% !TeX root = forth.tex \chapter{The optional Double-Number word set} % 8 \wordlist{double} \section{Introduction} % 8.1 Sixteen-bit Forth systems often use double-length numbers. However, many Forths on small embedded systems do not, and many users of Forth on systems with a cell size of 32 bits or more find that the use of double-length numbers is much diminished. Therefore, the words that manipulate double-length entities have been placed in this optional word set. \section{Additional terms and notation} % 8.2 None. \section{Additional usage requirements} % 8.3 \subsection{Text interpreter input number conversion} % 8.3.2 When the text interpreter processes a number, except a \arg{cnum}, that is immediately followed by a decimal point and is not found as a definition name, the text interpreter shall convert it to a double-cell number. For example, entering \word[core]{DECIMAL} \texttt{1234} leaves the single-cell number \texttt{1234} on the stack, and entering \word[core]{DECIMAL} \texttt{1234.} leaves the double-cell number \texttt{1234} \texttt{0} on the stack. See: \xref[3.4.1.3 Text interpreter input number conversion]{usage:numbers}. \section{Additional documentation requirements} % 8.4 \subsection{System documentation} % 8.4.1 \subsubsection{Implementation-defined options} % 8.4.1.1 \begin{itemize} \item no additional requirements. \end{itemize} \subsubsection{Ambiguous conditions} % 8.4.1.2 \begin{itemize} \item \param{d} outside range of \param{n} in \wref{double:DtoS}{D>S}. \end{itemize} \subsubsection{Other system documentation} % 8.4.1.3 \begin{itemize} \item no additional requirements. \end{itemize} \subsection{Program documentation} % 8.4.2 \begin{itemize} \item no additional requirements. \end{itemize} \section{Compliance and labeling} % 8.5 \subsection{Forth-\snapshot{} systems} % 8.5.1 The phrase ``Providing the Double-Number word set'' shall be appended to the label of any Standard System that provides all of the Double-Number word set. The phrase ``Providing \emph{name(s)} from the Double-Number Extensions word set'' shall be appended to the label of any Standard System that provides portions of the Double-Number Extensions word set. The phrase ``Providing the Double-Number Extensions word set'' shall be appended to the label of any Standard System that provides all of the Double-Number and Double-Number Extensions word sets. \subsection{Forth-\snapshot{} programs} % 8.5.2 The phrase ``Requiring the Double-Number word set'' shall be appended to the label of Standard Programs that require the system to provide the Double-Number word set. The phrase ``Requiring \emph{name(s)} from the Double-Number Extensions word set'' shall be appended to the label of Standard Programs that require the system to provide portions of the Double-Number Extensions word set. The phrase ``Requiring the Double-Number Extensions word set'' shall be appended to the