本ページには広告が含まれています。
目次
- 1 プログラム
- 2 Decimalモジュールとは
- 3 誤差
- 4 特殊値
- 5 プロパティ
- 6 関数一覧
- 7 メイン関数
- 7.1 absoluteValue関数
- 7.2 ceil関数
- 7.3 clampedTo関数
- 7.4 comparedTo関数
- 7.5 cosine関数
- 7.6 cubeRoot関数
- 7.7 decimalPlaces関数
- 7.8 dividedBy関数
- 7.9 dividedToIntegerBy関数
- 7.10 equals関数
- 7.11 floor関数
- 7.12 greaterThan関数
- 7.13 greaterThanOrEqualTo関数
- 7.14 hyperbolicCosine関数
- 7.15 hyperbolicSine関数
- 7.16 hyperbolicTangent関数
- 7.17 inverseCosine関数
- 7.18 inverseHyperbolicCosine関数
- 7.19 inverseHyperbolicSine関数
- 7.20 inverseHyperbolicTangent関数
- 7.21 inverseSine関数
- 7.22 inverseTangent関数
- 7.23 isFinite関数
- 7.24 isInteger関数
- 7.25 isNaN関数
- 7.26 isNegative関数
- 7.27 isPositive関数
- 7.28 isZero関数
- 7.29 lessThan関数
- 7.30 lessThanOrEqualTo関数
- 7.31 logarithm関数
- 7.32 minus関数
- 7.33 modulo関数
- 7.34 negated関数
- 7.35 plus関数
- 7.36 precision関数
- 7.37 round関数
- 7.38 sine関数
- 7.39 squareRoot関数
- 7.40 tangent関数
- 7.41 times関数
- 7.42 toBinary関数
- 7.43 toDecimalPlaces関数
- 7.44 toExponential関数
- 7.45 toFraction関数
- 7.46 toHexadecimal関数
- 7.47 toNumber関数
- 7.48 toOctal関数
- 7.49 toPower関数
- 7.50 toPrecision関数
- 8 ヘルパー関数
- 9 その他関数
- 10 自作関数
精度の高い計算を行います。
- 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 minE = -9E+15
PUBLIC maxE = 9E+15
PUBLIC quadrant = EMPTY
PUBLIC modulo = 1
DIM inexact = FALSE
PUBLIC toExpNeg = -7
PUBLIC toExpPos = 21
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
DIM external = 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(bitXor(x[1] > y[1], 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)
DIM path = folderspec + filename
IFB 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 OR COPY(n, 2) AND COPY(n, 0) = "5" THEN
// Truncate to the first rounding digit.
finalise(r, e + 1, 1)
m = !eq(times(times(r, 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 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, pr = NULL, rm = NULL, dp = NULL, _base = 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 _base <> NULL THEN
logBase = 1
e = x[1] - y[1]
ELSE
_base = 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 * _base + 0
ELSE
t = k * _base + 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 * _base + 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 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)
DIM path = folderspec + filename
IFB 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)
DIM path = folderspec + filename
IFB 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)
DIM path = folderspec + filename
IFB 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)
DIM path = folderspec + filename
IFB 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)
DIM path = folderspec + filename
IFB 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)
DIM path = folderspec + filename
IFB 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)
DIM path = folderspec + filename
IFB 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)
DIM path = folderspec + filename
IFB 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)
DIM path = folderspec + filename
IFB 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 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]
// x = finalise(x, pr, rm)
// y = finalise(y, pr, rm)
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))
ELSE
RESULT = SLICE(y)
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 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))
EXIT
ENDIF
// Calculate base 1e7 exponents.
// value = x[1]/LOG_BASE
// k = INT(value) + IIF(value<0 AND value <> INT(value), -1, 0)
// value = y[1]/LOG_BASE
// e = INT(value) + IIF(value<0 AND value- INT(value) <> 0, -1, 0)
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)
// i = LENGTH(yd)
//TEXTBLOCK
IFB i > len THEN
i = len
RESIZE(d, 1)
ENDIF
//ENDTEXTBLOCK
// 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))
ELSE
RESULT = SLICE(y)
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)
DIM path = folderspec + filename
IFB 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)
DIM path = folderspec + filename
IFB 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)
// x = divide(x, squareRoot(minus(Constructor(1), times(x, x))), pr + 10, 0)
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 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))
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))
ELSE
RESULT = SLICE(y)
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 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)
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)
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))
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
FUNCTION divide(dividend, divisor, pr = 20, rm = 4, dp = NULL, _base = NULL, isnumeric = FALSE)
RESULT = dividedBy(dividend, divisor, pr, rm, dp, _base, isnumeric)
FEND
FUNCTION div(dividend, divisor, pr = 20, rm = 4, dp = NULL, _base = NULL, isnumeric = FALSE)
RESULT = dividedBy(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
IF 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 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
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) _
) _
)
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, 1)
x[1] = EMPTY // 仮の値
// Underflow?
