backend: add double version of lgamma

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, 163 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 96aae039..52253fbb 100644
--- a/backend/src/libocl/tmpl/ocl_math_common.tmpl.cl
+++ b/backend/src/libocl/tmpl/ocl_math_common.tmpl.cl
@@ -1742,6 +1742,168 @@ OVERLOADABLE int ilogb(double x)
 	else return 0x80000000;
 }
 
+OVERLOADABLE double lgamma(double x)
+{
+	double two52=  4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */
+	halfD=  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
+	one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
+	pi  =  3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
+	a0  =  7.72156649015328655494e-02, /* 0x3FB3C467, 0xE37DB0C8 */
+	a1  =  3.22467033424113591611e-01, /* 0x3FD4A34C, 0xC4A60FAD */
+	a2  =  6.73523010531292681824e-02, /* 0x3FB13E00, 0x1A5562A7 */
+	a3  =  2.05808084325167332806e-02, /* 0x3F951322, 0xAC92547B */
+	a4  =  7.38555086081402883957e-03, /* 0x3F7E404F, 0xB68FEFE8 */
+	a5  =  2.89051383673415629091e-03, /* 0x3F67ADD8, 0xCCB7926B */
+	a6  =  1.19270763183362067845e-03, /* 0x3F538A94, 0x116F3F5D */
+	a7  =  5.10069792153511336608e-04, /* 0x3F40B6C6, 0x89B99C00 */
+	a8  =  2.20862790713908385557e-04, /* 0x3F2CF2EC, 0xED10E54D */
+	a9  =  1.08011567247583939954e-04, /* 0x3F1C5088, 0x987DFB07 */
+	a10 =  2.52144565451257326939e-05, /* 0x3EFA7074, 0x428CFA52 */
+	a11 =  4.48640949618915160150e-05, /* 0x3F07858E, 0x90A45837 */
+	tc  =  1.46163214496836224576e+00, /* 0x3FF762D8, 0x6356BE3F */
+	tf  = -1.21486290535849611461e-01, /* 0xBFBF19B9, 0xBCC38A42 */
+	/* tt = -(tail of tf) */
+	tt  = -3.63867699703950536541e-18, /* 0xBC50C7CA, 0xA48A971F */
+	t0  =  4.83836122723810047042e-01, /* 0x3FDEF72B, 0xC8EE38A2 */
+	t1  = -1.47587722994593911752e-01, /* 0xBFC2E427, 0x8DC6C509 */
+	t2  =  6.46249402391333854778e-02, /* 0x3FB08B42, 0x94D5419B */
+	t3  = -3.27885410759859649565e-02, /* 0xBFA0C9A8, 0xDF35B713 */
+	t4  =  1.79706750811820387126e-02, /* 0x3F9266E7, 0x970AF9EC */
+	t5  = -1.03142241298341437450e-02, /* 0xBF851F9F, 0xBA91EC6A */
+	t6  =  6.10053870246291332635e-03, /* 0x3F78FCE0, 0xE370E344 */
+	t7  = -3.68452016781138256760e-03, /* 0xBF6E2EFF, 0xB3E914D7 */
+	t8  =  2.25964780900612472250e-03, /* 0x3F6282D3, 0x2E15C915 */
+	t9  = -1.40346469989232843813e-03, /* 0xBF56FE8E, 0xBF2D1AF1 */
+	t10 =  8.81081882437654011382e-04, /* 0x3F4CDF0C, 0xEF61A8E9 */
+	t11 = -5.38595305356740546715e-04, /* 0xBF41A610, 0x9C73E0EC */
+	t12 =  3.15632070903625950361e-04, /* 0x3F34AF6D, 0x6C0EBBF7 */
+	t13 = -3.12754168375120860518e-04, /* 0xBF347F24, 0xECC38C38 */
