Rx

A Dynamic Automata Library

with excerpts from The GNU C Library reference manual

by Sandra Loosemore

with

Richard M. Stallman, Roland McGrath, and Andrew Oram

Copyright © 1995 Cygnus Support

Permission is granted to make and distribute verbatim copies of this manual provided the copyright notice and this permission notice are preserved on all copies.

Permission is granted to copy and distribute modified versions of this manual under the conditions for verbatim copying, provided that the entire resulting derived work is distributed under the terms of a permission notice identical to this one.

Permission is granted to copy and distribute translations of this manual into another language, under the above conditions for modified versions, except that this permission notice may be stated in a translation approved by the author.

Rx

This document describes Rx.

This document applies to version "Rx-diSpencer" of the library named librx.a

1 Regular Expression Matching

This section is excerpted from The GNU C Library reference manual by Sandra Loosemore with Richard M. Stallman, Roland McGrath, and Andrew Oram.

The GNU C library supports the standard POSIX.2 interface. Programs using this interface should include the header file ‘rxposix.h’.

1.1 POSIX Regular Expression Compilation

Before you can actually match a regular expression, you must compile it. This is not true compilation—it produces a special data structure, not machine instructions. But it is like ordinary compilation in that its purpose is to enable you to “execute” the pattern fast. (See section Matching a Compiled POSIX Regular Expression, for how to use the compiled regular expression for matching.)

There is a special data type for compiled regular expressions:

Data Type: regex_t

This type of object holds a compiled regular expression. It is actually a structure. It has just one field that your programs should look at:

re_nsub

This field holds the number of parenthetical subexpressions in the regular expression that was compiled.

There are several other fields, but we don’t describe them here, because only the functions in the library should use them.

After you create a regex_t object, you can compile a regular expression into it by calling regcomp.

Function: int regcomp (regex_t *compiled, const char *pattern, int cflags)

The function regcomp “compiles” a regular expression into a data structure that you can use with regexec to match against a string. The compiled regular expression format is designed for efficient matching. regcomp stores it into *compiled.

It’s up to you to allocate an object of type regex_t and pass its address to regcomp.

The argument cflags lets you specify various options that control the syntax and semantics of regular expressions. See section Flags for POSIX Regular Expressions.

If you use the flag REG_NOSUB, then regcomp omits from the compiled regular expression the information necessary to record how subexpressions actually match. In this case, you might as well pass 0 for the matchptr and nmatch arguments when you call regexec.

If you don’t use REG_NOSUB, then the compiled regular expression does have the capacity to record how subexpressions match. Also, regcomp tells you how many subexpressions pattern has, by storing the number in compiled->re_nsub. You can use that value to decide how long an array to allocate to hold information about subexpression matches.

regcomp returns 0 if it succeeds in compiling the regular expression; otherwise, it returns a nonzero error code (see the table below). You can use regerror to produce an error message string describing the reason for a nonzero value; see POSIX Regexp Matching Cleanup.

Here are the possible nonzero values that regcomp can return:

REG_BADBR

There was an invalid ‘\{…\}’ construct in the regular expression. A valid ‘\{…\}’ construct must contain either a single number, or two numbers in increasing order separated by a comma.

REG_BADPAT

There was a syntax error in the regular expression.

REG_BADRPT

A repetition operator such as ‘?’ or ‘*’ appeared in a bad position (with no preceding subexpression to act on).

REG_ECOLLATE

The regular expression referred to an invalid collating element (one not defined in the current locale for string collation).

REG_ECTYPE

The regular expression referred to an invalid character class name.

REG_EESCAPE

The regular expression ended with ‘\’.

REG_ESUBREG

There was an invalid number in the ‘\digit’ construct.

REG_EBRACK

There were unbalanced square brackets in the regular expression.

REG_EPAREN

An extended regular expression had unbalanced parentheses, or a basic regular expression had unbalanced ‘\(’ and ‘\)’.

REG_EBRACE

The regular expression had unbalanced ‘\{’ and ‘\}’.

REG_ERANGE

One of the endpoints in a range expression was invalid.

REG_ESPACE

regcomp ran out of memory.

1.2 Flags for POSIX Regular Expressions

These are the bit flags that you can use in the cflags operand when compiling a regular expression with regcomp.

REG_EXTENDED

Treat the pattern as an extended regular expression, rather than as a basic regular expression.

