Optimization of sine function's taylor expansion

[Bernard]

Hello!
While coding in assembly various series expansions of many functions i tried to optimize my code mainly by using rcpps instruction instead of divaps.When performing tests oncode which calculates sine function by taylor series i did a few measurements as explained here :"http://software.intel.com/en-us/forums/showthread.php?t=52482" and the result was between 10-12 cycles per first term of sine expansion(i used 14 terms).
I would like to ask you how can i rewrite this code in order to gain speed of execution improvment.
[bash]movups xmm0,argument movups xmm1,argument mulps xmm1,xmm1 mulps xmm1,xmm0 mov ebx,OFFSET coef movups xmm2,[ebx] rcpps xmm3,xmm2 ;rcpps used instead of divaps mulps xmm1,xmm3 subps xmm0,xmm1[/bash]

[Bernard]

>>> But, you're trying to use a Java-like style of programming especially when it comes to declarations of different helper types, like structures, and initialization of members of these helper types. I'll take a look at your function tomorrow.>>> Thanks for answer. Structures types can be accessed with pointers or with 'dot' operator.It is question of programming style.Today i will switch to the 2D ,3D,4D array types and try to eliminate those pesky structures if it works I can save more than 100 lines of code.I will post the update. Update on vectorised fastsin() with array type coefficients. Sadly I still cannot load xmm registers with an array type coefficients as I told you earlier only passing structure reference to xmm register works. I will investigate this issue with debugger today.

[Bernard]

I did preliminary tests on execution speed of _asm{} block.The tests were made with the help of RDTSC instructions beign executed inside _asm{} block.After a few tests I got ~1567 cycles even if latency of accessing and zeroing eax and edx registers and RDTSC and CPUID instructions is included it could not be more than ~300-400 cycles for executing whole block.Inline assembly code should be very fast and total latency in cpi per one Horner scheme polynomial term is not more than 4-5 cycles.So total time of calculation for 10 terms should be ~40-50 cycles excluding xoring xmm registers and copying x^2 value. Could you run set of tests on this?

[SergeyKostrov]

>> Tip #1 << Try to use 'typedef's for declaration of structures instead of 'struct': typedef struct tagSOMESTRUCT { } SOMESTRUCT; >> Tip # 2 << Lots of unnecesseary things in that piece of code: ... if(arg1.f1 >= HALF_PI_FLT || arg1.f2 >= HALF_PI_FLT || arg1.f3 >= HALF_PI_FLT || arg1.f4 >= HALF_PI_FLT) { vec4D vec; vec.f1 = arg1.f1; vec.f2 = arg1.f2; vec.f3 = arg1.f3; vec.f4 = arg1.f4; vec.f1 = (vec.f1 - vec.f1)/(vec.f1 - vec.f1); vec.f2 = (vec.f2 - vec.f2)/(vec.f2 - vec.f2); vec.f3 = (vec.f3 - vec.f3)/(vec.f3 - vec.f3); vec.f4 = (vec.f4 - vec.f4)/(vec.f4 - vec.f4); return vec; } ... Why don't you want to return just NULL: ... if(arg1.f1 >= HALF_PI_FLT || arg1.f2 >= HALF_PI_FLT || arg1.f3 >= HALF_PI_FLT || arg1.f4 >= HALF_PI_FLT) { return (vec &)NULL; } ... If there is an error with one of input parameters I try to leave a function / method as soon as possible without doing any calculations.

[SergeyKostrov]

>> Tip # 3 << inline struct vec4D fastsin4D( struct Argument4D arg1 ) { ... } This is a C-like, that is very obsolete, way of declaring a function. Also, why don't you want to have a class that wraps and consolidates all common things, variables, declarations, etc?

