This is ../info/lispref.info, produced by makeinfo version 4.0 from lispref/lispref.texi. INFO-DIR-SECTION XEmacs Editor START-INFO-DIR-ENTRY * Lispref: (lispref). XEmacs Lisp Reference Manual. END-INFO-DIR-ENTRY Edition History: GNU Emacs Lisp Reference Manual Second Edition (v2.01), May 1993 GNU Emacs Lisp Reference Manual Further Revised (v2.02), August 1993 Lucid Emacs Lisp Reference Manual (for 19.10) First Edition, March 1994 XEmacs Lisp Programmer's Manual (for 19.12) Second Edition, April 1995 GNU Emacs Lisp Reference Manual v2.4, June 1995 XEmacs Lisp Programmer's Manual (for 19.13) Third Edition, July 1995 XEmacs Lisp Reference Manual (for 19.14 and 20.0) v3.1, March 1996 XEmacs Lisp Reference Manual (for 19.15 and 20.1, 20.2, 20.3) v3.2, April, May, November 1997 XEmacs Lisp Reference Manual (for 21.0) v3.3, April 1998 Copyright (C) 1990, 1991, 1992, 1993, 1994, 1995 Free Software Foundation, Inc. Copyright (C) 1994, 1995 Sun Microsystems, Inc. Copyright (C) 1995, 1996 Ben Wing. 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 Foundation. 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 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 General Public License" may be included in a translation approved by the Free Software Foundation instead of in the original English.  File: lispref.info, Node: Specifier Type, Next: Font Instance Type, Prev: Glyph Type, Up: Window-System Types Specifier Type -------------- (not yet documented)  File: lispref.info, Node: Font Instance Type, Next: Color Instance Type, Prev: Specifier Type, Up: Window-System Types Font Instance Type ------------------ (not yet documented)  File: lispref.info, Node: Color Instance Type, Next: Image Instance Type, Prev: Font Instance Type, Up: Window-System Types Color Instance Type ------------------- (not yet documented)  File: lispref.info, Node: Image Instance Type, Next: Toolbar Button Type, Prev: Color Instance Type, Up: Window-System Types Image Instance Type ------------------- (not yet documented)  File: lispref.info, Node: Toolbar Button Type, Next: Subwindow Type, Prev: Image Instance Type, Up: Window-System Types Toolbar Button Type ------------------- (not yet documented)  File: lispref.info, Node: Subwindow Type, Next: X Resource Type, Prev: Toolbar Button Type, Up: Window-System Types Subwindow Type -------------- (not yet documented)  File: lispref.info, Node: X Resource Type, Prev: Subwindow Type, Up: Window-System Types X Resource Type --------------- (not yet documented)  File: lispref.info, Node: Type Predicates, Next: Equality Predicates, Prev: Window-System Types, Up: Lisp Data Types Type Predicates =============== The XEmacs Lisp interpreter itself does not perform type checking on the actual arguments passed to functions when they are called. It could not do so, since function arguments in Lisp do not have declared data types, as they do in other programming languages. It is therefore up to the individual function to test whether each actual argument belongs to a type that the function can use. All built-in functions do check the types of their actual arguments when appropriate, and signal a `wrong-type-argument' error if an argument is of the wrong type. For example, here is what happens if you pass an argument to `+' that it cannot handle: (+ 2 'a) error--> Wrong type argument: integer-or-marker-p, a If you want your program to handle different types differently, you must do explicit type checking. The most common way to check the type of an object is to call a "type predicate" function. Emacs has a type predicate for each type, as well as some predicates for combinations of types. A type predicate function takes one argument; it returns `t' if the argument belongs to the appropriate type, and `nil' otherwise. Following a general Lisp convention for predicate functions, most type predicates' names end with `p'. Here is an example which uses the predicates `listp' to check for a list and `symbolp' to check for a symbol. (defun add-on (x) (cond ((symbolp x) ;; If X is a symbol, put it on LIST. (setq list (cons x list))) ((listp x) ;; If X is a list, add its elements to LIST. (setq list (append x list))) (t ;; We only handle symbols and lists. (error "Invalid argument %s in add-on" x)))) Here is a table of predefined type predicates, in alphabetical order, with references to further information. `annotationp' *Note annotationp: Annotation Primitives. `arrayp' *Note arrayp: Array Functions. `atom' *Note atom: List-related Predicates. `bit-vector-p' *Note bit-vector-p: Bit Vector Functions. `bitp' *Note bitp: Bit Vector Functions. `boolean-specifier-p' *Note boolean-specifier-p: Specifier Types. `buffer-glyph-p' *Note buffer-glyph-p: Glyph Types. `buffer-live-p' *Note buffer-live-p: Killing Buffers. `bufferp' *Note bufferp: Buffer Basics. `button-event-p' *Note button-event-p: Event Predicates. `button-press-event-p' *Note button-press-event-p: Event Predicates. `button-release-event-p' *Note button-release-event-p: Event Predicates. `case-table-p' *Note case-table-p: Case Tables. `char-int-p' *Note char-int-p: Character Codes. `char-or-char-int-p' *Note char-or-char-int-p: Character Codes. `char-or-string-p' *Note char-or-string-p: Predicates for Strings. `char-table-p' *Note char-table-p: Char Tables. `characterp' *Note characterp: Predicates for Characters. `color-instance-p' *Note color-instance-p: Colors. `color-pixmap-image-instance-p' *Note color-pixmap-image-instance-p: Image Instance