# SOME DESCRIPTIVE TITLE # Copyright (C) YEAR Free Software Foundation, Inc. # This file is distributed under the same license as the PACKAGE package. # FIRST AUTHOR , YEAR. # #, fuzzy msgid "" msgstr "" "Project-Id-Version: PACKAGE VERSION\n" "POT-Creation-Date: 2021-11-07 12:11+0900\n" "PO-Revision-Date: YEAR-MO-DA HO:MI+ZONE\n" "Last-Translator: FULL NAME \n" "Language-Team: LANGUAGE \n" "Language: \n" "MIME-Version: 1.0\n" "Content-Type: text/plain; charset=UTF-8\n" "Content-Transfer-Encoding: 8bit\n" #. type: chapter #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:6 #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:7 #, no-wrap msgid "Numbers" msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:8 #, no-wrap msgid "integers" msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:9 #, no-wrap msgid "numbers" msgstr "" #. type: Plain text #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:20 msgid "" "GNU Emacs supports two numeric data types: @dfn{integers} and " "@dfn{floating-point numbers}. Integers are whole numbers such as @minus{}3, " "0, 7, 13, and 511. Floating-point numbers are numbers with fractional " "parts, such as @minus{}4.5, 0.0, and 2.71828. They can also be expressed in " "exponential notation: @samp{1.5e2} is the same as @samp{150.0}; here, " "@samp{e2} stands for ten to the second power, and that is multiplied by " "1.5. Integer computations are exact. Floating-point computations often " "involve rounding errors, as the numbers have a fixed amount of precision." msgstr "" #. type: section #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:32 #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:34 #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:35 #, no-wrap msgid "Integer Basics" msgstr "" #. type: menuentry #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:32 msgid "Representation and range of integers." msgstr "" #. type: node #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:32 #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:217 #, no-wrap msgid "Float Basics" msgstr "" #. type: menuentry #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:32 msgid "Representation and range of floating point." msgstr "" #. type: node #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:32 #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:342 #, no-wrap msgid "Predicates on Numbers" msgstr "" #. type: menuentry #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:32 msgid "Testing for numbers." msgstr "" #. type: section #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:32 #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:398 #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:399 #, no-wrap msgid "Comparison of Numbers" msgstr "" #. type: menuentry #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:32 msgid "Equality and inequality predicates." msgstr "" #. type: section #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:32 #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:511 #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:512 #, no-wrap msgid "Numeric Conversions" msgstr "" #. type: menuentry #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:32 msgid "Converting float to integer and vice versa." msgstr "" #. type: section #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:32 #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:606 #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:607 #, no-wrap msgid "Arithmetic Operations" msgstr "" #. type: menuentry #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:32 msgid "How to add, subtract, multiply and divide." msgstr "" #. type: section #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:32 #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:832 #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:833 #, no-wrap msgid "Rounding Operations" msgstr "" #. type: menuentry #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:32 msgid "Explicitly rounding floating-point numbers." msgstr "" #. type: node #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:32 #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:864 #, no-wrap msgid "Bitwise Operations" msgstr "" #. type: menuentry #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:32 msgid "Logical and, or, not, shifting." msgstr "" #. type: node #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:32 #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1120 #, no-wrap msgid "Math Functions" msgstr "" #. type: menuentry #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:32 msgid "Trig, exponential and logarithmic functions." msgstr "" #. type: section #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:32 #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1224 #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1225 #, no-wrap msgid "Random Numbers" msgstr "" #. type: menuentry #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:32 msgid "Obtaining random integers, predictable or not." msgstr "" #. type: Plain text #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:40 msgid "" "The Lisp reader reads an integer as a nonempty sequence of decimal digits " "with optional initial sign and optional final period." msgstr "" #. type: example #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:48 #, no-wrap msgid "" " 1 ; @r{The integer 1.}\n" " 1. ; @r{The integer 1.}\n" "+1 ; @r{Also the integer 1.}\n" "-1 ; @r{The integer @minus{}1.}\n" " 0 ; @r{The integer 0.}\n" "-0 ; @r{The integer 0.}\n" msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:50 #, no-wrap msgid "integers in specific radix" msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:51 #, no-wrap msgid "radix for reading an integer" msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:52 #, no-wrap msgid "base for reading an integer" msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:53 #, no-wrap msgid "hex numbers" msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:54 #, no-wrap msgid "octal numbers" msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:55 #, no-wrap msgid "reading numbers in hex, octal, and binary" msgstr "" #. type: Plain text #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:67 msgid "" "The syntax for integers in bases other than 10 consists of @samp{#} followed " "by a radix indication followed by one or more digits. The radix indications " "are @samp{b} for binary, @samp{o} for octal, @samp{x} for hex, and " "@samp{@var{radix}r} for radix @var{radix}. Thus, @samp{#b@var{integer}} " "reads @var{integer} in binary, and @samp{#@var{radix}r@var{integer}} reads " "@var{integer} in radix @var{radix}. Allowed values of @var{radix} run from " "2 to 36, and allowed digits are the first @var{radix} characters taken from " "@samp{0}--@samp{9}, @samp{A}--@samp{Z}. Letter case is ignored and there is " "no initial sign or final period. For example:" msgstr "" #. type: example #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:73 #, no-wrap msgid "" "#b101100 @result{} 44\n" "#o54 @result{} 44\n" "#x2c @result{} 44\n" "#24r1k @result{} 44\n" msgstr "" #. type: Plain text #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:78 msgid "" "To understand how various functions work on integers, especially the bitwise " "operators (@pxref{Bitwise Operations}), it is often helpful to view the " "numbers in their binary form." msgstr "" #. type: Plain text #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:80 msgid "In binary, the decimal integer 5 looks like this:" msgstr "" #. type: example #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:83 #, no-wrap msgid "@dots{}000101\n" msgstr "" #. type: Plain text #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:89 msgid "" "(The ellipsis @samp{@dots{}} stands for a conceptually infinite number of " "bits that match the leading bit; here, an infinite number of 0 bits. Later " "examples also use this @samp{@dots{}} notation.)" msgstr "" #. type: Plain text #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:91 msgid "The integer @minus{}1 looks like this:" msgstr "" #. type: example #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:94 #, no-wrap msgid "@dots{}111111\n" msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:97 #, no-wrap msgid "two's complement" msgstr "" #. type: Plain text #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:100 msgid "" "@minus{}1 is represented as all ones. (This is called @dfn{two's " "complement} notation.)" msgstr "" #. type: Plain text #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:104 msgid "" "Subtracting 4 from @minus{}1 returns the negative integer @minus{}5. In " "binary, the decimal integer 4 is 100. Consequently, @minus{}5 looks like " "this:" msgstr "" #. type: example #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:107 #, no-wrap msgid "@dots{}111011\n" msgstr "" #. type: Plain text #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:114 msgid "" "Many of the functions described in this chapter accept markers for arguments " "in place of numbers. (@xref{Markers}.) Since the actual arguments to such " "functions may be either numbers or markers, we often give these arguments " "the name @var{number-or-marker}. When the argument value is a marker, its " "position value is used and its buffer is ignored." msgstr "" #. type: Plain text #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:118 msgid "" "In Emacs Lisp, text characters are represented by integers. Any integer " "between zero and the value of @code{(max-char)}, inclusive, is considered to " "be valid as a character. @xref{Character Codes}." msgstr "" #. type: Plain text #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:129 msgid "" "Integers in Emacs Lisp are not limited to the machine word size. Under the " "hood, though, there are two kinds of integers: smaller ones, called " "@dfn{fixnums}, and larger ones, called @dfn{bignums}. Although Emacs Lisp " "code ordinarily should not depend on whether an integer is a fixnum or a " "bignum, older Emacs versions support only fixnums, some functions in Emacs " "still accept only fixnums, and older Emacs Lisp code may have trouble when " "given bignums. For example, while older Emacs Lisp code could safely " "compare integers for numeric equality with @code{eq}, the presence of " "bignums means that equality predicates like @code{eql} and @code{=} should " "now be used to compare integers." msgstr "" #. type: Plain text #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:137 msgid "" "The range of values for bignums is limited by the amount of main memory, by " "machine characteristics such as the size of the word used to represent a " "bignum's exponent, and by the @code{integer-width} variable. These limits " "are typically much more generous than the limits for fixnums. A bignum is " "never numerically equal to a fixnum; Emacs always represents an integer in " "fixnum range as a fixnum, not a bignum." msgstr "" #. type: Plain text #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:140 msgid "" "The range of values for a fixnum depends on the machine. The minimum range " "is @minus{}536,870,912 to 536,870,911 (30 bits; i.e.," msgstr "" #. type: ifnottex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:142 #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:183 msgid "@minus{}2**29" msgstr "" #. type: tex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:145 #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:186 #, no-wrap msgid "@math{-2^{29}}\n" msgstr "" #. type: Plain text #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:147 msgid "to" msgstr "" #. type: ifnottex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:149 msgid "2**29 @minus{} 1)," msgstr "" #. type: tex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:152 #, no-wrap msgid "@math{2^{29}-1}),\n" msgstr "" #. type: Plain text #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:154 msgid "but many machines provide a wider range." msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:155 #, no-wrap msgid "largest fixnum" msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:156 #, no-wrap msgid "maximum fixnum" msgstr "" #. type: defvar #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:157 #, no-wrap msgid "most-positive-fixnum" msgstr "" #. type: defvar #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:160 msgid "" "The value of this variable is the greatest ``small'' integer that Emacs Lisp " "can handle. Typical values are" msgstr "" #. type: ifnottex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:162 msgid "2**29 @minus{} 1" msgstr "" #. type: tex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:165 #, no-wrap msgid "@math{2^{29}-1}\n" msgstr "" #. type: defvar #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:167 #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:188 msgid "on 32-bit and" msgstr "" #. type: ifnottex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:169 msgid "2**61 @minus{} 1" msgstr "" #. type: tex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:172 #, no-wrap msgid "@math{2^{61}-1}\n" msgstr "" #. type: defvar #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:174 #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:195 msgid "on 64-bit platforms." msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:176 #, no-wrap msgid "smallest fixnum" msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:177 #, no-wrap msgid "minimum fixnum" msgstr "" #. type: defvar #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:178 #, no-wrap msgid "most-negative-fixnum" msgstr "" #. type: defvar #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:181 msgid "" "The value of this variable is the numerically least ``small'' integer that " "Emacs Lisp can handle. It is negative. Typical values are" msgstr "" #. type: ifnottex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:190 msgid "@minus{}2**61" msgstr "" #. type: tex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:193 #, no-wrap msgid "@math{-2^{61}}\n" msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:197 #, no-wrap msgid "bignum range" msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:198 #, no-wrap msgid "integer range" msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:199 #, no-wrap msgid "number of bignum bits, limit on" msgstr "" #. type: defvar #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:200 #, no-wrap msgid "integer-width" msgstr "" #. type: defvar #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:204 msgid "" "The value of this variable is a nonnegative integer that controls whether " "Emacs signals a range error when a large integer would be calculated. " "Integers with absolute values less than" msgstr "" #. type: ifnottex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:206 msgid "2**@var{n}," msgstr "" #. type: tex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:209 #, no-wrap msgid "@math{2^{n}},\n" msgstr "" #. type: defvar #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:215 msgid "" "where @var{n} is this variable's value, do not signal a range error. " "Attempts to create larger integers typically signal a range error, although " "there might be no signal if a larger integer can be created cheaply. " "Setting this variable to a large number can be costly if a computation " "creates huge integers." msgstr "" #. type: section #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:218 #, no-wrap msgid "Floating-Point Basics" msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:220 #, no-wrap msgid "@acronym{IEEE} floating point" msgstr "" #. type: Plain text #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:233 msgid "" "Floating-point numbers are useful for representing numbers that are not " "integral. The range of floating-point numbers is the same as the range of " "the C data type @code{double} on the machine you are using. On all " "computers supported by Emacs, this is @acronym{IEEE} binary64 floating point " "format, which is standardized by " "@url{https://standards.ieee.org/standard/754-2019.html,,IEEE Std 754-2019} " "and is discussed further in David Goldberg's paper " "``@url{https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html, What " "Every Computer Scientist Should Know About Floating-Point Arithmetic}''. On " "modern platforms, floating-point operations follow the IEEE-754 standard " "closely; however, results are not always rounded correctly on some " "obsolescent platforms, notably 32-bit x86." msgstr "" #. type: Plain text #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:243 msgid "" "The read syntax for floating-point numbers requires either a decimal point, " "an exponent, or both. Optional signs (@samp{+} or @samp{-}) precede the " "number and its exponent. For example, @samp{1500.0}, @samp{+15e2}, " "@samp{15.0e+2}, @samp{+1500000e-3}, and @samp{.15e4} are five ways of " "writing a floating-point number whose value is 1500. They are all " "equivalent. Like Common Lisp, Emacs Lisp requires at least one digit after " "a decimal point in a floating-point number that does not have an exponent; " "@samp{1500.