03-Jul-2023 17:05:40

vpa_test():
  MATLAB/Octave version 5.2.0.
  Use the Symbolic package for high precision calculations.

agm_pi_test()
  agm_pi() computes the value of pi using the 
  arithmetic-geometric-mean approach.

  Request PI to 10, 20, 40, 80 digits.

  Digits   PI:

Symbolic pkg v3.1.1: Python communication link active, SymPy v1.11.1.
p = (sym) 3.141592654
p = (sym) 3.1415926535897932385
p = (sym) 3.141592653589793238462643383279502884197
p = (sym)

  3.1415926535897932384626433832795028841971693993751058209749445923078164062862
  090


  How long does it take to compute PI to D digits?

          Digits    Seconds

   1           2        0.261889
   2           4        0.371268
   3           8        0.481268
   4          16        0.592613
   5          32        0.702933
   6          64        0.814228
   7         128        0.931292
   8         256         1.05974
   9         512         1.18304
  10        1024         1.36402
  11        2048         1.60449
  12        4096         2.17194
  13        8192          3.8248
  14       16384         9.52797
  15       32768         31.0163

agm_pi_test()
  Normal end of execution.

bbp_pi_test():
  bbp_pi() can compute 13 hexadecimal digits at a time
  in the value of pi using the Bailey-Borwein-Plouffe approach.
  Usually the first 11 or 12 digits are accurate.

  Request PI to 10, 20, 40, 80 hexadecimal digits.

  Digits   PI:

  0: 9  243F6A8885
  0:19  243F6A8885A308D31319
  0:29  243F6A8885A308D313198A2E037073
  0:39  243F6A8885A308D313198A2E03707344A4093822

  Correct hexadecimal representation of pi to 80 hexadecimal digits:
              1         2         3         4         5         6         7         8
    012345678901234567890123456789012345678901234567890123456789012345678901234567890
  3.243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89452821E638D01377B

  How long does it take to compute 13 digits of PI starting at digit D?

               D         Seconds

   1           2       0.0014112
   2           4      0.00199509
   3           8      0.00340414
   4          16      0.00661612
   5          32       0.0137711
   6          64       0.0298002
   7         128       0.0649939
   8         256        0.142051
   9         512        0.308394
  10        1024        0.667056
  11        2048         1.43361
  12        4096         3.06883
  13        8192         6.53818
  14       16384         13.8897
  15       32768         29.3835

  We skip chud_pi_test(), because there is some flaw
  in the code when executing under Octave with the
  symbolic package.

vpa_test():
  Normal end of execution.

03-Jul-2023 17:07:35