On Wed, 28 Mar 2012 12:20:51 -0500, Tim Wescott wrote:> On Wed, 28 Mar 2012 09:17:14 +0200, David Brown wrote: > >> On 27/03/2012 19:02, David T. Ashley wrote: >>> On Tue, 27 Mar 2012 18:52:09 +0300, upsidedown@downunder.com wrote: >>> >>>> On Tue, 27 Mar 2012 11:28:18 -0400, David T. Ashley >>>> <dashley@gmail.com> wrote: >>>> >>>> >>>>> Without FPU support, assuming that the processor has basic integer >>>>> multiplication instructions, integer operations are ALWAYS faster >>>>> than floating-point operations. Usually _far_ faster. And always >>>>> more precise. >>>> >>>> Floating point instructions MUL/DIV are trivial, just multiply/divide >>>> the mantissa and add/sub the exponent. >>>> >>>> With FP add/sub you have to denormalize one operand and then >>>> normalize the result, which can be quite time consuming, without >>>> sufficient HW support. >>>> >>>> This can be really time consuming, if the HW is designed by an idiot. >>> >>> Your observations are valid. But I have yet to see a practical >>> example of something that can be done faster and with equal accuracy >>> in floating point vs. using integer operations. >>> >>> >> It depends on the chip, the type of floating point hardware it has, the >> operations you need, the compiler, and the code quality. For a lot of >> heavy calculations done with integer arithmetic, you need a number of >> "extra" instructions as well as the basic add, subtract, multiply and >> divides. You might need shifts for scaling, mask operations, extra >> code to get the signs right, etc. And the paths for these are likely >> to be highly serialised, with each depending directly on the results of >> the previous operation, which slows down pipelining. With hardware >> floating point, you have a much simpler instruction stream, which can >> result in faster throughput even if the actual latency for the >> calculations is the same. >> >> This effect increases with the size and complexity of the processor. >> Obviously it is dependent on the processor having floating point >> hardware for the precision needed (single or double), but once you have >> any sort of hardware floating point you should re-check all your >> assumptions about speed differences. You could be wrong in either >> direction. > > The key point is "it is dependent on the processor having floating point > hardware for the precision needed". And, I might add, on other things > -- > see Walter Banks's comments in another sub-thread about 32-bit floating > point vs. 32-bit integer math. > > In my experience with signal processing and control loops, having a > library that implements fixed-point, fractional arithmetic with > saturation on addition and shift-up is often faster that floating point > _or_ "pure" integer math, and sidesteps a number of problems with both. > It's at the cost of a learning curve with anyone using the package, but > it works well. > > On all the processors I've tried it except for x86 processors, there's > been a 3-20x speedup once I've hand-written the assembly code to do the > computation (and that's without understanding or trying to accommodate > any pipelines that may exist).Weren't you the one that said that your (tuned) ARM C code was generally only a factor of 1.2 worse than the best hand-tweaked assembly code? Maybe not, but I've seen it said in these parts. Certainly, my experience is that that is quite good rule of thumb, and it is very difficult to get more than a factor of two between assembler and C unless the platform in question has a very poor C compiler or the assembly code is actually implementing a different algorithm (which is sometimes possible, but much rarer in these days of well-supplied intrinsic function libraries.)> But on the x86 -- which is the _only_ processor that I've tried it that > had floating point -- 32-bit fractional arithmetic is slower than 64-bit > floating point.One thing that gives float a particualr edge on the x86(32) (but which can also apply to other processors) is that using floating point means that you don't have to use the precious integer register set for data: it can be used for pointers, counters and other control periphera, leaving the working "data state" in the FPU registers. Modern SIMD units can do integer operations as well as floating point, so the "extra state" argument might seem weaker, but I've never seen a compiler use SIMD registers for integer calculations (unless forced to with intrinsic functions).