From: Lv Meng Date: Tue, 14 Jan 2014 03:04:57 +0000 (+0800) Subject: GBE: improve precision of rootn X-Git-Url: http://review.tizen.org/git/?a=commitdiff_plain;h=a0f277455862f2a12377e31c11d454b39b81a82e;p=contrib%2Fbeignet.git GBE: improve precision of rootn Signed-off-by: Lv Meng --- diff --git a/backend/src/ocl_stdlib.tmpl.h b/backend/src/ocl_stdlib.tmpl.h index 224cfc6..cea4700 100755 --- a/backend/src/ocl_stdlib.tmpl.h +++ b/backend/src/ocl_stdlib.tmpl.h @@ -3349,6 +3349,232 @@ INLINE_OVERLOADABLE float __gen_ocl_internal_fdim(float x, float y) { return y; return x > y ? (x - y) : +0.f; } + +INLINE_OVERLOADABLE float __gen_ocl_internal_pow(float x, float y) { + float z,ax,z_h,z_l,p_h,p_l; + float y1,t1,t2,r,s,sn,t,u,v,w; + int i,j,k,yisint,n; + int hx,hy,ix,iy,is; + float bp[2],dp_h[2],dp_l[2], + 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 = 6.93145752e-01, /* 0x3f317200 */ + lg2_l = 1.42860654e-06, /* 0x35bfbe8c */ + 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*/ + bp[0] = 1.0,bp[1] = 1.5, + dp_h[0] = 0.0,dp_h[1] = 5.84960938e-01, + dp_l[0] = 0.0,dp_l[1] = 1.56322085e-06; + GEN_OCL_GET_FLOAT_WORD(hx,x); + GEN_OCL_GET_FLOAT_WORD(hy,y); + ix = hx&0x7fffffff; iy = hy&0x7fffffff; + if (ix < 0x00800000) { /* x < 2**-126 */ + ix = 0;/* Gen does not support subnormal number now */ + } + if (iy < 0x00800000) { /* y < 2**-126 */ + iy = 0;/* Gen does not support subnormal number now */ + } + /* y==zero: x**0 = 1 */ + if(iy==0) return one; + if(hx==0x3f800000) return one; + /* +-NaN return x+y */ + if(ix > 0x7f800000 || iy > 0x7f800000) + return (x+0.0f)+y+(0.0f); + /* 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>=0x4b800000) yisint = 2; /* even integer y */ + else if(iy>=0x3f800000) { + k = (iy>>23)-0x7f; /* exponent */ + j = iy>>(23-k); + if((j<<(23-k))==iy) yisint = 2-(j&1); + } + } + /* special value of y */ + if (iy==0x7f800000) { /* y is +-inf */ + if (ix==0x3f800000) + //return y - y; /* inf**+-1 is NaN */ + return one; + else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */ + return (hy>=0)? y: zero; + else /* (|x|<1)**-,+inf = inf,0 */ + return (hy<0)?-y: zero; + } + if(iy==0x3f800000) { /* y is +-1 */ + if(hy<0) return one/x; else return x; + } + if(hy==0x40000000) return x*x; /* y is 2 */ + if(hy==0x3f000000) { /* y is 0.5 */ + if(hx>=0)return __gen_ocl_sqrt(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(hy<0) z = one/z; /* z = (1/|x|) */ + if(hx<0) { + if(((ix-0x3f800000)|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 = ((uint)hx>>31)-1; + + /* (x<0)**(non-int) is NaN */ + if((n|yisint)==0) return (x-x)/(x-x); + + sn = one; /* s (sign of result -ve**odd) = -1 else = 1 */ + if((n|(yisint-1))==0) sn = -one;/* (-ve)**(odd int) */ + + /* |y| is huge */ + if(iy>0x4d000000) { /* if |y| > 2**27 */ + /* over/underflow if x is not close to one */ + if(ix<0x3f7ffff8) return (hy<0)? sn*huge*huge:sn*tiny*tiny; + if(ix>0x3f800007) return (hy>0)? sn*huge*huge:sn*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*(0.333333333333f-t*0.25f)); + 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|>1)&0xfffff000)|0x20000000; + GEN_OCL_SET_FLOAT_WORD(t_h,is+0x00400000+(k<<21)); + 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 = 3.0f+s2+r; + GEN_OCL_GET_FLOAT_WORD(is,t_h); + GEN_OCL_SET_FLOAT_WORD(t_h,is&0xfffff000); + t_l = r-((t_h-3.0f)-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&0xfffff000); + 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&0xfffff000); + t2 = z_l-(((t1-t)-dp_h[k])-z_h); + } + + /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ + GEN_OCL_GET_FLOAT_WORD(is,y); + GEN_OCL_SET_FLOAT_WORD(y1,is&0xfffff000); + p_l = (y-y1)*t1+y*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; + } + t = p_l+p_h; + GEN_OCL_GET_FLOAT_WORD(is,t); + GEN_OCL_SET_FLOAT_WORD(t,is&0xffff8000); + 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; +} + + INLINE_OVERLOADABLE float hypot(float x, float y) { //return __gen_ocl_sqrt(x*x + y*y); float a,b,an,bn,cn; @@ -3479,7 +3705,36 @@ INLINE_OVERLOADABLE float pown(float x, int n) { return powr(x, n); } INLINE_OVERLOADABLE float rootn(float x, int n) { - return powr(x, 1.f / n); + float ax,re; + int sign = 0; + if( n == 0 )return NAN; + //rootn ( x, n ) returns a NaN for x < 0 and n is even. + if( x < 0 && 0 == (n&1) ) + return NAN; + if( x == 0.0 ){ + switch( n & 0x80000001 ){ + //rootn ( +-0, n ) is +0 for even n > 0. + case 0: + return 0.0f; + //rootn ( +-0, n ) is +-0 for odd n > 0. + case 1: + return x; + //rootn ( +-0, n ) is +inf for even n < 0. + case 0x80000000: + return INFINITY; + + //rootn ( +-0, n ) is +-inf for odd n < 0. + case 0x80000001: + return __gen_ocl_internal_copysign(INFINITY, x); + } + } + ax = __gen_ocl_fabs(x); + if(x <0.0f && (n&1)) + sign = 1; + re = __gen_ocl_internal_pow(ax,1.f/n); + if(sign) + re = -re; + return re; } /////////////////////////////////////////////////////////////////////////////