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llvm-mirror/lib/Target/PowerPC
Cong Hou 50c405416c [BPI] Replace weights by probabilities in BPI.
This patch removes all weight-related interfaces from BPI and replace
them by probability versions. With this patch, we won't use edge weight
anymore in either IR or MC passes. Edge probabilitiy is a better
representation in terms of CFG update and validation.


Differential revision: http://reviews.llvm.org/D15519 

llvm-svn: 256263
2015-12-22 18:56:14 +00:00
..
AsmParser Reduce the size of MCRelaxableFragment. 2015-11-14 06:35:56 +00:00
Disassembler
InstPrinter
MCTargetDesc Simplify. NFC. 2015-12-17 14:19:52 +00:00
TargetInfo
CMakeLists.txt [PPC64] Convert bool literals to i32 2015-12-07 20:50:29 +00:00
LLVMBuild.txt
Makefile
PPC.h [PPC64] Convert bool literals to i32 2015-12-07 20:50:29 +00:00
PPC.td Define a feature for __float128 support in the PPC back end 2015-12-15 12:19:34 +00:00
PPCAsmPrinter.cpp [PowerPC] OutStreamer cleanup in PPCAsmPrinter 2015-12-12 01:47:08 +00:00
PPCBoolRetToInt.cpp [PPC64] Convert bool literals to i32 2015-12-07 20:50:29 +00:00
PPCBranchSelector.cpp
PPCCallingConv.h
PPCCallingConv.td
PPCCTRLoops.cpp LPM: Stop threading Pass * through all of the loop utility APIs. NFC 2015-12-15 19:40:57 +00:00
PPCEarlyReturn.cpp [CodeGen] Make MachineInstrBuilder::copyImplicitOps const. NFC. 2015-12-16 22:15:30 +00:00
PPCFastISel.cpp Weak non-function symbols were being accessed directly, which is 2015-11-20 20:51:31 +00:00
PPCFrameLowering.cpp Replace uint16_t with the MCPhysReg typedef in many places. A lot of physical register arrays already use this typedef. 2015-12-05 07:13:35 +00:00
PPCFrameLowering.h Find available scratch register to use in function prologue and epilogue as part of shrink wrapping. 2015-11-16 20:22:15 +00:00
PPCHazardRecognizers.cpp
PPCHazardRecognizers.h
PPCInstr64Bit.td Introduce new @llvm.get.dynamic.area.offset.i{32, 64} intrinsics. 2015-12-01 11:40:55 +00:00
PPCInstrAltivec.td
PPCInstrBuilder.h
PPCInstrFormats.td
PPCInstrHTM.td
PPCInstrInfo.cpp Replace uint16_t with the MCPhysReg typedef in many places. A lot of physical register arrays already use this typedef. 2015-12-05 07:13:35 +00:00
PPCInstrInfo.h replace MachineCombinerPattern namespace and enum with enum class; NFCI 2015-11-05 19:34:57 +00:00
PPCInstrInfo.td Introduce new @llvm.get.dynamic.area.offset.i{32, 64} intrinsics. 2015-12-01 11:40:55 +00:00
PPCInstrQPX.td Start replacing vector_extract/vector_insert with extractelt/insertelt 2015-12-11 19:20:16 +00:00
PPCInstrSPE.td
PPCInstrVSX.td Bitcasts between FP and INT values using direct moves 2015-12-15 14:50:34 +00:00
PPCISelDAGToDAG.cpp [BPI] Replace weights by probabilities in BPI. 2015-12-22 18:56:14 +00:00
PPCISelLowering.cpp Bitcasts between FP and INT values using direct moves 2015-12-15 14:50:34 +00:00
PPCISelLowering.h [Power PC] llvm soft float support for ppc32 2015-12-14 17:57:33 +00:00
PPCLoopDataPrefetch.cpp
PPCLoopPreIncPrep.cpp LPM: Stop threading Pass * through all of the loop utility APIs. NFC 2015-12-15 19:40:57 +00:00
PPCMachineFunctionInfo.cpp
PPCMachineFunctionInfo.h
PPCMCInstLower.cpp
PPCMIPeephole.cpp [PowerPC] Add an MI SSA peephole pass. 2015-11-10 21:38:26 +00:00
PPCPerfectShuffle.h
PPCRegisterInfo.cpp Introduce new @llvm.get.dynamic.area.offset.i{32, 64} intrinsics. 2015-12-01 11:40:55 +00:00
PPCRegisterInfo.h Introduce new @llvm.get.dynamic.area.offset.i{32, 64} intrinsics. 2015-12-01 11:40:55 +00:00
PPCRegisterInfo.td
PPCSchedule440.td
PPCSchedule.td
PPCScheduleA2.td
PPCScheduleE500mc.td
PPCScheduleE5500.td
PPCScheduleG3.td
PPCScheduleG4.td
PPCScheduleG4Plus.td
PPCScheduleG5.td
PPCScheduleP7.td
PPCScheduleP8.td
PPCSubtarget.cpp Define a feature for __float128 support in the PPC back end 2015-12-15 12:19:34 +00:00
PPCSubtarget.h Define a feature for __float128 support in the PPC back end 2015-12-15 12:19:34 +00:00
PPCTargetMachine.cpp [Power PC] llvm soft float support for ppc32 2015-12-14 17:57:33 +00:00
PPCTargetMachine.h
PPCTargetObjectFile.cpp Drop prelink support. 2015-11-17 00:51:23 +00:00
PPCTargetObjectFile.h
PPCTargetStreamer.h
PPCTargetTransformInfo.cpp
PPCTargetTransformInfo.h
PPCTLSDynamicCall.cpp
PPCTOCRegDeps.cpp
PPCVSXCopy.cpp Bitcasts between FP and INT values using direct moves 2015-12-15 14:50:34 +00:00
PPCVSXFMAMutate.cpp PPC: Teach FMA mutate to respect register classes. 2015-12-10 21:28:40 +00:00
PPCVSXSwapRemoval.cpp [PPC64LE] Properly initialize instr-info in PPCVSXSwapRemoval pass 2015-11-02 22:43:57 +00:00
README_ALTIVEC.txt
README.txt

