y);
+  return k == 1 || k === 0;
+};
+
+
+/*
+ * Return a new Decimal whose value is the hyperbolic cosine of the value in radians of this
+ * Decimal.
+ *
+ * Domain: [-Infinity, Infinity]
+ * Range: [1, Infinity]
+ *
+ * cosh(x) = 1 + x^2/2! + x^4/4! + x^6/6! + ...
+ *
+ * cosh(0)         = 1
+ * cosh(-0)        = 1
+ * cosh(Infinity)  = Infinity
+ * cosh(-Infinity) = Infinity
+ * cosh(NaN)       = NaN
+ *
+ *  x        time taken (ms)   result
+ * 1000      9                 9.8503555700852349694e+433
+ * 10000     25                4.4034091128314607936e+4342
+ * 100000    171               1.4033316802130615897e+43429
+ * 1000000   3817              1.5166076984010437725e+434294
+ * 10000000  abandoned after 2 minute wait
+ *
+ * TODO? Compare performance of cosh(x) = 0.5 * (exp(x) + exp(-x))
+ *
+ */
+P.hyperbolicCosine = P.cosh = function () {
+  var k, n, pr, rm, len,
+    x = this,
+    Ctor = x.constructor,
+    one = new Ctor(1);
+
+  if (!x.isFinite()) return new Ctor(x.s ? 1 / 0 : NaN);
+  if (x.isZero()) return one;
+
+  pr = Ctor.precision;
+  rm = Ctor.rounding;
+  Ctor.precision = pr + Math.max(x.e, x.sd()) + 4;
+  Ctor.rounding = 1;
+  len = x.d.length;
+
+  // Argument reduction: cos(4x) = 1 - 8cos^2(x) + 8cos^4(x) + 1
+  // i.e. cos(x) = 1 - cos^2(x/4)(8 - 8cos^2(x/4))
+
+  // Estimate the optimum number of times to use the argument reduction.
+  // TODO? Estimation reused from cosine() and may not be optimal here.
+  if (len < 32) {
+    k = Math.ceil(len / 3);
+    n = (1 / tinyPow(4, k)).toString();
+  } else {
+    k = 16;
+    n = '2.3283064365386962890625e-10';
+  }
+
+  x = taylorSeries(Ctor, 1, x.times(n), new Ctor(1), true);
+
+  // Reverse argument reduction
+  var cosh2_x,
+    i = k,
+    d8 = new Ctor(8);
+  for (; i--;) {
+    cosh2_x = x.times(x);
+    x = one.minus(cosh2_x.times(d8.minus(cosh2_x.times(d8))));
+  }
+
+  return finalise(x, Ctor.precision = pr, Ctor.rounding = rm, true);
+};
+
+
+/*
+ * Return a new Decimal whose value is the hyperbolic sine of the value in radians of this
+ * Decimal.
+ *
+ * Domain: [-Infinity, Infinity]
+ * Range: [-Infinity, Infinity]
+ *
+ * sinh(x) = x + x^3/3! + x^5/5! + x^7/7! + ...
+ *
+ * sinh(0)         = 0
+ * sinh(-0)        = -0
+ * sinh(Infinity)  = Infinity
+ * sinh(-Infinity) = -Infinity
+ * sinh(NaN)       = NaN
+ *
+ * x        time taken (ms)
+ * 10       2 ms
+ * 100      5 ms
+ * 1000     14 ms
+ * 10000    82 ms
+ * 100000   886 ms            1.4033316802130615897e+43429
+ * 200000   2613 ms
+ * 300000   5407 ms
+ * 400000   8824 ms
+ * 500000   13026 ms          8.7080643612718084129e+217146
+ * 1000000  48543 ms
+ *
+ * TODO? Compare performance of sinh(x) = 0.5 * (exp(x) - exp(-x))
+ *
+ */
+P.hyperbolicSine = P.sinh = function () {
+  var k, pr, rm, len,
+    x = this,
+    Ctor = x.constructor;
+
+  if (!x.isFinite() || x.isZero()) return new Ctor(x);
+
+  pr = Ctor.precision;
+  rm = Ctor.rounding;
+  Ctor.precision = pr + Math.max(x.e, x.sd()) + 4;
+  Ctor.rounding = 1;
+  len = x.d.length;
+
+  if (len < 3) {
+    x = taylorSeries(Ctor, 2, x, x, true);
+  } else {
+
+    // Alternative argument reduction: sinh(3x) = sinh(x)(3 + 4sinh^2(x))
+    // i.e. sinh(x) = sinh(x/3)(3 + 4sinh^2(x/3))
+    // 3 multiplications and 1 addition
+
+    // Argument reduction: sinh(5x) = sinh(x)(5 + sinh^2(x)(20 + 16sinh^2(x)))
+    // i.e. sinh(x) = sinh(x/5)(5 + sinh^2(x/5)(20 + 16sinh^2(x/5)))
+    // 4 multiplications and 2 additions
+
+    // Estimate the optimum number of times to use the argument reduction.
+    k = 1.4 * Math.sqrt(len);
+    k = k > 16 ? 16 : k | 0;
+
+    x = x.times(1 / tinyPow(5, k));
+    x = taylorSeries(Ctor, 2, x, x, true);
+
+    // Reverse argument reduction
+    var sinh2_x,
+      d5 = new Ctor(5),
+      d16 = new Ctor(16),
+      d20 = new Ctor(20);
+    for (; k--;) {
+      sinh2_x = x.times(x);
+      x = x.times(d5.plus(sinh2_x.times(d16.times(sinh2_x).plus(d20))));
+    }
+  }
+
+  Ctor.precision = pr;
+  Ctor.rounding = rm;
+
+  return finalise(x, pr, rm, true);
+};
+
+
+/*
+ * Return a new Decimal whose value is the hyperbolic tangent of the value in radians of this
+ * Decimal.
+ *
+ * Domain: [-Infinity, Infinity]
+ * Range: [-1, 1]
+ *
+ * tanh(x) = sinh(x) / cosh(x)
+ *
+ * tanh(0)         = 0
+ * tanh(-0)        = -0
+ * tanh(Infinity)  = 1
+ * tanh(-Infinity) = -1
+ * tanh(NaN)       = NaN
+ *
+ */
+P.hyperbolicTangent = P.tanh = function () {
+  var pr, rm,
+    x = this,
+    Ctor = x.constructor;
+
+  if (!x.isFinite()) return new Ctor(x.s);
+  if (x.isZero()) return new Ctor(x);
+
+  pr = Ctor.precision;
+  rm = Ctor.rounding;
+  Ctor.precision = pr + 7;
+  Ctor.rounding = 1;
+
+  return divide(x.sinh(), x.cosh(), Ctor.precision = pr, Ctor.rounding = rm);
+};
+
+
+/*
+ * Return a new Decimal whose value is the arccosine (inverse cosine) in radians of the value of
+ * this Decimal.
+ *
+ * Domain: [-1, 1]
+ * Range: [0, pi]
+ *
+ * acos(x) = pi/2 - asin(x)
+ *
+ * acos(0)       = pi/2
+ * acos(-0)      = pi/2
+ * acos(1)       = 0
+ * acos(-1)      = pi
+ * acos(1/2)     = pi/3
+ * acos(-1/2)    = 2*pi/3
+ * acos(|x| > 1) = NaN
+ * acos(NaN)     = NaN
+ *
+ */
+P.inverseCosine = P.acos = function () {
+  var halfPi,
+    x = this,
+    Ctor = x.constructor,
+    k = x.abs().cmp(1),
+    pr = Ctor.precision,
+    rm = Ctor.rounding;
+
+  if (k !== -1) {
+    return k === 0
+      // |x| is 1
+      ? x.isNeg() ? getPi(Ctor, pr, rm) : new Ctor(0)
+      // |x| > 1 or x is NaN
+      : new Ctor(NaN);
+  }
+
+  if (x.isZero()) return getPi(Ctor, pr + 4, rm).times(0.5);
+
+  // TODO? Special case acos(0.5) = pi/3 and acos(-0.5) = 2*pi/3
+
+  Ctor.precision = pr + 6;
+  Ctor.rounding = 1;
+
+  x = x.asin();
+  halfPi = getPi(Ctor, pr + 4, rm).times(0.5);
+
+  Ctor.precision = pr;
+  Ctor.rounding = rm;
+
+  return halfPi.minus(x);
+};
+
+
+/*
+ * Return a new Decimal whose value is the inverse of the hyperbolic cosine in radians of the
+ * value of this Decimal.
+ *
+ * Domain: [1, Infinity]
+ * Range: [0, Infinity]
+ *
+ * acosh(x) = ln(x + sqrt(x^2 - 1))
+ *
+ * acosh(x < 1)     = NaN
+ * acosh(NaN)       = NaN
+ * acosh(Infinity)  = Infinity
+ * acosh(-Infinity) = NaN
+ * acosh(0)         = NaN
+ * acosh(-0)        = NaN
+ * acosh(1)         = 0
+ * acosh(-1)        = NaN
+ *
+ */
+P.inverseHyperbolicCosine = P.acosh = function () {
+  var pr, rm,
+    x = this,
+    Ctor = x.constructor;
+
+  if (x.lte(1)) return new Ctor(x.eq(1) ? 0 : NaN);
+  if (!x.isFinite()) return new Ctor(x);
+
+  pr = Ctor.precision;
+  rm = Ctor.rounding;
+  Ctor.precision = pr + Math.max(Math.abs(x.e), x.sd()) + 4;
+  Ctor.rounding = 1;
+  external = false;
+
+  x = x.times(x).minus(1).sqrt().plus(x);
+
+  external = true;
+  Ctor.precision = pr;
+  Ctor.rounding = rm;
+
+  return x.ln();
+};
+
+
+/*
+ * Return a new Decimal whose value is the inverse of the hyperbolic sine in radians of the value
+ * of this Decimal.
+ *
+ * Domain: [-Infinity, Infinity]
+ * Range: [-Infinity, Infinity]
+ *
+ * asinh(x) = ln(x + sqrt(x^2 + 1))
+ *
+ * asinh(NaN)       = NaN
+ * asinh(Infinity)  = Infinity
+ * asinh(-Infinity) = -Infinity
+ * asinh(0)         = 0
+ * asinh(-0)        = -0
+ *
+ */
+P.inverseHyperbolicSine = P.asinh = function () {
+  var pr, rm,
+    x = this,
+    Ctor = x.constructor;
+
+  if (!x.isFinite() || x.isZero()) return new Ctor(x);
+
+  pr = Ctor.precision;
+  rm = Ctor.rounding;
+  Ctor.precision = pr + 2 * Math.max(Math.abs(x.e), x.sd()) + 6;
+  Ctor.rounding = 1;
+  external = false;
+
+  x = x.times(x).plus(1).sqrt().plus(x);
+
+  external = true;
+  Ctor.precision = pr;
+  Ctor.rounding = rm;
+
+  return x.ln();
+};
+
+
+/*
+ * Return a new Decimal whose value is the inverse of the hyperbolic tangent in radians of the
+ * value of this Decimal.
+ *
+ * Domain: [-1, 1]
+ * Range: [-Infinity, Infinity]
+ *
+ * atanh(x) = 0.5 * ln((1 + x) / (1 - x))
+ *
+ * atanh(|x| > 1)   = NaN
+ * atanh(NaN)       = NaN
+ * atanh(Infinity)  = NaN
+ * atanh(-Infinity) = NaN
+ * atanh(0)         = 0
+ * atanh(-0)        = -0
+ * atanh(1)         = Infinity
+ * atanh(-1)        = -Infinity
+ *
+ */
+P.inverseHyperbolicTangent = P.atanh = function () {
+  var pr, rm, wpr, xsd,
+    x = this,
+    Ctor = x.constructor;
+
+  if (!x.isFinite()) return new Ctor(NaN);
+  if (x.e >= 0) return new Ctor(x.abs().eq(1) ? x.s / 0 : x.isZero() ? x : NaN);
+
+  pr = Ctor.precision;
+  rm = Ctor.rounding;
+  xsd = x.sd();
+
+  if (Math.max(xsd, pr) < 2 * -x.e - 1) return finalise(new Ctor(x), pr, rm, true);
+
+  Ctor.precision = wpr = xsd - x.e;
+
+  x = divide(x.plus(1), new Ctor(1).minus(x), wpr + pr, 1);
+
+  Ctor.precision = pr + 4;
+  Ctor.rounding = 1;
+
+  x = x.ln();
+
+  Ctor.precision = pr;
+  Ctor.rounding = rm;
+
+  return x.times(0.5);
+};
+
+
+/*
+ * Return a new Decimal whose value is the arcsine (inverse sine) in radians of the value of this
+ * Decimal.
+ *
+ * Domain: [-Infinity, Infinity]
+ * Range: [-pi/2, pi/2]
+ *
+ * asin(x) = 2*atan(x/(1 + sqrt(1 - x^2)))
+ *
+ * asin(0)       = 0
+ * asin(-0)      = -0
+ * asin(1/2)     = pi/6
+ * asin(-1/2)    = -pi/6
+ * asin(1)       = pi/2
+ * asin(-1)      = -pi/2
+ * asin(|x| > 1) = NaN
+ * asin(NaN)     = NaN
+ *
+ * TODO? Compare performance of Taylor series.
+ *
+ */
+P.inverseSine = P.asin = function () {
+  var halfPi, k,
+    pr, rm,
+    x = this,
+    Ctor = x.constructor;
+
+  if (x.isZero()) return new Ctor(x);
+
+  k = x.abs().cmp(1);
+  pr = Ctor.precision;
+  rm = Ctor.rounding;
+
+  if (k !== -1) {
+
+    // |x| is 1
+    if (k === 0) {
+      halfPi = getPi(Ctor, pr + 4, rm).times(0.5);
+      halfPi.s = x.s;
+      return halfPi;
+    }
+
+    // |x| > 1 or x is NaN
+    return new Ctor(NaN);
+  }
+
+  // TODO? Special case asin(1/2) = pi/6 and asin(-1/2) = -pi/6
+
+  Ctor.precision = pr + 6;
+  Ctor.rounding = 1;
+
+  x = x.div(new Ctor(1).minus(x.times(x)).sqrt().plus(1)).atan();
+
+  Ctor.precision = pr;
+  Ctor.rounding = rm;
+
+  return x.times(2);
+};
+
+
+/*
+ * Return a new Decimal whose value is the arctangent (inverse tangent) in radians of the value
+ * of this Decimal.
+ *
+ * Domain: [-Infinity, Infinity]
+ * Range: [-pi/2, pi/2]
+ *
+ * atan(x) = x - x^3/3 + x^5/5 - x^7/7 + ...
+ *
+ * atan(0)         = 0
+ * atan(-0)        = -0
+ * atan(1)         = pi/4
+ * atan(-1)        = -pi/4
+ * atan(Infinity)  = pi/2
+ * atan(-Infinity) = -pi/2
+ * atan(NaN)       = NaN
+ *
+ */
+P.inverseTangent = P.atan = function () {
+  var i, j, k, n, px, t, r, wpr, x2,
+    x = this,
+    Ctor = x.constructor,
+    pr = Ctor.precision,
+    rm = Ctor.rounding;
+
+  if (!x.isFinite()) {
+    if (!x.s) return new Ctor(NaN);
+    if (pr + 4 <= PI_PRECISION) {
+      r = getPi(Ctor, pr + 4, rm).times(0.5);
+      r.s = x.s;
+      return r;
+    }
+  } else if (x.isZero()) {
+    return new Ctor(x);
+  } else if (x.abs().eq(1) && pr + 4 <= PI_PRECISION) {
+    r = getPi(Ctor, pr + 4, rm).times(0.25);
+    r.s = x.s;
+    return r;
+  }
+
+  Ctor.precision = wpr = pr + 10;
+  Ctor.rounding = 1;
+
+  // TODO? if (x >= 1 && pr <= PI_PRECISION) atan(x) = halfPi * x.s - atan(1 / x);
+
+  // Argument reduction
+  // Ensure |x| < 0.42
+  // atan(x) = 2 * atan(x / (1 + sqrt(1 + x^2)))
+
+  k = Math.min(28, wpr / LOG_BASE + 2 | 0);
+
+  for (i = k; i; --i) x = x.div(x.times(x).plus(1).sqrt().plus(1));
+
+  external = false;
+
+  j = Math.ceil(wpr / LOG_BASE);
+  n = 1;
+  x2 = x.times(x);
+  r = new Ctor(x);
+  px = x;
+
+  // atan(x) = x - x^3/3 + x^5/5 - x^7/7 + ...
+  for (; i !== -1;) {
+    px = px.times(x2);
+    t = r.minus(px.div(n += 2));
+
+    px = px.times(x2);
+    r = t.plus(px.div(n += 2));
+
+    if (r.d[j] !== void 0) for (i = j; r.d[i] === t.d[i] && i--;);
+  }
+
+  if (k) r = r.times(2 << (k - 1));
+
+  external = true;
+
+  return finalise(r, Ctor.precision = pr, Ctor.rounding = rm, true);
+};
+
+
+/*
+ * Return true if the value of this Decimal is a finite number, otherwise return false.
