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08-25-2022, 09:37 PM
(This post was last modified: 08-25-2022, 11:02 PM by Kernelpanic.)
(08-25-2022, 08:12 PM)mnrvovrfc Wrote: Why not just "printf" instead of "__mingw_printf"? Because you're including "stdio.h" then "printf()" should be available. I tried to compile your program as it was, "gcc" asked me if I meant "builtin_printf()" or alike. After I forgot what option for linker so it links to math library...
"__mingw-printf" is for representing large numbers like l ong double.
So, "__mingw_printf("%.12 Lf"...) is for displayin great numbers.
![[Image: chud-in-C-2022-08-26-010015.jpg]](https://i.ibb.co/F59QQWF/chud-in-C-2022-08-26-010015.jpg)
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Pete
my only intention in posting the string version of Ramanujan was for you to incorporate it into your string-math routines
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08-26-2022, 03:16 AM
(This post was last modified: 08-26-2022, 01:42 PM by Pete.)
(08-26-2022, 12:50 AM)Jack Wrote: Pete
my only intention in posting the string version of Ramanujan was for you to incorporate it into your string-math routines
I did that, too.
Code: (Select All) WIDTH 180, 42
_SCREENMOVE 0, 0
DIM SHARED limit&&, betatest%
digits% = 10
limit&& = digits% + 7
betatest% = 0
DIM AS STRING n, m, c, sum, f, f4, f4k, c1, c2, c3, c34k, t1, t2, t3
DIM AS LONG k, k4
DIM t AS DOUBLE
FOR pete% = 0 TO 16
digits% = pete% + 10 + pete% * 8
limit&& = digits% + 7
t = TIMER
c1 = "1103"
c2 = "26390"
c3 = "396"
f = "1"
f4k = "1"
sum = "1103"
c34k = "1"
k4 = 0
t1 = c3
t2 = c3
sm t1, "*", t2, c3
t1 = c3
t2 = c3
sm t1, "*", t2, c3
FOR k = 1 TO digits% / (7.984)
t1 = f
sm STR$(k), "*", t1, f
IF betatest% THEN PRINT "results = "; f: SLEEP
t1 = f: t2 = f
sm t1, "*", t2, f4
IF betatest% THEN PRINT "results = "; f4: SLEEP
t1 = f4: t2 = f4
sm t1, "*", t2, f4
IF betatest% THEN PRINT "results = "; f4: SLEEP
t1 = c34k
sm c3, "*", t1, c34k
IF betatest% THEN PRINT "results = "; c34k: SLEEP
t1 = STR$(k4 + 1)
t2 = f4k
sm t1, "*", t2, f4k
IF betatest% THEN PRINT "results = "; f4k: SLEEP
t1 = STR$(k4 + 2)
t2 = f4k
sm t1, "*", t2, f4k
IF betatest% THEN PRINT "results = "; f4k: SLEEP
t1 = STR$(k4 + 3)
t2 = f4k
sm t1, "*", t2, f4k
IF betatest% THEN PRINT "results = "; f4k: SLEEP
t1 = STR$(k4 + 4)
t2 = f4k
sm t1, "*", t2, f4k
IF betatest% THEN PRINT "results = "; f4k: SLEEP
k4 = k4 + 4
t1 = STR$(k)
sm t1, "*", c2, t2
IF betatest% THEN PRINT "results = "; t2: SLEEP
sm c1, "+", t2, t1
IF betatest% THEN PRINT "results = "; t1: SLEEP
sm f4k, "*", t1, t2
IF betatest% THEN PRINT "results = "; t2: SLEEP
sm f4, "*", c34k, t1
IF betatest% THEN PRINT "results = "; t1: SLEEP
sm t2, "/", t1, t3
IF betatest% THEN PRINT "results = "; t3: SLEEP
t1 = sum
sm t1, "+", t3, sum
IF betatest% THEN PRINT "sum = "; sum: SLEEP
CALL pi(t1, sum, k)
NEXT
COLOR 14, 0: PRINT "Ramanujan pi = "; MID$("3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481", 1, 11 + (k - 2) * 8)
COLOR 7, 0
t = TIMER - t
PRINT "Time:"; t: PRINT
NEXT pete%
END
SUB pi (t1$, sum$, k)
square_root "8", t1$
IF betatest% THEN PRINT "Pi # = "; t1$: SLEEP
t2$ = "9801"
sm t1$, "/", t2$, t3$
IF betatest% THEN PRINT "Pi # = "; t3$: SLEEP
sm t3$, "*", sum$, t2$
IF betatest% THEN PRINT "Pi # = "; t2$: SLEEP
sm t1$, "/", t2$, t3$
IF betatest% THEN PRINT "Pi # = "; t3$: SLEEP
sm "1", "/", t2$, t1$
IF betatest% THEN PRINT "Pi # = "; t1$: SLEEP
PRINT "loop #"; LTRIM$(STR$(k));: LOCATE , 10: PRINT " pi = "; MID$(t1$, 1, 11 + (k - 1) * 8)
END SUB
SUB sm (s_var1$, operator$, s_var2$, runningtotal$)
DIM AS _INTEGER64 a, c, aa, cc, s, ss
stringmatha$ = s_var1$: stringmathb$ = s_var2$
SELECT CASE operator$
CASE "+", "-"
GOSUB string_add_subtract_new
CASE "*"
GOSUB string_multiply_new
CASE "/"
GOSUB string_divide
CASE ELSE
PRINT "Error, no operator selected. operator$ = "; operator$: END
END SELECT
EXIT SUB
string_divide:
terminating_decimal% = 0: divsign% = 0: divremainder& = 0: divremainder$ = "": divplace& = 0: divplace2& = 0: quotient$ = "": divcarry& = 0
divbuffer& = LEN(stringmathb$) - LEN(stringmatha$)
IF divbuffer& < 0 THEN divbuffer& = 0
d2dividend$ = stringmatha$
d1divisor$ = stringmathb$
IF LEFT$(d1divisor$, 1) = "0" AND LEN(d1divisor$) = 1 THEN PRINT "Division by zero not allowed.": divsign% = 0: EXIT SUB
IF LEFT$(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$
GOSUB string_multiply_new ' Gets runningtotal$
tempcutd$ = divremainder$ ' divremainder$ can be 00 or other leading zero values.
DO
IF LEN(tempcutd$) = 1 THEN EXIT DO
IF LEFT$(tempcutd$, 1) = "0" THEN
tempcutd$ = MID$(tempcutd$, 2)
ELSE
EXIT DO
END IF
LOOP
IF LEN(tempcutd$) > LEN(runningtotal$) OR LEN(tempcutd$) = LEN(runningtotal$) AND runningtotal$ <= tempcutd$ THEN EXIT FOR
NEXT
quotient$ = quotient$ + LTRIM$(STR$(div_i%))
stringmatha$ = LTRIM$(STR$(div_i%)): stringmathb$ = d1divisor$
GOSUB string_multiply_new ' Gets runningtotal$
stringmatha$ = divremainder$: stringmathb$ = runningtotal$
operator$ = "-": GOSUB string_add_subtract_new
divremainder$ = runningtotal$
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
stringmathb$ = quotient$: quotient$ = ""
IF stringmathb$ = "overflow" THEN divsign% = 0: EXIT SUB
runningtotal$ = stringmathb$: stringmathb$ = ""
IF divsign% THEN runningtotal$ = "-" + runningtotal$
IF stringmathround$ <> "" THEN runningtotal$ = runningtotal$ + stringmathround$
RETURN
string_add_subtract_new:
a1$ = stringmatha$: b1$ = stringmathb$
s = 18: i&& = 0: c = 0
a$ = stringmatha$: b$ = stringmathb$: op$ = operator$
IF op$ = "-" THEN
IF LEFT$(b$, 1) = "-" THEN b$ = MID$(b$, 2) ELSE b$ = "-" + b$
END IF
IF INSTR(a$, ".") <> 0 OR INSTR(b$, ".") <> 0 THEN
decimal% = -1
IF INSTR(a$, ".") <> 0 THEN
dec_a&& = LEN(MID$(a$, INSTR(a$, ".") + 1))
a$ = MID$(a$, 1, INSTR(a$, ".") - 1) + MID$(a$, INSTR(a$, ".") + 1)
END IF
IF INSTR(b$, ".") <> 0 THEN
dec_b&& = LEN(MID$(b$, INSTR(b$, ".") + 1))
b$ = MID$(b$, 1, INSTR(b$, ".") - 1) + MID$(b$, INSTR(b$, ".") + 1)
END IF
' Line up decimal places by inserting trailing zeros.
IF dec_b&& > dec_a&& THEN
j&& = dec_b&&
a$ = a$ + STRING$(dec_b&& - dec_a&&, "0")
ELSE
j&& = dec_a&&
b$ = b$ + STRING$(dec_a&& - dec_b&&, "0")
END IF
END IF
IF LEFT$(a$, 1) = "-" OR LEFT$(b$, 1) = "-" THEN
IF LEFT$(a$, 1) = "-" AND LEFT$(b$, 1) = "-" THEN
sign$ = "--": a$ = MID$(a$, 2): b$ = MID$(b$, 2)
ELSE
IF LEFT$(a$, 1) = "-" THEN a$ = MID$(a$, 2): sign_a$ = "-"
IF LEFT$(b$, 1) = "-" THEN b$ = MID$(b$, 2): sign_b$ = "-"
IF LEFT$(a1$, 1) = "-" THEN a1_x$ = MID$(a1$, 2) ELSE a1_x$ = a1$
IF LEFT$(b1$, 1) = "-" THEN b1_x$ = MID$(b1$, 2) ELSE b1_x$ = b1$
string_compare a1_x$, b1_x$, gl%
IF gl% < 0 THEN
IF LEN(sign_b$) THEN sign$ = "-": SWAP a$, b$
ELSE
IF LEN(sign_a$) THEN sign$ = "-": SWAP sign_a$, sign_b$
END IF
END IF
END IF
z$ = ""
DO
i&& = i&& + s
x1$ = MID$(a$, LEN(a$) - i&& + 1, s)
x2$ = MID$(b$, LEN(b$) - i&& + 1, s)
zeros% = LEN(x1$): IF LEN(x2$) > zeros% THEN zeros% = LEN(x2$)
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$(s, "9")) THEN a = a - 10 ^ s: c = 1
IF a < 0 THEN a = a + 10 ^ s: c = -1
tmp$ = LTRIM$(STR$(a))
z$ = STRING$(zeros% - LEN(tmp$), "0") + tmp$ + z$
LOOP
IF decimal% THEN
z$ = MID$(z$, 1, LEN(z$) - j&&) + "." + MID$(z$, LEN(z$) - j&& + 1)
END IF
' Remove any leading zeros.
