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Info file libg++.info, produced by Makeinfo, -*- Text -*- from input file libg++.texinfo. START-INFO-DIR-ENTRY * Libg++: (libg++). The g++ library. END-INFO-DIR-ENTRY This file documents the features and implementation of The GNU C++ library Copyright (C) 1988, 1991, 1992 Free Software Foundation, Inc. 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 also that the section entitled "GNU Library General Public License" is included exactly as in the original, and 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 the section entitled "GNU Library General Public License" and this permission notice may be included in translations approved by the Free Software Foundation instead of in the original English. File: libg++.info, Node: Obstack, Next: AllocRing, Prev: Stream, Up: Top The Obstack class ***************** The `Obstack' class is a simple rewrite of the C obstack macros and functions provided in the GNU CC compiler source distribution. Obstacks provide a simple method of creating and maintaining a string table, optimized for the very frequent task of building strings character-by-character, and sometimes keeping them, and sometimes not. They seem especially useful in any parsing application. One of the test files demonstrates usage. A brief summary: `grow' places something on the obstack without committing to wrap it up as a single entity yet. `finish' wraps up a constructed object as a single entity, and returns the pointer to its start address. `copy' places things on the obstack, and *does* wrap them up. `copy' is always equivalent to first grow, then finish. `free' deletes something, and anything else put on the obstack since its creation. The other functions are less commonly needed: `blank' is like grow, except it just grows the space by size units without placing anything into this space `alloc' is like `blank', but it wraps up the object and returns its starting address. `chunk_size, base, next_free, alignment_mask, size, room' returns the appropriate class variables. `grow_fast' places a character on the obstack without checking if there is enough room. `blank_fast' like `blank', but without checking if there is enough room. `shrink(int n)' shrink the current chunk by n bytes. `contains(void* addr)' returns true if the Obstack holds the address addr. Here is a lightly edited version of the original C documentation: These functions operate a stack of objects. Each object starts life small, and may grow to maturity. (Consider building a word syllable by syllable.) An object can move while it is growing. Once it has been "finished" it never changes address again. So the "top of the stack" is typically an immature growing object, while the rest of the stack is of mature, fixed size and fixed address objects. These routines grab large chunks of memory, using the GNU C++ `new' operator. On occasion, they free chunks, via `delete'. Each independent stack is represented by a Obstack. One motivation for this package is the problem of growing char strings in symbol tables. Unless you are a "fascist pig with a read-only mind" [Gosper's immortal quote from HAKMEM item 154, out of context] you would not like to put any arbitrary upper limit on the length of your symbols. In practice this often means you will build many short symbols and a few long symbols. At the time you are reading a symbol you don't know how long it is. One traditional method is to read a symbol into a buffer, `realloc()'ating the buffer every time you try to read a symbol that is longer than the buffer. This is beaut, but you still will want to copy the symbol from the buffer to a more permanent symbol-table entry say about half the time. With obstacks, you can work differently. Use one obstack for all symbol names. As you read a symbol, grow the name in the obstack gradually. When the name is complete, finalize it. Then, if the symbol exists already, free the newly read name. The way we do this is to take a large chunk, allocating memory from low addresses. When you want to build a symbol in the chunk you just add chars above the current "high water mark" in the chunk. When you have finished adding chars, because you got to the end of the symbol, you know how long the chars are, and you can create a new object. Mostly the chars will not burst over the highest address of the chunk, because you would typically expect a chunk to be (say) 100 times as long as an average object. In case that isn't clear, when we have enough chars to make up the object, *they are already contiguous in the chunk* (guaranteed) so we just point to it where it lies. No moving of chars is needed and this is the second win: potentially long strings need never be explicitly shuffled. Once an object is formed, it does not change its address during its lifetime. When the chars burst over a chunk boundary, we allocate a larger chunk, and then copy the partly formed object from the end of the old chunk to the beginning of the new larger chunk. We then carry on accreting characters to the end of the object as we normally would. A special version of grow is provided to add a single char at a time to a growing object. Summary: * We allocate large chunks. * We carve out one object at a time from the current chunk. * Once carved, an object never moves. * We are free to append data of any size to the currently growing object. * Exactly one object is growing in an obstack at any one time. * You can run one obstack per control block. * You may have as many control blocks as you dare. * Because of the way we do it, you can `unwind' a obstack back to a previous state. (You may remove objects much as you would with a stack.) The obstack data structure is used in many places in the GNU C++ compiler. Differences from the the GNU C version 1. The obvious differences stemming from the use of classes and inline functions instead of structs and macros. The C `init' and `begin' macros are replaced by constructors. 