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This is Info file ../../info/lispref.info, produced by Makeinfo-1.63 from the input file lispref.texi. 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 Copyright (C) 1990, 1991, 1992, 1993, 1994, 1995 Free Software Foundation, Inc. Copyright (C) 1994, 1995 Sun Microsystems, Inc. Copyright (C) 1995 Amdahl Corporation. Copyright (C) 1995 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: 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::.) (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: 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 and takes account of text properties as well as the characters in the strings. To compare two strings' characters without comparing their text properties, use `string=' (*note Text Comparison::.). (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, 7, 13, and 511. Their values are exact. 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 Emacs 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. Emacs 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' and `number-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: wholenump OBJECT The `wholenump' predicate (whose name comes from the phrase "whole-number-p") tests to see whether its argument is a nonnegative integer, and returns `t' if so, `nil' otherwise. 0 is considered non-negative. `natnump' is an obsolete synonym for `wholenump'. - 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 Emacs Lisp. Therefore, `eq' is equivalent `=' 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: (defvar 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. Emacs Lisp can have just one integer object for any given value because it has a limited range of integer values. - Function: = NUMBER-OR-MARKER1 NUMBER-OR-MARKER2 This function tests whether its arguments are numerically equal, and returns `t' if so, `nil' otherwise. - Function: /= NUMBER-OR-MARKER1 NUMBER-OR-MARKER2 This function tests whether its arguments are numerically equal, and returns `t' if they are not, and `nil' if they are. - Function: < NUMBER-OR-MARKER1 NUMBER-OR-MARKER2 This function tests whether its first argument is strictly less than its second argument. It returns `t' if so, `nil' otherwise. - Function: <= NUMBER-OR-MARKER1 NUMBER-OR-MARKER2 This function tests whether its first argument is less than or equal to its second argument. It returns `t' if so, `nil' otherwise. - Function: > NUMBER-OR-MARKER1 NUMBER-OR-MARKER2 This function tests whether its first argument is strictly greater than its second argument. It returns `t' if so, `nil' otherwise. - Function: >= NUMBER-OR-MARKER1 NUMBER-OR-MARKER2 This function tests whether its first argument is greater than or equal to its second argument. It returns `t' if so, `nil' otherwise. - Function: max NUMBER-OR-MARKER &rest NUMBERS-OR-MARKERS 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-OR-MARKER &rest NUMBERS-OR-MARKERS 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 ===================== Emacs 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 Emacs Lisp, arithmetic functions do not check for overflow. Thus `(1+ 134217727)' may evaluate to -134217728, depending on your hardware. - Function: 1+ NUMBER-OR-MARKER This function returns NUMBER-OR-MARKER plus 1. 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 - Function: 1- NUMBER-OR-MARKER This function returns NUMBER-OR-MARKER minus 1. - Function: abs NUMBER This returns the absolute value of NUMBER. - Function: + &rest NUMBERS-OR-MARKERS This function adds its arguments together. When given no arguments, `+' returns 0. (+) => 0 (+ 1) => 1 (+ 1 2 3 4) => 10 - Function: - &optional NUMBER-OR-MARKER &rest OTHER-NUMBERS-OR-MARKERS 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-OR-MARKERS from NUMBER-OR-MARKER, cumulatively. If there are no arguments, the result is 0. (- 10 1 2 3 4) => 0 (- 10) => -10 (-) => 0 - Function: * &rest NUMBERS-OR-MARKERS This function multiplies its arguments together, and returns the product. When given no arguments, `*' returns 1. (*) => 1 (* 1) => 1 (* 1 2 3 4) => 24 - Function: / DIVIDEND DIVISOR &rest DIVISORS This function divides DIVIDEND by DIVISOR and returns the quotient. If there are additional arguments DIVISORS, then it divides DIVIDEND by each divisor in turn. Each argument may be a number or a marker. If all the arguments are integers, then the result is an integer too. 