//===- README.txt - Notes for improving PowerPC-specific code gen ---------===//

TODO:
* lmw/stmw pass a la arm load store optimizer for prolog/epilog

===-------------------------------------------------------------------------===

This code:

unsigned add32carry(unsigned sum, unsigned x) {
 unsigned z = sum + x;
 if (sum + x < x)
     z++;
 return z;
}

Should compile to something like:

	addc r3,r3,r4
	addze r3,r3

instead we get:

	add r3, r4, r3
	cmplw cr7, r3, r4
	mfcr r4 ; 1
	rlwinm r4, r4, 29, 31, 31
	add r3, r3, r4

Ick.

===-------------------------------------------------------------------------===

We compile the hottest inner loop of viterbi to:

        li r6, 0
        b LBB1_84       ;bb432.i
LBB1_83:        ;bb420.i
        lbzx r8, r5, r7
        addi r6, r7, 1
        stbx r8, r4, r7
LBB1_84:        ;bb432.i
        mr r7, r6
        cmplwi cr0, r7, 143
        bne cr0, LBB1_83        ;bb420.i

The CBE manages to produce:

	li r0, 143
	mtctr r0
loop:
	lbzx r2, r2, r11
	stbx r0, r2, r9
	addi r2, r2, 1
	bdz later
	b loop

This could be much better (bdnz instead of bdz) but it still beats us.  If we
produced this with bdnz, the loop would be a single dispatch group.

===-------------------------------------------------------------------------===

Lump the constant pool for each function into ONE pic object, and reference
pieces of it as offsets from the start.  For functions like this (contrived
to have lots of constants obviously):

double X(double Y) { return (Y*1.23 + 4.512)*2.34 + 14.38; }

We generate:

_X:
        lis r2, ha16(.CPI_X_0)
        lfd f0, lo16(.CPI_X_0)(r2)
        lis r2, ha16(.CPI_X_1)
        lfd f2, lo16(.CPI_X_1)(r2)
        fmadd f0, f1, f0, f2
        lis r2, ha16(.CPI_X_2)
        lfd f1, lo16(.CPI_X_2)(r2)
        lis r2, ha16(.CPI_X_3)
        lfd f2, lo16(.CPI_X_3)(r2)
        fmadd f1, f0, f1, f2
        blr

It would be better to materialize .CPI_X into a register, then use immediates
off of the register to avoid the lis's.  This is even more important in PIC 
mode.