DO
IF LEFT$(z$, 1) = "0" THEN z$ = MID$(z$, 2) ELSE EXIT DO
LOOP
IF z$ = "" OR z$ = "0" THEN z$ = "0" ELSE z$ = LEFT$(sign$, 1) + z$
runningtotal$ = z$
sign$ = "": sign_a$ = "": sign_b$ = "": i&& = 0: j&& = 0: decimal% = 0: c = 0
RETURN
string_multiply_new:
z$ = "": sign$ = "": mult&& = 0: h&& = 0: i&& = 0: j&& = 0: c = 0: decimal% = 0
zz$ = "": ii&& = 0: jj&& = 0
s = 8: ss = 18
a$ = stringmatha$: b$ = stringmathb$
IF INSTR(a$, "-") <> 0 OR INSTR(b$, "-") <> 0 THEN
IF INSTR(a$, "-") <> 0 AND INSTR(b$, "-") <> 0 THEN
a$ = MID$(a$, 2): b$ = MID$(b$, 2)
ELSE
IF INSTR(a$, "-") <> 0 THEN a$ = MID$(a$, 2) ELSE b$ = MID$(b$, 2)
sign$ = "-"
END IF
END IF
IF INSTR(a$, ".") <> 0 OR INSTR(b$, ".") <> 0 THEN
decimal% = -1
IF INSTR(a$, ".") <> 0 THEN
dec_a&& = LEN(MID$(a$, INSTR(a$, ".") + 1))
a$ = MID$(a$, 1, INSTR(a$, ".") - 1) + MID$(a$, INSTR(a$, ".") + 1)
END IF
IF INSTR(b$, ".") <> 0 THEN
dec_b&& = LEN(MID$(b$, INSTR(b$, ".") + 1))
b$ = MID$(b$, 1, INSTR(b$, ".") - 1) + MID$(b$, INSTR(b$, ".") + 1)
END IF
END IF
IF LEN(a$) < LEN(b$) THEN SWAP a$, b$ ' Needed so x1$ is always the largest for leading zero replacements.
DO
h&& = h&& + s: i&& = 0
x2$ = MID$(b$, LEN(b$) - h&& + 1, s)
WHILE -1
i&& = i&& + s
x1$ = MID$(a$, LEN(a$) - i&& + 1, s)
a = VAL(sign_a$ + x1$) * VAL(sign_b$ + x2$) + c
c = 0
tmp$ = LTRIM$(STR$(a))
IF LEN(tmp$) > s THEN c = VAL(MID$(tmp$, 1, LEN(tmp$) - s)): tmp$ = MID$(tmp$, LEN(tmp$) - s + 1)
z$ = STRING$(LEN(x1$) - LEN(tmp$), "0") + tmp$ + z$
IF i&& >= LEN(a$) AND c = 0 THEN EXIT WHILE
WEND
jj&& = jj&& + 1
IF jj&& > 1 THEN
ii&& = 0: cc = 0
aa$ = holdaa$
bb$ = z$ + STRING$((jj&& - 1) * s, "0")
DO
ii&& = ii&& + ss
xx1$ = MID$(aa$, LEN(aa$) - ii&& + 1, ss)
xx2$ = MID$(bb$, LEN(bb$) - ii&& + 1, ss)
zeros% = LEN(xx1$): IF LEN(xx2$) > zeros% THEN zeros% = LEN(xx2$)
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$
zz$ = STRING$(zeros% - LEN(tmp$), "0") + tmp$ + zz$
LOOP
DO WHILE LEFT$(zz$, 1) = "0"
IF LEFT$(zz$, 1) = "0" THEN zz$ = MID$(zz$, 2)
LOOP
IF zz$ = "" THEN zz$ = "0"
holdaa$ = zz$
ELSE
holdaa$ = z$ + STRING$(jj&& - 1, "0")
END IF
z$ = "": zz$ = ""
LOOP UNTIL h&& >= LEN(b$)
z$ = holdaa$
IF decimal% THEN
DO UNTIL LEN(z$) >= dec_a&& + dec_b&&
z$ = "0" + z$
LOOP
z$ = MID$(z$, 0, LEN(z$) - (dec_a&& + dec_b&& - 1)) + "." + MID$(z$, LEN(z$) - (dec_a&& + dec_b&&) + 1)
DO UNTIL RIGHT$(z$, 1) <> "0" AND RIGHT$(z$, 1) <> "."
z$ = MID$(z$, 1, LEN(z$) - 1)
LOOP
END IF
IF z$ = "" OR z$ = "0" THEN z$ = "0" ELSE z$ = sign$ + z$
decimal% = 0: sign$ = ""
runningtotal$ = z$
RETURN
END SUB
SUB string_compare (compa$, compb$, gl%)
DO
' Remove trailing zeros after a decimal point.
IF INSTR(compa$, ".") THEN
DO UNTIL RIGHT$(compa$, 1) <> "0" AND RIGHT$(compa$, 1) <> "." AND RIGHT$(compa$, 1) <> "-"
compa$ = MID$(compa$, 1, LEN(compa$) - 1)
LOOP
END IF
IF INSTR(compb$, ".") THEN
DO UNTIL RIGHT$(compb$, 1) <> "0" AND RIGHT$(compb$, 1) <> "." AND RIGHT$(compb$, 1) <> "-"
compb$ = MID$(compb$, 1, LEN(compb$) - 1)
LOOP
END IF
IF MID$(compa$, 1, 2) = "-0" OR compa$ = "" OR compa$ = "-" THEN compa$ = "0"
IF MID$(compb$, 1, 2) = "-0" OR compb$ = "" OR compb$ = "-" THEN compb$ = "0"
' A - and +
IF LEFT$(compa$, 1) = "-" THEN j% = -1
IF LEFT$(compb$, 1) = "-" THEN k% = -1
IF k% = 0 AND j% THEN gl% = -1: EXIT DO
IF j% = 0 AND k% THEN gl% = 1: EXIT DO
' A decimal and non-decimal.
j% = INSTR(compa$, ".")
k% = INSTR(compb$, ".")
IF j% = 0 AND k% THEN
IF compa$ = "0" THEN gl% = -1 ELSE gl% = 1
EXIT DO
END IF
IF k% = 0 AND j% THEN
IF compb$ = "0" THEN gl% = 1 ELSE gl% = -1
EXIT DO
END IF
' Both decimals.
IF j% THEN
IF compa$ > compb$ THEN
gl% = 1
ELSEIF compa$ = compb$ THEN gl% = 0
ELSEIF compa$ < compb$ THEN gl% = -1
END IF
EXIT DO
END IF
' Both positive or both negative whole numbers.
SELECT CASE LEN(compa$)
CASE IS < LEN(compb$)
gl% = -1
CASE IS = LEN(compb$)
IF compa$ = compb$ THEN
gl% = 0
ELSEIF compa$ > compb$ THEN gl% = 1
ELSEIF compa$ < compb$ THEN gl% = -1
END IF
CASE IS > LEN(compb$)
gl% = 1
END SELECT
EXIT DO
LOOP
END SUB
SUB square_root (x$, sqrt$)
oldy$ = "": sqrt$ = ""
IF INSTR(x$, ".") THEN
decx$ = MID$(x$, 1, INSTR(x$, ".") - 1)
x$ = MID$(x$, 1, INSTR(x$, ".") - 1) + MID$(x$, INSTR(x$, ".") + 1)
IF LEN(x$) = 1 THEN x$ = x$ + "0"
ELSE
decx$ = x$
END IF
j&& = LEN(decx$)
' VAL() okay, one character eval.
IF VAL(RIGHT$(LTRIM$(STR$(j&&)), 1)) / 2 = VAL(RIGHT$(LTRIM$(STR$(j&&)), 1)) \ 2 THEN
i&& = 1 ' Even number length.
ELSE
i&& = 0 ' Odd number length.
END IF
DO
sm z$, "-", k$, runningtotal$
z$ = runningtotal$ + (MID$(x$, i&&, 2))
IF LEFT$(z$, 1) = "0" THEN z$ = MID$(z$, 2) ' Remove leading zeros
oldy$ = ""
FOR j&& = 1 TO 10
IF i&& > 1 THEN
sm sqrt$, "*", "2", y$
y$ = y$ + LTRIM$(STR$(j&&))
ELSE
y$ = LTRIM$(STR$(j&&))
END IF
sm y$, "*", LTRIM$(STR$(j&&)), runningtotal$
string_compare runningtotal$, z$, gl%
IF gl% > -1 THEN
IF gl% = 0 THEN
h% = 0: oldy$ = y$ ' Perfect square division.
ELSE
h% = 1
END IF
sm oldy$, "*", LTRIM$(STR$(j&& - h%)), runningtotal$
IF STRING$(LEN(z$), "0") = z$ AND runningtotal$ = "0" AND i&& >= LEN(decx$) THEN EXIT DO
IF dpx&& = 0 THEN ' Limited to && size unless converted to string.
IF i&& >= LEN(decx$) THEN
dpx&& = INT(LEN(decx$) / 2 + .5)
IF dpx&& = 0 THEN dpx&& = -1
END IF
END IF
IF betatest% < -1 THEN PRINT "Sqrt "; sqrt$; " * 2 = ";: COLOR 2, 0: PRINT LTRIM$(STR$(VAL(sqrt$) * 2));: COLOR 7, 0: PRINT LTRIM$(STR$(j&& - h%)); " * "; LTRIM$(STR$(j&& - h%)); " ="; VAL(oldy$) * (j&& - h%)
sqrt$ = sqrt$ + LTRIM$(STR$(j&& - h%))
sm oldy$, "*", LTRIM$(STR$(j&& - h%)), runningtotal$
k$ = runningtotal$
IF betatest% < -1 THEN PRINT "Remainder "; z$; " minus "; k$; " = ";
EXIT FOR
END IF
oldy$ = y$
NEXT
i&& = i&& + 2
IF LEN(z$) >= limit&& THEN EXIT DO
x$ = x$ + "00"
LOOP
IF dpx&& THEN
sqrt$ = MID$(sqrt$, 0, dpx&& + 1) + "." + MID$(sqrt$, dpx&& + 1)
END IF
END SUB
It isn't quite as fast. What I've noticed is my routines tend to take the decimal places out further than necessary for some calculations. My limit&& variable needs to be slightly more than the number of digits to obtain the desired results. Changing that variable has some impact on the final decimal places. My hunch is other methods of calculation use rounding for the final digits, and significant figures in the calculations. Mine does not use either.
