Decimalモジュール (自作関数)

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浮動小数点数の演算による誤差を防ぎ、正確な計算を行います。

構文

引数

戻り値

プログラム

//////////////////////////////////////////////////
// 【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】
//   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】
//   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】
//   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】
//   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】
//   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

Decimalモジュールとは

Decimalモジュール (自作関数)は精度の高い計算を行う必要があるときに使用します。JavaScriptで高精度な数値計算を行うdecimal.jsというライブラリをUWSCでも利用できるように作成したものです。

decimal.jsのダウンロードはGitHub - MikeMcl/decimal.js: An arbitrary-precision Decimal type for JavaScript · GitHub、公式ドキュメントはdecimal.js APIで確認できます。

UWSCの倍精度浮動小数点型（Double型）は15桁程度の精度がありますが、すべての実数を表現できるわけではないため期待値と異なる値になる場合もあります。

正しい計算結果を得られない原因については#errorの項目で記述しています。

Decimalインスタンス

Decimalインスタンスとは、浮動小数点数を厳密に表現するためのオブジェクトです。Decimalモジュール (自作関数)ではオブジェクトとして扱うことはできないので配列で数値を管理します。

Decimalモジュールの#ConstructorでDecimalインスタンスを生成することができます。

配列の0番目に符号、1番目に指数、2番目以降に指定桁ごと（デフォルト:7桁）に分割した仮数部が格納されます。

以下は#ConstructorでDecimalインスタンスを生成するプログラムです。戻り値は配列なのでJOIN関数でカンマで区切った文字列として出力します。

出力される結果の形式は符号,指数部,仮数部1,仮数部2,…です。仮数部は小数点の位置を中心として指定桁（7桁）ごとに区切られます。

結果

#Constructorで生成した符号、指数、仮数部で構成される#decimal-instanceを文字列に戻すには#finiteToStringを使います。

誤差

丸め誤差

丸め誤差とは、数値を有限の桁数で表すためにある桁以降を切り捨て、切り上げ、四捨五入することで生じる誤差。

例えば無限に続く円周率3.141592…を小数点以下3桁目を四捨五入して3.14として扱うことは、1592…が切り捨てられ丸め誤差となります。

打切り誤差

打切り誤差とは、本来無限に続く計算を途中で打ち切ることによって生じる誤差。

以下は1/3を計算した結果です。無限小数ですが、小数点以下16桁目以降は切り捨てられています。

結果

以下は2/3を計算した結果です。1/3の時と同様に無限小数ですが、小数点以下16桁目を四捨五入することで切り上げられています。

結果

#dividedByを使うと有効桁数を指定することができます。以下は1/3を有効桁数50桁に指定。

結果

以下は2/3を有効桁数20桁、#rmを1（0の方向へ丸める）を指定。

結果

情報落ち

情報落ちとは、絶対値の大きい数と小さい数を加減算したとき、小さい数の情報が結果に反映されずに生じる誤差。

10000000000000000 + 1 - 10000000000000000を計算する例です。$10^{16}$という大きい数に対して1という小さい数を加算しても結果に反映されず誤差が生じます。

結果

桁落ち

桁落ちとは、ほぼ等しい数を減算したときに生じる誤差。例えば0.123456789 - 0.123456788の計算を行ったとき0.123456789、0.123456788は有効桁数9桁だが、計算結果の0.000000001は有効桁数1桁というように有効桁数が極端に減少することをいいます。

以下のプログラムは桁落ち以前に小数値であるために丸め誤差が発生しているため、結果が正しく出力されません。

結果

Decimalモジュール (自作関数)を使うと正しい結果を得られます。

結果

オーバーフロー/アンダーフロー

オーバーフローは、データ型で扱える範囲の上限値を超えたときに発生します。Decimalモジュール (自作関数)ではデフォルトで9E+15まで扱うことができます。

一方でアンダーフローは、データ型で扱える範囲の下限値を下回ったときに発生します。Decimalモジュール (自作関数)ではデフォルトで-9E+15まで扱うことができます。

特殊値

Decimalモジュール (自作関数)では通常の値とは別に以下の特殊値があります。decimal.jsで無限大を表す値はInfinityですが、UWSCでは同じ無限大を表す値としてINFがあるのでそれを文字列形式の"INF"として扱うこととします。

特殊値		意味
decimal.js	UWSC	意味
Infinity	INF	正の無限大
-Infinity	-INF	負の無限大
NaN	NaN	非数

decimal.jsで値は符号、指数、仮数部の配列で構成で表現されますが、特殊値は普通の値では表現できないため配列構成も特殊です。

数値を配列に変換するには#Constructorを使います。

まずはdecimal.jsでの特殊値の配列構成です。Decimal{　}内が配列の値で、カンマ区切りで0〜2番目の値で特殊値を表します。

次にUWSCでの特殊値の配列構成です。decimal.jsではNaNやnullで表していた値をUWSCではNULLやFALSEとして扱っています。UWSCでNaNに該当する値がないのと、特殊値を判断する分岐処理での都合によるためです。

また特殊値を含む値の四則演算の結果は以下の表のようになります。

1行目は被演算数INF、演算数INFのときの結果が、加算はINF、減算はNaN、乗算はINF、除算はNaNということを表しています。

式		結果
被演算数	演算数	加算	減算	乗算	除算
INF	INF	INF	NaN	INF	NaN
INF	-INF	NaN	INF	-INF	NaN
INF	NaN	NaN	NaN	NaN	NaN
INF	0	INF	INF	NaN	INF
-INF	INF	NaN	-INF	-INF	NaN
-INF	-INF	-INF	NaN	INF	NaN
-INF	NaN	NaN	NaN	NaN	NaN
-INF	0	-INF	-INF	NaN	-INF
NaN	INF	NaN	NaN	NaN	NaN
NaN	-INF	NaN	NaN	NaN	NaN
NaN	NaN	NaN	NaN	NaN	NaN
NaN	0	NaN	NaN	NaN	NaN
0	INF	INF	-INF	NaN	0
0	-INF	-INF	INF	NaN	0
0	NaN	NaN	NaN	NaN	NaN
0	0	0	0	0	NaN

