⟦9893505e2⟧

TextFile

%!PS-Adobe-2.0
%%Title: PubTeX output 1990.12.13:1341
%%Creator: Pubps,       ArborText, Inc.
%%BoundingBox: (atend)
%%Pages: (atend)
%%DocumentFonts: (atend)
%%EndComments

%! 
%  Dvips.pro - included prolog for DviLaser-generated PostScript files.
% 
%  Copyright (c) 1986-89, ArborText, Inc.
%  Permission to copy is granted so long as the PostScript code
%  is not resold or used in a commercial product.
%
%  $Header: pubps.pro,v 1.14 90/04/10 12:27:08 jsg Exp $

systemdict /setpacking known  % use array packing mode if its available
  {/savepackingmode currentpacking def 
   true setpacking}
  if
 
/$DviLaser 400 dict def
 
% Begin document
/BeginDviLaserDoc {
  vmstatus pop pop 0 eq 
    { $DviLaser begin 
      InitializeState }
    { /DviLaserJob save def
      $DviLaser begin
      InitializeState
      /DviLaserFonts save def }
    ifelse
} bind def
 
% End document
/EndDviLaserDoc {
  vmstatus pop pop 0 eq 
    { end }
    { DviLaserFonts restore
      end
      DviLaserJob restore }
    ifelse
} bind def
 
$DviLaser begin

/tempstr 64 string def
/tempint 0 def
/tempmatrix matrix def
 
%
%  Debugging routines
%
/DebugMode false def

/PrintInt {
  tempstr cvs print
} bind def

/PrintLn {
  (\n) print flush
} bind def
 
/PrintVMStats {
  print
  PrintLn
  (VM status - ) print
  vmstatus
  3 copy
  PrintInt (\(total\), ) print
  PrintInt (\(used\), ) print
  pop
  exch sub 
  PrintInt (\(remaining\), ) print
  PrintInt (\(level\)) print
  PrintLn
} bind def
 
/VMS /PrintVMStats load def 
 
/VMSDebug {
  DebugMode
    {PrintVMStats}
    {pop}
    ifelse
} bind def
 
(beginning of common prolog) VMSDebug 

% Make it easy to bind definitions.
/bdef { bind def } bind def
/xdef { exch def } bdef

% Begin page
/BP {
  /Magnification xdef
  /DviLaserPage save def
  (beginning of page) VMSDebug 
} bdef
 
% End page
/EP {
  DviLaserPage restore
} bdef
 
% Exit page (temporarily) to add fonts/characters.
/XP {
  % Save current point information so it can be reset later. 
  /Xpos where {pop Xpos} {0} ifelse
  /Ypos where {pop Ypos} {0} ifelse
  /currentpoint cvx stopped {0 0 moveto currentpoint} if 
  /DviLaserPage where {pop DviLaserPage restore} if
  moveto
  /Ypos xdef
  /Xpos xdef
} bdef
 
% Resume page
/RP {
  /DviLaserPage save def
} bdef
 
% Purge all fonts to reclaim memory space. 
/PF {
  GlobalMode
  LocalMode
} bdef
 
% Switch to base save/restore level, saving state information. 
/GlobalMode {
  /UserSave where {pop UserSave} if  % invoke "UserSave" if available
  PortraitMode 
  PaperWidth 
  PaperHeight 
  PxlResolution 
  Resolution 
  Magnification
  Ymax
  RasterScaleFactor
  % Save current point information so it can be reset later. 
  /currentpoint cvx stopped {0 0 moveto currentpoint} if 
  /DviLaserPage where {pop DviLaserPage restore} if
  DviLaserFonts restore
  RecoverState
} bdef
 
% Preserve state at the base level.
/RecoverState {
  10 copy
  /Ypos xdef
  /Xpos xdef
  /RasterScaleFactor xdef
  /Ymax xdef
  /Magnification xdef
  /Resolution xdef
  /PxlResolution xdef
  /PaperHeight xdef
  /PaperWidth xdef
  /PortraitMode xdef
  DoInitialScaling
  PortraitMode not {PaperWidth 0 SetupLandscape} if
  Xpos Ypos moveto
} bdef

% Initialize state variables to default values.
/InitializeState {
  /Resolution 3600.0 def
  /PxlResolution 300.0 def
  /RasterScaleFactor PxlResolution Resolution div def
  /PortraitMode true def
  11.0 Resolution mul /PaperHeight xdef
  8.5 Resolution mul /PaperWidth xdef
  /Ymax PaperHeight def
  /Magnification 1000.0 def
  /Xpos 0.0 def
  /Ypos 0.0 def
  /InitialMatrix matrix currentmatrix def
} bdef

% Switch from base save/restore level, restoring state information. 
/LocalMode {
  /Ypos xdef
  /Xpos xdef
  /RasterScaleFactor xdef
  /Ymax xdef
  /Magnification xdef
  /Resolution xdef
  /PxlResolution xdef
  /PaperHeight xdef
  /PaperWidth xdef
  /PortraitMode xdef
  DoInitialScaling
  PortraitMode not {PaperWidth 0 SetupLandscape} if
  Xpos Ypos moveto
  /UserRestore where {pop UserRestore} if  % invoke "UserRestore" if available
  /DviLaserFonts save def
  /DviLaserPage save def
} bdef
 
% Abbreviations 
/S /show load def
/SV /save load def
/RST /restore load def
 
/Yadjust {Ymax exch sub} bdef
 
% (x,y) position absolute, just set Xpos & Ypos, don't move.
/SXY {
  Yadjust 
  /Ypos xdef /Xpos xdef
} bdef
 
% (x,y) position absolute
/XY {
  Yadjust 
  2 copy /Ypos xdef /Xpos xdef
  moveto
} bdef
 
% (x,0) position absolute
/X {
  currentpoint exch pop 
  2 copy /Ypos xdef /Xpos xdef
  moveto
} bdef
 
% (0,y) position absolute
/Y {
  currentpoint pop exch Yadjust 
  2 copy /Ypos xdef /Xpos xdef
  moveto
} bdef
 
% (x,y) position relative
/xy {
  neg rmoveto
  currentpoint /Ypos xdef /Xpos xdef
} bdef
 
% (x,0) position relative
/x {
  0.0 rmoveto
  currentpoint /Ypos xdef /Xpos xdef
} bdef
 
% (0,y) position relative
/y {
  0.0 exch neg rmoveto
  currentpoint /Ypos xdef /Xpos xdef
  } bdef
 
% Print a rule.  In order to get correct pixel size and positioning,
% we usually create a temporary font in which the rule is the only character.
% When the rule is large, however, we fill a rectangle instead.
/R {
  /ht xdef
  /wd xdef
  ht 1950 le wd 1950 le and
    {save
    /tfd 6 dict def
    tfd begin
      /FontType 3 def
      /FontMatrix [1 0 0 1 0 0] def
      /FontBBox [0 0 wd ht] def
      /Encoding 256 array dup 97 /a put def
      /BuildChar {
        pop   % ignore character code
        pop   % ignore font dict, too
        wd 0 0 0 wd ht setcachedevice
        wd ht true
        [1 0 0 -1 0 ht] {<FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF>} imagemask
        } def
      end % tfd
    /tf tfd definefont setfont
    (a) show
    restore
    }
    {gsave
    0 setgray
    currentpoint
    newpath
      moveto
      0.0 ht rlineto
      wd 0.0 rlineto
      0.0 ht neg rlineto
      wd neg 0.0 rlineto
    closepath fill
    grestore
    }
  ifelse
  wd 0.0 rmoveto
  currentpoint /Ypos xdef /Xpos xdef
} bdef

%
%  <PXL-file resolution(pix/inch)> <resolution(pix/inch)> RES
%
/RES {
  /Resolution xdef
  /PxlResolution xdef
  /RasterScaleFactor PxlResolution Resolution div def
  DoInitialScaling
} bdef

%
% Do initial scaling.
%
/DoInitialScaling {
  InitialMatrix setmatrix
  72.0 Resolution div dup scale   
} bdef
 
%
%  <paper-height(pix)> <paper-width(pix)> PM 
%
/PM { 
  XP
  /PaperWidth xdef 
  /PaperHeight xdef
  /Ymax PaperHeight def
  /PortraitMode true def
  DoInitialScaling
  RP
} bdef  
 
%
%  <paper-height(pix)> <paper-width(pix)> LM 
%
/LM {
  XP
  /PaperWidth xdef 
  /PaperHeight xdef
  /Ymax PaperWidth def
  /PortraitMode false def
  DoInitialScaling
  PaperWidth 0 SetupLandscape
  RP
} bdef  
  
% Change magnification setting
/MAG {
  XP
  /Magnification xdef
  RP
} bdef
 
%
%  Switch to landscape mode
%
/SetupLandscape {
  translate
  90.0 rotate
} bdef
 
%
%  <mode> SPB - begin "\special" mode
%
%  This is the PostScript procedure used to transfer from the internal
%  environment used for the DVI translation code emitted by DVIPS to
%  a standard PostScript environment.
%
%  Parameters: 0 - Local
%              1 - Global
%              2 - Inline
%
/SPB {
  /spc_mode xdef
  spc_mode 0 eq spc_mode 2 eq or
    {XP}
    {spc_mode 1 eq {GlobalMode} if} 
    ifelse
  Resolution 72.0 div dup scale        % Restore default scaling...
  Magnification 1000.0 div dup scale   % Adjust for any magnification...
  /Xpos Xpos 72.0 Resolution div mul 1000.0 Magnification div mul def
  /Ypos Ypos 72.0 Resolution div mul 1000.0 Magnification div mul def
} bdef
 
