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Xref: bloom-picayune.mit.edu comp.lang.c:62383 news.answers:4599 Newsgroups: comp.lang.c,news.answers Path: bloom-picayune.mit.edu!adam.mit.edu!scs From: scs@adam.mit.edu (Steve Summit) Subject: comp.lang.c Answers (Abridged) to Frequently Asked Questions (FAQ) Message-ID: <1992Dec15.160735.21337@athena.mit.edu> Followup-To: poster Sender: news@athena.mit.edu (News system) Supersedes: <1992Dec1.025558.25274@athena.mit.edu> Nntp-Posting-Host: adam.mit.edu Reply-To: scs@adam.mit.edu X-Archive-Name: C-faq/abridged Organization: none, at the moment Date: Tue, 15 Dec 1992 16:07:35 GMT X-Last-Modified: November 3, 1992 Approved: news-answers-request@MIT.Edu Expires: Wed, 6 Jan 1993 00:00:00 GMT Lines: 944 Archive-name: C-faq/abridged [Last modified November 3, 1992 by scs.] This article contains minimal answers to the comp.lang.c frequently- asked questions list. Please see the long version (posted on the first of each month, or see question 17.21) for more detailed explanations and references. Section 1. Null Pointers 1.1: What is this infamous null pointer, anyway? A: For each pointer type, there is a special value -- the "null pointer" -- which is distinguishable from all other pointer values and which is not the address of any object. 1.2: How do I "get" a null pointer in my programs? A: A constant 0 in a pointer context is converted into a null pointer at compile time. A "pointer context" is an initialization, assignment, or comparison with one side a variable or expression of pointer type, and (in ANSI standard C) a function argument which has a prototype in scope declaring a certain parameter as being of pointer type. In other contexts (function arguments without prototypes, or in the variable part of variadic function calls) a constant 0 with an appropriate explicit cast is required. 1.3: What is NULL and how is it #defined? A: NULL is simply a preprocessor macro, #defined as 0 (or (void *)0), which is used (as a stylistic convention, in preference to unadorned 0's) to generate null pointers, 1.4: How should NULL be #defined on a machine which uses a nonzero bit pattern as the internal representation of a null pointer? A: The same as any other machine: as 0 (or (void *)0). (The compiler makes the translation, upon seeing a 0, not the preprocessor.) 1.5: If NULL were defined as "(char *)0," wouldn't that make function calls which pass an uncast NULL work? A: Not in general. The problem is that there are machines which use different internal representations for pointers to different types of data. A cast is still required to tell the compiler which kind of null pointer is required, since it may be different from (char *)0. 1.6: I use the preprocessor macro "#define Nullptr(type) (type *)0" to help me build null pointers of the correct type. A: This trick, though valid, does not buy much. 1.7: Is the abbreviated pointer comparison "if(p)" to test for non- null pointers valid? What if the internal representation for null pointers is nonzero? A: The construction "if(p)" works, regardless of the internal representation of null pointers, because the compiler essentially rewrites it as "if(p != 0)" and goes on to convert 0 into the correct null pointer. 1.8: If "NULL" and "0" are equivalent, which should I use? A: Either; the distinction is entirely stylistic. 1.9: But wouldn't it be better to use NULL (rather than 0) in case the value of NULL changes, perhaps on a machine with nonzero null pointers? A: No. NULL is, and will always be, 0. 1.10: I'm confused. NULL is guaranteed to be 0, but the null pointer is not? A: A "null pointer" is a language concept whose particular internal value does not matter. A null pointer is requested in source code with the character "0". "NULL" is a preprocessor macro, which is always #defined as 0 (or (void *)0). 1.11: Why is there so much confusion surrounding null pointers? Why do these questions come up so often? A: The fact that null pointers are represented both in source code, and internally to most machines, as zero invites unwarranted assumptions. The use of a preprocessor macro (NULL) suggests that the value might change later, or on some weird machine. 1.12: I'm still confused. I just can't understand all this null pointer stuff. A: A simple rule is, "Always use `0' or `NULL' for null pointers, and always cast them when they are used as arguments in function calls." 1.13: Given all the confusion surrounding null pointers, wouldn't it be easier simply to require them to be represented internally by zeroes? A: Such a requirement would accomplish little. 1.14: Seriously, have any actual machines really used nonzero null pointers? A: Machines manufactured by Prime and by Honeywell-Bull, as well as Symbolics Lisp Machines, have done so. Section 2. Arrays and Pointers 2.1: I had the definition char a[6] in one source file, and in another I declared extern char *a. Why didn't it work? A: The declaration extern char *a simply does not match the actual definition. Use extern char a[]. 