以下の表は被演算数、演算数でまとめたもので内容は上の表と同じです。

被演算数	演算数
被演算数	INF	-INF	NaN	0
INF	+：INF -：NaN *：INF /：NaN	+：NaN -：INF *：-INF /：NaN	+：NaN -：NaN *：NaN /：NaN	+：INF -：INF *：NaN /：INF
-INF	+：NaN -：-INF *：-INF /：NaN	+：-INF -：NaN *：INF /：NaN	+：NaN -：NaN *：NaN /：NaN	+：-INF -：-INF *：NaN /：-INF
NaN	+：NaN -：NaN *：NaN /：NaN	+：NaN -：NaN *：NaN /：NaN	+：NaN -：NaN *：NaN /：NaN	+：NaN -：NaN *：NaN /：NaN
0	+：INF -：-INF *：NaN /：0	+：-INF -：INF *：NaN /：0	+：NaN -：NaN *：NaN /：NaN	+：0 -：0 *：0 /：NaN

プロパティ

演算精度や丸め方法、指数範囲などを制御します。

変数	説明	既定値
precision	有効桁数	20
rounding	#rm	4
modulo	剰余の定義を指定	1
toExpNeg	指数表記を使い始める負の指数の閾値しきいち	-7
toExpPos	指数表記を使い始める正の指数の閾値しきいち	21
minE	許容する最小指数。指数がこの数値以下になると0を返します。	-9E+15
maxE	許容する最大指数。指数がこの数値以上になるとINFを返します。	9E+15

プロパティ値は以下のように指定することで変更できます。

precision

有効桁数を指定します。演算結果がこの桁数に丸められます。デフォルトでは有効桁数20桁。

このプロパティはライブラリ全体の既定の有効桁数を設定するグローバル設定です。インスタンスやメソッド呼び出しで明示的に有効桁数を渡さない場合に使われます。

rounding

丸めモードを指定します。値は#rmの表にあるように0から8の値を指定できます。デフォルトでは四捨五入（4）。

このプロパティはライブラリ全体の既定の丸めモードを設定するグローバル設定です。インスタンスやメソッド呼び出しで明示的に丸めモードを渡さない場合に使われます。

modulo

剰余を求める際のモードを設定します。

プロパティ	値	説明
ROUND_UP	0	無限大方向へ丸める
ROUND_DOWN	1	0の方向へ丸める
ROUND_FLOOR	3	負の無限大方向へ丸める
ROUND_HALF_EVEN	6	偶数丸め
EUCLID	9	剰余は常に正数

以下の式は各モードでの基本形式です。

\[ q = \operatorname{round\_mode}\!\left(\frac{a}{n}\right),\qquad r = a - n\cdot q \]

被除数を$a$、除数を$n$、商を$q$、剰余を$r$とする。ただし$n \ne 0$。$\vert x \vert$は絶対値、$\lceil x \rceil$は天井関数、$\lfloor x \rfloor$は床関数、sgn(x)は符号関数（$x > 0 \to 1$、$x = 0 \to 0$、$x < 0 \to -1$）を表します。

指定したモードでの商を求めるには#quotient、剰余を求めるには#moduloを使います。

ROUND_UP

商を切り上げで丸めます。被除数が負なら剰余は正、被除数が正なら剰余は負となります。

丸め関数（無限大方向へ丸める）

\[ \operatorname{round\_up}(y) = \begin{cases} \lceil y\rceil & (y>0)\\ \lfloor y\rfloor & (y<0)\\ 0 & (y=0) \end{cases} \]

商と剰余

\[ q=\operatorname{round\_up}\!\left(\frac{a}{n}\right),\qquad r=a-nq \]

$a$を-5、$n$を3としたときの商と剰余を求めます。

\[ q=\operatorname{round\_up}\!\left(\frac{-5}{3}\right)=\lfloor -1.6\rfloor=-2 \] \[ \qquad r=a-nq=-5-3\times(-2)=-5+6=1 \]

以下はプロパティにROUND_UPを指定したときの剰余を求めるプログラムです。

結果

ROUND_DOWN

丸め関数（0の方向へ丸める）

\[ \operatorname{trunc}(y)=\begin{cases} \lfloor y\rfloor & (y\ge0)\\[4pt] \lceil y\rceil & (y<0) \end{cases} \]

商と剰余

\[ q=\operatorname{trunc}\!\left(\frac{a}{n}\right),\qquad r=a-nq \]

$a$を-5、$n$を3としたときの商と剰余を求めます。

\[ q=\operatorname{round\_up}\!\left(\frac{-5}{3}\right)=\lceil -1.6\rceil=-1 \] \[ \qquad r=a-nq=-5-3\times(-1)=-5+3=-2 \]

以下はプロパティにROUND_DOWNを指定したときの剰余を求めるプログラムです。

結果

ROUND_FLOOR

丸め関数（負の無限大方向へ丸める）

\[ \operatorname{floor}(y)=\lfloor y\rfloor \]

商と剰余

\[ q=\lfloor\tfrac{a}{n}\rfloor,\qquad r=a-nq \]

$a$を-5、$n$を3としたときの商と剰余を求めます。

\[ q=\lfloor\tfrac{-5}{3}\rfloor=\lfloor-1.6\rfloor=-2 \] \[ \qquad r=a-nq=-5-3\times(-2)=-5+6=1 \]

以下はプロパティにROUND_FLOORを指定したときの剰余を求めるプログラムです。

結果

ROUND_HALF_EVEN

補助量

\[ m=\lfloor y\rfloor,\qquad d=y-m\quad(0\le d<1) \]

丸め関数（最近接、端点は偶数に丸める）

\[ \operatorname{round\_half\_even}(y)= \begin{cases} m & (d<0.5),\\[6pt] m+1 & (d>0.5),\\[6pt] m & (d=0.5\ \text{かつ}\ m\ \text{が偶数}),\\[6pt] m+1 & (d=0.5\ \text{かつ}\ m\ \text{が奇数}). \end{cases} \]

