On May 23, 12:39*am, Andrew Lee <fiacre.patr...@gmail.comwrote:

Mensanator wrote:
On May 22, 11:32 am, "Dutton, Sam" <Sam.Dut...@itn.co.ukwrote:
I've noticed that the value of math.pi -- just entering it at the interactive prompt -- is returned as 3.1415926535897931, whereas (as every pi-obsessive knows) the value is 3.1415926535897932... (Note the 2 at the end.)

Is this a precision issue, or from the underlying C, or something else?How is math.pi calculated?

If you actually need that many digits, use a different library.

>>import gmpy

>>print gmpy.pi(64) # 64 bit precision

3.14159265358979323846
>>print gmpy.pi(128) # 128 bit precision

3.141592653589793238462643383279502884197
>>print gmpy.pi(16384) # 16384 bit precision

3.141592653589793238462643383279502884197169399375 10582097494459

23....

Heh!

I wonder who needs that many digits?

Pi digits specifically, or that many digits

in general? I generally don't use pi, but

I routinely work with numbers having that

many digits.

>

Certainly not number theorists (they need a LOT more).

That depends on the problem. What's important

to the number theorist is not how many digits

there are, but the fact that every single one

of them is significant. If pi is needed, the

mantissa must have as many digits as the number

to avoid loss of significance.

For example, in the Collatz Conjecture, there

is a nice closed form equation to tell you the

ith, kth Generation Type [1,2] Mersenne Hailstone:

a(i,k) = 2**(6*((i-1)*9**(k-1)+(9**(k-1)-1)/2+1)-1)-1

Which for a modest request like a(1,6) returns

a number with 53,338 decimal digits. And you

can't even compute the 11th generation without

getting an "Outrageous Exponent" exception

(the exponent exceeded 32 bits).

Now, it's true you can't count up to such a

number, but you can readily determine its Collatz

Sequence as they are logarithmic (for a(1,6) the

sequence contains 854,697 odd numbers and about

twice that many even numbers).

And since a(1,6) has only 177,149 bits, it's

easy to verify that it is, indeed, the first

of the infinite members of the 6th generation.

Certainly not

physicists -- they need about 30 digits to be within 1% of any

measurement from molecules to galaxies. *Certainly not engineers, they

need half the digits that physicists need. *Cryptographers are making a

dire mistake if they are using PI in any computations (possible

exception for elliptic curves -- see number theorists, above) ... so --

other than PI-philes, who needs PI to thousands of digits?- Hide quoted text -

- Show quoted text -