2. Overloaded function names are used for grow (and others), rather than the C `grow', `grow0', etc. 3. All dynamic allocation uses the the built-in `new' operator. This restricts flexibility by a little, but maintains compatibility with usual C++ conventions. 4. There are now two versions of finish: 1. finish() behaves like the C version. 2. finish(char terminator) adds `terminator', and then calls `finish()'. This enables the normal invocation of `finish(0)' to wrap up a string being grown character-by-character. 5. There are special versions of grow(const char* s) and copy(const char* s) that add the null-terminated string `s' after computing its length. 6. The shrink and contains functions are provided. File: libg++.info, Node: AllocRing, Next: String, Prev: Obstack, Up: Top The AllocRing class ******************* An AllocRing is a bounded ring (circular list), each of whose elements contains a pointer to some space allocated via `new char[some_size]'. The entries are used cyclicly. The size, n, of the ring is fixed at construction. After that, every nth use of the ring will reuse (or reallocate) the same space. AllocRings are needed in order to temporarily hold chunks of space that are needed transiently, but across constructor-destructor scopes. They mainly useful for storing strings containing formatted characters to print acrosss various functions and coercions. These strings are needed across routines, so may not be deleted in any one of them, but should be recovered at some point. In other words, an AllocRing is an extremely simple minded garbage collection mechanism. The GNU C++ library used to use one AllocRing for such formatting purposes, but it is being phased out, and is now only used by obsolete functions. These days, AllocRings are probably not very useful. Support includes: `AllocRing a(int n)' constructs an Alloc ring with n entries, all null. `void* mem = a.alloc(sz)' moves the ring pointer to the next entry, and reuses the space if their is enough, also allocates space via new char[sz]. `int present = a.contains(void* ptr)' returns true if ptr is held in one of the ring entries. `a.clear()' deletes all space pointed to in any entry. This is called automatically upon destruction. `a.free(void* ptr)' If ptr is one of the entries, calls delete of the pointer, and resets to entry pointer to null. File: libg++.info, Node: String, Next: Integer, Prev: AllocRing, Up: Top The String class **************** The `String' class is designed to extend GNU C++ to support string processing capabilities similar to those in languages like Awk. The class provides facilities that ought to be convenient and efficient enough to be useful replacements for `char*' based processing via the C string library (i.e., `strcpy, strcmp,' etc.) in many applications. Many details about String representations are described in the Representation section. A separate `SubString' class supports substring extraction and modification operations. This is implemented in a way that user programs never directly construct or represent substrings, which are only used indirectly via String operations. Another separate class, `Regex' is also used indirectly via String operations in support of regular expression searching, matching, and the like. The Regex class is based entirely on the GNU Emacs regex functions. *Note Syntax of Regular Expressions: (emacs.info)Regexps, for a full explanation of regular expression syntax. (For implementation details, see the internal documentation in files `regex.h' and `regex.c'.) Constructors ============ Strings are initialized and assigned as in the following examples: `String x; String y = 0; String z = "";' Set x, y, and z to the nil string. Note that either 0 or "" may always be used to refer to the nil string. `String x = "Hello"; String y("Hello");' Set x and y to a copy of the string "Hello". `String x = 'A'; String y('A');' Set x and y to the string value "A" `String u = x; String v(x);' Set u and v to the same string as String x `String u = x.at(1,4); String v(x.at(1,4));' Set u and v to the length 4 substring of x starting at position 1 (counting indexes from 0). `String x("abc", 2);' Sets x to "ab", i.e., the first 2 characters of "abc". `String x = dec(20);' Sets x to "20". As here, Strings may be initialized or assigned the results of any `char*' function. There are no directly accessible forms for declaring SubString variables. The declaration `Regex r("[a-zA-Z_][a-zA-Z0-9_]*");' creates a compiled regular expression suitable for use in String operations described below. (In this case, one that matches any C++ identifier). The first argument may also be a String. Be careful in distinguishing the role of backslashes in quoted GNU C++ char* constants versus those in Regexes. For example, a Regex that matches either one or more tabs or all strings beginning with "ba" and ending with any number of occurrences of "na" could be declared as `Regex r = "\\(\t+\\)\\|\\(ba\\(na\\)*\\)"' Note that only one backslash is needed to signify the tab, but two are needed for the parenthesization