Note that this (and the static variable version) is discussed here for GCC:
http://gcc.gnu.org/ml/gcc-patches/2006-02/msg00133.html

Here's another example (the sgn function):
double testf(double a) {
       return a == 0.0 ? 0.0 : (a > 0.0 ? 1.0 : -1.0);
}

it produces a BB like this:
LBB1_1: ; cond_true
        lis r2, ha16(LCPI1_0)
        lfs f0, lo16(LCPI1_0)(r2)
        lis r2, ha16(LCPI1_1)
        lis r3, ha16(LCPI1_2)
        lfs f2, lo16(LCPI1_2)(r3)
        lfs f3, lo16(LCPI1_1)(r2)
        fsub f0, f0, f1
        fsel f1, f0, f2, f3
        blr 

===-------------------------------------------------------------------------===

PIC Code Gen IPO optimization:

Squish small scalar globals together into a single global struct, allowing the 
address of the struct to be CSE'd, avoiding PIC accesses (also reduces the size
of the GOT on targets with one).

Note that this is discussed here for GCC:
http://gcc.gnu.org/ml/gcc-patches/2006-02/msg00133.html

===-------------------------------------------------------------------------===

Darwin Stub removal:

We still generate calls to foo$stub, and stubs, on Darwin.  This is not
necessary when building with the Leopard (10.5) or later linker, as stubs are
generated by ld when necessary.  Parameterizing this based on the deployment
target (-mmacosx-version-min) is probably enough.  x86-32 does this right, see
its logic.

===-------------------------------------------------------------------------===

Darwin Stub LICM optimization:

Loops like this:
  
  for (...)  bar();

Have to go through an indirect stub if bar is external or linkonce.  It would 
be better to compile it as:

     fp = &bar;
     for (...)  fp();

which only computes the address of bar once (instead of each time through the 
stub).  This is Darwin specific and would have to be done in the code generator.
Probably not a win on x86.

===-------------------------------------------------------------------------===

Simple IPO for argument passing, change:
  void foo(int X, double Y, int Z) -> void foo(int X, int Z, double Y)

the Darwin ABI specifies that any integer arguments in the first 32 bytes worth
of arguments get assigned to r3 through r10. That is, if you have a function
foo(int, double, int) you get r3, f1, r6, since the 64 bit double ate up the
argument bytes for r4 and r5. The trick then would be to shuffle the argument
order for functions we can internalize so that the maximum number of 
integers/pointers get passed in regs before you see any of the fp arguments.

Instead of implementing this, it would actually probably be easier to just 
implement a PPC fastcc, where we could do whatever we wanted to the CC, 
including having this work sanely.

===-------------------------------------------------------------------------===

Fix Darwin FP-In-Integer Registers ABI

Darwin passes doubles in structures in integer registers, which is very very 
bad.  Add something like a BITCAST to LLVM, then do an i-p transformation that
percolates these things out of functions.

Check out how horrible this is:
http://gcc.gnu.org/ml/gcc/2005-10/msg01036.html

This is an extension of "interprocedural CC unmunging" that can't be done with
just fastcc.

===-------------------------------------------------------------------------===

Fold add and sub with constant into non-extern, non-weak addresses so this:

static int a;
void bar(int b) { a = b; }
void foo(unsigned char *c) {
  *c = a;
}

So that 

_foo:
        lis r2, ha16(_a)
        la r2, lo16(_a)(r2)
        lbz r2, 3(r2)
        stb r2, 0(r3)
        blr

Becomes

_foo:
        lis r2, ha16(_a+3)
        lbz r2, lo16(_a+3)(r2)
        stb r2, 0(r3)
        blr

===-------------------------------------------------------------------------===

We should compile these two functions to the same thing:

#include <stdlib.h>
void f(int a, int b, int *P) {
  *P = (a-b)>=0?(a-b):(b-a);
}
void g(int a, int b, int *P) {
  *P = abs(a-b);
}

Further, they should compile to something better than:

_g:
        subf r2, r4, r3
        subfic r3, r2, 0
        cmpwi cr0, r2, -1
        bgt cr0, LBB2_2 ; entry
LBB2_1: ; entry
        mr r2, r3
LBB2_2: ; entry
        stw r2, 0(r5)
        blr

GCC produces:

_g:
        subf r4,r4,r3
        srawi r2,r4,31
        xor r0,r2,r4
        subf r0,r2,r0
        stw r0,0(r5)
        blr

... which is much nicer.

