Posts tagged ‘intrinsics’

Buy Spiriva Without Prescription, Although it's often considered one of the dustier branches of C++, the ?: ternary operator can sometimes compile to code that actually runs much faster than the equivalent if/else. Some compilers translate it directly to a hardware operation called a conditional move which allows the compiler to select between two values without having to perform any comparison or branch operations. As I'll show below, in some cases, particularly where floating point numbers are involved, this can result in really significant performance gains, no prescription Spiriva online.

The Slow Tree Is Full Of Branches

In opcode parlance, any instruction that causes the CPU to skip from one instruction to another is called a branch. If the jump occurs based on some condition being met, like in an if ( x == y ) { doSomething() ; } block, Spiriva from canadian pharmacy, it's called a conditional branch: in this case, the program branches to either run doSomething() or not depending on the result of a "compare x to y" operation.

For various reasons, a branch instruction can be pretty slow to execute, Buy Spiriva Without Prescription. The important one here is that modern CPUs process their instructions in many steps along a pipeline. Like parts moving along a conveyor belt in a factory, a CPU have as many as eighty program instructions in flight at once, each of them being processed a little bit more at each of the eighty steps along the assembly line until it is finished and the final results written back to memory, comprar en línea Spiriva, comprar Spiriva baratos.

When a conditional branch instruction executes, the CPU can't know which instructions are supposed to come after the branch on the assembly line. Usually instructions are executed in sequence, so that opcode #1000 is followed by #1001 and that by #1002 and so on, Spiriva over the counter, but if #1002 turns out to be a branch to instruction #2000, then any work the processor might have done on instructions #1003-#1010 at earlier stages in the pipeline has to be thrown away. Modern CPUs and compilers have gotten quite good at mitigating this effect through branch prediction Buy Spiriva Without Prescription, but in some cases, particularly involving floating-point numbers, branch prediction may be impossible in a way that causes the entire assembly line to be cleared out and restarted.

To understand this, first consider this pseudoassembly for how we could compile x = (a >= 0 . b : c) using a compare followed by a branch instruction:

// assume four registers named ra, rb, buy cheap Spiriva no rx, rc, rx
// where rx is the output
// and r0 contains zero
COMPARE ra, r0 // sets "ge" condition bit to 1 if ra >= 0
JUMPGE cbranch // executes a GOTO cbranch: if the "ge" bit is 1
MOVE rx, rb    // sets rx = rb
JUMP finish
MOVE rx, Purchase Spiriva online, rc    // sets rx = rc

There are a couple of ways that this can slow down the instruction pipeline. Firstly, it always executes at least one branch operation, which is expensive: on the PowerPC such a branch can stall execution for between five and twenty cycles depending on whether it is predicted correctly. Also, the conditional jump occurs immediately after the COMPARE operation, Spiriva treatment, which can lead to another stall if the result of the COMPARE isn't ready within a single cycle.

But with floating-point compares the situation can be much worse because float pipelines are often much longer than the integer/branch pipeline, Buy Spiriva Without Prescription. This means that the result of the COMPARE may not be available to the branch unit for many cycles after it dispatches. When the CPU tries to branch on a result that isn't available yet, it has no choice but to flush the entire pipeline, Online buying Spiriva, wait for the compare to finish and start over. For a modern 40-cycle long pipeline this can be quite costly indeed. For example, consider this simplified pipeline of a hypothetical machine. Buy Spiriva Without Prescription, The fetch stage takes six cycles, then instructions are dispatched after a three cycle delay to either an integer, branch, or float pipeline.

[caption id="attachment_65" align="aligncenter" width="600" caption="a float-compare enters the fetch stage, immediately followed by a branch-on-greater-or-equal"]a float-compare enters the fetch stage, <b>where to buy Spiriva</b>, immediately followed by a branch-on-greatereq[/caption]

The fcmp instruction begins to execute, but its results won't be ready until it leaves the eight-stage float pipeline. So, the branch instruction immediately following it can't execute yet. Spiriva used for, [caption id="attachment_66" align="aligncenter" width="600" caption="The fcmp begins to execute, but the branch pipeline can't evaluate until the results are ready."]The fcmp begins to execute, but the branch pipeline can't evaluate until the results are ready.[/caption]

It (and all the instructions behind it) gets flushed from the pipeline and has to start over from the beginning.

[caption id="attachment_67" align="aligncenter" width="600" caption="The fcmp continues to execute, while everything behind it in the pipeline is flushed altogether."]The fcmp continues to execute, while everything behind it in the pipeline is flushed altogether.[/caption]

Once the fcmp is done, online buying Spiriva hcl, the branch is allowed to enter the pipe again,

[caption id="attachment_68" align="aligncenter" width="600" caption="Branch instruction starts over while fcmp executes."]Branch instruction reenters pipeline[/caption]

and then finally executes some time later. Even though the branch immediately follows the fcmp in the program, it doesn't actually get executed until over twenty cycles later, Buy Spiriva Without Prescription.