> So, yes -- whether integer (or fixed point) arithmetic is going to be > faster than floating point depends _a lot_ on the processor. So instead > of automatically deciding to do everything "the hard way" and feeling > clever and virtuous thereby, you should _benchmark_ the performance of a > code sample with floating point vs. whatever fixed-point poison you > choose.Fast isn't always the only consideration, though. Floating point is *always* going to be more power-hungry than fixed point, simply because it is doing a bunch of extra work at run-time that fixed-point forces you to hoist to compile-time. The advice to benchmark is excellent, of course. Particularly because the results won't necessarily be what you expect. Cheers, -- Andrew
Floating point vs fixed arithmetics (signed 64-bit)
Started by ●March 26, 2012
Reply by ●March 28, 20122012-03-28
Reply by ●March 28, 20122012-03-28
On Wed, 28 Mar 2012 22:44:32 +0000, Andrew Reilly wrote:> On Wed, 28 Mar 2012 12:20:51 -0500, Tim Wescott wrote: > >> On Wed, 28 Mar 2012 09:17:14 +0200, David Brown wrote: >> >>> On 27/03/2012 19:02, David T. Ashley wrote: >>>> On Tue, 27 Mar 2012 18:52:09 +0300, upsidedown@downunder.com wrote: >>>> >>>>> On Tue, 27 Mar 2012 11:28:18 -0400, David T. Ashley >>>>> <dashley@gmail.com> wrote: >>>>> >>>>> >>>>>> Without FPU support, assuming that the processor has basic integer >>>>>> multiplication instructions, integer operations are ALWAYS faster >>>>>> than floating-point operations. Usually _far_ faster. And always >>>>>> more precise. >>>>> >>>>> Floating point instructions MUL/DIV are trivial, just >>>>> multiply/divide the mantissa and add/sub the exponent. >>>>> >>>>> With FP add/sub you have to denormalize one operand and then >>>>> normalize the result, which can be quite time consuming, without >>>>> sufficient HW support. >>>>> >>>>> This can be really time consuming, if the HW is designed by an >>>>> idiot. >>>> >>>> Your observations are valid. But I have yet to see a practical >>>> example of something that can be done faster and with equal accuracy >>>> in floating point vs. using integer operations. >>>> >>>> >>> It depends on the chip, the type of floating point hardware it has, >>> the operations you need, the compiler, and the code quality. For a >>> lot of heavy calculations done with integer arithmetic, you need a >>> number of "extra" instructions as well as the basic add, subtract, >>> multiply and divides. You might need shifts for scaling, mask >>> operations, extra code to get the signs right, etc. And the paths for >>> these are likely to be highly serialised, with each depending directly >>> on the results of the previous operation, which slows down pipelining. >>> With hardware floating point, you have a much simpler instruction >>> stream, which can result in faster throughput even if the actual >>> latency for the calculations is the same. >>> >>> This effect increases with the size and complexity of the processor. >>> Obviously it is dependent on the processor having floating point >>> hardware for the precision needed (single or double), but once you >>> have any sort of hardware floating point you should re-check all your >>> assumptions about speed differences. You could be wrong in either >>> direction. >> >> The key point is "it is dependent on the processor having floating >> point hardware for the precision needed". And, I might add, on other >> things -- >> see Walter Banks's comments in another sub-thread about 32-bit floating >> point vs. 32-bit integer math. >> >> In my experience with signal processing and control loops, having a >> library that implements fixed-point, fractional arithmetic with >> saturation on addition and shift-up is often faster that floating point >> _or_ "pure" integer math, and sidesteps a number of problems with both. >> It's at the cost of a learning curve with anyone using the package, but >> it works well. >> >> On all the processors I've tried it except for x86 processors, there's >> been a 3-20x speedup once I've hand-written the assembly code to do the >> computation (and