Floating point vs integer calculations on modern hardware

Question

I am doing some performance critical work in C    and we are currently using integer calculations for problems that are inherently floating point because  its faster   This causes a whole lot of annoying problems and adds a lot of annoying code   Now  I remember reading about how floating point calculations were so slow approximately circa the 386 days  where I believe  IIRC  that there was an optional co-proccessor  But surely nowadays with exponentially more complex and powerful CPUs it makes no difference in  speed  if doing floating point or integer calculation  Especially since the actual calculation time is tiny compared to something like causing a pipeline stall or fetching something from main memory   I know the correct answer is to benchmark on the target hardware  what would be a good way to test this  I wrote two tiny C   programs and compared their run time with  time  on Linux  but the actual run time is too variable  doesn t help I am running on a virtual server   Short of spending my entire day running hundreds of benchmarks  making graphs etc  is there something I can do to get a reasonable test of the relative speed  Any ideas or thoughts  Am I completely wrong   The programs I used as follows  they are not identical by any means    include  lt iostream gt   include  lt cmath gt   include  lt cstdlib gt   include  lt time h gt   int main  int argc  char   argv         int accum   0       srand  time  NULL           for  unsigned int i   0  i  lt  100000000    i                 accum    rand      365            std  cout  lt  lt  accum  lt  lt  std  endl       return 0      Program 2    include  lt iostream gt   include  lt cmath gt   include  lt cstdlib gt   include  lt time h gt   int main  int argc  char   argv          float accum   0      srand  time  NULL           for  unsigned int i   0  i  lt  100000000    i                 accum     float   rand      365              std  cout  lt  lt  accum  lt  lt  std  endl       return 0      Thanks in advance   Edit  The platform I care about is regular x86 or x86-64 running on desktop Linux and Windows machines   Edit 2 pasted from a comment below   We have an extensive code base currently  Really I have come up against the generalization that we  must not use float since integer calculation is faster   - and I am looking for a way  if this is even true  to disprove this generalized assumption  I realize that it would be impossible to predict the exact outcome for us short of doing all the work and profiling it afterwards   Anyway  thanks for all your excellent answers and help  Feel free to add anything else

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The floating point version will be much slower  if there is no remainder operation  Since all the adds are sequential  the cpu will not be able to parallelise the summation  The latency will be critical  FPU add latency is typically 3 cycles  while integer add is 1 cycle  However  the divider for the remainder operator will probably the critical part  as it is not fully pipelined on modern cpu s  so  assuming the divide remainder instruction will consume the bulk of the time  the difference due to add latency will be small

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There is likely to be a significant difference in real-world speed between fixed-point and floating-point math  but the theoretical best-case throughput of the ALU vs FPU is completely irrelevant   Instead  the number of integer and floating-point registers  real registers  not register names  on your architecture which are not otherwise used by your computation  e g  for loop control   the number of elements of each type which fit in a cache line  optimizations possible considering the different semantics for integer vs  floating point math -- these effects will dominate   The data dependencies of your algorithm play a significant role here  so that no general comparison will predict the performance gap on your problem   For example  integer addition is commutative  so if the compiler sees a loop like you used for a benchmark  assuming the random data was prepared in advance so it wouldn t obscure the results   it can unroll the loop and calculate partial sums with no dependencies  then add them when the loop terminates   But with floating point  the compiler has to do the operations in the same order you requested  you ve got sequence points in there so the compiler has to guarantee the same result  which disallows reordering  so there s a strong dependency of each addition on the result of the previous one   You re likely to fit more integer operands in cache at a time as well   So the fixed-point version might outperform the float version by an order of magnitude even on a machine where the FPU has theoretically higher throughput