I would also need to speed up the square root and division modules a bit. The chunk multiplication, addition, and subtraction are quite fast. That was a nice improvement. Over-all the work is progressing nicely, but I may be leaving my comfort zone when it comes to the mathematical mechanics.
Thanks for all your help on this. It is great for beta-testing my new string routines!
Pete
Edit: Found one bug and fixed the issue in the code.
Posts: 1,616
Threads: 157
Joined: Apr 2022
Reputation:
77
Interesting to note that with both string math routines, Treebeard's and mine, pi to 28 digits and 36 digits is incorrect by over 1 on the last digit, and I don't see it as a rounding situation. All other iterations of 10 to 150 appear to be correct, except these. So to correct this, both routines would have to lengthen the value of the square root of 8. I did that by an extra 20-digits, and it fixed the aforementioned discrepancies. Nice; however I wonder what the accepted value of the square root of 8 is for mathematicians who have worked with this formula?
Pete
Posts: 1,616
Threads: 157
Joined: Apr 2022
Reputation:
77
Okay, what I see is a need to have the square root of 8 always returned with more digit, and possibly at least the same number of digits, than the output of pi. To that end, I set that number to 200 digits for the square root calculation and noted all digits of pi 10, 18, 26, 34, 50... up to 150 are now all correct. This same adjustment would have to be applied using the Treebeard string math routines.
Updated code. The grey digits are not part of the comparison. I included them to check what the last significant pi digit should be.
Code: (Select All) WIDTH 180, 42
_SCREENMOVE 0, 0
DIM SHARED sqrt$, limit&&, betatest%
betatest% = 0
DIM AS STRING n, m, c, sum, f, f4, f4k, c1, c2, c3, c34k, t1, t2, t3
DIM AS LONG k, k4
DIM t AS DOUBLE
limit&& = 200: square_root "8", sqrt$ ' Limit must be as many or more digits than the max digits of the returned value for pi.
FOR pete% = 0 TO 16
digits% = pete% + 10 + pete% * 8
limit&& = digits% + 7
t = TIMER
c1 = "1103"
c2 = "26390"
c3 = "396"
f = "1"
f4k = "1"
sum = "1103"
c34k = "1"
k4 = 0
t1 = c3
t2 = c3
sm t1, "*", t2, c3
t1 = c3
t2 = c3
sm t1, "*", t2, c3
FOR k = 1 TO digits% / (7.984)
t1 = f
sm STR$(k), "*", t1, f
IF betatest% THEN PRINT "results = "; f: SLEEP
t1 = f: t2 = f
sm t1, "*", t2, f4
IF betatest% THEN PRINT "results = "; f4: SLEEP
t1 = f4: t2 = f4
sm t1, "*", t2, f4
IF betatest% THEN PRINT "results = "; f4: SLEEP
t1 = c34k
sm c3, "*", t1, c34k
IF betatest% THEN PRINT "results = "; c34k: SLEEP
t1 = STR$(k4 + 1)
t2 = f4k
sm t1, "*", t2, f4k
IF betatest% THEN PRINT "results = "; f4k: SLEEP
t1 = STR$(k4 + 2)
t2 = f4k
sm t1, "*", t2, f4k
IF betatest% THEN PRINT "results = "; f4k: SLEEP
t1 = STR$(k4 + 3)
t2 = f4k
sm t1, "*", t2, f4k
IF betatest% THEN PRINT "results = "; f4k: SLEEP
t1 = STR$(k4 + 4)
t2 = f4k
sm t1, "*", t2, f4k
IF betatest% THEN PRINT "results = "; f4k: SLEEP
k4 = k4 + 4
t1 = STR$(k)
sm t1, "*", c2, t2
IF betatest% THEN PRINT "results = "; t2: SLEEP
sm c1, "+", t2, t1
IF betatest% THEN PRINT "results = "; t1: SLEEP
sm f4k, "*", t1, t2
IF betatest% THEN PRINT "results = "; t2: SLEEP
sm f4, "*", c34k, t1
IF betatest% THEN PRINT "results = "; t1: SLEEP
sm t2, "/", t1, t3
IF betatest% THEN PRINT "results = "; t3: SLEEP
t1 = sum
sm t1, "+", t3, sum
IF betatest% THEN PRINT "sum = "; sum: SLEEP
CALL pi(t1, sum, k)
NEXT
COLOR 14, 0: PRINT "Ramanujan pi = "; MID$("3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481", 1, 11 + (k - 2) * 8)
COLOR 7, 0
t = TIMER - t
PRINT "Time:"; t: PRINT
NEXT pete%
END
SUB pi (t1$, sum$, k)
REM square_root "8", sqrt$
IF betatest% THEN PRINT "Pi # = "; sqrt$: SLEEP
t2$ = "9801"
sm sqrt$, "/", t2$, t3$
IF betatest% THEN PRINT "Pi # = "; t3$: SLEEP
sm t3$, "*", sum$, t2$
IF betatest% THEN PRINT "Pi # = "; t2$: SLEEP
sm t1$, "/", t2$, t3$
IF betatest% THEN PRINT "Pi # = "; t3$: SLEEP
sm "1", "/", t2$, t1$
IF betatest% THEN PRINT "Pi # = "; t1$: SLEEP
PRINT "loop #"; LTRIM$(STR$(k));: LOCATE , 10: PRINT " pi = "; MID$(t1$, 1, 11 + (k - 1) * 8);: COLOR 8, 0: PRINT MID$(t1$, 11 + (k - 1) * 8 + 1, 4): COLOR 7, 0
END SUB
SUB sm (s_var1$, operator$, s_var2$, runningtotal$)
DIM AS _INTEGER64 a, c, aa, cc, s, ss
stringmatha$ = s_var1$: stringmathb$ = s_var2$
SELECT CASE operator$
CASE "+", "-"
GOSUB string_add_subtract_new
CASE "*"
GOSUB string_multiply_new
CASE "/"
GOSUB string_divide
CASE ELSE
PRINT "Error, no operator selected. operator$ = "; operator$: END
END SELECT
EXIT SUB
string_divide:
terminating_decimal% = 0: divsign% = 0: divremainder& = 0: divremainder$ = "": divplace& = 0: divplace2& = 0: quotient$ = "": divcarry& = 0
divbuffer& = LEN(stringmathb$) - LEN(stringmatha$)
IF divbuffer& < 0 THEN divbuffer& = 0
d2dividend$ = stringmatha$
d1divisor$ = stringmathb$
IF LEFT$(d1divisor$, 1) = "0" AND LEN(d1divisor$) = 1 THEN PRINT "Division by zero not allowed.": divsign% = 0: EXIT SUB
IF LEFT$(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$
GOSUB string_multiply_new ' Gets runningtotal$
tempcutd$ = divremainder$ ' divremainder$ can be 00 or other leading zero values.
DO
IF LEN(tempcutd$) = 1 THEN EXIT DO
IF LEFT$(tempcutd$, 1) = "0" THEN
tempcutd$ = MID$(tempcutd$, 2)
ELSE
EXIT DO
END IF
LOOP
IF LEN(tempcutd$) > LEN(runningtotal$) OR LEN(tempcutd$) = LEN(runningtotal$) AND runningtotal$ <= tempcutd$ THEN EXIT FOR
NEXT
quotient$ = quotient$ + LTRIM$(STR$(div_i%))
stringmatha$ = LTRIM$(STR$(div_i%)): stringmathb$ = d1divisor$
GOSUB string_multiply_new ' Gets runningtotal$
stringmatha$ = divremainder$: stringmathb$ = runningtotal$
operator$ = "-": GOSUB string_add_subtract_new
divremainder$ = runningtotal$
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
stringmathb$ = quotient$: quotient$ = ""
IF stringmathb$ = "overflow" THEN divsign% = 0: EXIT SUB
runningtotal$ = stringmathb$: stringmathb$ = ""
IF divsign% THEN runningtotal$ = "-" + runningtotal$
IF stringmathround$ <> "" THEN runningtotal$ = runningtotal$ + stringmathround$
RETURN
string_add_subtract_new:
a1$ = stringmatha$: b1$ = stringmathb$
s = 18: i&& = 0: c = 0
a$ = stringmatha$: b$ = stringmathb$: op$ = operator$
IF op$ = "-" THEN
IF LEFT$(b$, 1) = "-" THEN b$ = MID$(b$, 2) ELSE b$ = "-" + b$
END IF
IF INSTR(a$, ".") <> 0 OR INSTR(b$, ".") <> 0 THEN
decimal% = -1
IF INSTR(a$, ".") <> 0 THEN
dec_a&& = LEN(MID$(a$, INSTR(a$, ".") + 1))
a$ = MID$(a$, 1, INSTR(a$, ".") - 1) + MID$(a$, INSTR(a$, ".") + 1)
END IF
IF INSTR(b$, ".") <> 0 THEN
dec_b&& = LEN(MID$(b$, INSTR(b$, ".") + 1))
b$ = MID$(b$, 1, INSTR(b$, ".") - 1) + MID$(b$, INSTR(b$, ".") + 1)
END IF
' Line up decimal places by inserting trailing zeros.