%
%  <mode> SPE - end "\special" mode
%
%  This is the PostScript procedure used to reenter the internal
%  environment used for the DVI translation code emitted by DVIPS from 
%  the standard PostScript environment provided for processing user-supplied
%  PostScript code.
%
%  Parameters: 0 - Local
%              1 - Global
%              2 - Inline
%
/SPE {
  /spc_mode xdef
  1000.0 Magnification div dup scale   % Un-adjust for any magnification...
  72.0 Resolution div dup scale        % Restore default internal scaling...
  spc_mode 0 eq spc_mode 2 eq or
    {RP}
    {spc_mode 1 eq {LocalMode} if} 
    ifelse
} bdef
 
%
%  <num-copies> PP
%
/PP {
  /#copies xdef
  showpage
  /#copies 1 def
} bdef
 
%
%  /font-name <point-size(pix)> DMF
%
/DMF {
  /psz xdef
  /nam xdef
  nam findfont psz scalefont setfont
} bdef
 
%
%  /abcd (xxx) str-concat  ==> /abcdxxx
%
/str-concatstr 64 string def

/str-concat {
  /xxx xdef
  /nam xdef
  /namstr nam str-concatstr cvs def
  /newnam namstr length xxx length add string def
  newnam 0 namstr putinterval
  newnam namstr length xxx putinterval
  newnam cvn 
} bdef
 
%
%  /abcdef 2 str-strip ==> /cdef
%
/str-strip {
  /num xdef
  /nam xdef
  /namstr nam tempstr cvs def
  /newlen namstr length num sub def
  namstr num newlen getinterval
  cvn
} bdef
 
%
%  <old-dict> copydict ==> new-dict on stack
%
/copydict {
  dup length 1 add dict /newdict xdef
    {1 index /FID ne
      {newdict 3 1 roll put}
      {pop pop}
     ifelse
    } forall 
  newdict
} bdef
 
%
%  <font-type> DefineCMEncoding
%
/DefineCMEncoding {
  /EncodeType xdef
 
  /CMEncoding 256 array def
  /Times-Roman findfont /Encoding get aload pop CMEncoding astore pop
 
  EncodeType 11 eq {Do-CM-rm-encoding} if
  EncodeType 12 eq {Do-CM-it-encoding} if
  EncodeType 13 eq {Do-CM-tt-encoding} if
} bdef
 
%
%  Do special mappings for the various CM-font types.  Characters that
%  get "covered up" are repositioned in the range (128,128+32).
%
/Do-standard-CM-encodings {
  CMEncoding
  dup 0 /.notdef put
  dup 1 /.notdef put
  dup 2 /.notdef put
  dup 3 /.notdef put
  dup 4 /.notdef put
  dup 5 /.notdef put
  dup 6 /.notdef put
  dup 7 /.notdef put
 
  dup 8 /.notdef put
  dup 9 /.notdef put
  dup 10 /.notdef put
  dup 11 /.notdef put
  dup 12 /fi put
  dup 13 /fl put
  dup 14 /.notdef put
  dup 15 /.notdef put
 
  dup 16 /dotlessi put
  dup 17 /.notdef put
  dup 18 /grave put
  dup 19 /acute put
  dup 20 /caron put
  dup 21 /breve put
  dup 22 /macron put
  dup 23 /ring put
 
  dup 24 /cedilla put
  dup 25 /germandbls put
  dup 26 /ae put
  dup 27 /oe put
  dup 28 /oslash put
  dup 29 /AE put
  dup 30 /OE put
  dup 31 /Oslash put

  dup 127 /dieresis put

  dup 128 /space put
  dup 129 /quotedbl put
  dup 130 /sterling put
  dup 131 /dollar put
  dup 132 /less put
  dup 133 /greater put
  dup 134 /backslash put
  dup 135 /asciicircum put

  dup 136 /underscore put
  dup 137 /braceleft put
  dup 138 /bar put
  dup 139 /braceright put
  dup 140 /asciitilde put
  pop
} bdef
 
/Do-CM-rm-encoding {
  Do-standard-CM-encodings
  CMEncoding
  dup 32 /.notdef put
  dup 34 /quotedblright put
  dup 60 /exclamdown put
  dup 62 /questiondown put
  dup 92 /quotedblleft put
  dup 94 /circumflex put
  dup 95 /dotaccent put
  dup 123 /endash put
  dup 124 /emdash put
  dup 125 /hungarumlaut put
  dup 126 /tilde put
  pop
} bdef
 
/Do-CM-it-encoding {
  Do-standard-CM-encodings
  CMEncoding
  dup 32 /.notdef put
  dup 34 /quotedblright put
  dup 36 /sterling put
  dup 60 /exclamdown put
  dup 62 /questiondown put
  dup 92 /quotedblleft put
  dup 94 /circumflex put
  dup 95 /dotaccent put
  dup 123 /endash put
  dup 124 /emdash put
  dup 125 /hungarumlaut put
  dup 126 /tilde put
  pop
} bdef
 
/Do-CM-tt-encoding {
  Do-standard-CM-encodings
  CMEncoding
  dup 12 /.notdef put
  dup 13 /quotesingle put
  dup 14 /exclamdown put
  dup 15 /questiondown put
  dup 94 /circumflex put
  dup 126 /tilde put
  pop
} bdef

%
% Routines to handle packing/unpacking numbers.
%
%  <target> <pos> <num> PackHW --> <new target>
%
/PackHW {
  /num xdef
  /pos xdef
  /target xdef
  num 16#0000FFFF and 1 pos sub 16 mul bitshift
    target or
} bdef

%
%  <target> <pos> <num> PackByte --> <new target>
%
/PackByte {
  /num xdef
  /pos xdef
  /target xdef
  num 16#000000FF and 3 pos sub 8 mul bitshift
    target or
} bdef

%
%  <pos> <num> UnpkHW --> <unpacked value>
%
/UnpkHW {
  /num xdef
  /pos xdef
  num 1 pos sub -16 mul bitshift 16#0000FFFF and
  dup 16#00007FFF gt {16#00010000 sub} if
} bdef

%
%  <pos> <num> UnpkByte --> <unpacked value>
%
/UnpkByte {
  /num xdef
  /pos xdef
  num 3 pos sub -8 mul bitshift 16#000000FF and
  dup 16#0000007F gt {16#00000100 sub} if
} bdef

%
%  <int-font-name> <ext-font-name> <pt-sz(pix)> <type> <loaded-fg> DefineCMFont
%
%    type 10: "as-is" PostScript font
%    type 11: CM-mapped PostScript font - roman
%    type 12: CM-mapped PostScript font - text italic 
%    type 13: CM-mapped PostScript font - typewriter type 
%
/int-dict-name {int (-dict) str-concat} bdef
/int-dict {int (-dict) str-concat cvx load} bdef

/DF {
  true  % signal that the font is already loaded
  DefineCMFont
} bdef
 
/DNF {
  false  % signal that the font is not already loaded
  DefineCMFont
} bdef

/DefineCMFont {
  /loaded xdef
  /typ xdef
  /psz xdef
  /ext xdef
  /int xdef
 
  typ 10 ne 
    { % font_type = 11, 12, 13
    loaded not
      { /fnam ext 3 str-strip def
        fnam findfont copydict /newdict xdef 
        typ DefineCMEncoding
        newdict /Encoding CMEncoding put
        ext newdict definefont pop
      } if
    int-dict-name ext findfont psz scalefont def
    currentdict int [int-dict /setfont cvx] cvx put
    }
    { % font_type = 10
    /fnam ext def
    int-dict-name fnam findfont psz scalefont def
    currentdict int [int-dict /setfont cvx] cvx put
    }
  ifelse
} bdef 
 
%
%  <int-font-name> <ext-font-name> <pt-sz(pix)> <PXL mag> <num-chars>
%      [llx lly urx ury] <newfont-fg> DefinePXLFont
%

/PXLF {
  true  % signal that the font is already loaded
  DefinePXLFont
} bdef
 
/PXLNF {
  false  % signal that the font is not already loaded
  DefinePXLFont
} bdef

/PXLBuildCharDict 17 dict def
 
/CMEncodingArray 256 array def
0 1 255 {CMEncodingArray exch dup tempstr cvs cvn put} for

/RasterConvert {RasterScaleFactor div} bdef
 
/TransformBBox {
  aload pop
 
  /BB-ury xdef
  /BB-urx xdef
  /BB-lly xdef
  /BB-llx xdef
 
  [BB-llx RasterConvert BB-lly RasterConvert 
   BB-urx RasterConvert BB-ury RasterConvert]
} bdef

/DefinePXLFont {
  /newfont xdef
  /bb xdef
  /num xdef
  /psz xdef
  /dsz xdef
  /pxlmag xdef
  /ext xdef
  /int xdef
 
  /fnam ext (-) str-concat pxlmag tempstr cvs str-concat def
 
  newfont not {
    int-dict-name 13 dict def
   
    int-dict begin
      /FontType 3 def
      /FontMatrix [1 dsz div 0 0 1 dsz div 0 0] def
      /FontBBox bb TransformBBox def
      /Encoding CMEncodingArray def
      /CharDict 1 dict def
      CharDict begin
        /Char-Info num array def
        end
  