[SergeyKostrov]

>> Tip # 4 << There are lots of declarations of some types and initializations of some constants inside of the function: inline struct vec4D fastsin4D( struct Argument4D arg1 ) { ... struct CoeffFlt1 { float c1,c2,c3,c4; } coeffflt1; ... struct CoeffFlt10 { float c1,c2,c3,c4; } coeffflt10; ... coeffflt1.c1 = -0.1666666; coeffflt1.c2 = -0.1666666; coeffflt1.c3 = -0.1666666; coeffflt1.c4 = -0.1666666; ... coeffflt10.c1 = -3.8681701e-23; coeffflt10.c2 = -3.8681701e-23; coeffflt10.c3 = -3.8681701e-23; coeffflt10.c4 = -3.8681701e-23; ... } - Declarations of some types should be done only once even if it is a compile time thing - Initializations of constants could be done only once during initialization of your library

[SergeyKostrov]

>> Tip # 5 << Think about applications and use cases of your API. Will a developer X be happy with your function(s) / class(es) or not? >> Tip # 6 << Have a test-case(s) for your API from the very beginning. >> Tip # 7 << Evaluate performance of your API from the very beginning. It will save time later and you won't need to do a re-design if some function doesn't work fast.

[Bernard]

>>>- Declarations of some types should be done only once even if it is a compile time thing - Initializations of constants could be done only once during initialization of your library>>> Thank You very much for your help I'm still learning and switching between 3 programming languages sometime confuses me:) Regarding declaration of those sine coefficients and their structures I will "typedef" them and move them to header file.Is this good solution to this problem?

[Bernard]

>>>This is a C-like, that is very obsolete, way of declaring a function. Also, why don't you want to have a class that wraps and consolidates all common things, variables, declarations, etc?>>> Yes I know this and I'm only at early stage of library design.Later I will create static library wrapped in classes with static function members. Now I only tested a few possible vectorization of input argument.

[Bernard]

I think that I will switch to intrinsics .

[Bernard]

>> Tip # 5 << Think about applications and use cases of your API. Will a developer X be happy with your function(s) / class(es) or not? >> Tip # 6 << Have a test-case(s) for your API from the very beginning. >> Tip # 7 << Evaluate performance of your API from the very beginning. It will save time later and you won't need to do a re-design if some function doesn't work fast. I will proceed with the design of library according to your advise. Today I tested large composed structure with four 4D inner structures put simply 4x4D vectors matrix.I was able to load them into XMM registers and perform various vector-wise and scalar-wise operation.I could try to calculate 16 scalar sine values and return pointer to such a matrix.

[Bernard]

>>>Try to use 'typedef's for declaration of structures instead of 'struct':>>> Yes I will do this.My intention is to wrap primitive types and data types in my own "typedefs". Btw Is it recommended to declare and initialize structure in header file? I tried to do this and even after using include guards I got compile errors. >>>Lots of unnecesseary things in that piece of code:>>> That piece of code simple fills and returns structure with NaN values,but I agree with you that this adds unnecesary clutter.I could also fix the values with for exmaple HALF_PI and did recursive call , but better option is simply return NULL.

[SergeyKostrov]

>>>>Try to use 'typedef's for declaration of structures instead of 'struct': >> >>Yes I will do this. My intention is to wrap primitive types and data types in my own "typedefs". >>Btw Is it recommended to declare and initialize structure in header file? - Declaration could be done in both. That is, in a header file or in a cpp-file - Initialization has to be done in a cpp-file Note: If you do initialization in a header file you can get a compilation error like 'A variable is already declared' or something like that ( every C++ compiler will display a different error ). >>I tried to do this and even after using include guards I got compile errors. Could you post a text of the compiler error? What about a really small reproducer?

