08-21-2022, 09:28 PM
WOW! this is great. I fixed two bugs in my new string math routine after rigorous testing by incorporating it into my square root calculator. Then I substituted the debugged code to the square root calculator and the speed improvement was blinding!
So I did a test on the square root of 2 to 5,000 places. It only took 45 seconds on my slow clunky laptop. If you like to try that out, change the limit&& variable to 5000, run the program, and input 2 at the number prompt.
Anyway, here's the square root program with the my new faster bulk number processing string math system.
Pete
So I did a test on the square root of 2 to 5,000 places. It only took 45 seconds on my slow clunky laptop. If you like to try that out, change the limit&& variable to 5000, run the program, and input 2 at the number prompt.
Anyway, here's the square root program with the my new faster bulk number processing string math system.
Code: (Select All)
WIDTH 160, 42
_SCREENMOVE 0, 0
DO
limit&& = 128
'betatest% = -1
IF betatest% THEN limit&& = 16
DO
INPUT "Number: "; x$: PRINT
IF x$ = "" THEN SYSTEM
IF LEFT$(x$, 1) = "-" THEN
PRINT "Negatives not allowed. Redo..": _DELAY 2: PRINT
ELSE
validate_string x$
IF INSTR(x$, "invalid") = 0 THEN EXIT DO
PRINT "Sorry, "; x$: _DELAY 1: PRINT
END IF
LOOP
x# = VAL(x$) ' Needed for QB64 SQR() comparison only.
oldy$ = ""
IF INSTR(x$, ".") THEN
decx$ = MID$(x$, 1, INSTR(x$, ".") - 1)
x$ = MID$(x$, 1, INSTR(x$, ".") - 1) + MID$(x$, INSTR(x$, ".") + 1)
IF LEN(x$) = 1 THEN x$ = x$ + "0"
ELSE
decx$ = x$
END IF
j&& = LEN(decx$)
' VAL() okay, one character eval.
IF VAL(RIGHT$(LTRIM$(STR$(j&&)), 1)) / 2 = VAL(RIGHT$(LTRIM$(STR$(j&&)), 1)) \ 2 THEN
i&& = 1 ' Even number length.
ELSE
i&& = 0 ' Odd number length.
END IF
DO
stringmatha$ = z$: stringmathb$ = k$
string_math z$, "-", k$, runningtotal$, terminating_decimal%, limit&&
z$ = runningtotal$ + (MID$(x$, i&&, 2))
IF LEFT$(z$, 1) = "0" THEN z$ = MID$(z$, 2) ' Remove leading zeros
oldy$ = ""
FOR j&& = 1 TO 10
IF i&& > 1 THEN
string_math sqrt$, "*", "2", y$, terminating_decimal%, limit&&
y$ = y$ + LTRIM$(STR$(j&&))
ELSE
y$ = LTRIM$(STR$(j&&))
END IF
string_math y$, "*", LTRIM$(STR$(j&&)), runningtotal$, terminating_decimal%, limit&&
string_compare runningtotal$, z$, gl%
IF gl% > -1 THEN
IF gl% = 0 THEN
h% = 0: oldy$ = y$ ' Perfect square division.
ELSE
h% = 1
END IF
string_math oldy$, "*", LTRIM$(STR$(j&& - h%)), runningtotal$, terminating_decimal%, limit&&
IF STRING$(LEN(z$), "0") = z$ AND runningtotal$ = "0" AND i&& >= LEN(decx$) THEN EXIT DO
IF dp&& = 0 THEN ' Limited to && size unless converted to string.
