Crypto.Number.Basic

sqrti returns two integers (l,b) so that l <= sqrt i <= b. The implementation is quite naive, use an approximation for the first number and use a dichotomy algorithm to compute the bound relatively efficiently.

Get the extended GCD of two integer using integer divMod

gcde a b find (x,y,gcd(a,b)) where ax + by = d

Check if a list of integer are all even

Compute the binary logarithm of a integer

Compute the number of bits for an integer

Compute the number of bytes for an integer

Out of numBits rather than out of GMP's own count in base 256. GHC's bignum sizes a number in base two by looking at its highest limb, and in any other base -- 256 included -- by dividing the number down to nothing: on a 2048-bit modulus that is 1.65 us against 0.01, and every serialization here asks for the size before it allocates. Eight bits to the byte does the rest.

Express an integer as an odd number and a power of 2