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[SCM] gawk branch, feature/cmp_scalars, updated. gawk-4.1.0-4169-g658ce0
|
From: |
Arnold Robbins |
|
Subject: |
[SCM] gawk branch, feature/cmp_scalars, updated. gawk-4.1.0-4169-g658ce05 |
|
Date: |
Wed, 4 Nov 2020 14:06:03 -0500 (EST) |
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The branch, feature/cmp_scalars has been updated
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- Log -----------------------------------------------------------------
http://git.sv.gnu.org/cgit/gawk.git/commit/?id=658ce05d5381f1d428971586d03b75e5343c3df3
commit 658ce05d5381f1d428971586d03b75e5343c3df3
Author: Arnold D. Robbins <arnold@skeeve.com>
Date: Wed Nov 4 21:05:41 2020 +0200
Revise doc on numeric values (inf, nan, etc.).
diff --git a/doc/ChangeLog b/doc/ChangeLog
index f2afd29..13b6cdf 100644
--- a/doc/ChangeLog
+++ b/doc/ChangeLog
@@ -1,3 +1,9 @@
+2020-11-04 Arnold D. Robbins <arnold@skeeve.com>
+
+ * gawktexi.in (Strange values): New section on NaN and infinity.
+ Update some other bits to point to it.
+ * wordlist: Updated with more words.
+
2020-10-31 Arnold D. Robbins <arnold@skeeve.com>
* texinfo.tex: Updated from GNULIB.
diff --git a/doc/gawk.info b/doc/gawk.info
index 03c3a88..244bbd8 100644
--- a/doc/gawk.info
+++ b/doc/gawk.info
@@ -546,6 +546,7 @@ in (a) below. A copy of the license is included in the
section entitled
* Inexact representation:: Numbers are not exactly represented.
* Comparing FP Values:: How to compare floating point values.
* Errors accumulate:: Errors get bigger as they go.
+* Strange values:: A few words about infinities and NaNs.
* Getting Accuracy:: Getting more accuracy takes some work.
* Try To Round:: Add digits and round.
* Setting precision:: How to set the precision.
@@ -6926,8 +6927,8 @@ width. Here is a list of the format-control letters:
On systems supporting IEEE 754 floating-point format, values
representing negative infinity are formatted as '-inf' or
'-infinity', and positive infinity as 'inf' or 'infinity'. The
- special "not a number" value formats as '-nan' or 'nan' (*note Math
- Definitions::).
+ special "not a number" value formats as '-nan' or 'nan' (*note
+ Strange values::).
'%F'
Like '%f', but the infinity and "not a number" values are spelled
@@ -12819,7 +12820,7 @@ brackets ([ ]):
'log(X)'
Return the natural logarithm of X, if X is positive; otherwise,
- return 'NaN' ("not a number") on IEEE 754 systems. Additionally,
+ return NaN ("not a number") on IEEE 754 systems. Additionally,
'gawk' prints a warning message when 'x' is negative.
'rand()'
@@ -24153,18 +24154,10 @@ material here:
another number and infinity produce infinity.
"NaN"
- "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
- systems return 'NaN'. Some examples:
-
- 'sqrt(-1)'
- This makes sense in the range of complex numbers, but not in
- the range of real numbers, so the result is 'NaN'.
-
- 'log(-8)'
- -8 is out of the domain of 'log()', so the result is 'NaN'.
+ "Not a number." A special value that results from attempting a
+ calculation that has no answer as a real number. *Note Strange
+ values::, for more information about infinity and not-a-number
+ values.
"Normalized"
How the significand (see later in this list) is usually stored.
@@ -24223,11 +24216,6 @@ Table 16.3: Basic IEEE format values
NOTE: The precision numbers include the implied leading one that
gives them one extra bit of significand.
- ---------- Footnotes ----------
-
- (1) Thanks to Michael Brennan for this description, which we have
-paraphrased, and for the examples.
-
File: gawk.info, Node: MPFR features, Next: FP Math Caution, Prev: Math
Definitions, Up: Arbitrary Precision Arithmetic
@@ -24320,6 +24308,7 @@ be sure of the number of significant decimal places in
the final result.
* Inexact representation:: Numbers are not exactly represented.
* Comparing FP Values:: How to compare floating point values.
* Errors accumulate:: Errors get bigger as they go.
+* Strange values:: A few words about infinities and NaNs.
File: gawk.info, Node: Inexact representation, Next: Comparing FP Values,
Up: Inexactness of computations
@@ -24384,7 +24373,7 @@ values with a delta, you should be sure to use
'difference < abs(delta)'
in case someone passes in a negative delta value.
-File: gawk.info, Node: Errors accumulate, Prev: Comparing FP Values, Up:
Inexactness of computations
+File: gawk.info, Node: Errors accumulate, Next: Strange values, Prev:
Comparing FP Values, Up: Inexactness of computations
16.4.1.3 Errors Accumulate
..........................