REG_ICASE

Ignore case when matching letters.

REG_NOSUB

Don’t bother storing the contents of the matches-ptr array.

REG_NEWLINE

Treat a newline in string as dividing string into multiple lines, so that ‘$’ can match before the newline and ‘^’ can match after. Also, don’t permit ‘.’ to match a newline, and don’t permit ‘[^…]’ to match a newline.

Otherwise, newline acts like any other ordinary character.

1.3 Matching a Compiled POSIX Regular Expression

Once you have compiled a regular expression, as described in POSIX Regular Expression Compilation, you can match it against strings using regexec. A match anywhere inside the string counts as success, unless the regular expression contains anchor characters (‘^’ or ‘$’).

Function: int regexec (regex_t *compiled, char *string, size_t nmatch, regmatch_t matchptr [], int eflags)

This function tries to match the compiled regular expression *compiled against string.

regexec returns 0 if the regular expression matches; otherwise, it returns a nonzero value. See the table below for what nonzero values mean. You can use regerror to produce an error message string describing the reason for a nonzero value; see POSIX Regexp Matching Cleanup.

The argument eflags is a word of bit flags that enable various options.

If you want to get information about what part of string actually matched the regular expression or its subexpressions, use the arguments matchptr and nmatch. Otherwise, pass 0 for nmatch, and NULL for matchptr. See section Match Results with Subexpressions.

You must match the regular expression with the same set of current locales that were in effect when you compiled the regular expression.

The function regexec accepts the following flags in the eflags argument:

REG_NOTBOL

Do not regard the beginning of the specified string as the beginning of a line; more generally, don’t make any assumptions about what text might precede it.

REG_NOTEOL

Do not regard the end of the specified string as the end of a line; more generally, don’t make any assumptions about what text might follow it.

Here are the possible nonzero values that regexec can return:

REG_NOMATCH

The pattern didn’t match the string. This isn’t really an error.

REG_ESPACE

regexec ran out of memory.

1.4 Match Results with Subexpressions

When regexec matches parenthetical subexpressions of pattern, it records which parts of string they match. It returns that information by storing the offsets into an array whose elements are structures of type regmatch_t. The first element of the array (index 0) records the part of the string that matched the entire regular expression. Each other element of the array records the beginning and end of the part that matched a single parenthetical subexpression.

Data Type: regmatch_t

This is the data type of the matcharray array that you pass to regexec. It containes two structure fields, as follows:

rm_so

The offset in string of the beginning of a substring. Add this value to string to get the address of that part.

rm_eo

The offset in string of the end of the substring.

Data Type: regoff_t

regoff_t is an alias for another signed integer type. The fields of regmatch_t have type regoff_t.

The regmatch_t elements correspond to subexpressions positionally; the first element (index 1) records where the first subexpression matched, the second element records the second subexpression, and so on. The order of the subexpressions is the order in which they begin.

When you call regexec, you specify how long the matchptr array is, with the nmatch argument. This tells regexec how many elements to store. If the actual regular expression has more than nmatch subexpressions, then you won’t get offset information about the rest of them. But this doesn’t alter whether the pattern matches a particular string or not.

If you don’t want regexec to return any information about where the subexpressions matched, you can either supply 0 for nmatch, or use the flag REG_NOSUB when you compile the pattern with regcomp.

1.5 Complications in Subexpression Matching

Sometimes a subexpression matches a substring of no characters. This happens when ‘f\(o*\)’ matches the string ‘fum’. (It really matches just the ‘f’.) In this case, both of the offsets identify the point in the string where the null substring was found. In this example, the offsets are both 1.

Sometimes the entire regular expression can match without using some of its subexpressions at all—for example, when ‘ba\(na\)*’ matches the string ‘ba’, the parenthetical subexpression is not used. When this happens, regexec stores -1 in both fields of the element for that subexpression.

Sometimes matching the entire regular expression can match a particular subexpression more than once—for example, when ‘ba\(na\)*’ matches the string ‘bananana’, the parenthetical subexpression matches three times. When this happens, regexec usually stores the offsets of the last part of the string that matched the subexpression. In the case of ‘bananana’, these offsets are 6 and 8.

