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Diffstat (limited to 'doc/gawk.info')
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1 files changed, 213 insertions, 218 deletions
diff --git a/doc/gawk.info b/doc/gawk.info index 21e8fd3b..a8e11ab9 100644 --- a/doc/gawk.info +++ b/doc/gawk.info @@ -21813,7 +21813,7 @@ Decimal arithmetic sides) of the decimal point, and the results of a computation are always exact. - Some modern system can do decimal arithmetic in hardware, but + Some modern systems can do decimal arithmetic in hardware, but usually you need a special software library to provide access to these instructions. There are also libraries that do decimal arithmetic entirely in software. @@ -21867,12 +21867,6 @@ Numeric representation Minimum value Maximum value 32-bit unsigned integer 0 4,294,967,295 64-bit signed integer -9,223,372,036,854,775,8089,223,372,036,854,775,807 64-bit unsigned integer 0 18,446,744,073,709,551,615 -Single-precision `1.175494e-38' `3.402823e+38' -floating point -(approximate) -Double-precision `2.225074e-308' `1.797693e+308' -floating point -(approximate) Table 15.1: Value ranges for different numeric representations @@ -21888,7 +21882,7 @@ File: gawk.info, Node: Math Definitions, Next: MPFR features, Prev: Computer The rest of this major node uses a number of terms. Here are some informal definitions that should help you work your way through the -material here. +material here: "Accuracy" A floating-point calculation's accuracy is how close it comes to @@ -21908,7 +21902,7 @@ material here. number and infinity produce infinity. "NaN" - "Not A Number."(1) A special value that results from attempting a + "Not a number."(1) A special value that results from attempting a calculation that has no answer as a real number. In such a case, programs can either receive a floating-point exception, or get `NaN' back as the result. The IEEE 754 standard recommends that @@ -21934,15 +21928,15 @@ material here. PREC = 3.322 * DPS - Here, PREC denotes the binary precision (measured in bits) and DPS - (short for decimal places) is the decimal digits. + Here, _prec_ denotes the binary precision (measured in bits) and + _dps_ (short for decimal places) is the decimal digits. "Rounding mode" How numbers are rounded up or down when necessary. More details are provided later. "Significand" - A floating-point value consists the significand multiplied by 10 + A floating-point value consists of the significand multiplied by 10 to the power of the exponent. For example, in `1.2345e67', the significand is `1.2345'. @@ -21964,7 +21958,7 @@ precision formats to allow greater precisions and larger exponent ranges. (`awk' uses only the 64-bit double-precision format.) *note table-ieee-formats:: lists the precision and exponent field -values for the basic IEEE 754 binary formats: +values for the basic IEEE 754 binary formats. Name Total bits Precision Minimum Maximum exponent exponent @@ -22029,7 +22023,7 @@ File: gawk.info, Node: FP Math Caution, Next: Arbitrary Precision Integers, P Math class is tough! -- Teen Talk Barbie, July 1992 - This minor node provides a high level overview of the issues + This minor node provides a high-level overview of the issues involved when doing lots of floating-point arithmetic.(1) The discussion applies to both hardware and arbitrary-precision floating-point arithmetic. @@ -22050,8 +22044,8 @@ floating-point arithmetic. (1) There is a very nice paper on floating-point arithmetic (http://www.validlab.com/goldberg/paper.pdf) by David Goldberg, "What -Every Computer Scientist Should Know About Floating-point Arithmetic," -`ACM Computing Surveys' *23*, 1 (1991-03), 5-48. This is worth reading +Every Computer Scientist Should Know About Floating-Point Arithmetic," +`ACM Computing Surveys' *23*, 1 (1991-03): 5-48. This is worth reading if you are interested in the details, but it does require a background in computer science. @@ -22105,7 +22099,7 @@ number as you assigned to it: Often the error is so small you do not even notice it, and if you do, you can always specify how much precision you would like in your output. -Usually this is a format string like `"%.15g"', which when used in the +Usually this is a format string like `"%.15g"', which, when used in the previous example, produces an output identical to the input. @@ -22145,7 +22139,7 @@ File: gawk.info, Node: Errors accumulate, Prev: Comparing FP