+ *
+ */
+P.isFinite = function () {
+  return !!this.d;
+};
+
+
+/*
+ * Return true if the value of this Decimal is an integer, otherwise return false.
+ *
+ */
+P.isInteger = P.isInt = function () {
+  return !!this.d && mathfloor(this.e / LOG_BASE) > this.d.length - 2;
+};
+
+
+/*
+ * Return true if the value of this Decimal is NaN, otherwise return false.
+ *
+ */
+P.isNaN = function () {
+  return !this.s;
+};
+
+
+/*
+ * Return true if the value of this Decimal is negative, otherwise return false.
+ *
+ */
+P.isNegative = P.isNeg = function () {
+  return this.s < 0;
+};
+
+
+/*
+ * Return true if the value of this Decimal is positive, otherwise return false.
+ *
+ */
+P.isPositive = P.isPos = function () {
+  return this.s > 0;
+};
+
+
+/*
+ * Return true if the value of this Decimal is 0 or -0, otherwise return false.
+ *
+ */
+P.isZero = function () {
+  return !!this.d && this.d[0] === 0;
+};
+
+
+/*
+ * Return true if the value of this Decimal is less than `y`, otherwise return false.
+ *
+ */
+P.lessThan = P.lt = function (y) {
+  return this.cmp(y) < 0;
+};
+
+
+/*
+ * Return true if the value of this Decimal is less than or equal to `y`, otherwise return false.
+ *
+ */
+P.lessThanOrEqualTo = P.lte = function (y) {
+  return this.cmp(y) < 1;
+};
+
+
+/*
+ * Return the logarithm of the value of this Decimal to the specified base, rounded to `precision`
+ * significant digits using rounding mode `rounding`.
+ *
+ * If no base is specified, return log[10](arg).
+ *
+ * log[base](arg) = ln(arg) / ln(base)
+ *
+ * The result will always be correctly rounded if the base of the log is 10, and 'almost always'
+ * otherwise:
+ *
+ * Depending on the rounding mode, the result may be incorrectly rounded if the first fifteen
+ * rounding digits are [49]99999999999999 or [50]00000000000000. In that case, the maximum error
+ * between the result and the correctly rounded result will be one ulp (unit in the last place).
+ *
+ * log[-b](a)       = NaN
+ * log[0](a)        = NaN
+ * log[1](a)        = NaN
+ * log[NaN](a)      = NaN
+ * log[Infinity](a) = NaN
+ * log[b](0)        = -Infinity
+ * log[b](-0)       = -Infinity
+ * log[b](-a)       = NaN
+ * log[b](1)        = 0
+ * log[b](Infinity) = Infinity
+ * log[b](NaN)      = NaN
+ *
+ * [base] {number|string|Decimal} The base of the logarithm.
+ *
+ */
+P.logarithm = P.log = function (base) {
+  var isBase10, d, denominator, k, inf, num, sd, r,
+    arg = this,
+    Ctor = arg.constructor,
+    pr = Ctor.precision,
+    rm = Ctor.rounding,
+    guard = 5;
+
+  // Default base is 10.
+  if (base == null) {
+    base = new Ctor(10);
+    isBase10 = true;
+  } else {
+    base = new Ctor(base);
+    d = base.d;
+
+    // Return NaN if base is negative, or non-finite, or is 0 or 1.
+    if (base.s < 0 || !d || !d[0] || base.eq(1)) return new Ctor(NaN);
+
+    isBase10 = base.eq(10);
+  }
+
+  d = arg.d;
+
+  // Is arg negative, non-finite, 0 or 1?
+  if (arg.s < 0 || !d || !d[0] || arg.eq(1)) {
+    return new Ctor(d && !d[0] ? -1 / 0 : arg.s != 1 ? NaN : d ? 0 : 1 / 0);
+  }
+
+  // The result will have a non-terminating decimal expansion if base is 10 and arg is not an
+  // integer power of 10.
+  if (isBase10) {
+    if (d.length > 1) {
+      inf = true;
+    } else {
+      for (k = d[0]; k % 10 === 0;) k /= 10;
+      inf = k !== 1;
+    }
+  }
+
+  external = false;
+  sd = pr + guard;
+  num = naturalLogarithm(arg, sd);
+  denominator = isBase10 ? getLn10(Ctor, sd + 10) : naturalLogarithm(base, sd);
+
+  // The result will have 5 rounding digits.
+  r = divide(num, denominator, sd, 1);
+
+  // If at a rounding boundary, i.e. the result's rounding digits are [49]9999 or [50]0000,
+  // calculate 10 further digits.
+  //
+  // If the result is known to have an infinite decimal expansion, repeat this until it is clear
+  // that the result is above or below the boundary. Otherwise, if after calculating the 10
+  // further digits, the last 14 are nines, round up and assume the result is exact.
+  // Also assume the result is exact if the last 14 are zero.
+  //
+  // Example of a result that will be incorrectly rounded:
+  // log[1048576](4503599627370502) = 2.60000000000000009610279511444746...
+  // The above result correctly rounded using ROUND_CEIL to 1 decimal place should be 2.7, but it
+  // will be given as 2.6 as there are 15 zeros immediately after the requested decimal place, so
+  // the exact result would be assumed to be 2.6, which rounded using ROUND_CEIL to 1 decimal
+  // place is still 2.6.
+  if (checkRoundingDigits(r.d, k = pr, rm)) {
+
+    do {
+      sd += 10;
+      num = naturalLogarithm(arg, sd);
+      denominator = isBase10 ? getLn10(Ctor, sd + 10) : naturalLogarithm(base, sd);
+      r = divide(num, denominator, sd, 1);
+
+      if (!inf) {
+
+        // Check for 14 nines from the 2nd rounding digit, as the first may be 4.
+        if (+digitsToString(r.d).slice(k + 1, k + 15) + 1 == 1e14) {
+          r = finalise(r, pr + 1, 0);
+        }
+
+        break;
+      }
+    } while (checkRoundingDigits(r.d, k += 10, rm));
+  }
+
+  external = true;
+
+  return finalise(r, pr, rm);
+};
+
+
+/*
+ * Return a new Decimal whose value is the maximum of the arguments and the value of this Decimal.
+ *
+ * arguments {number|string|Decimal}
+ *
+P.max = function () {
+  Array.prototype.push.call(arguments, this);
+  return maxOrMin(this.constructor, arguments, 'lt');
+};
+ */
+
+
+/*
+ * Return a new Decimal whose value is the minimum of the arguments and the value of this Decimal.
+ *
+ * arguments {number|string|Decimal}
+ *
+P.min = function () {
+  Array.prototype.push.call(arguments, this);
+  return maxOrMin(this.constructor, arguments, 'gt');
+};
+ */
+
+
+/*
+ *  n - 0 = n
+ *  n - N = N
+ *  n - I = -I
+ *  0 - n = -n
+ *  0 - 0 = 0
+ *  0 - N = N
+ *  0 - I = -I
+ *  N - n = N
+ *  N - 0 = N
+ *  N - N = N
+ *  N - I = N
+ *  I - n = I
+ *  I - 0 = I
+ *  I - N = N
+ *  I - I = N
+ *
+ * Return a new Decimal whose value is the value of this Decimal minus `y`, rounded to `precision`
+ * significant digits using rounding mode `rounding`.
+ *
+ */
+P.minus = P.sub = function (y) {
+  var d, e, i, j, k, len, pr, rm, xd, xe, xLTy, yd,
+    x = this,
+    Ctor = x.constructor;
+
+  y = new Ctor(y);
+
+  // If either is not finite...
+  if (!x.d || !y.d) {
+
+    // Return NaN if either is NaN.
+    if (!x.s || !y.s) y = new Ctor(NaN);
+
+    // Return y negated if x is finite and y is ±Infinity.
+    else if (x.d) y.s = -y.s;
+
+    // Return x if y is finite and x is ±Infinity.
+    // Return x if both are ±Infinity with different signs.
+    // Return NaN if both are ±Infinity with the same sign.
+    else y = new Ctor(y.d || x.s !== y.s ? x : NaN);
+
+    return y;
+  }
+
+  // If signs differ...
+  if (x.s != y.s) {
+    y.s = -y.s;
+    return x.plus(y);
+  }
+
+  xd = x.d;
+  yd = y.d;
+  pr = Ctor.precision;
+  rm = Ctor.rounding;
+
+  // If either is zero...
+  if (!xd[0] || !yd[0]) {
+
+    // Return y negated if x is zero and y is non-zero.
+    if (yd[0]) y.s = -y.s;
+
+    // Return x if y is zero and x is non-zero.
+    else if (xd[0]) y = new Ctor(x);
+
+    // Return zero if both are zero.
+    // From IEEE 754 (2008) 6.3: 0 - 0 = -0 - -0 = -0 when rounding to -Infinity.
+    else return new Ctor(rm === 3 ? -0 : 0);
+
+    return external ? finalise(y, pr, rm) : y;
+  }
+
+  // x and y are finite, non-zero numbers with the same sign.
+
+  // Calculate base 1e7 exponents.
+  e = mathfloor(y.e / LOG_BASE);
+  xe = mathfloor(x.e / LOG_BASE);
+
+  xd = xd.slice();
+  k = xe - e;
+
+  // If base 1e7 exponents differ...
+  if (k) {
+    xLTy = k < 0;
+
+    if (xLTy) {
+      d = xd;
+      k = -k;
+      len = yd.length;
+    } else {
+      d = yd;
+      e = xe;
+      len = xd.length;
+    }
+
+    // Numbers with massively different exponents would result in a very high number of
+    // zeros needing to be prepended, but this can be avoided while still ensuring correct
+    // rounding by limiting the number of zeros to `Math.ceil(pr / LOG_BASE) + 2`.
+    i = Math.max(Math.ceil(pr / LOG_BASE), len) + 2;
+
+    if (k > i) {
+      k = i;
+      d.length = 1;
+    }
+
+    // Prepend zeros to equalise exponents.
+    d.reverse();
+    for (i = k; i--;) d.push(0);
+    d.reverse();
+
+  // Base 1e7 exponents equal.
+  } else {
+
+    // Check digits to determine which is the bigger number.
+
+    i = xd.length;
+    len = yd.length;
+    xLTy = i < len;
+    if (xLTy) len = i;
+
+    for (i = 0; i < len; i++) {
+      if (xd[i] != yd[i]) {
+        xLTy = xd[i] < yd[i];
+        break;
+      }
+    }
+
+    k = 0;
+  }
+
+  if (xLTy) {
+    d = xd;
+    xd = yd;
+    yd = d;
+    y.s = -y.s;
+  }
+
+  len = xd.length;
+
+  // Append zeros to `xd` if shorter.
+  // Don't add zeros to `yd` if shorter as subtraction only needs to start at `yd` length.
+  for (i = yd.length - len; i > 0; --i) xd[len++] = 0;
+
+  // Subtract yd from xd.
+  for (i = yd.length; i > k;) {
+
+    if (xd[--i] < yd[i]) {
+      for (j = i; j && xd[--j] === 0;) xd[j] = BASE - 1;
+      --xd[j];
+      xd[i] += BASE;
+    }
+
+    xd[i] -= yd[i];
+  }
+
+  // Remove trailing zeros.
+  for (; xd[--len] === 0;) xd.pop();
+
+  // Remove leading zeros and adjust exponent accordingly.
+  for (; xd[0] === 0; xd.shift()) --e;
+
+  // Zero?
+  if (!xd[0]) return new Ctor(rm === 3 ? -0 : 0);
+
+  y.d = xd;
+  y.e = getBase10Exponent(xd, e);
+
+  return external ? finalise(y, pr, rm) : y;
+};
+
+
+/*
+ *   n % 0 =  N
+ *   n % N =  N
+ *   n % I =  n
+ *   0 % n =  0
+ *  -0 % n = -0
+ *   0 % 0 =  N
+ *   0 % N =  N
+ *   0 % I =  0
+ *   N % n =  N
+ *   N % 0 =  N
+ *   N % N =  N
+ *   N % I =  N
+ *   I % n =  N
+ *   I % 0 =  N
+ *   I % N =  N
+ *   I % I =  N
+ *
+ * Return a new Decimal whose value is the value of this Decimal modulo `y`, rounded to
+ * `precision` significant digits using rounding mode `rounding`.
+ *
+ * The result depends on the modulo mode.
+ *
+ */
+P.modulo = P.mod = function (y) {
+  var q,
+    x = this,
+    Ctor = x.constructor;
+
+  y = new Ctor(y);
+
+  // Return NaN if x is ±Infinity or NaN, or y is NaN or ±0.
+  if (!x.d || !y.s || y.d && !y.d[0]) return new Ctor(NaN);
+
+  // Return x if y is ±Infinity or x is ±0.
+  if (!y.d || x.d && !x.d[0]) {
+    return finalise(new Ctor(x), Ctor.precision, Ctor.rounding);
+  }
+
+  // Prevent rounding of intermediate calculations.
+  external = false;
+
+  if (Ctor.modulo == 9) {
+
+    // Euclidian division: q = sign(y) * floor(x / abs(y))
+    // result = x - q * y    where  0 <= result < abs(y)
+    q = divide(x, y.abs(), 0, 3, 1);
+    q.s *= y.s;
+  } else {
+    q = divide(x, y, 0, Ctor.modulo, 1);
+  }
+
+  q = q.times(y);
+
+  external = true;
+
+  return x.minus(q);
+};
+
+
+/*
+ * Return a new Decimal whose value is the natural exponential of the value of this Decimal,
+ * i.e. the base e raised to the power the value of this Decimal, rounded to `precision`
+ * significant digits using rounding mode `rounding`.
+ *
+ */
+P.naturalExponential = P.exp = function () {
+  return naturalExponential(this);
+};
+
+
+/*
+ * Return a new Decimal whose value is the natural logarithm of the value of this Decimal,
+ * rounded to `precision` significant digits using rounding mode `rounding`.
+ *
+ */
+P.naturalLogarithm = P.ln = function () {
+  return naturalLogarithm(this);
+};
+
+
+/*
+ * Return a new Decimal whose value is the value of this Decimal negated, i.e. as if multiplied by
+ * -1.
+ *
+ */
+P.negated = P.neg = function () {
+  var x = new this.constructor(this);
+  x.s = -x.s;
+  return finalise(x);
+};
+
+
+/*
+ *  n + 0 = n
+ *  n + N = N
+ *  n + I = I
+ *  0 + n = n
+ *  0 + 0 = 0
+ *  0 + N = N
+ *  0 + I = I
+ *  N + n = N
+ *  N + 0 = N
+ *  N + N = N
+ *  N + I = N
+ *  I + n = I
+ *  I + 0 = I
+ *  I + N = N
+ *  I + I = I
+ *
+ * Return a new Decimal whose value is the value of this Decimal plus `y`, rounded to `precision`
+ * significant digits using rounding mode `rounding`.
+ *
+ */
+P.plus = P.add = function (y) {
+  var carry, d, e, i, k, len, pr, rm, xd, yd,
+    x = this,
+    Ctor = x.constructor;
+
+  y = new Ctor(y);
+
+  // If either is not finite...
+  if (!x.d || !y.d) {
+
+    // Return NaN if either is NaN.
+    if (!x.s || !y.s) y = new Ctor(NaN);
+
+    // Return x if y is finite and x is ±Infinity.
+    // Return x if both are ±Infinity with the same sign.
+    // Return NaN if both are ±Infinity with different signs.
+    // Return y if x is finite and y is ±Infinity.
+    else if (!x.d) y = new Ctor(y.d || x.s === y.s ? x : NaN);
+
+    return y;
+  }
+
+   // If signs differ...
+  if (x.s != y.s) {
+    y.s = -y.s;
+    return x.minus(y);
+  }
+
+  xd = x.d;
+  yd = y.d;
+  pr = Ctor.precision;
+  rm = Ctor.rounding;
+
+  // If either is zero...
+  if (!xd[0] || !yd[0]) {
+
+    // Return x if y is zero.
+    // Return y if y is non-zero.
+    if (!yd[0]) y = new Ctor(x);
+
+    return external ? finalise(y, pr, rm) : y;
+  }
+
+  // x and y are finite, non-zero numbers with the same sign.
+
+  // Calculate base 1e7 exponents.
+  k = mathfloor(x.e / LOG_BASE);
+  e = mathfloor(y.e / LOG_BASE);
+
+  xd = xd.slice();
+  i = k - e;
+
+  // If base 1e7 exponents differ...
+  if (i) {
+
+    if (i < 0) {
+      d = xd;
+      i = -i;
+      len = yd.length;
+    } else {
+      d = yd;
+      e = k;
+      len = xd.length;
+    }
+
+    // Limit number of zeros prepended to max(ceil(pr / LOG_BASE), len) + 1.
+    k = Math.ceil(pr / LOG_BASE);
+    len = k > len ? k + 1 : len + 1;
+
+    if (i > len) {
+      i = len;
+      d.length = 1;
+    }
+
+    // Prepend zeros to equalise exponents. Note: Faster to use reverse then do unshifts.
+    d.reverse();
+    for (; i--;) d.push(0);
+    d.reverse();
+  }
+
+  len = xd.length;
+  i = yd.length;
+
+  // If yd is longer than xd, swap xd and yd so xd points to the longer array.
