I've seen online calculators that do this:
1 / 3 * 3 = .999...
and this:
1 / 3 * 3 = 1
Obviously, the second one takes into account 1 / 3 as an infinite repetend. So I was wondering if there was some algorithm I could apply to properly round all repetend situations. Well, I punted on that concept, as to identify a repetend that goes over 10,000 digits before repeating the number sequence, simply takes too much calculation time. Not to mention how far can we go? After all, Pi is a transcendental number, so that could take an eternity... or an eternity and a half, if you're using FreeBASIC.
So, I decided to approach this problem by going old-school. Although decimals can never be depended on to divide and multiply back symmetrically, fractions can. So I designed a string math calculator system that works with numerators and denominators, but displays the results in decimal form.
This is roughed out, which means I did not put much thought into variable and line number names, tricks to speed it up, or extensive optimization. Goal #1 for me is to always get it working, and I think this is either close or does meet my first goal...
Pete
1 / 3 * 3 = .999...
and this:
1 / 3 * 3 = 1
Obviously, the second one takes into account 1 / 3 as an infinite repetend. So I was wondering if there was some algorithm I could apply to properly round all repetend situations. Well, I punted on that concept, as to identify a repetend that goes over 10,000 digits before repeating the number sequence, simply takes too much calculation time. Not to mention how far can we go? After all, Pi is a transcendental number, so that could take an eternity... or an eternity and a half, if you're using FreeBASIC.
So, I decided to approach this problem by going old-school. Although decimals can never be depended on to divide and multiply back symmetrically, fractions can. So I designed a string math calculator system that works with numerators and denominators, but displays the results in decimal form.
This is roughed out, which means I did not put much thought into variable and line number names, tricks to speed it up, or extensive optimization. Goal #1 for me is to always get it working, and I think this is either close or does meet my first goal...
Code: (Select All)
DIM SHARED betatest%
REM betatest% = -1
WIDTH 160, 42
_SCREENMOVE 0, 0
DIM SHARED operator$, stringmatha$, stringmathb$, runningtotal$, limit&&
start:
display_as&& = 15
limit&& = 100
DO
IF sa$ = "" OR LEN(op$) THEN
LINE INPUT "Number: "; n$
IF op$ = "" THEN
sa$ = n$
ELSE
sb$ = n$
GOSUB calculate
op$ = ""
END IF
ELSE
' Input operation.
PRINT "[+-*/]: ";
DO
_LIMIT 30
mykey$ = INKEY$
IF LEN(mykey$) THEN
SELECT CASE mykey$
CASE "+", "="
op$ = "+": EXIT DO
CASE "-", "_"
op$ = "-": EXIT DO
CASE "*", "8"
op$ = "*": EXIT DO
CASE "/", "?"
op$ = "/": EXIT DO
CASE "c", "C"
PRINT: PRINT "Total = 0": CLEAR: GOTO start
CASE CHR$(27)
SYSTEM
END SELECT
END IF
LOOP
PRINT op$
END IF
LOOP
calculate:
SELECT CASE op$
CASE "+", "-"
IF nator_a$ = "" THEN
nator_a$ = sa$: nator_b$ = sb$
dator_a$ = "1": dator_b$ = "1"
ELSE
nator_b$ = sb$: dator_b$ = "1"
END IF
IF INSTR(nator_a$, ".") THEN
n$ = nator_a$
GOSUB convert_to_fraction
nator_a$ = numerator$: dator_a$ = denominator$
END IF
IF INSTR(sb$, ".") THEN
n$ = sb$
GOSUB convert_to_fraction
nator_b$ = numerator$: dator_b$ = denominator$
ELSE
nator_b$ = sb$: dator_b$ = "1"
END IF
' Cross multiply
IF dator_a$ <> datorb$ THEN
stringmatha$ = nator_a$: stringmathb$ = dator_b$: operator$ = "*"
CALL string_math
a$ = runningtotal$
stringmatha$ = dator_a$: stringmathb$ = dator_b$: operator$ = "*"
CALL string_math
dator_c$ = runningtotal$ ' Common denominator.
