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+--- Thread: KISS MY ASCII GOOD PI! (/showthread.php?tid=795)
KISS MY ASCII GOOD PI! - Pete - 08-22-2022
So I updated my pi approximation routine with my faster string math addition/subtraction/multiplication routine and got...
3.14149 and change in about 15-minutes. Now my system is Mem/CPU challenged, so I suspect your systems might be able to turn and burn the 10,000 iterations it took to achieve that in under 5-minutes. Anyway pi by Liebniz's method (1 - (1/3) + (1/5)... = pi /4) appears valid, but to get anything close to accurate would take maybe what, 50,000 iterations? Also, I cheated a bit by not increasing the digit limit to over 1,000 and I used the betatest% variable to direct the routine to cut the final division calculation to 32 digits. I did that because I have not addressed a faster way to do long division by chunks or some other method in my new improved string math routines. If I left that last cheat out, the difference would not be all that great and the calculation time would probably be a few hours and burn up the CPU.
Anyway, if you are impatient, just play around with lowering the loops. It will do 500 very fast.
Code: (Select All)
DIM SHARED betatest%: betatest% = -2
WIDTH 160, 43
_SCREENMOVE 0, 0
limit&& = 128
j = -1
FOR i = 1 TO 10000
IF betatest% <> -1 THEN IF i MOD 100 = 0 THEN PRINT "Loop"; i
j = j + 2
IF oldd$ = "" THEN
d$ = "1": oldd$ = "1": oldn$ = "1": n$ = "1"
ELSE
d$ = LTRIM$(STR$(j))
' 2nd denominator * 1st numerator.
a$ = d$: b$ = oldn$: op$ = "*"
CALL string_math(a$, op$, b$, x$, limit&&)
m1$ = x$
' 1st denominator * 2nd numerator.
a$ = oldd$: b$ = n$
CALL string_math(a$, op$, b$, x$, limit&&)
m2$ = x$
' Get common denominator
a$ = d$: b$ = oldd$
CALL string_math(a$, op$, b$, x$, limit&&)
d$ = x$
a$ = m1$: b$ = m2$: IF i / 2 = i \ 2 THEN op$ = "-" ELSE op$ = "+"
CALL string_math(a$, op$, b$, x$, limit&&)
REM PRINT "oldn$ = "; oldn$; " oldd$ = "; oldd$, "n$ = "; x$; " d$ = "; d$
IF betatest% = -1 THEN PRINT "n$ = "; x$; " d$ = "; d$;: COLOR 14, 0: PRINT " "; op$; " 1/"; LTRIM$(STR$(j)): COLOR 7, 0
oldn$ = x$: oldd$ = d$
END IF
NEXT
n$ = x$
a$ = x$: b$ = d$: op$ = "/"
IF betatest% = -1 THEN ' Reduce for speed increase
limit&& = 32
j&& = LEN(b$) - LEN(a$)
a$ = MID$(a$, 1, 32)
b$ = MID$(b$, 1, j&& + 32)
PRINT: PRINT "Numerator = "; a$; " "; "Denominator = "; b$
ELSE
IF betatest% = -2 THEN
limit&& = 32
j&& = LEN(b$) - LEN(a$)
a$ = MID$(a$, 1, 32)
b$ = MID$(b$, 1, j&& + 32)
PRINT: PRINT "Numerator = "; a$; " "; "Denominator = "; b$
ELSE
PRINT "Begin long division...": PRINT
END IF
END IF
CALL string_math(a$, op$, b$, x$, limit&&)
a$ = x$: b$ = "4": op$ = "*"
CALL string_math(a$, op$, b$, x$, limit&&)
PRINT: PRINT "pi = "; x$
END
SUB string_math (stringmatha$, operator$, stringmathb$, runningtotal$, limit&&)
DIM AS _INTEGER64 a, c, aa, cc, s, ss
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: m_product$ = 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$) > LEN(m_product$) 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: m_product$ = runningtotal$
operator$ = "-"
stringmatha$ = divremainder$
stringmathb$ = m_product$
GOSUB string_add_subtract_new
stringmatha$ = runningtotal$ '*'
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_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$) TO 1 STEP -1 ' Multiply each charater top and bottom.
m_k& = m_l&
m_x2$ = 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$: m_product$ = ""
IF stringmathb$ = "overflow" THEN EXIT SUB
runningtotal$ = stringmathb$: stringmathb$ = ""
IF m_sign% THEN runningtotal$ = "-" + runningtotal$: m_sign% = 0
EXIT SUB
string_add_subtract:
IF INSTR(stringmatha$, ".") <> 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)
GOSUB string_comp
IF gl% < 0 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)
GOSUB string_comp
IF gl% < 0 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)
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
IF stringmathb$ = "overflow" THEN n2sign$ = "": EXIT SUB
runningtotal$ = n2sign$ + stringmathb$: n2sign$ = ""
EXIT SUB
'------------------------------------------------------------------------
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$) - i&& + 1, s)
a = VAL(sign_a$ + 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
IF operationdivision% THEN RETURN
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
IF LEN(a$) < LEN(b$) THEN SWAP a$, b$
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$
IF operationdivision% THEN RETURN
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 SUBPete
PS Sorry about the title, Steve. (I might have got his hopes up it meant I was de-partying!)