Types. `color-specifier-p' *Note color-specifier-p: Specifier Types. `commandp' *Note commandp: Interactive Call. `compiled-function-p' *Note compiled-function-p: Compiled-Function Type. `console-live-p' *Note console-live-p: Connecting to a Console or Device. `consolep' *Note consolep: Consoles and Devices. `consp' *Note consp: List-related Predicates. `database-live-p' *Note database-live-p: Connecting to a Database. `databasep' *Note databasep: Databases. `device-live-p' *Note device-live-p: Connecting to a Console or Device. `device-or-frame-p' *Note device-or-frame-p: Basic Device Functions. `devicep' *Note devicep: Consoles and Devices. `eval-event-p' *Note eval-event-p: Event Predicates. `event-live-p' *Note event-live-p: Event Predicates. `eventp' *Note eventp: Events. `extent-live-p' *Note extent-live-p: Creating and Modifying Extents. `extentp' *Note extentp: Extents. `face-boolean-specifier-p' *Note face-boolean-specifier-p: Specifier Types. `facep' *Note facep: Basic Face Functions. `floatp' *Note floatp: Predicates on Numbers. `font-instance-p' *Note font-instance-p: Fonts. `font-specifier-p' *Note font-specifier-p: Specifier Types. `frame-live-p' *Note frame-live-p: Deleting Frames. `framep' *Note framep: Frames. `functionp' (not yet documented) `generic-specifier-p' *Note generic-specifier-p: Specifier Types. `glyphp' *Note glyphp: Glyphs. `hash-table-p' *Note hash-table-p: Hash Tables. `icon-glyph-p' *Note icon-glyph-p: Glyph Types. `image-instance-p' *Note image-instance-p: Images. `image-specifier-p' *Note image-specifier-p: Specifier Types. `integer-char-or-marker-p' *Note integer-char-or-marker-p: Predicates on Markers. `integer-or-char-p' *Note integer-or-char-p: Predicates for Characters. `integer-or-marker-p' *Note integer-or-marker-p: Predicates on Markers. `integer-specifier-p' *Note integer-specifier-p: Specifier Types. `integerp' *Note integerp: Predicates on Numbers. `itimerp' (not yet documented) `key-press-event-p' *Note key-press-event-p: Event Predicates. `keymapp' *Note keymapp: Creating Keymaps. `keywordp' (not yet documented) `listp' *Note listp: List-related Predicates. `markerp' *Note markerp: Predicates on Markers. `misc-user-event-p' *Note misc-user-event-p: Event Predicates. `mono-pixmap-image-instance-p' *Note mono-pixmap-image-instance-p: Image Instance Types. `motion-event-p' *Note motion-event-p: Event Predicates. `mouse-event-p' *Note mouse-event-p: Event Predicates. `natnum-specifier-p' *Note natnum-specifier-p: Specifier Types. `natnump' *Note natnump: Predicates on Numbers. `nlistp' *Note nlistp: List-related Predicates. `nothing-image-instance-p' *Note nothing-image-instance-p: Image Instance Types. `number-char-or-marker-p' *Note number-char-or-marker-p: Predicates on Markers. `number-or-marker-p' *Note number-or-marker-p: Predicates on Markers. `numberp' *Note numberp: Predicates on Numbers. `pointer-glyph-p' *Note pointer-glyph-p: Glyph Types. `pointer-image-instance-p' *Note pointer-image-instance-p: Image Instance Types. `process-event-p' *Note process-event-p: Event Predicates. `processp' *Note processp: Processes. `range-table-p' *Note range-table-p: Range Tables. `ringp' (not yet documented) `sequencep' *Note sequencep: Sequence Functions. `specifierp' *Note specifierp: Specifiers. `stringp' *Note stringp: Predicates for Strings. `subrp' *Note subrp: Function Cells. `subwindow-image-instance-p' *Note subwindow-image-instance-p: Image Instance Types. `subwindowp' *Note subwindowp: Subwindows. `symbolp' *Note symbolp: Symbols. `syntax-table-p' *Note syntax-table-p: Syntax Tables. `text-image-instance-p' *Note text-image-instance-p: Image Instance Types. `timeout-event-p' *Note timeout-event-p: Event Predicates. `toolbar-button-p' *Note toolbar-button-p: Toolbar. `toolbar-specifier-p' *Note toolbar-specifier-p: Toolbar. `user-variable-p' *Note user-variable-p: Defining Variables. `vectorp' *Note vectorp: Vectors. `weak-list-p' *Note weak-list-p: Weak Lists. `window-configuration-p' *Note window-configuration-p: Window Configurations. `window-live-p' *Note window-live-p: Deleting Windows. `windowp' *Note windowp: Basic Windows. The most general way to check the type of an object is to call the function `type-of'. Recall that each object belongs to one and only one primitive type; `type-of' tells you which one (*note Lisp Data Types::). But `type-of' knows nothing about non-primitive types. In most cases, it is more convenient to use type predicates than `type-of'. - Function: type-of object This function returns a symbol naming the primitive type of OBJECT. The value is one of `bit-vector', `buffer', `char-table', `character', `charset', `coding-system', `cons', `color-instance', `compiled-function', `console', `database', `device', `event', `extent', `face', `float', `font-instance', `frame', `glyph', `hash-table', `image-instance', `integer', `keymap', `marker', `process', `range-table', `specifier', `string', `subr', `subwindow', `symbol', `toolbar-button', `tooltalk-message', `tooltalk-pattern', `vector', `weak-list', `window', `window-configuration', or `x-resource'. (type-of 1) => integer (type-of 'nil) => symbol (type-of '()) ; `()' is `nil'. => symbol (type-of '(x)) => cons  File: lispref.info, Node: Equality Predicates, Prev: Type Predicates, Up: Lisp Data Types Equality Predicates =================== Here we describe two functions that test for equality between any two objects. Other functions test equality between objects of specific