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  • Committer: Arnold D. Robbins
  • Date: 2024-07-28 09:43:58 UTC
  • mto: (2057.4.2)
  • mto: This revision was merged to the branch mainline in revision 2125.
  • Revision ID: git-v1:84d2a184dd407cf68f554ee628232c47c44ae09e
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doc/gawk.info
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16.1 A General Description of Computer Arithmetic
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=================================================
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Until now, we have worked with data as either numbers or strings.
 
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     Have you ever considered that the plural of "half" is "whole"?
 
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                          -- _Allan Sherman_
 
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   Until now, we have worked with data as either numbers or strings.
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Ultimately, however, computers represent everything in terms of “binary
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digits”, or “bits”.  A decimal digit can take on any of 10 values: zero
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through nine.  A binary digit can take on any of two values, zero or
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                                                              (line   6)
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* arbitrary precision:                   Arbitrary Precision Arithmetic.
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                                                              (line   6)
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* arbitrary precision <1>:               Computer Arithmetic. (line  61)
 
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* arbitrary precision <1>:               Computer Arithmetic. (line  64)
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* arbitrary precision, integers:         Arbitrary Precision Integers.
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                                                              (line   6)
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* archaeologists:                        Bugs.                (line   6)
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                                                              (line  31)
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* double quote ("), in regexp constants: Computed Regexps.    (line  30)
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* double quote ("), in shell commands:   Quoting.             (line  54)
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* double-precision:                      Computer Arithmetic. (line  61)
 
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* double-precision:                      Computer Arithmetic. (line  64)
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* down debugger command:                 Execution Stack.     (line  23)
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* Drepper, Ulrich:                       Acknowledgments.     (line  52)
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* Duman, Patrice:                        Acknowledgments.     (line  75)
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* fixed-width data:                      Constant Size.       (line   6)
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* flag variables:                        Boolean Ops.         (line  69)
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* flag variables <1>:                    Tee Program.         (line  20)
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* floating-point, numbers:               Computer Arithmetic. (line  49)
 
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* floating-point, numbers:               Computer Arithmetic. (line  52)
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* floating-point, numbers, arbitrary-precision: Arbitrary Precision Arithmetic.
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                                                              (line   6)
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* floating-point, numbers, arbitrary-precision <1>: Computer Arithmetic.
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                                                              (line  61)
 
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                                                              (line  64)
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* floating-point, numbers, double-precision: Computer Arithmetic.
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                                                              (line  61)
 
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                                                              (line  64)
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* floating-point, numbers, single-precision: Computer Arithmetic.
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                                                              (line  61)
 
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                                                              (line  64)
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* flush buffered output:                 I/O Functions.       (line  28)
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* fnmatch() extension function:          Extension Sample Fnmatch.
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                                                              (line  12)
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                                                              (line  31)
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* integers, arbitrary precision:         Arbitrary Precision Integers.
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                                                              (line   6)
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* integers, unsigned:                    Computer Arithmetic. (line  41)
 
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* integers, unsigned:                    Computer Arithmetic. (line  44)
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* interacting with other programs:       I/O Functions.       (line 105)
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* internationalization:                  I18N Functions.      (line   6)
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* internationalization <1>:              I18N and L10N.       (line   6)
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* shells, sea:                           Undocumented.        (line   9)
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* shells, variables:                     Using Shell Variables.
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                                                              (line   6)
 
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* Sherman, Allan:                        Computer Arithmetic. (line   6)
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* shift, bitwise:                        Bitwise Functions.   (line  32)
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* short-circuit operators:               Boolean Ops.         (line  59)
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* show in debugger, all source files:    Debugger Info.       (line  45)
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* single records, treating files as:     gawk split records.  (line 102)
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* single-character fields:               Single Character Fields.
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                                                              (line   6)
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* single-precision:                      Computer Arithmetic. (line  61)
 
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* single-precision:                      Computer Arithmetic. (line  64)
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* single-step execution, in the debugger: Debugger Execution Control.
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                                                              (line  43)
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* Skywalker, Luke:                       Undocumented.        (line   6)
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* Unix awk, close() function and:        Close Return Value.  (line   6)
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* Unix awk, password files, field separators and: Command Line Field Separator.
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                                                              (line  62)
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* unsigned integers:                     Computer Arithmetic. (line  41)
 