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 you divide by 0, an `arith-error' error is signaled. (*Note Errors::.) (/ 6 2) => 3 (/ 5 2) => 2 (/ 25 3 2) => 4 (/ -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 FLOAT This function rounds FLOAT to the next lower integral value, and returns that value as a floating point number. - Function: fceiling FLOAT This function rounds FLOAT to the next higher integral value, and returns that value as a floating point number. - Function: ftruncate FLOAT This function rounds FLOAT towards zero to an integral value, and returns that value as a floating point number. - Function: fround FLOAT This function rounds FLOAT 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 Emacs 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 Emacs 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. They allow integers as well as floating point numbers as arguments. - Function: sin ARG - Function: cos ARG - Function: tan ARG These are the ordinary trigonometric functions, with argument measured in radians. - Function: asin ARG The value of `(asin ARG)' is a number between -pi/2 and pi/2 (inclusive) whose sine is ARG; if, however, ARG is out of range (outside [-1, 1]), then the result is a NaN. - Function: acos ARG The value of `(acos ARG)' is a number between 0 and pi (inclusive) whose cosine is ARG; if, however, ARG is out of range (outside [-1, 1]), then the result is a NaN. - Function: atan ARG The value of `(atan ARG)' is a number between -pi/2 and pi/2 (exclusive) whose tangent is ARG. - Function: exp ARG This is the exponential function; it returns e to the power ARG. e is a fundamental mathematical constant also called the base of natural logarithms. - Function: log ARG &optional BASE This function returns the logarithm of ARG, with base BASE. If you don't specify BASE, the base E is used. If ARG is negative, the result is a NaN. - Function: log10 ARG This function returns the logarithm of ARG, with base 10. If ARG 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 ARG This returns the square root of ARG. If ARG is negative, the value is a NaN. 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 Emacs 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 Emacs 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, Emacs Lisp has many functions expressly for manipulating them. Emacs Lisp programs use strings more often than individual characters. * Menu: * Basics: 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. * Text Comparison:: Comparing characters or strings. * String Conversion:: Converting characters or strings and vice versa. * Formatting Strings:: `format': XEmacs's analog of `printf'. * Character Case:: Case conversion functions. * Case Table:: Customizing case conversion. File: lispref.info, Node: String Basics, Next: Predicates for Strings, Up: Strings and Characters String and Character Basics =========================== Strings in Emacs Lisp are arrays that contain an ordered sequence of characters. Characters are represented in Emacs Lisp as integers; whether an integer was intended as a character or not is determined only by how it is used. Thus, strings really contain integers. The length of a string (like any array) is fixed and independent of the string contents, and cannot be altered. Strings in Lisp are *not* terminated by a distinguished character code. (By contrast, strings in C are terminated by a character with ASCII code 0.) This means that any character, including the null character (ASCII code 0), is a valid element of a string. Since strings are considered arrays, you can operate on them with the general array functions. (*Note Sequences Arrays Vectors::.) For example, you can access or change individual characters in a string using the functions `aref' and `aset' (*note Array Functions::.). Each character in a string is stored in a single byte. Therefore, numbers not in the range 0 to 255 are truncated when stored into a string. This means that a string takes up much less memory than a vector of the same length. Sometimes key sequences are represented as strings. When a string is a key sequence, string elements in the range 128 to 255 represent meta characters (which are extremely large integers) rather than keyboard events in the range 128 to 255. Strings cannot hold characters that have the hyper, super or alt modifiers; they can hold ASCII control characters, but no other control characters. They do not distinguish case in ASCII control characters. *Note Character Type::, for more information about representation of meta and other modifiers for keyboard input characters. Strings are useful for holding regular expressions. You can also match regular expressions against strings (*note Regexp Search::.). The functions `match-string' (*note Simple Match Data::.) and `replace-match' (*note Replacing Match::.) are useful for decomposing and modifying strings based on regular expression matching. Like a buffer, a string can contain extents in it. These extents are created when a function such as `buffer-substring' is called on a region with duplicable extents in it. When the string is inserted into a buffer, the extents are inserted along with it. *Note Duplicable Extents::. *Note Text::, for information about functions that display strings or copy them into buffers. *Note Character Type::, and *Note String Type::, for information about the syntax of characters and