A double-to-string conversion algorithm based on Schubfach and xjb with implementations in C and C++

• Round trip guarantee
• Shortest decimal representation
• Correct rounding
• High performance
• Small binary size
• Fast compile time
• IEEE 754 double and float support
• Safer API than classic dtoa
• User-friendly output format similar to Python's default representation
• Negative zero dependencies
• Small, clean codebase consisting of one source file and an optional header
• Permissive license

#include "zmij.h"
#include <stdio.h>

int main() {
  char buf[zmij::double_buffer_size + 1];
  auto end = zmij::write(buf, sizeof(buf), 5.0507837461e-27);
  *end = '\0';
  puts(buf);
}

On an Apple M5 Max running macOS, compiled with Clang 21.0, Żmij is more than 7x faster than Ryū, used by multiple C++ standard library implementations, ~13x faster than double-conversion and ~100x faster than sprintf on dtoa-benchmark.

Conversion time (smaller is better):

ostringstream and sprintf are left out of the charts to keep the faster methods readable.

On an AMD EPYC 7C13 (Milan) running Linux, compiled with GCC 13.3, Żmij is ~3.8x faster than Ryū, ~7x faster than double-conversion and ~34x faster than sprintf.

Conversion time (smaller is better):

ostringstream and sprintf are left out of the charts to keep the faster methods readable.

Compile time is ~135ms by default and ~180ms with optimizations enabled as measured by

% time c++ -c zmij.cc [-O2]

taking the best of 3 runs.

• C++: https://github.com/vitaut/zmij/blob/main/zmij.cc (reference implementation)
• C: https://github.com/vitaut/zmij/blob/main/zmij.c
• Rust: https://github.com/dtolnay/zmij
• Zig: https://github.com/de-sh/zmij

• 1 instead of 3 multiplications by a power of 10 in the common case
• Faster logarithm approximations
• Faster division and modulo
• Fewer conditional branches
• More efficient significand and exponent output
• Improved storage of powers of 10
• SIMD support

Żmij (pronounced roughly zhmeey or more precisely /ʐmij/) is a Polish word that refers to a mythical dragon- or serpent-like creature, continuing the dragon theme started by Steele and White.

A nice bonus is that the name even contains a "floating point" in its first letter. And to quote Aras Pranckevičius, "Żmij is also literally a beast."

We would like to express our gratitude to the individuals who have made Żmij possible:

• Victor Zverovich (@vitaut) - Original author and maintainer of Żmij.

• Tobias Schlüter (@TobiSchluter) - Contributed significant performance and portability improvements, including SIMD/SSE support and core algorithm refinements that enhance execution speed and cross-platform compatibility.

• Dougall Johnson (@dougallj) – Authored the NEON implementation and contributed many optimization ideas, substantially improving performance on ARM platforms.

• Alex Guteniev (@AlexGuteniev) - Contributed multiple fixes and improvements across build systems, platform compatibility, and testing infrastructure.

• Xiang JunBo (@xjb714) - Contributed high-performance BCD digit extraction algorithm and additional optimization ideas used across scalar and SIMD code paths. The double path uses xjb's $10^{-k-1}$ scaling to eliminate a division from the critical path.

• David Tolnay (@dtolnay) - Created and maintains the Rust port of Żmij, expanding the algorithm's reach and adoption in the Rust ecosystem.

• Raffaello Giulietti - Author of the Schubfach algorithm, whose work forms a foundational basis for Żmij.

• Yaoyuan Guo (@ibireme) - Author of the yy algorithm, whose ideas influenced key optimizations used in Żmij.

• Junekey Jeon (@jk-jeon) - Author of the Dragonbox algorithm, which informed design and benchmarking comparisons for Żmij, as well as the to_decimal API.

• Community contributors who provided feedback, issues, suggestions, and occasional commits, helping improve the robustness and performance of Żmij.