backend: add double version of pow

cp from fdlibm and pass the cft after refined

Signed-off-by: rander <rander.wang@intel.com>
Tested-by: Yang Rong <rong.r.yang@intel.com>

2 files changed, 260 insertions, 0 deletions

diff --git a/backend/src/libocl/tmpl/ocl_math_common.tmpl.cl b/backend/src/libocl/tmpl/ocl_math_common.tmpl.cl
index 31cb1bad..dc6306c6 100644
--- a/backend/src/libocl/tmpl/ocl_math_common.tmpl.cl
+++ b/backend/src/libocl/tmpl/ocl_math_common.tmpl.cl
@@ -2089,6 +2089,265 @@ OVERLOADABLE double fmod (double x, double y)
 
 }
 
+OVERLOADABLE double __ocl_internal_pow(double x, double y)
+{
+	double bp[] = {1.0, 1.5,},
+	dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
+	dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
+	zero	=  0.0,
+	one =  1.0,
+	two =  2.0,
+	two53   =  9007199254740992.0,  /* 0x43400000, 0x00000000 */
+	huge	=  1.0e300,
+	tiny	=  1.0e-300,
+		/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
+	L1  =  5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
+	L2  =  4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
+	L3  =  3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
+	L4  =  2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
+	L5  =  2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
+	L6  =  2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
+	P1   =  1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
+	P2   = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
+	P3   =  6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
+	P4   = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
+	P5   =  4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */
+	lg2  =  6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
+	lg2_h  =  6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
+	lg2_l  = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
+	ovt =  8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
+	cp	=  9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
+	cp_h  =  9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
+	cp_l  = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
+	ivln2	=  1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
+	ivln2_h  =  1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
+	ivln2_l  =  1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
+
+	double z,ax,z_h,z_l,p_h,p_l;
+	double y1,t1,t2,r,s,t,u,v,w;
+	int i0,i1,i,j,k,yisint,n;
+	int hx,hy,ix,iy;
+	unsigned lx,ly;
+
+	hx = __HI(x); lx = __LO(x);
+	hy = __HI(y); ly = __LO(y);
+	ix = hx&0x7fffffff;  iy = hy&0x7fffffff;
+
+	i0 = ((*(int*)&one)>>29)^1; i1=1-i0;
+
+	/* determine if y is an odd int when x < 0
+	 * yisint = 0   ... y is not an integer
+	 * yisint = 1   ... y is an odd int
+	 * yisint = 2   ... y is an even int
+	 */
+	yisint  = 0;
+	if(hx<0) {
+		if(iy>=0x43400000) yisint = 2; /* even integer y */
+		else if(iy>=0x3ff00000) {
+		k = (iy>>20)-0x3ff;	/* exponent */
+		if(k>20) {
+			j = ly>>(52-k);
+			if((j<<(52-k))==ly) yisint = 2-(j&1);
+		} else if(ly==0) {
+			j = iy>>(20-k);
+			if((j<<(20-k))==iy) yisint = 2-(j&1);
+		}
+		}
+	}
+
+	/* special value of y */
+	if(ly==0) {
+		if (iy==0x7ff00000) {   /* y is +-inf */
+			if(((ix-0x3ff00000)|lx)==0)
+			return  1.0;  /* inf**+-1 is NaN */
+			else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */
+			return (hy>=0)? y: zero;
+			else			/* (|x|<1)**-,+inf = inf,0 */
+			return (hy<0)?-y: zero;
+		}
+		if(iy==0x3ff00000) {	/* y is  +-1 */
+		if(hy<0) return one/x; else return x;
+		}
+		if(hy==0x40000000) return x*x; /* y is  2 */
+		if(hy==0x3fe00000) {	/* y is  0.5 */
+		if(hx>=0)   /* x >= +0 */
+		return sqrt(x);
+		}
+	}
+
+	ax   = fabs(x);
+	/* special value of x */
+	if(lx==0) {
+		if(ix==0x7ff00000||ix==0||ix==0x3ff00000){
+		z = ax;		 /*x is +-0,+-inf,+-1*/
+		if(hy<0) z = one/z; /* z = (1/|x|) */
+		if(hx<0) {
+			if(((ix-0x3ff00000)|yisint)==0) {
+			z = (z-z)/(z-z); /* (-1)**non-int is NaN */
+			} else if(yisint==1)
+			z = -z;	 /* (x<0)**odd = -(|x|**odd) */
+		}
+		return z;
+		}
+	}
+
+	n = (hx>>31)+1;
+
+	/* (x<0)**(non-int) is NaN */
+	if((n|yisint)==0) return (x-x)/(x-x);
+
+	s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
+	if((n|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */
+
+	/* |y| is huge */
+	if(iy>0x41e00000) { /* if |y| > 2**31 */