This theoretically may help improve twolf slightly (used in dimbox.c:142?).

===-------------------------------------------------------------------------===

PR5945: This: 
define i32 @clamp0g(i32 %a) {
entry:
        %cmp = icmp slt i32 %a, 0
        %sel = select i1 %cmp, i32 0, i32 %a
        ret i32 %sel
}

Is compile to this with the PowerPC (32-bit) backend:

_clamp0g:
        cmpwi cr0, r3, 0
        li r2, 0
        blt cr0, LBB1_2
; BB#1:                                                     ; %entry
        mr r2, r3
LBB1_2:                                                     ; %entry
        mr r3, r2
        blr

This could be reduced to the much simpler:

_clamp0g:
        srawi r2, r3, 31
        andc r3, r3, r2
        blr

===-------------------------------------------------------------------------===

int foo(int N, int ***W, int **TK, int X) {
  int t, i;
  
  for (t = 0; t < N; ++t)
    for (i = 0; i < 4; ++i)
      W[t / X][i][t % X] = TK[i][t];
      
  return 5;
}

We generate relatively atrocious code for this loop compared to gcc.

We could also strength reduce the rem and the div:
http://www.lcs.mit.edu/pubs/pdf/MIT-LCS-TM-600.pdf

===-------------------------------------------------------------------------===

We generate ugly code for this:

void func(unsigned int *ret, float dx, float dy, float dz, float dw) {
  unsigned code = 0;
  if(dx < -dw) code |= 1;
  if(dx > dw)  code |= 2;
  if(dy < -dw) code |= 4;
  if(dy > dw)  code |= 8;
  if(dz < -dw) code |= 16;
  if(dz > dw)  code |= 32;
  *ret = code;
}

===-------------------------------------------------------------------------===

%struct.B = type { i8, [3 x i8] }

define void @bar(%struct.B* %b) {
entry:
        %tmp = bitcast %struct.B* %b to i32*              ; <uint*> [#uses=1]
        %tmp = load i32* %tmp          ; <uint> [#uses=1]
        %tmp3 = bitcast %struct.B* %b to i32*             ; <uint*> [#uses=1]
        %tmp4 = load i32* %tmp3                ; <uint> [#uses=1]
        %tmp8 = bitcast %struct.B* %b to i32*             ; <uint*> [#uses=2]
        %tmp9 = load i32* %tmp8                ; <uint> [#uses=1]
        %tmp4.mask17 = shl i32 %tmp4, i8 1          ; <uint> [#uses=1]
        %tmp1415 = and i32 %tmp4.mask17, 2147483648            ; <uint> [#uses=1]
        %tmp.masked = and i32 %tmp, 2147483648         ; <uint> [#uses=1]
        %tmp11 = or i32 %tmp1415, %tmp.masked          ; <uint> [#uses=1]
        %tmp12 = and i32 %tmp9, 2147483647             ; <uint> [#uses=1]
        %tmp13 = or i32 %tmp12, %tmp11         ; <uint> [#uses=1]
        store i32 %tmp13, i32* %tmp8
        ret void
}

We emit:

_foo:
        lwz r2, 0(r3)
        slwi r4, r2, 1
        or r4, r4, r2
        rlwimi r2, r4, 0, 0, 0
        stw r2, 0(r3)
        blr

We could collapse a bunch of those ORs and ANDs and generate the following
equivalent code:

_foo:
        lwz r2, 0(r3)
        rlwinm r4, r2, 1, 0, 0
        or r2, r2, r4
        stw r2, 0(r3)
        blr

===-------------------------------------------------------------------------===

Consider a function like this:

float foo(float X) { return X + 1234.4123f; }

The FP constant ends up in the constant pool, so we need to get the LR register.
 This ends up producing code like this:

_foo:
.LBB_foo_0:     ; entry
        mflr r11
***     stw r11, 8(r1)
        bl "L00000$pb"
"L00000$pb":
        mflr r2
        addis r2, r2, ha16(.CPI_foo_0-"L00000$pb")
        lfs f0, lo16(.CPI_foo_0-"L00000$pb")(r2)
        fadds f1, f1, f0
***     lwz r11, 8(r1)
        mtlr r11
        blr

This is functional, but there is no reason to spill the LR register all the way
to the stack (the two marked instrs): spilling it to a GPR is quite enough.