that's without understanding or trying to accommodate >> any pipelines that may exist). > > Weren't you the one that said that your (tuned) ARM C code was generally > only a factor of 1.2 worse than the best hand-tweaked assembly code? > Maybe not, but I've seen it said in these parts. Certainly, my > experience is that that is quite good rule of thumb, and it is very > difficult to get more than a factor of two between assembler and C > unless the platform in question has a very poor C compiler or the > assembly code is actually implementing a different algorithm (which is > sometimes possible, but much rarer in these days of well-supplied > intrinsic function libraries.)When the compiler can figure out what I mean, yes, it is usually at least almost as good as I can do, and sometimes better (I don't carry around all the instruction reordering rules in my head: the compiler does). With fixed-point arithmetic stuff, though, the compiler never seems to "get it".>> But on the x86 -- which is the _only_ processor that I've tried it that >> had floating point -- 32-bit fractional arithmetic is slower than >> 64-bit floating point. > > One thing that gives float a particualr edge on the x86(32) (but which > can also apply to other processors) is that using floating point means > that you don't have to use the precious integer register set for data: > it can be used for pointers, counters and other control periphera, > leaving the working "data state" in the FPU registers. Modern SIMD > units can do integer operations as well as floating point, so the "extra > state" argument might seem weaker, but I've never seen a compiler use > SIMD registers for integer calculations (unless forced to with intrinsic > functions).So, the next time I try this on x86 I should use the SIMD registers. Actually, if you know you're going to be doing things like vector dot products, then you could probably get some significant speed-up by doing a spot of assembly here and there. I haven't had occasion to try this on an x86, though.>> So, yes -- whether integer (or fixed point) arithmetic is going to be >> faster than floating point depends _a lot_ on the processor. So >> instead of automatically deciding to do everything "the hard way" and >> feeling clever and virtuous thereby, you should _benchmark_ the >> performance of a code sample with floating point vs. whatever >> fixed-point poison you choose. > > Fast isn't always the only consideration, though. Floating point is > *always* going to be more power-hungry than fixed point, simply because > it is doing a bunch of extra work at run-time that fixed-point forces > you to hoist to compile-time.It'll be power hungry twice if you select a chip that has floating point hardware. I never seem to have the budget -- either dollars or watts -- to use such processors.> The advice to benchmark is excellent, of course. Particularly because > the results won't necessarily be what you expect.Yes. Even when I expect anti-intuitive results, I can still be astonished by benchmarks. -- My liberal friends think I'm a conservative kook. My conservative friends think I'm a liberal kook. Why am I not happy that they have found common ground? Tim Wescott, Communications, Control, Circuits & Software http://www.wescottdesign.com
Reply by ●March 29, 20122012-03-29
On 28 Mar 2012 22:44:32 GMT, Andrew Reilly <areilly---@bigpond.net.au> wrote:>Weren't you the one that said that your (tuned) ARM C code was generally >only a factor of 1.2 worse than the best hand-tweaked assembly code? >Maybe not, but I've seen it said in these parts. Certainly, my >experience is that that is quite good rule of thumb, and it is very >difficult to get more than a factor of two between assembler and C unless >the platform in question has a very poor C compiler or the assembly code >is actually implementing a different algorithm (which is sometimes >possible, but much rarer in these days of well-supplied intrinsic >function libraries.)The main problem trying to write _low_level_ math routines in C is that you do not have access to the carry bit or use any rotate instruction. The C-compiler would have to be very clever to convert a sequence of C-statement into a single rotate instruction or shifting multiple bits into two registers.