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* unsigned integers:                     Computer Arithmetic. (line  44)
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* until debugger command:                Debugger Execution Control.
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                                                              (line  82)
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* unwatch debugger command:              Viewing And Changing Data.
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Node: Namespace Summary1046273
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Node: Arbitrary Precision Arithmetic1047784
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Node: Computer Arithmetic1049303
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Ref: table-numeric-ranges1053111
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Ref: table-floating-point-ranges1053608
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Ref: Computer Arithmetic-Footnote-11054266
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Node: Math Definitions1054323
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Ref: table-ieee-formats1057355
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Node: MPFR features1057928
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Node: MPFR On Parole1058381
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Ref: MPFR On Parole-Footnote-11059222
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Node: MPFR Intro1059381
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Node: FP Math Caution1061065
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Ref: FP Math Caution-Footnote-11062137
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Node: Inexactness of computations1062510
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Node: Inexact representation1063541
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Node: Comparing FP Values1064922
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Node: Errors accumulate1066180
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Node: Strange values1067645
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Ref: Strange values-Footnote-11070299
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Node: Getting Accuracy1070404
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Node: Try To Round1073141
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Node: Setting precision1074048
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Ref: table-predefined-precision-strings1074753
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Node: Setting the rounding mode1076637
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Ref: table-gawk-rounding-modes1077019
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Ref: Setting the rounding mode-Footnote-11081071
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Node: Arbitrary Precision Integers1081254
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Ref: Arbitrary Precision Integers-Footnote-11084464
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Node: Checking for MPFR1084617
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Node: POSIX Floating Point Problems1086107
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Ref: POSIX Floating Point Problems-Footnote-11090927
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Node: Floating point summary1090965
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Node: Dynamic Extensions1093221
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Node: Extension Intro1094818
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Node: Plugin License1096120
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Node: Extension Mechanism Outline1096933
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Ref: figure-load-extension1097384
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Ref: figure-register-new-function1098962
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Ref: figure-call-new-function1100071
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Node: Extension API Description1102186
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Node: Extension API Functions Introduction1103915
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Ref: table-api-std-headers1105809
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Node: General Data Types1110250
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Ref: General Data Types-Footnote-11119396
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Node: Memory Allocation Functions1119699
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Ref: Memory Allocation Functions-Footnote-11124416
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Node: Constructor Functions1124515
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Node: API Ownership of MPFR and GMP Values1128416
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Node: Registration Functions1129969
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Node: Extension Functions1130673
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Node: Exit Callback Functions1136247
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Node: Extension Version String1137561
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Node: Input Parsers1138256
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Node: Output Wrappers1152875
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Node: Two-way processors1157717
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Node: Printing Messages1160070
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Ref: Printing Messages-Footnote-11161281
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Node: Updating ERRNO1161434
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Node: Requesting Values1162233
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Ref: table-value-types-returned1162986
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Node: Accessing Parameters1165045
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Node: Symbol Table Access1166326
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Node: Symbol table by name1166838
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Ref: Symbol table by name-Footnote-11170039
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Node: Symbol table by cookie1170171
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Ref: Symbol table by cookie-Footnote-11174440
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Node: Cached values1174504
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Ref: Cached values-Footnote-11178136
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Node: Array Manipulation1178293
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Ref: Array Manipulation-Footnote-11179392
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Node: Array Data Types1179429
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Ref: Array Data Types-Footnote-11182247
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Node: Array Functions1182343
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Node: Flattening Arrays1187372
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Node: Creating Arrays1194420
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Node: Redirection API1199262
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Node: Extension API Variables1202279
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Node: Extension Versioning1203002
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Ref: gawk-api-version1203431
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Node: Extension GMP/MPFR Versioning1205218
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Node: Extension API Informational Variables1206922
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Node: Extension API Boilerplate1208175
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Node: Changes from API V11212305
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Node: Finding Extensions1213937
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Node: Extension Example1214512
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Node: Internal File Description1215334
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Node: Internal File Ops1219626
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Ref: Internal File Ops-Footnote-11231176
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Node: Using Internal File Ops1231324
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Ref: Using Internal File Ops-Footnote-11233755
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Node: Extension Samples1234033
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Node: Extension Sample File Functions1235602
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Node: Extension Sample Fnmatch1243727
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Node: Extension Sample Fork1245322
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Node: Extension Sample Inplace1246598
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Node: Extension Sample Ord1250700
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Node: Extension Sample Readdir1251576
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Ref: table-readdir-file-types1252365
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Node: Extension Sample Revout1253721
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Node: Extension Sample Rev2way1254318
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Node: Extension Sample Read write array1255070
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Node: Extension Sample Readfile1258344
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Node: Extension Sample Time1259475
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Node: Extension Sample API Tests1261475
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Node: gawkextlib1261983
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Node: Extension summary1265015
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Node: Extension Exercises1268863
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Node: Language History1270133
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Node: V7/SVR3.11271845
40429
 