IF dec_b&& > dec_a&& THEN
j&& = dec_b&&
a$ = a$ + STRING$(dec_b&& - dec_a&&, "0")
ELSE
j&& = dec_a&&
b$ = b$ + STRING$(dec_a&& - dec_b&&, "0")
END IF
END IF
IF LEFT$(a$, 1) = "-" OR LEFT$(b$, 1) = "-" THEN
IF LEFT$(a$, 1) = "-" AND LEFT$(b$, 1) = "-" THEN
sign$ = "--": a$ = MID$(a$, 2): b$ = MID$(b$, 2)
ELSE
IF LEFT$(a$, 1) = "-" THEN a$ = MID$(a$, 2): sign_a$ = "-"
IF LEFT$(b$, 1) = "-" THEN b$ = MID$(b$, 2): sign_b$ = "-"
IF LEFT$(a1$, 1) = "-" THEN a1_x$ = MID$(a1$, 2) ELSE a1_x$ = a1$
IF LEFT$(b1$, 1) = "-" THEN b1_x$ = MID$(b1$, 2) ELSE b1_x$ = b1$
string_compare a1_x$, b1_x$, gl%
IF gl% < 0 THEN
IF LEN(sign_b$) THEN sign$ = "-": SWAP a$, b$
ELSE
IF LEN(sign_a$) THEN sign$ = "-": SWAP sign_a$, sign_b$
END IF
END IF
END IF
z$ = ""
DO
i&& = i&& + s
x1$ = MID$(a$, LEN(a$) - i&& + 1, s)
x2$ = MID$(b$, LEN(b$) - i&& + 1, s)
zeros% = LEN(x1$): IF LEN(x2$) > zeros% THEN zeros% = LEN(x2$)
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$(s, "9")) THEN a = a - 10 ^ s: c = 1
IF a < 0 THEN a = a + 10 ^ s: c = -1
tmp$ = LTRIM$(STR$(a))
z$ = STRING$(zeros% - LEN(tmp$), "0") + tmp$ + z$
LOOP
IF decimal% THEN
z$ = MID$(z$, 1, LEN(z$) - j&&) + "." + MID$(z$, LEN(z$) - j&& + 1)
END IF
' Remove any leading zeros.
DO
IF LEFT$(z$, 1) = "0" THEN z$ = MID$(z$, 2) ELSE EXIT DO
LOOP
IF z$ = "" OR z$ = "0" THEN z$ = "0" ELSE z$ = LEFT$(sign$, 1) + z$
runningtotal$ = z$
sign$ = "": sign_a$ = "": sign_b$ = "": i&& = 0: j&& = 0: decimal% = 0: c = 0
RETURN
string_multiply_new:
z$ = "": sign$ = "": mult&& = 0: h&& = 0: i&& = 0: j&& = 0: c = 0: decimal% = 0
zz$ = "": ii&& = 0: jj&& = 0
s = 8: ss = 18
a$ = stringmatha$: b$ = stringmathb$
IF INSTR(a$, "-") <> 0 OR INSTR(b$, "-") <> 0 THEN
IF INSTR(a$, "-") <> 0 AND INSTR(b$, "-") <> 0 THEN
a$ = MID$(a$, 2): b$ = MID$(b$, 2)
ELSE
IF INSTR(a$, "-") <> 0 THEN a$ = MID$(a$, 2) ELSE b$ = MID$(b$, 2)
sign$ = "-"
END IF
END IF
IF INSTR(a$, ".") <> 0 OR INSTR(b$, ".") <> 0 THEN
decimal% = -1
IF INSTR(a$, ".") <> 0 THEN
dec_a&& = LEN(MID$(a$, INSTR(a$, ".") + 1))
a$ = MID$(a$, 1, INSTR(a$, ".") - 1) + MID$(a$, INSTR(a$, ".") + 1)
END IF
IF INSTR(b$, ".") <> 0 THEN
dec_b&& = LEN(MID$(b$, INSTR(b$, ".") + 1))
b$ = MID$(b$, 1, INSTR(b$, ".") - 1) + MID$(b$, INSTR(b$, ".") + 1)
END IF
END IF
IF LEN(a$) < LEN(b$) THEN SWAP a$, b$ ' Needed so x1$ is always the largest for leading zero replacements.
DO
h&& = h&& + s: i&& = 0
x2$ = MID$(b$, LEN(b$) - h&& + 1, s)
WHILE -1
i&& = i&& + s
x1$ = MID$(a$, LEN(a$) - i&& + 1, s)
a = VAL(sign_a$ + x1$) * VAL(sign_b$ + x2$) + c
c = 0
tmp$ = LTRIM$(STR$(a))
IF LEN(tmp$) > s THEN c = VAL(MID$(tmp$, 1, LEN(tmp$) - s)): tmp$ = MID$(tmp$, LEN(tmp$) - s + 1)
z$ = STRING$(LEN(x1$) - LEN(tmp$), "0") + tmp$ + z$
IF i&& >= LEN(a$) AND c = 0 THEN EXIT WHILE
WEND
jj&& = jj&& + 1
IF jj&& > 1 THEN
ii&& = 0: cc = 0
aa$ = holdaa$
bb$ = z$ + STRING$((jj&& - 1) * s, "0")
DO
ii&& = ii&& + ss
xx1$ = MID$(aa$, LEN(aa$) - ii&& + 1, ss)
xx2$ = MID$(bb$, LEN(bb$) - ii&& + 1, ss)
zeros% = LEN(xx1$): IF LEN(xx2$) > zeros% THEN zeros% = LEN(xx2$)
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$
zz$ = STRING$(zeros% - LEN(tmp$), "0") + tmp$ + zz$
LOOP
DO WHILE LEFT$(zz$, 1) = "0"
IF LEFT$(zz$, 1) = "0" THEN zz$ = MID$(zz$, 2)
LOOP
IF zz$ = "" THEN zz$ = "0"
holdaa$ = zz$
ELSE
holdaa$ = z$ + STRING$(jj&& - 1, "0")
END IF
z$ = "": zz$ = ""
LOOP UNTIL h&& >= LEN(b$)
z$ = holdaa$
IF decimal% THEN
DO UNTIL LEN(z$) >= dec_a&& + dec_b&&
z$ = "0" + z$
LOOP
z$ = MID$(z$, 0, LEN(z$) - (dec_a&& + dec_b&& - 1)) + "." + MID$(z$, LEN(z$) - (dec_a&& + dec_b&&) + 1)
DO UNTIL RIGHT$(z$, 1) <> "0" AND RIGHT$(z$, 1) <> "."
z$ = MID$(z$, 1, LEN(z$) - 1)
LOOP
END IF
IF z$ = "" OR z$ = "0" THEN z$ = "0" ELSE z$ = sign$ + z$
decimal% = 0: sign$ = ""
runningtotal$ = z$
RETURN
END SUB
SUB string_compare (compa$, compb$, gl%)
DO
' Remove trailing zeros after a decimal point.
IF INSTR(compa$, ".") THEN
DO UNTIL RIGHT$(compa$, 1) <> "0" AND RIGHT$(compa$, 1) <> "." AND RIGHT$(compa$, 1) <> "-"
compa$ = MID$(compa$, 1, LEN(compa$) - 1)
LOOP
END IF
IF INSTR(compb$, ".") THEN
DO UNTIL RIGHT$(compb$, 1) <> "0" AND RIGHT$(compb$, 1) <> "." AND RIGHT$(compb$, 1) <> "-"
compb$ = MID$(compb$, 1, LEN(compb$) - 1)
LOOP
END IF
IF MID$(compa$, 1, 2) = "-0" OR compa$ = "" OR compa$ = "-" THEN compa$ = "0"
IF MID$(compb$, 1, 2) = "-0" OR compb$ = "" OR compb$ = "-" THEN compb$ = "0"
' A - and +
IF LEFT$(compa$, 1) = "-" THEN j% = -1
IF LEFT$(compb$, 1) = "-" THEN k% = -1
IF k% = 0 AND j% THEN gl% = -1: EXIT DO
IF j% = 0 AND k% THEN gl% = 1: EXIT DO
' A decimal and non-decimal.
j% = INSTR(compa$, ".")
k% = INSTR(compb$, ".")
IF j% = 0 AND k% THEN
IF compa$ = "0" THEN gl% = -1 ELSE gl% = 1
EXIT DO
END IF
IF k% = 0 AND j% THEN
IF compb$ = "0" THEN gl% = 1 ELSE gl% = -1
EXIT DO
END IF
' Both decimals.
IF j% THEN
IF compa$ > compb$ THEN
gl% = 1
ELSEIF compa$ = compb$ THEN gl% = 0
ELSEIF compa$ < compb$ THEN gl% = -1
END IF
EXIT DO
END IF
' Both positive or both negative whole numbers.
SELECT CASE LEN(compa$)
CASE IS < LEN(compb$)
gl% = -1
CASE IS = LEN(compb$)
IF compa$ = compb$ THEN
gl% = 0
ELSEIF compa$ > compb$ THEN gl% = 1
ELSEIF compa$ < compb$ THEN gl% = -1
END IF
CASE IS > LEN(compb$)
gl% = 1
END SELECT
EXIT DO
LOOP
END SUB
SUB square_root (x$, sqrt$)
oldy$ = "": sqrt$ = "": custom_limit&& = 200
IF INSTR(x$, ".") THEN
decx$ = MID$(x$, 1, INSTR(x$, ".") - 1)
x$ = MID$(x$, 1, INSTR(x$, ".") - 1) + MID$(x$, INSTR(x$, ".") + 1)
IF LEN(x$) = 1 THEN x$ = x$ + "0"
ELSE
decx$ = x$
END IF
j&& = LEN(decx$)
' VAL() okay, one character eval.
IF VAL(RIGHT$(LTRIM$(STR$(j&&)), 1)) / 2 = VAL(RIGHT$(LTRIM$(STR$(j&&)), 1)) \ 2 THEN
i&& = 1 ' Even number length.
ELSE
i&& = 0 ' Odd number length.
END IF
DO
sm z$, "-", k$, runningtotal$
z$ = runningtotal$ + (MID$(x$, i&&, 2))
IF LEFT$(z$, 1) = "0" THEN z$ = MID$(z$, 2) ' Remove leading zeros
oldy$ = ""
FOR j&& = 1 TO 10
IF i&& > 1 THEN
sm sqrt$, "*", "2", y$
y$ = y$ + LTRIM$(STR$(j&&))
ELSE
y$ = LTRIM$(STR$(j&&))
END IF
sm y$, "*", LTRIM$(STR$(j&&)), runningtotal$
string_compare runningtotal$, z$, gl%
IF gl% > -1 THEN
IF gl% = 0 THEN
h% = 0: oldy$ = y$ ' Perfect square division.
ELSE
h% = 1
END IF
sm oldy$, "*", LTRIM$(STR$(j&& - h%)), runningtotal$
IF STRING$(LEN(z$), "0") = z$ AND runningtotal$ = "0" AND i&& >= LEN(decx$) THEN EXIT DO
IF dpx&& = 0 THEN ' Limited to && size unless converted to string.
