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Just finished calculating pi to 30 trillion places.
#21
"Actually, 8 new correct digits should appear with each run"
you need high precision arithmetic for that, perhaps you were thinking of the spigot algorithm? http://www.cs.williams.edu/~heeringa/cla...spigot.pdf page 9 has code that you can convert to QB64
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#22
(08-16-2022, 05:42 PM)Jack Wrote: "Actually, 8 new correct digits should appear with each run"
you need high precision arithmetic for that, perhaps you were thinking of the spigot algorithm? http://www.cs.williams.edu/~heeringa/cla...spigot.pdf page 9 has code that you can convert to QB64

Thanks for trusting my math skills,  Wink  but I've never heard of that until now.

For me, "programming" is just a distraction, something to take my mind off things for a while. To do this, I choose something, or I come across something, and then try to solve it. Sometimes it works, but often it doesn't. Well, what the heck.

I'll see if I wil tackle the problem again.
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#23
here's a translation and mod of this c spigot program https://cs.fit.edu/~mmahoney/cse3101/pi.c.txt all credit goes to that author
the program compiled with -O2 runs in about half a second
you could use this in your string-math by changing the printpi sub to simply convert to string
Code: (Select All)
Const maxdigits = 10000
Dim n As Long: n = ((maxdigits + 3) / 12) + 3
Dim As _Unsigned _Integer64 pi(n)
Dim As Long i, j
Dim As _Unsigned _Integer64 t, m, dq, dm
Dim As Double tm

tm = Timer
pi(1) = 4
i = CLng((3.321928094887362 * 12) * n)
While i > 0
    t = 0
    j = n - 1
    While j >= 0
        t = t + pi(j) * i
        pi(j) = t Mod 1000000000000~&&
        t = t \ 1000000000000~&&
        j = j - 1
    Wend
    dq = 0
    dm = 0
    j = 0
    While j < n
        m = pi(j) + (dm * 1000000000000~&&)
        dq = m \ ((i + i) + 1)
        dm = m Mod ((i + i) + 1)
        pi(j) = dq
        j = j + 1
    Wend
    pi(1) = pi(1) + 2
    i = i - 1
Wend
tm = Timer - tm
printpi pi(), n
Print tm

Sub printpi (pi() As _Unsigned _Integer64, n As Long)
    Dim As Long i, l
    Dim As String s

    Print pi(1); ".";
    i = 2
    While i < (n - 1)
        s = _Trim$(Str$(pi(i)))
        l = Len(s)
        s = String$(12 - l, "0") + s
        Print s;
        i = i + 1
    Wend
    Print
End Sub
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#24
(08-15-2022, 04:40 PM)Kernelpanic Wrote: @Pete, I think your path is a dead end. There are several formulas for calculating pi, one of which seems quite workable to me - if the program works. It is the formel by Ramanujan.

Maybe someone will find the error in the calculation?

Ramanujan’s Formula for Pi and Kreiszahl Wikipedia - below

Code: (Select All)
'pi berechnen - 15. Aug. 2022

Dim n As Integer
Dim pi, pir, x As Double
Dim rampi As _Integer64

Print
pir = Sqr(2) * (9801 / 4412)
Print Using "pi SR = ###.########"; pir
Print

n = 2
'Nach Wikipedia - Ramanujan -- correct
pi = (Sqr(n) * (9801) / (4412))
Print Using "Wiki pi = ###.#######"; pi
Print

'Where is the mistake?
pi = (0.0002885855652225477 + (24 * (1103 + 26390)) / (1 * 24591257856))
Print Using "Ramanu ausgerechnet pi = ###.#######"; pi

Print
pi = (Sqr(8) / 9801) + ((24 * (1103 + 26390)) / (1 * (396 ^ 4)))
Print Using "Ramanu pi = ###.#######"; pi

Print
x = 396 ^ 4
Print "x = "; x


I ran your equations through my string math routines and here are the results...



Code: (Select All)
DIM SHARED betatest: betatest% = 0
limit&& = 128
WIDTH 160, 42
_SCREENMOVE 0, 0
'--------------------------------- End pete's DIM / variable assignment.

DIM n AS INTEGER
DIM pi, pir, x AS _INTEGER64
DIM rampi AS _INTEGER64

PRINT

pir = SQR(2) * (9801 / 4412)

PRINT

PRINT USING "pi SR = ###.########"; pir
PRINT

n = 2
'Nach Wikipedia - Ramanujan -- correct
pi = (SQR(n) * (9801) / (4412))
PRINT USING "Wiki pi = ###.#######"; pi
PRINT

'Where is the mistake?
pi = (0.0002885855652225477 + (24 * (1103 + 26390)) / (1 * 24591257856))
PRINT USING "Ramanu ausgerechnet pi = ###.#######"; pi

PRINT
pi = (SQR(8) / 9801) + ((24 * (1103 + 26390)) / (1 * (396 ^ 4)))
PRINT USING "Ramanu pi = ###.#######"; pi

PRINT
x = 396 ^ 4
PRINT "x = "; x
PRINT

' Pete's routine ------------------------------------------------------------
CALL square_root("2", sqrt$, limit&&)
stringmatha$ = "9801"
stringmathb$ = "4412"
operator$ = "/"
CALL string_math(stringmatha$, operator$, stringmathb$, runningtotal$, terminating_decimal%, limit&&)
stringmatha$ = sqrt$
stringmathb$ = runningtotal$
operator$ = "*"
CALL string_math(stringmatha$, operator$, stringmathb$, runningtotal$, terminating_decimal%, limit&&)
COLOR 14, 0: PRINT "Pete's Pi based on the formula: SQR(2) * (9801 / 4412)"; runningtotal$
_CLIPBOARD$ = runningtotal$ ' Save pi to clipboard.
COLOR 7, 0: PRINT

PRINT "Next evaluation: (.0002885855652225477 + (24 * (1103 + 26390)) / (1 * 24591257856))": PRINT

stringmatha$ = "1103": stringmathb$ = "26390": operator$ = "+"
CALL string_math(stringmatha$, operator$, stringmathb$, runningtotal$, terminating_decimal%, limit&&)
stringmatha$ = "24": stringmathb$ = runningtotal$: operator$ = "*"
CALL string_math(stringmatha$, operator$, stringmathb$, runningtotal$, terminating_decimal%, limit&&)
stringmatha$ = runningtotal$: stringmathb$ = "24591257856": operator$ = "/"
CALL string_math(stringmatha$, operator$, stringmathb$, runningtotal$, terminating_decimal%, limit&&)
stringmatha$ = runningtotal$: stringmathb$ = ".0002885855652225477": operator$ = "+"
CALL string_math(stringmatha$, operator$, stringmathb$, runningtotal$, terminating_decimal%, limit&&)
COLOR 3, 0: PRINT "Ramanu ausgerechnet pi: "; runningtotal$: PRINT: COLOR 7, 0
_CLIPBOARD$ = runningtotal$ ' Save pi to clipboard.

PRINT "Next evaluation: (SQR(8) / 9801) + ((24 * (1103 + 26390)) / (1 * 1 * 24591257856))"

stringmatha$ = "1103": stringmathb$ = "26390": operator$ = "+"
CALL string_math(stringmatha$, operator$, stringmathb$, runningtotal$, terminating_decimal%, limit&&)
stringmatha$ = "24": stringmathb$ = runningtotal$: operator$ = "*"
CALL string_math(stringmatha$, operator$, stringmathb$, runningtotal$, terminating_decimal%, limit&&)
stringmatha$ = runningtotal$: stringmathb$ = "24591257856": operator$ = "/"
CALL string_math(stringmatha$, operator$, stringmathb$, runningtotal$, terminating_decimal%, limit&&)
hold$ = runningtotal$

sqrt$ = "": CALL square_root("8", sqrt$, limit&&)

stringmatha$ = sqrt$: stringmathb$ = "9801": operator$ = "/"
CALL string_math(stringmatha$, operator$, stringmathb$, runningtotal$, terminating_decimal%, limit&&)
stringmatha$ = runningtotal$: stringmathb$ = hold$: operator$ = "+"
CALL string_math(stringmatha$, operator$, stringmathb$, runningtotal$, terminating_decimal%, limit&&)

COLOR 2, 0: PRINT "Ramanu ausgerechnet pi: "; runningtotal$: COLOR 7, 0
_CLIPBOARD$ = runningtotal$ ' Save pi to clipboard.
END

SUB square_root (x$, sqrt$, limit&&)
    oldy$ = ""

    IF INSTR(x$, ".") THEN
        decx$ = MID$(x$, 1, INSTR(x$, ".") - 1)
        x$ = MID$(x$, 1, INSTR(x$, ".") - 1) + MID$(x$, INSTR(x$, ".") + 1)
        IF LEN(x$) = 1 THEN x$ = x$ + "0"
    ELSE
        decx$ = x$
    END IF

    j&& = LEN(decx$)

    ' VAL() okay, one character eval.
    IF VAL(RIGHT$(LTRIM$(STR$(j&&)), 1)) / 2 = VAL(RIGHT$(LTRIM$(STR$(j&&)), 1)) \ 2 THEN
        i&& = 1 ' Even number length.
    ELSE
        i&& = 0 ' Odd number length.
    END IF