ELSEIF x[1] < minE THEN
x[1] = 0
RESIZE(x, 2)
x[2] = 0
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)
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)
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[2] = NULL
x[1] = NULL
// 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 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
// 【戻り値】
// 10進数に変換した値
//////////////////////////////////////////////////
FUNCTION binToDec(bin, signFlg = TRUE)
DIM dec = 0
DIM decimalFlg = IIF(POS(".", bin), TRUE, FALSE)
IFB COPY(bin, 1, 1) = "1" AND signFlg THEN
DIM msb = IIF(decimalFlg, POS(".", bin) - 1, LENGTH(bin))
DIM lsb = IIF(decimalFlg, POS(".", bin) - LENGTH(bin), 0)
DIM dec2 = POWER(2, msb) - 1
FOR i = -1 TO lsb STEP -1
dec2 = dec2 + POWER(2, i)
NEXT
DIM a = binToDec(bin, FALSE)
DIM b = dec2
dec = -1 * (bitXor(a, b) + POWER(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)
dec = dec + COPY(integer, i, 1) * POWER(2, LENGTH(integer) - i)
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)
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)) 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)
// 負数で符号なしならばエラー値を返す
IFB 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 = IIF(POS(".", dec) <> 0, TRUE, FALSE)
DIM negativeFlg = IIF(dec < 0, TRUE, FALSE)
dec = ABS(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 = (integer MOD 2) + bin
integer = INT(integer / 2)
UNTIL 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】
// 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) + ")")
FENDDecimalモジュールとは
Decimalモジュール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、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 (スクリプト関数)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。
PRINT JOIN(Decimal.Constructor("123"), ",")
PRINT JOIN(Decimal.Constructor("65536"), ",")
PRINT JOIN(Decimal.Constructor("12345678901234567890"), ",")
Decimal.Constructor("12345678901234.123456789012")- 結果
1,2,123 1,4,65536 1,19,123456,7890123,4567890 1,13,1234567,8901234,1234567,8901200
#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。
DIM array = Decimal.Constructor("1250")
PRINT JOIN(array, ",")
PRINT Decimal.finiteToString(array)pr：有効桁数（Precision）
演算結果の有効桁数を表します。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。
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。
FOR pr = 1 TO 20
PRINT pr + "<#TAB>" + Decimal.dividedBy("1", "9", pr)
NEXT- 結果
1 0.1 2 0.11 3 0.111 4 0.1111 5 0.11111 6 0.111111 7 0.1111111 8 0.11111111 9 0.111111111 10 0.1111111111 11 0.11111111111 12 0.111111111111 13 0.1111111111111 14 0.11111111111111 15 0.111111111111111 16 0.1111111111111111 17 0.11111111111111111 18 0.111111111111111111 19 0.1111111111111111111 20 0.11111111111111111111
有効桁数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。
FOR pr = 1 TO 20
PRINT pr + "<#TAB>" + Decimal.dividedBy("1234567", "6", pr)
NEXT- 結果
1 200000 2 210000 3 206000 4 205800 5 205760 6 205761 7 205761.2 8 205761.17 9 205761.167 10 205761.1667 11 205761.16667 12 205761.166667 13 205761.1666667 14 205761.16666667 15 205761.166666667 16 205761.1666666667 17 205761.16666666667 18 205761.166666666667 19 205761.1666666666667 20 205761.16666666666667
rm：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。
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 |
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。
PRINT 1/3- 結果
0.333333333333333
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。
PRINT 2/3- 結果
0.666666666666667
#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。