商と剰余

\[ q = \operatorname{round\_half\_even}\!\left(\frac{a}{n}\right),r=a-nq \]

$a$を-5、$n$を3としたときの商と剰余を求めます。

\[ q = \operatorname{round\_half\_even}\!\left(\frac{-5}{3}\right)=\lfloor -1.6\rfloor=-2 \] \[ r=a-nq=-5-3\times(-2)=-5+6=1 \]

以下はプロパティにROUND_HALF_EVENを指定したときの剰余を求めるプログラムです。

結果

EUCLID

商

\[ q = \operatorname{sgn}(n)\cdot\left\lfloor\frac{a}{|n|}\right\rfloor \]

これにより剰余は必ず非負となる（0 ≤ r < |n|）。

剰余

\[ r = a - n\cdot\Big(\operatorname{sgn}(n)\cdot\left\lfloor\frac{a}{|n|}\right\rfloor\Big) \] \[ r \equiv a \pmod{|n|},\qquad 0\le r<|n| \]

$a$を-5、$n$を3としたときの商と剰余を求めます。

\[ q = \operatorname{sgn}(3)\cdot\left\lfloor\frac{-5}{|3|}\right\rfloor = 1\cdot\left\lfloor-1.6\right\rfloor=-2 \] \[ r = -5-3\cdot\Big(\operatorname{sgn}(3)\cdot\left\lfloor\frac{-5}{|3|}\right\rfloor\Big)=-5-3\cdot\Big(1\cdot\left\lfloor-1.6\right\rfloor\Big)=-5-3\cdot\Big(1\cdot(-2)\Big)=-5-3\cdot-2=-5+6=1 \]

以下はプロパティにEUCLIDを指定したときの剰余を求めるプログラムです。

結果

toExpNeg

負数で指数を使い始める値を指定します。

負数では指数を使い始める値（toExpNeg）は-7乗がデフォルトになっているため指数の値がそれ以下のときは指数表記となります。-6乗までは固定小数点で出力されます。

結果

以下は$2^{-20}$を求めるプログラムです。デフォルトでは-7乗で指数表記となります。

結果

toExpNegに負数を指定することで指数を使い始める値を指定できます。以下は負の指数の閾値を-10としています。

結果

toExpPos

正数で指数を使い始める値を指定します。

正数では指数を使い始める値（toExpPos）は21乗がデフォルトになっているため指数の値がそれ以上のときは指数表記となります。20乗までは固定小数点で出力されます。

結果

以下は$2^{100}$を求めるプログラムです。デフォルトでは有効桁数（precision）が20桁、正数では指数を使い始めるの値（toExpPos）が21乗なので以下のように丸められてしまいます。

結果

関数を実行する前にプロパティに値を指定することで結果の精度を変更できます。

以下は有効桁数を35桁、指数を使い始める値を50乗としています。大きい値を指定することで結果を丸めずに求めることができます。

結果

minE

許容する指数の下限値を指定します。これを下回る値はアンダフローとして扱われ0を返します。

以下は0.01、0.001を指数表記にするプログラムです。

結果

eの右側の数値が指数を表しています。

以下は指数が-3以下のときはアンダーフローとし0を返します。0.01は指数表記だと1e-2なので0.01を返しますが、0.001は指数表記だと1e-3となりminEで指定された-3以下となるので0を返します。

結果

maxE

許容する指数の上限値を指定します。これを上回る値はオーバーフローとして扱われINFを返します。

以下は10000000、100000000を指数表記にするプログラムです。

結果

minEのときと同様、eの右側の数値が指数を表しています。

以下は指数が8以上のときはオーバーフローとしてINFを返します。10000000は指数表記だと1e+7なので10000000を返しますが、100000000は指数表記だと1e+8となりmaxEで指定された8以上となるのでINFを返します。

結果

引数

精度（Precision）

演算結果の精度を表します。この設定値を超える桁数が必要になった場合、#rmのルールに従って丸められます。デフォルトは20桁です。

特定の関数の呼び出しごとに適用するローカルな有効桁数のオーバーライドです。該当呼び出しだけに適用され、他の操作や既定値は変わりません。

演算時に一時的に計算精度を制御したいときに使います。

以下は引数にprを持つ関数です。

#dividedBy
#div
#minus
#sub
#plus
#add
#times
#mul
#divide
#getLN10
#intPow
#calculate
#calcRPN
#toRPN

以下は除算の結果を指定した桁数で丸めるプログラムです。

結果

精度が整数の桁数よりも小さい場合、先頭からprで指定された桁以降は0になります。丸めモードはデフォルトでは四捨五入（4）が指定されています。

結果

有効桁数（significant digits）

演算後の最終的な丸め・フォーマットを行うときに使います。

以下は引数にsdを持つ関数です。

#toBinary
#toHexadecimal
#toOctal
#toPrecision
#toSignificantDigits
#finalise
#finiteToString
#getLN10
#getPI
#naturalExponential
#naturalLogarithm
#toStringBinary

丸めモード（Rounding Mode）

演算結果を有効桁数に合わせる際の丸め方を表す整数を指定します。デフォルトは4の四捨五入です。

特定の丸め操作を行うメソッド呼び出しごとに使うローカルな丸めモードのオーバーライドです。該当呼び出しだけに適用され、他の操作や既定値は変わりません。

定数名はUWSCでは定義していないので0〜8の値を直接指定してください。

値	定数名	説明
0	ROUND_UP	無限大方向へ丸める
1	ROUND_DOWN	0の方向へ丸める
2	ROUND_CEIL	正の無限大方向へ丸める
3	ROUND_FLOOR	負の無限大方向へ丸める
4	ROUND_HALF_UP	四捨五入（境界値は無限大方向へ丸める）
5	ROUND_HALF_DOWN	五捨六入（境界値は0の方向へ丸める）
6	ROUND_HALF_EVEN	偶数丸め
7	ROUND_HALF_CEIL	正の方向へ丸める
8	ROUND_HALF_FLOOR	負の方向へ丸める