    DO
        stringmatha$ = z$: stringmathb$ = k$

        string_math z$, "-", k$, runningtotal$, terminating_decimal%, limit&&
        z$ = runningtotal$ + (MID$(x$, i&&, 2))
        IF LEFT$(z$, 1) = "0" THEN z$ = MID$(z$, 2) ' Remove leading zeros

        oldy$ = ""
        FOR j&& = 1 TO 10
            IF i&& > 1 THEN
                string_math sqrt$, "*", "2", y$, terminating_decimal%, limit&&
                y$ = y$ + LTRIM$(STR$(j&&))
            ELSE
                y$ = LTRIM$(STR$(j&&))
            END IF

            string_math y$, "*", LTRIM$(STR$(j&&)), runningtotal$, terminating_decimal%, limit&&

            string_compare runningtotal$, z$, gl%
            IF gl% > -1 THEN
                IF gl% = 0 THEN
                    h% = 0: oldy$ = y$ ' Perfect square division.
                ELSE
                    h% = 1
                END IF
                string_math oldy$, "*", LTRIM$(STR$(j&& - h%)), runningtotal$, terminating_decimal%, limit&&
                IF STRING$(LEN(z$), "0") = z$ AND runningtotal$ = "0" AND i&& >= LEN(decx$) THEN EXIT DO

                IF dp&& = 0 THEN ' Limited to && size unless converted to string.
                    IF i&& >= LEN(decx$) THEN
                        dp&& = INT(LEN(decx$) / 2 + .5)
                        IF dp&& = 0 THEN dp&& = -1
                    END IF
                END IF

                IF betatest% THEN PRINT "Sqrt "; sqrt$; " * 2 = ";: COLOR 2, 0: PRINT LTRIM$(STR$(VAL(sqrt$) * 2));: COLOR 7, 0: PRINT LTRIM$(STR$(j&& - h%)); " * "; LTRIM$(STR$(j&& - h%)); " ="; VAL(oldy$) * (j&& - h%)
                sqrt$ = sqrt$ + LTRIM$(STR$(j&& - h%))

                string_math oldy$, "*", LTRIM$(STR$(j&& - h%)), runningtotal$, terminating_decimal%, limit&&
                k$ = runningtotal$

                IF betatest% THEN PRINT "Remainder "; z$; " minus "; k$; " = ";
                EXIT FOR
            END IF
            oldy$ = y$
        NEXT

        IF betatest% THEN
            string_math stringmatha$, "-", stringmathb$, runningtotal$, terminating_decimal%, limit&&
            PRINT runningtotal$; " sqrt = "; sqrt$
        END IF

        i&& = i&& + 2
        IF LEN(z$) >= limit&& THEN EXIT DO
        x$ = x$ + "00"
    LOOP

    PRINT

    IF dp&& THEN
        sqrt$ = MID$(sqrt$, 0, dp&& + 1) + "." + MID$(sqrt$, dp&& + 1)
    END IF

    _CLIPBOARD$ = sqrt$
END SUB

SUB string_math (stringmatha$, operator$, stringmathb$, runningtotal$, terminating_decimal%, limit&&)
    DIM AS _INTEGER64 a, c, aa, cc, s, ss

    SELECT CASE operator$
        CASE "+", "-"
            GOTO string_add_subtract_new
        CASE "*"
            GOTO string_multiply_new
        CASE "/"
            GOTO string_divide
        CASE ELSE
            PRINT "Error, no operator selected. operator$ = "; operator$
    END SELECT

    string_divide:
    terminating_decimal% = 0: divsign% = 0: divremainder& = 0: divremainder$ = "": divplace& = 0: divplace2& = 0: quotient$ = "": divcarry& = 0
    operationdivision% = -1
    divbuffer& = LEN(stringmathb$) - LEN(stringmatha$)
    IF divbuffer& < 0 THEN divbuffer& = 0
    d2dividend$ = stringmatha$
    d1divisor$ = stringmathb$
    IF LEFT$(d1divisor$, 1) = "0" AND LEN(d1divisor$) = 1 THEN PRINT "Division by zero not allowed.": divsign% = 0: operationdivision% = 0: EXIT SUB
    IF LEFT$(d1divisor$, 1) = "-" THEN divsign% = -1: d1divisor$ = MID$(d1divisor$, 2)
    IF LEFT$(d2dividend$, 1) = "-" THEN
        IF divsign% THEN
            divsign% = 0
        ELSE
            divsign% = -1
        END IF
        d2dividend$ = MID$(d2dividend$, 2)
    END IF
    IF INSTR(d1divisor$, ".") <> 0 THEN
        DO UNTIL RIGHT$(d1divisor$, 1) <> "0"
            d1divisor$ = MID$(d1divisor$, 1, LEN(d1divisor$) - 1) ' Strip off trailing zeros
        LOOP
        divplace& = LEN(d1divisor$) - INSTR(d1divisor$, ".")
        d1divisor$ = MID$(d1divisor$, 1, INSTR(d1divisor$, ".") - 1) + MID$(d1divisor$, INSTR(d1divisor$, ".") + 1) ' Strip off decimal point.
        DO UNTIL LEFT$(d1divisor$, 1) <> "0"
            d1divisor$ = MID$(d1divisor$, 2) ' Strip off leading zeros for divisors smaller than .1
        LOOP
    END IF

    IF INSTR(d2dividend$, ".") <> 0 THEN
        d2dividend$ = d2dividend$ + STRING$(divplace& - LEN(d2dividend$) - INSTR(d2dividend$, "."), "0") ' Add any zeros based on the length of dividend at decimal - length of divisor at decimal. If less than zero, nothing added.
        divplace2& = INSTR(d2dividend$, ".")
        DO UNTIL RIGHT$(d2dividend$, 1) <> "0"
            d2dividend$ = MID$(d2dividend$, 1, LEN(d2dividend$) - 1) ' Strip off trailing zeros
        LOOP
        d2dividend$ = MID$(d2dividend$, 1, INSTR(d2dividend$, ".") - 1) + MID$(d2dividend$, INSTR(d2dividend$, ".") + 1) ' Strip off decimal point.
    ELSE
        d2dividend$ = d2dividend$ + STRING$(divplace&, "0") ' Add any zeros based on the length of dividend at decimal - length of divisor at decimal. If less than zero, nothing added.
        divplace& = 0
    END IF
    DO
        DO
            divremainder& = divremainder& + 1: divremainder$ = divremainder$ + MID$(d2dividend$, divremainder&, 1)
            IF MID$(d2dividend$, divremainder&, 1) = "" THEN
                IF divremainder$ = STRING$(LEN(divremainder$), "0") AND LEN(quotient$) > LEN(d2dividend$) THEN
                    divflag% = -1
                    terminating_decimal% = -1
                    EXIT DO
                END IF
                divcarry& = divcarry& + 1
                IF divcarry& = 1 THEN divplace3& = divremainder& - 1
                IF divcarry& > limit&& + 1 + divbuffer& THEN
                    divflag% = -2: EXIT DO
                END IF
                divremainder$ = divremainder$ + "0" ' No more digits to bring down.
            END IF
            IF LEN(divremainder$) > LEN(d1divisor$) OR LEN(divremainder$) = LEN(d1divisor$) AND divremainder$ >= d1divisor$ THEN EXIT DO
            quotient$ = quotient$ + "0"
        LOOP
        IF divflag% THEN divflag% = 0: EXIT DO
        FOR div_i% = 9 TO 1 STEP -1
            stringmatha$ = LTRIM$(STR$(div_i%)): stringmathb$ = d1divisor$
            m_product$ = "": GOSUB string_multiply_new: m_product$ = runningtotal$
            tempcutd$ = divremainder$ ' divremainder$ can be 00 or other leading zero values.
            DO
                IF LEN(tempcutd$) = 1 THEN EXIT DO
                IF LEFT$(tempcutd$, 1) = "0" THEN
                    tempcutd$ = MID$(tempcutd$, 2)
                ELSE
                    EXIT DO
                END IF
            LOOP
            IF LEN(tempcutd$) > LEN(m_product$) OR LEN(tempcutd$) = LEN(m_product$) AND m_product$ <= tempcutd$ THEN EXIT FOR
        NEXT
        quotient$ = quotient$ + LTRIM$(STR$(div_i%))
        stringmatha$ = LTRIM$(STR$(div_i%)): stringmathb$ = d1divisor$
        m_product$ = "": GOSUB string_multiply: m_product$ = runningtotal$
        operator$ = "-"
        stringmatha$ = divremainder$
        stringmathb$ = m_product$
        GOSUB string_add_subtract_new
        stringmatha$ = runningtotal$ '*'
        divremainder$ = stringmatha$
        operator$ = "/"
    LOOP

    IF divplace& = 0 AND divplace2& = 0 THEN divplace& = divplace3&
    IF divplace2& THEN divplace& = divplace& + divplace2& - 1
    IF quotient$ = "" THEN divplace& = 0 ' dividend is zero.
    IF divplace& OR divplace2& THEN
        quotient$ = MID$(quotient$, 1, divplace&) + "." + MID$(quotient$, divplace& + 1)
        DO UNTIL RIGHT$(quotient$, 1) <> "0"
            quotient$ = MID$(quotient$, 1, LEN(quotient$) - 1) ' Strip off trailing zeros
        LOOP
        IF RIGHT$(quotient$, 1) = "." THEN quotient$ = MID$(quotient$, 1, LEN(quotient$) - 1) ' Strip off abandoned decimal.
    END IF
    DO UNTIL LEFT$(quotient$, 1) <> "0"
        quotient$ = MID$(quotient$, 2) ' Strip off leading zeros
    LOOP
    IF quotient$ = "" THEN quotient$ = "0": divsign% = 0
    operationdivision% = 0
    stringmathb$ = quotient$: quotient$ = ""

    IF stringmathb$ = "overflow" THEN divsign% = 0: operationdivision% = 0: EXIT SUB

    runningtotal$ = stringmathb$: stringmathb$ = ""
    IF divsign% THEN runningtotal$ = "-" + runningtotal$

