\documentclass[12pt,titlepage]{article} \usepackage{amsmath} \usepackage{mathrsfs} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsthm} \usepackage{mathtools} \usepackage{graphicx} \usepackage{color} \usepackage{ucs} \usepackage[utf8x]{inputenc} \usepackage{xparse} \usepackage{tikz} \usepackage{hyperref} %----Macros---------- % % Unresolved issues: % % \righttoleftarrow % \lefttorightarrow % % \color{} with HTML colorspec % \bgcolor % \array with options (without options, it's equivalent to the matrix environment) % Of the standard HTML named colors, white, black, red, green, blue and yellow % are predefined in the color package. 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\newcommand{\bottom}{\bot} \newcommand{\minusb}{\boxminus} \newcommand{\plusb}{\boxplus} \newcommand{\timesb}{\boxtimes} \newcommand{\intersection}{\cap} \newcommand{\union}{\cup} \newcommand{\Del}{\nabla} \newcommand{\odash}{\circleddash} \newcommand{\negspace}{\!} \newcommand{\widebar}{\overline} \newcommand{\textsize}{\normalsize} \renewcommand{\scriptsize}{\scriptstyle} \newcommand{\scriptscriptsize}{\scriptscriptstyle} \newcommand{\mathfr}{\mathfrak} \newcommand{\statusline}[2]{#2} \newcommand{\tooltip}[2]{#2} \newcommand{\toggle}[2]{#2} % Theorem Environments \theoremstyle{plain} \newtheorem{theorem}{Theorem} \newtheorem{lemma}{Lemma} \newtheorem{prop}{Proposition} \newtheorem{cor}{Corollary} \newtheorem*{utheorem}{Theorem} \newtheorem*{ulemma}{Lemma} \newtheorem*{uprop}{Proposition} \newtheorem*{ucor}{Corollary} \theoremstyle{definition} \newtheorem{defn}{Definition} \newtheorem{example}{Example} \newtheorem*{udefn}{Definition} \newtheorem*{uexample}{Example} \theoremstyle{remark} \newtheorem{remark}{Remark} \newtheorem{note}{Note} \newtheorem*{uremark}{Remark} \newtheorem*{unote}{Note} %------------------------------------------------------------------- \begin{document} %------------------------------------------------------------------- \section*{ieee_arithmetic} The module {\colorbox[rgb]{1.00,0.93,1.00}{\tt ieee\char95arithmetic}} is an intrinsic module defined in the technical report ISO/IEC TR 15580:1998(E) which provides IEEE arithmetic facilities. \hypertarget{ieee_datatype_selection}{}\subsection*{{IEEE Datatype Selection}}\label{ieee_datatype_selection} \hypertarget{ieee_selected_real_kind}{}\subsubsection*{{ieee\_selected\_real\_kind}}\label{ieee_selected_real_kind} \begin{verbatim}integer function ieee_selected_real_kind(p,r) integer(kind1), optional :: p integer(kind2), optional :: r\end{verbatim} This function behaves like the {\colorbox[rgb]{1.00,0.93,1.00}{\tt selected\char95real\char95kind}} intrinsic, but only returns numbers of of IEEE kinds of reals. \hypertarget{general_inquiry_functions}{}\subsection*{{General Inquiry Functions}}\label{general_inquiry_functions} \hypertarget{ieee_support_datatype}{}\subsubsection*{{ieee\_support\_datatype}}\label{ieee_support_datatype} \begin{verbatim}logical function ieee_support_datatype(x) real(kind), optional :: x\end{verbatim} Returns {\colorbox[rgb]{1.00,0.93,1.00}{\tt \char46true\char46}} if IEEE arithmetic is supported for the same kind of {\colorbox[rgb]{1.00,0.93,1.00}{\tt real}} as {\colorbox[rgb]{1.00,0.93,1.00}{\tt x}} (or for all {\colorbox[rgb]{1.00,0.93,1.00}{\tt real}} kinds if {\colorbox[rgb]{1.00,0.93,1.00}{\tt x}} is absent). \hypertarget{ieee_support_denormal}{}\subsubsection*{{ieee\_support\_denormal}}\label{ieee_support_denormal} \begin{verbatim}logical function ieee_support_denormal(x) real(kind), optional :: X\end{verbatim} Returns {\colorbox[rgb]{1.00,0.93,1.00}{\tt \char46true\char46}} if IEEE denormal values are supported for the same kind of {\colorbox[rgb]{1.00,0.93,1.00}{\tt real}} as {\colorbox[rgb]{1.00,0.93,1.00}{\tt x}} (or for all {\colorbox[rgb]{1.00,0.93,1.00}{\tt real}} kinds if {\colorbox[rgb]{1.00,0.93,1.00}{\tt x}} is absent). \hypertarget{ieee_support_divide}{}\subsubsection*{{ieee\_support\_divide}}\label{ieee_support_divide} \begin{verbatim}logical function ieee_support_divide(x) real(kind), optional :: x\end{verbatim} Returns {\colorbox[rgb]{1.00,0.93,1.00}{\tt \char46true\char46}} if division up to IEEE-specified accuracy is supported for the same kind of {\colorbox[rgb]{1.00,0.93,1.00}{\tt real}} as {\colorbox[rgb]{1.00,0.93,1.00}{\tt x}} (or for all {\colorbox[rgb]{1.00,0.93,1.00}{\tt real}} kinds if {\colorbox[rgb]{1.00,0.93,1.00}{\tt x}} is absent). \hypertarget{ieee_support_inf}{}\subsubsection*{{ieee\_support\_inf}}\label{ieee_support_inf} \begin{verbatim}logical function ieee_support_inf(x) real(kind), optional :: x\end{verbatim} Returns {\colorbox[rgb]{1.00,0.93,1.00}{\tt \char46true\char46}} if IEEE infinite values are supported for the same kind of {\colorbox[rgb]{1.00,0.93,1.00}{\tt real}} as {\colorbox[rgb]{1.00,0.93,1.00}{\tt x}} (or for all {\colorbox[rgb]{1.00,0.93,1.00}{\tt real}} kinds if {\colorbox[rgb]{1.00,0.93,1.00}{\tt x}} is absent). \hypertarget{ieee_support_nan}{}\subsubsection*{{ieee\_support\_nan}}\label{ieee_support_nan} \begin{verbatim}logical function ieee_support_nan(x) real(kind), optional :: x\end{verbatim} Returns {\colorbox[rgb]{1.00,0.93,1.00}{\tt \char46true\char46}} if IEEE NaN (Not-a-Number) values are supported for the same kind of {\colorbox[rgb]{1.00,0.93,1.00}{\tt real}} as {\colorbox[rgb]{1.00,0.93,1.00}{\tt x}} (or for all {\colorbox[rgb]{1.00,0.93,1.00}{\tt real}} kinds if {\colorbox[rgb]{1.00,0.93,1.00}{\tt x}} is absent). \hypertarget{ieee_support_sqrt}{}\subsubsection*{{ieee\_support\_sqrt}}\label{ieee_support_sqrt} \begin{verbatim}logical function ieee_support_sqrt(x) real(kind), optional :: x\end{verbatim} Returns {\colorbox[rgb]{1.00,0.93,1.00}{\tt \char46true\char46}} if {\colorbox[rgb]{1.00,0.93,1.00}{\tt sqrt}} follows the IEEE standard for the same kind of {\colorbox[rgb]{1.00,0.93,1.00}{\tt real}} as {\colorbox[rgb]{1.00,0.93,1.00}{\tt x}} (or for all {\colorbox[rgb]{1.00,0.93,1.00}{\tt real}} kinds if {\colorbox[rgb]{1.00,0.93,1.00}{\tt x}} is absent). \hypertarget{ieee_support_standard}{}\subsubsection*{{ieee\_support\_standard}}\label{ieee_support_standard} \begin{verbatim}logical function ieee_support_standard(x) real(kind), optional :: x\end{verbatim} Returns {\colorbox[rgb]{1.00,0.93,1.00}{\tt \char46true\char46}} if all the IEEE facilities are supported for the same kind of {\colorbox[rgb]{1.00,0.93,1.00}{\tt real}} as {\colorbox[rgb]{1.00,0.93,1.00}{\tt x}} (or for all {\colorbox[rgb]{1.00,0.93,1.00}{\tt real}} kinds if {\colorbox[rgb]{1.00,0.93,1.00}{\tt x}} is absent). \hypertarget{rounding_modes}{}\subsection*{{Rounding Modes}}\label{rounding_modes} \hypertarget{number_classification}{}\subsection*{{Number Classification}}\label{number_classification} The module also contains the following [[Elemental function|elemental functions]] for reals {\colorbox[rgb]{1.00,0.93,1.00}{\tt x}} and {\colorbox[rgb]{1.00,0.93,1.00}{\tt y}} for which {\colorbox[rgb]{1.00,0.93,1.00}{\tt ieee\char95support\char95datatype}} is true: \begin{itemize}% \item {\colorbox[rgb]{1.00,0.93,1.00}{\tt