@@ -24432,6 +24421,58 @@ representations yield an unexpected result:
-| 4
+File: gawk.info, Node: Strange values, Prev: Errors accumulate, Up:
Inexactness of computations
+
+16.4.1.4 Floating Point Values They Didn't Talk About In School
+...............................................................
+
+Both IEEE 754 floating-point hardware, and MPFR, support two kinds of
+values that you probably didn't learn about in school. The first is
+"infinity", a special value, that can be either negative or positive,
+and which is either smaller than any other value (negative infinity), or
+larger than any other value (positive infinity). When such values are
+generated, 'gawk' prints them as either '-inf' or '+inf', respectively.
+It accepts those strings as data input and converts them to the proper
+floating-point values internally.
+
+ Infinity values of the same sign compare as equal to each other.
+Otherwise, operations (addition, subtraction, etc.) involving another
+number and infinity produce infinity.
+
+ The second kind of value is "not a number", or NaN for short.(1)
+This is 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 systems return NaN. Some examples:
+
+'sqrt(-1)'
+ This makes sense in the range of complex numbers, but not in the
+ range of real numbers, so the result is NaN.
+
+'log(-8)'
+ -8 is out of the domain of 'log()', so the result is NaN.
+
+ NaN values are strange. In particular, they cannot be compared with
+other floating point values; any such comparison, except for "is not
+equal to", returns false. NaN values are so much unequal to other
+values that even comparing two identical NaN values with '!=' returns
+true!
+
+ NaN values can also be signed, although it depends upon the
+implementation as to which sign you get for any operation that returns a
+NaN. For example, on some systems, 'sqrt(-1)' returns a negative NaN. On
+others, it returns a positive NaN.
+
+ When such values are generated, 'gawk' prints them as either '-nan'
+or '+nan', respectively. Here too, 'gawk' accepts those strings as data
+input and converts them to the proper floating-point values internally.
+
+ ---------- Footnotes ----------
+
+ (1) Thanks to Michael Brennan for this description, which we have
+paraphrased, and for the examples.
+
+
File: gawk.info, Node: Getting Accuracy, Next: Try To Round, Prev:
Inexactness of computations, Up: FP Math Caution
16.4.2 Getting the Accuracy You Need
@@ -37934,602 +37975,603 @@ Index
Tag Table:
Node: Top1200
-Node: Foreword344474
-Node: Foreword448916
-Node: Preface50448
-Ref: Preface-Footnote-153307
-Ref: Preface-Footnote-253416
-Ref: Preface-Footnote-353650
-Node: History53792
-Node: Names56144
-Ref: Names-Footnote-157248
-Node: This Manual57395
-Ref: This Manual-Footnote-164034
-Node: Conventions64134
-Node: Manual History66503
-Ref: Manual History-Footnote-169500
-Ref: Manual History-Footnote-269541
-Node: How To Contribute69615
-Node: Acknowledgments70541
-Node: Getting Started75478
-Node: Running gawk77917
-Node: One-shot79107
-Node: Read Terminal80370
-Node: Long82363
-Node: Executable Scripts83876
-Ref: Executable Scripts-Footnote-186509
-Node: Comments86612
-Node: Quoting89096
-Node: DOS Quoting94622
-Node: Sample Data Files96678
-Node: Very Simple99273
-Node: Two Rules105375
-Node: More Complex107260
-Node: Statements/Lines109592
-Ref: Statements/Lines-Footnote-1114076
-Node: Other Features114341
-Node: When115277
-Ref: When-Footnote-1117031
-Node: Intro Summary117096
-Node: Invoking Gawk117980
-Node: Command Line119494
-Node: Options120292
-Ref: Options-Footnote-1138206
-Ref: Options-Footnote-2138437
-Node: Other Arguments138462
-Node: Naming Standard Input142473
-Node: Environment Variables143683
-Node: AWKPATH Variable144241
-Ref: AWKPATH Variable-Footnote-1147653
-Ref: AWKPATH Variable-Footnote-2147687
-Node: AWKLIBPATH Variable148058
-Ref: AWKLIBPATH Variable-Footnote-1149755
-Node: Other Environment Variables150130
-Node: Exit Status153951
-Node: Include Files154628
-Node: Loading Shared Libraries158318
-Node: Obsolete159746
-Node: Undocumented160438
-Node: Invoking Summary160735
-Node: Regexp163576
-Node: Regexp Usage165030
-Node: Escape Sequences167067
-Node: Regexp Operators173308
-Node: Regexp Operator Details173793
-Ref: Regexp Operator Details-Footnote-1180225