    IF stringmathround$ <> "" THEN runningtotal$ = runningtotal$ + stringmathround$
    operationdivision% = 0

    EXIT SUB
    '------------------------------------------------------------------------
    string_multiply:
    m_decimal_places& = 0: m_product$ = ""
    fac1$ = stringmatha$: fac2$ = stringmathb$ ' Make numbers whole numbers and remove any - sign.
    IF LEFT$(fac1$, 1) = "-" THEN fac1$ = MID$(fac1$, 2): m_sign% = -1
    IF LEFT$(fac2$, 1) = "-" THEN fac2$ = MID$(fac2$, 2): IF m_sign% THEN m_sign% = 0 ELSE m_sign% = -1
    IF INSTR(fac1$, ".") <> 0 THEN m_decimal_places& = LEN(fac1$) - INSTR(fac1$, "."): fac1$ = MID$(fac1$, 1, INSTR(fac1$, ".") - 1) + MID$(fac1$, INSTR(fac1$, ".") + 1)
    IF INSTR(fac2$, ".") <> 0 THEN m_decimal_places& = m_decimal_places& + LEN(fac2$) - INSTR(fac2$, "."): fac2$ = MID$(fac2$, 1, INSTR(fac2$, ".") - 1) + MID$(fac2$, INSTR(fac2$, ".") + 1)
    FOR m_i& = LEN(fac2$) TO 1 STEP -1 ' Multiply each charater top and bottom.
        m_k& = m_l&
        m_x2$ = MID$(fac2$, m_i&, 1)
        FOR m_j& = LEN(fac1$) TO 1 STEP -1
            m_x1$ = MID$(fac1$, m_j&, 1)
            IF m_product$ <> "" THEN
                m_add$ = LTRIM$(STR$(VAL(m_x1$) * VAL(m_x2$))) + STRING$(m_k&, "0")
                m_t& = 0: m_xproduct$ = "": m_carry% = 0
                DO ' Add multiplied characters together.
                    m_x3$ = MID$(m_add$, LEN(m_add$) - m_t&, 1)
                    m_x4$ = MID$(m_product$, LEN(m_product$) - m_t&, 1)
                    IF m_x3$ = "" AND m_x4$ = "" THEN
                        IF m_carry% THEN m_xproduct$ = "1" + m_xproduct$
                        EXIT DO
                    END IF
                    m_g% = VAL(m_x3$) + VAL(m_x4$) + m_carry%
                    IF m_g% >= 10 THEN m_g% = m_g% - 10: m_carry% = 1 ELSE m_carry% = 0
                    m_xproduct$ = LTRIM$(STR$(m_g%)) + m_xproduct$
                    m_t& = m_t& + 1
                LOOP
                m_product$ = m_xproduct$: m_xproduct$ = ""
            ELSE
                m_product$ = LTRIM$(STR$(VAL(m_x1$) * VAL(m_x2$))) + STRING$(m_k&, "0") ' First loop makes variable here.
            END IF
            m_k& = m_k& + 1 ' Adds trailing zeros multiplication
        NEXT
        m_l& = m_l& + 1 ' Used to reset value for m_k& adding one trailing zer for each loop.
    NEXT
    fac1$ = "": fac2$ = "": m_l& = 0: m_k& = 0: m_t& = 0
    IF m_decimal_places& > LEN(m_product$) THEN m_product$ = STRING$(m_decimal_places& - LEN(m_product$), "0") + m_product$ ' Add any leading zeros to a decimal. Ex: .02 * .01 is factored as 002. It needs one leading zero before adding the decimal point, .0002.
    IF m_decimal_places& AND m_product$ <> "0" THEN ' Replace any decimal point.
        m_product$ = MID$(m_product$, 1, LEN(m_product$) - m_decimal_places&) + "." + MID$(m_product$, LEN(m_product$) - m_decimal_places& + 1)
    END IF
    DO UNTIL LEFT$(m_product$, 1) <> "0" ' Remove leading zeros.
        m_product$ = MID$(m_product$, 2)
    LOOP
    IF m_decimal_places& THEN
        DO UNTIL RIGHT$(m_product$, 1) <> "0" ' Remove trailing zeros in a decimal sum.
            m_product$ = MID$(m_product$, 1, LEN(m_product$) - 1)
        LOOP
    END IF
    IF m_product$ = "" THEN m_product$ = "0": m_sign% = 0
    IF RIGHT$(m_product$, 1) = "." THEN m_product$ = MID$(m_product$, 1, LEN(m_product$) - 1) ' Remove decimal from the end of an integer total.
    IF operationdivision% THEN m_sign% = 0: RETURN
    stringmathb$ = m_product$: m_product$ = ""

    IF stringmathb$ = "overflow" THEN EXIT SUB

    runningtotal$ = stringmathb$: stringmathb$ = ""
    IF m_sign% THEN runningtotal$ = "-" + runningtotal$: m_sign% = 0
    EXIT SUB

    string_add_subtract:
    IF INSTR(stringmatha$, ".") <> 0 THEN ' Evaluate sum for decimal fraction.
        sumplace& = LEN(stringmatha$) - INSTR(stringmatha$, ".")
        stringmatha$ = MID$(stringmatha$, 1, INSTR(stringmatha$, ".") - 1) + MID$(stringmatha$, INSTR(stringmatha$, ".") + 1) ' Strip out decimal
    END IF
    IF INSTR(stringmathb$, ".") <> 0 THEN ' Evaluate number for decimal fraction.
        numplace& = LEN(stringmathb$) - INSTR(stringmathb$, ".")
        stringmathb$ = MID$(stringmathb$, 1, INSTR(stringmathb$, ".") - 1) + MID$(stringmathb$, INSTR(stringmathb$, ".") + 1) ' Strip out decimal
    END IF
    IF sumplace& > numplace& THEN addsubplace& = sumplace& ELSE addsubplace& = numplace&
    IF sumplace& > addsubplace& THEN
        stringmatha$ = stringmatha$ + STRING$(sumplace& - addsubplace&, "0")
    ELSEIF addsubplace& > sumplace& THEN
        stringmatha$ = stringmatha$ + STRING$(addsubplace& - sumplace&, "0")
    END IF
    IF numplace& > addsubplace& THEN
        stringmathb$ = stringmathb$ + STRING$(numplace& - addsubplace&, "0")
    ELSEIF addsubplace& > numplace& THEN
        stringmathb$ = stringmathb$ + STRING$(addsubplace& - numplace&, "0")
    END IF ' END Decimal evaluations.

    IF LEFT$(stringmatha$, 1) = "-" THEN sign_input$ = "-" ELSE sign_input$ = "+"
    IF LEFT$(stringmathb$, 1) = "-" THEN sign_total$ = "-" ELSE sign_total$ = "+"

    addsubsign% = 0
    SELECT CASE sign_input$ + operator$ + sign_total$
        CASE "+++", "+--"
            operator$ = "+"
            IF LEFT$(stringmathb$, 1) = "-" THEN stringmathb$ = MID$(stringmathb$, 2)
        CASE "++-", "+-+"
            operator$ = "-"
            IF LEFT$(stringmathb$, 1) = "-" THEN stringmathb$ = MID$(stringmathb$, 2)
            GOSUB string_comp
            IF gl% < 0 THEN SWAP stringmatha$, stringmathb$: addsubsign% = -1
        CASE "---", "-++"
            operator$ = "-"
            IF LEFT$(stringmatha$, 1) = "-" THEN stringmatha$ = MID$(stringmatha$, 2)
            IF LEFT$(stringmathb$, 1) = "-" THEN stringmathb$ = MID$(stringmathb$, 2)
            GOSUB string_comp
            IF gl% < 0 THEN SWAP stringmatha$, stringmathb$: addsubsign% = -1
        CASE "--+", "-+-"
            operator$ = "+"
            IF LEFT$(stringmatha$, 1) = "-" THEN stringmatha$ = MID$(stringmatha$, 2)
            IF LEFT$(stringmathb$, 1) = "-" THEN stringmathb$ = MID$(stringmathb$, 2)
            addsubsign% = -1
    END SELECT

    IF LEN(stringmatha$) > LEN(stringmathb$) THEN
        stringmathb$ = STRING$(LEN(stringmatha$) - LEN(stringmathb$), "0") + stringmathb$
    ELSEIF LEN(stringmatha$) < LEN(stringmathb$) THEN
        stringmatha$ = STRING$(LEN(stringmathb$) - LEN(stringmatha$), "0") + stringmatha$
    END IF
    addsubx1$ = ""

    SELECT CASE operator$
        CASE "+", "="
            FOR addsubii& = LEN(stringmatha$) TO 1 STEP -1
                addsubx1% = VAL(MID$(stringmatha$, addsubii&, 1)) + VAL(MID$(stringmathb$, addsubii&, 1)) + addsubcarry%
                IF addsubx1% > 9 THEN addsubx1% = addsubx1% - 10: addsubcarry% = 1 ELSE addsubcarry% = 0
                addsubx1$ = LTRIM$(STR$(addsubx1%)) + addsubx1$
            NEXT
            IF addsubcarry% THEN addsubx1$ = "1" + addsubx1$: addsubcarry% = 0
            GOSUB replace_decimal
        CASE "-"
            FOR addsubii& = LEN(stringmatha$) TO 1 STEP -1
                addsubx1% = VAL(MID$(stringmatha$, addsubii&, 1)) - VAL(MID$(stringmathb$, addsubii&, 1)) + addsubcarry%
                IF addsubx1% < 0 THEN addsubx1% = addsubx1% + 10: addsubcarry% = -1 ELSE addsubcarry% = 0
                addsubx1$ = LTRIM$(STR$(addsubx1%)) + addsubx1$
            NEXT
            IF addsubx1$ <> "" AND addsubx1$ <> STRING$(LEN(addsubx1$), "0") THEN GOSUB replace_decimal
            DO UNTIL LEFT$(addsubx1$, 1) <> "0" ' Remove leading zeros.
                addsubx1$ = MID$(addsubx1$, 2)
            LOOP
            IF addsubx1$ = "" THEN
                addsubx1$ = "0": addsubsign% = 0
            ELSE
                IF addsubcarry% THEN addsubx1$ = "-" + addsubx1$: addsubcarry% = 0
            END IF
    END SELECT

