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+\chapter{Compiler Overview} % -*- Dictionary: design -*-
+
+The structure of the compiler may be broadly characterized by describing the
+compilation phases and the data structures that they manipulate.  The steps in
+the compilation are called phases rather than passes since they don't
+necessarily involve a full pass over the code.  The data structure used to
+represent the code at some point is called an {\it intermediate
+representation.}
+
+Two major intermediate representations are used in the compiler:
+\begin{itemize}
+
+\item The Implicit Continuation Representation (ICR) represents the lisp-level
+semantics of the source code during the initial phases.  Partial evaluation and
+semantic analysis are done on this representation.  ICR is roughly equivalent
+to a subset of Common Lisp, but is represented as a flow-graph rather than a
+syntax tree.  Phases which only manipulate ICR comprise the "front end".  It
+would be possible to use a different back end such as one that directly
+generated code for a stack machine.
+
+\item The Virtual Machine Representation (VMR) represents the implementation of
+the source code on a virtual machine.  The virtual machine may vary depending
+on the the target hardware, but VMR is sufficiently stylized that most of the
+phases which manipulate it are portable.
+\end{itemize}
+
+Each phase is briefly described here.  The phases from local call analysis''
+to constraint propagation'' all interact; for maximum optimization, they
+are generally repeated until nothing new is discovered.  The source files which
+primarily contain each phase are listed after Files: ''.
+\begin{description}
+
+\item[ICR conversion]
+Convert the source into ICR, doing macroexpansion and simple source-to-source
+transformation.  All names are resolved at this time, so we don't have to worry
+about name conflicts later on.  Files: {\tt ir1tran, srctran, typetran}
+
+\item[Local call analysis] Find calls to local functions and convert them to
+local calls to the correct entry point, doing keyword parsing, etc.  Recognize
+once-called functions as lets.  Create {\it external entry points} for
+entry-point functions.  Files: {\tt locall}
+
+\item[Find components]
+Find flow graph components and compute depth-first ordering.  Separate
+top-level code from run-time code, and determine which components are top-level
+components.  Files: {\tt dfo}
+
+\item[ICR optimize] A grab-bag of all the non-flow ICR optimizations.  Fold
+constant functions, propagate types and eliminate code that computes unused
+values.  Special-case calls to some known global functions by replacing them
+with a computed function.  Merge blocks and eliminate IF-IFs.  Substitute let
+variables.  Files: {\tt ir1opt, ir1tran, typetran, seqtran, vm/vm-tran}
+
+\item[Type constraint propagation]
+Use global flow analysis to propagate information about lexical variable
+types.   Eliminate unnecessary type checks and tests.  Files: {\tt constraint}
+
+\item[Type check generation]
+Emit explicit ICR code for any necessary type checks that are too complex to be
+easily generated on the fly by the back end.  Files: {\tt checkgen}
+
+\item[Event driven operations]
+Various parts of ICR are incrementally recomputed, either eagerly on
+modification of the ICR, or lazily, when the relevant information is needed.
+\begin{itemize}
+\item Check that type assertions are satisfied, marking places where type
+checks need to be done.
+
+\item Locate let calls.
+
+\item Delete functions and variables with no references
+\end{itemize}
+Files: {\tt ir1util}, {\tt ir1opt}
+
+\item[ICR finalize]
+This phase is run after all components have been compiled.  It scans the
+global variable references, looking for references to undefined variables
+and incompatible function redefinitions.  Files: {\tt ir1final}, {\tt main}.
+
+\item[Environment analysis]
+Determine which distinct environments need to be allocated, and what
+context needed to be closed over by each environment.  We detect non-local
+exits and set closure variables.  We also emit cleanup code as funny
+function calls.  This is the last pure ICR pass.  Files: {\tt envanal}
+
+\item[Global TN allocation (GTN)]
+Iterate over all defined functions, determining calling conventions
+and assigning TNs to local variables.  Files: {\tt gtn}
+
+\item[Local TN allocation (LTN)]
+Use type and policy information to determine which VMR translation to use
+for known functions, and then create TNs for expression evaluation
+temporaries.  We also accumulate some random information needed by VMR
+conversion.  Files: {\tt ltn}
+
+\item[Control analysis]
+Linearize the flow graph in a way that minimizes the number of branches.  The
+block-level structure of the flow graph is basically frozen at this point.
+Files: {\tt control}
+
+\item[Stack analysis]
+Maintain stack discipline for unknown-values continuation in the presence
+of local exits.  Files: {\tt stack}
+
+\item[Entry analysis]
+Collect some back-end information for each externally callable function.
+
+\item[VMR conversion] Convert ICR into VMR by translating nodes into VOPs.
+Emit type checks.  Files: {\tt ir2tran, vmdef}
+
+\item[Copy propagation] Use flow analysis to eliminate unnecessary copying of
+TN values.  Files: {\tt copyprop}
+
+\item[Representation selection]
+Look at all references to each TN to determine which representation has the
+lowest cost.  Emit appropriate move and coerce VOPS for that representation.
+
+Do flow analysis to find the set of TNs whose lifetimes
+overlap with the lifetimes of each TN being packed.  Annotate call VOPs with
+the TNs that need to be saved.  Files: {\tt life}
+
+\item[Pack]
+Find a legal register allocation, attempting to minimize unnecessary moves.
+Files: {\tt pack}
+
+\item[Code generation]
+Call the VOP generators to emit assembly code.  Files: {\tt codegen}
+
+\item[Pipeline reorganization] On some machines, move memory references
+backward in the code so that they can overlap with computation.  On machines
+with delayed branch instructions, locate instructions that can be moved into
+delay slots.  Files: {\tt assem-opt}
+
+\item[Assembly]
+Resolve branches and convert in to object code and fixup information.
+Files: {\tt assembler}
+
+\item[Dumping] Convert the compiled code into an object file or in-core
+function.  Files: {\tt debug-dump}, {\tt dump}, {\tt vm/core}
+
+\end{description}
+
+\chapter{The Implicit Continuation Representation}
+
+The set of special forms recognized is exactly that specified in the Common
+Lisp manual.  Everything that is described as a macro in CLTL is a macro.
+
+Large amounts of syntactic information are thrown away by the conversion to an
+anonymous flow graph representation.  The elimination of names eliminates the
