[R] Precision

[Josef Eschgfaeller]

How precise is R numerically? For example I
wrote the following function for calculating
the volume of the ball inscribed in the
unit cube in m dimensions. In order to see what
happens in 40 dimensions, I created an output
of 24 digits. But how many are precise?

Thanks
Josef Eschgfäller
Ferrara
---------------------------------------
Vol = function (m)
{if (m<=1) 1
else Vol(m-2)*pi/(m+m)}


for (m in 1:40)
{x=sprintf('%2d   %.24f',m,Vol(m))
print(x)}
---------------------------------------
   1   1.000000000000000000000000
   2   0.785398163397448278999491
   3   0.523598775598298815658893
   4   0.308425137534042437259529
   5   0.164493406684822623953224
   6   0.080745512188280771370685
   7   0.036912234143214060766436
   8   0.015854344243815498421979
   9   0.006442400200661534299951
  10   0.002490394570192719803786
  11   0.000919972597358349329817
  12   0.000325991886927389960208
  13   0.000111160736667881195885
  14   0.000036576204182177245747
  15   0.000011640725122781503579
  16   0.000003590860448591509251
  17   0.000001075600486123191399
  18   0.000000313361689037812061
  19   0.000000088923646984269168
  20   0.000000024611369504941992
  21   0.000000006651473240385528
  22   0.000000001757247673443401
  23   0.000000000454265640598788
  24   0.000000000115011591279740
  25   0.000000000028542351985668
  26   0.000000000006948453273887
  27   0.000000000001660526728044
  28   0.000000000000389807317126
  29   0.000000000000089943078792
  30   0.000000000000020410263397
  31   0.000000000000004557492187
  32   0.000000000000001001886462
  33   0.000000000000000216936121
  34   0.000000000000000046287046
  35   0.000000000000000009736070
  36   0.000000000000000002019653
  37   0.000000000000000000413335
  38   0.000000000000000000083486
  39   0.000000000000000000016648
  40   0.000000000000000000003278