This version is based on pow() implementation ported from msun. I just modify it to support a floating point to the power of an integer.
Signed-off-by: Ruiling Song <[email protected]> --- backend/src/libocl/tmpl/ocl_math.tmpl.cl | 237 +++++++++++++++++++++++++++++- 1 file changed, 232 insertions(+), 5 deletions(-) diff --git a/backend/src/libocl/tmpl/ocl_math.tmpl.cl b/backend/src/libocl/tmpl/ocl_math.tmpl.cl index d857890..321d469 100644 --- a/backend/src/libocl/tmpl/ocl_math.tmpl.cl +++ b/backend/src/libocl/tmpl/ocl_math.tmpl.cl @@ -2986,6 +2986,21 @@ OVERLOADABLE float __gen_ocl_internal_fdim(float x, float y) { return y; return x > y ? (x - y) : +0.f; } +/* + * the pow/pown high precision implementation are copied from msun library. + * Conversion to float by Ian Lance Taylor, Cygnus Support, [email protected]. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ OVERLOADABLE float __gen_ocl_internal_pow(float x, float y) { float z,ax,z_h,z_l,p_h,p_l; @@ -3213,6 +3228,209 @@ OVERLOADABLE float __gen_ocl_internal_pow(float x, float y) { return sn*z; } +float __gen_ocl_internal_pown(float x, int y) { + const float + bp[] = {1.0, 1.5,}, + dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */ + dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */ + 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 = 0x1.62ep-1, + lg2_l = 0x1.0bfbe8p-15, + 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*/ + + float z,ax,z_h,z_l,p_h,p_l; + float y1,t1,t2,r,s,t,u,v,w; + int i,j,k,yisint,n; + int hx,ix,iy,is; + + GEN_OCL_GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + iy = y > 0 ? y&0x7fffffff : (-y)&0x7fffffff; + /* y==zero: x**0 = 1 */ + if(y==0) return one; + + /* +-NaN return NAN */ + if(ix > 0x7f800000) + return NAN; + + /* determine if y is an odd int + * yisint = 1 ... y is an odd int + * yisint = 2 ... y is an even int + */ + yisint = y&1 ? 1 : 2; + + if (y == 1) return x; + if (y == -1) return one/x; + if (y == 2) return x*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(y<0) z = one/z; /* z = (1/|x|) */ + if(hx<0) { + if(yisint==1) + z = -z; /* (x<0)**odd = -(|x|**odd) */ + } + return z; + } + + float sn = one; /* s (sign of result -ve**odd) = -1 else = 1 */ + if(((((unsigned)hx>>31)-1)|(yisint-1))==0) + sn = -one; /* (-ve)**(odd int) */ + + /* |y| is huge */ + if(iy>0x08000000) { /* if |y| > 2**27 */ + /* over/underflow if x is not close to one */ + if(ix<0x3f7ffff8) return (y<0)? sn*huge*huge:tiny*tiny; + if(ix>0x3f800007) return (y>0)? sn*huge*huge: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*((float)0.333333333333-t*(float)0.25)); + 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|<sqrt(3/2) */ + else if(j<0x5db3d7) k=1; /* |x|<sqrt(3) */ + else {k=0;n+=1;ix -= 0x00800000;} + GEN_OCL_SET_FLOAT_WORD(ax,ix); + + /* compute s = 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]); + s = u*v; + s_h = s; + GEN_OCL_GET_FLOAT_WORD(is,s_h); + GEN_OCL_SET_FLOAT_WORD(s_h,is&0xfffff000); + + /* t_h=ax+bp[k] High */ + GEN_OCL_SET_FLOAT_WORD(t_h, (((ix>>1)|0x20000000)+0x00400000+(k<<21)) &0xfffff000); + 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 = (float)3.0+s2+r; + GEN_OCL_GET_FLOAT_WORD(is,t_h); + GEN_OCL_SET_FLOAT_WORD(t_h,is&0xffffe000); + t_l = r-((t_h-(float)3.0)-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&0xffffe000); + 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&0xffffe000); + t2 = z_l-(((t1-t)-dp_h[k])-z_h); + } + + /* split up y into y1+y2+y3 and compute (y1+y2+y3)*(t1+t2) */ + + float fy = (float)y; + float y3 = (float)(y-(int)fy); + GEN_OCL_GET_FLOAT_WORD(is,fy); + GEN_OCL_SET_FLOAT_WORD(y1,is&0xfffff000); + + p_l = (fy-y1)*t1 + y3*t1 + fy*t2 + y3*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; + + z -= n; + } + + t = z; + GEN_OCL_GET_FLOAT_WORD(is,t); + GEN_OCL_SET_FLOAT_WORD(t,is&0xfffff000); + 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; +} OVERLOADABLE float hypot(float x, float y) { if (__ocl_math_fastpath_flag) @@ -3392,11 +3610,20 @@ OVERLOADABLE float powr(float x, float y) { } OVERLOADABLE float pown(float x, int n) { - if (x == 0.f && n == 0) - return 1.f; - if (x < 0.f && (n&1) ) - return -powr(-x, n); - return powr(x, n); + if (__ocl_math_fastpath_flag) { + if (x == 0.f && n == 0) + return 1.f; + if (x < 0.f && (n&1) ) + return -powr(-x, n); + return powr(x, n); + } else { + int ix; + GEN_OCL_GET_FLOAT_WORD(ix, x); + float sign = ix < 0 ? -1.0f : 1.0f; + if (x == 0.0f) x = sign * 0.0f; + + return __gen_ocl_internal_pown(x, n); + } } OVERLOADABLE float pow(float x, float y) { -- 1.7.10.4 _______________________________________________ Beignet mailing list [email protected] http://lists.freedesktop.org/mailman/listinfo/beignet