PRINT Decimal.dividedBy("1", "3", 50)- 結果
0.33333333333333333333333333333333333333333333333333
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。
PRINT Decimal.dividedBy("2", "3", 20, 1)- 結果
0.66666666666666666666
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。
PRINT 1E+16 + 1 - 1E+16- 結果
0
PRINT Decimal.minus(Decimal.plus("10000000000000000", "1"), "10000000000000000")- 結果
1
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。
PRINT 0.123456789 - 0.123456788- 結果
9.99999999473644E-10
Decimalモジュールを使うと正しい結果を得られます。
PRINT Decimal.minus("0.123456789", "0.123456788")- 結果
1e-9
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。
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。
特殊値
Decimalモジュール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 | |
| 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。
0 Decimal{ 1, 0, 0}
123 Decimal{ 1, 2, 123}
NaN Decimal{ NaN, NaN, null}
Infinity Decimal{ 1, NaN, null}
-Infinity Decimal{ -1, NaN, null}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。
0 Decimal{ 1, 0, 0}
123 Decimal{ 1, 2, 123}
NaN Decimal{NULL, NULL, FALSE}
INF Decimal{ 1, NULL, FALSE}
-INF Decimal{ -1, NULL, FALSE}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 | |||
|---|---|---|---|---|
| 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 |
|---|---|
| precision | 有効桁数（デフォルト：20） |
| rounding | #rm |
| minE | 許容する最小指数 |
| maxE | 許容する最大指数 |
| toExpNeg | 指数表記を使い始める負の指数の閾値（デフォルト：-7） |
| toExpPos | 指数表記を使い始める正の指数の閾値（デフォルト：21） |
| modulo |
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。
Decimal.precision = 30 // 有効桁数30桁
Decimal.rounding = 6 // 丸めモード偶数丸め
Decimal.toExpNeg = -10 // 負数の指数表記を開始する値-10
Decimal.toExpPos = 30 // 正数の指数表記を開始する値30precision
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。
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）。
toExpNeg
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。
PRINT Decimal.plus("0.000001", "0")
PRINT Decimal.plus("0.0000001", "0")- 結果
0.000001 1e-7
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。
PRINT Decimal.toPower(2, -20)- 結果
9.5367431640625e-7
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。
Decimal.toExpNeg = -10
PRINT Decimal.toPower(2, -20)- 結果
0.00000095367431640625
toExpPos
正数では指数を使い始める値（toExpNeg）は20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。19乗までは固定小数点で出力されます。
PRINT Decimal.plus("100000000000000000000", "0")
PRINT Decimal.plus("1000000000000000000000", "0")- 結果
100000000000000000000 1e+21
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。
PRINT Decimal.toPower(2, 100)- 結果
1.2676506002282294015e+30
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を変えることができます。
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。
Decimal.precision = 35
Decimal.toExpPos = 50
PRINT Decimal.toPower(2, 100)- 結果
1267650600228229401496703205376
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 | |
| #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 |
| #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。
Decimal.absoluteValue(x, isnumeric)- x
- 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。
PRINT Decimal.absoluteValue("-12.5") // 12.5
PRINT Decimal.absoluteValue("1.5") // 1.5ceil関数
xを正の無限大方向へ丸めます。
Decimal.ceil(x, isnumeric)- x
- 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。
PRINT Decimal.ceil("5.4") // 6
PRINT Decimal.ceil("-4.9") // -4clampedTo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。
Decimal.clampedTo(x, min, max)- x
- 範囲内に収める対象となる数値、文字列もしくは#decimal-instance
- min
- 下限値
- max
- 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。
