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+--- Thread: Roots and powers playing nicely together... (/showthread.php?tid=929)
Roots and powers playing nicely together... - Pete - 09-28-2022
So I decided on the long division methods over the approximation methods for nth roots then thought, why not apply these to decimal powers? It worked, because of the inverse relationship. So this is really choppy right now, and needs more work, but it looks like it is getting the digits correct.
What does it do?
Nth roots for whole numbers greater than zero.
Decimal roots for whole numbers greater than zero.
Mixed roots (Number >1 with decimal) for whole numbers greater than zero.
Powers for whole numbers greater than zero.
Decimal powers for whole numbers greater than zero.
Mixed powers (Power >1 with decimal) for whole numbers greater than zero.
So after I debug this for a bit, I want to see if I can figure out what needs to be done to go from whole numbers to mixed numbers with decimals and negative numbers.
Code: (Select All)
$CONSOLE:ONLY
DIM SHARED limit&&
PRINT "Demo does not display decimal point yet, and fails with zero roots/powers.": PRINT
DO
INPUT "Input 1 for general roots or 2 for decimal powers: "; k$
SELECT CASE k$
CASE "1"
LINE INPUT "Whole number: "; n$
LINE INPUT "Root: "; r$
j&& = INSTR(r$, ".")
IF j&& THEN ' Decimal or mixed whole and decimal.
IF j&& = 1 THEN ' Decimal only root. OKAY
pow$ = "1" + STRING$(LEN(r$) - 1, "0")
r$ = MID$(r$, INSTR(r$, ".") + 1)
''PRINT n$, r$, pow$
greatest_common_factor pow$, r$
''PRINT n$, r$, pow$: SLEEP
IF r$ <> "1" THEN GOSUB root_calc ELSE d$ = n$
tmp$ = d$
FOR i&& = 1 TO VAL(pow$) - 1
d$ = sm_mult$(tmp$, d$)
NEXT
sm_rt$ = d$
EXIT DO
ELSE ' Mixed whole and decimal root. OKAY
r_whole$ = MID$(r$, 1, INSTR(r$, ".") - 1)
r$ = MID$(r$, INSTR(r$, ".") + 1)
pow$ = "1" + STRING$(LEN(r$), "0")
''PRINT n$, r$, pow$
greatest_common_factor pow$, r$
''PRINT n$, r$, pow$
tmp$ = sm_mult$(r_whole$, pow$)
r$ = sm_add$(tmp$, r$)
''PRINT n$, r$: SLEEP
IF r$ <> "1" THEN GOSUB root_calc ELSE d$ = n$
''PRINT d$: SLEEP
tmp$ = d$ ' Combine both parts.
FOR i&& = 1 TO VAL(pow$) - 1
tmp$ = sm_mult$(tmp$, d$)
NEXT
sm_rt$ = tmp$
''PRINT sm_rt$
EXIT DO
END IF
ELSE ' Whole root. OKAY
IF r$ <> "1" THEN GOSUB root_calc ELSE d$ = n$
END IF
sm_rt$ = d$
EXIT DO
CASE "2"
LINE INPUT "Number: "; n$
LINE INPUT "Power: "; pow$
j&& = INSTR(pow$, ".")
IF j&& THEN ' Decimal or mixed whole and decimal.
IF j&& = 1 THEN ' Decimal only. OKAY
r$ = "1" + STRING$(LEN(pow$) - 1, "0")
pow$ = MID$(pow$, INSTR(pow$, ".") + 1)
''PRINT pow$, r$
greatest_common_factor pow$, r$
''PRINT pow$, r$: SLEEP
IF r$ <> "1" THEN GOSUB root_calc ELSE d$ = n$
sm_rt$ = d$
EXIT DO
ELSE ' Mixed whole number and decimal. OKAY
d_whole$ = n$
FOR i&& = 1 TO VAL(MID$(pow$, 1, INSTR(pow$, ".") - 1)) - 1
d_whole$ = sm_mult$(d_whole$, n$)
NEXT
pow$ = MID$(pow$, INSTR(pow$, ".") + 1)
r$ = "1" + STRING$(LEN(pow$), "0")
greatest_common_factor pow$, r$
''PRINT n$, d_whole$, r$, pow$: SLEEP
IF r$ <> "1" THEN GOSUB root_calc ELSE d$ = n$
''PRINT d$, d_whole$: SLEEP
d$ = sm_mult$(d_whole$, d$)
sm_rt$ = d$
EXIT DO
END IF
ELSE ' Whole number OKAY
d$ = n$
FOR i&& = 1 TO VAL(pow$) - 1
d$ = sm_mult$(d$, n$)
NEXT
sm_rt$ = d$
EXIT DO
END IF
END SELECT
LOOP
PRINT "Answer: "; sm_rt$: PRINT
RUN
root_calc:
' Decimal root conversion.
r = VAL(r$)
nu&& = INSTR(n$, ".") - 1: IF nu&& < 0 THEN nu&& = LEN(n$)
h&& = (r - (r - nu&& MOD r)) + 1
t$ = MID$(n$, 1, h&& - 1): d$ = "0"
limit&& = 16
' Calculate Pascal's Triangle.
REDIM p$(r + 1)
FOR i1&& = 1 TO r + 1
p&& = 1
FOR j1&& = 1 TO i1&&
p$(j1&&) = LTRIM$(STR$(p&&))
p&& = p&& * (i1&& - j1&&) \ j1&&
NEXT
NEXT
DO
oldx$ = "0"
lcnt&& = lcnt&& + 1
FOR j = 1 TO 10
x$ = "0"
FOR i&& = 1 TO r
REM PRINT "(10 ^"; (i&& - 1); "*"; p$(i&&); "* d ^"; i&& - 1; " * j ^"; (r + 1 - i&&); ") + ";
REM x = x + 10 ^ (i&& - 1) * VAL(p$(i&&)) * d ^ (i&& - 1) * j ^ (r + 1 - i&&)
tmp$ = "1"
FOR k% = 1 TO i&& - 1
tmp$ = sm_mult$(tmp$, "10")
NEXT
tmp$ = sm_mult$(tmp$, p$(i&&))
tmp2$ = "1"
FOR k% = 1 TO i&& - 1
tmp2$ = sm_mult$(tmp2$, d$)
NEXT
IF d$ = "0" AND k% = 1 THEN tmp2$ = "1" ' zero^0 = 1
tmp3$ = sm_mult$(tmp$, tmp2$)
tmp$ = "1"
FOR k% = 1 TO r + 1 - i&&
tmp$ = sm_mult$(tmp$, LTRIM$(STR$(j)))
NEXT
tmp2$ = sm_mult$(tmp3$, tmp$)
x$ = sm_add(x$, tmp2$)
NEXT
IF LEN(x$) > LEN(t$) OR LEN(x$) = LEN(t$) AND x$ > t$ THEN EXIT FOR
oldx$ = x$
NEXT
d$ = d$ + LTRIM$(STR$(j - 1))
IF LEFT$(d$, 1) = "0" THEN d$ = MID$(d$, 2) ' Remove leading zero.
tmp1$ = sm_sub$(t$, oldx$)
tmp2$ = MID$(n$, h&&, r) + STRING$(r - LEN(MID$(n$, h&&, r)), "0")
t$ = tmp1$ + tmp2$
IF LEFT$(t$, 1) = "0" THEN t$ = MID$(t$, 2) 'Remove leading zero.
h&& = h&& + r
IF t$ = STRING$(LEN(t$), "0") AND h&& >= LEN(n$) OR lcnt&& = limit&& THEN EXIT DO
IF dpx&& = 0 THEN ' Decimal point relocator. Limited to && size unless converted to string.
IF h&& >= nu&& THEN
dpx&& = INT(nu&& / 2 + .5)
IF dpx&& = 0 THEN dpx&& = -1 ' Do not set to zero as -1 accomplishes the same thing and prevents ongoing loops here.
END IF
END IF
LOOP
dpx&& = 0 ' Remove this when all decimal situations are included.
IF dpx&& THEN
sm_rt$ = MID$(d$, 0, dpx&& + 1) + "." + MID$(d$, dpx&& + 1)
ELSE
sm_rt$ = d$
END IF
RETURN
SUB sm_greater_lesser (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 +
j% = 0: k% = 0
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
j&& = INSTR(compa$, ".")
k&& = INSTR(compb$, ".")
' A starting decimal and non-decimal.
IF j&& = 0 AND k&& = 1 THEN
IF compa$ = "0" THEN gl% = -1 ELSE gl% = 1
EXIT DO
END IF
IF k&& = 0 AND j&& = 1 THEN
IF compb$ = "0" THEN gl% = 1 ELSE gl% = -1
EXIT DO
END IF
' remove decimals and align.
j2&& = 0: k2&& = 0
IF j&& <> 0 OR k&& <> 0 THEN
IF j&& THEN compa$ = MID$(compa$, 1, INSTR(compa$, ".") - 1) + MID$(compa$, INSTR(compa$, ".") + 1): j2&& = LEN(compa$) - j&& + 1
IF k&& THEN compb$ = MID$(compb$, 1, INSTR(compb$, ".") - 1) + MID$(compb$, INSTR(compb$, ".") + 1): k2&& = LEN(compb$) - k&& + 1
compa$ = compa$ + STRING$(k2&& - j2&&, "0")
compb$ = compb$ + STRING$(j2&& - k2&&, "0")
END IF
EXIT WHILE
WEND
' Remove leading zeros if any.
