[Beignet] [PATCH] libocl: implement high precision pown()
Zhigang Gong
zhigang.gong at linux.intel.com
Tue Dec 23 23:36:07 PST 2014
This patch LGTM, pushed, thanks.
On Wed, Dec 24, 2014 at 11:33:17AM +0800, Ruiling Song wrote:
> This version is based on pow() implementation ported from msun.
> I just modify it to support a floating point to the power of an integer.
>
> Signed-off-by: Ruiling Song <ruiling.song at intel.com>
> ---
> backend/src/libocl/tmpl/ocl_math.tmpl.cl | 237 +++++++++++++++++++++++++++++-
> 1 file changed, 232 insertions(+), 5 deletions(-)
>
> diff --git a/backend/src/libocl/tmpl/ocl_math.tmpl.cl b/backend/src/libocl/tmpl/ocl_math.tmpl.cl
> index d857890..321d469 100644
> --- a/backend/src/libocl/tmpl/ocl_math.tmpl.cl
> +++ b/backend/src/libocl/tmpl/ocl_math.tmpl.cl
> @@ -2986,6 +2986,21 @@ OVERLOADABLE float __gen_ocl_internal_fdim(float x, float y) {
> return y;
> return x > y ? (x - y) : +0.f;
> }
> +/*
> + * the pow/pown high precision implementation are copied from msun library.
> + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian at cygnus.com.
> + */
> +
> +/*
> + * ====================================================
> + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
> + *
> + * Developed at SunPro, a Sun Microsystems, Inc. business.
> + * Permission to use, copy, modify, and distribute this
> + * software is freely granted, provided that this notice
> + * is preserved.
> + * ====================================================
> + */
>
> OVERLOADABLE float __gen_ocl_internal_pow(float x, float y) {
> float z,ax,z_h,z_l,p_h,p_l;
> @@ -3213,6 +3228,209 @@ OVERLOADABLE float __gen_ocl_internal_pow(float x, float y) {
> return sn*z;
> }
>
> +float __gen_ocl_internal_pown(float x, int y) {
> + const float
> + bp[] = {1.0, 1.5,},
> + dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */
> + dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */
> + zero = 0.0,
> + one = 1.0,
> + two = 2.0,
> + two24 = 16777216.0, /* 0x4b800000 */
> + huge = 1.0e30,
> + tiny = 1.0e-30,
> + /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
> + L1 = 6.0000002384e-01, /* 0x3f19999a */
> + L2 = 4.2857143283e-01, /* 0x3edb6db7 */
> + L3 = 3.3333334327e-01, /* 0x3eaaaaab */
> + L4 = 2.7272811532e-01, /* 0x3e8ba305 */
> + L5 = 2.3066075146e-01, /* 0x3e6c3255 */
> + L6 = 2.0697501302e-01, /* 0x3e53f142 */
> + 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 */
> + lg2 = 6.9314718246e-01, /* 0x3f317218 */
> + lg2_h = 0x1.62ep-1,
> + lg2_l = 0x1.0bfbe8p-15,
> + ovt = 4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */
> + cp = 9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */
> + cp_h = 9.6179199219e-01, /* 0x3f763800 =head of cp */
> + cp_l = 4.7017383622e-06, /* 0x369dc3a0 =tail of cp_h */
> + ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
> + ivln2_h = 1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/
> + ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
> +
> + float z,ax,z_h,z_l,p_h,p_l;
> + float y1,t1,t2,r,s,t,u,v,w;
> + int i,j,k,yisint,n;
> + int hx,ix,iy,is;
> +
> + GEN_OCL_GET_FLOAT_WORD(hx,x);
> + ix = hx&0x7fffffff;
> + iy = y > 0 ? y&0x7fffffff : (-y)&0x7fffffff;
> + /* y==zero: x**0 = 1 */
> + if(y==0) return one;
> +
> + /* +-NaN return NAN */
> + if(ix > 0x7f800000)
> + return NAN;
> +
> + /* determine if y is an odd int
> + * yisint = 1 ... y is an odd int
> + * yisint = 2 ... y is an even int
> + */
> + yisint = y&1 ? 1 : 2;
> +
> + if (y == 1) return x;
> + if (y == -1) return one/x;
> + if (y == 2) return x*x;
> +
> + ax = __gen_ocl_fabs(x);
> +
> + /* special value of x */
> + if(ix==0x7f800000||ix==0||ix==0x3f800000){
> + z = ax; /*x is +-0,+-inf,+-1*/
> + if(y<0) z = one/z; /* z = (1/|x|) */
> + if(hx<0) {
> + if(yisint==1)
> + z = -z; /* (x<0)**odd = -(|x|**odd) */
> + }
> + return z;
> + }
> +
> + float sn = one; /* s (sign of result -ve**odd) = -1 else = 1 */
> + if(((((unsigned)hx>>31)-1)|(yisint-1))==0)
> + sn = -one; /* (-ve)**(odd int) */
> +
> + /* |y| is huge */
> + if(iy>0x08000000) { /* if |y| > 2**27 */
> + /* over/underflow if x is not close to one */
> + if(ix<0x3f7ffff8) return (y<0)? sn*huge*huge:tiny*tiny;
> + if(ix>0x3f800007) return (y>0)? sn*huge*huge:tiny*tiny;
> + /* now |1-x| is tiny <= 2**-20, suffice to compute
> + log(x) by x-x^2/2+x^3/3-x^4/4 */
> + t = ax-1; /* t has 20 trailing zeros */
> + w = (t*t)*((float)0.5-t*((float)0.333333333333-t*(float)0.25));
> + u = ivln2_h*t; /* ivln2_h has 16 sig. bits */
> + v = t*ivln2_l-w*ivln2;
> + t1 = u+v;
> + GEN_OCL_GET_FLOAT_WORD(is,t1);
> + GEN_OCL_SET_FLOAT_WORD(t1,is&0xfffff000);
> + t2 = v-(t1-u);
> + } else {
> + float s2,s_h,s_l,t_h,t_l;
> + n = 0;
> + /* take care subnormal number */
> +// if(ix<0x00800000)
> +// {ax *= two24; n -= 24; GEN_OCL_GET_FLOAT_WORD(ix,ax); }
> + n += ((ix)>>23)-0x7f;
> + j = ix&0x007fffff;
> + /* determine interval */
> + ix = j|0x3f800000; /* normalize ix */
> + if(j<=0x1cc471) k=0; /* |x|<sqrt(3/2) */
> + else if(j<0x5db3d7) k=1; /* |x|<sqrt(3) */
> + else {k=0;n+=1;ix -= 0x00800000;}
> + GEN_OCL_SET_FLOAT_WORD(ax,ix);
> +
> + /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
> + u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
> + v = one/(ax+bp[k]);
> + s = u*v;
> + s_h = s;
> + GEN_OCL_GET_FLOAT_WORD(is,s_h);
> + GEN_OCL_SET_FLOAT_WORD(s_h,is&0xfffff000);
> +
> + /* t_h=ax+bp[k] High */
> + GEN_OCL_SET_FLOAT_WORD(t_h, (((ix>>1)|0x20000000)+0x00400000+(k<<21)) &0xfffff000);
> + t_l = ax - (t_h-bp[k]);
> + s_l = v*((u-s_h*t_h)-s_h*t_l);
> +
> +
> + /* compute log(ax) */
> + s2 = s*s;
> + r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
> + r += s_l*(s_h+s);
> + s2 = s_h*s_h;
> + t_h = (float)3.0+s2+r;
> + GEN_OCL_GET_FLOAT_WORD(is,t_h);
> + GEN_OCL_SET_FLOAT_WORD(t_h,is&0xffffe000);
> + t_l = r-((t_h-(float)3.0)-s2);
