# This is a shell archive. Remove anything before this line, # then unpack it by saving it in a file and typing "sh file". # # Wrapped by (C) Jim Thomas on Tue Nov 5 16:12:13 1996 # # This archive contains: # type_generic_math.ps # LANG=""; export LANG PATH=/bin:/usr/bin:$PATH; export PATH echo x - type_generic_math.ps sed 's/^@//' >type_generic_math.ps <<'@EOF' %!PS-Adobe-3.0 %%Title: (Microsoft Word - type-generic\311) %%Creator: (Microsoft Word: PSPrinter 8.1.1) %%CreationDate: (4:08 PM Tuesday, November 5, 1996) %%For: () %%Pages: 5 %%DocumentFonts: Times-Roman Times-Bold Times-Italic Courier-Bold Courier-BoldOblique %%DocumentNeededFonts: Times-Roman Times-Bold Times-Italic Courier-Bold Courier-BoldOblique %%DocumentSuppliedFonts: %%DocumentData: Clean7Bit %%PageOrder: Ascend %%Orientation: Portrait %ADO_PaperArea: -31 -30 761 582 %ADO_ImageableArea: 0 0 730 552 %%EndComments /md 183 dict def md begin /currentpacking where {pop /sc_oldpacking currentpacking def true setpacking}if %%BeginFile: adobe_psp_basic %%Copyright: Copyright 1990-1993 Adobe Systems Incorporated. All Rights Reserved. /bd{bind def}bind def /xdf{exch def}bd /xs{exch store}bd /ld{load def}bd /Z{0 def}bd /T/true /F/false /:L/lineto /lw/setlinewidth /:M/moveto /rl/rlineto /rm/rmoveto /:C/curveto /:T/translate /:K/closepath /:mf/makefont /gS/gsave /gR/grestore /np/newpath 14{ld}repeat /$m matrix def /av 81 def /por true def /normland false def /psb-nosave{}bd /pse-nosave{}bd /us Z /psb{/us save store}bd /pse{us restore}bd /level2 /languagelevel where { pop languagelevel 2 ge }{ false }ifelse def /featurecleanup { stopped cleartomark countdictstack exch sub dup 0 gt { {end}repeat }{ pop }ifelse }bd /noload Z /startnoload { {/noload save store}if }bd /endnoload { {noload restore}if }bd level2 startnoload /setjob { statusdict/jobname 3 -1 roll put }bd /setcopies { userdict/#copies 3 -1 roll put }bd level2 endnoload level2 not startnoload /setjob { 1 dict begin/JobName xdf currentdict end setuserparams }bd /setcopies { 1 dict begin/NumCopies xdf currentdict end setpagedevice }bd level2 not endnoload /pm Z /mT Z /sD Z /realshowpage Z /initializepage { /pm save store mT concat }bd /endp { pm restore showpage }def /$c/DeviceRGB def /rectclip where { pop/rC/rectclip ld }{ /rC { np 4 2 roll :M 1 index 0 rl 0 exch rl neg 0 rl :K clip np }bd }ifelse /rectfill where { pop/rF/rectfill ld }{ /rF { gS np 4 2 roll :M 1 index 0 rl 0 exch rl neg 0 rl fill gR }bd }ifelse /rectstroke where { pop/rS/rectstroke ld }{ /rS { gS np 4 2 roll :M 1 index 0 rl 0 exch rl neg 0 rl :K stroke gR }bd }ifelse %%EndFile %%BeginFile: adobe_psp_colorspace_level1 %%Copyright: Copyright 1991-1993 Adobe Systems Incorporated. All Rights Reserved. /G/setgray ld /:F/setrgbcolor ld %%EndFile %%BeginFile: adobe_psp_uniform_graphics %%Copyright: Copyright 1990-1993 Adobe Systems Incorporated. All Rights Reserved. /@a { np :M 0 rl :L 0 exch rl 0 rl :L fill }bd /@b { np :M 0 rl 0 exch rl :L 0 rl 0 exch rl fill }bd /arct where { pop }{ /arct { arcto pop pop pop pop }bd }ifelse /x1 Z /x2 Z /y1 Z /y2 Z /rad Z /@q { /rad xs /y2 xs /x2 xs /y1 xs /x1 xs np x2 x1 add 2 div y1 :M x2 y1 x2 y2 rad arct x2 y2 x1 y2 rad arct x1 y2 x1 y1 rad arct x1 y1 x2 y1 rad arct fill }bd /@s { /rad xs /y2 xs /x2 xs /y1 xs /x1 xs np x2 x1 add 2 div y1 :M x2 y1 x2 y2 rad arct x2 y2 x1 y2 rad arct x1 y2 x1 y1 rad arct x1 y1 x2 y1 rad arct :K stroke }bd /@i { np 0 360 arc fill }bd /@j { gS np :T scale 0 0 .5 0 360 arc fill gR }bd /@e { np 0 360 arc :K stroke }bd /@f { np $m currentmatrix pop :T scale 0 0 .5 0 360 arc :K $m setmatrix stroke }bd /@k { gS np :T 0 0 :M 0 0 5 2 roll arc fill gR }bd /@l { gS np :T 0 0 :M scale 0 0 .5 5 -2 roll arc fill gR }bd /@m { np arc stroke }bd /@n { np $m currentmatrix pop :T scale 0 0 .5 5 -2 roll arc $m setmatrix stroke }bd %%EndFile %%BeginFile: adobe_psp_basic_text %%Copyright: Copyright 1990-1993 Adobe Systems Incorporated. All Rights Reserved. /S/show ld /A{ 0.0 exch ashow }bd /R{ 0.0 exch 32 exch widthshow }bd /W{ 0.0 3 1 roll widthshow }bd /J{ 0.0 32 4 2 roll 0.0 exch awidthshow }bd /V{ 0.0 4 1 roll 0.0 exch awidthshow }bd /fcflg true def /fc{ fcflg{ vmstatus exch sub 50000 lt{ (%%[ Warning: Running out of memory ]%%\r)print flush/fcflg false store }if pop }if }bd /$f[1 0 0 -1 0 0]def /:ff{$f :mf}bd /MacEncoding StandardEncoding 256 array copy def MacEncoding 39/quotesingle put MacEncoding 96/grave put /Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute /agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute/egrave /ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde/oacute /ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex/udieresis /dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/notequal/AE/Oslash /infinity/plusminus/lessequal/greaterequal/yen/mu/partialdiff/summation /product/pi/integral/ordfeminine/ordmasculine/Omega/ae/oslash /questiondown/exclamdown/logicalnot/radical/florin/approxequal/Delta/guillemotleft /guillemotright/ellipsis/space/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide/lozenge /ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright/fi/fl /daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex/Idieresis/Igrave /Oacute/Ocircumflex/apple/Ograve/Uacute/Ucircumflex/Ugrave/dotlessi/circumflex/tilde /macron/breve/dotaccent/ring/cedilla/hungarumlaut/ogonek/caron MacEncoding 128 128 getinterval astore pop level2 startnoload /copyfontdict { findfont dup length dict begin { 1 index/FID ne{def}{pop pop}ifelse }forall }bd level2 endnoload level2 not startnoload /copyfontdict { findfont dup length dict copy begin }bd level2 not endnoload md/fontname known not{ /fontname/customfont def }if /Encoding Z /:mre { copyfontdict /Encoding MacEncoding def fontname currentdict end definefont :ff def }bd /:bsr { copyfontdict /Encoding Encoding 256 array copy def Encoding dup }bd /pd{put dup}bd /:esr { pop pop fontname currentdict end definefont :ff def }bd /scf { scalefont def }bd /scf-non { $m scale :mf setfont }bd /ps Z /fz{/ps xs}bd /sf/setfont ld /cF/currentfont ld /mbf { /makeblendedfont where { pop makeblendedfont /ABlend exch definefont }{ pop }ifelse def }def %%EndFile %%BeginFile: adobe_psp_derived_styles %%Copyright: Copyright 1990-1993 Adobe Systems Incorporated. All Rights Reserved. /wi version(23.0)eq { { gS 0 0 0 0 rC stringwidth gR }bind }{ /stringwidth load }ifelse def /$o 1. def /gl{$o G}bd /ms{:M S}bd /condensedmtx[.82 0 0 1 0 0]def /:mc { condensedmtx :mf def }bd /extendedmtx[1.18 0 0 1 0 0]def /:me { extendedmtx :mf def }bd /basefont Z /basefonto Z /dxa Z /dxb Z /dxc Z /dxd Z /dsdx2 Z /bfproc Z /:fbase { dup/FontType get 0 eq{ dup length dict begin dup{1 index/FID ne 2 index/UniqueID ne and{def}{pop pop}ifelse}forall /FDepVector exch/FDepVector get[exch/:fbase load forall]def }/bfproc load ifelse /customfont currentdict end definefont }bd /:mo { /bfproc{ dup dup length 2 add dict begin { 1 index/FID ne 2 index/UniqueID ne and{def}{pop pop}ifelse }forall /PaintType 2 def /StrokeWidth .012 0 FontMatrix idtransform pop def /customfont currentdict end definefont 8 dict begin /basefonto xdf /basefont xdf /FontType 3 def /FontMatrix[1 0 0 1 0 0]def /FontBBox[0 0 1 1]def /Encoding StandardEncoding def /BuildChar { exch begin basefont setfont ( )dup 0 4 -1 roll put dup wi setcharwidth 0 0 :M gS gl dup show gR basefonto setfont show end }def }store :fbase }bd /:mso { /bfproc{ 7 dict begin /basefont xdf /FontType 3 def /FontMatrix[1 0 0 1 0 0]def /FontBBox[0 0 1 1]def /Encoding StandardEncoding def /BuildChar { exch begin sD begin /dxa 1 ps div def basefont setfont ( )dup 0 4 -1 roll put dup wi 1 index 0 ne { exch dxa add exch }if setcharwidth dup 0 0 ms dup dxa 0 ms dup dxa dxa ms dup 0 dxa ms gl dxa 2. div