+need to represent most environment manipulation special forms.  The explicit
+representation of control eliminates the need to represent BLOCK and GO, and
+makes flow analysis easy.  The full Common Lisp LAMBDA is implemented with a
+simple fixed-arg lambda, which greatly simplifies later code.
+
+The elimination of syntactic information eliminates the need for most of the
+"beta transformation" optimizations in Rabbit.  There are no progns, no
+tagbodys and no returns.  There are no "close parens" which get in the way of
+determining which node receives a given value.
+
+In ICR, computation is represented by Nodes.  These are the node types:
+\begin{description}
+\item[if]  Represents all conditionals.
+
+\item[set] Represents a {\tt setq}.
+
+\item[ref] Represents a constant or variable reference.
+
+\item[combination] Represents a normal function call.
+
+\item[MV-combination] Represents a {\tt multiple-value-call}.  This is used to
+implement all multiple value receiving forms except for {\tt
+multiple-value-prog1}, which is implicit.
+
+\item[bind]
+This represents the allocation and initialization of the variables in
+a lambda.
+
+\item[return]
+This collects the return value from a lambda and represents the
+control transfer on return.
+
+\item[entry] Marks the start of a dynamic extent that can have non-local exits
+to it.  Dynamic state can be saved at this point for restoration on re-entry.
+
+\item[exit] Marks a potentially non-local exit.  This node is interposed
+between the non-local uses of a continuation and the {\tt dest} so that code to
+do a non-local exit can be inserted if necessary.
+\end{description}
+
+Some slots are shared between all node types (via defstruct inheritance.)  This
+information held in common between all nodes often makes it possible to avoid
+special-casing nodes on the basis of type.  This shared information is
+primarily concerned with the order of evaluation and destinations and
+properties of results.  This control and value flow is indicated in the node
+primarily by pointing to continuations.
+
+The {\tt continuation} structure represents information sufficiently related
+to the normal notion of a continuation that naming it so seems sensible.
+Basically, a continuation represents a place in the code, or alternatively the
+destination of an expression result and a transfer of control.  These two
+notions are bound together for the same reasons that they are related in the
+standard functional continuation interpretation.
+
+A continuation may be deprived of either or both of its value or control
+significance.  If the value of a continuation is unused due to evaluation for
+effect, then the continuation will have a null {\tt dest}.  If the {\tt next}
+node for a continuation is deleted by some optimization, then {\tt next} will
+be {\tt :none}.
+
+  [\#\#\# Continuation kinds...]
+
+The {\tt block} structure represents a basic block, in the the normal sense.
+Control transfers other than simple sequencing are represented by information
+in the block structure.  The continuation for the last node in a block
+represents only the destination for the result.
+
+It is very difficult to reconstruct anything resembling the original source
+from ICR, so we record the original source form in each node.  The location of
+the source form within the input is also recorded, allowing for interfaces such
+as "Edit Compiler Warnings".  See section \ref{source-paths}.
+
+Forms such as special-bind and catch need to have cleanup code executed at all
+exit points from the form.  We represent this constraint in ICR by annotating
+the code syntactically within the form with a Cleanup structure describing what
+needs to be cleaned up.  Environment analysis determines the cleanup locations
+by watching for a change in the cleanup between two continuations.  We can't
+emit cleanup code during ICR conversion, since we don't know which exits will
+be local until after ICR optimizations are done.
+
+Special binding is represented by a call to the funny function %Special-Bind.
+The first argument is the Global-Var structure for the variable bound and the
+second argument is the value to bind it to.
+
+Some subprimitives are implemented using a macro-like mechanism for translating
+%PRIMITIVE forms into arbitrary lisp code.  Subprimitives special-cased by VMR
+conversion are represented by a call to the funny function %%Primitive.  The
+corresponding Template structure is passed as the first argument.
+
+We check global function calls for syntactic legality with respect to any
+defined function type function.  If the call is illegal or we are unable to
+tell if it is legal due to non-constant keywords, then we give a warning and
+mark the function reference as :notinline to force a full call and cause
+subsequent phases to ignore the call.  If the call is legal and is to a known
+function, then we annotate the Combination node with the Function-Info
+structure that contains the compiler information for the function.
+
+
+\section{Tail sets}
+\#|
+Probably want to have a GTN-like function result equivalence class mechanism
+for ICR type inference.  This would be like the return value propagation being
+done by Propagate-From-Calls, but more powerful, less hackish, and known to
+terminate.  The ICR equivalence classes could probably be used by GTN, as well.
+
+What we do is have local call analysis eagerly maintain the equivalence classes
+of functions that return the same way by annotating functions with a Tail-Info
+structure shared between all functions whose value could be the value of this
+function.  We don't require that the calls actually be tail-recursive, only
+that the call deliver its value to the result continuation.  [\#\#\# Actually
+now done by ICR-OPTIMIZE-RETURN, which is currently making ICR optimize
+mandatory.]
+
+We can then use the Tail-Set during ICR type inference.  It would have a type
+that is the union across all equivalent functions of the types of all the uses
+other than in local calls.  This type would be recomputed during optimization
+of return nodes.  When the type changes, we would propagate it to all calls to
+any of the equivalent functions.  How do we know when and how to recompute the
+type for a tail-set?  Recomputation is driven by type propagation on the result
+continuation.
+
+This is really special-casing of RETURN nodes.  The return node has the type
+which is the union of all the non-call uses of the result.  The tail-set is
+found though the lambda.  We can then recompute the overall union by taking the
+union of the type per return node, rather than per-use.
+
+
+How do result type assertions work?  We can't intersect the assertions across
+all functions in the equivalence class, since some of the call combinations may