PRINT Decimal.clampedTo("150", "0", "100")- 結果
100
-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。
PRINT Decimal.clampedTo("-5", "0", "100")- 結果
0
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。
PRINT Decimal.clampedTo("25", "0", "100")- 結果
25
comparedTo関数
x、yの値を比較し、大小関係を数値で返します。
Decimal.comparedTo(x, y)- x
- 大小を比較する1つ目の数値、文字列もしくは#decimal-instance
- y
- 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。
PRINT Decimal.comparedTo("5", "1")- 結果
1
-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。
PRINT Decimal.comparedTo("-5", "20")- 結果
-1
5と5を比較します。同値なので0を返します。
PRINT Decimal.comparedTo("5", "5")- 結果
0
10とNaNを比較します。一方がNaNなのでNaNを返します。
PRINT Decimal.comparedTo("10", "NaN")- 結果
NaN
cosine関数
x（弧度法）の余弦（斜辺と底辺の比）を求めます。
Decimal.cosine(x, isnumeric)- x
- 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。
PRINT Decimal.cosine("0.25")- 結果
0.96891242171064478414
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。
PRINT Decimal.cosine(degToRad("30"))- 結果
0.86602540378443864676
cubeRoot関数
xの三乗根を返します。
cubeRoot(x)- x
- 三乗根を求める対象となる数値、文字列もしくは#decimal-instance
125の三乗根を返します。
PRINT Decimal.cubeRoot("125")- 結果
5
decimalPlaces関数
xの小数部の桁数を返します。
decimalPlaces(x)- x
- 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。
PRINT Decimal.decimalPlaces("1.235") // 3
PRINT Decimal.decimalPlaces("-27") // 0dividedBy関数
dividendをdivisorで割った値を返します。
String = Decimal.dividedBy(dividend, divisor, pr, rm, dp, _base, isnumeric)
String = Decimal.div(dividend, divisor, pr, rm, dp, _base, isnumeric)- dividend
- 被除数となる数値、文字列もしくは#decimal-instance
- divisor
- 除数となる数値、文字列もしくは#decimal-instance
- pr
- 有効桁数
- rm
- 丸めモード
- dp
- 小数点以下の桁数
- _base
- 基数
1を3で割った値を返します。デフォルトではprに20が指定されているので20桁まで返します。
PRINT Decimal.dividedBy("1", "3")- 結果
0.33333333333333333333
prで有効桁数を指定することができます。以下は5桁に設定しています。
PRINT Decimal.dividedBy("1", "3", 5)- 結果
0.33333
特殊値同士の計算結果は以下のようになります。
DIM dividends[] = "INF", "-INF", "NaN", "0"
DIM divisors[] = "INF", "-INF", "NaN", "0"
FOR dividend IN dividends
FOR divisor IN divisors
PRINT dividend + " / " + divisor + " = " + Decimal.dividedBy(dividend, divisor)
NEXT
PRINT "--------------------"
NEXT- 結果
INF / INF = NaN INF / -INF = NaN INF / NaN = NaN INF / 0 = INF -------------------- -INF / INF = NaN -INF / -INF = NaN -INF / NaN = NaN -INF / 0 = -INF -------------------- NaN / INF = NaN NaN / -INF = NaN NaN / NaN = NaN NaN / 0 = NaN -------------------- 0 / INF = 0 0 / -INF = 0 0 / NaN = NaN 0 / 0 = NaN --------------------
dividedToIntegerBy関数
xをyで除算した整数部を返します。
Decimal.dividedToIntegerBy(x, y, isNumeric)- x
- 被除数となる数値、文字列もしくは#decimal-instance
- y
- 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。
PRINT Decimal.dividedToIntegerBy("12", "5")- 結果
2
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。
equals(x, y)- x
- 比較する1つ目の数値、文字列もしくは#decimal-instance
- y
- 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。
PRINT Decimal.equals("1.0", "1")- 結果
True
floor関数
xを負の無限大方向へ丸めた値を返します。
Decimal.floor(x)- x
- 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。
PRINT Decimal.floor("4.2")- 結果
4
-2.1を負の無限大方向へ丸めた値を求めます。
PRINT Decimal.floor("-2.1")- 結果
-3
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。
Boolean = Decimal.greaterThan(x, y)- x
- 大小を比較する1つ目の数値、文字列もしくは#decimal-instance
- y
- 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。
PRINT Decimal.greaterThan("0.1", "0.2")- 結果
False
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。
Boolean = Decimal.greaterThanOrEqualTo(x, y)- x
- 大小を比較する1つ目の数値、文字列もしくは#decimal-instance
- y
- 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。