But the last match is not always the one that is chosen. It’s more accurate to say that the last opportunity to match is the one that takes precedence. What this means is that when one subexpression appears within another, then the results reported for the inner subexpression reflect whatever happened on the last match of the outer subexpression. For an example, consider ‘\(ba\(na\)*s \)*’ matching the string ‘bananas bas ’. The last time the inner expression actually matches is near the end of the first word. But it is considered again in the second word, and fails to match there. regexec reports nonuse of the “na” subexpression.

Another place where this rule applies is when the regular expression ‘\(ba\(na\)*s \|nefer\(ti\)* \)*’ matches ‘bananas nefertiti’. The “na” subexpression does match in the first word, but it doesn’t match in the second word because the other alternative is used there. Once again, the second repetition of the outer subexpression overrides the first, and within that second repetition, the “na” subexpression is not used. So regexec reports nonuse of the “na” subexpression.

1.6 POSIX Regexp Matching Cleanup

When you are finished using a compiled regular expression, you can free the storage it uses by calling regfree.

Function: void regfree (regex_t *compiled)

Calling regfree frees all the storage that *compiled points to. This includes various internal fields of the regex_t structure that aren’t documented in this manual.

regfree does not free the object *compiled itself.

You should always free the space in a regex_t structure with regfree before using the structure to compile another regular expression.

When regcomp or regexec reports an error, you can use the function regerror to turn it into an error message string.

Function: size_t regerror (int errcode, regex_t *compiled, char *buffer, size_t length)

This function produces an error message string for the error code errcode, and stores the string in length bytes of memory starting at buffer. For the compiled argument, supply the same compiled regular expression structure that regcomp or regexec was working with when it got the error. Alternatively, you can supply NULL for compiled; you will still get a meaningful error message, but it might not be as detailed.

If the error message can’t fit in length bytes (including a terminating null character), then regerror truncates it. The string that regerror stores is always null-terminated even if it has been truncated.

The return value of regerror is the minimum length needed to store the entire error message. If this is less than length, then the error message was not truncated, and you can use it. Otherwise, you should call regerror again with a larger buffer.

Here is a function which uses regerror, but always dynamically allocates a buffer for the error message:

char *get_regerror (int errcode, regex_t *compiled)
{
  size_t length = regerror (errcode, compiled, NULL, 0);
  char *buffer = xmalloc (length);
  (void) regerror (errcode, compiled, buffer, length);
  return buffer;
}

2 Performance Considerations

In order to use the Rx implementation of Posix regexp functions most effectively, it may help to know a bit about performance tuning in Rx.

2.1 Avoiding Redundant Compilations

Rx implements the Posix regexp entry points regcomp, regerror, regexec, and regfree. Some special considerations apply when using the Rx versions.

First, regcomp is a comparatively expensive operation. Addiitonally, regexec tends to perform better when a compiled expression is compiled once and used twice than when the pattern is compiled twice and used twice. Internally, Rx caches that information about a pattern which is constructed dynamicly by regexec. You can save on compilation costs and maximize the effectiveness of the Rx cache by re-using compiled expressions when it is convenient.

For example, for reasons unrelated to Rx, it has long been the practice in GNU emacs to always save one compiled regular expression (the most recent). Before compiling a new expression, Emacs checks to see if the new pattern is the same as the one that is already compiled. This is the sort of optimization that Rx likes. (It may even win, in some cases, to cache more than a single compiled regexp.)

In the long-run, Rx should be modified to cache compilations on its own. (See section Improvements to Make.)

Sometimes programmers write programs with many regexps, all known staticly at compile time. This can be a problem with Rx because when the program starts up, or as it runs, all of those staticly known regexps have to be compiled, which may be too time consuming.

One easy fix for programs with many static regexps is to use flex or another lexical-analyzer generator program instead. Lexer-generators are optimized for the case of compiling staticly known regexps.

There are still reasons why staticly known regexps may not be convertable to flex input – for example, the Posix pattern language is more general than flex’s. In the long-run, it may be a good idea to extend Rx to support static compilation of regexps. (See section Improvements to Make.)

2.2 Controlling Memory Use

The size of the cache used by regexec is subject to control by programmers. Additionally, by using lower level entry points, programmers can create multiple, distinct Rx caches.

This part of the code is subject to change and so is not yet documented.

See "default_cache" in rxsuper.c and the parameters at the top of "rxbasic.c" to find some parameters you can tune or hints about creating alternative regexec caches.