and virgule, since the GNU C++ lexical analyzer decodes and strips backslashes before they are seen by Regex. There are three additional optional arguments to the Regex constructor that are less commonly useful: `fast (default 0)' `fast' may be set to true (1) if the Regex should be "fast-compiled". This causes an additional compilation step that is generally worthwhile if the Regex will be used many times. `bufsize (default max(40, length of the string))' This is an estimate of the size of the internal compiled expression. Set it to a larger value if you know that the expression will require a lot of space. If you do not know, do not worry: realloc is used if necessary. `transtable (default none == 0)' The address of a byte translation table (a char[256]) that translates each character before matching. As a convenience, several Regexes are predefined and usable in any program. Here are their declarations from `String.h'. extern Regex RXwhite; // = "[ \n\t]+" extern Regex RXint; // = "-?[0-9]+" extern Regex RXdouble; // = "-?\\(\\([0-9]+\\.[0-9]*\\)\\| // \\([0-9]+\\)\\| // \\(\\.[0-9]+\\)\\) // \\([eE][---+]?[0-9]+\\)?" extern Regex RXalpha; // = "[A-Za-z]+" extern Regex RXlowercase; // = "[a-z]+" extern Regex RXuppercase; // = "[A-Z]+" extern Regex RXalphanum; // = "[0-9A-Za-z]+" extern Regex RXidentifier; // = "[A-Za-z_][A-Za-z0-9_]*" Examples ======== Most `String' class capabilities are best shown via example. The examples below use the following declarations. String x = "Hello"; String y = "world"; String n = "123"; String z; char* s = ","; String lft, mid, rgt; Regex r = "e[a-z]*o"; Regex r2("/[a-z]*/"); char c; int i, pos, len; double f; String words[10]; words[0] = "a"; words[1] = "b"; words[2] = "c"; Comparing, Searching and Matching ================================= The usual lexicographic relational operators (`==, !=, <, <=, >, >=') are defined. A functional form `compare(String, String)' is also provided, as is `fcompare(String, String)', which compares Strings without regard for upper vs. lower case. All other matching and searching operations are based on some form of the (non-public) `match' and `search' functions. `match' and `search' differ in that `match' attempts to match only at the given starting position, while `search' starts at the position, and then proceeds left or right looking for a match. As seen in the following examples, the second optional `startpos' argument to functions using `match' and `search' specifies the starting position of the search: If non-negative, it results in a left-to-right search starting at position `startpos', and if negative, a right-to-left search starting at position `x.length() + startpos'. In all cases, the index returned is that of the beginning of the match, or -1 if there is no match. Three String functions serve as front ends to `search' and `match'. `index' performs a search, returning the index, `matches' performs a match, returning nonzero (actually, the length of the match) on success, and `contains' is a boolean function performing either a search or match, depending on whether an index argument is provided: `x.index("lo")' returns the zero-based index of the leftmost occurrence of substring "lo" (3, in this case). The argument may be a String, SubString, char, char*, or Regex. `x.index("l", 2)' returns the index of the first of the leftmost occurrence of "l" found starting the search at position x[2], or 2 in this case. `x.index("l", -1)' returns the index of the rightmost occurrence of "l", or 3 here. `x.index("l", -3)' returns the index of the rightmost occurrence of "l" found by starting the search at the 3rd to the last position of x, returning 2 in this case. `pos = r.search("leo", 3, len, 0)' returns the index of r in the `char*' string of length 3, starting at position 0, also placing the length of the match in reference parameter len. `x.contains("He")' returns nonzero if the String x contains the substring "He". The argument may be a String, SubString, char, char*, or Regex. `x.contains("el", 1)' returns nonzero if x contains the substring "el" at position 1. As in this example, the second argument to `contains', if present, means to match the substring only at that position, and not to search elsewhere in the string. `x.contains(RXwhite);' returns nonzero if x contains any whitespace (space, tab, or newline). Recall that `RXwhite' is a global whitespace Regex. `x.matches("lo", 3)' returns nonzero if x starting at position 3 exactly matches "lo", with no trailing characters (as it does in this example). `x.matches(r)' returns nonzero if String x as a whole matches Regex r. `int f = x.freq("l")' returns the number of distinct, nonoverlapping matches to the argument (2 in this case). Substring extraction ==================== Substrings may be extracted via the `at', `before', `through', `from', and `after' functions. These behave as either lvalues or rvalues. `z = x.at(2, 3)' sets String z to be equal to the length 3 substring of String x starting at zero-based position 2, setting z to "llo" in this case. A nil String is returned if the arguments don't make sense. `x.at(2, 2) = "r"' Sets what was in positions 2 to 3 of x to "r", setting x to "Hero" in this case. As indicated here, SubString assignments may be of different lengths. `x.at("He") = "je";' x("He") is the substring of x that matches the first occurrence of it's argument. The substitution sets x to "jello". If "He" did not occur, the substring would be nil, and the assignment would have no