PRINT Decimal.greaterThanOrEqualTo("0.3", "0.2")- 結果
True
hyperbolicCosine関数
双曲線余弦（ハイパボリック コサイン）を求めます。
String = hyperbolicCosine(x, isNumeric)- x
- 弧度法による角度を表す数値、文字列もしくは#decimal-instance
PRINT Decimal.hyperbolicCosine("1")- 結果
1.5430806348152437785
PRINT Decimal.hyperbolicCosine("0")- 結果
1
hyperbolicSine関数
双曲線正弦（ハイパボリック サイン）を求めます。
String = hyperbolicSine(x, isNumeric)- x
- 弧度法による角度を表す数値、文字列もしくは#decimal-instance
PRINT Decimal.hyperbolicSine(1)- 結果
1.1752011936438014569
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。
String = hyperbolicTangent(x, isNumeric)- x
- 弧度法による角度を表す数値、文字列もしくは#decimal-instance
PRINT Decimal.hyperbolicTangent(1)- 結果
0.76159415595576488812
inverseCosine関数
逆余弦（アークコサイン）を求めます。
String = Decimal.inverseCosine(x)- x
- 弧度法による角度を表す数値、文字列もしくは#decimal-instance
PRINT Decimal.inverseCosine(0)- 結果
1.5707963267948966192
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。
String = Decimal.inverseHyperbolicCosine(x)- x
- 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。
String = Decimal.inverseHyperbolicSine(x)- x
- 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。
PRINT Decimal.inverseHyperbolicSine(0)- 結果
0
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。
String = Decimal.inverseHyperbolicTangent(x)- x
- 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。
PRINT Decimal.inverseHyperbolicTangent(0)- 結果
0
inverseSine関数
逆正弦（アークサイン）を求めます。
String = Decimal.inverseSine(x)- x
- 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。
PRINT Decimal.inverseSine(0)- 結果
0
inverseTangent関数
逆正接（アークタンジェント）を求めます。
String = Decimal.inverseTangent(x)0ラジアンの逆正接を求めます。
PRINT Decimal.inverseTangent(0)- 結果
0
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。
Boolean = Decimal.isFinite(x)- x
- 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。
DIM x = Decimal.Constructor("2")
PRINT Decimal.isFinite(x)- 結果
True
-INFが有限値かを求めます。
DIM x = Decimal.Constructor("-INF")
PRINT Decimal.isFinite(x)- 結果
False
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。
Decimal.isInteger(x)- x
- 整数値かを求める数値、文字列もしくは#decimal-instance
256が整数かを求めます。
DIM x = Decimal.Constructor("256")
PRINT Decimal.isInteger(x)- 結果
True
3.14が整数かを求めます。
DIM x = Decimal.Constructor("3.14")
PRINT Decimal.isInteger(x)- 結果
False
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。
Decimal.isNaN(x)- x
- 非数かを求める数値、文字列もしくは#decimal-instance
DIM x = Decimal.Constructor("NaN")
PRINT Decimal.isNaN(x)- 結果
True
DIM x = Decimal.Constructor("-INF")
PRINT Decimal.isNaN(x)- 結果
False
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。
Boolean = Decimal.isNegative(x)- x
- 負数かを求める数値、文字列もしくは#decimal-instance
PRINT Decimal.isNegative(Decimal.Constructor("12")) // False
PRINT Decimal.isNegative(Decimal.Constructor("-14")) // TrueisPositive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。
Boolean = Decimal.isPositive(x)- x
- 正数かを求める数値、文字列もしくは#decimal-instance
PRINT Decimal.isPositive(Decimal.Constructor("452")) // True
PRINT Decimal.isPositive(Decimal.Constructor("-510")) // FalseisZero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。
Decimal.isZero(x)- x
- 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
Boolean = Decimal.lessThan(x, y)- x
- 大小を比較する1つ目の数値、文字列もしくは#decimal-instance
- y
- 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。
Boolean = Decimal.lessThanOrEqualTo(x, y)- x
- 大小を比較する1つ目の数値、文字列もしくは#decimal-instance
- y
- 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。
Decimal.logarithm(x, base)- x
- 真数
- base
- 底（省略時は10）
\(\log_{2}{8}\)を求めます。
PRINT Decimal.logarithm("8", "2")- 結果
3
