Algorithm to convert an IEEE 754 double to a string?

Question

Many programming languages that use IEEE 754 doubles provide a library function to convert those doubles to strings. For example, C has sprintf, C++ has

Answer 1

The code used by various software environments to convert floating-point numbers to string representations is typically based on the following publications (the work by Steele and White is particularly frequently cited):

Jerome T. Coonen: "An Implementation Guide to a Proposed Standard for Floating-Point Arithmetic." Computer, Vol. 13, No. 1, January 1980, pp. 68-79

Guy. L. Steele Jr. and J. L. White: "How to print floating-point numbers accurately". In proceedings of ACM SIGPLAN '90 Conference on Programming Language Design and Implementation, White Plains, New York, June 1990, pp. 112-126

David M. Gay: "Correctly rounded binary-decimal and decimal-binary conversions." Technical Report 90-10, AT&T Bell Laboratories, November 1990.

Some relevant followup work:

Robert G. Burger and R. Kent Dybvig: "Printing floating-point numbers quickly and accurately." In proceedings of ACM SIGPLAN 1996 conference on Programming Language Design and Implementation, Philadelphia, PA, USA, May 1996, pp. 108-116

Guy L. Steele Jr. and Jon L. White: "Retrospective: How to print floating-point numbers accurately." ACM SIGPLAN Notices, Vol. 39, No. 4, April 2004, pp. 372–389

Florian Loitsch: "Printing floating-point numbers quickly and accurately with integers." In proceedings of 2010 ACM SIGPLAN Conference on Programming Language Design and Implementation, Toronto, ON, Canada, June 2010, pp. 233-243

Marc Andrysco, Ranjit Jhala, and Sorin Lerner: "Printing floating-point numbers: a faster, always correct method." ACM SIGPLAN Notices, Vol. 51, No. 1, January 2016, pp. 555-567

Ulf Adams: "Ryū: fast float-to-string conversion." ACM SIGPLAN Notices, Vol. 53, No. 4, April 2018, pp. 270-282

Answer 2

I believe you are looking for Printing Floating-Point Numbers Quickly and Accurately

I found that link on another post: here.

Answer 3

For most example languages you quote the source is freely consultable online as they're available in open source.

For Java, the class java.lang.Double delegates this work to sun.misc.FloatingDecimal. Check out its constructor and toJavaFormatString() method.

For C, glibc is always a good example, and there we see that floating point output is located in its own source file.

Answer 4

See Ryan Juckett's Printing Floating-Point Numbers (2014), which describes history and implementations of floating-point to string conversions. In this four-part post, Ryan also provides a C++ implementation of Dragon4 based on Steele and White (1990), which is an efficient algorithm to convert a binary number in floating point format to a decimal number in string format.

You can also see a C implementation of Ryan's Dragon4 for Numpy here, and use it within Python/Numpy 1.14 format_float_positional and format_float_scientific functions.

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In 2018, an algorithm/library Ryu was published, with bindings in many modern programming languages (C, Java, C++, C#, Scala, Rust, Julia, Go, ...)