RE: KISS MY ASCII GOOD PI! - Kernelpanic - 08-22-2022
Something may be wrong with your solution. Even after 2500 iterations, the result is still far from a correct result.
![[Image: PI-Pete-vs-Ramanujan.jpg]](https://i.ibb.co/vmWYjv8/PI-Pete-vs-Ramanujan.jpg)
RE: KISS MY ASCII GOOD PI! - Pete - 08-22-2022
Well, if you rad the post, my routine calculates pi using Liebniz's method. My gripe with his method is it takes 10,000 iterations to get to 3.14149, which is close to 3.14159, but still not quite there yet. So what I don't like about his method is that by the time you get 10,000, you have hundreds of decimal places present in the output, but only the first 3 are correct. So his method may be valid if you can continue it over a few million iterations to what, maybe 20 or 30 decimal places? How many iterations before 128-digits can be produced correctly? Frankly, I conclude the Liebniz method to simple algorithm for a pi estimator, but not a good practical pi calculator. It certainly can't be used for any of the mega-math pi calculations we see with correct output to trillions of digits.
An issue I would have with Ramanujan's method is it depends on constantly using the square root of 2, which is an irrational number. So we have an irrational number essentially corrupting proper fractions to obtain a transcendental (irrational) number, pi. What I do like about his method is it approximates pi for the first 5-digits with many less iterations as Liebniz's method.
Out of curiosity, do you know the calculations needed to obtain the numerators and denominators in each iteration in that table of Ramanujan's method? My hunch is they are log created, which I could not use, as I have not yet created a string math log routine.
Pete
RE: KISS MY ASCII GOOD PI! - Kernelpanic - 08-22-2022
Quote:Out of curiosity, do you know the calculations needed to obtain the numerators and denominators in each iteration in that table of Ramanujan's method? My hunch is they are log created, which I could not use, as I have not yet created a string math log routine.
That's the problem, my problem, I can't get this damn formula converted into a computer program. There is a mistake somewhere in my implementation so far, but where?
The formula isn't any more complicated than the financial mathematical formulas that I implemented in C over 20 years ago.
Example - Now bplus gets upset again because it is a German text.
![[Image: Finanzformeln-KL.jpg]](https://i.ibb.co/5T4t2QC/Finanzformeln-KL.jpg)
beste bildersuche web
RE: KISS MY ASCII GOOD PI! - Pete - 08-22-2022
Hey, I did better than Mark (bplus), because I recognized one word... Damit. Well damn it, I never knew that was a German word!
Well my mad math skills are 40 years behind me, so that example is lost on me in present time, damit.
Pete
RE: KISS MY ASCII GOOD PI! - Kernelpanic - 08-22-2022
(08-22-2022, 03:49 PM)Pete Wrote: Hey, I did better than Mark (bplus), because I recognized one word... Damit. Well damn it, I never knew that was a German word!
Well my mad math skills are 40 years behind me, so that example is lost on me in present time, damit.
Pete
You enjoy math: It could be this formula conversion (photo), but I'm not sure.
Maybe I'll try to implement this in Basic.
Do you know what "gift" means in German?