2.2: But I heard that char a[] was identical to char *a. A: Not at all. Arrays are not pointers. A reference like x[3] generates different code depending on whether x is an array or a pointer. 2.3: So what is meant by the "equivalence of pointers and arrays" in C? A: An lvalue of type array-of-T which appears in an expression decays into a pointer to its first element; the type of the resultant pointer is pointer-to-T. So for an array a and pointer p, you can say "p = a;" and then p[3] and a[3] will access the same element. 2.4: Why are array and pointer declarations interchangeable as function formal parameters? A: Since functions can never receive arrays as parameters, any parameter declarations which "look like" arrays are treated by the compiler as if they were pointers. 2.5: Why doesn't sizeof properly report the size of an array which is a parameter to a function? A: The sizeof operator reports the size of the pointer parameter which the function actually receives. 2.6: Someone explained to me that arrays were really just constant pointers. A: An array name is "constant" in that it cannot be assigned to, but an array is _not_ a pointer. 2.7: I came across some "joke" code containing the "expression" 5["abcdef"] . How can this be legal C? A: Yes, array subscripting is commutative in C. The array subscripting operation a[e] is defined as being equivalent to *((a)+(e)). 2.8: My compiler complained when I passed a two-dimensional array to a routine expecting a pointer to a pointer. A: The rule by which arrays decay into pointers is not applied recursively. An array of arrays (i.e. a two-dimensional array in C) decays into a pointer to an array, not a pointer to a pointer. 2.9: How do I declare a pointer to an array? A: Usually, you don't want to. Consider using a pointer to one of the array's elements instead. 2.10: How can I dynamically allocate a multidimensional array? A: It is usually best to allocate an array of pointers, and then initialize each pointer to a dynamically-allocated "row." See the full list for code samples. 2.11: Can I simulate a non-0-based array with a pointer? A: Not if the pointer points outside of the block of memory it is intended to access. 2.12: I passed a pointer to a function which initialized it, but the pointer in the caller was unchanged. A: The called function probably altered only the passed copy of the pointer. 2.13: I have a char * pointer that happens to point to some ints, and I want to step it over them. Why doesn't "((int *)p)++;" work? A: In C, a cast operator is a conversion operator, and by definition it yields an rvalue, which cannot be assigned to, or incremented with ++. Section 3. Memory Allocation 3.1: Why doesn't the code "char *answer; gets(answer);" work? A: The pointer variable "answer" has not been set to point to any valid storage. The simplest way to correct this fragment is to use a local array, instead of a pointer. 3.2: I can't get strcat to work. I tried "char *s1 = "Hello, ", *s2 = "world!", *s3 = strcat(s1, s2);" but I got strange results. A: Again, the problem is that space for the concatenated result is not properly allocated. 3.3: But the man page for strcat says that it takes two char *'s as arguments. How am I supposed to know to allocate things? A: In general, when using pointers you _always_ have to consider memory allocation, at least to make sure that the compiler is doing it for you. 3.4: I have a function that is supposed to return a string, but when it returns to its caller, the returned string is garbage. A: Make sure that the memory to which the function returns a pointer is correctly (i.e. not locally) allocated. 3.5: You can't use dynamically-allocated memory after you free it, can you? A: No. Some early man pages implied otherwise, but the claim is no longer valid. 3.6: How does free() know how many bytes to free? A: The malloc/free package remembers the size of each block it allocates and returns. 3.7: So can I query the malloc package to find out how big an allocated block is? A: Not portably. 3.8: Is it legal to pass a null pointer as the first argument to realloc()? A: ANSI C sanctions this usage, but several earlier implementations do not support it. 3.9: Is it safe to use calloc's zero-fill guarantee for pointer and floating-point values? A: No. 3.10: What is alloca and why is its use discouraged? A: alloca allocates memory which is automatically freed when the function which called alloca returns. alloca cannot be written portably, is difficult to implement on machines without a stack, and fails under certain conditions if implemented simply. Section 4. Expressions 4.1: Why doesn't the code "a[i] = i++;" work? A: The variable i is both referenced and modified in the same expression. 4.2: Under my compiler, the code "int i = 7; printf("%d\n", i++ * i++);" prints 49. Regardless of the order of evaluation, shouldn't it print 56? A: The operations implied by the postincrement and postdecrement operators ++ and -- are performed at some time after the operand's former values are yielded and before the end of the expression, but not necessarily immediately after, or before other parts of the expression are evaluated. 