3 Semantic Tests

The distribution of Rx includes a test-suite, aimed at testing the conformance of an implementation of the Posix regexp functions to the standard.

Currently, the tests come from two sources: a test-suite started by Henry Spencer, and the "Khadafy" test suite by Scott Anderson.

The tests come in three files:

• runtests.c – The driver program.
• TESTS – The list of test cases
• TESTS2C.sed – A script to convert test cases into C.

3.1 Running the Tests

To build the test program, use make runtests. (Detailed configuration and build instructions can be found in INSTALL).

Invoked with no arguments, runtests runs all test-cases. For each test case, a sequence number is printed. If there is a problem with that case, more information is printed. Output like this:

#0
#1
#2
...

indicates a successful run. (The output format is likely to change in the future to make it easier to automate testing of Rx.)

With a single numeric argument, runtests executes just that test and no others. This is handy when debugging.

Sometimes a bug will occur when all tests are run, but disappear when just the problematic test is run. Usually this has to do with memory or cache corruption.

3.2 Adding New Tests

This list of tests used by runtests is found in the file TESTS. Each line of that file is a list of colon separated fields similar to:

1:^(ab|cd)e:abcde

The first field is the expected return value of regexec, or ’2’ meaning that the pattern is not valid.

The second field is the regular expression being tested.

The third field is the string to which the pattern is to be compared.

The file TESTS2C.sed is used to convert the test cases into initializers for an array of structures (which is automated in the Makefile).

To add a new test case, add lines to TESTS and recompile runtests.

4 General Functions

Here is a whirlwind tour of the lower-level Rx entry points and data structures. This is not intended to be complete, but rather to be a help to anyone reading the code itself.

These are presented in the same order in which they might typically be used.

4.1 Compiling Expressions

Internal Function: reg_errcode_t rx_parse (struct rexp_node ** rexp_p, __const__ char *pattern, int size, unsigned long syntax, int cset_size, unsigned char *translate);

Compile a regular expression.

rexp_p will return a syntax tree for the pattern. See "rxnode.h" to learn about syntax trees. Minimally, you should know that syntax trees are reference counted using rx_save_rexp and rx_free_rexp.

pattern and size are the expression and its length. The expression need not be 0-terminated.

The bits set in syntax control details of the language understood by the parser. The meaning of each bit is described in "rxgnucomp.h".

cset_size is usually 256. It should not be much larger than that or space-performance will suffer badly.

translate is a translation table – an array of characters. Characters in the pattern are looked up in translate as they are read. Additionally, the pattern is compiled presuming that the same translation table will be applied to characters in the string being searched (meaning that the pattern is compiled in such a way that the effect will be as if every character in the target string is looked up in the translation table, even though the expense of that lookup is usually avoided).

A return of 0 indicates success, otherwise, the error can be looked up in the rx_error_msg array.

Internal Function: int rx_posix_analyze_rexp (struct rexp_node *** subexps, int * n_subexps, struct rexp_node * node, int id)

Staticly analyze a regular expression in preparation for matching.

This function fills in some fields of the nodes of a syntax tree.

subexps and n_subexps return a malloced array of pointers into the syntax tree, one per parenthesized subexpression. The caller must eventually free this array.

node is the pattern to be analyzed. The tree returned by rx_parse is suitable for this.

id should be 1.

Ignore the return value.

This function is not robust in the case that malloc or realloc returns 0 (which should be fixed).

You might expect that rx_posix_analyze_rexp and rx_parse should be combined. They are not because the actions of rx_posix_analyze_rexp make sense for any syntax tree, regardless of how it is constructed. rx_parse is just one way to build a syntax tree – it is subject to replacement and trees can be built without using a parser at all (c.f. "rxnode.h").