\(\log_{10}{100}\)を求めます。baseは省略されているので10となります。
PRINT Decimal.logarithm("100")- 結果
2
minus関数
minuendからsubtrahendを引いた値を返します。
String = Decimal.minus(minuend, subtrahend, pr, rm, isnumeric)
String = Decimal.sub(minuend, subtrahend, pr, rm, isnumeric)- minuend
- 被減数となる数値、文字列もしくは#decimal-instance
- subtrahend
- 減数となる数値、文字列もしくは#decimal-instance
- pr
- 有効桁数
- rm
- 丸めモード
1.00から0.33を引いた値を返します。
PRINT Decimal. minus("1.00", "0.33")- 結果
0.67
特殊値同士の計算結果は以下のようになります。
DIM minuends[] = "INF", "-INF", "NaN", "0"
DIM subtrahends[] = "INF", "-INF", "NaN", "0"
FOR minuend IN minuends
FOR subtrahend IN subtrahends
PRINT minuend + " - " + subtrahend + " = " + Decimal.minus(minuend, subtrahend)
NEXT
PRINT "--------------------"
NEXT- 結果
INF - INF = NaN INF - -INF = INF INF - NaN = NaN INF - 0 = INF -------------------- -INF - INF = -INF -INF - -INF = NaN -INF - NaN = NaN -INF - 0 = -INF -------------------- NaN - INF = NaN NaN - -INF = NaN NaN - NaN = NaN NaN - 0 = NaN -------------------- 0 - INF = -INF 0 - -INF = INF 0 - NaN = NaN 0 - 0 = 0 --------------------
modulo関数
xをyで割ったときのあまりを求めます。
modulo(x, y)- x
- 被除数となる数値、文字列もしくは#decimal-instance
- y
- 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。
PRINT Decimal.modulo("19", "5")- 結果
4
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。
PRINT Decimal.modulo("1", "0.3")- 結果
0.1
negated関数
xの正負を反転した値を返します。
String = Decimal.negated(x)- x
- 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。
PRINT Decimal.negated("1.5")- 結果
-1.5
-3.1の正負を反転させます。
PRINT Decimal.negated("-3.1")- 結果
3.1
plus関数
augendにaddendを加えた値を返します。
String = Decimal.plus(augend, addend, pr, rm, isnumeric)
String = Decimal.add(augend, addend, pr, rm, isnumeric)- augend
- 被加数となる数値、文字列もしくは#decimal-instance
- addend
- 加数となる数値、文字列もしくは#decimal-instance
- pr
- 有効桁数
- rm
- 丸めモード
0.1に0.2を加えた値を返します。
PRINT Decimal.plus("0.1", "0.2")- 結果
0.3
特殊値同士の計算結果は以下のようになります。
DIM augends[] = "INF", "-INF", "NaN", "0"
DIM addends[] = "INF", "-INF", "NaN", "0"
FOR augend IN augends
FOR addend IN addends
PRINT augend + " + " + addend + " = " + Decimal.plus(augend, addend)
NEXT
PRINT "--------------------"
NEXT- 結果
INF + INF = INF INF + -INF = NaN INF + NaN = NaN INF + 0 = INF -------------------- -INF + INF = NaN -INF + -INF = -INF -INF + NaN = NaN -INF + 0 = -INF -------------------- NaN + INF = NaN NaN + -INF = NaN NaN + NaN = NaN NaN + 0 = NaN -------------------- 0 + INF = INF 0 + -INF = -INF 0 + NaN = NaN 0 + 0 = 0 --------------------
precision関数
xの有効桁数を返します。
Decimal.precision(x, z)- x
- 有効桁数を求める数値、文字列もしくは#decimal-instance
- z
- 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。
PRINT Decimal.precision("1.23")- 結果
3
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。
PRINT Decimal.precision("5640000")
PRINT Decimal.precision("5640000", TRUE)- 結果
3 7
round関数
#rmを使用しxを整数に丸めます。
Decimal.round(x)- x
- 丸める数値、文字列もしくは#decimal-instance
10.4を丸めます。
PRINT Decimal.round("10.4")- 結果
10
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。
Decimal.sine(x, isnumeric)- x
- 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。
PRINT Decimal.sine("0")- 結果
0
squareRoot関数
xの平方根を返します。
squareRoot(x, isnumeric)- x
- 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。
PRINT Decimal.squareRoot("4")- 結果
2
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。
tangent(x, isnumeric)- x
- 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。
PRINT Decimal.tangent(degToRad("45"))- 結果
1
times関数
multiplierにmultiplicandを掛けた値を返します。
String = Decimal.times(multiplier, multiplicand, pr, rm, isnumeric)
