Make scalar comparisons match doubles for NaN and INF.dead-branches/revamp-scalar-comparisons

10 files changed, 1065 insertions, 594 deletions

diff --git a/ChangeLog b/ChangeLog
index 11b398fa..72866a1d 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,13 @@
+2018-07-19         Arnold D. Robbins     <arnold@skeeve.com>
+
+	Revamp scalar comparisons to be like hardware doubles.
+
+	* eval.c (mpg_cmp_scalars): New routine.
+	(cmp_scalars): Change return type to bool. Rework code to take
+	NaNs and INFs and type of comparison into account. Call mpg_cmp_scalars
+	if necessary.
+	* interpret.h (r_interpret): Change calls to cmp_scalars().
+
 2018-07-13         Arnold D. Robbins     <arnold@skeeve.com>
 
 	* builtin.c (format_nan_inf): New function to generate +nan, -nan,
diff --git a/doc/ChangeLog b/doc/ChangeLog
index a8d885db..10032499 100644
--- a/doc/ChangeLog
+++ b/doc/ChangeLog
@@ -1,3 +1,8 @@
+2018-07-19         Arnold D. Robbins     <arnold@skeeve.com>
+
+	* gawktexi.in (IEEE 754 Special Values): New subsubsection on
+	NaNs and INFs.
+
 2018-07-10         Arnold D. Robbins     <arnold@skeeve.com>
 
 	* gawktexi.in (Control Letters): Add a note about output of NaN and
diff --git a/doc/gawk.info b/doc/gawk.info
index f9219634..9ea649cf 100644
--- a/doc/gawk.info
+++ b/doc/gawk.info
@@ -293,6 +293,7 @@ in (a) below.  A copy of the license is included in the section entitled
                                         strings with '<', etc.
 * Variable Typing::                     String type versus numeric type.
 * Comparison Operators::                The comparison operators.
+* IEEE 754 Special Values::             Comparing IEEE 754 Special Floating-Point Values and Regular Numbers.
 * POSIX String Comparison::             String comparison with POSIX rules.
 * Boolean Ops::                         Combining comparison expressions using
                                         boolean operators '||' ("or"),
@@ -8693,6 +8694,7 @@ variables are typed, and how 'awk' compares variables.
 
 * Variable Typing::             String type versus numeric type.
 * Comparison Operators::        The comparison operators.
+* IEEE 754 Special Values::     Comparing IEEE 754 Special Floating-Point Values and Regular Numbers.
 * POSIX String Comparison::     String comparison with POSIX rules.
 
 
@@ -8864,7 +8866,7 @@ program text comprise a string constant.  The following examples print
 thing.
 
 
-File: gawk.info,  Node: Comparison Operators,  Next: POSIX String Comparison,  Prev: Variable Typing,  Up: Typing and Comparison
+File: gawk.info,  Node: Comparison Operators,  Next: IEEE 754 Special Values,  Prev: Variable Typing,  Up: Typing and Comparison
 
 6.3.2.2 Comparison Operators
 ............................
@@ -8977,9 +8979,57 @@ expression:
 Constant Regexps::, where this is discussed in more detail.
 
 
-File: gawk.info,  Node: POSIX String Comparison,  Prev: Comparison Operators,  Up: Typing and Comparison
+File: gawk.info,  Node: IEEE 754 Special Values,  Next: POSIX String Comparison,  Prev: Comparison Operators,  Up: Typing and Comparison
 
-6.3.2.3 String Comparison Based on Locale Collating Order
+6.3.2.3 Comparing IEEE 754 Special Floating-Point Values and Regular Numbers
+............................................................................
+
+Modern computing platforms use floating-point arithmatic as defined by
+the IEEE 754 standard (*FIXME: web link or two here*).  Besides regular
+numbers, like -57 and 42, the standard defines two "special" values:
+"Infinity", and "Not-A-Number".  (The latter is usally referred to as a
+"NaN".) These special values come in both positive and negative flavors.
+
+   Infinity values are easy to understand: negative infinity is smaller
+than any other possible negative value, and postive infinity is greater
+than any other possible positive value.
+
+   NaN values are harder to comprehend.  They represent impossible
+values.  A canonical example is 'sqrt(-1)'.  This value doesn't exist,
+so the result of calling 'sqrt(-1)' is a NaN.
+
+   When comparing infinity values with '<', '<=', and so on, the results
+make sense.  But when comparing NaN values, things are more surprising.
+In particular, _the only comparison that returns true for a NaN is_
+'!='.  Every other comparison returns false.  Most surprising of all, is
+that if you have two NaN values, they do *not* compare equal!  They are
+not equal to each other, even if obtained in the same way.  Consider
+this file, 'nan.awk':
+
+     BEGIN {
+         nan1 = sqrt(-1)
+         nan2 = sqrt(-1)
+         print nan1, nan2
+         print "nan1 == nan2 -->", (nan1 == nan2)
+         print "nan1 != nan2 -->", (nan1 != nan2)
+     }
+
+Here is what happens when it's run:
+
+     $ gawk -f nan.awk
+     -| gawk: x.awk:2: warning: sqrt: called with negative argument -1
+     -| gawk: x.awk:3: warning: sqrt: called with negative argument -1
+     -| -nan -nan
+     -| nan1 == nan2 --> 0
+     -| nan1 != nan2 --> 1
+
+   In short, remember that computer arithmetic is _not_ the same as
+paper-and-pencil arithmetic!
+
+
+File: gawk.info,  Node: POSIX String Comparison,  Prev: IEEE 754 Special Values,  Up: Typing and Comparison
+
+6.3.2.4 String Comparison Based on Locale Collating Order
 .........................................................
 