types, e.g., strings. For these predicates, see the appropriate chapter describing the data type. - Function: eq object1 object2 This function returns `t' if OBJECT1 and OBJECT2 are the same object, `nil' otherwise. The "same object" means that a change in one will be reflected by the same change in the other. `eq' returns `t' if OBJECT1 and OBJECT2 are integers with the same value. Also, since symbol names are normally unique, if the arguments are symbols with the same name, they are `eq'. For other types (e.g., lists, vectors, strings), two arguments with the same contents or elements are not necessarily `eq' to each other: they are `eq' only if they are the same object. (The `make-symbol' function returns an uninterned symbol that is not interned in the standard `obarray'. When uninterned symbols are in use, symbol names are no longer unique. Distinct symbols with the same name are not `eq'. *Note Creating Symbols::.) NOTE: Under XEmacs 19, characters are really just integers, and thus characters and integers are `eq'. Under XEmacs 20, it was necessary to preserve remnants of this in function such as `old-eq' in order to maintain byte-code compatibility. Byte code compiled under any Emacs 19 will automatically have calls to `eq' mapped to `old-eq' when executed under XEmacs 20. (eq 'foo 'foo) => t (eq 456 456) => t (eq "asdf" "asdf") => nil (eq '(1 (2 (3))) '(1 (2 (3)))) => nil (setq foo '(1 (2 (3)))) => (1 (2 (3))) (eq foo foo) => t (eq foo '(1 (2 (3)))) => nil (eq [(1 2) 3] [(1 2) 3]) => nil (eq (point-marker) (point-marker)) => nil - Function: old-eq object1 object2 This function exists under XEmacs 20 and is exactly like `eq' except that it suffers from the char-int confoundance disease. In other words, it returns `t' if given a character and the equivalent integer, even though the objects are of different types! You should _not_ ever call this function explicitly in your code. However, be aware that all calls to `eq' in byte code compiled under version 19 map to `old-eq' in XEmacs 20. (Likewise for `old-equal', `old-memq', `old-member', `old-assq' and `old-assoc'.) ;; Remember, this does not apply under XEmacs 19. ?A => ?A (char-int ?A) => 65 (old-eq ?A 65) => t ; Eek, we've been infected. (eq ?A 65) => nil ; We are still healthy. - Function: equal object1 object2 This function returns `t' if OBJECT1 and OBJECT2 have equal components, `nil' otherwise. Whereas `eq' tests if its arguments are the same object, `equal' looks inside nonidentical arguments to see if their elements are the same. So, if two objects are `eq', they are `equal', but the converse is not always true. (equal 'foo 'foo) => t (equal 456 456) => t (equal "asdf" "asdf") => t (eq "asdf" "asdf") => nil (equal '(1 (2 (3))) '(1 (2 (3)))) => t (eq '(1 (2 (3))) '(1 (2 (3)))) => nil (equal [(1 2) 3] [(1 2) 3]) => t (eq [(1 2) 3] [(1 2) 3]) => nil (equal (point-marker) (point-marker)) => t (eq (point-marker) (point-marker)) => nil Comparison of strings is case-sensitive. Note that in FSF GNU Emacs, comparison of strings takes into account their text properties, and you have to use `string-equal' if you want only the strings themselves compared. This difference does not exist in XEmacs; `equal' and `string-equal' always return the same value on the same strings. (equal "asdf" "ASDF") => nil Two distinct buffers are never `equal', even if their contents are the same. The test for equality is implemented recursively, and circular lists may therefore cause infinite recursion (leading to an error).  File: lispref.info, Node: Numbers, Next: Strings and Characters, Prev: Lisp Data Types, Up: Top Numbers ******* XEmacs supports two numeric data types: "integers" and "floating point numbers". Integers are whole numbers such as -3, 0, #b0111, #xFEED, #o744. Their values are exact. The number prefixes `#b', `#o', and `#x' are supported to represent numbers in binary, octal, and hexadecimal notation (or radix). Floating point numbers are numbers with fractional parts, such as -4.5, 0.0, or 2.71828. They can also be expressed in exponential notation: 1.5e2 equals 150; in this example, `e2' stands for ten to the second power, and is multiplied by 1.5. Floating point values are not exact; they have a fixed, limited amount of precision. * Menu: * Integer Basics:: Representation and range of integers. * Float Basics:: Representation and range of floating point. * Predicates on Numbers:: Testing for numbers. * Comparison of Numbers:: Equality and inequality predicates. * Numeric Conversions:: Converting float to integer and vice versa. * Arithmetic Operations:: How to add, subtract, multiply and divide. * Rounding Operations:: Explicitly rounding floating point numbers. * Bitwise Operations:: Logical and, or, not, shifting. * Math Functions:: Trig, exponential and logarithmic functions. * Random Numbers:: Obtaining random integers, predictable or not.  File: lispref.info, Node: Integer Basics, Next: Float Basics, Up: Numbers Integer Basics ============== The range of values for an integer depends on the machine. The minimum range is -134217728 to 134217727 (28 bits; i.e., -2**27 to 2**27 - 1), but some machines may provide a wider range. Many examples in this chapter assume an integer has 28 bits. The Lisp reader reads an integer as a sequence of digits with optional initial sign and optional final period. 1 ; The integer 1. 1. ; The integer 1. +1 ; Also the integer 1. -1 ; The integer -1. 268435457 ; Also the integer 1, due to overflow. 