DO UNTIL LEFT$(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$)
gl% = 1
END SELECT
EXIT DO
LOOP
END SUB
SUB sm_add_subtract_router (stringmatha$, operator$, stringmathb$, runningtotal$)
DIM AS _INTEGER64 a, c, s
a1$ = 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$
sm_greater_lesser 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
END SUB
FUNCTION sm_add$ (stringmatha$, stringmathb$)
operator$ = "+"
sm_add_subtract_router stringmatha$, operator$, stringmathb$, runningtotal$
sm_add$ = runningtotal$
END FUNCTION
FUNCTION sm_sub$ (stringmatha$, stringmathb$)
operator$ = "-"
sm_add_subtract_router stringmatha$, operator$, stringmathb$, runningtotal$
sm_sub$ = runningtotal$
END FUNCTION
FUNCTION sm_mult$ (stringmatha$, stringmathb$)
DIM AS _INTEGER64 a, c, aa, cc, s, ss
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$
sm_mult$ = z$
END FUNCTION
FUNCTION sm_div$ (stringmatha$, stringmathb$)
hold_stringmatha$ = stringmatha$: hold_stringmathb$ = stringmathb$
q$ = "": divisor$ = stringmathb$: dividend$ = stringmatha$
DO ' Falx loop.
'Strip off neg(s) and determine quotent sign.
IF LEFT$(divisor$, 1) = "-" THEN divisor$ = MID$(divisor$, 2): q$ = "-"
IF LEFT$(dividend$, 1) = "-" THEN dividend$ = MID$(dividend$, 2): IF q$ = "-" THEN q$ = "" ELSE q$ = "-"
' Quick results for divisor 1 or 0.
IF dividend$ = "0" THEN q$ = "0": EXIT DO
IF divisor$ = "1" THEN q$ = dividend$: EXIT DO
IF divisor$ = "0" THEN q$ = "Division by zero not possible.": EXIT DO
' Determine decimal direction. -1 to left, +1 to right.
gl% = 0: sm_greater_lesser divisor$, dividend$, gl%
IF betatest% AND gl% = 1 THEN PRINT divisor$; " > "; dividend$; " Move decimal to the left"
IF betatest% AND gl% = 0 THEN PRINT divisor$; " = "; dividend$
IF betatest% AND gl% = -1 THEN PRINT divisor$; " < "; dividend$; " Move deciml to the right."
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(divisor$, ".")
IF temp&& THEN
divisor$ = MID$(divisor$, 1, temp&& - 1) + MID$(divisor$, temp&& + 1)
IF temp&& = 1 THEN
DO UNTIL LEFT$(divisor$, 1) <> "0" ' Strip off any leading zeros on divisor only.
divisor$ = MID$(divisor$, 2)
dp&& = dp&& + 1
LOOP
dp&& = dp&& + 1
ELSE
dp&& = -(temp&& - 2)
END IF
ELSE
dp&& = -(LEN(divisor$) - 1)
END IF
temp&& = INSTR(dividend$, ".")
IF temp&& THEN
dividend$ = MID$(dividend$, 1, temp&& - 1) + MID$(dividend$, temp&& + 1)
IF temp&& = 1 THEN
DO UNTIL LEFT$(dividend$, 1) <> "0" ' Strip off any leading zeros on divisor only.
dividend$ = MID$(dividend$, 2)
dp2&& = dp2&& + 1
LOOP
dp2&& = dp2&& + 1
ELSE
dp2&& = -(temp&& - 2)
END IF
ELSE
dp2&& = -(LEN(dividend$) - 1)
END IF
IF betatest% THEN COLOR 11: PRINT "Divisor decimal moves "; LTRIM$(STR$(dp&&)); ". Dividend decimal moves"; LTRIM$(STR$(dp2&&)); ". Quotent decimal ABS("; LTRIM$(STR$(dp&&)); " - "; LTRIM$(STR$(dp2&&)); ") =";: COLOR 14: PRINT ABS(dp&& - dp2&&);: COLOR 11: PRINT "+ any adjustment.": COLOR 7
dp&& = ABS(dp&& - dp2&&)
IF betatest% THEN PRINT "Divisor 1st# = "; MID$(divisor$, 1, 1); " Remainder 1st# = "; MID$(dividend$, 1, 1)
' Adjust decimal place for instances when divisor is larger than remainder the length of the divisor.
j% = 0
IF MID$(divisor$, 1, 1) > MID$(dividend$, 1, 1) THEN
j% = 1
IF betatest% THEN PRINT "Larger divisor, so move quotent decimal one place back to: ";: COLOR 14: PRINT LTRIM$(STR$(dp&&)): COLOR 7
ELSEIF MID$(divisor$, 1, 1) = MID$(dividend$, 1, 1) THEN
IF LEN(divisor$) = LEN(dividend$) THEN
IF divisor$ > dividend$ THEN j% = 1
ELSE
IF LEN(divisor$) > LEN(dividend$) THEN
temp$ = dividend$ + STRING$(LEN(divisor$) - LEN(dividend$), "0")
ELSE
temp$ = MID$(dividend$, 1, LEN(divisor$))
END IF
IF divisor$ > temp$ THEN j% = 1
END IF
IF betatest% THEN
IF j% THEN PRINT "Larger divisor than dividend at LEN(divisor$), so move quotent decimal one place back to: ";: COLOR 14: PRINT LTRIM$(STR$(dp&&)): COLOR 7
IF j% = 0 THEN PRINT "Smaller divisor than dividend at LEN(divisor$), so no quotent decimal place adjustment needed. Quotent decimal place = ";: COLOR 14: PRINT LTRIM$(STR$(dp&&)): COLOR 7
END IF
ELSE
j% = 0
IF betatest% THEN PRINT "Smaller divisor, so no quotent decimal place adjustment needed. Quotent decimal place = ";: COLOR 14: PRINT LTRIM$(STR$(dp&&)): COLOR 7
END IF
IF j% THEN dp&& = dp&& - div_decimal%
origdividend$ = dividend$
' Determine length of divisor and dividend to begin initial long divison step.
gl% = 2: sm_greater_lesser divisor$, MID$(dividend$, 1, LEN(divisor$)) + STRING$(LEN(divisor$) - LEN(dividend$), "0"), gl%
divisor_ratio_dividend% = gl%
IF gl% = 1 AND MID$(dividend$, 1, 1) <> "0" THEN
dividend$ = MID$(dividend$, 1, LEN(divisor$) + 1) + STRING$(LEN(divisor$) + 1 - LEN(dividend$), "0")
ELSE
dividend$ = MID$(dividend$, 1, LEN(divisor$)) + STRING$(LEN(divisor$) - LEN(dividend$), "0")
END IF
' Long divison loop. Mult and subtraction of dividend and remainder.
k&& = 0
IF betatest% THEN PRINT "Begin long divison loop..."
DO
SELECT CASE MID$(divisor$, 1, 1)
CASE IS < MID$(dividend$, 1, 1)
adj_rem_len% = 0
CASE IS = MID$(dividend$, 1, 1)
gl% = 2: sm_greater_lesser divisor$, MID$(dividend$, 1, LEN(divisor$)), gl%
IF gl% = 1 THEN adj_rem_len% = 1 ELSE adj_rem_len% = 0
CASE IS > MID$(dividend$, 1, 1)
adj_rem_len% = 1
END SELECT
IF j2&& = 0 THEN j2&& = LEN(divisor$) + adj_rem_len%
DO
IF LEN(divisor$) > LEN(dividend$) THEN
w3&& = 0: runningtotal$ = dividend$: stringmathb$ = "0"
IF betatest% THEN PRINT: COLOR 3: PRINT "Divisor is larger so "; dividend$; " \ "; divisor$; " =";: COLOR 5: PRINT w3&&: COLOR 7
EXIT DO
END IF
IF LEN(divisor$) = LEN(dividend$) THEN
gl% = 2: sm_greater_lesser divisor$, dividend$, gl%
IF gl% = 1 THEN
w3&& = 0: runningtotal$ = dividend$: stringmathb$ = "0"
IF betatest% THEN COLOR 9: PRINT "Length of divisor is the same as remainder but remainder is smaller so w3&& = ";: COLOR 5: PRINT "0": COLOR 7
EXIT DO
END IF
END IF
SELECT CASE LEN(dividend$)
CASE IS > 2
w3&& = VAL(MID$(dividend$, 1, 2 + adj_rem_len%)) \ VAL(MID$(divisor$, 1, 2))
IF betatest% THEN PRINT MID$(dividend$, 1, 2 + adj_rem_len%); " \ "; MID$(divisor$, 1, 2); " =";
CASE ELSE
w3&& = VAL(MID$(dividend$, 1, 1 + adj_rem_len%)) \ VAL(MID$(divisor$, 1, 1))
IF betatest% THEN PRINT MID$(dividend$, 1, 1 + adj_rem_len%); " \ "; MID$(divisor$, 1, 1); " =";
END SELECT
IF betatest% THEN COLOR 5: PRINT " " + LTRIM$(STR$(w3&&));: COLOR 7: PRINT ". Begin mult est. at or one above this number."
