TODO.md

TODO

• crtp
• divide sequence.hpp into smaller pieces
• bigint
  • bit operations
    • inplace bit operations
  • add
    • add_with_carry
      • with intrinsics
        • x86
        • cuda
    • add_with_carry inplace
      • with intrinsics
    • add: $c = a + b \pmod{\mathrm{LIMB_BITS}}$
    • add inplace: $a = a + b \pmod{\mathrm{LIMB_BITS}}$
    • add group add: $c = a + b \pmod{M}$
    • add group add inplace: $a = a + b \pmod{M}$
  • sub
    • sub_with_borrow
      • with intrinsics
    • sub_with_borrow inplace
      • with intrinsics
    • sub: $a = b - c \pmod{\mathrm{LIMB_BITS}}$
    • sub inplace: $a = a - b \pmod{\mathrm{LIMB_BITS}}$
    • add group sub: $a = b - c \pmod{M}$
    • add group sub inplace: $a = a - b \pmod{M}$
  • mul
    • Interleaved Multiplication-reduction Method
    • Montgomery Multiplication
      • Q: What about $N$ that is not coprime with $b$?
        • Q: Is mon-mul capable of handling this?
          A: No
          • Q: If not, what's a good alternative?
            A: A possible alternative is to use Interleaved Multiplication-reduction Method instead
          • Q: Is mon-arithmetic + $\mathbb{F}_{2^q}$ arithmetic + CRT a probable or even a good solution?
  • inv
    • Montgomery Inversion
• hashing
  • working implementation
    • bigint
    • point
  • hash_combine
  • hasher
• hash table
  • static
    • perfect hash function
      • CHD algorithm
      • HIT algorithm
      • Fredman algorithm
• remove all non-constant indexing of array in __device__ function
• replace array based interface with sequence based (Maybe 2.0?)
• refactor operations for heterogeneous data structures (Maybe 2.0?)
• fix segment fault under Clang in release mode