4.3: But what about the &&, ||, and comma operators? A: There is a special exception for those operators, (as well as ?: ); left-to-right evaluation is guaranteed. 4.4: If I'm not using the value of the expression, should I use i++ or ++i to increment a variable? A: Since the two forms differ only in the value yielded, they are entirely equivalent when only their side effect is needed. 4.5: Why doesn't the code "int a = 1000, b = 1000; long int c = a * b;" work? A: You must manually cast one of the operands to (long). Section 5. ANSI C 5.1: What is the "ANSI C Standard?" A: In 1983, the American National Standards Institute commissioned a committee, X3J11, to standardize the C language. After a long, arduous process, the committee's work was finally ratified as an American National Standard, X3.159-1989, on December 14, 1989, and published in the spring of 1990. The Standard has also been adopted as ISO/IEC 9899:1990. 5.2: How can I get a copy of the Standard? A: Copies are available from the American National Standards Institute in New York, or from Global Engineering Documents in Irvine, CA. See the unabridged list for addresses. 5.3: Does anyone have a tool for converting old-style C programs to ANSI C, or for automatically generating prototypes? A: See the full list for details. 5.4: How do I keep the ANSI "stringizing" preprocessing operator from stringizing the macro's name rather than its value? A: You must use a two-step #definition to force the macro to be expanded as well as stringized. 5.5: What's the difference between "char const *p" and "char * const p"? A: The former is a pointer to a constant character; the latter is a constant pointer to a character. 5.6: My ANSI compiler complains about a mismatch when it sees extern int func(float); int func(x) float x; {... A: You have mixed the new-style prototype declaration "extern int func(float);" with the old-style definition "int func(x) float x;". "Narrow" types are treated differently according to which syntax is used. The problem can be fixed by using either new-style (prototype) or old-style syntax consistently. 5.7: I'm getting strange syntax errors inside code which I've #ifdeffed out. A: Under ANSI C, #ifdeffed-out text must still consist of "valid preprocessing tokens." This means that there must be no unterminated comments or quotes (i.e. no single apostrophes), and no newlines inside quotes. 5.8: Can I declare main as void, to shut off these annoying "main returns no value" messages? A: No. 5.9: Why does the ANSI Standard not guarantee more than six monocase characters of external identifier significance? A: The problem is older linkers which cannot be forced (by mere words in a Standard) to upgrade. 5.10: What is the difference between memcpy and memmove? A: memmove offers guaranteed behavior if the source and destination arguments overlap. 5.11: My compiler is rejecting the simplest possible test programs, with all kinds of syntax errors. A: Perhaps it is a pre-ANSI compiler. 5.12: Why won't frobozz-cc, which claims to be ANSI compliant, accept this code? A: Are you sure that the code being rejected doesn't rely on some non-Standard extension? 5.13: What are #pragmas and what are they good for? A: The #pragma directive provides a single, well-defined "escape hatch" which can be used for extensions. Section 6. C Preprocessor 6.1: How can I write a generic macro to swap two values? A: There is no good answer to this question. The best all-around solution is probably to forget about using a macro. 6.2: I have some old code that tries to construct identifiers with a macro like "#define Paste(a, b) a/**/b ", but it doesn't work any more. A: Try the ANSI token-pasting operator ##. 6.3: What's the best way to write a multi-statement cpp macro? A: #define Func() do {stmt1; stmt2; ... } while(0) /* (no trailing ;) */ 6.4: Is it acceptable for one header file to #include another? A: There has been considerable debate surrounding this question. 6.5: Does the sizeof operator work in preprocessor #if directives? A: No. 6.6: How can I use a preprocessor #if expression to detect endianness? A: You probably can't. 6.7: I've got this tricky processing I want to do at compile time and I can't figure out a way to get cpp to do it. A: Consider writing your own little special-purpose preprocessing tool, instead. 6.8: How can I write a cpp macro which takes a variable number of arguments? A: Here is one popular trick. Note that the parentheses around printf's argument list are in the macro call, not the definition. #define DEBUG(args) (printf("DEBUG: "), printf args) if(n != 0) DEBUG(("n is %d\n", n)); Section 7. Variable-Length Argument Lists 7.1: How can I write a function that takes a variable number of arguments? A: Use the <stdarg.h> (or older <varargs.h>) header. 7.2: How can I write a function that takes a format string and a variable number of arguments, like printf, and passes them to printf to do most of the work? A: Use vprintf, vfprintf, or vsprintf. 