JDToYMD関数 (自作関数)

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ユリウス日をグレゴリオ暦に変換します。

構文: JDToYMD( JD )

引数

JD 必須: ユリウス日

戻り値: グレゴリオ暦を格納した配列（0 : 年, 1 : 月, 2 : 日, 3 : 時, 4 : 分, 5 : 秒）

プログラム

プログラム実行例

今年の春分の日の日付を求める

春分の日は太陽黄経が0度なので、翌年1月1日の直前の太陽黄経0度の日付を求める。

Main
FUNCTIONS

//////////////////////////////////////////////////
// 【引数】
//   arr : 追加される配列（参照引数）
//   tmp : 追加する配列
// 【戻り値】
//   追加した後の配列の要素数
//////////////////////////////////////////////////
FUNCTION arrayMerge(Var arr[], tmp[])
	FOR n = 0 TO UBound(tmp)
		arrayPush(arr, tmp[n])
	NEXT
	RESULT = UBound(arr)
FEND

//////////////////////////////////////////////////
// 【引数】
//   array : 配列。参照引数。
// 【戻り値】
//   引数に指定した配列の最後の要素
//////////////////////////////////////////////////
FUNCTION arrayPop(Var array[])
	DIM n = UBound(array)
	DIM res = array[n]
	RESIZE(array, n-1)
	RESULT = res
FEND

//////////////////////////////////////////////////
// 【引数】
//   array : 要素を追加する配列（参照引数）
//   values : 追加する要素をvalue1から指定
// 【戻り値】
//   処理後の配列の要素の数
//////////////////////////////////////////////////
FUNCTION arrayPush(var array[], value1 = EMPTY, value2 = EMPTY, value3 = EMPTY, value4 = EMPTY, value5 = EMPTY, value6 = EMPTY, value7 = EMPTY, value8 = EMPTY, value9 = EMPTY, value10 = EMPTY, value11 = EMPTY, value12 = EMPTY, value13 = EMPTY, value14 = EMPTY, value15 = EMPTY, value16 = EMPTY)
    DIM i = 1
    WHILE EVAL("value" + i) <> EMPTY
	  DIM res = RESIZE(array, UBound(array) + 1)
	  array[res] = EVAL("value" + i)
	  i = i + 1
	WEND
	RESULT = LENGTH(array)
FEND

//////////////////////////////////////////////////
// 【引数】
//   array : 逆順にする配列
// 【戻り値】
//////////////////////////////////////////////////
PROCEDURE arrayReverse(Var array[])
	DIM cnt = LENGTH(array)
	FOR i = 0 TO INT(cnt / 2) - 1
		swap(array[i], array[cnt-(i+1)])
	NEXT
FEND

//////////////////////////////////////////////////
// 【引数】
//   needle : 検索する値
//   haystack : 配列
// 【戻り値】
//   needleが見つかった場合に配列のキー
//////////////////////////////////////////////////
FUNCTION arraySearch(needle, haystack[])
	DIM i = 0
	FOR item IN haystack
		IFB item = needle THEN
			RESULT = i
			EXIT
		ENDIF
		i = i + 1
	NEXT
FEND

//////////////////////////////////////////////////
// 【引数】
//   array : 配列
// 【戻り値】
//   arrayの最初の値。配列arrayは、要素一つ分だけ短くなり、全ての要素は前にずれます。
//////////////////////////////////////////////////
FUNCTION arrayShift(Var array[])
	DIM res = array[0]
	SHIFTARRAY(array, -1)
	RESIZE(array, UBound(array) - 1)
	RESULT = res
FEND

//////////////////////////////////////////////////
// 【引数】
//   array : 要素を加えられる配列
//   values : 加える値をvalue1から順に指定
// 【戻り値】
//   処理後の配列の要素の数
//////////////////////////////////////////////////
FUNCTION arrayUnshift(var array[], value1 = EMPTY, value2 = EMPTY, value3 = EMPTY, value4 = EMPTY, value5 = EMPTY, value6 = EMPTY, value7 = EMPTY, value8 = EMPTY, value9 = EMPTY, value10 = EMPTY, value11 = EMPTY, value12 = EMPTY, value13 = EMPTY, value14 = EMPTY, value15 = EMPTY, value16 = EMPTY)
	DIM tmp[-1]
	DIM i = 1
	WHILE EVAL("value" + i) <> EMPTY
		arrayPush(tmp, EVAL("value" + i))
		i = i + 1
	WEND
	arrayMerge(tmp, array)
	RESIZE(array, UBound(tmp))
	SETCLEAR(array, EMPTY)
	FOR i = 0 TO UBound(tmp)
		array[i] = tmp[i]
	NEXT
	RESULT = LENGTH(array)
FEND

//////////////////////////////////////////////////
// 【引数】
//   bin : 2進数
//   signFlg : 符号付きならばTrue
//   digits : 変換する2進数の桁数合わせを自動で行うかを示すブール値、もしくは桁数を表す数値（8,16,24,32,64のいずれか）を指定
// 【戻り値】
//   10進数に変換した値
//////////////////////////////////////////////////
FUNCTION binToDec(bin, signFlg = TRUE, digits = TRUE)
	DIM dec = 0
	DIM decimalFlg = IIF(POS(".", bin), TRUE, FALSE)
	// 桁合わせ
	IFB digits THEN
		IFB decimalFlg THEN
			keta = LENGTH(COPY(bin, POS(".", bin) + 1)) MOD 4
			IF keta <> 0 THEN bin = bin + strRepeat("0", 4 - keta)
		ENDIF
		DIM nums[] = 8, 16, 24, 32, 64
		FOR num IN nums
			IFB LENGTH(REPLACE(bin, ".", "")) <= num THEN
				bin = strPad(bin, num + decimalFlg, "0", LEFT)
				BREAK
			ENDIF
		NEXT
	ENDIF
	IFB COPY(bin, 1, 1) = "1" AND signFlg THEN
		DIM msb = VAL(IIF(decimalFlg, POS(".", bin) - 1, LENGTH(bin)))
		DIM lsb = VAL(IIF(decimalFlg, POS(".", bin) - LENGTH(bin), 0))
		DIM dec2 = Decimal.minus(Decimal.toPower(2, msb), 1)
		FOR i = -1 TO lsb STEP -1
			dec2 = Decimal.plus(dec2, Decimal.toPower(2, i))
		NEXT
		DIM a = binToDec(bin, FALSE)
		DIM b = dec2
		dec = Decimal.times("-1", Decimal.plus(bitXor(a, b), Decimal.toPower(2, lsb)))
	ELSE
		IFB decimalFlg THEN
			DIM integer = COPY(bin, 1, POS(".", bin) - 1)
			DIM decimal = COPY(bin, POS(".", bin) + 1)
			FOR i = 1 TO LENGTH(decimal)
				dec = dec + COPY(decimal, i, 1) * POWER(2, -1 * i)
			NEXT
		ELSE
			integer = bin
		ENDIF
		FOR i = 1 TO LENGTH(integer)
			WITH Decimal
				dec = .plus(dec, .times(COPY(integer, i, 1), .toPower(2, LENGTH(integer) - i)))
			ENDWITH
		NEXT
	ENDIF
	RESULT = dec
FEND

//////////////////////////////////////////////////
// 【引数】
//   arg1 : 数値1（10進数）
//   arg2 : 数値2（10進数）
// 【戻り値】
//   2つの数値のビット毎の論理積
//////////////////////////////////////////////////
FUNCTION bitAnd(arg1, arg2)
	DIM args[1] = arg1, arg2
	DIM bins[1]
	DIM decimals[1]
	DIM integers[1]
	DIM keta[1]
	IFB ABS(arg1) <> arg1 OR ABS(arg2) <> arg2 THEN
		RESULT = ERR_VALUE
		EXIT
	ENDIF
	FOR i = 0 TO 1
		bins[i] = decToBin(args[i])
		decimals[i] = 0
		IFB POS(".", bins[i]) <> 0 THEN
			integers[i] = COPY(bins[i], 1, POS(".", bins[i]) - 1)
			decimals[i] = COPY(bins[i], POS(".", bins[i]) + 1)
		ELSE
			integers[i] = bins[i]
		ENDIF
	NEXT
	keta[0] = IIF(LENGTH(integers[0]) > LENGTH(integers[1]), LENGTH(integers[0]), LENGTH(integers[1]))
	integers[0] = strPad(integers[0], keta[0], "0", LEFT)
	integers[1] = strPad(integers[1], keta[0], "0", LEFT)
	keta[1] = IIF(LENGTH(decimals[0]) > LENGTH(decimals[1]), LENGTH(decimals[0]), LENGTH(decimals[1]))
	decimals[0] = strPad(decimals[0], keta[1], "0", RIGHT)
	decimals[1] = strPad(decimals[1], keta[1], "0", RIGHT)
	DIM bin = ""
	FOR i = 1 TO keta[0]
		bin = bin + (VAL(COPY(integers[0], i, 1)) AND VAL(COPY(integers[1], i, 1)))
	NEXT
	bin = bin + "."
	FOR i = 1 TO keta[1]
		bin = bin + (VAL(COPY(decimals[0], i, 1)) AND VAL(COPY(decimals[1], i, 1)))
	NEXT
	RESULT = binToDec(bin)
FEND

//////////////////////////////////////////////////
// 【引数】
//   num : 10進数もしくは2進数の値
//   bit : ビット
// 【戻り値】
//   ビットを反転した値
//////////////////////////////////////////////////
FUNCTION bitNot(num, bit = EMPTY)
	IFB isString(num) THEN
		DIM res = ""
		FOR i = 1 TO LENGTH(num)
			DIM str = COPY(num, i, 1)
			IFB str = "0" OR str = "1" THEN
				res = res + (1 - VAL(str))
			ELSE
				res = res + str
			ENDIF
		NEXT
		RESULT = res
	ELSE
		DIM exponent = IIF(bit = EMPTY, CEIL(LOGN(2, num + 1)), bit)
		RESULT = POWER(2, exponent) - num - 1
	ENDIF
FEND

//////////////////////////////////////////////////
// 【引数】
//   arg1 : 数値1（10進数）
//   arg2 : 数値2（10進数）
// 【戻り値】
//   2つの数値のビット毎の排他的論理和
//////////////////////////////////////////////////
FUNCTION bitXor(arg1, arg2)
	IFB arg1 = arg2 THEN
		RESULT = 0
		EXIT
	ENDIF
	DIM args[1] = arg1, arg2
	DIM bins[1]
	DIM decimals[1]
	DIM integers[1]
	DIM keta[1]
	FOR i = 0 TO 1
		bins[i] = decToBin(args[i])
		decimals[i] = 0
		IFB POS(".", bins[i]) <> 0 THEN
			integers[i] = COPY(bins[i], 1, POS(".", bins[i]) - 1)
			decimals[i] = COPY(bins[i], POS(".", bins[i]) + 1)
		ELSE
			integers[i] = bins[i]
		ENDIF
	NEXT
	keta[0] = IIF(LENGTH(integers[0]) > LENGTH(integers[1]), LENGTH(integers[0]), LENGTH(integers[1]))
	integers[0] = strPad(integers[0], keta[0], "0", LEFT)
	integers[1] = strPad(integers[1], keta[0], "0", LEFT)
	keta[1] = IIF(LENGTH(decimals[0]) > LENGTH(decimals[1]), LENGTH(decimals[0]), LENGTH(decimals[1]))
	decimals[0] = strPad(decimals[0], keta[1], "0", RIGHT)
	decimals[1] = strPad(decimals[1], keta[1], "0", RIGHT)
	DIM bin = ""
	FOR i = 1 TO keta[0]
		bin = bin + (VAL(COPY(integers[0], i, 1)) XOR VAL(COPY(integers[1], i, 1)))
	NEXT
	bin = bin + "."
	FOR i = 1 TO keta[1]
		bin = bin + (VAL(COPY(decimals[0], i, 1)) XOR VAL(COPY(decimals[1], i, 1)))
	NEXT
	RESULT = binToDec(bin)
FEND

//////////////////////////////////////////////////
// 【引数】
//   num : 単位換算する数値
//   before : 変換前の単位
//   after : 変換後の単位
// 【戻り値】
//   指定した単位に変換した数値
//////////////////////////////////////////////////
FUNCTION convert(num, before, after)
	HASHTBL unit
	
	// 重量
	unit["g,sg"] = "num * 6.85217658567918 * POWER(10, -5)"
	unit["g,lbm"] = "num * 2.20462262184878 * POWER(10, -3)"
	unit["g,u"] = "num * 6.02217 * POWER(10, +23)"
	unit["g,ozm"] = "num * 3.52739619495804 * POWER(10, -2)"
	unit["sg,g"] = "num * 1.45939029372064 * POWER(10, +4)"
	unit["sg,lbm"] = "num * 3.21740485564304 * POWER(10, +1)"
	unit["sg,u"] = "num * 8.78869644513561 * POWER(10, +27)"
	unit["sg,ozm"] = "num * 5.14784776902887 * POWER(10, +2)"
	unit["lbm,g"] = "num * 4.5359237 * POWER(10, +2)"
	unit["lbm,sg"] = "num * 3.10809501715673 * POWER(10, -2)"
	unit["lbm,u"] = "num * 2.7316103628429 * POWER(10, +26)"
	unit["lbm,ozm"] = "num * 1.6 * POWER(10, +1)"
	unit["u,g"] = "num * 1.66053100460465 * POWER(10, -24)"
	unit["u,sg"] = "num * 1.13782516695463 * POWER(10, -28)"
	unit["u,lbm"] = "num * 3.66084421703269 * POWER(10, -27)"
	unit["u,ozm"] = "num * 5.8573507472523 * POWER(10, -26)"
	unit["ozm,g"] = "num * 2.8349523125 * POWER(10, +1)"
	unit["ozm,sg"] = "num * 1.94255938572295 * POWER(10, -3)"
	unit["ozm,lbm"] = "num * 6.25 * POWER(10, -2)"
	unit["ozm,u"] = "num * 1.70725647677681 * POWER(10, +25)"
	
	// 距離
	unit["m,mi"] = "num * 6.21371192237334 * POWER(10, -4)"
	unit["m,Nmi"] = "num * 5.39956803455724 * POWER(10, -4)"
	unit["m,in"] = "num * 3.93700787401575 * POWER(10, +1)"
	unit["m,ft"] = "num * 3.28083989501312 * POWER(10, +0)"
	unit["m,yd"] = "num * 1.09361329833771 * POWER(10, +0)"
	unit["m,ang"] = "num * 1 * POWER(10, +10)"
	unit["m,pica"] = "num * 2.36220472440945 * POWER(10, +2)"
	unit["mi,m"] = "num * 1.609344 * POWER(10, +3)"
	unit["mi,Nmi"] = "num * 8.68976241900648 * POWER(10, -1)"
	unit["mi,in"] = "num * 6.336 * POWER(10, +4)"
	unit["mi,ft"] = "num * 5.28 * POWER(10, +3)"
	unit["mi,yd"] = "num * 1.76 * POWER(10, +3)"
	unit["mi,ang"] = "num * 1.609344 * POWER(10, +13)"
	unit["mi,pica"] = "num * 3.8016 * POWER(10, +5)"
	unit["Nmi,m"] = "num * 1.852 * POWER(10, +3)"
	unit["Nmi,mi"] = "num * 1.15077944802354 * POWER(10, +0)"
	unit["Nmi,in"] = "num * 7.29133858267717 * POWER(10, +4)"
	unit["Nmi,ft"] = "num * 6.0761154855643 * POWER(10, +3)"
	unit["Nmi,yd"] = "num * 2.02537182852143 * POWER(10, +3)"
	unit["Nmi,ang"] = "num * 1.852 * POWER(10, +13)"
	unit["Nmi,pica"] = "num * 4.3748031496063 * POWER(10, +5)"
	unit["in,m"] = "num * 2.54 * POWER(10, -2)"
	unit["in,mi"] = "num * 1.57828282828283 * POWER(10, -5)"
	unit["in,Nmi"] = "num * 1.37149028077754 * POWER(10, -5)"
	unit["in,ft"] = "num * 8.33333333333333 * POWER(10, -2)"
	unit["in,yd"] = "num * 2.77777777777778 * POWER(10, -2)"
	unit["in,ang"] = "num * 2.54 * POWER(10, +8)"
	unit["in,pica"] = "num * 6 * POWER(10, +0)"
	unit["ft,m"] = "num * 3.048 * POWER(10, -1)"
	unit["ft,mi"] = "num * 1.89393939393939 * POWER(10, -4)"
	unit["ft,Nmi"] = "num * 1.64578833693305 * POWER(10, -4)"
	unit["ft,in"] = "num * 1.2 * POWER(10, +1)"
	unit["ft,yd"] = "num * 3.33333333333333 * POWER(10, -1)"
	unit["ft,ang"] = "num * 3.048 * POWER(10, +9)"
	unit["ft,pica"] = "num * 7.2 * POWER(10, +1)"
	unit["yd,m"] = "num * 9.144 * POWER(10, -1)"
	unit["yd,mi"] = "num * 5.68181818181818 * POWER(10, -4)"
	unit["yd,Nmi"] = "num * 4.93736501079914 * POWER(10, -4)"
	unit["yd,in"] = "num * 3.6 * POWER(10, +1)"
	unit["yd,ft"] = "num * 3 * POWER(10, +0)"
	unit["yd,ang"] = "num * 9.144 * POWER(10, +9)"
	unit["yd,pica"] = "num * 2.16 * POWER(10, +2)"
	unit["ang,m"] = "num * 1 * POWER(10, -10)"
	unit["ang,mi"] = "num * 6.21371192237334 * POWER(10, -14)"
	unit["ang,Nmi"] = "num * 5.39956803455724 * POWER(10, -14)"
	unit["ang,in"] = "num * 3.93700787401575 * POWER(10, -9)"
	unit["ang,ft"] = "num * 3.28083989501312 * POWER(10, -10)"
	unit["ang,yd"] = "num * 1.09361329833771 * POWER(10, -10)"
	unit["ang,pica"] = "num * 2.36220472440945 * POWER(10, -8)"
	unit["pica,m"] = "num * 4.23333333333333 * POWER(10, -3)"
	unit["pica,mi"] = "num * 2.63047138047138 * POWER(10, -6)"
	unit["pica,Nmi"] = "num * 2.28581713462923 * POWER(10, -6)"
	unit["pica,in"] = "num * 1.66666666666667 * POWER(10, -1)"
	unit["pica,ft"] = "num * 1.38888888888889 * POWER(10, -2)"
	unit["pica,yd"] = "num * 4.62962962962963 * POWER(10, -3)"
	unit["pica,ang"] = "num * 4.23333333333333 * POWER(10, +7)"

// 時間
	unit["yr,day"] = "num * 3.6525 * POWER(10, +2)"
	unit["yr,hr"] = "num * 8.766 * POWER(10, +3)"
	unit["yr,mn"] = "num * 5.2596 * POWER(10, +5)"
	unit["yr,sec"] = "num * 3.15576 * POWER(10, +7)"
	unit["day,yr"] = "num * 2.7378507871321 * POWER(10, -3)"
	unit["day,hr"] = "num * 2.4 * POWER(10, +1)"
	unit["day,mn"] = "num * 1.44 * POWER(10, +3)"
	unit["day,sec"] = "num * 8.64 * POWER(10, +4)"
	unit["hr,yr"] = "num * 1.14077116130504 * POWER(10, -4)"
	unit["hr,day"] = "num * 4.16666666666667 * POWER(10, -2)"
	unit["hr,mn"] = "num * 6 * POWER(10, +1)"
	unit["hr,sec"] = "num * 3.6 * POWER(10, +3)"
	unit["mn,yr"] = "num * 1.90128526884174 * POWER(10, -6)"
	unit["mn,day"] = "num * 6.94444444444444 * POWER(10, -4)"
	unit["mn,hr"] = "num * 1.66666666666667 * POWER(10, -2)"
	unit["mn,sec"] = "num * 6 * POWER(10, +1)"
	unit["sec,yr"] = "num * 3.16880878140289 * POWER(10, -8)"
	unit["sec,day"] = "num * 1.15740740740741 * POWER(10, -5)"
	unit["sec,hr"] = "num * 2.77777777777778 * POWER(10, -4)"
	unit["sec,mn"] = "num * 1.66666666666667 * POWER(10, -2)"
	
	// 圧力
	unit["Pa,atm"] = "num * 9.86923266716013 * POWER(10, -6)"
	unit["Pa,mmHg"] = "num * 7.5006168270417 * POWER(10, -3)"
	unit["atm,Pa"] = "num * 1.01325 * POWER(10, +5)"
	unit["atm,mmHg"] = "num * 7.6 * POWER(10, +2)"
	unit["mmHg,Pa"] = "num * 1.33322368421053 * POWER(10, +2)"
	unit["mmHg,atm"] = "num * 1.31578947368421 * POWER(10, -3)"
	
	// 物理的な力
	unit["N,dyn"] = "num * 1 * POWER(10, +5)"
	unit["N,lbf"] = "num * 2.2480894309971 * POWER(10, -1)"
	unit["dyn,N"] = "num * 1 * POWER(10, -5)"
	unit["dyn,lbf"] = "num * 2.2480894309971 * POWER(10, -6)"
	unit["lbf,N"] = "num * 4.4482216152605 * POWER(10, +0)"
	unit["lbf,dyn"] = "num * 4.4482216152605 * POWER(10, +5)"
	
	// エネルギー
	unit["J,e"] = "num * 1 * POWER(10, +7)"
	unit["J,cal"] = "num * 2.38845896627496 * POWER(10, -1)"
	unit["J,eV"] = "num * 6.241457 * POWER(10, +18)"
	unit["J,HPh"] = "num * 3.72506135998619 * POWER(10, -7)"
	unit["J,Wh"] = "num * 2.77777777777778 * POWER(10, -4)"
	unit["J,flb"] = "num * 7.37562149277265 * POWER(10, -1)"
	unit["J,BTU"] = "num * 9.47817120313317 * POWER(10, -4)"
	unit["J,c"] = "num * 2.39005736137667 * POWER(10, -1)"
	unit["e,J"] = "num * 1 * POWER(10, -7)"
	unit["e,cal"] = "num * 2.38845896627496 * POWER(10, -8)"
	unit["e,eV"] = "num * 6.241457 * POWER(10, +11)"
	unit["e,HPh"] = "num * 3.72506135998619 * POWER(10, -14)"
	unit["e,Wh"] = "num * 2.77777777777778 * POWER(10, -11)"
	unit["e,flb"] = "num * 7.37562149277265 * POWER(10, -8)"
	unit["e,BTU"] = "num * 9.47817120313317 * POWER(10, -11)"
	unit["e,c"] = "num * 2.39005736137667 * POWER(10, -8)"
	unit["cal,J"] = "num * 4.1868 * POWER(10, +0)"
	unit["cal,e"] = "num * 4.1868 * POWER(10, +7)"
	unit["cal,eV"] = "num * 2.61317321676 * POWER(10, +19)"
	unit["cal,HPh"] = "num * 1.55960869019902 * POWER(10, -6)"
	unit["cal,Wh"] = "num * 1.163 * POWER(10, -3)"
	unit["cal,flb"] = "num * 3.08802520659405 * POWER(10, +0)"
	unit["cal,BTU"] = "num * 3.9683207193278 * POWER(10, -3)"
	unit["cal,c"] = "num * 1.00066921606119 * POWER(10, +0)"
	unit["eV,J"] = "num * 1.60219000146921 * POWER(10, -19)"
	unit["eV,e"] = "num * 1.60219000146921 * POWER(10, -12)"
	unit["eV,cal"] = "num * 3.82676507468522 * POWER(10, -20)"
	unit["eV,HPh"] = "num * 5.96825606582916 * POWER(10, -26)"
	unit["eV,Wh"] = "num * 4.45052778185891 * POWER(10, -23)"
	unit["eV,flb"] = "num * 1.18171470103417 * POWER(10, -19)"
	unit["eV,BTU"] = "num * 1.51858311338733 * POWER(10, -22)"
	unit["eV,c"] = "num * 3.82932600733558 * POWER(10, -20)"
	unit["HPh,J"] = "num * 2.68451953769617 * POWER(10, +6)"
	unit["HPh,e"] = "num * 2.68451953769617 * POWER(10, +13)"
	unit["HPh,cal"] = "num * 6.41186475995073 * POWER(10, +5)"
	unit["HPh,eV"] = "num * 1.67553132601905 * POWER(10, +25)"
	unit["HPh,Wh"] = "num * 7.4569987158227 * POWER(10, +2)"
	unit["HPh,flb"] = "num * 1.98 * POWER(10, +6)"
	unit["HPh,BTU"] = "num * 2.54443357764402 * POWER(10, +3)"
	unit["HPh,c"] = "num * 6.41615568283024 * POWER(10, +5)"
	unit["Wh,J"] = "num * 3.6 * POWER(10, +3)"
	unit["Wh,e"] = "num * 3.6 * POWER(10, +10)"
	unit["Wh,cal"] = "num * 8.59845227858985 * POWER(10, +2)"
	unit["Wh,eV"] = "num * 2.24692452 * POWER(10, +22)"
	unit["Wh,HPh"] = "num * 1.34102208959503 * POWER(10, -3)"
	unit["Wh,flb"] = "num * 2.65522373739816 * POWER(10, +3)"
	unit["Wh,BTU"] = "num * 3.41214163312794 * POWER(10, +0)"
	unit["Wh,c"] = "num * 8.60420650095602 * POWER(10, +2)"
	unit["flb,J"] = "num * 1.3558179483314 * POWER(10, +0)"
	unit["flb,e"] = "num * 1.3558179483314 * POWER(10, +7)"
	unit["flb,cal"] = "num * 3.23831553532865 * POWER(10, -1)"
	unit["flb,eV"] = "num * 8.46227942433866 * POWER(10, +18)"
	unit["flb,HPh"] = "num * 5.05050505050505 * POWER(10, -7)"
	unit["flb,Wh"] = "num * 3.76616096758722 * POWER(10, -4)"
	unit["flb,BTU"] = "num * 1.28506746345658 * POWER(10, -3)"
	unit["flb,c"] = "num * 3.24048266809608 * POWER(10, -1)"
	unit["BTU,J"] = "num * 1.05505585262 * POWER(10, +3)"
	unit["BTU,e"] = "num * 1.05505585262 * POWER(10, +10)"
	unit["BTU,cal"] = "num * 2.51995761111111 * POWER(10, +2)"
	unit["BTU,eV"] = "num * 6.58508573672607 * POWER(10, +21)"
	unit["BTU,HPh"] = "num * 3.93014778922204 * POWER(10, -4)"
	unit["BTU,Wh"] = "num * 2.93071070172222 * POWER(10, -1)"
	unit["BTU,flb"] = "num * 7.78169262265965 * POWER(10, +2)"
	unit["BTU,c"] = "num * 2.52164400721797 * POWER(10, +2)"
	unit["c,J"] = "num * 4.184 * POWER(10, +0)"
	unit["c,e"] = "num * 4.184 * POWER(10, +7)"
	unit["c,cal"] = "num * 9.99331231489443 * POWER(10, -1)"
	unit["c,eV"] = "num * 2.6114256088 * POWER(10, +19)"
	unit["c,HPh"] = "num * 1.55856567301822 * POWER(10, -6)"
	unit["c,Wh"] = "num * 1.16222222222222 * POWER(10, -3)"
	unit["c,flb"] = "num * 3.08596003257608 * POWER(10, +0)"
	unit["c,BTU"] = "num * 3.96566683139092 * POWER(10, -3)"
	
	// 仕事率
	unit["HP,W"] = "num * 7.4569987158227 * POWER(10, +2)"
	unit["W,HP"] = "num * 1.34102208959503 * POWER(10, -3)"
	
	// 磁力
	unit["T,ga"] = "num * 1 * POWER(10, +4)"
	unit["ga,T"] = "num * 1 * POWER(10, -4)"
	
	// 温度
	unit["C,F"] = "num * (9/5) + 32"
	unit["C,K"] = "num + 273.15"
	unit["F,C"] = "(num - 32) * (9/5)"
	unit["F,K"] = "(num - 32) * (5/9) + 273.15"
	unit["K,C"] = "num - 23373.15"
	unit["K,F"] = "(num - 273.15) * (9/5) + 32"
	
	// 体積（容積）
	unit["tsp,tbs"] = "num * 3.33333333333333 * POWER(10, -1)"
	unit["tsp,oz"] = "num * 1.66666666666667 * POWER(10, -1)"
	unit["tsp,cup"] = "num * 2.08333333333333 * POWER(10, -2)"
	unit["tsp,us_pt"] = "num * 1.04166666666667 * POWER(10, -2)"
	unit["tsp,uk_pt"] = "num * 8.67368942321863 * POWER(10, -3)"
	unit["tsp,qt"] = "num * 5.20833333333333 * POWER(10, -3)"
	unit["tsp,gal"] = "num * 1.30208333333333 * POWER(10, -3)"
	unit["tbs,tsp"] = "num * 3 * POWER(10, +0)"
	unit["tbs,oz"] = "num * 5 * POWER(10, -1)"
	unit["tbs,cup"] = "num * 6.25 * POWER(10, -2)"
	unit["tbs,us_pt"] = "num * 3.125 * POWER(10, -2)"
	unit["tbs,uk_pt"] = "num * 2.60210682696559 * POWER(10, -2)"
	unit["tbs,qt"] = "num * 1.5625 * POWER(10, -2)"
	unit["tbs,gal"] = "num * 3.90625 * POWER(10, -3)"
	unit["oz,tsp"] = "num * 6 * POWER(10, +0)"
	unit["oz,tbs"] = "num * 2 * POWER(10, +0)"
	unit["oz,cup"] = "num * 1.25 * POWER(10, -1)"
	unit["oz,us_pt"] = "num * 6.25 * POWER(10, -2)"
	unit["oz,uk_pt"] = "num * 5.20421365393118 * POWER(10, -2)"
	unit["oz,qt"] = "num * 3.125 * POWER(10, -2)"
	unit["oz,gal"] = "num * 7.8125 * POWER(10, -3)"
	unit["cup,tsp"] = "num * 4.8 * POWER(10, +1)"
	unit["cup,tbs"] = "num * 1.6 * POWER(10, +1)"
	unit["cup,oz"] = "num * 8 * POWER(10, +0)"
	unit["cup,us_pt"] = "num * 5 * POWER(10, -1)"
	unit["cup,uk_pt"] = "num * 4.16337092314494 * POWER(10, -1)"
	unit["cup,qt"] = "num * 2.5 * POWER(10, -1)"
	unit["cup,gal"] = "num * 6.25 * POWER(10, -2)"
	unit["us_pt,tsp"] = "num * 9.6 * POWER(10, +1)"
	unit["us_pt,tbs"] = "num * 3.2 * POWER(10, +1)"
	unit["us_pt,oz"] = "num * 1.6 * POWER(10, +1)"
	unit["us_pt,cup"] = "num * 2 * POWER(10, +0)"
	unit["us_pt,uk_pt"] = "num * 8.32674184628989 * POWER(10, -1)"
	unit["us_pt,qt"] = "num * 5 * POWER(10, -1)"
	unit["us_pt,gal"] = "num * 1.25 * POWER(10, -1)"
	unit["uk_pt,tsp"] = "num * 1.15291192848466 * POWER(10, +2)"
	unit["uk_pt,tbs"] = "num * 3.84303976161554 * POWER(10, +1)"
	unit["uk_pt,oz"] = "num * 1.92151988080777 * POWER(10, +1)"
	unit["uk_pt,cup"] = "num * 2.40189985100971 * POWER(10, +0)"
	unit["uk_pt,us_pt"] = "num * 1.20094992550486 * POWER(10, +0)"
	unit["uk_pt,qt"] = "num * 6.00474962752428 * POWER(10, -1)"
	unit["uk_pt,gal"] = "num * 1.50118740688107 * POWER(10, -1)"
	unit["qt,tsp"] = "num * 1.92 * POWER(10, +2)"
	unit["qt,tbs"] = "num * 6.4 * POWER(10, +1)"
	unit["qt,oz"] = "num * 3.2 * POWER(10, +1)"
	unit["qt,cup"] = "num * 4 * POWER(10, +0)"
	unit["qt,us_pt"] = "num * 2 * POWER(10, +0)"
	unit["qt,uk_pt"] = "num * 1.66534836925798 * POWER(10, +0)"
	unit["qt,gal"] = "num * 2.5 * POWER(10, -1)"
	unit["gal,tsp"] = "num * 7.68 * POWER(10, +2)"
	unit["gal,tbs"] = "num * 2.56 * POWER(10, +2)"
	unit["gal,oz"] = "num * 1.28 * POWER(10, +2)"
	unit["gal,cup"] = "num * 1.6 * POWER(10, +1)"
	unit["gal,us_pt"] = "num * 8 * POWER(10, +0)"
	unit["gal,uk_pt"] = "num * 6.66139347703191 * POWER(10, +0)"
	unit["gal,qt"] = "num * 4 * POWER(10, +0)"