    IF addsubsign% THEN
        IF LEFT$(addsubx1$, 1) = "-" THEN addsubx1$ = MID$(addsubx1$, 2) ELSE addsubx1$ = "-" + addsubx1$
    END IF
    stringmatha$ = addsubx1$: addsubx1$ = ""
    IF operationdivision% THEN RETURN
    stringmathb$ = stringmatha$: stringmatha$ = ""
    IF LEFT$(stringmathb$, 1) = "-" THEN
        stringmathb$ = MID$(stringmathb$, 2)
        n2sign$ = "-"
    ELSE
        n2sign$ = ""
    END IF

    IF stringmathb$ = "overflow" THEN n2sign$ = "": EXIT SUB

    runningtotal$ = n2sign$ + stringmathb$: n2sign$ = ""
    EXIT SUB


    '------------------------------------------------------------------------
    string_add_subtract_new:
    a1$ = stringmatha$: b1$ = stringmathb$
    s = 18: i&& = 0: c = 0

    a$ = stringmatha$: b$ = stringmathb$: op$ = operator$

    IF op$ = "-" THEN
        IF LEFT$(b$, 1) = "-" THEN b$ = MID$(b$, 2) ELSE b$ = "-" + b$
    END IF

    IF INSTR(a$, ".") <> 0 OR INSTR(b$, ".") <> 0 THEN
        decimal% = -1
        IF INSTR(a$, ".") <> 0 THEN
            dec_a&& = LEN(MID$(a$, INSTR(a$, ".") + 1))
            a$ = MID$(a$, 1, INSTR(a$, ".") - 1) + MID$(a$, INSTR(a$, ".") + 1)
        END IF
        IF INSTR(b$, ".") <> 0 THEN
            dec_b&& = LEN(MID$(b$, INSTR(b$, ".") + 1))
            b$ = MID$(b$, 1, INSTR(b$, ".") - 1) + MID$(b$, INSTR(b$, ".") + 1)
        END IF
        ' Line up decimal places by inserting trailing zeros.
        IF dec_b&& > dec_a&& THEN
            j&& = dec_b&&
            a$ = a$ + STRING$(dec_b&& - dec_a&&, "0")
        ELSE
            j&& = dec_a&&
            b$ = b$ + STRING$(dec_a&& - dec_b&&, "0")
        END IF
    END IF

    IF LEFT$(a$, 1) = "-" OR LEFT$(b$, 1) = "-" THEN
        IF LEFT$(a$, 1) = "-" AND LEFT$(b$, 1) = "-" THEN
            sign$ = "--": a$ = MID$(a$, 2): b$ = MID$(b$, 2)
        ELSE
            IF LEFT$(a$, 1) = "-" THEN a$ = MID$(a$, 2): sign_a$ = "-"
            IF LEFT$(b$, 1) = "-" THEN b$ = MID$(b$, 2): sign_b$ = "-"

            IF LEFT$(a1$, 1) = "-" THEN a1_x$ = MID$(a1$, 2) ELSE a1_x$ = a1$
            IF LEFT$(b1$, 1) = "-" THEN b1_x$ = MID$(b1$, 2) ELSE b1_x$ = b1$

            string_compare a1_x$, b1_x$, gl%

            IF gl% < 0 THEN
                IF LEN(sign_b$) THEN sign$ = "-": SWAP a$, b$
            ELSE
                IF LEN(sign_a$) THEN sign$ = "-": SWAP sign_a$, sign_b$
            END IF
        END IF
    END IF

    z$ = ""

    DO
        i&& = i&& + s
        x1$ = MID$(a$, LEN(a$) - i&& + 1, s)
        x2$ = MID$(b$, LEN(b$) - i&& + 1, s)
        a = VAL(sign_a$ + x1$) + VAL(sign_b$ + x2$) + c
        IF x1$ + x2$ = "" AND c = 0 THEN EXIT DO
        c = 0
        IF a > VAL(STRING$(s, "9")) THEN a = a - 10 ^ s: c = 1
        IF a < 0 THEN a = a + 10 ^ s: c = -1
        tmp$ = LTRIM$(STR$(a))
        z$ = STRING$(LEN(x1$) - LEN(tmp$), "0") + tmp$ + z$
    LOOP

    IF decimal% THEN
        z$ = MID$(z$, 1, LEN(z$) - j&&) + "." + MID$(z$, LEN(z$) - j&& + 1)
    END IF

    ' Remove any leading zeros.
    DO
        IF LEFT$(z$, 1) = "0" THEN z$ = MID$(z$, 2) ELSE EXIT DO
    LOOP

    IF z$ = "" OR z$ = "0" THEN z$ = "0" ELSE z$ = LEFT$(sign$, 1) + z$

    runningtotal$ = z$ '*'

    sign$ = "": sign_a$ = "": sign_b$ = "": i&& = 0: j&& = 0: decimal% = 0: c = 0
    IF operationdivision% THEN RETURN
    EXIT SUB

    '------------------------------------------------------------------------
    string_multiply_new:
    z$ = "": sign$ = "": mult&& = 0: h&& = 0: i&& = 0: j&& = 0: c = 0: decimal% = 0
    zz$ = "": ii&& = 0: jj&& = 0
    s = 8: ss = 18

    a$ = stringmatha$: b$ = stringmathb$

    IF INSTR(a$, "-") <> 0 OR INSTR(b$, "-") <> 0 THEN
        IF INSTR(a$, "-") <> 0 AND INSTR(b$, "-") <> 0 THEN
            a$ = MID$(a$, 2): b$ = MID$(b$, 2)
        ELSE
            IF INSTR(a$, "-") <> 0 THEN a$ = MID$(a$, 2) ELSE b$ = MID$(b$, 2)
            sign$ = "-"
        END IF
    END IF

    IF INSTR(a$, ".") <> 0 OR INSTR(b$, ".") <> 0 THEN
        decimal% = -1
        IF INSTR(a$, ".") <> 0 THEN
            dec_a&& = LEN(MID$(a$, INSTR(a$, ".") + 1))
            a$ = MID$(a$, 1, INSTR(a$, ".") - 1) + MID$(a$, INSTR(a$, ".") + 1)
        END IF
        IF INSTR(b$, ".") <> 0 THEN
            dec_b&& = LEN(MID$(b$, INSTR(b$, ".") + 1))
            b$ = MID$(b$, 1, INSTR(b$, ".") - 1) + MID$(b$, INSTR(b$, ".") + 1)
        END IF
    END IF

    IF LEN(a$) < LEN(b$) THEN SWAP a$, b$

    DO
        h&& = h&& + s: i&& = 0
        x2$ = MID$(b$, LEN(b$) - h&& + 1, s)
        WHILE -1
            i&& = i&& + s
            x1$ = MID$(a$, LEN(a$) - i&& + 1, s)
            a = VAL(sign_a$ + x1$) * VAL(sign_b$ + x2$) + c
            c = 0
            tmp$ = LTRIM$(STR$(a))
            IF LEN(tmp$) > s THEN c = VAL(MID$(tmp$, 1, LEN(tmp$) - s)): tmp$ = MID$(tmp$, LEN(tmp$) - s + 1)
            z$ = STRING$(LEN(x1$) - LEN(tmp$), "0") + tmp$ + z$
            IF i&& >= LEN(a$) AND c = 0 THEN EXIT WHILE
        WEND

        jj&& = jj&& + 1

        IF jj&& > 1 THEN
            ii&& = 0: cc = 0
            aa$ = holdaa$
            bb$ = z$ + STRING$((jj&& - 1) * s, "0")

            DO
                ii&& = ii&& + ss
                xx1$ = MID$(aa$, LEN(aa$) - ii&& + 1, ss)
                xx2$ = MID$(bb$, LEN(bb$) - ii&& + 1, ss)
                aa = VAL(xx1$) + VAL(xx2$) + cc
                IF xx1$ + xx2$ = "" AND cc = 0 THEN EXIT DO ' Prevents leading zeros.
                cc = 0
                IF aa > VAL(STRING$(ss, "9")) THEN aa = aa - 10 ^ ss: cc = 1
                tmp$ = LTRIM$(STR$(aa))
                zz$ = STRING$(LEN(xx1$) - LEN(tmp$), "0") + tmp$ + zz$
            LOOP

            DO WHILE LEFT$(zz$, 1) = "0"
                IF LEFT$(zz$, 1) = "0" THEN zz$ = MID$(zz$, 2)
            LOOP
            IF zz$ = "" THEN zz$ = "0"

            holdaa$ = zz$
        ELSE
            holdaa$ = z$ + STRING$(jj&& - 1, "0")
        END IF

        z$ = "": zz$ = ""

    LOOP UNTIL h&& >= LEN(b$)

    z$ = holdaa$

    IF decimal% THEN
        DO UNTIL LEN(z$) >= dec_a&& + dec_b&&
            z$ = "0" + z$
        LOOP

        z$ = MID$(z$, 0, LEN(z$) - (dec_a&& + dec_b&& - 1)) + "." + MID$(z$, LEN(z$) - (dec_a&& + dec_b&&) + 1)