以下は引数にrmを持つ関数です。

小数点以下の桁数（decimal places）

小数点以下の桁数を何桁に丸めるかを指定します。

以下は引数にdpを持つ関数です。

#dividedBy
#toDecimalPlaces
#toExponential
#toFixed
#divide
#div

数値型（isNumeric）

計算結果（戻り値）を数値型で返す場合はTrueを指定します。

デフォルト値はFalseで文字列型で返します。

関数一覧

メイン関数

関数名	説明	カテゴリ	短縮形
#absoluteValue	絶対値		abs
#ceil	正の無限大方向へ丸める	丸め処理
#clampedTo	数値を範囲内に収める	丸め処理	clamp
#comparedTo	`x`と`y`を比較	比較	cmp
#cosine	余弦関数	三角関数	cos
#cubeRoot	三乗根	冪根（累乗根）	cbrt
#decimalPlaces	小数部の桁数		dp
#dividedBy	除算	四則演算	div
#dividedToIntegerBy	`x`を`y`で除算した整数部		divToInt
#equals	`x`と`y`が等しいか	比較	eq
#floor	負の無限大方向へ丸める	丸め処理
#greaterThan	`x`が`y`より大きいか	比較	gt
#greaterThanOrEqualTo	`x`が`y`以上か	比較	gte
#hyperbolicCosine	双曲余弦関数	双曲線関数	cosh
#hyperbolicSine	双曲正弦関数	双曲線関数	sinh
#hyperbolicTangent	双曲正接関数	双曲線関数	tanh
#inverseCosine	逆余弦関数	逆関数	acos
#inverseHyperbolicCosine	逆双曲線余弦関数	逆双曲線関数	acosh
#inverseHyperbolicSine	逆双曲線正弦関数	逆双曲線関数	asinh
#inverseHyperbolicTangent	逆双曲線正接関数	逆双曲線関数	atanh
#inverseSine	逆正弦関数	逆関数	asin
#inverseTangent	逆正接関数	逆関数	atan
#isFinite	有限値か	真偽値
#isInteger	整数か	真偽値	isInt
#isNaN	NaNか	真偽値
#isNegative	負数か	真偽値	isNeg
#isPositive	正数か	真偽値	isPos
#isZero	0か	真偽値
#lessThan	`x`が`y`より小さいか	比較	lt
#lessThanOrEqualTo	`x`が`y`以下か	比較	lte
#logarithm	対数もしくは常用対数	対数	log
#minus	減算	四則演算
#modulo	剰余（余り）		mod
#negated	`x`の正負を反転		neg
#plus	加算	四則演算
#precision	有効桁数		sd
#round	#rmを使用した丸め処理	丸め処理
#sine	正弦関数	三角関数	sin
#squareRoot	平方根	冪根（累乗根）	sqrt
#tangent	正接関数	三角関数	tan
#times	乗算	四則演算
#toBinary	10進数を2進数に変換	進数変換
#toDecimalPlaces	小数点以下を丸める	丸め処理	toDP
#toExponential	指数表記に変換
#toFixed	小数点以下を丸める	丸め処理
#toFraction	既約分数にした配列を求める
#toHexadecimal	10進数を16進数に変換	進数変換	toHex
#toJSON
#toNearest	指定した倍数に最も近い値への丸め処理	丸め処理
#toNumber	#decimal-instance
#toOctal	10進数を8進数に変換	進数変換
#toPower	累乗		pow
#toPrecision	指定した有効桁数、丸めモードで丸めた文字列を返す
#toSignificantDigits	指定した有効桁数、丸めモードで丸めた#decimal-instanceを返す		toSD
#toString	#decimal-instanceを文字列型に変換
#truncated	小数点以下を切り捨て、0の方向へ丸める。		trunc
#valueOf

ヘルパー関数

#main-functionの内部で補助するために使われている関数。

関数名	説明
#digitsToString	配列`d`に格納されている数字を桁合わせして結合
#checkInt32	数値が32ビット符号付き整数（-2,147,483,648 ～ 2,147,483,647）、もしくは`min`以上`max`以下の範囲内にあるか
#checkRoundingDigits	丸め処理の妥当性を検証
#convertBase	`str`に指定された文字列を`baseIn`の進数から`baseOut`の進数に変換します
#cosine2	#cosineのヘルパー関数
#divide	#dividedByのヘルパー関数
#finalise	#decimal-instanceを指定した有効桁数、丸めモードで丸めます
#finiteToString	#decimal-instanceを文字列型に変換します
#getBase10Exponent	$\log_{10}{digits}$を求める
#getLn10	$\log_{e}{10}$を`sd`の有効桁数で返す
#getPi	円周率を`sd`の有効桁数で返す。
#getPrecision	`x`の有効桁数を返す。
#getZeroString	0を`k`の数だけ結合した文字列
#intPow	$k^{n}$を返します。
#isOdd	`x`が奇数か
#maxOrMin
#naturalExponential	ネイピア数$e$を底、`x`を指数とする$e^{x}$
#naturalLogarithm	ネイピア数を底とした$\log_{e}{y}$
#nonFiniteToString
#parseDecimal	数値または文字列を#decimal-instanceに変換します
#parseOther	特殊値を#decimal-instanceに変換します
#sine2	#sineのヘルパー関数
#taylorSeries	テイラー展開を計算します。正弦関数、余弦関数、双曲線正弦関数、双曲線余弦関数の計算に使用。
#tinyPow	$b^{e}$を求める
#toLessThanHalfPi	三角関数の計算で入力された角度を$0 〜 \frac{\pi}{2}$の範囲に正規化します
#toLessThanHalfPi2	#toLessThanHalfPiの補助関数
#toStringBinary
#truncate

その他関数

#helper-functionに記載はないがdecimal.jsで定義されているその他関数。

関数名	説明
#compare	`a`と`b`を大小関係を比較
#Constructor	`v`を符号、指数、仮数部で構成される配列（#decimal-instance）に変換
#isDecimalInstance	`v`が#decimal-instanceか
#multiplyInteger	整数同士の乗算を行う
#subtract	減算