strings. File: lispref.info, Node: Predicates for Strings, Next: Creating Strings, Prev: String Basics, Up: Strings and Characters The Predicates for Strings ========================== For more information about general sequence and array predicates, see *Note Sequences Arrays Vectors::, and *Note Arrays::. - Function: stringp OBJECT This function returns `t' if OBJECT is a string, `nil' otherwise. - Function: char-or-string-p OBJECT This function returns `t' if OBJECT is a string or a character (i.e., an integer), `nil' otherwise. File: lispref.info, Node: Creating Strings, Next: Text Comparison, Prev: Predicates for Strings, Up: Strings and Characters Creating Strings ================ The following functions create strings, either from scratch, or by putting strings together, or by taking them apart. - Function: make-string COUNT CHARACTER This function returns a string made up of COUNT repetitions of CHARACTER. If COUNT is negative, an error is signaled. (make-string 5 ?x) => "xxxxx" (make-string 0 ?x) => "" Other functions to compare with this one include `char-to-string' (*note String Conversion::.), `make-vector' (*note Vectors::.), and `make-list' (*note Building Lists::.). - Function: substring STRING START &optional END This function returns a new string which consists of those characters from STRING in the range from (and including) the character at the index START up to (but excluding) the character at the index END. The first character is at index zero. (substring "abcdefg" 0 3) => "abc" Here the index for `a' is 0, the index for `b' is 1, and the index for `c' is 2. Thus, three letters, `abc', are copied from the string `"abcdefg"'. The index 3 marks the character position up to which the substring is copied. The character whose index is 3 is actually the fourth character in the string. A negative number counts from the end of the string, so that -1 signifies the index of the last character of the string. For example: (substring "abcdefg" -3 -1) => "ef" In this example, the index for `e' is -3, the index for `f' is -2, and the index for `g' is -1. Therefore, `e' and `f' are included, and `g' is excluded. When `nil' is used as an index, it stands for the length of the string. Thus, (substring "abcdefg" -3 nil) => "efg" Omitting the argument END is equivalent to specifying `nil'. It follows that `(substring STRING 0)' returns a copy of all of STRING. (substring "abcdefg" 0) => "abcdefg" But we recommend `copy-sequence' for this purpose (*note Sequence Functions::.). If the characters copied from STRING have text properties, the properties are copied into the new string also. *Note Text Properties::. A `wrong-type-argument' error is signaled if either START or END is not an integer or `nil'. An `args-out-of-range' error is signaled if START indicates a character following END, or if either integer is out of range for STRING. Contrast this function with `buffer-substring' (*note Buffer Contents::.), which returns a string containing a portion of the text in the current buffer. The beginning of a string is at index 0, but the beginning of a buffer is at index 1. - Function: concat &rest SEQUENCES This function returns a new string consisting of the characters in the arguments passed to it (along with their text properties, if any). The arguments may be strings, lists of numbers, or vectors of numbers; they are not themselves changed. If `concat' receives no arguments, it returns an empty string. (concat "abc" "-def") => "abc-def" (concat "abc" (list 120 (+ 256 121)) [122]) => "abcxyz" ;; `nil' is an empty sequence. (concat "abc" nil "-def") => "abc-def" (concat "The " "quick brown " "fox.") => "The quick brown fox." (concat) => "" The second example above shows how characters stored in strings are taken modulo 256. In other words, each character in the string is stored in one byte. The `concat' function always constructs a new string that is not `eq' to any existing string. When an argument is an integer (not a sequence of integers), it is converted to a string of digits making up the decimal printed representation of the integer. *Don't use this feature; we plan to eliminate it. If you already use this feature, change your programs now!