IF i&& >= LEN(decx$) THEN
dpx&& = INT(LEN(decx$) / 2 + .5)
IF dpx&& = 0 THEN dpx&& = -1
END IF
END IF
IF betatest% < -1 THEN PRINT "Sqrt "; sqrt$; " * 2 = ";: COLOR 2, 0: PRINT LTRIM$(STR$(VAL(sqrt$) * 2));: COLOR 7, 0: PRINT LTRIM$(STR$(j&& - h%)); " * "; LTRIM$(STR$(j&& - h%)); " ="; VAL(oldy$) * (j&& - h%)
sqrt$ = sqrt$ + LTRIM$(STR$(j&& - h%))
sm oldy$, "*", LTRIM$(STR$(j&& - h%)), runningtotal$
k$ = runningtotal$
IF betatest% < -1 THEN PRINT "Remainder "; z$; " minus "; k$; " = ";
EXIT FOR
END IF
oldy$ = y$
NEXT
i&& = i&& + 2
IF LEN(z$) >= custom_limit&& THEN EXIT DO
x$ = x$ + "00"
LOOP
IF dpx&& THEN
sqrt$ = MID$(sqrt$, 0, dpx&& + 1) + "." + MID$(sqrt$, dpx&& + 1)
END IF
END SUB
Pete
Posts: 336
Threads: 24
Joined: Apr 2022
Reputation:
19
08-26-2022, 04:24 PM
(This post was last modified: 08-26-2022, 04:24 PM by Jack.)
Pete
if I set digits% to 100 then your program calculates Pi to about 154 decimals, in your previous version it would only give 51 correct decimals
I think that your precision tracking needs work
Posts: 1,616
Threads: 157
Joined: Apr 2022
Reputation:
77
(08-26-2022, 04:24 PM)Jack Wrote: Pete
if I set digits% to 100 then your program calculates Pi to about 154 decimals, in your previous version it would only give 51 correct decimals
I think that your precision tracking needs work
In the previous, somewhat different, version, I limited the output to the screen to 51 decimals. So that's about demo presentation, not precision.
I'm now looking into how particular statements slow down calculation loops. I found that setting a variable to the length of a small string, for some weird reason, makes a big noticeable difference in loop speed. Weird. I don't have enough testing yet to conclude why, or what could be used to speed things up. What I do know but don't want to get into now is considering what it would take to do fixed string replacement instead of string concatenation. That definitely increases speed, but it would need to be bullet-proof, meaning it must work in all possible conditions.
Pete
Posts: 336
Threads: 24
Joined: Apr 2022
Reputation:
19
08-26-2022, 05:31 PM
(This post was last modified: 08-26-2022, 05:53 PM by Jack.)
Pete
I think the following was your previous version except that I changed limit&& and digits%, limit&& was 52 and digits% was 50, I also changed to console output
loop #13 is the last loop, loop #12 is accurate to 86 decimals
Quote:loop #12 pi = 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628031244133064023
loop #13 pi = 3.141592704753823286968106636310008090364871048493655060239030000194318500280725372036486027296712004
Code: (Select All) $Console:Only
_Dest _Console
Dim Shared digits%, limit&&, betatest%
limit&& = 102: betatest% = 0
Rem Jack's Ramanujan pi calculation algorithm with Pete's string math routine.
Dim As String n, m, c, sum, f, f4, f4k, c1, c2, c3, c34k, t1, t2, t3
Dim As Long k, k4
Dim t As Double
t = Timer
digits% = 100
c1 = "1103"
c2 = "26390"
c3 = "396"
f = "1"
f4k = "1"
sum = "1103"
c34k = "1"
k4 = 0
t1 = c3
t2 = c3
sm t1, "*", t2, c3
t1 = c3
t2 = c3
sm t1, "*", t2, c3
For k = 1 To digits% / 7.984
t1 = f
sm Str$(k), "*", t1, f
If betatest% Then Print "results = "; f: Sleep
t1 = f: t2 = f
sm t1, "*", t2, f4
If betatest% Then Print "results = "; f4: Sleep
t1 = f4: t2 = f4
sm t1, "*", t2, f4
If betatest% Then Print "results = "; f4: Sleep
t1 = c34k
sm c3, "*", t1, c34k
If betatest% Then Print "results = "; c34k: Sleep
t1 = Str$(k4 + 1)
t2 = f4k
sm t1, "*", t2, f4k
If betatest% Then Print "results = "; f4k: Sleep
t1 = Str$(k4 + 2)
t2 = f4k
sm t1, "*", t2, f4k
If betatest% Then Print "results = "; f4k: Sleep
t1 = Str$(k4 + 3)
t2 = f4k
sm t1, "*", t2, f4k
If betatest% Then Print "results = "; f4k: Sleep
t1 = Str$(k4 + 4)
t2 = f4k
sm t1, "*", t2, f4k
If betatest% Then Print "results = "; f4k: Sleep
k4 = k4 + 4
t1 = Str$(k)
sm t1, "*", c2, t2
If betatest% Then Print "results = "; t2: Sleep
sm c1, "+", t2, t1
If betatest% Then Print "results = "; t1: Sleep
sm f4k, "*", t1, t2
If betatest% Then Print "results = "; t2: Sleep
sm f4, "*", c34k, t1
If betatest% Then Print "results = "; t1: Sleep
sm t2, "/", t1, t3
If betatest% Then Print "results = "; t3: Sleep
t1 = sum
sm t1, "+", t3, sum
If betatest% Then Print "sum = "; sum: Sleep
Call pi(t1, sum, k)
Next
Color 14, 0: Print "Ramanujan pi = 3.1415926535897932384626433832795028841971693993751"
Color 7, 0
t = Timer - t
Print: Print "Time:"; t
End
Sub pi (t1$, sum$, k)
square_root "8", t1$
If betatest% Then Print "Pi # = "; t1$: Sleep
t2$ = "9801"
sm t1$, "/", t2$, t3$
If betatest% Then Print "Pi # = "; t3$: Sleep
sm t3$, "*", sum$, t2$
If betatest% Then Print "Pi # = "; t2$: Sleep
sm t1$, "/", t2$, t3$
If betatest% Then Print "Pi # = "; t3$: Sleep
sm "1", "/", t2$, t1$
If betatest% Then Print "Pi # = "; t1$: Sleep
Print "loop #"; LTrim$(Str$(k));: Locate , 10: Print " pi = "; Mid$(t1$, 1, digits% + 1)
End Sub
Sub sm (s_var1$, operator$, s_var2$, runningtotal$)
Dim As _Integer64 a, c, aa, cc, s, ss
stringmatha$ = s_var1$: stringmathb$ = s_var2$
Select Case operator$
Case "+", "-"
GoSub string_add_subtract_new
Case "*"
GoSub string_multiply_new
Case "/"
GoSub string_divide
Case Else
Print "Error, no operator selected. operator$ = "; operator$: End
End Select
Exit Sub
string_divide:
terminating_decimal% = 0: divsign% = 0: divremainder& = 0: divremainder$ = "": divplace& = 0: divplace2& = 0: quotient$ = "": divcarry& = 0
divbuffer& = Len(stringmathb$) - Len(stringmatha$)
If divbuffer& < 0 Then divbuffer& = 0
d2dividend$ = stringmatha$
d1divisor$ = stringmathb$
If Left$(d1divisor$, 1) = "0" And Len(d1divisor$) = 1 Then Print "Division by zero not allowed.": divsign% = 0: Exit Sub
If Left$(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$
GoSub string_multiply_new ' Gets runningtotal$
tempcutd$ = divremainder$ ' divremainder$ can be 00 or other leading zero values.
Do
If Len(tempcutd$) = 1 Then Exit Do
If Left$(tempcutd$, 1) = "0" Then
tempcutd$ = Mid$(tempcutd$, 2)
Else
Exit Do
End If
Loop
If Len(tempcutd$) > Len(runningtotal$) Or Len(tempcutd$) = Len(runningtotal$) And runningtotal$ <= tempcutd$ Then Exit For
Next
quotient$ = quotient$ + LTrim$(Str$(div_i%))
stringmatha$ = LTrim$(Str$(div_i%)): stringmathb$ = d1divisor$
GoSub string_multiply_new ' Gets runningtotal$
stringmatha$ = divremainder$: stringmathb$ = runningtotal$
operator$ = "-": GoSub string_add_subtract_new
divremainder$ = runningtotal$
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
stringmathb$ = quotient$: quotient$ = ""
If stringmathb$ = "overflow" Then divsign% = 0: Exit Sub
runningtotal$ = stringmathb$: stringmathb$ = ""
If divsign% Then runningtotal$ = "-" + runningtotal$
If stringmathround$ <> "" Then runningtotal$ = runningtotal$ + stringmathround$
Return
string_add_subtract_new:
a1$ = stringmatha$: b1$ = stringmathb$
s = 18: i&& = 0: c = 0
a$ = stringmatha$: b$ = stringmathb$: op$ = operator$
If op$ = "-" Then
If Left$(b$, 1) = "-" Then b$ = Mid$(b$, 2) Else b$ = "-" + b$
End If
If InStr(a$, ".") <> 0 Or InStr(b$, ".") <> 0 Then
decimal% = -1
If InStr(a$, ".") <> 0 Then
dec_a&& = Len(Mid$(a$, InStr(a$, ".") + 1))
a$ = Mid$(a$, 1, InStr(a$, ".") - 1) + Mid$(a$, InStr(a$, ".") + 1)
End If
If InStr(b$, ".") <> 0 Then
dec_b&& = Len(Mid$(b$, InStr(b$, ".") + 1))
b$ = Mid$(b$, 1, InStr(b$, ".") - 1) + Mid$(b$, InStr(b$, ".") + 1)
End If
' Line up decimal places by inserting trailing zeros.
If dec_b&& > dec_a&& Then
j&& = dec_b&&
a$ = a$ + String$(dec_b&& - dec_a&&, "0")
Else
j&& = dec_a&&
b$ = b$ + String$(dec_a&& - dec_b&&, "0")
End If
End If
If Left$(a$, 1) = "-" Or Left$(b$, 1) = "-" Then
If Left$(a$, 1) = "-" And Left$(b$, 1) = "-" Then
sign$ = "--": a$ = Mid$(a$, 2): b$ = Mid$(b$, 2)
Else
If Left$(a$, 1) = "-" Then a$ = Mid$(a$, 2): sign_a$ = "-"
If Left$(b$, 1) = "-" Then b$ = Mid$(b$, 2): sign_b$ = "-"
If Left$(a1$, 1) = "-" Then a1_x$ = Mid$(a1$, 2) Else a1_x$ = a1$
If Left$(b1$, 1) = "-" Then b1_x$ = Mid$(b1$, 2) Else b1_x$ = b1$
string_compare a1_x$, b1_x$, gl%
If gl% < 0 Then
If Len(sign_b$) Then sign$ = "-": Swap a$, b$
Else
If Len(sign_a$) Then sign$ = "-": Swap sign_a$, sign_b$
End If
End If
End If
z$ = ""
Do
i&& = i&& + s
x1$ = Mid$(a$, Len(a$) - i&& + 1, s)
x2$ = Mid$(b$, Len(b$) - i&& + 1, s)
zeros% = Len(x1$): If Len(x2$) > zeros% Then zeros% = Len(x2$)
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$(s, "9")) Then a = a - 10 ^ s: c = 1
If a < 0 Then a = a + 10 ^ s: c = -1
tmp$ = LTrim$(Str$(a))
z$ = String$(zeros% - Len(tmp$), "0") + tmp$ + z$
Loop
If decimal% Then
z$ = Mid$(z$, 1, Len(z$) - j&&) + "." + Mid$(z$, Len(z$) - j&& + 1)
End If
' Remove any leading zeros.
