'============================================================================
'   G.H. George                                                 1992 JUL 17
'                                SALAMIN.BAS          Modified  1998 APR 27
'   - Gauss-Salamin algorithm for the value of  Pi.
'   From the Mathematical Gazette, Vol. 76 (Number 476), pages 231-242,
'   1992 July.
'=============================================================================

'  Procedures:
'      <none>

'  Variables:
'    a, b, c, x, y:  variables in the algorithm
'    Iteration:      loop counter = number of iterations

DEFDBL A-Z
DIM Iteration AS INTEGER
CLS
PRINT "Gauss-Salamin Estimation of Pi:"
PRINT

LET a = 1
LET b = 1 / SQR(2)
LET c = 1 / 4
LET x = 1
PRINT "Iteration", "Estimate of Pi": PRINT

FOR Iteration = 1 TO 10
    LET y = a
    LET a = (a + b) / 2
    LET b = SQR(y * b)
    LET c = c - x * (a - y) * (a - y)
    LET x = 2 * x
    PRINT Iteration, (a + b) * (a + b) / (4 * c)
NEXT Iteration

END

'============================================================================

'Iteration           Estimate of pi

'    1             3.140579250522169
'    2             3.141592646213542
'    3             3.141592653589794
'    4             3.141592653589794
'    5             3.141592653589794            
'    6             3.141592653589794
'    7             3.141592653589794
'    8             3.141592653589794
'    9             3.141592653589794
'   10             3.141592653589794        pi = 3.141 592 653 589 794