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Today  integer operations are usually a little bit faster than floating point operations  So if you can do a calculation with the same operations in integer and floating point  use integer  HOWEVER you are saying  This causes a whole lot of annoying problems and adds a lot of annoying code   That sounds like you need more operations because you use integer arithmetic instead of floating point  In that case  floating point will run faster because   as soon as you need more integer operations  you probably need a lot more  so the slight speed advantage is more than eaten up by the additional operations the floating-point code is simpler  which means it is faster to write the code  which means that if it is speed critical  you can spend more time optimising the code

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For example  lesser numbers are faster    64-bit Intel Xeon X5550   2 67GHz  gcc 4 1 2 -O3  short add sub  1 005460  0  short mul div  3 926543  0  long add sub  0 000000  0  long mul div  7 378581  0  long long add sub  0 000000  0  long long mul div  7 378593  0  float add sub  0 993583  0  float mul div  1 821565  0  double add sub  0 993884  0  double mul div  1 988664  0    32-bit Dual Core AMD Opteron tm  Processor 265   1 81GHz  gcc 3 4 6 -O3  short add sub  0 553863  0  short mul div  12 509163  0  long add sub  0 556912  0  long mul div  12 748019  0  long long add sub  5 298999  0  long long mul div  20 461186  0  float add sub  2 688253  0  float mul div  4 683886  0  double add sub  2 700834  0  double mul div  4 646755  0    As Dan pointed out  even once you normalize for clock frequency  which can be misleading in itself in pipelined designs   results will vary wildly based on CPU architecture  individual ALU FPU performance  as well as actual number of ALUs FPUs available per core in superscalar designs which influences how many independent operations can execute in parallel -- the latter factor is not exercised by the code below as all operations below are sequentially dependent    Poor man s FPU ALU operation benchmark    include  lt stdio h gt   ifdef  WIN32  include  lt sys timeb h gt   else  include  lt sys time h gt   endif  include  lt time h gt   include  lt cstdlib gt   double mygettime void      ifdef  WIN32   struct  timeb tb     ftime  amp tb     return  double tb time    0 001    double tb millitm     else   struct timeval tv    if gettimeofday  amp tv  0   lt  0        perror  oops          return  double tv tv sec    0 000001    double tv tv usec     endif    template lt  typename Type  gt  void my test const char  name      Type v    0       Do not use constants or repeating values       to avoid loop unroll optimizations       All values  gt 0 to avoid division by 0      Perform ten ops iteration to reduce       impact of   i below on measurements   Type v0    Type  rand     256  16   1    Type v1    Type  rand     256  16   1    Type v2    Type  rand     256  16   1    Type v3    Type  rand     256  16   1    Type v4    Type  rand     256  16   1    Type v5    Type  rand     256  16   1    Type v6    Type  rand     256  16   1    Type v7    Type  rand     256  16   1    Type v8    Type  rand     256  16   1    Type v9    Type  rand     256  16   1     double t1   mygettime      for  size t i   0  i  lt  100000000    i        v    v0      v -  v1      v    v2      v -  v3      v    v4      v -  v5      v    v6      v -  v7      v    v8      v -  v9           Pretend we make use of v so compiler doesn t optimize out       the loop completely   printf   s add sub   f   d  n   name  mygettime   - t1   int v amp 1     t1   mygettime      for  size t i   0  i  lt  100000000    i        v    v0      v    v1      v    v2      v    v3      v    v4      v    v5      v    v6      v    v7      v    v8      v    v9           Pretend we make use of v so compiler doesn t optimize out       the loop completely   printf   s mul div   f   d  n   name  mygettime   - t1   int v amp 1      int main       my test lt  short  gt   short      my test lt  long  gt   long      my test lt  long long  gt   long long      my test lt  float  gt   float      my test lt  double  gt   double       return 0

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Addition is much faster than rand  so your program is  especially  useless   You need to identify performance hotspots and incrementally modify your program  It sounds like you have problems with your development environment that will need to be solved first  Is it impossible to run your program on your PC for a small problem set   Generally  attempting FP jobs with integer arithmetic is a recipe for slow