      /BuildChar
        { 
          PXLBuildCharDict begin
            /char xdef
            /fontdict xdef
   
            fontdict /CharDict get /Char-Info get char get aload pop
   
            /rasters xdef
            /PackedWord1 xdef
   
            0 PackedWord1 UnpkHW 16#7FFF ne
              { /PackedWord2 xdef
                /wx 0 PackedWord1 UnpkHW def
                /rows 2 PackedWord1 UnpkByte def
                /cols 3 PackedWord1 UnpkByte def
                /llx 0 PackedWord2 UnpkByte def
                /lly 1 PackedWord2 UnpkByte def
                /urx 2 PackedWord2 UnpkByte def
                /ury 3 PackedWord2 UnpkByte def }
              { /PackedWord2 xdef
                /PackedWord3 xdef
                /PackedWord4 xdef
                /wx 1 PackedWord1 UnpkHW def
                /rows 0 PackedWord2 UnpkHW def
                /cols 1 PackedWord2 UnpkHW def
                /llx 0 PackedWord3 UnpkHW def
                /lly 1 PackedWord3 UnpkHW def
                /urx 0 PackedWord4 UnpkHW def
                /ury 1 PackedWord4 UnpkHW def }
               ifelse

            rows 0 lt
              { /rows rows neg def
                /runlength 1 def }
              { /runlength 0 def }
             ifelse
 
            wx 0 
            llx RasterConvert lly RasterConvert 
            urx RasterConvert ury RasterConvert setcachedevice
            rows 0 ne
              {
              gsave
                cols rows true 
                RasterScaleFactor 0 0 RasterScaleFactor neg llx neg ury 
                  tempmatrix astore
                {GenerateRasters} imagemask
              grestore
              } if
            end
        } def
      end
   
      fnam int-dict definefont pop 
    } if 
 
  int-dict-name fnam findfont psz scalefont def
  currentdict int [int-dict /setfont cvx] cvx put
} bdef 
 
%
%  <int-font-name> <code> <wx> <llx> <lly> <urx> <ury> <rows> <cols> <runlength> <rasters> PXLC
%
/PXLC {
 
  /rasters xdef
  /runlength xdef
  /cols xdef
  /rows xdef
  /ury xdef
  /urx xdef
  /lly xdef
  /llx xdef
  /wx xdef
  /code xdef
  /int xdef
 
  % See if the long or short format is required
  true cols CKSZ rows CKSZ ury CKSZ urx CKSZ lly CKSZ llx CKSZ 
    TackRunLengthToRows
    { int-dict /CharDict get /Char-Info get code 
        [0 0 llx PackByte 1 lly PackByte 2 urx PackByte 3 ury PackByte
         0 0 wx PackHW 2 rows PackByte 3 cols PackByte
         rasters] put}
    { int-dict /CharDict get /Char-Info get code 
        [0 0 urx PackHW 1 ury PackHW
         0 0 llx PackHW 1 lly PackHW
         0 0 rows PackHW 1 cols PackHW
         0 0 16#7FFF PackHW 1 wx PackHW
         rasters] put} 
    ifelse
} bdef
 
/CKSZ {abs 127 le and} bdef
/TackRunLengthToRows {runlength 0 ne {/rows rows neg def} if} bdef
 
%
%  <wx> <dsz> <psz> <llx> <lly> <urx> <ury> <rows> <cols> <runlength> <rasters> PLOTC
%
/PLOTC {
  /rasters xdef
  /runlength xdef
  /cols xdef
  /rows xdef
  /ury xdef
  /urx xdef
  /lly xdef
  /llx xdef
  /psz xdef
  /dsz xdef
  /wx xdef
 
  % "Plot" a character's raster pattern.
  rows 0 ne
    {
    gsave
      currentpoint translate
      psz dsz div dup scale
      cols rows true 
      RasterScaleFactor 0 0 RasterScaleFactor neg llx neg ury 
        tempmatrix astore
      {GenerateRasters} imagemask
    grestore
    } if
  wx x
} bdef
 
% Routine to generate rasters for "imagemask".
/GenerateRasters {
  rasters
  runlength 1 eq {RunLengthToRasters} if
} bdef
 
% Routine to convert from runlength encoding back to rasters.
/RunLengthToRasters {
  % ...not done yet...
} bdef
 
%
%  These procedures handle bitmap processing.
%
%  <bitmap columns> <bitmap rows> <bitmap pix/inch> <magnification> BMbeg
%
/BMbeg {
  /BMmagnification xdef
  /BMresolution xdef
  /BMrows xdef
  /BMcols xdef

  /BMcurrentrow 0 def
  gsave
    0.0 setgray
    Resolution BMresolution div dup scale
    currentpoint translate
    BMmagnification 1000.0 div dup scale
    0.0 BMrows moveto
    BMrows dup scale
    currentpoint translate
    /BMCheckpoint save def
  } bdef

/BMend {
  BMCheckpoint restore
  grestore
  } bdef

%
%  <hex raster bitmap> <rows> BMswath 
%
/BMswath {
  /rows xdef
  /rasters xdef

  BMcols rows true
  [BMrows 0 0 BMrows neg 0 BMcurrentrow neg]
  {rasters}
  imagemask

  /BMcurrentrow BMcurrentrow rows add def
  BMcurrentrow % save this on the stack around a restore...
  BMCheckpoint restore
  /BMcurrentrow xdef
  /BMCheckpoint save def
  } bdef

%
%  Procedures for implementing the "rotate <theta>" special:
%  <theta> ROTB -
%        - ROTE -

/ROTB {
  XP
  gsave
  Xpos Ypos translate
  rotate % using <theta> from the stack
  Xpos neg Ypos neg translate
  RP
  } bdef

/ROTE {XP grestore RP} bdef

%
%  Procedures for implementing the "epsfile <filename> [<mag>]" special:
%  <llx> <lly> <mag> EPSB -
%  - EPSE -

/EPSB {
  0 SPB
  save
  4 1 roll % push the savelevel below the parameters
  /showpage {} def
  Xpos Ypos translate
  1000 div dup scale % using <mag> from the stack
  neg exch neg exch translate % using <llx> <lly> from the stack
  } bdef

/EPSE {restore 0 SPE} bdef

%
%  Procedure for implementing revision bars:
%  <bary1> <bary2> <barx> <barw> REVB -
%  The bar is a line of width barw drawn from (barx,bary1) to (barx,bary2).

/REVB {
  /barw xdef
  /barx xdef
  /bary2 xdef
  /bary1 xdef
  gsave
    barw setlinewidth
    barx bary1 Yadjust moveto
    barx bary2 Yadjust lineto
    stroke
  grestore
  } bdef

%
%  A small dictionary to facilitate The Publisher's implementation
%  of gray table cells.

/grpm 40 dict def

%
%  Procedures for implementing the "paper <source>" option:
%  <name> <eop> SPS          -
%         <eop> paper-manual -
%  etc.  The boolean <eop> is passed so that a paper source procedure
%  knows if it is being called at the beginning (false) or end
%  (true) of a page.

/SPS {
  /eop xdef
  /name xdef
  name where {pop eop name cvx exec} if
  } bdef

/paper-manual {
    {statusdict /manualfeed known
      {statusdict /manualfeed true put}
    if}
  if
  } bdef

