# Modern ways to store a number (float)
public: true
tags: IEEE754, DataSystems
time: 2026-01-06 05:08:56

2. Next-Generation Alternatives
The debate over replacing the 40-year-old IEEE 754 standard continues in 2026 with new mathematical approaches.
Posits (Type III Unum): Designed as a "drop-in replacement" for standard floats. Unlike IEEE 754, posits use tapered precision: they provide more accuracy for numbers close to 1 (where most math happens) and less for extremely large or small numbers. Proponents argue they offer bitwise identical results across all hardware, solving the "it works on my machine but not yours" problem in scientific computing.
Takum: A newer format emerging in 2025–2026 research that aims to match or exceed Posit's performance while maintaining better backward compatibility with existing IEEE 754 hardware. 
3. Specialized Database and Transmission Formats
Beyond PostgreSQL, other systems use specialized ways to store and move numbers.
Varint (Variable-length Integer): Used in Google’s Protocol Buffers (Protobuf) and SQLite. It uses only as many bytes as needed to store a number (e.g., the number 5 takes 1 byte, while 1,000,000 might take 3). This is highly efficient for network transmission where most values are small.
Columnar Compression (Apache Parquet/ORC): In big data systems, numbers are often stored in columns rather than rows. This allows the system to use "Delta Encoding," where it only stores the difference between consecutive numbers (e.g., storing 100, 101, 102 as 100, +1, +1), dramatically reducing disk space. 
4. The Continuing Debates (2026)
Accuracy vs. Silicon Space: Posits require more complex decoding logic in hardware compared to the "fixed" structure of IEEE 754. While they save memory, they can be 30–60% slower to process on current chip designs.
Power Efficiency in Data Centers: With US data center power demand expected to hit 75.8 GW in 2026, there is a push toward formats like bfloat16 and FP8 because they require fewer gate delays and less electricity per calculation.
The "NaN" Controversy: IEEE 754 has 14 different ways to represent "Not a Number" (NaN), which critics call wasteful. Posits replace this with a single "NaR" (Not a Real) value to simplify error handling