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Two points to consider -  Modern hardware can overlap instructions  execute them in parallel and reorder them to make best use of the hardware  And also  any significant floating point program is likely to have significant integer work too even if it s only calculating indices into arrays  loop counter etc  so even if you have a slow floating point instruction it may well be running on a separate bit of hardware overlapped with some of the integer work  My point being that even if the floating point instructions are slow that integer ones  your overall program may run faster because it can make use of more of the hardware    As always  the only way to be sure is to profile your actual program   Second point is that most CPUs these days have SIMD instructions for floating point that can operate on multiple floating point values all at the same time  For example you can load 4 floats into a single SSE register and the perform 4 multiplications on them all in parallel  If you can rewrite parts of your code to use SSE instructions then it seems likely it will be faster than an integer version  Visual c   provides compiler intrinsic functions to do this  see http   msdn microsoft com en-us library x5c07e2a v VS 80  aspx for some information

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Based of that oh-so-reliable  something I ve heard   back in the old days  integer calculation were about 20 to 50 times faster that floating point  and these days it s less than twice as faster

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I ran a test that just added 1 to the number instead of rand     Results  on an x86-64  were    short      4 260s int        4 020s long long  3 350s float      7 330s double     7 210s

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TIL This varies  a lot   Here are some results using gnu compiler  btw I also checked by compiling on machines  gnu g   5 4 from xenial is a hell of a lot faster than 4 6 3 from linaro on precise   Intel i7 4700MQ xenial  short add  0 822491 short sub  0 832757 short mul  1 007533 short div  3 459642 long add  0 824088 long sub  0 867495 long mul  1 017164 long div  5 662498 long long add  0 873705 long long sub  0 873177 long long mul  1 019648 long long div  5 657374 float add  1 137084 float sub  1 140690 float mul  1 410767 float div  2 093982 double add  1 139156 double sub  1 146221 double mul  1 405541 double div  2 093173   Intel i3 2370M has similar results  short add  1 369983 short sub  1 235122 short mul  1 345993 short div  4 198790 long add  1 224552 long sub  1 223314 long mul  1 346309 long div  7 275912 long long add  1 235526 long long sub  1 223865 long long mul  1 346409 long long div  7 271491 float add  1 507352 float sub  1 506573 float mul  2 006751 float div  2 762262 double add  1 507561 double sub  1 506817 double mul  1 843164 double div  2 877484   Intel R  Celeron R  2955U  Acer C720 Chromebook running xenial   short add  1 999639 short sub  1 919501 short mul  2 292759 short div  7 801453 long add  1 987842 long sub  1 933746 long mul  2 292715 long div  12 797286 long long add  1 920429 long long sub  1 987339 long long mul  2 292952 long long div  12 795385 float add  2 580141 float sub  2 579344 float mul  3 152459 float div  4 716983 double add  2 579279 double sub  2 579290 double mul  3 152649 double div  4 691226   DigitalOcean 1GB Droplet Intel R  Xeon R  CPU E5-2630L v2  running trusty   short add  1 094323 short sub  1 095886 short mul  1 356369 short div  4 256722 long add  1 111328 long sub  1 079420 long mul  1 356105 long div  7 422517 long long add  1 057854 long long sub  1 099414 long long mul  1 368913 long long div  7 424180 float add  1 516550 float sub  1 544005 float mul  1 879592 float div  2 798318 double add  1 534624 double sub  1 533405 double mul  1 866442 double div  2 777649   AMD Opteron tm  Processor 4122  precise   short add  3 396932 short sub  3 530665 short mul  3 524118 short div  15 226630 long add  3 522978 long sub  3 439746 long mul  5 051004 long div  15 125845 long long add  4 008773 long long sub  4 138124 long long mul  5 090263 long long div  14 769520 float add  6 357209 float sub  6 393084 float mul  6 303037 float div  17 541792 double add  6 415921 double sub  6 342832 double mul  6 321899 double div  15 362536   This uses code from http   pastebin com Kx8WGUfg as benchmark-pc c  g   -fpermissive -O3 -o benchmark-pc benchmark-pc c   I ve run multiple passes  but this seems to be the case that general numbers are the same   One notable exception seems to be ALU mul vs FPU mul  Addition and subtraction seem trivially different   Here is the above in chart form  click for full size  lower is faster and preferable      Update to accomodate  Peter Cordes  https   gist github com Lewiscowles1986 90191c59c9aedf3d08bf0b129065cccc  i7 4700MQ Linux Ubuntu Xenial 64-bit  all patches to 2018-03-13 applied       short add  0 773049     short sub  0 789793     short mul  0 960152     short div  3 273668       int add  0 837695       int sub  0 804066       int mul  0 960840       int div  3 281113      long add  0 829946      long sub  0 829168      long mul  0 960717      long div  5 363420 long long add  0 828654 long long sub  0 805897 long long mul  0 964164 long long div  5 359342     float add  1 081649     float sub  1 080351     float mul  1 323401     float div  1 984582    double add  1 081079    double sub  1 082572    double mul  1 323857    double div  1 968488   AMD Opteron tm  Processor 4122  precise  DreamHost shared-hosting       short add  1 235603     short sub  1 235017     short mul  1 280661     short div  5 535520       int add  1 233110       int sub  1 232561       int mul  1 280593       int div  5 350998      long add  1 281022      long sub  1 251045      long mul  1 834241      long div  5 350325 long long add  1 279738 long long sub  1 249189 long long mul  1 841852 long long div  5 351960     float add  2 307852     float sub  2 305122     float mul  2 298346     float div  4 833562    double add  2 305454    double sub  2 307195    double mul  2 302797    double div  5 485736   Intel Xeon E5-2630L v2   2 4GHz  Trusty 64-bit  DigitalOcean VPS       short add  1 040745     short sub  0 998255     short mul  1 240751     short div  3 900671       int add  1 054430       int sub  1 000328       int mul  1 250496       int div  3 904415      long add  0 995786      long sub  1 021743      long mul  1 335557      long div  7 693886 long long add  1 139643 long long sub  1 103039 long long mul  1 409939 long long div  7 652080     float add  1 572640     float sub  1 532714     float mul  1 864489     float div  2 825330    double add  1 535827    double sub  1 535055    double mul  1 881584    double div  2 777245

