ippsTanh_32f_A11 at x64

[max-divulskiy]

Interesting fact. Two functions that calculate the tanh with almost equal accuracy. Why is the performance of the approximated function is twice as high at x64?

[bash]void function_1( float* lq, size_t lq_size ) { #pragma ivdep #pragma vector always for (size_t i = 0; i < lq_size; i++) lq /= 2.0f; ippsTanh_32f_A11( lq, lq, lq_size ); return ; }[/bash]
and another

[bash]float tanh_approximared( float x ) // excellent { float xa = abs( x ); // do not optimization this line float x2 = xa * xa; float x3 = xa * x2; float x4 = x2 * x2; float x7 = x3 * x4; float res = (1.0f - 1.0f / (1.0f + xa + x2 + 0.58576695f * x3 + 0.55442112f * x4 + 0.057481508f * x7)); return (x > 0.0f ? res : -res); } void function_2( float* lq, size_t lq_size ) { #pragma ivdep #pragma vector always for (size_t i = 0; i < lq_size; i++) lq = tanh_approximared( lq / 2.0f ); return ; }[/bash]

[Ying_H_Intel]

Hi Muved,

Could you pleasetell more test details, like OS, the problem size and how do you link the ipp?

ora completed test casewill behelpful.

Thanks
Ying

[SergeyKostrov]

Two improvements could be done for the approximated tanhfunction:

- don't use local variables x2, x3, x4 andx7
- normalize the polynomial in order to reduce number of multiplications, that is, x^2+x^4 = x^2 * ( 1 + x^2 )

I use these improvements in my high-performance sin, cos, tan, etc functions.

Best regards,
Sergey

[Andrey_K_Intel]

Hi Muved,

Your appriximation of tanhf is simple 7-degree polynomial one without any range reduction.It cannot be accurate on whole input range andit doesn'tsatisfy accuracy requirements for IPP A11 functions (at least 11 correct mantissa bits which corresponds to ~ 4096 ulp).

There arecouple oferror arguments, for example:

Input: 0.248947113752365 [0x3e7eebfe]
Output: 0.243623077869415 [0x3e797854]
Reference: 0.24392868578434 [0x3e79c871]
Error:20508.53 ulp

Input: 4.333872457e-019 [0x20ffd3a1]
Output: 0.0000000[0x00000000]
Reference: 4.333872457e-019 [0x20ffd3a1]
Error: -1.68e+007 ulp

That's why IPP implementation is slower.

Regards,
Andrey K.

[max-divulskiy]

Thanks all.