.\" ********** dictionary **********
.\" B0 size of wide figure just diverted
.\" B1 size of figure at top full wdith
.\" B2 if figure at full width bottom
.\" B3 name of full width top figure for next page
.\" B4 full width bottom figure
.\" B5 wide top figure size scheduled for this page
.\" B6 true if a wide figure being diverted
.\" B8 if at EM end up macro stage
.\" BM width bottom margin
.\" BX full width top figure, this page
.\" CS begin caption; center if 1 line, else paragraph.
.\" D1 amount of text left column
.\" D2 amount of text right column
.\" D3 arithmetic scratch, typically whether went past page footer
.\" D9 scratch, remembers length of diverted keep
.\" DN name of current diversion trap
.\" DO default page offset
.\" EE string to be prefixed to an equation to indent it two spaces if wanted
.\" EZ rathole to throw equations down
.\" F0 argument to GS specifying quadrant
.\" F1 biggest space available in left column
.\" F2 biggest space available in right column
.\" F5 position of top of 2 2col section
.\" F6 argument to BS specifying top/bottom
.\" (2) size of just entered figure
.\" G1 size figure top left next page
.\" G2 size figure top right next page
.\" G3 size left bottom figure
.\" G4 size right bottom figure
.\" G5 true if next top narrow figure goes to right side (next page)
.\" G6 true if next bottom narrow figure goes to right side
.\" G7 (1) amount space before bottom wide figure to sit on baseline
.\" (2) flag for doubled up narrow figures into a wide one
.\" G8 true if figure has been placed
.\" GD buffer where narrow figure is placed
.\" GJ figure top left next page
.\" GK figure top right next page
.\" GL content left bottom figure
.\" GM content right bottom figure
.\" GP left half of a figure pair
.\" GQ right half of a figure pair
.\" H0 section numbers for numbered headings
.\" H1 size of figure at top left this page
.\" H2 size of figure top right this page
.\" HJ figure at top left this page
.\" HK figure at top right this page
.\" HS true if just at a section heading
.\" IK true if inside a KS/KE
.\" L1 shortest legal amount of two column material
.\" L2 amount of 2 column stuff expected
.\" L4 amount being diverted
.\" L5 amount of text diverted in double-column hunt
.\" L6 zero if right column, true if too short to split up
.\" L7 minimum length of a split column
.\" LC position of left column bottom
.\" LE computation of column lengths \" LE should be F3
.\" LE true if equations are labeled
.\" LS general looseness parameter
.\" NB number of columns possible
.\" NC number of columns being set
.\" ND have been in double column before, not first break to it.
.\" P1 (1) height left col
.\" (2) amount to pad total
.\" P2 height right column
.\" P3 amount of extra space at a 1C-2C transition
.\" P4 temporary in filling columns calcuations
.\" PS standard point size
.\" Q1 number of places to pad
.\" Q2 number padding points right column
.\" RO position of right column (offset for)
.\" S1 position of space in column
.\" T1 true if top figure position forced by GS arg
.\" T2 true if bottom figure position forced by GS arg
.\" TB true if there is to be a turnover bar here.
.\" TP true if still at document title (turnover bar decision)
.\" TQ position at top of page
.\" TT >0 if figure, etc. doesn't fit this page
.\" TT right running head (title)
.\" TW table width (set by TBL)
.\" VS standard vertical spacing
.\" X1 diversion to hold left column
.\" X2 diversion to hold right column
.\" XI value of indent to be restored after abstract
.\" XQ register in which padding points are counted
.\" XR true (1) if past the very first paragraph
.\" XX diversion to hold input text in preparation for formatting
.\" YE past very top: avoids a break in the EQ/EN macro before startup.
.\" y place of footer trap
.\" ********** environments *********
.\" 2 while columns are arranged
.\" ********** macros **********
.\" for user which invoke
.\" TL,AU,AI,AB,AE IZ, EA, AX, AY
.\" 2C 2D, 2S, C4, C3, LA
.\" 1C 1D, 1E, 1S, C6, C7
.\" GS, GE GA,GB,GG,GU,GV,GW,GX,GY,GZ,GN,GO,C8,MR,BR
.\" -----------------------------
.de RT \" reset params to normal state
.\" -----------------------------
.if !\\n(L1 .nr L1 1.5i \"minimum amount of double column
.\" -----------------------------
.de EQ \"equation, breakout and display
.if "\\$1"I" .ds EE \\h'4n'
.if "\\$1"I" .if !"\\$3"" .ds EE \\h'\\$3'
.\" -----------------------------
.de EN \" end of a displayed equation
.if !"\\n(.z"EZ" .tm EN not preceded by EQ, disaster follows.
.if \\n(ZN=0 .if !"\\*(EL"" .nr ZN 1
.if \\n(ZN>0 .if !\\n(.d=\\n(PE .SP 0.5
.if \\n(BD>0 .nr LE 0 \" can't mean centering in this case.
.if \\n(ZN>0 .if \\n(LE>0 .tl \(ts\(ts\\*(10\(ts\\*(EL\(ts
.if \\n(ZN>0 .if \\n(LE=0 .if \\n(BD=0 .tl \(ts\\*(EE\\*(10\(ts\(ts\\*(EL\(ts
.if \\n(ZN>0 .if \\n(LE=0 .if \\n(BD>0 \!\\*(10\\\\t\\*(EL
.if \\n(ZN>0 .if \\n(LE=0 .if \\n(BD>0 .if \\n(BD<\\w'\\*(10' .nr BD \\w'\\*(10'
.if \\n(YE>0 .if \\n(EF>0 .fi
.\" -----------------------------
.de TL \"title of document
.if !"xx\\n(.z"xx" \!.bd 1 3
.if !"xx\\n(.z"xx" \!.bd 2 3
.\" -----------------------------
.de AU \"author(s) name(s)
.if !"xx\\n(.z"xx" \!.bd 1
.if !"xx\\n(.z"xx" \!.bd 2
.\" -----------------------------
.de AI \"authors institution
.\" -----------------------------
.\" -----------------------------
.\" No default table macro now.
.\" . -----------------------------