Easy Accurate Reading and Writing of Floating-Point Numbers

TL;DR

This paper introduces simplified algorithms for converting between decimal scientific notation and IEEE-754 double-precision floating-point numbers, ensuring stability and minimal mantissa digits compared to previous methods.

Contribution

The paper presents new, simpler algorithms for floating-point conversions that are stable and use minimal mantissa digits, improving upon prior approaches.

Findings

Algorithms are simpler than previous methods.

Conversions are stable under repeated operations.

Scientific representations use minimal mantissa digits.

Abstract

Presented here are algorithms for converting between (decimal) scientific-notation and (binary) IEEE-754 double-precision floating-point numbers. By employing a rounding integer quotient operation these algorithms are much simpler than those previously published. The values are stable under repeated conversions between the formats. Unlike Java-1.8, the scientific representations generated use only the minimum number of mantissa digits needed to convert back to the original binary values.