Values, Up: Inex The loss of accuracy during a single computation with floating-point numbers usually isn't enough to worry about. However, if you compute a -value which is the result of a sequence of floating-point operations, +value that is the result of a sequence of floating-point operations, the error can accumulate and greatly affect the computation itself. Here is an attempt to compute the value of pi using one of its many series representations: @@ -22196,7 +22190,7 @@ easy answers. The standard rules of algebra often do not apply when using floating-point arithmetic. Among other things, the distributive and associative laws do not hold completely, and order of operation may be important for your computation. Rounding error, cumulative precision -loss and underflow are often troublesome. +loss, and underflow are often troublesome. When `gawk' tests the expressions `0.1 + 12.2' and `12.3' for equality using the machine double-precision arithmetic, it decides that @@ -22231,8 +22225,9 @@ illustrated by our earlier attempt to compute the value of pi. Extra precision can greatly enhance the stability and the accuracy of your computation in such cases. - Repeated addition is not necessarily equivalent to multiplication in -floating-point arithmetic. In the example in *note Errors accumulate::: + Additionally, you should understand that repeated addition is not +necessarily equivalent to multiplication in floating-point arithmetic. +In the example in *note Errors accumulate::: $ gawk 'BEGIN { > for (d = 1.1; d <= 1.5; d += 0.1) # loop five times (?) @@ -22287,7 +22282,7 @@ set the value to one of the predefined case-insensitive strings shown in *note table-predefined-precision-strings::, to emulate an IEEE 754 binary format. -`PREC' IEEE 754 Binary Format +`PREC' IEEE 754 binary format --------------------------------------------------- `"half"' 16-bit half-precision `"single"' Basic 32-bit single precision @@ -22320,14 +22315,14 @@ on arithmetic operations: example illustrates the differences among various ways to print a floating-point constant: - $ gawk -M 'BEGIN { PREC = 113; printf("%0.25f\n", 0.1) }' - -| 0.1000000000000000055511151 - $ gawk -M -v PREC=113 'BEGIN { printf("%0.25f\n", 0.1) }' - -| 0.1000000000000000000000000 - $ gawk -M 'BEGIN { PREC = 113; printf("%0.25f\n", "0.1") }' - -| 0.1000000000000000000000000 - $ gawk -M 'BEGIN { PREC = 113; printf("%0.25f\n", 1/10) }' - -| 0.1000000000000000000000000 + $ gawk -M 'BEGIN { PREC = 113; printf("%0.25f\n", 0.1) }' + -| 0.1000000000000000055511151 + $ gawk -M -v PREC=113 'BEGIN { printf("%0.25f\n", 0.1) }' + -| 0.1000000000000000000000000 + $ gawk -M 'BEGIN { PREC = 113; printf("%0.25f\n", "0.1") }' + -| 0.1000000000000000000000000 + $ gawk -M 'BEGIN { PREC = 113; printf("%0.25f\n", 1/10) }' + -| 0.1000000000000000000000000 File: gawk.info, Node: Setting the rounding mode, Prev: Setting precision, Up: FP Math Caution @@ -22335,15 +22330,15 @@ File: gawk.info, Node: Setting the rounding mode, Prev: Setting precision, Up 15.4.5 Setting the Rounding Mode -------------------------------- -The `ROUNDMODE' variable provides program level control over the +The `ROUNDMODE' variable provides program-level control over the rounding mode. The correspondence between `ROUNDMODE' and the IEEE rounding modes is shown in *note table-gawk-rounding-modes::. -Rounding Mode IEEE Name `ROUNDMODE' +Rounding mode IEEE name `ROUNDMODE' --------------------------------------------------------------------------- Round to nearest, ties to even `roundTiesToEven' `"N"' or `"n"' -Round toward plus Infinity `roundTowardPositive' `"U"' or `"u"' -Round toward negative Infinity `roundTowardNegative' `"D"' or `"d"' +Round toward positive infinity `roundTowardPositive' `"U"' or `"u"' +Round toward negative infinity `roundTowardNegative' `"D"' or `"d"' Round toward zero `roundTowardZero' `"Z"' or `"z"' Round to nearest, ties away `roundTiesToAway' `"A"' or `"a"' from zero @@ -22394,8 +22389,8 @@ distributes upward and downward rounds of exact halves, which might cause any accumulating round-off error to cancel itself out. This is the default rounding mode for IEEE 754 computing functions and operators. - The other rounding modes are rarely used. Round toward positive -infinity (`roundTowardPositive') and round toward negative infinity + The other rounding modes are rarely used. Rounding toward positive +infinity (`roundTowardPositive') and