Double precision in C++ (or pow(2, 1000))

Question

I\'m working on Project Euler to brush up on my C++ coding skills in preparation for the programming challenge(s) we\'ll be having this next semester (since they don\'t let

Answer 1

You need a bignum library, such as this one.

Answer 2

If you want to do this sort of thing on a practical basis, you're looking for an arbitrary precision arithmetic package. There are a number around, including NTL, lip, GMP, and MIRACL.

If you're just after something for Project Euler, you can write your own code for raising to a power. The basic idea is to store your large number in quite a few small pieces, and implement your own carries, borrows, etc., between the pieces.

Answer 3

UPDATE: I just browsed to the Euler Problem site and found that Problem 13 is about summing large integers. The iterated method can become very tricky after a short while, so I'd suggest to use the code from Problem #13 you should have already to solve this, because 2**N => 2**(N-1) + 2**(N-1)

Using bignums is cheating and not a solution. Also, you don't need to compute 2**1000 or anything like that to get to the result. I'll give you a hint:

Take the first few values of 2**N:

0 1 2 4 8 16 32 64 128 256 ...

Now write down for each number the sum of its digits:

1 2 4 8 7 5 10 11 13 ...

You should notice that (x~=y means x and y have the same sum of digits)

1+1=2, 1+(1+2)=4, 1+(1+2+4)=8, 1+(1+2+4+8)=16~=7 1+(1+2+4+8+7)=23~=5

Now write a loop.

Project Euler = Think before Compute!

Answer 4

C/C++ operates on fundamental data types. You are using a double which has only 64 bits to store a 1000 bit number. double uses 51 bit for the significant digits and 11 bit for the magnitude.

The only solution for you is to either use a library like bignum mentioned elsewhere or to roll out your own.

Answer 5

You probably need a pointer here (pun intended)

In C++ you would need to create your own bigint lib in order to do the same as in python.

Answer 6

Isn't pow(2, 1000) just 2 left-shifted 1000 times, essentially? It should have an exact binary representation in a double float. It shouldn't require a bignum library.