Reply by ●March 29, 20122012-03-29
On 28/03/2012 19:20, Tim Wescott wrote:> On Wed, 28 Mar 2012 09:17:14 +0200, David Brown wrote: > >> On 27/03/2012 19:02, David T. Ashley wrote: >>> On Tue, 27 Mar 2012 18:52:09 +0300, upsidedown@downunder.com wrote: >>> >>>> On Tue, 27 Mar 2012 11:28:18 -0400, David T. Ashley >>>> <dashley@gmail.com> wrote: >>>> >>>> >>>>> Without FPU support, assuming that the processor has basic integer >>>>> multiplication instructions, integer operations are ALWAYS faster >>>>> than floating-point operations. Usually _far_ faster. And always >>>>> more precise. >>>> >>>> Floating point instructions MUL/DIV are trivial, just multiply/divide >>>> the mantissa and add/sub the exponent. >>>> >>>> With FP add/sub you have to denormalize one operand and then normalize >>>> the result, which can be quite time consuming, without sufficient HW >>>> support. >>>> >>>> This can be really time consuming, if the HW is designed by an idiot. >>> >>> Your observations are valid. But I have yet to see a practical example >>> of something that can be done faster and with equal accuracy in >>> floating point vs. using integer operations. >>> >>> >> It depends on the chip, the type of floating point hardware it has, the >> operations you need, the compiler, and the code quality. For a lot of >> heavy calculations done with integer arithmetic, you need a number of >> "extra" instructions as well as the basic add, subtract, multiply and >> divides. You might need shifts for scaling, mask operations, extra code >> to get the signs right, etc. And the paths for these are likely to be >> highly serialised, with each depending directly on the results of the >> previous operation, which slows down pipelining. With hardware floating >> point, you have a much simpler instruction stream, which can result in >> faster throughput even if the actual latency for the calculations is the >> same. >> >> This effect increases with the size and complexity of the processor. >> Obviously it is dependent on the processor having floating point >> hardware for the precision needed (single or double), but once you have >> any sort of hardware floating point you should re-check all your >> assumptions about speed differences. You could be wrong in either >> direction. > > The key point is "it is dependent on the processor having floating point > hardware for the precision needed". And, I might add, on other things -- > see Walter Banks's comments in another sub-thread about 32-bit floating > point vs. 32-bit integer math. >Yes (see my reply on that thread).> In my experience with signal processing and control loops, having a > library that implements fixed-point, fractional arithmetic with > saturation on addition and shift-up is often faster that floating point > _or_ "pure" integer math, and sidesteps a number of problems with both. > It's at the cost of a learning curve with anyone using the package, but > it works well. >When you add things like saturation into the mix, it gets more complicated. That is going to be much less overhead for integer arithmetic than for floating point (unless you have a processor that has hardware support for floating point saturated instructions). But yes, a well-written library is normally going to be better than poorly written "direct" code, as well as saving you from having to get all the little details correct (you shouldn't worry about your code being fast until you are sure it is correct!). A lot of ready-made libraries are not well written, however, or have other disadvantages. I've seen libraries that were compiled without optimisation - and were thus far slower than necessary. And many libraries are full of hand-made assembly that is out of date, yet remains there for historic reasons even when it now does more harm than good. Like everything in this field, there are no simple answers.> On all the processors I've tried it except for x86 processors, there's > been a 3-20x speedup once I've hand-written the assembly code to do the > computation (and that's without understanding or trying to accommodate > any pipelines that may exist).While x86 typically means "desktop" rather than "embedded", there are steadily more powerful cpu's making their way into the embedded space. I've been using some PowerPC cores recently, and see there's a large number of factors that affect the real-world speed of the code. Often floating point (when supported by hardware) will be faster than scaled integer code, and C code will often be much faster than hand-written assembly (because it is hard for the assembly programmer to track pipelines or to make full use of the core's weirder instructions).> > But on the x86 -- which is the _only_ processor that I've tried it that > had floating point -- 32-bit fractional arithmetic is slower than 64-bit > floating point. > > So, yes -- whether integer (or fixed point) arithmetic is going to be > faster than floating point depends _a lot_ on the processor. So instead > of automatically deciding to do everything "the hard way" and feeling > clever and virtuous thereby, you should _benchmark_ the performance of a > code sample with floating point vs. whatever fixed-point poison you > choose.Absolutely.> > Then, even if fixed point is significantly faster, you should look at the > time consumed by floating point and ask if it's really necessary to save > that time: even cheapo 8-bit processors run pretty fast these days, and > can implement fairly complex control laws at 10 or even 100Hz using > double-precision floating point arithmetic. If floating point will do, > fixed point is a waste of effort. And if floating point is _faster_, > fixed point is just plain stupid. >It's always tempting to worry too much about speed, and work hard to get the fastest solution. But if you've got code that works correctly, is high quality (clear, reliable, maintainable, etc.), and runs fast enough for the job - then you are finished. It doesn't matter if you could run faster by switching to floating point or fixed point - good enough is good enough.> So, benchmark, think, make an informed decision, and then that virtuous > glow that surrounds you after you make your decision will be earned. >Yes.