+  if (len - i < 0) {
+    i = len;
+    d = yd;
+    yd = xd;
+    xd = d;
+  }
+
+  // Only start adding at yd.length - 1 as the further digits of xd can be left as they are.
+  for (carry = 0; i;) {
+    carry = (xd[--i] = xd[i] + yd[i] + carry) / BASE | 0;
+    xd[i] %= BASE;
+  }
+
+  if (carry) {
+    xd.unshift(carry);
+    ++e;
+  }
+
+  // Remove trailing zeros.
+  // No need to check for zero, as +x + +y != 0 && -x + -y != 0
+  for (len = xd.length; xd[--len] == 0;) xd.pop();
+
+  y.d = xd;
+  y.e = getBase10Exponent(xd, e);
+
+  return external ? finalise(y, pr, rm) : y;
+};
+
+
+/*
+ * Return the number of significant digits of the value of this Decimal.
+ *
+ * [z] {boolean|number} Whether to count integer-part trailing zeros: true, false, 1 or 0.
+ *
+ */
+P.precision = P.sd = function (z) {
+  var k,
+    x = this;
+
+  if (z !== void 0 && z !== !!z && z !== 1 && z !== 0) throw Error(invalidArgument + z);
+
+  if (x.d) {
+    k = getPrecision(x.d);
+    if (z && x.e + 1 > k) k = x.e + 1;
+  } else {
+    k = NaN;
+  }
+
+  return k;
+};
+
+
+/*
+ * Return a new Decimal whose value is the value of this Decimal rounded to a whole number using
+ * rounding mode `rounding`.
+ *
+ */
+P.round = function () {
+  var x = this,
+    Ctor = x.constructor;
+
+  return finalise(new Ctor(x), x.e + 1, Ctor.rounding);
+};
+
+
+/*
+ * Return a new Decimal whose value is the sine of the value in radians of this Decimal.
+ *
+ * Domain: [-Infinity, Infinity]
+ * Range: [-1, 1]
+ *
+ * sin(x) = x - x^3/3! + x^5/5! - ...
+ *
+ * sin(0)         = 0
+ * sin(-0)        = -0
+ * sin(Infinity)  = NaN
+ * sin(-Infinity) = NaN
+ * sin(NaN)       = NaN
+ *
+ */
+P.sine = P.sin = function () {
+  var pr, rm,
+    x = this,
+    Ctor = x.constructor;
+
+  if (!x.isFinite()) return new Ctor(NaN);
+  if (x.isZero()) return new Ctor(x);
+
+  pr = Ctor.precision;
+  rm = Ctor.rounding;
+  Ctor.precision = pr + Math.max(x.e, x.sd()) + LOG_BASE;
+  Ctor.rounding = 1;
+
+  x = sine(Ctor, toLessThanHalfPi(Ctor, x));
+
+  Ctor.precision = pr;
+  Ctor.rounding = rm;
+
+  return finalise(quadrant > 2 ? x.neg() : x, pr, rm, true);
+};
+
+
+/*
+ * Return a new Decimal whose value is the square root of this Decimal, rounded to `precision`
+ * significant digits using rounding mode `rounding`.
+ *
+ *  sqrt(-n) =  N
+ *  sqrt(N)  =  N
+ *  sqrt(-I) =  N
+ *  sqrt(I)  =  I
+ *  sqrt(0)  =  0
+ *  sqrt(-0) = -0
+ *
+ */
+P.squareRoot = P.sqrt = function () {
+  var m, n, sd, r, rep, t,
+    x = this,
+    d = x.d,
+    e = x.e,
+    s = x.s,
+    Ctor = x.constructor;
+
+  // Negative/NaN/Infinity/zero?
+  if (s !== 1 || !d || !d[0]) {
+    return new Ctor(!s || s < 0 && (!d || d[0]) ? NaN : d ? x : 1 / 0);
+  }
+
+  external = false;
+
+  // Initial estimate.
+  s = Math.sqrt(+x);
+
+  // Math.sqrt underflow/overflow?
+  // Pass x to Math.sqrt as integer, then adjust the exponent of the result.
+  if (s == 0 || s == 1 / 0) {
+    n = digitsToString(d);
+
+    if ((n.length + e) % 2 == 0) n += '0';
+    s = Math.sqrt(n);
+    e = mathfloor((e + 1) / 2) - (e < 0 || e % 2);
+
+    if (s == 1 / 0) {
+      n = '5e' + e;
+    } else {
+      n = s.toExponential();
+      n = n.slice(0, n.indexOf('e') + 1) + e;
+    }
+
+    r = new Ctor(n);
+  } else {
+    r = new Ctor(s.toString());
+  }
+
+  sd = (e = Ctor.precision) + 3;
+
+  // Newton-Raphson iteration.
+  for (;;) {
+    t = r;
+    r = t.plus(divide(x, t, sd + 2, 1)).times(0.5);
+
+    // TODO? Replace with for-loop and checkRoundingDigits.
+    if (digitsToString(t.d).slice(0, sd) === (n = digitsToString(r.d)).slice(0, sd)) {
+      n = n.slice(sd - 3, sd + 1);
+
+      // The 4th rounding digit may be in error by -1 so if the 4 rounding digits are 9999 or
+      // 4999, i.e. approaching a rounding boundary, continue the iteration.
+      if (n == '9999' || !rep && n == '4999') {
+
+        // On the first iteration only, check to see if rounding up gives the exact result as the
+        // nines may infinitely repeat.
+        if (!rep) {
+          finalise(t, e + 1, 0);
+
+          if (t.times(t).eq(x)) {
+            r = t;
+            break;
+          }
+        }
+
+        sd += 4;
+        rep = 1;
+      } else {
+
+        // If the rounding digits are null, 0{0,4} or 50{0,3}, check for an exact result.
+        // If not, then there are further digits and m will be truthy.
+        if (!+n || !+n.slice(1) && n.charAt(0) == '5') {
+
+          // Truncate to the first rounding digit.
+          finalise(r, e + 1, 1);
+          m = !r.times(r).eq(x);
+        }
+
+        break;
+      }
+    }
+  }
+
+  external = true;
+
+  return finalise(r, e, Ctor.rounding, m);
+};
+
+
+/*
+ * Return a new Decimal whose value is the tangent of the value in radians of this Decimal.
+ *
+ * Domain: [-Infinity, Infinity]
+ * Range: [-Infinity, Infinity]
+ *
+ * tan(0)         = 0
+ * tan(-0)        = -0
+ * tan(Infinity)  = NaN
+ * tan(-Infinity) = NaN
+ * tan(NaN)       = NaN
+ *
+ */
+P.tangent = P.tan = function () {
+  var pr, rm,
+    x = this,
+    Ctor = x.constructor;
+
+  if (!x.isFinite()) return new Ctor(NaN);
+  if (x.isZero()) return new Ctor(x);
+
+  pr = Ctor.precision;
+  rm = Ctor.rounding;
+  Ctor.precision = pr + 10;
+  Ctor.rounding = 1;
+
+  x = x.sin();
+  x.s = 1;
+  x = divide(x, new Ctor(1).minus(x.times(x)).sqrt(), pr + 10, 0);
+
+  Ctor.precision = pr;
+  Ctor.rounding = rm;
+
+  return finalise(quadrant == 2 || quadrant == 4 ? x.neg() : x, pr, rm, true);
+};
+
+
+/*
+ *  n * 0 = 0
+ *  n * N = N
+ *  n * I = I
+ *  0 * n = 0
+ *  0 * 0 = 0
+ *  0 * N = N
+ *  0 * I = N
+ *  N * n = N
+ *  N * 0 = N
+ *  N * N = N
+ *  N * I = N
+ *  I * n = I
+ *  I * 0 = N
+ *  I * N = N
+ *  I * I = I
+ *
+ * Return a new Decimal whose value is this Decimal times `y`, rounded to `precision` significant
+ * digits using rounding mode `rounding`.
+ *
+ */
+P.times = P.mul = function (y) {
+  var carry, e, i, k, r, rL, t, xdL, ydL,
+    x = this,
+    Ctor = x.constructor,
+    xd = x.d,
+    yd = (y = new Ctor(y)).d;
+
+  y.s *= x.s;
+
+   // If either is NaN, ±Infinity or ±0...
+  if (!xd || !xd[0] || !yd || !yd[0]) {
+
+    return new Ctor(!y.s || xd && !xd[0] && !yd || yd && !yd[0] && !xd
+
+      // Return NaN if either is NaN.
+      // Return NaN if x is ±0 and y is ±Infinity, or y is ±0 and x is ±Infinity.
+      ? NaN
+
+      // Return ±Infinity if either is ±Infinity.
+      // Return ±0 if either is ±0.
+      : !xd || !yd ? y.s / 0 : y.s * 0);
+  }
+
+  e = mathfloor(x.e / LOG_BASE) + mathfloor(y.e / LOG_BASE);
+  xdL = xd.length;
+  ydL = yd.length;
+
+  // Ensure xd points to the longer array.
+  if (xdL < ydL) {
+    r = xd;
+    xd = yd;
+    yd = r;
+    rL = xdL;
+    xdL = ydL;
+    ydL = rL;
+  }
+
+  // Initialise the result array with zeros.
+  r = [];
+  rL = xdL + ydL;
+  for (i = rL; i--;) r.push(0);
+
+  // Multiply!
+  for (i = ydL; --i >= 0;) {
+    carry = 0;
+    for (k = xdL + i; k > i;) {
+      t = r[k] + yd[i] * xd[k - i - 1] + carry;
+      r[k--] = t % BASE | 0;
+      carry = t / BASE | 0;
+    }
+
+    r[k] = (r[k] + carry) % BASE | 0;
+  }
+
+  // Remove trailing zeros.
+  for (; !r[--rL];) r.pop();
+
+  if (carry) ++e;
+  else r.shift();
+
+  y.d = r;
+  y.e = getBase10Exponent(r, e);
+
+  return external ? finalise(y, Ctor.precision, Ctor.rounding) : y;
+};
+
+
+/*
+ * Return a string representing the value of this Decimal in base 2, round to `sd` significant
+ * digits using rounding mode `rm`.
+ *
+ * If the optional `sd` argument is present then return binary exponential notation.
+ *
+ * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.
+ * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+ *
+ */
+P.toBinary = function (sd, rm) {
+  return toStringBinary(this, 2, sd, rm);
+};
+
+
+/*
+ * Return a new Decimal whose value is the value of this Decimal rounded to a maximum of `dp`
+ * decimal places using rounding mode `rm` or `rounding` if `rm` is omitted.
+ *
+ * If `dp` is omitted, return a new Decimal whose value is the value of this Decimal.
+ *
+ * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive.
+ * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+ *
+ */
+P.toDecimalPlaces = P.toDP = function (dp, rm) {
+  var x = this,
+    Ctor = x.constructor;
+
+  x = new Ctor(x);
+  if (dp === void 0) return x;
+
+  checkInt32(dp, 0, MAX_DIGITS);
+
+  if (rm === void 0) rm = Ctor.rounding;
+  else checkInt32(rm, 0, 8);
+
+  return finalise(x, dp + x.e + 1, rm);
+};
+
+
+/*
+ * Return a string representing the value of this Decimal in exponential notation rounded to
+ * `dp` fixed decimal places using rounding mode `rounding`.
+ *
+ * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive.
+ * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+ *
+ */
+P.toExponential = function (dp, rm) {
+  var str,
+    x = this,
+    Ctor = x.constructor;
+
+  if (dp === void 0) {
+    str = finiteToString(x, true);
+  } else {
+    checkInt32(dp, 0, MAX_DIGITS);
+
+    if (rm === void 0) rm = Ctor.rounding;
+    else checkInt32(rm, 0, 8);
+
+    x = finalise(new Ctor(x), dp + 1, rm);
+    str = finiteToString(x, true, dp + 1);
+  }
+
+  return x.isNeg() && !x.isZero() ? '-' + str : str;
+};
+
+
+/*
+ * Return a string representing the value of this Decimal in normal (fixed-point) notation to
+ * `dp` fixed decimal places and rounded using rounding mode `rm` or `rounding` if `rm` is
+ * omitted.
+ *
+ * As with JavaScript numbers, (-0).toFixed(0) is '0', but e.g. (-0.00001).toFixed(0) is '-0'.
+ *
+ * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive.
+ * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+ *
+ * (-0).toFixed(0) is '0', but (-0.1).toFixed(0) is '-0'.
+ * (-0).toFixed(1) is '0.0', but (-0.01).toFixed(1) is '-0.0'.
+ * (-0).toFixed(3) is '0.000'.
+ * (-0.5).toFixed(0) is '-0'.
+ *
+ */
+P.toFixed = function (dp, rm) {
+  var str, y,
+    x = this,
+    Ctor = x.constructor;
+
+  if (dp === void 0) {
+    str = finiteToString(x);
+  } else {
+    checkInt32(dp, 0, MAX_DIGITS);
+
+    if (rm === void 0) rm = Ctor.rounding;
+    else checkInt32(rm, 0, 8);
+
+    y = finalise(new Ctor(x), dp + x.e + 1, rm);
+    str = finiteToString(y, false, dp + y.e + 1);
+  }
+
+  // To determine whether to add the minus sign look at the value before it was rounded,
+  // i.e. look at `x` rather than `y`.
+  return x.isNeg() && !x.isZero() ? '-' + str : str;
+};
+
+
+/*
+ * Return an array representing the value of this Decimal as a simple fraction with an integer
+ * numerator and an integer denominator.
+ *
+ * The denominator will be a positive non-zero value less than or equal to the specified maximum
+ * denominator. If a maximum denominator is not specified, the denominator will be the lowest
+ * value necessary to represent the number exactly.
+ *
+ * [maxD] {number|string|Decimal} Maximum denominator. Integer >= 1 and < Infinity.
+ *
+ */
+P.toFraction = function (maxD) {
+  var d, d0, d1, d2, e, k, n, n0, n1, pr, q, r,
+    x = this,
+    xd = x.d,
+    Ctor = x.constructor;
+
+  if (!xd) return new Ctor(x);
+
+  n1 = d0 = new Ctor(1);
+  d1 = n0 = new Ctor(0);
+
+  d = new Ctor(d1);
+  e = d.e = getPrecision(xd) - x.e - 1;
+  k = e % LOG_BASE;
+  d.d[0] = mathpow(10, k < 0 ? LOG_BASE + k : k);
+
+  if (maxD == null) {
+
+    // d is 10**e, the minimum max-denominator needed.
+    maxD = e > 0 ? d : n1;
+  } else {
+    n = new Ctor(maxD);
+    if (!n.isInt() || n.lt(n1)) throw Error(invalidArgument + n);
+    maxD = n.gt(d) ? (e > 0 ? d : n1) : n;
+  }
+
+  external = false;
+  n = new Ctor(digitsToString(xd));
+  pr = Ctor.precision;
+  Ctor.precision = e = xd.length * LOG_BASE * 2;
+
+  for (;;)  {
+    q = divide(n, d, 0, 1, 1);
+    d2 = d0.plus(q.times(d1));
+    if (d2.cmp(maxD) == 1) break;
+    d0 = d1;
+    d1 = d2;
+    d2 = n1;
+    n1 = n0.plus(q.times(d2));
+    n0 = d2;
+    d2 = d;
+    d = n.minus(q.times(d2));
+    n = d2;
+  }
+
+  d2 = divide(maxD.minus(d0), d1, 0, 1, 1);
+  n0 = n0.plus(d2.times(n1));
+  d0 = d0.plus(d2.times(d1));
+  n0.s = n1.s = x.s;
+
+  // Determine which fraction is closer to x, n0/d0 or n1/d1?
+  r = divide(n1, d1, e, 1).minus(x).abs().cmp(divide(n0, d0, e, 1).minus(x).abs()) < 1
+      ? [n1, d1] : [n0, d0];
+
+  Ctor.precision = pr;
+  external = true;
+
+  return r;
+};
+
+
+/*
+ * Return a string representing the value of this Decimal in base 16, round to `sd` significant
+ * digits using rounding mode `rm`.
+ *
+ * If the optional `sd` argument is present then return binary exponential notation.
+ *
+ * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.
+ * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+ *
+ */
+P.toHexadecimal = P.toHex = function (sd, rm) {
+  return toStringBinary(this, 16, sd, rm);
+};
+
+
+/*
+ * Returns a new Decimal whose value is the nearest multiple of `y` in the direction of rounding
+ * mode `rm`, or `Decimal.rounding` if `rm` is omitted, to the value of this Decimal.
+ *
+ * The return value will always have the same sign as this Decimal, unless either this Decimal
+ * or `y` is NaN, in which case the return value will be also be NaN.
+ *
+ * The return value is not affected by the value of `precision`.
+ *
+ * y {number|string|Decimal} The magnitude to round to a multiple of.
+ * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+ *
+ * 'toNearest() rounding mode not an integer: {rm}'
+ * 'toNearest() rounding mode out of range: {rm}'
+ *
+ */
+P.toNearest = function (y, rm) {
+  var x = this,
+    Ctor = x.constructor;
+
+  x = new Ctor(x);
+
+  if (y == null) {
+
+    // If x is not finite, return x.