 The POSIX standard used to say that all string comparisons are performed
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-Node: Adding Code1213594
-Node: New Ports1219813
-Node: Derived Files1224301
-Ref: Derived Files-Footnote-11229947
-Ref: Derived Files-Footnote-21229982
-Ref: Derived Files-Footnote-31230580
-Node: Future Extensions1230694
-Node: Implementation Limitations1231352
-Node: Extension Design1232535
-Node: Old Extension Problems1233689
-Ref: Old Extension Problems-Footnote-11235207
-Node: Extension New Mechanism Goals1235264
-Ref: Extension New Mechanism Goals-Footnote-11238628
-Node: Extension Other Design Decisions1238817
-Node: Extension Future Growth1240930
-Node: Old Extension Mechanism1241766
-Node: Notes summary1243529
-Node: Basic Concepts1244711
-Node: Basic High Level1245392
-Ref: figure-general-flow1245674
-Ref: figure-process-flow1246359
-Ref: Basic High Level-Footnote-11249660
-Node: Basic Data Typing1249845
-Node: Glossary1253173
-Node: Copying1285011
-Node: GNU Free Documentation License1322554
-Node: Index1347674
+Node: Foreword343509
+Node: Foreword447951
+Node: Preface49483
+Ref: Preface-Footnote-152342
+Ref: Preface-Footnote-252449
+Ref: Preface-Footnote-352683
+Node: History52825
+Node: Names55177
+Ref: Names-Footnote-156271
+Node: This Manual56418
+Ref: This Manual-Footnote-162903
+Node: Conventions63003
+Node: Manual History65358
+Ref: Manual History-Footnote-168355
+Ref: Manual History-Footnote-268396
+Node: How To Contribute68470
+Node: Acknowledgments69396
+Node: Getting Started74304
+Node: Running gawk76743
+Node: One-shot77933
+Node: Read Terminal79196
+Node: Long81189
+Node: Executable Scripts82702
+Ref: Executable Scripts-Footnote-185497
+Node: Comments85600
+Node: Quoting88084
+Node: DOS Quoting93601
+Node: Sample Data Files95657
+Node: Very Simple98252
+Node: Two Rules103154
+Node: More Complex105039
+Node: Statements/Lines107905
+Ref: Statements/Lines-Footnote-1112364
+Node: Other Features112629
+Node: When113565
+Ref: When-Footnote-1115319
+Node: Intro Summary115384
+Node: Invoking Gawk116268
+Node: Command Line117782
+Node: Options118580
+Ref: Options-Footnote-1135142
+Ref: Options-Footnote-2135373
+Node: Other Arguments135398
+Node: Naming Standard Input138345
+Node: Environment Variables139438
+Node: AWKPATH Variable139996
+Ref: AWKPATH Variable-Footnote-1143408
+Ref: AWKPATH Variable-Footnote-2143442
+Node: AWKLIBPATH Variable143703
+Node: Other Environment Variables145361
+Node: Exit Status149182
+Node: Include Files149859
+Node: Loading Shared Libraries153384
+Node: Obsolete154812
+Node: Undocumented155504
+Node: Invoking Summary155801
+Node: Regexp157461
+Node: Regexp Usage158915
+Node: Escape Sequences160952
+Node: Regexp Operators167184
+Ref: Regexp Operators-Footnote-1174600
+Ref: Regexp Operators-Footnote-2174747
+Node: Bracket Expressions174845
+Ref: table-char-classes177321
+Node: Leftmost Longest180726
+Node: Computed Regexps182029
+Node: GNU Regexp Operators185456
+Node: Case-sensitivity189135
+Ref: Case-sensitivity-Footnote-1192022
+Ref: Case-sensitivity-Footnote-2192257
+Node: Regexp Summary192365
+Node: Reading Files193831
+Node: Records196100
+Node: awk split records197175
+Node: gawk split records202450
+Ref: gawk split records-Footnote-1207036
+Node: Fields207073
+Node: Nonconstant Fields209814
+Ref: Nonconstant Fields-Footnote-1212050
+Node: Changing Fields212254
+Node: Field Separators218182
+Node: Default Field Splitting220880
+Node: Regexp Field Splitting221998
+Node: Single Character Fields225351
+Node: Command Line Field Separator226411
+Node: Full Line Fields229629
+Ref: Full Line Fields-Footnote-1231151
+Ref: Full Line Fields-Footnote-2231197
+Node: Field Splitting Summary231298
+Node: Constant Size233372
+Node: Fixed width data234104
+Node: Skipping intervening237571
+Node: Allowing trailing data238369
+Node: Fields with fixed data239406
+Node: Splitting By Content240924
+Ref: Splitting By Content-Footnote-1244574
+Node: Testing field creation244737
+Node: Multiple Line246362
+Ref: Multiple Line-Footnote-1252246
+Node: Getline252425
+Node: Plain Getline254894
+Node: Getline/Variable257535
+Node: Getline/File258686
+Node: Getline/Variable/File260074
+Ref: Getline/Variable/File-Footnote-1261679
+Node: Getline/Pipe261767
+Node: Getline/Variable/Pipe264474
+Node: Getline/Coprocess265609
+Node: Getline/Variable/Coprocess266876
+Node: Getline Notes267618
+Node: Getline Summary270415
+Ref: table-getline-variants270839
+Node: Read Timeout271587
+Ref: Read Timeout-Footnote-1275493
+Node: Retrying Input275551
+Node: Command-line directories276750
+Node: Input Summary277656
+Node: Input Exercises280828
+Node: Printing281556
+Node: Print283390
+Node: Print Examples284847
+Node: Output Separators287627
+Node: OFMT289644
+Node: Printf291000
+Node: Basic Printf291785
+Node: Control Letters293359
+Node: Format Modifiers298486
+Node: Printf Examples304501
+Node: Redirection306987
+Node: Special FD313828
+Ref: Special FD-Footnote-1316996
+Node: Special Files317070
+Node: Other Inherited Files317687
+Node: Special Network318688
+Node: Special Caveats319548
+Node: Close Files And Pipes320497
+Ref: table-close-pipe-return-values327404
+Ref: Close Files And Pipes-Footnote-1328217
+Ref: Close Files And Pipes-Footnote-2328365
+Node: Nonfatal328517
+Node: Output Summary330855
+Node: Output Exercises332077
+Node: Expressions332756
+Node: Values333944
+Node: Constants334622
+Node: Scalar Constants335313
+Ref: Scalar Constants-Footnote-1336177
+Node: Nondecimal-numbers336427
+Node: Regexp Constants339428
+Node: Using Constant Regexps339954
+Node: Standard Regexp Constants340576
+Node: Strong Regexp Constants343764
+Node: Variables346722
+Node: Using Variables347379
+Node: Assignment Options349289
+Node: Conversion351162
+Node: Strings And Numbers351686
+Ref: Strings And Numbers-Footnote-1354749
+Node: Locale influences conversions354858
+Ref: table-locale-affects357616
+Node: All Operators358234
+Node: Arithmetic Ops358863
+Node: Concatenation361369
+Ref: Concatenation-Footnote-1364216
+Node: Assignment Ops364323
+Ref: table-assign-ops369314
+Node: Increment Ops370627
+Node: Truth Values and Conditions374087
+Node: Truth Values375161
+Node: Typing and Comparison376209
+Node: Variable Typing377131
+Ref: Variable Typing-Footnote-1383594
+Ref: Variable Typing-Footnote-2383666
+Node: Comparison Operators383743
+Ref: table-relational-ops384162
+Node: IEEE 754 Special Values387657
+Node: POSIX String Comparison389700
+Ref: POSIX String Comparison-Footnote-1391398
+Ref: POSIX String Comparison-Footnote-2391537
