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.NH
Number Registers and Arithmetic
.PP
.UL troff
has a facility for doing arithmetic,
and for defining and using variables with numeric values,
called
.ul
number registers.
Number registers, like strings and macros, can be useful in setting up a document
so it is easy to change later.
And of course they serve for any sort of arithmetic computation.
.PP
Like strings, number registers have one or two character names.
They are set by the
.BD .nr
command,
and are referenced anywhere by
.BD \enx
(one character name) or
.BD \en(xy
(two character name).
.PP
There are quite a few pre-defined number registers maintained by
.UL troff ,
among them
.BD %
for the current page number;
.BD nl
for the current vertical position on the page;
.BD dy ,
.BD mo
and
.BD yr
for the current day, month and year; and
.BD .s
and
.BD .f
for the current size and font.
(The font is a number from 1 to 4.)
Any of these can be used in computations like any other register,
but some, like
.BD .s
and
.BD .f ,
cannot be changed with
.BD .nr .
.PP
As an example of the use of number registers,
in the
.BD \-ms
macro package [4],
most significant parameters are defined in terms of the values
of a handful of number registers.
These include the point size for text, the vertical spacing,
and the line and title lengths.
To set the point size and vertical spacing for the following paragraphs, for example, a user may say
.P1
^nr PS 9
^nr VS 11
.P2
The paragraph macro
.BD .PP
is defined (roughly) as follows:
.P1
.ta  1i
^de PP
^ps \e\en(PS	\e" reset size
^vs \e\en(VSp	\e" spacing
^ft R	\e" font
^sp 0.5v	\e" half a line
^ti +3m
^^
.P2
This sets the font to Roman and the point size and line spacing
to whatever values are stored in the number registers
.BD PS
and
.BD VS .
.PP
Why are there two backslashes?
This is the eternal problem of how to quote a quote.
When
.UL troff
originally reads the macro definition,
it peels off one backslash
to see what's coming next.
To ensure that another is left in the definition when the 
macro is
.ul
used,
we have to put in two backslashes in the definition.
If only one backslash is used, 
point size and vertical spacing will be frozen at the time the macro
is defined, not when it is used.
.PP
Protecting by an extra layer of backslashes
is only needed for
.BD \en ,
.BD \e* ,
.BD \e$
(which we haven't come to yet),
and
.BD \e
itself.
Things like
.BD \es ,
.BD \ef ,
.BD \eh ,
.BD \ev ,
and so on do not need an extra backslash,
since they are converted by
.UL troff
to an internal code immediately upon being seen.
.WS
.PP
Arithmetic expressions can appear anywhere that
a number is expected.
As a trivial example,
.P1
^nr PS \e\en(PS\-2
.P2
decrements PS by 2.
Expressions can use the arithmetic operators +, \-, *, /, % (mod),
the relational operators >, >=, <, <=, =, and != (not equal),
and parentheses.
.PP
Although the arithmetic we have done so far
has been straightforward,
more complicated things are somewhat tricky.
First,
number registers hold only integers.
.UL troff
arithmetic uses truncating integer division, just like Fortran.
Second, in the absence of parentheses,
evaluation is done left-to-right
without any operator precedence
(including relational operators).
Thus
.P1
7*\-4+3/13
.P2
becomes `\-1'.
Number registers can occur anywhere in an expression,
and so can scale indicators like
.BD p ,
.BD i ,
.BD m ,
and so on (but no spaces).
Although integer division causes truncation,
each number and its scale indicator is converted
to machine units (1/432 inch) before any arithmetic is done,
so
1i/2u
evaluates to
0.5i
correctly.
.PP
The scale indicator
.BD u
often has to appear
when you wouldn't expect it _
in particular, when arithmetic is being done
in a context that implies horizontal or vertical dimensions.
For example,
.P1
^ll 7/2i
.P2
would seem obvious enough _
3\(12 inches.
Sorry.
Remember that the default units for horizontal parameters like
.BD .ll
are ems.
That's really `7 ems / 2 inches',
and when translated into machine units, it becomes zero.
How about
.P1
^ll 7i/2
.P2
Sorry, still no good _
the `2' is `2 ems', so `7i/2' is small,
although not zero.
You
.ul
must
use
.P1
^ll 7i/2u
.P2
So again, a safe rule is to
attach a scale indicator to every number,
even constants.
.PP
For arithmetic done within a
.BD .nr
command,
there is no implication of horizontal or vertical dimension,
so the default units are `units',
and 7i/2 and 7i/2u
mean the same thing.
Thus
.P1
^nr ll 7i/2
^ll \e\en(llu
.P2
does just what you want,
so long as you
don't forget the
.BD u
on the
.BD .ll
command.