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Unless you re writing code that will be called millions of times per second  such as  e g   drawing a line to the screen in a graphics application   integer vs  floating-point arithmetic is rarely the bottleneck   The usual first step to the efficiency questions is to profile your code to see where the run-time is really spent  The linux command for this is gprof   Edit   Though I suppose you can always implement the line drawing algorithm using integers and floating-point numbers  call it a large number of times and see if it makes a difference   http   en wikipedia org wiki Bresenham s algorithm

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Alas  I can only give you an  it depends  answer     From my experience  there are many  many variables to performance   especially between integer  amp  floating point math   It varies strongly from processor to processor  even within the same family such as x86  because different processors have different  pipeline  lengths   Also  some operations are generally very simple  such as addition  and have an accelerated route through the processor  and others  such as division  take much  much longer   The other big variable is where the data reside   If you only have a few values to add  then all of the data can reside in cache  where they can be quickly sent to the CPU   A very  very slow floating point operation that already has the data in cache will be many times faster than an integer operation where an integer needs to be copied from system memory   I assume that you are asking this question because you are working on a performance critical application   If you are developing for the x86 architecture  and you need extra performance  you might want to look into using the SSE extensions   This can greatly speed up single-precision floating point arithmetic  as the same operation can be performed on multiple data at once  plus there is a separate  bank of registers for the SSE operations    I noticed in your second example you used  float  instead of  double   making me think you are using single-precision math      Note   Using the old MMX instructions would actually slow down programs  because those old instructions actually used the same registers as the FPU does  making it impossible to use both the FPU and MMX at the same time

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