0 ; The integer 0. -0 ; The integer 0. To understand how various functions work on integers, especially the bitwise operators (*note Bitwise Operations::), it is often helpful to view the numbers in their binary form. In 28-bit binary, the decimal integer 5 looks like this: 0000 0000 0000 0000 0000 0000 0101 (We have inserted spaces between groups of 4 bits, and two spaces between groups of 8 bits, to make the binary integer easier to read.) The integer -1 looks like this: 1111 1111 1111 1111 1111 1111 1111 -1 is represented as 28 ones. (This is called "two's complement" notation.) The negative integer, -5, is creating by subtracting 4 from -1. In binary, the decimal integer 4 is 100. Consequently, -5 looks like this: 1111 1111 1111 1111 1111 1111 1011 In this implementation, the largest 28-bit binary integer is the decimal integer 134,217,727. In binary, it looks like this: 0111 1111 1111 1111 1111 1111 1111 Since the arithmetic functions do not check whether integers go outside their range, when you add 1 to 134,217,727, the value is the negative integer -134,217,728: (+ 1 134217727) => -134217728 => 1000 0000 0000 0000 0000 0000 0000 Many of the following functions accept markers for arguments as well as integers. (*Note Markers::.) More precisely, the actual arguments to such functions may be either integers or markers, which is why we often give these arguments the name INT-OR-MARKER. When the argument value is a marker, its position value is used and its buffer is ignored.  File: lispref.info, Node: Float Basics, Next: Predicates on Numbers, Prev: Integer Basics, Up: Numbers Floating Point Basics ===================== XEmacs supports floating point numbers. The precise range of floating point numbers is machine-specific; it is the same as the range of the C data type `double' on the machine in question. The printed representation for floating point numbers requires either a decimal point (with at least one digit following), an exponent, or both. For example, `1500.0', `15e2', `15.0e2', `1.5e3', and `.15e4' are five ways of writing a floating point number whose value is 1500. They are all equivalent. You can also use a minus sign to write negative floating point numbers, as in `-1.0'. Most modern computers support the IEEE floating point standard, which provides for positive infinity and negative infinity as floating point values. It also provides for a class of values called NaN or "not-a-number"; numerical functions return such values in cases where there is no correct answer. For example, `(sqrt -1.0)' returns a NaN. For practical purposes, there's no significant difference between different NaN values in XEmacs Lisp, and there's no rule for precisely which NaN value should be used in a particular case, so this manual doesn't try to distinguish them. XEmacs Lisp has no read syntax for NaNs or infinities; perhaps we should create a syntax in the future. You can use `logb' to extract the binary exponent of a floating point number (or estimate the logarithm of an integer): - Function: logb number This function returns the binary exponent of NUMBER. More precisely, the value is the logarithm of NUMBER base 2, rounded down to an integer.  File: lispref.info, Node: Predicates on Numbers, Next: Comparison of Numbers, Prev: Float Basics, Up: Numbers Type Predicates for Numbers =========================== The functions in this section test whether the argument is a number or whether it is a certain sort of number. The functions `integerp' and `floatp' can take any type of Lisp object as argument (the predicates would not be of much use otherwise); but the `zerop' predicate requires a number as its argument. See also `integer-or-marker-p', `integer-char-or-marker-p', `number-or-marker-p' and `number-char-or-marker-p', in *Note Predicates on Markers::. - Function: floatp object This predicate tests whether its argument is a floating point number and returns `t' if so, `nil' otherwise. `floatp' does not exist in Emacs versions 18 and earlier. - Function: integerp object This predicate tests whether its argument is an integer, and returns `t' if so, `nil' otherwise. - Function: numberp object This predicate tests whether its argument is a number (either integer or floating point), and returns `t' if so, `nil' otherwise. - Function: natnump object The `natnump' predicate (whose name comes from the phrase "natural-number-p") tests to see whether its argument is a nonnegative integer, and returns `t' if so, `nil' otherwise. 0 is considered non-negative. - Function: zerop number This predicate tests whether its argument is zero, and returns `t' if so, `nil' otherwise. The argument must be a number. These two forms are equivalent: `(zerop x)' == `(= x 0)'.  