RESULT = EVAL(unit[before + "," + after])
FEND

//////////////////////////////////////////////////
// 【引数】
//   folderspec : 作成するフォルダのパス
// 【戻り値】
//////////////////////////////////////////////////
PROCEDURE CreateFolders(folderspec)
	WITH CREATEOLEOBJ("Scripting.FileSystemObject")
		folderspec = .GetAbsolutePathName(folderspec)
		IF !.DriveExists(.GetDriveName(folderspec)) THEN EXIT
		DIM parentPath = .GetParentFolderName(folderspec)
		IF !.FolderExists(parentPath) THEN CreateFolders(parentPath)
		IF !.FolderExists(folderspec) THEN .CreateFolder(folderspec)
	ENDWITH
FEND

//////////////////////////////////////////////////
// 【引数】
//   interval : 加算する時間間隔を表す文字列式（yyyy：年、m：月、d：日、ww：週、h：時、n：分、s：秒）
//   num : dateに加算する値。未来は正、過去は負で指定
//   date : 時間間隔を加算する日付
// 【戻り値】
//   日時（date）に、指定した単位（interval）の時間（num）を加算して返します
//////////////////////////////////////////////////
FUNCTION dateAdd(interval, num, date)
	DIM year, month, day, d
	GETTIME(0, date)
	DIM time = G_TIME_HH2 + ":" + G_TIME_NN2 + ":" + G_TIME_SS2
	SELECT interval
		CASE "yyyy"
			d = (G_TIME_YY + num) + "/" + G_TIME_MM2 + "/" + G_TIME_DD2
			IF time <> "00:00:00" THEN d = d + " " + time
		CASE "m"
			IFB num > 0 THEN
				year = G_TIME_YY + INT((G_TIME_MM + num) / 12)
				month = REPLACE(FORMAT(((G_TIME_MM + num) MOD 12), 2), " ", "0")
			ELSE
				year = G_TIME_YY + CEIL((G_TIME_MM + num) / 12 - 1)
				month = REPLACE(FORMAT(G_TIME_MM - (ABS(num) MOD 12), 2), " ", "0")
			ENDIF
			IF month = "00" THEN month = 12
			day = G_TIME_DD2
			d = "" + year + month + day
			IFB !isDate(d) THEN
				d = year + "/" + month + "/" + "01"
				d = getEndOfMonth(d)
			ELSE
				d = year + "/" + month + "/" + day
			ENDIF
			IF time <> "00:00:00" THEN d = d + " " + time
		CASE "d"
			t = GETTIME(num, date)
			d = G_TIME_YY4 + "/" + G_TIME_MM2 + "/" + G_TIME_DD2 + IIF(t MOD 86400, " " + G_TIME_HH2 + ":" + G_TIME_NN2 + ":" + G_TIME_SS2, "")
		CASE "ww"
			t = GETTIME(num * 7, date)
			d = G_TIME_YY4 + "/" + G_TIME_MM2 + "/" + G_TIME_DD2 + IIF(t MOD 86400, " " + G_TIME_HH2 + ":" + G_TIME_NN2 + ":" + G_TIME_SS2, "")
		CASE "h"
			t = GETTIME(num / 24, date)
			d = G_TIME_YY4 + "/" + G_TIME_MM2 + "/" + G_TIME_DD2 + IIF(t MOD 86400, " " + G_TIME_HH2 + ":" + G_TIME_NN2 + ":" + G_TIME_SS2, "")
		CASE "n"
			t = GETTIME(num / 1440, date)
			d = G_TIME_YY4 + "/" + G_TIME_MM2 + "/" + G_TIME_DD2 + IIF(t MOD 86400, " " + G_TIME_HH2 + ":" + G_TIME_NN2 + ":" + G_TIME_SS2, "")
		CASE "s"
			t = GETTIME(num / 86400, date)
			d = G_TIME_YY4 + "/" + G_TIME_MM2 + "/" + G_TIME_DD2 + IIF(t MOD 86400, " " + G_TIME_HH2 + ":" + G_TIME_NN2 + ":" + G_TIME_SS2, "")
	SELEND
	RESULT = d
FEND

//////////////////////////////////////////////////
// 【引数】
//   interval : 時間単位（yyyy︰年、q：四半期、m︰月、d︰日、w：週日、ww：週、h：時、n：分、s：秒）
//   date1 : 日時1
//   date2 : 日時2
// 【戻り値】
//   date2からdate1を引いた時間間隔を求めます。
//////////////////////////////////////////////////
FUNCTION dateDiff(interval, date1, date2)
	DIM y1, y2, m1, m2, d1, d2, d
	SELECT interval
		CASE "yyyy"
			GETTIME(0, date1)
			y1 = G_TIME_YY
			GETTIME(0, date2)
			y2 = G_TIME_YY
			d = y2 - y1
		CASE "q"
			GETTIME(0, date1)
			y1 = G_TIME_YY
			m1 = G_TIME_MM
			GETTIME(0, date2)
			y2 = G_TIME_YY
			m2 = G_TIME_MM
			d = y2 * 4 + CEIL(m2/3) - (y1 * 4 + CEIL(m1/3))
		CASE "m"
			GETTIME(0, date1)
			y1 = G_TIME_YY
			m1 = G_TIME_MM
			GETTIME(0, date2)
			y2 = G_TIME_YY
			m2 = G_TIME_MM
			d = (y2 - y1) * 12 + m2 - m1
		CASE "d"
			d1 = GETTIME(0, date1)
			d2 = GETTIME(0, date2)
			d = (d2 - d1) / 86400
		CASE "w"
			d = INT(dateDiff("d", date1, date2) / 7)
		CASE "ww"
			date1 = dateAdd("d", -1 * getWeekday(date1), date1)
			d = INT(dateDiff("d", date1, date2) / 7)
		CASE "h"
			d = dateDiff("d", date1, date2) * 24
		CASE "n"
			d = dateDiff("d", date1, date2) * 1440
		CASE "s"
			d = dateDiff("d", date1, date2) * 86400
	SELEND
	RESULT = d
FEND

