xjb: Fast Float to String Algorithm

xjb is a high-performance algorithm for converting floating-point numbers (float/double) to strings, designed for speed and correctness. It provides single-file implementations for both general use and JSON-specific formatting.

1.Key Features

• High Performance: Optimized algorithm with low branch prediction failure rate and SIMD acceleration
• Correctness: Satisfies RFC8259 and ECMAScript standards for JSON number formatting
• Small Footprint: Compact lookup tables for both float and double conversions
• Versatility: Support for both float (IEEE754-binary32) and double (IEEE754-binary64) types
• Modern Design: Low instruction dependency and high IPC (Instructions Per Cycle)

2.Implementation Files

Core Implementations

• General float/double to string: src/ftoa.cpp
• JSON-specific formatting: src/ftoa_json.cpp (satisfies RFC8259 and ECMAScript standards)

Algorithm Variants

Float to Decimal Conversion Algorithms

• xjb32: For float (IEEE754-binary32) - bench/xjb/float_to_decimal/xjb32_i.cpp
• xjb64: For double (IEEE754-binary64) - bench/xjb/float_to_decimal/xjb64_i.cpp

Float to String Conversion Algorithms

• Full lookup table: bench/xjb/float_to_string/ftoa.cpp
• Compressed lookup table: bench/xjb/float_to_string/ftoa_comp.cpp

Lookup Table Sizes

Type	Full Table (ftoa.cpp)	Compressed Table (ftoa_comp.cpp)
float	1352 bytes	64 bytes
double	15336 bytes	368 bytes

3.Usage Examples

Here are some examples of how the double to string algorithm handles various inputs:

Input	Output
123.45	"123.45"
1000	"1000.0"
123	"123.0"
123000	"123000.0"
1.2e23	"1.2e23"
1e100	"1e100"
0.0123	"0.0123"
0.001	"0.001"
0.000123	"0.000123"
1.2e-08	"1.2e-08"
0	"0.0"
NaN	"nan"
Inf	"inf"

4.Algorithm Characteristics

xjb is based on the schubfach algorithm and inspired by other state-of-the-art algorithms like yy, dragonbox, and grisu. Key characteristics include:

1. Dual Precision Support: Handles both float and double types
2. Optimized Process: Streamlined algorithm flow for maximum performance
3. Low Branch Misprediction: Designed to minimize pipeline stalls
4. SIMD Acceleration: Leverages SIMD instruction sets for faster processing
5. High Instruction Level Parallelism: Low dependency between instructions
6. Efficient Instruction Count: Minimizes the number of operations

5.Algorithm Correctness

Algorithm Principle Introduction Document : xjb
To verify the correctness of the algorithm, run the following command:

cd bench
make check

6.Benchmark Results

Benchmark tests are located in the bench directory. Build the benchmark program with make and run bench/main.cpp to test performance.

Latest benchmark results (as of 2026.4.8) on various CPUs:

on Apple M5:

ramdom float on Apple M5 compiler: apple clang 21.0.0

ramdom double on Apple M5 compiler: apple clang 21.0.0

fixed-length double on Apple M5 compiler: apple clang 21.0.0

on Apple M1:

ramdom float on Apple M1 compiler: apple clang 21.0.0

ramdom double on Apple M1 compiler: apple clang 21.0.0

fixed-length double on Apple M1 compiler: apple clang 21.0.0

on AMD R7-7840H:

ramdom float on AMD R7-7840H compiler: icpx 2025.0.4

ramdom double on AMD R7-7840H compiler: icpx 2025.0.4

fixed-length double on AMD R7-7840H compiler: icpx 2025.0.4

For detailed benchmark results and charts, please refer to the bench directory.

Related Algorithms

Algorithm	Description
schubfach	Raffaello Giulietti's algorithm. Original source: https://github.com/c4f7fcce9cb06515/Schubfach
schubfach_xjb	Improved version of schubfach with identical output results
ryu	Ulf Adams's Ryū algorithm
dragonbox	Junekey Jeon's C++ implementation
fmt	Victor Zverovich's formatting library (version: 12.1.0)
yy_double	yy's algorithm from https://github.com/ibireme/c_numconv_benchmark/blob/master/vendor/yy_double/yy_double.c
yy_json	yy's algorithm for JSON
teju	Algorithm with upcoming academic paper for correctness proof
xjb	XiangJunBo's algorithm (this project)
schubfach_vitaut	Vitaut's implementation of schubfach
zmij	Vitaut's algorithm
jnum	Jing Leng's algorithm
uscale	Russ Cox's algorithm ,document

Acknowledgements

Special thanks to the following contributors and inspirations:

• Yaoyuan Guo (@ibireme) - Author of yyjson and yy_double algorithms, provided benchmark data and test code. This project was inspired by the yy algorithm.

• Dougall Johnson (@dougallj) - Authored the NEON implementation used in xjb.

• Daniel Lemire (@lemire) - Authored the AVX512IFMA implementation for converting integers to decimal strings, used in xjb.

• Raffaello Giulietti (@rgiulietti) - Author of the Schubfach algorithm, which forms the foundation of xjb.

• Victor Zverovich (@vitaut) - Author of the zmij algorithm and fmt library. Parts of this implementation are derived from zmij.

Projects Using xjb

• ssrJSON - A SIMD-boosted high-performance Python JSON parsing library
• jsoniter-scala - Scala macros for compile-time generation of fast JSON codecs

Roadmap

• Big-endian support
• f16, f128, and f256 support

Contributing

Contributions are welcome! Please feel free to submit issues or pull requests to help improve this project.

License

MIT License