label of Standard Programs that require the system to provide all of the Double-Number and Double-Number Extensions word sets. \section{Glossary} % 8.6 \subsection{Double-Number words} % 8.6.1 \begin{worddef}{0360}{2CONSTANT}[two-constant] \item \stack{x_1 x_2 "name"}{} Skip leading space delimiters. Parse \param{name} delimited by a space. Create a definition for \param{name} with the execution semantics defined below. \param{name} is referred to as a ``two-constant''. \execute[name] \stack{}{x_1 x_2} Place cell pair \param{x_1 x_2} on the stack. \see \xref[3.4.1 Parsing]{usage:parsing}, \rref{double:2CONSTANT}{}. \begin{rationale} % A.8.6.1.0360 2CONSTANT Typical use: \texttt{x1} \texttt{x2} \word{2CONSTANT} \emph{name} \end{rationale} \begin{testing} \test{1 2 \word{2CONSTANT} 2c1}{} \\ \test{2c1}{1 2} \test{\word{:} cd1 2c1 \word{;}}{} \\ \test{cd1}{1 2} \test{\word{:} cd2 \word{2CONSTANT} \word{;}}{} \\ \test{-1 -2 cd2 2c2}{} \\ \test{2c2}{-1 -2} \test{4 5 \word{2CONSTANT} 2c3 \word{IMMEDIATE} 2c3}{4 5} \\ \test{\word{:} cd6 2c3 \word{2LITERAL} \word{;} cd6}{4 5} \end{testing} \end{worddef} \begin{worddef}{0390}{2LITERAL}[two-literal] \interpret Interpretation semantics for this word are undefined. \compile \stack{x_1 x_2}{} Append the run-time semantics below to the current definition. \runtime \stack{}{x_1 x_2} Place cell pair \param{x_1 x_2} on the stack. \see \rref{double:2LITERAL}{}. \begin{rationale} % A.8.6.1.0390 2LITERAL \setwordlist{core} Typical use: \word{:} \texttt{X} {\ldots} \word{[} \texttt{x1} \texttt{x2} \word{]} \word[double]{2LITERAL} {\ldots} \word{;} \setwordlist{double} \end{rationale} \begin{testing} \test{\word{:} cd1 \word{[} MAX-2INT \word{]} \word{2LITERAL} \word{;}}{}\\ \test{cd1}{MAX-2INT} \test{\word{2VARIABLE} 2v4 \word{IMMEDIATE} 5 6 2v4 \word{2!}}{} \\ \test{\word{:} cd7 2v4 \word{[} \word{2@} \word{]} \word{2LITERAL} \word{;} cd7}{5 6} \\ \test{\word{:} cd8 \word{[} 6 7 \word{]} 2v4 \word{[} \word{2!} \word{]} \word{;} 2v4 \word{2@}}{6 7} \end{testing} \end{worddef} \begin{worddef}{0440}{2VARIABLE}[two-variable] \item \stack{"name"}{} Skip leading space delimiters. Parse \param{name} delimited by a space. Create a definition for \param{name} with the execution semantics defined below. Reserve two consecutive cells of data space. \param{name} is referred to as a ``two-variable''. \execute[name] \stack{}{a-addr} \param{a-addr} is the address of the first (lowest address) cell of two consecutive cells in data space reserved by \word{2VARIABLE} when it defined \param{name}. A program is responsible for initializing the contents. \see \xref[3.4.1 Parsing]{usage:parsing}, \wref{core:VARIABLE}{VARIABLE}, \rref{double:2VARIABLE}{}. \begin{rationale} % A.8.6.1.0440 2VARIABLE Typical use: \word{2VARIABLE} \param{name} \end{rationale} \begin{testing} \test{\word{2VARIABLE} 2v1}{} \\ \test{0. 2v1 \word{2!}}{ } \\ \test{ 2v1 \word{2@}}{0.