IF w3&& < 9 THEN w3&& = w3&& + 1 ELSE IF w3&& = 10 THEN w3&& = 9
DO
stringmatha$ = divisor$: stringmathb$ = LTRIM$(STR$(w3&&))
runningtotal$ = sm_mult$(divisor$, LTRIM$(STR$(w3&&)))
gl% = 2: sm_greater_lesser runningtotal$, dividend$, gl%
IF gl% <= 0 OR w3&& = 0 THEN EXIT DO
IF betatest% THEN COLOR 8: PRINT "Mult loop:"; w3&&; "* "; divisor$; " = "; runningtotal$: COLOR 7
w3&& = w3&& - 1
LOOP
stringmatha$ = dividend$: stringmathb$ = runningtotal$
sm_add_subtract_router dividend$, "-", stringmathb$, runningtotal$
EXIT DO
LOOP
IF betatest% THEN PRINT LTRIM$(STR$(w3&&)); " * "; divisor$; " = "; stringmathb$; " | "; stringmatha$; " - "; stringmathb$; " = "; runningtotal$; " Remainder and drop-down = ";
j2&& = j2&& + 1
drop$ = "0": MID$(drop$, 1, 1) = MID$(origdividend$, j2&&, 1)
IF runningtotal$ <> "0" THEN remainder$ = runningtotal$ ELSE remainder$ = ""
dividend$ = 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$
IF betatest% AND remainder$ = "" THEN betatemp$ = CHR$(34) + CHR$(34) ELSE IF betatest% THEN betatemp$ = remainder$
IF betatest% AND MID$(origdividend$, j2&&, 1) = "" THEN betatemp2$ = CHR$(34) + CHR$(34) ELSE IF betatest% THEN betatemp2$ = MID$(origdividend$, j2&&, 1)
IF betatest% THEN PRINT dividend$; " ("; betatemp$; " + "; drop$; ") at:"; j2&&; "of "; origdividend$; " Loop"; k&& + 1; "Quotent = ";: COLOR 14, 4: PRINT q$;: COLOR 7, 0: PRINT: SLEEP
' Check to terminate
IF div_decimal% = -1 THEN
' Decimal to left.
IF remainder$ = "" AND MID$(origdividend$, j2&&, 1) = "" OR LEN(q$) >= limit&& THEN EXIT DO
ELSE
' Decimal to right.
IF remainder$ = "" AND MID$(origdividend$, j2&&, 1) = "" AND k&& >= dp&& OR LEN(q$) >= limit&& THEN EXIT DO
END IF
IF INKEY$ = " " THEN EXIT DO
k&& = k&& + 1
LOOP
EXIT DO
LOOP
IF RIGHT$(q$, 1) = "." AND divisor$ <> "0" THEN runningtotal$ = MID$(q$, 1, LEN(q$) - 1) ELSE runningtotal$ = q$
sm_div$ = runningtotal$
stringmatha$ = hold_stringmatha$: stringmathb$ = hold_stringmathb$
END FUNCTION
SUB greatest_common_factor (gfca$, gfcb$)
IF betatest% THEN PRINT "Pre-GFC "; gfca$; " / "; gfcb$
numerator$ = gfca$: denominator$ = gfcb$
' Make both numbers positive.
IF MID$(gfca$, 1, 1) = "-" THEN gfca$ = MID$(gfca$, 2)
IF MID$(gfcb$, 1, 1) = "-" THEN gfcb$ = MID$(gfcb$, 2)
CALL sm_greater_lesser(gfca$, gfcb$, gl%)
IF gl% THEN SWAP gfca$, gfcb$
DO
stringmatha$ = gfca$: stringmathb$ = gfcb$
runningtotal$ = sm_div$(stringmatha$, stringmathb$)
IF INSTR(runningtotal$, ".") THEN runningtotal$ = MID$(runningtotal$, 1, INSTR(runningtotal$, ".") - 1)
stringmatha$ = runningtotal$: stringmathb$ = gfcb$
runningtotal$ = sm_mult$(stringmatha$, stringmathb$)
stringmatha$ = gfca$: stringmathb$ = runningtotal$
runningtotal$ = sm_sub$(stringmatha$, stringmathb$)
SWAP gfca$, gfcb$: gfcb$ = runningtotal$
IF runningtotal$ = "0" THEN EXIT DO
LOOP
stringmatha$ = numerator$: stringmathb$ = gfca$
IF betatest% THEN PRINT "GFC = "; gfca$
numerator$ = sm_div$(stringmatha$, stringmathb$)
stringmatha$ = denominator$: stringmathb$ = gfca$
denominator$ = sm_div$(stringmatha$, stringmathb$)
gfca$ = numerator$: gfcb$ = denominator$ ' Needed to pass back.
IF betatest% THEN PRINT "Fraction: "; numerator$; " / "; denominator$
END SUBWat I like is this format reduces fractions, which helps eliminates some rounding errors. For example, if the computation requires something like find the .2 root of 6, well, 2/10 root of 6 would be square root of 6 = 2.449489742783178 ^ 10 = 7,775.9999999999968826892081723528 whereas reducing 2/10 to 1/5 leaves us with 6^5 = 7,776.
Again, to solve for the discrepancy if reducing the fraction is not possible, or just doesn't matter, means I would have to get numbers lik the square root of 6 in either enough digits to reach the terminating decimal or convert the remainder and digits calculated to a fraction. So yes, Virginia, there is a Santa Clause, and I'd bet he'd rather shove his fat ascii down chimneys all night than mess with stuff.
Pete
EDIT: Screwy forum didn't register post contents.
RE: Roots and powers playing nicely together... - Pete - 09-28-2022
Okay, so with mixed numbers you have to line up the number for root division. Groups per root both left and right of the decimal point. This little routine helps visualize the process...
Code: (Select All)
WIDTH 140, 25
DO
INPUT "Root: "; r
' How to line up root equations.
' 23.0347 root = 3 instr() = 3 dp (3 - 1) = 2 digits = (7 - 1) = 6
' 23|034|7 ' root 3 example.
' .0024768
' |002|467|8 ' root 3 example.
' 3509875.45
' 3|509|875|45 ' root 3 example.
REDIM a1$(3)
a1$(1) = "23.0347"
a1$(2) = ".0024768"
a1$(3) = "3509875.45"
FOR h = 1 TO 3
PRINT a1$(h),
i = INSTR(a1$(h), ".") - 1 ' digits before decimal.
j = LEN(a1$(h)) - 1 ' Number of digits.
a$ = MID$(a1$(h), 1, INSTR(a1$(h), ".") - 1) + MID$(a1$(h), INSTR(a1$(h), ".") + 1)
PRINT "Digits before decimal ="; i; " Number of digits ="; j; "Number: "; a1$(h); SPACE$(14 - LEN(a1$(h)));
FOR k = 1 TO j
IF (k - (i - r + 1)) MOD r = 0 THEN PRINT "|";
PRINT MID$(a$, k, 1);
NEXT
PRINT
NEXT h
PRINT
CLEAR
LOOPPete
RE: Roots and powers playing nicely together... - Pete - 09-29-2022
Finished adding mixed numbers to all functions. Preliminary attempt to add decimals, fingers crossed but I'll bet I'll find some exceptions I need to address. Once I get settled with tat, I need to add the restrictions for no illegal roots. I don't want to wander into imaginary numbers.
Anyway, this is where I'm at so far...
Code: (Select All)
$CONSOLE:ONLY
DIM SHARED limit&&
DO
INPUT "Input 1 for general roots or 2 for decimal powers: "; k$
SELECT CASE k$
CASE "1"
LINE INPUT "Number: "; n$
LINE INPUT "Root: "; r$
orig_n$ = n$
j&& = INSTR(r$, ".")
IF j&& THEN ' Decimal or mixed whole and decimal root.
IF j&& = 1 THEN ' Decimal only root. OKAY
pow$ = "1" + STRING$(LEN(r$) - 1, "0")
r$ = MID$(r$, INSTR(r$, ".") + 1)
greatest_common_factor pow$, r$
IF r$ <> "1" THEN GOSUB root_calc ELSE sm_rt$ = orig_n$
tmp$ = sm_rt$
FOR i&& = 1 TO VAL(pow$) - 1
sm_rt$ = sm_mult$(tmp$, sm_rt$)
NEXT
EXIT DO
ELSE ' Mixed whole and decimal root. OKAY
r_whole$ = MID$(r$, 1, INSTR(r$, ".") - 1)
r$ = MID$(r$, INSTR(r$, ".") + 1)
pow$ = "1" + STRING$(LEN(r$), "0")
greatest_common_factor pow$, r$
tmp$ = sm_mult$(r_whole$, pow$)
r$ = sm_add$(tmp$, r$)
IF r$ <> "1" THEN GOSUB root_calc ELSE sm_rt$ = orig_n$
tmp$ = sm_rt$ ' Combine both parts.
FOR i&& = 1 TO VAL(pow$) - 1
sm_rt$ = sm_mult$(tmp$, sm_rt$)
NEXT
EXIT DO
END IF
ELSE ' Whole root. OKAY
IF r$ <> "1" THEN GOSUB root_calc ELSE sm_rt$ = orig_n$
EXIT DO
END IF
CASE "2"
LINE INPUT "Number: "; n$
LINE INPUT "Power: "; pow$
orig_n$ = n$
j&& = INSTR(pow$, ".")
IF j&& THEN ' Decimal or mixed whole and decimal power.
IF j&& = 1 THEN ' Decimal only. OKAY
r$ = "1" + STRING$(LEN(pow$) - 1, "0") ' Make denominator.
pow$ = MID$(pow$, INSTR(pow$, ".") + 1) ' Strip out decimal from power.
greatest_common_factor pow$, r$
IF r$ <> "1" THEN GOSUB root_calc ELSE sm_rt$ = orig_n$
tmp$ = sm_rt$
FOR i&& = 1 TO VAL(pow$) - 1
sm_rt$ = sm_mult$(sm_rt$, tmp$)
NEXT
EXIT DO
ELSE ' Mixed whole number and decimal power. OKAY
d_whole$ = orig_n$
' Raise the entire number to the whole number portion of the power. Ex: 8.5^2.4 is 8.5^2.