7.3: How can I discover how many arguments a function was actually called with? A: Any function which takes a variable number of arguments must be able to determine from the arguments themselves how many of them there are. 7.4: How can I write a function which takes a variable number of arguments and passes them to some other function (which takes a variable number of arguments)? A: In general, you cannot. 7.5: How can I call a function with an argument list built up at run time? A: You can't. Section 8. Boolean Expressions and Variables 8.1: What is the right type to use for boolean values in C? Why isn't it a standard type? Should #defines or enums be used for the true and false values? A: C does not provide a standard boolean type, because picking one involves a space/time tradeoff which is best decided by the programmer. The choice between #defines and enums is arbitrary and not terribly interesting. 8.2: Isn't #defining TRUE to be 1 dangerous, since any nonzero value is considered "true" in C? What if a built-in boolean or relational operator "returns" something other than 1? A: It is true (sic) that any nonzero value is considered true in C, but this applies only "on input", i.e. where a boolean value is expected. When a boolean value is generated by a built-in operator, it is guaranteed to be 1 or 0. (This is _not_ true for some library routines such as isalpha.) Section 9. Structs, Enums, and Unions 9.1: What is the difference between an enum and a series of preprocessor #defines? A: At the present time, there is little difference. The ANSI standard states that enumerations are compatible with integral types. 9.2: I heard that structures could be assigned to variables and passed to and from functions, but K&R I says not. A: These operations are supported by all modern compilers. 9.3: How does struct passing and returning work? A: If you really need to know, see the unabridged list. 9.4: I have a program which works correctly, but dumps core after it finishes. Why? A: Check to see if a structure type declaration just before main is missing its trailing semicolon, causing the compiler to believe that main returns a structure. See also question 17.15. 9.5: Why can't you compare structs? A: There is no reasonable way for a compiler to implement struct comparison which is consistent with C's low-level flavor. 9.6: I came across some code that declared a structure with the last member an array of one element, and then did some tricky allocation to make the array act like it had several elements. Is this legal and/or portable? A: The ANSI C standard allows it, but only implicitly. 9.7: How can I determine the byte offset of a field within a structure? A: ANSI C defines the offsetof macro, which should be used if available. 9.8: How can I access structure fields by name at run time? A: Build a table of names and offsets, using the offsetof() macro. 9.9: Why does sizeof report a larger size than I expect for a structure type, as if there was padding at the end? A: The alignment of arrays of structures must be preserved. 9.10: How can I turn off structure padding? A: There is no standard method. 9.11: Can I initialize unions? A: ANSI Standard C allows an initializer for the first member. Section 10. Declarations 10.1: How do you decide which integer type to use? A: If you might need large values, use long. Otherwise, if space is very important, use short. Otherwise, use int. 10.2: I can't seem to define a linked list node which contains a pointer to itself. A: Structs in C can certainly contain pointers to themselves; the discussion and example in section 6.5 of K&R make this clear. Problems arise if an attempt is made to define (and use) a typedef in the midst of such a declaration; avoid this. 10.3: How do I declare an array of pointers to functions returning pointers to functions returning pointers to characters? A: char *(*(*a[5])())(); Using a chain of typedefs, or the cdecl program, makes these declarations easier. 10.4: How can I declare a function that returns a pointer to a function of its own type? A: You can't do it directly. 10.5: What's the best way to declare and define global variables? A: It is best to place the definition in some central .c file, with an external declaration in a header file. 10.6: How do I initialize a pointer to a function? A: Use something like "extern int func(); int (*fp)() = func;" . 10.7: I've seen different methods used for calling through pointers to functions. A: The extra parentheses and explicit * are now officially optional, although some older implementations require them. Section 11. Stdio 11.1: Why doesn't the code "char c; while((c = getchar()) != EOF)..." work? A: The variable to hold getchar's return value must be an int. 11.2: Why does errno contain ENOTTY after a call to printf? A: Don't worry about it. It is only meaningful for a program to inspect the contents of errno after an error has occurred. 