Node: SVR41274195
40430
 
Node: POSIX1275727
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Node: BTL1277152
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Node: POSIX/GNU1277919
40433
 
Node: Feature History1284574
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Node: Common Extensions1304415
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Node: Ranges and Locales1305890
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Ref: Ranges and Locales-Footnote-11310675
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Ref: Ranges and Locales-Footnote-21310702
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Ref: Ranges and Locales-Footnote-31310937
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Node: Contributors1311160
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Node: History summary1317351
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Node: Installation1318793
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Node: Gawk Distribution1319757
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Node: Getting1320249
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Node: Extracting1321248
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Node: Distribution contents1322954
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Node: Unix Installation1330844
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Node: Quick Installation1331664
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Node: Compiling with MPFR1334204
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Node: Shell Startup Files1334910
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Node: Additional Configuration Options1336067
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Node: Configuration Philosophy1338450
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Node: Compiling from Git1340950
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Node: Building the Documentation1341509
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Node: Non-Unix Installation1342921
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Node: PC Installation1343397
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Node: PC Binary Installation1344266
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Node: PC Compiling1345159
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Node: PC Using1346337
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Node: Cygwin1350053
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Node: MSYS1351305
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Node: OpenVMS Installation1351931
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Node: OpenVMS Compilation1352612
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Ref: OpenVMS Compilation-Footnote-11354095
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Node: OpenVMS Dynamic Extensions1354153
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Node: OpenVMS Installation Details1355789
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Node: OpenVMS Running1358220
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Node: OpenVMS GNV1362357
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Node: Bugs1363112
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Node: Bug definition1364032
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Node: Bug address1367633
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Node: Usenet1371202
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Node: Performance bugs1372415
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Node: Asking for help1375431
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Node: Maintainers1377418
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Node: Other Versions1378445
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Node: Installation summary1388049
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Node: Notes1389431
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Node: Compatibility Mode1390241
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Node: Additions1391063
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Node: Accessing The Source1392008
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Node: Adding Code1393539
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Node: New Ports1400650
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Node: Derived Files1405153
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Ref: Derived Files-Footnote-11410964
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Ref: Derived Files-Footnote-21410999
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Ref: Derived Files-Footnote-31411610
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Node: Future Extensions1411724
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Node: Implementation Limitations1412394
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Node: Extension Design1413636
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Node: Old Extension Problems1414796
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Ref: Old Extension Problems-Footnote-11416368
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Node: Extension New Mechanism Goals1416429
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Ref: Extension New Mechanism Goals-Footnote-11419899
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Node: Extension Other Design Decisions1420100
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Node: Extension Future Growth1422297
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Node: Notes summary1422917
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Node: Basic Concepts1424127
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Node: Basic High Level1424812
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Ref: figure-general-flow1425094
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Ref: figure-process-flow1425796
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Ref: Basic High Level-Footnote-11429166
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Node: Basic Data Typing1429355
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Node: Glossary1432763
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Node: Copying1465641
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Node: GNU Free Documentation License1503199
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Node: Index1528322
 
40326
Ref: table-numeric-ranges1053228
 
40327
Ref: table-floating-point-ranges1053725
 
40328
Ref: Computer Arithmetic-Footnote-11054383
 
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Node: Math Definitions1054440
 