+    if (!x.d) return x;
+
+    y = new Ctor(1);
+    rm = Ctor.rounding;
+  } else {
+    y = new Ctor(y);
+    if (rm === void 0) {
+      rm = Ctor.rounding;
+    } else {
+      checkInt32(rm, 0, 8);
+    }
+
+    // If x is not finite, return x if y is not NaN, else NaN.
+    if (!x.d) return y.s ? x : y;
+
+    // If y is not finite, return Infinity with the sign of x if y is Infinity, else NaN.
+    if (!y.d) {
+      if (y.s) y.s = x.s;
+      return y;
+    }
+  }
+
+  // If y is not zero, calculate the nearest multiple of y to x.
+  if (y.d[0]) {
+    external = false;
+    x = divide(x, y, 0, rm, 1).times(y);
+    external = true;
+    finalise(x);
+
+  // If y is zero, return zero with the sign of x.
+  } else {
+    y.s = x.s;
+    x = y;
+  }
+
+  return x;
+};
+
+
+/*
+ * Return the value of this Decimal converted to a number primitive.
+ * Zero keeps its sign.
+ *
+ */
+P.toNumber = function () {
+  return +this;
+};
+
+
+/*
+ * Return a string representing the value of this Decimal in base 8, round to `sd` significant
+ * digits using rounding mode `rm`.
+ *
+ * If the optional `sd` argument is present then return binary exponential notation.
+ *
+ * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.
+ * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+ *
+ */
+P.toOctal = function (sd, rm) {
+  return toStringBinary(this, 8, sd, rm);
+};
+
+
+/*
+ * Return a new Decimal whose value is the value of this Decimal raised to the power `y`, rounded
+ * to `precision` significant digits using rounding mode `rounding`.
+ *
+ * ECMAScript compliant.
+ *
+ *   pow(x, NaN)                           = NaN
+ *   pow(x, ±0)                            = 1
+
+ *   pow(NaN, non-zero)                    = NaN
+ *   pow(abs(x) > 1, +Infinity)            = +Infinity
+ *   pow(abs(x) > 1, -Infinity)            = +0
+ *   pow(abs(x) == 1, ±Infinity)           = NaN
+ *   pow(abs(x) < 1, +Infinity)            = +0
+ *   pow(abs(x) < 1, -Infinity)            = +Infinity
+ *   pow(+Infinity, y > 0)                 = +Infinity
+ *   pow(+Infinity, y < 0)                 = +0
+ *   pow(-Infinity, odd integer > 0)       = -Infinity
+ *   pow(-Infinity, even integer > 0)      = +Infinity
+ *   pow(-Infinity, odd integer < 0)       = -0
+ *   pow(-Infinity, even integer < 0)      = +0
+ *   pow(+0, y > 0)                        = +0
+ *   pow(+0, y < 0)                        = +Infinity
+ *   pow(-0, odd integer > 0)              = -0
+ *   pow(-0, even integer > 0)             = +0
+ *   pow(-0, odd integer < 0)              = -Infinity
+ *   pow(-0, even integer < 0)             = +Infinity
+ *   pow(finite x < 0, finite non-integer) = NaN
+ *
+ * For non-integer or very large exponents pow(x, y) is calculated using
+ *
+ *   x^y = exp(y*ln(x))
+ *
+ * Assuming the first 15 rounding digits are each equally likely to be any digit 0-9, the
+ * probability of an incorrectly rounded result
+ * P([49]9{14} | [50]0{14}) = 2 * 0.2 * 10^-14 = 4e-15 = 1/2.5e+14
+ * i.e. 1 in 250,000,000,000,000
+ *
+ * If a result is incorrectly rounded the maximum error will be 1 ulp (unit in last place).
+ *
+ * y {number|string|Decimal} The power to which to raise this Decimal.
+ *
+ */
+P.toPower = P.pow = function (y) {
+  var e, k, pr, r, rm, s,
+    x = this,
+    Ctor = x.constructor,
+    yn = +(y = new Ctor(y));
+
+  // Either ±Infinity, NaN or ±0?
+  if (!x.d || !y.d || !x.d[0] || !y.d[0]) return new Ctor(mathpow(+x, yn));
+
+  x = new Ctor(x);
+
+  if (x.eq(1)) return x;
+
+  pr = Ctor.precision;
+  rm = Ctor.rounding;
+
+  if (y.eq(1)) return finalise(x, pr, rm);
+
+  // y exponent
+  e = mathfloor(y.e / LOG_BASE);
+
+  // If y is a small integer use the 'exponentiation by squaring' algorithm.
+  if (e >= y.d.length - 1 && (k = yn < 0 ? -yn : yn) <= MAX_SAFE_INTEGER) {
+    r = intPow(Ctor, x, k, pr);
+    return y.s < 0 ? new Ctor(1).div(r) : finalise(r, pr, rm);
+  }
+
+  s = x.s;
+
+  // if x is negative
+  if (s < 0) {
+
+    // if y is not an integer
+    if (e < y.d.length - 1) return new Ctor(NaN);
+
+    // Result is positive if x is negative and the last digit of integer y is even.
+    if ((y.d[e] & 1) == 0) s = 1;
+
+    // if x.eq(-1)
+    if (x.e == 0 && x.d[0] == 1 && x.d.length == 1) {
+      x.s = s;
+      return x;
+    }
+  }
+
+  // Estimate result exponent.
+  // x^y = 10^e,  where e = y * log10(x)
+  // log10(x) = log10(x_significand) + x_exponent
+  // log10(x_significand) = ln(x_significand) / ln(10)
+  k = mathpow(+x, yn);
+  e = k == 0 || !isFinite(k)
+    ? mathfloor(yn * (Math.log('0.' + digitsToString(x.d)) / Math.LN10 + x.e + 1))
+    : new Ctor(k + '').e;
+
+  // Exponent estimate may be incorrect e.g. x: 0.999999999999999999, y: 2.29, e: 0, r.e: -1.
+
+  // Overflow/underflow?
+  if (e > Ctor.maxE + 1 || e < Ctor.minE - 1) return new Ctor(e > 0 ? s / 0 : 0);
+
+  external = false;
+  Ctor.rounding = x.s = 1;
+
+  // Estimate the extra guard digits needed to ensure five correct rounding digits from
+  // naturalLogarithm(x). Example of failure without these extra digits (precision: 10):
+  // new Decimal(2.32456).pow('2087987436534566.46411')
+  // should be 1.162377823e+764914905173815, but is 1.162355823e+764914905173815
+  k = Math.min(12, (e + '').length);
+
+  // r = x^y = exp(y*ln(x))
+  r = naturalExponential(y.times(naturalLogarithm(x, pr + k)), pr);
+
+  // r may be Infinity, e.g. (0.9999999999999999).pow(-1e+40)
+  if (r.d) {
+
+    // Truncate to the required precision plus five rounding digits.
+    r = finalise(r, pr + 5, 1);
+
+    // If the rounding digits are [49]9999 or [50]0000 increase the precision by 10 and recalculate
+    // the result.
+    if (checkRoundingDigits(r.d, pr, rm)) {
+      e = pr + 10;
+
+      // Truncate to the increased precision plus five rounding digits.
+      r = finalise(naturalExponential(y.times(naturalLogarithm(x, e + k)), e), e + 5, 1);
+
+      // Check for 14 nines from the 2nd rounding digit (the first rounding digit may be 4 or 9).
+      if (+digitsToString(r.d).slice(pr + 1, pr + 15) + 1 == 1e14) {
+        r = finalise(r, pr + 1, 0);
+      }
+    }
+  }
+
+  r.s = s;
+  external = true;
+  Ctor.rounding = rm;
+
+  return finalise(r, pr, rm);
+};
+
+
+/*
+ * Return a string representing the value of this Decimal rounded to `sd` significant digits
+ * using rounding mode `rounding`.
+ *
+ * Return exponential notation if `sd` is less than the number of digits necessary to represent
+ * the integer part of the value in normal notation.
+ *
+ * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.
+ * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+ *
+ */
+P.toPrecision = function (sd, rm) {
+  var str,
+    x = this,
+    Ctor = x.constructor;
+
+  if (sd === void 0) {
+    str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos);
+  } else {
+    checkInt32(sd, 1, MAX_DIGITS);
+
+    if (rm === void 0) rm = Ctor.rounding;
+    else checkInt32(rm, 0, 8);
+
+    x = finalise(new Ctor(x), sd, rm);
+    str = finiteToString(x, sd <= x.e || x.e <= Ctor.toExpNeg, sd);
+  }
+
+  return x.isNeg() && !x.isZero() ? '-' + str : str;
+};
+
+
+/*
+ * Return a new Decimal whose value is the value of this Decimal rounded to a maximum of `sd`
+ * significant digits using rounding mode `rm`, or to `precision` and `rounding` respectively if
+ * omitted.
+ *
+ * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.
+ * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+ *
+ * 'toSD() digits out of range: {sd}'
+ * 'toSD() digits not an integer: {sd}'
+ * 'toSD() rounding mode not an integer: {rm}'
+ * 'toSD() rounding mode out of range: {rm}'
+ *
+ */
+P.toSignificantDigits = P.toSD = function (sd, rm) {
+  var x = this,
+    Ctor = x.constructor;
+
+  if (sd === void 0) {
+    sd = Ctor.precision;
+    rm = Ctor.rounding;
+  } else {
+    checkInt32(sd, 1, MAX_DIGITS);
+
+    if (rm === void 0) rm = Ctor.rounding;
+    else checkInt32(rm, 0, 8);
+  }
+
+  return finalise(new Ctor(x), sd, rm);
+};
+
+
+/*
+ * Return a string representing the value of this Decimal.
+ *
+ * Return exponential notation if this Decimal has a positive exponent equal to or greater than
+ * `toExpPos`, or a negative exponent equal to or less than `toExpNeg`.
+ *
+ */
+P.toString = function () {
+  var x = this,
+    Ctor = x.constructor,
+    str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos);
+
+  return x.isNeg() && !x.isZero() ? '-' + str : str;
+};
+
+
+/*
+ * Return a new Decimal whose value is the value of this Decimal truncated to a whole number.
+ *
+ */
+P.truncated = P.trunc = function () {
+  return finalise(new this.constructor(this), this.e + 1, 1);
+};
+
+
+/*
+ * Return a string representing the value of this Decimal.
+ * Unlike `toString`, negative zero will include the minus sign.
+ *
+ */
+P.valueOf = P.toJSON = function () {
+  var x = this,
+    Ctor = x.constructor,
+    str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos);
+
+  return x.isNeg() ? '-' + str : str;
+};
+
+
+// Helper functions for Decimal.prototype (P) and/or Decimal methods, and their callers.
+
+
+/*
+ *  digitsToString           P.cubeRoot, P.logarithm, P.squareRoot, P.toFraction, P.toPower,
+ *                           finiteToString, naturalExponential, naturalLogarithm
+ *  checkInt32               P.toDecimalPlaces, P.toExponential, P.toFixed, P.toNearest,
+ *                           P.toPrecision, P.toSignificantDigits, toStringBinary, random
+ *  checkRoundingDigits      P.logarithm, P.toPower, naturalExponential, naturalLogarithm
+ *  convertBase              toStringBinary, parseOther
+ *  cos                      P.cos
+ *  divide                   P.atanh, P.cubeRoot, P.dividedBy, P.dividedToIntegerBy,
+ *                           P.logarithm, P.modulo, P.squareRoot, P.tan, P.tanh, P.toFraction,
+ *                           P.toNearest, toStringBinary, naturalExponential, naturalLogarithm,
+ *                           taylorSeries, atan2, parseOther
+ *  finalise                 P.absoluteValue, P.atan, P.atanh, P.ceil, P.cos, P.cosh,
+ *                           P.cubeRoot, P.dividedToIntegerBy, P.floor, P.logarithm, P.minus,
+ *                           P.modulo, P.negated, P.plus, P.round, P.sin, P.sinh, P.squareRoot,
+ *                           P.tan, P.times, P.toDecimalPlaces, P.toExponential, P.toFixed,
+ *                           P.toNearest, P.toPower, P.toPrecision, P.toSignificantDigits,
+ *                           P.truncated, divide, getLn10, getPi, naturalExponential,
+ *                           naturalLogarithm, ceil, floor, round, trunc
+ *  finiteToString           P.toExponential, P.toFixed, P.toPrecision, P.toString, P.valueOf,
+ *                           toStringBinary
+ *  getBase10Exponent        P.minus, P.plus, P.times, parseOther
+ *  getLn10                  P.logarithm, naturalLogarithm
+ *  getPi                    P.acos, P.asin, P.atan, toLessThanHalfPi, atan2
+ *  getPrecision             P.precision, P.toFraction
+ *  getZeroString            digitsToString, finiteToString
+ *  intPow                   P.toPower, parseOther
+ *  isOdd                    toLessThanHalfPi
+ *  maxOrMin                 max, min
+ *  naturalExponential       P.naturalExponential, P.toPower
+ *  naturalLogarithm         P.acosh, P.asinh, P.atanh, P.logarithm, P.naturalLogarithm,
+ *                           P.toPower, naturalExponential
+ *  nonFiniteToString        finiteToString, toStringBinary
+ *  parseDecimal             Decimal
+ *  parseOther               Decimal
+ *  sin                      P.sin
+ *  taylorSeries             P.cosh, P.sinh, cos, sin
+ *  toLessThanHalfPi         P.cos, P.sin
+ *  toStringBinary           P.toBinary, P.toHexadecimal, P.toOctal
+ *  truncate                 intPow
+ *
+ *  Throws:                  P.logarithm, P.precision, P.toFraction, checkInt32, getLn10, getPi,
+ *                           naturalLogarithm, config, parseOther, random, Decimal
+ */
+
+
+function digitsToString(d) {
+  var i, k, ws,
+    indexOfLastWord = d.length - 1,
+    str = '',
+    w = d[0];
+
+  if (indexOfLastWord > 0) {
+    str += w;
+    for (i = 1; i < indexOfLastWord; i++) {
+      ws = d[i] + '';
+      k = LOG_BASE - ws.length;
+      if (k) str += getZeroString(k);
+      str += ws;
+    }
+
+    w = d[i];
+    ws = w + '';
+    k = LOG_BASE - ws.length;
+    if (k) str += getZeroString(k);
+  } else if (w === 0) {
+    return '0';
+  }
+
+  // Remove trailing zeros of last w.
+  for (; w % 10 === 0;) w /= 10;
+
+  return str + w;
+}
+
+
+function checkInt32(i, min, max) {
+  if (i !== ~~i || i < min || i > max) {
+    throw Error(invalidArgument + i);
+  }
+}
+
+
+/*
+ * Check 5 rounding digits if `repeating` is null, 4 otherwise.
+ * `repeating == null` if caller is `log` or `pow`,
+ * `repeating != null` if caller is `naturalLogarithm` or `naturalExponential`.
+ */
+function checkRoundingDigits(d, i, rm, repeating) {
+  var di, k, r, rd;
+
+  // Get the length of the first word of the array d.
+  for (k = d[0]; k >= 10; k /= 10) --i;
+
+  // Is the rounding digit in the first word of d?
+  if (--i < 0) {
+    i += LOG_BASE;
+    di = 0;
+  } else {
+    di = Math.ceil((i + 1) / LOG_BASE);
+    i %= LOG_BASE;
+  }
+
+  // i is the index (0 - 6) of the rounding digit.
+  // E.g. if within the word 3487563 the first rounding digit is 5,
+  // then i = 4, k = 1000, rd = 3487563 % 1000 = 563
+  k = mathpow(10, LOG_BASE - i);
+  rd = d[di] % k | 0;
+
+  if (repeating == null) {
+    if (i < 3) {
+      if (i == 0) rd = rd / 100 | 0;
+      else if (i == 1) rd = rd / 10 | 0;
+      r = rm < 4 && rd == 99999 || rm > 3 && rd == 49999 || rd == 50000 || rd == 0;
+    } else {
+      r = (rm < 4 && rd + 1 == k || rm > 3 && rd + 1 == k / 2) &&
+        (d[di + 1] / k / 100 | 0) == mathpow(10, i - 2) - 1 ||
+          (rd == k / 2 || rd == 0) && (d[di + 1] / k / 100 | 0) == 0;
+    }
+  } else {
+    if (i < 4) {
+      if (i == 0) rd = rd / 1000 | 0;
+      else if (i == 1) rd = rd / 100 | 0;
+      else if (i == 2) rd = rd / 10 | 0;
+      r = (repeating || rm < 4) && rd == 9999 || !repeating && rm > 3 && rd == 4999;
+    } else {
+      r = ((repeating || rm < 4) && rd + 1 == k ||
+      (!repeating && rm > 3) && rd + 1 == k / 2) &&
+        (d[di + 1] / k / 1000 | 0) == mathpow(10, i - 3) - 1;
+    }
+  }
+
+  return r;
+}
+
+
+// Convert string of `baseIn` to an array of numbers of `baseOut`.
+// Eg. convertBase('255', 10, 16) returns [15, 15].
+// Eg. convertBase('ff', 16, 10) returns [2, 5, 5].