自作関数

Decimalモジュール (自作関数)の関数を使った計算処理を簡潔に記述するために当サイトの管理人が定義した関数。

関数名	説明
#calculate	#tokenize、#toRPN、#calcRPNの3つをまとめた関数で、文字列型で指定された計算式を逆ポーランド記法で計算した結果を返します。
#calcRPN	逆ポーランド記法を計算します
#cmpPrecedence
#isOperator	演算子か
#quotient	除算の商の整数部を返す
#tokenize	数式をトークンに分割します
#toRPN	トークンを逆ポーランド記法に変換します

メイン関数

absoluteValue関数

xの絶対値を返します。

x必須: 絶対値を返す数値、文字列もしくは#decimal-instance

-12.5、1.5の絶対値を求めます。

ceil関数

xを正の無限大方向へ丸めます。

x必須: 丸め対象となる数値、文字列もしくは#decimal-instance

5.4、-4.9を正の無限大方向へ丸めます。

clampedTo関数

数値を指定した範囲内に収めます。xがminより小さい場合はminに、maxよりも大きい場合はmaxに丸め込み、それ以外はそのまま返します。

x必須: 範囲内に収める対象となる数値、文字列もしくは#decimal-instance
min必須: 下限値
max必須: 上限値

150を0から100の範囲内に収めます。上限値の100を上回っているので100となります。

結果

-5を0から100の範囲内に収めます。下限値の0を下回っているので0となります。

結果

25を0から100の範囲内に収めます。下限値の0を上回っていて、上限値の100を下回っているので、25をそのまま返します。

結果

comparedTo関数

x、yの値を比較し、大小関係を数値で返します。

x必須: 大小を比較する1つ目の数値、文字列もしくは#decimal-instance
y必須: 大小を比較する2つ目の数値、文字列もしくは#decimal-instance

戻り値は以下の表に示すとおりです。

戻り値	説明
1	`x`が`y`より大きい
-1	`x`が`y`より小さい
0	`x`と`y`は同値
NaN	どちらか一方または両方が`NaN`

5と1を比較します。xがyより大きいので1を返します。

結果

-5と20を比較します。xがyより小さいので-1を返します。

結果

5と5を比較します。同値なので0を返します。

結果

10とNaNを比較します。一方がNaNなのでNaNを返します。

結果

cosine関数

x（弧度法）の余弦（斜辺と底辺の比）を求めます。

x必須: 弧度法による角度を表す数値、文字列もしくは#decimal-instance

0.25ラジアンの余弦を求めます。

結果

弧度法（ラジアン単位）で指定する場合はdegToRad関数 (自作関数)を使って度数法を弧度法に変換します。以下は度数法で30°の余弦を求めています。cos30°の値は$\frac{\sqrt{3}}{2} = 0.8660254038$です。

結果

cubeRoot関数

xの三乗根を返します。

x必須: 三乗根を求める対象となる数値、文字列もしくは#decimal-instance

9、125、-1000の三乗根を返します。

decimalPlaces関数

xの小数部の桁数を返します。

x必須: 小数部の桁数を求める対象となる数値、文字列もしくは#decimal-instance

1.235、-27の小数部の桁数を返します。

dividedBy関数

dividendをdivisorで割った値を返します。

dividend必須: 被除数となる数値、文字列もしくは#decimal-instance
divisor必須: 除数となる数値、文字列もしくは#decimal-instance

6を9で割った値を返します。

結果

精度を指定するにはprecisionプロパティを使います。精度を5桁に指定しています。

結果

丸めモードで丸め方を指定することもできます。デフォルトでは四捨五入ですが、以下ではDecimal.ROUND_FLOORで負の無限大方向へ丸めています。

結果

特殊値同士の計算結果は以下のようになります。

結果

dividedToIntegerBy関数

xをyで除算した整数部を返します。

x必須: 被除数となる数値、文字列もしくは#decimal-instance
y必須: 除数となる数値、文字列もしくは#decimal-instance

12を5で除算した整数部を返します。

結果

equals関数

xとyが等しいかを示すブール値を返します。xとyが等しければTrue、等しくなければFalseを返します。

x必須: 比較する1つ目の数値、文字列もしくは#decimal-instance
y必須: 比較する2つ目の数値、文字列もしくは#decimal-instance

1.0と1が等しいかを示すブール値を返します。表記が違っていても数値的に等しければTrueを返します。

結果

floor関数

xを負の無限大方向へ丸めた値を返します。

x必須: 丸め対象となる数値、文字列もしくは#decimal-instance

4.2を負の無限大方向へ丸めた値を求めます。

結果

-2.1を負の無限大方向へ丸めた値を求めます。

結果

greaterThan関数

xがyより大きいかを示すブール値を返します。xがyよりも大きければTrue、小さければFalseを返します。

x必須: 大小を比較する1つ目の数値、文字列もしくは#decimal-instance
y必須: 大小を比較する2つ目の数値、文字列もしくは#decimal-instance

0.1が0.2より大きいかを示すブール値を返します。0.1 > 0.2は成り立たないのでFalseを返します。

結果

greaterThanOrEqualTo関数

xがy以上かを示すブール値を返します。xがyと等しいか、もしくは大きければTrue、そうでなければFalseを返します。

x必須: 大小を比較する1つ目の数値、文字列もしくは#decimal-instance
y必須: 大小を比較する2つ目の数値、文字列もしくは#decimal-instance