} \\ \test{-1 -2 2v1 \word{2!}}{ } \\ \test{ 2v1 \word{2@}}{-1 -2} \test{\word{:} cd2 \word{2VARIABLE} \word{;}}{} \\ \test{cd2 2v2}{} \\ \test{\word{:} cd3 2v2 \word{2!} \word{;}}{} \\ \test{-2 -1 cd3}{} \\ \test{2v2 \word{2@}}{-2 -1} \test{\word{2VARIABLE} 2v3 \word{IMMEDIATE} 5 6 2v3 \word{2!}}{} \\ \test{2v3 \word{2@}}{5 6} \end{testing} \end{worddef} \begin{worddef}{1040}{D+}[d-plus] \item \stack{d_1|ud_1 d_2|ud_2}{d_3|ud_3} Add \param{d_2|ud_2} to \param{d_1|ud_1}, giving the sum \param{d_3|ud_3}. \begin{testing} \test{ 0. 5. \word{D+}}{ 5.} \tab[11.5] \word{bs} small integers \\ \test{-5. 0. \word{D+}}{-5.} \\ \test{ 1. 2. \word{D+}}{ 3.} \\ \test{ 1. -2. \word{D+}}{-1.} \\ \test{-1. 2. \word{D+}}{ 1.} \\ \test{-1. -2. \word{D+}}{-3.} \\ \test{-1. 1. \word{D+}}{ 0.} \test{ 0 0 0 5 \word{D+}}{ 0 5} \tab[8] \word{bs} mid range integers \\ \test{-1 5 0 0 \word{D+}}{-1 5} \\ \test{ 0 0 0 -5 \word{D+}}{ 0 -5} \\ \test{ 0 -5 -1 0 \word{D+}}{-1 -5} \\ \test{ 0 1 0 2 \word{D+}}{ 0 3} \\ \test{-1 1 0 -2 \word{D+}}{-1 -1} \\ \test{ 0 -1 0 2 \word{D+}}{ 0 1} \\ \test{ 0 -1 -1 -2 \word{D+}}{-1 -3} \\ \test{-1 -1 0 1 \word{D+}}{-1 0} \test{MIN-INT 0 \word{2DUP} \word{D+}}{0 1} \\ \test{MIN-INT \word{StoD} MIN-INT 0 \word{D+}}{0 0} \test{ HI-2INT 1.\ \word{D+}}{0 HI-INT \word{1+}} \tab \word{bs} large double integers \\ \test{ HI-2INT \word{2DUP} \word{D+}}{1S \word{1-} MAX-INT} \\ \test{MAX-2INT MIN-2INT \word{D+}}{-1.} \\ \test{MAX-2INT LO-2INT \word{D+}}{HI-2INT} \\ \test{ LO-2INT \word{2DUP} \word{D+}}{MIN-2INT} \\ \test{ HI-2INT MIN-2INT \word{D+} 1.\ \word{D+}}{LO-2INT} \end{testing} \end{worddef} \begin{worddef}{1050}{D-}[d-minus] \item \stack{d_1|ud_1 d_2|ud_2}{d_3|ud_3} Subtract \param{d_2|ud_2} from \param{d_1|ud_1}, giving the difference \param{d_3|ud_3}. \begin{testing} \test{ 0. 5. \word{D-}}{-5.} \tab[6] \word{bs} small integers \\ \test{ 5. 0. \word{D-}}{ 5.} \\ \test{ 0. -5. \word{D-}}{ 5.} \\ \test{ 1. 2. \word{D-}}{-1.} \\ \test{ 1. -2. \word{D-}}{ 3.} \\ \test{-1. 2. \word{D-}}{-3.} \\ \test{-1. -2. \word{D-}}{ 1.} \\ \test{-1. -1. \word{D-}}{ 0.} \\ \test{ 0 0 0 5 \word{D-}}{ 0 -5} \tab[2.5] \word{bs} mid-range integers \\ \test{-1 5 0 0 \word{D-}}{-1 5} \\ \test{ 0 0 -1 -5 \word{D-}}{ 1 4} \\ \test{ 0 -5 0 0 \word{D-}}{ 0 -5} \\ \test{-1 1 0 2 \word{D-}}{-1 -1} \\ \test{ 0 1 -1 -2 \word{D-}}{ 1 2} \\ \test{ 0 -1 0 2 \word{D-}}{ 0 -3} \\ \test{ 0 -1 0 -2 \word{D-}}{ 0 1} \\ \test{ 0 0 0 1 \word{D-}}{ 0 -1} \test{MIN-INT 0 \word{2DUP} \word{D-}}{0.} \\ \test{MIN-INT \word{StoD} MAX-INT 0\word{D-}}{1 1s} \\ \test{MAX-2INT max-2INT \word{D-}}{0.} \tab \word{bs} large integers \\ \test{MIN-2INT min-2INT \word{D-}}{0.} \\ \test{MAX-2INT hi-2INT \word{D-}}{lo-2INT \word{DNEGATE}} \\ \test{ HI-2INT lo-2INT \word{D-}}{max-2INT} \\ \test{ LO-2INT hi-2INT \word{D-}}{min-2INT 1. \word{D+}} \\ \test{MIN-2INT min-2INT \word{D-}}{0.