[SergeyKostrov]

Hi Iliya, Here are a couple of more tips: - Use of macros help in reducing the overall size of sources ( Note: macros can't be debugged! ) - Try to use a Hungarian Notation when declaring variables or members of a class - Consider C++ templates ( one implementation will cover many different types ) - If possible, consider portability ( Portability is always a challenge! ) I could provide some little examples and just let me know what you need. Best regards, Sergey

[SergeyKostrov]

>>Regarding declaration of those sine coefficients and their structures I will "typedef" them and move them to header file. Is this >>good solution to this problem? Here is an example: [cpp] template < class T > class TSomeClass { public: TSomeClass( void ) { InitData(); }; virtual ~TSomeClass( void ) { }; private: inline void InitData( void ) { m_tNF2 = ( T )1.0 / ( T )2.0; m_tNF3 = ( T )1.0 / ( T )6.0; m_tNF4 = ( T )1.0 / ( T )24.0; m_tNF5 = ( T )1.0 / ( T )120.0; ... }; private: T m_tNF2; T m_tNF3; T m_tNF4; T m_tNF5; ... }; [/cpp]

[SergeyKostrov]

This is a test: #include void main( void ) { printf("Pasted from VS 2005"); }

[Bernard]

>>>- Use of macros help in reducing the overall size of sources ( Note: macros can't be debugged! )>>> I do not like macro definition.Usually I put in header file various constants and function declaration , regarding length of source code it does not matter for me:) >>>Try to use a Hungarian Notation when declaring variables or members of a class>>> I hate it but I will use it in order to prevent name conflicts. >>>- If possible, consider portability ( Portability is always a challenge! )>>> What do you mean by writing this? Are you talking about the hiding differences between various OS or between various compilers? I think that portability question is still too complicated to me. I have no more than 10 months of programming experience:)

[Bernard]

>>>- Declaration could be done in both. That is, in a header file or in a cpp-file - Initialization has to be done in a cpp-file Note: If you do initialization in a header file you can get a compilation error like 'A variable is already declared' or something like that ( every C++ compiler will display a different error ).>>> I could declare and initialize my own typedefs for various trigo and special functions pre-calculated coefficients(primitive types) and put them in .h file,but I won't be able to load them into XMM registers inside asm block.This is my main problem.Lets look at this from different perspective if I'm forced to use struct types I can declare them inside #include guarded "region" but I still need to initialize them in .cpp file probably as a global constants so I will use less lines of code spent of every function.Or simply keep initializing those structures inside function. As I wrote you earlier I was not able initialize even inside #ifdef block.

[Bernard]

Here is an example: This is good design I will use it as a template. My design will be based on static functions inside my own namespace.For such a library I still do not want to do full object orientation. I still love structured programming paradigm design:)

[SergeyKostrov]

>>...Are you talking about the hiding differences between various OS or between various compilers?.. The 2nd part of your question '...between various compilers...'. For example, Intel and MSC C++ compilers must compile the sources and results have to be the same ( or almost the same ).

[SergeyKostrov]

>>...I do not like macro definition.Usually I put in header file various constants and function declaration... I was talking about macros like this: ... #define HrtExchange( Value1, Value2, Unused ) \ { \ _asm MOV eax, [##Value1] \ _asm MOV edx, [##Value2] \ _asm MOV [##Value1], edx \ _asm MOV [##Value2], eax \ } ...

[Bernard]

I was talking about macros like this: ... #define HrtExchange( Value1, Value2, Unused ) \ { \ _asm MOV eax, [##Value1] \ _asm MOV edx, [##Value2] \ _asm MOV [##Value1], edx \ _asm MOV [##Value2], eax \ } Theoritically I could move simple scalar double argument trigo function computation to header file and define them as a macros,but what about the 4D double vectors and complex multi-vector structures?I studied a design of xnamath library which was fully implemented inside header file. What do You think about the such a design? Such a macros are good for removing burden of coeffs calculation/initialization ,but my intention is to vectorize calculation and not to speed up it Regarding initialization coeffs structure inside header file I abandoned it and simply will only declare them in .h file.Inside trigo function I will initialize/instatiate those structures by such a design it could be possible to reduce such a function to more than 100 lines of code. Now I'm testing large 4x4D structure with 16 sine scalar argument for now I was able to do simple vectors computation.