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Advanced - Number Theory Ā· 4:17
Arbitrary-Precision Integers
When a value outgrows 64 bits, store it as a vector of 9-digit limbs in base 10^9, least significant first, and print every limb but the top one padded to 9 digits. Addition and subtraction carry and borrow limb by limb, multiplication fills an O(nĀ·m) grid of 64-bit limb products, and division by a small number runs from the top limb down; the same thinking explains why trading systems keep prices as integer ticks and accumulate notional in 128 bits instead of doubles.
You will learn
- Store a big integer as base-10^9 limbs, least significant first, and print it correctly with %09d padding
- Implement addition, subtraction (with borrow and leading-zero stripping), multiplication in O(nĀ·m) and division by a short integer
- Avoid the classic bugs: missing 1LL in limb products, unsigned size_t underflow in downward loops, unpadded output
- Explain why prices are stored as integer ticks or fixed-point decimals rather than doubles, and when notional needs 128-bit accumulation