} \\ \test{MIN-2INT lo-2INT \word{D-}}{lo-2INT} \end{testing} \end{worddef} \begin{worddef}[Dd]{1060}{D.{}}[d-dot] \item \stack{d}{} Display \param{d} in free field format. \begin{testing} See \tref{double:D.R}{}. \end{testing} \end{worddef} \begin{worddef}{1070}{D.R}[d-dot-r] \item \stack{d n}{} Display \param{d} right aligned in a field \param{n} characters wide. If the number of characters required to display \param{d} is greater than \param{n}, all digits are displayed with no leading spaces in a field as wide as necessary. \see \rref{double:D.R}{}. \begin{rationale} % A.8.6.1.1070 D.R In \word{D.R}, the ``R'' is short for RIGHT. \end{rationale} \begin{testing}\ttfamily\obeyspaces MAX-2INT 71 73 \word{M*/} \word{2CONSTANT} dbl1 \\ MIN-2INT 73 79 \word{M*/} \word{2CONSTANT} dbl2 \word{:} d>ascii \word{p} d -{}- caddr u ) \\ \tab \word{DUP} \word{toR} \word{num-start} \word{DABS} \word{numS} \word{Rfrom} \word{SIGN} \word{num-end} \tab \word{p} -{}- caddr1 u ) \\ \tab \word{HERE} \word{SWAP} \word{2DUP} \word{2toR} \word{CHARS} \word{DUP} \word{ALLOT} \word{MOVE} \word{2Rfrom} \\ \word{;} dbl1 d>ascii \word{2CONSTANT} "dbl1" \\ dbl2 d>ascii \word{2CONSTANT} "dbl2" \word{:} DoubleOutput \\ \tab \word{CR} \word{.q} You should see lines duplicated:" \word{CR} \\ \tab 5 \word{SPACES} "dbl1" \word{TYPE} \word{CR} \\ \tab 5 \word{SPACES} dbl1 \word{Dd} \word{CR} \\ \tab 8 \word{SPACES} "dbl1" \word{DUP} \word{toR} \word{TYPE} \word{CR} \\ \tab 5 \word{SPACES} dbl1 \word{Rfrom} 3 \word{+} \word{D.R} \word{CR} \\ \tab 5 \word{SPACES} "dbl2" \word{TYPE} \word{CR} \\ \tab 5 \word{SPACES} dbl2 \word{Dd} \word{CR} \\ \tab 10 \word{SPACES} "dbl2" \word{DUP} \word{toR} \word{TYPE} \word{CR} \\ \tab 5 \word{SPACES} dbl2 \word{Rfrom} 5 \word{+} \word{D.R} \word{CR} \\ \word{;} \test{DoubleOutput}{} \end{testing} \end{worddef} \begin{worddef}[D0less]{1075}{D0<}[d-zero-less] \item \stack{d}{flag} \param{flag} is true if and only if \param{d} is less than zero. \begin{testing} \test{ 0. \word{D0less}}{} \\ \test{ 1. \word{D0less}}{} \\ \test{ MIN-INT 0 \word{D0less}}{} \\ \test{ 0 MAX-INT \word{D0less}}{} \\ \test{ MAX-2INT \word{D0less}}{} \\ \test{ -1. \word{D0less}}{ } \\ \test{ MIN-2INT \word{D0less}}{ } \end{testing} \end{worddef} \begin{worddef}{1080}{D0=}[d-zero-equals] \item \stack{xd}{flag} \param{flag} is true if and only if \param{xd} is equal to zero. \begin{testing} \test{ 1. \word{D0=}}{} \\ \test{MIN-INT 0 \word{D0=}}{} \\ \test{ MAX-2INT \word{D0=}}{} \\ \test{ -1 MAX-INT \word{D0=}}{} \\ \test{ 0. \word{D0=}}{ } \\ \test{ -1. \word{D0=}}{} \\ \test{ 0 MIN-INT \word{D0=}}{} \end{testing} \end{worddef} \begin{worddef}{1090}{D2*}[d-two-star] \item \stack{xd_1}{xd_2} \param{xd_2} is the result of shifting \param{xd_1} one bit toward the most-significant bit, filling the vacated least-significant bit with zero. \begin{testing} \test{ 0. \word{D2*}}{0. \word{D2*}} \\ \test{MIN-INT 0 \word{D2*}}{0 1} \\ \test{ HI-2INT \word{D2*}}{MAX-2INT 1. \word{D-}} \\ \test{ LO-2INT \word{D2*}}{MIN-2INT} \end{testing} \end{worddef} \begin{worddef}{1100}{D2/}[d-two-slash] \item \stack{xd_1}{xd_2} \param{xd_2} is the result of shifting \param{xd_1} one bit toward the least-significant bit, leaving the most-significant bit unchanged. \begin{testing} \test{ 0. \word{D2/}}{0. } \\ \test{ 1. \word{D2/}}{0. } \\ \test{ 0 1 \word{D2/}}{MIN-INT 0} \\ \test{MAX-2INT \word{D2/}}{HI-2INT } \\ \test{ -1. \word{D2/}}{-1. } \\ \test{MIN-2INT \word{D2/}}{LO-2INT } \end{testing} \end{worddef} \begin{worddef}[Dless]{1110}{D<}[d-less-than] \item \stack{d_1 d_2}{flag} \param{flag} is true if and only if \param{d_1} is less than \param{d_2}. \begin{testing} \test{ 0. 1. \word{Dless}}{ } \\ \test{ 0. 0. \word{Dless}}{} \\ \test{ 1. 0. \word{Dless}}{} \\ \test{ -1. 1. \word{Dless}}{ } \\ \test{ -1. 0. \word{Dless}}{ } \\ \test{ -2. -1. \word{Dless}}{ } \\ \test{ -1. -2. \word{Dless}}{} \\ \test{ -1. MAX-2INT \word{Dless}}{ } \\ \test{MIN-2INT MAX-2INT \word{Dless}}{ } \\ \test{MAX-2INT -1. \word{Dless}}{} \\ \test{MAX-2INT MIN-2INT \word{Dless}}{} \test{MAX-2INT \word{2DUP} -1. \word{D+} \word{Dless}}{} \\ \test{MIN-2INT \word{2DUP} 1. \word{D+} \word{Dless}}{ } \end{testing} \end{worddef} \begin{worddef}{1120}{D=}[d-equals] \item \stack{xd_1 xd_2}{flag} \param{flag} is true if and only if \param{xd_1} is bit-for-bit the same as \param{xd_2}. \begin{testing} \test{ -1. -1. \word{D=}}{ } \\ \test{ -1. 0. \word{D=}}{} \\ \test{ -1. 1. \word{D=}}{} \\ \test{ 0. -1. \word{D=}}{} \\ \test{ 0. 0. \word{D=}}{ } \\ \test{ 0. 1. \word{D=}}{} \\ \test{ 1. -1. \word{D=}}{} \\ \test{ 1. 0. \word{D=}}{} \\ \test{ 1. 1. \word{D=}}{ } \test{ 0 -1 0 -1 \word{D=}}{ } \\ \test{ 0 -1 0 0 \word{D=}}{} \\ \test{ 0 -1 0 1 \word{D=}}{} \\ \test{ 0 0 0 -1 \word{D=}}{} \\ \test{ 0 0 0 0 \word{D=}}{ } \\ \test{ 0 0 0 1 \word{D=}}{} \\ \test{ 0 1 0 -1 \word{D=}}{} \\ \test{ 0 1 0 0 \word{D=}}{} \\ \test{ 0 1 0 1 \word{D=}}{ } \test{MAX-2INT MIN-2INT \word{D=}}{} \\ \test{MAX-2INT 0. \word{D=}}{} \\ \test{MAX-2INT MAX-2INT \word{D=}}{ } \\ \test{MAX-2INT HI-2INT \word{D=}}{} \\ \test{MAX-2INT MIN-2INT \word{D=}}{} \\ \test{MIN-2INT MIN-2INT \word{D=}}{ } \\ \test{MIN-2INT LO-2INT \word{D=}}{} \\ \test{MIN-2INT MAX-2INT \word{D=}}{} \end{testing} \end{worddef} \begin{worddef}[DtoS]{1140}{D>S}[d-to-s] \item \stack{d}{n} \param{n} is the equivalent of \param{d}. An ambiguous condition exists if \param{d} lies outside the range of a signed single-cell number. \see \rref{double:DtoS}{}. \begin{rationale} % A.8.6.1.1140 D>S There exist number representations, e.g., the sign-magnitude representation, where reduction from double- to single-precision cannot simply be done with \word[core]{DROP}. This word, equivalent to \word[core]{DROP} on two's complement systems, desensitizes application code to number representation and facilitates