IF i&& >= LEN(decx$) THEN
dp&& = INT(LEN(decx$) / 2 + .5)
IF dp&& = 0 THEN dp&& = -1
END IF
END IF
IF betatest% THEN PRINT "Sqrt "; sqrt$; " * 2 = ";: COLOR 2, 0: PRINT LTRIM$(STR$(VAL(sqrt$) * 2));: COLOR 7, 0: PRINT LTRIM$(STR$(j&& - h%)); " * "; LTRIM$(STR$(j&& - h%)); " ="; VAL(oldy$) * (j&& - h%)
sqrt$ = sqrt$ + LTRIM$(STR$(j&& - h%))
string_math oldy$, "*", LTRIM$(STR$(j&& - h%)), runningtotal$, terminating_decimal%, limit&&
k$ = runningtotal$
IF betatest% THEN PRINT "Remainder "; z$; " minus "; k$; " = ";
EXIT FOR
END IF
oldy$ = y$
NEXT
IF betatest% THEN
string_math stringmatha$, "-", stringmathb$, runningtotal$, terminating_decimal%, limit&&
PRINT runningtotal$; " sqrt = "; sqrt$
END IF
i&& = i&& + 2
IF LEN(z$) >= limit&& THEN EXIT DO
x$ = x$ + "00"
LOOP
PRINT
IF dp&& THEN
sqrt$ = MID$(sqrt$, 0, dp&& + 1) + "." + MID$(sqrt$, dp&& + 1)
END IF
_CLIPBOARD$ = sqrt$
PRINT "QB64 SQR:"; SQR(x#)
PRINT "Pete SQR: "; sqrt$: _DELAY 1: CLEAR
PRINT
LOOP
SUB string_math (stringmatha$, operator$, stringmathb$, runningtotal$, terminating_decimal%, limit&&)
DIM AS _INTEGER64 a, b, c, aa, bb, cc, s, ss
a1$ = stringmatha$: b1$ = stringmathb$
SELECT CASE operator$
CASE "+", "-"
GOTO string_add_subtract_new
CASE "*"
GOTO string_multiply_new
CASE "/"
GOTO string_divide
CASE ELSE
PRINT "Error, no operator selected. operator$ = "; operator$
END SELECT
string_divide:
terminating_decimal% = 0: divsign% = 0: divremainder& = 0: divremainder$ = "": divplace& = 0: divplace2& = 0: quotient$ = "": divcarry& = 0
operationdivision% = -1
divbuffer& = LEN(stringmathb$) - LEN(stringmatha$)
IF divbuffer& < 0 THEN divbuffer& = 0
d2dividend$ = stringmatha$
d1divisor$ = stringmathb$
IF LEFT$(d1divisor$, 1) = "0" AND LEN(d1divisor$) = 1 THEN PRINT "Division by zero not allowed.": divsign% = 0: operationdivision% = 0: EXIT SUB
IF LEFT$(d1divisor$, 1) = "-" THEN divsign% = -1: d1divisor$ = MID$(d1divisor$, 2)
IF LEFT$(d2dividend$, 1) = "-" THEN
IF divsign% THEN
divsign% = 0
ELSE
divsign% = -1
END IF
d2dividend$ = MID$(d2dividend$, 2)
END IF
IF INSTR(d1divisor$, ".") <> 0 THEN
DO UNTIL RIGHT$(d1divisor$, 1) <> "0"
d1divisor$ = MID$(d1divisor$, 1, LEN(d1divisor$) - 1) ' Strip off trailing zeros
LOOP
divplace& = LEN(d1divisor$) - INSTR(d1divisor$, ".")
d1divisor$ = MID$(d1divisor$, 1, INSTR(d1divisor$, ".") - 1) + MID$(d1divisor$, INSTR(d1divisor$, ".") + 1) ' Strip off decimal point.
DO UNTIL LEFT$(d1divisor$, 1) <> "0"
d1divisor$ = MID$(d1divisor$, 2) ' Strip off leading zeros for divisors smaller than .1
LOOP
END IF
IF INSTR(d2dividend$, ".") <> 0 THEN
d2dividend$ = d2dividend$ + STRING$(divplace& - LEN(d2dividend$) - INSTR(d2dividend$, "."), "0") ' Add any zeros based on the length of dividend at decimal - length of divisor at decimal. If less than zero, nothing added.
divplace2& = INSTR(d2dividend$, ".")
DO UNTIL RIGHT$(d2dividend$, 1) <> "0"
d2dividend$ = MID$(d2dividend$, 1, LEN(d2dividend$) - 1) ' Strip off trailing zeros
LOOP
d2dividend$ = MID$(d2dividend$, 1, INSTR(d2dividend$, ".") - 1) + MID$(d2dividend$, INSTR(d2dividend$, ".") + 1) ' Strip off decimal point.