} is an integer, not a floating-point number." msgstr "" #. type: Plain text #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:249 msgid "" "Emacs Lisp treats @code{-0.0} as numerically equal to ordinary zero with " "respect to numeric comparisons like @code{=}. This follows the " "@acronym{IEEE} floating-point standard, which says @code{-0.0} and " "@code{0.0} are numerically equal even though other operations can " "distinguish them." msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:250 #, no-wrap msgid "positive infinity" msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:251 #, no-wrap msgid "negative infinity" msgstr "" #. type: item #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:252 #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:277 #, no-wrap msgid "infinity" msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:253 #, no-wrap msgid "NaN" msgstr "" #. type: Plain text #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:264 msgid "" "The @acronym{IEEE} floating-point standard supports 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, @code{(/ 0.0 " "0.0)} returns a NaN@. A NaN is never numerically equal to any value, not " "even to itself. NaNs carry a sign and a significand, and non-numeric " "functions treat two NaNs as equal when their signs and significands agree. " "Significands of NaNs are machine-dependent, as are the digits in their " "string representation." msgstr "" #. type: Plain text #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:273 msgid "" "When NaNs and signed zeros are involved, non-numeric functions like " "@code{eql}, @code{equal}, @code{sxhash-eql}, @code{sxhash-equal} and " "@code{gethash} determine whether values are indistinguishable, not whether " "they are numerically equal. For example, when @var{x} and @var{y} are the " "same NaN, @code{(equal x y)} returns @code{t} whereas @code{(= x y)} uses " "numeric comparison and returns @code{nil}; conversely, @code{(equal 0.0 " "-0.0)} returns @code{nil} whereas @code{(= 0.0 -0.0)} returns @code{t}." msgstr "" #. type: Plain text #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:275 msgid "Here are read syntaxes for these special floating-point values:" msgstr "" #. type: table #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:279 msgid "@samp{1.0e+INF} and @samp{-1.0e+INF}" msgstr "" #. type: item #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:279 #, no-wrap msgid "not-a-number" msgstr "" #. type: table #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:281 msgid "@samp{0.0e+NaN} and @samp{-0.0e+NaN}" msgstr "" #. type: Plain text #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:285 msgid "The following functions are specialized for handling floating-point numbers:" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:286 #, no-wrap msgid "isnan x" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:289 msgid "" "This predicate returns @code{t} if its floating-point argument is a NaN, " "@code{nil} otherwise." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:291 #, no-wrap msgid "frexp x" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:295 msgid "" "This function returns a cons cell @code{(@var{s} . @var{e})}, where @var{s} " "and @var{e} are respectively the significand and exponent of the " "floating-point number @var{x}." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:298 msgid "" "If @var{x} is finite, then @var{s} is a floating-point number between 0.5 " "(inclusive) and 1.0 (exclusive), @var{e} is an integer, and" msgstr "" #. type: ifnottex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:300 msgid "@var{x} = @var{s} * 2**@var{e}." msgstr "" #. type: tex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:303 #, no-wrap msgid "@math{x = s 2^e}.\n" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:307 msgid "" "If @var{x} is zero or infinity, then @var{s} is the same as @var{x}. If " "@var{x} is a NaN, then @var{s} is also a NaN@. If @var{x} is zero, then " "@var{e} is 0." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:309 #, no-wrap msgid "ldexp s e" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:312 msgid "" "Given a numeric significand @var{s} and an integer exponent @var{e}, this " "function returns the floating point number" msgstr "" #. type: ifnottex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:314 msgid "@var{s} * 2**@var{e}." msgstr "" #. type: tex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:317 #, no-wrap msgid "@math{s 2^e}.\n" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:320 #, no-wrap msgid "copysign x1 x2" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:323 msgid "" "This function copies the sign of @var{x2} to the value of @var{x1}, and " "returns the result. @var{x1} and @var{x2} must be floating point." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:325 #, no-wrap msgid "logb x" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:331 msgid "" "This function returns the binary exponent of @var{x}. More precisely, if " "@var{x} is finite and nonzero, the value is the logarithm base 2 of " "@math{|x|}, rounded down to an integer. If @var{x} is zero or infinite, the " "value is infinity; if @var{x} is a NaN, the value is a NaN." msgstr "" #. type: example #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:339 #, no-wrap msgid "" "(logb 10)\n" " @result{} 3\n" "(logb 10.0e20)\n" " @result{} 69\n" "(logb 0)\n" " @result{} -1.0e+INF\n" msgstr "" #. type: section #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:343 #, no-wrap msgid "Type Predicates for Numbers" msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:344 #, no-wrap msgid "predicates for numbers" msgstr "" #. type: Plain text #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:352 msgid "" "The functions in this section test for numbers, or for a specific type of " "number. The functions @code{integerp} and @code{floatp} can take any type " "of Lisp object as argument (they would not be of much use otherwise), but " "the @code{zerop} predicate requires a number as its argument. See also " "@code{integer-or-marker-p} and @code{number-or-marker-p}, in @ref{Predicates " "on Markers}." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:353 #, no-wrap msgid "bignump object" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:357 msgid "" "This predicate tests whether its argument is a large integer, and returns " "@code{t} if so, @code{nil} otherwise. Unlike small integers, large integers " "can be @code{=} or @code{eql} even if they are not @code{eq}." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:359 #, no-wrap msgid "fixnump object" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:363 msgid "" "This predicate tests whether its argument is a small integer, and returns " "@code{t} if so, @code{nil} otherwise. Small integers can be compared with " "@code{eq}." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:365 #, no-wrap msgid "floatp object" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:368 msgid "" "This predicate tests whether its argument is floating point and returns " "@code{t} if so, @code{nil} otherwise." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:370 #, no-wrap msgid "integerp object" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:373 msgid "" "This predicate tests whether its argument is an integer, and returns " "@code{t} if so, @code{nil} otherwise." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:375 #, no-wrap msgid "numberp object" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:378 msgid "" "This predicate tests whether its argument is a number (either integer or " "floating point), and returns @code{t} if so, @code{nil} otherwise." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:380 #, no-wrap msgid "natnump object" msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:381 #, no-wrap msgid "natural numbers" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:386 msgid "" "This predicate (whose name comes from the phrase ``natural number'') tests " "to see whether its argument is a nonnegative integer, and returns @code{t} " "if so, @code{nil} otherwise. 0 is considered non-negative." msgstr "" #. type: findex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:387 #, no-wrap msgid "wholenump" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:389 msgid "@code{wholenump} is a synonym for @code{natnump}." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:391 #, no-wrap msgid "zerop number" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:394 msgid "" "This predicate tests whether its argument is zero, and returns @code{t} if " "so, @code{nil} otherwise. The argument must be a number." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:396 msgid "@code{(zerop x)} is equivalent to @code{(= x 0)}." msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:400 #, no-wrap msgid "number comparison" msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:401 #, no-wrap msgid "comparing numbers" msgstr "" #. type: Plain text #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:413 msgid "" "To test numbers for numerical equality, you should normally use @code{=} " "instead of non-numeric comparison predicates like @code{eq}, @code{eql} and " "@code{equal}. Distinct floating-point and large integer objects can be " "numerically equal. If you use @code{eq} to compare them, you test whether " "they are the same @emph{object}; if you use @code{eql} or @code{equal}, you " "test whether their values are @emph{indistinguishable}. In contrast, " "@code{=} uses numeric comparison, and sometimes returns @code{t} when a " "non-numeric comparison would return @code{nil} and vice versa. @xref{Float " "Basics}." msgstr "" #. type: Plain text #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:422 msgid "" "In Emacs Lisp, if two fixnums are numerically equal, they are the same Lisp " "object. That is, @code{eq} is equivalent to @code{=} on fixnums. It is " "sometimes convenient to use @code{eq} for comparing an unknown value with a " "fixnum, because @code{eq} does not report an error if the unknown value is " "not a number---it accepts arguments of any type. By contrast, @code{=} " "signals an error if the arguments are not numbers or markers. However, it " "is better programming practice to use @code{=} if you can, even for " "comparing integers." msgstr "" #. type: Plain text #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:428 msgid "" "Sometimes it is useful to compare numbers with @code{eql} or @code{equal}, " "which treat two numbers as equal if they have the same data type (both " "integers, or both floating point) and the same value. By contrast, @code{=} " "can treat an integer and a floating-point number as equal. @xref{Equality " "Predicates}." msgstr "" #. type: Plain text #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:433 msgid "" "There is another wrinkle: because floating-point arithmetic is not exact, it " "is often a bad idea to check for equality of floating-point values. Usually " "it is better to test for approximate equality. Here's a function to do " "this:" msgstr "" #. type: example #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:441 #, no-wrap msgid "" "(defvar fuzz-factor 1.0e-6)\n" "(defun approx-equal (x y)\n" " (or (= x y)\n" " (< (/ (abs (- x y))\n" " (max (abs x) (abs y)))\n" " fuzz-factor)))\n" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:443 #, no-wrap msgid "= number-or-marker &rest number-or-markers" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:446 msgid "" "This function tests whether all its arguments are numerically equal, and " "returns @code{t} if so, @code{nil} otherwise." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:448 #, no-wrap msgid "eql value1 value2" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:458 msgid "" "This function acts like @code{eq} except when both arguments are numbers. " "It compares numbers by type and numeric value, so that @code{(eql 1.0 1)} " "returns @code{nil}, but @code{(eql 1.0 1.0)} and @code{(eql 1 1)} both " "return @code{t}. This can be used to compare large integers as well as " "small ones. Floating-point values with the same sign, exponent and fraction " "are @code{eql}. This differs from numeric comparison: @code{(eql 0.0 -0.0)} " "returns @code{nil} and @code{(eql 0.0e+NaN 0.0e+NaN)} returns @code{t}, " "whereas @code{=} does the opposite." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:460 #, no-wrap msgid "/= number-or-marker1 number-or-marker2" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:463 msgid "" "This function tests whether its arguments are numerically equal, and returns " "@code{t} if they are not, and @code{nil} if they are." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:465 #, no-wrap msgid "< number-or-marker &rest number-or-markers" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:468 msgid "" "This function tests whether each argument is strictly less than the " "following argument. It returns @code{t} if so, @code{nil} otherwise." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:470 #, no-wrap msgid "<= number-or-marker &rest number-or-markers" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:473 msgid "" "This function tests whether each argument is less than or equal to the " "following argument. It returns @code{t} if so, @code{nil} otherwise." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:475 #, no-wrap msgid "> number-or-marker &rest number-or-markers" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:478 msgid "" "This function tests whether each argument is strictly greater than the " "following argument. It returns @code{t} if so, @code{nil} otherwise." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:480 #, no-wrap msgid ">= number-or-marker &rest number-or-markers" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:483 msgid "" "This function tests whether each argument is greater than or equal to the " "following argument. It returns @code{t} if so, @code{nil} otherwise." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:485 #, no-wrap msgid "max number-or-marker &rest numbers-or-markers" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:487 msgid "This function returns the largest of its arguments." msgstr "" #. type: example #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:495 #, no-wrap msgid "" "(max 20)\n" " @result{} 20\n" "(max 1 2.5)\n" " @result{} 2.5\n" "(max 1 3 2.5)\n" " @result{} 3\n" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:498 #, no-wrap msgid "min number-or-marker &rest numbers-or-markers" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:500 msgid "This function returns the smallest of its arguments." msgstr "" #. type: example #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:504 #, no-wrap msgid "" "(min -4 1)\n" " @result{} -4\n" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:507 #, no-wrap msgid "abs number" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:509 msgid "This function returns the absolute value of @var{number}." msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:513 #, no-wrap msgid "rounding in conversions" msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:514 #, no-wrap msgid "number conversions" msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:515 #, no-wrap msgid "converting numbers" msgstr "" #. type: Plain text #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:518 msgid "To convert an integer to floating point, use the function @code{float}." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:519 #, no-wrap msgid "float number" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:523 msgid "" "This returns @var{number} converted to floating point. If @var{number} is " "already floating point, @code{float} returns it unchanged." msgstr "" #. type: Plain text #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:535 msgid "" "There are four functions to convert floating-point numbers to integers; they " "differ in how they round. All accept an argument @var{number} and an " "optional argument @var{divisor}. Both arguments may be integers or " "floating-point numbers. @var{divisor} may also be @code{nil}. If " "@var{divisor} is @code{nil} or omitted, these functions convert @var{number} " "to an integer, or return it unchanged if it already is an integer. If " "@var{divisor} is non-@code{nil}, they divide @var{number} by @var{divisor} " "and convert the result to an integer. If @var{divisor} is zero (whether " "integer or floating point), Emacs signals an @code{arith-error} error." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:536 #, no-wrap msgid "truncate number &optional divisor" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:539 msgid "This returns @var{number}, converted to an integer by rounding towards zero." msgstr "" #. type: example #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:549 #, no-wrap msgid "" "(truncate 1.2)\n" " @result{} 1\n" "(truncate 1.7)\n" " @result{} 1\n" "(truncate -1.2)\n" " @result{} -1\n" "(truncate -1.7)\n" " @result{} -1\n" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:552 #, no-wrap msgid "floor number &optional divisor" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:555 msgid "" "This returns @var{number}, converted to an integer by rounding downward " "(towards negative infinity)." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:558 msgid "" "If @var{divisor} is specified, this uses the kind of division operation that " "corresponds to @code{mod}, rounding downward." msgstr "" #. type: example #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:570 #, no-wrap msgid "" "(floor 1.2)\n" " @result{} 1\n" "(floor 1.7)\n" " @result{} 1\n" "(floor -1.2)\n" " @result{} -2\n" "(floor -1.7)\n" " @result{} -2\n" "(floor 5.99 3)\n" " @result{} 1\n" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:573 #, no-wrap msgid "ceiling number &optional divisor" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:576 msgid "" "This returns @var{number}, converted to an integer by rounding upward " "(towards positive infinity)." msgstr "" #. type: example #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:586 #, no-wrap msgid "" "(ceiling 1.2)\n" " @result{} 2\n" "(ceiling 1.7)\n" " @result{} 2\n" "(ceiling -1.2)\n" " @result{} -1\n" "(ceiling -1.7)\n" " @result{} -1\n" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:589 #, no-wrap msgid "round number &optional divisor" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:593 msgid "" "This returns @var{number}, converted to an integer by rounding towards the " "nearest integer. Rounding a value equidistant between two integers returns " "the even integer." msgstr "" #. type: example #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:603 #, no-wrap msgid "" "(round 1.2)\n" " @result{} 1\n" "(round 1.7)\n" " @result{} 2\n" "(round -1.2)\n" " @result{} -1\n" "(round -1.7)\n" " @result{} -2\n" msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:608 #, no-wrap msgid "arithmetic operations" msgstr "" #. type: Plain text #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:616 msgid "" "Emacs Lisp provides the traditional four arithmetic operations (addition, " "subtraction, multiplication, and division), as well as remainder and modulus " "functions, and functions to add or subtract 1. Except for @code{%}, each of " "these functions accepts both integer and floating-point arguments, and " "returns a floating-point number if any argument is floating point." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:617 #, no-wrap msgid "1+ number-or-marker" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:620 msgid "This function returns @var{number-or-marker} plus 1. For example," msgstr "" #. type: example #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:626 #, no-wrap msgid "" "(setq foo 4)\n" " @result{} 4\n" "(1+ foo)\n" " @result{} 5\n" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:630 msgid "" "This function is not analogous to the C operator @code{++}---it does not " "increment a variable. It just computes a sum. Thus, if we continue," msgstr "" #. type: example #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:634 #, no-wrap msgid "" "foo\n" " @result{} 4\n" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:638 msgid "If you want to increment the variable, you must use @code{setq}, like this:" msgstr "" #. type: example #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:642 #, no-wrap msgid "" "(setq foo (1+ foo))\n" " @result{} 5\n" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:645 #, no-wrap msgid "1- number-or-marker" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:647 msgid "This function returns @var{number-or-marker} minus 1." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:649 #, no-wrap msgid "+ &rest numbers-or-markers" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:652 msgid "" "This function adds its arguments together. When given no arguments, " "@code{+} returns 0." msgstr "" #. type: example #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:660 #, no-wrap msgid "" "(+)\n" " @result{} 0\n" "(+ 1)\n" " @result{} 1\n" "(+ 1 2 3 4)\n" " @result{} 10\n" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:663 #, no-wrap msgid "- &optional number-or-marker &rest more-numbers-or-markers" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:669 msgid "" "The @code{-} function serves two purposes: negation and subtraction. When " "@code{-} has a single argument, the value is the negative of the argument. " "When there are multiple arguments, @code{-} subtracts each of the " "@var{more-numbers-or-markers} from @var{number-or-marker}, cumulatively. If " "there are no arguments, the result is 0." msgstr "" #. type: example #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:677 #, no-wrap msgid "" "(- 10 1 2 3 4)\n" " @result{} 0\n" "(- 10)\n" " @result{} -10\n" "(-)\n" " @result{} 0\n" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:680 #, no-wrap msgid "* &rest numbers-or-markers" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:683 msgid "" "This function multiplies its arguments together, and returns the product. " "When given no arguments, @code{*} returns 1." msgstr "" #. type: example #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:691 #, no-wrap msgid "" "(*)\n" " @result{} 1\n" "(* 1)\n" " @result{} 1\n" "(* 1 2 3 4)\n" " @result{} 24\n" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:694 #, no-wrap msgid "/ number &rest divisors" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:700 msgid "" "With one or more @var{divisors}, this function divides @var{number} by each " "divisor in @var{divisors} in turn, and returns the quotient. With no " "@var{divisors}, this function returns 1/@var{number}, i.e., the " "multiplicative inverse of @var{number}. Each argument may be a number or a " "marker." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:703 msgid "" "If all the arguments are integers, the result is an integer, obtained by " "rounding the quotient towards zero after each division." msgstr "" #. type: group #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:708 #, no-wrap msgid "" "(/ 6 2)\n" " @result{} 3\n" msgstr "" #. type: group #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:712 #, no-wrap msgid "" "(/ 5 2)\n" " @result{} 2\n" msgstr "" #. type: group #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:716 #, no-wrap msgid "" "(/ 5.0 2)\n" " @result{} 2.5\n" msgstr "" #. type: group #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:720 #, no-wrap msgid "" "(/ 5 2.0)\n" " @result{} 2.5\n" msgstr "" #. type: group #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:724 #, no-wrap msgid "" "(/ 5.0 2.0)\n" " @result{} 2.5\n" msgstr "" #. type: group #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:728 #, no-wrap msgid "" "(/ 4.0)\n" " @result{} 0.25\n" msgstr "" #. type: group #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:732 #, no-wrap msgid "" "(/ 4)\n" " @result{} 0\n" msgstr "" #. type: group #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:736 #, no-wrap msgid "" "(/ 25 3 2)\n" " @result{} 4\n" msgstr "" #. type: group #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:740 #, no-wrap msgid "" "(/ -17 6)\n" " @result{} -2\n" msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:743 #, no-wrap msgid "@code{arith-error} in division" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:748 msgid "" "If you divide an integer by the integer 0, Emacs signals an " "@code{arith-error} error (@pxref{Errors}). Floating-point division of a " "nonzero number by zero yields either positive or negative infinity " "(@pxref{Float Basics})." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:750 #, no-wrap msgid "% dividend divisor" msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:751 #, no-wrap msgid "remainder" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:754 msgid "" "This function returns the integer remainder after division of @var{dividend} " "by @var{divisor}. The arguments must be integers or markers." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:756 msgid "For any two integers @var{dividend} and @var{divisor}," msgstr "" #. type: group #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:761 #, no-wrap msgid "" "(+ (% @var{dividend} @var{divisor})\n" " (* (/ @var{dividend} @var{divisor}) @var{divisor}))\n" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:766 msgid "always equals @var{dividend} if @var{divisor} is nonzero." msgstr "" #. type: example #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:776 #, no-wrap msgid "" "(% 9 4)\n" " @result{} 1\n" "(% -9 4)\n" " @result{} -1\n" "(% 9 -4)\n" " @result{} 1\n" "(% -9 -4)\n" " @result{} -1\n" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:779 #, no-wrap msgid "mod dividend divisor" msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:780 #, no-wrap msgid "modulus" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:785 msgid "" "This function returns the value of @var{dividend} modulo @var{divisor}; in " "other words, the remainder after division of @var{dividend} by " "@var{divisor}, but with the same sign as @var{divisor}. The arguments must " "be numbers or markers." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:789 msgid "" "Unlike @code{%}, @code{mod} permits floating-point arguments; it rounds the " "quotient downward (towards minus infinity) to an integer, and uses that " "quotient to compute the remainder." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:792 msgid "" "If @var{divisor} is zero, @code{mod} signals an @code{arith-error} error if " "both arguments are integers, and returns a NaN otherwise." msgstr "" #. type: group #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:797 #, no-wrap msgid "" "(mod 9 4)\n" " @result{} 1\n" msgstr "" #. type: group #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:801 #, no-wrap msgid "" "(mod -9 4)\n" " @result{} 3\n" msgstr "" #. type: group #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:805 #, no-wrap msgid "" "(mod 9 -4)\n" " @result{} -3\n" msgstr "" #. type: group #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:809 #, no-wrap msgid "" "(mod -9 -4)\n" " @result{} -1\n" msgstr "" #. type: group #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:813 #, no-wrap msgid "" "(mod 5.5 2.5)\n" " @result{} .5\n" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:817 msgid "For any two numbers @var{dividend} and @var{divisor}," msgstr "" #. type: group #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:822 #, no-wrap msgid "" "(+ (mod @var{dividend} @var{divisor})\n" " (* (floor @var{dividend} @var{divisor}) @var{divisor}))\n" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:830 msgid "" "always equals @var{dividend}, subject to rounding error if either argument " "is floating point and to an @code{arith-error} if @var{dividend} is an " "integer and @var{divisor} is 0. For @code{floor}, see @ref{Numeric " "Conversions}." msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:834 #, no-wrap msgid "rounding without conversion" msgstr "" #. type: Plain text #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:842 msgid "" "The functions @code{ffloor}, @code{fceiling}, @code{fround}, and " "@code{ftruncate} take a floating-point argument and return a floating-point " "result whose value is a nearby integer. @code{ffloor} returns the nearest " "integer below; @code{fceiling}, the nearest integer above; @code{ftruncate}, " "the nearest integer in the direction towards zero; @code{fround}, the " "nearest integer." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:843 #, no-wrap msgid "ffloor float" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:846 msgid "" "This function rounds @var{float} to the next lower integral value, and " "returns that value as a floating-point number." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:848 #, no-wrap msgid "fceiling float" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:851 msgid "" "This function rounds @var{float} to the next higher integral value, and " "returns that value as a floating-point number." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:853 #, no-wrap msgid "ftruncate float" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:856 msgid "" "This function rounds @var{float} towards zero to an integral value, and " "returns that value as a floating-point number." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:858 #, no-wrap msgid "fround float" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:862 msgid "" "This function rounds @var{float} to the nearest integral value, and returns " "that value as a floating-point number. Rounding a value equidistant between " "two integers returns the even integer." msgstr "" #. type: section #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:865 #, no-wrap msgid "Bitwise Operations on Integers" msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:866 #, no-wrap msgid "bitwise arithmetic" msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:867 #, no-wrap msgid "logical arithmetic" msgstr "" #. type: Plain text #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:876 msgid "" "In a computer, an integer is represented as a binary number, a sequence of " "@dfn{bits} (digits which are either zero or one). Conceptually the bit " "sequence is infinite on the left, with the most-significant bits being all " "zeros or all ones. A bitwise operation acts on the individual bits of such " "a sequence. For example, @dfn{shifting} moves the whole sequence left or " "right one or more places, reproducing the same pattern moved over." msgstr "" #. type: Plain text #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:878 msgid "The bitwise operations in Emacs Lisp apply only to integers." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:879 #, no-wrap msgid "ash integer1 count" msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:880 #, no-wrap msgid "arithmetic shift" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:886 msgid "" "@code{ash} (@dfn{arithmetic shift}) shifts the bits in @var{integer1} to the " "left @var{count} places, or to the right if @var{count} is negative. Left " "shifts introduce zero bits on the right; right shifts discard the rightmost " "bits. Considered as an integer operation, @code{ash} multiplies " "@var{integer1} by" msgstr "" #. type: ifnottex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:888 msgid "2**@var{count}," msgstr "" #. type: tex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:891 #, no-wrap msgid "@math{2^{count}},\n" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:894 msgid "" "and then converts the result to an integer by rounding downward, toward " "minus infinity." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:901 msgid "" "Here are examples of @code{ash}, shifting a pattern of bits one place to the " "left and to the right. These examples show only the low-order bits of the " "binary pattern; leading bits all agree with the highest-order bit shown. As " "you can see, shifting left by one is equivalent to multiplying by two, " "whereas shifting right by one is equivalent to dividing by two and then " "rounding toward minus infinity." msgstr "" #. type: group #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:909 #, no-wrap msgid "" "(ash 7 1) @result{} 14\n" ";; @r{Decimal 7 becomes decimal 14.