String = Decimal.mul(multiplier, multiplicand, pr, rm, isnumeric)- multiplier
- 被乗数となる数値、文字列もしくは#decimal-instance
- multiplicand
- 乗数となる数値、文字列もしくは#decimal-instance
- pr
- 有効桁数
- rm
- 丸めモード
3.5に2を掛けた値を返します。
PRINT Decimal.times("3.5", "2")- 結果
7
特殊値同士の計算結果は以下のようになります。
DIM multipliers[] = "INF", "-INF", "NaN", "0"
DIM multiplicands[] = "INF", "-INF", "NaN", "0"
FOR multiplier IN multipliers
FOR multiplicand IN multiplicands
PRINT multiplier + " * " + multiplicand + " = " + Decimal.times(multiplier, multiplicand)
NEXT
PRINT "--------------------"
NEXT- 結果
INF * INF = INF INF * -INF = -INF INF * NaN = NaN INF * 0 = NaN -------------------- -INF * INF = -INF -INF * -INF = INF -INF * NaN = NaN -INF * 0 = NaN -------------------- NaN * INF = NaN NaN * -INF = NaN NaN * NaN = NaN NaN * 0 = NaN -------------------- 0 * INF = NaN 0 * -INF = NaN 0 * NaN = NaN 0 * 0 = 0 --------------------
toBinary関数
10進数を2進数に変換します。
String = Decimal.toBinary(x, sd, rm)- x
- 2進数に変換する数値、文字列もしくは#decimal-instance
- sd
- 有効桁数
- rm
- #rm
10進数の8を2進数に変換します。
PRINT Decimal.toBinary("8")- 結果
0b1000
toDecimalPlaces関数
小数値を指定した桁、丸めモードで丸めます。
String = Decimal.toDecimalPlaces(x, dp, rm)- x
- 丸め対象となる数値、文字列もしくは#decimal-instance
- dp
- 小数点以下の桁数
- rm
- #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。
PRINT Decimal.toDecimalPlaces("8.125", 2)- 結果
8.13
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。
PRINT Decimal.toDecimalPlaces("8.125", 2, 1)- 結果
8.12
toExponential関数
指数表記に変換します。
String = toExponential(x, dp, rm)- x
- 数値、文字列もしくは#decimal-instance
- dp
- 小数点以下の桁数
- rm
- #rm
256を指数表記に変換します。
PRINT Decimal.toExponential("256")- 結果
2.56e+2
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。
Array = Decimal.toFraction(x, maxD)- x
- 数値、文字列もしくは#decimal-instance
- maxD
- 最大分母
0.131を既約分数にした配列を返します。
DIM array = Decimal.toFraction("0.131")
FOR item IN array
PRINT item
NEXT- 結果
131 1000
toFraction関数の戻り値を以下のようにJOIN関数 (スクリプト関数)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。
PRINT JOIN(Decimal.toFraction("0.131"), "/")- 結果
131/1000
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。
DIM array = Decimal.toFraction("0.131", "500")
FOR item IN array
PRINT item
NEXT- 結果
30 229
toHexadecimal関数
10進数を16進数に変換します。
String = Decimal.toHexadecimal(x, sd, rm)- x
- 数値、文字列もしくは#decimal-instance
- sd
- 有効桁数
- rm
- #rm
10進数の128を16進数に変換します。
PRINT Decimal.toHexadecimal("128")- 結果
0x80
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。
Decimal.toNumber(x)- x
- 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。
String = Decimal.toOctal(x, sd, rm)- x
- 8進数に変換する数値、文字列もしくは#decimal-instance
- sd
- 有効桁数
- rm
- #rm
10進数の128を8進数に変換します。
PRINT Decimal.toOctal("128")- 結果
0o200
toPower関数
baseのexponent乗の値を計算します。
String = Decimal.toPower(base, exponent)- base
- 底
- exponent
- 指数
\(2^{10}\)を計算します。
PRINT Decimal.toPower("2", "10")- 結果
1024
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。
PRINT Decimal.toPower("2", "100")- 結果
1.2676506002282294015e+30
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。
String = toPrecision(x, sd, rm)- x
- 丸める数値、文字列もしくは#decimal-instance
- sd
- 有効桁数
- rm
- 丸めモード
123.5を有効桁数2桁で丸めます。
DIM x = Decimal.Constructor("123.5")
PRINT Decimal.toPrecision(x, 2)- 結果
1.2e+2
123.5を有効桁数2桁、#rmを0（無限大の方向）で丸めます。
DIM x = Decimal.Constructor("123.5")
PRINT Decimal.toPrecision(x, 2, 0)- 結果
1.3e+3
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。
String = Decimal.digitsToString(d)- d
- 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。
DIM d = SAFEARRAY(0, 3)
d[0] = "81"
d[1] = "5184"
d[2] = "331778"
d[3] = "1234000"
PRINT Decimal.digitsToString(d)- 結果
