"The smallest state-of-the-art double-to-string implementation"

[jepler]

I think this may be more of a "minimal in terms of lines of source", rather than binary size; it relies on a 64x128->192-bit multiplication primitive and a 617(?)-element, 128-bit look-up table. Still, I thought it might be of interest to micropython folks.

The github repository states that "[t]he binary size is ~12kiB on an ARM-based macOS".

Converting floating-point numbers to their shortest decimal representations has long been a surprisingly challenging problem. For decades, developers relied on algorithms such as Dragon4 that used multi-precision arithmetic. More recently, a new generation of provably correct and high-performance algorithms emerged, including Ryu, Schubfach and Dragonbox.

In my earlier post, double to string conversion in 150 lines of code, I explored how compact a basic implementation can be while still maintaining correctness. The Schubfach algorithm pushes this idea much further: it enables fully proven, high-performance dtoa with an amount of code comparable to the naïve algorithm. This post gives a brief overview of Schubfach and then walks through the minimal C++ implementation in https://github.com/vitaut/schubfach.

https://vitaut.net/posts/2025/smallest-dtoa/

My own findings on object size, not actually running anything:

jepler@bert:/tmp/schubfach$ arm-none-eabi-g++ -std=gnu++23 -c -Oz schubfach.cc  -mcpu=cortex-m33
jepler@bert:/tmp/schubfach$ nm -C --defined-only --print-size --size-sort --radix=d schubfach.o 
00000000 00000070 t (anonymous namespace)::umul128(unsigned long long, unsigned long long)
00000162 00000078 t (anonymous namespace)::write8digits(char*, unsigned int)
00000070 00000092 t (anonymous namespace)::umul192_upper64_modified(unsigned long long, unsigned long long, unsigned long long)
00000000 00000144 r (anonymous namespace)::pow10
00000240 00000268 t (anonymous namespace)::write(char*, unsigned long long, int)
00000508 00000776 T schubfach::dtoa(double, char*)
00000144 00009872 r (anonymous namespace)::pow10_significands
jepler@bert:/tmp/schubfach$ arm-none-eabi-size schubfach.o
   text	   data	    bss	    dec	    hex	filename
  11350	      0	      0	  11350	   2c56	schubfach.o

A variant for 32-bit floats would probably be smaller: for one thing, I think the table would get by with 64-bit values and have a mere 77 entries.

[scruss]

There were improvements made to roundtripping floats in v1.26.0: https://github.com/micropython/micropython/releases/tag/v1.26.0