-Node: Interval Expressions180372
-Ref: Interval Expressions-Footnote-1181793
-Node: Bracket Expressions181891
-Ref: table-char-classes184367
-Node: Leftmost Longest187693
-Node: Computed Regexps188996
-Node: GNU Regexp Operators192423
-Node: Case-sensitivity196160
-Ref: Case-sensitivity-Footnote-1199026
-Ref: Case-sensitivity-Footnote-2199261
-Node: Regexp Summary199369
-Node: Reading Files200835
-Node: Records203104
-Node: awk split records204179
-Node: gawk split records209454
-Ref: gawk split records-Footnote-1214187
-Node: Fields214224
-Node: Nonconstant Fields216965
-Ref: Nonconstant Fields-Footnote-1219201
-Node: Changing Fields219405
-Node: Field Separators225436
-Node: Default Field Splitting228134
-Node: Regexp Field Splitting229252
-Node: Single Character Fields232605
-Node: Command Line Field Separator233665
-Node: Full Line Fields236883
-Ref: Full Line Fields-Footnote-1238405
-Ref: Full Line Fields-Footnote-2238451
-Node: Field Splitting Summary238552
-Node: Constant Size240626
-Node: Fixed width data241358
-Node: Skipping intervening244825
-Node: Allowing trailing data245623
-Node: Fields with fixed data246660
-Node: Splitting By Content248178
-Ref: Splitting By Content-Footnote-1251961
-Node: More CSV252124
-Node: Testing field creation253434
-Node: Multiple Line255059
-Node: Getline261336
-Node: Plain Getline263805
-Node: Getline/Variable266378
-Node: Getline/File267529
-Node: Getline/Variable/File268917
-Ref: Getline/Variable/File-Footnote-1270522
-Node: Getline/Pipe270610
-Node: Getline/Variable/Pipe273314
-Node: Getline/Coprocess274449
-Node: Getline/Variable/Coprocess275716
-Node: Getline Notes276458
-Node: Getline Summary279255
-Ref: table-getline-variants279679
-Node: Read Timeout280427
-Ref: Read Timeout-Footnote-1284333
-Node: Retrying Input284391
-Node: Command-line directories285590
-Node: Input Summary286496
-Node: Input Exercises289668
-Node: Printing290102
-Node: Print291936
-Node: Print Examples293393
-Node: Output Separators296173
-Node: OFMT298190
-Node: Printf299546
-Node: Basic Printf300331
-Node: Control Letters301905
-Node: Format Modifiers307069
-Node: Printf Examples313084
-Node: Redirection315570
-Node: Special FD322411
-Ref: Special FD-Footnote-1325579
-Node: Special Files325653
-Node: Other Inherited Files326270
-Node: Special Network327271
-Node: Special Caveats328131
-Node: Close Files And Pipes329080
-Ref: table-close-pipe-return-values335987
-Ref: Close Files And Pipes-Footnote-1336800
-Ref: Close Files And Pipes-Footnote-2336948
-Node: Nonfatal337100
-Node: Output Summary339438
-Node: Output Exercises340660
-Node: Expressions341339
-Node: Values342527
-Node: Constants343205
-Node: Scalar Constants343896
-Ref: Scalar Constants-Footnote-1346406
-Node: Nondecimal-numbers346656
-Node: Regexp Constants349657
-Node: Using Constant Regexps350183
-Node: Standard Regexp Constants350805
-Node: Strong Regexp Constants353993
-Node: Variables357005
-Node: Using Variables357662
-Node: Assignment Options359572
-Node: Conversion362043
-Node: Strings And Numbers362567
-Ref: Strings And Numbers-Footnote-1365630
-Node: Locale influences conversions365739
-Ref: table-locale-affects368497
-Node: All Operators369115
-Node: Arithmetic Ops369744
-Node: Concatenation372460
-Ref: Concatenation-Footnote-1375307
-Node: Assignment Ops375414
-Ref: table-assign-ops380405
-Node: Increment Ops381718
-Node: Truth Values and Conditions385178
-Node: Truth Values386252
-Node: Typing and Comparison387300
-Node: Variable Typing388120
-Ref: Variable Typing-Footnote-1394583
-Ref: Variable Typing-Footnote-2394655
-Node: Comparison Operators394732
-Ref: table-relational-ops395151
-Node: POSIX String Comparison398646
-Ref: POSIX String Comparison-Footnote-1400341
-Ref: POSIX String Comparison-Footnote-2400480
-Node: Boolean Ops400564
-Ref: Boolean Ops-Footnote-1405046
-Node: Conditional Exp405138
-Node: Function Calls406874
-Node: Precedence410751
-Node: Locales414410
-Node: Expressions Summary416042
-Node: Patterns and Actions418615
-Node: Pattern Overview419735
-Node: Regexp Patterns421412
-Node: Expression Patterns421954
-Node: Ranges425735
-Node: BEGIN/END428843
-Node: Using BEGIN/END429604
-Ref: Using BEGIN/END-Footnote-1432358
-Node: I/O And BEGIN/END432464
-Node: BEGINFILE/ENDFILE434777
-Node: Empty438008