[caption id="attachment_64" align="aligncenter" width="600" caption="Branch instruction finally executes after fcmp completes."]Branch instruction finally begins to execute[/caption]

To solve all of these issues and others, hardware designers have invented instructions that can perform all this work in a single branchless operation. Spiriva gel, ointment, cream, pill, spray, continuous-release, extended-release, Unfortunately, compilers aren't always smart enough to use them, so sometimes you need to do a little work yourself.

The conditional move

Because branches can be slow, many architectures implement a means of selecting between two different values based on a third without having to actually execute a comparison and jump operation. This is usually called a "conditional move" or "branchless select" and expresses the operation: if a ≥ 0 then b else c; in C++ that is

// int a, buy Spiriva without prescription, b, c;
int x = a >= 0 . b : c ;

Buy Spiriva Without Prescription, or, more LISPishly,

( if (>= a 0) b c )

There are numerous reasons why this is useful but from my point of view the best is improving performance by eliminating pipeline bubbles. Unlike an if/else implemented as a branch op, a conditional move doesn't change the flow of the program or cause it to jump from one instruction or another; it simply assigns either value a or b to the contents of register x in a single instruction. Real brand Spiriva online, Thus, it can never cause the pipeline to clear or invalidate any of the instructions that come after it.

The floating-point conditional move operator on the PPC is called fsel, which works like:

fsel f0, f1, f2, order Spiriva no prescription, f3 // f0 = ( f1 >= 0 . f2 : f3 )

The most recent version of the compiler I use is pretty good at compiling this automatically for cases like this:

return a >= 0 . b : c; fsel fr1,fr1,fr2,fr3

and it even does the right thing with this:

// float a, b, c, d, e, f;
return ( a >= 0, Buy Spiriva Without Prescription. b + 1 : c + 2 ) +
( d >= 0 . e + 1 : f + 2 ) ;

; fr1 = a, Where can i buy Spiriva online, fr2 = b, fr3 = c,
; fr4 = d, fr5 = e, fr6 = f
; fr0 = 1.0, fr13 = 2.0f
fadds fr12, buy Spiriva online no prescription,fr2,fr0 ; fr12 = a + 1
fadds fr11,fr3,fr13 ; fr11 = c + 2
fadds fr10, Get Spiriva, fr5,fr0 ; fr10 = e + 1
fadds fr9,fr6,fr13 ; fr9 = f + 2
fsel fr8,fr1,fr12, Spiriva schedule,fr11 ; fr8 = a >= 0 . fr12 : fr11
fsel fr7,fr4,fr10, Effects of Spiriva, fr9 ; fr7 = d >= 0 . fr10 : fr9
fadds fr1,fr8,fr7 ; return = fr8 + fr7

but it has trouble with more complicated scenarios like this:

// float a, b, c, kjøpe Spiriva på nett, köpa Spiriva online, d;

return a >= b . c : d;

 Buy Spiriva Without Prescription, ; fr1 = a, fr2 = b, fr3 = c, fr4 = d
fcmpu cr6,fr1,fr2 ; compare fr1 and fr2
blt cr6,$LN3 ; if compare result was
; "less than", GOTO $LN3
fmr fr1,fr3 ; move fr3 to fr1
blr ; return
fmr fr1,fr4 ; move fr4 to fr1
blr ; return

and if you use an if/else block instead of the ternary operator, all bets are off.

So, for these more complex cases, the compiler exposes as an intrinsic with a prototype something like:

float fsel( float a, Purchase Spiriva for sale, float x, float y );
// equivalent to { return a >= 0 . x : y ; }

A compiler intrinsic looks like an ordinary C++ function but compiles directly to the native hardware instruction, providing you with direct access to the opcode without having to actually write assembly. The caveat is that the hardware fcmp can only perform a ≥ 0 comparison (on the PPC anyway), so for complex conditionals like

if ( a / 2 < b + 3 ) { return c; } else { return d; }

you need to do a little algebra to transform the inequality a / 2 < b + 3 into a - 2b - 6 < 0 and then, herbal Spiriva, because x < 0 ≡ ¬(x . 0), flip the order of the operands to get return _fsel( a - 2*b - 6, d, Spiriva without a prescription, c );. Once you've got everything fed into the intrinsic, the compiler can do a good job of scheduling your other instructions, Buy Spiriva Without Prescription.

Life beyond if

The advantage of conditional moves comes when you use them to eliminate branching from a complex mathematical operation altogether. The most obvious cases are something like the good old min( float a, float b ) { return a <= b . a : b } which becomes return _fsel( b - a, a, buy Spiriva no prescription, b ); which means you get through something wacky like x += min(a,b) * max(c,d) without any branches at all.