+		if(iy>0x43f00000){  /* if |y| > 2**64, must o/uflow */
+		if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
+		if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
+		}
+	/* over/underflow if x is not close to one */
+		if(ix<0x3fefffff) return (hy<0)? s*huge*huge:s*tiny*tiny;
+		if(ix>0x3ff00000) return (hy>0)? s*huge*huge:s*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-one;	 /* t has 20 trailing zeros */
+		w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25));
+		u = ivln2_h*t;  /* ivln2_h has 21 sig. bits */
+		v = t*ivln2_l-w*ivln2;
+		t1 = u+v;
+		__setLow(&t1, 0);
+		t2 = v-(t1-u);
+	} else {
+		double ss,s2,s_h,s_l,t_h,t_l;
+		n = 0;
+	/* take care subnormal number */
+		if(ix<0x00100000)
+		{ax *= two53; n -= 53; ix = __HI(ax); }
+		n  += ((ix)>>20)-0x3ff;
+		j  = ix&0x000fffff;
+	/* determine interval */
+		ix = j|0x3ff00000;	  /* normalize ix */
+		if(j<=0x3988E) k=0;	 /* |x|<sqrt(3/2) */
+		else if(j<0xBB67A) k=1; /* |x|<sqrt(3)   */
+		else {k=0;n+=1;ix -= 0x00100000;}
+		__setHigh(&ax, ix);
+
+	/* compute ss = 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]);
+		ss = u*v;
+		s_h = ss;
+		__setLow(&s_h, 0);
+	/* t_h=ax+bp[k] High */
+		t_h = zero;
+		__setHigh(&t_h, ((ix>>1)|0x20000000)+0x00080000+(k<<18));
+		t_l = ax - (t_h-bp[k]);
+		s_l = v*((u-s_h*t_h)-s_h*t_l);
+	/* compute log(ax) */
+		s2 = ss*ss;
+		r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
+		r += s_l*(s_h+ss);
+		s2  = s_h*s_h;
+		t_h = 3.0+s2+r;
+		__setLow(&t_h, 0);
+		t_l = r-((t_h-3.0)-s2);
+	/* u+v = ss*(1+...) */
+		u = s_h*t_h;
+		v = s_l*t_h+t_l*ss;
+	/* 2/(3log2)*(ss+...) */
+		p_h = u+v;
+		__setLow(&p_h, 0);
+		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) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
+		t = (double)n;
+		t1 = (((z_h+z_l)+dp_h[k])+t);
+		__setLow(&t1, 0);
+		t2 = z_l-(((t1-t)-dp_h[k])-z_h);
+	}
+
+	/* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
+	y1  = y;
+	__setLow(&y1, 0);
+	p_l = (y-y1)*t1+y*t2;
+	p_h = y1*t1;
+	z = p_l+p_h;
+	j = __HI(z);
+	i = __LO(z);
+	if (j>=0x40900000) {				/* z >= 1024 */
+		if(((j-0x40900000)|i)!=0)		   /* if z > 1024 */
+		return s*huge*huge;		 /* overflow */
+		else {
+		if(p_l+ovt>z-p_h) return s*huge*huge;   /* overflow */
+		}
+	} else if((j&0x7fffffff)>=0x4090cc00 ) {	/* z <= -1075 */
+		if(((j-0xc090cc00)|i)!=0)	   /* z < -1075 */
+		return s*tiny*tiny;	 /* underflow */
+		else {
+		if(p_l<=z-p_h) return s*tiny*tiny;  /* underflow */
+		}
+	}
+	/*
+	 * compute 2**(p_h+p_l)
+	 */
+	i = j&0x7fffffff;
+	k = (i>>20)-0x3ff;
+	n = 0;
+	if(i>0x3fe00000) {	  /* if |z| > 0.5, set n = [z+0.5] */
+		n = j+(0x00100000>>(k+1));
+		k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */
+		t = zero;
+		__setHigh(&t, (n&~(0x000fffff>>k)));
+		n = ((n&0x000fffff)|0x00100000)>>(20-k);
+		if(j<0) n = -n;
+		p_h -= t;
+	}
+	t = p_l+p_h;
+	__setLow(&t, 0);
+	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);
+	j  = __HI(z);
+	j += (n<<20);
+	if((j>>20)<=0) z = __scalbn(z,n); /* subnormal output */
+	else __setHigh(&z, __HI(z)+(n<<20));
+	return s*z;
+}
+
+
+OVERLOADABLE double pow(double x, double y)
+{
+	int hx,hy,ix,iy;
+	unsigned lx,ly;
+
+	hx = __HI(x); lx = __LO(x);
+	hy = __HI(y); ly = __LO(y);
+	ix = hx&0x7fffffff;  iy = hy&0x7fffffff;
+
+	/* y==zero: x**0 = 1 */
+	if((iy|ly)==0) return 1.0;
+
+	/* +-NaN return x+y */
+	if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)))
+		return x+y;
+
+	if(iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0)))
+	{
+		if(x == 1.0)
+			return x;
+		else
+		return x + y;
+	}
+
+	return __ocl_internal_pow(x, y);
+}
+
 OVERLOADABLE double remainder(double x, double p)
 {
 	int hx,hp;
diff --git a/backend/src/libocl/tmpl/ocl_math_common.tmpl.h b/backend/src/libocl/tmpl/ocl_math_common.tmpl.h
index 6b6a741b..9a75d00a 100644
--- a/backend/src/libocl/tmpl/ocl_math_common.tmpl.h
+++ b/backend/src/libocl/tmpl/ocl_math_common.tmpl.h
@@ -57,6 +57,7 @@ OVERLOADABLE double lgamma(double x);
 OVERLOADABLE double mad(double a, double b, double c);
 OVERLOADABLE double nan(ulong code);
 OVERLOADABLE double nextafter(double x, double y);
+OVERLOADABLE double pow(double x, double y);
 OVERLOADABLE double remainder(double x, double p);
 OVERLOADABLE double rint(double x);
 OVERLOADABLE double round(double x);