effect. `x.at("l", -1) = "i";' replaces the rightmost occurrence of "l" with "i", setting x to "Helio". `z = x.at(r)' sets String z to the first match in x of Regex r, or "ello" in this case. A nil String is returned if there is no match. `z = x.before("o")' sets z to the part of x to the left of the first occurrence of "o", or "Hell" in this case. The argument may also be a String, SubString, or Regex. (If there is no match, z is set to "".) `x.before("ll") = "Bri";' sets the part of x to the left of "ll" to "Bri", setting x to "Brillo". `z = x.before(2)' sets z to the part of x to the left of x[2], or "He" in this case. `z = x.after("Hel")' sets z to the part of x to the right of "Hel", or "lo" in this case. `z = x.through("el")' sets z to the part of x up and including "el", or "Hel" in this case. `z = x.from("el")' sets z to the part of x from "el" to the end, or "ello" in this case. `x.after("Hel") = "p";' sets x to "Help"; `z = x.after(3)' sets z to the part of x to the right of x[3] or "o" in this case. `z = " ab c"; z = z.after(RXwhite)' sets z to the part of its old string to the right of the first group of whitespace, setting z to "ab c"; Use gsub(below) to strip out multiple occurrences of whitespace or any pattern. `x[0] = 'J';' sets the first element of x to 'J'. x[i] returns a reference to the ith element of x, or triggers an error if i is out of range. `common_prefix(x, "Help")' returns the String containing the common prefix of the two Strings or "Hel" in this case. `common_suffix(x, "to")' returns the String containing the common suffix of the two Strings or "o" in this case. Concatenation ============= `z = x + s + ' ' + y.at("w") + y.after("w") + ".";' sets z to "Hello, world." `x += y;' sets x to "Helloworld" `cat(x, y, z)' A faster way to say z = x + y. `cat(z, y, x, x)' Double concatenation; A faster way to say x = z + y + x. `y.prepend(x);' A faster way to say y = x + y. `z = replicate(x, 3);' sets z to "HelloHelloHello". `z = join(words, 3, "/")' sets z to the concatenation of the first 3 Strings in String array words, each separated by "/", setting z to "a/b/c" in this case. The last argument may be "" or 0, indicating no separation. Other manipulations =================== `z = "this string has five words"; i = split(z, words, 10, RXwhite);' sets up to 10 elements of String array words to the parts of z separated by whitespace, and returns the number of parts actually encountered (5 in this case). Here, words[0] = "this", words[1] = "string", etc. The last argument may be any of the usual. If there is no match, all of z ends up in words[0]. The words array is *not* dynamically created by split. `int nmatches x.gsub("l","ll")' substitutes all original occurrences of "l" with "ll", setting x to "Hellllo". The first argument may be any of the usual, including Regex. If the second argument is "" or 0, all occurrences are deleted. gsub returns the number of matches that were replaced. `z = x + y; z.del("loworl");' deletes the leftmost occurrence of "loworl" in z, setting z to "Held". `z = reverse(x)' sets z to the reverse of x, or "olleH". `z = upcase(x)' sets z to x, with all letters set to uppercase, setting z to "HELLO" `z = downcase(x)' sets z to x, with all letters set to lowercase, setting z to "hello" `z = capitalize(x)' sets z to x, with the first letter of each word set to uppercase, and all others to lowercase, setting z to "Hello" `x.reverse(), x.upcase(), x.downcase(), x.capitalize()' in-place, self-modifying versions of the above. Reading, Writing and Conversion =============================== `cout << x' writes out x. `cout << x.at(2, 3)' writes out the substring "llo". `cin >> x' reads a whitespace-bounded string into x. `x.length()' returns the length of String x (5, in this case). `s = (const char*)x' can be used to extract the `char*' char array. This coercion is useful for sending a String as an argument to any function expecting a `const char*' argument (like `atoi', and `File::open'). This operator must be used with care, since the conversion returns a pointer to `String' internals without copying the characters: The resulting `(char*)' is only valid until the next String operation, and you must not modify it. (The conversion is defined to return a const value so that GNU C++ will produce warning and/or error messages if changes are attempted.) File: libg++.info, Node: Integer, Next: Rational, Prev: String, Up: Top The Integer class. ****************** The `Integer' class provides multiple precision integer arithmetic facilities. Some representation details are discussed in the Representation section. `Integers' may be up to `b * ((1 << b) - 1)' bits long, where `b' is the number of bits per short (typically 1048560 bits when `b = 16'). The implementation assumes that a `long' is at least twice as long as a `short'. This assumption hides beneath almost all primitive operations, and would be very difficult to change. It also relies on correct behavior of *unsigned* arithmetic operations. Some of the arithmetic algorithms are very loosely based on those provided in the MIT Scheme `bignum.c' release, which is Copyright (c) 1987 Massachusetts Institute of Technology. Their use here falls within the provisions described in the Scheme release. Integers may be constructed in the following ways: `Integer x;' Declares an uninitialized Integer. `Integer x = 2; Integer y(2);' Set x and y to the Integer value 2; `Integer u(x); Integer v = x;' Set u and v to the same value as x. `Integers' may be coerced back into longs via the `long' coercion operator. If the Integer cannot fit into a long, this returns MINLONG or MAXLONG (depending on the sign) where MINLONG is the most negative, and MAXLONG is the most positive representable long. The member function `fits_in_long()' may be used to test this. `Integers' may also be coerced into `doubles', with potential loss of precision. `+/-HUGE' is returned if the Integer cannot fit into a double. `fits_in_double()' may be used to test this. All of the usual arithmetic operators are provided (`+, -, *, /, %, +=, ++, -=, --, *=, /=, %=, ==, !