-Node: Using Shell Variables438325
-Node: Action Overview440599
-Node: Statements442924
-Node: If Statement444772
-Node: While Statement446267
-Node: Do Statement448295
-Node: For Statement449443
-Node: Switch Statement452614
-Node: Break Statement455055
-Node: Continue Statement457147
-Node: Next Statement458974
-Node: Nextfile Statement461357
-Node: Exit Statement464009
-Node: Built-in Variables466412
-Node: User-modified467545
-Node: Auto-set475312
-Ref: Auto-set-Footnote-1492119
-Ref: Auto-set-Footnote-2492325
-Node: ARGC and ARGV492381
-Node: Pattern Action Summary496594
-Node: Arrays499024
-Node: Array Basics500353
-Node: Array Intro501197
-Ref: figure-array-elements503172
-Ref: Array Intro-Footnote-1505876
-Node: Reference to Elements506004
-Node: Assigning Elements508468
-Node: Array Example508959
-Node: Scanning an Array510718
-Node: Controlling Scanning513740
-Ref: Controlling Scanning-Footnote-1520196
-Node: Numeric Array Subscripts520512
-Node: Uninitialized Subscripts522696
-Node: Delete524315
-Ref: Delete-Footnote-1527067
-Node: Multidimensional527124
-Node: Multiscanning530219
-Node: Arrays of Arrays531810
-Node: Arrays Summary536578
-Node: Functions538671
-Node: Built-in539709
-Node: Calling Built-in540790
-Node: Numeric Functions542786
-Ref: Numeric Functions-Footnote-1546814
-Ref: Numeric Functions-Footnote-2547462
-Ref: Numeric Functions-Footnote-3547510
-Node: String Functions547782
-Ref: String Functions-Footnote-1571923
-Ref: String Functions-Footnote-2572051
-Ref: String Functions-Footnote-3572299
-Node: Gory Details572386
-Ref: table-sub-escapes574177
-Ref: table-sub-proposed575696
-Ref: table-posix-sub577059
-Ref: table-gensub-escapes578600
-Ref: Gory Details-Footnote-1579423
-Node: I/O Functions579577
-Ref: table-system-return-values586031
-Ref: I/O Functions-Footnote-1588111
-Ref: I/O Functions-Footnote-2588259
-Node: Time Functions588379
-Ref: Time Functions-Footnote-1599050
-Ref: Time Functions-Footnote-2599118
-Ref: Time Functions-Footnote-3599276
-Ref: Time Functions-Footnote-4599387
-Ref: Time Functions-Footnote-5599499
-Ref: Time Functions-Footnote-6599726
-Node: Bitwise Functions599992
-Ref: table-bitwise-ops600586
-Ref: Bitwise Functions-Footnote-1606649
-Ref: Bitwise Functions-Footnote-2606822
-Node: Type Functions607013
-Node: I18N Functions609876
-Node: User-defined611527
-Node: Definition Syntax612339
-Ref: Definition Syntax-Footnote-1618033
-Node: Function Example618104
-Ref: Function Example-Footnote-1621026
-Node: Function Calling621048
-Node: Calling A Function621636
-Node: Variable Scope622594
-Node: Pass By Value/Reference625588
-Node: Function Caveats628232
-Ref: Function Caveats-Footnote-1630279
-Node: Return Statement630399
-Node: Dynamic Typing633378
-Node: Indirect Calls634308
-Ref: Indirect Calls-Footnote-1644560
-Node: Functions Summary644688
-Node: Library Functions647393
-Ref: Library Functions-Footnote-1651000
-Ref: Library Functions-Footnote-2651143
-Node: Library Names651314
-Ref: Library Names-Footnote-1654981
-Ref: Library Names-Footnote-2655204
-Node: General Functions655290
-Node: Strtonum Function656393
-Node: Assert Function659415
-Node: Round Function662741
-Node: Cliff Random Function664281
-Node: Ordinal Functions665297
-Ref: Ordinal Functions-Footnote-1668360
-Ref: Ordinal Functions-Footnote-2668612
-Node: Join Function668822
-Ref: Join Function-Footnote-1670592
-Node: Getlocaltime Function670792
-Node: Readfile Function674534
-Node: Shell Quoting676511
-Node: Data File Management677912
-Node: Filetrans Function678544
-Node: Rewind Function682640
-Node: File Checking684549
-Ref: File Checking-Footnote-1685883
-Node: Empty Files686084
-Node: Ignoring Assigns688063
-Node: Getopt Function689613
-Ref: Getopt Function-Footnote-1704824
-Node: Passwd Functions705024
-Ref: Passwd Functions-Footnote-1713863
-Node: Group Functions713951
-Ref: Group Functions-Footnote-1721849
-Node: Walking Arrays722056
-Node: Library Functions Summary725064
-Node: Library Exercises726470
-Node: Sample Programs726935
-Node: Running Examples727705
-Node: Clones728433
-Node: Cut Program729657
-Node: Egrep Program739586
-Node: Id Program748597
-Node: Split Program758544
-Ref: Split Program-Footnote-1768318
-Node: Tee Program768491
-Node: Uniq Program771281
-Node: Wc Program778845
-Node: Bytes vs. Characters779242
