Re:How many decimals of pi do we need? (2016)
by kloch on Saturday July 02, 2022 @11:54PM
(#31964909)
It depends on the dynamic range you are working with and they type of operation. Dynamic range is critical with addition and subtraction but usually not important with multiplication and division (where only maximum exponent ranges are of concern).
For example, 1.0 + 1.616e-35 = 1.0 (exact) with double precision as the dynamic range is far too high to encode the sum within the ~16 decimal digits available. The second term just gets rounded out.
1.0 / 1.616e-35 however can be successfully encoded and you will not lose much precision, at most a rounding error in the last digit.
So, to answer your question double precision is usually sufficient even at Planck scale as long as you are not also adding/subtracting terms at much larger scales (like the 1 meter example above)
For example, 1.0 + 1.616e-35 = 1.0 (exact) with double precision as the dynamic range is far too high to encode the sum within the ~16 decimal digits available. The second term just gets rounded out.
1.0 / 1.616e-35 however can be successfully encoded and you will not lose much precision, at most a rounding error in the last digit.
So, to answer your question double precision is usually sufficient even at Planck scale as long as you are not also adding/subtracting terms at much larger scales (like the 1 meter example above)