+Node: Boolean Ops391621
+Ref: Boolean Ops-Footnote-1396103
+Node: Conditional Exp396195
+Node: Function Calls397931
+Node: Precedence401808
+Node: Locales405467
+Node: Expressions Summary407099
+Node: Patterns and Actions409672
+Node: Pattern Overview410792
+Node: Regexp Patterns412469
+Node: Expression Patterns413011
+Node: Ranges416792
+Node: BEGIN/END419900
+Node: Using BEGIN/END420661
+Ref: Using BEGIN/END-Footnote-1423397
+Node: I/O And BEGIN/END423503
+Node: BEGINFILE/ENDFILE425817
+Node: Empty428730
+Node: Using Shell Variables429047
+Node: Action Overview431321
+Node: Statements433646
+Node: If Statement435494
+Node: While Statement436989
+Node: Do Statement439017
+Node: For Statement440165
+Node: Switch Statement443336
+Node: Break Statement445722
+Node: Continue Statement447814
+Node: Next Statement449641
+Node: Nextfile Statement452024
+Node: Exit Statement454676
+Node: Built-in Variables457079
+Node: User-modified458212
+Node: Auto-set465979
+Ref: Auto-set-Footnote-1482281
+Ref: Auto-set-Footnote-2482487
+Node: ARGC and ARGV482543
+Node: Pattern Action Summary486756
+Node: Arrays489186
+Node: Array Basics490515
+Node: Array Intro491359
+Ref: figure-array-elements493334
+Ref: Array Intro-Footnote-1496038
+Node: Reference to Elements496166
+Node: Assigning Elements498630
+Node: Array Example499121
+Node: Scanning an Array500880
+Node: Controlling Scanning503902
+Ref: Controlling Scanning-Footnote-1509301
+Node: Numeric Array Subscripts509617
+Node: Uninitialized Subscripts511801
+Node: Delete513420
+Ref: Delete-Footnote-1516172
+Node: Multidimensional516229
+Node: Multiscanning519324
+Node: Arrays of Arrays520915
+Node: Arrays Summary525682
+Node: Functions527775
+Node: Built-in528813
+Node: Calling Built-in529894
+Node: Numeric Functions531890
+Ref: Numeric Functions-Footnote-1535918
+Ref: Numeric Functions-Footnote-2536275
+Ref: Numeric Functions-Footnote-3536323
+Node: String Functions536595
+Ref: String Functions-Footnote-1560304
+Ref: String Functions-Footnote-2560432
+Ref: String Functions-Footnote-3560680
+Node: Gory Details560767
+Ref: table-sub-escapes562558
+Ref: table-sub-proposed564077
+Ref: table-posix-sub565440
+Ref: table-gensub-escapes566981
+Ref: Gory Details-Footnote-1567804
+Node: I/O Functions567958
+Ref: table-system-return-values574426
+Ref: I/O Functions-Footnote-1576406
+Ref: I/O Functions-Footnote-2576554
+Node: Time Functions576674
+Ref: Time Functions-Footnote-1587345
+Ref: Time Functions-Footnote-2587413
+Ref: Time Functions-Footnote-3587571
+Ref: Time Functions-Footnote-4587682
+Ref: Time Functions-Footnote-5587794
+Ref: Time Functions-Footnote-6588021
+Node: Bitwise Functions588287
+Ref: table-bitwise-ops588881
+Ref: Bitwise Functions-Footnote-1594944
+Ref: Bitwise Functions-Footnote-2595117
+Node: Type Functions595308
+Node: I18N Functions598059
+Node: User-defined599710
+Node: Definition Syntax600515
+Ref: Definition Syntax-Footnote-1606202
+Node: Function Example606273
+Ref: Function Example-Footnote-1609195
+Node: Function Caveats609217
+Node: Calling A Function609735
+Node: Variable Scope610693
+Node: Pass By Value/Reference613687
+Node: Return Statement617186
+Node: Dynamic Typing620165
+Node: Indirect Calls621095
+Ref: Indirect Calls-Footnote-1631347
+Node: Functions Summary631475
+Node: Library Functions634180
+Ref: Library Functions-Footnote-1637787
+Ref: Library Functions-Footnote-2637930
+Node: Library Names638101
+Ref: Library Names-Footnote-1641561
+Ref: Library Names-Footnote-2641784
+Node: General Functions641870
+Node: Strtonum Function642973
+Node: Assert Function645995
+Node: Round Function649321
+Node: Cliff Random Function650861
+Node: Ordinal Functions651877
+Ref: Ordinal Functions-Footnote-1654940
+Ref: Ordinal Functions-Footnote-2655192
+Node: Join Function655402
+Ref: Join Function-Footnote-1657172
+Node: Getlocaltime Function657372
+Node: Readfile Function661114
+Node: Shell Quoting663091
+Node: Data File Management664492
+Node: Filetrans Function665124
+Node: Rewind Function669220
+Node: File Checking671130
+Ref: File Checking-Footnote-1672464
+Node: Empty Files672665
+Node: Ignoring Assigns674644
+Node: Getopt Function676194
+Ref: Getopt Function-Footnote-1687663
+Node: Passwd Functions687863
+Ref: Passwd Functions-Footnote-1696702
+Node: Group Functions696790
+Ref: Group Functions-Footnote-1704688
+Node: Walking Arrays704895
+Node: Library Functions Summary707903
+Node: Library Exercises709309
+Node: Sample Programs709774
+Node: Running Examples710544
+Node: Clones711272
+Node: Cut Program712496
+Node: Egrep Program722425
+Ref: Egrep Program-Footnote-1729937
+Node: Id Program730047
+Node: Split Program733727
+Ref: Split Program-Footnote-1737185
+Node: Tee Program737314
+Node: Uniq Program740104
+Node: Wc Program747530
+Ref: Wc Program-Footnote-1751785
+Node: Miscellaneous Programs751879
+Node: Dupword Program753092
+Node: Alarm Program755122
+Node: Translate Program759977
+Ref: Translate Program-Footnote-1764542
+Node: Labels Program764812
+Ref: Labels Program-Footnote-1768163
+Node: Word Sorting768247
+Node: History Sorting772319
+Node: Extract Program774154
+Node: Simple Sed782208
+Node: Igawk Program785282
+Ref: Igawk Program-Footnote-1799613
+Ref: Igawk Program-Footnote-2799815
+Ref: Igawk Program-Footnote-3799937
+Node: Anagram Program800052
+Node: Signature Program803114
+Node: Programs Summary804361
+Node: Programs Exercises805575
+Ref: Programs Exercises-Footnote-1809704
+Node: Advanced Features809795
+Node: Nondecimal Data811785
+Node: Array Sorting813376
+Node: Controlling Array Traversal814076
+Ref: Controlling Array Traversal-Footnote-1822444
+Node: Array Sorting Functions822562
+Ref: Array Sorting Functions-Footnote-1827653
+Node: Two-way I/O827849
+Ref: Two-way I/O-Footnote-1834401
+Ref: Two-way I/O-Footnote-2834588
+Node: TCP/IP Networking834670
+Node: Profiling837788
+Ref: Profiling-Footnote-1846460
+Node: Advanced Features Summary846783
+Node: Internationalization848627
+Node: I18N and L10N850107
+Node: Explaining gettext850794
+Ref: Explaining gettext-Footnote-1856686
+Ref: Explaining gettext-Footnote-2856871
+Node: Programmer i18n857036
+Ref: Programmer i18n-Footnote-1861985
+Node: Translator i18n862034
+Node: String Extraction862828
+Ref: String Extraction-Footnote-1863960
+Node: Printf Ordering864046
+Ref: Printf Ordering-Footnote-1866832
+Node: I18N Portability866896
+Ref: I18N Portability-Footnote-1869352
+Node: I18N Example869415
+Ref: I18N Example-Footnote-1872221
+Node: Gawk I18N872294
+Node: I18N Summary872939
+Node: Debugger874280
+Node: Debugging875303
+Node: Debugging Concepts875744