-Node: Using extensions780790
-Node: wc program781548
-Node: Miscellaneous Programs786413
-Node: Dupword Program787626
-Node: Alarm Program789656
-Node: Translate Program794511
-Ref: Translate Program-Footnote-1799076
-Node: Labels Program799346
-Ref: Labels Program-Footnote-1802697
-Node: Word Sorting802781
-Node: History Sorting806853
-Node: Extract Program809078
-Node: Simple Sed817132
-Node: Igawk Program820206
-Ref: Igawk Program-Footnote-1834537
-Ref: Igawk Program-Footnote-2834739
-Ref: Igawk Program-Footnote-3834861
-Node: Anagram Program834976
-Node: Signature Program838038
-Node: Programs Summary839285
-Node: Programs Exercises840499
-Ref: Programs Exercises-Footnote-1844629
-Node: Advanced Features844715
-Node: Nondecimal Data846705
-Node: Array Sorting848296
-Node: Controlling Array Traversal848996
-Ref: Controlling Array Traversal-Footnote-1857364
-Node: Array Sorting Functions857482
-Ref: Array Sorting Functions-Footnote-1862573
-Node: Two-way I/O862769
-Ref: Two-way I/O-Footnote-1870490
-Ref: Two-way I/O-Footnote-2870677
-Node: TCP/IP Networking870759
-Node: Profiling873877
-Node: Advanced Features Summary883191
-Node: Internationalization885035
-Node: I18N and L10N886515
-Node: Explaining gettext887202
-Ref: Explaining gettext-Footnote-1893094
-Ref: Explaining gettext-Footnote-2893279
-Node: Programmer i18n893444
-Ref: Programmer i18n-Footnote-1898393
-Node: Translator i18n898442
-Node: String Extraction899236
-Ref: String Extraction-Footnote-1900368
-Node: Printf Ordering900454
-Ref: Printf Ordering-Footnote-1903240
-Node: I18N Portability903304
-Ref: I18N Portability-Footnote-1905760
-Node: I18N Example905823
-Ref: I18N Example-Footnote-1909098
-Ref: I18N Example-Footnote-2909171
-Node: Gawk I18N909280
-Node: I18N Summary909929
-Node: Debugger911270
-Node: Debugging912270
-Node: Debugging Concepts912711
-Node: Debugging Terms914520
-Node: Awk Debugging917095
-Ref: Awk Debugging-Footnote-1918040
-Node: Sample Debugging Session918172
-Node: Debugger Invocation918706
-Node: Finding The Bug920092
-Node: List of Debugger Commands926566
-Node: Breakpoint Control927899
-Node: Debugger Execution Control931593
-Node: Viewing And Changing Data934955
-Node: Execution Stack938496
-Node: Debugger Info940133
-Node: Miscellaneous Debugger Commands944204
-Node: Readline Support949266
-Node: Limitations950162
-Node: Debugging Summary952716
-Node: Namespaces953995
-Node: Global Namespace955106
-Node: Qualified Names956504
-Node: Default Namespace957503
-Node: Changing The Namespace958244
-Node: Naming Rules959858
-Node: Internal Name Management961706
-Node: Namespace Example962748
-Node: Namespace And Features965310
-Node: Namespace Summary966745
-Node: Arbitrary Precision Arithmetic968222
-Node: Computer Arithmetic969709
-Ref: table-numeric-ranges973475
-Ref: table-floating-point-ranges973968
-Ref: Computer Arithmetic-Footnote-1974626
-Node: Math Definitions974683
-Ref: table-ieee-formats977999
-Ref: Math Definitions-Footnote-1978602
-Node: MPFR features978707
-Node: FP Math Caution980425
-Ref: FP Math Caution-Footnote-1981497
-Node: Inexactness of computations981866
-Node: Inexact representation982826
-Node: Comparing FP Values984186
-Node: Errors accumulate985427
-Node: Getting Accuracy986860
-Node: Try To Round989570
-Node: Setting precision990469
-Ref: table-predefined-precision-strings991166
-Node: Setting the rounding mode992996
-Ref: table-gawk-rounding-modes993370
-Ref: Setting the rounding mode-Footnote-1997301
-Node: Arbitrary Precision Integers997480
-Ref: Arbitrary Precision Integers-Footnote-11000655
-Node: Checking for MPFR1000804
-Node: POSIX Floating Point Problems1002278
-Ref: POSIX Floating Point Problems-Footnote-11006563
-Node: Floating point summary1006601
-Node: Dynamic Extensions1008791
-Node: Extension Intro1010344
-Node: Plugin License1011610
-Node: Extension Mechanism Outline1012407
-Ref: figure-load-extension1012846
-Ref: figure-register-new-function1014411
-Ref: figure-call-new-function1015503
-Node: Extension API Description1017565
-Node: Extension API Functions Introduction1019278
-Ref: table-api-std-headers1021114
-Node: General Data Types1025363
-Ref: General Data Types-Footnote-11033993
-Node: Memory Allocation Functions1034292
-Ref: Memory Allocation Functions-Footnote-11038793