4.2 Checking for Posixly Correct Matches with One-Piece Strings

Looking for a match that is Posixly correct is conceptually tricky. Here is one way to think of it:

The Posix expression languages, absent of any consideration of the meaning of "leftmost-longest", underspecify the return value of regexec. Consider the example:

Pattern:
	foo\(.*\)\(.*\)bar
Target string:
	fooxxxbar

Initially it is ambiguous how this should be matched. The ambiguity is exposed by considering the possible bindings for the subexpressions \1 and \2:

Possible outcomes:

	\1 == "xxx" \2 == ""
	\1 == "xx" \2 == "x"
	\1 == "x" \2 == "xx"
	\1 == "" \2 == "xxx"

Posix tells us that the first outcome is the prefered one if the illustrated pattern is used alone (this is a consequence of the "leftmost longest" rule). But Posix also says the answer may be different if the pattern is a sub-pattern of a larger pattern. For example:

Pattern:
	foo\(.*\)\(.*\)bar\2
Target string:
	fooxxxbarxx

Now the only acceptable outcome is:

	\1 == "x" \2 == "xx"

Three entry points provide a relatively simple interface to this moderately complicated situation:

Internal Function: struct rx_solutions * rx_basic_make_solutions (struct rx_registers * regs, struct rexp_node * expression, struct rexp_node ** subexps, int start, int end, struct rx_context_rules * rules, char * str)

Internal Function: void rx_basic_free_solutions (struct rx_solutions * solns);

Internal Function: enum rx_answers rx_next_solution (struct rx_solutions * solns)

Internal Function: void rx_basic_free_solutions (struct rx_solutions * solns)

make_solutions returns a lazilly constructed stream of possible solutions for a given regexp and target string.

next_solution constructs and returns the next solution from a list returned by make_solutions. Solutions are returned in order of preferability according to the Posix spec. So, the first solution is the leftmost-longest, and the last, the rightmost-shortest.

regs is where subexpression extents are tracked.

expression is the expression to solve.

subexps is as returned by rx_posix_analyze_rexp.

start and end are the integer addresses of the data to be compared to the pattern. A solution must match all characters starting at start and ending at end - 1.

rules are some bits that control the precise meaning of "^" and "$". See "rxcontext.h".

str is the data to be matched. Note that anchoring operators can cause the matcher to look beyond start and end when testing a match. It may make sense to pass start > 0, for example.

make_solutions returns a pointer to a solution list, or 0 if an allocation fails.

next_solution returns a status which can be:

rx_yes	-- The pattern matches exactly.
rx_maybe	-- The pattern does not match, but might 
		   if more characters were added to the string.
rx_no	-- The pattern does not match and could not be
		   made to match even by adding more characters.

In addition, regs is filled in by next_solution.

Finally, free_solutions is used to release resources consumed by a solution list.

4.3 Hairy Matches and Suspendable Searches

The functions rx_basic_make_solutions and rx_basic_free_solutions are used to find matches in a one-piece string. More general entry points are provided for multi-piece strings, which may or may not be entirely available in memory at one time:

Internal Function: struct rx_solutions * rx_make_solutions (struct rx_registers * regs, struct rx_unfaniverse * verse, struct rexp_node * expression, struct rexp_node ** subexps, int cset_size, int start, int end, rx_vmfn vmfn, rx_contextfn contextfn, void * closure)

Internal Function: void rx_free_solutions (struct rx_solutions * solns)

These functions are similar to their _basic_ analogues, but substitute some new parameters for the one piece string:

vmfn is a function provided by the caller that returns at least part of the string being matched.

contextfn is a function provided by the caller that does the work of the backreference operators, "^", and "$".

closure is data provided by the caller, passed through to vmfn and contextfn.

typedef enum rx_answers (*rx_vmfn)
     P((void * closure,
	unsigned char ** burst, int * len, int * offset,
	int start, int end, int need));

typedef enum rx_answers (*rx_contextfn)
     P((void * closure,
	int type,
	int start, int end,
	struct rx_registers * regs));

vmfn is asked for a range of characters from start to end. need is in that range and is the only position that must be returned by vmfn. burst, len, and offset are output parameters. offset will get the integer address of burst, and len the number of valid characters in the burst. vmfn may be asked for the empty string from end to end and should be able to handle that case.

If vmfn provides the needed character, it should return rx_yes.

If vmfn can’t provide the character now, but might be able to later, it should return rx_maybe. This will cause rx_next_solution to quickly return rx_maybe. If rx_next_solution is called again, it will retry the call to vmfn and possibly resume the search.

If vmfn can not provide the needed character, it should return rx_no. rx_next_solution will not normally ask for out-of-range characters, so usually there is no good reason to return rx_no, but the code is supposed to be robust in case you do.

The contextfn also returns a yes/no/maybe status. It tests whether the characters in start to end satisfy the operator type. type is an ascii value; one of the characters in "^$123456789".