Implementing this will require some codegen improvements.  Nate writes:

"So basically what we need to support the "no stack frame save and restore" is a
generalization of the LR optimization to "callee-save regs".

Currently, we have LR marked as a callee-save reg.  The register allocator sees
that it's callee save, and spills it directly to the stack.

Ideally, something like this would happen:

LR would be in a separate register class from the GPRs. The class of LR would be
marked "unspillable".  When the register allocator came across an unspillable
reg, it would ask "what is the best class to copy this into that I *can* spill"
If it gets a class back, which it will in this case (the gprs), it grabs a free
register of that class.  If it is then later necessary to spill that reg, so be
it.

===-------------------------------------------------------------------------===

We compile this:
int test(_Bool X) {
  return X ? 524288 : 0;
}

to: 
_test:
        cmplwi cr0, r3, 0
        lis r2, 8
        li r3, 0
        beq cr0, LBB1_2 ;entry
LBB1_1: ;entry
        mr r3, r2
LBB1_2: ;entry
        blr 

instead of:
_test:
        addic r2,r3,-1
        subfe r0,r2,r3
        slwi r3,r0,19
        blr

This sort of thing occurs a lot due to globalopt.

===-------------------------------------------------------------------------===

We compile:

define i32 @bar(i32 %x) nounwind readnone ssp {
entry:
  %0 = icmp eq i32 %x, 0                          ; <i1> [#uses=1]
  %neg = sext i1 %0 to i32              ; <i32> [#uses=1]
  ret i32 %neg
}

to:

_bar:
	cntlzw r2, r3
	slwi r2, r2, 26
	srawi r3, r2, 31
	blr 

it would be better to produce:

_bar: 
        addic r3,r3,-1
        subfe r3,r3,r3
        blr

===-------------------------------------------------------------------------===

We generate horrible ppc code for this:

#define N  2000000
double   a[N],c[N];
void simpleloop() {
   int j;
   for (j=0; j<N; j++)
     c[j] = a[j];
}

LBB1_1: ;bb
        lfdx f0, r3, r4
        addi r5, r5, 1                 ;; Extra IV for the exit value compare.
        stfdx f0, r2, r4
        addi r4, r4, 8

        xoris r6, r5, 30               ;; This is due to a large immediate.
        cmplwi cr0, r6, 33920
        bne cr0, LBB1_1

//===---------------------------------------------------------------------===//

This:
        #include <algorithm>
        inline std::pair<unsigned, bool> full_add(unsigned a, unsigned b)
        { return std::make_pair(a + b, a + b < a); }
        bool no_overflow(unsigned a, unsigned b)
        { return !full_add(a, b).second; }

Should compile to:

__Z11no_overflowjj:
        add r4,r3,r4
        subfc r3,r3,r4
        li r3,0
        adde r3,r3,r3
        blr

(or better) not:

__Z11no_overflowjj:
        add r2, r4, r3
        cmplw cr7, r2, r3
        mfcr r2
        rlwinm r2, r2, 29, 31, 31
        xori r3, r2, 1
        blr 

//===---------------------------------------------------------------------===//

We compile some FP comparisons into an mfcr with two rlwinms and an or.  For
example:
#include <math.h>
int test(double x, double y) { return islessequal(x, y);}
int test2(double x, double y) {  return islessgreater(x, y);}
int test3(double x, double y) {  return !islessequal(x, y);}

Compiles into (all three are similar, but the bits differ):

_test:
	fcmpu cr7, f1, f2
	mfcr r2
	rlwinm r3, r2, 29, 31, 31
	rlwinm r2, r2, 31, 31, 31
	or r3, r2, r3
	blr 

GCC compiles this into:

 _test:
	fcmpu cr7,f1,f2
	cror 30,28,30
	mfcr r3
	rlwinm r3,r3,31,1
	blr
        
which is more efficient and can use mfocr.  See PR642 for some more context.