-Node: Constructor Functions1038892
-Node: API Ownership of MPFR and GMP Values1042358
-Node: Registration Functions1043671
-Node: Extension Functions1044371
-Node: Exit Callback Functions1049693
-Node: Extension Version String1050943
-Node: Input Parsers1051606
-Node: Output Wrappers1064327
-Node: Two-way processors1068839
-Node: Printing Messages1071104
-Ref: Printing Messages-Footnote-11072275
-Node: Updating ERRNO1072428
-Node: Requesting Values1073167
-Ref: table-value-types-returned1073904
-Node: Accessing Parameters1074840
-Node: Symbol Table Access1076077
-Node: Symbol table by name1076589
-Ref: Symbol table by name-Footnote-11079613
-Node: Symbol table by cookie1079741
-Ref: Symbol table by cookie-Footnote-11083926
-Node: Cached values1083990
-Ref: Cached values-Footnote-11087526
-Node: Array Manipulation1087679
-Ref: Array Manipulation-Footnote-11088770
-Node: Array Data Types1088807
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-Node: Array Functions1091557
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-Node: Extension API Variables1110631
-Node: Extension Versioning1111342
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-Node: PC Installation1237154
-Node: PC Binary Installation1237992
-Node: PC Compiling1238427
-Node: PC Using1239544
-Node: Cygwin1243097
-Node: MSYS1244321
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-Node: VMS GNV1255218
-Node: VMS Old Gawk1255953
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-Node: Bug address1257087
-Node: Usenet1260069
-Node: Maintainers1261073
-Node: Other Versions1262258
-Node: Installation summary1269346
-Node: Notes1270555
-Node: Compatibility Mode1271349
-Node: Additions1272131
-Node: Accessing The Source1273056
-Node: Adding Code1274493
-Node: New Ports1280712
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-Node: Extension Design1293362
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-Node: Basic Data Typing1308645
-Node: Glossary1311973
-Node: Copying1343858
-Node: GNU Free Documentation License1381401
-Node: Index1406521
+Node: Foreword344553
+Node: Foreword448995
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+Node: Manual History66582
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+Node: Future Extensions1293567
+Node: Implementation Limitations1294225
+Node: Extension Design1295435
+Node: Old Extension Problems1296579
+Ref: Old Extension Problems-Footnote-11298097
+Node: Extension New Mechanism Goals1298154
+Ref: Extension New Mechanism Goals-Footnote-11301518
+Node: Extension Other Design Decisions1301707
+Node: Extension Future Growth1303820
+Node: Notes summary1304426
+Node: Basic Concepts1305584
+Node: Basic High Level1306265
+Ref: figure-general-flow1306547
+Ref: figure-process-flow1307232
+Ref: Basic High Level-Footnote-11310533
+Node: Basic Data Typing1310718
+Node: Glossary1314046
+Node: Copying1345931
+Node: GNU Free Documentation License1383474
+Node: Index1408594
End Tag Table
diff --git a/doc/gawk.texi b/doc/gawk.texi
index 2a1e65c..6c1f409 100644
--- a/doc/gawk.texi
+++ b/doc/gawk.texi
@@ -919,6 +919,7 @@ particular records in a file and perform operations upon
them.
* Inexact representation:: Numbers are not exactly represented.
* Comparing FP Values:: How to compare floating point values.
* Errors accumulate:: Errors get bigger as they go.
+* Strange values:: A few words about infinities and NaNs.
* Getting Accuracy:: Getting more accuracy takes some work.
* Try To Round:: Add digits and round.
* Setting precision:: How to set the precision.
@@ -8413,7 +8414,7 @@ FPAT = "([^,]*)|(\"[^\"]+\")"
@c Per email from Ed Morton <mortoneccc@comcast.net>
@c
@c WONTFIX: 10/2020
-@c This is too much work. FPAT and CSV files are very flakey and
+@c This is too much work. FPAT and CSV files are very flaky and
@c fragile. Doing something like this is merely inviting trouble.
As with @code{FS}, the @code{IGNORECASE} variable (@pxref{User-modified})
@@ -10063,7 +10064,7 @@ infinity are formatted as
and positive infinity as
@samp{inf} or @samp{infinity}.
The special ``not a number'' value formats as @samp{-nan} or @samp{nan}
-(@pxref{Math Definitions}).
+(@pxref{Strange values}).
@item @code{%F}
Like @samp{%f}, but the infinity and ``not a number'' values are spelled
@@ -18298,7 +18299,7 @@ compatibility mode (@pxref{Options}).
