C++存储超大整数的低编译时方法及无额外库实现咨询

Great question! When working with extremely large integers in C++ that go way beyond the limits of built-in types like long long, here are some practical, no-external-library approaches to store them efficiently while keeping compile times snappy:

1. Fixed-Size Arrays or std::array (Best for Known Maximum Lengths) #

• If you know the maximum number of digits or bits your large integer will have upfront, fixed-size arrays are the fastest option for compilation. The compiler can allocate stack space directly at compile time, with no dynamic memory overhead.
• Storage options:
  • Store individual decimal digits in a uint8_t array (e.g., uint8_t digits[20] = {1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9,0} for the number 12345678901234567890).
  • Use larger chunks (like uint64_t blocks) to store groups of bits/hex digits—this makes arithmetic operations faster later on, while still keeping compile times low.
• Compile time win: No template instantiation overhead (unlike some dynamic containers) and the compiler can optimize the array directly into your binary.

2. std::vector with Preallocation (For Dynamic Lengths) #

• If you don’t know the maximum size of your large integer upfront, std::vector is a flexible choice that still keeps compile times reasonable. The key is to use reserve() to preallocate enough space upfront, avoiding repeated reallocations.
• Example:

  std::vector<uint64_t> big_num_blocks;
  big_num_blocks.reserve(10); // Preallocate space for 10 64-bit blocks
  // Add blocks (starting from the least significant bits)
  big_num_blocks.push_back(0x1234567890ABCDEF);
  big_num_blocks.push_back(0xFEDCBA0987654321);
  

• Compile time note: std::vector is part of the standard library, so compilers have highly optimized implementations for it—you won’t see a big compile time hit compared to fixed arrays.

3. std::string (Simplest for Static Values) #

• For static large integers that you don’t need to perform arithmetic on often, storing them as a std::string literal is the quickest to compile. The compiler processes string literals directly at compile time, embedding them into your binary without extra code.
• Example:

  const std::string big_num = "1234567890123456789012345678901234567890";
  

• Caveat: Arithmetic operations on string-stored integers require逐位 processing, which is slower than array-based storage. But if your main goal is storage with minimal compile time, this is unbeatable.

4. Hash-Based Storage (For Verification/Indexing Only) #

• If you don’t need to recover the full large integer later—only need a unique identifier or checksum—you can compute a hash of the integer (in string or array form) and store that hash. This is extremely fast to compile, as hash calculations can even be done at compile time for static values.
• Example of compile-time hash for a string literal:

  constexpr size_t hash_big_num(const char* s) {
      size_t h = 0;
      while (*s) {
          h = h * 31 + static_cast<size_t>(*s++);
      }
      return h;
  }
  
  constexpr size_t big_num_hash = hash_big_num("12345678901234567890");
  

• Important: Hashes are one-way functions—you can’t reverse-engineer the original large integer from the hash. Use this only for use cases like checking data integrity or indexing.

Quick Compile Time Tips #

• Avoid overcomplicating with template metaprogramming: While templates can enable compile-time calculations, complex template structures will slow down compilation. Stick to simple containers for storage.
• Use constexpr for static values: If your large integer is a compile-time constant, initialize arrays or hashes with constexpr—the compiler will embed the final value directly into your binary, with no runtime initialization overhead.

内容的提问来源于stack exchange，提问作者mss