0.3が0.2以上かを示すブール値を返します。0.3 >= 0.2が成り立つのでTrueを返します。

結果

hyperbolicCosine関数

双曲線余弦（ハイパボリックコサイン）を求めます。

x必須: 弧度法による角度を表す数値、文字列もしくは#decimal-instance

結果

hyperbolicSine関数

双曲線正弦（ハイパボリックサイン）を求めます。

x必須: 弧度法による角度を表す数値、文字列もしくは#decimal-instance

結果

hyperbolicTangent関数

双曲線正接（ハイパボリックタンジェント）を求めます。

x必須: 弧度法による角度を表す数値、文字列もしくは#decimal-instance

結果

inverseCosine関数

逆余弦（アークコサイン）を求めます。

x必須: 弧度法による角度を表す数値、文字列もしくは#decimal-instance

結果

inverseHyperbolicCosine関数

逆双曲線余弦（アーク・ハイパボリック・コサイン）を求めます。

x必須: 弧度法による角度を表す数値、文字列もしくは#decimal-instance

inverseHyperbolicSine関数

逆双曲線正弦（アーク・ハイパボリック・サイン）を求めます。

x必須: 弧度法による角度を表す数値、文字列もしくは#decimal-instance

0ラジアンの逆双曲線正弦を求めます。

結果

inverseHyperbolicTangent関数

逆双曲線正接（アーク・ハイパボリック・タンジェント）を求めます。

x必須: 弧度法による角度を表す数値、文字列もしくは#decimal-instance

0ラジアンの逆双曲線正接を求めます。

結果

inverseSine関数

逆正弦（アークサイン）を求めます。

x必須: 弧度法による角度を表す数値、文字列もしくは#decimal-instance

0ラジアンの逆正弦を求めます。

結果

inverseTangent関数

逆正接（アークタンジェント）を求めます。

x必須: 弧度法による角度を表す数値、文字列もしくは#decimal-instance

0ラジアンの逆正接を求めます。

結果

isFinite関数

xが有限値かを示すブール値を返します。xが有限値であればTrue、有限値以外（NaN、INF、-INF）であればFalseを返します。

x必須: 有限値かを求める数値、文字列もしくは#decimal-instance

2が有限値かを求めます。

結果

-INFが有限値かを求めます。

結果

isInteger関数

xが整数かを示すブール値を返します。xが整数であればTrue、整数でなければFalseを返します。

x必須: 整数値かを求める数値、文字列もしくは#decimal-instance

256、256.0、3.14が整数かを求めます。

isNaN関数

xが非数（NaN）かを示すブール値を返します。xが非数であればTrue、非数でなければFalseを返します。

x必須: 非数かを求める数値、文字列もしくは#decimal-instance

結果

isNegative関数

xが負数かを示すブール値を返します。xが負数であればTrue、負数でなければFalseを返します。

x必須: 負数かを求める数値、文字列もしくは#decimal-instance

isPositive関数

xが正数かを示すブール値を返します。xが正数であればTrue、正数でなければFalseを返します。

x必須: 正数かを求める数値、文字列もしくは#decimal-instance

isZero関数

xが0かを示すブール値を返します。xが0であればTrue、0でなければFalseを返します。

x必須: 0かを求める数値、文字列もしくは#decimal-instance

lessThan関数

xがyよりも小さい値かを示すブール値を返します。xがyよりも小さい値であればTrue、それ以外であればFalseを返します

x必須: 大小を比較する1つ目の数値、文字列もしくは#decimal-instance
y必須: 大小を比較する2つ目の数値、文字列もしくは#decimal-instance

lessThanOrEqualTo関数

xがy以下の値かを示すブール値を返します。xがy以下の値であればTrue、それ以外であればFalseを返します。

x必須: 大小を比較する1つ目の数値、文字列もしくは#decimal-instance
y必須: 大小を比較する2つ目の数値、文字列もしくは#decimal-instance

logarithm関数

baseを底とする対数$\log_{base}{x}$を求めます。baseを省略した場合は、底をとする常用対数$\log_{10}{x}$を求めます。

x必須: 真数
base省略可: 底（省略時は10）

$\log_{2}{8}$を求めます。

結果

$\log_{10}{100}$を求めます。baseは省略されているので10となります。

結果

minus関数

minuendからsubtrahendを引いた値を返します。

minuend必須: 被減数となる数値、文字列もしくは#decimal-instance
subtrahend必須: 減数となる数値、文字列もしくは#decimal-instance

1.00から0.33を引いた値を返します。

結果

特殊値同士の計算結果は以下のようになります。

結果

modulo関数

xをyで割ったときのあまりを求めます。

x必須: 被除数となる数値、文字列もしくは#decimal-instance
y必須: 除数となる数値、文字列もしくは#decimal-instance

19を5で割った余りを求めます。$19 \div 5 = 3 \mod 4$なので4を返します。

結果

1を0.3で割った余りを求めます。$1 \div 0.3 = 3 \mod 0.1$なので0.1を返します。

結果

-10.2を2で割った余りを求めます。$-10.2 \div 2 = -5 \mod 0.2$なので0.2を返します。

結果

negated関数

xの正負を反転した値を返します。

x必須: 正負を反転する数値、文字列もしくは#decimal-instance

1.5の正負を反転させます。

結果

-3.1の正負を反転させます。

結果

plus関数

augendにaddendを加えた値を返します。

augend必須: 被加数となる数値、文字列もしくは#decimal-instance
addend必須: 加数となる数値、文字列もしくは#decimal-instance
pr省略可: 有効桁数
rm省略可: 丸めモード

0.1に0.2を加えた値を返します。

結果

特殊値同士の計算結果は以下のようになります。

結果

precision関数

xの有効桁数を返します。

x必須: 有効桁数を求める数値、文字列もしくは#decimal-instance
z省略可: 末尾の0を有効桁数としてカウントするかを示すブール値

1.23の有効桁数を求めます。

結果

5640000の有効桁数を求めます。sdを省略した場合は末尾の0を有効桁数としてカウントしないため564の桁数である3を返します。sdにTrueを指定した場合は末尾の0も有効桁数としてカウントするため5640000全体の桁数である7を返します。