@cindexawkfunc{log}
@cindex logarithm
Return the natural logarithm of @var{x}, if @var{x} is positive;
-otherwise, return @code{NaN} (``not a number'') on IEEE 754 systems.
+otherwise, return NaN (``not a number'') on IEEE 754 systems.
Additionally, @command{gawk} prints a warning message when @code{x}
is negative.
@@ -33586,21 +33587,9 @@ A special value representing infinity. Operations
involving another
number and infinity produce infinity.
@item NaN
-``Not a number.''@footnote{Thanks to Michael Brennan for this description,
-which we have paraphrased, and for the examples.} 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 @code{NaN} back as the result. The IEEE 754 standard recommends
-that systems return @code{NaN}. Some examples:
-
-@table @code
-@item sqrt(-1)
-This makes sense in the range of complex numbers, but not in the
-range of real numbers, so the result is @code{NaN}.
-
-@item log(-8)
-@minus{}8 is out of the domain of @code{log()}, so the result is @code{NaN}.
-@end table
+``Not a number.'' A special value that results from attempting a
+calculation that has no answer as a real number. @xref{Strange values},
+for more information about infinity and not-a-number values.
@item Normalized
How the significand (see later in this list) is usually stored. The
@@ -33769,6 +33758,7 @@ decimal places in the final result.
* Inexact representation:: Numbers are not exactly represented.
* Comparing FP Values:: How to compare floating point values.
* Errors accumulate:: Errors get bigger as they go.
+* Strange values:: A few words about infinities and NaNs.
@end menu
@node Inexact representation
@@ -33890,6 +33880,54 @@ $ @kbd{gawk 'BEGIN @{}
@print{} 4
@end example
+@node Strange values
+@subsubsection Floating Point Values They Didn't Talk About In School
+
+Both IEEE 754 floating-point hardware, and MPFR, support two kinds of
+values that you probably didn't learn about in school. The first is
+@dfn{infinity}, a special value, that can be either negative or positive,
+and which is either smaller than any other value (negative infinity),
+or larger than any other value (positive infinity). When such values
+are generated, @command{gawk} prints them as either @samp{-inf} or
+@samp{+inf}, respectively. It accepts those strings as data input and
+converts them to the proper floating-point values internally.
+
+Infinity values of the same sign compare as equal to each other.
+Otherwise, operations (addition, subtraction, etc.) involving another
+number and infinity produce infinity.
+
+The second kind of value is ``not a number'', or NaN for
+short.@footnote{Thanks to Michael Brennan for this description, which we
+have paraphrased, and for the examples.} This is 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 systems return NaN. Some examples:
+
+@table @code
+@item sqrt(-1)
+This makes sense in the range of complex numbers, but not in the
+range of real numbers, so the result is NaN.
+
+@item log(-8)
+@minus{}8 is out of the domain of @code{log()}, so the result is NaN.
+@end table
+
+NaN values are strange. In particular, they cannot be compared with other
+floating point values; any such comparison, except for ``is not equal
+to'', returns false. NaN values are so much unequal to other values that
+even comparing two identical NaN values with @code{!=} returns true!
+
+NaN values can also be signed, although it depends upon the implementation
+as to which sign you get for any operation that returns a NaN. For
+example, on some systems, @code{sqrt(-1)} returns a negative NaN. On
+others, it returns a positive NaN.
+
+When such values are generated, @command{gawk} prints them as either
+@samp{-nan} or @samp{+nan}, respectively. Here too, @command{gawk}
+accepts those strings as data input and converts them to the proper
+floating-point values internally.
+
@node Getting Accuracy
@subsection Getting the Accuracy You Need
diff --git a/doc/gawktexi.in b/doc/gawktexi.in
index e733c4e..eca3bea 100644
--- a/doc/gawktexi.in
+++ b/doc/gawktexi.in
@@ -914,6 +914,7 @@ particular records in a file and perform operations upon
them.
* Inexact representation:: Numbers are not exactly represented.
* Comparing FP Values:: How to compare floating point values.
* Errors accumulate:: Errors get bigger as they go.
+* Strange values:: A few words about infinities and NaNs.
* Getting Accuracy:: Getting more accuracy takes some work.
* Try To Round:: Add digits and round.
* Setting precision:: How to set the precision.
@@ -7966,7 +7967,7 @@ FPAT = "([^,]*)|(\"[^\"]+\")"
@c Per email from Ed Morton <mortoneccc@comcast.net>
@c
@c WONTFIX: 10/2020
-@c This is too much work. FPAT and CSV files are very flakey and
+@c This is too much work. FPAT and CSV files are very flaky and
@c fragile. Doing something like this is merely inviting trouble.
As with @code{FS}, the @code{IGNORECASE} variable (@pxref{User-modified})
@@ -9616,7 +9617,7 @@ infinity are formatted as
and positive infinity as
@samp{inf} or @samp{infinity}.