dup ms end end }def }store :fbase }bd /:ms { /bfproc{ dup dup length 2 add dict begin { 1 index/FID ne 2 index/UniqueID ne and{def}{pop pop}ifelse }forall /PaintType 2 def /StrokeWidth .012 0 FontMatrix idtransform pop def /customfont currentdict end definefont 8 dict begin /basefonto xdf /basefont xdf /FontType 3 def /FontMatrix[1 0 0 1 0 0]def /FontBBox[0 0 1 1]def /Encoding StandardEncoding def /BuildChar { exch begin sD begin /dxb .05 def basefont setfont ( )dup 0 4 -1 roll put dup wi exch dup 0 ne { dxb add }if exch setcharwidth dup dxb .01 add 0 ms 0 dxb :T gS gl dup 0 0 ms gR basefonto setfont 0 0 ms end end }def }store :fbase }bd /:mss { /bfproc{ 7 dict begin /basefont xdf /FontType 3 def /FontMatrix[1 0 0 1 0 0]def /FontBBox[0 0 1 1]def /Encoding StandardEncoding def /BuildChar { exch begin sD begin /dxc 1 ps div def /dsdx2 .05 dxc 2 div add def basefont setfont ( )dup 0 4 -1 roll put dup wi exch dup 0 ne { dsdx2 add }if exch setcharwidth dup dsdx2 .01 add 0 ms 0 .05 dxc 2 div sub :T dup 0 0 ms dup dxc 0 ms dup dxc dxc ms dup 0 dxc ms gl dxc 2 div dup ms end end }def }store :fbase }bd /:msb { /bfproc{ 7 dict begin /basefont xdf /FontType 3 def /FontMatrix[1 0 0 1 0 0]def /FontBBox[0 0 1 1]def /Encoding StandardEncoding def /BuildChar { exch begin sD begin /dxd .03 def basefont setfont ( )dup 0 4 -1 roll put dup wi 1 index 0 ne { exch dxd add exch }if setcharwidth dup 0 0 ms dup dxd 0 ms dup dxd dxd ms 0 dxd ms end end }def }store :fbase }bd /italicmtx[1 0 -.212557 1 0 0]def /:mi { italicmtx 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%%BeginFeature: *PageSize LetterSmall 1 dict dup /Policies 2 dict dup /PageSize 2 put dup /MediaType 0 put put setpagedevice 2 dict dup /PageSize [612 792] put dup /ImagingBBox null put setpagedevice %%EndFeature }featurecleanup ()setjob /pT[1 0 0 -1 30 761]def/mT[1 0 0 -1 30 761]def /sD 16 dict def 300 level2{1 dict dup/WaitTimeout 4 -1 roll put setuserparams}{statusdict/waittimeout 3 -1 roll put}ifelse %%IncludeFont: Times-Roman %%IncludeFont: Times-Bold %%IncludeFont: Times-Italic %%IncludeFont: Courier-Bold %%IncludeFont: Courier-BoldOblique /f0_1/Times-Roman :mre /f0_12 f0_1 12 scf /f0_10 f0_1 10 scf /f0_9 f0_1 9 scf /f0_5 f0_1 5 scf /f1_1/Times-Bold :mre /f1_18 f1_1 18 scf /f1_14 f1_1 14 scf /f1_12 f1_1 12 scf /f2_1/Times-Italic :mre /f2_12 f2_1 12 scf /f2_10 f2_1 10 scf /f3_1/Courier-Bold :mre /f3_14 f3_1 14 scf /f3_10 f3_1 10 scf /f3_9 f3_1 9 scf /f7_1/Courier-BoldOblique :mre /f7_10 f7_1 10 scf /Courier findfont[10 0 0 -10 0 0]:mf setfont %%EndSetup %%Page: 1 1 %%BeginPageSetup initializepage (; page: 1 of 5)setjob %%EndPageSetup gS 0 0 552 730 rC 504 710 :M f0_12 sf (1)S 177 55 :M f1_18 sf -.036(Type-Generic Math Functions)A 182 80 :M f1_12 sf -.024(WG14/N618 X3J11/96-82 \(Draft 10/13/96\))A 264 104 :M f0_12 sf -.11(Jim Thomas)A 54 104 :M (5)S 246 116 :M f3_10 sf (jthomas@best.com)S 78 157 :M f1_12 sf -.097(Synopsis)A 48 169 :M f0_12 sf (1)S 54 169 :M (0)S 96 181 :M 2.044 .204(Type-generic macros allow calling a function whose type is determined by the)J 78 193 :M @.313 .031(argument type, as is the case for C operators such as )J 338 193 :M f3_10 sf @.109(+)A f0_12 sf @.17 .017( and )J f3_10 sf @.109(*)A f0_12 sf @.277 .028(. For example, with a type-)J 78 205 :M @.408 .041(generic )J 118 205 :M f3_10 sf @.214(cos)A f0_12 sf @.628 .063( macro, the expression )J f3_10 sf @.214(cos\(\(float\)x\))A f0_12 sf @.471 .047( will have type )J f3_10 sf @.214(float)A f0_12 sf @.54 .054(. This feature)J 78 217 :M @.026 .003(enables writing more portably efficient code, and alleviates need for awkward casting and)J 78 229 :M @.944 .094(suffixing in the process of porting or adjusting precision. This is a proposal for type-)J 48 229 :M (1)S 54 229 :M (5)S 78 241 :M @.414 .041(generic macros for most of the functions in )J 294 241 :M f3_10 sf @.058()A