+not happen (or even be possible).  We can intersect the assertion of the result
+with the derived types for non-call uses.
+
+When we do a tail call, we obviously can't check that the returned value
+matches our assertion.  Although in principle, we would like to be able to
+check all assertions, to preserve system integrity, we only need to check
+assertions that we depend on.  We can afford to lose some assertion information
+as long as we entirely lose it, ignoring it for type inference as well as for
+type checking.
+
+Things will work out, since the caller will see the tail-info type as the
+derived type for the call, and will emit a type check if it needs a stronger
+result.
+
+A remaining question is whether we should intersect the assertion with
+per-RETURN derived types from the very beginning (i.e. before the type check
+pass).  I think the answer is yes.  We delay the type check pass so that we can
+get our best guess for the derived type before we decide whether a check is
+necessary.  But with the function return type, we aren't committing to doing
+any type check when we intersect with the type assertion; the need to type
+check is still determined in the type check pass by examination of the result
+continuation.
+
+What is the relationship between the per-RETURN types and the types in the
+result continuation?  The assertion is exactly the Continuation-Asserted-Type
+(note that the asserted type of result continuations will never change after
+ICR conversion).  The per-RETURN derived type is different than the
+Continuation-Derived-Type, since it is intersected with the asserted type even
+before Type Check runs.  Ignoring the Continuation-Derived-Type probably makes
+life simpler anyway, since this breaks the potential circularity of the
+Tail-Info-Type will affecting the Continuation-Derived-Type, which affects...
+
+When a given return has no non-call uses, we represent this by using
+*empty-type*.  This consistent with the interpretation that a return type of
+NIL means the function can't return.
+
+
+\section{Hairy function representation}
+
+Non-fixed-arg functions are represented using Optional-Dispatch.  An
+Optional-Dispatch has an entry-point function for each legal number of
+optionals, and one for when extra args are present.  Each entry point function
+is a simple lambda.  The entry point function for an optional is passed the
+arguments which were actually supplied; the entry point function is expected to
+default any remaining parameters and evaluate the actual function body.
+
+If no supplied-p arg is present, then we can do this fairly easily by having
+each entry point supply its default and call the next entry point, with the
+last entry point containing the body.  If there are supplied-p args, then entry
+point function is replaced with a function that calls the original entry
+function with T's inserted at the position of all the supplied args with
+supplied-p parameters.
+
+We want to be a bit clever about how we handle arguments declared special when
+doing optional defaulting, or we will emit really gross code for special
+optionals.  If we bound the arg specially over the entire entry-point function,
+then the entry point function would be caused to be non-tail-recursive.  What
+we can do is only bind the variable specially around the evaluation of the
+default, and then read the special and store the final value of the special
+into a lexical variable which we then pass as the argument.  In the common case
+where the default is a constant, we don't have to special-bind at all, since
+the computation of the default is not affected by and cannot affect any special
+bindings.
+
+Keyword and rest args are both implemented using a LEXPR-like "more args"
+convention.  The More-Entry takes two arguments in addition to the fixed and
+optional arguments: the argument context and count.  (ARG <context> <n>)
+accesses the N'th additional argument.  Keyword args are implemented directly
+using this mechanism.  Rest args are created by calling %Listify-Rest-Args with
+the context and count.
+
+The More-Entry parses the keyword arguments and passes the values to the main
+function as positional arguments.  If a keyword default is not constant, then
+we pass a supplied-p parameter into the main entry and let it worry about
+defaulting the argument.  Since the main entry accepts keywords in parsed form,
+we can parse keywords at compile time for calls to known functions.  We keep
+around the original parsed lambda-list and related information so that people
+can figure out how to call the main entry.
+
+
+\section{ICR representation of non-local exits}
+
+All exits are initially represented by EXIT nodes:
+    (defstruct (exit (:include node))
+      value)
+The Exit node uses the continuation that is to receive the thrown Value.
+During optimization, if we discover that the Cont's home-lambda is the same is
+the exit node's, then we can delete the Exit node, substituting the Cont for
+all of the Value's uses.
+
+The successor block of an EXIT is the entry block in the entered environment.
+So we use the Exit node to mark the place where exit code is inserted.  During
+environment analysis, we need only insert a single block containing the entry
+point stub.
+
+We ensure that all Exits that aren't for a NLX don't have any Value, so that
+local exits never require any value massaging.
+
+The Entry node marks the beginning of a block or tagbody:
+    (defstruct (entry (:include node))
+      (continuations nil :type list))
+
+It contains a list of all the continuations that the body could exit to.  The
+Entry node is used as a marker for the the place to snapshot state, including
+the control stack pointer.  Each lambda has a list of its Entries so
+that environment analysis can figure out which continuations are really being
+closed over.  There is no reason for optimization to delete Entry nodes,
+since they are harmless in the degenerate case: we just emit no code (like a
+no-var let).
+
+
+We represent CATCH using the lexical exit mechanism.  We do a transformation
+like this:
+   (catch 'foo xxx)  ==>
+   (block \#:foo
+     (%catch \#'(lambda () (return-from \#:foo (%unknown-values))) 'foo)
+     (%within-cleanup :catch
+       xxx))
+
+%CATCH just sets up the catch frame which points to the exit function.  %Catch
+is an ordinary function as far as ICR is concerned.  The fact that the catcher
+needs to be cleaned up is expressed by the Cleanup slots in the continuations
+in the body.  %UNKNOWN-VALUES is a dummy function call which represents the
+fact that we don't know what values will be thrown.
+
+%WITHIN-CLEANUP is a special special form that instantiates its first argument
+as the current cleanup when converting the body.  In reality, the lambda is