+function convertBase(str, baseIn, baseOut) {
+  var j,
+    arr = [0],
+    arrL,
+    i = 0,
+    strL = str.length;
+
+  for (; i < strL;) {
+    for (arrL = arr.length; arrL--;) arr[arrL] *= baseIn;
+    arr[0] += NUMERALS.indexOf(str.charAt(i++));
+    for (j = 0; j < arr.length; j++) {
+      if (arr[j] > baseOut - 1) {
+        if (arr[j + 1] === void 0) arr[j + 1] = 0;
+        arr[j + 1] += arr[j] / baseOut | 0;
+        arr[j] %= baseOut;
+      }
+    }
+  }
+
+  return arr.reverse();
+}
+
+
+/*
+ * cos(x) = 1 - x^2/2! + x^4/4! - ...
+ * |x| < pi/2
+ *
+ */
+function cosine(Ctor, x) {
+  var k, len, y;
+
+  if (x.isZero()) return x;
+
+  // Argument reduction: cos(4x) = 8*(cos^4(x) - cos^2(x)) + 1
+  // i.e. cos(x) = 8*(cos^4(x/4) - cos^2(x/4)) + 1
+
+  // Estimate the optimum number of times to use the argument reduction.
+  len = x.d.length;
+  if (len < 32) {
+    k = Math.ceil(len / 3);
+    y = (1 / tinyPow(4, k)).toString();
+  } else {
+    k = 16;
+    y = '2.3283064365386962890625e-10';
+  }
+
+  Ctor.precision += k;
+
+  x = taylorSeries(Ctor, 1, x.times(y), new Ctor(1));
+
+  // Reverse argument reduction
+  for (var i = k; i--;) {
+    var cos2x = x.times(x);
+    x = cos2x.times(cos2x).minus(cos2x).times(8).plus(1);
+  }
+
+  Ctor.precision -= k;
+
+  return x;
+}
+
+
+/*
+ * Perform division in the specified base.
+ */
+var divide = (function () {
+
+  // Assumes non-zero x and k, and hence non-zero result.
+  function multiplyInteger(x, k, base) {
+    var temp,
+      carry = 0,
+      i = x.length;
+
+    for (x = x.slice(); i--;) {
+      temp = x[i] * k + carry;
+      x[i] = temp % base | 0;
+      carry = temp / base | 0;
+    }
+
+    if (carry) x.unshift(carry);
+
+    return x;
+  }
+
+  function compare(a, b, aL, bL) {
+    var i, r;
+
+    if (aL != bL) {
+      r = aL > bL ? 1 : -1;
+    } else {
+      for (i = r = 0; i < aL; i++) {
+        if (a[i] != b[i]) {
+          r = a[i] > b[i] ? 1 : -1;
+          break;
+        }
+      }
+    }
+
+    return r;
+  }
+
+  function subtract(a, b, aL, base) {
+    var i = 0;
+
+    // Subtract b from a.
+    for (; aL--;) {
+      a[aL] -= i;
+      i = a[aL] < b[aL] ? 1 : 0;
+      a[aL] = i * base + a[aL] - b[aL];
+    }
+
+    // Remove leading zeros.
+    for (; !a[0] && a.length > 1;) a.shift();
+  }
+
+  return function (x, y, pr, rm, dp, base) {
+    var cmp, e, i, k, logBase, more, prod, prodL, q, qd, rem, remL, rem0, sd, t, xi, xL, yd0,
+      yL, yz,
+      Ctor = x.constructor,
+      sign = x.s == y.s ? 1 : -1,
+      xd = x.d,
+      yd = y.d;
+
+    // Either NaN, Infinity or 0?
+    if (!xd || !xd[0] || !yd || !yd[0]) {
+
+      return new Ctor(// Return NaN if either NaN, or both Infinity or 0.
+        !x.s || !y.s || (xd ? yd && xd[0] == yd[0] : !yd) ? NaN :
+
+        // Return ±0 if x is 0 or y is ±Infinity, or return ±Infinity as y is 0.
+        xd && xd[0] == 0 || !yd ? sign * 0 : sign / 0);
+    }
+
+    if (base) {
+      logBase = 1;
+      e = x.e - y.e;
+    } else {
+      base = BASE;
+      logBase = LOG_BASE;
+      e = mathfloor(x.e / logBase) - mathfloor(y.e / logBase);
+    }
+
+    yL = yd.length;
+    xL = xd.length;
+    q = new Ctor(sign);
+    qd = q.d = [];
+
+    // Result exponent may be one less than e.
+    // The digit array of a Decimal from toStringBinary may have trailing zeros.
+    for (i = 0; yd[i] == (xd[i] || 0); i++);
+
+    if (yd[i] > (xd[i] || 0)) e--;
+
+    if (pr == null) {
+      sd = pr = Ctor.precision;
+      rm = Ctor.rounding;
+    } else if (dp) {
+      sd = pr + (x.e - y.e) + 1;
+    } else {
+      sd = pr;
+    }
+
+    if (sd < 0) {
+      qd.push(1);
+      more = true;
+    } else {
+
+      // Convert precision in number of base 10 digits to base 1e7 digits.
+      sd = sd / logBase + 2 | 0;
+      i = 0;
+
+      // divisor < 1e7
+      if (yL == 1) {
+        k = 0;
+        yd = yd[0];
+        sd++;
+
+        // k is the carry.
+        for (; (i < xL || k) && sd--; i++) {
+          t = k * base + (xd[i] || 0);
+          qd[i] = t / yd | 0;
+          k = t % yd | 0;
+        }
+
+        more = k || i < xL;
+
+      // divisor >= 1e7
+      } else {
+
+        // Normalise xd and yd so highest order digit of yd is >= base/2
+        k = base / (yd[0] + 1) | 0;
+
+        if (k > 1) {
+          yd = multiplyInteger(yd, k, base);
+          xd = multiplyInteger(xd, k, base);
+          yL = yd.length;
+          xL = xd.length;
+        }
+
+        xi = yL;
+        rem = xd.slice(0, yL);
+        remL = rem.length;
+
+        // Add zeros to make remainder as long as divisor.
+        for (; remL < yL;) rem[remL++] = 0;
+
+        yz = yd.slice();
+        yz.unshift(0);
+        yd0 = yd[0];
+
+        if (yd[1] >= base / 2) ++yd0;
+
+        do {
+          k = 0;
+
+          // Compare divisor and remainder.
+          cmp = compare(yd, rem, yL, remL);
+
+          // If divisor < remainder.
+          if (cmp < 0) {
+
+            // Calculate trial digit, k.
+            rem0 = rem[0];
+            if (yL != remL) rem0 = rem0 * base + (rem[1] || 0);
+
+            // k will be how many times the divisor goes into the current remainder.
+            k = rem0 / yd0 | 0;
+
+            //  Algorithm:
+            //  1. product = divisor * trial digit (k)
+            //  2. if product > remainder: product -= divisor, k--
+            //  3. remainder -= product
+            //  4. if product was < remainder at 2:
+            //    5. compare new remainder and divisor
+            //    6. If remainder > divisor: remainder -= divisor, k++
+
+            if (k > 1) {
+              if (k >= base) k = base - 1;
+
+              // product = divisor * trial digit.
+              prod = multiplyInteger(yd, k, base);
+              prodL = prod.length;
+              remL = rem.length;
+
+              // Compare product and remainder.
+              cmp = compare(prod, rem, prodL, remL);
+
+              // product > remainder.
+              if (cmp == 1) {
+                k--;
+
+                // Subtract divisor from product.
+                subtract(prod, yL < prodL ? yz : yd, prodL, base);
+              }
+            } else {
+
+              // cmp is -1.
+              // If k is 0, there is no need to compare yd and rem again below, so change cmp to 1
+              // to avoid it. If k is 1 there is a need to compare yd and rem again below.
+              if (k == 0) cmp = k = 1;
+              prod = yd.slice();
+            }
+
+            prodL = prod.length;
+            if (prodL < remL) prod.unshift(0);
+
+            // Subtract product from remainder.
+            subtract(rem, prod, remL, base);
+
+            // If product was < previous remainder.
+            if (cmp == -1) {
+              remL = rem.length;
+
+              // Compare divisor and new remainder.
+              cmp = compare(yd, rem, yL, remL);
+
+              // If divisor < new remainder, subtract divisor from remainder.
+              if (cmp < 1) {
+                k++;
+
+                // Subtract divisor from remainder.
+                subtract(rem, yL < remL ? yz : yd, remL, base);
+              }
+            }
+
+            remL = rem.length;
+          } else if (cmp === 0) {
+            k++;
+            rem = [0];
+          }    // if cmp === 1, k will be 0
+
+          // Add the next digit, k, to the result array.
+          qd[i++] = k;
+
+          // Update the remainder.
+          if (cmp && rem[0]) {
+            rem[remL++] = xd[xi] || 0;
+          } else {
+            rem = [xd[xi]];
+            remL = 1;
+          }
+
+        } while ((xi++ < xL || rem[0] !== void 0) && sd--);
+
+        more = rem[0] !== void 0;
+      }
+
+      // Leading zero?
+      if (!qd[0]) qd.shift();
+    }
+
+    // logBase is 1 when divide is being used for base conversion.
+    if (logBase == 1) {
+      q.e = e;
+      inexact = more;
+    } else {
+
+      // To calculate q.e, first get the number of digits of qd[0].
+      for (i = 1, k = qd[0]; k >= 10; k /= 10) i++;
+      q.e = i + e * logBase - 1;
+
+      finalise(q, dp ? pr + q.e + 1 : pr, rm, more);
+    }
+
+    return q;
+  };
+})();
+
+
+/*
+ * Round `x` to `sd` significant digits using rounding mode `rm`.
+ * Check for over/under-flow.
+ */
+ function finalise(x, sd, rm, isTruncated) {
+  var digits, i, j, k, rd, roundUp, w, xd, xdi,
+    Ctor = x.constructor;
+
+  // Don't round if sd is null or undefined.
+  out: if (sd != null) {
+    xd = x.d;
+
+    // Infinity/NaN.
+    if (!xd) return x;
+
+    // rd: the rounding digit, i.e. the digit after the digit that may be rounded up.
+    // w: the word of xd containing rd, a base 1e7 number.
+    // xdi: the index of w within xd.
+    // digits: the number of digits of w.
+    // i: what would be the index of rd within w if all the numbers were 7 digits long (i.e. if
+    // they had leading zeros)
+    // j: if > 0, the actual index of rd within w (if < 0, rd is a leading zero).
+
+    // Get the length of the first word of the digits array xd.
+    for (digits = 1, k = xd[0]; k >= 10; k /= 10) digits++;
+    i = sd - digits;
+
+    // Is the rounding digit in the first word of xd?
+    if (i < 0) {
+      i += LOG_BASE;
+      j = sd;
+      w = xd[xdi = 0];
+
+      // Get the rounding digit at index j of w.
+      rd = w / mathpow(10, digits - j - 1) % 10 | 0;
+    } else {
+      xdi = Math.ceil((i + 1) / LOG_BASE);
+      k = xd.length;
+      if (xdi >= k) {
+        if (isTruncated) {
+
+          // Needed by `naturalExponential`, `naturalLogarithm` and `squareRoot`.
+          for (; k++ <= xdi;) xd.push(0);
+          w = rd = 0;
+          digits = 1;
+          i %= LOG_BASE;
+          j = i - LOG_BASE + 1;
+        } else {
+          break out;
+        }
+      } else {
+        w = k = xd[xdi];
+
+        // Get the number of digits of w.
+        for (digits = 1; k >= 10; k /= 10) digits++;
+
+        // Get the index of rd within w.
+        i %= LOG_BASE;
+
+        // Get the index of rd within w, adjusted for leading zeros.
+        // The number of leading zeros of w is given by LOG_BASE - digits.
+        j = i - LOG_BASE + digits;
+
+        // Get the rounding digit at index j of w.
+        rd = j < 0 ? 0 : w / mathpow(10, digits - j - 1) % 10 | 0;
+      }
+    }
+
+    // Are there any non-zero digits after the rounding digit?
+    isTruncated = isTruncated || sd < 0 ||
+      xd[xdi + 1] !== void 0 || (j < 0 ? w : w % mathpow(10, digits - j - 1));
+
+    // The expression `w % mathpow(10, digits - j - 1)` returns all the digits of w to the right
+    // of the digit at (left-to-right) index j, e.g. if w is 908714 and j is 2, the expression
+    // will give 714.
+
+    roundUp = rm < 4
+      ? (rd || isTruncated) && (rm == 0 || rm == (x.s < 0 ? 3 : 2))
+      : rd > 5 || rd == 5 && (rm == 4 || isTruncated || rm == 6 &&
+
+        // Check whether the digit to the left of the rounding digit is odd.
+        ((i > 0 ? j > 0 ? w / mathpow(10, digits - j) : 0 : xd[xdi - 1]) % 10) & 1 ||
+          rm == (x.s < 0 ? 8 : 7));
+
+    if (sd < 1 || !xd[0]) {
+      xd.length = 0;
+      if (roundUp) {
+
+        // Convert sd to decimal places.
+        sd -= x.e + 1;
+
+        // 1, 0.1, 0.01, 0.001, 0.0001 etc.
+        xd[0] = mathpow(10, (LOG_BASE - sd % LOG_BASE) % LOG_BASE);
+        x.e = -sd || 0;
+      } else {
+
+        // Zero.
+        xd[0] = x.e = 0;
+      }
+
+      return x;
+    }
+
+    // Remove excess digits.
+    if (i == 0) {
+      xd.length = xdi;
+      k = 1;
+      xdi--;
+    } else {
+      xd.length = xdi + 1;
+      k = mathpow(10, LOG_BASE - i);
+
+      // E.g. 56700 becomes 56000 if 7 is the rounding digit.
+      // j > 0 means i > number of leading zeros of w.
+      xd[xdi] = j > 0 ? (w / mathpow(10, digits - j) % mathpow(10, j) | 0) * k : 0;
+    }
+
+    if (roundUp) {
+      for (;;) {
+
+        // Is the digit to be rounded up in the first word of xd?
+        if (xdi == 0) {
+
+          // i will be the length of xd[0] before k is added.
+          for (i = 1, j = xd[0]; j >= 10; j /= 10) i++;
+          j = xd[0] += k;
+          for (k = 1; j >= 10; j /= 10) k++;
+
+          // if i != k the length has increased.
+          if (i != k) {
+            x.e++;
+            if (xd[0] == BASE) xd[0] = 1;
+          }
+
+          break;
+        } else {
+          xd[xdi] += k;
+          if (xd[xdi] != BASE) break;
+          xd[xdi--] = 0;
+          k = 1;
+        }
+      }
+    }
+
+    // Remove trailing zeros.
+    for (i = xd.length; xd[--i] === 0;) xd.pop();
+  }
+
+  if (external) {
+
+    // Overflow?
+    if (x.e > Ctor.maxE) {
+
+      // Infinity.
+      x.d = null;
+      x.e = NaN;
+
+    // Underflow?
+    } else if (x.e < Ctor.minE) {
+
+      // Zero.
+      x.e = 0;
+      x.d = [0];
+      // Ctor.underflow = true;
+    } // else Ctor.underflow = false;
+  }
+
+  return x;
+}
+
+
+function finiteToString(x, isExp, sd) {
+  if (!x.isFinite()) return nonFiniteToString(x);
+  var k,
+    e = x.e,
+    str = digitsToString(x.d),
+    len = str.length;
+
+  if (isExp) {
+    if (sd && (k = sd - len) > 0) {
+      str = str.charAt(0) + '.' + str.slice(1) + getZeroString(k);
+    } else if (len > 1) {
+      str = str.charAt(0) + '.' + str.slice(1);
+    }
+
+    str = str + (x.e < 0 ? 'e' : 'e+') + x.e;
+  } else if (e < 0) {
+    str = '0.' + getZeroString(-e - 1) + str;
+    if (sd && (k = sd - len) > 0) str += getZeroString(k);
+  } else if (e >= len) {
+    str += getZeroString(e + 1 - len);
+    if (sd && (k = sd - e - 1) > 0) str = str + '.' + getZeroString(k);
+  } else {
+    if ((k = e + 1) < len) str = str.slice(0, k) + '.' + str.slice(k);
+    if (sd && (k = sd - len) > 0) {
+      if (e + 1 === len) str += '.';
+      str += getZeroString(k);
+    }
+  }
+
+  return str;
+}
+
+
+// Calculate the base 10 exponent from the base 1e7 exponent.
+function getBase10Exponent(digits, e) {
+  var w = digits[0];
+
+  // Add the number of digits of the first word of the digits array.
+  for ( e *= LOG_BASE; w >= 10; w /= 10) e++;
+  return e;
+}
+
+
+function getLn10(Ctor, sd, pr) {
+  if (sd > LN10_PRECISION) {
+
+    // Reset global state in case the exception is caught.
+    external = true;
+    if (pr) Ctor.precision = pr;
+    throw Error(precisionLimitExceeded);
+  }
+  return finalise(new Ctor(LN10), sd, 1, true);
+}
+
+
+function getPi(Ctor, sd, rm) {
+  if (sd > PI_PRECISION) throw Error(precisionLimitExceeded);
+  return finalise(new Ctor(PI), sd, rm, true);
+}
+
+
+function getPrecision(digits) {
+  var w = digits.length - 1,
+    len = w * LOG_BASE + 1;
+
+  w = digits[w];
+
+  // If non-zero...