11.3: My program's prompts and intermediate output don't always show up on the screen, especially when I pipe the output through another program. A: It is best to use an explicit fflush(stdout) whenever output should definitely be visible. 11.4: When I read from the keyboard with scanf, it seems to hang until I type one extra line of input. A: scanf was designed for free-format input, which is seldom what you want when reading from the keyboard. 11.5: Will fflush(stdin) flush unread characters from the standard input stream? A: No. 11.6: Once I've used freopen, how can I get the original stdout back? A: It's not easy. Try avoiding freopen. 11.7: How can I recover the file name given an open file descriptor? A: This problem is, in general, insoluble. It is best to remember the names of files yourself when you open them. Section 12. Library Subroutines 12.1: I'm trying to sort an array of strings with qsort, using strcmp as the comparison function, but it's not working. A: You'll have to write a "helper" comparison function which takes two generic pointer arguments, converts them to char **, and dereferences them, yielding char *'s which can be usefully compared. 12.2: Now I'm trying to sort an array of structures with qsort. My comparison routine takes pointers to structures, but the compiler complains that the function is of the wrong type for qsort. How can I cast the function pointer to shut off the warning? A: The conversions must be in the comparison function, which must be declared as accepting "generic pointers" (void * or char *). 12.3: How can I convert numbers to strings? A: Just use sprintf. 12.4: How can I get the time of day in a C program? A: Just use the time, ctime, and/or localtime functions. 12.5: How can I convert a struct tm or a string into a time_t? A: The ANSI mktime routine converts a struct tm to a time_t. No standard routine exists to parse strings. 12.6: I need a random number generator. A: The standard C library has one: rand(). 12.7: Each time I run my program, I get the same sequence of random numbers. A: You can call srand() to seed the pseudo-random number generator with a more random initial value. 12.8: I need a random true/false value, so I'm taking rand() % 2, but it's just alternating 0, 1, 0, 1, 0... A: Try using the higher-order bits. 12.9-13: I'm trying to port this old program. Why do I get "undefined external" errors for some library routines? A: Some semistandard routines have been renamed or replaced over the years; see the full list for details. 12.14: How can I execute a command with system() and read its output into a program? A: Unix and some other systems provide a popen() routine. 12.15: How can I read a directory in a C program? A: See if you can use the opendir() and readdir() routines. Section 13. Lint 13.1: I just typed in this program, and it's acting strangely. Can you see anything wrong with it? A: Try running lint first. 13.2: How can I shut off the "warning: possible pointer alignment problem" message lint gives me for each call to malloc? A: It may be easier simply to ignore the message, perhaps in an automated way with grep -v. 13.3: Where can I get an ANSI-compatible lint? A: See the unabridged list for two commercial products. Section 14. Style 14.1: Is the code "if(!strcmp(s1, s2))" good style? A: Perhaps; perhaps not. 14.2: What's the best style for code layout in C? A: There is no one "best style," but see the full list for a few suggestions. 14.3: Where can I get the "Indian Hill Style Guide" and other coding standards? A: See the unabridged list. Section 15. Floating Point 15.1: My floating-point calculations are acting strangely and giving me different answers on different machines. A: First, make sure that you have #included <math.h>, and correctly declared other functions returning double. If the problem isn't that simple, see the full list for a brief explanation, or any good programming book for a better one. 15.2: I keep getting "undefined: _sin" compilation errors. A: Make sure you're linking against the correct math library. 15.3: Why doesn't C have an exponentiation operator? A: Try using the pow() function. 15.4: I'm having trouble with a Turbo C program which crashes and says something like "floating point formats not linked." A: Some compilers for small machines, including Turbo C, attempt to leave out floating point support if it looks like it will not be needed. The programmer must occasionally insert a dummy explicit floating-point call to force loading of floating-point support. Section 16. System Dependencies 16.1: How can I read a single character from the keyboard without waiting for a newline? A: Contrary to popular belief and many people's wishes, this is not a C-related question. How to do so is a function of the operating system in use. 16.2: How can I find out if there are characters available for reading (and if so, how many)? Alternatively, how can I do a read that will not block if there are no characters available? A: These, too, are entirely operating-system-specific. 16.3: How can I clear the screen? A: Such things depend on the output device you're using. 16.4: How do I read the mouse? A: What system are you using? 