40330
Ref: table-ieee-formats1057472
 
40331
Node: MPFR features1058045
 
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Node: MPFR On Parole1058498
 
40333
Ref: MPFR On Parole-Footnote-11059339
 
40334
Node: MPFR Intro1059498
 
40335
Node: FP Math Caution1061182
 
40336
Ref: FP Math Caution-Footnote-11062254
 
40337
Node: Inexactness of computations1062627
 
40338
Node: Inexact representation1063658
 
40339
Node: Comparing FP Values1065039
 
40340
Node: Errors accumulate1066297
 
40341
Node: Strange values1067762
 
40342
Ref: Strange values-Footnote-11070416
 
40343
Node: Getting Accuracy1070521
 
40344
Node: Try To Round1073258
 
40345
Node: Setting precision1074165
 
40346
Ref: table-predefined-precision-strings1074870
 
40347
Node: Setting the rounding mode1076754
 
40348
Ref: table-gawk-rounding-modes1077136
 
40349
Ref: Setting the rounding mode-Footnote-11081188
 
40350
Node: Arbitrary Precision Integers1081371
 
40351
Ref: Arbitrary Precision Integers-Footnote-11084581
 
40352
Node: Checking for MPFR1084734
 
40353
Node: POSIX Floating Point Problems1086224
 
40354
Ref: POSIX Floating Point Problems-Footnote-11091044
 
40355
Node: Floating point summary1091082
 
40356
Node: Dynamic Extensions1093338
 
40357
Node: Extension Intro1094935
 
40358
Node: Plugin License1096237
 
40359
Node: Extension Mechanism Outline1097050
 
40360
Ref: figure-load-extension1097501
 
40361
Ref: figure-register-new-function1099079
 
40362
Ref: figure-call-new-function1100188
 
40363
Node: Extension API Description1102303
 
40364
Node: Extension API Functions Introduction1104032
 
40365
Ref: table-api-std-headers1105926
 
40366
Node: General Data Types1110367
 
40367
Ref: General Data Types-Footnote-11119513
 
40368
Node: Memory Allocation Functions1119816
 
40369
Ref: Memory Allocation Functions-Footnote-11124533
 
40370
Node: Constructor Functions1124632
 
40371
Node: API Ownership of MPFR and GMP Values1128533
 
40372
Node: Registration Functions1130086
 
40373
Node: Extension Functions1130790
 
40374
Node: Exit Callback Functions1136364
 
40375
Node: Extension Version String1137678
 
40376
Node: Input Parsers1138373
 
40377
Node: Output Wrappers1152992
 
40378
Node: Two-way processors1157834
 
40379
Node: Printing Messages1160187
 
40380
Ref: Printing Messages-Footnote-11161398
 
40381
Node: Updating ERRNO1161551
 
40382
Node: Requesting Values1162350
 
40383
Ref: table-value-types-returned1163103
 
40384
Node: Accessing Parameters1165162
 
40385
Node: Symbol Table Access1166443
 
40386
Node: Symbol table by name1166955
 
40387
Ref: Symbol table by name-Footnote-11170156
 
40388
Node: Symbol table by cookie1170288
 
40389
Ref: Symbol table by cookie-Footnote-11174557
 
40390
Node: Cached values1174621
 
40391
Ref: Cached values-Footnote-11178253
 
40392
Node: Array Manipulation1178410
 
40393
Ref: Array Manipulation-Footnote-11179509
 
40394
Node: Array Data Types1179546
 
40395
Ref: Array Data Types-Footnote-11182364
 
40396
Node: Array Functions1182460
 
40397
Node: Flattening Arrays1187489
 
40398
Node: Creating Arrays1194537
 
40399
Node: Redirection API1199379
 
40400
Node: Extension API Variables1202396
 
40401
Node: Extension Versioning1203119
 
40402
Ref: gawk-api-version1203548
 
40403
Node: Extension GMP/MPFR Versioning1205335
 
40404
Node: Extension API Informational Variables1207039
 
40405
Node: Extension API Boilerplate1208292
 
40406
Node: Changes from API V11212422
 
40407
Node: Finding Extensions1214054
 
40408
Node: Extension Example1214629
 
40409
Node: Internal File Description1215451
 
40410
Node: Internal File Ops1219743
 
40411
Ref: Internal File Ops-Footnote-11231293
 
40412
Node: Using Internal File Ops1231441
 
40413
Ref: Using Internal File Ops-Footnote-11233872
 
40414
Node: Extension Samples1234150
 
40415
Node: Extension Sample File Functions1235719
 
40416