Reply by ●March 29, 20122012-03-29
On 29/03/2012 01:35, Tim Wescott wrote:> On Wed, 28 Mar 2012 22:44:32 +0000, Andrew Reilly wrote: > >> On Wed, 28 Mar 2012 12:20:51 -0500, Tim Wescott wrote: >> >>> On Wed, 28 Mar 2012 09:17:14 +0200, David Brown wrote: >>> >>>> On 27/03/2012 19:02, David T. Ashley wrote: >>>>> On Tue, 27 Mar 2012 18:52:09 +0300, upsidedown@downunder.com wrote: >>>>> >>>>>> On Tue, 27 Mar 2012 11:28:18 -0400, David T. Ashley >>>>>> <dashley@gmail.com> wrote: >>>>>> >>>>>> >>>>>>> Without FPU support, assuming that the processor has basic integer >>>>>>> multiplication instructions, integer operations are ALWAYS faster >>>>>>> than floating-point operations. Usually _far_ faster. And always >>>>>>> more precise. >>>>>> >>>>>> Floating point instructions MUL/DIV are trivial, just >>>>>> multiply/divide the mantissa and add/sub the exponent. >>>>>> >>>>>> With FP add/sub you have to denormalize one operand and then >>>>>> normalize the result, which can be quite time consuming, without >>>>>> sufficient HW support. >>>>>> >>>>>> This can be really time consuming, if the HW is designed by an >>>>>> idiot. >>>>> >>>>> Your observations are valid. But I have yet to see a practical >>>>> example of something that can be done faster and with equal accuracy >>>>> in floating point vs. using integer operations. >>>>> >>>>> >>>> It depends on the chip, the type of floating point hardware it has, >>>> the operations you need, the compiler, and the code quality. For a >>>> lot of heavy calculations done with integer arithmetic, you need a >>>> number of "extra" instructions as well as the basic add, subtract, >>>> multiply and divides. You might need shifts for scaling, mask >>>> operations, extra code to get the signs right, etc. And the paths for >>>> these are likely to be highly serialised, with each depending directly >>>> on the results of the previous operation, which slows down pipelining. >>>> With hardware floating point, you have a much simpler instruction >>>> stream, which can result in faster throughput even if the actual >>>> latency for the calculations is the same. >>>> >>>> This effect increases with the size and complexity of the processor. >>>> Obviously it is dependent on the processor having floating point >>>> hardware for the precision needed (single or double), but once you >>>> have any sort of hardware floating point you should re-check all your >>>> assumptions about speed differences. You could be wrong in either >>>> direction. >>> >>> The key point is "it is dependent on the processor having floating >>> point hardware for the precision needed". And, I might add, on other >>> things -- >>> see Walter Banks's comments in another sub-thread about 32-bit floating >>> point vs. 32-bit integer math. >>> >>> In my experience with signal processing and control loops, having a >>> library that implements fixed-point, fractional arithmetic with >>> saturation on addition and shift-up is often faster that floating point >>> _or_ "pure" integer math, and sidesteps a number of problems with both. >>> It's at the cost of a learning curve with anyone using the package, but >>> it works well. >>> >>> On all the processors I've tried it except for x86 processors, there's >>> been a 3-20x speedup once I've hand-written the assembly code to do the >>> computation (and that's without understanding or trying to accommodate >>> any pipelines that may exist). >> >> Weren't you the one that said that your (tuned) ARM C code was generally >> only a factor of 1.2 worse than the best hand-tweaked assembly code? >> Maybe not, but I've seen it said in these parts. Certainly, my >> experience is that that is quite good rule of thumb, and it is very >> difficult to get more than a factor of two between assembler and C >> unless the platform in question has a very poor C compiler or the >> assembly code is actually implementing a different algorithm (which is >> sometimes possible, but much rarer in these days of well-supplied >> intrinsic function libraries.) > > When the compiler can figure out what I mean, yes, it is usually at least > almost as good as I can do, and sometimes better (I don't carry around > all the instruction reordering rules in my head: the