[Beignet] [PATCH] GBE: Further optimize exp().

[Zhigang Gong]

LGTM, pushed, thanks.

On Tue, Jun 24, 2014 at 02:23:31PM +0800, Ruiling Song wrote:
> Use native_exp() as much as possible.
> 
> Signed-off-by: Ruiling Song <ruiling.song at intel.com>
> ---
>  backend/src/ocl_stdlib.tmpl.h |   40 +++++++++++-----------------------------
>  1 file changed, 11 insertions(+), 29 deletions(-)
> 
> diff --git a/backend/src/ocl_stdlib.tmpl.h b/backend/src/ocl_stdlib.tmpl.h
> index ec945e4..412966e 100755
> --- a/backend/src/ocl_stdlib.tmpl.h
> +++ b/backend/src/ocl_stdlib.tmpl.h
> @@ -2267,7 +2267,7 @@ INLINE_OVERLOADABLE float __gen_ocl_internal_tanpi(float x) {
>    return native_tan(x * M_PI_F);
>  }
>  INLINE_OVERLOADABLE float native_exp2(float x) { return __gen_ocl_exp(x); }
> -INLINE_OVERLOADABLE float native_exp(float x) { return __gen_ocl_pow(M_E_F, x); }
> +INLINE_OVERLOADABLE float native_exp(float x) { return __gen_ocl_exp(M_LOG2E_F*x); }
>  INLINE_OVERLOADABLE float native_exp10(float x) { return __gen_ocl_pow(10, x); }
>  INLINE_OVERLOADABLE float __gen_ocl_internal_cbrt(float x) {
>    /* copied from fdlibm */
> @@ -2640,7 +2640,7 @@ INLINE_OVERLOADABLE float __gen_ocl_internal_rint(float x) {
>  
>  INLINE_OVERLOADABLE float __gen_ocl_internal_exp(float x) {
>    //use native instruction when it has enough precision
> -  if (x > 128 || x < -128)
> +  if (x > -0x1.6p1 && x < 0x1.6p1)
>    {
>      return native_exp(x);
>    }
> @@ -2648,15 +2648,8 @@ INLINE_OVERLOADABLE float __gen_ocl_internal_exp(float x) {
>    float o_threshold = 8.8721679688e+01,  /* 0x42b17180 */
>    u_threshold = -1.0397208405e+02,  /* 0xc2cff1b5 */
>    twom100 = 7.8886090522e-31, 	 /* 2**-100=0x0d800000 */
> -  ivln2	 =	1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
> -  one = 1.0,
> -  huge = 1.0e+30,
> -  P1 = 1.6666667163e-01, /* 0x3e2aaaab */
> -  P2 = -2.7777778450e-03, /* 0xbb360b61 */
> -  P3 = 6.6137559770e-05, /* 0x388ab355 */
> -  P4 = -1.6533901999e-06, /* 0xb5ddea0e */
> -  P5 =	4.1381369442e-08; /* 0x3331bb4c */
> -  float y,hi=0.0,lo=0.0,c,t;
> +  ivln2	 =	1.4426950216e+00; /* 0x3fb8aa3b =1/ln2 */
> +  float y,hi=0.0,lo=0.0,t;
>    int k=0,xsb;
>    unsigned hx;
>    float ln2HI_0 = 6.9313812256e-01;	/* 0x3f317180 */
> @@ -2672,17 +2665,16 @@ INLINE_OVERLOADABLE float __gen_ocl_internal_exp(float x) {
>  
>    /* filter out non-finite argument */
>    if(hx >= 0x42b17218) {			/* if |x|>=88.721... */
> -    if(hx>0x7f800000)
> -      return x+x;			/* NaN */
> -    if(hx==0x7f800000)
> -      return (xsb==0)? x:0.0; 	/* exp(+-inf)={inf,0} */
> -    if(x > o_threshold) return huge*huge; /* overflow */
> -    if(x < u_threshold) return twom100*twom100; /* underflow */
> +    // native_exp already handled this
> +    return native_exp(x);
>    }
> +
>    /* argument reduction */
>    if(hx > 0x3eb17218) {		/* if  |x| > 0.5 ln2 */
>      if(hx < 0x3F851592) {	/* and |x| < 1.5 ln2 */
> -      hi = x-(xsb ==1 ? ln2HI_1 : ln2HI_0); lo= xsb == 1? ln2LO_1 : ln2LO_0; k = 1-xsb-xsb;
> +      hi = x-(xsb ==1 ? ln2HI_1 : ln2HI_0);
> +      lo= xsb == 1? ln2LO_1 : ln2LO_0;
> +      k = 1-xsb-xsb;
>      } else {
>        float tmp = xsb == 1 ? half_1 : half_0;
>        k  = ivln2*x+tmp;
> @@ -2692,18 +2684,8 @@ INLINE_OVERLOADABLE float __gen_ocl_internal_exp(float x) {
>      }
>      x  = hi - lo;
>    }
> -  else if(hx < 0x31800000)  { /* when |x|<2**-28 */
> -    if(huge+x>one) return one+x;/* trigger inexact */
> -  }
> -  else k = 0;
>  
> -  /* x is now in primary range */
> -  t  = x*x;
> -  c  = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
> -  if(k==0)
> -    return one-((x*c)/(c-(float)2.0)-x);
> -  else
> -    y = one-((lo-(x*c)/((float)2.0-c))-hi);
> +  y = native_exp(x);
>    if(k >= -125) {
>      unsigned hy;
>      GEN_OCL_GET_FLOAT_WORD(hy,y);
> -- 
> 1.7.10.4
> 
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