Insanely small decimals

Started by
18 comments, last by Rayno 18 years, 9 months ago
Ok, you asked for it. Its 301,648 characters and nearly 300KB long. I calculated using a programming language I'm working on which makes use of the GMP and MPFR libraries. Oh, it took 0.03 second to calculate.

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Quote:Original post by Colin Jeanne
It's hard to argue with Google [grin]

On a more serious note, your math is correct. The answer is going to be insanely small as 0.5^1000000 = 1/(2^1000000). For reference, 2^x is approximately 10^(x/3) so 2^1000000 is about the same as 10^333333.


It's funny how your approximation, though off by about thirthy thousand magnitude orders is actually pretty good.
Quote:Original post by Rayno
Ok, you asked for it. Its 301,648 characters and nearly 300KB long. I calculated using a programming language I'm working on which makes use of the GMP and MPFR libraries. Oh, it took 0.03 second to calculate.

*** Source Snippet Removed ***


What approximation is that supposed to be?? Its obviously not 0.5^1000000 exact.

Quote:Original post by HAM
What approximation is that supposed to be?? Its obviously not 0.5^1000000 exact.


How is that obvious? It's not a repeating decimal...
Quote:Original post by MaulingMonkey
Quote:Original post by HAM
What approximation is that supposed to be?? Its obviously not 0.5^1000000 exact.


How is that obvious? It's not a repeating decimal...


Well multiples of 5 have an end-digit of 5.

More specifically the last three digits of the Powers of 5 end in 125 and 625, for odd and even powers respectively.

The number given is obviously not a power of 5, nor is it even a multiple of 5. Whatever it is, its not exact.
I didn't have the precision set high enough. Its actually a could hundred digits longer but it wouldn't let me modify my post. It was timing out.
Is this enough precision?

unsigned int exponent = 0;unsigned double mantissa = 1;for(unsigned int counter = 0; counter <= 1000000; counter++){    mantissa /=2;    if(mantissa < 0.1)    {        mantissa *= 10;        exponent++;    }}printf("Answer is %lf x 10 ^ -%d", mantissa, exponent);


EDIT: double guarantees at least 15 digits of precision (52 bits of mantissa), while long double guarantees at least 19 digits of precision (64 bits of mantissa)
If speed isn't terribly important OCaml has a built-in Num type for arbitrarily precise calculations, the following calculation took about 1 minute:

# let a = num_of_string "1/2";;
val a : Num.num = Ratio <abstr>
# let b = num_of_string "1000000";;
val b : Num.num = Int 1000000
# let c = a **/ b;;
val c : Num.num = Ratio <abstr>
# approx_num_exp 20 c;;
- : string = "+0.10100340591980302247e-301029"
Ok, I cranked up the precision and generated the actual number. 1000001 digits long. Its in a text file right here. Just had to do:
var x;x: precision = 4000000;x = 0.5 ** 1000000;print x;

It took about 2 seconds to generate and print.

I don't mean to plug my language, the point I'm trying to make is the GMP/MPFR are good quality and extremely fast arbitrary precision libraries.

This topic is closed to new replies.

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