FOR i&& = 1 TO VAL(MID$(pow$, 1, INSTR(pow$, ".") - 1)) - 1
d_whole$ = sm_mult$(d_whole$, n$)
NEXT
pow$ = MID$(pow$, INSTR(pow$, ".") + 1) ' Root. Convert the power to the portion after the decimal place. Ex: ^2.4 is ^4
r$ = "1" + STRING$(LEN(pow$), "0") ' Power.
greatest_common_factor pow$, r$
IF betatest% THEN PRINT "Root = "; r$; " Power = "; pow$
IF r$ <> "12" THEN GOSUB root_calc ELSE sm_rt$ = orig_n$
tmp$ = sm_rt$
FOR i&& = 1 TO VAL(pow$) - 1
sm_rt$ = sm_mult$(sm_rt$, tmp$)
NEXT
sm_rt$ = sm_mult$(d_whole$, sm_rt$)
EXIT DO
END IF
ELSE ' Whole number power. Decimal is calulated in mult. function.
sm_rt$ = orig_n$
FOR i&& = 1 TO VAL(pow$) - 1
sm_rt$ = sm_mult$(sm_rt$, orig_n$)
NEXT
EXIT DO
END IF
END SELECT
LOOP
PRINT "Answer: "; sm_rt$: PRINT
RUN
root_calc:
r = VAL(r$)
nu&& = INSTR(orig_n$, ".") - 1
IF nu&& < 0 THEN
nu&& = LEN(orig_n$) ' Non-decimal. Locate any decimal point at end of number.
ELSE ' Remove decimal point.
n$ = MID$(orig_n$, 1, INSTR(n$, ".") - 1) + MID$(orig_n$, INSTR(orig_n$, ".") + 1)
END IF
h&& = (r - (r - nu&& MOD r)) + 1 ' Long division format. Ex: 8|456 for cube root of 8456.
IF betatest% THEN PRINT "nu&& ="; nu&&; " h&& ="; h&&
' Decimal point relocator. Limited to && size unless converted to string.
t$ = MID$(n$, 1, h&& - 1): d$ = "0" ' Initial target.
limit&& = 16
' Calculate Pascal's Triangle.
REDIM p$(r + 1)
FOR i1&& = 1 TO r + 1
p&& = 1
FOR j1&& = 1 TO i1&&
p$(j1&&) = LTRIM$(STR$(p&&))
p&& = p&& * (i1&& - j1&&) \ j1&&
NEXT
NEXT
IF betatest% THEN PRINT "n$ = "; n$; " r ="; r; " nu&& ="; nu&&; " h&& ="; h&&
DO
oldx$ = "0"
lcnt&& = lcnt&& + 1
IF betatest% THEN PRINT "Target ="; t$
FOR j = 1 TO 10
x$ = "0"
FOR i&& = 1 TO r
IF betatest% THEN PRINT "(10 ^"; (i&& - 1); "*"; p$(i&&); "* d ^"; i&& - 1; " * j ^"; (r + 1 - i&&); ") + "
REM x = x + 10 ^ (i&& - 1) * VAL(p$(i&&)) * d ^ (i&& - 1) * j ^ (r + 1 - i&&)
tmp$ = "1"
FOR k% = 1 TO i&& - 1
tmp$ = sm_mult$(tmp$, "10")
NEXT
tmp$ = sm_mult$(tmp$, p$(i&&))
tmp2$ = "1"
FOR k% = 1 TO i&& - 1
tmp2$ = sm_mult$(tmp2$, d$)
NEXT
IF d$ = "0" AND k% = 1 THEN tmp2$ = "1" ' zero^0 = 1
tmp3$ = sm_mult$(tmp$, tmp2$)
tmp$ = "1"
FOR k% = 1 TO r + 1 - i&&
tmp$ = sm_mult$(tmp$, LTRIM$(STR$(j)))
NEXT
tmp2$ = sm_mult$(tmp3$, tmp$)
x$ = sm_add(x$, tmp2$)
NEXT
IF betatest% THEN PRINT "<<<"; x$: SLEEP
IF LEN(x$) > LEN(t$) OR LEN(x$) = LEN(t$) AND x$ > t$ THEN EXIT FOR
oldx$ = x$
NEXT
d$ = d$ + LTRIM$(STR$(j - 1))
IF LEFT$(d$, 1) = "0" THEN d$ = MID$(d$, 2) ' Remove leading zero.
tmp1$ = sm_sub$(t$, oldx$)
tmp2$ = MID$(n$, h&&, r) + STRING$(r - LEN(MID$(n$, h&&, r)), "0")
IF betatest% THEN PRINT "t - oldx as: "; t$; " - "; oldx$; " = "; tmp1$,: COLOR 14: PRINT "d ="; d$: COLOR 7
t$ = tmp1$ + tmp2$
IF LEFT$(t$, 1) = "0" THEN t$ = MID$(t$, 2) 'Remove leading zero.
h&& = h&& + r
IF dp&& = 0 THEN ' Decimal point relocator. Limited to && size unless converted to string.
IF h&& >= nu&& THEN
dp&& = INT(nu&& / 2 + .5) + 1
IF betatest% THEN PRINT "dp&& ="; dp&&
END IF
END IF
IF t$ = STRING$(LEN(t$), "0") AND h&& >= LEN(n$) OR lcnt&& = limit&& THEN EXIT DO
LOOP
IF dp&& THEN
sm_rt$ = MID$(d$, 0, dp&&) + "." + MID$(d$, dp&&)
ELSE
sm_rt$ = d$
END IF
n$ = orig_n$
RETURN
SUB sm_greater_lesser (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 +
j% = 0: k% = 0
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
j&& = INSTR(compa$, ".")
k&& = INSTR(compb$, ".")
' A starting decimal and non-decimal.
IF j&& = 0 AND k&& = 1 THEN
IF compa$ = "0" THEN gl% = -1 ELSE gl% = 1
EXIT DO
END IF
IF k&& = 0 AND j&& = 1 THEN
IF compb$ = "0" THEN gl% = 1 ELSE gl% = -1
EXIT DO
END IF
' remove decimals and align.
j2&& = 0: k2&& = 0
IF j&& <> 0 OR k&& <> 0 THEN
IF j&& THEN compa$ = MID$(compa$, 1, INSTR(compa$, ".") - 1) + MID$(compa$, INSTR(compa$, ".") + 1): j2&& = LEN(compa$) - j&& + 1
IF k&& THEN compb$ = MID$(compb$, 1, INSTR(compb$, ".") - 1) + MID$(compb$, INSTR(compb$, ".") + 1): k2&& = LEN(compb$) - k&& + 1
compa$ = compa$ + STRING$(k2&& - j2&&, "0")
compb$ = compb$ + STRING$(j2&& - k2&&, "0")
END IF
EXIT WHILE
WEND
' Remove leading zeros if any.
DO UNTIL LEFT$(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$)
gl% = 1
END SELECT
EXIT DO
LOOP
END SUB
SUB sm_add_subtract_router (stringmatha$, operator$, stringmathb$, runningtotal$)
DIM AS _INTEGER64 a, c, s
a1$ = 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$
sm_greater_lesser 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
END SUB
FUNCTION sm_add$ (stringmatha$, stringmathb$)
operator$ = "+"
sm_add_subtract_router stringmatha$, operator$, stringmathb$, runningtotal$
sm_add$ = runningtotal$
END FUNCTION
FUNCTION sm_sub$ (stringmatha$, stringmathb$)
operator$ = "-"
sm_add_subtract_router stringmatha$, operator$, stringmathb$, runningtotal$
sm_sub$ = runningtotal$
END FUNCTION
FUNCTION sm_mult$ (stringmatha$, stringmathb$)
DIM AS _INTEGER64 a, c, aa, cc, s, ss
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$
sm_mult$ = z$
END FUNCTION
FUNCTION sm_div$ (stringmatha$, stringmathb$)
hold_stringmatha$ = stringmatha$: hold_stringmathb$ = stringmathb$
q$ = "": divisor$ = stringmathb$: dividend$ = stringmatha$
DO ' Falx loop.
'Strip off neg(s) and determine quotent sign.
IF LEFT$(divisor$, 1) = "-" THEN divisor$ = MID$(divisor$, 2): q$ = "-"
IF LEFT$(dividend$, 1) = "-" THEN dividend$ = MID$(dividend$, 2): IF q$ = "-" THEN q$ = "" ELSE q$ = "-"
' Quick results for divisor 1 or 0.
IF dividend$ = "0" THEN q$ = "0": EXIT DO
IF divisor$ = "1" THEN q$ = dividend$: EXIT DO
IF divisor$ = "0" THEN q$ = "Division by zero not possible.": EXIT DO
' Determine decimal direction. -1 to left, +1 to right.
gl% = 0: sm_greater_lesser divisor$, dividend$, gl%
IF betatest% AND gl% = 1 THEN PRINT divisor$; " > "; dividend$; " Move decimal to the left"
IF betatest% AND gl% = 0 THEN PRINT divisor$; " = "; dividend$
IF betatest% AND gl% = -1 THEN PRINT divisor$; " < "; dividend$; " Move deciml to the right."
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(divisor$, ".")