+also created by the special special form %ESCAPE-FUNCTION, which gives the
+lambda a special :ESCAPE kind so that the back end knows not to generate any
+code for it.
+
+
+We use a similar hack in Unwind-Protect to represent the fact that the cleanup
+forms can be invoked at arbitrarily random times.
+    (unwind-protect p c)  ==>
+    (flet ((\#:cleanup () c))
+      (block \#:return
+	(multiple-value-bind
+	    (\#:next \#:start \#:count)
+	    (block \#:unwind
+	      (%unwind-protect \#'(lambda (x) (return-from \#:unwind x)))
+	      (%within-cleanup :unwind-protect
+		(return-from \#:return p)))
+	  (\#:cleanup)
+	  (%continue-unwind \#:next \#:start \#:count))))
+
+We use the block \#:unwind to represent the entry to cleanup code in the case
+where we are non-locally unwound.  Calling of the cleanup function in the
+drop-through case (or any local exit) is handled by cleanup generation.  We
+make the cleanup a function so that cleanup generation can add calls at local
+exits from the protected form.  \#:next, \#:start and \#:count are state used in
+the case where we are unwound.  They indicate where to go after doing the
+cleanup and what values are being thrown.  The cleanup encloses only the
+protected form.  As in CATCH, the escape function is specially tagged as
+:ESCAPE.  The cleanup function is tagged as :CLEANUP to inhibit let conversion
+(since references are added in environment analysis.)
+
+Notice that implementing these forms using closures over continuations
+eliminates any need to special-case ICR flow analysis.  Obviously we don't
+really want to make heap-closures here.  In reality these functions are
+special-cased by the back-end according to their KIND.
+
+
+\section{Block compilation}
+
+One of the properties of ICR is that supports "block compilation" by allowing
+arbitrarily large amounts of code to be converted at once, with actual
+compilation of the code being done at will.
+
+
+In order to preserve the normal semantics we must recognize that proclamations
+(possibly implicit) are scoped.  A proclamation is in effect only from the time
+of appearance of the proclamation to the time it is contradicted.  The current
+global environment at the end of a block is not necessarily the correct global
+environment for compilation of all the code within the block.  We solve this
+problem by closing over the relevant information in the ICR at the time it is
+converted.  For example, each functional variable reference is marked as
+inline, notinline or don't care.  Similarly, each node contains a structure
+known as a Cookie which contains the appropriate settings of the compiler
+policy switches.
+
+We actually convert each form in the file separately, creating a separate
+"initial component" for each one.  Later on, these components are merged as
+needed.  The main reason for doing this is to cause EVAL-WHEN processing to be
+
+
+\section{Entry points}
+
+\#|
+
+Since we need to evaluate potentially arbitrary code in the XEP argument forms
+(for type checking), we can't leave the arguments in the wired passing
+locations.  Instead, it seems better to give the XEP max-args fixed arguments,
+with the passing locations being the true passing locations.  Instead of using
+%XEP-ARG, we reference the appropriate variable.
+
+Also, it might be a good idea to do argument count checking and dispatching
+with explicit conditional code in the XEP.  This would simplify both the code
+that creates the XEP and the VMR conversion of XEPs.  Also, argument count
+dispatching would automatically benefit from any cleverness in compilation of
+case-like forms (jump tables, etc).  On the downside, this would push some
+assumptions about how arg dispatching is done into ICR.  But then we are
+currently violating abstraction at least as badly in VMR conversion, which is
+also supposed to be implementation independent.
+|\#
+
+As a side-effect of finding which references to known functions can be
+converted to local calls, we find any references that cannot be converted.
+References that cannot be converted to a local call must evaluate to a
+"function object" (or function-entry) that can be called using the full call
+convention.  A function that can be called from outside the component is called
+an "entry-point".
+
+Lots of stuff that happens at compile-time with local function calls must be
+done at run-time when an entry-point is called.
+
+It is desirable for optimization and other purposes if all the calls to every
+function were directly present in ICR as local calls.  We cannot directly do
+this with entry-point functions, since we don't know where and how the
+entry-point will be called until run-time.
+
+What we do is represent all the calls possible from outside the component by
+local calls within the component.  For each entry-point function, we create a
+corresponding lambda called the external entry point or XEP.  This is a
+function which takes the number of arguments passed as the first argument,
+followed by arguments corresponding to each required or optional argument.
+
+If an optional argument is unsupplied, the value passed into the XEP is
+undefined.  The XEP is responsible for doing argument count checking and
+dispatching.
+
+In the case of a fixed-arg lambda, we emit a call to the %VERIFY-ARGUMENT-COUNT
+funny function (conditional on policy), then call the real function on the
+passed arguments.  Even in this simple case, we benefit several ways from
+having a separate XEP:
+ -- The argument count checking is factored out, and only needs to be done in
+    full calls.
+ -- Argument type checking happens automatically as a consequence of passing
+    the XEP arguments in a local call to the real function.  This type checking
+    is also only done in full calls.
+ -- The real function may use a non-standard calling convention for the benefit
+    of recursive or block-compiled calls.  The XEP converts arguments/return
+    values to/from the standard convention.  This also requires little
+    special-casing of XEPs.
+
+If the function has variable argument count (represented by an
+OPTIONAL-DISPATCH), then the XEP contains a COND which dispatches off of the
+argument count, calling the appropriate entry-point function (which then does
+defaulting).  If there is a more entry (for keyword or rest args), then the XEP
+obtains the more arg context and count by calling the %MORE-ARG-CONTEXT funny
+function.
+
+All non-local-call references to functions are replaced with references to the
+corresponding XEP.  ICR optimization may discover a local call that was
+previously a non-local reference.  When we delete the reference to the XEP, we
+may find that it has no references.  In this case, we can delete the XEP,
+causing the function to no longer be an entry-point.
+
+