+  if (w) {
+
+    // Subtract the number of trailing zeros of the last word.
+    for (; w % 10 == 0; w /= 10) len--;
+
+    // Add the number of digits of the first word.
+    for (w = digits[0]; w >= 10; w /= 10) len++;
+  }
+
+  return len;
+}
+
+
+function getZeroString(k) {
+  var zs = '';
+  for (; k--;) zs += '0';
+  return zs;
+}
+
+
+/*
+ * Return a new Decimal whose value is the value of Decimal `x` to the power `n`, where `n` is an
+ * integer of type number.
+ *
+ * Implements 'exponentiation by squaring'. Called by `pow` and `parseOther`.
+ *
+ */
+function intPow(Ctor, x, n, pr) {
+  var isTruncated,
+    r = new Ctor(1),
+
+    // Max n of 9007199254740991 takes 53 loop iterations.
+    // Maximum digits array length; leaves [28, 34] guard digits.
+    k = Math.ceil(pr / LOG_BASE + 4);
+
+  external = false;
+
+  for (;;) {
+    if (n % 2) {
+      r = r.times(x);
+      if (truncate(r.d, k)) isTruncated = true;
+    }
+
+    n = mathfloor(n / 2);
+    if (n === 0) {
+
+      // To ensure correct rounding when r.d is truncated, increment the last word if it is zero.
+      n = r.d.length - 1;
+      if (isTruncated && r.d[n] === 0) ++r.d[n];
+      break;
+    }
+
+    x = x.times(x);
+    truncate(x.d, k);
+  }
+
+  external = true;
+
+  return r;
+}
+
+
+function isOdd(n) {
+  return n.d[n.d.length - 1] & 1;
+}
+
+
+/*
+ * Handle `max` and `min`. `ltgt` is 'lt' or 'gt'.
+ */
+function maxOrMin(Ctor, args, ltgt) {
+  var y,
+    x = new Ctor(args[0]),
+    i = 0;
+
+  for (; ++i < args.length;) {
+    y = new Ctor(args[i]);
+    if (!y.s) {
+      x = y;
+      break;
+    } else if (x[ltgt](y)) {
+      x = y;
+    }
+  }
+
+  return x;
+}
+
+
+/*
+ * Return a new Decimal whose value is the natural exponential of `x` rounded to `sd` significant
+ * digits.
+ *
+ * Taylor/Maclaurin series.
+ *
+ * exp(x) = x^0/0! + x^1/1! + x^2/2! + x^3/3! + ...
+ *
+ * Argument reduction:
+ *   Repeat x = x / 32, k += 5, until |x| < 0.1
+ *   exp(x) = exp(x / 2^k)^(2^k)
+ *
+ * Previously, the argument was initially reduced by
+ * exp(x) = exp(r) * 10^k  where r = x - k * ln10, k = floor(x / ln10)
+ * to first put r in the range [0, ln10], before dividing by 32 until |x| < 0.1, but this was
+ * found to be slower than just dividing repeatedly by 32 as above.
+ *
+ * Max integer argument: exp('20723265836946413') = 6.3e+9000000000000000
+ * Min integer argument: exp('-20723265836946411') = 1.2e-9000000000000000
+ * (Math object integer min/max: Math.exp(709) = 8.2e+307, Math.exp(-745) = 5e-324)
+ *
+ *  exp(Infinity)  = Infinity
+ *  exp(-Infinity) = 0
+ *  exp(NaN)       = NaN
+ *  exp(±0)        = 1
+ *
+ *  exp(x) is non-terminating for any finite, non-zero x.
+ *
+ *  The result will always be correctly rounded.
+ *
+ */
+function naturalExponential(x, sd) {
+  var denominator, guard, j, pow, sum, t, wpr,
+    rep = 0,
+    i = 0,
+    k = 0,
+    Ctor = x.constructor,
+    rm = Ctor.rounding,
+    pr = Ctor.precision;
+
+  // 0/NaN/Infinity?
+  if (!x.d || !x.d[0] || x.e > 17) {
+
+    return new Ctor(x.d
+      ? !x.d[0] ? 1 : x.s < 0 ? 0 : 1 / 0
+      : x.s ? x.s < 0 ? 0 : x : 0 / 0);
+  }
+
+  if (sd == null) {
+    external = false;
+    wpr = pr;
+  } else {
+    wpr = sd;
+  }
+
+  t = new Ctor(0.03125);
+
+  // while abs(x) >= 0.1
+  while (x.e > -2) {
+
+    // x = x / 2^5
+    x = x.times(t);
+    k += 5;
+  }
+
+  // Use 2 * log10(2^k) + 5 (empirically derived) to estimate the increase in precision
+  // necessary to ensure the first 4 rounding digits are correct.
+  guard = Math.log(mathpow(2, k)) / Math.LN10 * 2 + 5 | 0;
+  wpr += guard;
+  denominator = pow = sum = new Ctor(1);
+  Ctor.precision = wpr;
+
+  for (;;) {
+    pow = finalise(pow.times(x), wpr, 1);
+    denominator = denominator.times(++i);
+    t = sum.plus(divide(pow, denominator, wpr, 1));
+
+    if (digitsToString(t.d).slice(0, wpr) === digitsToString(sum.d).slice(0, wpr)) {
+      j = k;
+      while (j--) sum = finalise(sum.times(sum), wpr, 1);
+
+      // Check to see if the first 4 rounding digits are [49]999.
+      // If so, repeat the summation with a higher precision, otherwise
+      // e.g. with precision: 18, rounding: 1
+      // exp(18.404272462595034083567793919843761) = 98372560.1229999999 (should be 98372560.123)
+      // `wpr - guard` is the index of first rounding digit.
+      if (sd == null) {
+
+        if (rep < 3 && checkRoundingDigits(sum.d, wpr - guard, rm, rep)) {
+          Ctor.precision = wpr += 10;
+          denominator = pow = t = new Ctor(1);
+          i = 0;
+          rep++;
+        } else {
+          return finalise(sum, Ctor.precision = pr, rm, external = true);
+        }
+      } else {
+        Ctor.precision = pr;
+        return sum;
+      }
+    }
+
+    sum = t;
+  }
+}
+
+
+/*
+ * Return a new Decimal whose value is the natural logarithm of `x` rounded to `sd` significant
+ * digits.
+ *
+ *  ln(-n)        = NaN
+ *  ln(0)         = -Infinity
+ *  ln(-0)        = -Infinity
+ *  ln(1)         = 0
+ *  ln(Infinity)  = Infinity
+ *  ln(-Infinity) = NaN
+ *  ln(NaN)       = NaN
+ *
+ *  ln(n) (n != 1) is non-terminating.
+ *
+ */
+function naturalLogarithm(y, sd) {
+  var c, c0, denominator, e, numerator, rep, sum, t, wpr, x1, x2,
+    n = 1,
+    guard = 10,
+    x = y,
+    xd = x.d,
+    Ctor = x.constructor,
+    rm = Ctor.rounding,
+    pr = Ctor.precision;
+
+  // Is x negative or Infinity, NaN, 0 or 1?
+  if (x.s < 0 || !xd || !xd[0] || !x.e && xd[0] == 1 && xd.length == 1) {
+    return new Ctor(xd && !xd[0] ? -1 / 0 : x.s != 1 ? NaN : xd ? 0 : x);
+  }
+
+  if (sd == null) {
+    external = false;
+    wpr = pr;
+  } else {
+    wpr = sd;
+  }
+
+  Ctor.precision = wpr += guard;
+  c = digitsToString(xd);
+  c0 = c.charAt(0);
+
+  if (Math.abs(e = x.e) < 1.5e15) {
+
+    // Argument reduction.
+    // The series converges faster the closer the argument is to 1, so using
+    // ln(a^b) = b * ln(a),   ln(a) = ln(a^b) / b
+    // multiply the argument by itself until the leading digits of the significand are 7, 8, 9,
+    // 10, 11, 12 or 13, recording the number of multiplications so the sum of the series can
+    // later be divided by this number, then separate out the power of 10 using
+    // ln(a*10^b) = ln(a) + b*ln(10).
+
+    // max n is 21 (gives 0.9, 1.0 or 1.1) (9e15 / 21 = 4.2e14).
+    //while (c0 < 9 && c0 != 1 || c0 == 1 && c.charAt(1) > 1) {
+    // max n is 6 (gives 0.7 - 1.3)
+    while (c0 < 7 && c0 != 1 || c0 == 1 && c.charAt(1) > 3) {
+      x = x.times(y);
+      c = digitsToString(x.d);
+      c0 = c.charAt(0);
+      n++;
+    }
+
+    e = x.e;
+
+    if (c0 > 1) {
+      x = new Ctor('0.' + c);
+      e++;
+    } else {
+      x = new Ctor(c0 + '.' + c.slice(1));
+    }
+  } else {
+
+    // The argument reduction method above may result in overflow if the argument y is a massive
+    // number with exponent >= 1500000000000000 (9e15 / 6 = 1.5e15), so instead recall this
+    // function using ln(x*10^e) = ln(x) + e*ln(10).
+    t = getLn10(Ctor, wpr + 2, pr).times(e + '');
+    x = naturalLogarithm(new Ctor(c0 + '.' + c.slice(1)), wpr - guard).plus(t);
+    Ctor.precision = pr;
+
+    return sd == null ? finalise(x, pr, rm, external = true) : x;
+  }
+
+  // x1 is x reduced to a value near 1.
+  x1 = x;
+
+  // Taylor series.
+  // ln(y) = ln((1 + x)/(1 - x)) = 2(x + x^3/3 + x^5/5 + x^7/7 + ...)
+  // where x = (y - 1)/(y + 1)    (|x| < 1)
+  sum = numerator = x = divide(x.minus(1), x.plus(1), wpr, 1);
+  x2 = finalise(x.times(x), wpr, 1);
+  denominator = 3;
+
+  for (;;) {
+    numerator = finalise(numerator.times(x2), wpr, 1);
+    t = sum.plus(divide(numerator, new Ctor(denominator), wpr, 1));
+
+    if (digitsToString(t.d).slice(0, wpr) === digitsToString(sum.d).slice(0, wpr)) {
+      sum = sum.times(2);
+
+      // Reverse the argument reduction. Check that e is not 0 because, besides preventing an
+      // unnecessary calculation, -0 + 0 = +0 and to ensure correct rounding -0 needs to stay -0.
+      if (e !== 0) sum = sum.plus(getLn10(Ctor, wpr + 2, pr).times(e + ''));
+      sum = divide(sum, new Ctor(n), wpr, 1);
+
+      // Is rm > 3 and the first 4 rounding digits 4999, or rm < 4 (or the summation has
+      // been repeated previously) and the first 4 rounding digits 9999?
+      // If so, restart the summation with a higher precision, otherwise
+      // e.g. with precision: 12, rounding: 1
+      // ln(135520028.6126091714265381533) = 18.7246299999 when it should be 18.72463.
+      // `wpr - guard` is the index of first rounding digit.
+      if (sd == null) {
+        if (checkRoundingDigits(sum.d, wpr - guard, rm, rep)) {
+          Ctor.precision = wpr += guard;
+          t = numerator = x = divide(x1.minus(1), x1.plus(1), wpr, 1);
+          x2 = finalise(x.times(x), wpr, 1);
+          denominator = rep = 1;
+        } else {
+          return finalise(sum, Ctor.precision = pr, rm, external = true);
+        }
+      } else {
+        Ctor.precision = pr;
+        return sum;
+      }
+    }
+
+    sum = t;
+    denominator += 2;
+  }
+}
+
+
+// ±Infinity, NaN.
+function nonFiniteToString(x) {
+  // Unsigned.
+  return String(x.s * x.s / 0);
+}
+
+
+/*
+ * Parse the value of a new Decimal `x` from string `str`.
+ */
+function parseDecimal(x, str) {
+  var e, i, len;
+
+  // Decimal point?
+  if ((e = str.indexOf('.')) > -1) str = str.replace('.', '');
+
+  // Exponential form?
+  if ((i = str.search(/e/i)) > 0) {
+
+    // Determine exponent.
+    if (e < 0) e = i;
+    e += +str.slice(i + 1);
+    str = str.substring(0, i);
+  } else if (e < 0) {
+
+    // Integer.
+    e = str.length;
+  }
+
+  // Determine leading zeros.
+  for (i = 0; str.charCodeAt(i) === 48; i++);
+
+  // Determine trailing zeros.
+  for (len = str.length; str.charCodeAt(len - 1) === 48; --len);
+  str = str.slice(i, len);
+
+  if (str) {
+    len -= i;
+    x.e = e = e - i - 1;
+    x.d = [];
+
+    // Transform base
+
+    // e is the base 10 exponent.
+    // i is where to slice str to get the first word of the digits array.
+    i = (e + 1) % LOG_BASE;
+    if (e < 0) i += LOG_BASE;
+
+    if (i < len) {
+      if (i) x.d.push(+str.slice(0, i));
+      for (len -= LOG_BASE; i < len;) x.d.push(+str.slice(i, i += LOG_BASE));
+      str = str.slice(i);
+      i = LOG_BASE - str.length;
+    } else {
+      i -= len;
+    }
+
+    for (; i--;) str += '0';
+    x.d.push(+str);
+
+    if (external) {
+
+      // Overflow?
+      if (x.e > x.constructor.maxE) {
+
+        // Infinity.
+        x.d = null;
+        x.e = NaN;
+
+      // Underflow?
+      } else if (x.e < x.constructor.minE) {
+
+        // Zero.
+        x.e = 0;
+        x.d = [0];
+        // x.constructor.underflow = true;
+      } // else x.constructor.underflow = false;
+    }
+  } else {
+
+    // Zero.
+    x.e = 0;
+    x.d = [0];
+  }
+
+  return x;
+}
+
+
+/*
+ * Parse the value of a new Decimal `x` from a string `str`, which is not a decimal value.
+ */
+function parseOther(x, str) {
+  var base, Ctor, divisor, i, isFloat, len, p, xd, xe;
+
+  if (str.indexOf('_') > -1) {
+    str = str.replace(/(\d)_(?=\d)/g, '$1');
+    if (isDecimal.test(str)) return parseDecimal(x, str);
+  } else if (str === 'Infinity' || str === 'NaN') {
+    if (!+str) x.s = NaN;
+    x.e = NaN;
+    x.d = null;
+    return x;
+  }
+
+  if (isHex.test(str))  {
+    base = 16;
+    str = str.toLowerCase();
+  } else if (isBinary.test(str))  {
+    base = 2;
+  } else if (isOctal.test(str))  {
+    base = 8;
+  } else {
+    throw Error(invalidArgument + str);
+  }
+
+  // Is there a binary exponent part?
+  i = str.search(/p/i);
+
+  if (i > 0) {
+    p = +str.slice(i + 1);
+    str = str.substring(2, i);
+  } else {
+    str = str.slice(2);
+  }
+
+  // Convert `str` as an integer then divide the result by `base` raised to a power such that the
+  // fraction part will be restored.
+  i = str.indexOf('.');
+  isFloat = i >= 0;
+  Ctor = x.constructor;
+
+  if (isFloat) {
+    str = str.replace('.', '');
+    len = str.length;
+    i = len - i;
+
+    // log[10](16) = 1.2041... , log[10](88) = 1.9444....
+    divisor = intPow(Ctor, new Ctor(base), i, i * 2);
+  }
+
+  xd = convertBase(str, base, BASE);
+  xe = xd.length - 1;
+
+  // Remove trailing zeros.
+  for (i = xe; xd[i] === 0; --i) xd.pop();
+  if (i < 0) return new Ctor(x.s * 0);
+  x.e = getBase10Exponent(xd, xe);
+  x.d = xd;
+  external = false;
+
+  // At what precision to perform the division to ensure exact conversion?
+  // maxDecimalIntegerPartDigitCount = ceil(log[10](b) * otherBaseIntegerPartDigitCount)
+  // log[10](2) = 0.30103, log[10](8) = 0.90309, log[10](16) = 1.20412
+  // E.g. ceil(1.2 * 3) = 4, so up to 4 decimal digits are needed to represent 3 hex int digits.
+  // maxDecimalFractionPartDigitCount = {Hex:4|Oct:3|Bin:1} * otherBaseFractionPartDigitCount
+  // Therefore using 4 * the number of digits of str will always be enough.
+  if (isFloat) x = divide(x, divisor, len * 4);
+
+  // Multiply by the binary exponent part if present.
+  if (p) x = x.times(Math.abs(p) < 54 ? mathpow(2, p) : Decimal.pow(2, p));
+  external = true;
+
+  return x;
+}
+
+
+/*
+ * sin(x) = x - x^3/3! + x^5/5! - ...
+ * |x| < pi/2
+ *
+ */
+function sine(Ctor, x) {
+  var k,
+    len = x.d.length;
+
+  if (len < 3) {
+    return x.isZero() ? x : taylorSeries(Ctor, 2, x, x);
+  }
+
+  // Argument reduction: sin(5x) = 16*sin^5(x) - 20*sin^3(x) + 5*sin(x)
+  // i.e. sin(x) = 16*sin^5(x/5) - 20*sin^3(x/5) + 5*sin(x/5)
+  // and  sin(x) = sin(x/5)(5 + sin^2(x/5)(16sin^2(x/5) - 20))
+
+  // Estimate the optimum number of times to use the argument reduction.
