论文信息 - Interval arithmetic with fixed rounding mode

Interval arithmetic with fixed rounding mode

We discuss several methods to simulate interval arithmetic operations using floatingpoint operations with fixed rounding mode. In particular we present formulas using only rounding to nearest and using only chop rounding (towards zero). The latter was the default and only rounding on GPU (Graphics Processing Unit) and cell processors, which in turn are very fast and therefore attractive in scientific computations.

Siegfried M. Rump | Shin'ichi Oishi | Takeshi Ogita | Yusuke Morikura

[1] Guillaume Melquiond,et al. Computing predecessor and successor in rounding to nearest , 2009 .

[2] Chenyi Hu,et al. Algorithm 737: INTLIB—a portable Fortran 77 interval standard-function library , 1994, TOMS.

[3] Yun Shang,et al. A Note on the Extended Rosenbrock Function , 2006 .

[4] Siegfried M. Rump,et al. Accurate Floating-Point Summation Part I: Faithful Rounding , 2008, SIAM J. Sci. Comput..

[5] H. Peter Hofstee,et al. Introduction to the Cell multiprocessor , 2005, IBM J. Res. Dev..

[6] Sang H. Dhong,et al. The vector floating-point unit in a synergistic processor element of a CELL processor , 2005, 17th IEEE Symposium on Computer Arithmetic (ARITH'05).