+Node: Debugging Terms877553
+Node: Awk Debugging880128
+Node: Sample Debugging Session881034
+Node: Debugger Invocation881568
+Node: Finding The Bug882954
+Node: List of Debugger Commands889432
+Node: Breakpoint Control890765
+Node: Debugger Execution Control894459
+Node: Viewing And Changing Data897821
+Node: Execution Stack901195
+Node: Debugger Info902832
+Node: Miscellaneous Debugger Commands906903
+Node: Readline Support911965
+Node: Limitations912861
+Node: Debugging Summary914970
+Node: Arbitrary Precision Arithmetic916249
+Node: Computer Arithmetic917734
+Ref: table-numeric-ranges921500
+Ref: table-floating-point-ranges921993
+Ref: Computer Arithmetic-Footnote-1922651
+Node: Math Definitions922708
+Ref: table-ieee-formats926024
+Ref: Math Definitions-Footnote-1926627
+Node: MPFR features926732
+Node: FP Math Caution928450
+Ref: FP Math Caution-Footnote-1929522
+Node: Inexactness of computations929891
+Node: Inexact representation930851
+Node: Comparing FP Values932211
+Node: Errors accumulate933293
+Node: Getting Accuracy934726
+Node: Try To Round937436
+Node: Setting precision938335
+Ref: table-predefined-precision-strings939032
+Node: Setting the rounding mode940862
+Ref: table-gawk-rounding-modes941236
+Ref: Setting the rounding mode-Footnote-1945167
+Node: Arbitrary Precision Integers945346
+Ref: Arbitrary Precision Integers-Footnote-1948521
+Node: Checking for MPFR948670
+Node: POSIX Floating Point Problems950144
+Ref: POSIX Floating Point Problems-Footnote-1954429
+Node: Floating point summary954467
+Node: Dynamic Extensions956657
+Node: Extension Intro958210
+Node: Plugin License959476
+Node: Extension Mechanism Outline960273
+Ref: figure-load-extension960712
+Ref: figure-register-new-function962277
+Ref: figure-call-new-function963369
+Node: Extension API Description965431
+Node: Extension API Functions Introduction967073
+Node: General Data Types972613
+Ref: General Data Types-Footnote-1980974
+Node: Memory Allocation Functions981273
+Ref: Memory Allocation Functions-Footnote-1985483
+Node: Constructor Functions985582
+Node: Registration Functions989168
+Node: Extension Functions989853
+Node: Exit Callback Functions995068
+Node: Extension Version String996318
+Node: Input Parsers996981
+Node: Output Wrappers1009702
+Node: Two-way processors1014214
+Node: Printing Messages1016479
+Ref: Printing Messages-Footnote-11017650
+Node: Updating ERRNO1017803
+Node: Requesting Values1018542
+Ref: table-value-types-returned1019279
+Node: Accessing Parameters1020215
+Node: Symbol Table Access1021450
+Node: Symbol table by name1021962
+Node: Symbol table by cookie1023751
+Ref: Symbol table by cookie-Footnote-11027936
+Node: Cached values1028000
+Ref: Cached values-Footnote-11031536
+Node: Array Manipulation1031689
+Ref: Array Manipulation-Footnote-11032780
+Node: Array Data Types1032817
+Ref: Array Data Types-Footnote-11035475
+Node: Array Functions1035567
+Node: Flattening Arrays1040065
+Node: Creating Arrays1047041
+Node: Redirection API1051808
+Node: Extension API Variables1054641
+Node: Extension Versioning1055352
+Ref: gawk-api-version1055781
+Node: Extension GMP/MPFR Versioning1057512
+Node: Extension API Informational Variables1059140
+Node: Extension API Boilerplate1060213
+Node: Changes from API V11064187
+Node: Finding Extensions1065759
+Node: Extension Example1066318
+Node: Internal File Description1067116
+Node: Internal File Ops1071196
+Ref: Internal File Ops-Footnote-11082546
+Node: Using Internal File Ops1082686
+Ref: Using Internal File Ops-Footnote-11085069
+Node: Extension Samples1085343
+Node: Extension Sample File Functions1086872
+Node: Extension Sample Fnmatch1094521
+Node: Extension Sample Fork1096008
+Node: Extension Sample Inplace1097226
+Node: Extension Sample Ord1100443
+Node: Extension Sample Readdir1101279
+Ref: table-readdir-file-types1102168
+Node: Extension Sample Revout1102973
+Node: Extension Sample Rev2way1103562
+Node: Extension Sample Read write array1104302
+Node: Extension Sample Readfile1106244
+Node: Extension Sample Time1107339
+Node: Extension Sample API Tests1108687
+Node: gawkextlib1109179
+Node: Extension summary1112097
+Node: Extension Exercises1115799
+Node: Language History1117297
+Node: V7/SVR3.11118953
+Node: SVR41121105
+Node: POSIX1122539
+Node: BTL1123919
+Node: POSIX/GNU1124648
+Node: Feature History1130426
+Node: Common Extensions1146285
+Node: Ranges and Locales1147568
+Ref: Ranges and Locales-Footnote-11152184
+Ref: Ranges and Locales-Footnote-21152211
+Ref: Ranges and Locales-Footnote-31152446
+Node: Contributors1152667
+Node: History summary1158612
+Node: Installation1159992
+Node: Gawk Distribution1160936
+Node: Getting1161420
+Node: Extracting1162383
+Node: Distribution contents1164021
+Node: Unix Installation1170501
+Node: Quick Installation1171183
+Node: Shell Startup Files1173597
+Node: Additional Configuration Options1174686
+Node: Configuration Philosophy1176851
+Node: Non-Unix Installation1179220
+Node: PC Installation1179680
+Node: PC Binary Installation1180518
+Node: PC Compiling1180953
+Node: PC Using1182070
+Node: Cygwin1185285
+Node: MSYS1186384
+Node: VMS Installation1186885
+Node: VMS Compilation1187676
+Ref: VMS Compilation-Footnote-11188905
+Node: VMS Dynamic Extensions1188963
+Node: VMS Installation Details1190648
+Node: VMS Running1192901
+Node: VMS GNV1197180
+Node: VMS Old Gawk1197915
+Node: Bugs1198386
+Node: Bug address1199049
+Node: Usenet1201841
+Node: Maintainers1202618
+Node: Other Versions1203879
+Node: Installation summary1210641
+Node: Notes1211843
+Node: Compatibility Mode1212708
+Node: Additions1213490
+Node: Accessing The Source1214415
+Node: Adding Code1215852
+Node: New Ports1222071
+Node: Derived Files1226559
+Ref: Derived Files-Footnote-11232205
+Ref: Derived Files-Footnote-21232240
+Ref: Derived Files-Footnote-31232838
+Node: Future Extensions1232952
+Node: Implementation Limitations1233610
+Node: Extension Design1234793
+Node: Old Extension Problems1235947
+Ref: Old Extension Problems-Footnote-11237465
+Node: Extension New Mechanism Goals1237522
+Ref: Extension New Mechanism Goals-Footnote-11240886
+Node: Extension Other Design Decisions1241075
+Node: Extension Future Growth1243188
+Node: Old Extension Mechanism1244024
+Node: Notes summary1245787
+Node: Basic Concepts1246969
+Node: Basic High Level1247650
+Ref: figure-general-flow1247932
+Ref: figure-process-flow1248617
+Ref: Basic High Level-Footnote-11251918
+Node: Basic Data Typing1252103
+Node: Glossary1255431
+Node: Copying1287269
+Node: GNU Free Documentation License1324812
+Node: Index1349932
 