//////////////////////////////////////////////////
// 【引数】
// 【戻り値】
//////////////////////////////////////////////////
MODULE Decimal
	CONST BASE = 1E+7
	CONST LOG_BASE = 7
	CONST MAX_SAFE_INTEGER = 1E+15 - 1
	CONST MAX_DIGITS = 1E+9
	PUBLIC precision = 20
	PUBLIC rounding = 4
	PUBLIC modulo = 1
	PUBLIC toExpNeg = -7
	PUBLIC toExpPos = 21
	PUBLIC minE = -9E+15
	PUBLIC maxE = 9E+15
	PUBLIC quadrant = EMPTY
	DIM inexact = FALSE
	CONST MathLN10 = 2.302585092994046
	CONST LN10 = "2.3025850929940456840179914546843642076011014886287729760333279009675726096773524802359972050895982983" + _
					"4196778404228624863340952546508280675666628736909878168948290720832555468084379989482623319852839350" + _
					"5308965377732628846163366222287698219886746543667474404243274365155048934314939391479619404400222105" + _
					"1017141748003688084012647080685567743216228355220114804663715659121373450747856947683463616792101806" + _
					"4450706480002775026849167465505868569356734206705811364292245544057589257242082413146956890167589402" + _
					"5677631135691929203337658714166023010570308963457207544037084746994016826928280848118428931484852494" + _
					"8644871927809676271275775397027668605952496716674183485704422507197965004714951050492214776567636938" + _
					"6629769795221107182645497347726624257094293225827985025855097852653832076067263171643095059950878075" + _
					"2371033310119785754733154142180842754386359177811705430982748238504564801909561029929182431823752535" + _
					"7709750539565187697510374970888692180205189339507238539205144634197265287286965110862571492198849978" + _
					"748873771345686209167058"
	CONST isBinary = "^0b([01]+(\.[01]*)?|\.[01]+)(p[+-]?\d+)?$"
	CONST isHex = "^0x([0-9a-f]+(\.[0-9a-f]*)?|\.[0-9a-f]+)(p[+-]?\d+)?$"
	CONST isOctal = "^0o([0-7]+(\.[0-7]*)?|\.[0-7]+)(p[+-]?\d+)?$"
	CONST isDecimal = "^(\d+(\.\d*)?|\.\d+)(e[+-]?\d+)?$"
	CONST LN10PRECISION = LENGTH(LN10) - 1
	CONST PI = "3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679" + _
					"8214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196" + _
					"4428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273" + _
					"7245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094" + _
					"3305727036575959195309218611738193261179310511854807446237996274956735188575272489122793818301194912" + _
					"9833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132" + _
					"0005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235" + _
					"4201995611212902196086403441815981362977477130996051870721134999999837297804995105973173281609631859" + _
					"5024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303" + _
					"5982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989" + _
					"380952572010654858632789"
	CONST PI_PRECISION = LENGTH(PI) - 1
	CONST ROUND_UP = 0
	CONST ROUND_DOWN = 1
	CONST ROUND_CEIL = 2
	CONST ROUND_FLOOR = 3
	CONST ROUND_HALF_UP = 4
	CONST ROUND_HALF_DOWN = 5
	CONST ROUND_HALF_EVEN = 6
	CONST ROUND_HALF_CEIL = 7
	CONST ROUND_HALF_FLOOR = 8
	CONST EUCLID = 9
	DIM external = TRUE
	DIM cacheFlg = TRUE
	DIM folderspec = "cache\decimal\"
	//////////////////////////////
	// メイン関数
	//////////////////////////////
	FUNCTION absoluteValue(x, isNumeric = FALSE)
		x = IIF(VARTYPE(x) < 8192, Constructor(x), x)
		IF x[0] < 0 THEN x[0] = 1
		RESULT = finalise(x)
		IF isNumeric = NULL THEN EXIT
		RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
	FEND
	FUNCTION ceil(x, isNumeric = FALSE)
		x = IIF(VARTYPE(x) < 8192, Constructor(x), x)
		RESULT = finalise(x, x[1] + 1, 2)
		RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
	FEND
	FUNCTION clampedTo(x, min, max, isNumeric = FALSE)
		x = Constructor(x)
		min = Constructor(min)
		max = Constructor(max)
		IFB !min[0] OR !max[0] THEN
			RESULT = Constructor("NaN")
			EXIT
		ENDIF
		IFB gt(min, max) THEN
			RESULT = ERR_VALUE
			EXIT
		ENDIF
		k = cmp(x, min)
		RESULT = IIF(k < 0, min, IIF(cmp(x, max) > 0, max, Constructor(x)))
		IF isNumeric = NULL THEN EXIT
		RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))		
	FEND
	FUNCTION comparedTo(x, y)
		x = IIF(VARTYPE(x) < 8192, Constructor(x), x)
		y = IIF(VARTYPE(y) < 8192, Constructor(y), y)
		xd = SLICE(x, 2)
		yd = SLICE(IIF(VARTYPE(y) < 8192, Constructor(y), y), 2)
		xs = x[0]
		ys = y[0]
		DIM xIsNum = CHKNUM(x[1])
		DIM yIsNum = CHKNUM(y[1])
		DIM xIsZero = x[0] = 1 AND x[1] = 0 AND x[2] = 0
		DIM yIsZero = y[0] = 1 AND y[1] = 0 AND y[2] = 0
		DIM xIsInf = x[0] <> NULL AND x[1] = NULL AND !x[2]
		DIM yIsInf = y[0] <> NULL AND y[1] = NULL AND !y[2]
		DIM xIsNaN = x[0] = NULL AND x[1] = NULL AND x[2] = FALSE
		DIM yIsNaN = y[0] = NULL AND y[1] = NULL AND y[2] = FALSE
		// Either NaN or ±Infinity?
		IFB (xIsNaN OR yIsNaN) OR(xIsInf OR yIsInf) THEN
			IFB xIsNaN OR yIsNaN THEN
				RESULT = "NaN"
			ELSEIF xs <> ys THEN
				RESULT = xs
			ELSEIF JOIN(xd, "") = JOIN(yd, "") THEN
				RESULT = 0
			ELSEIF POWER(VARTYPE(!xd[0], VAR_INTEGER), IIF(xs < 0, 1, 0)) THEN
				RESULT = 1
			ELSE
				RESULT = -1
			ENDIF
			EXIT
		ENDIF
		// Either zero?
		IFB xIsZero OR yIsZero THEN
			RESULT = IIF(xd[0], xs, IIF(yd[0], -1 * ys, 0))
			EXIT
		ENDIF
		// Signs differ?
		IFB xs <> ys THEN
			RESULT = xs
			EXIT
		ENDIF
		// Compare exponents.
		IFB x[1] <> y[1] THEN
			RESULT = IIF(x[1] > y[1] XOR xs < 0, 1, -1)
			EXIT
		ENDIF
		xdL = LENGTH(xd)
		ydL = LENGTH(yd)
		// Compare digit by digit.
		FOR i = 0 TO IIF(xdL < ydL, xdL, ydL) - 1
			IFB xd[i] <> yd[i] THEN
				RESULT = IIF(xd[i] > yd[i], 1, -1)
				RESULT = IIF(xs < 0, -1 * RESULT, RESULT)
				EXIT
			ENDIF
		NEXT
		// Compare lengths.
		RESULT = IIF(xdL = ydL, 0, IIF(xdL > POWER(ydL, xs) < 0, 1, -1))
	FEND
	FUNCTION cosine(x, isNumeric = FALSE)
		IFB isDecimalInstance(x) THEN
			str = toString(x)
		ELSE
			str = x
		ENDIF
		DIM filename = Hash.sha256("cosine,x=" + str + ",precision=" + precision + ",rounding=" + rounding + ",modulo=" + modulo + ",toExpNeg=" + toExpNeg + ",toExpPos=" + toExpPos + ",minE=" + minE + ",maxE=" + maxE)
		DIM path = folderspec + filename
		IFB cacheFlg AND FOPEN(path, F_EXISTS) THEN
			DIM FID = FOPEN(path, F_READ)
			str = VARTYPE(FGET(FID, 1), 258)
			RESULT = Constructor(str)
			FCLOSE(FID)
		ELSE
			x = Constructor(x)
			json = "{'precision':20, 'rounding':7}"
			Ctor = JSON.Parse(REPLACE(json, "'", "<#DBL>"))
			xd = SLICE(x, 2)
			IFB !LENGTH(xd) THEN
				RESULT = Constructor("NaN")
				EXIT
			ENDIF
			// cos(0) = cos(-0) = 1
			IFB !xd[0] THEN
				RESULT = Constructor(1)
				EXIT
			ENDIF
			pr = precision
			rm = rounding
			DIM array[] = VAL(x[1]), sd(x)
			precision = pr + large(array, 1) + LOG_BASE
			rounding = 1
			x = cosine2(Ctor, toLessThanHalfPi2(Ctor, x))
			precision = pr
			rounding = rm
			RESULT = finalise(IIF(quadrant = 2 OR quadrant = 3, neg(x), x), pr, rm, TRUE)
			CreateFolders(folderspec)
			FID = FOPEN(path, F_READ OR F_WRITE8)
			FPUT(FID, toString(RESULT))
			FCLOSE(FID)
		ENDIF
		RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
	FEND
	FUNCTION cubeRoot(x, isNumeric = FALSE)
		x = IIF(VARTYPE(x) < 8192, Constructor(x), x)
		rep = 0
		IFB !isFinite(x) OR isZero(x) THEN
			RESULT = Constructor(x)
			EXIT
		ENDIF
		external = FALSE
		// Initial estimate.
		s = x[0] * POWER(x[0] * toString(x), 1/3)
		// Math.cbrt underflow/overflow?
		// Pass x to Math.pow as integer, then adjust the exponent of the result.
		IFB !s OR ABS(s) = "INF" THEN
			xd = SLICE(x, 2)
			n = digitsToString(xd)
			e = x[1]
			// Adjust n exponent so it is a multiple of 3 away from x exponent.
			s = e - LENGTH(n) + 1
			IF s MOD 3 THEN n = n + IIF(s = 1 OR s = -2, "0", "00")
			s = POWER(n, 1 / 3)
			// Rarely, e may be one less than the result exponent value.
			e = GLOBAL.floor((e + 1) / 3) - (e MOD 3 = IIF(e < 0, -1, 2))
			IFB s = 1 / 0 THEN
				n = "5e" + e
			ELSE
				n = toExponential(s)
				n = COPY(n, 1, POS("e", n) + 1) + e
			ENDIF
			r = Constructor(n)
			r[0] = x[0]
		ELSE
			r = Constructor(s)
		ENDIF
		e = precision
		sd = e + 3
		// Halley's method.
		// TODO? Compare Newton's method.
		m = NULL
		WHILE TRUE
			t = r
			td = SLICE(t, 2)
			t3 = times(times(t, t), t)
			t3plusx = plus(t3, x)
			r = divide(times(plus(t3plusx, x), t), plus(t3plusx, t3), sd + 2, 1)
			rd = SLICE(r, 2)
			// TODO? Replace with for-loop and checkRoundingDigits.
			n = digitsToString(rd)
			IFB COPY(digitsToString(td), 1, sd) = COPY(n, 1, sd) THEN
				n = COPY(n, sd - 3 + 1, 4)
				// 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.
        		IFB n = "9999" OR !rep AND n = "4999" THEN
					// On the first iteration only, check to see if rounding up gives the exact result as the
					// nines may infinitely repeat.
					IFB !rep THEN
						t = finalise(t, e + 1, 0)
						IFB eq(times(times(t, t), t), x) THEN
							r = t
							BREAK
						ENDIF
					ENDIF
					sd = 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.
					IFB n <> "" THEN
						IFB COPY(n, 2) AND COPY(n, 1) = "5" THEN
							// Truncate to the first rounding digit.
							finalise(r, e + 1, 1)
							m = !eq(times(times(r, r), r), x)
						ENDIF
					ENDIF
					BREAK
				ENDIF
			ENDIF
		WEND
		external = TRUE
		RESULT = finalise(r, e, rounding, m)
		IF isNumeric = NULL THEN EXIT
		RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))		
	FEND
	FUNCTION decimalPlaces(x)
		x = IIF(VARTYPE(x) < 8192, Constructor(x), x)
		d = SLICE(x, 2)
		n = "NaN"
		IFB LENGTH(d) THEN
			DIM w = LENGTH(d) - 1
			n = (w - GLOBAL.floor(x[1] / LOG_BASE)) * LOG_BASE
			// Subtract the number of trailing zeros of the last word.
			w = d[w]
			IFB w THEN
				WHILE w MOD 10 = 0
					n = n - 1
					w = w / 10
				WEND
			ENDIF
			IF n < 0 THEN n = 0
		ENDIF
		RESULT = n
	FEND
	FUNCTION dividedBy(dividend, divisor, isNumeric = FALSE)
		RESULT = divide(dividend, divisor)
	FEND
	FUNCTION dividedToIntegerBy(x, y, isNumeric = FALSE)
		x = IIF(VARTYPE(x) < 8192, Constructor(x), x)
		y = IIF(VARTYPE(y) < 8192, Constructor(y), y)
		RESULT = finalise(divide(x, y, 0, 1, 1), precision, rounding)
		IF isNumeric = NULL THEN EXIT
		RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
	FEND
	FUNCTION equals(x, y)
		RESULT = cmp(x, y) = 0
	FEND
	FUNCTION floor(x, isNumeric = FALSE)
		x = IIF(VARTYPE(x) < 8192, Constructor(x), x)
		RESULT = finalise(x, x[1] + 1, 3)
		IF isNumeric = NULL THEN EXIT
		RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
	FEND
	FUNCTION greaterThan(x, y)
		RESULT = cmp(x, y) > 0
	FEND
	FUNCTION greaterThanOrEqualTo(x, y)
		k = cmp(x, y)
		RESULT = VARTYPE(k = 1 OR k = 0, VAR_BOOLEAN)
	FEND
	FUNCTION hyperbolicCosine(x, isNumeric = FALSE)
		IFB isDecimalInstance(x) THEN
			str = toString(x)
		ELSE
			str = x
		ENDIF
		DIM filename = Hash.sha256("hyperbolicCosine,x=" + str + ",precision=" + precision + ",rounding=" + rounding + ",modulo=" + modulo + ",toExpNeg=" + toExpNeg + ",toExpPos=" + toExpPos + ",minE=" + minE + ",maxE=" + maxE)
		DIM path = folderspec + filename
		IFB cacheFlg AND FOPEN(path, F_EXISTS) THEN
			DIM FID = FOPEN(path, F_READ)
			str = VARTYPE(FGET(FID, 1), 258)
			RESULT = Constructor(str)
			FCLOSE(FID)
		ELSE
			x = IIF(VARTYPE(x) < 8192, Constructor(x), x)
			json = "{'precision':20, 'rounding':7}"
			Ctor = JSON.Parse(REPLACE(json, "'", "<#DBL>"))
			one = Constructor(1)
			IFB !isFinite(x) THEN
				RESULT = IIF(x[0], "INF", "NaN")
				EXIT
			ENDIF
			IFB isZero(x) THEN
				RESULT = one
				IF isNumeric = NULL THEN EXIT
				RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
				EXIT
			ENDIF
			pr = precision
			rm = rounding
			DIM array[] = x[1], sd(x)
			precision = pr + large(array, 1) + 4
			rounding = 1
			xd = SLICE(x, 2)
			len = LENGTH(xd)
			// 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.
			IFB len < 32 THEN
				k = GLOBAL.CEIL(len / 3)
				n = "" + (1 / tinyPow(4, k))
			ELSE
				k = 16
				n = "2.3283064365386962890625e-10"
			ENDIF
			x = taylorSeries(Ctor, 1, times(x, n), Constructor(1), TRUE)
			// Reverse argument reduction
			i = k
			d8 = Constructor(8)
			WHILE i > 0
				i = i - 1
				cosh2x = times(x, x, NULL)
				x = times(cosh2x, d8, NULL)
				x = minus(d8, x, NULL)
				x = times(cosh2x, x, NULL)
				x = minus(one, x, NULL)
			WEND
			precision = pr
			rounding = rm
			RESULT = finalise(x, precision, rounding, TRUE)
			CreateFolders(folderspec)
			FID = FOPEN(path, F_READ OR F_WRITE8)
			FPUT(FID, toString(RESULT))
			FCLOSE(FID)
		ENDIF
		IF isNumeric = NULL THEN EXIT
		RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
	FEND
	FUNCTION hyperbolicSine(x, isNumeric = FALSE)
		IFB isDecimalInstance(x) THEN
			str = toString(x)
		ELSE
			str = x
		ENDIF
		DIM filename = Hash.sha256("hyperbolicSine,x=" + str + ",precision=" + precision + ",rounding=" + rounding + ",modulo=" + modulo + ",toExpNeg=" + toExpNeg + ",toExpPos=" + toExpPos + ",minE=" + minE + ",maxE=" + maxE)
		DIM path = folderspec + filename
		IFB cacheFlg AND FOPEN(path, F_EXISTS) THEN
			DIM FID = FOPEN(path, F_READ)
			str = VARTYPE(FGET(FID, 1), 258)
			RESULT = Constructor(str)
			FCLOSE(FID)
		ELSE
			x = IIF(VARTYPE(x) < 8192, Constructor(x), x)
			json = "{'precision':20, 'rounding':7}"
			Ctor = JSON.Parse(REPLACE(json, "'", "<#DBL>"))
			IFB !isFinite(x) OR isZero(x) THEN
				RESULT = Constructor(x)
				EXIT
			ENDIF
			pr = precision
			rm = rounding
			DIM array[] = x[1], sd(x)
			precision = pr + large(array, 1) + 4
			rounding = 1
			xd = SLICE(x, 2)
			len = LENGTH(xd)
			IFB len < 3 THEN
				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 * GLOBAL.SQRT(len)
				k = IIF(k > 16, 16, INT(k))
				x = times(x, 1 / tinyPow(5, k), NULL)
				x = taylorSeries(2, x, x, TRUE)
				// Reverse argument reduction
				d5 = Constructor(5)
				d16 = Constructor(16)
				d20 = Constructor(20)
				WHILE k > 0
					k = k - 1
					sinh2x = times(x, x)
					x = times(x, plus(d5, times(sinh2x, plus(times(d16, sinh2x), d20))))
				WEND
			ENDIF
			precision = pr
			rounding = rm
			RESULT = finalise(x, pr, rm, TRUE)
			CreateFolders(folderspec)
			FID = FOPEN(path, F_READ OR F_WRITE8)
			FPUT(FID, toString(RESULT))
			FCLOSE(FID)
		ENDIF
		IF isNumeric = NULL THEN EXIT
		RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
	FEND
	FUNCTION hyperbolicTangent(x, isNumeric = FALSE)
		IFB isDecimalInstance(x) THEN
			str = toString(x)
		ELSE
			str = x
		ENDIF
		DIM filename = Hash.sha256("hyperbolicTangent,x=" + str + ",precision=" + precision + ",rounding=" + rounding + ",modulo=" + modulo + ",toExpNeg=" + toExpNeg + ",toExpPos=" + toExpPos + ",minE=" + minE + ",maxE=" + maxE)
		DIM path = folderspec + filename
		IFB cacheFlg AND FOPEN(path, F_EXISTS) THEN
			DIM FID = FOPEN(path, F_READ)
			str = VARTYPE(FGET(FID, 1), 258)
			RESULT = Constructor(str)
			FCLOSE(FID)
		ELSE
			x = IIF(VARTYPE(x) < 8192, Constructor(x), x)
			IFB !isFinite(x) THEN
				RESULT = Constructor(x[0])
				EXIT
			ENDIF
			IFB isZero(x) THEN
				RESULT = Constructor(x)
				EXIT
			ENDIF
			pr = precision
			rm = rounding
			precision = pr + 7
			rounding = 1
			precision = pr
			rounding = rm
			RESULT = finalise(divide(sinh(x), cosh(x), pr, rm))
			CreateFolders(folderspec)
			FID = FOPEN(path, F_READ OR F_WRITE8)
			FPUT(FID, toString(RESULT))
			FCLOSE(FID)
		ENDIF
		IF isNumeric = NULL THEN EXIT
		RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
	FEND
	FUNCTION inverseCosine(x, isNumeric = FALSE)
		IFB isDecimalInstance(x) THEN
			str = toString(x)
		ELSE
			str = x
		ENDIF
		DIM filename = Hash.sha256("hyperbolicTangent,x=" + str + ",precision=" + precision + ",rounding=" + rounding + ",modulo=" + modulo + ",toExpNeg=" + toExpNeg + ",toExpPos=" + toExpPos + ",minE=" + minE + ",maxE=" + maxE)
		DIM path = folderspec + filename
		IFB cacheFlg AND FOPEN(path, F_EXISTS) THEN
			DIM FID = FOPEN(path, F_READ)
			str = VARTYPE(FGET(FID, 1), 258)
			RESULT = Constructor(str)
			FCLOSE(FID)
		ELSE
			x = IIF(VARTYPE(x) < 8192, Constructor(x), x)
			json = "{'precision':20, 'rounding':7}"
			Ctor = JSON.Parse(REPLACE(json, "'", "<#DBL>"))		
			k = cmp(absoluteValue(x), 1)
			pr = precision
			rm = rounding
			IFB k <> -1 THEN
				RESULT = IIF(k = 0, IIF(isNeg(x), getPi(Ctor, pr, rm), Constructor(0)), Constructor("NaN"))
				IF isNumeric = NULL THEN EXIT
				RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
				EXIT
			ENDIF
			IFB isZero(x) THEN
				RESULT = times(getPi(Ctor, pr + 4, rm), 0.5, NULL)
				IF isNumeric = NULL THEN EXIT
				RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
				EXIT
			ENDIF
			// TODO? Special case acos(0.5) = pi/3 and acos(-0.5) = 2*pi/3
			precision = pr + 6
			rounding = 1
			x = asin(x)
			halfPi = times(getPi(Ctor, pr + 4, rm), 0.5)
			precision = pr
			rounding = rm
			CreateFolders(folderspec)
			FID = FOPEN(path, F_READ OR F_WRITE8)
			FPUT(FID, toString(RESULT))
			FCLOSE(FID)
		ENDIF
		RESULT = minus(halfPi, x)
	FEND
	FUNCTION inverseHyperbolicCosine(x, isNumeric = FALSE)
		IFB isDecimalInstance(x) THEN
			str = toString(x)
		ELSE
			str = x
		ENDIF
		DIM filename = Hash.sha256("inverseHyperbolicCosine,x=" + str + ",precision=" + precision + ",rounding=" + rounding + ",modulo=" + modulo + ",toExpNeg=" + toExpNeg + ",toExpPos=" + toExpPos + ",minE=" + minE + ",maxE=" + maxE)
		DIM path = folderspec + filename
		IFB cacheFlg AND FOPEN(path, F_EXISTS) THEN
			DIM FID = FOPEN(path, F_READ)
			str = VARTYPE(FGET(FID, 1), 258)
			RESULT = Constructor(str)
			FCLOSE(FID)
		ELSE
			x = IIF(VARTYPE(x) < 8192, Constructor(x), x)
			IFB lte(x, 1) THEN
				RESULT = Constructor(IIF(eq(x, 1), 0, "NaN"))
				EXIT
			ENDIF
			IFB !isFinite(x) THEN
				RESULT = Constructor(x)
				EXIT
			ENDIF
			pr = precision
			rm = rounding
			DIM array[] = absoluteValue(x[1]), sd(x)
			precision = pr + large(array, 1) + 4
			rounding = 1
			external = FALSE
			x = plus(squareRoot(minus(times(x, x, NULL), "1", NULL)), x, NULL)
			external = TRUE
			precision = pr
			rounding = rm
			RESULT = naturalLogarithm(x, NULL, NULL)
			CreateFolders(folderspec)
			FID = FOPEN(path, F_READ OR F_WRITE8)
			FPUT(FID, toString(RESULT))
			FCLOSE(FID)
		ENDIF
		IF isNumeric = NULL THEN EXIT
		RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
	FEND
	FUNCTION inverseHyperbolicSine(x, isNumeric = FALSE)
		IFB isDecimalInstance(x) THEN
			str = toString(x)
		ELSE
			str = x
		ENDIF
		DIM filename = Hash.sha256("inverseHyperbolicSine,x=" + str + ",precision=" + precision + ",rounding=" + rounding + ",modulo=" + modulo + ",toExpNeg=" + toExpNeg + ",toExpPos=" + toExpPos + ",minE=" + minE + ",maxE=" + maxE)
		DIM path = folderspec + filename
		IFB cacheFlg AND FOPEN(path, F_EXISTS) THEN
			DIM FID = FOPEN(path, F_READ)
			str = VARTYPE(FGET(FID, 1), 258)
			RESULT = Constructor(str)
			FCLOSE(FID)
		ELSE
			x = IIF(VARTYPE(x) < 8192, Constructor(x), x)
			IFB !isFinite(x) OR isZero(x) THEN
				RESULT = Constructor(x)
				IF isNumeric = NULL THEN EXIT
				RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
				EXIT
			ENDIF
			pr = precision
			rm = rounding
			DIM array[] = absoluteValue(x[1]), sd(x)
			precision = pr + 2 * large(array, 1) + 6
			rounding = 1
			external = FALSE
			x = plus(squareRoot(plus(times(x, x), 1)), x)
			external = TRUE
			precision = pr
			rounding = rm
			RESULT = naturalLogarithm(x, NULL, NULL)
			CreateFolders(folderspec)
			FID = FOPEN(path, F_READ OR F_WRITE8)
			FPUT(FID, toString(RESULT))
			FCLOSE(FID)
		ENDIF
		IF isNumeric = NULL THEN EXIT
		RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
	FEND
	FUNCTION inverseHyperbolicTangent(x, isNumeric = FALSE)
		IFB isDecimalInstance(x) THEN
			str = toString(x)
		ELSE
			str = x
		ENDIF
		DIM filename = Hash.sha256("inverseHyperbolicTangent,x=" + str + ",precision=" + precision + ",rounding=" + rounding + ",modulo=" + modulo + ",toExpNeg=" + toExpNeg + ",toExpPos=" + toExpPos + ",minE=" + minE + ",maxE=" + maxE)
		DIM path = folderspec + filename
		IFB cacheFlg AND FOPEN(path, F_EXISTS) THEN
			DIM FID = FOPEN(path, F_READ)
			str = VARTYPE(FGET(FID, 1), 258)
			RESULT = Constructor(str)
			FCLOSE(FID)
		ELSE
			x = IIF(VARTYPE(x) < 8192, Constructor(x), x)
			IFB !isFinite(x) THEN
				RESULT = Constructor("NaN")
				IF isNumeric = NULL THEN EXIT
				RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
				EXIT
			ENDIF
			IFB x[1] >= 0 THEN
				RESULT = Constructor(IIF(eq(absoluteValue(x), 1), x[0] + "INF", IIF(isZero(x), x, "NaN")))
				IF isNumeric = NULL THEN EXIT
				RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
			EXIT
			ENDIF
			pr = precision
			rm = rounding
			xsd = sd(x)
			DIM array[] = xsd, pr
			IFB large(array, 1) < 2 * (-1 * x[1]) - 1 THEN
				RESULT = finalise(Constructor(x), pr, rm, TRUE)
				EXIT
			ENDIF
			wpr = xsd - x[1]
			precision = wpr
			x = divide(plus(x, 1, NULL), minus(Constructor(1), x, NULL), wpr + pr, 1)
			precision = pr + 4
			rounding = 1
			x = naturalLogarithm(Constructor(x))
			precision = pr
			rounding = rm
			RESULT = times(x, 0.5, NULL)
			CreateFolders(folderspec)
			FID = FOPEN(path, F_READ OR F_WRITE8)
			FPUT(FID, toString(RESULT))
			FCLOSE(FID)
		ENDIF
		IF isNumeric = NULL THEN EXIT
		RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
	FEND
	FUNCTION inverseSine(x, isNumeric = FALSE)
		IFB isDecimalInstance(x) THEN
			str = toString(x)
		ELSE
			str = x
		ENDIF
		DIM filename = Hash.sha256("inverseSine,x=" + str + ",precision=" + precision + ",rounding=" + rounding + ",modulo=" + modulo + ",toExpNeg=" + toExpNeg + ",toExpPos=" + toExpPos + ",minE=" + minE + ",maxE=" + maxE)
		DIM path = folderspec + filename
		IFB cacheFlg AND FOPEN(path, F_EXISTS) THEN
			DIM FID = FOPEN(path, F_READ)
			str = VARTYPE(FGET(FID, 1), 258)
			RESULT = Constructor(str)
			FCLOSE(FID)
		ELSE
			x = IIF(VARTYPE(x) < 8192, Constructor(x), x)
			json = "{'precision':20, 'rounding':7}"
			Ctor = JSON.Parse(REPLACE(json, "'", "<#DBL>"))
			IFB isZero(x) THEN
				RESULT = Constructor(x)
				IF isNumeric = NULL THEN EXIT
				RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
				EXIT
			ENDIF
			k = cmp(THIS.abs(x), 1)
			pr = precision
			rm = rounding
			IFB k <> -1 THEN
				// |x| is 1
				IFB k = 0 THEN
					halfPi = times(getPi(Ctor, pr + 4, rm), 0.5)
					halfPi[0] = x[0]
					RESULT = halfPi
				ELSE
					// |x| > 1 or x is NaN
					RESULT = Constructor("NaN")
					EXIT
				ENDIF
			ENDIF
			// TODO? Special case asin(1/2) = pi/6 and asin(-1/2) = -pi/6
			precision = pr + 6
			rounding = 1
			tmp = squareRoot(minus(Constructor(1), times(x, x, NULL), NULL), NULL)
			tmp = plus(tmp, 1, NULL)
			x = div(x, tmp, NULL, NULL, NULL, NULL, NULL)
			x = atan(x)
			precision = pr
			rounding = rm
			RESULT = times(x, 2, NULL)
			IF isNumeric = NULL THEN EXIT
			CreateFolders(folderspec)
			FID = FOPEN(path, F_READ OR F_WRITE8)
			FPUT(FID, toString(RESULT))
			FCLOSE(FID)
		ENDIF
		RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
	FEND
	FUNCTION inverseTangent(x, isNumeric = FALSE)
		IFB isDecimalInstance(x) THEN
			str = toString(x)
		ELSE
			str = x
		ENDIF
		DIM filename = Hash.sha256("inverseTangent,x=" + str + ",precision=" + precision + ",rounding=" + rounding + ",modulo=" + modulo + ",toExpNeg=" + toExpNeg + ",toExpPos=" + toExpPos + ",minE=" + minE + ",maxE=" + maxE)
		DIM path = folderspec + filename
		IFB cacheFlg AND FOPEN(path, F_EXISTS) THEN
			DIM FID = FOPEN(path, F_READ)
			str = VARTYPE(FGET(FID, 1), 258)
			RESULT = Constructor(str)
			FCLOSE(FID)
		ELSE
			x = IIF(VARTYPE(x) < 8192, Constructor(x), x)
			json = "{'precision':20, 'rounding':7}"
			Ctor = JSON.Parse(REPLACE(json, "'", "<#DBL>"))
			pr = precision
			rm = rounding
			IFB !isFinite(x) THEN
				IFB !x[0] THEN
					RESULT = Constructor("NaN")
					IF isNumeric = NULL THEN EXIT
					RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
					EXIT
				ENDIF
				IFB pr + 4 <= PI_PRECISION THEN
					r = times(getPi(Ctor, pr + 4, rm), 0.5)
					r[0] = x[0]
					RESULT = r
					EXIT
				ENDIF
			ELSEIF isZero(x) THEN
				RESULT = Constructor(x)
				IF isNumeric = NULL THEN EXIT
				RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
				EXIT
			ELSEIF eq(absoluteValue(x), 1) AND pr + 4 <= PI_PRECISION THEN
				r = times(getPi(Ctor, pr + 4, rm), 0.25)
				RESULT = r
			ENDIF
			wpr = pr + 10
			precision = wpr
			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)))
			DIM array[] = 28, INT(wpr / LOG_BASE + 2)
			k = small(array, 1)
			i = k
			WHILE i > 0
				i = i - 1
				tmp = times(x, x, NULL)
				tmp = plus(tmp, 1, NULL)
				tmp = squareRoot(tmp, NULL)
				tmp = plus(tmp, 1, NULL)
				x = div(x, tmp, NULL, NULL, NULL, NULL, NULL)
			WEND
			external = FALSE
			j = CEIL(wpr / LOG_BASE)
			n = 1
			x2 = times(x, x, NULL)
			r = Constructor(x)
			px = x
			// atan(x) = x - x^3/3 + x^5/5 - x^7/7 + ...
			WHILE i <> -1
				px = times(px, x2)
				n = n + 2
				tmp = div(px, n, NULL, NULL, NULL, NULL, NULL)
				t = minus(r, div(px, n, NULL, NULL, NULL, NULL, NULL), NULL)
				td = SLICE(t, 2)
				px = times(px, x2, NULL)
				n = n + 2
				r = plus(t, div(px, n, NULL, NULL, NULL, NULL, NULL), NULL)
				rd = SLICE(r, 2)
				IFB UBound(rd) >= j THEN
					i = j
					WHILE i >= 0 AND rd[i] = td[i]
						i = i - 1
						IF i = -1 THEN BREAK
					WEND
				ENDIF
			WEND
			IF k <> 0 THEN r = times(r, POWER(2, k))
			external = TRUE
			precision = pr
			rounding = rm
			RESULT = finalise(r, precision, rounding, TRUE)
			CreateFolders(folderspec)
			FID = FOPEN(path, F_READ OR F_WRITE8)
			FPUT(FID, toString(RESULT))
			FCLOSE(FID)
		ENDIF
		IF isNumeric = NULL THEN EXIT
		RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
	FEND
	FUNCTION isFinite(x)
		x = IIF(VARTYPE(x) < 8192, Constructor(x), x)
		RESULT = IIF(x[1] <> NULL, TRUE, FALSE)
	FEND
	FUNCTION isInteger(x)
		x = IIF(VARTYPE(x) < 8192, Constructor(x), x)
		RESULT = VARTYPE(LENGTH(x) >= 3 AND GLOBAL.floor(x[1] / LOG_BASE) > LENGTH(x) - 2 - 2, VAR_BOOLEAN)
	FEND
	FUNCTION isNaN(x)
		x = IIF(VARTYPE(x) < 8192, Constructor(x), x)
		RESULT = IIF(x[0] = NULL, TRUE, FALSE)
	FEND
	FUNCTION isNegative(x)
		x = IIF(VARTYPE(x) < 8192, Constructor(x), x)
		RESULT = IIF(x[0] < 0, TRUE, FALSE)
	FEND
	FUNCTION isPositive(x)
		x = IIF(VARTYPE(x) < 8192, Constructor(x), x)
		RESULT = IIF(x[0] > 0, TRUE, FALSE)
	FEND
	FUNCTION isZero(x)
		x = IIF(VARTYPE(x) < 8192, Constructor(x), x)
		RESULT = VARTYPE(VARTYPE(x[2]) = 5 AND x[2] = 0, VAR_BOOLEAN)
	FEND
	FUNCTION lessThan(x, y)
		RESULT = cmp(x, y) < 0
	FEND
	FUNCTION lessThanOrEqualTo(x, y)
		RESULT = cmp(x, y) < 1
	FEND
	FUNCTION logarithm(x, base = NULL, isNumeric = FALSE)
		arg = IIF(VARTYPE(x) < 8192, Constructor(x), x)
		json = "{'precision':20, 'rounding':7}"
		Ctor = JSON.Parse(REPLACE(json, "'", "<#DBL>"))
		pr = precision
		rm = rounding
		guard = 5
		// Default base is 10.
		IFB base = NULL THEN
			base = Constructor(10)
			isBase10 = TRUE
		ELSE
			base = Constructor(base)
			d = SLICE(base, 2)
			// Return NaN if base is negative, or non-finite, or is 0 or 1.
			IFB VAL(base[0]) < 0 OR LENGTH(d) >= 2 OR eq(base, 1) THEN
				RESULT = Constructor("NaN")
				EXIT
			ENDIF
			isBase10 = eq(base, 10)
		ENDIF
		d = SLICE(arg, 2)
		// The result will have a non-terminating decimal expansion if base is 10 and arg is not an
		// integer power of 10.
		inf = FALSE
		IFB isBase10 THEN
			IFB LENGTH(d) > 1 THEN
				inf = TRUE
			ELSE
				k = d[0]
				WHILE k MOD 10 = 0
					k = k / 10
				WEND
				inf = k <> 1
			ENDIF
		ENDIF
		external = FALSE
		sd = pr + guard
		num = naturalLogarithm(arg, sd)
		IFB isBase10 THEN
			denominator = getLn10(Ctor, sd + 10)
		ELSE
			denominator = naturalLogarithm(base, sd)
		ENDIF
		// The result will have 5 rounding digits.
		r = divide(num, denominator, sd, 1)
		rd = SLICE(r, 2)
		// 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.
		k = pr
		IFB checkRoundingDigits(rd, pr, rm) THEN
			REPEAT
				sd = sd + 10
				num = naturalLogarithm(arg, sd)
				denominator = IIF(isBase10, getLn10(Ctor, sd + 10), naturalLogarithm(base, sd))
				r = divide(num, denominator, sd, 1)
				rd = SLICE(r, 2)
				IFB !inf THEN
					// Check for 14 nines from the 2nd rounding digit, as the first may be 4.
					IFB VAL(COPY(digitsToString(rd), k + 2, 14)) + 1 = 1E+14 THEN
						r = finalise(r, pr + 1, 0)
					ENDIF
					BREAK
				ENDIF
				k = k + 10
			UNTIL !(checkRoundingDigits(rd, k, rm))
		ENDIF
		external = TRUE
		RESULT = finalise(r, pr, rm)
		IF isNumeric = NULL THEN EXIT
		RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
	FEND
	FUNCTION minus(minuend, subtrahend, isNumeric = FALSE)
		x = IIF(VARTYPE(minuend) < 8192, Constructor(minuend), minuend)
		y = IIF(VARTYPE(subtrahend) < 8192, Constructor(subtrahend), subtrahend)
		DIM filename = Hash.sha256("minus,minuend=" + toString(x) + ",subtrahend=" + toString(y) + ",precision=" + precision + ",rounding=" + rounding + ",modulo=" + modulo + ",toExpNeg=" + toExpNeg + ",toExpPos=" + toExpPos + ",minE=" + minE + ",maxE=" + maxE)
		DIM path = folderspec + filename
		IFB cacheFlg AND FOPEN(path, F_EXISTS) THEN
			DIM FID = FOPEN(path, F_READ)
			str = VARTYPE(FGET(FID, 1), 258)
			RESULT = Constructor(str)
			IF isNumeric = NULL THEN EXIT
			RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
			FCLOSE(FID)
		ELSE
			DIM xIsNum = CHKNUM(x[1])
			DIM yIsNum = CHKNUM(y[1])
			DIM xIsZero = x[0] = 1 AND x[1] = 0 AND x[2] = 0
			DIM yIsZero = y[0] = 1 AND y[1] = 0 AND y[2] = 0
			DIM xIsInf = x[0] <> NULL AND x[1] = NULL AND !x[2]
			DIM yIsInf = y[0] <> NULL AND y[1] = NULL AND !y[2]
			DIM xIsNaN = x[0] = NULL AND x[1] = NULL AND x[2] = FALSE
			DIM yIsNaN = y[0] = NULL AND y[1] = NULL AND y[2] = FALSE
			// If either is not finite...
			IFB !xIsNum OR !yIsNum THEN
				// Return NaN if either is NaN
				// どちらかがNaNならばNaNを返す
				IFB xIsNaN OR yIsNaN THEN
					RESULT = "NaN"
				// Return y negated if x is finite and y is ±Infinity.
				// xが有限値でyが無限値ならばyを否定して返す
				ELSEIF !xIsInf AND yIsInf THEN
					y[0] = -1 * y[0]
					RESULT = finiteToString(y)
				// Return x if y is finite and x is ±Infinity.
				// yが有限値でxが無限値ならばxを返す
				ELSEIF yIsNum AND xIsInf THEN
					RESULT = finiteToString(x)
				// Return x if both are ±Infinity with different signs.
				// 両方とも±∞で符号が違うならばxを返す
				ELSEIF x[0] <> y[0] AND xIsInf AND yIsInf THEN
					RESULT = finiteToString(x)
				// Return NaN if both are ±Infinity with the same sign.
				// 両方とも±∞で符号が同じならばNaNを返す
				ELSEIF x[0] = y[0] AND xIsInf AND yIsInf THEN
					RESULT = "NaN"
				ENDIF
				EXIT
			ENDIF
			// If signs differ...
			IFB x[0] <> y[0] THEN
				y[0] = -1 * y[0]
				RESULT = Decimal.plus(x, y, isNumeric)
				EXIT
			ENDIF
			xd = SLICE(x, 2)
			yd = SLICE(y, 2)
			pr = precision
			rm = rounding
			// If either is zero...
			IFB !xd[0] OR !yd[0] THEN
				// Return y negated if x is zero and y is non-zero.
				IFB yd[0] THEN
					y[0] = -1 * y[0]
				// Return x if y is zero and x is non-zero.
				ELSEIF xd[0] THEN
					y = x
				// Return zero if both are zero.
				// From IEEE 754 (2008) 6.3: 0 - 0 = -0 - -0 = -0 when rounding to -Infinity.
				ELSE
					RESULT = 0
					EXIT
				ENDIF
				RESULT = IIF(external, finalise(y, pr, rm), y)
				RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
				EXIT
			ENDIF
			// Calculate base 1e7 exponents.
			e = GLOBAL.floor(y[1] / LOG_BASE)
			xe = GLOBAL.floor(x[1] / LOG_BASE)
			k = xe - e
			// If base 1e7 exponents differ...
			IFB k <> 0 THEN
				xLTy = k < 0
				IFB xLTy THEN
					d = SLICE(xd)
					k = -1 * k
					len = LENGTH(yd)
				ELSE
					d = SLICE(yd)
					e = xe
					len = LENGTH(xd)
				ENDIF
				DIM tmp[] = CEIL(pr / LOG_BASE), len
				i = CALCARRAY(tmp, CALC_MAX) + 2
				IFB k > i THEN
					k = i
					RESIZE(d, 1)
				ENDIF
				// Prepend zeros to equalise exponents.
				arrayReverse(d)
				i = k - 1
				WHILE i >= 0
					arrayPush(d, 0)
					i = i - 1
				WEND
				arrayReverse(d)
				// copy
				IFB xLTy THEN
					xd = SLICE(d)
				ELSE
					yd = SLICE(d)
				ENDIF
			ELSE
				// Check digits to determine which is the bigger number.
				i = LENGTH(x) - 2
				len = LENGTH(y) - 2
				xLTy = i < len
				IF xLTy <> 0 THEN len = i
				FOR i = 0 TO len - 1
					IFB VAL(xd[i]) <> VAL(yd[i]) THEN
						xLTy = VAL(xd[i]) < VAL(yd[i])
						BREAK
					ENDIF
				NEXT
				k = 0
			ENDIF
			IFB xLTy <> 0 THEN
				d = SLICE(xd)
				xd = SLICE(yd)
				yd = SLICE(d)
				y[0] = -1 * y[0]
			ENDIF
			len = LENGTH(xd)
			// Append zeros to `xd` if shorter.
			// Don't add zeros to `yd` if shorter as subtraction only needs to start at `yd` length.
			i = LENGTH(yd) - len
			WHILE i > 0
				arrayPush(xd, 0)
				len = len + 1
				i = i - 1
			WEND
			// Subtract yd from xd.
			i = LENGTH(yd)
			WHILE i > k
				i = i - 1
				IFB VAL(xd[i]) < VAL(yd[i]) THEN
					j = i
					j = j - 1
					WHILE VARTYPE(j+1, VAR_BOOLEAN) AND VARTYPE(xd[j] = 0, VAR_BOOLEAN)
						xd[j] = BASE - 1
						j = j - 1
					WEND
					xd[j] = VAL(xd[j] )- 1
					xd[i] = VAL(xd[i]) + BASE
				ENDIF
				xd[i] = VAL(xd[i]) - VAL(yd[i])
			WEND
			// Remove trailing zeros.
			len = LENGTH(xd)
			WHILE len > 0
				IFB xd[len - 1] = 0 THEN
					arrayPop(xd)
					len = LENGTH(xd)
				ELSE
					BREAK
				ENDIF
			WEND
			// Remove leading zeros and adjust exponent accordingly.
			IFB LENGTH(xd) <> 0 THEN
				WHILE xd[0] = 0
					arrayShift(xd)
					e = e - 1
				WEND
			ENDIF
			// Zero?
			IFB LENGTH(xd) = 0 THEN
				RESULT = Constructor(IIF(rm=3, -0, 0))
				IF isNumeric = NULL THEN EXIT
				RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))		
				EXIT
			ENDIF
			RESIZE(y, 1)
			arrayMerge(y, xd)
			y[1] = getBase10Exponent(xd, e)
			IFB external THEN
				RESULT = finalise(y, pr, rm)
				IF isNumeric = NULL THEN EXIT
				RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
				CreateFolders(folderspec)
				FID = FOPEN(path, F_READ OR F_WRITE8)
				FPUT(FID, RESULT)
				FCLOSE(FID)
			ELSE
				RESULT = SLICE(y)
			ENDIF
		ENDIF
	FEND
	FUNCTION modulo(x, y)
		x = IIF(VARTYPE(x) < 8192, Constructor(x), x)		
		y = IIF(VARTYPE(y) < 8192, Constructor(y), y)		
		DIM xIsNum = CHKNUM(x[1])
		DIM yIsNum = CHKNUM(y[1])
		DIM xIsZero = x[0] = 1 AND x[1] = 0 AND x[2] = 0
		DIM yIsZero = y[0] = 1 AND y[1] = 0 AND y[2] = 0
		DIM xIsInf = x[0] <> NULL AND x[1] = NULL AND !x[2]
		DIM yIsInf = y[0] <> NULL AND y[1] = NULL AND !y[2]
		DIM xIsNaN = x[0] = NULL AND x[1] = NULL AND x[2] = FALSE
		DIM yIsNaN = y[0] = NULL AND y[1] = NULL AND y[2] = FALSE
		// Return NaN if x is ±Infinity or NaN, or y is NaN or ±0.
		IFB (xIsInf OR xIsNaN) OR (yIsNaN OR yIsZero) THEN
			RESULT = Constructor("NaN")
			EXIT
		ENDIF
		// Prevent rounding of intermediate calculations.
		external = FALSE
		IFB modulo = 9 THEN
			// Euclidian division: q = sign(y) * floor(x / abs(y))
			// result = x - q * y    where  0 <= result < abs(y)
			q = divide(x, absoluteValue(y), 0, 3, 1)
			q[0] = q[0] * y[0]
		ELSE
			q = divide(x, y, 0, modulo, 1)
		ENDIF
		q = times(q, y)
		external = TRUE
		RESULT = minus(x, q)
	FEND
	FUNCTION negated(x, isNumeric = FALSE)
		x = IIF(VARTYPE(x) < 8192, Constructor(x), x)		
		x[0] = -1 * x[0]
		RESULT = finalise(x)
		IF isNumeric = NULL THEN EXIT
		RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
	FEND
	FUNCTION plus(augend, addend, isNumeric = FALSE)
		x = IIF(VARTYPE(augend) < 8192, Constructor(augend), augend)
		y = IIF(VARTYPE(addend) < 8192, Constructor(addend), addend)
		DIM filename = Hash.sha256("plus,augend=" + toString(x) + ",addend=" + toString(y) + ",precision=" + precision + ",rounding=" + rounding + ",modulo=" + modulo + ",toExpNeg=" + toExpNeg + ",toExpPos=" + toExpPos + ",minE=" + minE + ",maxE=" + maxE)
		DIM path = folderspec + filename
		IFB cacheFlg AND FOPEN(path, F_EXISTS) THEN
			DIM FID = FOPEN(path, F_READ)
			str = VARTYPE(FGET(FID, 1), 258)
			RESULT = Constructor(str)
			IF isNumeric = NULL THEN EXIT
			RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
			FCLOSE(FID)
		ELSE
			DIM xIsNum = CHKNUM(x[1])
			DIM yIsNum = CHKNUM(y[1])
			DIM xIsZero = x[0] = 1 AND x[1] = 0 AND x[2] = 0
			DIM yIsZero = y[0] = 1 AND y[1] = 0 AND y[2] = 0
			DIM xIsInf = x[0] <> NULL AND x[1] = NULL AND !x[2]
			DIM yIsInf = y[0] <> NULL AND y[1] = NULL AND !y[2]
			DIM xIsNaN = x[0] = NULL AND x[1] = NULL AND x[2] = FALSE
			DIM yIsNaN = y[0] = NULL AND y[1] = NULL AND y[2] = FALSE
			// If either is not finite...
			IFB !xIsNum OR !yIsNum THEN
				// Return NaN if either is NaN.
				// どちらかがNaNならばNaNを返す
				IFB xIsNaN OR yIsNaN THEN
					RESULT = "NaN"
				// Return x if y is finite and x is ±Infinity.
				// yが有限でxが±∞ならばxを返す
				ELSEIF yIsNum AND xIsInf THEN
					RESULT = finiteToString(x)//IIF(isNegative(x), "-", "") + "INF"
				// Return x if both are ±Infinity with the same sign.
				// 両方とも±∞で符号が同じならばxを返す
				ELSEIF x[0] = y[0] AND xIsInf AND yIsInf THEN
					RESULT = finiteToString(x)//IIF(isNegative(x), "-", "") + "INF"
				// Return NaN if both are ±Infinity with different signs.
				// 両方とも±∞で符号が違うならばNaNを返す
				ELSEIF x[0] <> y[0] AND xIsInf AND yIsInf THEN
					RESULT = "NaN"
				// Return y if x is finite and y is ±Infinity.
				// xが有限でyが±∞ならばyを返す
				ELSEIF xIsNum AND yIsInf THEN
					RESULT = "INF"//finiteToString(y)//IIF(isNegative(y), "-", "") + "INF"//toString(finalise(y, pr, rm))
				ENDIF
				RESULT = Constructor(RESULT)
				EXIT
			ENDIF
			// If signs differ...
			IFB x[0] <> y[0] THEN
				y[0] = -1 * y[0]
				RESULT = Decimal.minus(x, y, isNumeric)
				EXIT
			ENDIF
			xd = SLICE(x, 2)
			yd = SLICE(y, 2)
			pr = precision
			rm = rounding
			// If either is zero...
			IFB !xd[0] OR !yd[0] THEN
				IF !yd[0] THEN y = x
				RESULT = IIF(external, finalise(y, pr, rm), y)
				IF isNumeric = NULL THEN EXIT
				RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
				CreateFolders(folderspec)
				FID = FOPEN(path, F_READ OR F_WRITE8)
				FPUT(FID, RESULT)
				FCLOSE(FID)
				EXIT
			ENDIF
			// Calculate base 1e7 exponents.
			k = GLOBAL.floor(x[1] / LOG_BASE)
			e = GLOBAL.floor(y[1] / LOG_BASE)
			i = k - e
			// If base 1e7 exponents differ
			IFB i <> 0 THEN
				IFB i < 0 THEN
					DIM d = SLICE(xd)
					i = -1 * i
					len = LENGTH(yd)
					flg = TRUE
				ELSE
					d = SLICE(yd)
					e = k
					len = LENGTH(xd)
					flg = FALSE
				ENDIF
				// Limit number of zeros prepended to max(ceil(pr / LOG_BASE), len) + 1.
				k = CEIL(pr/LOG_BASE)
				len = IIF(k > len, k + 1, len + 1)
				IFB i > len THEN
					i = len
					RESIZE(d, 1)
				ENDIF
				// Prepend zeros to equalise exponents. Note: Faster to use reverse then do unshifts.
				arrayReverse(d)
				WHILE i > 0
					arrayPush(d, 0)
					i = i - 1
				WEND
				arrayReverse(d)
				// copy
				IFB flg THEN
					xd = SLICE(d)
				ELSE
					yd = SLICE(d)
				ENDIF
			ENDIF
			len = LENGTH(xd)
			i = LENGTH(yd)
			// If yd is longer than xd, swap xd and yd so xd points to the longer array.
			IFB len - i < 0 THEN
				i = len
				d = SLICE(yd)
				yd = SLICE(xd)
				xd = SLICE(d)
			ENDIF
			// Only start adding at yd.length - 1 as the further digits of xd can be left as they are.
			DIM carry = 0
			WHILE i > 0
				i = i - 1
				xd[i] = VAL(xd[i]) + VAL(yd[i]) + carry
				carry = INT(xd[i] / BASE)
				xd[i] = xd[i] MOD BASE
			WEND
			IFB carry THEN
				// xd.unshift(carry)
				arrayUnshift(xd, carry)
				e = e + 1
			ENDIF
			// Remove trailing zeros.
			// No need to check for zero, as +x + +y != 0 && -x + -y != 0		RESULT = ERR_VALUE
			len = LENGTH(xd)
			WHILE len > 0
				IFB xd[len - 1] = 0 THEN
					arrayPop(xd)
					len = LENGTH(xd)
				ELSE
					BREAK
				ENDIF
			WEND
			RESIZE(y, 1)
			arrayMerge(y, xd)
			y[1] = getBase10Exponent(xd, e)
			IFB external THEN
				RESULT = finalise(y, pr, rm)
				IF isNumeric = NULL THEN EXIT
				RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
				CreateFolders(folderspec)
				FID = FOPEN(path, F_READ OR F_WRITE8)
				FPUT(FID, RESULT)
				FCLOSE(FID)
			ELSE
				RESULT = SLICE(y)
			ENDIF
		ENDIF
	FEND
	FUNCTION precision(x, z = NULL)
		x = IIF(VARTYPE(x) < 8192, Constructor(x), x)
		xd = SLICE(x, 2)
		IFB LENGTH(xd) THEN
			k = getPrecision(xd)
			IFB z <> NULL THEN
				IF z AND x[1] + 1 > k THEN k = x[1] + 1
			ENDIF
		ELSE
			k = "NaN"
		ENDIF
		RESULT = k
	FEND
	FUNCTION round(x, isNumeric = FALSE)
		x = Constructor(x)
		RESULT = finalise(x, x[1] + 1, rounding)
		IF isNumeric = NULL THEN EXIT
		RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
	FEND
	FUNCTION sine(x, isNumeric = FALSE)
		IFB isDecimalInstance(x) THEN
			str = toString(x)
		ELSE
			str = x
		ENDIF
		DIM filename = Hash.sha256("sine,x=" + str + ",precision=" + precision + ",rounding=" + rounding + ",modulo=" + modulo + ",toExpNeg=" + toExpNeg + ",toExpPos=" + toExpPos + ",minE=" + minE + ",maxE=" + maxE)
		DIM path = folderspec + filename
		IFB cacheFlg AND FOPEN(path, F_EXISTS) THEN
			DIM FID = FOPEN(path, F_READ)
			str = VARTYPE(FGET(FID, 1), 258)
			RESULT = Constructor(str)
			FCLOSE(FID)
		ELSE
			x = IIF(VARTYPE(x) < 8192, Constructor(x), x)
			json = "{'precision':20, 'rounding':7}"
			Ctor = JSON.Parse(REPLACE(json, "'", "<#DBL>"))
			IFB !isFinite(x) THEN
				RESULT = Constructor("NaN")
				EXIT
			ENDIF
			IFB isZero(x) THEN
				RESULT = Constructor(x)
				IF isNumeric = NULL THEN EXIT
				RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))		
				EXIT
			ENDIF
			pr = precision
			rm = rounding
			DIM array[] = x[1], sd(x)
			precision = pr + CALCARRAY(array, CALC_MAX) + LOG_BASE
			rounding = 1
			x = sine2(Ctor, toLessThanHalfPi(Ctor, x))
			precision = pr
			rounding = rm
			RESULT = finalise(IIF(quadrant > 2, neg(x), x), pr, rm, TRUE)
			CreateFolders(folderspec)
			FID = FOPEN(path, F_READ OR F_WRITE8)
			FPUT(FID, toString(RESULT))
			FCLOSE(FID)
		ENDIF
		IF isNumeric = NULL THEN EXIT
		RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))		
	FEND
	FUNCTION squareRoot(x, isNumeric = FALSE)
		x = Constructor(x)
		d = SLICE(x, 2)
		e = x[1]
		s = x[0]
		DIM xIsNum = CHKNUM(x[1])
		DIM xIsZero = x[0] = 1 AND x[1] = 0 AND x[2] = 0
		DIM xIsInf = x[0] <> NULL AND x[1] = NULL AND !x[2]
		DIM xIsNaN = x[0] = NULL AND x[1] = NULL AND x[2] = FALSE
		// Negative/NaN/Infinity/zero?
		IFB s <> 1 OR xIsNaN OR xIsInf OR xIsZero THEN
			RESULT = Constructor(IIF(!s OR s < 0 AND (!d OR d[0]), "NaN", IIF(d, x, 1 / 0)))
		ENDIF
		external = FALSE
		// Initial estimate.
		n = finiteToString(x)
//		s = GLOBAL.SQRT(n)
		DIM SC = CREATEOLEOBJ("ScriptControl")
		SC.Language = "JScript"
		s = SC.Eval("Math.sqrt(" + n + ").toPrecision(16)")