/paper-automatic {
    {statusdict /manualfeed known
      {statusdict /manualfeed false put}
    if}
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PXLC RP
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PXLC RP
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PXLC RP
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PXLC RP
1086 2498 XY F21(\013)S 13 x F6(is)S 13 x(not)S 14 x(representable)S
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PXLC RP
300 853 XY F22(j)S F21(\013)S F22(j)S
XP /F21 60 32 3 -2 28 22 24 32 0
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PXLC RP
363 853 XY F21(<)S 13 x F48(FLOAT_TYPE\015MACHINE_RADIX)S
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PXLC RP
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XP /F20 /cmr10 300 41.5 41.5 128 [-3 -11 41 31] PXLNF RP
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PXLC RP
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PXLC RP
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PXLC RP
1514 853 XY F48(1)S
XP /F20 41 16 2 -11 12 31 42 16 0
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PXLC RP
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F6(by)S 18 x(AI-00387\).)S 1724 Y 383 X(The)S 14 x(result)S 15 x(de)S
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15 x(this)S 50 y 300 X(same)S 15 x(restriction.)S 20 x(The)S 14 x
(raising)S 15 x(of)S 14 x F48(STORAGE_ERROR)S 12 x F6(during)S 15 x
(instantiation)S 15 x(is)S 15 x(only)S 15 x(allowed)S 15 x(for)S 
15 x(the)S 14 x(purpose)S 14 x(of)S 15 x(signaling)S 50 y 300 X(the)S
21 x(exhaustion)S 22 x(of)S 21 x(storage.)S 3127 Y 1265 X(7)S
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300 343 XY F73(8.)S 34 x(Speci\014cations)S 26 x(of)S 25 x(the)S 
26 x(subprograms)S 458 Y 383 X F6(Except)S 13 x(where)S 13 x(an)S 
13 x(approximation)S 13 x(is)S 13 x(explicitly)S 13 x(allowed)S 12 x
(and)S 13 x(de\014ned,)S 13 x(the)S 13 x(formulas)S 13 x(given)S 
13 x(below)S 13 x(under)S 13 x(the)S 13 x(heading)S 50 y 300 X F7
(De)S
(\014nition)S 16 x F6(specify)S 15 x(precise)S 15 x(mathematical)S
16 x(results.)S 22 x(In)S 16 x(a)S 16 x(few)S 16 x(cases,)S 16 x
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15 x(unde\014ned)S 16 x(for)S 50 y 300 X(certain)S 14 x(ar)S -1 x
(guments;)S 15 x(in)S 15 x(those)S 15 x(cases,)S 14 x(the)S 14 x
(subprogram)S 14 x(will)S 14 x(raise)S 14 x(an)S 15 x(exception,)S
15 x(as)S 14 x(stated)S 14 x(under)S 14 x(the)S 15 x(heading)S 14 x 
F7(Exceptions)S F6(,)S 49 y 300 X(instead)S 21 x(of)S 21 x
(delivering)S 22 x(a)S 22 x(result.)S 694 Y 383 X(In)S 13 x(the)S 
14 x(speci\014cations)S 13 x(of)S 14 x F48(EXPONENT)S F6(,)S 11 x 
F48(FRACTION)S F6(,)S 12 x F48(DECOMPOSE)S F6(,)S 12 x F48(COMPOSE)S
F6(,)S 12 x F48(SCALE)S F6(,)S 13 x(and)S 13 x F48(LEADING_PART)S 
F6(,)S 10 x(the)S 13 x(symbol)S
XP /F21 12 23 1 -8 24 29 37 24 0
<0001F0 000618 00080C 00100C 00200E 00400E 00800E 00801C 01001C
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 040038 080070 080070 080070 0800E0 1800E0 1800C0 140180 140300
 230E00 20F800 200000 200000 400000 400000 400000 400000 800000
 800000>
PXLC RP
300 744 XY F21(\014)S 22 x F6(stands)S 19 x(for)S 19 x(the)S 19 x
(value)S 19 x(of)S 18 x F48(FLOAT_TYPE\015MACHINE_RADIX)S -5 x F6(.)S
916 Y 300 X F73(8.1.)S 33 x(EXPONENT\320Exponent)S 19 x(of)S 19 x
(the)S 19 x(Canonical)S 19 x(Representation)S 70 y 808 X(of)S 22 x
(a)S 22 x(Floating-Point)S 22 x(Machine)S 22 x(Number)S 1158 Y 383 X 
F2(Speci\014cation:)S 1329 Y 466 X F48(function)S 20 x(EXPONENT)S 
20 x(\(X)S 22 x(:)S 21 x(FLOAT_TYPE\))S 20 x(return)S 20 x
(EXPONENT_TYPE;)S 1500 Y 383 X F2(De\014nition:)S 1635 Y 466 X F6
(\(a\))S 37 x F48(EXPONENT\()S
XP /F48 48 22 2 0 19 25 25 24 0
<03E000 0FF800 1FFC00 1E3C00 380E00 780F00 700700 700700 E00380
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PXLC RP
745 1635 XY F48(0)S
XP /F48 46 22 8 0 13 5 5 8 0
<70 F8 F8 F8 70>
PXLC RP
767 1635 XY F48(.0\))S
XP /F20 61 32 2 4 29 16 12 32 0
<7FFFFFC0 FFFFFFE0 00000000 00000000 00000000 00000000 00000000
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PXLC RP
852 1635 XY F20(=)S 19 x F48(0)S 62 y 466 X F6(\(b\))S 35 x(For)S 
15 x F48(X)S
XP /F22 54 0 6 -10 25 30 40 24 0
<000060 000060 0000E0 0000C0 0001C0 000180 000380 000300 000700
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 006000 00E000 00C000 00C000 01C000 018000 038000 030000 070000
 060000 0E0000 0C0000 0C0000 1C0000 180000 380000 300000 700000
 600000 E00000 C00000 C00000>
PXLC RP
658 1697 XY F22(6)S F20(=)S 13 x F48(0.0)S F6(,)S 16 x F48
(EXPONENT\(X\))S 11 x F20(=)S 16 x F6(the)S 15 x(unique)S 16 x
(integer)S
XP /F21 107 22 2 0 20 29 29 24 0
<0FC000 01C000 01C000 038000 038000 038000 038000 070000 070000
 070000 070000 0E0700 0E1880 0E21C0 0E23C0 1C4780 1C8300 1D0000
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 E06200 603C00>
PXLC RP
1422 1697 XY F21(k)S 16 x F6(such)S 16 x(that)S 15 x F21(\014)S
XP /F53 /cmmi7 300 29.1 29.1 128 [-1 -7 32 22] PXLNF RP
XP /F53 107 18 2 0 15 20 20 16 0
<3E00 0600 0C00 0C00 0C00 0C00 1800 1870 18B8 1938 3230 3400 3800
 3E00 6300 6310 6310 6310 C320 C1C0>
PXLC RP
1655 1682 XY F53(k)S
XP /F54 /cmsy7 300 29.1 29.1 128 [-1 -28 35 23] PXLNF RP
XP /F54 0 26 3 6 21 8 2 24 0
<FFFFC0 FFFFC0>
PXLC RP
1673 1682 XY F54(\000)S
XP /F32 /cmr10 300 41.5 29.1 128 [-3 -11 41 31] PXLF RP
XP /F32 49 21 4 0 17 28 28 16 0
<0300 0700 3F00 C700 0700 0700 0700 0700 0700 0700 0700 0700 0700
 0700 0700 0700 0700 0700 0700 0700 0700 0700 0700 0700 0700 0700
 0F80 FFF8>
PXLC RP
1699 1682 XY F32(1)S
XP /F22 20 32 3 -8 28 26 34 32 0
<00000180 00000780 00001E00 00007800 0001E000 00078000 001E0000
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PXLC RP
1729 1697 XY F22(\024)S 14 x(j)S F48(X)S F22(j)S 13 x F21(<)S 13 x
(\014)S -15 y 2 x F53(k)S 1869 Y 383 X F2(Notes:)S 2003 Y -53 x F6
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(FLOAT_TYPE)S
(\015MACHINE_EMIN)S -5 x F6(.)S 2176 Y 300 X F73(8.2.)S 33 x
(FRACTION)S
(\320Signed)S 20 x(Mantissa)S 20 x(of)S 19 x(the)S 19 x(Canonical)S
20 x(Representation)S 70 y 788 X(of)S 23 x(a)S 23 x(Floating-Point)S
22 x(Machine)S 22 x(Number)S 2417 Y 383 X F2(Speci\014cation:)S 
2589 Y 466 X F48(function)S 20 x(FRACTION)S 20 x(\(X)S 22 x(:)S 21 x
(FLOAT_TYPE\))S 20 x(return)S 20 x(FLOAT_TYPE;)S 2760 Y 383 X F2(De)S
(\014nition:)S 2895 Y 466 X F6(\(a\))S 37 x F48(FRACTION\(0.0\))S 
16 x F20(=)S 20 x F48(0.0)S 62 y 466 X F6(\(b\))S 35 x(For)S 14 x 
F48(X)S 11 x F22(6)S F20(=)S 12 x F48(0.0)S F6(,)S 14 x F48
(FRACTION\(X\))S 10 x F20(=)S 12 x F48(X)S
XP /F22 1 12 4 8 8 12 4 8 0