Node: Extension Sample Fnmatch1243844
 
40417
Node: Extension Sample Fork1245439
 
40418
Node: Extension Sample Inplace1246715
 
40419
Node: Extension Sample Ord1250817
 
40420
Node: Extension Sample Readdir1251693
 
40421
Ref: table-readdir-file-types1252482
 
40422
Node: Extension Sample Revout1253838
 
40423
Node: Extension Sample Rev2way1254435
 
40424
Node: Extension Sample Read write array1255187
 
40425
Node: Extension Sample Readfile1258461
 
40426
Node: Extension Sample Time1259592
 
40427
Node: Extension Sample API Tests1261592
 
40428
Node: gawkextlib1262100
 
40429
Node: Extension summary1265132
 
40430
Node: Extension Exercises1268980
 
40431
Node: Language History1270250
 
40432
Node: V7/SVR3.11271962
 
40433
Node: SVR41274312
 
40434
Node: POSIX1275844
 
40435
Node: BTL1277269
 
40436
Node: POSIX/GNU1278036
 
40437
Node: Feature History1284691
 
40438
Node: Common Extensions1304532
 
40439
Node: Ranges and Locales1306007
 
40440
Ref: Ranges and Locales-Footnote-11310792
 
40441
Ref: Ranges and Locales-Footnote-21310819
 
40442
Ref: Ranges and Locales-Footnote-31311054
 
40443
Node: Contributors1311277
 
40444
Node: History summary1317468
 
40445
Node: Installation1318910
 
40446
Node: Gawk Distribution1319874
 
40447
Node: Getting1320366
 
40448
Node: Extracting1321365
 
40449
Node: Distribution contents1323071
 
40450
Node: Unix Installation1330961
 
40451
Node: Quick Installation1331781
 
40452
Node: Compiling with MPFR1334321
 
40453
Node: Shell Startup Files1335027
 
40454
Node: Additional Configuration Options1336184
 
40455
Node: Configuration Philosophy1338567
 
40456
Node: Compiling from Git1341067
 
40457
Node: Building the Documentation1341626
 
40458
Node: Non-Unix Installation1343038
 
40459
Node: PC Installation1343514
 
40460
Node: PC Binary Installation1344383
 
40461
Node: PC Compiling1345276
 
40462
Node: PC Using1346454
 
40463
Node: Cygwin1350170
 
40464
Node: MSYS1351422
 
40465
Node: OpenVMS Installation1352048
 
40466
Node: OpenVMS Compilation1352729
 
40467
Ref: OpenVMS Compilation-Footnote-11354212
 
40468
Node: OpenVMS Dynamic Extensions1354270
 
40469
Node: OpenVMS Installation Details1355906
 
40470
Node: OpenVMS Running1358337
 
40471
Node: OpenVMS GNV1362474
 
40472
Node: Bugs1363229
 
40473
Node: Bug definition1364149
 
40474
Node: Bug address1367750
 
40475
Node: Usenet1371319
 
40476
Node: Performance bugs1372532
 
40477
Node: Asking for help1375548
 
40478
Node: Maintainers1377535
 
40479
Node: Other Versions1378562
 
40480
Node: Installation summary1388166
 
40481
Node: Notes1389548
 
40482
Node: Compatibility Mode1390358
 
40483
Node: Additions1391180
 
40484
Node: Accessing The Source1392125
 
40485
Node: Adding Code1393656
 
40486
Node: New Ports1400767
 
40487
Node: Derived Files1405270
 
40488
Ref: Derived Files-Footnote-11411081
 
40489
Ref: Derived Files-Footnote-21411116
 
40490
Ref: Derived Files-Footnote-31411727
 
40491
Node: Future Extensions1411841
 
40492
Node: Implementation Limitations1412511
 
40493
Node: Extension Design1413753
 
40494
Node: Old Extension Problems1414913
 
40495
Ref: Old Extension Problems-Footnote-11416485
 
40496
Node: Extension New Mechanism Goals1416546
 
40497
Ref: Extension New Mechanism Goals-Footnote-11420016
 
40498
Node: Extension Other Design Decisions1420217
 
40499
Node: Extension Future Growth1422414
 
40500
Node: Notes summary1423034
 
40501
Node: Basic Concepts1424244
 
40502
Node: Basic High Level1424929
 
40503
Ref: figure-general-flow1425211
 
40504
Ref: figure-process-flow1425913
 
40505
Ref: Basic High Level-Footnote-11429283
 
40506
Node: Basic Data Typing1429472
 
40507
Node: Glossary1432880
 
40508
Node: Copying1465758
 
40509
Node: GNU Free Documentation License1503316
 
40510
Node: Index1528439
40507
40511
 
40508
40512
End Tag Table
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