ELSE
d2dividend$ = d2dividend$ + STRING$(divplace&, "0") ' Add any zeros based on the length of dividend at decimal - length of divisor at decimal. If less than zero, nothing added.
divplace& = 0
END IF
DO
DO
divremainder& = divremainder& + 1: divremainder$ = divremainder$ + MID$(d2dividend$, divremainder&, 1)
IF MID$(d2dividend$, divremainder&, 1) = "" THEN
IF divremainder$ = STRING$(LEN(divremainder$), "0") AND LEN(quotient$) > LEN(d2dividend$) THEN
divflag% = -1
terminating_decimal% = -1
EXIT DO
END IF
divcarry& = divcarry& + 1
IF divcarry& = 1 THEN divplace3& = divremainder& - 1
IF divcarry& > limit&& + 1 + divbuffer& THEN
divflag% = -2: EXIT DO
END IF
divremainder$ = divremainder$ + "0" ' No more digits to bring down.
END IF
IF LEN(divremainder$) > LEN(d1divisor$) OR LEN(divremainder$) = LEN(d1divisor$) AND divremainder$ >= d1divisor$ THEN EXIT DO
quotient$ = quotient$ + "0"
LOOP
IF divflag% THEN divflag% = 0: EXIT DO
FOR div_i% = 9 TO 1 STEP -1
stringmatha$ = LTRIM$(STR$(div_i%)): stringmathb$ = d1divisor$
m_product$ = "": GOSUB string_multiply_new
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_new
operator$ = "-"
stringmatha$ = divremainder$
stringmathb$ = m_product$
GOSUB string_add_subtract_new
divremainder$ = stringmatha$
operator$ = "/"
LOOP
IF divplace& = 0 AND divplace2& = 0 THEN divplace& = divplace3&
IF divplace2& THEN divplace& = divplace& + divplace2& - 1
IF quotient$ = "" THEN divplace& = 0 ' dividend is zero.
IF divplace& OR divplace2& THEN
quotient$ = MID$(quotient$, 1, divplace&) + "." + MID$(quotient$, divplace& + 1)
DO UNTIL RIGHT$(quotient$, 1) <> "0"
quotient$ = MID$(quotient$, 1, LEN(quotient$) - 1) ' Strip off trailing zeros
LOOP
IF RIGHT$(quotient$, 1) = "." THEN quotient$ = MID$(quotient$, 1, LEN(quotient$) - 1) ' Strip off abandoned decimal.
END IF
DO UNTIL LEFT$(quotient$, 1) <> "0"
quotient$ = MID$(quotient$, 2) ' Strip off leading zeros
LOOP
IF quotient$ = "" THEN quotient$ = "0": divsign% = 0
operationdivision% = 0
stringmathb$ = quotient$: quotient$ = ""
IF stringmathb$ = "overflow" THEN divsign% = 0: operationdivision% = 0: EXIT SUB
runningtotal$ = stringmathb$: stringmathb$ = ""
IF divsign% THEN runningtotal$ = "-" + runningtotal$
IF stringmathround$ <> "" THEN runningtotal$ = runningtotal$ + stringmathround$
operationdivision% = 0
EXIT SUB
'------------------------------------------------------------------------
string_add_subtract_new:
s = 18
a$ = stringmatha$: b$ = stringmathb$: op$ = operator$
IF op$ = "-" THEN
IF LEFT$(b$, 1) = "-" THEN b$ = MID$(b$, 2) ELSE b$ = "-" + b$
END IF
IF INSTR(a$, ".") <> 0 OR INSTR(b$, ".") <> 0 THEN
decimal% = -1
IF INSTR(a$, ".") <> 0 THEN
dec_a&& = LEN(MID$(a$, INSTR(a$, ".") + 1))
a$ = MID$(a$, 1, INSTR(a$, ".") - 1) + MID$(a$, INSTR(a$, ".") + 1)
END IF
IF INSTR(b$, ".") <> 0 THEN
dec_b&& = LEN(MID$(b$, INSTR(b$, ".") + 1))
b$ = MID$(b$, 1, INSTR(b$, ".") - 1) + MID$(b$, INSTR(b$, ".") + 1)
END IF
' Line up decimal places by inserting trailing zeros.
