09-16-2022, 06:22 AM
Okay, here is a combo of decimal powers and general roots using the formula ...
...provided by @Kernelpanic in a previous post. Too tired tonight to test out much tonight, but I know it will be littered with rounding errors like cube root of 125 = 4.999something.
Pete
Code: (Select All)
x ^ (1 / n)...provided by @Kernelpanic in a previous post. Too tired tonight to test out much tonight, but I know it will be littered with rounding errors like cube root of 125 = 4.999something.
Code: (Select All)
WIDTH 170, 42
_SCREENMOVE 0, 0
DIM SHARED limit&&, betatest%
limit&& = 32
betatest% = 0
DO
PRINT "Press 1 for general roots or 2 for decimal powers: ";
DO
_LIMIT 30
k$ = INKEY$
IF LEN(k$) THEN
IF k$ = CHR$(27) THEN SYSTEM
IF k$ = "1" OR k$ = "2" THEN EXIT DO
END IF
LOOP
PRINT k$: PRINT
SELECT CASE k$
CASE "1"
LINE INPUT "Number: "; num$
LINE INPUT "Root: "; root$
temp$ = sm_div$("1", root$)
PRINT sm_pow$(num$, temp$)
PRINT
CASE "2"
LINE INPUT "Number: "; num$
LINE INPUT "Power: "; power$
PRINT sm_pow$(num$, power$)
PRINT
END SELECT
LOOP
SUB sm_greater_lesser (stringmatha$, 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 j% THEN
dp&& = dp&& - div_decimal%
IF betatest% THEN PRINT "Larger divisor than dividend at LEN(divisor$), so move quotent decimal one place back to: ";: COLOR 14: PRINT LTRIM$(STR$(dp&&)): COLOR 7
ELSE
IF betatest% THEN PRINT "Smaller divisor than dividend at LEN(divisor$), 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
FUNCTION sm_sqrt$ (sm_var$)
oldy$ = "": sqrt$ = "": custom_limit&& = limit&&: REM IF limit&& < 150 THEN custom_limit&& = 150 ELSE custom_limit&& = limit&&
sqrt_a$ = sm_var$
IF INSTR(sqrt_a$, ".") THEN
decx$ = MID$(sqrt_a$, 1, INSTR(sqrt_a$, ".") - 1)
sqrt_a$ = MID$(sqrt_a$, 1, INSTR(sqrt_a$, ".") - 1) + MID$(sqrt_a$, INSTR(sqrt_a$, ".") + 1)
IF LEN(sqrt_a$) = 1 THEN sqrt_a$ = sqrt_a$ + "0"
ELSE
decx$ = sqrt_a$
END IF
j&& = LEN(decx$)
' VAL() okay, one character eval.
IF VAL(RIGHT$(LTRIM$(STR$(j&&)), 1)) / 2 = VAL(RIGHT$(LTRIM$(STR$(j&&)), 1)) \ 2 THEN
i&& = 1 ' Even number length.
ELSE
i&& = 0 ' Odd number length.
END IF
DO
runningtotal$ = sm_sub$(z$, k$)
z$ = runningtotal$ + (MID$(sqrt_a$, 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
y$ = sm_mult$(sqrt$, "2")
y$ = y$ + LTRIM$(STR$(j&&))
ELSE
y$ = LTRIM$(STR$(j&&))
END IF
runningtotal$ = sm_mult$(y$, LTRIM$(STR$(j&&)))
sm_greater_lesser runningtotal$, z$, gl%
IF gl% > -1 THEN
IF gl% = 0 THEN
h% = 0: oldy$ = y$ ' Perfect square division.
ELSE
h% = 1
END IF
runningtotal$ = sm_mult$(oldy$, LTRIM$(STR$(j&& - h%)))
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%))
runningtotal$ = sm_mult$(oldy$, LTRIM$(STR$(j&& - h%)))
k$ = runningtotal$
IF betatest% < -1 THEN PRINT "Remainder "; z$; " minus "; k$; " = ";
EXIT FOR
END IF
oldy$ = y$
NEXT
i&& = i&& + 2
IF LEN(z$) >= custom_limit&& THEN EXIT DO
sqrt_a$ = sqrt_a$ + "00"
LOOP
IF dpx&& THEN sqrt$ = MID$(sqrt$, 0, dpx&& + 1) + "." + MID$(sqrt$, dpx&& + 1)
sm_sqrt$ = sqrt$
END FUNCTION
FUNCTION sm_pow$ (num$, power$)
IF INSTR(power$, ".") THEN
t$ = MID$(power$, INSTR(power$, "."))
power$ = MID$(power$, 1, INSTR(power$, ".") - 1)
a$ = "1"
b$ = num$
x$ = "0"
y$ = "1"
highc$ = b$
lowc$ = a$
highz$ = "1"
DO
t1$ = sm_mult$(a$, b$)
c$ = sm_sqrt$(t1$)
t1$ = sm_add(x$, y$)
z$ = sm_div(t1$, "2")
sm_greater_lesser z$, t$, gl%
IF gl% >= 0 THEN
highz$ = z$: highc$ = c$
ELSEIF gl% = -1 THEN
lowz$ = z$: lowc$ = c$
END IF
REM PRINT a$, b$, highc$, lowc$, z$, highz$, lowz$
a$ = highc$: b$ = lowc$
x$ = highz$: y$ = lowz$
LOOP UNTIL gl% = 0
IF LEN(power$) THEN
'a = num ^ VAL(power$) * a
temp$ = num$
FOR i&& = 1 TO VAL(power$) - 1
temp2$ = sm_mult$(temp$, num$): temp$ = temp2$
NEXT
a$ = sm_mult$(temp2$, a$)
END IF
ELSE
'num ^ VAL(power$)
temp$ = num$
FOR i&& = 1 TO VAL(power$) - 1
a$ = sm_mult$(temp$, num$): temp$ = a$
NEXT
END IF
sm_pow$ = a$
END FUNCTIONPete