 End Tag Table
diff --git a/doc/gawk.texi b/doc/gawk.texi
index 5081449a..74e8bbb2 100644
--- a/doc/gawk.texi
+++ b/doc/gawk.texi
@@ -665,6 +665,7 @@ particular records in a file and perform operations upon them.
                                         strings with @samp{<}, etc.
 * Variable Typing::                     String type versus numeric type.
 * Comparison Operators::                The comparison operators.
+* IEEE 754 Special Values::             Comparing IEEE 754 Special Floating-Point Values and Regular Numbers.
 * POSIX String Comparison::             String comparison with POSIX rules.
 * Boolean Ops::                         Combining comparison expressions using
                                         boolean operators @samp{||} (``or''),
@@ -12560,6 +12561,7 @@ compares variables.
 @menu
 * Variable Typing::             String type versus numeric type.
 * Comparison Operators::        The comparison operators.
+* IEEE 754 Special Values::     Comparing IEEE 754 Special Floating-Point Values and Regular Numbers.
 * POSIX String Comparison::     String comparison with POSIX rules.
 @end menu
 
@@ -13016,6 +13018,76 @@ One special place where @code{/foo/} is @emph{not} an abbreviation for
 @xref{Using Constant Regexps},
 where this is discussed in more detail.
 
+@c FIXME: Add indexing here and in other places in the doc.
+@node IEEE 754 Special Values
+@subsubsection Comparing IEEE 754 Special Floating-Point Values and Regular Numbers
+
+Modern computing platforms use floating-point arithmatic as defined by the
+IEEE 754 standard (@strong{FIXME: web link or two here}).  Besides regular
+numbers, like @minus{}57 and 42, the standard defines two ``special''
+values: @dfn{Infinity}, and @dfn{Not-A-Number}.  (The latter is usally
+referred to as a @dfn{NaN}.)  These special values come in both positive
+and negative flavors.
+
+Infinity values are easy to understand: negative infinity is smaller
+than any other possible negative value, and postive infinity is greater
+than any other possible positive value.
+
+NaN values are harder to comprehend.  They represent impossible values.
+A canonical example is
+@iftex
+@math{\sqrt{-1}}.
+@end iftex
+@ifdocbook
+@docbook
+&radic;&minus;1.
+@end docbook
+@end ifdocbook
+@ifhtml
+@html
+<span style="white-space: nowrap; font-size:larger">
+&radic;<span style="text-decoration:overline;">&nbsp;&minus;1&nbsp;</span>.
+</span>
+@end html
+@end ifhtml
+@ifinfo
+@samp{sqrt(-1)}.
+@end ifinfo
+This value doesn't exist, so the result of calling @samp{sqrt(-1)} is a NaN.
+
+When comparing infinity values with @code{<}, @code{<=}, and so on,
+the results make sense.  But when comparing NaN values, things are
+more surprising. In particular, @emph{the only comparison that returns
+true for a NaN is} @code{!=}.  Every other comparison returns false.
+Most surprising of all, is that if you have two NaN values, they do
+@strong{not} compare equal!  They are not equal to each other, even if
+obtained in the same way. Consider this file, @file{nan.awk}:
+
+@example
+BEGIN @{
+    nan1 = sqrt(-1)
+    nan2 = sqrt(-1)
+    print nan1, nan2
+    print "nan1 == nan2 -->", (nan1 == nan2)
+    print "nan1 != nan2 -->", (nan1 != nan2)
+@}
+@end example
+
+@noindent
+Here is what happens when it's run:
+
+@example
+$ @kbd{gawk -f nan.awk}
+@print{} gawk: x.awk:2: warning: sqrt: called with negative argument -1
+@print{} gawk: x.awk:3: warning: sqrt: called with negative argument -1
+@print{} -nan -nan
+@print{} nan1 == nan2 --> 0
+@print{} nan1 != nan2 --> 1
+@end example
+
+In short, remember that computer arithmetic is @emph{not} the same
+as paper-and-pencil arithmetic!
+
 @node POSIX String Comparison
 @subsubsection String Comparison Based on Locale Collating Order
 