IF dec_b&& > dec_a&& THEN
j&& = dec_b&&
a$ = a$ + STRING$(dec_b&& - dec_a&&, "0")
ELSE
j&& = dec_a&&
b$ = b$ + STRING$(dec_a&& - dec_b&&, "0")
END IF
END IF
IF LEFT$(a$, 1) = "-" OR LEFT$(b$, 1) = "-" THEN
IF LEFT$(a$, 1) = "-" AND LEFT$(b$, 1) = "-" THEN
sign$ = "--": a$ = MID$(a$, 2): b$ = MID$(b$, 2)
ELSE
IF LEFT$(a$, 1) = "-" THEN a$ = MID$(a$, 2): sign_a$ = "-"
IF LEFT$(b$, 1) = "-" THEN b$ = MID$(b$, 2): sign_b$ = "-"
IF LEFT$(a1$, 1) = "-" THEN a1_x$ = MID$(a1$, 2) ELSE a1_x$ = a1$
IF LEFT$(b1$, 1) = "-" THEN b1_x$ = MID$(b1$, 2) ELSE b1_x$ = b1$
string_compare a1_x$, b1_x$, gl%
IF gl% < 0 THEN
IF LEN(sign_b$) THEN sign$ = "-": SWAP a$, b$
ELSE
IF LEN(sign_a$) THEN sign$ = "-": SWAP sign_a$, sign_b$
END IF
END IF
END IF
s = 18: z$ = ""
DO
i&& = i&& + s
x1$ = MID$(a$, LEN(a$) - i&& + 1, s)
x2$ = MID$(b$, LEN(b$) - i&& + 1, s)
a = VAL(sign_a$ + x1$) + VAL(sign_b$ + x2$) + c
IF x1$ + x2$ = "" AND c = 0 THEN EXIT DO
c = 0
IF a > VAL(STRING$(s, "9")) THEN a = a - 10 ^ s: c = 1
IF a < 0 THEN a = a + 10 ^ s: c = -1
tmp$ = LTRIM$(STR$(a))
z$ = STRING$(LEN(x1$) - LEN(tmp$), "0") + tmp$ + z$
LOOP
IF decimal% THEN
z$ = MID$(z$, 1, LEN(z$) - j&&) + "." + MID$(z$, LEN(z$) - j&& + 1)
END IF
' Remove any leading zeros.
DO
IF LEFT$(z$, 1) = "0" THEN z$ = MID$(z$, 2) ELSE EXIT DO
LOOP
IF z$ = "" OR z$ = "0" THEN z$ = "0" ELSE z$ = LEFT$(sign$, 1) + z$
runningtotal$ = z$ '*'
sign$ = "": sign_a$ = "": sign_b$ = "": i&& = 0: j&& = 0: decimal% = 0: c = 0
EXIT SUB
'------------------------------------------------------------------------
string_multiply_new:
z$ = "": sign$ = "": mult&& = 0: h&& = 0: i&& = 0: j&& = 0: c = 0: decimal% = 0
zz$ = "": ii&& = 0: jj&& = 0
s = 8: ss = 18
a$ = stringmatha$: b$ = stringmathb$
IF INSTR(a$, "-") <> 0 OR INSTR(b$, "-") <> 0 THEN
IF INSTR(a$, "-") <> 0 AND INSTR(b$, "-") <> 0 THEN
a$ = MID$(a$, 2): b$ = MID$(b$, 2)
ELSE
IF INSTR(a$, "-") <> 0 THEN a$ = MID$(a$, 2) ELSE b$ = MID$(b$, 2)
sign$ = "-"
END IF
END IF
IF INSTR(a$, ".") <> 0 OR INSTR(b$, ".") <> 0 THEN
decimal% = -1
IF INSTR(a$, ".") <> 0 THEN
dec_a&& = LEN(MID$(a$, INSTR(a$, ".") + 1))
a$ = MID$(a$, 1, INSTR(a$, ".") - 1) + MID$(a$, INSTR(a$, ".") + 1)
END IF
IF INSTR(b$, ".") <> 0 THEN
dec_b&& = LEN(MID$(b$, INSTR(b$, ".") + 1))
b$ = MID$(b$, 1, INSTR(b$, ".") - 1) + MID$(b$, INSTR(b$, ".") + 1)
END IF
END IF
DO
h&& = h&& + s: i&& = 0