text:
# Three equations, three variables, three powers

Algebra Level 4

$\begin{cases} x + y + z = 10 \\ x^2 + y^2 + z^2 = 20 \\ x^3 + y^3 + z^3 = 100 \end{cases}$

Consider three complex numbers $$x, y$$ and $$z$$ that satisfy the system of equations above. Find the value of $$xyz$$.

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text:
# Storm：Running topologies on a production cluster

Running topologies on a production cluster is similar to running in Local mode. Here are the steps:

Define the topology (Use TopologyBuilder if defining using Java)

Use StormSubmitter to submit the topology to the cluster. StormSubmitter takes as input the name of the topology, a configuration for the topology, and the topology itself. For example:

Config conf = new Config();
conf.setNumWorkers(20);
conf.setMaxSpoutPending(5000);
StormSubmitter.submitTopology("mytopology", conf, topology);

Create a jar containing your code and all the dependencies of your code (except for Storm – the Storm jars will be added to the classpath on the worker nodes).

If you’re using Maven, the Maven Assembly Plugin can do the packaging for you. Just add this to your pom.xml:

  <plugin>
<artifactId>maven-assembly-plugin</artifactId>
<configuration>
<descriptorRefs>
<descriptorRef>jar-with-dependencies</descriptorRef>
</descriptorRefs>
<archive>
<manifest>
<mainClass>com.path.to.main.Class</mainClass>
</manifest>
</archive>
</configuration>
</plugin>

Then run mvn assembly:assembly to get an appropriately packaged jar. Make sure you exclude the Storm jars since the cluster already has Storm on the classpath.

Submit the topology to the cluster using the storm client, specifying the path to your jar, the classname to run, and any arguments it will use:

storm jar path/to/allmycode.jar org.me.MyTopology arg1 arg2 arg3

storm jar will submit the jar to the cluster and configure the StormSubmitter class to talk to the right cluster. In this example, after uploading the jar, storm jar calls the main function on org.me.MyTopology with the arguments “arg1”, “arg2”, and “arg3”.