//s = 4.898979485566356//GLOBAL.SQRT(VAL(JOIN(d, "")))
		// Math.sqrt underflow/overflow?
		// Pass x to Math.sqrt as integer, then adjust the exponent of the result.
		IFB s = 0 OR s = 1 / 0 THEN
			n = digitsToString(d)
			IF (LENGTH(n) + e) MOD 2 = 0 THEN n = n + "0"
			s = GLOBAL.SQRT(n)
			e = floor((e + 1) / 2) - (e < 0 OR e MOD 2)
			IFB s = 1 / 0 THEN
				n = "5E" + e
			ELSE
				n = toExponential(s)
				n = SLICE(n, 1, POS("e", n) + 1) + e
			ENDIF
			r = Constructor(n)
		ELSE
			r = Constructor("" + s)
		ENDIF
		e = precision
		sd = e + 3
		// Newton-Raphson iteration.
		rep = FALSE
		WHILE TRUE
			t = r
			td = SLICE(t, 2)
//			tmp = divide(x, t, sd + 2, 1)
//			tmp = plus(t, tmp)
//			r = times(tmp, 0.5)
			r = times(plus(t, divide(x, t, sd + 2, 1)), 0.5)
			rd = SLICE(r, 2)
			// TODO? Replace with for-loop and checkRoundingDigits.
			n = digitsToString(rd)
			m = COPY(digitsToString(td), 1, sd)
			IFB m = COPY(n, 1, sd) THEN
				n = COPY(n, sd - 3 + 1, 4)
				// 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.
				IFB n = "9999" OR !rep AND n = "4999" THEN
					// On the first iteration only, check to see if rounding up gives the exact result as the
					// nines may infinitely repeat.
					IFB !rep THEN
						finalise(t, e + 1, 0)
						IFB eq(times(t, t), x) THEN
							r = t
							BREAK
						ENDIF
					ENDIF
					sd = 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.
					IFB n <> 0 OR COPY(n, 2) <> "0" AND COPY(n, 1, 1) = "5" THEN
						// Truncate to the first rounding digit.
						finalise(r, e + 1, 1)
						m = !eq(times(r, r), x)
					ENDIF
					BREAK
				ENDIF
			ENDIF
		WEND
		external = TRUE
		RESULT = finalise(r, e, rounding, m)
		IF isNumeric = NULL THEN EXIT
		RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
	FEND
	FUNCTION tangent(x, isNumeric = FALSE)
		IFB isDecimalInstance(x) THEN
			str = toString(x)
		ELSE
			str = x
		ENDIF
		DIM filename = Hash.sha256("tangent,x=" + str + ",precision=" + precision + ",rounding=" + rounding + ",modulo=" + modulo + ",toExpNeg=" + toExpNeg + ",toExpPos=" + toExpPos + ",minE=" + minE + ",maxE=" + maxE)
		DIM path = folderspec + filename
		IFB cacheFlg AND FOPEN(path, F_EXISTS) THEN
			DIM FID = FOPEN(path, F_READ)
			str = VARTYPE(FGET(FID, 1), 258)
			RESULT = Constructor(str)
			FCLOSE(FID)
		ELSE
			x = Constructor(x)
			IFB !isFinite(x) THEN
				RESULT = Constructor("NaN")
				EXIT
			ENDIF
			IFB isZero(x) THEN
				RESULT = Constructor(x)
				EXIT
			ENDIF
			pr = precision
			rm = rounding
			precision = pr + 10
			rounding = 1
			x = sine(x, NULL)
			x[0] = 1
			tmp = times(x, x, NULL)
			tmp = minus(1, tmp, NULL)
			tmp = THIS.sqrt(tmp, NULL)
			x = divide(x, tmp)
			precision = pr
			rounding = rm
			RESULT = finalise(IIF(quadrant = 2 OR quadrant = 4, neg(x), x), pr, rm, TRUE)
			CreateFolders(folderspec)
			FID = FOPEN(path, F_READ OR F_WRITE8)
			FPUT(FID, toString(RESULT))
			FCLOSE(FID)
		ENDIF
		IF isNumeric = NULL THEN EXIT
		RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
	FEND
	FUNCTION times(multiplicand, multiplier, isNumeric = FALSE)
		x = IIF(VARTYPE(multiplicand) < 8192, Constructor(multiplicand), multiplicand)
		y = IIF(VARTYPE(multiplier) < 8192, Constructor(multiplier), multiplier)
		xd = SLICE(x, 2)
		yd = SLICE(y, 2)
		DIM filename = Hash.sha256("times,multiplicand=" + toString(x) + ",multiplier=" + toString(y) + ",precision=" + precision + ",rounding=" + rounding + ",modulo=" + modulo + ",toExpNeg=" + toExpNeg + ",toExpPos=" + toExpPos + ",minE=" + minE + ",maxE=" + maxE)
		DIM path = folderspec + filename
		IFB cacheFlg AND FOPEN(path, F_EXISTS) THEN
			DIM FID = FOPEN(path, F_READ)
			str = VARTYPE(FGET(FID, 1), 258)
			RESULT = Constructor(str)
			IF isNumeric = NULL THEN EXIT
			RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
			FCLOSE(FID)
		ELSE
			DIM xIsZero = x[0] = 1 AND x[1] = 0 AND x[2] = 0
			DIM yIsZero = y[0] = 1 AND y[1] = 0 AND y[2] = 0
			DIM xIsInf = x[0] <> NULL AND x[1] = NULL AND !x[2]
			DIM yIsInf = y[0] <> NULL AND y[1] = NULL AND !y[2]
			DIM xIsNaN = x[0] = NULL AND x[1] = NULL AND x[2] = FALSE
			DIM yIsNaN = y[0] = NULL AND y[1] = NULL AND y[2] = FALSE
			IFB xIsNaN OR yIsNan THEN
				y[0] = "NaN"
			ELSE
				y[0] = y[0] * x[0]
			ENDIF
			// If either is NaN, ±Infinity or ±0...
			IFB (xIsNaN OR yIsNaN) OR (xIsInf OR yIsInf) OR (xIsZero OR yIsZero) THEN
				// Return NaN if either is NaN.
				// どちらかがNaNならばNaNを返す
				IFB xIsNaN OR yIsNaN THEN
					RESULT = "NaN"
				// Return NaN if x is ±0 and y is ±Infinity, or y is ±0 and x is ±Infinity.
				// xが±0、yが±無限大、もしくはyが±0、xが±無限大ならばNaNを返す
				ELSEIF (xIsZero AND yIsInf) OR (yIsZero AND xIsInf) THEN
					RESULT = "NaN"
				// Return ±Infinity if either is ±Infinity.
				// どちらかが±無限大ならば±無限大を返す
				ELSEIF xIsInf OR yIsInf THEN
					RESULT = "INF"
				// Return ±0 if either is ±0.
				// どちらかが±0ならば±0を返す
				ELSEIF xIsZero OR yIsZero THEN
					RESULT = "0"
				ENDIF
				RESULT = Constructor(RESULT)
				IF isNumeric = NULL THEN EXIT
				RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
				CreateFolders(folderspec)
				FID = FOPEN(path, F_READ OR F_WRITE8)
				FPUT(FID, RESULT)
				FCLOSE(FID)
				EXIT
			ENDIF
			e = GLOBAL.floor(x[1] / LOG_BASE) + GLOBAL.floor(y[1] / LOG_BASE)
			xdL = LENGTH(xd)
			ydL = LENGTH(yd)
			// Ensure xd points to the longer array.
			IFB xdL < ydL THEN
				r = SLICE(xd)
				xd = SLICE(yd)
				yd = SLICE(r)
				rL = xdL
				xdL = ydL
				ydL = rL
			ENDIF
			// Initialise the result array with zeros.
			DIM r[-1]
			rL = xdL + ydL
			i = rL
			WHILE i > 0
				arrayPush(r, 0)
				i = i - 1
			WEND
			// Multiply!
			i = ydL
			WHILE i > 0
				i = i - 1
				carry = 0
				k = xdL + i
				WHILE k > i
					t = VAL(r[k]) + VAL(yd[i]) * VAL(xd[k-i-1]) + carry
					r[k] = t MOD BASE
					k = k - 1
					carry = INT(t / BASE)
				WEND
				r[k] = (r[k] + carry) MOD BASE
			WEND
			// Remove trailing zeros.
			rL = rL - 1
			WHILE r[rL] = 0
				arrayPop(r)
				rL = rL - 1
			WEND
			IFB carry <> 0 THEN
				e = e + 1
			ELSE
				arrayShift(r)
			ENDIF
			RESIZE(y, 1)
			arrayMerge(y, r)
			y[1] = getBase10Exponent(r, e)
			IFB external THEN
				RESULT = finalise(y, precision, rounding)
				IF isNumeric = NULL THEN EXIT
				RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
				CreateFolders(folderspec)
				FID = FOPEN(path, F_READ OR F_WRITE8)
				FPUT(FID, RESULT)
				FCLOSE(FID)
			ELSE
				RESULT = SLICE(y)
			ENDIF
		ENDIF
	FEND
	FUNCTION toBinary(x, sd = NULL, rm = NULL)
		RESULT = toStringBinary(x, 2, sd, rm)
	FEND
	FUNCTION toDecimalPlaces(x, dp = NULL, rm = NULL)
		x = IIF(VARTYPE(x) < 8192, Constructor(x), x)
		IFB dp = NULL THEN
			RESULT = SLICE(x)
			RESULT = toString(RESULT)
			EXIT
		ENDIF
		checkInt32(dp, 0, MAX_DIGITS)
		IFB rm = NULL THEN
			rm = rounding
		ELSE
			checkInt32(rm, 0, 8)
		ENDIF
		RESULT = finiteToString(finalise(x, dp + x[1] + 1, rm))
	FEND
	FUNCTION toExponential(x, dp = NULL, rm = NULL)
		x = IIF(VARTYPE(x) < 8192, Constructor(x), x)
		IFB dp = NULL THEN
			str = finiteToString(x, TRUE)
		ELSE
			checkInt32(dp, 0, MAX_DIGITS)
			IFB rm = NULL THEN
				rm = rounding 
			ELSE
				checkInt32(rm, 0, 8)
			ENDIF
			x = finalise(Constructor(x), dp + 1, rm)
			str = finiteToString(x, TRUE, dp + 1)
		ENDIF
		RESULT = IIF(isNeg(x) AND !isZero(x), "-" + str, str)
	FEND
	FUNCTION toFixed(x, dp = NULL, rm = NULL)
		x = IIF(VARTYPE(x) < 8192, Constructor(x), x)
		IFB dp = NULL THEN
			str = finiteToString(x)
		ELSE
			checkInt32(dp, 0, MAX_DIGITS)
			IFB rm = NULL THEN
				rm = rounding
			ELSE
				checkInt32(rm, 0, 8)
			ENDIF
			y = finalise(Constructor(x), dp + x[1] + 1, rm)
			str = finiteToString(y, FALSE, dp + y[1] + 1)
		ENDIF		
		// To determine whether to add the minus sign look at the value before it was rounded,
		// i.e. look at `x` rather than `y`.
		RESULT = IIF(isNeg(x) AND !isZero(x), "-" + str, str)
	FEND
	FUNCTION toFraction(x, maxD = NULL)
		x = IIF(VARTYPE(x) < 8192, Constructor(x), x)
		xd = SLICE(x, 2)
		IFB LENGTH(xd) = 0 THEN
			RESULT = Constructor(x)
		ENDIF
		d0 = Constructor(1)
		n1 = d0
		n0 = Constructor(0)
		d1 = n0	
		d = Constructor(d1)
		d[1] = getPrecision(xd) - x[1] - 1
		e = d[1]
		k = e MOD LOG_BASE
		d[2] = POW(10, IIF(k < 0, LOG_BASE + k, k))
		IFB maxD = NULL THEN
			// d is 10**e, the minimum max-denominator needed.
			maxD = IIF(e > 0, d, n1)
		ELSE
			n = Constructor(maxD)
			IFB !isInt(n) <> 0 OR lt(n, n1) THEN
				RESULT = ERR_VALUE
				EXIT
			ENDIF
			maxD = IIF(gt(n, d), IIF(e > 0, d, n1), n)
		ENDIF
		external = FALSE
		n = Constructor(digitsToString(xd))
		pr = precision
		e = LENGTH(xd) * LOG_BASE * 2
		precision = e
		WHILE TRUE
			q = divide(n, d, 0, 1, 1)
			d2 = plus(d0, times(q, d1), NULL)
			IF cmp(d2, maxD) = 1 THEN BREAK
			d0 = d1
			d1 = d2
			d2 = n1
			n1 = plus(n0, times(q, d2), NULL)
			n0 = d2
			d2 = d
			d = minus(n, times(q, d2))
			n = d2
		WEND
		d2 = divide(minus(maxD, d0), d1, 0, 1, 1)
		n0 = plus(n0, times(d2, n1), NULL)
		d0 = plus(d0, times(d2, d1), NULL)
		n1[0] = x[0]
		n0[0] = n1[0]
		// Determine which fraction is closer to x, n0/d0 or n1/d1?
		tmp1 = divide(n1, d1, e, 1)
		tmp1 = minus(tmp1, x)
		tmp1 = THIS.abs(tmp1)
		tmp2 = divide(n0, d0, e, 1)
		tmp2 = minus(tmp2, x)
		tmp2 = THIS.abs(tmp2)
		DIM r[-1]
		IFB cmp(tmp1, tmp2) < 1 THEN
			arrayPush(r, finiteToString(n1))
			arrayPush(r, finiteToString(d1))
		ELSE
			arrayPush(r, finiteToString(n0))
			arrayPush(r, finiteToString(d0))
		ENDIF
		precision = pr
		external = TRUE
		RESULT = SLICE(r)
	FEND
	FUNCTION toHexadecimal(x, sd = NULL, rm = NULL)
		RESULT = toStringBinary(x, 16, sd, rm)
	FEND
	FUNCTION toNearest(x, y = NULL, rm = NULL)
		x = IIF(VARTYPE(x) < 8192, Constructor(x), x)
		xd = SLICE(x, 2)
		IFB y = NULL THEN
			// If x is not finite, return x.
			IFB !LENGTH(xd) THEN
				RESULT = SLICE(x)
				EXIT
			ENDIF
			y = Constructor(1)
			rm = rounding
		ELSE
			y = Constructor(y)
			yd = SLICE(y, 2)
			IFB rm = NULL THEN
				rm = rounding
			ELSE
				checkInt32(rm, 0, 8)
			ENDIF
			// If x is not finite, return x if y is not NaN, else NaN.
			IFB !LENGTH(xd) THEN
				RESULT = IIF(y[0], x, y)
			ENDIF
			// If y is not finite, return Infinity with the sign of x if y is Infinity, else NaN.
			IFB !LENGTH(yd) THEN
				IF y[0] THEN y[0] = x[0]
				RESULT = SLICE(y)
			ENDIF
			// If y is not zero, calculate the nearest multiple of y to x.
			IFB yd[0] THEN
				external = FALSE
				x = times(divide(x, y, 0, rm, 1), y)
				external = TRUE
				finalise(x)
			ELSE
				// If y is zero, return zero with the sign of x.
				y[0] = x[0]
				x = y
			ENDIF
		ENDIF
		RESULT = SLICE(x)
		RESULT = .toNumber(RESULT)
	FEND
	FUNCTION toNumber(x)
		str = finiteToString(x)
		RESULT = VAL(IIF(isNegative(x), "-" + str, str))
	FEND
	FUNCTION toOctal(x, sd = NULL, rm = NULL)
		RESULT = toStringBinary(x, 8, sd, rm)
	FEND
	FUNCTION toPower(base, exponent, isNumeric = FALSE)
		DIM filename = Hash.sha256("toPower,exponent=" + exponent + ",precision=" + precision + ",rounding=" + rounding + ",modulo=" + modulo + ",toExpNeg=" + toExpNeg + ",toExpPos=" + toExpPos + ",minE=" + minE + ",maxE=" + maxE)
		DIM path = folderspec + filename
		IFB cacheFlg AND FOPEN(path, F_EXISTS) THEN
			DIM FID = FOPEN(path, F_READ)
			str = VARTYPE(FGET(FID, 1), 258)
			RESULT = Constructor(str)
			IF isNumeric = NULL THEN EXIT
			RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
			FCLOSE(FID)
		ELSE
			DIM x = Constructor(base)
			DIM y = Constructor(exponent)
			json = "{'precision':20, 'rounding':7}"
			Ctor = JSON.Parse(REPLACE(json, "'", "<#DBL>"))
			DIM yn = VAL(exponent)
			DIM xIsZero = x[0] = 1 AND x[1] = 0 AND x[2] = 0
			DIM yIsZero = y[0] = 1 AND y[1] = 0 AND y[2] = 0
			DIM xIsInf = x[0] <> NULL AND x[1] = NULL AND !x[2]
			DIM yIsInf = y[0] <> NULL AND y[1] = NULL AND !y[2]
			DIM xIsNaN = x[0] = NULL AND x[1] = NULL AND x[2] = FALSE
			DIM yIsNaN = y[0] = NULL AND y[1] = NULL AND y[2] = FALSE
			// Either ±Infinity, NaN or ±0?
			// どちらかが±Infinity、NaNもしくは±0
			IFB (xIsInf OR yIsInf) OR (xIsNaN OR yIsNaN) OR (xIsZero OR yIsZero) THEN
				RESULT = POWER(base, exponent)
				EXIT
			ENDIF
			IFB base = "1" THEN
				RESULT = x
				EXIT
			ENDIF
			pr = precision
			rm = rounding
			IFB exponent = "1" THEN
				RESULT = finalise(x, pr, rm)
				RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
				EXIT
			ENDIF
			// y exponent
			e = GLOBAL.floor(y[1]/LOG_BASE)
			// If y is a small integer use the 'exponentiation by squaring' algorithm.
			DIM k = IIF(yn < 0, -1 * yn, yn)
			IFB e >= LENGTH(y) - 2 - 1 AND k <= MAX_SAFE_INTEGER THEN
				DIM r = intPow(Ctor, x, k, pr)
				IFB VAL(y[0]) < 0 THEN
					RESULT = dividedBy("1", r)
				ELSE
					RESULT = toString(finalise(r, pr, rm))
//					RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
					CreateFolders(folderspec)
					FID = FOPEN(path, F_READ OR F_WRITE8)
					FPUT(FID, RESULT)
					FCLOSE(FID)
				ENDIF
//				RESULT = IIF(VAL(y[0]) < 0, dividedBy("1", r), toString(finalise(r, pr, rm)))
				EXIT
			ENDIF
			DIM s = x[0]
			// if x is negative
			IFB s < 0 THEN
				// if y is not an integer
				IFB e < LENGTH(y) - 2 - 1 THEN
					RESULT = "NaN"
					EXIT
				ENDIF
				// Result is positive if x is negative and the last digit of integer y is even.
				IF (y[e+2] AND 1) = 0 THEN s = 1
				// if x.eq(-1)
				IFB x[1] = 0 AND x[2] = 1 AND LENGTH(x) - 2 = 1 THEN
					x[0] = s
					RESULT = x
					EXIT
				ENDIF
			ENDIF
			// 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)
			xd = SLICE(x, 2)
			k = POWER(digitsToString(xd), yn)
			IFB k = 0 OR !isFinite(Constructor(k)) THEN
				e = floor(yn * (LN("0." + digitsToString(xd)) / VAL(LN10) + VAL(x[1]) + 1))
			ELSE
				e = Constructor(k)[1]
			ENDIF
			// Exponent estimate may be incorrect e.g. x: 0.999999999999999999, y: 2.29, e: 0, r.e: -1.
			// Overflow/underflow?
			IFB e > maxE + 1 OR e < minE - 1 THEN
				IFB e > 0 THEN
					RESULT = IIF(s >= 0, "INF", "-INF")
				ELSE
					RESULT = "0"
				ENDIF
				EXIT
			ENDIF
			external = FALSE
			x[0] = 1
			rounding = x[0]
			// 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
			DIM array[] = 12, LENGTH(e)
			k = small(array, 1)
			// r = x^y = exp(y*ln(x))
			r = naturalExponential(times(y, naturalLogarithm(x, pr + k)), pr)
			rd = SLICE(r, 2)
			// r may be Infinity, e.g. (0.9999999999999999).pow(-1e+40)
			IFB LENGTH(rd) THEN
				// 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.
				IFB checkRoundingDigits(rd, pr, rm) THEN
					e = pr + 10
					// Truncate to the increased precision plus five rounding digits.
					r = finalise(naturalExponential(times(y, 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).
					IFB COPY(digitsToString(rd), pr + 1 + 1, pr + 15 + 1) + 1 = 1E+14 THEN
						r = finalise(r, pr + 1, 0)
					ENDIF
				ENDIF
			ENDIF
			r[0] = s
			external = TRUE
			rounding = rm
			RESULT = finalise(r, pr, rm)
			RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
			CreateFolders(folderspec)
			FID = FOPEN(path, F_READ OR F_WRITE8)
			FPUT(FID, RESULT)
			FCLOSE(FID)
		ENDIF
	FEND
	FUNCTION toPrecision(x, sd = NULL, rm = NULL)
		x = IIF(VARTYPE(x) < 8192, Constructor(x), x)
		IFB sd = NULL THEN
			str = finiteToString(x, x[1] <= toExpNeg OR x[1] >= toExpPos)
		ELSE
			checkInt32(sd, 1, MAX_DIGITS)
			IFB rm = NULL THEN 
				rm = rounding
			ELSE
				checkInt32(rm, 0, 8)
			ENDIF
			x = finalise(Constructor(x), sd, rm)
			str = finiteToString(x, sd <= x[1] OR x[1] <= toExpNeg, sd)
		ENDIF
		RESULT = IIF(isNeg(x) AND isZero(x), "-" + str, str)
	FEND
	FUNCTION toSignificantDigits(x, sd = NULL, rm = NULL)
		x = IIF(VARTYPE(x) < 8192, Constructor(x), x)
		IFB sd = NULL THEN
			sd = precision
			rm = rounding
		ELSE
			checkInt32(sd, 1, MAX_DIGITS)
			IFB rm = NULL THEN
				rm = rounding
			ELSE
				checkInt32(rm, 0, 8)
			ENDIF
		ENDIF
		RESULT = toString(finalise(Constructor(x), sd, rm))
	FEND
	FUNCTION toString(x)
		str = finiteToString(x, x[1] <= toExpNeg OR x[1] >= toExpPos)
		RESULT = IIF(isNegative(x) AND !isZero(x), "-" + str, str)
	FEND
	FUNCTION truncated(x, isNumeric = FALSE)
		x = IIF(VARTYPE(x) < 8192, Constructor(x), x)
		RESULT = finalise(x, x[1] + 1, 1)
		IF isNumeric = NULL THEN EXIT
		RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
	FEND
	FUNCTION valueOf(x)
		x = IIF(VARTYPE(x) < 8192, Constructor(x), x)
		str = finiteToString(x, x[1] <= toExpNeg OR x[1] >= toExpPos)
		RESULT = IIF(isNeg(x), "-" + str, str)
	FEND
	//////////////////////////////
	// 短縮形
	//////////////////////////////
	FUNCTION abs(x)
		RESULT = absoluteValue(x)
	FEND
	FUNCTION acos(x)
		RESULT = inverseCosine(x)
	FEND
	FUNCTION acosh(x)
		RESULT = inverseHyperbolicCosine(x)
	FEND
	FUNCTION asin(x)
		RESULT = inverseSine(x)
	FEND
	FUNCTION asinh(x)
		RESULT = inverseHyperbolicSine(x)
	FEND
	FUNCTION atan(x)
		RESULT = inverseTangent(x)
	FEND	
	FUNCTION atanh(x)
		RESULT = inverseHyperbolicTangent(x)
	FEND
	FUNCTION add(augend, addend, isNumeric = FALSE)
		RESULT = plus(augend, addend, isNumeric)
	FEND
	FUNCTION calc(str, pr = 20, rm = 4)
		RESULT = calculate(str, pr, rm)
	FEND
	FUNCTION cbrt(x)
		RESULT = cubeRoot(x)
	FEND
	FUNCTION clamp(x, min, max)
		RESULT = clampedTo(x, min, max)
	FEND
	FUNCTION cmp(x, y)
		RESULT = comparedTo(x, y)
	FEND
	FUNCTION cos(x)
		RESULT = cosine(x)
	FEND
	FUNCTION cosh(x, isNumeric = FALSE)
		RESULT = hyperbolicCosine(x, isNumeric)
	FEND
TEXTBLOCK
	FUNCTION divide(dividend, divisor, pr = 20, rm = 4, dp = NULL, _base = NULL, isNumeric = FALSE)
		RESULT = dividedBy(dividend, divisor, pr, rm, dp, _base, isNumeric)
	FEND
ENDTEXTBLOCK
	FUNCTION div(dividend, divisor, pr = 20, rm = 4, dp = NULL, _base = NULL, isNumeric = FALSE)
		RESULT = divide(dividend, divisor, pr, rm, dp, _base, isNumeric)
	FEND
	FUNCTION divToInt(x, y)
		RESULT = dividedToIntegerBy(x, y)
	FEND
	FUNCTION dp(x)
		RESULT = decimalPlaces(x)
	FEND
	FUNCTION eq(x, y)
		RESULT = equals(x, y)
	FEND
	FUNCTION exp(x)
		RESULT = naturalExponential(x)
	FEND
	FUNCTION gt(x, y)
		RESULT = greaterThan(x, y)
	FEND
	FUNCTION gte(x, y)
		RESULT = greaterThanOrEqualTo(x, y)
	FEND
	FUNCTION isInt(x)
		RESULT = isInteger(x)
	FEND
	FUNCTION isNeg(x)
		RESULT = isNegative(x)
	FEND
	FUNCTION isPos(x)
		RESULT = isPositive(x)
	FEND
	FUNCTION ln(x)
		RESULT = naturalLogarithm(x)
	FEND
	FUNCTION log(arg, base)
		RESULT = logarithm(arg, base)
	FEND
	FUNCTION lt(x, y)
		RESULT = lessThan(x, y)
	FEND
	FUNCTION lte(x, y)
		RESULT = lessThanOrEqualTo(x, y)
	FEND
	FUNCTION mod(x, y)
		RESULT = modulo(x, y)
	FEND
	FUNCTION mul(multiplicand, multiplier, isNumeric = FALSE)
		RESULT = times(multiplicand, multiplier, isNumeric)
	FEND
	FUNCTION neg(x)
		RESULT = negated(x)
	FEND
	FUNCTION pow(base, exponent)
		RESULT = toPower(base, exponent)
	FEND
	FUNCTION sd(x, z = NULL)
		RESULT = precision(x, z)
	FEND
	FUNCTION sin(x)
		RESULT = sine(x)
	FEND
	FUNCTION sinh(x, isNumeric = FALSE)
		RESULT = hyperbolicSine(x, isNumeric)
	FEND
	FUNCTION sqrt(x, isNumeric = FALSE)
		RESULT = squareRoot(x, isNumeric)
	FEND
	FUNCTION sub(minuend, subtrahend, isNumeric = FALSE)
		RESULT = minus(minuend, subtrahend, isNumeric)
	FEND
	FUNCTION tan(x)
		RESULT = tangent(x)
	FEND
	FUNCTION tanh(x)
		RESULT = hyperbolicTangent(x)
	FEND
	//////////////////////////////
	// ヘルパー関数
	//////////////////////////////
	FUNCTION digitsToString(d)
		indexOfLastWord = LENGTH(d) - 1
		str = ""
		w = d[0]
		IFB indexOfLastWord > 0 THEN
			str = str + w
			DIM i = 1
			WHILE i < indexOfLastWord
				ws = d[i] + ""
				k = LOG_BASE - LENGTH(ws)
				IF k THEN str = str + getZeroString(k)
				str = str + ws
				i = i + 1
			WEND
			w = d[i]
			ws = w + ""
			k = LOG_BASE - LENGTH(ws)
			IF k THEN str = str + getZeroString(k)
		ELSEIF w = 0 THEN
			RESULT = "0"
			EXIT
		ENDIF
		// Remove trailing zeros of last w.
		WHILE w MOD 10 = 0 AND w <> 0
			w = w / 10
		WEND
		RESULT = str + w
	FEND
	FUNCTION checkInt32(i, min, max)
		IF i <> VARTYPE(i, VAR_INTEGER) OR i < min OR i > max THEN RESULT = ERR_VALUE
	FEND
	FUNCTION checkRoundingDigits(d, i, rm, repeating = NULL)
		// Get the length of the first word of the array d.
		k = d[0]
		WHILE k >= 10
			i = i - 1
			k = k / 10
		WEND
		// Is the rounding digit in the first word of d?
		i = i - 1
		IFB i < 0 THEN
			i = i + LOG_BASE
			di = 0
		ELSE
			di = VAL(CEIL((i + 1) / LOG_BASE))
			i = i MOD LOG_BASE
		ENDIF
		// 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		RESULT = ERR_VALUE
		k = POWER(10, LOG_BASE - i)
		IFB di > UBound(d) THEN
			rd = 0
		ELSE
			rd = d[di] MOD k
		ENDIF
		IFB repeating = NULL THEN
			IFB i < 3 THEN
				IFB i = 0 THEN
					rd = rd / 100
				ELSEIF i = 1 THEN
					rd = rd / 10
				ENDIF
				r = rm < 4 AND rd = 99999 OR rm > 3 AND rd = 49999 OR rd = 50000 OR rd = 0
			ELSE
				IFB di + 1 > UBound(d) THEN
					n = 0
				ELSE
					n = d[di + 1]
				ENDIF
				r = (rm < 4 AND rd + 1 = k OR rm > 3 AND rd + 1 = k / 2) AND (n / k / 100) = POWER(10, i - 2) - 1 OR (rd = k / 2 OR rd = 0) AND (n / k / 100) = 0
			ENDIF
		ELSE
			IFB i < 4 THEN
				IFB i = 0 THEN
					rd = rd / 1000
				ELSEIF i = 1 THEN
					rd = rd / 100
				ELSEIF i = 2 THEN
					rd = rd / 10
				ENDIF
				r = (repeating OR rm < 4) AND rd = 9999 OR !repeating AND rm > 3 AND rd = 4999
			ELSE
				IFB di + 1 > UBound(d) THEN
					n = 0
				ELSE
					n = d[di + 1]
				ENDIF
				r = ((repeating OR rm < 4) AND rd + 1 = k OR (!repeating AND rm > 3) AND rd + 1 = k / 2) AND (n / k / 1000) = POWER(10, i - 3) - 1
			ENDIF
		ENDIF
		RESULT = VARTYPE(r, VAR_BOOLEAN)
	FEND
	FUNCTION convertBase(str, baseIn, baseOut)
		CONST NUMERALS = "0123456789abcdef"
		DIM arr[0] = 0
		DIM i = 0
		DIM strL = LENGTH(str)
		WHILE i < strL
			arrL = LENGTH(arr)
			WHILE TRUE
				arrL = arrL - 1
				IF arrL < 0 THEN BREAK
				arr[arrL] = arr[arrL] * baseIn
			WEND
			arr[0] = arr[0] + (POS(COPY(str, i+1, 1), NUMERALS) - 1)
			i = i + 1
			j = 0
			WHILE j < LENGTH(arr)
				IFB arr[j] > baseOut - 1 THEN
					IFB j + 1 > UBound(arr) THEN
						RESIZE(arr, j + 1)
						arr[j+1] = 0
					ENDIF
					arr[j+1] = arr[j+1] + INT(arr[j] / baseOut)
					arr[j] = arr[j] MOD baseOut
				ENDIF
				j = j + 1
			WEND
		WEND
		arrayReverse(arr)
		RESULT = SLICE(arr)
	FEND
	FUNCTION cosine2(Ctor, x)
		IFB isZero(x) THEN
			RESULT = SLICE(x)
			EXIT
		ENDIF
		// 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.
		xd = x
		xd = SLICE(xd, 2)
		len = LENGTH(xd)
		IFB len < 32 THEN
			k = GLOBAL.CEIL(len / 3)
			y = "" + (1 / tinyPow(4, k))
		ELSE
			k = 16
			y = "2.3283064365386962890625e-10"
		ENDIF
		precision = precision + k
		x = taylorSeries(Ctor, 1, times(x, y), Constructor(1))
		// Reverse argument reduction
		i = k
		WHILE i > 0
			i = i - 1
			cos2x = times(x, x, NULL)
			x = times(cos2x, cos2x, NULL)
			x = minus(x, cos2x, NULL)
			x = times(x, 8, NULL)
			x = plus(x, 1, NULL)
		WEND
		precision = precision - k
		RESULT = SLICE(x)
	FEND
	FUNCTION divide(dividend, divisor, pr = NULL, rm = NULL, dp = NULL, radix = NULL, isNumeric = FALSE)
		x = IIF(VARTYPE(dividend) < 8192, Constructor(dividend), dividend)
		y = IIF(VARTYPE(divisor) < 8192, Constructor(divisor), divisor)
		DIM sign = IIF(x[0] = y[0], 1, -1)
		xd = SLICE(x, 2)
		yd = SLICE(y, 2)
		DIM xIsZero = x[0] = 1 AND x[1] = 0 AND x[2] = 0
		DIM yIsZero = y[0] = 1 AND y[1] = 0 AND y[2] = 0
		DIM xIsInf = x[0] <> NULL AND x[1] = NULL AND !x[2]
		DIM yIsInf = y[0] <> NULL AND y[1] = NULL AND !y[2]
		DIM xIsNaN = x[0] = NULL AND x[1] = NULL AND x[2] = FALSE
		DIM yIsNaN = y[0] = NULL AND y[1] = NULL AND y[2] = FALSE
		// Either NaN, Infinity or 0?
		IFB xIsNaN OR yIsNaN OR xIsInf OR yIsInf OR xIsZero OR yIsZero THEN
			// Return NaN if either NaN, or both Infinity or 0.
			// x,yのどちらかNaNならばNaN、両方ともInfinityか0ならNaNを返す
			IFB (xIsNaN OR yIsNaN) OR (xIsInf AND yIsInf) OR (xIsZero AND yIsZero) THEN
				RESULT = "NaN"
			// xが0、yが±∞ならば±0を返す
			ELSEIF xIsZero OR yIsInf THEN
				RESULT = 0
			// yが0ならば±∞を返す
			ELSEIF yIsZero THEN
				RESULT = IIF(isNegative(x), "-", "") + "INF"
			ENDIF
			RESULT = Constructor(RESULT)
			EXIT
		ENDIF
		IFB radix <> NULL THEN
			logBase = 1
			e = x[1] - y[1]
		ELSE
			radix = BASE
			logBase = LOG_BASE
			value1 = x[1] / logBase
			value2 = y[1] / logBase
			e = GLOBAL.floor(x[1] / logBase) - GLOBAL.floor(y[1] / logBase)
		ENDIF
		yL = LENGTH(yd)
		xL = LENGTH(xd)
		DIM q = SAFEARRAY(0, 1)
		q[0] = sign
		q[1] = 0
		DIM qd[-1]
		// Result exponent may be one less than e.
		// The digit array of a Decimal from toStringBinary may have trailing zeros.
		IFB LENGTH(yd) > LENGTH(xd) THEN
			DIM tmp[LENGTH(yd)]
			SETCLEAR(tmp, 0)
			FOR i = 0 TO UBound(xd)
				tmp[i] = xd[i]
			NEXT
		ELSE
			tmp = xd
		ENDIF
		i = 0
		WHILE yd[i] = tmp[i]
			i = i + 1
			IF i = LENGTH(yd) THEN BREAK
		WEND
		IFB UBound(xd) >= i AND UBound(yd) >= i THEN
			bool = IIF(VAL(yd[i]) > VAL(xd[i]), TRUE, FALSE)
		ELSE
			bool = FALSE
		ENDIF
		IF bool THEN e = e - 1
		IFB pr = NULL THEN
			pr = precision
			sd = pr
			rm = rounding
		ELSEIF dp <> NULL THEN
			sd = pr + (x[1] - y[1]) + 1
		ELSE
			sd = pr
		ENDIF
		IFB sd < 0 THEN
			arrayPush(qd, 1)
			more = TRUE
		ELSE
			// Convert precision in number of base 10 digits to base 1e7 digits.
			sd = INT(sd / logBase + 2)
			i = 0
			// divisor < 1e7
			IFB yL = 1 THEN
				k = 0
				yd = yd[0]
				sd = sd + 1
				// k is the carry.
				WHILE (i < xL OR k) AND VARTYPE(sd, VAR_BOOLEAN)
					sd = sd - 1
					IF sd < 0 THEN BREAK
					IFB i > UBound(xd) THEN
						t = k * radix + 0
					ELSE
						t = k * radix + VAL(xd[i])
					ENDIF
					RESIZE(qd, i)
					qd[i] = INT(t / yd)
					k = INT(t MOD yd)
					i = i + 1
				WEND
				arrayMerge(q, qd)
				more = k OR i < xL
			ELSE
				// Normalise xd and yd so highest order digit of yd is >= base/2
				k = INT(base / (VAL(yd[0]) + 1))
				IFB k > 1 THEN
					yd = multiplyInteger(yd, k, base)
					xd = multiplyInteger(xd, k, base)
					yL = LENGTH(yd)
					xL = LENGTH(xd)
				ENDIF
				xi = yl
				rem = SLICE(xd, 0, yL - 1)
				remL = LENGTH(rem)
				// Add zeros to make remainder as long as divisor.
				WHILE remL < yL
					RESIZE(rem, remL)
					rem[remL] = 0
					remL = remL + 1
				WEND
				yz = SLICE(yd)
				arrayUnshift(yz, 0)
				yd0 = yd[0]
				IF yd[1] >= base / 2 THEN yd0 = VAL(yd0) + 1
				WHILE TRUE
					k = 0
					// Compare divisor and remainder.
					cmp = compare(yd, rem, yL, remL)
					// If divisor < remainder.
					IFB cmp < 0 THEN
						// Calculate trial digit, k.
						rem0 = rem[0]
						IF yL <> remL THEN rem0 = rem0 * radix + INT(rem[1])
						// k will be how many times the divisor goes into the current remainder.
						k = INT(rem0 / yd0)
						IFB k > 1 THEN
							IF k >= base THEN k = base - 1
							// product = divisor * trial digit.
							prod = multiplyInteger(yd, k, base)
							prodL = LENGTH(prod)
							remL = LENGTH(rem)
							// Compare product and remainder.
							cmp = compare(prod, rem, prodL, remL)
							// product > remainder.
							IFB cmp = 1 THEN
								k = k - 1
								// Subtract divisor from product.
								subtract(prod, IIF(yL < prodL, yz, yd), prodL, base)
							ENDIF
						ELSE
							IFB k = 0 THEN
								k = 1
								cmp = k
							ENDIF
							prod = SLICE(yd)
						ENDIF
						prodL = LENGTH(prod)
						IF prodL < remL THEN arrayUnshift(prod, 0)
						// Subtract product from remainder.
						subtract(rem, prod, remL, base)
						IFB cmp = -1 THEN
							remL = LENGTH(rem)
							cmp = compare(yd, rem, yL, remL)
							IFB cmp < 1 THEN
								k = k + 1
								subtract(rem, IIF(yL < remL, yz, yd), remL, base)
							ENDIF
						ENDIF
						remL = LENGTH(rem)
					ELSEIF cmp = 0 THEN
						k = k + 1
						rem = SAFEARRAY(-1)
						rem[0] = 0
					ENDIF
					IF LENGTH(qd) >= i THEN RESIZE(qd, i)
					IF LENGTH(q) >= i+2 THEN RESIZE(q, i+2)
					qd[i] = k
					q[i+2] = k
					i = i + 1
					IFB VARTYPE(cmp, VAR_BOOLEAN) AND VARTYPE(rem[0], VAR_BOOLEAN) THEN
						IF UBound(rem) < remL THEN RESIZE(rem, remL)
						IFB xi > UBound(xd) THEN
							rem[remL] = 0
						ELSE
							rem[remL] = xd[xi]
						ENDIF
						remL = remL + 1
					ELSE
						TRY
							rem[0] = xd[xi]
						EXCEPT
							rem[0] = NULL
						ENDTRY
						remL = 1
					ENDIF
					IFB (xi < xL OR UBound(rem) > 0) AND VARTYPE(sd, VAR_BOOLEAN) THEN
						xi = xi + 1
						sd = sd - 1
					ELSE
						BREAK
					ENDIF
				WEND
				more = IIF(rem[0]<>NULL, TRUE, FALSE)
			ENDIF
			IFB !qd[0] THEN
				arrayShift(qd)
				RESIZE(q, 1)
				arrayMerge(q, qd)
			ENDIF
		ENDIF
		// logBase is 1 when divide is being used for base conversion.
		IFB logBase = 1 THEN
			q[1] = e
			inexact = more
			RESULT = SLICE(q)
			EXIT
		ELSE
			// To calculate q.e, first get the number of digits of qd[0].
			i = 1
			k = qd[0]
			WHILE k >= 10
				k = k / 10
				i = i + 1
			WEND
			q[1] = i + e * logBase - 1
			q = SLICE(q)
			dp = IIF(dp = NULL, FALSE, dp)
			RESULT = finalise(q, IIF(dp, pr + q[1] + 1, pr), rm, more)
			IFB external THEN
				IF isNumeric = NULL THEN EXIT
				RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
			ELSE
				RESULT = SLICE(RESULT)
			ENDIF
			EXIT
		ENDIF
	FEND
	FUNCTION finalise(x, sd = NULL, rm = NULL, isTruncated = FALSE)
		x = IIF(VARTYPE(x) < 8192, Constructor(x), x)
		xd = SLICE(x, 2)
		WHILE sd <> NULL
			// Get the length of the first word of the digits array xd.
			digits = 1
			k = VAL(xd[0])
			WHILE k >= 10
				digits = digits + 1
				k = k / 10
			WEND
			i = sd - digits
			// Is the rounding digit in the first word of xd?
			IFB i < 0 THEN
				i = i + LOG_BASE
				j = sd
				xdi = 0
				w = xd[xdi]
				// Get the rounding digit at index j of w.
				rd = w / POWER(10, digits - j - 1) MOD 10
			ELSE
				xdi = GLOBAL.CEIL((i+1)/LOG_BASE)
				k = LENGTH(xd)
				IFB xdi >= k THEN
					IFB isTruncated THEN
						// Needed by `naturalExponential`, `naturalLogarithm` and `squareRoot`.
						WHILE k <= xdi
							arrayPush(xd, 0)
							k = k + 1
						WEND
						rd = 0
						w = rd
						digits = 1
						i = i MOD LOG_BASE
						j = i - LOG_BASE + 1
					ELSE
						BREAK
					ENDIF
				ELSE
					k = xd[xdi]
					w = k
					// Get the number of digits of w.
					digits = 1
					WHILE k >= 10
						digits = digits + 1
						k = k / 10
					WEND
					// Get the index of rd within w.
					i = i MOD 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 = IIF(j < 0, 0, INT(w / POWER(10, digits - j - 1)) MOD 10)
				ENDIF
			ENDIF
			// Are there any non-zero digits after the rounding digit?
			// isTruncated = 
			//IF isTruncated OR sd < 0 OR x[xdi+3] = EMPTY THEN 
			//isTruncated = FALSE
			IFB isTruncated THEN
			ELSEIF sd < 0 THEN
				isTruncated = TRUE
			ELSEIF xdi > UBound(xd) THEN
				isTruncated = TRUE
			ELSEIF IIF(j < 0, w, w MOD POWER(10, digits - j - 1)) THEN
				isTruncated = TRUE
			ENDIF
			// 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.
			IFB i > 0 THEN
				tmp = IIF(j > 0, w / POWER(10, digits - j), 0)
			ELSE
				IFB xdi = 0 THEN
					tmp = 0
				ELSE
					tmp = xd[xdi - 1] MOD 10
				ENDIF
			ENDIF
			IF isTruncated = NULL THEN isTruncated = FALSE
			IFB rm < 4 THEN
				roundUp = (VARTYPE(rd, VAR_BOOLEAN) OR VARTYPE(isTruncated, VAR_BOOLEAN)) AND (rm = 0 OR VARTYPE(rm = IIF(x[0] < 0, 3, 2), VAR_BOOLEAN))
			ELSE
				roundUp1 = rd > 5
				roundUp2 = rd = 5
				roundUp3 = rm = 4
				roundUp4 = isTruncated
				roundUp5 = rm = 6
				roundUp6 = VARTYPE(bitAnd("" + tmp, "1"), VAR_BOOLEAN)
				roundUp7= (rm = IIF(x[0] < 8, 8, 7))
				roundUp = (roundUp1 OR roundUp2 AND (roundUp3 OR roundUp4 OR roundUp5 AND roundUp6 OR roundUp7))
			ENDIF
TEXTBLOCK
IFB rm < 4 THEN
	roundUp = (VARTYPE(rd, VAR_BOOLEAN) OR VARTYPE(isTruncated, VAR_BOOLEAN)) AND (rm = 0 OR VARTYPE(rm = IIF(x[0] < 0, 3, 2), VAR_BOOLEAN))
ELSE
	roundUp = rd > 5 OR rd = 5 AND (rm = 4 OR isTruncated OR rm = 6 AND _
			// Check whether the digit to the left of the rounding digit is odd.
			bitAnd(tmp, 1) OR rm = IIF(x[0] < 0, 8, 7) _
		)
ENDIF
ENDTEXTBLOCK
TEXTBLOCK
			roundUp = IIF(rm < 4, _
							// truepart
							(VARTYPE(rd, VAR_BOOLEAN) OR VARTYPE(isTruncated, VAR_BOOLEAN)) AND (rm = 0 OR VARTYPE(rm = IIF(x[0] < 0, 3, 2), VAR_BOOLEAN)), _
							// falsepart
							rd > 5 OR rd = 5 AND (rm = 4 OR isTruncated OR rm = 6 AND _
								// Check whether the digit to the left of the rounding digit is odd.
								bitAnd(tmp, 1) OR rm = IIF(x[0] < 0, 8, 7) _
							) _
						)
ENDTEXTBLOCK
			IFB sd < 1 OR !xd[0] THEN
				RESIZE(xd, 0)
				IFB roundUp THEN
					// Convert sd to decimal places.
					sd = sd - (x[1] + 1)
					// 1, 0.1, 0.01, 0.001, 0.0001 etc.
					x[2] = POWER(10, (LOG_BASE - sd MOD LOG_BASE) MOD LOG_BASE)
					x[1] = -1 * sd
				ELSE
					// Zero.
					RESIZE(x, 2)
					x[2] = 0
					x[1] = 0
				ENDIF
				RESULT = SLICE(x)
				EXIT
			ENDIF
			// Remove excess digits.
			IFB i = 0 THEN
				RESIZE(xd, xdi-1)
				RESIZE(x, 1)
				arrayMerge(x, xd)
				k = 1
				xdi = xdi - 1
			ELSE
				RESIZE(xd, xdi)
				RESIZE(x, 1)
				arrayMerge(x, xd)
				k = POWER(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.
				IFB j > 0 THEN
					RESIZE(x, xdi+2)
					xd[xdi] = INT(INT(w / POWER(10, digits-j)) MOD POWER(10, j)) * k
					x[xdi+2] = xd[xdi]
				ELSE
					RESIZE(x, xdi+2)
					xd[xdi] = 0
					x[xdi+2] = xd[xdi]
				ENDIF
			ENDIF
			IFB roundUp THEN
				WHILE TRUE
					// Is the digit to be rounded up in the first word of xd?
					IFB xdi = 0 THEN
						// i will be the length of xd[0] before k is added.
						i = 1
						j = VAL(xd[0])
						WHILE j >= 10
							i = i + 1
							j = j / 10
						WEND
						xd[0] = VAL(xd[0]) + k
						x[2] = xd[0]
						j = VAL(xd[0])
						k = 1
						WHILE j >= 10
							k = k + 1
							j = j / 10
						WEND
						// if i != k the length has increased.
						IFB i <> k THEN
							x[1] = x[1] + 1
							IF x[2] = BASE THEN x[2] = 1
						ENDIF
						BREAK
					ELSE
						xd[xdi] = xd[xdi] + k
						IF xd[xdi] <> BASE THEN BREAK
						xd[xdi] = 0
						xdi = xdi - 1
						k = 1
					ENDIF
				WEND
			ENDIF
			// Remove trailing zeros.
			FOR i = UBound(xd) TO 0 STEP -1
				IFB xd[i] = 0 THEN
					arrayPop(xd)
				ELSE
					BREAK
				ENDIF
			NEXT
			BREAK
		WEND
		IFB external THEN
			// Overflow?
			IFB x[1] > maxE THEN
				// Infinity
				RESIZE(x, 2)
				x[1] = NULL
				x[2] = FALSE
				RESULT = SLICE(x)
				EXIT
			// Underflow?
			ELSEIF x[1] < minE THEN
				RESIZE(x, 2)
				x[1] = 0
				x[2] = 0
				RESULT = SLICE(x)
				EXIT
			ENDIF
		ENDIF
		RESIZE(x, 1)
		arrayMerge(x, xd)
		RESULT = SLICE(x)
	FEND
	FUNCTION finiteToString(x, isExp = FALSE, sd = EMPTY)
		IFB !isFinite(x) THEN
			RESULT = nonFiniteToString(x)
			EXIT
		ENDIF
		e = x[1]
		xd = SLICE(x, 2)
		str = digitsToString(xd)
		len = LENGTH(str)
		IFB isExp THEN
			k = sd - len
			IFB sd AND k > 0 THEN
				str = COPY(str, 1, 1) + "." + COPY(str, 2) + getZeroString(k)
			ELSEIF len > 1 THEN
				str = COPY(str, 1, 1) + "." + COPY(str, 2)
			ENDIF
			str = str + IIF(x[1] < 0, "e", "e+") + x[1]
		ELSEIF e < 0 THEN
			str = "0." + getZeroString(-1 * e - 1) + str
			k = sd - len
			IF sd AND k > 0 THEN str = str + getZeroString(k)
		ELSEIF e >= len THEN
			str = str + getZeroString(e + 1 - len)
			k = sd - e - 1
			IF sd AND k > 0 THEN str = str + "." + getZeroString(k)
		ELSE
			k = e + 1
			IF k < len THEN str = COPY(str, 1, k) + "." + COPY(str, k+1)
			k = sd - len
			IFB sd AND k > 0 THEN
				IF e + 1 = len THEN str = str + "."
				str = str + getZeroString(k)
			ENDIF
		ENDIF
		RESULT = str
	FEND
	FUNCTION getBase10Exponent(digits[], e)
		DIM w = digits[0]
		e = e * LOG_BASE
		WHILE w >= 10
			e = e + 1
			w = w / 10
		WEND
		RESULT = e
	FEND
	FUNCTION getLN10(Ctor, sd, pr = NULL)
		IFB sd > LN10PRECISION THEN
			// Reset global state in case the exception is caught.
			external = TRUE
			IF pr THEN precision = pr
		ENDIF
		RESULT = finalise(Constructor(LN10), sd, 1, TRUE)
	FEND
	FUNCTION getPI(Ctor, sd, rm)
		IFB sd > PI_PRECISION THEN
			RESULT = ERR_VALUE
		ELSE
			RESULT = finalise(Constructor(PI), sd, rm, TRUE)
		ENDIF
	FEND
	FUNCTION getPrecision(digits)
		w = LENGTH(digits) - 1
		len = w * LOG_BASE + 1
		w = digits[w]
		// If non-zero...
		IFB w <> 0 THEN
			// Subtract the number of trailing zeros of the last word.
			WHILE w MOD 10 = 0
				len = len - 1
				w = w / 10
			WEND
			// Add the number of digits of the first word.
			w = digits[0]
			WHILE VAL(w) >= 10
				len = len + 1
				w = w / 10
			WEND
		ENDIF
		RESULT = len
	FEND
	FUNCTION getZeroString(k)
		zs = ""
		WHILE k > 0
			zs = zs + "0"
			k = k - 1
		WEND
		RESULT = zs
	FEND
	FUNCTION intPow(Ctor, x, n, pr)
		DIM isTruncated
		DIM r = Constructor("1")
		// Max n of 9007199254740991 takes 53 loop iterations.
		// Maximum digits array length; leaves [28, 34] guard digits.
		DIM k = CEIL(pr / LOG_BASE + 4)
		external = FALSE
		WHILE TRUE
			IFB n MOD 2 THEN
				r = times(r, x, NULL)
				rd = SLICE(r, 2)
				IF truncate(rd, k) THEN isTruncated = TRUE
			ENDIF
			n = GLOBAL.floor(n/2)
			IFB n = 0 THEN
				rd = SLICE(r, 2)
				// To ensure correct rounding when r.d is truncated, increment the last word if it is zero.
				n = LENGTH(rd) - 1
				IF isTruncated AND rd[n] = 0 THEN rd[n] = rd[n] + 1
				BREAK
			ENDIF
			x = times(x, x, NULL)
			xd = SLICE(x, 2)
			truncate(xd, k)
		WEND
		external = TRUE
		RESULT = r
	FEND
	FUNCTION isOdd(n)
		IFB !isInteger(n) THEN
			RESULT = ERR_VALUE
			EXIT
		ENDIF
		RESULT = IIF(modulo(n, 2) = "0", FALSE, TRUE)
	FEND
	FUNCTION maxOrMin(Ctor, args, ltgt)
		RESULT = ERR_VALUE
	FEND
	FUNCTION naturalExponential(x, sd = NULL, isNumeric = FALSE)
		x = IIF(VARTYPE(x) < 8192, Constructor(x), x)				
		rep = 0
		i = 0
		k = 0
		rm = rounding
		pr = precision
		// 0/NaN/Infinity
		IFB (x[0] = 1 AND x[1] = 0 AND x[2] = 0) OR x[1] = NULL OR x[1] > 17 THEN
			
