[Beignet] [PATCH] libocl: implement high precision pown()
Ruiling Song
ruiling.song at intel.com
Tue Dec 23 19:33:17 PST 2014
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
More information about the Beignet
mailing list