[Beignet] [PATCH] backend: add double version of cosh
rander
rander.wang at intel.com
Thu Mar 30 07:09:53 UTC 2017
Also add double version of exp & expm1, for cosh depends on them
cp from fdlibm and pass the cft after refined
Signed-off-by: rander <rander.wang at intel.com>
---
backend/src/libocl/tmpl/ocl_math_common.tmpl.cl | 218 ++++++++++++++++++++++++
backend/src/libocl/tmpl/ocl_math_common.tmpl.h | 3 +
2 files changed, 221 insertions(+)
diff --git a/backend/src/libocl/tmpl/ocl_math_common.tmpl.cl b/backend/src/libocl/tmpl/ocl_math_common.tmpl.cl
index 4f0fb90..ee1cf0b 100644
--- a/backend/src/libocl/tmpl/ocl_math_common.tmpl.cl
+++ b/backend/src/libocl/tmpl/ocl_math_common.tmpl.cl
@@ -432,6 +432,178 @@ OVERLOADABLE double atanh(double x)
return 0.0;
}
+OVERLOADABLE double exp(double x)
+{
+ double one = 1.0,
+ halF[2] = {0.5,-0.5,},
+ huge = 1.0e+300,
+ twom1000= 9.33263618503218878990e-302, /* 2**-1000=0x01700000,0*/
+ o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */
+ u_threshold= -7.45133219101941108420e+02, /* 0xc0874910, 0xD52D3051 */
+ ln2HI[2] ={ 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */
+ -6.93147180369123816490e-01,},/* 0xbfe62e42, 0xfee00000 */
+ ln2LO[2] ={ 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */
+ -1.90821492927058770002e-10,},/* 0xbdea39ef, 0x35793c76 */
+ invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */
+ 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 */
+
+ double y,hi,lo,c,t;
+ int k,xsb;
+ unsigned hx;
+
+ hx = __HI(x); /* high word of x */
+ xsb = (hx>>31)&1; /* sign bit of x */
+ hx &= 0x7fffffff; /* high word of |x| */
+
+ /* filter out non-finite argument */
+ if(hx >= 0x40862E42) { /* if |x|>=709.78... */
+ if(hx>=0x7ff00000) {
+ if(((hx&0xfffff)|__LO(x))!=0)
+ return x+x; /* NaN */
+ else return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */
+ }
+ if(x > o_threshold) return huge*huge; /* overflow */
+ if(x < u_threshold) return twom1000*twom1000; /* underflow */
+ }
+
+ /* argument reduction */
+ if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
+ if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */
+ hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
+ } else {
+ k = (int)(invln2*x+halF[xsb]);
+ t = k;
+ hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
+ lo = t*ln2LO[0];
+ }
+ x = hi - lo;
+ }
+ else if(hx < 0x3e300000) { /* when |x|<2**-28 */
+ if(huge+x>one) return one+x;/* trigger inexact */
+ }
+ else k = 0;
+
+ /* x is now in primary range */
+ t = x*x;
+ c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
+ if(k==0) return one-((x*c)/(c-2.0)-x);
+ else y = one-((lo-(x*c)/(2.0-c))-hi);
+ if(k >= -1021) {
+ __setHigh(&y, __HI(y) + (k<<20)); /* add k to y's exponent */
+ return y;
+ } else {
+ __setHigh(&y, __HI(y) + ((k+1000)<<20));/* add k to y's exponent */
+ return y*twom1000;
+ }
+
+}
+
+OVERLOADABLE double expm1(double x)
+{
+ double one = 1.0,
+ huge = 1.0e+300,
+ tiny = 1.0e-300,
+ o_threshold = 7.09782712893383973096e+02,/* 0x40862E42, 0xFEFA39EF */
+ ln2_hi = 6.93147180369123816490e-01,/* 0x3fe62e42, 0xfee00000 */
+ ln2_lo = 1.90821492927058770002e-10,/* 0x3dea39ef, 0x35793c76 */
+ invln2 = 1.44269504088896338700e+00,/* 0x3ff71547, 0x652b82fe */
+ /* scaled coefficients related to expm1 */
+ Q1 = -3.33333333333331316428e-02, /* BFA11111 111110F4 */
+ Q2 = 1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */
+ Q3 = -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */
+ Q4 = 4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */
+ Q5 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */
+
+ double y,hi,lo,c,t,e,hxs,hfx,r1;
+ int k,xsb;
+ unsigned hx;
+
+ hx = __HI(x); /* high word of x */
+ xsb = hx&0x80000000; /* sign bit of x */
+ if(xsb==0) y=x; else y= -x; /* y = |x| */
+ hx &= 0x7fffffff; /* high word of |x| */
+
+ /* filter out huge and non-finite argument */
+ if(hx >= 0x4043687A) { /* if |x|>=56*ln2 */