compiler does). > > With fixed-point arithmetic stuff, though, the compiler never seems to > "get it". > >>> But on the x86 -- which is the _only_ processor that I've tried it that >>> had floating point -- 32-bit fractional arithmetic is slower than >>> 64-bit floating point. >> >> One thing that gives float a particualr edge on the x86(32) (but which >> can also apply to other processors) is that using floating point means >> that you don't have to use the precious integer register set for data: >> it can be used for pointers, counters and other control periphera, >> leaving the working "data state" in the FPU registers. Modern SIMD >> units can do integer operations as well as floating point, so the "extra >> state" argument might seem weaker, but I've never seen a compiler use >> SIMD registers for integer calculations (unless forced to with intrinsic >> functions). > > So, the next time I try this on x86 I should use the SIMD registers. >This is one of the reasons why it is best to use a modern compiler for big processors - it is hard to keep up with them when working by hand. On small devices, you can learn all you need to know about the cpu - but for modern x86 devices, it is just too much effort. And if you are trying to generate the fastest possible code, it varies significantly between different x86 models - your fine-tuned hand-coded assembly may run optimally on the cpu you have on your machine today, but poorly on another machine.> Actually, if you know you're going to be doing things like vector dot > products, then you could probably get some significant speed-up by doing > a spot of assembly here and there. I haven't had occasion to try this on > an x86, though.For particularly complex vector work, hand-coding the SIMD instructions is essential for optimal speed. But compilers are getting surprisingly good at generating some of this stuff semi-automatically - it is worth trying the compiler's SIMD support before doing it by hand. The other option is libraries - Intel in particular provides optimised libraries for this sort of stuff.> >>> So, yes -- whether integer (or fixed point) arithmetic is going to be >>> faster than floating point depends _a lot_ on the processor. So >>> instead of automatically deciding to do everything "the hard way" and >>> feeling clever and virtuous thereby, you should _benchmark_ the >>> performance of a code sample with floating point vs. whatever >>> fixed-point poison you choose. >> >> Fast isn't always the only consideration, though. Floating point is >> *always* going to be more power-hungry than fixed point, simply because >> it is doing a bunch of extra work at run-time that fixed-point forces >> you to hoist to compile-time. >That is a wildly inaccurate generalisation. For small processors, the power consumption is going to depend on the speed of the calculations - these cores are all-or-nothing in their power usage, so doing the work faster means you can go to sleep sooner. So faster is lower power. For larger processors, there may be dynamic clock enabling of different parts - if the hardware floating point unit is not used, it can be powered-down. Then there is a trade-off - do you spend extra time in the integer units, or do you do the job faster with the power-hungry floating point unit? The answer will vary there too, but typically faster means less energy overall. It is obviously correct that the more work that is done at compile time the better - it is only run-time that takes power (on the target). But I can think of no justification for claiming that fixed-point algorithms will do more at compile-time than floating-point algorithms - I would expect the floating-point code to do far more compile-time optimisation and pre-calculation (since the compiler has a better understanding of the code in question).> It'll be power hungry twice if you select a chip that has floating point > hardware. I never seem to have the budget -- either dollars or watts -- > to use such processors. > >> The advice to benchmark is excellent, of course. Particularly because >> the results won't necessarily be what you expect. > > Yes. Even when I expect anti-intuitive results, I can still be > astonished by benchmarks. >