stringmatha$ = nator_b$: stringmathb$ = dator_a$: operator$ = "*"
CALL string_math
b$ = runningtotal$
stringmatha$ = a$: stringmathb$ = b$: operator$ = op$
CALL string_math
nator_c$ = runningtotal$
END IF
CASE "*"
IF nator_a$ = "" THEN
nator_a$ = sa$: nator_b$ = sb$
dator_a$ = "1": dator_b$ = "1"
ELSE
nator_b$ = sb$: dator_b$ = "1"
END IF
IF INSTR(nator_a$, ".") THEN
n$ = nator_a$
GOSUB convert_to_fraction
nator_a$ = numerator$: dator_a$ = denominator$
END IF
IF INSTR(sb$, ".") THEN
n$ = sb$
GOSUB convert_to_fraction
nator_b$ = numerator$: dator_b$ = denominator$
ELSE
nator_b$ = sb$: dator_b$ = "1"
END IF
stringmatha$ = nator_a$: stringmathb$ = nator_b$: operator$ = "*"
CALL string_math
nator_c$ = runningtotal$
stringmatha$ = dator_a$: stringmathb$ = dator_b$: operator$ = "*"
CALL string_math
dator_c$ = runningtotal$
CASE "/"
IF nator_a$ = "" THEN
nator_a$ = sa$: nator_b$ = sb$
dator_a$ = "1": dator_b$ = "1"
ELSE
nator_b$ = sb$: dator_b$ = "1"
END IF
IF INSTR(nator_a$, ".") THEN
n$ = nator_a$
GOSUB convert_to_fraction
nator_a$ = numerator$: dator_a$ = denominator$
END IF
IF INSTR(sb$, ".") THEN
n$ = sb$
GOSUB convert_to_fraction
nator_b$ = numerator$: dator_b$ = denominator$
ELSE
nator_b$ = sb$: dator_b$ = "1"
END IF
SWAP nator_b$, dator_b$
stringmatha$ = nator_a$: stringmathb$ = nator_b$: operator$ = "*"
CALL string_math
nator_c$ = runningtotal$
stringmatha$ = dator_a$: stringmathb$ = dator_b$: operator$ = "*"
CALL string_math
dator_c$ = runningtotal$
END SELECT
IF betatest% THEN
PRINT "nator_a$: "; nator_a$
PRINT "dator_a$: "; dator_a$
PRINT "nator_b$: "; nator_b$
PRINT "dator_b$: "; dator_b$
PRINT "nator_c$: "; nator_c$
PRINT "dator_c$: "; dator_c$
END IF
a$ = nator_c$: b$ = dator_c$: GOSUB greatest_common_factor
nator_c$ = numerator$: dator_c$ = denominator$
stringmatha$ = nator_c$: stringmathb$ = dator_c$: operator$ = "/"
CALL string_math
sa$ = runningtotal$
COLOR 15, 0: PRINT:
IF LEFT$(sa$, 1) = "-" THEN PRINT "Total: "; sa$ ELSE PRINT "Total: "; sa$
COLOR 7, 0
nator_a$ = nator_c$
dator_a$ = dator_c$
IF betatest% THEN COLOR 2, 0: PRINT: PRINT "nator_a$ ="; nator_a$, "dator_a$ = "; dator_a$: PRINT: COLOR 7, 0
RETURN
'=================================================================================
convert_to_fraction:
i = 0: j = 0: k = 0: msg$ = ""
IF MID$(n$, 1, 1) = "-" THEN j = 3 ELSE j = 2 ' Look for negative sign.
x1$ = MID$(n$, 1, INSTR(n$, ".") - 1)
IF j = 3 THEN x1$ = MID$(x1$, 2)
x2$ = MID$(n$, INSTR(n$, ".") + 1)
b$ = "1" + STRING$(LEN(x2$), "0")
x1$ = x1$ + x2$
DO UNTIL LEFT$(x1$, 1) <> "0"
x1$ = MID$(x1$, 2) ' Strip off any leading zeros
LOOP
IF j = 2 THEN a$ = x1$ ELSE a$ = "-" + x1$
z$ = ""
IF betatest% THEN PRINT "numerator and denomintor: "; a$, b$
numerator$ = a$: denominator$ = b$
RETURN
greatest_common_factor:
' GFC algorithm. -------------------------------------------------------------
gfca$ = a$: gfcb$ = b$
IF betatest% THEN PRINT "PRE GFC "; a$; " / "; b$
' Make both numbers positive.