Because math is costly, it may seem like a good idea to use an if statement to prevent unnecessary calculations from being performed, Taking Spiriva, but this can be the wrong thing to do. Sometimes using a floating-point branch to early-out of some calculations may actually hurt performance. Buy Spiriva Without Prescription, In some cases, the cost of the branch may be much greater than the cost of the calculation itself, and so if you're using if/else to choose between performing one of two different calculations, it may be better to do both calculations and use fsel to choose between them afterwards.

Often the compiler can interleave the calculations so the cost of both is the same as doing only one, and you avoid the pipeline clear caused by the fcmp. For example, this code:

float out[N], online Spiriva without a prescription, inA[N], inB[N], cond[N];
for (int i = 0 ; i < N ; ++i )
if ( cond[i] >= 0 )
{ out[i] = cond[i] + inA[i]; }
{ out[i] = cond[i] + inB[i]; }

can be turned into:
for (int i = 0 ; i < N ; ++i )
out[i] = fsel( cond[i], cond[i] + inA[i], Spiriva coupon, cond[i] + inB[i] );

In the top version, we choose to do one of two additions based on the sign of cond[i]. In the bottom version, we perform two additions and throw away one result, but even so it is much faster. When I tested 200, Spiriva long term,000,000 iterations of the above code, the if/else version took 5.243 seconds compared with 0.724 seconds for the fsel version: a 7x speedup for not avoiding an addition.

Another example is if you have a large quantity of such assignments to do one after another, like
struct CFoo { float x, y, z, w; }
// CFoo out, A, B
// float cond[4]; (some number that acts as a selector)
out.x += fsel( cond[0], A.x, B.x );
out.y += fsel( cond[1], A.y, B.y );
out.z += fsel( cond[2], A.z, B.z );
out.w += fsel( cond[3], A.w, B.w );

In this case, because all of the fsel operations are independent (the result of one line does not depend on the result of another), they can all be scheduled to occur immediately after one another for a throughput of one per cycle, Buy Spiriva Without Prescription. Had if/else been used instead (eg if ( cond[0] >= 0 ) out.x += A.x; else out.x += B.x;), Spiriva online cod, then each branch would have depended on the result of the preceding comparison, meaning that we would need to pay the full 60-cycle fcmp/branch penalty for each line before starting the next one.

By now you're probably looking at the example above and thinking, "for four floats packed together like that, I could use a SIMD instruction to compare and assign them all at once," and if so you're absolutely right, buy Spiriva without a prescription. Both VMX (on the PowerPC) and SSE (on the x86) also have conditional move instructions that work very similarly to the scalar float operations I've described above. Consult your documentation for the exact semantics, but in general they work by performing a comparison operation to create a mask which is then fed into a subsequent "select" operation. Buy Spiriva Without Prescription, The general principle is that it can be better to perform both arms of a calculation and then select between them afterwards than to use an if/else to perform only one arm of the calculation. This is even more true for SIMD units since the pipelines are often deeper. Buy generic Spiriva,

Integer Conditional Move

All the discussion above has focused on floating-point conditional move operations. The x86 platform offers an analogous integer conditional move, called CMOV, but some PowerPC implementations lack this native opcode. Instead, you can manufacture one yourself by creating a mask and then using a bitwise-and to select between two values, Spiriva from mexico.

The key is to remember that for any signed int a < 0, the leftmost (most significant) bit of a will be 1, and that the C++ arithmetic-shift operator >> always preserves the sign of the word you are shifting, Buy Spiriva Without Prescription. So, int mask = a >> 31; means the same as int mask = (a < 0 . -1 : 0).

Once you have your mask, Spiriva from canada, you can combine it with a bitwise-and and an add to make your conditional move. Given that x + ( y - x ) = y, you can generate your integer select function like so:

// if a >= 0, return x, else y
int isel( int a, int x, Spiriva cost, int y )
int mask = a >> 31; // arithmetic shift right, splat out the sign bit
// mask is 0xFFFFFFFF if (a < 0) and 0x00 otherwise.
return x + ((y - x) & mask);
Buy Spiriva Without Prescription, The assembly for this works out to about four instructions. The performance gain usually isn't as great as with fsel, because the integer pipeline tends to be much shorter and so there's no pipeline clear on an integer compared followed by a branch; however this construction does give the compiler more latitude in scheduling instructions, and lets you avoid the innate prediction penalty that always occurs with any branch.

In addition to this most PowerPCs have a "count leading zeroes" instruction that lets a smart compiler do something really cool with return a + ( (b - a) & ((Q == W) . 0 : -1) );. Try it out in your disassembler and see.

Further Reading

Mike Acton writes extensively about branch elimination at his CellPerformance blog. In addition to fsel specifically, he describes many other techniques of branchless programming.

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