Do
If Left$(z$, 1) = "0" Then z$ = Mid$(z$, 2) Else Exit Do
Loop
If z$ = "" Or z$ = "0" Then z$ = "0" Else z$ = Left$(sign$, 1) + z$
runningtotal$ = z$
sign$ = "": sign_a$ = "": sign_b$ = "": i&& = 0: j&& = 0: decimal% = 0: c = 0
Return
string_multiply_new:
z$ = "": sign$ = "": mult&& = 0: h&& = 0: i&& = 0: j&& = 0: c = 0: decimal% = 0
zz$ = "": ii&& = 0: jj&& = 0
s = 8: ss = 18
a$ = stringmatha$: b$ = stringmathb$
If InStr(a$, "-") <> 0 Or InStr(b$, "-") <> 0 Then
If InStr(a$, "-") <> 0 And InStr(b$, "-") <> 0 Then
a$ = Mid$(a$, 2): b$ = Mid$(b$, 2)
Else
If InStr(a$, "-") <> 0 Then a$ = Mid$(a$, 2) Else b$ = Mid$(b$, 2)
sign$ = "-"
End If
End If
If InStr(a$, ".") <> 0 Or InStr(b$, ".") <> 0 Then
decimal% = -1
If InStr(a$, ".") <> 0 Then
dec_a&& = Len(Mid$(a$, InStr(a$, ".") + 1))
a$ = Mid$(a$, 1, InStr(a$, ".") - 1) + Mid$(a$, InStr(a$, ".") + 1)
End If
If InStr(b$, ".") <> 0 Then
dec_b&& = Len(Mid$(b$, InStr(b$, ".") + 1))
b$ = Mid$(b$, 1, InStr(b$, ".") - 1) + Mid$(b$, InStr(b$, ".") + 1)
End If
End If
If Len(a$) < Len(b$) Then Swap a$, b$ ' Needed so x1$ is always the largest for leading zero replacements.
Do
h&& = h&& + s: i&& = 0
x2$ = Mid$(b$, Len(b$) - h&& + 1, s)
While -1
i&& = i&& + s
x1$ = Mid$(a$, Len(a$) - i&& + 1, s)
a = Val(sign_a$ + x1$) * Val(sign_b$ + x2$) + c
c = 0
tmp$ = LTrim$(Str$(a))
If Len(tmp$) > s Then c = Val(Mid$(tmp$, 1, Len(tmp$) - s)): tmp$ = Mid$(tmp$, Len(tmp$) - s + 1)
z$ = String$(Len(x1$) - Len(tmp$), "0") + tmp$ + z$
If i&& >= Len(a$) And c = 0 Then Exit While
Wend
jj&& = jj&& + 1
If jj&& > 1 Then
ii&& = 0: cc = 0
aa$ = holdaa$
bb$ = z$ + String$((jj&& - 1) * s, "0")
Do
ii&& = ii&& + ss
xx1$ = Mid$(aa$, Len(aa$) - ii&& + 1, ss)
xx2$ = Mid$(bb$, Len(bb$) - ii&& + 1, ss)
aa = Val(xx1$) + Val(xx2$) + cc
If xx1$ + xx2$ = "" And cc = 0 Then Exit Do ' Prevents leading zeros.
cc = 0
If aa > Val(String$(ss, "9")) Then aa = aa - 10 ^ ss: cc = 1
tmp$ = LTrim$(Str$(aa))
zz$ = String$(Len(xx1$) - Len(tmp$), "0") + tmp$ + zz$
Loop
Do While Left$(zz$, 1) = "0"
If Left$(zz$, 1) = "0" Then zz$ = Mid$(zz$, 2)
Loop
If zz$ = "" Then zz$ = "0"
holdaa$ = zz$
Else
holdaa$ = z$ + String$(jj&& - 1, "0")
End If
z$ = "": zz$ = ""
Loop Until h&& >= Len(b$)
z$ = holdaa$
If decimal% Then
Do Until Len(z$) >= dec_a&& + dec_b&&
z$ = "0" + z$
Loop
z$ = Mid$(z$, 0, Len(z$) - (dec_a&& + dec_b&& - 1)) + "." + Mid$(z$, Len(z$) - (dec_a&& + dec_b&&) + 1)
Do Until Right$(z$, 1) <> "0" And Right$(z$, 1) <> "."
z$ = Mid$(z$, 1, Len(z$) - 1)
Loop
End If
If z$ = "" Or z$ = "0" Then z$ = "0" Else z$ = sign$ + z$
decimal% = 0: sign$ = ""
runningtotal$ = z$
Return
End Sub
Sub string_compare (compa$, compb$, gl%)
Do
' Remove trailing zeros after a decimal point.
If InStr(compa$, ".") Then
Do Until Right$(compa$, 1) <> "0" And Right$(compa$, 1) <> "." And Right$(compa$, 1) <> "-"
compa$ = Mid$(compa$, 1, Len(compa$) - 1)
Loop
End If
If InStr(compb$, ".") Then
Do Until Right$(compb$, 1) <> "0" And Right$(compb$, 1) <> "." And Right$(compb$, 1) <> "-"
compb$ = Mid$(compb$, 1, Len(compb$) - 1)
Loop
End If
If Mid$(compa$, 1, 2) = "-0" Or compa$ = "" Or compa$ = "-" Then compa$ = "0"
If Mid$(compb$, 1, 2) = "-0" Or compb$ = "" Or compb$ = "-" Then compb$ = "0"
' A - and +
If Left$(compa$, 1) = "-" Then j% = -1
If Left$(compb$, 1) = "-" Then k% = -1
If k% = 0 And j% Then gl% = -1: Exit Do
If j% = 0 And k% Then gl% = 1: Exit Do
' A decimal and non-decimal.
j% = InStr(compa$, ".")
k% = InStr(compb$, ".")
If j% = 0 And k% Then
If compa$ = "0" Then gl% = -1 Else gl% = 1
Exit Do
End If
If k% = 0 And j% Then
If compb$ = "0" Then gl% = 1 Else gl% = -1
Exit Do
End If
' Both decimals.
If j% Then
If compa$ > compb$ Then
gl% = 1
ElseIf compa$ = compb$ Then gl% = 0
ElseIf compa$ < compb$ Then gl% = -1
End If
Exit Do
End If
' Both positive or both negative whole numbers.
Select Case Len(compa$)
Case Is < Len(compb$)
gl% = -1
Case Is = Len(compb$)
If compa$ = compb$ Then
gl% = 0
ElseIf compa$ > compb$ Then gl% = 1
ElseIf compa$ < compb$ Then gl% = -1
End If
Case Is > Len(compb$)
gl% = 1
End Select
Exit Do
Loop
End Sub
Sub square_root (x$, sqrt$)
oldy$ = "": sqrt$ = ""
If InStr(x$, ".") Then
decx$ = Mid$(x$, 1, InStr(x$, ".") - 1)
x$ = Mid$(x$, 1, InStr(x$, ".") - 1) + Mid$(x$, InStr(x$, ".") + 1)
If Len(x$) = 1 Then x$ = x$ + "0"
Else
decx$ = x$
End If
j&& = Len(decx$)
' VAL() okay, one character eval.
If Val(Right$(LTrim$(Str$(j&&)), 1)) / 2 = Val(Right$(LTrim$(Str$(j&&)), 1)) \ 2 Then
i&& = 1 ' Even number length.
Else
i&& = 0 ' Odd number length.
End If
Do
sm z$, "-", k$, runningtotal$
z$ = runningtotal$ + (Mid$(x$, i&&, 2))
If Left$(z$, 1) = "0" Then z$ = Mid$(z$, 2) ' Remove leading zeros
oldy$ = ""
For j&& = 1 To 10
If i&& > 1 Then
sm sqrt$, "*", "2", y$
y$ = y$ + LTrim$(Str$(j&&))
Else
y$ = LTrim$(Str$(j&&))
End If
sm y$, "*", LTrim$(Str$(j&&)), runningtotal$
string_compare runningtotal$, z$, gl%
If gl% > -1 Then
If gl% = 0 Then
h% = 0: oldy$ = y$ ' Perfect square division.
Else
h% = 1
End If
sm oldy$, "*", LTrim$(Str$(j&& - h%)), runningtotal$
If String$(Len(z$), "0") = z$ And runningtotal$ = "0" And i&& >= Len(decx$) Then Exit Do
If dpx&& = 0 Then ' Limited to && size unless converted to string.
If i&& >= Len(decx$) Then
dpx&& = Int(Len(decx$) / 2 + .5)
If dpx&& = 0 Then dpx&& = -1
End If
End If
If betatest% Then Print "Sqrt "; sqrt$; " * 2 = ";: Color 2, 0: Print LTrim$(Str$(Val(sqrt$) * 2));: Color 7, 0: Print LTrim$(Str$(j&& - h%)); " * "; LTrim$(Str$(j&& - h%)); " ="; Val(oldy$) * (j&& - h%)
sqrt$ = sqrt$ + LTrim$(Str$(j&& - h%))
sm oldy$, "*", LTrim$(Str$(j&& - h%)), runningtotal$
k$ = runningtotal$
If betatest% Then Print "Remainder "; z$; " minus "; k$; " = ";
Exit For
End If
oldy$ = y$
Next
i&& = i&& + 2
If Len(z$) >= limit&& Then Exit Do
x$ = x$ + "00"
Loop
If dpx&& Then
sqrt$ = Mid$(sqrt$, 0, dpx&& + 1) + "." + Mid$(sqrt$, dpx&& + 1)
End If
End Sub
Posts: 1,616
Threads: 157
Joined: Apr 2022
Reputation:
77
08-26-2022, 07:50 PM
(This post was last modified: 08-26-2022, 07:51 PM by Pete.)