f0_12 sf @.093 .009( and )J 367 241 :M f3_10 sf @.059()A f0_12 sf @.166 .017(. The proposed)J 78 253 :M (header )S f3_10 sf -.006()A f0_12 sf -.005( includes the headers )A 313 253 :M f3_10 sf -.008()A f0_12 sf ( and )S f3_10 sf -.008()A f0_12 sf -.008( and extends)A 78 265 :M -.006(them by defining the type-generic macros.)A 48 289 :M (2)S 54 289 :M (0)S 78 301 :M f1_12 sf -.038(Background)A 96 325 :M f0_12 sf @.064 .006(As recent as December 1995, the floating-point and complex arithmetic specifications)J 78 337 :M @.204 .02(included type-generic macros, under the name of overloading macros. Then, in response)J 78 349 :M 1.51 .151(to the wishes of the C committees, these specifications were redrafted removing the)J 48 349 :M (2)S 54 349 :M (5)S 78 361 :M @.052 .005(overloading macros, with the intention of later considering them as a separate feature. At)J 78 373 :M 1.537 .154(the Amsterdam meeting, the committees accepted in principle the floating-point and)J 78 385 :M 1.893 .189(complex arithmetic specifications \(sans overloading\) into the C9X draft; and they)J 78 397 :M @.514 .051(requested a newly written proposal for the extracted facility, but under a different name)J 78 409 :M -.019(than overloading. This document is that proposal.)A 48 409 :M (3)S 54 409 :M (0)S 78 445 :M f1_12 sf -.047(Proposal)A 96 469 :M f0_12 sf 1.593 .159(Rationale given here pertains to this presentation of the type-generic feature. It)J 48 469 :M (3)S 54 469 :M (5)S 78 481 :M @.294 .029(supplements the rationale in the earlier specification for overloading, and is not intended)J 78 493 :M -.006(as a complete rationale for the feature.)A 78 529 :M f2_12 sf -.036(In 7, insert this subclause:)A 48 529 :M f0_12 sf (4)S 54 529 :M (0)S 78 564 :M f1_18 sf -.011(7.x Type-generic math )A 96 595 :M f0_12 sf -.063(The header )A 153 595 :M f3_10 sf -.008()A f0_12 sf -.006( includes the headers )A 353 595 :M f3_10 sf -.024()A f0_12 sf -.018( and )A f3_10 sf -.024()A f0_12 sf -.027( and)A 78 607 :M -.041(defines several )A 153 607 :M f2_12 sf -.014(type-generic macros)A f0_12 sf (.)S 48 607 :M (4)S 54 607 :M (5)S 114 631 :M f0_10 sf @.852 .085([The name )J 163 631 :M f2_10 sf -.088(type-generic)A 213 631 :M f0_10 sf @.934 .093( was chosen as more specific than the suggested name )J 447 631 :M f2_10 sf -.086(intrinsic)A f0_10 sf (,)S 114 642 :M -.012(which already is widely used with a more general meaning.)A 114 664 :M @.39 .039(The macros are placed in their own header in order not to silently break old programs that)J 48 664 :M f0_12 sf (5)S 54 664 :M (0)S 114 675 :M f0_10 sf -.133(include )A 146 675 :M f3_9 sf -.271()A f0_10 sf -.196(, for example with )A f3_9 sf -.271(printf\("%e", sin\(x\)\);)A f0_10 sf -.209( .])A endp %%Page: 2 2 %%BeginPageSetup initializepage (; page: 2 of 5)setjob %%EndPageSetup gS 0 0 552 730 rC 42 14 :M f0_12 sf -.032(WG14/N618 X3J11/96-82)A 431 14 :M -.095(10/13/96)A 42 722 :M (2)S 379 722 :M -.059(Type-Generic Math)A 42 68 :M f1_14 sf -.022(7.x.1 Type-generic macros)A 60 95 :M f0_12 sf 2.992 .299(Of the )J f3_10 sf 1.454()A f0_12 sf 2.356 .236( and )J 189 95 :M f3_10 sf @.892()A f0_12 sf 2.55 .255( functions without an )J 386 95 :M f3_10 sf 1.717(f)A f0_12 sf 1.669 .167( \()J f3_10 sf 1.717(float)A f0_12 sf 2.384 .238(\) or )J 468 95 :M f3_10 sf (l)S 42 107 :M f0_12 sf (\()S 46 107 :M f3_10 sf @.272(long\312double)A f0_12 sf @.92 .092(\) suffix, several have one or more parameters whose corresponding real)J 18 107 :M (5)S 42 119 :M @.866 .087(type is )J 80 119 :M f3_10 sf @.251(double)A f0_12 sf @.694 .069( and return a result whose corresponding real type is )J 383 119 :M f3_10 sf @.233(double)A f0_12 sf @.492 .049(. For each)J 42 131 :M @.915 .092(such function, except for )J f3_10 sf @.296(modf)A f0_12 sf @.461 .046( and )J f3_10 sf @.296(nextafterd)A f0_12 sf @.806 .081(, there is a corresponding )J 414 131 :M f2_12 sf -.087(type-generic)A 42 145 :M -.164(macro)A 73 142 :M f0_9 sf (1)S 77 145 :M f0_12 sf 2.127 .213(. The parameters whose corresponding real type is )J 355 145 :M f3_10 sf @.552(double)A f0_12 sf 1.492 .149( in the function)J 42 157 :M 2.819 .282(synopsis are )J 114 157 :M f2_12 sf 1.618 .162(generic parameters)J 213 157 :M f0_12 sf 3.264 .326(. Use of the macro invokes a function whose)J 42 169 :M @.074 .007(corresponding real type and type-domain are determined by the arguments for the generic)J 12 169 :M (1)S 18 169 :M (0)S 42 181 :M -.063(parameters.)A 78 205 :M f0_10 sf -.22([)A f3_9 sf -.374(modf\(double, double*\))A 188 205 :M f0_10 sf @.726 .073( is excluded because no way was seen to make it safe without)J 78 216 :M -.029(complicating the type resolution.])A 12 227 :M f0_12 sf (1)S 18 227 :M (5)S 60 239 :M -.01(Use of the macro invokes a function whose corresponding real type is the wider of)A 42 263 :M (\321)S 60 263 :M -.011(the corresponding real types of floating arguments for generic parameters)A 42 275 :M (\321)S 60 275 :M -.22(the )A 78 275 :M f3_10 sf -.073(float)A f0_12 sf -.072( type)A 12 287 :M (2)S 18 287 :M (0)S 78 299 :M f0_10 sf @.42 .042([This differs from the earlier overloading proposal in that the type is determined solely by)J 78 310 :M @.577 .058(the argument, and may be narrower than the type for expression evaluation. This change)J 78 321 :M -.008(was made because the performance costs for computing functions with narrow arguments to)A 78 332 :M 1.91 .191(wide range and precision might be too high, even if the implementation efficiently)J 78 343 :M -.013(evaluates basic operations to wide precision.])A 12 343 :M f0_12 sf (2)S 18 343 :M (5)S 60 366 :M 3.185 .319(For each unsuffixed function in )J f3_10 sf 1.016()A f0_12 sf 2.505 .251( for which there is a function in)J 42 378 :M f3_10 sf @.155()A f0_12 sf @.368 .037( with the same name except for a )J f3_10 sf @.155(c)A f0_12 sf @.619 .062( prefix, the corresponding type-generic)J 42 390 :M 2.015 .201(macro \(for both functions\) has the same name as the function in )J f3_10 sf @.719()A f0_12 sf 1.326 .133(. The)J 42 402 :M -.016(corresponding type-generic macro for )A 227 402 :M f3_10 sf -.017(fabs)A f0_12 sf -.013( and )A f3_10 sf -.017(cabs)A f0_12 sf ( is )S f3_10 sf -.017(fabs)A f0_12 sf (.)S 12 402 :M (3)S 18 402 :M (0)S 78 426 :M f3_10 sf ()S 186 426 :M ()S 294 426 :M f0_12 sf -.087(type-generic)A 78 438 :M -.141(function)A 186 438 :M -.141(function)A 294 438 :M -.245(macro)A 78 450 :M -.103(----------)A 186 450 :M -.076(-------------)A 294 450 :M -.135(--------)A 326 450 :M -.159(-------)A 78 462 :M f3_10 sf (acos)S 186 462 :M (cacos)S 294 462 :M (acos)S 12 462 :M f0_12 sf (3)S 18 462 :M (5)S 78 473 :M f3_10 sf (asin)S 186 473 :M (casin)S 294 473 :M (asin)S 78 484 :M (atan)S 186 484 :M (catan)S 294 484 :M (atan)S 78 495 :M (acosh)S 186 495 :M (cacosh)S 294 495 :M (acosh)S 78 506 :M (asinh)S 186 506 :M (casinh)S 294 506 :M (asinh)S 78 517 :M (atanh)S 186 517 :M (catanh)S 294 517 :M (atanh)S 12 517 :M f0_12 sf (4)S 18 517 :M (0)S 78 528 :M f3_10 sf (cos)S 186 528 :M (ccos)S 294 528 :M (cos)S 78 539 :M (sin)S 186 539 :M (csin)S 294 539 :M (sin)S 78 550 :M (tan)S 186 550 :M (ctan)S 294 550 :M (tan)S 78 561 :M (cosh)S 186 561 :M (ccosh)S 294 561 :M (cosh)S 78 572 :M (sinh)S 186 572 :M (csinh)S 294 572 :M (sinh)S 12 572 :M f0_12 sf (4)S 18 572 :M (5)S 78 583 :M f3_10 sf (tanh)S 186 583 :M (ctanh)S 294 583 :M (tanh)S 78 594 :M (exp)S 186 594 :M (cexp)S 294 594 :M (exp)S 78 605 :M (log)S 186 605 :M (clog)S 294 605 :M (log)S 78 616 :M (pow)S 186 616 :M (cpow)S 294 616 :M (pow)S 78 627 :M (sqrt)S 186 627 :M (csqrt)S 294 627 :M (sqrt)S 12 627 :M f0_12 sf (5)S 18 627 :M (0)S 78 638 :M f3_10 sf (fabs)S 186 638 :M (cabs)S 294 638 :M (fabs)S 42 662 :M f0_12 sf ( )S 42 659.48 -.48 .48 186.48 659 .48 42 