Code: (Select All)
void effektivZins( double nominal_zins, double kurs, double p_annu, int t_frei )
{
int x, tz;
double AZ, Co, q, t, n;
double p, pi, g, r, rl;
double fk1, fk2, fg1, fg2, pa;
double pd1, pd2, qi1, qi2;
double C1, C2, dy;
char puffer[64]; //AZ=Abschluázahlung
//Co=Ausgabekurs
//p=Nominalzins
//pi=Effektivzins
//q=Aufzinsfaktor, q=1+i
//fg=nachsch. Rentenbarwertfaktor
//fk, fk2=Hilfsvariablen
//r=Laufzeit
//g=ganzzahliger Teil der Laufzeit
//rl=restl. Laufzeit
//t=Tilgungssatz
//n=g+1
//pa=Prozentannuit„t
//pd1,2 qi1,2 C1,2 dy=Hilfsvariable
printf( "\nDie Effektivverzinsung der Annuitaetenschuld mit %d tilgungsfreien ", t_frei);
printf( "Jahr(en) \nbetraegt : " );
p = nominal_zins;
pa = p_annu;
tz = t_frei;
Co = kurs;
//------------------------------------
q = 1 + (p / 100);
t = pa - p; //Tilgungssatz
//Laufzeit (6-31) S.228
r = (log(pa) - log(t)) / log(q);
x = 1;
//... und ganzzahlige Tilgungsdauer ermitteln
rl = fmod(r, x);
g = r - rl;
//** Effektivzins bei P.-annuität mit tilgungsfreier Zeit S.232(77) **
//====================================================================
//Abschlußzahlung (6-30) und S.228
AZ = ((100 * pow(q, g)) - (pa * ((pow(q, g) - 1) / (q - 1)))) * q;
//Laufzeit mit Abschluázahlung S.230 unten
n = g + 1;
//Effektivzins nach Nährungsformel (6-7) "Faustformel"
pi = ((p + ((100 - Co) / n)) / Co) * 100;
x = 1;
//Zwei Zinsätze fr C1 und C2 ermitteln
dy = fmod(pi, x); //Nachkommarest ermitteln
//Bandbreite der Zinss„tze z.B.: pi=7.2 --> pd1=7.0 -- pd2=7.5
if ( dy > 0.5 )
{
pd1 = pi - (dy / 2);
pd2 = pi + (dy / 2);
}
else
{
pd1 = pi - dy;
pd2 = pi + dy + 0.1;
}
//Effekt.- Aufzinsfaktoren der beiden Zinss„tze fr C1, C2 bestimmen
qi1 = 1 + (pd1 / 100);
qi2 = 1 + (pd2 / 100);
//** Jeweils 2 (fk,fg) und nach! den Eff.-aufzinsfaktoren **
//'fk' (6-32), wie nachschüssiger Rentenbarwertfaktor (6-18) S.215
fk1 = (1 / pow(qi1, tz)) * ((pow(qi1, tz) - 1) / (qi1 - 1));
fk2 = (1 / pow(qi2, tz)) * ((pow(qi2, tz) - 1) / (qi2 - 1));
//'fg'(6-32), wie oben
fg1 = (1 / pow(qi1, g)) * ((pow(qi1, g) - 1) / (qi1 - 1));
fg2 = (1 / pow(qi2, g)) * ((pow(qi2, g) - 1) / (qi2 - 1));
//Ausgabekurs (6-34) S.230, fr beide Zinss„tze
C1 = p * fk1 + ((pa * fg1 + (AZ * (1 / pow(qi1, n)))) * (1 / pow(qi1, tz)));
C2 = p * fk2 + ((pa * fg2 + (AZ * (1 / pow(qi2, n)))) * (1 / pow(qi2, tz)));
//Eff.-zins Nährungslösung durch lineare Interpolation (Kopie S.642)
pi = pd1 + ((pd2 - pd1) * ((C1 - Co) / (C1 - C2)));
printf( "%7.5f", pi);
printf( " %%\n" );
//getch();
}RE: KISS MY ASCII GOOD PI! - Pete - 08-22-2022
Gift in German? As in the Democrat Party is a gift to America? Yeah, that's about as toxic as it gets.
So for math fun, I ran your code in the other pi post through my string math routines: https://qb64phoenix.com/forum/showthread.php?tid=770&pid=5669#pid5669
I haven't got to the point of making it very user friendly yet, but you are welcome to use it if it helps you in your projects.
Pete
RE: KISS MY ASCII GOOD PI! - Kernelpanic - 08-22-2022
There is a misconception somewhere in the implementation of Rama's formula - but where? See screenshot.
That's right. Also the last digit is OK too. But how one get there with n = 1? (German Wiki) - I can't even do it with n = 0.
Code: (Select All)
Dim As Double pi
pi = Sqr(2) * (2510613731736 / 1130173253125)
Print pi![[Image: PI-All-unclear-I-hope.jpg]](https://i.ibb.co/0GCBMJt/PI-All-unclear-I-hope.jpg)
RE: KISS MY ASCII GOOD PI! - Kernelpanic - 08-22-2022
@Pete - You're thinking too complicated, I'm thinking mathematically wrong.
It's like the Gordian Knot! Where is an Alexander?
Good night, and keep cool:
RE: KISS MY ASCII GOOD PI! - SMcNeill - 08-22-2022
Here's my little attempt at finding Pi. This relies on some very impressive math formulas and such, but it can calculate up to a million digits of PI for us in about 1/10th of a second! (Just expect QB64 to spend quite a bit longer to print the results to screen for you than that -- our print routine isn't very quick at all!)
![[Image: image.png]](https://i.ibb.co/xD6N7H9/image.png)
The program here is a little too large to fit and play nicely inside a code box, so I'll attached it below for ease of download and reference.
I hope you appreciate all the time and effort I put into this for you @Pete! I doubt you'll ever find another method any more accurate or faster than this one!!