}\n" "@dots{}000111\n" " @result{}\n" "@dots{}001110\n" msgstr "" #. type: group #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:916 #, no-wrap msgid "" "(ash 7 -1) @result{} 3\n" "@dots{}000111\n" " @result{}\n" "@dots{}000011\n" msgstr "" #. type: group #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:923 #, no-wrap msgid "" "(ash -7 1) @result{} -14\n" "@dots{}111001\n" " @result{}\n" "@dots{}110010\n" msgstr "" #. type: group #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:930 #, no-wrap msgid "" "(ash -7 -1) @result{} -4\n" "@dots{}111001\n" " @result{}\n" "@dots{}111100\n" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:934 msgid "Here are examples of shifting left or right by two bits:" msgstr "" #. type: group #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:942 #, no-wrap msgid "" " ; @r{ binary values}\n" "(ash 5 2) ; 5 = @r{@dots{}000101}\n" " @result{} 20 ; = @r{@dots{}010100}\n" "(ash -5 2) ; -5 = @r{@dots{}111011}\n" " @result{} -20 ; = @r{@dots{}101100}\n" msgstr "" #. type: group #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:946 #, no-wrap msgid "" "(ash 5 -2)\n" " @result{} 1 ; = @r{@dots{}000001}\n" msgstr "" #. type: group #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:950 #, no-wrap msgid "" "(ash -5 -2)\n" " @result{} -2 ; = @r{@dots{}111110}\n" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:954 #, no-wrap msgid "lsh integer1 count" msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:955 #, no-wrap msgid "logical shift" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:965 msgid "" "@code{lsh}, which is an abbreviation for @dfn{logical shift}, shifts the " "bits in @var{integer1} to the left @var{count} places, or to the right if " "@var{count} is negative, bringing zeros into the vacated bits. If " "@var{count} is negative, then @var{integer1} must be either a fixnum or a " "positive bignum, and @code{lsh} treats a negative fixnum as if it were " "unsigned by subtracting twice @code{most-negative-fixnum} before shifting, " "producing a nonnegative result. This quirky behavior dates back to when " "Emacs supported only fixnums; nowadays @code{ash} is a better choice." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:969 msgid "" "As @code{lsh} behaves like @code{ash} except when @var{integer1} and " "@var{count1} are both negative, the following examples focus on these " "exceptional cases. These examples assume 30-bit fixnums." msgstr "" #. type: group #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:977 #, no-wrap msgid "" " ; @r{ binary values}\n" "(ash -7 -1) ; -7 = @r{@dots{}111111111111111111111111111001}\n" " @result{} -4 ; = @r{@dots{}111111111111111111111111111100}\n" "(lsh -7 -1)\n" " @result{} 536870908 ; = @r{@dots{}011111111111111111111111111100}\n" msgstr "" #. type: group #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:983 #, no-wrap msgid "" "(ash -5 -2) ; -5 = @r{@dots{}111111111111111111111111111011}\n" " @result{} -2 ; = @r{@dots{}111111111111111111111111111110}\n" "(lsh -5 -2)\n" " @result{} 268435454 ; = @r{@dots{}001111111111111111111111111110}\n" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:987 #, no-wrap msgid "logand &rest ints-or-markers" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:991 msgid "" "This function returns the bitwise AND of the arguments: the @var{n}th bit is " "1 in the result if, and only if, the @var{n}th bit is 1 in all the " "arguments." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:998 msgid "" "For example, using 4-bit binary numbers, the bitwise AND of 13 and 12 is 12: " "1101 combined with 1100 produces 1100. In both the binary numbers, the " "leftmost two bits are both 1 so the leftmost two bits of the returned value " "are both 1. However, for the rightmost two bits, each is 0 in at least one " "of the arguments, so the rightmost two bits of the returned value are both " "0." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1001 msgid "Therefore," msgstr "" #. type: group #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1006 #, no-wrap msgid "" "(logand 13 12)\n" " @result{} 12\n" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1013 msgid "" "If @code{logand} is not passed any argument, it returns a value of " "@minus{}1. This number is an identity element for @code{logand} because its " "binary representation consists entirely of ones. If @code{logand} is passed " "just one argument, it returns that argument." msgstr "" #. type: group #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1017 #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1047 #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1072 #, no-wrap msgid "" " ; @r{ binary values}\n" "\n" msgstr "" #. type: group #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1021 #, no-wrap msgid "" "(logand 14 13) ; 14 = @r{@dots{}001110}\n" " ; 13 = @r{@dots{}001101}\n" " @result{} 12 ; 12 = @r{@dots{}001100}\n" msgstr "" #. type: group #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1028 #, no-wrap msgid "" "(logand 14 13 4) ; 14 = @r{@dots{}001110}\n" " ; 13 = @r{@dots{}001101}\n" " ; 4 = @r{@dots{}000100}\n" " @result{} 4 ; 4 = @r{@dots{}000100}\n" msgstr "" #. type: group #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1033 #, no-wrap msgid "" "(logand)\n" " @result{} -1 ; -1 = @r{@dots{}111111}\n" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1037 #, no-wrap msgid "logior &rest ints-or-markers" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1043 msgid "" "This function returns the bitwise inclusive OR of its arguments: the " "@var{n}th bit is 1 in the result if, and only if, the @var{n}th bit is 1 in " "at least one of the arguments. If there are no arguments, the result is 0, " "which is an identity element for this operation. If @code{logior} is passed " "just one argument, it returns that argument." msgstr "" #. type: group #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1051 #, no-wrap msgid "" "(logior 12 5) ; 12 = @r{@dots{}001100}\n" " ; 5 = @r{@dots{}000101}\n" " @result{} 13 ; 13 = @r{@dots{}001101}\n" msgstr "" #. type: group #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1058 #, no-wrap msgid "" "(logior 12 5 7) ; 12 = @r{@dots{}001100}\n" " ; 5 = @r{@dots{}000101}\n" " ; 7 = @r{@dots{}000111}\n" " @result{} 15 ; 15 = @r{@dots{}001111}\n" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1062 #, no-wrap msgid "logxor &rest ints-or-markers" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1068 msgid "" "This function returns the bitwise exclusive OR of its arguments: the " "@var{n}th bit is 1 in the result if, and only if, the @var{n}th bit is 1 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 @code{logxor} is passed " "just one argument, it returns that argument." msgstr "" #. type: group #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1076 #, no-wrap msgid "" "(logxor 12 5) ; 12 = @r{@dots{}001100}\n" " ; 5 = @r{@dots{}000101}\n" " @result{} 9 ; 9 = @r{@dots{}001001}\n" msgstr "" #. type: group #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1083 #, no-wrap msgid "" "(logxor 12 5 7) ; 12 = @r{@dots{}001100}\n" " ; 5 = @r{@dots{}000101}\n" " ; 7 = @r{@dots{}000111}\n" " @result{} 14 ; 14 = @r{@dots{}001110}\n" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1087 #, no-wrap msgid "lognot integer" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1092 msgid "" "This function returns the bitwise complement of its argument: the @var{n}th " "bit is one in the result if, and only if, the @var{n}th bit is zero in " "@var{integer}, and vice-versa. The result equals @minus{}1 @minus{} " "@var{integer}." msgstr "" #. type: example #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1099 #, no-wrap msgid "" "(lognot 5)\n" " @result{} -6\n" ";; 5 = @r{@dots{}000101}\n" ";; @r{becomes}\n" ";; -6 = @r{@dots{}111010}\n" msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1102 #, no-wrap msgid "popcount" msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1103 #, no-wrap msgid "Hamming weight" msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1104 #, no-wrap msgid "counting set bits" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1105 #, no-wrap msgid "logcount integer" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1111 msgid "" "This function returns the @dfn{Hamming weight} of @var{integer}: the number " "of ones in the binary representation of @var{integer}. If @var{integer} is " "negative, it returns the number of zero bits in its two's complement binary " "representation. The result is always nonnegative." msgstr "" #. type: example #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1117 #, no-wrap msgid "" "(logcount 43) ; 43 = @r{@dots{}000101011}\n" " @result{} 4\n" "(logcount -43) ; -43 = @r{@dots{}111010101}\n" " @result{} 3\n" msgstr "" #. type: section #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1121 #, no-wrap msgid "Standard Mathematical Functions" msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1122 #, no-wrap msgid "transcendental functions" msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1123 #, no-wrap msgid "mathematical functions" msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1124 #, no-wrap msgid "floating-point functions" msgstr "" #. type: Plain text #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1128 msgid "" "These mathematical functions allow integers as well as floating-point " "numbers as arguments." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1129 #, no-wrap msgid "sin arg" msgstr "" #. type: defunx #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1130 #, no-wrap msgid "cos arg" msgstr "" #. type: defunx #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1131 #, no-wrap msgid "tan arg" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1134 msgid "" "These are the basic trigonometric functions, with argument @var{arg} " "measured in radians." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1136 #, no-wrap msgid "asin arg" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1138 msgid "The value of @code{(asin @var{arg})} is a number between" msgstr "" #. type: ifnottex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1140 #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1171 msgid "@minus{}pi/2" msgstr "" #. type: tex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1143 #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1174 #, no-wrap msgid "@math{-\\pi/2}\n" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1145 #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1176 msgid "and" msgstr "" #. type: ifnottex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1147 #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1178 msgid "pi/2" msgstr "" #. type: tex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1150 #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1181 #, no-wrap msgid "@math{\\pi/2}\n" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1153 msgid "" "(inclusive) whose sine is @var{arg}. If @var{arg} is out of range (outside " "[@minus{}1, 1]), @code{asin} returns a NaN." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1155 #, no-wrap msgid "acos arg" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1157 msgid "The value of @code{(acos @var{arg})} is a number between 0 and" msgstr "" #. type: ifnottex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1159 msgid "pi" msgstr "" #. type: tex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1162 #, no-wrap msgid "@math{\\pi}\n" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1165 msgid "" "(inclusive) whose cosine is @var{arg}. If @var{arg} is out of range " "(outside [@minus{}1, 1]), @code{acos} returns a NaN." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1167 #, no-wrap msgid "atan y &optional x" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1169 msgid "The value of @code{(atan @var{y})} is a number between" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1186 msgid "" "(exclusive) whose tangent is @var{y}. If the optional second argument " "@var{x} is given, the value of @code{(atan y x)} is the angle in radians " "between the vector @code{[@var{x}, @var{y}]} and the @code{X} axis." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1188 #, no-wrap msgid "exp arg" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1191 msgid "" "This is the exponential function; it returns @math{e} to the power " "@var{arg}." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1193 #, no-wrap msgid "log arg &optional base" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1198 msgid "" "This function returns the logarithm of @var{arg}, with base @var{base}. If " "you don't specify @var{base}, the natural base @math{e} is used. If " "@var{arg} or @var{base} is negative, @code{log} returns a NaN." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1200 #, no-wrap msgid "expt x y" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1206 msgid "" "This function returns @var{x} raised to power @var{y}. If both arguments " "are integers and @var{y} is nonnegative, the result is an integer; in this " "case, overflow signals an error, so watch out. If @var{x} is a finite " "negative number and @var{y} is a finite non-integer, @code{expt} returns a " "NaN." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1208 #, no-wrap msgid "sqrt arg" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1211 msgid "" "This returns the square root of @var{arg}. If @var{arg} is finite and less " "than zero, @code{sqrt} returns a NaN." msgstr "" #. type: Plain text #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1215 msgid "In addition, Emacs defines the following common mathematical constants:" msgstr "" #. type: defvar #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1216 #, no-wrap msgid "float-e" msgstr "" #. type: defvar #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1218 msgid "The mathematical constant @math{e} (2.71828@dots{})." msgstr "" #. type: defvar #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1220 #, no-wrap msgid "float-pi" msgstr "" #. type: defvar #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1222 msgid "The mathematical constant @math{pi} (3.14159@dots{})." msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1226 #, no-wrap msgid "random numbers" msgstr "" #. type: Plain text #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1234 msgid "" "A deterministic computer program cannot generate true random numbers. For " "most purposes, @dfn{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." msgstr "" #. type: cindex #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1235 #, no-wrap msgid "seed, for random number generation" msgstr "" #. type: Plain text #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1241 msgid "" "Pseudo-random numbers are generated from a @dfn{seed value}. Starting from " "any given seed, the @code{random} function always generates the same " "sequence of numbers. By default, Emacs initializes the random seed at " "startup, in such a way that the sequence of values of @code{random} (with " "overwhelming likelihood) differs in each Emacs run." msgstr "" #. type: Plain text #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1249 msgid "" "Sometimes you want the random number sequence to be repeatable. For " "example, when debugging a program whose behavior depends on the random " "number sequence, it is helpful to get the same behavior in each program " "run. To make the sequence repeat, execute @code{(random \"\")}. This sets " "the seed to a constant value for your particular Emacs executable (though it " "may differ for other Emacs builds). You can use other strings to choose " "various seed values." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1250 #, no-wrap msgid "random &optional limit" msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1253 msgid "" "This function returns a pseudo-random integer. Repeated calls return a " "series of pseudo-random integers." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1258 msgid "" "If @var{limit} is a positive integer, the value is chosen to be nonnegative " "and less than @var{limit}. Otherwise, the value might be any fixnum, i.e., " "any integer from @code{most-negative-fixnum} through " "@code{most-positive-fixnum} (@pxref{Integer Basics})." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1263 msgid "" "If @var{limit} is @code{t}, it means to choose a new seed as if Emacs were " "restarting, typically from the system entropy. On systems lacking entropy " "pools, choose the seed from less-random volatile data such as the current " "time." msgstr "" #. type: defun #: /Users/suzume/Documents/Repositories/Projet OmegaT de Documentation Emacs - #: Sources/doc/lispref/numbers.texi:1266 msgid "" "If @var{limit} is a string, it means to choose a new seed based on the " "string's contents." msgstr ""