        DO UNTIL RIGHT$(z$, 1) <> "0" AND RIGHT$(z$, 1) <> "."
            z$ = MID$(z$, 1, LEN(z$) - 1)
        LOOP
    END IF

    IF z$ = "" OR z$ = "0" THEN z$ = "0": ELSE z$ = sign$ + z$

    decimal% = 0: sign$ = ""

    runningtotal$ = z$
    IF operationdivision% THEN RETURN
    EXIT SUB

    replace_decimal:
    IF addsubplace& THEN
        addsubx1$ = STRING$(addsubplace& - LEN(addsubx1$), "0") + addsubx1$
        addsubx1$ = MID$(addsubx1$, 1, LEN(addsubx1$) - addsubplace&) + "." + MID$(addsubx1$, LEN(addsubx1$) - addsubplace& + 1)
        DO UNTIL RIGHT$(addsubx1$, 1) <> "0" ' Remove trailing zeros in a decimal sum.
            addsubx1$ = MID$(addsubx1$, 1, LEN(addsubx1$) - 1)
            addsubplace& = addsubplace& - 1
        LOOP
        IF RIGHT$(addsubx1$, 1) = "." THEN addsubx1$ = MID$(addsubx1$, 1, LEN(addsubx1$) - 1) ' Number is now an integer.
    END IF
    RETURN

    string_comp:
    DO
        ' Remove trailing zeros after a decimal point.
        IF INSTR(acomp$, ".") THEN
            DO UNTIL RIGHT$(acomp$, 1) <> "0" AND RIGHT$(acomp$, 1) <> "." AND RIGHT$(acomp$, 1) <> "-"
                acomp$ = MID$(acomp$, 1, LEN(acomp$) - 1)
            LOOP
        END IF
        IF INSTR(bcomp$, ".") THEN
            DO UNTIL RIGHT$(bcomp$, 1) <> "0" AND RIGHT$(bcomp$, 1) <> "." AND RIGHT$(bcomp$, 1) <> "-"
                bcomp$ = MID$(bcomp$, 1, LEN(bcomp$) - 1)
            LOOP
        END IF

        IF MID$(acomp$, 1, 2) = "-0" OR acomp$ = "" OR acomp$ = "-" THEN acomp$ = "0"
        IF MID$(bcomp$, 1, 2) = "-0" OR bcomp$ = "" OR bcomp$ = "-" THEN bcomp$ = "0"

        ' A - and +
        IF LEFT$(acomp$, 1) = "-" THEN j% = -1
        IF LEFT$(bcomp$, 1) = "-" THEN k% = -1
        IF k% = 0 AND j% THEN gl% = -1: EXIT DO
        IF j% = 0 AND k% THEN gl% = 1: EXIT DO

        ' A decimal and non-decimal.
        j% = INSTR(acomp$, ".")
        k% = INSTR(bcomp$, ".")
        IF j% = 0 AND k% THEN
            IF acomp$ = "0" THEN gl% = -1 ELSE gl% = 1
            EXIT DO
        END IF
        IF k% = 0 AND j% THEN
            IF bcomp$ = "0" THEN gl% = 1 ELSE gl% = -1
            EXIT DO
        END IF

        ' Both decimals.
        IF j% THEN
            IF acomp$ > bcomp$ THEN
                gl% = 1
            ELSEIF acomp$ = bcomp$ THEN gl% = 0
            ELSEIF acomp$ < bcomp$ THEN gl% = -1
            END IF
            EXIT DO
        END IF

        ' Both positive or both negative whole numbers.
        SELECT CASE LEN(acomp$)
            CASE IS < LEN(bcomp$)
                gl% = -1
            CASE IS = LEN(bcomp$)
                IF acomp$ = bcomp$ THEN
                    gl% = 0
                ELSEIF acomp$ > bcomp$ THEN gl% = 1
                ELSEIF acomp$ < bcomp$ THEN gl% = -1
                END IF
            CASE IS > LEN(bcomp$)
                gl% = 1
        END SELECT
        EXIT DO
    LOOP
    RETURN
END SUB

SUB string_compare (compa$, compb$, gl%)
    DO
        ' Remove trailing zeros after a decimal point.
        IF INSTR(compa$, ".") THEN
            DO UNTIL RIGHT$(compa$, 1) <> "0" AND RIGHT$(compa$, 1) <> "." AND RIGHT$(compa$, 1) <> "-"
                compa$ = MID$(compa$, 1, LEN(compa$) - 1)
            LOOP
        END IF
        IF INSTR(compb$, ".") THEN
            DO UNTIL RIGHT$(compb$, 1) <> "0" AND RIGHT$(compb$, 1) <> "." AND RIGHT$(compb$, 1) <> "-"
                compb$ = MID$(compb$, 1, LEN(compb$) - 1)
            LOOP
        END IF

        IF MID$(compa$, 1, 2) = "-0" OR compa$ = "" OR compa$ = "-" THEN compa$ = "0"
        IF MID$(compb$, 1, 2) = "-0" OR compb$ = "" OR compb$ = "-" THEN compb$ = "0"

        ' A - and +
        IF LEFT$(compa$, 1) = "-" THEN j% = -1
        IF LEFT$(compb$, 1) = "-" THEN k% = -1
        IF k% = 0 AND j% THEN gl% = -1: EXIT DO
        IF j% = 0 AND k% THEN gl% = 1: EXIT DO

        ' A decimal and non-decimal.
        j% = INSTR(compa$, ".")
        k% = INSTR(compb$, ".")

        IF j% = 0 AND k% THEN
            IF compa$ = "0" THEN gl% = -1 ELSE gl% = 1
            EXIT DO
        END IF
        IF k% = 0 AND j% THEN
            IF compb$ = "0" THEN gl% = 1 ELSE gl% = -1
            EXIT DO
        END IF

        ' Both decimals.
        IF j% THEN
            IF compa$ > compb$ THEN
                gl% = 1
            ELSEIF compa$ = compb$ THEN gl% = 0
            ELSEIF compa$ < compb$ THEN gl% = -1
            END IF
            EXIT DO
        END IF

        ' Both positive or both negative whole numbers.
        SELECT CASE LEN(compa$)
            CASE IS < LEN(compb$)
                gl% = -1
            CASE IS = LEN(compb$)
                IF compa$ = compb$ THEN
                    gl% = 0
                ELSEIF compa$ > compb$ THEN gl% = 1
                ELSEIF compa$ < compb$ THEN gl% = -1
                END IF
            CASE IS > LEN(compb$)
                gl% = 1
        END SELECT
        EXIT DO
    LOOP
END SUB




Pete


Attached Files Image(s)
   
Reply
#25
(08-16-2022, 05:11 PM)Kernelpanic Wrote: Thanks! This works, but only once. "n" and "m" apparently have no meaning.
Actually, 8 new correct digits should appear with each run.
The screenshot of the code indicates you've declared nothing AS DOUBLE or AS _FLOAT. They're all SINGLE-precision, that's why the output quickly comes up with incorrect values. It wouldn't be really useful anyway, requires more horsepower as @Pete has cleverly displayed. ::u:
Reply
#26
Well guess what? I've been away for a bit. Straight jackets aren't as simple to slip out of as they used to be. Lucky for me, mine was made in China.

So I've been fiddling around with a new improved method of string division. My hunch was it would be about twice as fast on calculating pi in this thread. That would have made it about 35% faster than treebeard's routine. Well that hunch was exceeded significantly, to a 700% speed increase! My old code ran pi in the last loop of 160 digits in 14 seconds on my clunky machine, [b]but this new routine can do it in just 2![/]

Code: (Select All)
'Jack's Ramanujan's Pi Estimator with Pete's String Math Routines.
WIDTH 175, 42
_SCREENMOVE 0, 0
DIM SHARED sqrt$, limit&&, betatest%
betatest% = 0
DIM AS STRING sum, f, f4, f4k, c1, c2, c3, c34k, t1, t2, t3
DIM AS LONG k, k4
DIM t AS DOUBLE

limit&& = 150: square_root "8", sqrt$ ' Limit must be as many or more digits than the max digits of the returned value for pi.