=, <, <=, >, >='). All operators support special versions for mixed arguments of Integers and regular C++ longs in order to avoid useless coercions, as well as to allow automatic promotion of shorts and ints to longs, so that they may be applied without additional Integer coercion operators. The only operators that behave differently than the corresponding int or long operators are `++' and `--'. Because C++ does not distinguish prefix from postfix application, these are declared as `void' operators, so that no confusion can result from applying them as postfix. Thus, for Integers x and y, ` ++x; y = x; ' is correct, but ` y = ++x; ' and ` y = x++; ' are not. Bitwise operators (`~', `&', `|', `^', `<<', `>>', `&=', `|=', `^=', `<<=', `>>=') are also provided. However, these operate on sign-magnitude, rather than two's complement representations. The sign of the result is arbitrarily taken as the sign of the first argument. For example, `Integer(-3) & Integer(5)' returns `Integer(-1)', not -3, as it would using two's complement. Also, `~', the complement operator, complements only those bits needed for the representation. Bit operators are also provided in the BitSet and BitString classes. One of these classes should be used instead of Integers when the results of bit manipulations are not interpreted numerically. The following utility functions are also provided. (All arguments are Integers unless otherwise noted). `void divide(x, y, q, r);' Sets q to the quotient and r to the remainder of x and y. (q and r are returned by reference). `Integer pow(Integer x, Integer p)' returns x raised to the power p. `Integer Ipow(long x, long p)' returns x raised to the power p. `Integer gcd(x, y)' returns the greatest common divisor of x and y. `Integer lcm(x, y)' returns the least common multiple of x and y. `Integer abs(x);' returns the absolute value of x. `void x.negate();' negates x. `Integer sqr(x)' returns x * x; `Integer sqrt(x)' returns the floor of the square root of x. `long lg(x);' returns the floor of the base 2 logarithm of abs(x) `int sign(x)' returns -1 if x is negative, 0 if zero, else +1. Using `if (sign(x) == 0)' is a generally faster method of testing for zero than using relational operators. `int even(x)' returns true if x is an even number `int odd(x)' returns true if x is an odd number. `void setbit(Integer& x, long b)' sets the b'th bit (counting right-to-left from zero) of x to 1. `void clearbit(Integer& x, long b)' sets the b'th bit of x to 0. `int testbit(Integer x, long b)' returns true if the b'th bit of x is 1. `Integer atoI(char* asciinumber, int base = 10);' converts the base base char* string into its Integer form. `void Integer::printon(ostream& s, int base = 10, int width = 0);' prints the ascii string value of `(*this)' as a base `base' number, in field width at least `width'. `ostream << x;' prints x in base ten format. `istream >> x;' reads x as a base ten number. `int compare(Integer x, Integer y)' returns a negative number if x<y, zero if x==y, or positive if x>y. `int ucompare(Integer x, Integer y)' like compare, but performs unsigned comparison. `add(x, y, z)' A faster way to say z = x + y. `sub(x, y, z)' A faster way to say z = x - y. `mul(x, y, z)' A faster way to say z = x * y. `div(x, y, z)' A faster way to say z = x / y. `mod(x, y, z)' A faster way to say z = x % y. `and(x, y, z)' A faster way to say z = x & y. `or(x, y, z)' A faster way to say z = x | y. `xor(x, y, z)' A faster way to say z = x ^ y. `lshift(x, y, z)' A faster way to say z = x << y. `rshift(x, y, z)' A faster way to say z = x >> y. `pow(x, y, z)' A faster way to say z = pow(x, y). `complement(x, z)' A faster way to say z = ~x. `negate(x, z)' A faster way to say z = -x. File: libg++.info, Node: Rational, Next: Complex, Prev: Integer, Up: Top The Rational Class ****************** Class `Rational' provides multiple precision rational number arithmetic. All rationals are maintained in simplest form (i.e., with the numerator and denominator relatively prime, and with the denominator strictly positive). Rational arithmetic and relational operators are provided (`+, -, *, /, +=, -=, *=, /=, ==, !