Aa1S&HH SKI`R     dFootnote TableFootnote**. . / -  ]6]6LOT TableTitleLOFFigureTOC1Headingyyz{|}~-. !-=/- 42084: TableTitle: TABLE 2.. L90797: AppendixHead: Appendix I Sample C-language code implementing special-% y{} !% k42084: TableTitle: TABLE 2.؆L90797: AppendixHead: Appendix I Sample C-language code implementing special- <$paratext[Title]> <$paratext[Heading]> <$curpagenum><$lastpagenum><$daynum> <$monthname> <$year> (Continued)+ (Sheet <$tblsheetnum> of <$tblsheetcount>)<$daynum> <$monthname> <$year>"<$daynum>/<$monthnum>/<$shortyear>5<$daynum> <$monthname> <$year> <$hour24>:<$minute00> Fi<$daynum> <$monthname> <$year>"<$daynum>/<$monthnum>/<$shortyear> <$fullfilename> <$filename> <$marker1> <$marker2>Pagepage<$pagenum>Heading & Page <$paratext> on page<$pagenum>See Heading & Page%See <$paratext> on page<$pagenum>. Table & Page'Table<$paranumonly> on page<$pagenum>p Figure & Page(Figure<$paranumonly> on page<$pagenum>Section & Page%Section<$paranum> on page<$pagenum>Equation NumberTHeading<$paranumonly>x A nspTOC  Tle aAe  uAm<$a..nLOF00bLOTtnu33tIXU8aAm!Av!> <"#num$num%yea&5' <$(> <)hou*nut+,num-nam.>/$da0ont1hor2 3lfi4  5!ena6" 7%>8&$ma9:Page;gen<He=age TABLE 2. >ge?>@ HeAageBpar Appendix IaC>.Dle EablFumoGageHm>pIureJ(FiKranLn pMenuNSeOageP<$Qon RgenSEqTmbeUtioVWdinXanuY TABLE 1.Z[\n]^TO_`lea bc defghmij&k.lm0ntnuo3pq8arvstuwxyz{|}~genHeageLE ge> HeageparpenCDE ReferencesGHIJKLMNOPQRSTUVWXY TAZ[\]^_`abcdefgh9;SKI`e SKI`eSKI`e 6ixf 6ix`!0 6)n6) )6.1&f 6.1&Heh$6 yz 6A=pl6A=pA6m 6 J6 I f 6 I h%P04Q ofP 5RQ Hix f  Hix`#0 H) n H))fH.1& f  ;H.1&h&6K {| HA l HAAHm fHH I f H I h'Q9}Running H/F 1~P#Q of P4 1cnQ\(f 1cnQ\(UU`(. Hhnyhf HhnyhH)nH))6H0$yQf H0$yQh)6Q24 February 1993 H\hroH\hr\hrHmnH)SKI`e1&1H~6f- H~6 UU`"."<$paranum><$paratext><$pagenum> `,-"<$paranum><$paratext><$pagenum> )US UT`-S"<$paranum><$paratext><$pagenum> H I f H I 'h*P#Q of P4  SKI`e6ixf 6ixV6`Y5+Numerical values of special formats on VAX 4UU`<.(SpecialValueApproximate decimal value GU> UTUU`:.G+Infinity27126. 9+.8.50705917302346169 *. 10737 Y UTUU`;9ebS-.Infinity9-.27126.9-.8.50705917302346169 *. 10737 l UTUU`[.MsNaN1.49218759 *. 27126. 1.26941273597459479 *. 10738 eU9 UTUU`\.LqNaN1.99218759 *. 27126.1.69476569462576779 *. 10738 U8UU`]. KThe use of 9-.0.0 as a signaling pattern on the VAX is discouraged. `,U7UUh`.$pQThe present definitions correspond to the bit patterns shown in Table 2. Iתwh=5!Bit masks of special formats U!UU`a.(+Infinity9-.InfinitysNaNqNaN U UU`>.Single (& Double on VAX): UUU`d.Sign0100 UUU`e.-Exponent11111111111111111111111111111111 /UUU`f.7Fraction (most00000000-00000000-01111110-11111110- ?UUU`g.2sig. 16 bits)00000000000000000000000000000000 OUUU`h.in _UUU`A.+Double: 91oUUU`?. Sign0100 UUU`l.-9Exponent11111111111111111111111111111111111111111111 1UUU`@.377Fraction (most00000000-00000000-01110000-11110000- 26UUU`n.451sig 16 bits)00000000000000000000000000000000 1UUU(p. 2`An example of C code implementing this standard is given in Appendix I. (Note the pecu aUUUp.er[liarities of internal bit addressing differ on VAX and MIPS machines, even though they are he UUU@p. iboth "little-endian".) h`:ma  U!UU`.RANSI/IEEE Standard 754-1985: "IEEE Standard for Binary Floating-Point Arithmetic" SKI`eU,0HA3K ^f neHHD1Footnote11H-f (Footnote11msi000Hf"  ! 