File: lispref.info, Node: Comparison of Numbers, Next: Numeric Conversions, Prev: Predicates on Numbers, Up: Numbers Comparison of Numbers ===================== To test numbers for numerical equality, you should normally use `=', not `eq'. There can be many distinct floating point number objects with the same numeric value. If you use `eq' to compare them, then you test whether two values are the same _object_. By contrast, `=' compares only the numeric values of the objects. At present, each integer value has a unique Lisp object in XEmacs Lisp. Therefore, `eq' is equivalent to `=' where integers are concerned. It is sometimes convenient to use `eq' for comparing an unknown value with an integer, because `eq' does not report an error if the unknown value is not a number--it accepts arguments of any type. By contrast, `=' signals an error if the arguments are not numbers or markers. However, it is a good idea to use `=' if you can, even for comparing integers, just in case we change the representation of integers in a future XEmacs version. There is another wrinkle: because floating point arithmetic is not exact, it is often a bad idea to check for equality of two floating point values. Usually it is better to test for approximate equality. Here's a function to do this: (defconst fuzz-factor 1.0e-6) (defun approx-equal (x y) (or (and (= x 0) (= y 0)) (< (/ (abs (- x y)) (max (abs x) (abs y))) fuzz-factor))) Common Lisp note: Comparing numbers in Common Lisp always requires `=' because Common Lisp implements multi-word integers, and two distinct integer objects can have the same numeric value. XEmacs Lisp can have just one integer object for any given value because it has a limited range of integer values. In addition to numbers, all of the following functions also accept characters and markers as arguments, and treat them as their number equivalents. - Function: = number &rest more-numbers This function returns `t' if all of its arguments are numerically equal, `nil' otherwise. (= 5) => t (= 5 6) => nil (= 5 5.0) => t (= 5 5 6) => nil - Function: /= number &rest more-numbers This function returns `t' if no two arguments are numerically equal, `nil' otherwise. (/= 5 6) => t (/= 5 5 6) => nil (/= 5 6 1) => t - Function: < number &rest more-numbers This function returns `t' if the sequence of its arguments is monotonically increasing, `nil' otherwise. (< 5 6) => t (< 5 6 6) => nil (< 5 6 7) => t - Function: <= number &rest more-numbers This function returns `t' if the sequence of its arguments is monotonically nondecreasing, `nil' otherwise. (<= 5 6) => t (<= 5 6 6) => t (<= 5 6 5) => nil - Function: > number &rest more-numbers This function returns `t' if the sequence of its arguments is monotonically decreasing, `nil' otherwise. - Function: >= number &rest more-numbers This function returns `t' if the sequence of its arguments is monotonically nonincreasing, `nil' otherwise. - Function: max number &rest more-numbers This function returns the largest of its arguments. (max 20) => 20 (max 1 2.5) => 2.5 (max 1 3 2.5) => 3 - Function: min number &rest more-numbers This function returns the smallest of its arguments. (min -4 1) => -4  File: lispref.info, Node: Numeric Conversions, Next: Arithmetic Operations, Prev: Comparison of Numbers, Up: Numbers Numeric Conversions =================== To convert an integer to floating point, use the function `float'. - Function: float number This returns NUMBER converted to floating point. If NUMBER is already a floating point number, `float' returns it unchanged. There are four functions to convert floating point numbers to integers; they differ in how they round. These functions accept integer arguments also, and return such arguments unchanged. - Function: truncate number This returns NUMBER, converted to an integer by rounding towards zero. - Function: floor number &optional divisor This returns NUMBER, converted to an integer by rounding downward (towards negative infinity). If DIVISOR is specified, NUMBER is divided by DIVISOR before the floor is taken; this is the division operation that corresponds to `mod'. An `arith-error' results if DIVISOR is 0. - Function: ceiling number This returns NUMBER, converted to an integer by rounding upward (towards positive infinity). - Function: round number This returns NUMBER, converted to an integer by rounding towards the nearest integer. Rounding a value equidistant between two integers may choose the integer closer to zero, or it may prefer an even integer, depending on your machine.  File: lispref.info, Node: Arithmetic Operations, Next: Rounding Operations, Prev: Numeric Conversions, Up: Numbers Arithmetic Operations ===================== XEmacs Lisp provides the traditional four arithmetic operations: addition, subtraction, multiplication, and division. Remainder and modulus functions supplement the division functions. The functions to add or subtract 1 are provided because they are traditional in Lisp and commonly used. All of these functions except `%' return a floating point value if any argument is floating. It is important to note that in XEmacs Lisp, arithmetic functions do not check for overflow. Thus `(1+ 134217727)' may evaluate to -134217728, depending on your hardware. - Function: 1+ number This function returns NUMBER plus one. NUMBER may be a number, character or marker. Markers and characters are converted to integers. For example, (setq foo 4) => 4 (1+ foo) => 5 This function is not analogous to the C operator `++'--it does not increment a variable. It just computes a sum. Thus, if we continue, foo => 4 If you want to increment the variable, you must use `setq', like this: (setq foo (1+ foo)) => 5 Now that the `cl' package is always available from lisp code, a more convenient and natural way to increment a variable is `(incf foo)'. - Function: 1- number This function returns NUMBER minus one. NUMBER may be a number, character or marker. Markers and characters are converted to integers. - Function: abs number This returns the absolute value of NUMBER. - Function: + &rest numbers This function adds its arguments together. When given no arguments, `+' returns 0. If any of the arguments are characters or markers, they are first converted to integers. (+) => 0 (+ 1) => 1 (+ 1 2 3 