backend: add double version of erfc

cp from fdlibm and refine it

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

2 files changed, 124 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 624f5036..96aae039 100644
--- a/backend/src/libocl/tmpl/ocl_math_common.tmpl.cl
+++ b/backend/src/libocl/tmpl/ocl_math_common.tmpl.cl
@@ -718,6 +718,129 @@ OVERLOADABLE double erf(double x)
 
 }
 
+OVERLOADABLE double erfc(double x)
+{
+	double erx =  8.45062911510467529297e-01, /* 0x3FEB0AC1, 0x60000000 */
+	efx =  1.28379167095512586316e-01, /* 0x3FC06EBA, 0x8214DB69 */
+	efx8=  1.02703333676410069053e+00, /* 0x3FF06EBA, 0x8214DB69 */
+	pp0  =  1.28379167095512558561e-01, /* 0x3FC06EBA, 0x8214DB68 */
+	pp1  = -3.25042107247001499370e-01, /* 0xBFD4CD7D, 0x691CB913 */
+	pp2  = -2.84817495755985104766e-02, /* 0xBF9D2A51, 0xDBD7194F */
+	pp3  = -5.77027029648944159157e-03, /* 0xBF77A291, 0x236668E4 */
+	pp4  = -2.37630166566501626084e-05, /* 0xBEF8EAD6, 0x120016AC */
+	qq1  =  3.97917223959155352819e-01, /* 0x3FD97779, 0xCDDADC09 */
+	qq2  =  6.50222499887672944485e-02, /* 0x3FB0A54C, 0x5536CEBA */
+	qq3  =  5.08130628187576562776e-03, /* 0x3F74D022, 0xC4D36B0F */
+	qq4  =  1.32494738004321644526e-04, /* 0x3F215DC9, 0x221C1A10 */
+	qq5  = -3.96022827877536812320e-06, /* 0xBED09C43, 0x42A26120 */
+	pa0  = -2.36211856075265944077e-03, /* 0xBF6359B8, 0xBEF77538 */
+	pa1  =  4.14856118683748331666e-01, /* 0x3FDA8D00, 0xAD92B34D */
+	pa2  = -3.72207876035701323847e-01, /* 0xBFD7D240, 0xFBB8C3F1 */
+	pa3  =  3.18346619901161753674e-01, /* 0x3FD45FCA, 0x805120E4 */
+	pa4  = -1.10894694282396677476e-01, /* 0xBFBC6398, 0x3D3E28EC */
+	pa5  =  3.54783043256182359371e-02, /* 0x3FA22A36, 0x599795EB */
+	pa6  = -2.16637559486879084300e-03, /* 0xBF61BF38, 0x0A96073F */
+	qa1  =  1.06420880400844228286e-01, /* 0x3FBB3E66, 0x18EEE323 */
+	qa2  =  5.40397917702171048937e-01, /* 0x3FE14AF0, 0x92EB6F33 */
+	qa3  =  7.18286544141962662868e-02, /* 0x3FB2635C, 0xD99FE9A7 */
+	qa4  =  1.26171219808761642112e-01, /* 0x3FC02660, 0xE763351F */
+	qa5  =  1.36370839120290507362e-02, /* 0x3F8BEDC2, 0x6B51DD1C */
+	qa6  =  1.19844998467991074170e-02, /* 0x3F888B54, 0x5735151D */
+	ra0  = -9.86494403484714822705e-03, /* 0xBF843412, 0x600D6435 */
+	ra1  = -6.93858572707181764372e-01, /* 0xBFE63416, 0xE4BA7360 */
+	ra2  = -1.05586262253232909814e+01, /* 0xC0251E04, 0x41B0E726 */
+	ra3  = -6.23753324503260060396e+01, /* 0xC04F300A, 0xE4CBA38D */
+	ra4  = -1.62396669462573470355e+02, /* 0xC0644CB1, 0x84282266 */
+	ra5  = -1.84605092906711035994e+02, /* 0xC067135C, 0xEBCCABB2 */
+	ra6  = -8.12874355063065934246e+01, /* 0xC0545265, 0x57E4D2F2 */
+	ra7  = -9.81432934416914548592e+00, /* 0xC023A0EF, 0xC69AC25C */
+	sa1  =  1.96512716674392571292e+01, /* 0x4033A6B9, 0xBD707687 */
+	sa2  =  1.37657754143519042600e+02, /* 0x4061350C, 0x526AE721 */
+	sa3  =  4.34565877475229228821e+02, /* 0x407B290D, 0xD58A1A71 */
+	sa4  =  6.45387271733267880336e+02, /* 0x40842B19, 0x21EC2868 */
+	sa5  =  4.29008140027567833386e+02, /* 0x407AD021, 0x57700314 */
+	sa6  =  1.08635005541779435134e+02, /* 0x405B28A3, 0xEE48AE2C */
+	sa7  =  6.57024977031928170135e+00, /* 0x401A47EF, 0x8E484A93 */
+	sa8  = -6.04244152148580987438e-02, /* 0xBFAEEFF2, 0xEE749A62 */
+	rb0  = -9.86494292470009928597e-03, /* 0xBF843412, 0x39E86F4A */
+	rb1  = -7.99283237680523006574e-01, /* 0xBFE993BA, 0x70C285DE */