<60 F0 F0 60>
PXLC RP
1115 2957 XY F22(\001)S 9 x F21(\014)S -15 y 2 x F54(\000)S F53(k)S
15 y 3 x F6(,)S 14 x(where)S 14 x F21(k)S 15 x F6(is)S 14 x(the)S 
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3128 Y 1265 X F6(8)S
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300 343 XY F73(8.3.)S 33 x(DECOMPOSE\320Extract)S 19 x(the)S 19 x
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(Representation)S 19 x(of)S 20 x(a)S 19 x(Floating-Point)S 19 x
(Machine)S 70 y 866 X(Number)S 633 Y 383 X F2(Speci\014cation:)S 
781 Y 466 X F48(procedure)S 20 x(DECOMPOSE)S 20 x(\(X)S 1120 X(:)S
21 x(in)S 44 x(FLOAT_TYPE;)S 50 y 924 X(FRACTION)S 20 x(:)S 21 x
(out)S 22 x(FLOAT_TYPE;)S 50 y 924 X(EXPONENT)S 20 x(:)S 21 x(out)S
22 x(EXPONENT_TYPE\);)S 1030 Y 383 X F2(De\014nition:)S 1147 Y 466 X 
F6(\(a\))S 37 x F48(FRACTION)S 52 x F20(=)S 54 x F48(0.0)S 51 x F6
(and)S 52 x F48(EXPONENT)S 52 x F20(=)S 54 x F48(0)S 51 x F6(upon)S
52 x(return)S 52 x(from)S 51 x(an)S 51 x(invocation)S 51 x(of)S 50 y 
549 X F48(DECOMPOSE\(0.0,)S 18 x(FRACTION,)S 19 x(EXPONENT\))S 62 y 
466 X F6(\(b\))S 35 x(For)S 18 x F48(X)S 15 x F22(6)S F20(=)S 16 x 
F48(0.0)S F6(,)S 19 x F48(FRACTION)S 14 x F20(=)S 16 x F48(X)S 11 x 
F22(\001)S 10 x F21(\014)S -15 y 2 x F54(\000)S F53(k)S 15 y 21 x 
F6(and)S 18 x F48(EXPONENT)S 14 x F20(=)S 16 x F21(k)S 1 x F6(,)S 
18 x(where)S 18 x F21(k)S 19 x F6(is)S 17 x(the)S 18 x(unique)S 18 x
(integer)S 18 x(such)S 18 x(that)S 50 y 549 X F21(\014)S -15 y 2 x 
F53(k)S 1 x F54(\000)S F32(1)S 15 y 14 x F22(\024)S 12 x(j)S F48(X)S
F22(j)S 11 x F21(<)S 12 x(\014)S -15 y 2 x F53(k)S 15 y 3 x F6(,)S
14 x(upon)S 15 x(return)S 14 x(from)S 14 x(an)S 15 x(invocation)S 
14 x(of)S 14 x F48(DECOMPOSE\(X,)S 18 x(FRACTION,)S 19 x(EXPONENT\))S
1457 Y 383 X F2(Notes:)S 1575 Y -53 x F6(When)S 21 x F48(X)S 20 x 
F6(is)S 20 x(a)S 20 x(denormalized)S 21 x(number,)S 21 x F48
(EXPONENT)S 17 x F21(<)S 20 x F48(FLOAT_TYPE\015MACHINE_EMIN)S 15 x 
F6(upon)S 21 x(return)S 21 x(from)S 21 x(an)S 50 y 466 X(invocation)S
19 x(of)S 18 x F48(DECOMPOSE\(X,)S 19 x(FRACTION,)S 19 x(EXPONENT\))S
-2 x F6(.)S 1780 Y 300 X F73(8.4.)S 33 x(COMPOSE\320Construct)S 19 x
(a)S 20 x(Floating-Point)S 20 x(Machine)S 20 x(Number)S 20 x(from)S
70 y 785 X(the)S 20 x(Components)S 20 x(of)S 20 x(its)S 20 x
(Canonical)S 21 x(Representation)S 1999 Y 383 X F2(Speci\014cation:)S
2147 Y 466 X F48(function)S 20 x(COMPOSE)S 21 x(\(FRACTION)S 19 x(:)S
22 x(FLOAT_TYPE;)S 50 y 858 X(EXPONENT)S 20 x(:)S 22 x
(EXPONENT_TYPE\))S 19 x(return)S 20 x(FLOAT_TYPE;)S 2346 Y 383 X F2
(De)S
(\014nition:)S 2463 Y 466 X F6(\(a\))S 37 x F48(COMPOSE\(0.0,)S 18 x
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18 x F48(EXPONENT)S 63 y 466 X F6(\(b\))S 35 x(For)S 19 x F48
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(\001)S 11 x F21(\014)S
XP /F63 /cmtt10 300 41.5 29.1 128 [0 -10 22 29] PXLF RP
XP /F63 69 21 1 0 20 25 25 24 0
<7FFFC0 FFFFC0 7FFFC0 1C01C0 1C01C0 1C01C0 1C01C0 1C0000 1C0000
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 1C00E0 1C00E0 1C00E0 1C00E0 7FFFE0 FFFFE0 7FFFE0>
PXLC RP
1350 2510 XY F63(E)S
XP /F63 88 21 1 0 20 25 25 24 0
<7F1F80 7F3F80 7F1F80 0E1E00 0E1C00 073C00 073800 03B800 03F000
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 071C00 0E0E00 0E0E00 1C0700 7F1FC0 FF1FE0 7F1FC0>
PXLC RP
1365 2510 XY F63(X)S
XP /F63 80 21 1 0 19 25 25 24 0
<7FF800 FFFE00 7FFF00 1C0F80 1C0380 1C03C0 1C01C0 1C01C0 1C01C0
 1C03C0 1C0380 1C0F80 1FFF00 1FFE00 1FF800 1C0000 1C0000 1C0000
 1C0000 1C0000 1C0000 1C0000 7F0000 FF8000 7F0000>
PXLC RP
1381 2510 XY F63(P)S
XP /F63 79 21 2 0 19 25 25 24 0
<1FFC00 3FFE00 7FFF00 780F00 F00780 E00380 E00380 E00380 E00380
 E00380 E00380 E00380 E00380 E00380 E00380 E00380 E00380 E00380
 E00380 F00780 F00780 780F00 7FFF00 3FFE00 1FFC00>
PXLC RP
1396 2510 XY F63(O)S
XP /F63 78 21 1 0 20 25 25 24 0
<7E1FC0 FF3FE0 7F1FC0 1D0700 1D8700 1D8700 1D8700 1DC700 1DC700
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 1C3700 1C3700 1C3700 1C1700 7F1F00 FF9F00 7F0F00>
PXLC RP
1411 2510 XY F63(NEN)S
XP /F63 84 21 1 0 20 25 25 24 0
<7FFFE0 FFFFE0 FFFFE0 E0E0E0 E0E0E0 E0E0E0 E0E0E0 00E000 00E000
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 00E000 00E000 00E000 00E000 07FC00 0FFE00 07FC00>
PXLC RP
1457 2510 XY F63(T)S F54(\000)S F53(k)S 16 y 2 x F6(,)S 19 x(where)S
19 x F21(k)S 19 x F6(is)S 19 x(the)S 19 x(unique)S 19 x(integer)S 
19 x(such)S 19 x(that)S 49 y 549 X F21(\014)S -15 y 2 x F53(k)S 1 x 
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F22(j)S 11 x F21(<)S 12 x(\014)S -15 y 2 x F53(k)S 15 y 3 x F6(.)S
18 x(If)S 12 x F21(\013)S 12 x F6(is)S 12 x(exactly)S 12 x
(representable)S 12 x(as)S 12 x(a)S 12 x(\015oating-point)S 12 x
(machine)S 12 x(number)S 12 x(\(cf.)S 14 x(Sec-)S 50 y 549 X(tion)S
20 x(5\),)S 21 x F48(COMPOSE\(FRACTION,)S 18 x(EXPONENT\))S 17 x F20
(=)S 19 x F21(\013)S F6(;)S 22 x(otherwise,)S 21 x F48
(COMPOSE\(FRACTION,)S 18 x(EXPONENT\))S 17 x F20(=)S 50 y 549 X F6
(either)S 14 x(one)S 14 x(of)S 14 x(the)S 14 x(machine)S 14 x
(numbers)S 14 x(neighboring)S 14 x F21(\013)S F6(,)S 14 x(provided)S
14 x(that)S 14 x F22(j)S F21(\013)S F22(j)S 11 x F21(<)S 12 x F48
(FLOAT_TYPE)S
(\015BASE\015LAST)S -4 x F6(.)S 2823 Y 383 X F2(Exceptions:)S 2941 Y 
466 X F6(When)S 18 x F21(\013)S 18 x F6(as)S 18 x(de\014ned)S 18 x
(above)S 18 x(is)S 18 x(such)S 17 x(that)S 18 x F22(j)S -1 x F21
(\013)S F22(j)S
XP /F21 62 32 3 -2 28 22 24 32 0
<E0000000 78000000 1E000000 07800000 01E00000 00780000 001E0000
 00078000 0001E000 00007800 00001E00 00000780 00000780 00001E00
 00007800 0001E000 00078000 001E0000 00780000 01E00000 07800000
 1E000000 78000000 E0000000>
PXLC RP
1224 2941 XY F21(>)S 16 x F48(FLOAT_TYPE\015BASE\015LAST)S -4 x F6
(,)S 19 x F48(COMPOSE)S 16 x F6(raises)S 18 x(the)S 18 x(exception)S
50 y 466 X(speci\014ed)S 15 x(by)S 15 x(Ada)S 16 x(for)S 16 x
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15 x(instead)S 15 x(of)S 15 x(delivering)S 15 x(a)S 15 x(result.)S
3128 Y 1265 X(9)S
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(approximation)S 22 x(\(possibly)S 21 x(zero\))S 21 x(to)S 21 x(the)S
21 x(exact)S 50 y 549 X(mathematical)S 24 x(result)S 25 x F21(\013)S
24 x F6(only)S 24 x(when)S 25 x F48(EXPONENT)S 23 x F6(is)S 25 x
(suf)S -1 x(\014ciently)S 25 x(negative)S 24 x(to)S 24 x(force)S 
25 x F21(\013)S 24 x F6(to)S 25 x(be)S 25 x(in)S 24 x(the)S 50 y 
549 X(denormalized)S 24 x(range,)S 25 x(and)S 23 x(either)S 24 x
(the)S 24 x(implementation)S 24 x(does)S 24 x(not)S 23 x(recognize)S
23 x(denormalized)S 24 x(numbers,)S 50 y 549 X(or)S 16 x F21(\013)S