1Heading Rule_ m!U11~!l U~000H(SNd ^"l# 0-H_jH_jD5 1Heading Rule0H0 #f"% 1$$ Chapter Rulef $l#isiv theHJ ^%l#& itH(2H(2Dr Chapter RuleonHc&f%)h '( Table Topi_'m(&RAN~(l'&taar~metEZS(8 ^)l&* EZ\_jEZ\_jD Table TopH ,*f),++ TableFootnote+m*HHRb ^,l* H_H_D0 TableFootnoteHn(C ^-f. HwjHwjDTable of Contents SpecificationH-.f-/ 1H-UU`.."<$paranum><$paratext><$pagenum> H ^/f.0 diHEHEDList of Figures Specification$H60f/1 H6UU`/."<$paranum><$paratext><$pagenum> HJh ^1f0 HEHEDList of Tables SpecificationTaSKI`2e34H~3f42 H~`08(1, 23 l`18Z$<$symbols><$numerics><$alphabetics> `28 Level3IX &`38Ta Level2IX 0`48m Level1IX C`56LSymbols[\ ];Numerics[0];A;B;C;D;E;F;G;H;I;J;K;L;M;N;O;P;Q;R;S;T;U;V;W;X;Y;Z L`68e <$pagenum> ^HlAmN ^4f32 jHuHuDeIndex SpecificationHSKI`5e66Hix6f5 UUHix8> 3hB:Sample C-language code DUU`C;Sp#if defined IEEE_EL +UU`E; typedef union { 7UU`F; double d; CUU`G; struct { pOUU`H;>  unsigned int frac2:32; [UU`I;E unsigned int frac1:16; igUU`J;K unsigned int frac: 3; sUU`K; unsigned int quiet: 1; UU`L; unsigned int exp:11; UU`M;( unsigned int sign: 1; UU`N;ri } NaN_mask; UU`O; struct { UU`P;Le unsigned int frac1:32; eUU`R; unsigned int frac :20; 0ǪUU`S;I; unsigned int exp:11; Y;ӪUU`T;6 unsigned int sign: 1; ߪUU`U; } fp_mask; 모UU`V;ec } dNaN; UU`W; typedef union { UU`Z; float f; fUU`^; struct { UU`_; unsigned int frac1:16; 'UU`b;gu unsigned int frac: 6; p3UU`c;_E unsigned int quiet: 1; e?UU`i; unsigned int exp: 8; KUU`k;  unsigned int sign: 1; WUU`m;nt } NaN_mask; cUU`o; struct { aoUU`q;UU unsigned int frac :23; a{UU`r;UU unsigned int exp: 8; uiUU`s;UU unsigned int sign: 1; pUU`t;UU } fp_mask; iUU`u; } fNaN; NUU`w;ma#elif defined IEEE_EB UU`x; typedef union { êUU`y;ra double d; ϪUU`z; struct { a۪UU`{;UU unsigned int sign: 1; p窓UU`|;UU unsigned int exp:11; igUU`};UU unsigned int quiet: 1; UU`~;  unsigned int frac: 3;  UU`;{  unsigned int frac1:16; UU`;^ unsigned int frac2:32; U#UU`;si } NaN_mask; /UU`;gu struct { d;UU`; unsigned int sign: 1; dGUU`; unsigned int exp:11; edSUU`; unsigned int frac:20; d_UU`; unsigned int frac1:32; akUU`;o } fp_mask; aSKI`7eed886ix8f7 xp6ix6ed4igUU`;UU } dNaN; UU`; typedef union { UU`;UU float f; *UU`; struct { 6UU`;{  unsigned int sign: 1; eBUU`;z unsigned int exp: 8; UUNUU`;si unsigned int quiet: 1; UZUU`;si unsigned int frac: 6; UfUU`;si unsigned int frac1:16; UrUU`;si } NaN_mask; ~UU`;{ struct { dUU`; unsigned int sign: 1; dUU`; unsigned int exp: 8; maUU`; unsigned int frac:23; UUU`;si } fp_mask; dUU`; } fNaN; edƪUU`;#elif defined vax ҪUU`;ra typedef union { ުUU`;si double d; ꪗUU`; struct { pUU`;K unsigned int frac: 6; UU`; unsigned int quiet: 1; pUU`; unsigned int exp: 8; igUU`;UU unsigned int sign: 1; &UU`;io unsigned int frac1:16; l2UU`;UU unsigned int frac2:32; >UU`;  } NaN_mask; JUU`; struct { iVUU`;UU unsigned int frac: 7; ibUU`; U unsigned int exp: 8; sinUU`; U unsigned int sign: 1; izUU`; U unsigned int frac1:16; aUU`;UU unsigned int frac2:32; UU`;  } fp_mask; UU`; } dNaN; siUU`;ma typedef union { UU`;nt float f; ªUU`; struct { dΪUU`; unsigned int frac: 6; ڪUU`;d  unsigned int quiet: 1; e檂UU`; unsigned int exp: 8; UU`;  unsigned int sign: 1; UU`;nt unsigned int frac1:16;  UU`;nt } NaN_mask; ~UU`; struct { p"}UU`;UU unsigned int frac: 7; g.