That older version had a bug in the loop that followed: IF jj&& > 1 THEN
The latest version works, so far, as tested. Post #25 https://staging.qb64phoenix.com/showthre...25#pid5825
Pete
Posts: 1,616
Threads: 157
Joined: Apr 2022
Reputation:
77
@Jack
This is the latest update, made for console display, which allows scrolling to see all the results.
I haven't found a tweak yet that would make it process faster than the one using Treebeard's string math, but his routine would need to have the too small of a SQR(8) situation addressed, which is easy.
Code: (Select All) $CONSOLE:ONLY
_DEST _CONSOLE
DIM SHARED sqrt$, limit&&, betatest%
betatest% = 0
DIM AS STRING n, m, c, sum, f, f4, f4k, c1, c2, c3, c34k, t1, t2, t3
DIM AS LONG k, k4
DIM t AS DOUBLE
limit&& = 200: square_root "8", sqrt$ ' Limit must be as many or more digits than the max digits of the returned value for pi.
FOR pete% = 0 TO 16
digits% = pete% + 10 + pete% * 8
limit&& = digits% + 7
t = TIMER
c1 = "1103"
c2 = "26390"
c3 = "396"
f = "1"
f4k = "1"
sum = "1103"
c34k = "1"
k4 = 0
t1 = c3
t2 = c3
sm t1, "*", t2, c3
t1 = c3
t2 = c3
sm t1, "*", t2, c3
FOR k = 1 TO digits% / (7.984)
t1 = f
sm STR$(k), "*", t1, f
IF betatest% THEN PRINT "results = "; f: SLEEP
t1 = f: t2 = f
sm t1, "*", t2, f4
IF betatest% THEN PRINT "results = "; f4: SLEEP
t1 = f4: t2 = f4
sm t1, "*", t2, f4
IF betatest% THEN PRINT "results = "; f4: SLEEP
t1 = c34k
sm c3, "*", t1, c34k
IF betatest% THEN PRINT "results = "; c34k: SLEEP
t1 = STR$(k4 + 1)
t2 = f4k
sm t1, "*", t2, f4k
IF betatest% THEN PRINT "results = "; f4k: SLEEP
t1 = STR$(k4 + 2)
t2 = f4k
sm t1, "*", t2, f4k
IF betatest% THEN PRINT "results = "; f4k: SLEEP
t1 = STR$(k4 + 3)
t2 = f4k
sm t1, "*", t2, f4k
IF betatest% THEN PRINT "results = "; f4k: SLEEP
t1 = STR$(k4 + 4)
t2 = f4k
sm t1, "*", t2, f4k
IF betatest% THEN PRINT "results = "; f4k: SLEEP
k4 = k4 + 4
t1 = STR$(k)
sm t1, "*", c2, t2
IF betatest% THEN PRINT "results = "; t2: SLEEP
sm c1, "+", t2, t1
IF betatest% THEN PRINT "results = "; t1: SLEEP
sm f4k, "*", t1, t2
IF betatest% THEN PRINT "results = "; t2: SLEEP
sm f4, "*", c34k, t1
IF betatest% THEN PRINT "results = "; t1: SLEEP
sm t2, "/", t1, t3
IF betatest% THEN PRINT "results = "; t3: SLEEP
t1 = sum
sm t1, "+", t3, sum
IF betatest% THEN PRINT "sum = "; sum: SLEEP
CALL pi(t1, sum, k)
NEXT
COLOR 14, 0: PRINT "Ramanujan pi = "; MID$("3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481", 1, 11 + (k - 2) * 8)
COLOR 7, 0
t = TIMER - t
PRINT "Time:"; t: PRINT
NEXT pete%
END
SUB pi (t1$, sum$, k)
REM square_root "8", sqrt$
IF betatest% THEN PRINT "Pi # = "; sqrt$: SLEEP
t2$ = "9801"
sm sqrt$, "/", t2$, t3$
IF betatest% THEN PRINT "Pi # = "; t3$: SLEEP
sm t3$, "*", sum$, t2$
IF betatest% THEN PRINT "Pi # = "; t2$: SLEEP
sm t1$, "/", t2$, t3$
IF betatest% THEN PRINT "Pi # = "; t3$: SLEEP
sm "1", "/", t2$, t1$
IF betatest% THEN PRINT "Pi # = "; t1$: SLEEP
PRINT "loop #"; LTRIM$(STR$(k));: LOCATE , 10: PRINT " pi = "; MID$(t1$, 1, 11 + (k - 1) * 8);: COLOR 8, 0: PRINT MID$(t1$, 11 + (k - 1) * 8 + 1, 4): COLOR 7, 0
END SUB
SUB sm (s_var1$, operator$, s_var2$, runningtotal$)
DIM AS _INTEGER64 a, c, aa, cc, s, ss
stringmatha$ = s_var1$: stringmathb$ = s_var2$
SELECT CASE operator$
CASE "+", "-"
GOSUB string_add_subtract_new
CASE "*"
GOSUB string_multiply_new
CASE "/"
GOSUB string_divide
CASE ELSE
PRINT "Error, no operator selected. operator$ = "; operator$: END
END SELECT
EXIT SUB
string_divide:
terminating_decimal% = 0: divsign% = 0: divremainder& = 0: divremainder$ = "": divplace& = 0: divplace2& = 0: quotient$ = "": divcarry& = 0
divbuffer& = LEN(stringmathb$) - LEN(stringmatha$)
IF divbuffer& < 0 THEN divbuffer& = 0
d2dividend$ = stringmatha$
d1divisor$ = stringmathb$
IF LEFT$(d1divisor$, 1) = "0" AND LEN(d1divisor$) = 1 THEN PRINT "Division by zero not allowed.": divsign% = 0: EXIT SUB
IF LEFT$(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$
GOSUB string_multiply_new ' Gets runningtotal$
tempcutd$ = divremainder$ ' divremainder$ can be 00 or other leading zero values.
DO
IF LEN(tempcutd$) = 1 THEN EXIT DO
IF LEFT$(tempcutd$, 1) = "0" THEN
tempcutd$ = MID$(tempcutd$, 2)
ELSE
EXIT DO
END IF
LOOP
IF LEN(tempcutd$) > LEN(runningtotal$) OR LEN(tempcutd$) = LEN(runningtotal$) AND runningtotal$ <= tempcutd$ THEN EXIT FOR
NEXT
quotient$ = quotient$ + LTRIM$(STR$(div_i%))
stringmatha$ = LTRIM$(STR$(div_i%)): stringmathb$ = d1divisor$
GOSUB string_multiply_new ' Gets runningtotal$
stringmatha$ = divremainder$: stringmathb$ = runningtotal$
operator$ = "-": GOSUB string_add_subtract_new
divremainder$ = runningtotal$
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
stringmathb$ = quotient$: quotient$ = ""
IF stringmathb$ = "overflow" THEN divsign% = 0: EXIT SUB
runningtotal$ = stringmathb$: stringmathb$ = ""
IF divsign% THEN runningtotal$ = "-" + runningtotal$
IF stringmathround$ <> "" THEN runningtotal$ = runningtotal$ + stringmathround$
RETURN
string_add_subtract_new:
a1$ = stringmatha$: b1$ = stringmathb$
s = 18: i&& = 0: c = 0
a$ = stringmatha$: b$ = stringmathb$: op$ = operator$
IF op$ = "-" THEN
IF LEFT$(b$, 1) = "-" THEN b$ = MID$(b$, 2) ELSE b$ = "-" + b$
END IF
IF INSTR(a$, ".") <> 0 OR INSTR(b$, ".") <> 0 THEN
decimal% = -1
IF INSTR(a$, ".") <> 0 THEN
dec_a&& = LEN(MID$(a$, INSTR(a$, ".") + 1))
a$ = MID$(a$, 1, INSTR(a$, ".") - 1) + MID$(a$, INSTR(a$, ".") + 1)
END IF
IF INSTR(b$, ".") <> 0 THEN
dec_b&& = LEN(MID$(b$, INSTR(b$, ".") + 1))
b$ = MID$(b$, 1, INSTR(b$, ".") - 1) + MID$(b$, INSTR(b$, ".") + 1)
END IF
' Line up decimal places by inserting trailing zeros.
IF dec_b&& > dec_a&& THEN
j&& = dec_b&&
a$ = a$ + STRING$(dec_b&& - dec_a&&, "0")
ELSE
j&& = dec_a&&
b$ = b$ + STRING$(dec_a&& - dec_b&&, "0")
END IF
END IF
IF LEFT$(a$, 1) = "-" OR LEFT$(b$, 1) = "-" THEN
IF LEFT$(a$, 1) = "-" AND LEFT$(b$, 1) = "-" THEN
sign$ = "--": a$ = MID$(a$, 2): b$ = MID$(b$, 2)
ELSE
IF LEFT$(a$, 1) = "-" THEN a$ = MID$(a$, 2): sign_a$ = "-"
IF LEFT$(b$, 1) = "-" THEN b$ = MID$(b$, 2): sign_b$ = "-"
IF LEFT$(a1$, 1) = "-" THEN a1_x$ = MID$(a1$, 2) ELSE a1_x$ = a1$
IF LEFT$(b1$, 1) = "-" THEN b1_x$ = MID$(b1$, 2) ELSE b1_x$ = b1$
string_compare a1_x$, b1_x$, gl%
IF gl% < 0 THEN
IF LEN(sign_b$) THEN sign$ = "-": SWAP a$, b$
ELSE
IF LEN(sign_a$) THEN sign$ = "-": SWAP sign_a$, sign_b$
END IF
END IF
END IF
z$ = ""
' Addition and subtraction of digits.
DO
i&& = i&& + s
x1$ = MID$(a$, LEN(a$) - i&& + 1, s)
x2$ = MID$(b$, LEN(b$) - i&& + 1, s)
zeros% = LEN(x1$): IF LEN(x2$) > zeros% THEN zeros% = LEN(x2$)
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$(zeros% - LEN(tmp$), "0") + tmp$ + z$
LOOP
IF decimal% THEN
z$ = MID$(z$, 1, LEN(z$) - j&&) + "." + MID$(z$, LEN(z$) - j&& + 1)
END IF
' Remove any leading zeros.