You can find out how to configure your storm client to talk to a Storm cluster on Setting up development environment.

notes(ningg)：说两点：

• 本地Storm充当client向远端cluster提交topol时，只需要在本地Storm的storm.yaml文件中配置nimbus.host:123.45.678.890即可，具体参考：Storm：setting up a development environment
• 具体在windows的CMD下，我无法正确执行storm jar命令，转而，我在windows下安装了Cygwin，并在其中执行storm jar ...命令，向远端的Storm cluster提交topol以及依赖的代码；

## Common configurations

There are a variety of configurations you can set per topology. A list of all the configurations you can set can be found here. The ones prefixed with “TOPOLOGY” can be overridden on a topology-specific basis (the other ones are cluster configurations and cannot be overridden). Here are some common ones that are set for a topology:

• Config.TOPOLOGY_WORKERS: This sets the number of worker processes to use to execute the topology. For example, if you set this to 25, there will be 25 Java processes across the cluster executing all the tasks. If you had a combined 150 parallelism across all components in the topology, each worker process will have 6 tasks running within it as threads.
• Config.TOPOLOGY_ACKERS: This sets the number of tasks that will track tuple trees and detect when a spout tuple has been fully processed. Ackers are an integral part of Storm’s reliability model and you can read more about them on Guaranteeing message processing.
• Config.TOPOLOGY_MAX_SPOUT_PENDING: This sets the maximum number of spout tuples that can be pending on a single spout task at once (pending means the tuple has not been acked or failed yet). It is highly recommended you set this config to prevent queue explosion.
• Config.TOPOLOGY_MESSAGE_TIMEOUT_SECS: This is the maximum amount of time a spout tuple has to be fully completed before it is considered failed. This value defaults to 30 seconds, which is sufficient for most topologies. See Guaranteeing message processing for more information on how Storm’s reliability model works.
• Config.TOPOLOGY_SERIALIZATIONS: You can register more serializers to Storm using this config so that you can use custom types within tuples.

## Killing a topology

To kill a topology, simply run:

storm kill {stormname}

Give the same name to storm kill as you used when submitting the topology.

Storm won’t kill the topology immediately. Instead, it deactivates all the spouts so that they don’t emit any more tuples, and then Storm waits Config.TOPOLOGY_MESSAGE_TIMEOUT_SECS seconds before destroying all the workers. This gives the topology enough time to complete any tuples it was processing when it got killed.

## Updating a running topology

To update a running topology, the only option currently is to kill the current topology and resubmit a new one. A planned feature is to implement a storm swap command that swaps a running topology with a new one, ensuring minimal downtime and no chance of both topologies processing tuples at the same time.

## Monitoring topologies

The best place to monitor a topology is using the Storm UI. The Storm UI provides information about errors happening in tasks and fine-grained stats on the throughput and latency performance of each component of each running topology.

You can also look at the worker logs on the cluster machines.

Top


text:
# Different ways for modular exponentiation $A^E$ with negative A's

I was looking at a way for modular exponentiation $X=A^e \mod{n}$ with negative base $A$ in order to evaluate how it needs to be changed so I can use it with my hardware acceleration unit.

The crypto library I was looking at deals with negative base $A$ (MPI) as follows:

• Check if A was negative and if it was, remember that it was negative and invert its sign (e.g. -5 --> 5)
• Perform the actual modular exponentiation using a specific algorithm (e.g. sliding window method) with the positively signed $A$
• If $A$ was positive at the beginning, you're done
• If $A$ was negative at the beginning and the exponent $e$ was odd compensate by performing $X = n-X$

This library can work with arbitrarily large (or small) values of $A$. However my crypto core which accelerates moudular exponentiation expects the input parameters $e$ and $A \in [0 \dots n-1]$ which is why I came up with following solution:

• At the beginning always perform $A = A \mod{n}$. This would reduce $A$ if $A \ge n$. In case $A \lt 0$ this would make $A$'s sign positive.
• Perform the actual modular exponentiation using a specific algorithm (e.g. sliding window method) with the positively signed $A$

I think that performing the reduction at the beginning to reduce A and make its sign positive should not change the final result as $A^e \mod{n} = (A \mod{n})^e \mod{n}$. However I wanted to make sure, that I did not forget anything.

• Yea, i edited it to $X= n - X$, which is what the crypto library is doing. – TrinityTonic Jun 29 '17 at 6:30
• If the library is doing $X = n - x$, then it's broken (or you're looking at the modular multiplication routine, not the modular exponentiation). As written, they'd have $X^{-1} = n - X$, which is wrong, as we know $X \cdot X^{-1} = X^0 = 1$, and $X \cdot (n - X)$ is not 1 in general. What they'd need to do at this set is known as a 'modular inverse', that's certainly doable, but is considerably more complex that $X = n-x$. – poncho Aug 28 '17 at 22:57

For any integer $A$ we have the congruence $A \equiv A + kn \text{ mod } n$ for all integers k. This means a generic algorithm to get $A$ (where $A < 0$) into the range $[0, n)$ would be something like:

function(A):
while(A < 0):
A = A + n
return A

Doing A = A % n will work in some languages as well (e.g. python) but not all languages (e.g. C).