+	rb2  = -1.77579549177547519889e+01, /* 0xC031C209, 0x555F995A */
+	rb3  = -1.60636384855821916062e+02, /* 0xC064145D, 0x43C5ED98 */
+	rb4  = -6.37566443368389627722e+02, /* 0xC083EC88, 0x1375F228 */
+	rb5  = -1.02509513161107724954e+03, /* 0xC0900461, 0x6A2E5992 */
+	rb6  = -4.83519191608651397019e+02, /* 0xC07E384E, 0x9BDC383F */
+	sb1  =  3.03380607434824582924e+01, /* 0x403E568B, 0x261D5190 */
+	sb2  =  3.25792512996573918826e+02; /* 0x40745CAE, 0x221B9F0A */
+	double sb3  =  1.53672958608443695994e+03, /* 0x409802EB, 0x189D5118 */
+	sb4  =  3.19985821950859553908e+03, /* 0x40A8FFB7, 0x688C246A */
+	sb5  =  2.55305040643316442583e+03, /* 0x40A3F219, 0xCEDF3BE6 */
+	sb6  =  4.74528541206955367215e+02, /* 0x407DA874, 0xE79FE763 */
+	sb7  = -2.24409524465858183362e+01; /* 0xC03670E2, 0x42712D62 */
+
+	double tiny = 1e-300;
+	double halfD =  5.00000000000000000000e-01;/* 0x3FE00000, 0x00000000 */
+	double one =  1.00000000000000000000e+00; /* 0x3FF00000, 0x00000000 */
+	double two =  2.00000000000000000000e+00; /* 0x40000000, 0x00000000 */
+
+	int hx,ix;
+	double R,S,P,Q,s,y,z,r;
+	hx = __HI(x);
+	ix = hx&0x7fffffff;
+	if(ix>=0x7ff00000) {			/* erfc(nan)=nan */
+						/* erfc(+-inf)=0,2 */
+		return (double)(((unsigned)hx>>31)<<1)+one/x;
+	}
+
+	if(ix < 0x3feb0000) {		/* |x|<0.84375 */
+		if(ix < 0x3c700000)  	/* |x|<2**-56 */
+		return one-x;
+		z = x*x;
+		r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
+		s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
+		y = r/s;
+		if(hx < 0x3fd00000) {  	/* x<1/4 */
+		return one-(x+x*y);
+		} else {
+		r = x*y;
+		r += (x-halfD);
+			return halfD - r ;
+		}
+	}
+	if(ix < 0x3ff40000) {		/* 0.84375 <= |x| < 1.25 */
+		s = fabs(x)-one;
+		P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
+		Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
+		if(hx>=0) {
+			z  = one-erx; return z - P/Q;
+		} else {
+		z = erx+P/Q; return one+z;
+		}
+	}
+	if (ix < 0x403c0000) {		/* |x|<28 */
+		x = fabs(x);
+		s = one/(x*x);
+		if(ix< 0x4006DB6D) {	/* |x| < 1/.35 ~ 2.857143*/
+			R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
+				ra5+s*(ra6+s*ra7))))));
+			S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
+				sa5+s*(sa6+s*(sa7+s*sa8)))))));
+		} else {			/* |x| >= 1/.35 ~ 2.857143 */
+		if(hx<0&&ix>=0x40180000) return two-tiny;/* x < -6 */
+			R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
+				rb5+s*rb6)))));
+			S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
+				sb5+s*(sb6+s*sb7))))));
+		}
+		z  = x;
+		__setLow(&z, 0);
+		r  =  exp(-z*z-0.5625)*
+			exp((z-x)*(z+x)+R/S);
+		if(hx>0) return r/x; else return two-r/x;
+	} else {
+		if(hx>0) return tiny*tiny; else return two-tiny;
+	}
+}
+
 OVERLOADABLE double cbrt(double x)
 {
 	double B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
diff --git a/backend/src/libocl/tmpl/ocl_math_common.tmpl.h b/backend/src/libocl/tmpl/ocl_math_common.tmpl.h
index 325ca1be..2cea5130 100644
--- a/backend/src/libocl/tmpl/ocl_math_common.tmpl.h
+++ b/backend/src/libocl/tmpl/ocl_math_common.tmpl.h
@@ -34,6 +34,7 @@ OVERLOADABLE double atanh(double x);
 OVERLOADABLE double exp(double x);
 OVERLOADABLE double expm1(double x);
 OVERLOADABLE double erf(double x);
+OVERLOADABLE double erfc(double x);
 OVERLOADABLE double cbrt(double x);
 OVERLOADABLE double ceil(double x);
 OVERLOADABLE double copysign(double x, double y);