結果

round関数

#rmを使用しxを整数に丸めます。

x必須: 丸める数値、文字列もしくは#decimal-instance

10.4を丸めます。

結果

sine関数

xの正弦（斜辺と対辺の比）を求めます。xはラジアン単位で指定します。

x必須: 弧度法による角度を表す数値、文字列もしくは#decimal-instance

0ラジアンの正弦を求めます。

結果

squareRoot関数

xの平方根を返します。

x必須: 平方根を求める対象となる数値、文字列もしくは#decimal-instance

4の平方根を求めます。

結果

tangent関数

xの正接（底辺と対辺の比）を求めます。xはラジアン単位で指定します。

x必須: 弧度法による角度を表す数値、文字列もしくは#decimal-instance

45°の正接を求めます。

結果

times関数

multiplierにmultiplicandを掛けた値を返します。

multiplier必須: 被乗数となる数値、文字列もしくは#decimal-instance
multiplicand必須: 乗数となる数値、文字列もしくは#decimal-instance

3.5に2を掛けた値を返します。

結果

特殊値同士の計算結果は以下のようになります。

結果

toBinary関数

10進数を2進数に変換します。

x必須: 2進数に変換する数値、文字列もしくは#decimal-instance
sd省略可: 有効桁数
rm省略可: #rm

10進数の8を2進数に変換します。

結果

toDecimalPlaces関数

小数値を指定した桁、丸めモードで丸めます。

x必須: 丸め対象となる数値、文字列もしくは#decimal-instance
dp省略可: 小数点以下の桁数
rm省略可: #rm（デフォルト：4の四捨五入）

8.125を小数点以下2桁に丸めます。

結果

8.125を小数点以下2桁に切り捨てで（0の方向へ）丸めます。

結果

toExponential関数

指数表記に変換します。

x必須: 数値、文字列もしくは#decimal-instance
dp省略可: 小数点以下の桁数
rm省略可: #rm

256を指数表記に変換します。

結果

toFixed関数

小数点以下の数値を丸めます。

x必須: 数値、文字列もしくは#decimal-instance
dp省略可: 小数点以下の桁数
rm省略可: #rm

12.3456を小数点以下0桁（整数）に丸めます。

結果

12.3456を小数点以下2桁に丸めます。

結果

-22.8を整数に丸めます。

結果

toFraction関数

xに指定された数値を既約分数にした配列を返します。配列の0番目が分子、1番目が分母となります。

x必須: 数値、文字列もしくは#decimal-instance
maxD省略可: 最大分母

0.131を既約分数にした配列を返します。

結果

toFraction関数の戻り値を以下のようにJOIN関数で結合すると分数の形式にすることができます。0.131は131/1000で表すことができます。

結果

maxDを指定すると分母がその値を超えない範囲で表されます。

maxDに500を指定したことで131/1000で表されていた値が30/229となります。この値は小数に直すと0.131004366812227074となり誤差が発生します。

結果

toHexadecimal関数

10進数を16進数に変換します。

x必須: 数値、文字列もしくは#decimal-instance
sd省略可: 精度
rm省略可: #rm

10進数の128を16進数に変換します。

結果

toNumber関数

x（#decimal-instance）を数値型に変換します。数値として表現できない部分は丸められる可能性があります。

x必須: 数値、文字列もしくは#decimal-instance

toOctal関数

10進数の値を8進数に変換します。

x必須: 8進数に変換する数値、文字列もしくは#decimal-instance
sd省略可: 有効桁数
rm省略可: #rm

10進数の128を8進数に変換します。

結果

toPower関数

baseのexponent乗の値を計算します。

base必須: 底
exponent必須: 指数

$2^{10}$を計算します。

結果

以下は$2^{100}$を求めるプログラムです。桁数が多くなる場合は指数表記となります。

結果

toPrecision関数

xをsd、rmで指定された有効桁数、丸めモードで丸めた値を文字列型で返します。

x必須: 丸める数値、文字列もしくは#decimal-instance
sd省略可: 有効桁数
rm省略可: 丸めモード

123.5を有効桁数2桁で丸めます。

結果

123.5を有効桁数2桁、#rmを0（無限大の方向）で丸めます。

結果

toSignificantDigits関数

xをsd、rmで指定された有効桁数、丸めモードで丸めた値の#decimal-instanceを返します。

x必須: 丸める数値、文字列もしくは#decimal-instance
sd省略可: 有効桁数
rm省略可: 丸めモード

1234.567を有効桁数5桁に丸めます。

結果

1234.6/result]

toString関数

xに指定されたDecimalインスタンスを文字列型に変換します。

x必須: 数値、文字列もしくは#decimal-instance

truncated関数

小数点以下を切り捨て、0の方向へ丸めます。

x必須: 丸める対象となる数値、文字列もしくは#decimal-instance

123

valueOf関数

x必須

[/login]

ヘルパー関数

digitsToString関数

配列dに格納されている値を整えて文字列として返します。配列の0番目を除く各要素をLOGBASEに定義されている桁数（デフォルト：7）になるまで0埋めして結合します。結合したあと末尾の0は削除します。

d必須: 結合する数字を格納した配列

以下は1/123456を計算する過程で出てくるdの値を例にしています。

配列の0番目を除く各要素（5184、331778、1234000）を7桁に0埋め（0005184、0331778、1234000）して結合します。

0番目の要素も含めて結合、末尾の0を取り除くと結果は81000518403317781234となります。

結果

convertBase関数

strに指定された文字列をbaseInの進数からbaseOutの進数に変換します

str必須: 進数変換する文字列
baseIn必須: 変換前の進数
baseOut必須: 変換後の進数

以下は16進数のFFを10進数に変換するプログラムです。

結果

2進数の0101を10進数に変換します。

結果

getPI関数

円周率をsd、rmに指定したの精度、丸めモードで返す。

Ctor必須
sd必須: 精度
rm必須: #rm

結果

getZeroString関数

引数kに指定された値だけ0を結合した文字列を返します。

k必須

結果

naturalExponential関数

ネイピア数$e$を底、xを指数とする$e^{x}$を求めます。

x必須: 指数を表す数値、文字列もしくは#decimal-instance
sd省略可

$e^{1}$を求めます。

結果

naturalLogarithm関数

ネイピア数$e$を底とした自然対数$\log_{e}{y}$を求めます。

y必須: 真数を表す数値、文字列もしくは#decimal-instance
sd省略可

nonFiniteToString関数

配列xの非有限値を文字列型に変換します。NaN、INF、-INFのいずれかの値を返します。

x必須: 非有限値か求める数値、文字列もしくは#decimal-instance

parseDecimal関数

引数strに指定された値を指数、仮数部の配列に変換し配列xに格納します。

parseDecimal関数を実行するよりも前に配列xに符号を示す値を格納しておく必要があります。

x必須: 数値、文字列もしくは#decimal-instance
str必須

\[ 符号 \times 仮数部 \times 10^{指数} \]