659 @a 42 673 :M f0_9 sf (1)S 46 676 :M f0_10 sf -.004( Like other function-like macros in the Standard libraries, each type-generic macro can be suppressed to)A 42 687 :M -.007(make available the corresponding ordinary function.)A endp %%Page: 3 3 %%BeginPageSetup initializepage (; page: 3 of 5)setjob %%EndPageSetup gS 0 0 552 730 rC 78 14 :M f0_12 sf -.075(Draft 10/13/96)A 382 14 :M -.032(WG14/N618 X3J11/96-82)A 78 722 :M -.059(Type-Generic Math)A 504 722 :M (3)S 78 50 :M 1.712 .171(If at least one argument for a generic parameter is complex, then use of the macro)J 78 62 :M -.002(invokes a complex function; otherwise, use of the macro invokes a real function.)A 114 86 :M 1.077 .108(For each unsuffixed function in )J 278 86 :M f3_10 sf @.218()A f0_12 sf @.451 .045( without a )J f3_10 sf @.218(c)A f0_12 sf @.973 .097(-prefixed counter-part in)J 78 98 :M f3_10 sf @.111()A f0_12 sf @.364 .036(, the corresponding type-generic macro has the same name as the function.)J 54 98 :M (5)S 78 110 :M -.032(These type-generic macros are)A 78 134 :M ( )S 114 134 :M f3_10 sf (atan2)S 114 145 :M (exp2)S 114 156 :M (expm1)S 57 156 :M f0_12 sf (1)S 63 156 :M (0)S 114 167 :M f3_10 sf (frexp)S 114 178 :M (ldexp)S 114 189 :M (log10)S 114 200 :M (log1p)S 114 211 :M (log2)S 57 211 :M f0_12 sf (1)S 63 211 :M (5)S 114 222 :M f3_10 sf (logb)S 114 233 :M (scalb)S 270 134 :M (hypot)S 270 145 :M (erf)S 270 156 :M (erfc)S 213 156 :M f0_12 sf (2)S 219 156 :M (0)S 270 167 :M f3_10 sf (gamma)S 270 178 :M (lgamma)S 270 189 :M (ceil)S 270 200 :M (floor)S 270 211 :M (fmod)S 213 211 :M f0_12 sf (2)S 219 211 :M (5)S 270 222 :M f3_10 sf (nearbyint)S 270 233 :M (rint)S 426 134 :M (round)S 426 145 :M (trunc)S 426 156 :M (remainder)S 369 156 :M f0_12 sf (3)S 375 156 :M (0)S 426 167 :M f3_10 sf (remquo)S 426 178 :M (copysign)S 426 189 :M (nextafter)S 426 200 :M (fdim)S 426 211 :M (fmax)S 369 211 :M f0_12 sf (3)S 375 211 :M (5)S 426 222 :M f3_10 sf (fmin)S 78 256 :M f0_12 sf @.355 .035(If at least one argument for a generic parameter is not real, then use of the macro results)J 78 268 :M -.009(in implementation-defined behavior; otherwise, use of the macro invokes a real function.)A 48 280 :M (4)S 54 280 :M (0)S 114 292 :M f0_10 sf @.67 .067([The intention here is to allow, but not require, extensions for complex versions of these)J 114 303 :M @.353 .035(functions. Alternatively, the implementation might just pass a complex argument to a real)J 114 314 :M -.001(function, thereby converting the complex argument to real.])A 96 337 :M f0_12 sf @.339 .034(For each unsuffixed function in )J f3_10 sf @.108()A f0_12 sf @.174 .017( that is not a )J 385 337 :M f3_10 sf @.052(c)A f0_12 sf @.233 .023(-prefixed counter-part to)J 48 337 :M (4)S 54 337 :M (5)S 78 349 :M @.314 .031(a function in )J 144 349 :M f3_10 sf @.097()A f0_12 sf @.312 .031(, the corresponding type-generic macro has the same name as the)J 78 361 :M -.023(function. These type-generic macros are)A 114 385 :M f3_10 sf (carg)S 114 396 :M (conj)S 57 396 :M f0_12 sf (5)S 63 396 :M (0)S 270 385 :M f3_10 sf (cimag)S 270 396 :M (cproj)S 426 385 :M (creal)S 78 419 :M f0_12 sf -.014(Use of the macro with any real or complex arguments invokes a )A 388 419 :M f3_10 sf -.052()A f0_12 sf -.044( function.)A 48 419 :M (5)S 54 419 :M (5)S 78 443 :M f1_12 sf -.142(Examples)A 96 467 :M f0_12 sf -.031(With the declarations)A 48 479 :M (6)S 54 479 :M (0)S 114 491 :M f3_10 sf (#include )S 114 502 :M (int n;)S 114 513 :M (float f;)S 114 524 :M (double d;)S 114 535 :M (long double ld;)S 48 535 :M f0_12 sf (6)S 54 535 :M (5)S 114 546 :M f3_10 sf (float complex fc;)S 114 557 :M (double complex dc;)S 114 568 :M (long double complex ldc;)S 78 591 :M f0_12 sf -.008(functions invoked by use of type-generic macros are shown in the table:)A 48 591 :M (7)S 54 591 :M (0)S 96 615 :M -.122(macro use)A 222 615 :M -.054(invokes)A 96 627 :M -.064(---------------)A 222 627 :M -.083(------------)A 96 639 :M f3_10 sf (exp\(n\))S 222 639 :M (expf\(n\))S 96 650 :M (acosh\(f\))S 222 650 :M (acoshf\(f\))S 48 650 :M f0_12 sf (7)S 54 650 :M (5)S 96 661 :M f3_10 sf (sin\(d\))S 222 661 :M -.038(sin\(d\))A f0_12 sf -.031(, the function)A 96 673 :M f3_10 sf (atan\(ld\))S 222 673 :M (atanl\(ld\))S 96 684 :M (log\(fc\))S 222 684 :M (clogf\(fc\))S endp %%Page: 4 4 %%BeginPageSetup initializepage (; page: 4 of 5)setjob %%EndPageSetup gS 0 0 552 730 rC 42 14 :M f0_12 sf -.032(WG14/N618 X3J11/96-82)A 431 14 :M -.095(10/13/96)A 42 722 :M (4)S 379 722 :M -.059(Type-Generic Math)A 60 50 :M f3_10 sf (sqrt\(dc\))S 186 50 :M (csqrt\(dc\))S 60 61 :M (pow\(ldc, f\))S 186 61 :M (cpowl\(ldc, f\))S 60 72 :M (remainder\(n, n\))S 186 72 :M (remainderf\(n, n\))S 60 83 :M (nextafter\(d, f\))S 186 83 :M -.024(nextafter\(d, f\))A f0_12 sf -.02(, the function)A 60 95 :M f3_10 sf (copysign\(n, ld\))S 186 95 :M (copysignl\(n, ld\))S 18 95 :M f0_12 sf (5)S 60 106 :M f3_10 sf (exp2\(fc\))S 186 106 :M f0_12 sf -.014(implementation-defined)A 60 118 :M f3_10 sf (fabs\(dc\))S 186 118 :M f0_12 sf -.014(implementation-defined)A 60 130 :M f3_10 sf (gamma\(ldc\))S 186 130 :M f0_12 sf -.014(implementation-defined)A 60 142 :M f3_10 sf (carg\(n\))S 186 142 :M (cargf\(n\))S 60 153 :M (cproj\(f\))S 186 153 :M (cprojf\(f\))S 12 153 :M f0_12 sf (1)S 18 153 :M (0)S 60 164 :M f3_10 sf (creal\(d\))S 186 164 :M -.034(creal\(d\))A f0_12 sf -.028(, the function)A 60 176 :M f3_10 sf (cimag\(ld\))S 186 176 :M (cimagl\(ld\))S 60 187 :M (cabs\(fc\))S 186 187 :M (cabsf\(fc\))S 60 198 :M (carg\(dc\))S 186 198 :M -.034(carg\(dc\))A f0_12 sf -.028(, the function)A 60 210 :M f3_10 sf (cproj\(ldc\))S 186 210 :M (cprojl\(ldc\))S 12 210 :M f0_12 sf (1)S 18 210 :M (5)S 42 257 :M f2_12 sf -.007(Replace 7.x.11.3 in the floating-point document \(N595\) with the following \(footnote 14 is)A 42 269 :M -.027(already in the floating-point spec\):)A 12 269 :M f0_12 sf (2)S 18 269 :M (0)S 78 293 :M f0_10 sf -.051([This is essentially the )A f3_9 sf -.074(nextafter)A f0_10 sf -.054( spec prior to the extraction of overloading.])A 42 316 :M f1_12 sf -.009(7.x.11.3 The )A f3_10 sf -.011(nextafter)A f1_12 sf -.01( functions)A 12 328 :M f0_12 sf (2)S 18 328 :M (5)S 42 340 :M f1_12 sf -.097(Synopsis)A 78 364 :M f3_10 sf (#include )S 78 375 :M (double)S f7_10 sf ( )S f3_10 sf (nextafter\(double)S f7_10 sf ( )S f3_10 sf (x, long double y\);)S 78 386 :M (float nextafterf\(float x, float y\);)S 12 386 :M f0_12 sf (3)S 18 386 :M (0)S 78 397 :M f3_10 sf (double nextafterd\(double x, double y\);)S 78 408 :M (long double nextafterl\(long double x, long double y\);)S 42 431 :M f1_12 sf -.031(Description)A 12 443 :M f0_12 sf (3)S 18 443 :M (5)S 60 455 :M @.264 .026(The )J 83 455 :M f3_10 sf @.22(nextafter)A f0_12 sf @.665 .067( function determines the next representable value, in the type of the)J 42 467 :M (function, after )S 114 467 :M f3_10 sf @.139(x)A f0_12 sf @.299 .03( in the direction of )J f3_10 sf @.139(y)A f0_12 sf @.332 .033(, where x and y are first converted to the type of the)J 42 479 :M -.123(function.)A 85 475 :M f0_5 sf -.05(14)A f0_12 sf 0 4 rm -.111( The )A 0 -4 rm 118 479 :M f3_10 sf -.019(nextafter)A f0_12 sf -.014( function returns )A f3_10 sf (y)S f0_12 sf ( if )S f3_10 sf -.019(x\312==\312y)A f0_12 sf (.)S 60 503 :M 1.546 .155(The functions )J f3_10 sf @.455(nextafterf)A f0_12 sf @.379 .038(, )J f3_10 sf @.455(nextafterd)A f0_12 sf @.768 .077(, and )J f3_10 sf @.455(nextafterl)A f0_12 sf 1.077 .108( each is similar to the)J 12 503 :M (4)S 18 503 :M (0)S 42 515 :M f3_10 sf @.069(nextafter)A f0_12 sf @.193 .019( function except the type for both parameters and the returned value is )J 441 515 :M f3_10 sf (float)S f0_12 sf (,)S 42 527 :M f3_10 sf -.107(double)A f0_12 sf -.085(, or )A 97 527 :M f3_10 sf -.043(long\312double)A f0_12 sf -.034(, respectively.)A 42 551 :M f1_12 sf -.053(Returns)A 12 563 :M f0_12 sf (4)S 18 563 :M (5)S 60 575 :M @.492 .049(The functions )J f3_10 sf @.145(nextafter)A f0_12 sf @.121 .012(, )J f3_10 sf @.145(nextafterf)A f0_12 sf @.132 .013(, )J 261 575 :M f3_10 sf @.156(nextafterd)A f0_12 sf @.264 .026(, and )J f3_10 sf @.156(nextafterl)A f0_12 sf @.499 .05( each returns)J 42 587 :M -.009(the next representable value in the specified format after )A 316 587 :M f3_10 sf (x)S f0_12 sf -.03( in the direction of )A 414 587 :M f3_10 sf (y)S f0_12 sf (.)S 42 623 :M f2_12 sf -.003(In the Annex Y: IEC 559-Compatible Complex Arithmetic, append the subclause:)A 12 623 :M f0_12 sf (5)S 18 623 :M (0)S endp %%Page: 5 5 %%BeginPageSetup initializepage (; page: 5 of 5)setjob %%EndPageSetup gS 0 0 552 730 rC 78 14 :M f0_12 sf -.075(Draft 10/13/96)A 382 14 :M -.032(WG14/N618 X3J11/96-82)A 78 722 :M -.059(Type-Generic Math)A 504 722 :M (5)S 78 55 :M f1_18 sf -.287(Y.7 )A f3_14 sf -.362()A 96 83 :M f0_12 sf 3.523 .352(Type-generic macros that accept complex arguments also accept imaginary)J 78 95 :M @.2 .02(arguments. If an argument is imaginary, the macro expands to an expression whose type)J 78 107 :M @.181 .018(is real, imaginary, or complex, as appropriate for the particular function: if the argument)J 54 107 :M (5)S 78 119 :M @.518 .052(is imaginary, then the types of )J 232 119 :M f3_10 sf (cos)S f0_12 sf (, )S 257 119 :M f3_10 sf (cosh)S f0_12 sf (, )S 288 119 :M f3_10 sf (fabs)S f0_12 sf (, )S 319 119 :M f3_10 sf (carg)S f0_12 sf (, )S 350 119 :M f3_10 sf @.077(cimag)A f0_12 sf @.213 .021(, and)J 403 119 :M f3_10 sf @.388 .039( creal )J 447 119 :M f0_12 sf @.554 .055(are real; the)J 78 131 :M @.804 .08(types of )J f3_10 sf @.338(sin)A f0_12 sf @.308 .031(, )J 148 131 :M f3_10 sf @.223(tan)A f0_12 sf @.186 .019(, )J f3_10 sf @.223(sinh)A f0_12 sf @.203 .02(, )J 205 131 :M f3_10 sf @.201(tanh)A f0_12 sf @.168 .017(, )J f3_10 sf @.201(asin)A f0_12 sf @.183 .018(, )J 268 131 :M f3_10 sf @.289(atan)A f0_12 sf @.241 .024(, )J f3_10 sf @.289(asinh)A f0_12 sf @.488 .049(, and )J f3_10 sf @.289(atanh)A f0_12 sf @.75 .075( are imaginary; and the)J 78 143 :M -.009(types of the others are complex.)A 96 167 :M @.41 .041(Given an imaginary argument, each of the type-generic macros )J 409 167 :M f3_10 sf (cos)S f0_12 sf (, )S f3_10 sf (sin)S f0_12 sf (, )S 458 167 :M f3_10 sf (tan)S f0_12 sf (, )S 483 167 :M f3_10 sf (cosh)S f0_12 sf (,)S 48 167 :M (1)S 54 167 :M (0)S 78 179 :M f3_10 sf @.201(sinh)A f0_12 sf @.183 .018(, )J 110 179 :M f3_10 sf @.201(tanh)A f0_12 sf @.183 .018(, )J 142 179 :M f3_10 sf @.201(asin)A f0_12 sf @.183 .018(, )J 174 179 :M f3_10 sf @.201(atan)A f0_12 sf @.183 .018(, )J 206 179 :M f3_10 sf @.392(asinh)A f0_12 sf @.688 .069(, and )J 265 179 :M f3_10 sf @.433(atanh)A f0_12 sf 1.081 .108( is specified by a formula in terms of real)J 78 191 :M -.11(functions:)A 96 215 :M -.045(cos\(i*y\))A 150 215 :M (=)S 186 215 :M -.163(cosh\(y\))A 96 227 :M -.046(sin\(i*y\))A 150 227 :M (=)S 186 227 :M -.04(i*sinh\(y\))A 48 227 :M (1)S 54 227 :M (5)S 96 239 :M -.14(tan\(i*y\))A 150 239 :M (=)S 186 239 :M -.123(i*tanh\(y\))A 96 251 :M -.039(cosh\(i*y\))A 150 251 :M (=)S 186 251 :M -.196(cos\(y\))A 96 263 :M -.04(sinh\(i*y\))A 150 263 :M (=)S 186 263 :M -.046(i*sin\(y\))A 96 275 :M -.123(tanh\(i*y\))A 150 275 :M (=)S 186 275 :M -.14(i*tan\(y\))A 96 287 :M -.081(asin\(i*y\))A 150 287 :M (=)S 186 287 :M -.072(i*asinh\(y\))A 48 287 :M (2)S 54 287 :M (0)S 96 299 :M -.038(atan\(i*y\))A 150 299 :M (=)S 186 299 :M -.034(i*atanh\(y\))A 96 311 :M -.072(asinh\(i*y\))A 150 311 :M (=)S 186 311 :M -.081(i*asin\(y\))A 96 323 :M -.034(atanh\(i*y\))A 150 323 :M (=)S 186 323 :M -.038(i*atan\(y\))A 48 347 :M (2)S 54 347 :M (5)S endp %%Trailer end % md %%EOF @EOF chmod 640 type_generic_math.ps exit 0