IF temp&& THEN
divisor$ = MID$(divisor$, 1, temp&& - 1) + MID$(divisor$, temp&& + 1)
IF temp&& = 1 THEN
DO UNTIL LEFT$(divisor$, 1) <> "0" ' Strip off any leading zeros on divisor only.
divisor$ = MID$(divisor$, 2)
dp&& = dp&& + 1
LOOP
dp&& = dp&& + 1
ELSE
dp&& = -(temp&& - 2)
END IF
ELSE
dp&& = -(LEN(divisor$) - 1)
END IF
temp&& = INSTR(dividend$, ".")
IF temp&& THEN
dividend$ = MID$(dividend$, 1, temp&& - 1) + MID$(dividend$, temp&& + 1)
IF temp&& = 1 THEN
DO UNTIL LEFT$(dividend$, 1) <> "0" ' Strip off any leading zeros on divisor only.
dividend$ = MID$(dividend$, 2)
dp2&& = dp2&& + 1
LOOP
dp2&& = dp2&& + 1
ELSE
dp2&& = -(temp&& - 2)
END IF
ELSE
dp2&& = -(LEN(dividend$) - 1)
END IF
IF betatest% THEN COLOR 11: PRINT "Divisor decimal moves "; LTRIM$(STR$(dp&&)); ". Dividend decimal moves"; LTRIM$(STR$(dp2&&)); ". Quotent decimal ABS("; LTRIM$(STR$(dp&&)); " - "; LTRIM$(STR$(dp2&&)); ") =";: COLOR 14: PRINT ABS(dp&& - dp2&&);: COLOR 11: PRINT "+ any adjustment.": COLOR 7
dp&& = ABS(dp&& - dp2&&)
IF betatest% THEN PRINT "Divisor 1st# = "; MID$(divisor$, 1, 1); " Remainder 1st# = "; MID$(dividend$, 1, 1)
' Adjust decimal place for instances when divisor is larger than remainder the length of the divisor.
j% = 0
IF MID$(divisor$, 1, 1) > MID$(dividend$, 1, 1) THEN
j% = 1
IF betatest% THEN PRINT "Larger divisor, so move quotent decimal one place back to: ";: COLOR 14: PRINT LTRIM$(STR$(dp&&)): COLOR 7
ELSEIF MID$(divisor$, 1, 1) = MID$(dividend$, 1, 1) THEN
IF LEN(divisor$) = LEN(dividend$) THEN
IF divisor$ > dividend$ THEN j% = 1
ELSE
IF LEN(divisor$) > LEN(dividend$) THEN
temp$ = dividend$ + STRING$(LEN(divisor$) - LEN(dividend$), "0")
ELSE
temp$ = MID$(dividend$, 1, LEN(divisor$))
END IF
IF divisor$ > temp$ THEN j% = 1
END IF
IF betatest% THEN
IF j% THEN PRINT "Larger divisor than dividend at LEN(divisor$), so move quotent decimal one place back to: ";: COLOR 14: PRINT LTRIM$(STR$(dp&&)): COLOR 7
IF j% = 0 THEN PRINT "Smaller divisor than dividend at LEN(divisor$), so no quotent decimal place adjustment needed. Quotent decimal place = ";: COLOR 14: PRINT LTRIM$(STR$(dp&&)): COLOR 7
END IF
ELSE
j% = 0
IF betatest% THEN PRINT "Smaller divisor, so no quotent decimal place adjustment needed. Quotent decimal place = ";: COLOR 14: PRINT LTRIM$(STR$(dp&&)): COLOR 7
END IF
IF j% THEN dp&& = dp&& - div_decimal%
origdividend$ = dividend$
' Determine length of divisor and dividend to begin initial long divison step.
gl% = 2: sm_greater_lesser divisor$, MID$(dividend$, 1, LEN(divisor$)) + STRING$(LEN(divisor$) - LEN(dividend$), "0"), gl%
divisor_ratio_dividend% = gl%
IF gl% = 1 AND MID$(dividend$, 1, 1) <> "0" THEN
dividend$ = MID$(dividend$, 1, LEN(divisor$) + 1) + STRING$(LEN(divisor$) + 1 - LEN(dividend$), "0")
ELSE
dividend$ = MID$(dividend$, 1, LEN(divisor$)) + STRING$(LEN(divisor$) - LEN(dividend$), "0")
END IF
' Long divison loop. Mult and subtraction of dividend and remainder.
k&& = 0
IF betatest% THEN PRINT "Begin long divison loop..."
DO
SELECT CASE MID$(divisor$, 1, 1)
CASE IS < MID$(dividend$, 1, 1)
adj_rem_len% = 0
CASE IS = MID$(dividend$, 1, 1)
gl% = 2: sm_greater_lesser divisor$, MID$(dividend$, 1, LEN(divisor$)), gl%
IF gl% = 1 THEN adj_rem_len% = 1 ELSE adj_rem_len% = 0
CASE IS > MID$(dividend$, 1, 1)
adj_rem_len% = 1
END SELECT
IF j2&& = 0 THEN j2&& = LEN(divisor$) + adj_rem_len%
DO
IF LEN(divisor$) > LEN(dividend$) THEN
w3&& = 0: runningtotal$ = dividend$: stringmathb$ = "0"
IF betatest% THEN PRINT: COLOR 3: PRINT "Divisor is larger so "; dividend$; " \ "; divisor$; " =";: COLOR 5: PRINT w3&&: COLOR 7
EXIT DO
END IF
IF LEN(divisor$) = LEN(dividend$) THEN
gl% = 2: sm_greater_lesser divisor$, dividend$, gl%
IF gl% = 1 THEN
w3&& = 0: runningtotal$ = dividend$: stringmathb$ = "0"
IF betatest% THEN COLOR 9: PRINT "Length of divisor is the same as remainder but remainder is smaller so w3&& = ";: COLOR 5: PRINT "0": COLOR 7
EXIT DO
END IF
END IF
SELECT CASE LEN(dividend$)
CASE IS > 2
w3&& = VAL(MID$(dividend$, 1, 2 + adj_rem_len%)) \ VAL(MID$(divisor$, 1, 2))
IF betatest% THEN PRINT MID$(dividend$, 1, 2 + adj_rem_len%); " \ "; MID$(divisor$, 1, 2); " =";
CASE ELSE
w3&& = VAL(MID$(dividend$, 1, 1 + adj_rem_len%)) \ VAL(MID$(divisor$, 1, 1))
IF betatest% THEN PRINT MID$(dividend$, 1, 1 + adj_rem_len%); " \ "; MID$(divisor$, 1, 1); " =";
END SELECT
IF betatest% THEN COLOR 5: PRINT " " + LTRIM$(STR$(w3&&));: COLOR 7: PRINT ". Begin mult est. at or one above this number."
IF w3&& < 9 THEN w3&& = w3&& + 1 ELSE IF w3&& = 10 THEN w3&& = 9
DO
stringmatha$ = divisor$: stringmathb$ = LTRIM$(STR$(w3&&))
runningtotal$ = sm_mult$(divisor$, LTRIM$(STR$(w3&&)))
gl% = 2: sm_greater_lesser runningtotal$, dividend$, gl%
IF gl% <= 0 OR w3&& = 0 THEN EXIT DO
IF betatest% THEN COLOR 8: PRINT "Mult loop:"; w3&&; "* "; divisor$; " = "; runningtotal$: COLOR 7
w3&& = w3&& - 1
LOOP
stringmatha$ = dividend$: stringmathb$ = runningtotal$
sm_add_subtract_router dividend$, "-", stringmathb$, runningtotal$
EXIT DO
LOOP
IF betatest% THEN PRINT LTRIM$(STR$(w3&&)); " * "; divisor$; " = "; stringmathb$; " | "; stringmatha$; " - "; stringmathb$; " = "; runningtotal$; " Remainder and drop-down = ";
j2&& = j2&& + 1
drop$ = "0": MID$(drop$, 1, 1) = MID$(origdividend$, j2&&, 1)
IF runningtotal$ <> "0" THEN remainder$ = runningtotal$ ELSE remainder$ = ""
dividend$ = 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$
IF betatest% AND remainder$ = "" THEN betatemp$ = CHR$(34) + CHR$(34) ELSE IF betatest% THEN betatemp$ = remainder$
IF betatest% AND MID$(origdividend$, j2&&, 1) = "" THEN betatemp2$ = CHR$(34) + CHR$(34) ELSE IF betatest% THEN betatemp2$ = MID$(origdividend$, j2&&, 1)
IF betatest% THEN PRINT dividend$; " ("; betatemp$; " + "; drop$; ") at:"; j2&&; "of "; origdividend$; " Loop"; k&& + 1; "Quotent = ";: COLOR 14, 4: PRINT q$;: COLOR 7, 0: PRINT: SLEEP
' Check to terminate
IF div_decimal% = -1 THEN
' Decimal to left.
IF remainder$ = "" AND MID$(origdividend$, j2&&, 1) = "" OR LEN(q$) >= limit&& THEN EXIT DO
ELSE
' Decimal to right.
IF remainder$ = "" AND MID$(origdividend$, j2&&, 1) = "" AND k&& >= dp&& OR LEN(q$) >= limit&& THEN EXIT DO
END IF
IF INKEY$ = " " THEN EXIT DO
k&& = k&& + 1
LOOP
EXIT DO
LOOP
IF RIGHT$(q$, 1) = "." AND divisor$ <> "0" THEN runningtotal$ = MID$(q$, 1, LEN(q$) - 1) ELSE runningtotal$ = q$
sm_div$ = runningtotal$
stringmatha$ = hold_stringmatha$: stringmathb$ = hold_stringmathb$
END FUNCTION
SUB greatest_common_factor (gfca$, gfcb$)
IF betatest% THEN PRINT "Pre-GFC "; gfca$; " / "; gfcb$
numerator$ = gfca$: denominator$ = gfcb$
' Make both numbers positive.