DO
IF LEFT$(z$, 1) = "0" THEN z$ = MID$(z$, 2) ELSE EXIT DO
LOOP
IF z$ = "" OR z$ = "0" THEN z$ = "0" ELSE z$ = LEFT$(sign$, 1) + z$
runningtotal$ = z$
sign$ = "": sign_a$ = "": sign_b$ = "": i&& = 0: j&& = 0: decimal% = 0: c = 0
RETURN
string_multiply_new:
z$ = "": sign$ = "": mult&& = 0: h&& = 0: i&& = 0: j&& = 0: c = 0: decimal% = 0
zz$ = "": ii&& = 0: jj&& = 0
s = 8: ss = 18
a$ = stringmatha$: b$ = stringmathb$
IF INSTR(a$, "-") <> 0 OR INSTR(b$, "-") <> 0 THEN
IF INSTR(a$, "-") <> 0 AND INSTR(b$, "-") <> 0 THEN
a$ = MID$(a$, 2): b$ = MID$(b$, 2)
ELSE
IF INSTR(a$, "-") <> 0 THEN a$ = MID$(a$, 2) ELSE b$ = MID$(b$, 2)
sign$ = "-"
END IF
END IF
IF INSTR(a$, ".") <> 0 OR INSTR(b$, ".") <> 0 THEN
decimal% = -1
IF INSTR(a$, ".") <> 0 THEN
dec_a&& = LEN(MID$(a$, INSTR(a$, ".") + 1))
a$ = MID$(a$, 1, INSTR(a$, ".") - 1) + MID$(a$, INSTR(a$, ".") + 1)
END IF
IF INSTR(b$, ".") <> 0 THEN
dec_b&& = LEN(MID$(b$, INSTR(b$, ".") + 1))
b$ = MID$(b$, 1, INSTR(b$, ".") - 1) + MID$(b$, INSTR(b$, ".") + 1)
END IF
END IF
IF LEN(a$) < LEN(b$) THEN SWAP a$, b$ ' Needed so x1$ is always the largest for leading zero replacements.
' Multiplication of digits.
DO
h&& = h&& + s: i&& = 0
x2$ = MID$(b$, LEN(b$) - h&& + 1, s)
DO
i&& = i&& + s
x1$ = MID$(a$, LEN(a$) - i&& + 1, s)
a = VAL(x1$) * VAL(x2$) + c
c = 0
tmp$ = LTRIM$(STR$(a))
IF LEN(tmp$) > s THEN c = VAL(MID$(tmp$, 1, LEN(tmp$) - s)): tmp$ = MID$(tmp$, LEN(tmp$) - s + 1)
z$ = STRING$(LEN(x1$) - LEN(tmp$), "0") + tmp$ + z$
LOOP UNTIL i&& >= LEN(a$) AND c = 0
jj&& = jj&& + 1
IF jj&& > 1 THEN
ii&& = 0: cc = 0
aa$ = holdaa$
bb$ = z$ + STRING$((jj&& - 1) * s, "0")
' Addition only of digits.
DO
ii&& = ii&& + ss
xx1$ = MID$(aa$, LEN(aa$) - ii&& + 1, ss)
xx2$ = MID$(bb$, LEN(bb$) - ii&& + 1, ss)
IF LEN(xx1$) < LEN(xx2$) THEN SWAP xx1$, xx2$
aa = VAL(xx1$) + VAL(xx2$) + cc
IF xx1$ + xx2$ = "" AND cc = 0 THEN EXIT DO ' Prevents leading zeros.
cc = 0
IF aa > VAL(STRING$(ss, "9")) THEN aa = aa - 10 ^ ss: cc = 1
tmp$ = LTRIM$(STR$(aa))
zz$ = STRING$(LEN(xx1$) - LEN(tmp$), "0") + tmp$ + zz$
LOOP
DO WHILE LEFT$(zz$, 1) = "0"
IF LEFT$(zz$, 1) = "0" THEN zz$ = MID$(zz$, 2)
LOOP
IF zz$ = "" THEN zz$ = "0"
holdaa$ = zz$
ELSE
holdaa$ = z$ + STRING$(jj&& - 1, "0")
END IF
z$ = "": zz$ = ""
LOOP UNTIL h&& >= LEN(b$)
z$ = holdaa$
IF decimal% THEN
DO UNTIL LEN(z$) >= dec_a&& + dec_b&&
z$ = "0" + z$
LOOP
z$ = MID$(z$, 0, LEN(z$) - (dec_a&& + dec_b&& - 1)) + "." + MID$(z$, LEN(z$) - (dec_a&& + dec_b&&) + 1)
DO UNTIL RIGHT$(z$, 1) <> "0" AND RIGHT$(z$, 1) <> "."
z$ = MID$(z$, 1, LEN(z$) - 1)
LOOP
END IF
IF z$ = "" OR z$ = "0" THEN z$ = "0" ELSE z$ = sign$ + z$
decimal% = 0: sign$ = ""
runningtotal$ = z$
RETURN
END SUB
SUB string_compare (compa$, compb$, gl%)
DO
' Remove trailing zeros after a decimal point.
IF INSTR(compa$, ".") THEN
DO UNTIL RIGHT$(compa$, 1) <> "0" AND RIGHT$(compa$, 1) <> "." AND RIGHT$(compa$, 1) <> "-"
compa$ = MID$(compa$, 1, LEN(compa$) - 1)
LOOP
END IF
IF INSTR(compb$, ".") THEN
DO UNTIL RIGHT$(compb$, 1) <> "0" AND RIGHT$(compb$, 1) <> "." AND RIGHT$(compb$, 1) <> "-"
compb$ = MID$(compb$, 1, LEN(compb$) - 1)
LOOP
END IF
IF MID$(compa$, 1, 2) = "-0" OR compa$ = "" OR compa$ = "-" THEN compa$ = "0"
IF MID$(compb$, 1, 2) = "-0" OR compb$ = "" OR compb$ = "-" THEN compb$ = "0"
' A - and +
IF LEFT$(compa$, 1) = "-" THEN j% = -1
IF LEFT$(compb$, 1) = "-" THEN k% = -1
IF k% = 0 AND j% THEN gl% = -1: EXIT DO
IF j% = 0 AND k% THEN gl% = 1: EXIT DO
' A decimal and non-decimal.
j% = INSTR(compa$, ".")
k% = INSTR(compb$, ".")
IF j% = 0 AND k% THEN
IF compa$ = "0" THEN gl% = -1 ELSE gl% = 1
EXIT DO
END IF
IF k% = 0 AND j% THEN
IF compb$ = "0" THEN gl% = 1 ELSE gl% = -1
EXIT DO
END IF
' Both decimals.
IF j% THEN
IF compa$ > compb$ THEN
gl% = 1
ELSEIF compa$ = compb$ THEN gl% = 0
ELSEIF compa$ < compb$ THEN gl% = -1
END IF
EXIT DO
END IF
' Both positive or both negative whole numbers.
SELECT CASE LEN(compa$)
CASE IS < LEN(compb$)
gl% = -1
CASE IS = LEN(compb$)
IF compa$ = compb$ THEN
gl% = 0
ELSEIF compa$ > compb$ THEN gl% = 1
ELSEIF compa$ < compb$ THEN gl% = -1
END IF
CASE IS > LEN(compb$)
gl% = 1
END SELECT
EXIT DO
LOOP
END SUB
SUB square_root (x$, sqrt$)
oldy$ = "": sqrt$ = "": custom_limit&& = 200
IF INSTR(x$, ".") THEN
decx$ = MID$(x$, 1, INSTR(x$, ".") - 1)
x$ = MID$(x$, 1, INSTR(x$, ".") - 1) + MID$(x$, INSTR(x$, ".") + 1)
IF LEN(x$) = 1 THEN x$ = x$ + "0"
ELSE
decx$ = x$
END IF
j&& = LEN(decx$)
' VAL() okay, one character eval.
IF VAL(RIGHT$(LTRIM$(STR$(j&&)), 1)) / 2 = VAL(RIGHT$(LTRIM$(STR$(j&&)), 1)) \ 2 THEN
i&& = 1 ' Even number length.
ELSE
i&& = 0 ' Odd number length.
END IF
DO
sm z$, "-", k$, runningtotal$
z$ = runningtotal$ + (MID$(x$, i&&, 2))
IF LEFT$(z$, 1) = "0" THEN z$ = MID$(z$, 2) ' Remove leading zeros
oldy$ = ""
FOR j&& = 1 TO 10
IF i&& > 1 THEN
sm sqrt$, "*", "2", y$
y$ = y$ + LTRIM$(STR$(j&&))
ELSE
y$ = LTRIM$(STR$(j&&))
END IF
sm y$, "*", LTRIM$(STR$(j&&)), runningtotal$
string_compare runningtotal$, z$, gl%
IF gl% > -1 THEN
IF gl% = 0 THEN
h% = 0: oldy$ = y$ ' Perfect square division.
ELSE
h% = 1
END IF
sm oldy$, "*", LTRIM$(STR$(j&& - h%)), runningtotal$
IF STRING$(LEN(z$), "0") = z$ AND runningtotal$ = "0" AND i&& >= LEN(decx$) THEN EXIT DO
IF dpx&& = 0 THEN ' Limited to && size unless converted to string.
IF i&& >= LEN(decx$) THEN
dpx&& = INT(LEN(decx$) / 2 + .5)
IF dpx&& = 0 THEN dpx&& = -1
END IF
END IF
IF betatest% < -1 THEN PRINT "Sqrt "; sqrt$; " * 2 = ";: COLOR 2, 0: PRINT LTRIM$(STR$(VAL(sqrt$) * 2));: COLOR 7, 0: PRINT LTRIM$(STR$(j&& - h%)); " * "; LTRIM$(STR$(j&& - h%)); " ="; VAL(oldy$) * (j&& - h%)
sqrt$ = sqrt$ + LTRIM$(STR$(j&& - h%))
sm oldy$, "*", LTRIM$(STR$(j&& - h%)), runningtotal$
k$ = runningtotal$
IF betatest% < -1 THEN PRINT "Remainder "; z$; " minus "; k$; " = ";
EXIT FOR
END IF
oldy$ = y$
NEXT
i&& = i&& + 2
IF LEN(z$) >= custom_limit&& THEN EXIT DO
x$ = x$ + "00"
LOOP
IF dpx&& THEN
sqrt$ = MID$(sqrt$, 0, dpx&& + 1) + "." + MID$(sqrt$, dpx&& + 1)
END IF
END SUB
Pete
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