diff --git a/doc/gawktexi.in b/doc/gawktexi.in
index dff0e18c..0f5895dc 100644
--- a/doc/gawktexi.in
+++ b/doc/gawktexi.in
@@ -660,6 +660,7 @@ particular records in a file and perform operations upon them.
                                         strings with @samp{<}, etc.
 * Variable Typing::                     String type versus numeric type.
 * Comparison Operators::                The comparison operators.
+* IEEE 754 Special Values::             Comparing IEEE 754 Special Floating-Point Values and Regular Numbers.
 * POSIX String Comparison::             String comparison with POSIX rules.
 * Boolean Ops::                         Combining comparison expressions using
                                         boolean operators @samp{||} (``or''),
@@ -11878,6 +11879,7 @@ compares variables.
 @menu
 * Variable Typing::             String type versus numeric type.
 * Comparison Operators::        The comparison operators.
+* IEEE 754 Special Values::     Comparing IEEE 754 Special Floating-Point Values and Regular Numbers.
 * POSIX String Comparison::     String comparison with POSIX rules.
 @end menu
 
@@ -12334,6 +12336,76 @@ One special place where @code{/foo/} is @emph{not} an abbreviation for
 @xref{Using Constant Regexps},
 where this is discussed in more detail.
 
+@c FIXME: Add indexing here and in other places in the doc.
+@node IEEE 754 Special Values
+@subsubsection Comparing IEEE 754 Special Floating-Point Values and Regular Numbers
+
+Modern computing platforms use floating-point arithmatic as defined by the
+IEEE 754 standard (@strong{FIXME: web link or two here}).  Besides regular
+numbers, like @minus{}57 and 42, the standard defines two ``special''
+values: @dfn{Infinity}, and @dfn{Not-A-Number}.  (The latter is usally
+referred to as a @dfn{NaN}.)  These special values come in both positive
+and negative flavors.
+
+Infinity values are easy to understand: negative infinity is smaller
+than any other possible negative value, and postive infinity is greater
+than any other possible positive value.
+
+NaN values are harder to comprehend.  They represent impossible values.
+A canonical example is
+@iftex
+@math{\sqrt{-1}}.
+@end iftex
+@ifdocbook
+@docbook
+&radic;&minus;1.
+@end docbook
+@end ifdocbook
+@ifhtml
+@html
+<span style="white-space: nowrap; font-size:larger">
+&radic;<span style="text-decoration:overline;">&nbsp;&minus;1&nbsp;</span>.
+</span>
+@end html
+@end ifhtml
+@ifinfo
+@samp{sqrt(-1)}.
+@end ifinfo
+This value doesn't exist, so the result of calling @samp{sqrt(-1)} is a NaN.
+
+When comparing infinity values with @code{<}, @code{<=}, and so on,
+the results make sense.  But when comparing NaN values, things are
+more surprising. In particular, @emph{the only comparison that returns
+true for a NaN is} @code{!=}.  Every other comparison returns false.
+Most surprising of all, is that if you have two NaN values, they do
+@strong{not} compare equal!  They are not equal to each other, even if
+obtained in the same way. Consider this file, @file{nan.awk}:
+
+@example
+BEGIN @{
+    nan1 = sqrt(-1)
+    nan2 = sqrt(-1)
+    print nan1, nan2
+    print "nan1 == nan2 -->", (nan1 == nan2)
+    print "nan1 != nan2 -->", (nan1 != nan2)
+@}
+@end example
+
+@noindent
+Here is what happens when it's run:
+
+@example
+$ @kbd{gawk -f nan.awk}
+@print{} gawk: x.awk:2: warning: sqrt: called with negative argument -1
+@print{} gawk: x.awk:3: warning: sqrt: called with negative argument -1
+@print{} -nan -nan
+@print{} nan1 == nan2 --> 0
+@print{} nan1 != nan2 --> 1
+@end example
+
+In short, remember that computer arithmetic is @emph{not} the same
+as paper-and-pencil arithmetic!
+
 @node POSIX String Comparison
 @subsubsection String Comparison Based on Locale Collating Order
 
diff --git a/eval.c b/eval.c
index 34ba174c..9ed088be 100644
--- a/eval.c
+++ b/eval.c
@@ -24,10 +24,8 @@
  */
 