toward negative infinity (`roundTowardNegative') are often used to implement interval arithmetic, where you adjust the rounding mode to calculate upper and lower bounds for the range of output. The `roundTowardZero' mode can be @@ -22443,7 +22438,7 @@ floating-point values: If instead you were to compute the same value using arbitrary-precision floating-point values, the precision needed for -correct output (using the formula `prec = 3.322 * dps'), would be 3.322 +correct output (using the formula `prec = 3.322 * dps') would be 3.322 x 183231, or 608693. The result from an arithmetic operation with an integer and a @@ -22474,7 +22469,7 @@ interface to process arbitrary-precision integers or mixed-mode numbers as needed by an operation or function. In such a case, the precision is set to the minimum value necessary for exact conversion, and the working precision is not used for this purpose. If this is not what you need or -want, you can employ a subterfuge, and convert the integer to floating +want, you can employ a subterfuge and convert the integer to floating point first, like this: gawk -M 'BEGIN { n = 13; print (n + 0.0) % 2.0 }' @@ -22557,7 +22552,7 @@ File: gawk.info, Node: POSIX Floating Point Problems, Next: Floating point sum 15.6 Standards Versus Existing Practice ======================================= -Historically, `awk' has converted any non-numeric looking string to the +Historically, `awk' has converted any nonnumeric-looking string to the numeric value zero, when required. Furthermore, the original definition of the language and the original POSIX standards specified that `awk' only understands decimal numbers (base 10), and not octal @@ -22571,8 +22566,8 @@ These features are: hexadecimal notation (e.g., `0xDEADBEEF'). (Note: data values, _not_ source code constants.) - * Support for the special IEEE 754 floating-point values "Not A - Number" (NaN), positive Infinity ("inf"), and negative Infinity + * Support for the special IEEE 754 floating-point values "not a + number" (NaN), positive infinity ("inf"), and negative infinity ("-inf"). In particular, the format for these values is as specified by the ISO 1999 C standard, which ignores case and can allow implementation-dependent additional characters after the @@ -22589,21 +22584,21 @@ historical practice: values is also a very severe departure from historical practice. The second problem is that the `gawk' maintainer feels that this -interpretation of the standard, which requires a certain amount of +interpretation of the standard, which required a certain amount of "language lawyering" to arrive at in the first place, was not even -intended by the standard developers. In other words, "we see how you +intended by the standard developers. In other words, "We see how you got where you are, but we don't think that that's where you want to be." Recognizing these issues, but attempting to provide compatibility with the earlier versions of the standard, the 2008 POSIX standard added explicit wording to allow, but not require, that `awk' support -hexadecimal floating-point values and special values for "Not A Number" +hexadecimal floating-point values and special values for "not a number" and infinity. Although the `gawk' maintainer continues to feel that providing those features is inadvisable, nevertheless, on systems that support IEEE floating point, it seems reasonable to provide _some_ way to -support NaN and Infinity values. The solution implemented in `gawk' is +support NaN and infinity values. The solution implemented in `gawk' is as follows: * With the `--posix' command-line option, `gawk' becomes "hands @@ -22618,7 +22613,7 @@ as follows: $ echo 0xDeadBeef | gawk --posix '{ print $1 + 0 }' -| 3735928559 - * Without `--posix', `gawk' interprets the four strings `+inf', + * Without `--posix', `gawk' interprets the four string values `+inf', `-inf', `+nan', and `-nan' specially, producing the corresponding special numeric values. The leading sign acts a signal to `gawk' (and the user) that the value is really numeric. Hexadecimal @@ -22632,7 +22627,7 @@ as follows: $ echo 0xDeadBeef | gawk '{ print $1 + 0 }' -| 0 - `gawk' ignores case in the four special values. Thus `+nan' and + `gawk' ignores case in the four special values. Thus, `+nan' and `+NaN' are the same. ---------- Footnotes ---------- @@ -22649,9 +22644,9 @@ File: gawk.info, Node: Floating point summary, Prev: POSIX Floating Point Prob floating-point values. Standard `awk' uses double-precision floating-point values. - * In the early 1990s, Barbie mistakenly said "Math class is tough!" + * In the early 1990s Barbie mistakenly said, "Math class is tough!" Although math isn't tough, floating-point arithmetic isn't the same - as pencil and paper math, and care must be taken: + as pencil-and-paper math, and care must be taken: - Not all numbers can be represented exactly. @@ -22672,7 +22667,7 @@ File: gawk.info, Node: Floating point summary, Prev: POSIX Floating Point Prob rounding mode. * With `-M', `gawk' performs arbitrary-precision integer arithmetic - using the GMP library. This is faster and more space efficient + using the GMP library. This is faster and more space-efficient than using MPFR for the same calculations. * There are several "dark corners" with respect to floating-point @@ -22683,7 +22678,7 @@ File: gawk.info, Node: Floating point summary, Prev: POSIX Floating Point Prob results from floating-point arithmetic. The lesson to remember is that floating-point arithmetic is always more complex than arithmetic using pencil and paper. In order to take advantage of - the power of computer floating point, you need to know its + the power of floating-point arithmetic, you need to know its limitations and work within them. For most casual use of floating-point arithmetic, you will often get the expected result if you simply round the display of your final results to the @@ -35044,172 +35039,172 @@ Node: Limitations874675 Node: Debugging Summary876790 Node: Arbitrary Precision Arithmetic877964 Node: Computer Arithmetic879380 -Ref: table-numeric-ranges882978 -Ref: Computer Arithmetic-Footnote-1883837 -Node: Math Definitions883894 -Ref: table-ieee-formats887182 -Ref: Math Definitions-Footnote-1887786 -Node: MPFR features887891 -Node: FP Math Caution889562 -Ref: FP Math Caution-Footnote-1890612 -Node: Inexactness of computations890981 -Node: Inexact representation891940 -Node: Comparing FP Values893297 -Node: Errors accumulate894379 -Node: Getting Accuracy895812 -Node: Try To Round898474 -Node: Setting precision899373 -Ref: table-predefined-precision-strings900057 -Node: Setting the rounding mode901846 -Ref: table-gawk-rounding-modes902210 -Ref: Setting the rounding mode-Footnote-1905665 -Node: Arbitrary Precision Integers905844 -Ref: Arbitrary Precision Integers-Footnote-1910744 -Node: POSIX Floating Point Problems910893 -Ref: POSIX Floating Point Problems-Footnote-1914766 -Node: Floating point summary914804 -Node: Dynamic Extensions916998 -Node: Extension Intro918550 -Node: Plugin License919816 -Node: Extension Mechanism Outline920613 -Ref: figure-load-extension921041 -Ref: figure-register-new-function922521 -Ref: figure-call-new-function923525 -Node: Extension API Description925511 -Node: Extension API Functions Introduction926961 -Node: General Data Types931785 -Ref: General Data Types-Footnote-1937524 -Node: Memory Allocation Functions937823 -Ref: Memory Allocation Functions-Footnote-1940662 -Node: Constructor Functions940758 -Node: Registration Functions942492 -Node: Extension Functions943177 -Node: Exit Callback Functions945474 -Node: Extension Version String946722 -Node: Input Parsers947387 -Node: Output Wrappers957266 -Node: Two-way processors961781 -Node: Printing 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Extracting1097444 +Node: Distribution contents1099079 +Node: Unix Installation1105144 +Node: Quick Installation1105827 +Node: Shell Startup Files1108238 +Node: Additional Configuration Options1109317 +Node: Configuration Philosophy1111056 +Node: Non-Unix Installation1113425 +Node: PC Installation1113883 +Node: PC Binary Installation1115202 +Node: PC Compiling1117050 +Ref: PC Compiling-Footnote-11120071 +Node: PC Testing1120180 +Node: PC Using1121356 +Node: Cygwin1125471 +Node: MSYS1126294 +Node: VMS Installation1126794 +Node: VMS Compilation1127586 +Ref: VMS Compilation-Footnote-11128808 +Node: VMS Dynamic Extensions1128866 +Node: VMS Installation Details1130550 +Node: VMS Running1132802 +Node: VMS GNV1135638 +Node: VMS Old Gawk1136372 +Node: Bugs1136842 +Node: Other Versions1140725 +Node: Installation summary1147149 +Node: Notes1148205 +Node: Compatibility Mode1149070 +Node: Additions1149852 +Node: Accessing The Source1150777 +Node: Adding Code1152212 +Node: New Ports1158369 +Node: 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