4) => 10 - Function: - &optional number &rest other-numbers The `-' function serves two purposes: negation and subtraction. When `-' has a single argument, the value is the negative of the argument. When there are multiple arguments, `-' subtracts each of the OTHER-NUMBERS from NUMBER, cumulatively. If there are no arguments, an error is signaled. If any of the arguments are characters or markers, they are first converted to integers. (- 10 1 2 3 4) => 0 (- 10) => -10 (-) => 0 - Function: * &rest numbers This function multiplies its arguments together, and returns the product. When given no arguments, `*' returns 1. If any of the arguments are characters or markers, they are first converted to integers. (*) => 1 (* 1) => 1 (* 1 2 3 4) => 24 - Function: / dividend &rest divisors The `/' function serves two purposes: inversion and division. When `/' has a single argument, the value is the inverse of the argument. When there are multiple arguments, `/' divides DIVIDEND by each of the DIVISORS, cumulatively, returning the quotient. If there are no arguments, an error is signaled. If none of the arguments are floats, then the result is an integer. This means the result has to be rounded. On most machines, the result is rounded towards zero after each division, but some machines may round differently with negative arguments. This is because the Lisp function `/' is implemented using the C division operator, which also permits machine-dependent rounding. As a practical matter, all known machines round in the standard fashion. If any of the arguments are characters or markers, they are first converted to integers. If you divide by 0, an `arith-error' error is signaled. (*Note Errors::.) (/ 6 2) => 3 (/ 5 2) => 2 (/ 25 3 2) => 4 (/ 3.0) => 0.3333333333333333 (/ -17 6) => -2 The result of `(/ -17 6)' could in principle be -3 on some machines. - Function: % dividend divisor This function returns the integer remainder after division of DIVIDEND by DIVISOR. The arguments must be integers or markers. For negative arguments, the remainder is in principle machine-dependent since the quotient is; but in practice, all known machines behave alike. An `arith-error' results if DIVISOR is 0. (% 9 4) => 1 (% -9 4) => -1 (% 9 -4) => 1 (% -9 -4) => -1 For any two integers DIVIDEND and DIVISOR, (+ (% DIVIDEND DIVISOR) (* (/ DIVIDEND DIVISOR) DIVISOR)) always equals DIVIDEND. - Function: mod dividend divisor This function returns the value of DIVIDEND modulo DIVISOR; in other words, the remainder after division of DIVIDEND by DIVISOR, but with the same sign as DIVISOR. The arguments must be numbers or markers. Unlike `%', `mod' returns a well-defined result for negative arguments. It also permits floating point arguments; it rounds the quotient downward (towards minus infinity) to an integer, and uses that quotient to compute the remainder. An `arith-error' results if DIVISOR is 0. (mod 9 4) => 1 (mod -9 4) => 3 (mod 9 -4) => -3 (mod -9 -4) => -1 (mod 5.5 2.5) => .5 For any two numbers DIVIDEND and DIVISOR, (+ (mod DIVIDEND DIVISOR) (* (floor DIVIDEND DIVISOR) DIVISOR)) always equals DIVIDEND, subject to rounding error if either argument is floating point. For `floor', see *Note Numeric Conversions::.  File: lispref.info, Node: Rounding Operations, Next: Bitwise Operations, Prev: Arithmetic Operations, Up: Numbers Rounding Operations =================== The functions `ffloor', `fceiling', `fround' and `ftruncate' take a floating point argument and return a floating point result whose value is a nearby integer. `ffloor' returns the nearest integer below; `fceiling', the nearest integer above; `ftruncate', the nearest integer in the direction towards zero; `fround', the nearest integer. - Function: ffloor number This function rounds NUMBER to the next lower integral value, and returns that value as a floating point number. - Function: fceiling number This function rounds NUMBER to the next higher integral value, and returns that value as a floating point number. - Function: ftruncate number This function rounds NUMBER towards zero to an integral value, and returns that value as a floating point number. - Function: fround number This function rounds NUMBER to the nearest integral value, and returns that value as a floating point number.  File: lispref.info, Node: Bitwise Operations, Next: Math Functions, Prev: Rounding Operations, Up: Numbers Bitwise Operations on Integers ============================== In a computer, an integer is represented as a binary number, a sequence of "bits" (digits which are either zero or one). A bitwise operation acts on the individual bits of such a sequence. For example, "shifting" moves the whole sequence left or right one or more places, reproducing the same pattern "moved over". The bitwise operations in XEmacs Lisp apply only to integers. - Function: lsh integer1 count `lsh', which is an abbreviation for "logical shift", shifts the bits in INTEGER1 to the left COUNT places, or to the right if COUNT is negative, bringing zeros into the vacated bits. If COUNT is negative, `lsh' shifts zeros into the leftmost (most-significant) bit, producing a positive result even if INTEGER1 is negative. Contrast this with `ash', below. Here are two examples of `lsh', shifting a pattern of bits one place to the left. We show only the low-order eight bits of the binary pattern; the rest are all zero. (lsh 5 1) => 10 ;; Decimal 5 becomes decimal 10. 00000101 => 00001010 (lsh 7 1) => 14 ;; Decimal 7 becomes decimal 14. 