IF MID$(gfca$, 1, 1) = "-" THEN gfca$ = MID$(gfca$, 2)
IF MID$(gfcb$, 1, 1) = "-" THEN gfcb$ = MID$(gfcb$, 2)
CALL sm_greater_lesser(gfca$, gfcb$, gl%)
IF gl% THEN SWAP gfca$, gfcb$
DO
stringmatha$ = gfca$: stringmathb$ = gfcb$
runningtotal$ = sm_div$(stringmatha$, stringmathb$)
IF INSTR(runningtotal$, ".") THEN runningtotal$ = MID$(runningtotal$, 1, INSTR(runningtotal$, ".") - 1)
stringmatha$ = runningtotal$: stringmathb$ = gfcb$
runningtotal$ = sm_mult$(stringmatha$, stringmathb$)
stringmatha$ = gfca$: stringmathb$ = runningtotal$
runningtotal$ = sm_sub$(stringmatha$, stringmathb$)
SWAP gfca$, gfcb$: gfcb$ = runningtotal$
IF runningtotal$ = "0" THEN EXIT DO
LOOP
stringmatha$ = numerator$: stringmathb$ = gfca$
IF betatest% THEN PRINT "GFC = "; gfca$
numerator$ = sm_div$(stringmatha$, stringmathb$)
stringmatha$ = denominator$: stringmathb$ = gfca$
denominator$ = sm_div$(stringmatha$, stringmathb$)
gfca$ = numerator$: gfcb$ = denominator$ ' Needed to pass back.
IF betatest% THEN PRINT "Fraction: "; numerator$; " / "; denominator$
END SUBPete
RE: Roots and powers playing nicely together... - Kernelpanic - 09-29-2022
Mighty mighty, Pete! But I can't see through it. How is the root value created? See the screenshot. One can't find out the exponent without it.
It's not a mistake, because otherwise one wouldn't get to the exponent. Then what is it?
Code: (Select All)
'Kubikwurzel berechnen - 23. Sept. 2022
'$Debug
Dim As Double n, nDummy, x, rootx, potenz
Print
Input "Wurzelexponent: ", n
Input "Radikand : ", x
rootx = x ^ (1 / n)
Print Using "Kubikwurzel: ###.##########"; rootx
Print
potenz = (rootx ^ n)
Print Using "Und zurueck: ########.###"; potenz
Print
'Exponent ermitteln nach Pete
'nDummy = rootx ^ x
nDummy = 1.06675811 ^ x
Print Using "Exponent anzeigen: ###.##########"; nDummy
End![[Image: String-Mathe-Pete.jpg]](https://i.ibb.co/Y2rgZ5D/String-Mathe-Pete.jpg)
RE: Roots and powers playing nicely together... - Pete - 09-29-2022
Well one problem I anticipated, but I thought would take higher numbers is Pascal's Triangle. I tried 90 root 104 and the program froze. Somewhere between 1 and 104 INTEGER64 craps out. Tat means when I find the breaking point, I need to calculate Pascal's Triangle using string math.
Pete
RE: Roots and powers playing nicely together... - Kernelpanic - 09-29-2022
Well, but it crashes already before. - I've only checked a few variations, so I can't say when the program starts to crash really.
![[Image: String-Mathe30-Pete.jpg]](https://i.ibb.co/wyt2rsS/String-Mathe30-Pete.jpg)
RE: Roots and powers playing nicely together... - Pete - 09-30-2022
It crashes because Pascal's Triangle is being limited by _INTEGER64. I'm writing a string routine to get past that. What held me up is the algorithm I used to calculate Pascal's triangle utilized integer division, an I don't have a string routine for that. So, I'm going to re-tool the algorithm using arrays. The old arrays building the next row. Hope to have it up sometime tonight.
Pete
RE: Roots and powers playing nicely together... - Pete - 09-30-2022
Okay, this solved for the limits on the triangle situation. It's a bit slow for mixed powers and roots 50, 100, etc. Speed optimization will come later. Right now, It's all about trying to obtain accuracy.
Code: (Select All)
$CONSOLE:ONLY
DIM SHARED limit&&, betatest%
'betatest% = 3
DO
INPUT "Input 1 for general roots or 2 for decimal powers: "; k$
SELECT CASE k$
CASE "1"
LINE INPUT "Number: "; n$
LINE INPUT "Root: "; r$
orig_n$ = n$
j&& = INSTR(r$, ".")
IF j&& THEN ' Decimal or mixed whole and decimal root.
IF j&& = 1 THEN ' Decimal only root. OKAY
pow$ = "1" + STRING$(LEN(r$) - 1, "0")
r$ = MID$(r$, INSTR(r$, ".") + 1)
greatest_common_factor pow$, r$
IF r$ <> "1" THEN GOSUB root_calc ELSE sm_rt$ = orig_n$
tmp$ = sm_rt$
FOR i&& = 1 TO VAL(pow$) - 1
sm_rt$ = sm_mult$(tmp$, sm_rt$)
NEXT
EXIT DO
ELSE ' Mixed whole and decimal root. OKAY
r_whole$ = MID$(r$, 1, INSTR(r$, ".") - 1)
r$ = MID$(r$, INSTR(r$, ".") + 1)
pow$ = "1" + STRING$(LEN(r$), "0")
greatest_common_factor pow$, r$
tmp$ = sm_mult$(r_whole$, pow$)
r$ = sm_add$(tmp$, r$)
IF r$ <> "1" THEN GOSUB root_calc ELSE sm_rt$ = orig_n$
tmp$ = sm_rt$ ' Combine both parts.
FOR i&& = 1 TO VAL(pow$) - 1
sm_rt$ = sm_mult$(tmp$, sm_rt$)
NEXT
EXIT DO
END IF
ELSE ' Whole root. OKAY
IF r$ <> "1" THEN GOSUB root_calc ELSE sm_rt$ = orig_n$
EXIT DO
END IF
CASE "2"
LINE INPUT "Number: "; n$
LINE INPUT "Power: "; pow$
orig_n$ = n$
j&& = INSTR(pow$, ".")
IF j&& THEN ' Decimal or mixed whole and decimal power.
IF j&& = 1 THEN ' Decimal only. OKAY
r$ = "1" + STRING$(LEN(pow$) - 1, "0") ' Make denominator.
pow$ = MID$(pow$, INSTR(pow$, ".") + 1) ' Strip out decimal from power.
greatest_common_factor pow$, r$
IF r$ <> "1" THEN GOSUB root_calc ELSE sm_rt$ = orig_n$
tmp$ = sm_rt$
FOR i&& = 1 TO VAL(pow$) - 1
sm_rt$ = sm_mult$(sm_rt$, tmp$)
NEXT
EXIT DO
ELSE ' Mixed whole number and decimal power. OKAY
d_whole$ = orig_n$
' Raise the entire number to the whole number portion of the power. Ex: 8.5^2.4 is 8.5^2.
FOR i&& = 1 TO VAL(MID$(pow$, 1, INSTR(pow$, ".") - 1)) - 1
d_whole$ = sm_mult$(d_whole$, n$)
NEXT
pow$ = MID$(pow$, INSTR(pow$, ".") + 1) ' Root. Convert the power to the portion after the decimal place. Ex: ^2.4 is ^4
r$ = "1" + STRING$(LEN(pow$), "0") ' Power.
greatest_common_factor pow$, r$
IF betatest% = 3 THEN PRINT "Root = "; r$; " Power = "; pow$
IF r$ <> "12" THEN GOSUB root_calc ELSE sm_rt$ = orig_n$
tmp$ = sm_rt$
FOR i&& = 1 TO VAL(pow$) - 1
sm_rt$ = sm_mult$(sm_rt$, tmp$)
NEXT
sm_rt$ = sm_mult$(d_whole$, sm_rt$)
EXIT DO
END IF
ELSE ' Whole number power. Decimal is calulated in mult. function.
sm_rt$ = orig_n$
FOR i&& = 1 TO VAL(pow$) - 1
sm_rt$ = sm_mult$(sm_rt$, orig_n$)
NEXT
EXIT DO
END IF
END SELECT
LOOP
PRINT "Answer: "; sm_rt$: PRINT
RUN
root_calc:
r = VAL(r$)
nu&& = INSTR(orig_n$, ".") - 1
IF nu&& < 0 THEN
nu&& = LEN(orig_n$) ' Non-decimal. Locate any decimal point at end of number.
n$ = orig_n$
ELSE ' Remove decimal point.
n$ = MID$(orig_n$, 1, INSTR(n$, ".") - 1) + MID$(orig_n$, INSTR(orig_n$, ".") + 1)
END IF
h&& = (r - (r - nu&& MOD r)) ' Long division format. Ex: 8|456 for cube root of 8456.
IF h&& = 0 THEN h&& = r
IF betatest% = 3 THEN PRINT "nu&& ="; nu&&; " h&& ="; h&&; " r ="; r
' Decimal point relocator. Limited to && size unless converted to string.
t$ = MID$(n$, 1, h&&): d$ = "0" ' Initial target.
limit&& = 16
' Calculate Pascal's Triangle.