> + /* u+v = s*(1+...) */
> + u = s_h*t_h;
> + v = s_l*t_h+t_l*s;
> + /* 2/(3log2)*(s+...) */
> + p_h = u+v;
> + GEN_OCL_GET_FLOAT_WORD(is,p_h);
> + GEN_OCL_SET_FLOAT_WORD(p_h,is&0xffffe000);
> + p_l = v-(p_h-u);
> + z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
> + z_l = cp_l*p_h+p_l*cp+dp_l[k];
> + /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
> + t = (float)n;
> + t1 = (((z_h+z_l)+dp_h[k])+t);
> + GEN_OCL_GET_FLOAT_WORD(is,t1);
> + GEN_OCL_SET_FLOAT_WORD(t1,is&0xffffe000);
> + t2 = z_l-(((t1-t)-dp_h[k])-z_h);
> + }
> +
> + /* split up y into y1+y2+y3 and compute (y1+y2+y3)*(t1+t2) */
> +
> + float fy = (float)y;
> + float y3 = (float)(y-(int)fy);
> + GEN_OCL_GET_FLOAT_WORD(is,fy);
> + GEN_OCL_SET_FLOAT_WORD(y1,is&0xfffff000);
> +
> + p_l = (fy-y1)*t1 + y3*t1 + fy*t2 + y3*t2;
> + p_h = y1*t1;
> + z = p_l+p_h;
> +
> + GEN_OCL_GET_FLOAT_WORD(j,z);
> + if (j>0x43000000) /* if z > 128 */
> + return sn*huge*huge; /* overflow */
> + else if (j==0x43000000) { /* if z == 128 */
> + if(p_l+ovt>z-p_h) return sn*huge*huge; /* overflow */
> + }
> + else if ((j&0x7fffffff)>0x43160000) /* z <= -150 */
> + return sn*tiny*tiny; /* underflow */
> + else if (j==0xc3160000){ /* z == -150 */
> + if(p_l<=z-p_h) return sn*tiny*tiny; /* underflow */
> + }
> + /*
> + * compute 2**(p_h+p_l)
> + */
> + i = j&0x7fffffff;
> + k = (i>>23)-0x7f;
> + n = 0;
> + if(i>0x3f000000) { /* if |z| > 0.5, set n = [z+0.5] */
> + n = j+(0x00800000>>(k+1));
> + k = ((n&0x7fffffff)>>23)-0x7f; /* new k for n */
> + GEN_OCL_SET_FLOAT_WORD(t,n&~(0x007fffff>>k));
> + n = ((n&0x007fffff)|0x00800000)>>(23-k);
> + if(j<0) n = -n;
> + p_h -= t;
> +
> + z -= n;
> + }
> +
> + t = z;
> + GEN_OCL_GET_FLOAT_WORD(is,t);
> + GEN_OCL_SET_FLOAT_WORD(t,is&0xfffff000);
> + u = t*lg2_h;
> + v = (p_l-(t-p_h))*lg2+t*lg2_l;
> + z = u+v;
> + w = v-(z-u);
> + t = z*z;
> + t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
> + r = (z*t1)/(t1-two)-(w+z*w);
> + z = one-(r-z);
> + GEN_OCL_GET_FLOAT_WORD(j,z);
> + j += (n<<23);
> + if((j>>23)<=0) z = __gen_ocl_scalbnf(z,n); /* subnormal output */
> + else GEN_OCL_SET_FLOAT_WORD(z,j);
> + return sn*z;
> +}
>
> OVERLOADABLE float hypot(float x, float y) {
> if (__ocl_math_fastpath_flag)
> @@ -3392,11 +3610,20 @@ OVERLOADABLE float powr(float x, float y) {
> }
>
> OVERLOADABLE float pown(float x, int n) {
> - if (x == 0.f && n == 0)
> - return 1.f;
> - if (x < 0.f && (n&1) )
> - return -powr(-x, n);
> - return powr(x, n);
> + if (__ocl_math_fastpath_flag) {
> + if (x == 0.f && n == 0)
> + return 1.f;
> + if (x < 0.f && (n&1) )
> + return -powr(-x, n);
> + return powr(x, n);
> + } else {
> + int ix;
> + GEN_OCL_GET_FLOAT_WORD(ix, x);
> + float sign = ix < 0 ? -1.0f : 1.0f;
> + if (x == 0.0f) x = sign * 0.0f;
> +
> + return __gen_ocl_internal_pown(x, n);
> + }
> }
>
> OVERLOADABLE float pow(float x, float y) {
> --
> 1.7.10.4
>
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