16.5: How can my program discover the complete pathname to the executable file from which it was invoked? A: argv[0] may contain all or part of the pathname. You may be able to duplicate the command language interpreter's search path logic to locate the executable. 16.6: How can a process change an environment variable in its caller? A: In general, it cannot. 16.7: How can I find out the size of a file, prior to reading it in? A: You might be able to get an estimate using stat() or fseek/ftell. 16.8: How can a file be shortened in-place without completely clearing or rewriting it? A: There are various ways to do this, but there is no truly portable solution. 16.9: How can I implement a delay, or time a user's response, with sub-second resolution? A: Unfortunately, there is no portable way. 16.10: How can I read in an object file and jump to routines in it? A: You want a dynamic linker and/or loader. Section 17. Miscellaneous 17.1: What can I safely assume about the initial values of variables which are not explicitly initialized? A: Variables with "static" duration start out as 0, as if the programmer had initialized them. Variables with "automatic" duration, and dynamically-allocated memory, start out containing garbage (with the exception of calloc). 17.2: How can I write data files which can be read on other machines with different data formats? A: The best solution is to use text files. 17.3: How can I return several values from a function? A: Either pass pointers to locations which the function can fill in, or have the function return a structure containing the desired values. 17.4: How can I call a function, given its name as a string? A: The most straightforward thing to do is maintain a correspondence table of names and function pointers. 17.5: I seem to be missing the system header file <sgtty.h>. Can someone send me a copy? A: You cannot just pick up a copy of someone else's header file and expect it to work, since the definitions within header files are frequently system-dependent. Contact your vendor. 17.6: How can I call FORTRAN (C++, BASIC, Pascal, Ada, LISP) functions from C? A: The answer is entirely dependent on the machine and the specific calling sequences of the various compilers in use. 17.7: Does anyone know of a program for converting Pascal or FORTRAN to C? A: Several public-domain programs are available, namely ptoc, p2c, and f2c. See the full list for details. 17.8: Where can I get copies of all these public-domain programs? A: See the regular postings in the comp.sources.unix and comp.sources.misc newsgroups for information. 17.9: When will the next Obfuscated C Code Contest be held How can I get a copy of the previous winning entries? A: See the full list, or send e-mail to obfuscate@toad.com . 17.10: Why don't C comments nest? Are they legal inside quoted strings? A: Nested comments would cause more harm than good. The character sequences /* and */ are not special within double-quoted strings. 17.11: How can I implement sets and/or arrays of bits? A: Use arrays of char or int, with a few macros to access the right bit at the right index. 17.12: What is the most efficient way to count the number of bits which are set in a value? A: This and many other similar bit-twiddling problems can often be sped up and streamlined using lookup tables. 17.13: How can I make this code more efficient? A: Efficiency is not important nearly as often as people tend to think it is. Most of the time, by simply paying attention to good algorithm choices, perfectly acceptable results can be achieved. 17.14: Are pointers really faster than arrays? How much do function calls slow things down? A: Precise answers to these and many similar questions depend of course on the processor and compiler in use. 17.15: This program crashes before it even runs! A: Look for very large, local arrays. (See also question 9.4.) 17.16: What does "Segmentation violation" mean? A: It generally means that your program tried to access memory it shouldn't have. 17.17: Does anyone have a C compiler test suite I can use? A: Plum Hall, among others, sells one. 17.18: Where can I get a YACC grammar for C? A: See the ANSI Standard, or the unabridged list. 17.19: How do you pronounce "char"? A: Like the English words "char," "care," or "car" (your choice). 17.20: What's a good book for learning C? A: There are far too many to list here; the full list contains a few pointers. 17.21: Where can I get extra copies of this list? A: For now, just pull it off the net; the unabridged version is normally posted on the first of each month, with an Expiration: line which should keep it around all month. It can also be found in the newsgroup news.answers . Several sites archive news.answers postings and other FAQ lists, including this one; the archie server should help you find them. Steve Summit scs@adam.mit.edu scs%adam.mit.edu@mit.edu mit-eddie!adam.mit.edu!scs This article is Copyright 1988, 1990-1992 by Steve Summit. It may be freely redistributed so long as the author's name, and this notice, are retained.