cubic root

[clamicun]

I am "playing around" with FPU instructions.
Trying to build a small calculator.
It exists FSQRT to get the square root of the value in ST(0).
But I am breaking my head to get a cubic root.
There is no FPU instruction.
Any ideas ?

[FORTRANS]

Hi,

Any ideas ?

   Look at the exponential function and raise your value to the
one third power.

Cheers,

Steve N.

[clamicun]

Thank you Steve,

if you say "function" do you refer to
Logarithmic and exponential instructions ?

F2XM1     2 to the X power Minus 1
FSCALE    SCALE ST(0) by ST(1)
FYL2X     Y*Log2X
FYL2XP1   Y*Log2(X+1)

[FORTRANS]

Hi,

   Yes.  Particularly F2XM1.  FSCALE uses only integer exponents.

HTH,

Steve

[clamicun]

Thanks ... will try it

[jj2007]

Example:

include \masm32\MasmBasic\MasmBasic.inc      ; download
  Init

  fld FP10(0.33333333333333333333333333333)
  fld FP10(8.0)      ; 2^3
  fyl2x
  f2xm1
  fld1
  fadd
  Print Str$("The result is %Jf\n", ST(0))

  fld FP10(0.33333333333333333333333333333)
  fld FP10(1.8816763723536577724902657494247)      ; 1.2345^3
  fyl2x
  f2xm1
  fld1
  fadd
  Print Str$("The result is %Jf\n", ST(0))

EndOfCode

Output:

Code Select Expand

The result is 2.000000000000000000
The result is 1.234567890123456789

There is a more detailed example Posted on 2003-08-20 12:59:18 by Raymond, plus a fairly complex function that does not have the limitations of the log functions - see attachment (opens in WordPad in case you don't have RichMasm).

[Mikl__]

Root of the N-th power of the number

Code Select Expand

      fld Exponent
      fld st ;st=st(1)
      fabs ;st=|exp|
      fld Max
      fcompp ;leave exp in st(0)
      fstsw ax
      sahf
      jb @@RealPower ;exp > MaxInt?
      fld st ;exp=st(0)=st(1)
      frndint ;round(exp)
      fcomp ;compare exp and round(exp)
      fstsw ax
      sahf
      jne @@RealPower
      fistp IntExp
      mov eax, IntExp ;eax=Trunc(Exponent)
      mov ecx, eax
      cdq
      fld1 ;st(0)=1
      xor eax, edx
      sub eax, edx ;eax=|exp|
      jz @@Exit
      fld Base
      jmp @@Entry
@@Loop:fmul st, st ;st(0)=Base^2
@@Entry:shr eax, 1
      jnc @@Loop
      fmul st(1), st ;Result * X
      jnz @@Loop
      fstp st
      cmp ecx, 0
      jge @@Exit
      fld1
      fdivrp ;st(0)=1/Result
      jmp @@Exit
@@RealPower:fld Base
      ftst
      fstsw ax
      sahf
      jz @@Done
      fldln2
      fxch
      fyl2x
      fxch
      fmulp st(1), st
      fldl2e
      fmulp st(1), st
      fld st(0)
      frndint
      fsub st(1), st
      fxch st(1)
      f2xm1
      fld1
      faddp st(1), st
      fscale
@@Done:fstp st(1)
@@Exit:

[clamicun]

JJ,
fld FP10(8.0)      ; 2^3 ok.
If I change this to e.g.
fld FP10(27.0)      ; 3^3 not ok.
fld FP10(64.0)      ; 4^3 not ok.
??

[raymond]

If you have the MASM32 FDK,  you can use the FpuXexpY function of the provided Fpu.lib library, with 1/3 as the exponent. Or, if you want to code the FPU yourself, you can always look at the source code of that function and adapt it to your own specific needs.

[clamicun]

Mikl__

.data ???

[Mikl__]

Guten Abend, clamicun!
Wählen Sie die Daten auf eigene Faust. Das Programm berechnet nicht nur die Wurzel des Würfels

[clamicun]

Mikl__ Danke,
aber was ist der "Input" ? --- also der Wert aus dem die 3Wurzel berechnet werden soll --- Max ?

intExp ??
base  ??

[jj2007]

JJ,
fld FP10(8.0)      ; 2^3 ok.
If I change this to e.g.
fld FP10(27.0)      ; 3^3 not ok.
fld FP10(64.0)      ; 4^3 not ok.
??

There is a more detailed example Posted on 2003-08-20 12:59:18 by Raymond, plus a fairly complex function that does not have the limitations of the log functions

There is no easy way out

[clamicun]

JJ,
"CubeLogA"  from Raymond works perfekt  with integers ...
wonder how floats are working.

[Mikl__]

Code Select Expand

; GUI #
include win64a.inc
include msvcrt.inc
includelib msvcrt.lib
.data
n dd 3.0,3.0,3.0,3.0;exponent
y dd 125.0,?,?,?;number
x dd ?,?,?,?;result
.code
WinMain proc
sub esp,28h
movups xmm0,y
rcpps xmm1,n ;xmm1=1/exponent
invoke powf;float powf(float x, float y);Calculates x raised to the power of y 
        movups x,xmm0;x=y^{1/n}
fld x
fistp x
mov eax,x
invoke ExitProcess,0
WinMain endp
end