15 x F6(is)S 16 x(not)S 16 x(exactly)S 16 x(representable)S 16 x(as)S
15 x(a)S 16 x(denormalized)S 16 x(number)S 16 x(\(cf.)S 14 x
(Section)S 16 x(6\).)S 62 y 466 X(\(b\))S 35 x(The)S 13 x(name)S 
13 x F48(FRACTION)S 11 x F6(is)S 13 x(not)S 13 x(meant)S 13 x(to)S
14 x(suggest)S 13 x(that)S 13 x(the)S 13 x(\014rst)S 13 x(ar)S -1 x
(gument)S 13 x(is)S 14 x(restricted)S 13 x(to)S 13 x(fractional)S 
13 x(values;)S 50 y 549 X(rather,)S 15 x(it)S 14 x(is)S 14 x(meant)S
14 x(to)S 14 x(suggest)S 14 x(that)S 15 x(the)S 15 x(\014rst)S 15 x
(ar)S -1 x(gument)S 14 x(supplies)S 15 x(\(via)S 15 x(its)S 15 x
(fractional)S 14 x(part)S 14 x(in)S 15 x(the)S 15 x(canonical)S 50 y 
549 X(form\))S 19 x(the)S 19 x(fractional)S 19 x(part)S 19 x(of)S 
19 x(the)S 19 x(result.)S 930 Y 300 X F73(8.5.)S 33 x
(SCALE\320Increment/Decrement)S 20 x(the)S 19 x(Exponent)S 19 x(of)S
20 x(the)S 19 x(Canonical)S 70 y 685 X(Representation)S 20 x(of)S 
20 x(a)S 20 x(Floating-Point)S 20 x(Machine)S 21 x(Number)S 1151 Y 
383 X F2(Speci\014cation:)S 1303 Y 466 X F48(function)S 20 x(SCALE)S
21 x(\(X)S 1011 X(:)S 21 x(FLOAT_TYPE;)S 49 y 815 X(EXPONENT)S 20 x
(:)S 21 x(EXPONENT_TYPE\))S 19 x(return)S 21 x(FLOAT_TYPE;)S 1504 Y 
383 X F2(De\014nition:)S 1623 Y 466 X F6(Let)S 17 x F21(\013)S 14 x 
F20(=)S 14 x F48(X)S 11 x F22(\001)S 9 x F21(\014)S -15 y 2 x F63
(EXPONENT)S 15 y 5 x F6(.)S 23 x(If)S 16 x F21(\013)S 16 x F6(is)S
16 x(exactly)S 16 x(representable)S 16 x(as)S 16 x(a)S 17 x
(\015oating-point)S 16 x(machine)S 16 x(number)S 16 x(\(cf.)S 14 x
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15 x F20(=)S 18 x F21(\013)S F6(;)S 19 x(otherwise,)S 19 x F48
(SCALE\(X,)S 19 x(EXPONENT\))S 15 x F20(=)S 20 x F6(either)S 19 x
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50 y 466 X(speci\014ed)S 15 x(by)S 15 x(Ada)S 16 x(for)S 16 x
(signaling)S 15 x(over\015ow)S 15 x(\(cf.)S 14 x(Section)S 16 x
(7\),)S 15 x(instead)S 15 x(of)S 16 x(delivering)S 15 x(a)S 15 x
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13 x(when)S 49 y 466 X F48(EXPONENT)S 8 x F6(is)S 10 x(suf)S -1 x
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3128 Y 1254 X F6(10)S
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17 x F22(j)S F48(X)S F22(j)S -1 x F6(,)S 17 x(this)S 17 x(function)S
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914 Y 300 X F73(8.7.)S 33 x(CEILING\320Least)S 19 x(Integer)S 19 x
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724 X(Machine)S 22 x(Number,)S 22 x(as)S 22 x(a)S 21 x
(Floating-Point)S 21 x(Number)S 1143 Y 383 X F2(Speci\014cation:)S
1302 Y 466 X F48(function)S 20 x(CEILING)S 21 x(\(X)S 21 x(:)S 21 x
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(d)S 1 x F48(X)S F22(e)S 1745 Y 383 X F2(Notes:)S 1870 Y -53 x F6
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300 X F73(8.8.)S 33 x(ROUND\320Integer)S 19 x(Nearest)S 19 x(to)S 
19 x(a)S 19 x(Floating-Point)S 19 x(Machine)S 20 x(Number,)S 71 y 
701 X(as)S 25 x(a)S 25 x(Floating-Point)S 25 x(Number)S 2262 Y 383 X 
F2(Speci\014cation:)S 2421 Y 466 X F48(function)S 20 x(ROUND)S 21 x
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2580 Y 383 X F2(De\014nition:)S 2705 Y 466 X F48(ROUND\(X\))S 10 x 
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17 x(function)S 18 x(merely)S 17 x(returns)S 17 x(its)S 17 x(ar)S 
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(Number,)S 71 y 804 X(as)S 24 x(a)S 24 x(Floating-Point)S 24 x
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20 x(return)S 20 x(FLOAT_TYPE;)S 862 Y 383 X F2(De\014nition:)S 
993 Y 466 X F48(TRUNCATE\(X\))S 16 x F20(=)S
XP /F23 /cmex10 300 41.5 41.5 128 [-1 -123 60 32] PXLNF RP
XP /F23 26 31 5 -97 25 2 99 24 0
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PXLC RP
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<60 F0 F0 70 10 10 10 10 20 20 40 80>
PXLC RP
872 968 XY F21(;)S 41 x F48(X)S
XP /F22 21 32 3 -8 28 26 34 32 0
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PXLC RP
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1798 Y 466 X F48(function)S 20 x(REMAINDER)S 20 x(\(X,)S 21 x(Y)S 
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XP /F22 0 32 3 9 28 11 2 32 0
<FFFFFF80 FFFFFF80>
PXLC RP
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<381F00 4E6180 4681C0 4701C0 8F01C0 8E01C0 0E01C0 0E01C0 1C0380
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PXLC RP
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XP /F21 61 21 2 -10 18 31 41 16 0
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PXLC RP
2145 2066 XY F21(=)S F48(Y)S F6(;)S 26 x(if)S 50 y 466 X F22(j)S F21
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F22(j)S 11 x F20(=)S
XP /F20 49 21 4 0 17 28 28 16 0
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 0F80 FFF8>
PXLC RP
717 2116 XY F20(1)S F21(=)S
XP /F20 50 21 2 0 18 28 28 16 0
<07C0 1830 201C 400C 400E F00F F80F F807 F807 7007 000F 000E 000E
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PXLC RP
758 2116 XY F20(2)S F6(,)S 14 x(then)S 14 x F21(n)S 13 x F6(is)S 
14 x(chosen)S 13 x(to)S 13 x(be)S 14 x(even.)S 18 x(If)S 13 x F21
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15 x F48(REMAINDER\(X,)S 18 x(Y\))S 13 x F20(=)S 14 x F48(0.0)S 
2315 Y 383 X F2(Exceptions:)S 2433 Y 466 X F6(For)S 18 x(any)S 18 x 
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20 x(close)S 20 x(to)S 19 x(a)S 19 x(multiple)S 19 x(of)S 19 x F48
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F2(Speci\014cation:)S 765 Y 466 X F48(function)S 20 x(ADJACENT)S 
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20 x(FLOAT_TYPE;)S 906 Y 383 X F2(De\014nition:)S 1017 Y 466 X F6
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63 y 466 X F6(\(b\))S 35 x(For)S 22 x F48(TOWARDS)S 20 x F22(6)S F20
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19 x F20(=)S 23 x F6(the)S 23 x(\015oating-point)S 22 x(machine)S 
22 x(number)S 22 x(\(cf.)S 13 x(Section)S 49 y 549 X(5\))S 18 x
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549 X(\(cf.)S 13 x(Section)S 18 x(4\),)S 18 x(a)S 17 x(zero)S 18 x
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(ADJACENT\()S
XP /F22 6 32 2 -1 29 27 28 32 0
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PXLC RP
2043 1643 XY F22(\006)S
XP /F21 27 24 2 0 23 18 18 24 0
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PXLC RP
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549 X(implementation)S 16 x(recognizes)S 16 x(denormalized)S 16 x
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17 x(a)S 17 x(negatively)S 18 x(signed)S 17 x(zero)S 2735 Y 383 X 