4.4 NFA Functions and Super-NFA Functions

Not really documented yet.

rx.h, rxnfa.h		-- translating an expression into an NFA.

rxsuper.h		-- optimizing the NFA into a DFA, or at least
			   an NFA with fewer branch points.

rxanal.h		-- how to use DFAs to find longest matches,
			   matches of a specific length, the shortest
			   match, etc.

rxsimp.h		-- Translating a Posix "regular
			   expression" into a true regular expression
			   that describes a superset language.

5 Rx Theory

There are two match algorithms. One is for truly regular regexps (those that can be reduced to a dfa). The other is for non-regular regexps.

The dfa algorithm implements the idea suggested in Compilers by Aho, Sethi and Ullman:

[One] approach [to pattern matching regular expressions] is to use a DFA, but avoid constructing all of the transition table by using a technique called "lazy transition evaluation". Here, transitions are computed at run time [when] actually needed. [T]ransitions are stored in a cache. [....] If the cache becomes full, we can erase some previously computed transition to make room for the new transition.

The implementation in Rx is generalized from that, but the above description covers what is used for Posix patterns.

The non-dfa algorithm implements a "recursive decomposition" technique described in email by Henry Spencer. For a given pattern, this algorithm first checks to see if a simpler, superset language, DFA-pattern matches. If it does, then this algorithm does the detail-work to see if the non-DFA pattern matches.

The detail work usually involves recursing on subpatterns. For example, a concatentation of two subexpressions matches a string if the string can be divided into two parts, each matching one subexpression, in the right order. More than one solution is often possible for a given pattern. This ambiguity is the subject of the "leftmost longest" rules in the spec, and the back-tracking oriented stream-of-solution functions rx_make_solutions, rx_next_solution and rx_free_solutions.

rxspencer.[ch]	 			-- The non-DFA algorithm
rxanal.[ch] rxsuper.[ch] rxnfa.[ch]	-- The DFA algorithm

6 Improvements to Make

An approximation of the GNU entry points is needed. This can not easily be an exact approximation because the GNU entry points have no function for freeing a compiled expression – they assume that compiled expressions can be freed using a single call to "free(3)". For that reason, do not use the names of the old GNU entry points ...use "rx_" instead.

This version of Rx hasn’t been profiled and tuned.

It might be nice to have some C++ types to hide reference counting and provide handy constructors for rexp_nodes and nfa parts.

Right now, the regexp->regular regexp mapping in rxsimp.[ch] is cached for a particular input expression. I think it would probably be a big win in many situations if it were cached, like unique nfas (c.f. rxunfa.[ch]), for equivalent expressions.

It would speed up matching to lift the non-regular constructs to the top of the syntax tree. e.g., if you have:

pattern:  "abc$"

syntax tree: (concat (cset "a")
	             (concat (cset "b")
			     (concat (cset "c")
				     (operator "$"))))

it involves a lot more work (in "next_solution) than if you have the equivalent:

same pattern:  "abc$"

syntax tree: (concat (concat (cset "a")
			     (concat (cset "b")
				     (cset "c")))
		     (operator "$"))

in fact, while doing that, notice that subtrees of nothing-but-concat can conceivably be optimized so that next_solution just uses "strcmp".

For that matter, a tree which is a disjunction of conjunction (a tree of "|" whose leaves are trees of concat nodes) could be optimized to use a table method (Boyer/Moore?). Again, this would be for next_solution but might involve adding stuff to rx_posix_analyze_rexp.

As more and more optimizations are added, programmers should be given simple control over which optimizations are important for a particular pattern. For example, packages in emacs often include a few regexps that are used heavily – it would be worth the trouble to arrange for those regexps to be compiled specially.

Static compilation of regexps is mostly a job for lex, but posix patterns are more general and have a nicer interface. What’s more, it’d be nice to have the benefits of static compilation even for dynamicly loaded regexps (e.g., imagine if when an emacs lisp file is byte-compiled, the regexps it contains are also compiled).

A lot of optimizations apply to just syntax trees. One approach to static compilation is to make an ugly but fast-reading syntax for trees, and a printer for that syntax. Then, after optimiztaions, a pattern could be stored as a string and later read back in, already optimized.

A similar trick could be done for the nfa built in rxnfa.c.

next_solution already considers the length of a fixed-length subexpression, but many more lenght optimizations are possible. I’d guess these will pay off well.

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