+  k = 1.4 * Math.sqrt(len);
+  k = k > 16 ? 16 : k | 0;
+
+  x = x.times(1 / tinyPow(5, k));
+  x = taylorSeries(Ctor, 2, x, x);
+
+  // Reverse argument reduction
+  var sin2_x,
+    d5 = new Ctor(5),
+    d16 = new Ctor(16),
+    d20 = new Ctor(20);
+  for (; k--;) {
+    sin2_x = x.times(x);
+    x = x.times(d5.plus(sin2_x.times(d16.times(sin2_x).minus(d20))));
+  }
+
+  return x;
+}
+
+
+// Calculate Taylor series for `cos`, `cosh`, `sin` and `sinh`.
+function taylorSeries(Ctor, n, x, y, isHyperbolic) {
+  var j, t, u, x2,
+    i = 1,
+    pr = Ctor.precision,
+    k = Math.ceil(pr / LOG_BASE);
+
+  external = false;
+  x2 = x.times(x);
+  u = new Ctor(y);
+
+  for (;;) {
+    t = divide(u.times(x2), new Ctor(n++ * n++), pr, 1);
+    u = isHyperbolic ? y.plus(t) : y.minus(t);
+    y = divide(t.times(x2), new Ctor(n++ * n++), pr, 1);
+    t = u.plus(y);
+
+    if (t.d[k] !== void 0) {
+      for (j = k; t.d[j] === u.d[j] && j--;);
+      if (j == -1) break;
+    }
+
+    j = u;
+    u = y;
+    y = t;
+    t = j;
+    i++;
+  }
+
+  external = true;
+  t.d.length = k + 1;
+
+  return t;
+}
+
+
+// Exponent e must be positive and non-zero.
+function tinyPow(b, e) {
+  var n = b;
+  while (--e) n *= b;
+  return n;
+}
+
+
+// Return the absolute value of `x` reduced to less than or equal to half pi.
+function toLessThanHalfPi(Ctor, x) {
+  var t,
+    isNeg = x.s < 0,
+    pi = getPi(Ctor, Ctor.precision, 1),
+    halfPi = pi.times(0.5);
+
+  x = x.abs();
+
+  if (x.lte(halfPi)) {
+    quadrant = isNeg ? 4 : 1;
+    return x;
+  }
+
+  t = x.divToInt(pi);
+
+  if (t.isZero()) {
+    quadrant = isNeg ? 3 : 2;
+  } else {
+    x = x.minus(t.times(pi));
+
+    // 0 <= x < pi
+    if (x.lte(halfPi)) {
+      quadrant = isOdd(t) ? (isNeg ? 2 : 3) : (isNeg ? 4 : 1);
+      return x;
+    }
+
+    quadrant = isOdd(t) ? (isNeg ? 1 : 4) : (isNeg ? 3 : 2);
+  }
+
+  return x.minus(pi).abs();
+}
+
+
+/*
+ * Return the value of Decimal `x` as a string in base `baseOut`.
+ *
+ * If the optional `sd` argument is present include a binary exponent suffix.
+ */
+function toStringBinary(x, baseOut, sd, rm) {
+  var base, e, i, k, len, roundUp, str, xd, y,
+    Ctor = x.constructor,
+    isExp = sd !== void 0;
+
+  if (isExp) {
+    checkInt32(sd, 1, MAX_DIGITS);
+    if (rm === void 0) rm = Ctor.rounding;
+    else checkInt32(rm, 0, 8);
+  } else {
+    sd = Ctor.precision;
+    rm = Ctor.rounding;
+  }
+
+  if (!x.isFinite()) {
+    str = nonFiniteToString(x);
+  } else {
+    str = finiteToString(x);
+    i = str.indexOf('.');
+
+    // Use exponential notation according to `toExpPos` and `toExpNeg`? No, but if required:
+    // maxBinaryExponent = floor((decimalExponent + 1) * log[2](10))
+    // minBinaryExponent = floor(decimalExponent * log[2](10))
+    // log[2](10) = 3.321928094887362347870319429489390175864
+
+    if (isExp) {
+      base = 2;
+      if (baseOut == 16) {
+        sd = sd * 4 - 3;
+      } else if (baseOut == 8) {
+        sd = sd * 3 - 2;
+      }
+    } else {
+      base = baseOut;
+    }
+
+    // Convert the number as an integer then divide the result by its base raised to a power such
+    // that the fraction part will be restored.
+
+    // Non-integer.
+    if (i >= 0) {
+      str = str.replace('.', '');
+      y = new Ctor(1);
+      y.e = str.length - i;
+      y.d = convertBase(finiteToString(y), 10, base);
+      y.e = y.d.length;
+    }
+
+    xd = convertBase(str, 10, base);
+    e = len = xd.length;
+
+    // Remove trailing zeros.
+    for (; xd[--len] == 0;) xd.pop();
+
+    if (!xd[0]) {
+      str = isExp ? '0p+0' : '0';
+    } else {
+      if (i < 0) {
+        e--;
+      } else {
+        x = new Ctor(x);
+        x.d = xd;
+        x.e = e;
+        x = divide(x, y, sd, rm, 0, base);
+        xd = x.d;
+        e = x.e;
+        roundUp = inexact;
+      }
+
+      // The rounding digit, i.e. the digit after the digit that may be rounded up.
+      i = xd[sd];
+      k = base / 2;
+      roundUp = roundUp || xd[sd + 1] !== void 0;
+
+      roundUp = rm < 4
+        ? (i !== void 0 || roundUp) && (rm === 0 || rm === (x.s < 0 ? 3 : 2))
+        : i > k || i === k && (rm === 4 || roundUp || rm === 6 && xd[sd - 1] & 1 ||
+          rm === (x.s < 0 ? 8 : 7));
+
+      xd.length = sd;
+
+      if (roundUp) {
+
+        // Rounding up may mean the previous digit has to be rounded up and so on.
+        for (; ++xd[--sd] > base - 1;) {
+          xd[sd] = 0;
+          if (!sd) {
+            ++e;
+            xd.unshift(1);
+          }
+        }
+      }
+
+      // Determine trailing zeros.
+      for (len = xd.length; !xd[len - 1]; --len);
+
+      // E.g. [4, 11, 15] becomes 4bf.
+      for (i = 0, str = ''; i < len; i++) str += NUMERALS.charAt(xd[i]);
+
+      // Add binary exponent suffix?
+      if (isExp) {
+        if (len > 1) {
+          if (baseOut == 16 || baseOut == 8) {
+            i = baseOut == 16 ? 4 : 3;
+            for (--len; len % i; len++) str += '0';
+            xd = convertBase(str, base, baseOut);
+            for (len = xd.length; !xd[len - 1]; --len);
+
+            // xd[0] will always be be 1
+            for (i = 1, str = '1.'; i < len; i++) str += NUMERALS.charAt(xd[i]);
+          } else {
+            str = str.charAt(0) + '.' + str.slice(1);
+          }
+        }
+
+        str =  str + (e < 0 ? 'p' : 'p+') + e;
+      } else if (e < 0) {
+        for (; ++e;) str = '0' + str;
+        str = '0.' + str;
+      } else {
+        if (++e > len) for (e -= len; e-- ;) str += '0';
+        else if (e < len) str = str.slice(0, e) + '.' + str.slice(e);
+      }
+    }
+
+    str = (baseOut == 16 ? '0x' : baseOut == 2 ? '0b' : baseOut == 8 ? '0o' : '') + str;
+  }
+
+  return x.s < 0 ? '-' + str : str;
+}
+
+
+// Does not strip trailing zeros.
+function truncate(arr, len) {
+  if (arr.length > len) {
+    arr.length = len;
+    return true;
+  }
+}
+
+
+// Decimal methods
+
+
+/*
+ *  abs
+ *  acos
+ *  acosh
+ *  add
+ *  asin
+ *  asinh
+ *  atan
+ *  atanh
+ *  atan2
+ *  cbrt
+ *  ceil
+ *  clamp
+ *  clone
+ *  config
+ *  cos
+ *  cosh
+ *  div
+ *  exp
+ *  floor
+ *  hypot
+ *  ln
+ *  log
+ *  log2
+ *  log10
+ *  max
+ *  min
+ *  mod
+ *  mul
+ *  pow
+ *  random
+ *  round
+ *  set
+ *  sign
+ *  sin
+ *  sinh
+ *  sqrt
+ *  sub
+ *  sum
+ *  tan
+ *  tanh
+ *  trunc
+ */
+
+
+/*
+ * Return a new Decimal whose value is the absolute value of `x`.
+ *
+ * x {number|string|Decimal}
+ *
+ */
+function abs(x) {
+  return new this(x).abs();
+}
+
+
+/*
+ * Return a new Decimal whose value is the arccosine in radians of `x`.
+ *
+ * x {number|string|Decimal}
+ *
+ */
+function acos(x) {
+  return new this(x).acos();
+}
+
+
+/*
+ * Return a new Decimal whose value is the inverse of the hyperbolic cosine of `x`, rounded to
+ * `precision` significant digits using rounding mode `rounding`.
+ *
+ * x {number|string|Decimal} A value in radians.
+ *
+ */
+function acosh(x) {
+  return new this(x).acosh();
+}
+
+
+/*
+ * Return a new Decimal whose value is the sum of `x` and `y`, rounded to `precision` significant
+ * digits using rounding mode `rounding`.
+ *
+ * x {number|string|Decimal}
+ * y {number|string|Decimal}
+ *
+ */
+function add(x, y) {
+  return new this(x).plus(y);
+}
+
+
+/*
+ * Return a new Decimal whose value is the arcsine in radians of `x`, rounded to `precision`
+ * significant digits using rounding mode `rounding`.
+ *
+ * x {number|string|Decimal}
+ *
+ */
+function asin(x) {
+  return new this(x).asin();
+}
+
+
+/*
+ * Return a new Decimal whose value is the inverse of the hyperbolic sine of `x`, rounded to
+ * `precision` significant digits using rounding mode `rounding`.
+ *
+ * x {number|string|Decimal} A value in radians.
+ *
+ */
+function asinh(x) {
+  return new this(x).asinh();
+}
+
+
+/*
+ * Return a new Decimal whose value is the arctangent in radians of `x`, rounded to `precision`
+ * significant digits using rounding mode `rounding`.
+ *
+ * x {number|string|Decimal}
+ *
+ */
+function atan(x) {
+  return new this(x).atan();
+}
+
+
+/*
+ * Return a new Decimal whose value is the inverse of the hyperbolic tangent of `x`, rounded to
+ * `precision` significant digits using rounding mode `rounding`.
+ *
+ * x {number|string|Decimal} A value in radians.
+ *
+ */
+function atanh(x) {
+  return new this(x).atanh();
+}
+
+
+/*
+ * Return a new Decimal whose value is the arctangent in radians of `y/x` in the range -pi to pi
+ * (inclusive), rounded to `precision` significant digits using rounding mode `rounding`.
+ *
+ * Domain: [-Infinity, Infinity]
+ * Range: [-pi, pi]
+ *
+ * y {number|string|Decimal} The y-coordinate.
+ * x {number|string|Decimal} The x-coordinate.
+ *
+ * atan2(±0, -0)               = ±pi
+ * atan2(±0, +0)               = ±0
+ * atan2(±0, -x)               = ±pi for x > 0
+ * atan2(±0, x)                = ±0 for x > 0
+ * atan2(-y, ±0)               = -pi/2 for y > 0
+ * atan2(y, ±0)                = pi/2 for y > 0
+ * atan2(±y, -Infinity)        = ±pi for finite y > 0
+ * atan2(±y, +Infinity)        = ±0 for finite y > 0
+ * atan2(±Infinity, x)         = ±pi/2 for finite x
+ * atan2(±Infinity, -Infinity) = ±3*pi/4
+ * atan2(±Infinity, +Infinity) = ±pi/4
+ * atan2(NaN, x) = NaN
+ * atan2(y, NaN) = NaN
+ *
+ */
+function atan2(y, x) {
+  y = new this(y);
+  x = new this(x);
+  var r,
+    pr = this.precision,
+    rm = this.rounding,
+    wpr = pr + 4;
+
+  // Either NaN
+  if (!y.s || !x.s) {
+    r = new this(NaN);
+
+  // Both ±Infinity
+  } else if (!y.d && !x.d) {
+    r = getPi(this, wpr, 1).times(x.s > 0 ? 0.25 : 0.75);
+    r.s = y.s;
+
+  // x is ±Infinity or y is ±0
+  } else if (!x.d || y.isZero()) {
+    r = x.s < 0 ? getPi(this, pr, rm) : new this(0);
+    r.s = y.s;
+
+  // y is ±Infinity or x is ±0
+  } else if (!y.d || x.isZero()) {
+    r = getPi(this, wpr, 1).times(0.5);
+    r.s = y.s;
+
+  // Both non-zero and finite
+  } else if (x.s < 0) {
+    this.precision = wpr;
+    this.rounding = 1;
+    r = this.atan(divide(y, x, wpr, 1));
+    x = getPi(this, wpr, 1);
+    this.precision = pr;
+    this.rounding = rm;
+    r = y.s < 0 ? r.minus(x) : r.plus(x);
+  } else {
+    r = this.atan(divide(y, x, wpr, 1));
+  }
+
+  return r;
+}
+
+
+/*
+ * Return a new Decimal whose value is the cube root of `x`, rounded to `precision` significant
+ * digits using rounding mode `rounding`.
+ *
+ * x {number|string|Decimal}
+ *
+ */
+function cbrt(x) {
+  return new this(x).cbrt();
+}
+
+
+/*
+ * Return a new Decimal whose value is `x` rounded to an integer using `ROUND_CEIL`.
+ *
+ * x {number|string|Decimal}
+ *
+ */
+function ceil(x) {
+  return finalise(x = new this(x), x.e + 1, 2);
+}
+
+
+/*
+ * Return a new Decimal whose value is `x` clamped to the range delineated by `min` and `max`.
+ *
+ * x {number|string|Decimal}
+ * min {number|string|Decimal}
+ * max {number|string|Decimal}
+ *
+ */
+function clamp(x, min, max) {
+  return new this(x).clamp(min, max);
+}
+
+
+/*
+ * Configure global settings for a Decimal constructor.
+ *
+ * `obj` is an object with one or more of the following properties,
+ *
+ *   precision  {number}
+ *   rounding   {number}
+ *   toExpNeg   {number}
+ *   toExpPos   {number}
+ *   maxE       {number}
+ *   minE       {number}
+ *   modulo     {number}
+ *   crypto     {boolean|number}
+ *   defaults   {true}
+ *
+ * E.g. Decimal.config({ precision: 20, rounding: 4 })
+ *
+ */
+function config(obj) {
+  if (!obj || typeof obj !== 'object') throw Error(decimalError + 'Object expected');
+  var i, p, v,
+    useDefaults = obj.defaults === true,
+    ps = [
+      'precision', 1, MAX_DIGITS,
+      'rounding', 0, 8,
+      'toExpNeg', -EXP_LIMIT, 0,
+      'toExpPos', 0, EXP_LIMIT,
+      'maxE', 0, EXP_LIMIT,
+      'minE', -EXP_LIMIT, 0,
+      'modulo', 0, 9
+    ];
+
+  for (i = 0; i < ps.length; i += 3) {
+    if (p = ps[i], useDefaults) this[p] = DEFAULTS[p];
+    if ((v = obj[p]) !== void 0) {
+      if (mathfloor(v) === v && v >= ps[i + 1] && v <= ps[i + 2]) this[p] = v;
+      else throw Error(invalidArgument + p + ': ' + v);
+    }
+  }
+
+  if (p = 'crypto', useDefaults) this[p] = DEFAULTS[p];
+  if ((v = obj[p]) !== void 0) {
+    if (v === true || v === false || v === 0 || v === 1) {
+      if (v) {
+        if (typeof crypto != 'undefined' && crypto &&
+          (crypto.getRandomValues || crypto.randomBytes)) {
+          this[p] = true;
+        } else {
+          throw Error(cryptoUnavailable);
+        }
+      } else {
+        this[p] = false;
+      }
+    } else {
+      throw Error(invalidArgument + p + ': ' + v);
+    }
+  }
+
+  return this;
+}
+
+
+/*
+ * Return a new Decimal whose value is the cosine of `x`, rounded to `precision` significant
+ * digits using rounding mode `rounding`.
+ *
+ * x {number|string|Decimal} A value in radians.
+ *
+ */
+function cos(x) {
+  return new this(x).cos();
+}
+
+
+/*
+ * Return a new Decimal whose value is the hyperbolic cosine of `x`, rounded to precision
+ * significant digits using rounding mode `rounding`.
+ *
+ * x {number|string|Decimal} A value in radians.
+ *
+ */
+function cosh(x) {
+  return new this(x).cosh();
+}
+
+
+/*
+ * Create and return a Decimal constructor with the same configuration properties as this Decimal
+ * constructor.
+ *
+ */
+function clone(obj) {
+  var i, p, ps;
+
+  /*
+   * The Decimal constructor and exported function.