REDIM p$(r + 1), x$(r + 1)
FOR i1&& = 1 TO r + 1
p&& = 1: x$(1) = "1"
FOR j1&& = 1 TO i1&&
p$(j1&&) = sm_add$(x$(j1&& - 1), x$(j1&&))
NEXT
FOR h&& = 1 TO j1&& - 1
x$(h&&) = p$(h&&)
NEXT
NEXT
IF betatest% = 3 THEN PRINT "n$ = "; n$; " r ="; r; " nu&& ="; nu&&; " h&& ="; h&&
DO
oldx$ = "0"
lcnt&& = lcnt&& + 1
IF betatest% = 3 THEN PRINT "Target = "; t$: SLEEP
FOR j = 1 TO 10
x$ = "0"
FOR i&& = 1 TO r
IF betatest% = 3 THEN PRINT "(10 ^"; (i&& - 1); "*";: COLOR 14: PRINT p$(i&&);: COLOR 7: PRINT "* d ^"; i&& - 1; " * j ^"; (r + 1 - i&&); ") + "
REM x = x + 10 ^ (i&& - 1) * VAL(p$(i&&)) * d ^ (i&& - 1) * j ^ (r + 1 - i&&)
tmp$ = "1"
FOR k% = 1 TO i&& - 1
tmp$ = sm_mult$(tmp$, "10")
NEXT
tmp$ = sm_mult$(tmp$, p$(i&&))
tmp2$ = "1"
FOR k% = 1 TO i&& - 1
tmp2$ = sm_mult$(tmp2$, d$)
NEXT
IF d$ = "0" AND k% = 1 THEN tmp2$ = "1" ' zero^0 = 1
tmp3$ = sm_mult$(tmp$, tmp2$)
tmp$ = "1"
FOR k% = 1 TO r + 1 - i&&
tmp$ = sm_mult$(tmp$, LTRIM$(STR$(j)))
NEXT
tmp2$ = sm_mult$(tmp3$, tmp$)
x$ = sm_add(x$, tmp2$)
NEXT
IF betatest% = 3 THEN PRINT "<<<"; x$: SLEEP
IF LEN(x$) > LEN(t$) OR LEN(x$) = LEN(t$) AND x$ > t$ THEN EXIT FOR
oldx$ = x$
NEXT
d$ = d$ + LTRIM$(STR$(j - 1))
IF LEFT$(d$, 1) = "0" THEN d$ = MID$(d$, 2) ' Remove leading zero.
tmp1$ = sm_sub$(t$, oldx$)
tmp2$ = MID$(n$, h&&, r) + STRING$(r - LEN(MID$(n$, h&&, r)), "0")
IF betatest% = 3 THEN PRINT "t - oldx as: "; t$; " - "; oldx$; " = "; tmp1$,: COLOR 14: PRINT "d = "; d$: COLOR 7
t$ = tmp1$ + tmp2$
IF LEFT$(t$, 1) = "0" THEN t$ = MID$(t$, 2) 'Remove leading zero.
h&& = h&& + r
IF dp&& = 0 THEN ' Decimal point relocator. Limited to && size unless converted to string.
IF h&& >= nu&& THEN
dp&& = INT(nu&& / 2 + .5) + 1
IF betatest% = 3 THEN PRINT "dp&& ="; dp&&
END IF
END IF
IF t$ = STRING$(LEN(t$), "0") AND h&& >= LEN(n$) OR lcnt&& = limit&& THEN EXIT DO
LOOP
IF dp&& THEN
sm_rt$ = MID$(d$, 0, dp&&) + "." + MID$(d$, dp&&)
ELSE
sm_rt$ = d$
END IF
n$ = orig_n$
RETURN
SUB sm_greater_lesser (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 +
j% = 0: k% = 0
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
j&& = INSTR(compa$, ".")
k&& = INSTR(compb$, ".")
' A starting decimal and non-decimal.
IF j&& = 0 AND k&& = 1 THEN
IF compa$ = "0" THEN gl% = -1 ELSE gl% = 1
EXIT DO
END IF
IF k&& = 0 AND j&& = 1 THEN
IF compb$ = "0" THEN gl% = 1 ELSE gl% = -1
EXIT DO
END IF
' remove decimals and align.
j2&& = 0: k2&& = 0
IF j&& <> 0 OR k&& <> 0 THEN
IF j&& THEN compa$ = MID$(compa$, 1, INSTR(compa$, ".") - 1) + MID$(compa$, INSTR(compa$, ".") + 1): j2&& = LEN(compa$) - j&& + 1
IF k&& THEN compb$ = MID$(compb$, 1, INSTR(compb$, ".") - 1) + MID$(compb$, INSTR(compb$, ".") + 1): k2&& = LEN(compb$) - k&& + 1
compa$ = compa$ + STRING$(k2&& - j2&&, "0")
compb$ = compb$ + STRING$(j2&& - k2&&, "0")
END IF
EXIT WHILE
WEND
' Remove leading zeros if any.
DO UNTIL LEFT$(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$)
gl% = 1
END SELECT
EXIT DO
LOOP
END SUB
SUB sm_add_subtract_router (stringmatha$, operator$, stringmathb$, runningtotal$)
DIM AS _INTEGER64 a, c, s
a1$ = 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$
sm_greater_lesser 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
END SUB
FUNCTION sm_add$ (stringmatha$, stringmathb$)
operator$ = "+"
sm_add_subtract_router stringmatha$, operator$, stringmathb$, runningtotal$
sm_add$ = runningtotal$
END FUNCTION
FUNCTION sm_sub$ (stringmatha$, stringmathb$)
operator$ = "-"
sm_add_subtract_router stringmatha$, operator$, stringmathb$, runningtotal$
sm_sub$ = runningtotal$
END FUNCTION
FUNCTION sm_mult$ (stringmatha$, stringmathb$)
DIM AS _INTEGER64 a, c, aa, cc, s, ss
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$
sm_mult$ = z$
END FUNCTION
FUNCTION sm_div$ (stringmatha$, stringmathb$)
hold_stringmatha$ = stringmatha$: hold_stringmathb$ = stringmathb$
q$ = "": divisor$ = stringmathb$: dividend$ = stringmatha$
DO ' Falx loop.
'Strip off neg(s) and determine quotent sign.
IF LEFT$(divisor$, 1) = "-" THEN divisor$ = MID$(divisor$, 2): q$ = "-"
IF LEFT$(dividend$, 1) = "-" THEN dividend$ = MID$(dividend$, 2): IF q$ = "-" THEN q$ = "" ELSE q$ = "-"
' Quick results for divisor 1 or 0.
IF dividend$ = "0" THEN q$ = "0": EXIT DO
IF divisor$ = "1" THEN q$ = dividend$: EXIT DO
IF divisor$ = "0" THEN q$ = "Division by zero not possible.": EXIT DO
' Determine decimal direction. -1 to left, +1 to right.
gl% = 0: sm_greater_lesser divisor$, dividend$, gl%
IF betatest% < 0 AND gl% = 1 THEN PRINT divisor$; " > "; dividend$; " Move decimal to the left"
IF betatest% < 0 AND gl% = 0 THEN PRINT divisor$; " = "; dividend$
IF betatest% < 0 AND gl% = -1 THEN PRINT divisor$; " < "; dividend$; " Move deciml to the right."
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(divisor$, ".")
IF temp&& THEN
divisor$ = MID$(divisor$, 1, temp&& - 1) + MID$(divisor$, temp&& + 1)
IF temp&& = 1 THEN
DO UNTIL LEFT$(divisor$, 1) <> "0" ' Strip off any leading zeros on divisor only.
divisor$ = MID$(divisor$, 2)
dp&& = dp&& + 1
LOOP
dp&& = dp&& + 1
ELSE
dp&& = -(temp&& - 2)
END IF
ELSE
dp&& = -(LEN(divisor$) - 1)
END IF
temp&& = INSTR(dividend$, ".")
IF temp&& THEN
dividend$ = MID$(dividend$, 1, temp&& - 1) + MID$(dividend$, temp&& + 1)
IF temp&& = 1 THEN
DO UNTIL LEFT$(dividend$, 1) <> "0" ' Strip off any leading zeros on divisor only.
dividend$ = MID$(dividend$, 2)
dp2&& = dp2&& + 1
LOOP
dp2&& = dp2&& + 1
ELSE
dp2&& = -(temp&& - 2)
END IF
ELSE
dp2&& = -(LEN(dividend$) - 1)
END IF
IF betatest% < 0 THEN COLOR 11: PRINT "Divisor decimal moves "; LTRIM$(STR$(dp&&)); ". Dividend decimal moves"; LTRIM$(STR$(dp2&&)); ". Quotent decimal ABS("; LTRIM$(STR$(dp&&)); " - "; LTRIM$(STR$(dp2&&)); ") =";: COLOR 14: PRINT ABS(dp&& - dp2&&);: COLOR 11: PRINT "+ any adjustment.": COLOR 7
dp&& = ABS(dp&& - dp2&&)
IF betatest% < 0 THEN PRINT "Divisor 1st# = "; MID$(divisor$, 1, 1); " Remainder 1st# = "; MID$(dividend$, 1, 1)
' Adjust decimal place for instances when divisor is larger than remainder the length of the divisor.