仮数部は$1 \leq d < 10$の範囲の値です。

Decimalモジュール (自作関数)では配列の0番目に符号、1番目に指数、2番目以降に仮数部を格納しています。

以下はarrayに格納された値をparseDecimal関数で変換するプログラムです。

仮数部は小数点の位置を中心として7桁区切りで格納されます。7桁に満たない部分は0で残りの桁を埋めます。

結果

tinyPow関数

$b^{e}$を求めます。

b必須: 底
e必須: 指数

$2^{10}$を求めます。

結果

その他関数

compare関数（division）

aとbを比較し、aが大きければ1、bが大きければ-1、同じであれば0を返します。

a必須: 数値a
b必須: 数値b
aL必須: 数値aの長さ
bL必須: 数値bの長さ

Constructor関数

vの数値を符号、指数、仮数部で構成される配列に変換します。符号は正数であれば1、負数であれば-1、仮数部はデフォルトでは7桁区切りの配列となります。

v必須: 数値

以下は12345を配列にするプログラムです。出力される値は1が符号、4が指数、12345が仮数部です。

結果

以下は-0.00225634を配列にするプログラムです。

vが負の値なので符号は-1、指数は-3、仮数部は22563、4000000となります。

結果

multiplyInteger関数（division）

整数同士の乗算を行うための関数です。引数xはセーフ配列、引数kは整数、引数baseは係数配列の基数を指定します。

x必須: 数値、文字列もしくは#decimal-instance
k必須
base必須

以下は123125000×5の計算を行うプログラムです。

Constructor関数で取得した配列xの0番目は符号、1番目は指数、2番目以降が仮数部が格納されていて符号と指数は不要なので、arrayShift関数 (自作関数)を2回実行して先頭2つの要素を削除します。

結果

自作関数

calculate関数

decimal.jsで複雑な計算を行う場合はメソッドチェーンで記述することができますが、UWSCではメソッドチェーンを定義できないので、その代わりとなる関数です。

str必須: 計算式
pr省略可: 有効桁数
rm省略可: 丸めモード

以下は#calculateで使える演算子です。

演算子	記号	説明
加算	+	2値を足し算する
減算	-	2値を引き算する
乗算	*	2値を掛ける
除算	/	2値を割る
整数除算	//	除算した整数部を返す
剰余	%	除算した余りを返す

以下は#calculateで使用できる関数です。

関数名	説明
floor関数	小数点以下を切り捨てる
ceil関数	小数点以下を切り上げる

式を文字列で指定することでその計算結果を返します。

結果

calcRPN関数

#torpnで生成した逆ポーランド記法のトークン（token）から計算した結果を出力します。

tokens必須: トークン
pr必須: 有効桁数
rm必須: #rm

cmpPrecedence関数

token1必須
token2必須

isOperator関数

引数tokenが演算子（+、-、*、/、%、^のいずれか）ならばTrueを返します。

token必須: 演算子かを調べる文字列

quotient関数

除算の商の整数部を返します。

dividend必須: 被除数
divisor必須: 除数

tokenize関数

引数exprに指定された数式をトークンに分解した配列を生成します。

トークンとは意味のある最小単位の文字の並びのことで、tokenize関数では数式を数値、演算子、括弧に分割した配列を生成します。

expr必須: 文字列型の計算式

以下のプログラムは数式(123+456)*10をトークンに分割した配列の各要素を出力します。

結果

toRPN関数

#tokenizeで生成した配列を逆ポーランド記法（RPN）に変換します。

逆ポーランド記法とは、数式を記述する際に演算子を被演算子の後ろに記述する記法です。例えば普段使われる中置記法で2 + 3と書く数式を逆ポーランド記法では2 3 +と記述します。

演算子の優先順位を考慮する必要がなく、数式の評価を効率的に行うことができます。

tokens必須: #tokenizeで生成した配列
pr省略可: 有効桁数
rm省略可: #rm

Decimalデシマルモジュール

プログラム

Decimalモジュールとは

Decimalインスタンス

誤差

丸め誤差

打切り誤差

情報落ち

桁落ち

オーバーフロー/アンダーフロー

特殊値

プロパティ

precision

rounding

modulo

ROUND_UP

ROUND_DOWN

ROUND_FLOOR

ROUND_HALF_EVEN

EUCLID

toExpNeg

toExpPos

minE

maxE

引数

精度（Precision）

有効桁数（significant digits）

丸めモード（Rounding Mode）

小数点以下の桁数（decimal places）

数値型（isNumeric）

関数一覧

メイン関数

ヘルパー関数

その他関数

自作関数

メイン関数

absoluteValue関数

ceil関数

clampedTo関数

comparedTo関数

cosine関数

cubeRoot関数

decimalPlaces関数

dividedBy関数

dividedToIntegerBy関数

equals関数

floor関数

greaterThan関数

greaterThanOrEqualTo関数

hyperbolicCosine関数

hyperbolicSine関数

hyperbolicTangent関数

inverseCosine関数

inverseHyperbolicCosine関数

inverseHyperbolicSine関数

inverseHyperbolicTangent関数

inverseSine関数

inverseTangent関数

isFinite関数

isInteger関数

isNaN関数

isNegative関数

isPositive関数

isZero関数

lessThan関数

lessThanOrEqualTo関数

logarithm関数

minus関数

modulo関数

negated関数

plus関数

precision関数

round関数

sine関数

squareRoot関数

tangent関数

times関数

toBinary関数

toDecimalPlaces関数

toExponential関数