 #include "awk.h"
+#include <math.h>
 
-extern double pow(double x, double y);
-extern double modf(double x, double *yp);
-extern double fmod(double x, double y);
 NODE **fcall_list = NULL;
 long fcall_count = 0;
 int currule = 0;
@@ -1489,13 +1487,84 @@ eval_condition(NODE *t)
 }
 
 typedef enum {
-	SCALAR_EQ_NEQ,
-	SCALAR_RELATIONAL
+	SCALAR_EQ,
+	SCALAR_NE,
+	SCALAR_LT,
+	SCALAR_LE,
+	SCALAR_GT,
+	SCALAR_GE,
 } scalar_cmp_t;
 
+#ifdef HAVE_MPFR
+/* mpg_cmp_scalars -- compare two MPG / MPFR nodes on the stack */
+
+static inline bool
+mpg_cmp_scalars(NODE *t1, NODE *t2, scalar_cmp_t comparison_type)
+{
+	// Do regular comparison of mpg numbers
+
+	int ret = 0;
+	if (is_mpg_float(t1)) {
+		if (mpfr_nan_p(t1->mpg_numbr))
+			return (comparison_type == SCALAR_NE);	// true for !=, false for everything else
+		else if (is_mpg_float(t2)) {
+			if (mpfr_nan_p(t2->mpg_numbr))
+				return (comparison_type == SCALAR_NE);	// true for !=, false for everything else
+			ret = mpfr_cmp(t1->mpg_numbr, t2->mpg_numbr);
+			// fall through to switch
+		} else if (is_mpg_integer(t2)) {
+			ret = mpfr_cmp_z(t1->mpg_numbr, t2->mpg_i);
+			// fall through to switch
+		} else
+			assert(false);
+	} else if (is_mpg_float(t2)) {
+		if (mpfr_nan_p(t2->mpg_numbr))
+			return (comparison_type == SCALAR_NE);	// true for !=, false for everything else
+		ret = mpfr_cmp_z(t2->mpg_numbr, t1->mpg_i);
+		// fall through to switch
+	} else if (is_mpg_integer(t1)) {
+		ret =  mpz_cmp(t1->mpg_i, t2->mpg_i);
+		// fall through to switch
+	} else {
+		// t1 and t2 are AWKNUMs
+		ret = cmp_awknums(t1, t2);
+		// fall through to switch
+	}
+
+	bool result = false;
+	switch (comparison_type) {
+	case SCALAR_EQ:
+		result = (ret == 0);
+		break;
+	case SCALAR_NE:
+		result = (ret != 0);
+		break;
+	case SCALAR_LT:
+		result = (ret <  0);
+		break;
+	case SCALAR_LE:
+		result = (ret <= 0);
+		break;
+	case SCALAR_GT:
+		result = (ret >  0);
+		break;
+	case SCALAR_GE:
+		result = (ret >= 0);
+		break;
+	default:
+		fatal(_("mpg_cmp_scalars: bad value for comparison_type: %d"),
+			comparison_type);
+		break;
+	}
+
+	return result;
+
+}
+#endif
+
 /* cmp_scalars -- compare two nodes on the stack */
 
-static inline int
+static inline bool
 cmp_scalars(scalar_cmp_t comparison_type)
 {
 	NODE *t1, *t2;
@@ -1507,10 +1576,77 @@ cmp_scalars(scalar_cmp_t comparison_type)
 		DEREF(t2);
 		fatal(_("attempt to use array `%s' in a scalar context"), array_vname(t1));
 	}
-	di = cmp_nodes(t1, t2, comparison_type == SCALAR_EQ_NEQ);
+
+
+	fixtype(t1);
+	fixtype(t2);
+
+	bool result = false;
+#ifdef HAVE_MPFR
+	if (is_mpg_number(t1) || is_mpg_number(t2)) {
+		result = mpg_cmp_scalars(t1, t2, comparison_type);
+	} else
+#endif
+	if (isnan(t1->numbr) || isnan(t2->numbr))
+		result = (comparison_type == SCALAR_NE);	// true for !=, false for everything else
+	else if (isinf(t1->numbr) || isinf(t2->numbr)) {
+		switch (comparison_type) {
+		case SCALAR_EQ:
+			result = (t1->numbr == t2->numbr);
+			break;
+		case SCALAR_NE:
+			result = (t1->numbr != t2->numbr);
+			break;
+		case SCALAR_LT:
+			result = (t1->numbr <  t2->numbr);
+			break;
+		case SCALAR_LE:
+			result = (t1->numbr <= t2->numbr);
+			break;
+		case SCALAR_GT:
+			result = (t1->numbr >  t2->numbr);
+			break;
+		case SCALAR_GE:
+			result = (t1->numbr >= t2->numbr);
+			break;
+		default:
+			fatal(_("cmp_scalars: bad value for comparison_type: %d"),
+				comparison_type);
+			break;
+		}
+	} else {
+		di = cmp_nodes(t1, t2,
+			comparison_type == SCALAR_EQ || comparison_type == SCALAR_NE);
+
+		switch (comparison_type) {
+		case SCALAR_EQ:
+			result = (di == 0);
+			break;
+		case SCALAR_NE:
+			result = (di != 0);
+			break;
+		case SCALAR_LT:
+			result = (di <  0);
+			break;
+		case SCALAR_LE:
+			result = (di <= 0);
+			break;
+		case SCALAR_GT:
+			result = (di >  0);
+			break;
+		case SCALAR_GE:
+			result = (di >= 0);
+			break;
+		default:
+			fatal(_("cmp_scalars: bad value for comparison_type: %d"),
+				comparison_type);
+			break;
+		}
+	}
+
 	DEREF(t1);
 	DEREF(t2);
-	return di;
+	return result;
 }
 