x2$ = MID$(b$, LEN(b$) - h&& + 1, s)
WHILE -1
i&& = i&& + s
x1$ = MID$(a$, LEN(a$) - i&& + 1, s)
a = VAL(sign_a$ + x1$) * VAL(sign_b$ + x2$) + c
IF betatest% THEN PRINT "x1$ = "; x1$;: LOCATE , 20: PRINT "x2$ = "; x2$;: LOCATE , 35: PRINT VAL(x1$) * VAL(x2$) + c;: LOCATE , 55: PRINT "c = "; c;: LOCATE , 75: PRINT "val = "; a,
c = 0
tmp$ = LTRIM$(STR$(a))
IF LEN(tmp$) > s THEN c = VAL(MID$(tmp$, 1, LEN(tmp$) - s)): tmp$ = MID$(tmp$, LEN(tmp$) - s + 1)
z$ = STRING$(LEN(x1$) - LEN(tmp$), "0") + tmp$ + z$
IF betatest% THEN LOCATE , 100: PRINT a;: LOCATE , 120: PRINT z$
IF i&& >= LEN(a$) AND c = 0 THEN EXIT WHILE
WEND
jj&& = jj&& + 1
IF jj&& > 1 THEN
ii&& = 0: cc = 0
aa$ = holdaa$
bb$ = z$ + STRING$((jj&& - 1) * s, "0")
IF betatest% THEN PRINT "aa$ "; aa$; " + bb$ "; z$;: COLOR 14, 0: PRINT STRING$(jj&& - 1, "0"); " = ";: COLOR 7, 0: SLEEP
DO
ii&& = ii&& + ss
xx1$ = MID$(aa$, LEN(aa$) - ii&& + 1, ss)
xx2$ = MID$(bb$, LEN(bb$) - ii&& + 1, ss)
aa = VAL(xx1$) + VAL(xx2$) + cc
IF xx1$ + xx2$ = "" AND cc = 0 THEN EXIT DO ' Prevents leading zeros.
cc = 0
IF aa > VAL(STRING$(ss, "9")) THEN aa = aa - 10 ^ ss: cc = 1
tmp$ = LTRIM$(STR$(aa))
zz$ = STRING$(LEN(xx1$) - LEN(tmp$), "0") + tmp$ + zz$
LOOP
DO WHILE LEFT$(zz$, 1) = "0"
IF LEFT$(zz$, 1) = "0" THEN zz$ = MID$(zz$, 2)
LOOP
IF zz$ = "" THEN zz$ = "0"
holdaa$ = zz$
IF betatest% THEN COLOR 2, 0: PRINT holdaa$: COLOR 7, 0
ELSE
holdaa$ = z$ + STRING$(jj&& - 1, "0")
END IF
z$ = "": zz$ = ""
LOOP UNTIL h&& >= LEN(b$)
z$ = holdaa$
IF decimal% THEN
DO UNTIL LEN(z$) >= dec_a&& + dec_b&&
z$ = "0" + z$
LOOP
z$ = MID$(z$, 0, LEN(z$) - (dec_a&& + dec_b&& - 1)) + "." + MID$(z$, LEN(z$) - (dec_a&& + dec_b&&) + 1)
DO UNTIL RIGHT$(z$, 1) <> "0" AND RIGHT$(z$, 1) <> "."
z$ = MID$(z$, 1, LEN(z$) - 1)
LOOP
END IF
IF z$ = "" OR z$ = "0" THEN z$ = "0": ELSE z$ = sign$ + z$
decimal% = 0: sign$ = ""
runningtotal$ = z$
EXIT SUB
replace_decimal:
IF addsubplace& THEN
addsubx1$ = STRING$(addsubplace& - LEN(addsubx1$), "0") + addsubx1$
addsubx1$ = MID$(addsubx1$, 1, LEN(addsubx1$) - addsubplace&) + "." + MID$(addsubx1$, LEN(addsubx1$) - addsubplace& + 1)
DO UNTIL RIGHT$(addsubx1$, 1) <> "0" ' Remove trailing zeros in a decimal sum.
addsubx1$ = MID$(addsubx1$, 1, LEN(addsubx1$) - 1)
addsubplace& = addsubplace& - 1
LOOP
IF RIGHT$(addsubx1$, 1) = "." THEN addsubx1$ = MID$(addsubx1$, 1, LEN(addsubx1$) - 1) ' Number is now an integer.