j% = 0
IF MID$(divisor$, 1, 1) > MID$(dividend$, 1, 1) THEN
j% = 1
IF betatest% < 0 THEN PRINT "Larger divisor, so move quotent decimal one place back to: ";: COLOR 14: PRINT LTRIM$(STR$(dp&&)): COLOR 7
ELSEIF MID$(divisor$, 1, 1) = MID$(dividend$, 1, 1) THEN
IF LEN(divisor$) = LEN(dividend$) THEN
IF divisor$ > dividend$ THEN j% = 1
ELSE
IF LEN(divisor$) > LEN(dividend$) THEN
temp$ = dividend$ + STRING$(LEN(divisor$) - LEN(dividend$), "0")
ELSE
temp$ = MID$(dividend$, 1, LEN(divisor$))
END IF
IF divisor$ > temp$ THEN j% = 1
END IF
IF betatest% < 0 THEN
IF j% THEN PRINT "Larger divisor than dividend at LEN(divisor$), so move quotent decimal one place back to: ";: COLOR 14: PRINT LTRIM$(STR$(dp&&)): COLOR 7
IF j% = 0 THEN PRINT "Smaller divisor than dividend at LEN(divisor$), so no quotent decimal place adjustment needed. Quotent decimal place = ";: COLOR 14: PRINT LTRIM$(STR$(dp&&)): COLOR 7
END IF
ELSE
j% = 0
IF betatest% < 0 THEN PRINT "Smaller divisor, so no quotent decimal place adjustment needed. Quotent decimal place = ";: COLOR 14: PRINT LTRIM$(STR$(dp&&)): COLOR 7
END IF
IF j% THEN dp&& = dp&& - div_decimal%
origdividend$ = dividend$
' Determine length of divisor and dividend to begin initial long divison step.
gl% = 2: sm_greater_lesser divisor$, MID$(dividend$, 1, LEN(divisor$)) + STRING$(LEN(divisor$) - LEN(dividend$), "0"), gl%
divisor_ratio_dividend% = gl%
IF gl% = 1 AND MID$(dividend$, 1, 1) <> "0" THEN
dividend$ = MID$(dividend$, 1, LEN(divisor$) + 1) + STRING$(LEN(divisor$) + 1 - LEN(dividend$), "0")
ELSE
dividend$ = MID$(dividend$, 1, LEN(divisor$)) + STRING$(LEN(divisor$) - LEN(dividend$), "0")
END IF
' Long divison loop. Mult and subtraction of dividend and remainder.
k&& = 0
IF betatest% < 0 THEN PRINT "Begin long divison loop..."
DO
SELECT CASE MID$(divisor$, 1, 1)
CASE IS < MID$(dividend$, 1, 1)
adj_rem_len% = 0
CASE IS = MID$(dividend$, 1, 1)
gl% = 2: sm_greater_lesser divisor$, MID$(dividend$, 1, LEN(divisor$)), gl%
IF gl% = 1 THEN adj_rem_len% = 1 ELSE adj_rem_len% = 0
CASE IS > MID$(dividend$, 1, 1)
adj_rem_len% = 1
END SELECT
IF j2&& = 0 THEN j2&& = LEN(divisor$) + adj_rem_len%
DO
IF LEN(divisor$) > LEN(dividend$) THEN
w3&& = 0: runningtotal$ = dividend$: stringmathb$ = "0"
IF betatest% < 0 THEN PRINT: COLOR 3: PRINT "Divisor is larger so "; dividend$; " \ "; divisor$; " =";: COLOR 5: PRINT w3&&: COLOR 7
EXIT DO
END IF
IF LEN(divisor$) = LEN(dividend$) THEN
gl% = 2: sm_greater_lesser divisor$, dividend$, gl%
IF gl% = 1 THEN
w3&& = 0: runningtotal$ = dividend$: stringmathb$ = "0"
IF betatest% < 0 THEN COLOR 9: PRINT "Length of divisor is the same as remainder but remainder is smaller so w3&& = ";: COLOR 5: PRINT "0": COLOR 7
EXIT DO
END IF
END IF
SELECT CASE LEN(dividend$)
CASE IS > 2
w3&& = VAL(MID$(dividend$, 1, 2 + adj_rem_len%)) \ VAL(MID$(divisor$, 1, 2))
IF betatest% < 0 THEN PRINT MID$(dividend$, 1, 2 + adj_rem_len%); " \ "; MID$(divisor$, 1, 2); " =";
CASE ELSE
w3&& = VAL(MID$(dividend$, 1, 1 + adj_rem_len%)) \ VAL(MID$(divisor$, 1, 1))
IF betatest% < 0 THEN PRINT MID$(dividend$, 1, 1 + adj_rem_len%); " \ "; MID$(divisor$, 1, 1); " =";
END SELECT
IF betatest% < 0 THEN COLOR 5: PRINT " " + LTRIM$(STR$(w3&&));: COLOR 7: PRINT ". Begin mult est. at or one above this number."
IF w3&& < 9 THEN w3&& = w3&& + 1 ELSE IF w3&& = 10 THEN w3&& = 9
DO
stringmatha$ = divisor$: stringmathb$ = LTRIM$(STR$(w3&&))
runningtotal$ = sm_mult$(divisor$, LTRIM$(STR$(w3&&)))
gl% = 2: sm_greater_lesser runningtotal$, dividend$, gl%
IF gl% <= 0 OR w3&& = 0 THEN EXIT DO
IF betatest% < 0 THEN COLOR 8: PRINT "Mult loop:"; w3&&; "* "; divisor$; " = "; runningtotal$: COLOR 7
w3&& = w3&& - 1
LOOP
stringmatha$ = dividend$: stringmathb$ = runningtotal$
sm_add_subtract_router dividend$, "-", stringmathb$, runningtotal$
EXIT DO
LOOP
IF betatest% < 0 THEN PRINT LTRIM$(STR$(w3&&)); " * "; divisor$; " = "; stringmathb$; " | "; stringmatha$; " - "; stringmathb$; " = "; runningtotal$; " Remainder and drop-down = ";
j2&& = j2&& + 1
drop$ = "0": MID$(drop$, 1, 1) = MID$(origdividend$, j2&&, 1)
IF runningtotal$ <> "0" THEN remainder$ = runningtotal$ ELSE remainder$ = ""
dividend$ = 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$
IF betatest% < 0 AND remainder$ = "" THEN betatemp$ = CHR$(34) + CHR$(34) ELSE IF betatest% THEN betatemp$ = remainder$
IF betatest% < 0 AND MID$(origdividend$, j2&&, 1) = "" THEN betatemp2$ = CHR$(34) + CHR$(34) ELSE IF betatest% THEN betatemp2$ = MID$(origdividend$, j2&&, 1)
IF betatest% < 0 THEN PRINT dividend$; " ("; betatemp$; " + "; drop$; ") at:"; j2&&; "of "; origdividend$; " Loop"; k&& + 1; "Quotent = ";: COLOR 14, 4: PRINT q$;: COLOR 7, 0: PRINT: SLEEP
' Check to terminate
IF div_decimal% = -1 THEN
' Decimal to left.
IF remainder$ = "" AND MID$(origdividend$, j2&&, 1) = "" OR LEN(q$) >= limit&& THEN EXIT DO
ELSE
' Decimal to right.
IF remainder$ = "" AND MID$(origdividend$, j2&&, 1) = "" AND k&& >= dp&& OR LEN(q$) >= limit&& THEN EXIT DO
END IF
IF INKEY$ = " " THEN EXIT DO
k&& = k&& + 1
LOOP
EXIT DO
LOOP
IF RIGHT$(q$, 1) = "." AND divisor$ <> "0" THEN runningtotal$ = MID$(q$, 1, LEN(q$) - 1) ELSE runningtotal$ = q$
sm_div$ = runningtotal$
stringmatha$ = hold_stringmatha$: stringmathb$ = hold_stringmathb$
END FUNCTION
SUB greatest_common_factor (gfca$, gfcb$)
IF betatest% < 0 THEN PRINT "Pre-GFC "; gfca$; " / "; gfcb$
numerator$ = gfca$: denominator$ = gfcb$
' Make both numbers positive.
IF MID$(gfca$, 1, 1) = "-" THEN gfca$ = MID$(gfca$, 2)
IF MID$(gfcb$, 1, 1) = "-" THEN gfcb$ = MID$(gfcb$, 2)
CALL sm_greater_lesser(gfca$, gfcb$, gl%)
IF gl% THEN SWAP gfca$, gfcb$
DO
stringmatha$ = gfca$: stringmathb$ = gfcb$
runningtotal$ = sm_div$(stringmatha$, stringmathb$)
IF INSTR(runningtotal$, ".") THEN runningtotal$ = MID$(runningtotal$, 1, INSTR(runningtotal$, ".") - 1)
stringmatha$ = runningtotal$: stringmathb$ = gfcb$
runningtotal$ = sm_mult$(stringmatha$, stringmathb$)
stringmatha$ = gfca$: stringmathb$ = runningtotal$
runningtotal$ = sm_sub$(stringmatha$, stringmathb$)
SWAP gfca$, gfcb$: gfcb$ = runningtotal$
IF runningtotal$ = "0" THEN EXIT DO
LOOP
stringmatha$ = numerator$: stringmathb$ = gfca$
IF betatest% < 0 THEN PRINT "GFC = "; gfca$
numerator$ = sm_div$(stringmatha$, stringmathb$)
stringmatha$ = denominator$: stringmathb$ = gfca$
denominator$ = sm_div$(stringmatha$, stringmathb$)
gfca$ = numerator$: gfcb$ = denominator$ ' Needed to pass back.
IF betatest% < 0 THEN PRINT "Fraction: "; numerator$; " / "; denominator$
END SUBPete
RE: Roots and powers playing nicely together... - Pete - 09-30-2022
Next is to try and figure out how to handle powers like .03, .005, etc. Right now, .zero any power will cause the system to crash.
Pete
RE: Roots and powers playing nicely together... - bplus - 09-30-2022
Pete can you do x^1/100? Then x^.03 = x ^ 1/100 * x ^ 1/100 * x ^ 1/100, I think?
Yah