81000518403317781234
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
safearray = Decimal.convertBase(str, baseIn, baseOut)- str
- 進数変換する文字列
- baseIn
- 変換前の進数
- baseOut
- 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。
FOR item IN Decimal.ConvertBase("FF", 16, Decimal.Base)
PRINT item
NEXT- 結果
255
2進数の0101を10進数に変換します。
FOR item IN Decimal.ConvertBase("0101", 2, Decimal.Base)
PRINT item
NEXT- 結果
5
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。
Decimal.getZeroString(k)- k
PRINT Decimal.getZeroString(3)
PRINT Decimal.getZeroString(5)- 結果
000 00000
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。
Decimal.naturalExponential(x, sd)- x
- 指数を表す数値、文字列もしくは#decimal-instance
- sd
\(e^{1}\)を求めます。
PRINT Decimal.naturalExponential("1")- 結果
2.7182818284590452354
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。
Decimal.naturalLogarithm(y, sd)- y
- 真数を表す数値、文字列もしくは#decimal-instance
- sd
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。
Decimal.nonFiniteToString(x[])- x
- 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。
safearray = Decimal.parseDecimal(x, str)- x
- 数値、文字列もしくは#decimal-instance
- str
仮数部は\(1 \leq d < 10\)の範囲の値です。
Decimalモジュールでは配列の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。
DIM array[] = "0", "123", "-123", "299792458", "3.1415926535", "602214076000000000000000"
PRINT "v,s,e,[d]"
FOR item IN array
DIM num = item
DIM x = SAFEARRAY(-1)
x[0] = IIF(COPY(num, 1, 1) = "-", "-1", "1")
IF x[0] = -1 THEN num = COPY(num, 2)
x = Decimal.parseDecimal(x, num)
PRINT item + "," + JOIN(x, ",")
NEXT- 結果
v,s,e,[d] 0,1,0,0 123,1,2,123 -123,-1,2,123 299792458,1,8,29,9792458 3.1415926535,1,0,3,1415926,5350000 602214076000000000000000,1,23,602,2140760
tinyPow関数
\(b^{e}\)を求めます。
Decimal.tinyPow(b, e)- b
- 底
- e
- 指数
\(2^{10}\)を求めます。
PRINT Decimal.tinyPow("2", "10")- 結果
1024
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。
Decimal.compare(a, b, aL, bL)- a
- 数値a
- b
- 数値b
- aL
- 数値aの長さ
- bL
- 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。
safearray = Decimal.Constructor(v)- v
- 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。
DIM x = Decimal.Constructor("12345")
FOR item IN x
PRINT item
NEXT- 結果
1 4 12345
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。
DIM x = Decimal.Constructor("-0.00225634")
FOR item IN x
PRINT item
NEXT- 結果
-1 -3 22563 4000000
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。
Decimal.multiplyInteger(x, k, base)- x
- 数値、文字列もしくは#decimal-instance
- k
- base
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。
DIM x = Decimal.Constructor("123125000")
arrayShift(x)
arrayShift(x)
x = Decimal.multiplyInteger(x, 5, Decimal.BASE)
PRINT JOIN(x, "")- 結果
615625000
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。
String = Decimal.calculate(str, pr, rm)- str
- 計算式
- pr
- 有効桁数
- rm
- 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。
PRINT Decimal.calculate("1 / 3 * 3")- 結果
1
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。
String = Decimal.calcRPN(tokens, pr, rm)- tokens
- トークン
- pr
- 有効桁数
- rm
- #rm
cmpPrecedence関数
Decimal.cmpPrecedence(token1, token2)- token1
- token2
isOperator関数
引数tokenが演算子（+、-、*、/、%、^のいずれか）ならばTrueを返します。
Boolean = Decimal.isOperator(token)- token
- 演算子かを調べる文字列
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。
Decimal.tokenize(expr)- expr
- 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。
FOR item IN Decimal.tokenize("(123+456)*10")
PRINT item
NEXT- 結果
( 123 + 456 ) * 10
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。
Decimal.toRPN(tokens, pr, rm, isnumeric)