FOR pete% = 0 TO 16
    limit&& = pete% + 10 + pete% * 8
    t = TIMER
    c1 = "1103"
    c2 = "26390"
    c3 = "396"
    f = "1"
    f4k = "1"
    sum = "1103"
    c34k = "1"
    k4 = 0
    t1 = c3
    t2 = c3
    sm t1, "*", t2, c3
    t1 = c3
    t2 = c3
    sm t1, "*", t2, c3

    FOR k = 1 TO limit&& / (7.984)
        t1 = f
        sm STR$(k), "*", t1, f
        IF betatest% THEN PRINT "results = "; f: SLEEP
        t1 = f: t2 = f
        sm t1, "*", t2, f4
        IF betatest% THEN PRINT "results = "; f4: SLEEP
        t1 = f4: t2 = f4
        sm t1, "*", t2, f4
        IF betatest% THEN PRINT "results = "; f4: SLEEP
        t1 = c34k
        sm c3, "*", t1, c34k
        IF betatest% THEN PRINT "results = "; c34k: SLEEP
        t1 = STR$(k4 + 1)
        t2 = f4k
        sm t1, "*", t2, f4k
        IF betatest% THEN PRINT "results = "; f4k: SLEEP
        t1 = STR$(k4 + 2)
        t2 = f4k
        sm t1, "*", t2, f4k
        IF betatest% THEN PRINT "results = "; f4k: SLEEP
        t1 = STR$(k4 + 3)
        t2 = f4k
        sm t1, "*", t2, f4k
        IF betatest% THEN PRINT "results = "; f4k: SLEEP
        t1 = STR$(k4 + 4)
        t2 = f4k
        sm t1, "*", t2, f4k
        IF betatest% THEN PRINT "results = "; f4k: SLEEP
        k4 = k4 + 4
        t1 = STR$(k)
        sm t1, "*", c2, t2
        IF betatest% THEN PRINT "results = "; t2: SLEEP
        sm c1, "+", t2, t1
        IF betatest% THEN PRINT "results = "; t1: SLEEP
        sm f4k, "*", t1, t2
        IF betatest% THEN PRINT "results = "; t2: SLEEP
        sm f4, "*", c34k, t1
        IF betatest% THEN PRINT "results = "; t1: SLEEP
        sm t2, "/", t1, t3
        IF betatest% THEN PRINT "divide results = "; t3: SLEEP
        t1 = sum
        sm t1, "+", t3, sum
        IF betatest% THEN PRINT "sum =   "; sum: SLEEP
        CALL pi(t1, sum, k)
    NEXT
    COLOR 14, 0: PRINT "Ramanujan pi = "; MID$("3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481", 1, 11 + (k - 2) * 8)
    COLOR 7, 0
    t = TIMER - t
    PRINT "Time:"; t: PRINT
NEXT pete%
END

SUB pi (t1$, sum$, k)
    REM square_root "8", sqrt$
    IF betatest% THEN PRINT "sqrt Pi # = "; sqrt$: SLEEP
    t2$ = "9801"
    sm sqrt$, "/", t2$, t3$
    IF betatest% THEN PRINT "Pi # = "; t3$: SLEEP
    sm t3$, "*", sum$, t2$
    IF betatest% THEN PRINT "Pi # = "; t2$: SLEEP
    sm t1$, "/", t2$, t3$
    IF betatest% THEN PRINT "Pi # = "; t3$: SLEEP
    sm "1", "/", t2$, t1$
    IF betatest% THEN PRINT "Pi # = "; t1$: SLEEP
    PRINT "loop #"; LTRIM$(STR$(k));: LOCATE , 10: PRINT " pi = "; MID$(t1$, 1, 11 + (k - 1) * 8);: COLOR 8, 0: PRINT MID$(t1$, 11 + (k - 1) * 8 + 1, 4): COLOR 7, 0
END SUB

DEFINT A-Z
SUB sm (s_var1$, operator$, s_var2$, runningtotal$)
    DIM AS _INTEGER64 a, c, aa, cc, s, ss
    stringmatha$ = s_var1$: stringmathb$ = s_var2$

    SELECT CASE operator$
        CASE "+", "-"
            GOSUB string_add_subtract_new
        CASE "*"
            GOSUB string_multiply_new
        CASE "/"
            GOSUB string_divide_new
        CASE ELSE
            PRINT "Error, no operator selected. operator$ = "; operator$: END
    END SELECT
    EXIT SUB

    string_divide_new:
    q$ = "": az$ = stringmathb$: bz$ = stringmatha$
    DO ' Falx loop.
        'Strip off neg(s) and determine quotent sign.
        IF LEFT$(az$, 1) = "-" THEN az$ = MID$(az$, 2): q$ = "-"
        IF LEFT$(bz$, 1) = "-" THEN bz$ = MID$(bz$, 2): IF q$ = "-" THEN q$ = "" ELSE q$ = "-"

        ' Quick results for divisor 1 or 0.
        IF az$ = "0" THEN q$ = "0": EXIT DO
        IF az$ = "1" THEN q$ = bz$: EXIT DO
        IF bz$ = "0" THEN q$ = "Division by zero not possible.": EXIT DO

        ' Determine decimal direction. -1 to left, +1 to right.
        gl% = 0: string_compare az$, bz$, gl%
        IF gl% = 1 THEN ' Divisor is larger than dividend so decimal moves to the left.
            div_decimal% = -1 ' Move decimal point to the left.
        ELSEIF gl% = -1 THEN
            div_decimal% = 1 ' Move decimal point to the right.
        ELSE
            ' Divisor and dividend are the same number.
            q$ = q$ + "1": EXIT DO
        END IF
        divisor_ratio_dividend% = gl%

        ' Strip off decimal point(s) and determine places in these next 2 routines.
        dp&& = 0: dp2&& = 0: j2&& = 0
        temp&& = INSTR(az$, ".")
        IF temp&& THEN
            az$ = MID$(az$, 1, temp&& - 1) + MID$(az$, temp&& + 1)
            IF temp&& = 1 THEN
                DO UNTIL LEFT$(az$, 1) <> "0" ' Strip off any leading zeros on divisor only.
                    az$ = MID$(az$, 2)
                    dp&& = dp&& + 1
                LOOP
                dp&& = dp&& + 1
            ELSE
                dp&& = -(temp&& - 2)
            END IF
        ELSE
            dp&& = -(LEN(az$) - 1)
        END IF
        temp&& = INSTR(bz$, ".")
        IF temp&& THEN
            bz$ = MID$(bz$, 1, temp&& - 1) + MID$(bz$, temp&& + 1)
            IF temp&& = 1 THEN
                DO UNTIL LEFT$(bz$, 1) <> "0" ' Strip off any leading zeros on divisor only.
                    bz$ = MID$(bz$, 2)
                    dp2&& = dp2&& + 1
                LOOP
                dp2&& = dp2&& + 1
            ELSE
                dp2&& = -(temp&& - 2)
            END IF
        ELSE
            dp2&& = -(LEN(bz$) - 1)
        END IF
        dp&& = ABS(dp&& - dp2&&)

        ' Adjust decimal place for instances when divisor is larger than remainder.
        IF MID$(az$, 1, 1) > MID$(bz$, 1, 1) THEN
            dp&& = dp&& - div_decimal%
        ELSEIF MID$(az$, 1, 1) = MID$(bz$, 1, 1) THEN
            IF divisor_ratio_dividend% = 1 THEN
                dp&& = dp&& - div_decimal%
            END IF
        END IF
        origbz$ = bz$
        ' Determine length of divisor and dividend to begin initial long divison step.
        gl% = 2: string_compare az$, MID$(bz$, 1, LEN(az$)) + STRING$(LEN(az$) - LEN(bz$), "0"), gl%
        divisor_ratio_dividend% = gl%
        IF gl% = 1 AND MID$(bz$, 1, 1) <> "0" THEN
            bz$ = MID$(bz$, 1, LEN(az$) + 1) + STRING$(LEN(az$) + 1 - LEN(bz$), "0")
        ELSE
            bz$ = MID$(bz$, 1, LEN(az$)) + STRING$(LEN(az$) - LEN(bz$), "0")
        END IF

        ' Long divison loop. Mult and subtraction of dividend and remainder.
        k&& = 0
        DO
            SELECT CASE MID$(az$, 1, 1)
                CASE IS < MID$(bz$, 1, 1)
                    adj_rem_len% = 0
                CASE IS = MID$(bz$, 1, 1)
                    gl% = 2: string_compare az$, MID$(bz$, 1, LEN(az$)), gl%
                    IF gl% = 1 THEN adj_rem_len% = 1 ELSE adj_rem_len% = 0
                CASE IS > MID$(bz$, 1, 1)
                    adj_rem_len% = 1
            END SELECT
            IF j2&& = 0 THEN j2&& = LEN(az$) + adj_rem_len%
            DO
                IF LEN(az$) > LEN(bz$) THEN
                    w3&& = 0: runningtotal$ = bz$: stringmathb$ = "0"
                    EXIT DO
                END IF
                IF LEN(az$) = LEN(bz$) THEN
                    gl% = 2: string_compare az$, bz$, gl%
                    IF gl% = 1 THEN
                        w3&& = 0: runningtotal$ = bz$: stringmathb$ = "0"
                        EXIT DO
                    END IF
                END IF
                SELECT CASE LEN(bz$)
                    CASE IS > 2
                        w3&& = VAL(MID$(bz$, 1, 2 + adj_rem_len%)) \ VAL(MID$(az$, 1, 2))
                    CASE ELSE
                        w3&& = VAL(MID$(bz$, 1, 1 + adj_rem_len%)) \ VAL(MID$(az$, 1, 1))
                END SELECT
                IF w3&& < 9 THEN w3&& = w3&& + 1 ELSE IF w3&& = 10 THEN w3&& = 9
                DO
                    stringmatha$ = az$: stringmathb$ = LTRIM$(STR$(w3&&))
                    GOSUB string_multiply_new
                    IF bz$ = "" THEN BEEP: BEEP
                    gl% = 2: string_compare runningtotal$, bz$, gl%
                    IF gl% <= 0 OR w3&& = 0 THEN EXIT DO
                    w3&& = w3&& - 1
                LOOP
                stringmatha$ = bz$: stringmathb$ = runningtotal$
                operator$ = "-": GOSUB string_add_subtract_new
                EXIT DO
            LOOP
            j2&& = j2&& + 1
            drop$ = "0": MID$(drop$, 1, 1) = MID$(origbz$, j2&&, 1)
            IF runningtotal$ <> "0" THEN remainder$ = runningtotal$ ELSE remainder$ = ""
            bz$ = remainder$ + drop$
            w3$ = LTRIM$(STR$(w3&&))
            temp$ = ""
            IF div_decimal% = -1 THEN
                IF dp&& AND k&& = 0 THEN
                    q$ = q$ + "." + STRING$(dp&& - 1, "0")
                    IF w3&& = 0 THEN w3$ = ""
                END IF
            END IF
            IF div_decimal% >= 0 THEN
                IF dp&& = k&& THEN
                    temp$ = "."
                END IF
            END IF
            q$ = q$ + w3$ + temp$

