PI and accuracy of a floating-point number

Question

A single/double/extended-precision floating-point representation of Pi is accurate up to how many decimal places?

Answer 1

World of PI have PI to 100,000,000,000 digits, you could just print and compare. For a slightly easier to read version Joy of PI have 10,000 digits. And if you want to remember the digits youself you could try lerning the Cadaeic Cadenza poem.

Answer 2

In the x86 floating-point unit (x87) there are instructions for loading certain floating point constants. "fldz" and "fld1" load 0.0 and 1.0 onto the stack top "st" (aka "st(0)") for example. Another is "fldpi".

All these values have a mantissa that's 64 bits long which translates into close to 20 decimal digits. The 64 bits are possible through the 80-bit tempreal floating point format used internally in the x87. The x87 can load tempreals from and store them to 10 byte memory locations as well.

Answer 3

6 places and 14 places.1 place is over 0 for the 3, and the last place although stored can't be considered as a precision point.

And sorry but I don't know what extended means without more context. Do you mean C#'s decimal?

Answer 4

#include <stdio.h>

#define E_PI 3.1415926535897932384626433832795028841971693993751058209749445923078164062

int main(int argc, char** argv)
{
    long double pild = E_PI;
    double pid = pild;
    float pif = pid;
    printf("%s\n%1.80f\n%1.80f\n%1.80Lf\n",
    "3.14159265358979323846264338327950288419716939937510582097494459230781640628620899",
    pif, pid, pild);
    return 0;
}

Results:

[quassnoi #] gcc --version
gcc (GCC) 4.3.2 20081105 (Red Hat 4.3.2-7)

[quassnoi #] ./test

3.14159265358979323846264338327950288419716939937510582097494459230781640628620899

3.14159274101257324218750000000000000000000000000000000000000000000000000000000000
        ^
3.14159265358979311599796346854418516159057617187500000000000000000000000000000000
                 ^
3.14159265358979311599796346854418516159057617187500000000000000000000000000000000
                 ^
  0000000001111111
  1234567890123456