🐉 Żmij

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

Features

• Round trip guarantee
• Shortest decimal representation
• Correct rounding
• High performance
• Fast compile time
• IEEE 754 double and float support
• Safer API than classic dtoa
• Negative zero dependencies
• Small, clean codebase consisting of one source file and an optional header
• Permissive license

Usage

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

int main() {
  char buf[zmij::double_buffer_size];
  zmij::write(buf, sizeof(buf), 5.0507837461e-27);
  puts(buf);
}

Performance

Żmij v1 is more than 4x faster than Ryū used by multiple C++ standard library implementations, 9x faster than double-conversion and ~2.5x faster than Schubfach on dtoa-benchmark run on Apple M1.

Function	Time (ns)	Speedup
ostringstream	871.431	1.00x
sprintf	735.292	1.19x
double-conversion	83.332	10.46x
to_chars	42.808	20.36x
ryu	36.809	23.67x
schubfach	24.721	35.25x
fmt	22.224	39.21x
dragonbox	20.532	42.44x
yy	14.006	62.22x
xjb64	10.542	82.66x
zmij	8.661	100.62x
null	0.946	921.13x

Conversion time (smaller is better):

ostringstream and sprintf are excluded due to their significantly slower performance.

On EPYC Milan (AMD64) running Linux, Żmij is approximately 2.8× faster than Ryū and 5× faster than double-conversion when compiled with GCC 11.5.

Function	Time (ns)	Speedup
ostringstream	958.889	1.00x
sprintf	563.022	1.70x
double-conversion	95.706	10.02x
to_chars	67.115	14.29x
ryu	54.144	17.71x
schubfach	44.435	21.58x
fmt	40.098	23.91x
dragonbox	30.896	31.04x
yy	26.959	35.57x
xjb64	19.275	49.75x
zmij	19.194	49.96x
null	2.766	346.72x

Compile time

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.

Languages

• 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

Differences from Schubfach

• 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

Name

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."

Acknowledgements

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.

• 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.

• Cassio Neri (@cassioneri) - Proposed the single-candidate rounding strategy 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.