            ' Check to terminate
            IF div_decimal% = -1 THEN
                ' Decimal to left.
                IF remainder$ = "" AND MID$(origbz$, j2&&, 1) = "" OR LEN(q$) >= limit&& + 8 THEN EXIT DO
            ELSE
                ' Decimal to right.
                IF remainder$ = "" AND MID$(origbz$, j2&&, 1) = "" AND k&& >= dp&& OR LEN(q$) >= limit&& + 8 THEN EXIT DO
            END IF
            IF INKEY$ = " " THEN EXIT DO
            k&& = k&& + 1
        LOOP
        EXIT DO
    LOOP
    IF RIGHT$(q$, 1) = "." THEN runningtotal$ = MID$(q$, 1, LEN(q$) - 1) ELSE runningtotal$ = q$
    RETURN

    string_add_subtract_new:
    a1$ = stringmatha$: b1$ = stringmathb$
    s = 18: i&& = 0: c = 0

    a$ = stringmatha$: b$ = stringmathb$: op$ = operator$

    IF op$ = "-" THEN
        IF LEFT$(b$, 1) = "-" THEN b$ = MID$(b$, 2) ELSE b$ = "-" + b$
    END IF

    IF INSTR(a$, ".") <> 0 OR INSTR(b$, ".") <> 0 THEN
        decimal% = -1
        IF INSTR(a$, ".") <> 0 THEN
            dec_a&& = LEN(MID$(a$, INSTR(a$, ".") + 1))
            a$ = MID$(a$, 1, INSTR(a$, ".") - 1) + MID$(a$, INSTR(a$, ".") + 1)
        END IF
        IF INSTR(b$, ".") <> 0 THEN
            dec_b&& = LEN(MID$(b$, INSTR(b$, ".") + 1))
            b$ = MID$(b$, 1, INSTR(b$, ".") - 1) + MID$(b$, INSTR(b$, ".") + 1)
        END IF
        ' Line up decimal places by inserting trailing zeros.
        IF dec_b&& > dec_a&& THEN
            j&& = dec_b&&
            a$ = a$ + STRING$(dec_b&& - dec_a&&, "0")
        ELSE
            j&& = dec_a&&
            b$ = b$ + STRING$(dec_a&& - dec_b&&, "0")
        END IF
    END IF

    IF LEFT$(a$, 1) = "-" OR LEFT$(b$, 1) = "-" THEN
        IF LEFT$(a$, 1) = "-" AND LEFT$(b$, 1) = "-" THEN
            sign$ = "": a$ = MID$(a$, 2): b$ = MID$(b$, 2)
        ELSE
            IF LEFT$(a$, 1) = "-" THEN a$ = MID$(a$, 2): sign_a$ = "-"
            IF LEFT$(b$, 1) = "-" THEN b$ = MID$(b$, 2): sign_b$ = "-"

            IF LEFT$(a1$, 1) = "-" THEN a1_x$ = MID$(a1$, 2) ELSE a1_x$ = a1$
            IF LEFT$(b1$, 1) = "-" THEN b1_x$ = MID$(b1$, 2) ELSE b1_x$ = b1$

            string_compare a1_x$, b1_x$, gl%

            IF gl% < 0 THEN
                IF LEN(sign_b$) THEN sign$ = "-": SWAP a$, b$
            ELSE
                IF LEN(sign_a$) THEN sign$ = "-": SWAP sign_a$, sign_b$
            END IF
        END IF
    END IF

    z$ = ""
    ' Addition and subtraction of digits.
    DO
        i&& = i&& + s
        x1$ = MID$(a$, LEN(a$) - i&& + 1, s)
        x2$ = MID$(b$, LEN(b$) - i&& + 1, s)
        IF LEN(x2$) > LEN(x1$) THEN SWAP x1$, x2$
        a = VAL(sign_a$ + x1$) + VAL(sign_b$ + x2$) + c
        IF x1$ + x2$ = "" AND c = 0 THEN EXIT DO
        c = 0
        IF a > VAL(STRING$(s, "9")) THEN a = a - 10 ^ s: c = 1
        IF a < 0 THEN a = a + 10 ^ s: c = -1 ' a will never be less than 0.
        tmp$ = LTRIM$(STR$(a))
        z$ = STRING$(LEN(x1$) - LEN(tmp$), "0") + tmp$ + z$
    LOOP

    IF decimal% THEN
        z$ = MID$(z$, 1, LEN(z$) - j&&) + "." + MID$(z$, LEN(z$) - j&& + 1)
    END IF

    ' Remove any leading zeros.
    DO
        IF LEFT$(z$, 1) = "0" THEN z$ = MID$(z$, 2) ELSE EXIT DO
    LOOP

    IF z$ = "" OR z$ = "0" THEN z$ = "0" ELSE z$ = LEFT$(sign$, 1) + z$

    runningtotal$ = z$

    sign$ = "": sign_a$ = "": sign_b$ = "": i&& = 0: j&& = 0: decimal% = 0: c = 0
    RETURN

    string_multiply_new:
    z$ = "": sign$ = "": mult&& = 0: h&& = 0: i&& = 0: j&& = 0: c = 0: decimal% = 0
    zz$ = "": ii&& = 0: jj&& = 0
    s = 8: ss = 18

    a$ = stringmatha$: b$ = stringmathb$

    IF INSTR(a$, "-") <> 0 OR INSTR(b$, "-") <> 0 THEN
        IF INSTR(a$, "-") <> 0 AND INSTR(b$, "-") <> 0 THEN
            a$ = MID$(a$, 2): b$ = MID$(b$, 2)
        ELSE
            IF INSTR(a$, "-") <> 0 THEN a$ = MID$(a$, 2) ELSE b$ = MID$(b$, 2)
            sign$ = "-"
        END IF
    END IF

    IF INSTR(a$, ".") <> 0 OR INSTR(b$, ".") <> 0 THEN
        decimal% = -1
        IF INSTR(a$, ".") <> 0 THEN
            dec_a&& = LEN(MID$(a$, INSTR(a$, ".") + 1))
            a$ = MID$(a$, 1, INSTR(a$, ".") - 1) + MID$(a$, INSTR(a$, ".") + 1)
        END IF
        IF INSTR(b$, ".") <> 0 THEN
            dec_b&& = LEN(MID$(b$, INSTR(b$, ".") + 1))
            b$ = MID$(b$, 1, INSTR(b$, ".") - 1) + MID$(b$, INSTR(b$, ".") + 1)
        END IF
    END IF

    IF LEN(a$) < LEN(b$) THEN SWAP a$, b$ ' Needed so x1$ is always the largest for leading zero replacements.
    ' Multiplication of digits.
    DO
        h&& = h&& + s: i&& = 0
        x2$ = MID$(b$, LEN(b$) - h&& + 1, s)
        DO
            i&& = i&& + s
            x1$ = MID$(a$, LEN(a$) - i&& + 1, s)
            a = VAL(x1$) * VAL(x2$) + c
            c = 0
            tmp$ = LTRIM$(STR$(a))
            IF LEN(tmp$) > s THEN c = VAL(MID$(tmp$, 1, LEN(tmp$) - s)): tmp$ = MID$(tmp$, LEN(tmp$) - s + 1)
            z$ = STRING$(LEN(x1$) - LEN(tmp$), "0") + tmp$ + z$
        LOOP UNTIL i&& >= LEN(a$) AND c = 0

        jj&& = jj&& + 1

        IF jj&& > 1 THEN
            ii&& = 0: cc = 0
            aa$ = holdaa$
            bb$ = z$ + STRING$((jj&& - 1) * s, "0")
            ' Addition only of digits.
            DO
                ii&& = ii&& + ss
                xx1$ = MID$(aa$, LEN(aa$) - ii&& + 1, ss)
                xx2$ = MID$(bb$, LEN(bb$) - ii&& + 1, ss)
                IF LEN(xx1$) < LEN(xx2$) THEN SWAP xx1$, xx2$
                aa = VAL(xx1$) + VAL(xx2$) + cc
                IF xx1$ + xx2$ = "" AND cc = 0 THEN EXIT DO ' Prevents leading zeros.
                cc = 0
                IF aa > VAL(STRING$(ss, "9")) THEN aa = aa - 10 ^ ss: cc = 1
                tmp$ = LTRIM$(STR$(aa))
                zz$ = STRING$(LEN(xx1$) - LEN(tmp$), "0") + tmp$ + zz$
            LOOP

            DO WHILE LEFT$(zz$, 1) = "0"
                IF LEFT$(zz$, 1) = "0" THEN zz$ = MID$(zz$, 2)
            LOOP
            IF zz$ = "" THEN zz$ = "0"

            holdaa$ = zz$
        ELSE
            holdaa$ = z$ + STRING$(jj&& - 1, "0")
        END IF

        z$ = "": zz$ = ""

    LOOP UNTIL h&& >= LEN(b$)

    z$ = holdaa$

    IF decimal% THEN
        DO UNTIL LEN(z$) >= dec_a&& + dec_b&&
            z$ = "0" + z$
        LOOP

        z$ = MID$(z$, 0, LEN(z$) - (dec_a&& + dec_b&& - 1)) + "." + MID$(z$, LEN(z$) - (dec_a&& + dec_b&&) + 1)