F2(Exceptions:)S 2847 Y 466 X F6(Since)S 18 x(there)S 18 x(is)S 18 x
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18 x(the)S 18 x(positive)S 49 y 466 X(direction)S 26 x(\(a)S 27 x
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16 x(the)S 15 x(result)S 15 x(depends)S 16 x(on)S 15 x(whether)S 
16 x(or)S 16 x(not)S 16 x(the)S 15 x(implementation)S 50 y 466 X
(recognizes)S 13 x(denormalized)S 14 x(numbers)S 13 x(\(cf.)S 13 x
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50 y 466 X(number)S 18 x(if)S 18 x(the)S 18 x(implementation)S 18 x
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(number)S 15 x(if)S 15 x(the)S 16 x(implementation)S 16 x
(recognizes)S 16 x(denormalized)S 15 x(numbers,)S 15 x(and)S 16 x
(zero)S 16 x(otherwise.)S 819 Y 300 X F73(8.13.)S 33 x(PREDECESSOR)S
(\320Floating-Point)S 19 x(Machine)S 19 x(Number)S 19 x(Next)S 19 x
(Below)S 20 x(a)S 71 y 966 X(Given)S 21 x(Floating-Point)S 21 x
(Machine)S 21 x(Number)S 1042 Y 383 X F2(Speci\014cation:)S 1194 Y 
466 X F48(function)S 20 x(PREDECESSOR)S 20 x(\(X)S 21 x(:)S 22 x
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(\014nition:)S 1467 Y 466 X F48(PREDECESSOR\(X\))S 14 x F20(=)S 20 x 
F6(the)S 19 x(\015oating-point)S 19 x(machine)S 19 x(number)S 19 x
(\(cf.)S 14 x(Section)S 19 x(5\))S 19 x(neighboring)S 19 x F48(X)S
19 x F6(in)S 19 x(the)S 19 x(negative)S 50 y 466 X(direction,)S 19 x
(provided)S 18 x(that)S 19 x F48(X)S 16 x F22(6)S F20(=)S 16 x F48
(FLOAT_TYPE)S
(\015BASE\015FIRST)S -4 x F6(;)S 19 x(in)S 18 x(an)S 18 x
(implementation)S 18 x(exploiting)S 18 x(signed)S 18 x(zeros)S 50 y 
466 X(\(cf.)S 14 x(Section)S 17 x(4\),)S 18 x(a)S 17 x(zero)S 17 x
(result)S 17 x(must)S 18 x(be)S 17 x(a)S 17 x(positively)S 18 x
(signed)S 18 x(zero)S 1719 Y 383 X F2(Exceptions:)S 1840 Y 466 X F6
(Since)S 15 x(there)S 15 x(is)S 15 x(no)S 15 x(\015oating-point)S 
15 x(machine)S 15 x(number)S 15 x(neighboring)S 15 x F48(FLOAT_TYPE)S
(\015BASE\015FIRST)S 10 x F6(in)S 15 x(the)S 15 x(negative)S 49 y 
466 X(direction)S 23 x(\(a)S 23 x(consequence)S 24 x(of)S 23 x(the)S
23 x(assumption)S 24 x(and)S 24 x(restriction)S 23 x(in)S 24 x
(Section)S 23 x(5\),)S 25 x F48(PREDECESSOR)S 21 x F6(raises)S 23 x
(the)S 50 y 466 X(exception)S 18 x(speci\014ed)S 18 x(by)S 18 x(Ada)S
17 x(for)S 17 x(signaling)S 18 x(over\015ow)S 18 x(\(cf.)S 14 x
(Section)S 17 x(7\),)S 18 x(instead)S 17 x(of)S 17 x(delivering)S 
18 x(a)S 18 x(result,)S 18 x(when)S 50 y 466 X F48(X)S 19 x F20(=)S
19 x F48(FLOAT_TYPE\015BASE\015FIRST)S -5 x F6(.)S 2141 Y 383 X F2
(Notes:)S 2262 Y -53 x F6(For)S 15 x(certain)S 16 x(ar)S -1 x
(guments,)S 17 x(the)S 16 x(numerical)S 16 x(value)S 16 x(of)S 16 x
(the)S 15 x(result)S 15 x(depends)S 16 x(on)S 15 x(whether)S 16 x
(or)S 16 x(not)S 16 x(the)S 15 x(implementation)S 50 y 466 X
(recognizes)S 33 x(denormalized)S 33 x(numbers)S 33 x(\(cf.)S 14 x
(Section)S 33 x(6\).)S 57 x(For)S 33 x(example,)S 36 x F48
(PREDECESSOR\(0.0\))S 29 x F6(yields)S 33 x(a)S 50 y 466 X
(denormalized)S 13 x(number)S 13 x(if)S 13 x(the)S 13 x
(implementation)S 14 x(recognizes)S 13 x(denormalized)S 14 x
(numbers,)S 13 x(and)S 14 x(a)S 13 x(normalized)S 13 x(number)S 49 y 
466 X(otherwise.)S 25 x(Similarly,)S 17 x F48(PREDECESSOR\()S -2 x 
F21(\033)S 1 x F48(\))S F6(,)S 18 x(where)S 17 x F21(\033)S 18 x F6
(is)S 17 x(the)S 17 x(smallest)S 17 x(positive)S 17 x(normalized)S
17 x(number,)S 17 x(yields)S 18 x(a)S 50 y 466 X(denormalized)S 14 x
(number)S 14 x(if)S 14 x(the)S 14 x(implementation)S 14 x
(recognizes)S 14 x(denormalized)S 14 x(numbers,)S 14 x(and)S 14 x
(zero)S 14 x(otherwise.)S 2619 Y 300 X F73(8.14.)S 33 x
(COPY\210SIGN)S
(\320T)S -3 x(ransfer)S 19 x(of)S 19 x(Sign)S 19 x(from)S 20 x(One)S
19 x(Floating-Point)S 19 x(Machine)S 71 y 860 X(Number)S 26 x(to)S
25 x(Another)S 2842 Y 383 X F2(Speci\014cation:)S 2994 Y 466 X F48
(function)S 20 x(COPY_SIGN)S 20 x(\(VALUE,)S 20 x(SIGN)S 21 x(:)S 
22 x(FLOAT_TYPE\))S 20 x(return)S 20 x(FLOAT_TYPE;)S 3128 Y 1254 X 
F6(14)S
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1000 BP 3300 2550 PM /paper-automatic false SPS 383 0 XY
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383 342 XY F2(De\014nition:)S 491 Y 466 X F6(\(a\))S 37 x(For)S 14 x 
F48(VALUE)S 12 x F22(6)S F20(=)S 12 x F48(0.0)S F6(,)S 15 x F48
(COPY_SIGN\(VALUE,)S 17 x(SIGN\))S 11 x F20(=)S
XP /F23 56 37 16 -38 29 -1 37 16 0
<0018 0078 00F0 01E0 03C0 0780 0F00 1F00 1E00 3E00 3C00 7C00 7C00
 7800 F800 F800 F800 F800 F800 F800 F800 F800 F800 F800 F800 F800
 F800 F800 F800 F800 F800 F800 F800 F800 F800 F800 F800>
PXLC RP
1413 406 XY F23(8)S
XP /F23 60 37 7 -76 21 1 77 16 0
<007C 007C 007C 007C 007C 007C 007C 007C 007C 007C 007C 007C 007C
 007C 007C 007C 007C 007C 007C 007C 007C 007C 007C 007C 00F8 00F8
 00F8 00F0 01F0 01E0 03E0 03C0 0780 0700 0E00 1C00 3800 F000 C000
 F000 3800 1C00 0E00 0700 0780 03C0 03E0 01E0 01F0 00F0 00F8 00F8
 00F8 007C 007C 007C 007C 007C 007C 007C 007C 007C 007C 007C 007C
 007C 007C 007C 007C 007C 007C 007C 007C 007C 007C 007C 007C>
PXLC RP
1413 443 XY F23(<)S
XP /F23 58 37 16 -36 29 1 37 16 0
<F800 F800 F800 F800 F800 F800 F800 F800 F800 F800 F800 F800 F800
 F800 F800 F800 F800 F800 F800 F800 F800 F800 F800 7800 7C00 7C00
 3C00 3E00 1E00 1F00 0F00 0780 03C0 01E0 00F0 0078 0018>
PXLC RP
1413 518 XY F23(:)S 441 Y 7 x F22(j)S -1 x F48(VALUE)S -1 x F22(j)S
F21(;)S 1898 X F48(SIGN)S 11 x F21(>)S 11 x F48(0.0)S 50 y 1457 X 
F22(\006j)S F48(VALUE)S -1 x F22(j)S 20 x F20(\()S F6(see)S 14 x
(note)S 14 x(a)S F20(\))S F21(;)S 41 x F48(SIGN)S 11 x F20(=)S 11 x 
F48(0.0)S 50 y 1457 X F22(\000j)S F48(VALUE)S -1 x F22(j)S -1 x F21
(;)S 1898 X F48(SIGN)S 11 x F21(<)S 11 x F48(0.0)S 59 y 466 X F6
(\(b\))S 35 x F48(COPY_SIGN\(0.0,)S 18 x(SIGN\))S 16 x F20(=)S 17 x 
F48(0.0)S 27 x F20(\()S 1 x F6(see)S 13 x(note)S 14 x(b)S F20(\))S
741 Y 383 X F2(Exceptions:)S 854 Y 466 X F6(Since)S 20 x(the)S 20 x
(negation)S 19 x(of)S 20 x(some)S 20 x(representable)S 19 x(values)S
19 x(causes)S 19 x(over\015ow)S 19 x(on)S 20 x(some)S 20 x(hardware)S
19 x(\(e.g.,)S 20 x(when)S 19 x(2's-)S 49 y 466 X(complement)S 15 x
(representation)S 15 x(is)S 15 x(used)S 15 x(for)S 15 x
(\015oating-point\),)S 15 x F48(COPY_SIGN)S 13 x F6(raises)S 15 x
(the)S 15 x(exception)S 15 x(speci\014ed)S 15 x(by)S 15 x(Ada)S 50 y 
466 X(for)S 16 x(signaling)S 15 x(over\015ow)S 16 x(\(cf.)S 14 x
(Section)S 16 x(7\),)S 16 x(instead)S 16 x(of)S 16 x(delivering)S 
16 x(a)S 16 x(value,)S 16 x(in)S 16 x(that)S 16 x(case.)S 1094 Y 
383 X F2(Notes:)S 1206 Y -53 x F6(\(a\))S 37 x(T)S -3 x(wo)S 19 x
(cases)S 17 x(arise)S 18 x(when)S 18 x F48(VALUE)S 15 x F22(6)S F20