portability. \end{rationale} \begin{testing} \test{ 1234 0 \word{DtoS}}{ 1234 } \\ \test{ -1234 -1 \word{DtoS}}{-1234 } \\ \test{MAX-INT 0 \word{DtoS}}{MAX-INT} \\ \test{MIN-INT -1 \word{DtoS}}{MIN-INT} \end{testing} \end{worddef} \begin{worddef}{1160}{DABS}[d-abs] \item \stack{d}{ud} \param{ud} is the absolute value of \param{d}. \begin{testing} \test{ 1. \word{DABS}}{1. } \\ \test{ -1. \word{DABS}}{1. } \\ \test{MAX-2INT \word{DABS}}{MAX-2INT} \\ \test{MIN-2INT 1. \word{D+} \word{DABS}}{MAX-2INT} \end{testing} \end{worddef} \begin{worddef}{1210}{DMAX}[d-max] \item \stack{d_1 d_2}{d_3} \param{d_3} is the greater of \param{d_1} and \param{d_2}. \begin{testing} \test{ 1. 2. \word{DMAX}}{ 2. } \\ \test{ 1. 0. \word{DMAX}}{ 1. } \\ \test{ 1. -1. \word{DMAX}}{ 1. } \\ \test{ 1. 1. \word{DMAX}}{ 1. } \\ \test{ 0. 1. \word{DMAX}}{ 1. } \\ \test{ 0. -1. \word{DMAX}}{ 0. } \\ \test{ -1. 1. \word{DMAX}}{ 1. } \\ \test{ -1. -2. \word{DMAX}}{-1. } \test{MAX-2INT HI-2INT \word{DMAX}}{MAX-2INT} \\ \test{MAX-2INT MIN-2INT \word{DMAX}}{MAX-2INT} \\ \test{MIN-2INT MAX-2INT \word{DMAX}}{MAX-2INT} \\ \test{MIN-2INT LO-2INT \word{DMAX}}{LO-2INT } \test{MAX-2INT 1. \word{DMAX}}{MAX-2INT} \\ \test{MAX-2INT -1. \word{DMAX}}{MAX-2INT} \\ \test{MIN-2INT 1. \word{DMAX}}{ 1. } \\ \test{MIN-2INT -1. \word{DMAX}}{-1. } \end{testing} \end{worddef} \begin{worddef}{1220}{DMIN}[d-min] \item \stack{d_1 d_2}{d_3} \param{d_3} is the lesser of \param{d_1} and \param{d_2}. \begin{testing} \test{ 1. 2. \word{DMIN}}{ 1. } \\ \test{ 1. 0. \word{DMIN}}{ 0. } \\ \test{ 1. -1. \word{DMIN}}{-1. } \\ \test{ 1. 1. \word{DMIN}}{ 1. } \\ \test{ 0. 1. \word{DMIN}}{ 0. } \\ \test{ 0. -1. \word{DMIN}}{-1. } \\ \test{ -1. 1. \word{DMIN}}{-1. } \\ \test{ -1. -2. \word{DMIN}}{-2. } \test{MAX-2INT HI-2INT \word{DMIN}}{HI-2INT } \\ \test{MAX-2INT MIN-2INT \word{DMIN}}{MIN-2INT} \\ \test{MIN-2INT MAX-2INT \word{DMIN}}{MIN-2INT} \\ \test{MIN-2INT LO-2INT \word{DMIN}}{MIN-2INT} \test{MAX-2INT 1. \word{DMIN}}{ 1. } \\ \test{MAX-2INT -1. \word{DMIN}}{-1. } \\ \test{MIN-2INT 1. \word{DMIN}}{MIN-2INT} \\ \test{MIN-2INT -1. \word{DMIN}}{MIN-2INT} \end{testing} \end{worddef} \begin{worddef}{1230}{DNEGATE}[d-negate] \item \stack{d_1}{d_2} \param{d_2} is the negation of \param{d_1}. \begin{testing} \test{ 0.\ \word{DNEGATE}}{ 0.} \\ \test{ 1.\ \word{DNEGATE}}{-1.} \\ \test{ -1.\ \word{DNEGATE}}{ 1.} \\ \test{max-2int \word{DNEGATE}}{min-2int \word{SWAP} \word{1+} \word{SWAP}} \\ \test{min-2int \word{SWAP} \word{1+} \word{SWAP} \word{DNEGATE}}{max-2int} \end{testing} \end{worddef} \begin{worddef}{1820}{M*/}[m-star-slash] \item \stack{d_1 n_1 +n_2}{d_2} Multiply \param{d_1} by \param{n_1} producing the triple-cell intermediate result $t$. Divide $t$ by \param{+n_2} giving the double-cell quotient \param{d_2}. An ambiguous condition exists if \param{+n_2} is zero or negative, or the quotient lies outside of the range of a