		ENDIF
		IFB sd = NULL THEN
			external = FALSE
			wpr = pr
		ELSE
			wpr = sd
		ENDIF
		t = Constructor(0.03125)
		// while abs(x) >= 0.1
		WHILE x[1] > -2
			// x = x / 2^5
			x = times(x, t)
			k = k + 5
		WEND
		// 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 = INT(GLOBAL.LN(POWER(2, k)) / MathLN10 * 2 + 5)
		wpr = wpr + guard
		sum = Constructor("1")
		pow = sum
		denominator = pow
		precision = wpr
		WHILE TRUE
			pow = finalise(times(pow, x), wpr, 1)
			i = i + 1
			denominator = times(denominator, i)
			t = plus(sum, divide(pow, denominator, wpr, 1))
			td = SLICE(t, 2)
			sumd = SLICE(sum, 2)
			IFB COPY(digitsToString(td), 1, wpr) = COPY(digitsToString(sumd), 1, wpr) THEN
				j = k
				j = j - 1
				WHILE j >= 0
					sum = finalise(times(sum, sum), wpr, 1)
					j = j - 1
				WEND
				// 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.				
				IFB sd = NULL THEN
					sumd = SLICE(sum, 2)
					IFB rep < 3 AND checkRoundingDigits(sumd, wpr - guard, rm, rep) THEN
						precision = wpr = wpr + 10
						t = Constructor(1)
						pow = t
						denominator = pow
						i = 0
						rep = rep + 1
					ELSE
						precision = pr
						RESULT = finalise(sum, precision, rm, external = TRUE)
						IF isNumeric = NULL THEN EXIT
						RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))						
						EXIT
					ENDIF
				ELSE
					precision = pr
					RESULT = sum
					IF isNumeric = NULL THEN EXIT
					RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
					EXIT
				ENDIF
			ENDIF
			sum = t
		WEND
	FEND
	FUNCTION naturalLogarithm(y, sd = NULL, isNumeric = FALSE)
		y = IIF(VARTYPE(y) < 8192, Constructor(y), y)		
		n = 1
		guard = 10
		x = y
		xd = SLICE(x, 2)
		json = "{'precision':20, 'rounding':7}"
		Ctor = JSON.Parse(REPLACE(json, "'", "<#DBL>"))
		rm = rounding
		pr = precision
		// Is x negative or Infinity, NaN, 0 or 1?
		IFB x[0] < 0 THEN
//			RESULT = Constructor(0)
			EXIT
		ENDIF
		IFB sd = NULL THEN
			external = FALSE
			wpr = pr
		ELSE
			wpr = sd
		ENDIF
		wpr = wpr + guard
		precision = wpr
		c = digitsToString(xd)
		c0 = COPY(c, 1, 1)
		e = x[1]
		IFB .lessThan(GLOBAL.ABS(e), "1.5e+15") THEN
			// 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 AND c0 <> 1 OR c0 = 1 AND COPY(c, 1, 1) > 3
				x = times(x, y)
				xd = SLICE(x, 2)
				c = digitsToString(xd)
				c0 = COPY(c, 1, 1)
				n = n + 1
			WEND
			e = x[1]
			IFB c0 > 1 THEN
				x = Constructor("0." + c)
				e = e + 1
			ELSE
				x = Constructor(c0 + "." + COPY(c, 2))
			ENDIF
		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 = times(getLn10(Ctor, wpr + 2, pr), e)
			x = plus(naturalLogarithm(Constructor(c0 + "." + COPY(c, 2)), wpr - guard), t)
			precision = pr
			external = TRUE
			RESULT = IIF(sd = NULL, finalise(x, pr, rm, external), x)
			EXIT
		ENDIF
		// 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)
		x = divide(minus(x, "1"), plus(x, "1"), wpr, 1)
		numerator = x
		sum = numerator
		sumd = SLICE(sum, 2)
		x2 = finalise(times(x, x), wpr, 1)
		denominator = 3
		WHILE TRUE
			numerator = finalise(times(numerator, x2), wpr, 1)
			t = plus(sum, divide(numerator, constructor(denominator), wpr, 1, NULL, NULL, NULL), NULL)
			td = SLICE(t, 2)
			IFB COPY(digitsToString(td), 1, wpr) = COPY(digitstoString(sumd), 1, wpr) THEN
				sum = times(sum, "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 THEN sum = plus(sum, times(getLn10(Ctor, wpr + 2, pr), e, NULL), NULL)
				sum = divide(sum, Constructor(n), wpr, 1)
				sumd = SLICE(sum, 2)
				// 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.
				IFB sd = NULL THEN
					rep = 0
					IFB checkRoundingDigits(sumd, wpr - guard, rm, rep) THEN
						wpr = wpr + guard
						precision = wpr
						x = divide(minus(x1, "1"), plus(x1, "1"), wpr, 1)
						numerator = x
						t = numerator
						x2 = finalise(times(x, x), wpr, 1)
						rep = 1
						denominator = wpr
					ELSE
						precision = pr
						external = TRUE
						RESULT = finalise(sum, precision, rm, external)
						IF isNumeric = NULL THEN EXIT
						RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
						EXIT
					ENDIF
				ELSE
					precision = pr
					RESULT = sum
					IF isNumeric = NULL THEN EXIT
					RESULT = IIF(isNumeric, toNumber(RESULT), toString(RESULT))
					EXIT
				ENDIF
			ENDIF
			sum = t
			sumd = SLICE(sum, 2)
			denominator = denominator + 2
		WEND
	FEND
	FUNCTION nonFiniteToString(x[])
		IFB x[0] = NULL AND x[1] = NULL AND x[2] = FALSE THEN
			RESULT = "NaN"
		ELSEIF CHKNUM(x[0]) AND x[1] = NULL AND x[2] = FALSE THEN
			RESULT = IIF(x[0] > 0, "", "-") + "INF"
		ENDIF
	FEND
	FUNCTION parseDecimal(x, str)
		// Decimal point?
		e = POS(".", str) - 1
		IF e <> 0 THEN str = REPLACE(str, ".", "")
		// Exponential form?
		DIM i = POS("e", str)
		IFB i <> 0 THEN
			// Determine exponent.
			IF e < 0 THEN e = i
			e = VAL(COPY(str, i+1))
			str = COPY(str, 1, i-1)
		ELSEIF e < 0 THEN
			// Integer
			e = LENGTH(str)
		ENDIF
		// Determine leading zeros.
		i = 0
		WHILE COPY(str, i+1, 1) = "0"
			i = i + 1
		WEND
		// Determine trailing zeros.
		len = LENGTH(str)
		WHILE COPY(str, len, 1) = "0"
			len = len - 1
			IF len = 0 THEN BREAK
		WEND
		str = COPY(str, i+1, len-i)
		IFB str <> 0 AND str <> "" THEN
			len = len - i
			e = e - i - 1
			RESIZE(x, 1)
			x[1] = e
			//x[2] = 0
			// 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) MOD LOG_BASE
			IF e < 0 THEN i = i + LOG_BASE
			IFB i < len THEN
				IF i THEN arrayPush(x, VAL(COPY(str, 1, i)))
				len = len - LOG_BASE
				WHILE i < len
					arrayPush(x, VAL(COPY(str, i+1, LOG_BASE)))
					i = i + LOG_BASE
				WEND
				str = COPY(str, i+1)
				i = LOG_BASE - LENGTH(str)
			ELSE
				i = i - len
			ENDIF
			WHILE i > 0
				str = str + "0"
				i = i - 1
			WEND
			arrayPush(x, VAL(str))
			IFB external THEN
				// Overflow?
				IFB x[1] = maxE THEN
					// Infinity.
					x[1] = NULL
					x[2] = FALSE
				// Underflow?
				ELSEIF x[1] = minE THEN
					// Zero.
					x[1] = 0
					x[2] = 0
				ENDIF
			ENDIF
		ELSE
			// Zero.
			RESIZE(x, 2)
			x[1] = 0
			x[2] = 0
		ENDIF
		RESULT = SLICE(x)
	FEND
	FUNCTION parseOther(x, str)
		IF POS("Infinity", str) THEN str = REPLACE(str, "Infinity", "INF")
		IFB POS("_", str) <> 0 THEN
			