(=)S 16 x F48(0.0)S 17 x F6(and)S 18 x F48(SIGN)S 15 x F20(=)S 16 x 
F48(0.0)S F6(:)S 75 y 549 X(\(i\))S 44 x(in)S 12 x(an)S 12 x
(implementation)S 12 x(exploiting)S 12 x(signed)S 12 x(zeros)S 12 x
(\(cf.)S 12 x(Section)S 12 x(4\),)S 12 x F48(COPY_SIGN)S 10 x F6
(must)S 12 x(deliver)S 12 x F22(\000j)S F48(VALUE)S -2 x F22(j)S 
50 y 632 X F6(when)S 14 x F48(SIGN)S 13 x F6(is)S 14 x(a)S 14 x
(negatively)S 14 x(signed)S 15 x(zero)S 14 x(and)S 14 x F22(j)S F48
(VALUE)S -1 x F22(j)S 13 x F6(when)S 14 x F48(SIGN)S 14 x F6(is)S 
15 x(a)S 14 x(positively)S 14 x(signed)S 15 x(zero;)S 50 y 549 X
(\(ii\))S 32 x(in)S 15 x(an)S 15 x(implementation)S 14 x(not)S 14 x
(exploiting)S 14 x(signed)S 15 x(zeros,)S 14 x F48(COPY_SIGN)S 13 x 
F6(must)S 15 x(deliver)S 15 x F22(j)S -1 x F48(VALUE)S -1 x F22(j)S
F6(.)S 1468 Y 466 X(\(b\))S 35 x(In)S 14 x(an)S 15 x(implementation)S
15 x(exploiting)S 14 x(signed)S 14 x(zeros,)S 14 x(the)S 15 x(zero)S
14 x(delivered)S 14 x(by)S 14 x F48(COPY_SIGN\(0.0,)S 18 x(SIGN\))S
13 x F6(must)S 50 y 549 X(be)S 18 x(a)S 17 x(negatively)S 17 x
(signed)S 17 x(zero)S 18 x(when)S 17 x(either)S 18 x F48(SIGN)S 14 x 
F21(<)S 16 x F48(0.0)S 16 x F6(or)S 17 x F48(SIGN)S 17 x F6(is)S 
18 x(a)S 17 x(negatively)S 18 x(signed)S 17 x(zero,)S 18 x(and)S 
17 x(it)S 49 y 549 X(must)S 14 x(be)S 15 x(a)S 14 x(positively)S 
14 x(signed)S 14 x(zero)S 14 x(when)S 14 x(either)S 14 x F48(SIGN)S
11 x F21(>)S 12 x F48(0.0)S 14 x F6(or)S 14 x F48(SIGN)S 14 x F6(is)S
15 x(a)S 14 x(positively)S 14 x(signed)S 14 x(zero.)S 1717 Y 300 X 
F73(8.15.)S 33 x(LEADING\210P)S -4 x(ART\320Floating-Point)S 19 x
(Machine)S 19 x(Number)S 19 x(with)S 20 x(its)S 71 y 968 X(Mantissa)S
19 x(\(in)S 20 x(the)S 19 x(Canonical)S 19 x(Representation\))S 70 y 
968 X(T)S -3 x(runcated)S 20 x(to)S 20 x(a)S 20 x(Given)S 20 x
(Number)S 20 x(of)S 19 x(Radix-Digits)S 1999 Y 383 X F2
(Speci\014cation:)S 2140 Y 466 X F48(function)S 20 x(LEADING_PART)S
19 x(\(X)S 1251 X(:)S 21 x(FLOAT_TYPE;)S 50 y 967 X(RADIX_DIGITS)S
20 x(:)S 21 x(POSITIVE\))S 20 x(return)S 21 x(FLOAT_TYPE;)S 2331 Y 
383 X F2(De\014nition:)S 2443 Y 466 X F6(\(a\))S 37 x F48
(LEADING_PART\(0.0,)S 17 x(RADIX_DIGITS\))S 12 x F20(=)S 15 x F48
(0.0)S 15 x F6(for)S 16 x(any)S 17 x F48(RADIX_DIGITS)S 63 y 466 X 
F6(\(b\))S 35 x(For)S 13 x F48(X)S 11 x F21(>)S 12 x F48(0.0)S -1 x 
F6(,)S 13 x F48(LEADING_PART\(X,)S 18 x(RADIX_DIGITS\))S 9 x F20(=)S
XP /F23 4 20 8 -47 18 2 49 16 0
<C000 C000 C000 C000 C000 C000 C000 C000 C000 C000 C000 C000 C000
 C000 C000 C000 C000 C000 C000 C000 C000 C000 C000 C000 C000 C000
 C000 C000 C000 C000 C000 C000 C000 C000 C000 C000 C000 C000 C000
 C000 C000 C000 C000 C000 C000 C000 C000 FFC0 FFC0>
PXLC RP
1472 2472 XY F23(\004)S 34 y -1 x F48(X)S F21(=\014)S -15 y 2 x F53
(k)S 1 x F54(\000)S
XP /F63 82 21 1 0 21 25 25 24 0
<7FE000 FFF800 7FFC00 1C1E00 1C0F00 1C0700 1C0700 1C0700 1C0700
 1C0F00 1C1E00 1FFC00 1FF800 1FFC00 1C1C00 1C0E00 1C0E00 1C0E00
 1C0E00 1C0E20 1C0E70 1C0E70 7F07E0 FF87E0 7F03C0>
PXLC RP
1604 2491 XY F63(R)S
XP /F63 65 21 1 0 20 25 25 24 0
<00E000 01F000 01F000 01B000 01B000 03B800 03B800 03B800 031800
 071C00 071C00 071C00 071C00 071C00 0E0E00 0E0E00 0FFE00 0FFE00
 1FFF00 1C0700 1C0700 1C0700 7F1FC0 FF1FE0 7F1FC0>
PXLC RP
1619 2491 XY F63(A)S
XP /F63 68 21 0 0 19 25 25 24 0
<7FF800 FFFE00 7FFF00 1C0F00 1C0780 1C03C0 1C01C0 1C01C0 1C01E0
 1C00E0 1C00E0 1C00E0 1C00E0 1C00E0 1C00E0 1C00E0 1C00E0 1C01C0
 1C01C0 1C03C0 1C0780 1C0F80 7FFF00 FFFE00 7FF800>
PXLC RP
1634 2491 XY F63(D)S
XP /F63 73 21 3 0 18 25 25 16 0
<FFFE FFFE FFFE 0380 0380 0380 0380 0380 0380 0380 0380 0380 0380
 0380 0380 0380 0380 0380 0380 0380 0380 0380 FFFE FFFE FFFE>
PXLC RP
1650 2491 XY F63(IX)S
XP /F63 95 21 2 -4 19 -1 3 24 0
<FFFF80 FFFF80 FFFF80>
PXLC RP
1680 2491 XY F63(_DI)S
XP /F63 71 21 2 0 20 25 25 24 0
<03E300 07FF00 1FFF00 3E1F00 3C0F00 780F00 780700 700700 F00000
 E00000 E00000 E00000 E00000 E03F80 E07FC0 E03F80 F00700 700700
 780F00 780F00 3C0F00 3E1F00 1FFF00 07FF00 03E700>
PXLC RP
1726 2491 XY F63(GIT)S
XP /F63 83 21 2 0 19 25 25 24 0
<07E300 1FFF00 7FFF00 781F00 F00F00 E00700 E00700 E00000 F00000
 780000 7F8000 1FF000 07FC00 00FE00 000F00 000780 000380 000380
 E00380 E00380 F00780 F80F00 FFFE00 FFFC00 C7F000>
PXLC RP
1772 2491 XY F63(S)S
XP /F23 5 20 1 -47 11 2 49 16 0
<00C0 00C0 00C0 00C0 00C0 00C0 00C0 00C0 00C0 00C0 00C0 00C0 00C0
 00C0 00C0 00C0 00C0 00C0 00C0 00C0 00C0 00C0 00C0 00C0 00C0 00C0
 00C0 00C0 00C0 00C0 00C0 00C0 00C0 00C0 00C0 00C0 00C0 00C0 00C0
 00C0 00C0 00C0 00C0 00C0 00C0 00C0 00C0 FFC0 FFC0>
PXLC RP
1789 2472 XY F23(\005)S 34 y 7 x F22(\001)S 6 x F21(\014)S -15 y 
2 x F53(k)S 1 x F54(\000)S F63(RADIX_DIGITS)S 15 y 6 x F6(,)S 13 x
(where)S 13 x F21(k)S 51 y 549 X F6(is)S 18 x(the)S 18 x(unique)S 
18 x(integer)S 18 x(such)S 18 x(that)S 18 x F21(\014)S -15 y 2 x F53
(k)S 1 x F54(\000)S F32(1)S 15 y 18 x F22(\024)S 17 x(j)S -1 x F48
(X)S F22(j)S 16 x F21(<)S 17 x(\014)S -15 y 2 x F53(k)S 2619 Y 466 X 
F6(\(c\))S 37 x(For)S 13 x F48(X)S 11 x F21(<)S 12 x F48(0.0)S -1 x 
F6(,)S 13 x F48(LEADING_PART\(X,)S 18 x(RADIX_DIGITS\))S 9 x F20(=)S
XP /F23 6 20 8 -47 18 2 49 16 0
<FFC0 FFC0 C000 C000 C000 C000 C000 C000 C000 C000 C000 C000 C000
 C000 C000 C000 C000 C000 C000 C000 C000 C000 C000 C000 C000 C000
 C000 C000 C000 C000 C000 C000 C000 C000 C000 C000 C000 C000 C000
 C000 C000 C000 C000 C000 C000 C000 C000 C000 C000>
PXLC RP
1472 2585 XY F23(\006)S 34 y -1 x F48(X)S F21(=\014)S -15 y 2 x F53
(k)S 1 x F54(\000)S F63(RADIX_DIGITS)S
XP /F23 7 20 1 -47 11 2 49 16 0
<FFC0 FFC0 00C0 00C0 00C0 00C0 00C0 00C0 00C0 00C0 00C0 00C0 00C0
 00C0 00C0 00C0 00C0 00C0 00C0 00C0 00C0 00C0 00C0 00C0 00C0 00C0
 00C0 00C0 00C0 00C0 00C0 00C0 00C0 00C0 00C0 00C0 00C0 00C0 00C0
 00C0 00C0 00C0 00C0 00C0 00C0 00C0 00C0 00C0 00C0>
PXLC RP
1789 2585 XY F23(\007)S 34 y 7 x F22(\001)S 6 x F21(\014)S -15 y 
2 x F53(k)S 1 x F54(\000)S F63(RADIX_DIGITS)S 15 y 6 x F6(,)S 13 x
(where)S 13 x F21(k)S 51 y 549 X F6(is)S 18 x(the)S 18 x(unique)S 
18 x(integer)S 18 x(such)S 18 x(that)S 18 x F21(\014)S -15 y 2 x F53
(k)S 1 x F54(\000)S F32(1)S 15 y 18 x F22(\024)S 17 x(j)S -1 x F48
(X)S F22(j)S 16 x F21(<)S 17 x(\014)S -15 y 2 x F53(k)S 2811 Y 383 X 
F2(Notes:)S 2923 Y -53 x F6(For)S 14 x F48(RADIX_DIGITS)S 9 x F22
(\025)S 11 x F48(FLOAT_TYPE\015MACHINE_MANTISSA)S -5 x F6(,)S 14 x
(this)S 14 x(function)S 14 x(merely)S 14 x(returns)S 14 x(its)S 13 x
(\014rst)S 14 x(ar)S -1 x(gument.)S 3128 Y 1254 X(15)S
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DataMuseum.dk

Rational R1000/400

⟦9893505e2⟧ TextFile

Derivation

TextFile