* The proper way to convert an integer to a decimal number in this way is with `format' (*note Formatting Strings::.) or `number-to-string' (*note String Conversion::.). (concat 137) => "137" (concat 54 321) => "54321" For information about other concatenation functions, see the description of `mapconcat' in *Note Mapping Functions::, `vconcat' in *Note Vectors::, and `append' in *Note Building Lists::. File: lispref.info, Node: Text Comparison, Next: String Conversion, Prev: Creating Strings, Up: Strings and Characters Comparison of Characters and Strings ==================================== - Function: char-equal CHARACTER1 CHARACTER2 This function returns `t' if the arguments represent the same character, `nil' otherwise. This function ignores differences in case if `case-fold-search' is non-`nil'. (char-equal ?x ?x) => t (char-to-string (+ 256 ?x)) => "x" (char-equal ?x (+ 256 ?x)) => t - Function: string= STRING1 STRING2 This function returns `t' if the characters of the two strings match exactly; case is significant. (string= "abc" "abc") => t (string= "abc" "ABC") => nil (string= "ab" "ABC") => nil The function `string=' ignores the text properties of the two strings. To compare strings in a way that compares their text properties also, use `equal' (*note Equality Predicates::.). - Function: string-equal STRING1 STRING2 `string-equal' is another name for `string='. - Function: string< STRING1 STRING2 This function compares two strings a character at a time. First it scans both the strings at once to find the first pair of corresponding characters that do not match. If the lesser character of those two is the character from STRING1, then STRING1 is less, and this function returns `t'. If the lesser character is the one from STRING2, then STRING1 is greater, and this function returns `nil'. If the two strings match entirely, the value is `nil'. Pairs of characters are compared by their ASCII codes. Keep in mind that lower case letters have higher numeric values in the ASCII character set than their upper case counterparts; numbers and many punctuation characters have a lower numeric value than upper case letters. (string< "abc" "abd") => t (string< "abd" "abc") => nil (string< "123" "abc") => t When the strings have different lengths, and they match up to the length of STRING1, then the result is `t'. If they match up to the length of STRING2, the result is `nil'. A string of no characters is less than any other string. (string< "" "abc") => t (string< "ab" "abc") => t (string< "abc" "") => nil (string< "abc" "ab") => nil (string< "" "") => nil - Function: string-lessp STRING1 STRING2 `string-lessp' is another name for `string<'. See also `compare-buffer-substrings' in *Note Comparing Text::, for a way to compare text in buffers. The function `string-match', which matches a regular expression against a string, can be used for a kind of string comparison; see *Note Regexp Search::. File: lispref.info, Node: String Conversion, Next: Formatting Strings, Prev: Text Comparison, Up: Strings and Characters Conversion of Characters and Strings ==================================== This section describes functions for conversions between characters, strings and integers. `format' and `prin1-to-string' (*note Output Functions::.) can also convert Lisp objects into strings. `read-from-string' (*note Input Functions::.) can "convert" a string representation of a Lisp object into an object. *Note Documentation::, for functions that produce textual descriptions of text characters and general input events (`single-key-description' and `text-char-description'). These functions are used primarily for making help messages. - Function: char-to-string CHARACTER This function returns a new string with a length of one character. The value of CHARACTER, modulo 256, is used to initialize the element of the string. This function is similar to `make-string' with an integer argument of 1. (*Note Creating Strings::.) This conversion can also be done with `format' using the `%c' format specification. (*Note Formatting Strings::.) (char-to-string ?x) => "x" (char-to-string (+ 256 ?x)) => "x" (make-string 1 ?x) => "x" - Function: string-to-char STRING This function returns the first character in STRING. If the string is empty, the function returns 0. The value is also 0 when the first character of STRING is the null character, ASCII code 0. (string-to-char "ABC") => 65 (string-to-char "xyz") => 120 (string-to-char "") => 0 (string-to-char "\000") => 0 This function may be eliminated in the future if it does not seem useful enough to retain. - Function: number-to-string NUMBER This function returns a string consisting of the printed representation of NUMBER, which may be an integer or a floating point number. The value starts with a sign if the argument is negative. (number-to-string 256) => "256" (number-to-string -23) => "-23" (number-to-string -23.5) => "-23.5" `int-to-string' is a semi-obsolete alias for this function. See also the function `format' in *Note Formatting Strings::. - Function: string-to-number STRING This function returns the numeric value of the characters in STRING, read in base ten. It skips spaces and tabs at the beginning of STRING, then reads as much of STRING as it can interpret as a number. (On some systems it ignores other whitespace at the beginning, not just spaces and tabs.) If the first character after the ignored whitespace is not a digit or a minus sign, this function returns 0. (string-to-number "256") => 256 (string-to-number "25 is a perfect square.") => 25 (string-to-number "X256") => 0 (string-to-number "-4.5") => -4.5 `string-to-int' is an obsolete alias for this function.