Fortran 2018 conformance with ISO/IEC/IEEE 60559:2011

Ieee Standard ◽

A large number of changes to the intrinsic modules ieee_arithmetic, ieee_exceptions, and ieee_features have been made for conformance with the new IEEE standard for floating-point arithmetic (ISO/IEC/IEEE 60559:2011), including hexadecimal-significand I/O.

On fixpoints of Higham’s function

Carpathian Journal of Mathematics ◽

10.37193/cjm.2021.02.20 ◽

2021 ◽

Vol 37 (2) ◽

pp. 355-360

Author(s):

RADU T. TRÎMBIŢAŞ

Keyword(s):

Floating Point ◽

Double Precision ◽

Square Roots ◽

Ieee Standard ◽

Point Arithmetic ◽

Floating Point Numbers

We study the strange behavior in floating-point arithmetic of a function proposed by Nicholas Higham, consisting of repeated square roots extraction followed by the same number of times squaring and find its fixpoints. For IEEE standard double precision floating point numbers the fixpoints have the form \[ x \in \left\{\left( 1+k\mathrm{eps}\right) ^{\frac{1}{\mathrm{eps}}},\quad k=\left[ -745:\frac{1}{2}:-\frac{1}{2},0:709\right]\right\} \cup \{0\} , \] where \mathrm{eps} is the machine epsilon."

Algorithm 722: Functions to support the IEEE standard for binary floating-point arithmetic

ACM Transactions on Mathematical Software ◽

10.1145/168173.168185 ◽

1993 ◽

Vol 19 (4) ◽

pp. 443-451 ◽

Cited By ~ 4

Author(s):

W. J. Cody ◽

Jerome T. Coonen

Keyword(s):

Floating Point ◽

Ieee Standard ◽

IEEE Standard for Radix-Independent Floating-Point Arithmetic

10.1109/ieeestd.1987.81037 ◽

1987 ◽

Keyword(s):

Floating Point ◽

Ieee Standard ◽

Der Arithmetik-Prozessor INTEL 8087: eine komplette Implementierung des vorgeschlagenen IEEE-Standards für Gleitpunktarithmetik / The arithmetic processor INTEL 8087: a complete implementation of the proposed IEEE standard for floating-point arithmetic

it - Information Technology ◽

10.1524/itit.1981.23.16.173 ◽

1981 ◽

Vol 23 (1-6) ◽

Author(s):

C. REINSCH

Keyword(s):

Floating Point ◽

Ieee Standard ◽

Ieee Standards ◽

Arithmetic Processor ◽

IEEE Standard for Binary Floating-Point Arithmetic

10.1109/ieeestd.1985.82928 ◽

1985 ◽

Cited By ~ 26

Keyword(s):

Floating Point ◽

Ieee Standard ◽

Floating-point exception handling

10.1093/oso/9780198811893.003.0018 ◽

2018 ◽

Author(s):

Michael Metcalf ◽

John Reid ◽

Malcolm Cohen

Keyword(s):

Exception Handling ◽

Floating Point ◽

Iso Standard ◽

Numerical Software ◽

Ieee Standard ◽

Principal Application ◽

Point Arithmetic ◽

Efficient Software

Exception handling is required for the development of robust and efficient numerical software, a principal application of Fortran. Indeed, the existence of such a facility makes it possible to develop more efficient software than would otherwise be possible. Most computers nowadays have hardware based on the IEEE standard for binary floating-point arithmetic, which later became an ISO standard. Therefore, the Fortran exception handling features are based on the ability to test and set the five flags for floating-point exceptions that the IEEE standard specifies.