00000111 => 00001110 As the examples illustrate, shifting the pattern of bits one place to the left produces a number that is twice the value of the previous number. Shifting a pattern of bits two places to the left produces results like this (with 8-bit binary numbers): (lsh 3 2) => 12 ;; Decimal 3 becomes decimal 12. 00000011 => 00001100 On the other hand, shifting one place to the right looks like this: (lsh 6 -1) => 3 ;; Decimal 6 becomes decimal 3. 00000110 => 00000011 (lsh 5 -1) => 2 ;; Decimal 5 becomes decimal 2. 00000101 => 00000010 As the example illustrates, shifting one place to the right divides the value of a positive integer by two, rounding downward. The function `lsh', like all XEmacs Lisp arithmetic functions, does not check for overflow, so shifting left can discard significant bits and change the sign of the number. For example, left shifting 134,217,727 produces -2 on a 28-bit machine: (lsh 134217727 1) ; left shift => -2 In binary, in the 28-bit implementation, the argument looks like this: ;; Decimal 134,217,727 0111 1111 1111 1111 1111 1111 1111 which becomes the following when left shifted: ;; Decimal -2 1111 1111 1111 1111 1111 1111 1110 - Function: ash integer1 count `ash' ("arithmetic shift") shifts the bits in INTEGER1 to the left COUNT places, or to the right if COUNT is negative. `ash' gives the same results as `lsh' except when INTEGER1 and COUNT are both negative. In that case, `ash' puts ones in the empty bit positions on the left, while `lsh' puts zeros in those bit positions. Thus, with `ash', shifting the pattern of bits one place to the right looks like this: (ash -6 -1) => -3 ;; Decimal -6 becomes decimal -3. 1111 1111 1111 1111 1111 1111 1010 => 1111 1111 1111 1111 1111 1111 1101 In contrast, shifting the pattern of bits one place to the right with `lsh' looks like this: (lsh -6 -1) => 134217725 ;; Decimal -6 becomes decimal 134,217,725. 1111 1111 1111 1111 1111 1111 1010 => 0111 1111 1111 1111 1111 1111 1101 Here are other examples: ; 28-bit binary values (lsh 5 2) ; 5 = 0000 0000 0000 0000 0000 0000 0101 => 20 ; = 0000 0000 0000 0000 0000 0001 0100 (ash 5 2) => 20 (lsh -5 2) ; -5 = 1111 1111 1111 1111 1111 1111 1011 => -20 ; = 1111 1111 1111 1111 1111 1110 1100 (ash -5 2) => -20 (lsh 5 -2) ; 5 = 0000 0000 0000 0000 0000 0000 0101 => 1 ; = 0000 0000 0000 0000 0000 0000 0001 (ash 5 -2) => 1 (lsh -5 -2) ; -5 = 1111 1111 1111 1111 1111 1111 1011 => 4194302 ; = 0011 1111 1111 1111 1111 1111 1110 (ash -5 -2) ; -5 = 1111 1111 1111 1111 1111 1111 1011 => -2 ; = 1111 1111 1111 1111 1111 1111 1110 - Function: logand &rest ints-or-markers This function returns the "logical and" of the arguments: the Nth bit is set in the result if, and only if, the Nth bit is set in all the arguments. ("Set" means that the value of the bit is 1 rather than 0.) For example, using 4-bit binary numbers, the "logical and" of 13 and 12 is 12: 1101 combined with 1100 produces 1100. In both the binary numbers, the leftmost two bits are set (i.e., they are 1's), so the leftmost two bits of the returned value are set. However, for the rightmost two bits, each is zero in at least one of the arguments, so the rightmost two bits of the returned value are 0's. Therefore, (logand 13 12) => 12 If `logand' is not passed any argument, it returns a value of -1. This number is an identity element for `logand' because its binary representation consists entirely of ones. If `logand' is passed just one argument, it returns that argument. ; 28-bit binary values (logand 14 13) ; 14 = 0000 0000 0000 0000 0000 0000 1110 ; 13 = 0000 0000 0000 0000 0000 0000 1101 => 12 ; 12 = 0000 0000 0000 0000 0000 0000 1100 (logand 14 13 4) ; 14 = 0000 0000 0000 0000 0000 0000 1110 ; 13 = 0000 0000 0000 0000 0000 0000 1101 ; 4 = 0000 0000 0000 0000 0000 0000 0100 => 4 ; 4 = 0000 0000 0000 0000 0000 0000 0100 (logand) => -1 ; -1 = 1111 1111 1111 1111 1111 1111 1111 - Function: logior &rest ints-or-markers This function returns the "inclusive or" of its arguments: the Nth bit is set in the result if, and only if, the Nth bit is set in at least one of the arguments. If there are no arguments, the result is zero, which is an identity element for this operation. If `logior' is passed just one argument, it returns that argument. ; 28-bit binary values (logior 12 5) ; 12 = 0000 0000 0000 0000 0000 0000 1100 ; 5 = 0000 0000 0000 0000 0000 0000 0101 => 13 ; 13 = 0000 0000 0000 0000 0000 0000 1101 (logior 12 5 7) ; 12 = 0000 0000 0000 0000 0000 0000 1100 ; 5 = 0000 0000 0000 0000 0000 0000 0101 ; 7 = 0000 0000 0000 0000 0000 0000 0111 => 15 ; 15 = 0000 0000 0000 0000 0000 0000 1111 - Function: logxor &rest ints-or-markers This function returns the "exclusive or" of its arguments: the Nth bit is set in the result if, and only if, the Nth bit is set in an odd number of the arguments. If there are no arguments, the result is 0, which is an identity element for this operation. If `logxor' is passed just one argument, it returns that argument. ; 28-bit binary values (logxor 12 5) ; 12 = 0000 0000 0000 0000 0000 0000 1100 ; 5 = 0000 0000 0000 0000 0000 0000 0101 => 9 ; 9 = 0000 0000 0000 0000 0000 0000 1001 (logxor 12 5 7) ; 12 = 0000 0000 0000 0000 0000 0000 1100 ; 5 = 0000 0000 0000 0000 0000 0000 0101 ; 7 = 0000 0000 0000 0000 0000 0000 0111 => 14 ; 14 = 0000 0000 0000 0000 0000 0000 1110 - Function: lognot integer This function returns the logical complement of its argument: the Nth bit is one in the result if, and only if, the Nth bit