=, <, <=, >, >='). Operations resulting in a rational number with zero denominator trigger an exception. Rationals may be constructed and used in the following ways: `Rational x;' Declares an uninitialized Rational. `Rational x = 2; Rational y(2);' Set x and y to the Rational value 2/1; `Rational x(2, 3);' Sets x to the Rational value 2/3; `Rational x = 1.2;' Sets x to a Rational value close to 1.2. Any double precision value may be used to construct a Rational. The Rational will possess exactly as much precision as the double. Double values that do not have precise floating point equivalents (like 1.2) produce similarly imprecise rational values. `Rational x(Integer(123), Integer(4567));' Sets x to the Rational value 123/4567. `Rational u(x); Rational v = x;' Set u and v to the same value as x. `double(Rational x)' A Rational may be coerced to a double with potential loss of precision. +/-HUGE is returned if it will not fit. `Rational abs(x)' returns the absolute value of x. `void x.negate()' negates x. `void x.invert()' sets x to 1/x. `int sign(x)' returns 0 if x is zero, 1 if positive, and -1 if negative. `Rational sqr(x)' returns x * x. `Rational pow(x, Integer y)' returns x to the y power. `Integer x.numerator()' returns the numerator. `Integer x.denominator()' returns the denominator. `Integer floor(x)' returns the greatest Integer less than x. `Integer ceil(x)' returns the least Integer greater than x. `Integer trunc(x)' returns the Integer part of x. `Integer round(x)' returns the nearest Integer to x. `int compare(x, y)' returns a negative, zero, or positive number signifying whether x is less than, equal to, or greater than y. `ostream << x;' prints x in the form num/den, or just num if the denominator is one. `istream >> x;' reads x in the form num/den, or just num in which case the denominator is set to one. `add(x, y, z)' A faster way to say z = x + y. `sub(x, y, z)' A faster way to say z = x - y. `mul(x, y, z)' A faster way to say z = x * y. `div(x, y, z)' A faster way to say z = x / y. `pow(x, y, z)' A faster way to say z = pow(x, y). `negate(x, z)' A faster way to say z = -x. File: libg++.info, Node: Complex, Next: Fix, Prev: Rational, Up: Top The Complex class. ****************** Class `Complex' is implemented in a way similar to that described by Stroustrup. In keeping with libg++ conventions, the class is named `Complex', not `complex'. Complex arithmetic and relational operators are provided (`+, -, *, /, +=, -=, *=, /=, ==, !='). Attempted division by (0, 0) triggers an exception. Complex numbers may be constructed and used in the following ways: `Complex x;' Declares an uninitialized Complex. `Complex x = 2; Complex y(2.0);' Set x and y to the Complex value (2.0, 0.0); `Complex x(2, 3);' Sets x to the Complex value (2, 3); `Complex u(x); Complex v = x;' Set u and v to the same value as x. `double real(Complex& x);' returns the real part of x. `double imag(Complex& x);' returns the imaginary part of x. `double abs(Complex& x);' returns the magnitude of x. `double norm(Complex& x);' returns the square of the magnitude of x. `double arg(Complex& x);' returns the argument (amplitude) of x. `Complex polar(double r, double t = 0.0);' returns a Complex with abs of r and arg of t. `Complex conj(Complex& x);' returns the complex conjugate of x. `Complex cos(Complex& x);' returns the complex cosine of x. `Complex sin(Complex& x);' returns the complex sine of x. `Complex cosh(Complex& x);' returns the complex hyperbolic cosine of x. `Complex sinh(Complex& x);' returns the complex hyperbolic sine of x. `Complex exp(Complex& x);' returns the exponential of x. `Complex log(Complex& x);' returns the natural log of x. `Complex pow(Complex& x, long p);' returns x raised to the p power. `Complex pow(Complex& x, Complex& p);' returns x raised to the p power. `Complex sqrt(Complex& x);' returns the square root of x. `ostream << x;' prints x in the form (re, im). `istream >> x;' reads x in the form (re, im), or just (re) or re in which case the imaginary part is set to zero. File: libg++.info, Node: Fix, Next: Bit, Prev: Complex, Up: Top Fixed precision numbers *********************** Classes `Fix16', `Fix24', `Fix32', and `Fix48' support operations on 16, 24, 32, or 48 bit quantities that are considered as real numbers in the range [-1, +1). Such numbers are often encountered in digital signal processing applications. The classes may be be used in isolation or together. Class `Fix32' operations are entirely self-contained. Class `Fix16' operations are self-contained except that the multiplication operation `Fix16 * Fix16' returns a `Fix32'. `Fix24' and `Fix48' are similarly related. The standard arithmetic and relational operations are supported (`=', `+', `-', `*', `/', `<<', `>>', `+=', `-=', `*=', `/=', `<<=', `>>=', `==', `!=', `<', `<=', `>', `>='). All operations include provisions for special handling in cases where the result exceeds +/- 1.0. There are two cases that may be handled separately: "overflow" where the results of addition and subtraction operations go out of range, and all other "range errors" in which resulting values go off-scale (as with division operations, and assignment or initialization with off-scale values). In signal processing applications, it is often useful to handle these two cases differently. Handlers take one argument, a reference to the integer mantissa of the offending value, which may then be manipulated. In cases of overflow, this value is the result of the (integer) arithmetic computation on the mantissa; in others it is a fully saturated (i.e., most positive or most negative) value. Handling may be reset to any of several provided functions or any other user-defined function via `set_overflow_handler' and `set_range_error_handler'. The provided functions for `Fix16' are as follows (corresponding functions are also supported for the others). `Fix16_overflow_saturate' The default overflow handler. Results are "saturated": positive results are set to the largest representable value (binary 0.111111...), and negative values to -1.0. `Fix16_ignore' Performs no action. For overflow, this will allow addition and subtraction operations to "wrap around" in the same manner as integer arithmetic, and for saturation, will leave values saturated. `Fix16_overflow_warning_saturate' Prints a warning message on