.NH 2
Heuristic rules
.PP
Using the information described
in the previous section,
we can find all calls that can
be expanded in line, and for which
this expansion is desirable.
In general, we cannot expand all these calls,
so we have to choose the 'best' ones.
With every CAL instruction
that may be expanded, we associate
a \fIpay off\fR,
which expresses how desirable it is
to expand this specific CAL.
.sp
Let Tc denote the portion of EM text involved
in a specific call, i.e. the pushing of the actual
parameter expressions, the CAL itself,
the popping of the parameters and the
pushing of the result (if any, via an LFR).
Let Te denote the EM text that would be obtained
by expanding the call in line.
Let Pc be the original program and Pe the program
with Te substituted for Tc.
The pay off of the CAL depends on two factors:
.IP -
T = execution_time(Pe) - execution_time(Pc)
.IP -
S = code_size(Pe) - code_size(Pc)
.LP
The change in execution time (T) depends on:
.IP -
T1 = execution_time(Te) - execution_time(Tc)
.IP -
N = number of times Te or Tc get executed.
.LP
We assume that T1 will be the same every
time the code gets executed.
This is a reasonable assumption.
(Note that we are talking about one CAL,
not about different calls to the same procedure).
Hence
.DS
T = N * T1
.DE
T1 can be estimated by a careful analysis
of the transformations that are performed.
Below, we list everything that will be
different when a call is expanded in line:
.IP -
The CAL instruction is not executed.
This saves a subroutine jump.
.IP -
The instructions in the procedure prolog
are not executed.
These instructions, generated from the PRO pseudo,
save some machine registers 
(including the old LB), set the new LB and allocate space
for the locals of the called routine.
The savings may be less if there are no
locals to allocate.
.IP -
In line parameters are not evaluated before the call
and are not pushed on the stack.
.IP -
All remaining parameters are stored in local variables,
instead of being pushed on the stack.
.IP -
If the number of parameters is nonzero,
the ASP instruction after the CAL is not executed.
.IP -
Every reference to an in line parameter is
substituted by the parameter expression.
.IP -
RET (return) instructions are replaced by
BRA (branch) instructions.
If the called procedure 'falls through'
(i.e. it has only one RET, at the end of its code),
even the BRA is not needed.
.IP -
The LFR (fetch function result) is not executed
.PP
Besides these changes, which are caused directly by IL,
other changes may occur as IL influences other optimization
techniques, such as Register Allocation and Constant Propagation.
Our heuristic rules do not take into account the quite
inpredictable effects on Register Allocation.
It does, however, favour calls that have numeric \fIconstants\fR
as parameter; especially the constant "0" as an inline
parameter gets high scores,
as further optimizations may often be possible.
.PP
It cannot be determined statically how often a CAL instruction gets
executed.
We will use \fIloop nesting\fR information here.
The nesting level of the loop in which
the CAL appears (if any) will be used as an
indication for the number of times it gets executed.
.PP
Based on all these facts,
the pay off of a call will be computed.
The following model was developed empirically.
Assume procedure P calls procedure Q.
The call takes place in basic block B.
.DS
ZP = # zero parameters
CP = # constant parameters - ZP
LN = Loop Nesting level (0 if outside any loop)
F  = \fIif\fR # formal parameters of Q > 0 \fIthen\fR 1 \fIelse\fR 0
FT = \fIif\fR Q falls through \fIthen\fR 1 \fIelse\fR 0
S  = size(Q) - 1 - # inline_parameters - F
L  = \fIif\fR # local variables of P > 0 \fIthen\fR 0 \fIelse\fR -1
A  = CP + 2 * ZP
N  = \fIif\fR LN=0 and P is never called from a loop \fIthen\fR 0 \fIelse\fR (LN+1)**2
FM = \fIif\fR B is a firm block \fIthen\fR 2 \fIelse\fR 1

pay_off = (100/S + FT + F + L + A) * N * FM
.DE
S stands for the size increase of the program,
which is slightly less than the size of Q.
The size of a procedure is taken to be its number
of (non-pseudo) EM instructions.
The terms "loop nesting level" and "firm" were defined
in the chapter on the Intermediate Code (section "loop tables").
If a call is not inside a loop and the calling procedure
is itself never called from a loop (transitively),
then the call will probably be executed at most once.
Such a call is never expanded in line (its pay off is zero).
If the calling procedure doesn't have local variables, a penalty (L)
is introduced, as it will most likely get local variables if the
call gets expanded.