double-precision signed integer. \see \rref{double:M*/}{}. \begin{rationale} % A.8.6.1.1820 M*/ \word{M*/} was once described by Chuck Moore as the most useful arithmetic operator in Forth. It is the main workhorse in most computations involving double-cell numbers. Note that some systems allow signed divisors. This can cost a lot in performance on some CPUs. The requirement for a positive divisor has not proven to be a problem. \end{rationale} \begin{testing}\ttfamily \textdf{To correct the result if the division is floored, only used when necessary, i.e., negative quotient and remainder $\not=$ 0.} \word{:} ?floored \word{[} -3 2 \word{/} -2 \word{=} \word{]} \word{LITERAL} \word{IF} 1.\ \word{D-} \word{THEN} \word{;} \small \test{ 5. 7 11 \word{M*/}}{ 3.} \\ \test{ 5. -7 11 \word{M*/}}{-3. ?floored} \\ %\tab \word{bs} \textdf{floored -4.} \\ \test{ -5. 7 11 \word{M*/}}{-3. ?floored} \\ %\tab \word{bs} \textdf{floored -4.} \\ \test{ -5. -7 11 \word{M*/}}{ 3.} \\ \test{MAX-2INT 8 16 \word{M*/}}{HI-2INT} \\ \test{MAX-2INT -8 16 \word{M*/}}{HI-2INT \word{DNEGATE} ?floored} \\ %\tab \word{bs} \textdf{floored subtract 1} \\ \test{MIN-2INT 8 16 \word{M*/}}{LO-2INT} \\ \test{MIN-2INT -8 16 \word{M*/}}{LO-2INT \word{DNEGATE}} \test{MAX-2INT MAX-INT MAX-INT \word{M*/}}{MAX-2INT} \\ \test{MAX-2INT MAX-INT \word{2/} MAX-INT \word{M*/}}{MAX-INT 1- HI-2INT \word{NIP}} \\ \test{MIN-2INT LO-2INT \word{NIP} \word{DUP} \word{NEGATE} \word{M*/}}{MIN-2INT} \\ \test{MIN-2INT LO-2INT \word{NIP} \word{1-} MAX-INT \word{M*/}}{MIN-INT 3 + HI-2INT \word{NIP} 2 \word{+}} \\ \test{MAX-2INT LO-2INT \word{NIP} \word{DUP} \word{NEGATE} \word{M*/}}{MAX-2INT \word{DNEGATE}} \\ \test{MIN-2INT MAX-INT \word{DUP} \word{M*/}}{MIN-2INT} \end{testing} \end{worddef} \begin{worddef}{1830}{M+}[m-plus] \item \stack{d_1|ud_1 n}{d_2|ud_2} Add \param{n} to \param{d_1|ud_1}, giving the sum \param{d_2|ud_2}. \see \rref{double:M+}{}. \begin{rationale} % A.8.6.1.1830 M+ \word{M+} is the classical method for integrating. \end{rationale} \begin{testing} \test{HI-2INT 1 \word{M+}}{HI-2INT 1. \word{D+}} \\ \test{MAX-2INT -1 \word{M+}}{MAX-2INT -1. \word{D+}} \\ \test{MIN-2INT 1 \word{M+}}{MIN-2INT 1. \word{D+}} \\ \test{LO-2INT -1 \word{M+}}{LO-2INT -1. \word{D+}} \end{testing} \end{worddef} \newpage \subsection{Double-Number extension words} % 8.6.2 \extended \begin{worddef}{0420}{2ROT}[two-rote] \item \stack{x_1 x_2 x_3 x_4 x_5 x_6}{x_3 x_4 x_5 x_6 x_1 x_2} Rotate the top three cell pairs on the stack bringing cell pair \param{x_1 x_2} to the top of the stack. \begin{testing} \test{ 1. 2. 3. \word{2ROT}}{ 2. 3. 1.