Josef Eschgfaeller wrote:
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?
For most floating point operations R uses "double precision", which gives about 18-19 significant digit precision. Leading zeros don't count.
Duncan Murdoch
Thanks Josef Eschgf�ller 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
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