The special ``not a number'' value formats as @samp{-nan} or @samp{nan}
-(@pxref{Math Definitions}).
+(@pxref{Strange values}).
@item @code{%F}
Like @samp{%f}, but the infinity and ``not a number'' values are spelled
@@ -17523,7 +17524,7 @@ compatibility mode (@pxref{Options}).
@cindexawkfunc{log}
@cindex logarithm
Return the natural logarithm of @var{x}, if @var{x} is positive;
-otherwise, return @code{NaN} (``not a number'') on IEEE 754 systems.
+otherwise, return NaN (``not a number'') on IEEE 754 systems.
Additionally, @command{gawk} prints a warning message when @code{x}
is negative.
@@ -32552,21 +32553,9 @@ A special value representing infinity. Operations
involving another
number and infinity produce infinity.
@item NaN
-``Not a number.''@footnote{Thanks to Michael Brennan for this description,
-which we have paraphrased, and for the examples.} 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 @code{NaN} back as the result. The IEEE 754 standard recommends
-that systems return @code{NaN}. Some examples:
-
-@table @code
-@item sqrt(-1)
-This makes sense in the range of complex numbers, but not in the
-range of real numbers, so the result is @code{NaN}.
-
-@item log(-8)
-@minus{}8 is out of the domain of @code{log()}, so the result is @code{NaN}.
-@end table
+``Not a number.'' A special value that results from attempting a
+calculation that has no answer as a real number. @xref{Strange values},
+for more information about infinity and not-a-number values.
@item Normalized
How the significand (see later in this list) is usually stored. The
@@ -32735,6 +32724,7 @@ decimal places in the final result.
* Inexact representation:: Numbers are not exactly represented.
* Comparing FP Values:: How to compare floating point values.
* Errors accumulate:: Errors get bigger as they go.
+* Strange values:: A few words about infinities and NaNs.
@end menu
@node Inexact representation
@@ -32856,6 +32846,54 @@ $ @kbd{gawk 'BEGIN @{}
@print{} 4
@end example
+@node Strange values
+@subsubsection Floating Point Values They Didn't Talk About In School
+
+Both IEEE 754 floating-point hardware, and MPFR, support two kinds of
+values that you probably didn't learn about in school. The first is
+@dfn{infinity}, a special value, that can be either negative or positive,
+and which is either smaller than any other value (negative infinity),
+or larger than any other value (positive infinity). When such values
+are generated, @command{gawk} prints them as either @samp{-inf} or
+@samp{+inf}, respectively. It accepts those strings as data input and
+converts them to the proper floating-point values internally.
+
+Infinity values of the same sign compare as equal to each other.
+Otherwise, operations (addition, subtraction, etc.) involving another
+number and infinity produce infinity.
+
+The second kind of value is ``not a number'', or NaN for
+short.@footnote{Thanks to Michael Brennan for this description, which we
+have paraphrased, and for the examples.} This is 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 systems return NaN. Some examples:
+
+@table @code
+@item sqrt(-1)
+This makes sense in the range of complex numbers, but not in the
+range of real numbers, so the result is NaN.
+
+@item log(-8)
+@minus{}8 is out of the domain of @code{log()}, so the result is NaN.
+@end table
+
+NaN values are strange. In particular, they cannot be compared with other
+floating point values; any such comparison, except for ``is not equal
+to'', returns false. NaN values are so much unequal to other values that
+even comparing two identical NaN values with @code{!=} returns true!
+
+NaN values can also be signed, although it depends upon the implementation
+as to which sign you get for any operation that returns a NaN. For
+example, on some systems, @code{sqrt(-1)} returns a negative NaN. On
+others, it returns a positive NaN.
+
+When such values are generated, @command{gawk} prints them as either
+@samp{-nan} or @samp{+nan}, respectively. Here too, @command{gawk}
+accepts those strings as data input and converts them to the proper
+floating-point values internally.
+
@node Getting Accuracy
@subsection Getting the Accuracy You Need
diff --git a/doc/wordlist b/doc/wordlist
index c93eda5..9ce3118 100644
--- a/doc/wordlist
+++ b/doc/wordlist
@@ -316,6 +316,7 @@ NR
NT
NUMCUR
NaN
+NaNs
Nachum
Neacsu
Neacsu's
@@ -483,6 +484,7 @@ VT
Versioning
Vinschen
WIPO
+WONTFIX
Walamazoo
Wallin
Watchpoint
-----------------------------------------------------------------------
Summary of changes:
doc/ChangeLog | 6 +
doc/gawk.info | 1276 ++++++++++++++++++++++++++++---------------------------
doc/gawk.texi | 74 +++-
doc/gawktexi.in | 74 +++-
doc/wordlist | 2 +
5 files changed, 779 insertions(+), 653 deletions(-)
hooks/post-receive
--
gawk
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