+	t14 =  3.35529192635519073543e-04, /* 0x3F35FD3E, 0xE8C2D3F4 */
+	u0  = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */
+	u1  =  6.32827064025093366517e-01, /* 0x3FE4401E, 0x8B005DFF */
+	u2  =  1.45492250137234768737e+00, /* 0x3FF7475C, 0xD119BD6F */
+	u3  =  9.77717527963372745603e-01, /* 0x3FEF4976, 0x44EA8450 */
+	u4  =  2.28963728064692451092e-01, /* 0x3FCD4EAE, 0xF6010924 */
+	u5  =  1.33810918536787660377e-02, /* 0x3F8B678B, 0xBF2BAB09 */
+	v1  =  2.45597793713041134822e+00, /* 0x4003A5D7, 0xC2BD619C */
+	v2  =  2.12848976379893395361e+00, /* 0x40010725, 0xA42B18F5 */
+	v3  =  7.69285150456672783825e-01, /* 0x3FE89DFB, 0xE45050AF */
+	v4  =  1.04222645593369134254e-01, /* 0x3FBAAE55, 0xD6537C88 */
+	v5  =  3.21709242282423911810e-03, /* 0x3F6A5ABB, 0x57D0CF61 */
+	s0  = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */
+	s1  =  2.14982415960608852501e-01, /* 0x3FCB848B, 0x36E20878 */
+	s2  =  3.25778796408930981787e-01, /* 0x3FD4D98F, 0x4F139F59 */
+	s3  =  1.46350472652464452805e-01, /* 0x3FC2BB9C, 0xBEE5F2F7 */
+	s4  =  2.66422703033638609560e-02, /* 0x3F9B481C, 0x7E939961 */
+	s5  =  1.84028451407337715652e-03, /* 0x3F5E26B6, 0x7368F239 */
+	s6  =  3.19475326584100867617e-05, /* 0x3F00BFEC, 0xDD17E945 */
+	r1  =  1.39200533467621045958e+00, /* 0x3FF645A7, 0x62C4AB74 */
+	r2  =  7.21935547567138069525e-01, /* 0x3FE71A18, 0x93D3DCDC */
+	r3  =  1.71933865632803078993e-01, /* 0x3FC601ED, 0xCCFBDF27 */
+	r4  =  1.86459191715652901344e-02, /* 0x3F9317EA, 0x742ED475 */
+	r5  =  7.77942496381893596434e-04, /* 0x3F497DDA, 0xCA41A95B */
+	r6  =  7.32668430744625636189e-06, /* 0x3EDEBAF7, 0xA5B38140 */
+	w0  =  4.18938533204672725052e-01, /* 0x3FDACFE3, 0x90C97D69 */
+	w1  =  8.33333333333329678849e-02, /* 0x3FB55555, 0x5555553B */
+	w2  = -2.77777777728775536470e-03, /* 0xBF66C16C, 0x16B02E5C */
+	w3  =  7.93650558643019558500e-04, /* 0x3F4A019F, 0x98CF38B6 */
+	w4  = -5.95187557450339963135e-04, /* 0xBF4380CB, 0x8C0FE741 */
+	w5  =  8.36339918996282139126e-04, /* 0x3F4B67BA, 0x4CDAD5D1 */
+	w6  = -1.63092934096575273989e-03; /* 0xBF5AB89D, 0x0B9E43E4 */
+
+	double zero=  0.00000000000000000000e+00;
+
+	double t,y,z,nadj,p,p1,p2,p3,q,r,w;
+	int i,hx,lx,ix;
+
+	hx = __HI(x);
+	lx = __LO(x);
+
+	/* purge off +-inf, NaN, +-0, and negative arguments */
+	ix = hx&0x7fffffff;
+	if(ix>=0x7ff00000) return x*x;
+	if((ix|lx)==0) return one/zero;
+	if(ix<0x3b900000) {	/* |x|<2**-70, return -log(|x|) */
+		if(hx<0) {
+			return -log(-x);
+		} else return -log(x);
+	}
+	if(hx<0) {
+		if(ix>=0x43300000) 	/* |x|>=2**52, must be -integer */
+		return one/zero;
+		t = sinpi(x);
+		if(t==zero) return one/zero; /* -integer */