        DO UNTIL RIGHT$(z$, 1) <> "0" AND RIGHT$(z$, 1) <> "."
            z$ = MID$(z$, 1, LEN(z$) - 1)
        LOOP
    END IF

    IF STRING$(LEN(z$), "0") = z$ OR z$ = "" OR z$ = "0" THEN z$ = "0" ELSE z$ = sign$ + z$

    decimal% = 0: sign$ = ""

    runningtotal$ = z$
    RETURN
END SUB

SUB string_compare (stringmatha$, stringmathb$, gl%)
    compa$ = stringmatha$: compb$ = stringmathb$ ' So original variables do not get changed.
    DO
        WHILE -1 ' Falx loop.
            IF gl% = 2 THEN EXIT WHILE ' For bypassing sign and decimal adjustments when only positive non-decimal numbers are being evaluated.
            ' Remove trailing zeros after a decimal point.
            IF INSTR(compa$, ".") THEN
                DO UNTIL RIGHT$(compa$, 1) <> "0" AND RIGHT$(compa$, 1) <> "." AND RIGHT$(compa$, 1) <> "-"
                    compa$ = MID$(compa$, 1, LEN(compa$) - 1)
                LOOP
            END IF
            IF INSTR(compb$, ".") THEN
                DO UNTIL RIGHT$(compb$, 1) <> "0" AND RIGHT$(compb$, 1) <> "." AND RIGHT$(compb$, 1) <> "-"
                    compb$ = MID$(compb$, 1, LEN(compb$) - 1)
                LOOP
            END IF

            IF MID$(compa$, 1, 2) = "-0" OR compa$ = "" OR compa$ = "-" THEN compa$ = "0"
            IF MID$(compb$, 1, 2) = "-0" OR compb$ = "" OR compb$ = "-" THEN compb$ = "0"

            ' A - and +
            IF LEFT$(compa$, 1) = "-" THEN j% = -1
            IF LEFT$(compb$, 1) = "-" THEN k% = -1
            IF k% = 0 AND j% THEN gl% = -1: EXIT DO
            IF j% = 0 AND k% THEN gl% = 1: EXIT DO

            ' A decimal and non-decimal.
            j% = INSTR(compa$, ".")
            k% = INSTR(compb$, ".")

            IF j% = 0 AND k% THEN
                IF compa$ = "0" THEN gl% = -1 ELSE gl% = 1
                EXIT DO
            END IF
            IF k% = 0 AND j% THEN
                IF compb$ = "0" THEN gl% = 1 ELSE gl% = -1
                EXIT DO
            END IF

            ' Both decimals.
            IF j% THEN
                SELECT CASE INSTR(compa$, ".")
                    CASE IS > INSTR(compb$, ".")
                        gl% = 1
                    CASE IS = INSTR(compb$, ".")
                        IF compa$ = compb$ THEN
                            gl% = 0
                        ELSEIF compa$ < compb$ THEN gl% = -1
                        ELSE
                            gl% = 1
                        END IF
                    CASE IS < INSTR(compb$, ".")
                        gl% = -1
                END SELECT
                EXIT DO
            END IF
            EXIT WHILE
        WEND

        ' Remove leading zeros if any.
        DO UNTIL LEFT$(compa$, 1) <> "0"
            compa$ = MID$(compa$, 2)
        LOOP
        IF compa$ = "" THEN compa$ = "0"
        DO UNTIL LEFT$(compb$, 1) <> "0"
            compb$ = MID$(compb$, 2)
        LOOP
        IF compb$ = "" THEN compb$ = "0"

        ' Both positive or both negative whole numbers.

        SELECT CASE LEN(compa$)
            CASE IS < LEN(compb$)
                gl% = -1
            CASE IS = LEN(compb$)
                IF compa$ = compb$ THEN
                    gl% = 0
                ELSEIF compa$ > compb$ THEN gl% = 1
                ELSEIF compa$ < compb$ THEN gl% = -1
                END IF
            CASE IS > LEN(compb$)
                gl% = 1
        END SELECT
        EXIT DO
    LOOP
END SUB

DEFINT A-Z
SUB square_root (x$, sqrt$)
    oldy$ = "": sqrt$ = "": custom_limit&& = limit&& + 50

    IF INSTR(x$, ".") THEN
        decx$ = MID$(x$, 1, INSTR(x$, ".") - 1)
        x$ = MID$(x$, 1, INSTR(x$, ".") - 1) + MID$(x$, INSTR(x$, ".") + 1)
        IF LEN(x$) = 1 THEN x$ = x$ + "0"
    ELSE
        decx$ = x$
    END IF

    j&& = LEN(decx$)

    ' VAL() okay, one character eval.
    IF VAL(RIGHT$(LTRIM$(STR$(j&&)), 1)) / 2 = VAL(RIGHT$(LTRIM$(STR$(j&&)), 1)) \ 2 THEN
        i&& = 1 ' Even number length.
    ELSE
        i&& = 0 ' Odd number length.
    END IF

    DO
        sm z$, "-", k$, runningtotal$
        z$ = runningtotal$ + (MID$(x$, i&&, 2))
        IF LEFT$(z$, 1) = "0" THEN z$ = MID$(z$, 2) ' Remove leading zeros

        oldy$ = ""
        FOR j&& = 1 TO 10
            IF i&& > 1 THEN
                sm sqrt$, "*", "2", y$
                y$ = y$ + LTRIM$(STR$(j&&))
            ELSE
                y$ = LTRIM$(STR$(j&&))
            END IF

            sm y$, "*", LTRIM$(STR$(j&&)), runningtotal$

            string_compare runningtotal$, z$, gl%
            IF gl% > -1 THEN
                IF gl% = 0 THEN
                    h% = 0: oldy$ = y$ ' Perfect square division.
                ELSE
                    h% = 1
                END IF
                sm oldy$, "*", LTRIM$(STR$(j&& - h%)), runningtotal$

                IF STRING$(LEN(z$), "0") = z$ AND runningtotal$ = "0" AND i&& >= LEN(decx$) THEN EXIT DO

                IF dpx&& = 0 THEN ' Limited to && size unless converted to string.
                    IF i&& >= LEN(decx$) THEN
                        dpx&& = INT(LEN(decx$) / 2 + .5)
                        IF dpx&& = 0 THEN dpx&& = -1
                    END IF
                END IF

                IF betatest% < -1 THEN PRINT "Sqrt "; sqrt$; " * 2 = ";: COLOR 2, 0: PRINT LTRIM$(STR$(VAL(sqrt$) * 2));: COLOR 7, 0: PRINT LTRIM$(STR$(j&& - h%)); " * "; LTRIM$(STR$(j&& - h%)); " ="; VAL(oldy$) * (j&& - h%)
                sqrt$ = sqrt$ + LTRIM$(STR$(j&& - h%))

                sm oldy$, "*", LTRIM$(STR$(j&& - h%)), runningtotal$
                k$ = runningtotal$

                IF betatest% < -1 THEN PRINT "Remainder "; z$; " minus "; k$; " = ";
                EXIT FOR
            END IF
            oldy$ = y$
        NEXT

        i&& = i&& + 2
        IF LEN(z$) >= custom_limit&& THEN EXIT DO
        x$ = x$ + "00"
    LOOP

    IF dpx&& THEN
        sqrt$ = MID$(sqrt$, 0, dpx&& + 1) + "." + MID$(sqrt$, dpx&& + 1)
    END IF
END SUB

Pete
Reply
#27
Hi Pete
that's fast indeed, would care to explain your division routine?
Reply
#28
I kept a beta version of it that prints out what it is doing. I'm thinking I might post it in a new discussion thread on string math division. Basically what I did was to shortcut zero and 1 divisors, chop out leading zeros in small decimal numbers making less digits to calculate, estimate the mult loop by using just the first one or two digits of the divisor and the dividend or remainder so it usually only takes two tries to get the right multiplier before subtracting to obtain the remainder and, of course, working with chunks of numbers with multiplication and subtraction in the long division process.

I knew it would be faster, I'm just amazed it's so much faster.

Now I'm wondering how much faster it could be if I switched from string concatenation to fixed string replacement? I did that once with a c keyboard WP routine (about the only complicated C/C++ prog I've ever written) and the speed increase was pretty impressive. Converting for string math might be a bit of a challenge, and if too many conditions need to be added, it might end up being a push.

The only miss I had on this new routine was the bloat of about 40 more lines than my previous division code. I really wanted to do this one in about the same number of lines but no dice. In contrast, I think I cut code in both the multiplication and add/subtract routines.

Thanks,

Pete
Reply
#29
I think that posting your string division in a new thread is a good idea, looking forward to it
Reply
#30
(09-11-2022, 01:48 AM)Pete Wrote: I kept a beta version of it that prints out what it is doing. I'm thinking I might post it in a new discussion thread on string math division. Basically what I did was to shortcut zero and 1 divisors, chop out leading zeros in small decimal numbers making less digits to calculate, estimate the mult loop by using just the first one or two digits of the divisor and the dividend or remainder so it usually only takes two tries to get the right multiplier before subtracting to obtain the remainder and, of course, working with chunks of numbers with multiplication and subtraction in the long division process.

I knew it would be faster, I'm just amazed it's so much faster.

Now I'm wondering how much faster it could be if I switched from string concatenation to fixed string replacement? I did that once with a c keyboard WP routine (about the only complicated C/C++ prog I've ever written) and the speed increase was pretty impressive. Converting for string math might be a bit of a challenge, and if too many conditions need to be added, it might end up being a push.

The only miss I had on this new routine was the bloat of about 40 more lines than my previous division code. I really wanted to do this one in about the same number of lines but no dice. In contrast, I think I cut code in both the multiplication and add/subtract routines.

Thanks,

Pete
@Pete Hmm, that sounds pretty straight-forward! I was gunna try that next! Tongue
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