Reply by ●March 29, 20122012-03-29
On Thu, 29 Mar 2012 07:19:02 +0300, upsidedown wrote:> On 28 Mar 2012 22:44:32 GMT, Andrew Reilly <areilly---@bigpond.net.au> > wrote: > >>Weren't you the one that said that your (tuned) ARM C code was generally >>only a factor of 1.2 worse than the best hand-tweaked assembly code? >>Maybe not, but I've seen it said in these parts. Certainly, my >>experience is that that is quite good rule of thumb, and it is very >>difficult to get more than a factor of two between assembler and C >>unless the platform in question has a very poor C compiler or the >>assembly code is actually implementing a different algorithm (which is >>sometimes possible, but much rarer in these days of well-supplied >>intrinsic function libraries.) > > The main problem trying to write _low_level_ math routines in C is that > you do not have access to the carry bit or use any rotate instruction. > The C-compiler would have to be very clever to convert a sequence of > C-statement into a single rotate instruction or shifting multiple bits > into two registers.It's a funny old world. I've seen several compilers recognise the pair of shifts and an or combination as a rotate, and emit that instruction. I've also replaced carefully asm-"optimised" maths routines (on x86) that used the carry flag with "vanilla" C equivalents, and the overall effect was a fairly dramatic performance improvement. Not sure whether it was a side effect of the assembly code pinning registers that could otherwise have been reassigned, or some subtle consequence of reduced dependency, but the result was clear. Guessing performace on massively superscalar, out-of-order processors like modern x86-64 is very difficult, IMO. Intrinsic functions (to get access to things like clz and similar) also help a lot. Benchmarking is important. Milage will definitely vary with target and toolchain... Cheers, -- Andrew
Reply by ●March 29, 20122012-03-29
upsidedown@downunder.com wrote:> On 28 Mar 2012 22:44:32 GMT, Andrew Reilly <areilly---@bigpond.net.au> > wrote: > > >Weren't you the one that said that your (tuned) ARM C code was generally > >only a factor of 1.2 worse than the best hand-tweaked assembly code? > >Maybe not, but I've seen it said in these parts. Certainly, my > >experience is that that is quite good rule of thumb, and it is very > >difficult to get more than a factor of two between assembler and C unless > >the platform in question has a very poor C compiler or the assembly code > >is actually implementing a different algorithm (which is sometimes > >possible, but much rarer in these days of well-supplied intrinsic > >function libraries.) > > The main problem trying to write _low_level_ math routines in C is > that you do not have access to the carry bit or use any rotate > instruction. The C-compiler would have to be very clever to convert a > sequence of C-statement into a single rotate instruction or shifting > multiple bits into two registers.C compilers have been gaining performance in part because compiler designers are targeting with both a target and a subset of applications in mind. Most compiler developers are benchmarking "real" applications that are tending to direct the compiler to optimize those applications. The result is compilers used in the embedded systems market can often do some very low level optimization very well that would not be available or even considered for compilers used in other applications. For embedded systems specifically most if not all commercial compilers have some mechanism to access the processor condition codes. Most embedded system compilers do well at using the whole processor instruction set. Walter.. -- Walter Banks Byte Craft Limited http://www.bytecraft.com
Reply by ●March 29, 20122012-03-29
Andrew Reilly wrote:> Benchmarking is important. > > Milage will definitely vary with target and toolchain... >Nothing wakes me up faster than strong coffee than last nights benchmark results. Benchmarking code fragments are important, but benchmarking applications can be a real eyeopener. There is nothing more humbling than adding a clever optimization to a compiler and discovering that 75% of the regression applications just got slower and larger as a result. Walter..
