Editing Floating-point arithmetic (section)

=== Binary-to-decimal conversion with minimal number of digits ===
Converting a double-precision binary floating-point number to a decimal string is a common operation, but an algorithm producing results that are both accurate and minimal did not appear in print until 1990, with Steele and White's Dragon4. Some of the improvements since then include:
* David M. Gay's ''dtoa.c'', a practical open-source implementation of many ideas in Dragon4.<ref name="Gay_1990"/>
* Grisu3, with a 4&times; speedup as it removes the use of [[bignum]]s. Must be used with a fallback, as it fails for ~0.5% of cases.<ref name="Loitsch_2010"/>
* Errol3, an always-succeeding algorithm similar to, but slower than, Grisu3. Apparently not as good as an early-terminating Grisu with fallback.<ref name="mazong"/>
* Ryū, an always-succeeding algorithm that is faster and simpler than Grisu3.<ref name="Adams_2018"/>
* Schubfach, an always-succeeding algorithm that is based on a similar idea to Ryū, developed almost simultaneously and independently.<ref name="Giulietti"/> Performs better than Ryū and Grisu3 in certain benchmarks.<ref name="abolz"/>

Many modern language runtimes use Grisu3 with a Dragon4 fallback.<ref name="double_conversion_2020"/>