		ELSEIF str = "INF" OR str = "NaN" THEN
			IF str = "NaN" THEN x[0] = NULL
			RESIZE(x, 2)
			x[1] = NULL
			x[2] = FALSE
			RESULT = SLICE(x)
			EXIT
		ENDIF
		IFB reTest(str, isHex) THEN
			_base = 16
			str = STRCONV(str, SC_LOWERCASE)
		ELSEIF reTest(str, isBinary) THEN
			_base = 2
		ELSEIF reTest(str, isOctal) THEN
			_base = 8
		ELSE
			
			EXIT
		ENDIF
		// Is there a binary exponent part?
		i = POS("p", str)
		IFB i > 0 THEN
			p = COPY(str, (i+1)+1)
			str = COPY(str, 2+1, i+1)
		ELSE
			p = NULL
			str = COPY(str, 2+1)
		ENDIF
		// Convert `str` as an integer then divide the result by `base` raised to a power such that the
		// fraction part will be restored.
		i = POS(".", str)
		isFloat = i >= 1
		json = "{'precision':20, 'rounding':7}"
		Ctor = JSON.Parse(REPLACE(json, "'", "<#DBL>"))
		IFB isFloat THEN
			str = REPLACE(str, ".", "")
			len = LENGTH(str)
			i = len - i
			// log[10](16) = 1.2041... , log[10](88) = 1.9444....
			divisor = intPow(Ctor, Constructor(base), i, i * 2)
		ELSE
			len = NULL
			divisor = NULL
		ENDIF
		xd = convertBase(str, _base, base)
		xe = LENGTH(xd) - 1
		// Remove trailing zeros.
		i = xe
		WHILE xd[i] = 0
			i = i - 1
			arrayPop(xd)
		WEND
		IFB i < 0 THEN
//			RESULT = 
			EXIT
		ENDIF
		RESIZE(x, 1)
		x[1] = getBase10Exponent(xd, xe)
		arrayMerge(x, 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 THEN x = divide(x, divisor, len * 4)
		// Multiply by the binary exponent part if present.
		IF p <> NULL THEN x = times(x, POWER(2, p))
		external = TRUE
		RESULT = SLICE(x)
	FEND
	FUNCTION sine2(Ctor, x)
		xd = x
		xd = SLICE(xd, 2)
		len = LENGTH(xd)
		IFB len < 3 THEN
			RESULT = IIF(isZero(x), x, taylorSeries(Ctor, 2, x, x))
			EXIT
		ENDIF
		// 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 * GLOBAL.SQRT(len)
		k = INT(IIF(k > 16, 16, k))
		x = times(x, 1 / tinyPow(5, k), NULL)
		x = taylorSeries(Ctor, 2, x, x)
		// Reverse argument reduction
		d5 = Constructor(5)
		d16 = Constructor(16)
		d20 = Constructor(20)
		WHILE k > 0
			k = k - 1
			sin2x = times(x, x, NULL)
			x = times(x, plus(d5, times(sin2x, minus(times(d16, sin2x, NULL), d20, NULL), NULL), NULL), NULL)
		WEND
		RESULT = SLICE(x)
	FEND
	FUNCTION taylorSeries(Ctor, n, x, y, isHyperbolic = NULL)
		i = 1
		pr = precision
		k = GLOBAL.CEIL(pr / LOG_BASE)
		external = FALSE
		x2 = times(x, x)
		u = Constructor(y)
		WHILE TRUE
			multiplicand = times(u, x2)
			multiplier = Constructor(n * (n + 1))
			t = divide(multiplicand, multiplier, pr, 1)
			n = n + 2
			isHyperbolic = IIF(isHyperbolic = NULL, FALSE, isHyperbolic)
			u = IIF(isHyperbolic, plus(y, t), minus(y, t))
			y = divide(times(t, x2), Constructor(n * (n + 1)), pr, 1)
			n = n + 2
			t = plus(u, y)
			td = SLICE(t, 2)
			ud = SLICE(u, 2)
			IFB !(UBound(td) < k) THEN
				j = k
				TRY
					WHILE td[j] = ud[j] AND j >= 0
						j = j - 1
						IF j = 0 THEN BREAK 2
					WEND
				EXCEPT
				ENDTRY
				IF j = -1 THEN BREAK
			ENDIF
			j = u
			u = y
			y = t
			t = j
			i = i + 1			
		WEND
		external = TRUE
		RESIZE(td, k)
		RESIZE(t, 1)
		arrayMerge(t, td)
		RESULT = SLICE(t)
	FEND
	FUNCTION tinyPow(b, e)
		DIM n = b
		e = e - 1
		WHILE e > 0
			n = n * b
			e = e - 1
		WEND
		RESULT = n
	FEND
	FUNCTION toLessThanHalfPi(Ctor, x)
		isNeg = x[0] < 0
		_pi = getPi(Ctor, Ctor.precision, 1)
		halfPi = times(_pi, "0.5", NULL)
		x = absoluteValue(x, NULL)
		IFB lte(x, halfPi) THEN
			quadrant = IIF(isNeg, 4, 1)
			RESULT = SLICE(x)
			EXIT
		ENDIF
		t = divToInt(x, pi)
		IFB isZero(t) THEN
			quadrant = IIF(isNeg, 3, 2)
		ELSE
			x = minus(x, times(t, pi))
			// 0 <= x <pi
			IFB lte(x, halfPi) THEN
				quadrant = IIF(isOdd(t), IIF(isNeg, 2, 3), IIF(isNeg, 4, 1))
				RESULT = SLICE(x)
				EXIT
			ENDIF
			quadrant = IIF(isOdd(t), IIF(isNeg, 1, 4), IIF(isNeg, 3, 2))
		ENDIF
		RESULT = abs(minus(x, pi))
	FEND
	FUNCTION toLessThanHalfPi2(Ctor, x)
		isNeg = x[0] < 0
		_pi = getPi(Ctor, precision, 1)
		halfPi = times(_pi, "0.5", NULL)
		x = absoluteValue(x, NULL)
		IFB lte(x, halfPi) THEN
			quadrant = IIF(isNeg, 4, 1)
			RESULT = SLICE(x)
			EXIT
		ENDIF
		t = divToInt(x, pi)
		IFB isZero(t) THEN
			quadrant = IIF(isNeg, 3, 2)
		ELSE
			x = minus(x, times(t, pi), NULL)
			// 0 <= x <pi
			IFB lte(x, halfPi) THEN
				quadrant = IIF(isOdd(t), IIF(isNeg, 2, 3), IIF(isNeg, 4, 1))
				RESULT = SLICE(x)
				EXIT
			ENDIF
			quadrant = IIF(isOdd(t), IIF(isNeg, 1, 4), IIF(isNeg, 3, 2))
		ENDIF
		RESULT = abs(minus(x, pi))
	FEND
	FUNCTION toStringBinary(x, baseOut, sd, rm)
		x = IIF(VARTYPE(x) < 8192, Constructor(x), x)
		isExp = IIF(sd <> NULL, TRUE, FALSE)
		IFB isExp THEN
			checkInt32(sd, 1, MAX_DIGITS)
			IFB rm = NULL THEN
				rm = rounding
			ELSE
				checkInt32(rm, 0, 8)
			ENDIF
		ELSE
			sd = precision
			rm = rounding
		ENDIF
		IFB !isFinite(x) THEN
			str = nonFiniteToString(x)
		ELSE
			str = finiteToString(x)
			i = POS(".", str) - 1
			// 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
			IFB isExp THEN
				_base = 2
				IFB baseOut = 16 THEN
					sd = sd * 4 - 3
				ELSEIF baseOut = 8 THEN
					sd = sd * 3 - 2
				ENDIF
			ELSE
				_base = baseOut
			ENDIF
		ENDIF
		// 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.
		IFB i >= 0 THEN
			str = REPLACE(str, ".", "")
			y = Constructor(1)
			y[1] = LENGTH(str) - i
			yd = convertBase(finiteToString(y), 10, _base)
			RESIZE(y, 1)
			arrayMerge(y, yd)
			y[1] = LENGTH(yd)
		ENDIF
		xd = convertBase(str, 10, _base)
		len = LENGTH(xd)
		e = len
		// Remove trailing zeros.
		len = len - 1
		WHILE xd[len] = 0
			arrayPop(xd)
			IF len = 0 THEN BREAK
			len = len - 1
		WEND
		IFB !xd[0] THEN
			str = IIF(isExp, "0p+0", "0")
		ELSE
			IFB i < 0 THEN
				e = e - 1
				roundUp = FALSE
			ELSE
				// 修正
				x = Constructor(x)
				x = RESIZE(x, 1)
				arrayMerge(x, xd)
				x[1] = e
				x = divide(x, y, sd, rm, 0, base)
				xd = SLICE(x)
				e = x[1]
				roundUp = inexact
			ENDIF
			// The rounding digit, i.e. the digit after the digit that may be rounded up.
			IFB sd > UBound(xd) THEN
				i = NULL
				roundUp = roundUp OR FALSE
			ELSE
				i = xd[sd]
				roundUp = roundUp OR xd[sd + 1] <> NULL
			ENDIF
			k = _base / 2
			IFB rm < 4 THEN
				// (i !== void 0 || roundUp) && (rm === 0 || rm === (x.s < 0 ? 3 : 2))
				roundUp = (i = NULL OR roundUp) AND (rm = 0 OR rm = IIF(x[0] < 0, 3, 2))
			ELSE
				// i > k || i === k && (rm === 4 || roundUp || rm === 6 && xd[sd - 1] & 1 ||
            	// rm === (x.s < 0 ? 8 : 7));
				bit = IIF(sd - 1 > UBound(xd), 0, 1)
				roundUp = (i > k OR i = k AND (rm = 4 OR roundUp OR rm = 6 AND bitAnd(bit, 1)) OR rm = IIF(x[0] < 0, 8, 7))
			ENDIF
//			roundUp = IIF(rm < 4, _
//						(i <> NULL OR roundUp) AND (rm = 0 OR rm = IIF(x[0] < 0, 3, 2)), _
//						i > k OR i = k AND (rm = 4 OR roundUp OR rm = 6 AND xd[sd - 1] AND 1 OR rm = IIF(x[0] < 0, 8, 7))
			RESIZE(xd, sd)
			IFB roundUp THEN
				// Rounding up may mean the previous digit has to be rounded up and so on.
				sd = sd - 1
				WHILE xd[sd] > base - 1
					xd[sd] = 0
					IFB !sd THEN
						e = e + 1
						arrayUnshift(xd)
					ENDIF
				WEND
			ENDIF
			// Determine trailing zeros.
			len = LENGTH(xd)
			WHILE !xd[len - 1]
				len = len - 1
			WEND
			// E.g. [4, 11, 15] becomes 4bf.
			str = ""
			FOR i = 0 TO len - 1
				str = str + COPY(NUMERALS, VAL(xd[i]) + 1, 1)
			NEXT
			// Add binary exponent suffix?
			IFB isExp THEN
				IFB len > 1 THEN
					IFB baseOut = 16 OR baseOut = 8 THEN
						i = IIF(baseOut = 16, 4, 3)
						WHILE len MOD i
							str = str + "0"
							len = len + 1
						WEND
						xd = convertBase(str, base, baseOut)
						len = xd
						WHILE !xd[len - 1]
							len = len - 1
						WEND
						// xd[0] will always be be 1
						str = "1"
						FOR i = 1 TO len
							str = str + COPY(NUMERALS, xd[i], 1)
						NEXT
					ELSE
						str = COPY(str, 1, 1) + "." + COPY(str, 2)
					ENDIF
				ENDIF
			ELSEIF e < 0 THEN
				WHILE e < 0
					str = "'0" + str
					e = e + 1
				WEND
				str = "0." + str
			ELSE
				e = e + 1
				IFB e > len THEN
					FOR e = e - len TO 1 STEP -1
						str = str + "0"
					NEXT
				ELSEIF e < len THEN
					str = COPY(str, 1, e) + "." + COPY(str, e)
				ENDIF
			ENDIF
			str = IIF(baseOut = 16, "0x", IIF(baseOut = 2, "0b", IIF(baseOut = 8, "0o", ""))) + str
		ENDIF
		RESULT = IIF(x[0] < 0, "-" + str, str)
	FEND
	FUNCTION truncate(arr, len)
		IFB LENGTH(arr) > len THEN
			RESIZE(arr, len)
			RESULT = TRUE
			EXIT
		ENDIF
	FEND
	//////////////////////////////
	// その他
	//////////////////////////////
	FUNCTION compare(a, b, aL, bL)
		IFB aL <> bL THEN
			r = IIF(aL > bL, 1, -1)
		ELSE
			r = 0
			i = r
			WHILE i < aL
				IFB a[i] <> b[i] THEN
					r = IIF(a[i] > b[i], 1, -1)
					BREAK
				ENDIF
				i = i + 1
			WEND
		ENDIF
		RESULT = r
	FEND
	FUNCTION Constructor(v)
		CONST number = 5
		CONST string = 258
		DIM x = SAFEARRAY(-1)
		// Duplicate.
		IFB isDecimalInstance(v) THEN
			x[0] = v[0]
			vd = SLICE(v, 2)
			IFB external THEN
				IFB !LENGTH(vd) OR v[1] > maxE THEN
					// Infinity.
					RESIZE(x, 2)
					x[1] = NULL
					x[2] = NULL
				ELSEIF v[1] < minE THEN
					// Zero.
					RESIZE(x, 2)
					x[1] = 0
					x[2] = 0
				ELSE
					RESIZE(x, 1)
					x[1] = v[1]
					arrayMerge(x, vd)
				ENDIF
			ELSE
				RESIZE(x, 1)
				x[1] = v[1]
				arrayMerge(x, vd)
			ENDIF
			RESULT = SLICE(x)
			EXIT
		ENDIF
		t = VARTYPE(v)
		IFB t = number THEN
			IFB v = 0 THEN
				RESIZE(x, 2)
				x[0] = IIF(1/v<0, -1, 1)
				x[1] = 0
				x[2] = 0
				RESULT = SLICE(x)
				EXIT
			ENDIF
			IFB v < 0 THEN
				v = -1 * v
				x[0] = -1
			ELSE
				x[0] = 1
			ENDIF
			// Fast path for small integers.
			IFB v < POWER(10, 7) THEN
				IFB v = VARTYPE(v, VAR_INTEGER) THEN
					e = 0
					i = v
					WHILE i >= 10
						e = e + 1
						i = i / 10
					WEND
					IFB external THEN
						IFB e > maxE THEN
							RESIZE(x, 2)
							x[1] = NULL
							x[2] = NULL
						ELSEIF e < minE THEN
							RESIZE(x, 2)
							x[1] = 0
							x[2] = 0
						ELSE
							RESIZE(x, 1)
							x[1] = e
							arrayPush(x, v)
						ENDIF
					ELSE
						RESIZE(x, 1)
						x[1] = e
						DIM tmp[] = v
						arrayMerge(x, tmp)
					ENDIF
					RESULT = SLICE(x)
					EXIT
				// Infinity, NaN
				ELSEIF v * 0 <> 0 THEN
					IF !v THEN x[0] = NULL
					x[1] = NULL
					x[2] = NULL
					EXIT
				ENDIF
			ENDIF
			RESULT = parseDecimal(x, v)
			EXIT
		ELSEIF v = "NaN" THEN
			RESIZE(x, 2)
			x[0] = NULL
			x[1] = NULL
			x[2] = FALSE
			RESULT = SLICE(x)
			EXIT
		ELSEIF t <> string THEN
			RESULT = ERR_VALUE
			EXIT
		ENDIF
		// Minus sign?
		i = COPY(v, 1, 1)
		IFB i = "-" THEN
			v = COPY(v, 2)
			x[0] = -1
		ELSE
			// Plus sign?
			IF i = "+" THEN v = COPY(v, 1)
			x[0] = 1
		ENDIF
		RESULT = IIF(reTest(v, "^(\d+(\.\d*)?|\.\d+)(e[+-]?\d+)?$"), parseDecimal(x, v), parseOther(x, v))
	FEND
	FUNCTION isDecimalInstance(v)
		RESULT = IIF(isArray(v), TRUE, FALSE)
	FEND
	FUNCTION multiplyInteger(x, k, base)
		DIM carry = 0
		DIM i = UBound(x)
		WHILE i >= 0
			temp = x[i] * k + carry
			x[i] = INT(temp MOD base)
			carry = INT(temp / base)
			i = i - 1
		WEND
		IF carry <> 0 THEN arrayUnshift(x, carry)
		RESULT = SLICE(x)
	FEND
	PROCEDURE subtract(Var a, b, aL, base)
		DIM i = 0
		// Subtract b from a.
		WHILE aL > 0
			aL = aL - 1
			a[aL] = a[aL] - i
			i = IIF(a[aL] < b[aL], 1, 0)
			a[aL] = i * base + a[aL] - b[aL]
		WEND
		// Remove leading zeros.
		WHILE !a[0] AND LENGTH(a) > 1
			arrayShift(a)
		WEND
	FEND
	//////////////////////////////
	// 自作関数
	//////////////////////////////
	FUNCTION calculate(str, pr = 20, rm = 4)
		RESULT = tokenize(str)
		RESULT = toRPN(RESULT)
		RESULT = calcRPN(RESULT, pr, rm)
	FEND
	FUNCTION calcRPN(tokens, pr, rm)
		DIM denominator[-1]
		DIM numerator[-1]
		FOR token IN tokens
			IFB reTest(token, "[0-9.]+") THEN
				arrayPush(denominator, "" + 1)
				arrayPush(numerator, "" + token)
			ELSEIF token = "u-" THEN
				arrayPush(numerator, times("-1", arrayPop(numerator)))
			ELSEIF token = "floor" THEN
				bottom = arrayPop(denominator)
				top = arrayPop(numerator)
				arrayPush(denominator, "1")
				arrayPush(numerator, floor(dividedBy(top, bottom)))
			ELSEIF token = "ceil" THEN
				bottom = arrayPop(denominator)
				top = arrayPop(numerator)
				arrayPush(denominator, "1")				
				arrayPush(numerator, THIS.ceil(dividedBy(top, bottom)))
			ELSE
				IFB token = "+" OR token = "-" THEN
					DIM du = UBound(denominator)
					DIM nu = UBound(numerator)
					bottom = times(denominator[du], denominator[du-1])
					top = EVAL(denominator[du] * numerator[nu-1] + token + numerator[nu] * denominator[du-1])
					arrayPop(denominator)
					arrayPop(denominator)
					arrayPop(numerator)
					arrayPop(numerator)
					arrayPush(denominator, bottom)
					arrayPush(numerator, top)
				ELSEIF token = "*" THEN
					arrayPush(denominator, times(arrayPop(denominator), arrayPop(denominator)))
					arrayPush(numerator, times(arrayPop(numerator), arrayPop(numerator)))					
				ELSEIF token = "/" THEN
					swap(denominator[UBound(denominator)], numerator[UBound(numerator)])
					arrayPush(denominator, times(arrayPop(denominator), arrayPop(denominator)))
					arrayPush(numerator, times(arrayPop(numerator), arrayPop(numerator)))
				ELSEIF token = "//" THEN
					swap(denominator[UBound(denominator)], numerator[UBound(numerator)])
					arrayPush(denominator, times(arrayPop(denominator), arrayPop(denominator)))
					arrayPush(numerator, times(arrayPop(numerator), arrayPop(numerator)))
					bottom = arrayPop(denominator)
					top = arrayPop(numerator)
					arrayPush(denominator, "1")
					arrayPush(numerator, THIS.floor(dividedBy(top, bottom)))
				ELSEIF token = "%" THEN
					bottom = dividedBy(arrayPop(numerator), arrayPop(denominator))
					top = dividedBy(arrayPop(numerator), arrayPop(denominator))
					arrayPush(denominator, "1")
					arrayPush(numerator, modulo(top, bottom ))
				ENDIF
			ENDIF
			IFB COPY(denominator[UBound(denominator)], 1, 1) = "-" THEN
				denominator[UBound(denominator)] = times("-1", denominator[UBound(denominator)])
				numerator[UBound(numerator)] = times("-1", numerator[UBound(numerator)])
			ENDIF
		NEXT
		DIM x = SAFEARRAY(-1)
		DIM n = dividedBy(numerator[0], denominator[0])
		x = Constructor(n)
		RESULT = toString(finalise(x, pr, rm))
	FEND
	FUNCTION cmpPrecedence(token1, token2)
		DIM operators[] = "+", 0, LEFT, "-", 0, LEFT, "*", 5, LEFT, "/", 5, LEFT, "%", 5, LEFT, "^", 10, RIGHT
		IFB isOperator(token1) AND isOperator(token2) THEN
			RESULT = operators[arraySearch(token1, operators)+1] - operators[arraySearch(token2, operators)+1]
		ELSE
			RESULT = ERR_VALUE
		ENDIF
	FEND
	FUNCTION isOperator(token)
		RESULT = reTest(token, "[+\-*/%^]")
	FEND
	FUNCTION quotient(dividend, divisor)
		WITH Decimal
			RESULT = (dividend - (.modulo(dividend, divisor))) / divisor
		ENDWITH
	FEND

FUNCTION tokenize(expr)
		DIM tokens[-1]
		DIM i = 1
		DIM str = ""
		WHILE i <= LENGTH(expr)
			char = COPY(expr, i, 1)
			IFB reTest(char, "\s") THEN
				i = i + 1
				CONTINUE
			ENDIF
			IFB reTest(char, "[0-9.]") THEN
				num = char
				i = i + 1
				WHILE i <= LENGTH(expr) AND reTest(COPY(expr, i, 1), "[0-9.]")
					num = num + COPY(expr, i, 1)
					i = i + 1
				WEND
				arrayPush(tokens, VAL(num))
				CONTINUE
			ENDIF
			IFB reTest(char, "[+\-*/^%]") THEN
				IFB COPY(expr, i, 2) = "//" THEN
					arrayPush(tokens, "//")
					i = i + 2
				ELSE
					DIM prev = ""
					IF LENGTH(tokens) >= 1 THEN prev = tokens[LENGTH(tokens)-1]
					IFB char = "-" AND (LENGTH(tokens) = 0 OR (VARTYPE(prev) = 258 AND (isOperator(prev) OR prev = "(")))
						arrayPush(tokens, "u-")
					ELSE
						arrayPush(tokens, char)
					ENDIF
					i = i + 1
				ENDIF
				CONTINUE
			ENDIF
			IFB reTest(char, "[A-Za-z0-9]") THEN
				str = str + char
				i = i + 1
				WHILE i <= LENGTH(expr) AND reTest(COPY(expr, i, 1), "[A-Za-z0-9]")
					str = str + COPY(expr, i, 1)
					i = i + 1
				WEND
				arrayPush(tokens, str)
				str = ""
				CONTINUE
			ENDIF
			IFB reTest(char, "[()]") THEN
				IFB str <> "" THEN
					arrayPush(tokens, str)
					str = ""
				ENDIF
				arrayPush(tokens, char)
				i = i + 1
				CONTINUE
			ENDIF
		WEND
		RESULT = SLICE(tokens)
	FEND
	FUNCTION toRPN(tokens, pr = 20, rm = 4, isNumeric = FALSE)
		HASHTBL precedence
		precedence["^"] = 4
		precedence["u-"] = 3
		precedence["*"] = 2
		precedence["/"] = 2
		precedence["%"] = 2
		precedence["+"] = 1
		precedence["-"] = 1
		HASHTBL rightAssociative
		rightAssociative["u-"] = TRUE
		rightAssociative["^"] = TRUE
		DIM output[-1]
		DIM stack[-1]
		FOR token IN tokens
			IFB reTest(token, "[0-9]+") THEN
				arrayPush(output, token)
			ELSEIF token = "floor" OR token = "ceil" THEN
				arrayPush(stack, token)
			ELSEIF token ="(" THEN
				arrayPush(stack, token)
			ELSEIF token = ")" THEN
				WHILE LENGTH(stack) <> 0 AND stack[LENGTH(stack)-1] <> "("
					arrayPush(output, arrayPop(stack))
				WEND
				arrayPop(stack)
				IFB LENGTH(stack) <> 0 THEN
					IF stack[LENGTH(stack) - 1] = "floor" OR stack[LENGTH(stack) - 1] = "ceil" THEN arrayPush(output, arrayPop(stack))
				ENDIF
			ELSE
				WHILE LENGTH(stack)
					IFB stack[LENGTH(stack)-1] <> "(" AND _
						( _
							precedence[token] < precedence[stack[LENGTH(stack)-1]] OR _
							( _
								precedence[token] = precedence[stack[LENGTH(stack)-1]] AND _
								!rightAssociative[token] _
							) _
						) THEN
						arrayPush(output, arrayPop(stack))
					ELSE
						BREAK
					ENDIF
				WEND
				arrayPush(stack, token)
			ENDIF
		NEXT
		WHILE LENGTH(stack)
			arrayPush(output, arrayPop(stack))
		WEND
		RESULT = SLICE(output)
	FEND
ENDMODULE

//////////////////////////////////////////////////
// 【引数】
//   num : 数値
// 【戻り値】
//////////////////////////////////////////////////
FUNCTION decimalDigits(num)
	DIM str = fixed(num)
	RESULT = IIF(POS(".", str), LENGTH(BETWEENSTR(str, ".")), 0)
FEND

//////////////////////////////////////////////////
// 【引数】
//   dec : 10進数
//   signFlg : 符号付きならばTrueを指定
//   digits : 変換した2進数の桁数合わせを自動で行うかを示すブール値、もしくは桁数を表す数値（8,16,24,32,64のいずれか）を指定
//   errorMsg : エラーメッセージを出力するかを示すブール値
// 【戻り値】
//   2進数に変換した値
//////////////////////////////////////////////////
FUNCTION decToBin(dec, signFlg = FALSE, digits = FALSE, errorMsg = FALSE)
	// 64bitを超えてエラー判定になるので例外処理
	IFB dec = "-9223372036854775808" THEN
		RESULT = "1000000000000000000000000000000000000000000000000000000000000000"
		EXIT
	ENDIF

// 負数で符号なしならばエラー値を返す
	IFB Decimal.lessThan(dec, 0) AND signFlg = FALSE THEN
		PRINT "負数の場合signFlgにTrueを指定してください"
		RESULT = ERR_VALUE
		EXIT
	ENDIF
	
	// digitsのビット数が足りなければエラー値を返す、負数なら1桁多く取る
	IFB VARTYPE(digits) <> VAR_BOOLEAN AND digits < CEIL(LOGN(2, ABS(dec))) + IIF(dec < 0, 1, 0) THEN
		PRINT "ビット数が足りません"
		RESULT = ERR_VALUE
		EXIT
	ENDIF
	
	// signFlgがTrueかつdigitsがFalseならばエラー値を返す
	IFB signFlg AND !digits THEN
		PRINT "signFlgがTrueのときdigitsはFalse以外を選択してください"
		RESULT = ERR_VALUE
		EXIT
	ENDIF

// bin：2進数に変換した結果を代入する変数
	DIM bin = ""
	DIM msg = ""
	DIM isError = FALSE
	DIM decimalFlg = !Decimal.isInteger(dec)
	DIM negativeFlg = Decimal.isNegative(dec)
	dec = Decimal.absoluteValue(dec)
	
	// (1) 10進数を整数部と小数部に分ける
	DIM integer = IIF(decimalFlg, COPY(dec, 1, POS(".", dec) - 1), dec)
	DIM decimal = IIF(decimalFlg, "0." + COPY(dec, POS(".", dec) + 1), 0)

// (2) 10進数（整数部）を2進数に変換する。
	REPEAT
		bin = Decimal.modulo(integer, 2) + bin
		integer = Decimal.truncated(Decimal.dividedBy(integer, 2))
	UNTIL Decimal.eq(integer, "0")

// (3) 10進数（小数部）を2進数に変換する。
	IFB decimalFlg THEN
		bin = bin + "."
		DIM loop = 0
		REPEAT
			loop = loop + 1
			decimal = decimal * 2
			bin = bin + IIF(decimal >= 1, "1", "0")
			IF decimal > 1 THEN decimal = decimal - 1
		UNTIL decimal = 1 OR loop > 64
	ENDIF

// digitsがFALSE以外なら
	IFB digits THEN
		// (4) 2進数の桁合わせを行う
		DIM tmp = bin
		DIM binInteger = TOKEN(".", tmp)
		DIM binDecimal = TOKEN(".", tmp)
		// 整数部、小数部を4bit単位になるまで拡張
		// 整数部、4の倍数になるまで整数部の先頭に'0'を追加
		IF LENGTH(binInteger) MOD 4 <> 0 THEN binInteger = strRepeat("0", 4 - LENGTH(binInteger) MOD 4) + binInteger
		// 小数部、4の倍数になるまで小数部の末尾に'0'を追加
		IF LENGTH(binDecimal) MOD 4 <> 0 THEN binDecimal = binDecimal + strRepeat("0", 4 - LENGTH(binDecimal) MOD 4)
		DIM digit = LENGTH(binInteger + binDecimal)

// 10進数の場合、一旦自動調整を行う
		integer = INT(dec)

IF signFlg AND COPY(binInteger, 1, 1) = "1" THEN binInteger = strRepeat("0", 4) + binInteger

IFB signFlg THEN
			IFB integer >= -128 AND integer <= 127 THEN						// -2^7〜2^7-1
				binInteger = strRepeat("0", 8 - LENGTH(binInteger)) + binInteger
			ELSEIF integer >= -32768 AND integer <= 32767 THEN				// -2^15〜2^15-1
				binInteger = strRepeat("0", 16 - LENGTH(binInteger)) + binInteger
			ELSEIF integer >= -8388608 AND integer <= 8388607 THEN			// -2^23〜2^23-1
				binInteger = strRepeat("0", 24 - LENGTH(binInteger)) + binInteger
			ELSEIF integer >= -2147783648 AND integer <= 2147483647 THEN	// -2^31〜2^31-1
				binInteger = strRepeat("0", 32 - LENGTH(binInteger)) + binInteger
			ELSE
				binInteger = strRepeat("0", 64 - LENGTH(binInteger)) + binInteger
			ENDIF
		ELSE
			IFB integer <= 255 THEN				// 2^8-1
				binInteger = strRepeat("0", 8 - LENGTH(binInteger)) + binInteger		
			ELSEIF integer <= 65535 THEN		// 2^16-1
				binInteger = strRepeat("0", 16 - LENGTH(binInteger)) + binInteger		
			ELSEIF integer <= 16777215 THEN		// 2^24-1
				binInteger = strRepeat("0", 24 - LENGTH(binInteger)) + binInteger
			ELSEIF integer <= 4294967295 THEN	// 2^32-1
				binInteger = strRepeat("0", 32 - LENGTH(binInteger)) + binInteger
			ELSE
				binInteger = strRepeat("0", 64 - LENGTH(binInteger)) + binInteger
			ENDIF
		ENDIF

totalDigits = LENGTH(binInteger + binDecimal)