ieee\char95class\char40x\char41}}--ieee class. \item {\colorbox[rgb]{1.00,0.93,1.00}{\tt ieee\char95value\char40x\char44class\char41}}--generate a sample IEEE value of the specified class. \item {\colorbox[rgb]{1.00,0.93,1.00}{\tt ieee\char95is\char95finite\char40x\char41}}--determine if a value is finite. \item {\colorbox[rgb]{1.00,0.93,1.00}{\tt ieee\char95is\char95nan\char40x\char41}}--determine if a value is IEEE NaN. \item {\colorbox[rgb]{1.00,0.93,1.00}{\tt ieee\char95is\char95negative\char40x\char41}}--determine if a value is negative. \item {\colorbox[rgb]{1.00,0.93,1.00}{\tt ieee\char95is\char95normal\char40x\char41}}--determine if a value is ``normal,'' neither an Inf, NaN, nor denormalized. \item {\colorbox[rgb]{1.00,0.93,1.00}{\tt ieee\char95unordered\char40x\char44y\char41}}--IEEE unordered function. True if either {\colorbox[rgb]{1.00,0.93,1.00}{\tt x}} or {\colorbox[rgb]{1.00,0.93,1.00}{\tt y}} is {\colorbox[rgb]{1.00,0.93,1.00}{\tt NaN}} and false otherwise. \end{itemize} Values of type {\colorbox[rgb]{1.00,0.93,1.00}{\tt ieee\char95class\char95type}} indicate the IEEE class of a number which can be one of the following \begin{verbatim}type(ieee_class_type), parameter :: ieee_negative_denormal type(ieee_class_type), parameter :: ieee_negative_inf type(ieee_class_type), parameter :: ieee_negative_normal type(ieee_class_type), parameter :: ieee_negative_zero type(ieee_class_type), parameter :: ieee_positive_denormal type(ieee_class_type), parameter :: ieee_positive_inf type(ieee_class_type), parameter :: ieee_positive_normal type(ieee_class_type), parameter :: ieee_positive_zero type(ieee_class_type), parameter :: ieee_quiet_nan type(ieee_class_type), parameter :: ieee_signaling_nan \end{verbatim} The module {\colorbox[rgb]{1.00,0.93,1.00}{\tt ieee\char95arithmetic}} also defines the {\colorbox[rgb]{1.00,0.93,1.00}{\tt \char61\char61}} and {\colorbox[rgb]{1.00,0.93,1.00}{\tt \char47\char61}} operators for the {\colorbox[rgb]{1.00,0.93,1.00}{\tt ieee\char95class\char95type}}. These may be used to test the return value of the {\colorbox[rgb]{1.00,0.93,1.00}{\tt ieee\char95class}} function. For example: \begin{verbatim}if (ieee_class(x) == ieee_quiet_nan) then ! ... end if\end{verbatim} \hypertarget{arithmetic_operations}{}\subsection*{{Arithmetic operations}}\label{arithmetic_operations} \begin{itemize}% \item {\colorbox[rgb]{1.00,0.93,1.00}{\tt ieee\char95copy\char95sign\char40x\char44y\char41}}--IEEE copysign function. \item {\colorbox[rgb]{1.00,0.93,1.00}{\tt ieee\char95logb\char40x\char41}}--unbiased exponent in the IEEE floating point format. \item {\colorbox[rgb]{1.00,0.93,1.00}{\tt ieee\char95next\char95after\char40x\char44y\char41}}--returns the next representable neighbor of {\colorbox[rgb]{1.00,0.93,1.00}{\tt x}} in the direction toward {\colorbox[rgb]{1.00,0.93,1.00}{\tt y}}. \item {\colorbox[rgb]{1.00,0.93,1.00}{\tt ieee\char95rem\char40x\char44y\char41}}--the IEEE {\colorbox[rgb]{1.00,0.93,1.00}{\tt rem}} function, that is {\colorbox[rgb]{1.00,0.93,1.00}{\tt x\char32\char45\char32y\char42n}}, where {\colorbox[rgb]{1.00,0.93,1.00}{\tt n}} is the integer nearest to the exact value {\colorbox[rgb]{1.00,0.93,1.00}{\tt x\char47y}}. \item {\colorbox[rgb]{1.00,0.93,1.00}{\tt ieee\char95rint\char40x\char41}}--round to an integer value according to the current rounding mode. \item {\colorbox[rgb]{1.00,0.93,1.00}{\tt ieee\char95scalb\char40x\char44i\char41}}--Returns {\colorbox[rgb]{1.00,0.93,1.00}{\tt x\char42\char50i}}. \end{itemize} \end{document}