END IF
RETURN
string_comp:
DO
' Remove trailing zeros after a decimal point.
IF INSTR(acomp$, ".") THEN
DO UNTIL RIGHT$(acomp$, 1) <> "0" AND RIGHT$(acomp$, 1) <> "." AND RIGHT$(acomp$, 1) <> "-"
acomp$ = MID$(acomp$, 1, LEN(acomp$) - 1)
LOOP
END IF
IF INSTR(bcomp$, ".") THEN
DO UNTIL RIGHT$(bcomp$, 1) <> "0" AND RIGHT$(bcomp$, 1) <> "." AND RIGHT$(bcomp$, 1) <> "-"
bcomp$ = MID$(bcomp$, 1, LEN(bcomp$) - 1)
LOOP
END IF
IF MID$(acomp$, 1, 2) = "-0" OR acomp$ = "" OR acomp$ = "-" THEN acomp$ = "0"
IF MID$(bcomp$, 1, 2) = "-0" OR bcomp$ = "" OR bcomp$ = "-" THEN bcomp$ = "0"
' A - and +
IF LEFT$(acomp$, 1) = "-" THEN j% = -1
IF LEFT$(bcomp$, 1) = "-" THEN k% = -1
IF k% = 0 AND j% THEN gl% = -1: EXIT DO
IF j% = 0 AND k% THEN gl% = 1: EXIT DO
' A decimal and non-decimal.
j% = INSTR(acomp$, ".")
k% = INSTR(bcomp$, ".")
IF j% = 0 AND k% THEN
IF acomp$ = "0" THEN gl% = -1 ELSE gl% = 1
EXIT DO
END IF
IF k% = 0 AND j% THEN
IF bcomp$ = "0" THEN gl% = 1 ELSE gl% = -1
EXIT DO
END IF
' Both decimals.
IF j% THEN
IF acomp$ > bcomp$ THEN
gl% = 1
ELSEIF acomp$ = bcomp$ THEN gl% = 0
ELSEIF acomp$ < bcomp$ THEN gl% = -1
END IF
EXIT DO
END IF
' Both positive or both negative whole numbers.
SELECT CASE LEN(acomp$)
CASE IS < LEN(bcomp$)
gl% = -1
CASE IS = LEN(bcomp$)
IF acomp$ = bcomp$ THEN
gl% = 0
ELSEIF acomp$ > bcomp$ THEN gl% = 1
ELSEIF acomp$ < bcomp$ THEN gl% = -1
END IF
CASE IS > LEN(bcomp$)
gl% = 1
END SELECT
EXIT DO
LOOP
RETURN
END SUB
SUB string_compare (compa$, compb$, gl%)
DO
' Remove trailing zeros after a decimal point.
IF INSTR(compa$, ".") THEN
DO UNTIL RIGHT$(compa$, 1) <> "0" AND RIGHT$(compa$, 1) <> "." AND RIGHT$(compa$, 1) <> "-"
compa$ = MID$(compa$, 1, LEN(compa$) - 1)
LOOP
END IF
IF INSTR(compb$, ".") THEN
DO UNTIL RIGHT$(compb$, 1) <> "0" AND RIGHT$(compb$, 1) <> "." AND RIGHT$(compb$, 1) <> "-"
compb$ = MID$(compb$, 1, LEN(compb$) - 1)
LOOP
END IF
IF MID$(compa$, 1, 2) = "-0" OR compa$ = "" OR compa$ = "-" THEN compa$ = "0"
IF MID$(compb$, 1, 2) = "-0" OR compb$ = "" OR compb$ = "-" THEN compb$ = "0"
' A - and +
IF LEFT$(compa$, 1) = "-" THEN j% = -1
IF LEFT$(compb$, 1) = "-" THEN k% = -1
IF k% = 0 AND j% THEN gl% = -1: PRINT "1*": EXIT DO
IF j% = 0 AND k% THEN gl% = 1: PRINT "2*": EXIT DO
' A decimal and non-decimal.
j% = INSTR(compa$, ".")
k% = INSTR(compb$, ".")