IFB totalDigits > 64 THEN
			DIM del32 = totalDigits - 32
			DIM del64 = totalDigits - 64
			IFB del32 = LENGTH(binDecimal) AND digits <> 64 THEN
				binDecimal = ""
				msg = "32bitを超えたため、小数点以下を削除しました"
			ELSEIF del32 < LENGTH(binDecimal) AND digits <> 64 THEN
				binDecimal = COPY(binDecimal, 1, LENGTH(binDecimal) - del32)
				msg = "32bitを超えたため、小数点以下の一部を削除しました"
			ELSEIF del64 = LENGTH(binDecimal) AND del64 <> 0 THEN
				binDecimal = ""
				msg = "64bitを超えたため、小数点以下を削除しました"
			ELSEIF del64 < LENGTH(binDecimal) THEN
				binDecimal = COPY(binDecimal, 1, LENGTH(binDecimal) - del64)
				msg = "64bitを超えたため、小数点以下の一部を削除しました"
			ELSE
				msg = "64bitを超えるため、変換できません"
				isError = TRUE
			ENDIF
		ENDIF

// 整数部、小数部の合計桁数を8,16,24,32,64bit単位になるまで拡張
		digit = LENGTH(binInteger + binDecimal)
		DIM array[] = 8, 16, 24, 32, 64
		FOR item IN array
			IFB digit <= item THEN
				binInteger = strRepeat("0", item - digit) + binInteger
				BREAK
			ENDIF
		NEXT

// 指定ビットに調整
		// 合計桁数の再設定
		totalDigits = LENGTH(binInteger + binDecimal)
		
		IFB digits = TRUE THEN
			// 桁合わせを自動調整
			IFB totalDigits > 64 THEN
				len = LENGTH(binInteger + binDecimal)
				WHILE LENGTH(binInteger) > 8 AND len > digits
					IFB COPY(binInteger, 1, 4) = "0000" THEN
						binInteger = COPY(binInteger, 5)
						len = len - 4
					ELSE
						BREAK
					ENDIF
				WEND
	
				WHILE LENGTH(binDecimal) > 4 AND LENGTH(binInteger + binDecimal) > digits
				IFB COPY(binDecimal, LENGTH(binDecimal) - 4) = "0000" THEN
					binDecimal = COPY(binDecimal, 1, LENGTH(binDecimal) - 4)
					ELSE
						BREAK
					ENDIF
				WEND
				tmp = binInteger + "." + binDecimal

binInteger = COPY(tmp, 1, POS(".", tmp) - 1)
				binDecimal = COPY(tmp, POS(".", tmp) + 1)
				totalDigits = LENGTH(binInteger + binDecimal)
				IFB totalDigits > 64 THEN
					isError = TRUE
					msg = "64bitを超えたため変換できません"
				ENDIF
			ENDIF
		ELSE
			// 指定ビットに調整
			IFB totalDigits <= digits THEN
				binInteger = strPad(binInteger, digits - LENGTH(binDecimal), "0", LEFT)
			ELSE
				// 桁あふれ調整
				totalDigits = LENGTH(binInteger + binDecimal)

len = LENGTH(binInteger + binDecimal)
				WHILE LENGTH(binInteger) > 8 AND len > digits
					IFB COPY(binInteger, 1, 4) = "0000" THEN
						binInteger = COPY(binInteger, 5)
						len = len - 4
					ELSE
						BREAK
					ENDIF
				WEND
	
				WHILE LENGTH(binDecimal) > 4 AND LENGTH(binInteger + binDecimal) > digits
				IFB COPY(binDecimal, LENGTH(binDecimal) - 4) = "0000" THEN
					binDecimal = COPY(binDecimal, 1, LENGTH(binDecimal) - 4)
					ELSE
						BREAK
					ENDIF
				WEND
				tmp = binInteger + "." + binDecimal

binInteger = COPY(tmp, 1, POS(".", tmp) - 1)
				binDecimal = COPY(tmp, POS(".", tmp) + 1)
				len = LENGTH(binInteger + binDecimal)
				IFB len > digits THEN
					DIM deleteLength = len - digits
					IFB deleteLength = LENGTH(binDecimal) THEN
						binDecimal = ""
						msg = "指定ビット数にするため小数点以下を削除しました"
					ELSEIF deleteLength < LENGTH(binDecimal) THEN
						binDecimal = COPY(binDecimal, 1, LENGTH(binDecimal) - deleteLength)
						msg = "指定ビット数にするため小数点以下の一部を削除しました"
					ELSE
						isError = TRUE
						msg = "指定ビット数では変換できません"
					ENDIF
				ENDIF
			ENDIF
		ENDIF

bin = binInteger + IIF(binDecimal <> "", "." + binDecimal, "")

// (5) 入力値がマイナスのため、2進数をマイナス値に変換する
		IFB negativeFlg THEN
			// 1の補数
			bin = bitNot(bin)
			// 2の補数
			DIM res = ""
			DIM carry = "1"
			FOR i = LENGTH(bin) TO 1 STEP -1
				IFB carry = "1" THEN
					SELECT COPY(bin, i, 1)
						CASE "0"
							res = "1" + res
							carry = 0
						CASE "1"
							res = "0" + res
						DEFAULT
							res = COPY(bin, i, 1) + res
					SELEND
				ELSE
					res = COPY(bin, i, 1) + res
				ENDIF
			NEXT
			bin = res
		ENDIF
	ENDIF

IF errorMsg AND msg <> "" THEN PRINT msg
	RESULT = IIF(isError, ERR_VALUE, bin)
FEND

//////////////////////////////////////////////////
// 【引数】
//   deg : 角度（度数法）
// 【戻り値】
//   度数法から弧度法に変換した値
//////////////////////////////////////////////////
FUNCTION degToRad(deg)
	WITH Decimal
		pr = .precision
		.precision = 25
		RESULT = .times(deg, .dividedBy(Decimal.PI, "180"))
		.precision = pr
	ENDWITH
FEND

//////////////////////////////////////////////////
// 【引数】
//   dividend : 被除数
//   divisor : 除数
// 【戻り値】
//////////////////////////////////////////////////
FUNCTION division(dividend, divisor)
	DIM array[] = dividend, divisor
	DIM g = GCD(array)
	DIM tmp = divisor / g

DIM dat[] = 10, 5, 2
	DIM position = 0

FOR i = 0 TO UBound(dat)
		WHILE tmp MOD dat[i] = 0
			tmp = INT(tmp / dat[i])
			position = position + 1
		WEND
	NEXT

DIM repetend = ""
	DIM res = ""
	tmp = 0

i = 0
	WHILE TRUE
		DIM quotient = INT(dividend/divisor)
		DIM remainder = dividend MOD divisor
		IF i = position THEN tmp = remainder
		IFB i > position THEN
			repetend = repetend + quotient
		ELSE
			res = res + quotient
			IF i = 0 THEN res = res + "."
		ENDIF
		IF i > position AND tmp = remainder THEN BREAK
		dividend  = remainder * 10
		i = i  + 1
	WEND

RESULT = res + IIF(repetend<>0, "[" + repetend + "]", "")
FEND

//////////////////////////////////////////////////
// 【引数】
//   num : 数値
//   digits : 小数点以下の桁数
// 【戻り値】
//////////////////////////////////////////////////
FUNCTION fixed(num, digits = EMPTY)
	num = VAL(num)		// 指数表記を整える
	IFB POS("E-", num) THEN
		DIM mantissa = BETWEENSTR(num,, "E")
		DIM exponent = BETWEENSTR(num, "E")		
		RESULT = "0." + strRepeat("0", VAL(ABS(exponent) - 1)) + REPLACE(mantissa, ".", "")
	ELSEIF POS("E", num) THEN
		RESULT = ROUND(num, -1 *digits)
		mantissa = BETWEENSTR(num,, "E")
		exponent = BETWEENSTR(num, "E")
		RESULT = REPLACE(mantissa, ".", "") + strRepeat("0", VAL(exponent) - decimalDigits(mantissa))
	ELSEIF LENGTH(BETWEENSTR(num, ".")) < digits THEN
		DIM keta = digits - LENGTH(BETWEENSTR(num, "."))
		RESULT = num + IIF(POS(".", num) OR keta = 0, "", ".") + strRepeat("0", keta)
	ELSE
		IF digits = EMPTY THEN digits = LENGTH(BETWEENSTR(num, "."))
		RESULT = "" + roundOff(num, digits)
	ENDIF
FEND

//////////////////////////////////////////////////
// 【引数】
//   num : 丸め処理を行う値
// 【戻り値】
//   負の方向に丸めた値
//////////////////////////////////////////////////
FUNCTION floor(num)
	RESULT = INT(num) + IIF(num < 0 AND num <> INT(num), -1, 0)
FEND

//////////////////////////////////////////////////
// 【引数】
//   array : 最大公約数を求める数値を格納した配列
// 【戻り値】
//   最大公約数
//////////////////////////////////////////////////
FUNCTION GCD(array[])
	DIM c = LENGTH(array)
	DIM rem = array[c-1] MOD array[c-2]
	IFB rem = 0 THEN
		IFB LENGTH(array) = 2 THEN
			RESULT = array[c-2]
			EXIT
		ENDIF
		RESIZE(array, c-2)
		RESULT = GCD(array)
		EXIT
	ENDIF
	array[c-1] = array[c-2]
	array[c-2] = rem
	RESULT = GCD(array)
FEND

//////////////////////////////////////////////////
// 【引数】
//   date : 日付（”YYYYMMDD” or “YYYY/MM/DD” or “YYYY-MM-DD” or “YYYYMMDDHHNNSS” or “YYYY/MM/DD HH:NN:SS”）
//   m : 第一引数の指定日からプラスマイナスm月とする
// 【戻り値】
//   dateからm月後の月末の日付
//////////////////////////////////////////////////
FUNCTION getEndOfMonth(date, m = 0)
	date = dateAdd("m", m + 1, date)
	GETTIME(0, date)
	GETTIME(-G_TIME_DD, date)
	RESULT = G_TIME_YY4 + "/" + G_TIME_MM2 + "/" + G_TIME_DD2
FEND

//////////////////////////////////////////////////
// 【引数】
//   date : 日付文字列（”YYYYMMDD” or “YYYY/MM/DD” or “YYYY-MM-DD” or “YYYYMMDDHHNNSS” or “YYYY/MM/DD HH:NN:SS”）もしくはシリアル値
//   type : 取得する曜日番号の種類を示す0〜3または11〜17の値。1と17は日曜日を1、2と11は月曜日を1とカウントします。11以降はExcel2010で追加された値で、互換性を保つために重複した値があります。
// 【戻り値】
//   typeで指定した種類によって以下の値を返します。 : （0 : 0(日曜)〜6(土曜)、1 : 1(日曜)～7(土曜)、2 : 1(月曜)～7(日曜)、3 : 0(月曜)〜6(日曜)、11 : 1(月曜)～7(日曜)、12 : 1(火曜)～7(月曜)、13 : 1(水曜)～7(火曜)、14 : 1(木曜)～7(水曜)、15 : 1(金曜)～7(木曜)、16 : 1(土曜)～7(金曜)、17 : 1(日曜)～7(土曜)）
//////////////////////////////////////////////////
FUNCTION getWeekday(date, type = 1)
	IF VARTYPE(date) <> 258 THEN date = text(date, "yyyy/mm/dd")
	GETTIME(0, date)
	DIM w = G_TIME_WW
	SELECT TRUE
		CASE type = 0
			RESULT = w
		CASE type = 1
			RESULT = w + 1
		CASE type = 2
			RESULT = IIF(w=0, 7, w)
		CASE type = 3
			RESULT = (w+6) MOD 7
		CASE type >= 11
			RESULT = ((getWeekday(date, 2) + 17 - type) MOD 7) + 1
	SELEND
FEND

//////////////////////////////////////////////////
// 【引数】
//   str : ハッシュ化する文字列
// 【戻り値】
//   ハッシュ化した文字列
//////////////////////////////////////////////////
MODULE Hash
	DIM FSO = CREATEOLEOBJ("Scripting.FileSystemObject")
	DIM path
	PROCEDURE Hash()
		CONST TemporaryFolder = 2
		DIM Folder = FSO.GetSpecialFolder(TemporaryFolder)
		DIM folderspec = Folder.Path
		DIM filename = FSO.GetTempName
		path = FSO.BuildPath(folderspec, filename)
	FEND
	FUNCTION md2(str)
		DIM TextStream = FSO.CreateTextFile(path)
		TextStream.Write(str)
		TextStream.Close
		RESULT = TRIM(DOSCMD("CertUtil -hashfile <#DBL>" + path + "<#DBL> MD2 | findstr /R <#DBL>^[0-9A-Fa-f][0-9A-Fa-f]*$<#DBL>"))
		FSO.DeleteFile(path)
	FEND
	FUNCTION md4(str)
		DIM TextStream = FSO.CreateTextFile(path)
		TextStream.Write(str)
		TextStream.Close
		RESULT = TRIM(DOSCMD("CertUtil -hashfile <#DBL>" + path + "<#DBL> MD4 | findstr /R <#DBL>^[0-9A-Fa-f][0-9A-Fa-f]*$<#DBL>"))
		FSO.DeleteFile(path)
	FEND
	FUNCTION md5(str)
		DIM TextStream = FSO.CreateTextFile(path)
		TextStream.Write(str)
		TextStream.Close
		RESULT = TRIM(DOSCMD("CertUtil -hashfile <#DBL>" + path + "<#DBL> MD5 | findstr /R <#DBL>^[0-9A-Fa-f][0-9A-Fa-f]*$<#DBL>"))
		FSO.DeleteFile(path)
	FEND
	FUNCTION sha1(str)
		DIM TextStream = FSO.CreateTextFile(path)
		TextStream.Write(str)
		TextStream.Close
		RESULT = TRIM(DOSCMD("CertUtil -hashfile <#DBL>" + path + "<#DBL> SHA1 | findstr /R <#DBL>^[0-9A-Fa-f][0-9A-Fa-f]*$<#DBL>"))
		FSO.DeleteFile(path)
	FEND
	FUNCTION sha256(str)
		DIM TextStream = FSO.CreateTextFile(path)
		TextStream.Write(str)
		TextStream.Close
		RESULT = TRIM(DOSCMD("CertUtil -hashfile <#DBL>" + path + "<#DBL> SHA256 | findstr /R <#DBL>^[0-9A-Fa-f][0-9A-Fa-f]*$<#DBL>"))
		FSO.DeleteFile(path)
	FEND
	FUNCTION sha384(str)
		DIM TextStream = FSO.CreateTextFile(path)
		TextStream.Write(str)
		TextStream.Close
		RESULT = TRIM(DOSCMD("CertUtil -hashfile <#DBL>" + path + "<#DBL> SHA384 | findstr /R <#DBL>^[0-9A-Fa-f][0-9A-Fa-f]*$<#DBL>"))
		FSO.DeleteFile(path)
	FEND
	FUNCTION sha512(str)
		DIM TextStream = FSO.CreateTextFile(path)
		TextStream.Write(str)
		TextStream.Close
		RESULT = TRIM(DOSCMD("CertUtil -hashfile <#DBL>" + path + "<#DBL> SHA512 | findstr /R <#DBL>^[0-9A-Fa-f][0-9A-Fa-f]*$<#DBL>"))
		FSO.DeleteFile(path)
	FEND
ENDMODULE

//////////////////////////////////////////////////
// 【引数】
//   serial : シリアル値もしくは時刻文字列
// 【戻り値】
//   時刻から時間を表す0〜23の範囲の値
//////////////////////////////////////////////////
FUNCTION Hour(serial)
	IF VARTYPE(serial) = 258 THEN serial = timeValue(serial)
	RESULT = INT(serial * 24) MOD 24
FEND

//////////////////////////////////////////////////
// 【引数】
//   expr : 評価する式
//   truepart : 評価した式がTrueのときに返す値
//   falsepart : 評価した式がFalseのときに返す値
// 【戻り値】
//   truepart : 評価した式がTrueのとき、falsepart : 評価した式がFalseのとき
//////////////////////////////////////////////////
FUNCTION IIF(expr, truepart, falsepart)
	IFB EVAL(expr) THEN
		RESULT = truepart
	ELSE
		RESULT = falsepart
	ENDIF
FEND

//////////////////////////////////////////////////
// 【引数】
//   variable : 型を調べる変数
// 【戻り値】
//////////////////////////////////////////////////
FUNCTION isArray(variable[])
	RESULT = IIF(VARTYPE(variable) AND 8192, TRUE, FALSE)
FEND

//////////////////////////////////////////////////
// 【引数】
//   variable : 型を調べる変数
// 【戻り値】
//    : TRUE : 与えられた変数がブール型である、
//   FALSE : 与えられた変数がブール型でない、 :
//////////////////////////////////////////////////
FUNCTION isBoolean(variable)
	RESULT = IIF(VARTYPE(variable) = VAR_BOOLEAN, TRUE, FALSE)
FEND

//////////////////////////////////////////////////
// 【引数】
//   date : 存在するかを調べる日付文字列。YYYYMMDD or YYYY/MM/DD or YYYY-MM-DDのいずれかの形式。
// 【戻り値】
//   TRUE : 日付として認識できる、FALSE : 日付として認識できない
//////////////////////////////////////////////////
FUNCTION isDate(date)
	TRY
		GETTIME(0, date)
		RESULT = TRUE
	EXCEPT
		RESULT = FALSE
	ENDTRY
FEND

//////////////////////////////////////////////////
// 【引数】
//   variable : 型を調べる変数
// 【戻り値】
//////////////////////////////////////////////////
FUNCTION isFloat(variable)
	IFB VAL(variable) <> ERR_VALUE THEN
		RESULT = IIF((VARTYPE(variable) = VAR_SINGLE OR VARTYPE(variable) = VAR_DOUBLE) AND INT(variable) <> variable, TRUE, FALSE)
	ELSE
		RESULT = FALSE
	ENDIF
FEND

//////////////////////////////////////////////////
// 【引数】
//   variable : 型を調べる変数
// 【戻り値】
//    : TRUE : 与えられた変数が整数型である、
//   FALSE : 与えられた変数が整数型でない、 :
//////////////////////////////////////////////////
FUNCTION isInt(variable)
	IFB VAL(variable) <> ERR_VALUE AND !isBoolean(variable) AND !isString(variable) THEN
		RESULT = IIF(variable - INT(variable) = 0, TRUE, FALSE)
	ELSE
		RESULT = FALSE
	ENDIF
FEND

//////////////////////////////////////////////////
// 【引数】
//   variable : 型を調べる変数
// 【戻り値】
//    : TRUE : 与えられた変数が文字列型である、
//   FALSE : 与えられた変数が文字列型でない、 :
//////////////////////////////////////////////////
FUNCTION isString(variable)
	RESULT = IIF(VARTYPE(variable) = VAR_ASTR OR VARTYPE(variable) = VAR_USTR, TRUE, FALSE)
FEND

//////////////////////////////////////////////////
// 【引数】
//   JD : ユリウス日
// 【戻り値】
//   グレゴリオ暦を格納した配列（0 : 年, 1 : 月, 2 : 日, 3 : 時, 4 : 分, 5 : 秒）
//////////////////////////////////////////////////
FUNCTION JDToYMD(JD)
	DIM x0 = INT(JD + 68570)
	DIM x1 = INT(x0 / 36524.25)
	DIM x2 = x0 - INT(36524.25 * x1 + 0.75)
	DIM x3 = INT((x2 + 1) / 365.2425)
	DIM x4 = x2 - INT(365.25 * x3) + 31
	DIM x5 = INT(INT(x4) / 30.59)
	DIM x6 = INT(INT(x5) / 11)
	
	DIM t2 = x4 - INT(30.59 * x5)
	DIM t1 = x5 - 12 * x6 + 2
	DIM t0 = 100 * (x1 - 49) + x3 + x6
	
	IFB t1 = 2 AND t2 > 28 THEN
		SELECT TRUE
			CASE t0 MOD 100 = 0 AND t0 MOD 400 = 0
				t2 = 29
			CASE t0 MOD 4 = 0
				t2 = 29
			DEFAULT
				t2 = 28
		SELEND
	ENDIF
	
	DIM tm = 86400 * (JD - INT(JD))
	DIM t3 = INT(tm / 3600)
	DIM t4 = INT((tm - 3600 * t3) / 60)
	DIM t5 = INT(tm - 3600 * t3 - 60 * t4)
	DIM t[] = t0, t1, t2, t3, t4, t5
	
	RESULT = SLICE(t)
FEND

//////////////////////////////////////////////////
// 【引数】
//   text : JSONとして解析する文字列
//   value : JSON文字列に変換する値
//   reviver : 使用不可
//   replacer : 使用不可
//   space : 出力するJSON文字列に空白を挿入するための文字列もしくは数値
// 【戻り値】
//    : Parse : JSON文字列をオブジェクトに変換、
//   Stringify : オブジェクトをJSON文字列に変換、 :
//////////////////////////////////////////////////
MODULE JSON
	DIM SC, CodeObject
	PROCEDURE JSON
		SC = CREATEOLEOBJ("ScriptControl")
		WITH SC
			.Language = "JScript"
			.ExecuteStatement(json2)
			.ExecuteStatement(statement)
			CodeObject = .CodeObject
		ENDWITH
	FEND
	FUNCTION Parse(text, reviver = NULL)
		RESULT = CodeObject.JSON.parse(text, reviver)
	FEND
	FUNCTION Stringify(value, replacer = "", space = FALSE)
		RESULT = CodeObject.JSON.stringify(value, NULL, replacer)
		IF space THEN RESULT = REPLACE(RESULT, CHR(10), "<#CR>")
	FEND
ENDMODULE

TEXTBLOCK statement
Array.prototype.Item = function(i, value){
	if(value === undefined) return this[i]; this[i] = value;
}
Array.prototype.item = Array.prototype.Item;
ENDTEXTBLOCK

TEXTBLOCK json2
//  json2.js
//  2023-05-10
//  Public Domain.
//  NO WARRANTY EXPRESSED OR IMPLIED. USE AT YOUR OWN RISK.

//  USE YOUR OWN COPY. IT IS EXTREMELY UNWISE TO LOAD CODE FROM SERVERS YOU DO
//  NOT CONTROL.

//  This file creates a global JSON object containing two methods: stringify
//  and parse. This file provides the ES5 JSON capability to ES3 systems.
//  If a project might run on IE8 or earlier, then this file should be included.
//  This file does nothing on ES5 systems.

//      JSON.stringify(value, replacer, space)
//          value       any JavaScript value, usually an object or array.
//          replacer    an optional parameter that determines how object
//                      values are stringified for objects. It can be a
//                      function or an array of strings.
//          space       an optional parameter that specifies the indentation
//                      of nested structures. If it is omitted, the text will
//                      be packed without extra whitespace. If it is a number,
//                      it will specify the number of spaces to indent at each
//                      level. If it is a string (such as "\t" or " "),
//                      it contains the characters used to indent at each level.
//          This method produces a JSON text from a JavaScript value.
//          When an object value is found, if the object contains a toJSON
//          method, its toJSON method will be called and the result will be
//          stringified. A toJSON method does not serialize: it returns the
//          value represented by the name/value pair that should be serialized,
//          or undefined if nothing should be serialized. The toJSON method
//          will be passed the key associated with the value, and this will be
//          bound to the value.

//          For example, this would serialize Dates as ISO strings.

//              Date.prototype.toJSON = function (key) {
//                  function f(n) {
//                      // Format integers to have at least two digits.
//                      return (n < 10)
//                          ? "0" + n
//                          : n;
//                  }
//                  return this.getUTCFullYear()   + "-" +
//                       f(this.getUTCMonth() + 1) + "-" +
//                       f(this.getUTCDate())      + "T" +
//                       f(this.getUTCHours())     + ":" +
//                       f(this.getUTCMinutes())   + ":" +
//                       f(this.getUTCSeconds())   + "Z";
//              };

//          You can provide an optional replacer method. It will be passed the
//          key and value of each member, with this bound to the containing
//          object. The value that is returned from your method will be
//          serialized. If your method returns undefined, then the member will
//          be excluded from the serialization.

//          If the replacer parameter is an array of strings, then it will be
//          used to select the members to be serialized. It filters the results
//          such that only members with keys listed in the replacer array are
//          stringified.

//          Values that do not have JSON representations, such as undefined or
//          functions, will not be serialized. Such values in objects will be
//          dropped; in arrays they will be replaced with null. You can use
//          a replacer function to replace those with JSON values.

//          JSON.stringify(undefined) returns undefined.

//          The optional space parameter produces a stringification of the
//          value that is filled with line breaks and indentation to make it
//          easier to read.

//          If the space parameter is a non-empty string, then that string will
//          be used for indentation. If the space parameter is a number, then
//          the indentation will be that many spaces.

//          Example:

//          text = JSON.stringify(["e", {pluribus: "unum"}]);
//          // text is '["e",{"pluribus":"unum"}]'

//          text = JSON.stringify(["e", {pluribus: "unum"}], null, "\t");
//          // text is '[\n\t"e",\n\t{\n\t\t"pluribus": "unum"\n\t}\n]'

//          text = JSON.stringify([new Date()], function (key, value) {
//              return this[key] instanceof Date
//                  ? "Date(" + this[key] + ")"
//                  : value;
//          });
//          // text is '["Date(---current time---)"]'

//      JSON.parse(text, reviver)
//          This method parses a JSON text to produce an object or array.
//          It can throw a SyntaxError exception.

//          The optional reviver parameter is a function that can filter and
//          transform the results. It receives each of the keys and values,
//          and its return value is used instead of the original value.
//          If it returns what it received, then the structure is not modified.
//          If it returns undefined then the member is deleted.

//          Example:

//          // Parse the text. Values that look like ISO date strings will
//          // be converted to Date objects.

//          myData = JSON.parse(text, function (key, value) {
//              var a;
//              if (typeof value === "string") {
//                  a =
//   /^(\d{4})-(\d{2})-(\d{2})T(\d{2}):(\d{2}):(\d{2}(?:\.\d*)?)Z$/.exec(value);
//                  if (a) {
//                      return new Date(Date.UTC(
//                         +a[1], +a[2] - 1, +a[3], +a[4], +a[5], +a[6]
//                      ));
//                  }
//                  return value;
//              }
//          });

//          myData = JSON.parse(
//              "[\"Date(09/09/2001)\"]",
//              function (key, value) {
//                  var d;
//                  if (
//                      typeof value === "string"
//                      && value.slice(0, 5) === "Date("
//                      && value.slice(-1) === ")"
//                  ) {
//                      d = new Date(value.slice(5, -1));
//                      if (d) {
//                          return d;
//                      }
//                  }
//                  return value;
//              }
//          );

//  This is a reference implementation. You are free to copy, modify, or
//  redistribute.

/*jslint
    eval, for, this
*/

/*property
    JSON, apply, call, charCodeAt, getUTCDate, getUTCFullYear, getUTCHours,
    getUTCMinutes, getUTCMonth, getUTCSeconds, hasOwnProperty, join,
    lastIndex, length, parse, prototype, push, replace, slice, stringify,
    test, toJSON, toString, valueOf
*/

// Create a JSON object only if one does not already exist. We create the
// methods in a closure to avoid creating global variables.

if (typeof JSON !== "object") {
    JSON = {};
}

(function () {
    "use strict";

var rx_one = /^[\],:{}\s]*$/;
    var rx_two = /\\(?:["\\\/bfnrt]|u[0-9a-fA-F]{4})/g;
    var rx_three = /"[^"\\\n\r]*"|true|false|null|-?\d+(?:\.\d*)?(?:[eE][+\-]?\d+)?/g;
    var rx_four = /(?:^|:|,)(?:\s*\[)+/g;
    var rx_escapable = /[\\"\u0000-\u001f\u007f-\u009f\u00ad\u0600-\u0604\u070f\u17b4\u17b5\u200c-\u200f\u2028-\u202f\u2060-\u206f\ufeff\ufff0-\uffff]/g;
    var rx_dangerous = /[\u0000\u00ad\u0600-\u0604\u070f\u17b4\u17b5\u200c-\u200f\u2028-\u202f\u2060-\u206f\ufeff\ufff0-\uffff]/g;

function f(n) {
        // Format integers to have at least two digits.
        return (n < 10)
            ? "0" + n
            : n;
    }

function this_value() {
        return this.valueOf();
    }

if (typeof Date.prototype.toJSON !== "function") {

Date.prototype.toJSON = function () {

return isFinite(this.valueOf())
                ? (
                    this.getUTCFullYear()
                    + "-"
                    + f(this.getUTCMonth() + 1)
                    + "-"
                    + f(this.getUTCDate())
                    + "T"
                    + f(this.getUTCHours())
                    + ":"
                    + f(this.getUTCMinutes())
                    + ":"
                    + f(this.getUTCSeconds())
                    + "Z"
                )
                : null;
        };

Boolean.prototype.toJSON = this_value;
        Number.prototype.toJSON = this_value;
        String.prototype.toJSON = this_value;
    }

var gap;
    var indent;
    var meta;
    var rep;

function quote(string) {

// If the string contains no control characters, no quote characters, and no
// backslash characters, then we can safely slap some quotes around it.
// Otherwise we must also replace the offending characters with safe escape
// sequences.

rx_escapable.lastIndex = 0;
        return rx_escapable.test(string)
            ? "\"" + string.replace(rx_escapable, function (a) {
                var c = meta[a];
                return typeof c === "string"
                    ? c
                    : "\\u" + ("0000" + a.charCodeAt(0).toString(16)).slice(-4);
            }) + "\""
            : "\"" + string + "\"";
    }

function str(key, holder) {

// Produce a string from holder[key].

var i;          // The loop counter.
        var k;          // The member key.
        var v;          // The member value.
        var length;
        var mind = gap;
        var partial;
        var value = holder[key];

// If the value has a toJSON method, call it to obtain a replacement value.

if (
            value
            && typeof value === "object"
            && typeof value.toJSON === "function"
        ) {
            value = value.toJSON(key);
        }

// If we were called with a replacer function, then call the replacer to
// obtain a replacement value.

if (typeof rep === "function") {
            value = rep.call(holder, key, value);
        }

// What happens next depends on the value's type.

switch (typeof value) {
        case "string":
            return quote(value);

case "number":

// JSON numbers must be finite. Encode non-finite numbers as null.

return (isFinite(value))
                ? String(value)
                : "null";

case "boolean":
        case "null":

// If the value is a boolean or null, convert it to a string. Note:
// typeof null does not produce "null". The case is included here in
// the remote chance that this gets fixed someday.

return String(value);

// If the type is "object", we might be dealing with an object or an array or
// null.

case "object":

// Due to a specification blunder in ECMAScript, typeof null is "object",
// so watch out for that case.

if (!value) {
                return "null";
            }

// Make an array to hold the partial results of stringifying this object value.

gap += indent;
            partial = [];

// Is the value an array?

if (Object.prototype.toString.apply(value) === "[object Array]") {

// The value is an array. Stringify every element. Use null as a placeholder
// for non-JSON values.

length = value.length;
                for (i = 0; i < length; i += 1) {
                    partial[i] = str(i, value) || "null";
                }

// Join all of the elements together, separated with commas, and wrap them in
// brackets.

v = partial.length === 0
                    ? "[]"
                    : gap
                        ? (
                            "[\n"
                            + gap
                            + partial.join(",\n" + gap)
                            + "\n"
                            + mind
                            + "]"
                        )
                        : "[" + partial.join(",") + "]";
                gap = mind;
                return v;
            }

// If the replacer is an array, use it to select the members to be stringified.

if (rep && typeof rep === "object") {
                length = rep.length;
                for (i = 0; i < length; i += 1) {
                    if (typeof rep[i] === "string") {
                        k = rep[i];
                        v = str(k, value);
                        if (v) {
                            partial.push(quote(k) + (
                                (gap)
                                    ? ": "
                                    : ":"
                            ) + v);
                        }
                    }
                }
            } else {

// Otherwise, iterate through all of the keys in the object.

for (k in value) {
                    if (Object.prototype.hasOwnProperty.call(value, k)) {
                        v = str(k, value);
                        if (v) {
                            partial.push(quote(k) + (
                                (gap)
                                    ? ": "
                                    : ":"
                            ) + v);
                        }
                    }
                }
            }

// Join all of the member texts together, separated with commas,
// and wrap them in braces.

v = partial.length === 0
                ? "{}"
                : gap
                    ? "{\n" + gap + partial.join(",\n" + gap) + "\n" + mind + "}"
                    : "{" + partial.join(",") + "}";
            gap = mind;
            return v;
        }
    }

// If the JSON object does not yet have a stringify method, give it one.

if (typeof JSON.stringify !== "function") {
        meta = {    // table of character substitutions
            "\b": "\\b",
            "\t": "\\t",
            "\n": "\\n",
            "\f": "\\f",
            "\r": "\\r",
            "\"": "\\\"",
            "\\": "\\\\"
        };
        JSON.stringify = function (value, replacer, space) {

// The stringify method takes a value and an optional replacer, and an optional
// space parameter, and returns a JSON text. The replacer can be a function
// that can replace values, or an array of strings that will select the keys.
// A default replacer method can be provided. Use of the space parameter can
// produce text that is more easily readable.

var i;
            gap = "";
            indent = "";

// If the space parameter is a number, make an indent string containing that
// many spaces.

if (typeof space === "number") {
                for (i = 0; i < space; i += 1) {
                    indent += " ";
                }

// If the space parameter is a string, it will be used as the indent string.