+ if(hx >= 0x40862E42) { /* if |x|>=709.78... */
+ if(hx>=0x7ff00000) {
+ if(((hx&0xfffff)|__LO(x))!=0)
+ return x+x; /* NaN */
+ else return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
+ }
+ if(x > o_threshold) return huge*huge; /* overflow */
+ }
+ if(xsb!=0) { /* x < -56*ln2, return -1.0 with inexact */
+ if(x+tiny<0.0) /* raise inexact */
+ return tiny-one; /* return -1 */
+ }
+ }
+
+ /* argument reduction */
+ if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
+ if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */
+ if(xsb==0)
+ {hi = x - ln2_hi; lo = ln2_lo; k = 1;}
+ else
+ {hi = x + ln2_hi; lo = -ln2_lo; k = -1;}
+ } else {
+ k = invln2*x+((xsb==0)?0.5:-0.5);
+ t = k;
+ hi = x - t*ln2_hi; /* t*ln2_hi is exact here */
+ lo = t*ln2_lo;
+ }
+ x = hi - lo;
+ c = (hi-x)-lo;
+ }
+ else if(hx < 0x3c900000) { /* when |x|<2**-54, return x */
+ t = huge+x; /* return x with inexact flags when x!=0 */
+ return x - (t-(huge+x));
+ }
+ else k = 0;
+
+ /* x is now in primary range */
+ hfx = 0.5*x;
+ hxs = x*hfx;
+ r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
+ t = 3.0-r1*hfx;
+ e = hxs*((r1-t)/(6.0 - x*t));
+ if(k==0) return x - (x*e-hxs); /* c is 0 */
+ else {
+ e = (x*(e-c)-c);
+ e -= hxs;
+ if(k== -1) return 0.5*(x-e)-0.5;
+ if(k==1)
+ {
+ if(x < -0.25)
+ return -2.0*(e-(x+0.5));
+ else
+ return one+2.0*(x-e);
+ }
+
+ if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */
+ y = one-(e-x);
+ __setHigh(&y, __HI(y) + (k<<20));; /* add k to y's exponent */
+ return y-one;
+ }
+ t = one;
+ if(k<20) {
+ __setHigh(&t, 0x3ff00000 - (0x200000>>k)); /* t=1-2^-k */
+ y = t-(e-x);
+ __setHigh(&y, __HI(y) + (k<<20)); /* add k to y's exponent */
+ } else {
+ __setHigh(&t, ((0x3ff-k)<<20)); /* 2^-k */
+ y = x-(e+t);
+ y += one;
+ __setHigh(&y, __HI(y) + (k<<20)); /* add k to y's exponent */
+ }
+ }
+ return y;
+}
+
OVERLOADABLE double ceil(double x)
{
double ret;
@@ -871,6 +1043,52 @@ OVERLOADABLE double cos(double x)
}
}
+OVERLOADABLE double cosh(double x)
+{
+ double one = 1.0, dHalf=0.5, huge = 1.0e300;
+
+ double t,w;
+ int ix;
+ unsigned lx;
+
+ /* High word of |x|. */
+ ix = __HI(x);
+ ix &= 0x7fffffff;
+
+ /* x is INF or NaN */
+ if(ix>=0x7ff00000) return x*x;
+
+ /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
+ if(ix<0x3fd62e43) {
+ t = expm1(fabs(x));
+ w = one+t;
+ if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */
+ return one+(t*t)/(w+w);
+ }
+
+ /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
+ if (ix < 0x40360000) {
+ t = exp(fabs(x));
+ return dHalf*t+dHalf/t;
+ }
+
+ /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
+ if (ix < 0x40862E42) return dHalf*exp(fabs(x));
+
+ /* |x| in [log(maxdouble), overflowthresold] */
+ lx = *( (((*(unsigned*)&one)>>29)) + (unsigned*)&x);
+ if (ix<0x408633CE ||
+ ((ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d))) {
+ w = exp(dHalf*fabs(x));
+ t = dHalf*w;
+ return t*w;
+ }
+
+ /* |x| > overflowthresold, cosh(x) overflow */
+ return huge*huge;
+
+}
+
OVERLOADABLE double fabs(double x)
{
long qw = as_ulong(x);
diff --git a/backend/src/libocl/tmpl/ocl_math_common.tmpl.h b/backend/src/libocl/tmpl/ocl_math_common.tmpl.h
index 1802533..d1c7fd0 100644
--- a/backend/src/libocl/tmpl/ocl_math_common.tmpl.h
+++ b/backend/src/libocl/tmpl/ocl_math_common.tmpl.h
@@ -31,9 +31,12 @@ OVERLOADABLE double atan2(double x, double y);
OVERLOADABLE double atanpi(double x);
OVERLOADABLE double atan2pi(double x, double y);
OVERLOADABLE double atanh(double x);
+OVERLOADABLE double exp(double x);
+OVERLOADABLE double expm1(double x);
OVERLOADABLE double ceil(double x);
OVERLOADABLE double copysign(double x, double y);
OVERLOADABLE double cos(double x);
+OVERLOADABLE double cosh(double x);
OVERLOADABLE double fabs(double x);
OVERLOADABLE double fdim(double x, double y);
OVERLOADABLE double floor(double x);
--
2.7.4
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