IF j% = 0 AND k% THEN
IF compa$ = "0" THEN gl% = -1: PRINT "4*" ELSE gl% = 1: PRINT "5*"
EXIT DO
END IF
IF k% = 0 AND j% THEN
IF compb$ = "0" THEN gl% = 1: PRINT "6*" ELSE gl% = -1: PRINT "7*"
EXIT DO
END IF
' Both decimals.
IF j% THEN
IF compa$ > compb$ THEN
gl% = 1: PRINT "8*"
ELSEIF compa$ = compb$ THEN gl% = 0: PRINT "9*"
ELSEIF compa$ < compb$ THEN gl% = -1: PRINT "10*"
END IF
EXIT DO
END IF
' Both positive or both negative whole numbers.
SELECT CASE LEN(compa$)
CASE IS < LEN(compb$)
gl% = -1
CASE IS = LEN(compb$)
IF compa$ = compb$ THEN
gl% = 0
ELSEIF compa$ > compb$ THEN gl% = 1
ELSEIF compa$ < compb$ THEN gl% = -1
END IF
CASE IS > LEN(compb$)
gl% = 1
END SELECT
EXIT DO
LOOP
END SUB
SUB validate_string (stringmathb$)
DO ' Faux loop.
vsn_negcnt& = 0: vsn_poscnt& = 0: vsn_depresent& = 0: decimalcnt& = 0: vsn_numberpresent& = 0: vsn_zerospresent& = 0
IF LEFT$(stringmathb$, 1) = "-" THEN stringmathb$ = MID$(stringmathb$, 2): sm_sign$ = "-" ELSE sm_sign$ = ""
IF LEFT$(stringmathb$, 1) = "+" THEN IF sm_sign$ <> "-" THEN stringmathb$ = MID$(stringmathb$, 2) ELSE stringmathb$ = "invalid number": EXIT DO
IF INSTR(UCASE$(stringmathb$), "D") OR INSTR(UCASE$(stringmathb$), "E") THEN ' Evaluate for Scientific Notation.
FOR sm_i& = 1 TO LEN(stringmathb$)
validatenum$ = MID$(UCASE$(stringmathb$), sm_i&, 1)
SELECT CASE validatenum$
CASE "+"
IF vsn_depresent& THEN vsn_poscnt& = vsn_poscnt& + 1 ELSE stringmathb$ = "invalid number": EXIT DO
CASE "-"
IF vsn_depresent& THEN vsn_negcnt& = vsn_negcnt& + 1 ELSE stringmathb$ = "invalid number": EXIT DO
CASE "0" TO "9"
vsn_numberpresent& = -1
CASE "D", "E"
vsn_depresent& = vsn_depresent& + 1
IF decimalcnt& = 0 AND sm_i& <> 2 OR vsn_depresent& > 1 OR vsn_numberpresent& = 0 OR vsn_negcnt& > 1 OR vsn_poscnt& > 1 OR vsn_negcnt& = 1 AND vsn_poscnt& >= 1 THEN vsn_numberpresent& = 0: EXIT FOR
vsn_numberpresent& = 0
MID$(stringmathb$, sm_i&, 1) = "e" ' Standardize
CASE "."
decimalcnt& = decimalcnt& + 1
IF sm_i& <> 2 THEN vsn_numberpresent& = 0: EXIT FOR
CASE ELSE
vsn_numberpresent& = 0: EXIT FOR
END SELECT
NEXT
IF decimalcnt& = 0 THEN stringmathb$ = MID$(stringmathb$, 1, 1) + "." + MID$(stringmathb$, 2) ' Standardize "."