Here is a way to see that the library performs correctly. Assume $A$ (seen as an integer) be negative. Define $B = (-A)^e \bmod n$. Then: \begin{align*} A^e \bmod n &= [(-1)*(-A)]^e \bmod n\\ &= (-1)^e (-A)^e \bmod n\\ &= (-1)^e B \bmod n\\ &=\begin{cases} B \bmod n = B&\text{if $e$ is even}\\ -B \bmod n = n - B & \text{if $e$ is odd}\end{cases} \end{align*}

Note that the result remains correct if $-A$ is replaced with $-A \bmod n$ since $(-A)^e \bmod n = (-A \bmod n)^e \bmod n$.


text:
# Basic Percentage Question

• April 1st 2013, 01:30 PM
cmf0106
Basic Percentage Question
If you have the fraction $\frac{7}{18}$ how do you figure out what percentage that is? I know the answer is about 39% but how do you do the work to figure it out? Thanks
• April 1st 2013, 01:49 PM
Plato
Re: Basic Percentage Question
Quote:

Originally Posted by cmf0106
If you have the fraction $\frac{7}{18}$ how do you figure out what percentage that is? I know the answer is about 39% but how do you do the work to figure it out? Thanks

Can you do this question: $700 \div 18~?$
• April 1st 2013, 01:51 PM
cmf0106
Re: Basic Percentage Question
Quote:

Originally Posted by Plato
Can you do this question: $700 \div 18~?$

Yes, my question would be why are you able to do 700/18 ?
• April 1st 2013, 01:55 PM
Plato
Re: Basic Percentage Question
Quote:

Originally Posted by cmf0106
Yes, my question would be why are you able to do 700/18 ?

Well if you can do, the do it and see what you get.
• April 1st 2013, 01:56 PM
cmf0106
Re: Basic Percentage Question
yes 700/18 = 39%, but my question is why can you use 700?
• April 1st 2013, 02:28 PM
Plato
Re: Basic Percentage Question
Quote:

Originally Posted by cmf0106
yes 700/18 = 39%, but my question is why can you use 700?

Percent means per one hundred.

If you want $\frac{31}{81}$ changed to $\%$ then what is $3100 \div 81=~?$
• April 1st 2013, 03:53 PM
Prove It
Re: Basic Percentage Question
Quote:

Originally Posted by cmf0106
If you have the fraction $\frac{7}{18}$ how do you figure out what percentage that is? I know the answer is about 39% but how do you do the work to figure it out? Thanks

You want to write this as a percentage, which is an equivalent way to write a proportion, meaning "per hundred". You need to remember that 100% is the same as 1. You also need to remember that multiplying by 1 keeps your fraction the same. So that means:

\displaystyle \begin{align*} \frac{7}{18} &= \frac{7}{18} \cdot 1 \\ &= \frac{7}{18} \cdot 100\% \\ &= \frac{700}{18}\% \end{align*}


text:
Last edited by Kajiktilar
Friday, July 31, 2020 | History

2 edition of Single Variable Calculus, Volume 2 found in the catalog.

Single Variable Calculus, Volume 2

Jon Rogawski

# Single Variable Calculus, Volume 2

## by Jon Rogawski

Written in English

Subjects:
• Mathematics / Calculus,
• Calculus,
• Mathematics,
• Science/Mathematics

• The Physical Object
FormatPaperback
Number of Pages600
ID Numbers
Open LibraryOL11896832M
ISBN 101429204176
ISBN 109781429204170

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text:
134 meters in miles

Conversion

134 meters is equivalent to 0.0832637397598028 miles.[1]

Conversion formula How to convert 134 meters to miles?

We know (by definition) that: $1\mathrm{m}\approx 0.00062137119\mathrm{mile}$

We can set up a proportion to solve for the number of miles.

$1  m 134  m ≈ 0.00062137119  mile x  mile$

Now, we cross multiply to solve for our unknown $x$:

$x\mathrm{mile}\approx \frac{134\mathrm{m}}{1\mathrm{m}}*0.00062137119\mathrm{mile}\to x\mathrm{mile}\approx 0.08326373946\mathrm{mile}$

Conclusion: $134  m ≈ 0.08326373946  mile$

Conversion in the opposite direction

The inverse of the conversion factor is that 1 mile is equal to 12.0100298507463 times 134 meters.

It can also be expressed as: 134 meters is equal to $\frac{1}{\mathrm{12.0100298507463}}$ miles.

Approximation

An approximate numerical result would be: one hundred and thirty-four meters is about zero point zero eight miles, or alternatively, a mile is about twelve point zero zero times one hundred and thirty-four meters.

Footnotes

[1] The precision is 15 significant digits (fourteen digits to the right of the decimal point).

Results may contain small errors due to the use of floating point arithmetic.


text:
# Reading an external file failed with dimension related errors

I want to read an external file one line per read and insert each line as an item. I failed to do so because of dimension related errors. How to solve it?

\documentclass{article}
\def\trimtok i{}
\def\trimmer#1{\expandafter\trimtok #1}

\immediate\write18{tlmgr list --only-installed > installed-packages.txt}
\begin{document}
\makeatletter
\begin{enumerate}
\loop
\item \trimmer{\data}
\repeat
\end{enumerate}
\makeatother
\end{document}

-
By replacing installed-packages.txt by a random file containing a list, and adding curly braces aroud i{}in the definition of \trimtok, I get an output. I wonder if your problem wouldn't be related to the various backslashes and @ you get in installed-packages. – T. Verron Sep 24 '12 at 7:37

The text file you create contains TeX commands, which are present in the descriptions of some of the packages. Thus you need to detokenize somewhere. If you do it after reading, TeX will insert spaces after the control sequences. So I'd read as strings, and then deal with the i and end-of-line as 'other' characters in your tidy-up macros:

\documentclass{article}
\usepackage[T1]{fontenc}
\begingroup
\catcode\^^M=12\relax%
\expandafter\gdef\expandafter\trimtok\detokenize{i}#1^^M{#1}%
\gdef\trimmer#1{\expandafter\trimtok #1}%
\endgroup

\immediate\write18{tlmgr list --only-installed > installed-packages.txt}
\begin{document}
\makeatletter
\begin{enumerate}
\loop
\item \trimmer{\data}
\repeat

i addlines: A user-friendly wrapper around \enlargethispage.

which tries to execute \enlargethispage` without a suitable argument!


text:
# Linear and quadratic approximation. a. Find the linear approximating polynomial for the following functions centered at the given point a.

a. Find the linear approximating polynomial for the following functions centered at the given point a.
b. Find the quadratic approximating polynomial for the following functions centered at a.
c. Use the polynomials obtained in parts (a) and (b) to approximate the given quantity.
$$\displaystyle{f{{\left({x}\right)}}}={x}^{{\frac{{1}}{{3}}}},{a}={8}$$ approximiate $$\displaystyle{7.5}^{{\frac{{1}}{{3}}}}$$

• Questions are typically answered in as fast as 30 minutes

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Margot Mill
Given function:
$$\displaystyle{f{{\left({x}\right)}}}={x}^{{\frac{{1}}{{3}}}},{a}={8}$$
a) The linear approximating polynomial for the functions is given by
$$\displaystyle{p}_{{1}}{\left({x}\right)}={f{{\left({a}\right)}}}+{f}'{\left({a}\right)}{\left({x}-{a}\right)}$$
$$\displaystyle{p}_{{1}}{\left({x}\right)}={8}^{{\frac{{1}}{{3}}}}+{\frac{{{1}}}{{{3}}}}{8}^{{-\frac{{2}}{{3}}}}{\left({x}-{a}\right)}$$
$$\displaystyle{p}_{{1}}{\left({x}\right)}={2}+{\frac{{{1}}}{{{2}}}}{\left({x}-{a}\right)}$$
b) The quadratic approximating polynomial for the function is given by
$$\displaystyle{p}_{{2}}{\left({x}\right)}={f{{\left({a}\right)}}}+{\frac{{{1}}}{{{2}}}}{f}{''}{\left({a}\right)}{\left({x}-{8}\right)}^{{2}}$$
$$\displaystyle{p}_{{2}}{\left({x}\right)}={2}+{\frac{{{1}}}{{{12}}}}{\left({x}-{8}\right)}+{\frac{{{1}}}{{{2}}}}\times{\frac{{-{2}}}{{{9}}}}\times{8}^{{-\frac{{5}}{{3}}}}{\left({x}-{8}\right)}^{{2}}$$
$$\displaystyle{p}_{{2}}{\left({x}\right)}={2}+{\frac{{{1}}}{{{12}}}}{\left({x}-{8}\right)}-{\frac{{{1}}}{{{288}}}}{\left({x}-{8}\right)}^{{2}}$$
c) The polynomials obtained in parts (a) and (b) to approximate the given quantity.
$$\displaystyle{p}_{{1}}{\left({x}\right)}={2}+{\frac{{{1}}}{{{12}}}}{\left({x}-{8}\right)}$$
Substitute the value of $$\displaystyle{x}={7.5}$$
$$\displaystyle{p}_{{1}}{\left({7.5}\right)}={2}+{\frac{{{1}}}{{{12}}}}{\left({7.5}-{8}\right)}$$
$$\displaystyle{p}_{{1}}{\left({7.5}\right)}={1.9583}$$
$$\displaystyle{p}_{{2}}{\left({x}\right)}={2}+{\frac{{{1}}}{{{12}}}}{\left({x}-{8}\right)}-{\frac{{{1}}}{{{288}}}}{\left({x}-{8}\right)}^{{2}}$$
Substitute the value of x=7.5
$$\displaystyle{p}_{{2}}{\left({7.5}\right)}={2}+{\frac{{{1}}}{{{12}}}}{\left({7.5}-{8}\right)}-{\frac{{{1}}}{{{288}}}}{\left({7.5}-{8}\right)}^{{2}}$$
$$\displaystyle{p}_{{2}}{\left({7.5}\right)}={1.95747}$$


text:
The locally invariant infidelity between two KAK vectors.

This is the quantity

\min 1 - F_e( exp(i k_a · (XX,YY,ZZ)) kL exp(i k_b · (XX,YY,ZZ)) kR)

where F_e is the entanglement (process) fidelity and the minimum is taken over all 1-local unitaries kL, kR.

k_vec_a A 3-vector or tensor of 3-vectors with shape (...,3).
k_vec_b A 3-vector or tensor of 3-vectors with shape (...,3). If both k_vec_a and k_vec_b are tensors, their shapes must be compatible for broadcasting.
ignore_equivalent_vectors If True, the calculation ignores any other KAK vectors that are equivalent to the inputs under local unitaries. The resulting infidelity is then only an upper bound to the true infidelity.

An ndarray storing the locally invariant infidelity between the inputs. If k_vec_a or k_vec_b is a tensor, the result is vectorized.