standard error, then saturates the results. `Fix16_warning' The default range_error handler. Prints a warning message on standard error; otherwise leaving the argument unmodified. `Fix16_abort' prints an error message on standard error, then aborts execution. In addition to arithmetic operations, the following are provided: `Fix16 a = 0.5;' Constructs fixed precision objects from double precision values. Attempting to initialize to a value outside the range invokes the range_error handler, except, as a convenience, initialization to 1.0 sets the variable to the most positive representable value (binary 0.1111111...) without invoking the handler. `short& mantissa(a); long& mantissa(b);' return a * pow(2, 15) or b * pow(2, 31) as an integer. These are returned by reference, to enable "manual" data manipulation. `double value(a); double value(b);' return a or b as floating point numbers. File: libg++.info, Node: Bit, Next: Random, Prev: Fix, Up: Top Classes for Bit manipulation **************************** libg++ provides several different classes supporting the use and manipulation of collections of bits in different ways. * Class `Integer' provides "integer" semantics. It supports manipulation of bits in ways that are often useful when treating bit arrays as numerical (integer) quantities. This class is described elsewhere. * Class `BitSet' provides "set" semantics. It supports operations useful when treating collections of bits as representing potentially infinite sets of integers. * Class `BitSet32' supports fixed-length BitSets holding exactly 32 bits. * Class `Bitset256'supports fixed-length BitSets holding exactly 256 bits. * Class `BitString' provides "string" (or "vector") semantics. It supports operations useful when treating collections of bits as strings of zeros and ones. These classes also differ in the following ways: * BitSets are logically infinite. Their space is dynamically altered to adjust to the smallest number of consecutive bits actually required to represent the sets. Integers also have this property. BitStrings are logically finite, but their sizes are internally dynamically managed to maintain proper length. This means that, for example, BitStrings are concatenatable while BitSets and Integers are not. * BitSet32 and BitSet256 have precisely the same properties as BitSets, except that they use constant fixed length bit vectors. * While all classes support basic unary and binary operations `~, &, |, ^, -', the semantics differ. BitSets perform bit operations that precisely mirror those for infinite sets. For example, complementing an empty BitSet returns one representing an infinite number of set bits. Operations on BitStrings and Integers operate only on those bits actually present in the representation. For BitStrings and Integers, the the `&' operation returns a BitString with a length equal to the minimum length of the operands, and `|, ^' return one with length of the maximum. * Only BitStrings support substring extraction and bit pattern matching. BitSet ====== Bitsets are objects that contain logically infinite sets of nonnegative integers. Representational details are discussed in the Representation chapter. Because they are logically infinite, all BitSets possess a trailing, infinitely replicated 0 or 1 bit, called the "virtual bit", and indicated via 0* or 1*. BitSet32 and BitSet256 have they same properties, except they are of fixed length, and thus have no virtual bit. BitSets may be constructed as follows: `BitSet a;' declares an empty BitSet. `BitSet a = atoBitSet("001000");' sets a to the BitSet 0010*, reading left-to-right. The "0*" indicates that the set ends with an infinite number of zero (clear) bits. `BitSet a = atoBitSet("00101*");' sets a to the BitSet 00101*, where "1*" means that the set ends with an infinite number of one (set) bits. `BitSet a = longtoBitSet((long)23);' sets a to the BitSet 111010*, the binary representation of decimal 23. `BitSet a = utoBitSet((unsigned)23);' sets a to the BitSet 111010*, the binary representation of decimal 23. The following functions and operators are provided (Assume the declaration of BitSets a = 0011010*, b = 101101*, throughout, as examples). `~a' returns the complement of a, or 1100101* in this case. `a.complement()' sets a to ~a. `a & b; a &= b;' returns a intersected with b, or 0011010*. `a | b; a |= b;' returns a unioned with b, or 1011111*. `a - b; a -= b;' returns the set difference of a and b, or 000010*. `a ^ b; a ^= b;' returns the symmetric difference of a and b, or 1000101*. `a.empty()' returns true if a is an empty set. `a == b;' returns true if a and b contain the same set. `a <= b;' returns true if a is a subset of b. `a < b;' returns true if a is a proper subset of b; `a != b; a >= b; a > b;' are the converses of the above. `a.set(7)' sets the 7th (counting from 0) bit of a, setting a to 001111010* `a.clear(2)' clears the 2nd bit bit of a, setting a to 00011110* `a.clear()' clears all bits of a; `a.set()' sets all bits of a; `a.invert(0)' complements the 0th bit of a, setting a to 10011110* `a.set(0,1)' sets the 0th through 1st bits of a, setting a to 110111110* The two-argument versions of clear and invert are similar. `a.test(3)' returns true if the 3rd bit of a is set. `a.test(3, 5)' returns true if any of bits 3 through 5 are set. `int i = a[3]; a[3] = 0;' The subscript operator allows bits to be inspected and changed via standard subscript semantics, using a friend class BitSetBit. The use of the subscript operator a[i] rather than a.test(i) requires somewhat greater overhead. `a.first(1) or a.first()' returns the index of the first set bit of a (2 in this case), or -1 if no bits are set. `a.first(0)' returns the index of the first clear bit of a (0 in this case), or -1 if no bits are clear. `a.next(2, 1) or a.next(2)' returns the index of the next bit after position 2 that is set (3 in this case) or -1. `first' and `next' may be used as iterators, as in `for (int i = a.first(); i >= 0; i = a.next(i))...'