We searched for the worst cases for correct rounding of the exponential function in the IEEE 754r decimal64 format, and computed all the bad cases whose distance from a breakpoint (for all rounding modes) is less than 10 ulp, and we give the worst ones. In particular, the worst case for |x| ≥ 3 × 10 is exp(9.407822313572878 × 10) = 1.098645682066338 5 0000000000000000 278 . . .. This work can b...

This paper is in the form of a Draft Standard, patterned somewhat after the IEEE Standard for Binary Floating-Point Arithmetic [17]. The proposals of this paper are based on a previously published paper [15] which canvasses the need for, and the possibilities of, a standard for general purpose arithmetic. The proposals of this paper relate to one of the representational forms to be used in the ...

For more than 450 years, toxicologists have relied on an idea expressed by Paracelsus in the fifteenth century: "The dose makes the poison."[1] By this, Paracelsus meant that everything is poisonous in a high enough dose and, "Even strong poisons are harmless if the dose is low enough." Implicit in these two ideas is a third, "The higher the dose, the stronger the poison." Together, these ideas...

Two DNA markers, a random DNA fragment 754 and the cDNA sequence encoding the gene for ornithine transcarbamylase (OTC) have been studied in kindreds segregating for Duchenne muscular dystrophy. 754 and OTC are located close physically to the mutation in the region Xp21 below the breakpoints in two Duchenne females. The genetic distance was found to be approximately 10cM between 754 and DMD (tw...

There are several ways to represent real numbers on computers. Fixed point places a radix point somewhere in the middle of the digits, and is equivalent to using integers that represent portions of some unit. For example, one might represent 1/100ths of a unit; if you have four decimal digits, you could represent 10.82, or 00.01. Another approach is to use rationals, and represent every number ...

It is widely believed that the rate of profit across industrial sectors, while not in fact uniform as stipulated in the theory of prices of production, is independent of the sectoral organic composition of capital. It follows that the simple labour theory of value must be systematically in error as a predictor of actual sectoral aggregate prices. We offer empirical evidence from the US economy ...

This thesis examines a modern concept for machine numbers based on interval arithmetic called 'Unums' and compares it to IEEE 754 floating-point arithmetic, evaluating possible uses of this format where floating-point numbers are inadequate. In the course of this examination, this thesis builds theoretical foundations for IEEE 754 floating-point numbers, interval arithmetic based on the project...

Address for correspondence and proofs: Nipavan Chiamvimonvat Division of Cardiovascular Medicine, Department of Medicine University of California, Davis Genome and Biomedical Sciences Facility 451 East Health Sciences Drive, Room 6315 Davis, CA 95616 voice: (530) 754-7158 fax: (530) 754-7167 email: [email protected] Articles in PresS. Am J Physiol Heart Circ Physiol (July 29, 2005). do...