IF MID$(gfca$, 1, 1) = "-" THEN gfca$ = MID$(gfca$, 2)
IF MID$(gfcb$, 1, 1) = "-" THEN gfcb$ = MID$(gfcb$, 2)
' STRING MATH < or > EVAL NOT NEEDED AS NEG NUMBERS ARE CONVERTED TO POS AND NO CHANCE OF 0 AND < 1 > 0 LIKE 0 AND .1 OCCURRING.
IF gfca$ < gfcb$ THEN SWAP gfca$, gfcb$
' MOD operation in string math.
DO
stringmatha$ = gfca$: stringmathb$ = gfcb$
operator$ = "/": CALL string_math
m1$ = runningtotal$
IF INSTR(m1$, ".") THEN m1$ = MID$(m1$, 1, INSTR(m1$, ".") - 1)
stringmatha$ = m1$
stringmathb$ = gfcb$
operator$ = "*": CALL string_math
m2$ = runningtotal$
stringmatha$ = gfca$: stringmathb$ = m2$
operator$ = "-": CALL string_math
SWAP gfca$, gfcb$: gfcb$ = runningtotal$
IF runningtotal$ = "0" THEN EXIT DO
LOOP
stringmatha$ = a$: stringmathb$ = gfca$
operator$ = "/": CALL string_math
numerator$ = runningtotal$
stringmatha$ = b$: stringmathb$ = gfca$
operator$ = "/": CALL string_math
denominator$ = runningtotal$
IF betatest% THEN COLOR 14, 0: PRINT "GFC "; numerator$; " / "; denominator$: COLOR 7, 0
RETURN
'===============================================================================
SUB string_math
SELECT CASE operator$
CASE "+", "-"
GOTO string_add_subtract
CASE "*"
GOTO string_multiply
CASE "/"
GOTO string_divide
CASE ELSE
PRINT "Error, no operator selected. operator$ = "; operator$
END SELECT
string_divide:
divsign% = 0 '''''''''''''''
divremainder& = 0: divremainder$ = "": divplace& = 0 AND 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$) = 1 THEN PRINT "Division by zero not allowed.": divsign% = 0: operationdivision% = 0: EXIT SUB: RETURN '*'
IF LEFT$(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: EXIT DO
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
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
operator$ = "-"
stringmatha$ = divremainder$
stringmathb$ = m_product$
GOSUB string_add_subtract
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$: quotient$ = ""
'''GOSUB limit_round_convert
IF stringmathb$ = "overflow" THEN divsign% = 0: operationdivision% = 0: EXIT SUB: RETURN '*'
'''GOSUB sm_converter
runningtotal$ = stringmathb$: stringmathb$ = ""
IF divsign% THEN runningtotal$ = "-" + runningtotal$
IF stringmathround$ <> "" THEN runningtotal$ = runningtotal$ + stringmathround$
operationdivision% = 0 '''''
EXIT SUB ''' or RETURN to select case if goto changed to gosub.
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$) TO 1 STEP -1 ' Multiply each charter top and bottom.
m_k& = m_l&
m_x2$ = 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$: m_product$ = ""
'''GOSUB limit_round_convert
IF stringmathb$ = "overflow" THEN EXIT SUB: RETURN '*'
'''GOSUB sm_converter
runningtotal$ = stringmathb$: stringmathb$ = ""
IF m_sign% THEN runningtotal$ = "-" + runningtotal$: m_sign% = 0
EXIT SUB ''' or RETURN to select case if goto changed to gosub.
string_add_subtract:
IF INSTR(stringmatha$, ".") <> 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)
IF VAL(stringmathb$) > VAL(stringmatha$) 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)
IF VAL(stringmathb$) > VAL(stringmatha$) THEN SWAP stringmatha$, stringmathb$ ELSE 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
''' GOSUB limit_round_convert
IF stringmathb$ = "overflow" THEN n2sign$ = "": EXIT SUB: RETURN '*'
''' GOSUB sm_converter
runningtotal$ = n2sign$ + stringmathb$: n2sign$ = ""
EXIT SUB ''' or RETURN to select case if goto changed to gosub.
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
END SUBPete