is zero in INTEGER, and vice-versa. (lognot 5) => -6 ;; 5 = 0000 0000 0000 0000 0000 0000 0101 ;; becomes ;; -6 = 1111 1111 1111 1111 1111 1111 1010  File: lispref.info, Node: Math Functions, Next: Random Numbers, Prev: Bitwise Operations, Up: Numbers Standard Mathematical Functions =============================== These mathematical functions are available if floating point is supported (which is the normal state of affairs). They allow integers as well as floating point numbers as arguments. - Function: sin number - Function: cos number - Function: tan number These are the ordinary trigonometric functions, with argument measured in radians. - Function: asin number The value of `(asin NUMBER)' is a number between -pi/2 and pi/2 (inclusive) whose sine is NUMBER; if, however, NUMBER is out of range (outside [-1, 1]), then the result is a NaN. - Function: acos number The value of `(acos NUMBER)' is a number between 0 and pi (inclusive) whose cosine is NUMBER; if, however, NUMBER is out of range (outside [-1, 1]), then the result is a NaN. - Function: atan number &optional number2 The value of `(atan NUMBER)' is a number between -pi/2 and pi/2 (exclusive) whose tangent is NUMBER. If optional argument NUMBER2 is supplied, the function returns `atan2(NUMBER,NUMBER2)'. - Function: sinh number - Function: cosh number - Function: tanh number These are the ordinary hyperbolic trigonometric functions. - Function: asinh number - Function: acosh number - Function: atanh number These are the inverse hyperbolic trigonometric functions. - Function: exp number This is the exponential function; it returns e to the power NUMBER. e is a fundamental mathematical constant also called the base of natural logarithms. - Function: log number &optional base This function returns the logarithm of NUMBER, with base BASE. If you don't specify BASE, the base E is used. If NUMBER is negative, the result is a NaN. - Function: log10 number This function returns the logarithm of NUMBER, with base 10. If NUMBER is negative, the result is a NaN. `(log10 X)' == `(log X 10)', at least approximately. - Function: expt x y This function returns X raised to power Y. If both arguments are integers and Y is positive, the result is an integer; in this case, it is truncated to fit the range of possible integer values. - Function: sqrt number This returns the square root of NUMBER. If NUMBER is negative, the value is a NaN. - Function: cube-root number This returns the cube root of NUMBER.  File: lispref.info, Node: Random Numbers, Prev: Math Functions, Up: Numbers Random Numbers ============== A deterministic computer program cannot generate true random numbers. For most purposes, "pseudo-random numbers" suffice. A series of pseudo-random numbers is generated in a deterministic fashion. The numbers are not truly random, but they have certain properties that mimic a random series. For example, all possible values occur equally often in a pseudo-random series. In XEmacs, pseudo-random numbers are generated from a "seed" number. Starting from any given seed, the `random' function always generates the same sequence of numbers. XEmacs always starts with the same seed value, so the sequence of values of `random' is actually the same in each XEmacs run! For example, in one operating system, the first call to `(random)' after you start XEmacs always returns -1457731, and the second one always returns -7692030. This repeatability is helpful for debugging. If you want truly unpredictable random numbers, execute `(random t)'. This chooses a new seed based on the current time of day and on XEmacs's process ID number. - Function: random &optional limit This function returns a pseudo-random integer. Repeated calls return a series of pseudo-random integers. If LIMIT is a positive integer, the value is chosen to be nonnegative and less than LIMIT. If LIMIT is `t', it means to choose a new seed based on the current time of day and on XEmacs's process ID number. On some machines, any integer representable in Lisp may be the result of `random'. On other machines, the result can never be larger than a certain maximum or less than a certain (negative) minimum.  File: lispref.info, Node: Strings and Characters, Next: Lists, Prev: Numbers, Up: Top Strings and Characters ********************** A string in XEmacs Lisp is an array that contains an ordered sequence of characters. Strings are used as names of symbols, buffers, and files, to send messages to users, to hold text being copied between buffers, and for many other purposes. Because strings are so important, XEmacs Lisp has many functions expressly for manipulating them. XEmacs Lisp programs use strings more often than individual characters. * Menu: * String Basics:: Basic properties of strings and characters. * Predicates for Strings:: Testing whether an object is a string or char. * Creating Strings:: Functions to allocate new strings. * Predicates for Characters:: Testing whether an object is a character. * Character Codes:: Each character has an equivalent integer. * Text Comparison:: Comparing characters or strings. * String Conversion:: Converting characters or strings and vice versa. * Modifying Strings:: Changing characters in a string. * String Properties:: Additional information attached to strings. * Formatting Strings:: `format': XEmacs's analog of `printf'. * Character Case:: Case conversion functions. * Case Tables:: Customizing case conversion. * Char Tables:: Mapping from characters to Lisp objects.