|UU`;UU unsigned int exp: 8; ra:{UU`;UU unsigned int sign: 1; aFzUU`;UU unsigned int frac1:16; RyUU`;  } fp_mask; ^xUU`; } fNaN; rajwUU`;UU#endif  SKI`TeUVsi1cnQ\(UfVT 1cnQ\(V  7NA Standard for Binary Floating-; 7N Point Arithmetic and (@7NRepresentations peFUU`jM R. S. Bogart cUU`8MSOI Technical Note TN-90-103 UU 9. TThis Note defines the standard for representation of floating-point numbers used by UU9. LSOI programs. The representation adopted is the IEEE standard. Distinctions UU9. Qbetween Signaling and Quiet NaNs are defined, and bit patterns are reserved for UU@9. p)NaN and Infinity under VAX architecture. aHhnyhVfUT HhnyhUUU UU +.: [Coding of floating-point arithmetic routines for pipeline processing and for internal data ; UU+. Vretrieval should make use of the ANSI IEEE Standard for Binary Floating-Point ArithmeUU+.siWtic, ANSI/IEEE Std 754-1985, with such extensions or modifications as may be adopted. *UU+.UUUThe single format and double format representations for all regular and denormalized 6UU+.ta\numbers, zero, and signed Infinity should obey the Standard explicitly unless the coding is BUU+. Vfor a machine architecture (such as VAX) which does not support the Standard. Use of NUU+. Xsigned Infinity, Signaling NaNs, and Quiet NaNs is to be supported on any machine impleUUZUU+.SiRmentation of SOI-DRAC code in accordance with the Standard. Quiet NaNs are to be fUU@+.InUUQ.t Xand single representations of Infinity and NaN will be numerically equal on a VAX. On a e JUU@Q.fo4VAX the numeric representations will be as follows: thbUU`X.D d SKI`inLeftSKI` fRightothSKI`anFirstUUSKI`ct Referencee. SKI`reTOCnSKI`2usIXSKI`T cFirst alSKI`anSKI`5exSKI`7UU)<fffSE  stff s u1Step Step Number S:.\tStep~ fHQ  `Zue.Be~th3HeadingH:\t..\t FirstBodyfh >Footnote~~ fE  thEquationEquation Numbers E:(EQ )bllfD  FirstBodyBodyfffff CBullet f.@U fAbstract1HeadingfS tep CellHeading~;fHQ  u~>.1Heading 1Heading RuleH:\t.\t FirstBodyZ f@   AuthorPurposell fq n+>Bodyfffff dyCStepofff CBExtractf@ Ab0angG f%VQAppendixAppendix fFA  Figure Table Top Step NumberF:FIGURE .\tBodyfHQ  u~2HeadingH:\t.\t FirstBodyhorf@  Purpose FirstBodyfffS ffCS oStep Step Number S:.\tff  TableFootnotellfD fTableTablef@< Title Chapter RuleAuthor~;fQ  u~ ReferenceHead 1Heading Rule\t\tReferences Referencesf8f CellBody fTA   TableTitle Table Top Step NumberT:TABLE .\tTable f@ Abstract1Heading~;fAQ  u~ AppendixHead 1Heading RuleaA:\tAppendix \tAppendixffuf leffr Bullet Bullet Symbol\tf6   header firstll f. fBodyll f.f Body f8p Level2IX fATA Hea TableTitle Table Top Step NumberT:TABLE .\tTablellf.Dd R+>ixffTableTablellf.D ;2fqTableTable~;f:AQ  u~ AppendixHead 1Heading RuleA:\tAppendix \tAppendixf;@ 0BoaG f%VQAppendixAppendix~lf.Df  References References~lfDL  References References~;f:Qf  lu~f ReferenceHead 1Heading Rule\t\tReferences Referencesfe CellBodyf @   TNTaglAbstract Z f0@;  AuthorTNTagof6  lheaderfQ  ere footer leftfQ  ces footer rightfQ  Hea footer rightfF  CellHeadingfffff. ff ff N 3HeadingTOCfff-; or ffTN o 2HeadingTOCcfS ~  f 1HeadingTOCcf.  f FigureLOFcf.  f TableTitleLOTQf8g f SeparatorsIXf8n f SortOrderIX$f8 ffLevel3IXf 8  oLevel1IX f!6   GroupTitlesIX1Hf"8 IndexIXZ f%0@   AuthorTNTagf&M@  TNTaggAbstract-]< - F .  /  Bullet Symbol 0  $1Callout= 2 Emphasisff3 Equation Number 4   Run-In Heading 5 6  7  8 tleX 9 f :  ;In <  Step Number$=  First Letter= > TN Subscript= ?  Superscript @Appendix A  Step Number D F  J   Default Bold M <N  P sff Q Eqti R 4S eugef@l@mnoThinMediumDoubleThick@ Very ThinYiZlY6 6=6N6Format B$[6666Format AM]MComment Courier  Helvetica Symbol Times-RegularRegular BoldRegularObliqueItalicނϧ=bUcp`[/i&Lb+oܳxD{mPȡ^9㿇08NZRT:ϲQ~woĖ:q;27x_X5Wk>