Calculating the cube root of a number

[Dreamland Fantasy]

Here is some code that I converted from C to calculate cube roots:

Code: Select all

Procedure.f CubeRoot(num.f)
  
  ; This procedure is based on code by John T. Hannon Jr
  ; published in EDN January 15, 1998
  ;
  ; Article link: http://www.edn.com/archives/1998/011598/02di.pdf
  
  error.f = 0.00001                   ; SET UP MAXIMUM ERROR
  root.f = 2.0                        ; SET STARTING VALUE
  negflag = 0
  count = 0
  
  If num < 0                          ; IF NUMBER IS NEGATIVE
    num = -num                        ; CHANGE TO POSITIVE &
    negflag = 1                       ; SET NEG. NUMBER FLAG
  EndIf
  
  While (Abs(root * root * root - num)) >= error
    root = (num / (root * root) + root) / 2
    count + 1
    If count > 25                     ; IF NO MINIMUM ERROR AFTER 25
      Break                           ; ITERATIONS, EXIT THE FUNCTION
    EndIf                             ; THIS COULD BE LARGER FOR VERY LARGE NUMBERS
  Wend
  
  If negflag = 1                      ; IF ORIGINAL NUMBER WAS NEGATIVE
    root = -root                      ; SET ROOT TO NEGATIVE NUMBER
  EndIf
  
  ProcedureReturn root
  
EndProcedure

Kind regards,

Francis.

[Derek]

And here's mine

Code: Select all

Debug Pow(100,0.3333333333)

Won't work with negative numbers though.

[Dreamland Fantasy]

And here's mine

Code: Select all

Debug Pow(100,0.3333333333)

Won't work with negative numbers though.

I know that you can do cube roots using powers to the third, but I thought the procedure I posted would of interest to some people (e.g. the basis of a high-precision cube root function or whatever).

For negative numbers using powers just use this:

Code: Select all

Procedure.f CubeRoot(n.f)
  
  If n < 0
    Negative = 1
  EndIf
  
  Root.f = Pow(Abs(n), 1/3)
  
  If Negative
    Root = -Root
  EndIf
  
  ProcedureReturn Root
  
EndProcedure

Debug CubeRoot(-27)

Kind regards,

Francis.

[Derek]

Just joking with you, I'm sure your routine will be of use to someone.

With a couple of tweaks it probably would be more useful than the pow() one as that is not very accurate, using doubles and a lower error tolerance would probably work.

Probably about time that PureBasic got itself a scientific maths dll built in.

[joske]

Thanks for sharing. This routine with Newton-Rapson iteration is much faster and more precise than the general pow(), that can be useful. You can rewrite this function very easy to calculate the square root.

I just doubt if giving an answer for a negative value makes sense - shouldn't it be better to return NaN or NotDefined in that case?

[Derek]

Cuberoot of -27 equals -3

-3 * -3 * -3 = -27

so returning NotDefined is not technically right.

[Dreamland Fantasy]

Thanks for sharing. This routine with Newton-Rapson iteration is much faster and more precise than the general pow(), that can be useful. You can rewrite this function very easy to calculate the square root.

I just doubt if giving an answer for a negative value makes sense - shouldn't it be better to return NaN or NotDefined in that case?

Glad you like it.

As Derek points out a cube root of a negative number is perfectly feasible. You only run into problems when trying to get the square root of negative numbers.

Kind regards,

Francis.