The algorithms developed ten years ago in preparation for IBM’s support of IEEE Floating-Point on its mainframe S/390 processors use an overly conservative intermediate precision to guarantee correctly-rounded results across the entire exponent range. Here we study the minimal requirement for both bounded and unbounded precision on the decimal side (converting to machine precision on the binary side). An interesting new theorem on Continued Fraction expansions is offered, as well as an open problem on the growth of partial quotients for ratios of powers of two and five. Key words: Floating-Point conversion, Continued Fractions 1

Regardless of how accurately a computer performs floating-point operations, if the data to operate on must be initially converted from the decimal-based representation used by humans into the internal representation used by the machine, then errors in that conversion will irrevocably pollute the results of subsequent

Inferno is an operating system well suited to applications that need to be portable, graphical, and networked. This paper describes the fundamental �oating point facilities of the system, including: tight rules on expression evaluation, binary�decimal conversion, exceptions and rounding, and the elementary function library. Although the focus of Inferno is interactive media, its portability across hardware and operating platforms, its relative simplicity, and its strength in distributed computing make itattractive for advanced scienti�c computing as well. Since the appearance of a new operating system is a relatively uncommon event, this is a special opportunity for numerical analysts to voice their opinion about what fundamental facilities they need. The purpose of this short paper is to describe numerical aspects of the initial release of Inferno, and to invite comment before the tyranny of backward compatibility makes changes impossible. Overviews can be found at