version 1.1, 1999/12/23 10:25:09 |
version 1.11, 2000/01/16 06:39:39 |
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% $OpenXM$ |
% $OpenXM: OpenXM/doc/issac2000/openxm-stackmachines.tex,v 1.10 2000/01/16 06:02:41 takayama Exp $ |
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\section{OpenXM Stack machines}\label{sec:ox-stackmachines} |
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In OpenXM specification, all servers are stack machines. |
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%These are called OpenXM stack machines. |
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When a server ox\_xyz gets an OX data message, |
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it translates the data into a local object of ox\_xyz |
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and pushes the object onto the stack. |
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According to the OpenMath specification, |
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the translation scheme |
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%% together with definitions of mathematical operations |
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%% of the system ox\_xyz |
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is called the {\it PhraseBook} of ox\_xyz. |
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For example, the Asir command {\tt ox\_push\_cmo(P,1)} |
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(push integer $1$ onto the server $P$) |
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sends an OX data message |
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{\tt (OX\_DATA,(CMO\_ZZ,1))} to the server $P$. |
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Here, |
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{\tt OX\_DATA} stands for {\tt OX\_DATA} header and |
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{\tt (CMO\_ZZ,1)} is a body standing for $1$ expressed |
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by the CMO. |
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The server tranlates {\tt (CMO\_ZZ, 1)} to its internal object of |
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the integer $1$ |
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and pushes the object onto the stack. |
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If the server gets an {\it OX command} message, then the server |
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executes the command. |
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Any OX command message starts with the int32 tag OX\_COMMAND. |
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The body is a stack machine operation code expressed by int32. |
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The codes are listed below \cite{noro-takayama}. |
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\begin{verbatim} |
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#define SM_popSerializedLocalObject 258 |
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#define SM_popCMO 262 |
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#define SM_popString 263 |
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#define SM_mathcap 264 |
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#define SM_pops 265 |
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#define SM_setName 266 |
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#define SM_evalName 267 |
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#define SM_executeStringByLocalParser 268 |
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#define SM_executeFunction 269 |
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#define SM_beginBlock 270 |
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#define SM_endBlock 271 |
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#define SM_shutdown 272 |
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#define SM_setMathCap 273 |
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#define SM_executeStringByLocalParserInBatchMode 274 |
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#define SM_getsp 275 |
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#define SM_dupErrors 276 |
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#define SM_control_kill 1024 |
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#define SM_control_to_debug_mode 1025 |
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#define SM_control_exit_debug_mode 1026 |
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#define SM_control_reset_connection 1030 |
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\end{verbatim} |
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OpenXM does not have a standard for mathematical operation sets |
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while it is a work in progress in the GAP group \cite{gap}. |
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Each OpenXM server has its own set of mathematical operations, |
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which are performed as follows. |
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First, arguments for a mathematical operation |
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and the number of the arguments are pushed. |
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Second, |
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the mathematical operator name, |
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such as {\tt fctr} (the factorization command of Asir), |
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is pushed as a string. |
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Finally, the stack machine command |
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{\tt SM\_executeFunction} (269) evaluates the operator and |
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pushes the result onto the stack |
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after poping the operator name, the number of arguments |
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and arguments. |
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For example, the following code factorizes $x^{100}-1$ by calling |
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{\tt ox\_asir} from Asir. |
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\begin{verbatim} |
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P = ox_launch(); |
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ox_push_cmo(P,x^100-1); ox_push_cmo(P,ntoint32(1)); |
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ox_push_cmd(P,269); |
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Ans = ox_pop_cmo(P); |
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\end{verbatim} |
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When an error has occurred on an OpenXM server, |
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an error object is pushed onto the stack |
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instead of a result of the computation. |
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The error object consists of the serial number of the OX message |
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which caused the error, and an error message. |
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\begin{verbatim} |
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[340] P = ox_launch()$ |
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[341] ox_rpc(P,"fctr",1.2*x)$ |
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[342] ox_pop_cmo(P); |
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error([8,fctr : invalid argument]) |
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\end{verbatim} |
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OpenXM server won't send error messages to the client |
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except when it receives a {\tt SM\_pop*} command. |
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OX stackmachines work in the asynchronous mode which is similar |
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to X servers. |
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For servers of graphic and sound applications, |
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it may be an advantageous feature. |
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It is also possible to emulate RPC and a web server for MCP \cite{iamc} |
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on our asynchronous OX stackmachines. |
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