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t_cubert.bas

Uploader:	Volta
Datum/Zeit:	30.09.2010 20:42:05

'PROGRAM test_cube_root

#Include "quad_1x.bi"

Using quad_precision

#define EPSILON_HALF 2.22044604925031308E-016



Declare Function cube_root(y As quad) As quad



Dim As quad x, lhs, rhs, diff

Dim As Double  r

Dim As Integer i

Screen 0

Width 90,25

Color 15,1

Cls



Randomize 4711



For i = 1 To 20

  x.hi=Rnd

  r=Rnd

  x.hi = (x.hi - 0.5) / r

  x.lo = x.hi * EPSILON_HALF

  lhs = cube_root(x)

  If (x.hi >= 0.0) Then

    rhs = Exp( Log(x) / 3.0)

  Else

    rhs = - Exp( Log(- x) / 3.0)

  End If

  diff = lhs - rhs

  Print "lhs ="; lhs, "  Diff. ="; diff

Next

Sleep



Function cube_root(y As quad) As quad 'RESULT(x)

  '     Calculates the cube root of y in quadruple-precision.

  ' Programmer : Alan Miller, CSIRO Mathematical Information Sciences

  ' Latest revision - 6 December 1996



  Dim As quad f, xsq, x

  Dim As Double one_third = 0.33333333333333330

  '     First approximation is the double-precision cube root.

  '     Only one iteration is necessary.



  x.hi = Abs(y.hi)^ one_third

  If Sgn(y.hi) < 0.0 Then x.hi= -x.hi

  ' Put f(x) = x**3 - y

  ' Then Newton's iterative method uses:

  ' new x = x - f(x) / f'(x)

  ' Halley's method uses:

  ' new x = x - f / (f' - 0.5 * f * f'' / f')

  ' In this case

  ' new x = x - x * f / (3.x^3 - f)



  x.lo = 0.0

  xsq  = exactmul2(x.hi, x.hi)

  f    = x * xsq - y

  x    = x - x * f / (3.0 * x * xsq - f)

  Return x

End Function' cube_root

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