} else if (typeof space === "string") {
                indent = space;
            }

// If there is a replacer, it must be a function or an array.
// Otherwise, throw an error.

rep = replacer;
            if (replacer && typeof replacer !== "function" && (
                typeof replacer !== "object"
                || typeof replacer.length !== "number"
            )) {
                throw new Error("JSON.stringify");
            }

// Make a fake root object containing our value under the key of "".
// Return the result of stringifying the value.

return str("", {"": value});
        };
    }

// If the JSON object does not yet have a parse method, give it one.

if (typeof JSON.parse !== "function") {
        JSON.parse = function (text, reviver) {

// The parse method takes a text and an optional reviver function, and returns
// a JavaScript value if the text is a valid JSON text.

var j;

function walk(holder, key) {

// The walk method is used to recursively walk the resulting structure so
// that modifications can be made.

var k;
                var v;
                var value = holder[key];
                if (value && typeof value === "object") {
                    for (k in value) {
                        if (Object.prototype.hasOwnProperty.call(value, k)) {
                            v = walk(value, k);
                            if (v !== undefined) {
                                value[k] = v;
                            } else {
                                delete value[k];
                            }
                        }
                    }
                }
                return reviver.call(holder, key, value);
            }

// Parsing happens in four stages. In the first stage, we replace certain
// Unicode characters with escape sequences. JavaScript handles many characters
// incorrectly, either silently deleting them, or treating them as line endings.

text = String(text);
            rx_dangerous.lastIndex = 0;
            if (rx_dangerous.test(text)) {
                text = text.replace(rx_dangerous, function (a) {
                    return (
                        "\\u"
                        + ("0000" + a.charCodeAt(0).toString(16)).slice(-4)
                    );
                });
            }

// In the second stage, we run the text against regular expressions that look
// for non-JSON patterns. We are especially concerned with "()" and "new"
// because they can cause invocation, and "=" because it can cause mutation.
// But just to be safe, we want to reject all unexpected forms.

// We split the second stage into 4 regexp operations in order to work around
// crippling inefficiencies in IE's and Safari's regexp engines. First we
// replace the JSON backslash pairs with "@" (a non-JSON character). Second, we
// replace all simple value tokens with "]" characters. Third, we delete all
// open brackets that follow a colon or comma or that begin the text. Finally,
// we look to see that the remaining characters are only whitespace or "]" or
// "," or ":" or "{" or "}". If that is so, then the text is safe for eval.

if (
                rx_one.test(
                    text
                        .replace(rx_two, "@")
                        .replace(rx_three, "]")
                        .replace(rx_four, "")
                )
            ) {

// In the third stage we use the eval function to compile the text into a
// JavaScript structure. The "{" operator is subject to a syntactic ambiguity
// in JavaScript: it can begin a block or an object literal. We wrap the text
// in parens to eliminate the ambiguity.

j = eval("(" + text + ")");

// In the optional fourth stage, we recursively walk the new structure, passing
// each name/value pair to a reviver function for possible transformation.

return (typeof reviver === "function")
                    ? walk({"": j}, "")
                    : j;
            }

// If the text is not JSON parseable, then a SyntaxError is thrown.

throw new SyntaxError("JSON.parse");
        };
    }
}());
ENDTEXTBLOCK

//////////////////////////////////////////////////
// 【引数】
//   array : 配列
//   rank : 抽出する値の大きい方から数えた順位
// 【戻り値】
//////////////////////////////////////////////////
FUNCTION large(array[], rank)
	IFB rank >= 1 AND rank <= LENGTH(array) THEN
		shellSort(array)
		RESULT = array[LENGTH(array) - rank]
	ELSE
		RESULT = ERR_VALUE
	ENDIF
FEND

//////////////////////////////////////////////////
// 【引数】
//   JC : ユリウス世紀
// 【戻り値】
//   太陽黄経（λsun）
//////////////////////////////////////////////////
FUNCTION longitudeSun(JC)
	DIM A[18] = 0.0004, 0.0004, 0.0005, 0.0005, 0.0006, 0.0007, 0.0007, 0.0007, 0.0013, 0.0015, 0.0018, 0.0018, 0.0020, 0.0200, -0.0048*JC, 1.9147, 36000.7695*JC, 280.4659
	DIM k[18] = 31557.0, 29930.0, 2281.0, 155.0, 33718.0, 9038.0, 3035.0, 65929.0, 22519.0, 45038.0, 445267.0, 19.0, 32964.0, 71998.1, 35999.05, 35999.05, 0, 0
	DIM θ0[18] = 161.0, 48.0, 221.0, 118.0, 316.0, 64.0, 110.0, 45.0, 352.0, 254.0, 208.0, 159.0, 158.0, 265.1, 267.52, 267.52, 0, 0
	DIM λsun[18]
	FOR n = 0 TO 15
		DIM ang = normalizeAngle(k[n] * JC + θ0[n])
		λsun[n] = A[n] * COS(degToRad(ang))
	NEXT
	λsun[16] = normalizeAngle(A[16])
	λsun[17] = normalizeAngle(A[17])
	RESULT = normalizeAngle(CALCARRAY(λsun, CALC_ADD))
FEND

//////////////////////////////////////////////////
// 【引数】
//   JD : ユリウス日
// 【戻り値】
//   指定したユリウス日の直前の二至二分の日時
//////////////////////////////////////////////////
FUNCTION nishiNibun(JD)
	// ユリウス日を力学時に変換
	DIM TD = JD - 9/24
	DIM n = 1
	REPEAT
		// 力学時をユリウス世紀に変換
		DIM JC = (TD + 0.5 - 2451545) / 36525
		DIM λsun = longitudeSun(JC)
		IF n = 1 THEN DIM λsun0 = INT(λsun / 90) * 90
		DIM Δλ = λsun - λsun0
		SELECT TRUE
			CASE Δλ > 180
				Δλ = Δλ - 360
			CASE Δλ < -180
				Δλ = Δλ + 180
		SELEND
		DIM Δt = Δλ * (365.2/360)
		TD = TD - Δt
		n = n + 1
	UNTIL ABS(Δt) <= 1/86400
	DIM arr[1]
	arr[0] = TD + 9/24
	arr[1] = λsun0
	RESULT = SLICE(arr)
FEND

//////////////////////////////////////////////////
// 【引数】
//   deg : 度数法
//   offset : 0～360°の範囲からずらす場合のオフセット
// 【戻り値】
//   度単位の角度を0～360度に正規化
//////////////////////////////////////////////////
FUNCTION normalizeAngle(deg, offset = 0)
	deg = deg - offset
	SELECT TRUE
		CASE deg >= 360 + offset
			deg = deg - INT(deg / 360) * 360
		CASE deg < 0
			deg = deg + INT(ABS(deg / 360) + 1) * 360
	SELEND
	RESULT = deg + offset
FEND

//////////////////////////////////////////////////
// 【引数】
//   str : 正規表現による検索の対象となる文字列
//   Pattern : 正規表現で使用するパターンを設定
//   IgnoreCase : 大文字・小文字を区別しない場合はTrue、区別する場合はFalse
//   Global : 文字列全体を検索する場合はTrue、しない場合はFalse
// 【戻り値】
//   正規表現で検索した結果をMatchesコレクションとして返します。
//////////////////////////////////////////////////
FUNCTION reExecute(str, Pattern, IgnoreCase = TRUE, Global = TRUE)
	DIM re = CREATEOLEOBJ("VBScript.RegExp")
	re.Pattern = Pattern
	re.IgnoreCase = IgnoreCase
	re.Global = Global
	RESULT = re.Execute(str)
FEND

//////////////////////////////////////////////////
// 【引数】
//   str : 正規表現による検索の対象となる文字列
//   Pattern : 正規表現で使用するパターンを設定
//   IgnoreCase : 大文字・小文字を区別しない場合はTrue、区別する場合はFalse
//   Global : 文字列全体を検索する場合はTrue、しない場合はFalse
// 【戻り値】
//   正規表現にマッチするかどうかを示すブール値
//////////////////////////////////////////////////
FUNCTION reTest(str, Pattern, IgnoreCase = TRUE, Global = TRUE)
	DIM re = CREATEOLEOBJ("VBScript.RegExp")
	re.Pattern = Pattern
	re.IgnoreCase = IgnoreCase
	re.Global = Global
	RESULT = re.Test(str)
FEND

//////////////////////////////////////////////////
// 【引数】
//   num : 数値
//   digit : 四捨五入する位置（マイナスで整数方向）
// 【戻り値】
//   四捨五入した値
//////////////////////////////////////////////////
FUNCTION roundOff(num, digit = 0)
	DIM sign = sign(num)
	num = ABS(num)
	DIM offset = POWER(10, digit)
	DIM n = num * offset - INT(num * offset)
	RESULT = sign * IIF(n >= 0.5, CEIL(num * offset) / offset, INT(num * offset) / offset)
FEND

//////////////////////////////////////////////////
// 【引数】
//   serial : 時間を表すシリアル値を指定
// 【戻り値】
//////////////////////////////////////////////////
FUNCTION Second(serial)
	RESULT = REPLACE(FORMAT(INT(serial * 86400) MOD 60, 2), " ", "0")
FEND

//////////////////////////////////////////////////
// 【引数】
//   array : ソートする数値を格納した配列。参照引数。
// 【戻り値】
//////////////////////////////////////////////////
PROCEDURE shellSort(Var array[])
	DIM i, j, inc, temp
	
	inc = 4
	WHILE INT(inc) > 0
		FOR i = 0 TO UBound(array)
			j = i
			temp = array[i]
			WHILE j >= inc AND array[zcut(j-inc)] > temp
				array[j] = array[j-inc]
				j = j - inc
			WEND
			array[j] = temp
		NEXT
		IFB inc / 2 <> 0 THEN
			inc = inc / 2
		ELSEIF inc = 1 THEN
			inc = 0
		ELSE
			inc = 1
		ENDIF
	WEND
FEND

//////////////////////////////////////////////////
// 【引数】
//   num : 符号を求める数値
// 【戻り値】
//   1 : 正の数、0 : ゼロ、-1 : 負の数、ERR_VALUE : それ以外
//////////////////////////////////////////////////
FUNCTION sign(num)
	SELECT TRUE
		CASE !CHKNUM(num)
			RESULT = ERR_VALUE
		CASE num > 0
			RESULT = 1
		CASE num = 0
			RESULT = 0
		CASE num < 0
			RESULT = -1
	SELEND
FEND

//////////////////////////////////////////////////
// 【引数】
//   array : 配列
//   rank : 抽出する値の小さい方から数えた順位
// 【戻り値】
//////////////////////////////////////////////////
FUNCTION small(array[], rank)
	IFB rank >= 1 AND rank <= LENGTH(array) THEN
		shellSort(array)
		RESULT = array[rank-1]
	ELSE
		RESULT = ERR_VALUE
	ENDIF
FEND

//////////////////////////////////////////////////
// 【引数】
//   input : 入力文字列
//   length : 埋めたあとの長さ
//   str : 埋める文字
//   type : 埋める方向
// 【戻り値】
//   指定文字で埋めた文字列
//////////////////////////////////////////////////
FUNCTION strPad(input, length, str = " ", type = RIGHT)
	DIM s = ""
	SELECT type
		CASE LEFT
			FOR i = 1 TO CEIL((length - LENGTH(input)) / LENGTH(str))
				s = s + str
			NEXT
			input = COPY(s, 1, length - LENGTH(input)) + input
		CASE RIGHT
			FOR i = 1 TO CEIL((length - LENGTH(input)) / LENGTH(str))
				s = s + str
			NEXT
			input = input + COPY(s, 1, length - LENGTH(input))
	SELEND
	RESULT = input
FEND

//////////////////////////////////////////////////
// 【引数】
//   inputs : 繰り返す文字列
//   multiplier : inputsを繰り返す回数
// 【戻り値】
//   inputsをmultiplier回を繰り返した文字列を返します
//////////////////////////////////////////////////
FUNCTION strRepeat(inputs, multiplier)
	DIM res = ""
	FOR n = 1 TO multiplier
		res = res + inputs
	NEXT
	RESULT = res
FEND

//////////////////////////////////////////////////
// 【引数】
//   a : bと交換する値。参照引数。
//   b : aと交換する値。参照引数。
// 【戻り値】
//////////////////////////////////////////////////
PROCEDURE swap(Var a, Var b)
	DIM tmp = a
	a = b
	b = tmp
FEND

//////////////////////////////////////////////////
// 【引数】
//   serial : シリアル値
//   format : フォーマット
// 【戻り値】
//   数値を表示書式に基づいて変換した文字列
//////////////////////////////////////////////////
FUNCTION text(serial, format, hour12 = FALSE)
	HASHTBL startDate
	startDate["明治"] = "1868/01/25"
	startDate["大正"] = "1912/07/30"
	startDate["昭和"] = "1926/12/25"
	startDate["平成"] = "1989/01/08"
	startDate["令和"] = "2019/05/01"
	
	DIM baseDate = "1899/12/30"
	serial = VAL(serial)
	SELECT TRUE
		CASE reTest(format, "\[h+\]")
			Matches = reExecute(format, "\[(h+)\]")
			DIM hour = iif(hour12, Hour(serial) MOD 12, Hour(serial))
			RESULT = text(hour, strRepeat("0", LENGTH(Matches.Item(0).SubMatches(0))))
		CASE reTest(format, "^h+$")
			Matches = reExecute(format, "^(h+)$")
			hour = iif(hour12, Hour(serial) MOD 12, Hour(serial))
			RESULT = text(hour MOD 24, strRepeat("0", LENGTH(Matches.Item(0).SubMatches(0))))
		CASE reTest(format, "\[m+\]")
			Matches = reExecute(format, "\[(m+)\]")
			RESULT = text(serial * 1440, strRepeat("0", LENGTH(Matches.Item(0).SubMatches(0))))
		CASE format = "m"
			GETTIME(serial, baseDate)
			RESULT = text(G_TIME_MM, "0")
		CASE format = "mm"
			GETTIME(serial, baseDate)
			RESULT = G_TIME_MM2
		CASE format = "n"
			GETTIME(serial, baseDate)
			RESULT = G_TIME_NN
		CASE format = "nn"
			GETTIME(serial, baseDate)
			RESULT = G_TIME_NN2
		CASE format = "s"
			GETTIME(serial, baseDate)
			RESULT = text(G_TIME_SS, "0")
		CASE format = "ss"
			GETTIME(serial, baseDate)
			RESULT = G_TIME_SS2
		CASE format = "yyyy"
			GETTIME(serial, baseDate)
			RESULT = G_TIME_YY4
		CASE format = "yy"
			GETTIME(serial, baseDate)
			RESULT = COPY(G_TIME_YY4, 3, 2)
		CASE format = "e"
			SELECT TRUE
				CASE dateDiff("d", startDate["令和"], text(serial, "yyyy/mm/dd")) >= 0
					RESULT = text(serial, "yyyy") - 2018
				CASE dateDiff("d", startDate["平成"], text(serial, "yyyy/mm/dd")) >= 0
					RESULT = text(serial, "yyyy") - 1988
				CASE dateDiff("d", startDate["昭和"], text(serial, "yyyy/mm/dd")) >= 0
					RESULT = text(serial, "yyyy") - 1925
				CASE dateDiff("d", startDate["大正"], text(serial, "yyyy/mm/dd")) >= 0
					RESULT = text(serial, "yyyy") - 1911
				CASE dateDiff("d", startDate["明治"], text(serial, "yyyy/mm/dd")) >= 0
					RESULT = text(serial, "yyyy") - 1867
			SELEND
		CASE format = "ee"
			SELECT TRUE
				CASE dateDiff("d", startDate["令和"], text(serial, "yyyy/mm/dd")) >= 0
					RESULT = text(text(serial, "yyyy") - 2018, "00")
				CASE dateDiff("d", startDate["平成"], text(serial, "yyyy/mm/dd")) >= 0
					RESULT = text(text(serial, "yyyy") - 1988, "00")
				CASE dateDiff("d", startDate["昭和"], text(serial, "yyyy/mm/dd")) >= 0
					RESULT = text(text(serial, "yyyy") - 1925, "00")
				CASE dateDiff("d", startDate["大正"], text(serial, "yyyy/mm/dd")) >= 0
					RESULT = text(text(serial, "yyyy") - 1911, "00")
				CASE dateDiff("d", startDate["明治"], text(serial, "yyyy/mm/dd")) >= 0
					RESULT = text(text(serial, "yyyy") - 1867, "00")
			SELEND
		CASE format = "g"
			SELECT TRUE
				CASE dateDiff("d", startDate["令和"], text(serial, "yyyy/mm/dd")) >= 0;		RESULT = "R"
				CASE dateDiff("d", startDate["平成"], text(serial, "yyyy/mm/dd")) >= 0;		RESULT = "H"
				CASE dateDiff("d", startDate["昭和"], text(serial, "yyyy/mm/dd")) >= 0;		RESULT = "S"
				CASE dateDiff("d", startDate["大正"], text(serial, "yyyy/mm/dd")) >= 0;		RESULT = "T"
				CASE dateDiff("d", startDate["明治"], text(serial, "yyyy/mm/dd")) >= 0;		RESULT = "M"
			SELEND
		CASE format = "gg"
			RESULT = COPY(text(serial, "ggg"), 1, 1)
		CASE format = "ggg"
			SELECT TRUE
				CASE dateDiff("d", startDate["令和"], text(serial, "yyyy/mm/dd")) >= 0;		RESULT = "令和"
				CASE dateDiff("d", startDate["平成"], text(serial, "yyyy/mm/dd")) >= 0;		RESULT = "平成"
				CASE dateDiff("d", startDate["昭和"], text(serial, "yyyy/mm/dd")) >= 0;		RESULT = "昭和"
				CASE dateDiff("d", startDate["大正"], text(serial, "yyyy/mm/dd")) >= 0;		RESULT = "大正"
				CASE dateDiff("d", startDate["明治"], text(serial, "yyyy/mm/dd")) >= 0;		RESULT = "明治"
			SELEND
		CASE format = "mmmmm"
			RESULT = COPY(text(serial, "mmmm"), 1, 1)
		CASE format = "mmmm"
			DIM month[] = "January", "February", "March", "April", "May", "June", "July", "August", "September", "October", "November", "December"
			RESULT = month[text(serial, "m") - 1]
		CASE format = "mmm"
			RESULT = COPY(text(serial, "mmmm"), 1, 3)
		CASE format = "dd"
			GETTIME(serial, baseDate)
			RESULT = text(G_TIME_DD2, "00")
		CASE format = "d"
			GETTIME(serial, baseDate)
			RESULT = text(G_TIME_DD, "0")
		CASE reTest(format, "^[ad]{3,4}$")
			Matches = reExecute(format, "([ad]{3,4})")
			GETTIME(serial, baseDate)
			DIM aaa[] = "日", "月", "火", "水", "木", "金", "土"
			DIM aaaa[] = "日曜日", "月曜日", "火曜日", "水曜日", "木曜日", "金曜日", "土曜日"
			DIM ddd[] = "Sun", "Mon", "Tue", "Wed", "Thu", "Fri", "Sat"
			DIM dddd[] = "Sunday", "Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday"
			RESULT = EVAL(Matches.Item(0).SubMatches(0) + "[" + getWeekday(G_TIME_WW, 1) + "]")
		CASE reTest(format, "(0+\.?0+)?%")
			Matches = reExecute(format, "(0+\.?0+)?%")
			RESULT = text(serial * 100, Matches.Item(0).SubMatches(0)) + "%"
		CASE reTest(format, "^\[DBNum\d{1,4}\](.*?)$")
			Matches = reExecute(format, "^\[DBNum(\d{1,4})\](.*?)$")
			DIM value = VAL(Matches.Item(0).SubMatches(0))
			DIM sss = text(serial, Matches.Item(0).SubMatches(1))
			Matches = reExecute(sss, "(\D+)?(\d+)(\D+)?")
			DIM res = ""
			FOR m = 0 TO Matches.Count - 1
				serial = Matches.Item(m).SubMatches(1)
				SELECT value
					CASE 1, 2
						DIM n[][9] = "〇", "一", "二", "三", "四", "五", "六", "七", "八", "九", _
										"", "壱", "弐", "参", "四", "伍", "六", "七", "八", "九"
						DIM a[][3] = "", "十", "百", "千",  _
										"", "拾", "百", "阡"
						DIM b[][3] = "", "万", "億", "兆", _
										"", "萬", "億", "兆"
						DIM r = ""
						DIM j = 0
						type = value - 1
						REPEAT
							DIM str = ""
							DIM n4 = serial MOD 10000
							FOR i = LENGTH(n4) TO 1 STEP -1
								s = COPY(n4, i, 1)
								IFB s = 1 AND a[type][LENGTH(n4)-i] <> "" THEN
									str = IIF(s, a[type][LENGTH(n4)-i], "") + str
								ELSE	
									str = n[type][s] + IIF(s, a[type][LENGTH(n4)-i], "") + str
								ENDIF
							NEXT
							IF str <> "" THEN r = str + b[type][j] + r
							j = j + 1
							serial = INT(serial / 10000)
						UNTIL serial = 0
						res = res + Matches.Item(m).SubMatches(0) + r + Matches.Item(m).SubMatches(2)
					CASE 3
						res = res + Matches.Item(m).SubMatches(0) + STRCONV(serial, SC_FULLWIDTH) + Matches.Item(m).SubMatches(2)
					CASE 4
						res = res + Matches.Item(m).SubMatches(0) + STRCONV(serial, SC_HALFWIDTH) + Matches.Item(m).SubMatches(2)
				SELEND
			NEXT
			RESULT = res
		CASE reTest(format, "^(.*?)(AM\/PM|am\/pm|A\/P|a\/p)(.*?)$")
			Matches = reExecute(format, "^(.*?)(AM\/PM|am\/pm|A\/P|a\/p)(.*?)$")
			DIM array = SPLIT(Matches.Item(0).SubMatches(1), "/")
			ampm = array[IIF(serial - INT(serial) >= 0.5, 1, 0)]
			hour12 = TRUE
			res = ""
			WITH Matches.Item(0)
				res = text(serial, .SubMatches(0), hour12) + ampm + text(serial, .SubMatches(2), hour12)
			ENDWITH
			RESULT = res
		CASE reTest(format, "([^ymdagehns]{0,})?(([ymdagehns])\3{0,})([^ymdagehns]+)?")
			Matches = reExecute(format, "([^ymdagehns]{0,})?(([ymdagehns])\3{0,})([^ymdagehns]+)?")
			FOR n = 0 TO Matches.Count - 1
				IF n = 0 THEN res = Matches.Item(n).SubMatches(0)
			NEXT
			FOR n = 0 TO Matches.Count - 1
				WITH Matches.Item(n)
					res = res + text(serial, .SubMatches(1), hour12) + .SubMatches(3)
				ENDWITH
			NEXT
			RESULT = res
		CASE format = "0/0"
			DIM separator = POS(".", serial)
			DIM g = 0
			IFB separator <> 0 THEN
				DIM keta = LENGTH(serial)
				DIM shift = POWER(10, keta - separator)
				IFB shift >= POWER(10, 15) THEN
					DIM position = 0
					FOR i = 0 TO 14
						IFB serial * POWER(10, i) - serial >= 1 THEN
							position = i
							BREAK
						ENDIF
					NEXT
					tmp = serial * POWER(10, position)
					FOR i = 1 TO 15
						r = (tmp * POWER(10, i)) / serial - (tmp / serial)
						a1 = tmp * POWER(10, i) - tmp
						IF a1 = INT(a1) THEN BREAK 
					NEXT
					DIM frac[] = a1, r
					g = GCD(frac)
					RESULT = (a1/g) + "/" + (r/g)
				ELSE
					DIM molecule = serial * shift	// 分子
					DIM denominator = shift		// 分母
					DIM nums[] = molecule, denominator
					g = GCD(nums)
					molecule = molecule / g
					denominator = denominator / g
					RESULT = molecule + "/" + denominator
				ENDIF
			ELSE
				RESULT = serial + "/1"
			ENDIF
		CASE reTest(format, "(0+)\.?(0+)?") AND UBound(SPLIT(format, ".")) <= 1 
			Matches = reExecute(format, "(0+)\.?(0+)?")
			len1 = LENGTH(Matches.Item(0).SubMatches(0))
			len2 = LENGTH(Matches.Item(0).SubMatches(1))
			DIM arr[] = LENGTH(INT(serial)), len1
			IFB POS(".", format) THEN
				RESULT = REPLACE(FORMAT(serial, CALCARRAY(arr, CALC_MAX) + len2 + 1, len2), " ", "0")
			ELSE
				RESULT = REPLACE(FORMAT(serial, CALCARRAY(arr, CALC_MAX)), " ", "0")
			ENDIF
	SELEND
FEND

//////////////////////////////////////////////////
// 【引数】
//   str : 時刻文字列。hh:nn:ss AM/PM、hh:nn AM/PM、hh AM/PM、hh:nn:ss、hh:nn、hh時nn分ss秒、hh時nn分のいずれかの形式を指定。
// 【戻り値】
//   シリアル値　（例）0…00:00:00、0.5…12:00:00、0.999988425925926…23:59:59
//////////////////////////////////////////////////
FUNCTION timeValue(str)
	DIM serial = 0
	DIM Matches
	DIM pattern = "(\d+)"
	DIM hh = "(0?[0-9]|1[0-2])"
	DIM ampm = "([AP]M|[ap]m)"
	SELECT TRUE
		CASE reTest(str, "\b" + hh + ":" + pattern + ":" + pattern + " " + ampm + "\b")
			Matches = reExecute(str, "\b" + hh + ":" + pattern + ":" + pattern + " " + ampm + "\b")
			WITH Matches.Item(0)
				serial = timeValue(.SubMatches(0) + " " + .SubMatches(3)) + VAL(.SubMatches(1)) / 1440 + VAL(.SubMatches(2)) / 86400
			ENDWITH
		CASE reTest(str, "\b" + hh + ":" + pattern + " " + ampm + "\b")
			Matches = reExecute(str, "\b" + hh + ":" + pattern + " " + ampm + "\b")
			WITH Matches.Item(0)
				serial = timeValue(.SubMatches(0) + " " + .SubMatches(2)) + VAL(.SubMatches(1)) / 1440
			ENDWITH
		CASE reTest(str, "\b" + hh + " " + ampm + "\b")
			Matches = reExecute(str, "\b" + hh + " " + ampm + "\b")
			WITH Matches.Item(0)
				serial = VAL(.SubMatches(0) MOD 12) + IIF(reTest(.SubMatches(1), "AM|am"), 0, 12)
				serial = serial / 24
			ENDWITH
		CASE reTest(str, "\b" + pattern + ":" + pattern + ":" + pattern + "\b")
			Matches = reExecute(str, "\b" + pattern + ":" + pattern + ":" + pattern + "\b")
			WITH Matches.Item(0)
				serial = VAL(.SubMatches(0)) / 24 + VAL(.SubMatches(1)) / 1440 + VAL(.SubMatches(2)) / 86400
			ENDWITH
		CASE reTest(str, "\b" + pattern + ":" + pattern + "\b")
			Matches = reExecute(str, "\b" + pattern + ":" + pattern + "\b")
			WITH Matches.Item(0)
				serial = VAL(.SubMatches(0)) / 24 + VAL(.SubMatches(1)) / 1440
			ENDWITH
		CASE reTest(str, "\b" + pattern + "時" + pattern + "分" + pattern + "秒")
			Matches = reExecute(str, "\b" + pattern + "時" + pattern + "分" + pattern + "秒")
			WITH Matches.Item(0)
				serial = VAL(.SubMatches(0)) / 24 + VAL(.SubMatches(1)) / 1440 + VAL(.SubMatches(2)) / 86400
			ENDWITH
		CASE reTest(str, "\b" + pattern + "時" + pattern + "分")
			Matches = reExecute(str, "\b" + pattern + "時" + pattern + "分")
			WITH Matches.Item(0)
				serial = VAL(.SubMatches(0)) / 24 + VAL(.SubMatches(1)) / 1440
			ENDWITH
		DEFAULT
			serial = ERR_VALUE
	SELEND
	RESULT = serial - INT(serial)
FEND

//////////////////////////////////////////////////
// 【引数】
//   arrayname : 上限値を求める配列の名前
//   dimension : 返す次元を示す整数
// 【戻り値】
//   配列の上限値
//////////////////////////////////////////////////
FUNCTION UBound(arrayname[], dimension = 1)
	RESULT = EVAL("RESIZE(arrayname" + strRepeat("[0]", dimension - 1) + ")")
FEND

//////////////////////////////////////////////////
// 【引数】
//   year : 年
//   month : 月
//   day : 日
//   hour : 時
//   minute : 分
//   second : 秒
// 【戻り値】
//   ユリウス日
//////////////////////////////////////////////////
FUNCTION YMDToJD(year, month, day, hour = 0, minute = 0, second = 0)
	year = VAL(year);	month = VAL(month);		day = VAL(day)
	hour = VAL(hour);	minute = VAL(minute);	second = VAL(second)
	IFB month < 3 THEN
		year = year - 1
		month = month + 12
	ENDIF
	DIM JD = INT(year * 365.25)
	JD = JD + INT(year / 400)
	JD = JD - INT(year / 100)
	JD = JD + INT((month - 2) * 30.59)
	JD = JD + 1721088
	JD = JD + day
	DIM t = second / 3600
	t = t + minute / 60
	t = t + hour
	t = t / 24
	JD = JD + t
	RESULT = JD
FEND

結果

使用関数

今年の秋分の日の日付を求める

秋分の日は太陽黄経が180度なので、翌年1月1日の直前の太陽黄経180度の日付を求める。

Main
FUNCTIONS