 /* op_assign --- assignment operators excluding = */
diff --git a/helpers/ChangeLog b/helpers/ChangeLog
index d54de869..2c07b068 100644
--- a/helpers/ChangeLog
+++ b/helpers/ChangeLog
@@ -1,3 +1,7 @@
+2018-07-19         Arnold D. Robbins     <arnold@skeeve.com>
+
+	* gen-float-table.c, gen-table.awk: New files.
+
 2018-02-25         Arnold D. Robbins     <arnold@skeeve.com>
 
 	* 4.2.1: Release tar ball made.
diff --git a/helpers/gen-float-table.c b/helpers/gen-float-table.c
new file mode 100755
index 00000000..95985422
--- /dev/null
+++ b/helpers/gen-float-table.c
@@ -0,0 +1,62 @@
+#include <stdio.h>
+#include <math.h>
+#include <stdbool.h>
+
+#define def_func(name, op) \
+	bool name(double left, double right) { \
+		return left op right; \
+	}
+
+def_func(eq, ==)
+def_func(ne, !=)
+def_func(lt, <)
+def_func(le, <=)
+def_func(gt, >)
+def_func(ge, >=)
+
+struct {
+	const char *name;
+	bool (*func)(double left, double right);
+} functions[] = {
+	{ "==", eq },
+	{ "!=", ne },
+	{ "< ", lt },
+	{ "<=", le },
+	{ "> ", gt },
+	{ ">=", ge },
+	{ 0, 0 }
+};
+
+int main()
+{
+	double values[] = {
+		-sqrt(-1),     // nan
+		sqrt(-1),      // -nan
+		-log(0.0),     // inf
+		log(0.0)       // -inf
+	};
+	double compare[] = {
+		2.0,
+		-sqrt(-1),     // nan
+		sqrt(-1),      // -nan
+		-log(0.0),     // inf
+		log(0.0)       // -inf
+	};
+
+	int i, j, k;
+
+	for (i = 0; i < 4; i++) {
+		for (j = 0; j < 5; j++) {
+			for (k = 0; functions[k].name != NULL; k++) {
+				printf("%g %s %g -> %s\n",
+					values[i],
+					functions[k].name,
+					compare[j],
+					functions[k].func(values[i], compare[j]) ? "true" : "false");
+			}
+			printf("\n");
+		}
+	}
+
+	return 0;
+}
diff --git a/helpers/gen-table.awk b/helpers/gen-table.awk
new file mode 100644
index 00000000..6998ae0e
--- /dev/null
+++ b/helpers/gen-table.awk
@@ -0,0 +1,59 @@
+function eq(left, right)
+{
+        return left == right
+}
+
+function ne(left, right)
+{
+        return left != right
+}
+
+function lt(left, right)
+{
+        return left <  right
+}
+
+function le(left, right)
+{
+        return left <= right
+}
+
+function gt(left, right)
+{
+        return left >  right
+}
+
+function ge(left, right)
+{
+        return left >= right
+}
+
+BEGIN {
+	nan = sqrt(-1)
+	inf = -log(0)
+        split("== != < <= > >=", names)
+	names[3] = names[3] " "
+	names[5] = names[5] " "
+        split("eq ne lt le gt ge", funcs)
+
+	compare[1] =              2.0
+        compare[2] = values[1] = -sqrt(-1.0)	# nan
+        compare[3] = values[2] =  sqrt(-1.0)	# -nan
+        compare[4] = values[3] = -log(0.0)	# inf
+        compare[5] = values[4] =  log(0.0)	# -inf
+
+	for (i = 1; i in values; i++) {
+		for (j = 1; j in compare; j++) {
+			for (k = 1; k in names; k++) {
+				the_func = funcs[k]
+				result = @the_func(values[i], compare[j])
+				printf("%g %s %g -> %s\n",
+                                                values[i],
+						names[k],
+						compare[j],
+					        result ?  "true" : "false");
+			}
+			printf("\n");
+		}
+	}
+}
diff --git a/interpret.h b/interpret.h
index 8408a532..866bf7b7 100644
--- a/interpret.h
+++ b/interpret.h
@@ -459,37 +459,37 @@ uninitialized_scalar:
 			break;
 
 		case Op_equal:
-			r = node_Boolean[cmp_scalars(SCALAR_EQ_NEQ) == 0];
+			r = node_Boolean[cmp_scalars(SCALAR_EQ)];
 			UPREF(r);
 			REPLACE(r);
 			break;
 
 		case Op_notequal:
-			r = node_Boolean[cmp_scalars(SCALAR_EQ_NEQ) != 0];
+			r = node_Boolean[cmp_scalars(SCALAR_NE)];
 			UPREF(r);
 			REPLACE(r);
 			break;
 
 		case Op_less:
-			r = node_Boolean[cmp_scalars(SCALAR_RELATIONAL) < 0];
+			r = node_Boolean[cmp_scalars(SCALAR_LT)];
 			UPREF(r);
 			REPLACE(r);
 			break;
 
 		case Op_greater:
-			r = node_Boolean[cmp_scalars(SCALAR_RELATIONAL) > 0];
+			r = node_Boolean[cmp_scalars(SCALAR_GT)];
 			UPREF(r);
 			REPLACE(r);
 			break;
 
 		case Op_leq:
-			r = node_Boolean[cmp_scalars(SCALAR_RELATIONAL) <= 0];
+			r = node_Boolean[cmp_scalars(SCALAR_LE)];
 			UPREF(r);
 			REPLACE(r);
 			break;
 
 		case Op_geq:
-			r = node_Boolean[cmp_scalars(SCALAR_RELATIONAL) >= 0];
+			r = node_Boolean[cmp_scalars(SCALAR_GE)];
 			UPREF(r);
 			REPLACE(r);
 			break;