//===---------------------------------------------------------------------===//

void foo(float *data, float d) {
   long i;
   for (i = 0; i < 8000; i++)
      data[i] = d;
}
void foo2(float *data, float d) {
   long i;
   data--;
   for (i = 0; i < 8000; i++) {
      data[1] = d;
      data++;
   }
}

These compile to:

_foo:
	li r2, 0
LBB1_1:	; bb
	addi r4, r2, 4
	stfsx f1, r3, r2
	cmplwi cr0, r4, 32000
	mr r2, r4
	bne cr0, LBB1_1	; bb
	blr 
_foo2:
	li r2, 0
LBB2_1:	; bb
	addi r4, r2, 4
	stfsx f1, r3, r2
	cmplwi cr0, r4, 32000
	mr r2, r4
	bne cr0, LBB2_1	; bb
	blr 

The 'mr' could be eliminated to folding the add into the cmp better.

//===---------------------------------------------------------------------===//
Codegen for the following (low-probability) case deteriorated considerably 
when the correctness fixes for unordered comparisons went in (PR 642, 58871).
It should be possible to recover the code quality described in the comments.

; RUN: llvm-as < %s | llc -march=ppc32  | grep or | count 3
; This should produce one 'or' or 'cror' instruction per function.

; RUN: llvm-as < %s | llc -march=ppc32  | grep mfcr | count 3
; PR2964

define i32 @test(double %x, double %y) nounwind  {
entry:
	%tmp3 = fcmp ole double %x, %y		; <i1> [#uses=1]
	%tmp345 = zext i1 %tmp3 to i32		; <i32> [#uses=1]
	ret i32 %tmp345
}

define i32 @test2(double %x, double %y) nounwind  {
entry:
	%tmp3 = fcmp one double %x, %y		; <i1> [#uses=1]
	%tmp345 = zext i1 %tmp3 to i32		; <i32> [#uses=1]
	ret i32 %tmp345
}

define i32 @test3(double %x, double %y) nounwind  {
entry:
	%tmp3 = fcmp ugt double %x, %y		; <i1> [#uses=1]
	%tmp34 = zext i1 %tmp3 to i32		; <i32> [#uses=1]
	ret i32 %tmp34
}
//===----------------------------------------------------------------------===//
; RUN: llvm-as < %s | llc -march=ppc32 | not grep fneg

; This could generate FSEL with appropriate flags (FSEL is not IEEE-safe, and 
; should not be generated except with -enable-finite-only-fp-math or the like).
; With the correctness fixes for PR642 (58871) LowerSELECT_CC would need to
; recognize a more elaborate tree than a simple SETxx.

define double @test_FNEG_sel(double %A, double %B, double %C) {
        %D = fsub double -0.000000e+00, %A               ; <double> [#uses=1]
        %Cond = fcmp ugt double %D, -0.000000e+00               ; <i1> [#uses=1]
        %E = select i1 %Cond, double %B, double %C              ; <double> [#uses=1]
        ret double %E
}

//===----------------------------------------------------------------------===//
The save/restore sequence for CR in prolog/epilog is terrible:
- Each CR subreg is saved individually, rather than doing one save as a unit.
- On Darwin, the save is done after the decrement of SP, which means the offset
from SP of the save slot can be too big for a store instruction, which means we
need an additional register (currently hacked in 96015+96020; the solution there
is correct, but poor).
- On SVR4 the same thing can happen, and I don't think saving before the SP
decrement is safe on that target, as there is no red zone.  This is currently
broken AFAIK, although it's not a target I can exercise.
The following demonstrates the problem:
extern void bar(char *p);
void foo() {
  char x[100000];
  bar(x);
  __asm__("" ::: "cr2");
}

//===-------------------------------------------------------------------------===
Naming convention for instruction formats is very haphazard.
We have agreed on a naming scheme as follows:

<INST_form>{_<OP_type><OP_len>}+

Where:
INST_form is the instruction format (X-form, etc.)
OP_type is the operand type - one of OPC (opcode), RD (register destination),
                              RS (register source),
                              RDp (destination register pair),
                              RSp (source register pair), IM (immediate),
                              XO (extended opcode)
OP_len is the length of the operand in bits

VSX register operands would be of length 6 (split across two fields),
condition register fields of length 3.
We would not need denote reserved fields in names of instruction formats.

//===----------------------------------------------------------------------===//

Instruction fusion was introduced in ISA 2.06 and more opportunities added in
ISA 2.07.  LLVM needs to add infrastructure to recognize fusion opportunities
and force instruction pairs to be scheduled together.