Reply by ●March 29, 20122012-03-29
In article <oKCdnSXl7OPQPe7SnZ2dnUVZ_gednZ2d@web-ster.com>, tim@seemywebsite.com says...> > On Wed, 28 Mar 2012 22:44:32 +0000, Andrew Reilly wrote: ><<SNIP>>> > Fast isn't always the only consideration, though. Floating point is > > *always* going to be more power-hungry than fixed point, simply because > > it is doing a bunch of extra work at run-time that fixed-point forces > > you to hoist to compile-time. > > It'll be power hungry twice if you select a chip that has floating point > hardware. I never seem to have the budget -- either dollars or watts -- > to use such processors.Cortex M4 chips,like the STM32F405 have lowered the bars quite a bit for FPU availability. STm32F405 is about $11.5 qty 1 at DigiKey. The STM32F205 Cortex M3 is about the same price. I've got one of the chips, and it's compatible with the F205 board I designed, so I'll be trying it out soon. More RAM, more Flash, faster clock----everything we look forward to in a new generation of chips. (since I'm not using an OS or big USB or ethernet stacks, I'll have LOTS of flash left over for things like lookup tables, etc.) Right now, I'm just happy to read an SD card and send bit-banged data to an FT232H at about 6MB/second. I can even use the same drivers and host I use with the FT245 chips which do the same thing at about 200KB/s. The 4-bit SD interface on the STM chips can do multi-block reads at upwards of 10MB/s. Hard to match that with SPI mode!> > > The advice to benchmark is excellent, of course. Particularly because > > the results won't necessarily be what you expect. > > Yes. Even when I expect anti-intuitive results, I can still be > astonished by benchmarks.I think the FPU availability will greatly simplify coding of things like Extended Kalman Filters and digital signal processing apps. You can write and test code on a PC while specifying 32-bit floats and port pretty easily to the MPU system. Mark Borgerson
Reply by ●March 29, 20122012-03-29
On 29/03/2012 16:28, Walter Banks wrote:> > > upsidedown@downunder.com wrote: > >> On 28 Mar 2012 22:44:32 GMT, Andrew Reilly<areilly---@bigpond.net.au> >> wrote: >> >>> Weren't you the one that said that your (tuned) ARM C code was generally >>> only a factor of 1.2 worse than the best hand-tweaked assembly code? >>> Maybe not, but I've seen it said in these parts. Certainly, my >>> experience is that that is quite good rule of thumb, and it is very >>> difficult to get more than a factor of two between assembler and C unless >>> the platform in question has a very poor C compiler or the assembly code >>> is actually implementing a different algorithm (which is sometimes >>> possible, but much rarer in these days of well-supplied intrinsic >>> function libraries.) >> >> The main problem trying to write _low_level_ math routines in C is >> that you do not have access to the carry bit or use any rotate >> instruction. The C-compiler would have to be very clever to convert a >> sequence of C-statement into a single rotate instruction or shifting >> multiple bits into two registers. > > C compilers have been gaining performance in part because compiler > designers are targeting with both a target and a subset of applications > in mind. > > Most compiler developers are benchmarking "real" applications that > are tending to direct the compiler to optimize those applications. The > result is compilers used in the embedded systems market can often > do some very low level optimization very well that would not be > available or even considered for compilers used in other applications. > > For embedded systems specifically most if not all commercial compilers > have some mechanism to access the processor condition codes. Most > embedded system compilers do well at using the whole processor > instruction set. >I think it is a bit of an exaggeration to say this applies to "most" commercial compilers - and it is certainly not all. I think it applies to a /few/ commercial compilers targeted at particularly small processors. For larger processors, you don't get access to the condition codes from C - it would mess up the compiler code generation patterns too much. For big processors, a compiler needs to track condition codes over series of instructions - if the programmer can fiddle with condition codes in the middle of an instruction stream, the compiler would lose track. Also for larger processors, there are often many instruction codes (or addressing modes) that are never generated by the compiler. Some instructions are just too weird to map properly to C code, others cannot be expressed in C at all. As a programmer, you access these using library calls, inline assembly, or "intrinsic" functions (which are simply ready-made inline assembly functions). You write compilers targeted for small and limited processors, and have very fine-tuned optimisations and extensions to let developers squeeze maximum performance from such devices. But don't judge "most if not all" commercial compilers by your own standards - most do not measure up in those areas.