IF vsn_numberpresent& = 0 OR vsn_negcnt& = 1 AND vsn_poscnt& = 1 OR decimalcnt& > 1 OR INSTR(stringmathb$, ".") <> 2 THEN stringmathb$ = "invalid number": EXIT DO
vsn_depresent& = INSTR(stringmathb$, "e")
sm_x$ = MID$(stringmathb$, vsn_depresent& + 1, 1) ' Standardize exponent "+" these two lines.
IF sm_x$ <> "+" AND sm_x$ <> "-" THEN stringmathb$ = MID$(stringmathb$, 1, vsn_depresent&) + "+" + MID$(stringmathb$, vsn_depresent& + 1)
IF MID$(stringmathb$, vsn_depresent& + 2, 1) = "0" THEN
IF MID$(stringmathb$, vsn_depresent& + 3, 1) <> "" THEN stringmathb$ = "invalid number": EXIT DO ' No leading zeros allowed in exponent notation.
END IF
jjed& = INSTR(stringmathb$, "e") ' Get position of notation.
valexpside$ = MID$(stringmathb$, jjed&) ' These two lines break up into number and notation
stringmathb$ = MID$(stringmathb$, 1, jjed& - 1) ' stringmathb$ is +- single digit whole number, decimal point and decimal number. valexpside$ is notation, sign and exponent.
DO UNTIL RIGHT$(stringmathb$, 1) <> "0" ' Remove any trailing zeros for number. Example 1.0d3 or 1.0000d3, etc.
stringmathb$ = MID$(stringmathb$, 1, LEN(stringmathb$) - 1)
LOOP
IF VAL(MID$(stringmathb$, 1, INSTR(stringmathb$, ".") - 1)) = 0 THEN
IF RIGHT$(stringmathb$, 1) = "." THEN
stringmathb$ = "0.e+0" ' Handles all types of zero entries.
ELSE
stringmathb$ = "invalid number": EXIT DO
END IF
EXIT DO
END IF
stringmathb$ = sm_sign$ + stringmathb$ + valexpside$
EXIT DO
ELSE
FOR sm_i& = 1 TO LEN(stringmathb$)
validatenum$ = MID$(stringmathb$, sm_i&, 1)
SELECT CASE validatenum$
CASE "."
decimalcnt& = decimalcnt& + 1
CASE "0"
vsn_zerospresent& = -1
CASE "1" TO "9"
vsn_numberpresent& = -1
CASE "$"
CASE ELSE
stringmathb$ = "invalid number": EXIT DO
END SELECT
NEXT
IF decimalcnt& > 1 OR vsn_negcnt& > 1 OR vsn_poscnt& > 1 OR vsn_negcnt& >= 1 AND vsn_poscnt& >= 1 THEN
stringmathb$ = "invalid number": EXIT DO
END IF
REM IF INSTR(stringmathb$, "$") THEN GOSUB currency_validate
REM IF INSTR(stringmathb$, ",") THEN
REM GOSUB comma_validation
REM IF stringmathb$ = "invalid number" THEN exit do
REM GOSUB comma_removal
REM END IF
IF RIGHT$(stringmathb$, 1) = "." THEN stringmathb$ = MID$(stringmathb$, 1, LEN(stringmathb$) - 1)
DO UNTIL LEFT$(stringmathb$, 1) <> "0" ' Strip off any leading zeros.
stringmathb$ = MID$(stringmathb$, 2)
LOOP
stringmathb$ = sm_sign$ + stringmathb$
IF INSTR(stringmathb$, ".") THEN
DO UNTIL RIGHT$(stringmathb$, 1) <> "0" ' Strip off any trailing zeros in a decimal.
stringmathb$ = MID$(stringmathb$, 1, LEN(stringmathb$) - 1)
LOOP
END IF
IF RIGHT$(stringmathb$, 1) = "." THEN stringmathb$ = MID$(stringmathb$, 1, LEN(stringmathb$) - 1)
IF vsn_numberpresent& = 0 THEN
IF vsn_zerospresent& THEN
stringmathb$ = "0"
ELSE
stringmathb$ = "invalid number"
END IF
END IF
END IF
EXIT DO
LOOP
END SUBPete