Newton had a fun way to approximate general roots...

[Pete]

Well back to working with Euler approximations. So based on his work, I put together what I think is a pretty cool way to get decimal roots like 7^2.3, 8 ^.7, etc. calculated without using logs.

So if this works, it can be adopted to use with string math routines I have already made.

DECIMAL POWERS ROUTINE

Code: (Select All)

WIDTH 120, 42
_SCREENMOVE 0, 0
DO
    INPUT "Number: "; num
    LINE INPUT "Power: "; power$
    IF INSTR(power$, ".") THEN
        t = VAL(MID$(power$, INSTR(power$, ".")))
        power$ = MID$(power$, 1, INSTR(power$, ".") - 1)

        a = 1
        b = num
        x = 0
        y = 1

        highc = b
        lowc = a
        highz = 1

        DO
            t1 = a * b
            c = SQR(t1)
            t1 = x + y
            z = t1 / 2
            IF z = t THEN EXIT DO
            IF z > t THEN
                highz = z: highc = c
            ELSEIF z < t THEN
                lowz = z: lowc = c
            END IF
            PRINT a, b, highc, lowc, z, highz, lowz
            a = highc: b = lowc
            x = highz: y = lowz
        LOOP
        IF LEN(power$) THEN
            a = num ^ VAL(power$) * a
        END IF
        PRINT "Results = "; a
    ELSE
        PRINT "Results = "; num ^ VAL(power$)
    END IF
    PRINT
LOOP

Pete