+		nadj = log(pi/fabs(t*x));
+		x = -x;
+	}
+
+	/* purge off 1 and 2 */
+	if((((ix-0x3ff00000)|lx)==0)||(((ix-0x40000000)|lx)==0)) r = 0;
+	/* for x < 2.0 */
+	else if(ix<0x40000000) {
+		if(ix<=0x3feccccc) { 	/* lgamma(x) = lgamma(x+1)-log(x) */
+		r = -log(x);
+		if(ix>=0x3FE76944) {y = one-x; i= 0;}
+		else if(ix>=0x3FCDA661) {y= x-(tc-one); i=1;}
+		else {y = x; i=2;}
+		} else {
+		r = zero;
+			if(ix>=0x3FFBB4C3) {y=2.0-x;i=0;} /* [1.7316,2] */
+			else if(ix>=0x3FF3B4C4) {y=x-tc;i=1;} /* [1.23,1.73] */
+		else {y=x-one;i=2;}
+		}
+		switch(i) {
+		  case 0:
+		z = y*y;
+		p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10))));
+		p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11)))));
+		p  = y*p1+p2;
+		r  += (p-0.5*y); break;
+		  case 1:
+		z = y*y;
+		w = z*y;
+		p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12)));	/* parallel comp */
+		p2 = t1+w*(t4+w*(t7+w*(t10+w*t13)));
+		p3 = t2+w*(t5+w*(t8+w*(t11+w*t14)));
+		p  = z*p1-(tt-w*(p2+y*p3));
+		r += (tf + p); break;
+		  case 2:
+		p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5)))));
+		p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5))));
+		r += (-0.5*y + p1/p2);
+		}
+	}
+	else if(ix<0x40200000) { 			/* x < 8.0 */
+		i = (int)x;
+		t = zero;
+		y = x-(double)i;
+		p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6))))));
+		q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6)))));
+		r = halfD*y+p/q;
+		z = one;	/* lgamma(1+s) = log(s) + lgamma(s) */
+		switch(i) {
+		case 7: z *= (y+6.0);	/* FALLTHRU */
+		case 6: z *= (y+5.0);	/* FALLTHRU */
+		case 5: z *= (y+4.0);	/* FALLTHRU */
+		case 4: z *= (y+3.0);	/* FALLTHRU */
+		case 3: z *= (y+2.0);	/* FALLTHRU */
+			r += log(z); break;
+		}
+	/* 8.0 <= x < 2**58 */
+	} else if (ix < 0x43900000) {
+		t = log(x);
+		z = one/x;
+		y = z*z;
+		w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6)))));
+		r = (x-halfD)*(t-one)+w;
+	} else
+	/* 2**58 <= x <= inf */
+		r =  x*(log(x)-one);
+	if(hx<0) r = nadj - r;
+	return r;
+
+}
+
 CONST OVERLOADABLE double __gen_ocl_mad(double a, double b, double c) __asm("llvm.fma" ".f64");
 OVERLOADABLE double mad(double a, double b, double c)
 {
diff --git a/backend/src/libocl/tmpl/ocl_math_common.tmpl.h b/backend/src/libocl/tmpl/ocl_math_common.tmpl.h
index 2cea5130..de459465 100644
--- a/backend/src/libocl/tmpl/ocl_math_common.tmpl.h
+++ b/backend/src/libocl/tmpl/ocl_math_common.tmpl.h
@@ -53,6 +53,7 @@ OVERLOADABLE double log10(double x);
 OVERLOADABLE double log1p(double x);
 OVERLOADABLE double logb(double x);
 OVERLOADABLE int ilogb(double x);
+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);