. `a.last(1)' returns the index of the rightmost set bit, or -1 if there or no set bits or all set bits. `a.previous(3, 0)' returns the index of the previous clear bit before position 3. `a.count(1)' returns the number of set bits in a, or -1 if there are an infinite number. `a.virtual_bit()' returns the trailing (infinitely replicated) bit of a. `a = atoBitSet("ababX", 'a', 'b', 'X');' converts the char* string into a bitset, with 'a' denoting false, 'b' denoting true, and 'X' denoting infinite replication. `a.printon(cout, '-', '.', 0)' prints `a' to `cout' represented with `'-'' for falses, `'.'' for trues, and no replication marker. `cout << a' prints `a' to `cout' (representing lases by `'f'', trues by `'t'', and using `'*'' as the replication marker). `diff(x, y, z)' A faster way to say z = x - y. `and(x, y, z)' A faster way to say z = x & y. `or(x, y, z)' A faster way to say z = x | y. `xor(x, y, z)' A faster way to say z = x ^ y. `complement(x, z)' A faster way to say z = ~x. BitString ========= BitStrings are objects that contain arbitrary-length strings of zeroes and ones. BitStrings possess some features that make them behave like sets, and others that behave as strings. They are useful in applications (such as signature-based algorithms) where both capabilities are needed. Representational details are discussed in the Representation chapter. Most capabilities are exact analogs of those supported in the BitSet and String classes. A BitSubString is used with substring operations along the same lines as the String SubString class. A BitPattern class is used for masked bit pattern searching. Only a default constructor is supported. The declaration `BitString a;' initializes a to be an empty BitString. BitStrings may often be initialized via `atoBitString' and `longtoBitString'. Set operations (` ~, complement, &, &=, |, |=, -, ^, ^=') behave just as the BitSet versions, except that there is no "virtual bit": complementing complements only those bits in the BitString, and all binary operations across unequal length BitStrings assume a virtual bit of zero. The `&' operation returns a BitString with a length equal to the minimum length of the operands, and `|, ^' return one with length of the maximum. Set-based relational operations (`==, !=, <=, <, >=, >') follow the same rules. A string-like lexicographic comparison function, `lcompare', tests the lexicographic relation between two BitStrings. For example, lcompare(1100, 0101) returns 1, since the first BitString starts with 1 and the second with 0. Individual bit setting, testing, and iterator operations (`set, clear, invert, test, first, next, last, previous') are also like those for BitSets. BitStrings are automatically expanded when setting bits at positions greater than their current length. The string-based capabilities are just as those for class String. BitStrings may be concatenated (`+, +='), searched (`index, contains, matches'), and extracted into BitSubStrings (`before, at, after') which may be assigned and otherwise manipulated. Other string-based utility functions (`reverse, common_prefix, common_suffix') are also provided. These have the same capabilities and descriptions as those for Strings. String-oriented operations can also be performed with a mask via class BitPattern. BitPatterns consist of two BitStrings, a pattern and a mask. On searching and matching, bits in the pattern that correspond to 0 bits in the mask are ignored. (The mask may be shorter than the pattern, in which case trailing mask bits are assumed to be 0). The pattern and mask are both public variables, and may be individually subjected to other bit operations. Converting to char* and printing (`(atoBitString, atoBitPattern, printon, ostream <<)') are also as in BitSets, except that no virtual bit is used, and an 'X' in a BitPattern means that the pattern bit is masked out. The following features are unique to BitStrings. Assume declarations of BitString a = atoBitString("01010110") and b = atoBitSTring("1101"). `a = b + c;' Sets a to the concatenation of b and c; `a = b + 0; a = b + 1;' sets a to b, appended with a zero (one). `a += b;' appends b to a; `a += 0; a += 1;' appends a zero (one) to a. `a << 2; a <<= 2' return a with 2 zeros prepended, setting a to 0001010110. (Note the necessary confusion of << and >> operators. For consistency with the integer versions, << shifts low bits to high, even though they are printed low bits first.) `a >> 3; a >>= 3' return a with the first 3 bits deleted, setting a to 10110. `a.left_trim(0)' deletes all 0 bits on the left of a, setting a to 1010110. `a.right_trim(0)' deletes all trailing 0 bits of a, setting a to 0101011. `cat(x, y, z)' A faster way to say z = x + y. `diff(x, y, z)' A faster way to say z = x - y. `and(x, y, z)' A faster way to say z = x & y. `or(x, y, z)' A faster way to say z = x | y. `xor(x, y, z)' A faster way to say z = x ^ y. `lshift(x, y, z)' A faster way to say z = x << y. `rshift(x, y, z)' A faster way to say z = x >> y. `complement(x, z)' A faster way to say z = ~x.