How can I use VPA to do 32 digit precision computations?

I need to do very high precision computation (32 digit) and therefore I started to work with vpa. I eaither can't get it right or there is some bug with this function. Here is a simple test that I run:

>> clear all;syms p; f=p^10; vpa(subs(f,p,0.1),32)

 ans =
 0.000000000100000000000000055342008016114

>> clear all;syms p; f=p^10; vpa(subs(f,p,0.1),16)

 ans =
 0.0000000001000000000000001

>> clear all;syms p; f=p^10; vpa(subs(f,p,0.1),8)

 ans =
 0.0000000001

One would hope that the high precision of 32 digits, would give correct result for 10^(-10). Can you please help me understand what is goin on here?

Answer 1

[Walter Roberson]

For further reading on this topic, please see the FAQ

When you are doing the subs(), you are substituting in the binary floating point representation of 0.1 . The closest to 0.1 that can be represented is 0.1000000000000000055511151231257827021181583404541015625 .

You can fix your code by using sym('0.1') instead of 0.1