} \\ \test{MAX-2INT MIN-2INT 1. \word{2ROT}}{MIN-2INT 1. MAX-2INT} \end{testing} \end{worddef} % --------------------------------------------------------- \begin{worddef}{0435}{2VALUE}[two-value][X:2value] \item \stack{x_1 x_2 "name"}{} Skip leading space delimiters. Parse \param{name} delimited by a space. Create a definition for \param{name} with the execution semantics defined below, with an initial value of \param{x_1 x_2}. \param{name} is referred to as a ``two-value''. \execute[name] \stack{}{x_1 x_2} Place cell pair \param{x_1 x_2} on the stack. The value of \param{x_1 x_2} is that given when \param{name} was created, until the phrase ``\param{x_1 x_2} \word{TO} \param{name}'' is executed, causing a new cell pair \param{x_1 x_2} to be assigned to \param{name}. \runtime[\word{TO} \param{name}] \stack{x_1 x_2}{} Assign the cell pair \param{x_1 x_2} to \param{name}. \see \xref{usage:parsing} and \wref{core:TO}{}, \rref{double:2VALUE}{}. \begin{rationale} Typical use: \begin{quote}\ttfamily \word{:} fn1 \word{Sq} filename" \word{;} \\ fn1 \word{2VALUE} myfile \\ myfile \word[file]{INCLUDED} \\[2ex] \word{:} fn2 \word{Sq} filename2" \word{;} \\ fn2 \word{TO} myfile \\ myfile \word[file]{INCLUDED} \end{quote} \end{rationale} \begin{implement} \dffamily The implementation of \word{TO} to include \word{2VALUE}s requires detailed knowledge of the host implementation of \word{VALUE} and \word{TO}, which is the main reason why \word{2VALUE} should be standardized. The order in which the two cells are stored in memory is not specified in the definition for \word{2VALUE} but this reference implementation has to assume one ordering --- this is not intended to be definitive. \begin{quote}\ttfamily \word{:} \word{2VALUE} \word{p} x1 x2 -{}- ) \\ \tab \word{CREATE} \word{,} \word{,} \\ \tab \word{DOES} \word{2@} \word{p} -{}- x1 x2 ) \\ \word{;} \end{quote} The corresponding implementation of \word{TO} disregards the issue that \word{TO} must also work for integer \word{VALUE}s and locals. \begin{quote}\ttfamily \word{:} \word{TO} \word{p} x1 x2 "name" -{}- ) \\ \tab \word{'} \word{toBODY} \\ \tab \word{STATE} \word{@} \word{IF} \\ \tab[2] \word{POSTPONE} \word{2LITERAL} \word{POSTPONE} \word{2!} \\ \tab \word{ELSE} \\ \tab[2] \word{2!} \\ \tab \word{THEN} \\ \word{;} \word{IMMEDIATE} \end{quote} \end{implement} \begin{testing}\ttfamily \test{1 2 \word{2VALUE} t2val}{} \\ \test{t2val}{1 2} \\[2ex] \test{3 4 \word{TO} t2val}{} \\ \test{t2val}{3 4} \\[2ex] \word{:} sett2val t2val \word{2SWAP} \word{TO} t2val \word{;} \\ \test{5 6 sett2val t2val}{3 4 5 6} \end{testing} \end{worddef} % --------------------------------------------------------- \begin{worddef}[DUless]{1270}{DU<}[d-u-less] \item \stack{ud_1 ud_2}{flag} \param{flag} is true if and only if \param{ud_1} is less than \param{ud_2}. \begin{testing} \test{ 1. 1. \word{DUless}}{} \\ \test{ 1. -1. \word{DUless}}{ } \\ \test{ -1. 1. \word{DUless}}{} \\ \test{ -1. -2. \word{DUless}}{} \test{MAX-2INT HI-2INT \word{DUless}}{} \\ \test{ HI-2INT MAX-2INT \word{DUless}}{ } \\ \test{MAX-2INT MIN-2INT \word{DUless}}{ } \\ \test{MIN-2INT MAX-2INT \word{DUless}}{} \\ \test{MIN-2INT LO-2INT \word{DUless}}{ } \end{testing} \end{worddef}