+   * Return a new Decimal instance.
+   *
+   * v {number|string|Decimal} A numeric value.
+   *
+   */
+  function Decimal(v) {
+    var e, i, t,
+      x = this;
+
+    // Decimal called without new.
+    if (!(x instanceof Decimal)) return new Decimal(v);
+
+    // Retain a reference to this Decimal constructor, and shadow Decimal.prototype.constructor
+    // which points to Object.
+    x.constructor = Decimal;
+
+    // Duplicate.
+    if (isDecimalInstance(v)) {
+      x.s = v.s;
+
+      if (external) {
+        if (!v.d || v.e > Decimal.maxE) {
+
+          // Infinity.
+          x.e = NaN;
+          x.d = null;
+        } else if (v.e < Decimal.minE) {
+
+          // Zero.
+          x.e = 0;
+          x.d = [0];
+        } else {
+          x.e = v.e;
+          x.d = v.d.slice();
+        }
+      } else {
+        x.e = v.e;
+        x.d = v.d ? v.d.slice() : v.d;
+      }
+
+      return;
+    }
+
+    t = typeof v;
+
+    if (t === 'number') {
+      if (v === 0) {
+        x.s = 1 / v < 0 ? -1 : 1;
+        x.e = 0;
+        x.d = [0];
+        return;
+      }
+
+      if (v < 0) {
+        v = -v;
+        x.s = -1;
+      } else {
+        x.s = 1;
+      }
+
+      // Fast path for small integers.
+      if (v === ~~v && v < 1e7) {
+        for (e = 0, i = v; i >= 10; i /= 10) e++;
+
+        if (external) {
+          if (e > Decimal.maxE) {
+            x.e = NaN;
+            x.d = null;
+          } else if (e < Decimal.minE) {
+            x.e = 0;
+            x.d = [0];
+          } else {
+            x.e = e;
+            x.d = [v];
+          }
+        } else {
+          x.e = e;
+          x.d = [v];
+        }
+
+        return;
+
+      // Infinity, NaN.
+      } else if (v * 0 !== 0) {
+        if (!v) x.s = NaN;
+        x.e = NaN;
+        x.d = null;
+        return;
+      }
+
+      return parseDecimal(x, v.toString());
+
+    } else if (t !== 'string') {
+      throw Error(invalidArgument + v);
+    }
+
+    // Minus sign?
+    if ((i = v.charCodeAt(0)) === 45) {
+      v = v.slice(1);
+      x.s = -1;
+    } else {
+      // Plus sign?
+      if (i === 43) v = v.slice(1);
+      x.s = 1;
+    }
+
+    return isDecimal.test(v) ? parseDecimal(x, v) : parseOther(x, v);
+  }
+
+  Decimal.prototype = P;
+
+  Decimal.ROUND_UP = 0;
+  Decimal.ROUND_DOWN = 1;
+  Decimal.ROUND_CEIL = 2;
+  Decimal.ROUND_FLOOR = 3;
+  Decimal.ROUND_HALF_UP = 4;
+  Decimal.ROUND_HALF_DOWN = 5;
+  Decimal.ROUND_HALF_EVEN = 6;
+  Decimal.ROUND_HALF_CEIL = 7;
+  Decimal.ROUND_HALF_FLOOR = 8;
+  Decimal.EUCLID = 9;
+
+  Decimal.config = Decimal.set = config;
+  Decimal.clone = clone;
+  Decimal.isDecimal = isDecimalInstance;
+
+  Decimal.abs = abs;
+  Decimal.acos = acos;
+  Decimal.acosh = acosh;        // ES6
+  Decimal.add = add;
+  Decimal.asin = asin;
+  Decimal.asinh = asinh;        // ES6
+  Decimal.atan = atan;
+  Decimal.atanh = atanh;        // ES6
+  Decimal.atan2 = atan2;
+  Decimal.cbrt = cbrt;          // ES6
+  Decimal.ceil = ceil;
+  Decimal.clamp = clamp;
+  Decimal.cos = cos;
+  Decimal.cosh = cosh;          // ES6
+  Decimal.div = div;
+  Decimal.exp = exp;
+  Decimal.floor = floor;
+  Decimal.hypot = hypot;        // ES6
+  Decimal.ln = ln;
+  Decimal.log = log;
+  Decimal.log10 = log10;        // ES6
+  Decimal.log2 = log2;          // ES6
+  Decimal.max = max;
+  Decimal.min = min;
+  Decimal.mod = mod;
+  Decimal.mul = mul;
+  Decimal.pow = pow;
+  Decimal.random = random;
+  Decimal.round = round;
+  Decimal.sign = sign;          // ES6
+  Decimal.sin = sin;
+  Decimal.sinh = sinh;          // ES6
+  Decimal.sqrt = sqrt;
+  Decimal.sub = sub;
+  Decimal.sum = sum;
+  Decimal.tan = tan;
+  Decimal.tanh = tanh;          // ES6
+  Decimal.trunc = trunc;        // ES6
+
+  if (obj === void 0) obj = {};
+  if (obj) {
+    if (obj.defaults !== true) {
+      ps = ['precision', 'rounding', 'toExpNeg', 'toExpPos', 'maxE', 'minE', 'modulo', 'crypto'];
+      for (i = 0; i < ps.length;) if (!obj.hasOwnProperty(p = ps[i++])) obj[p] = this[p];
+    }
+  }
+
+  Decimal.config(obj);
+
+  return Decimal;
+}
+
+
+/*
+ * Return a new Decimal whose value is `x` divided by `y`, rounded to `precision` significant
+ * digits using rounding mode `rounding`.
+ *
+ * x {number|string|Decimal}
+ * y {number|string|Decimal}
+ *
+ */
+function div(x, y) {
+  return new this(x).div(y);
+}
+
+
+/*
+ * Return a new Decimal whose value is the natural exponential of `x`, rounded to `precision`
+ * significant digits using rounding mode `rounding`.
+ *
+ * x {number|string|Decimal} The power to which to raise the base of the natural log.
+ *
+ */
+function exp(x) {
+  return new this(x).exp();
+}
+
+
+/*
+ * Return a new Decimal whose value is `x` round to an integer using `ROUND_FLOOR`.
+ *
+ * x {number|string|Decimal}
+ *
+ */
+function floor(x) {
+  return finalise(x = new this(x), x.e + 1, 3);
+}
+
+
+/*
+ * Return a new Decimal whose value is the square root of the sum of the squares of the arguments,
+ * rounded to `precision` significant digits using rounding mode `rounding`.
+ *
+ * hypot(a, b, ...) = sqrt(a^2 + b^2 + ...)
+ *
+ * arguments {number|string|Decimal}
+ *
+ */
+function hypot() {
+  var i, n,
+    t = new this(0);
+
+  external = false;
+
+  for (i = 0; i < arguments.length;) {
+    n = new this(arguments[i++]);
+    if (!n.d) {
+      if (n.s) {
+        external = true;
+        return new this(1 / 0);
+      }
+      t = n;
+    } else if (t.d) {
+      t = t.plus(n.times(n));
+    }
+  }
+
+  external = true;
+
+  return t.sqrt();
+}
+
+
+/*
+ * Return true if object is a Decimal instance (where Decimal is any Decimal constructor),
+ * otherwise return false.
+ *
+ */
+function isDecimalInstance(obj) {
+  return obj instanceof Decimal || obj && obj.toStringTag === tag || false;
+}
+
+
+/*
+ * Return a new Decimal whose value is the natural logarithm of `x`, rounded to `precision`
+ * significant digits using rounding mode `rounding`.
+ *
+ * x {number|string|Decimal}
+ *
+ */
+function ln(x) {
+  return new this(x).ln();
+}
+
+
+/*
+ * Return a new Decimal whose value is the log of `x` to the base `y`, or to base 10 if no base
+ * is specified, rounded to `precision` significant digits using rounding mode `rounding`.
+ *
+ * log[y](x)
+ *
+ * x {number|string|Decimal} The argument of the logarithm.
+ * y {number|string|Decimal} The base of the logarithm.
+ *
+ */
+function log(x, y) {
+  return new this(x).log(y);
+}
+
+
+/*
+ * Return a new Decimal whose value is the base 2 logarithm of `x`, rounded to `precision`
+ * significant digits using rounding mode `rounding`.
+ *
+ * x {number|string|Decimal}
+ *
+ */
+function log2(x) {
+  return new this(x).log(2);
+}
+
+
+/*
+ * Return a new Decimal whose value is the base 10 logarithm of `x`, rounded to `precision`
+ * significant digits using rounding mode `rounding`.
+ *
+ * x {number|string|Decimal}
+ *
+ */
+function log10(x) {
+  return new this(x).log(10);
+}
+
+
+/*
+ * Return a new Decimal whose value is the maximum of the arguments.
+ *
+ * arguments {number|string|Decimal}
+ *
+ */
+function max() {
+  return maxOrMin(this, arguments, 'lt');
+}
+
+
+/*
+ * Return a new Decimal whose value is the minimum of the arguments.
+ *
+ * arguments {number|string|Decimal}
+ *
+ */
+function min() {
+  return maxOrMin(this, arguments, 'gt');
+}
+
+
+/*
+ * Return a new Decimal whose value is `x` modulo `y`, rounded to `precision` significant digits
+ * using rounding mode `rounding`.
+ *
+ * x {number|string|Decimal}
+ * y {number|string|Decimal}
+ *
+ */
+function mod(x, y) {
+  return new this(x).mod(y);
+}
+
+
+/*
+ * Return a new Decimal whose value is `x` multiplied by `y`, rounded to `precision` significant
+ * digits using rounding mode `rounding`.
+ *
+ * x {number|string|Decimal}
+ * y {number|string|Decimal}
+ *
+ */
+function mul(x, y) {
+  return new this(x).mul(y);
+}
+
+
+/*
+ * Return a new Decimal whose value is `x` raised to the power `y`, rounded to precision
+ * significant digits using rounding mode `rounding`.
+ *
+ * x {number|string|Decimal} The base.
+ * y {number|string|Decimal} The exponent.
+ *
+ */
+function pow(x, y) {
+  return new this(x).pow(y);
+}
+
+
+/*
+ * Returns a new Decimal with a random value equal to or greater than 0 and less than 1, and with
+ * `sd`, or `Decimal.precision` if `sd` is omitted, significant digits (or less if trailing zeros
+ * are produced).
+ *
+ * [sd] {number} Significant digits. Integer, 0 to MAX_DIGITS inclusive.
+ *
+ */
+function random(sd) {
+  var d, e, k, n,
+    i = 0,
+    r = new this(1),
+    rd = [];
+
+  if (sd === void 0) sd = this.precision;
+  else checkInt32(sd, 1, MAX_DIGITS);
+
+  k = Math.ceil(sd / LOG_BASE);
+
+  if (!this.crypto) {
+    for (; i < k;) rd[i++] = Math.random() * 1e7 | 0;
+
+  // Browsers supporting crypto.getRandomValues.
+  } else if (crypto.getRandomValues) {
+    d = crypto.getRandomValues(new Uint32Array(k));
+
+    for (; i < k;) {
+      n = d[i];
+
+      // 0 <= n < 4294967296
+      // Probability n >= 4.29e9, is 4967296 / 4294967296 = 0.00116 (1 in 865).
+      if (n >= 4.29e9) {
+        d[i] = crypto.getRandomValues(new Uint32Array(1))[0];
+      } else {
+
+        // 0 <= n <= 4289999999
+        // 0 <= (n % 1e7) <= 9999999
+        rd[i++] = n % 1e7;
+      }
+    }
+
+  // Node.js supporting crypto.randomBytes.
+  } else if (crypto.randomBytes) {
+
+    // buffer
+    d = crypto.randomBytes(k *= 4);
+
+    for (; i < k;) {
+
+      // 0 <= n < 2147483648
+      n = d[i] + (d[i + 1] << 8) + (d[i + 2] << 16) + ((d[i + 3] & 0x7f) << 24);
+
+      // Probability n >= 2.14e9, is 7483648 / 2147483648 = 0.0035 (1 in 286).
+      if (n >= 2.14e9) {
+        crypto.randomBytes(4).copy(d, i);
+      } else {
+
+        // 0 <= n <= 2139999999
+        // 0 <= (n % 1e7) <= 9999999
+        rd.push(n % 1e7);
+        i += 4;
+      }
+    }
+
+    i = k / 4;
+  } else {
+    throw Error(cryptoUnavailable);
+  }
+
+  k = rd[--i];
+  sd %= LOG_BASE;
+
+  // Convert trailing digits to zeros according to sd.
+  if (k && sd) {
+    n = mathpow(10, LOG_BASE - sd);
+    rd[i] = (k / n | 0) * n;
+  }
+
+  // Remove trailing words which are zero.
+  for (; rd[i] === 0; i--) rd.pop();
+
+  // Zero?
+  if (i < 0) {
+    e = 0;
+    rd = [0];
+  } else {
+    e = -1;
+
+    // Remove leading words which are zero and adjust exponent accordingly.
+    for (; rd[0] === 0; e -= LOG_BASE) rd.shift();
+
+    // Count the digits of the first word of rd to determine leading zeros.
+    for (k = 1, n = rd[0]; n >= 10; n /= 10) k++;
+
+    // Adjust the exponent for leading zeros of the first word of rd.
+    if (k < LOG_BASE) e -= LOG_BASE - k;
+  }
+
+  r.e = e;
+  r.d = rd;
+
+  return r;
+}
+
+
+/*
+ * Return a new Decimal whose value is `x` rounded to an integer using rounding mode `rounding`.
+ *
+ * To emulate `Math.round`, set rounding to 7 (ROUND_HALF_CEIL).
+ *
+ * x {number|string|Decimal}
+ *
+ */
+function round(x) {
+  return finalise(x = new this(x), x.e + 1, this.rounding);
+}
+
+
+/*
+ * Return
+ *   1    if x > 0,
+ *  -1    if x < 0,
+ *   0    if x is 0,
+ *  -0    if x is -0,
+ *   NaN  otherwise
+ *
+ * x {number|string|Decimal}
+ *
+ */
+function sign(x) {
+  x = new this(x);
+  return x.d ? (x.d[0] ? x.s : 0 * x.s) : x.s || NaN;
+}
+
+
+/*
+ * Return a new Decimal whose value is the sine of `x`, rounded to `precision` significant digits
+ * using rounding mode `rounding`.
+ *
+ * x {number|string|Decimal} A value in radians.
+ *
+ */
+function sin(x) {
+  return new this(x).sin();
+}
+
+
+/*
+ * Return a new Decimal whose value is the hyperbolic sine of `x`, rounded to `precision`
+ * significant digits using rounding mode `rounding`.
+ *
+ * x {number|string|Decimal} A value in radians.
+ *
+ */
+function sinh(x) {
+  return new this(x).sinh();
+}
+
+
+/*
+ * Return a new Decimal whose value is the square root of `x`, rounded to `precision` significant
+ * digits using rounding mode `rounding`.
+ *
+ * x {number|string|Decimal}
+ *
+ */
+function sqrt(x) {
+  return new this(x).sqrt();
+}
+
+
+/*
+ * Return a new Decimal whose value is `x` minus `y`, rounded to `precision` significant digits
+ * using rounding mode `rounding`.
+ *
+ * x {number|string|Decimal}
+ * y {number|string|Decimal}
+ *
+ */
+function sub(x, y) {
+  return new this(x).sub(y);
+}
+
+
+/*
+ * Return a new Decimal whose value is the sum of the arguments, rounded to `precision`
+ * significant digits using rounding mode `rounding`.
+ *
+ * Only the result is rounded, not the intermediate calculations.
+ *
+ * arguments {number|string|Decimal}
+ *
+ */
+function sum() {
+  var i = 0,
+    args = arguments,
+    x = new this(args[i]);
+
+  external = false;
+  for (; x.s && ++i < args.length;) x = x.plus(args[i]);
+  external = true;
+
+  return finalise(x, this.precision, this.rounding);
+}
+
+
+/*
+ * Return a new Decimal whose value is the tangent of `x`, rounded to `precision` significant
+ * digits using rounding mode `rounding`.
+ *
+ * x {number|string|Decimal} A value in radians.
+ *
+ */
+function tan(x) {
+  return new this(x).tan();
+}
+
+
+/*
+ * Return a new Decimal whose value is the hyperbolic tangent of `x`, rounded to `precision`
+ * significant digits using rounding mode `rounding`.
+ *
+ * x {number|string|Decimal} A value in radians.
+ *
+ */
+function tanh(x) {
+  return new this(x).tanh();
+}
+
+
+/*
+ * Return a new Decimal whose value is `x` truncated to an integer.
+ *
+ * x {number|string|Decimal}
+ *
+ */
+function trunc(x) {
+  return finalise(x = new this(x), x.e + 1, 1);
+}
+
+
+P[Symbol.for('nodejs.util.inspect.custom')] = P.toString;
+P[Symbol.toStringTag] = 'Decimal';
+
+// Create and configure initial Decimal constructor.
+export var Decimal = P.constructor = clone(DEFAULTS);
+
+// Create the internal constants from their string values.
+LN10 = new Decimal(LN10);
+PI = new Decimal(PI);
+
+export default Decimal;