Nice patch, now on my ivb machine strict mode luxmark on SALA scene could get more than 92% of the non-strict mode.
Just pushed, Thanks. On Wed, Jan 07, 2015 at 01:33:01PM +0800, Ruiling Song wrote: > Previous version was ported from msun which derived from fdlibm, > which is good for cpu, with lots of if-condition check to try to > optimize for different input data. But it is really bad for gpu. > So I reimplement these functions based on well-known payne & Hanek's > algorithm. > > Compared with previous version, it could reduce the static ASM > instruction number of sin/cos from about 1700 to 400. > > Signed-off-by: Ruiling Song <[email protected]> > --- > backend/src/libocl/tmpl/ocl_math.tmpl.cl | 550 > ++++++++++-------------------- > 1 file changed, 172 insertions(+), 378 deletions(-) > > diff --git a/backend/src/libocl/tmpl/ocl_math.tmpl.cl > b/backend/src/libocl/tmpl/ocl_math.tmpl.cl > index ed26b3c..82636f5 100644 > --- a/backend/src/libocl/tmpl/ocl_math.tmpl.cl > +++ b/backend/src/libocl/tmpl/ocl_math.tmpl.cl > @@ -19,6 +19,7 @@ > #include "ocl_float.h" > #include "ocl_relational.h" > #include "ocl_common.h" > +#include "ocl_integer.h" > > constant int __ocl_math_fastpath_flag = 1; > > @@ -399,340 +400,161 @@ float __gen_ocl_scalbnf (float x, int n){ > return x*twom25; > } > > - > -__constant const float PIo2[] = { > - 1.5703125000e+00, /* 0x3fc90000 */ > - 4.5776367188e-04, /* 0x39f00000 */ > - 2.5987625122e-05, /* 0x37da0000 */ > - 7.5437128544e-08, /* 0x33a20000 */ > - 6.0026650317e-11, /* 0x2e840000 */ > - 7.3896444519e-13, /* 0x2b500000 */ > - 5.3845816694e-15, /* 0x27c20000 */ > - 5.6378512969e-18, /* 0x22d00000 */ > - 8.3009228831e-20, /* 0x1fc40000 */ > - 3.2756352257e-22, /* 0x1bc60000 */ > - 6.3331015649e-25, /* 0x17440000 */ > +const __constant unsigned int two_over_pi[] = { > +0, 0, 0xA2F, 0x983, 0x6E4, 0xe44, 0x152, 0x9FC, > +0x275, 0x7D1, 0xF53, 0x4DD, 0xC0D, 0xB62, > +0x959, 0x93C, 0x439, 0x041, 0xFE5, 0x163, > }; > > +// The main idea is from "Radian Reduction for Trigonometric Functions" > +// written by Mary H. Payne and Robert N. Hanek. Also another reference > +// is "A Continued-Fraction Analysis of Trigonometric Argument Reduction" > +// written by Roger Alan Smith, who gave the worst case in this paper. > +// for single float, worst x = 0x1.47d0fep34, and there are 29 bit > +// leading zeros in the fraction part of x*(2.0/pi). so we need at least > +// 29 (leading zero)+ 24 (fraction )+12 (integer) + guard bits. that is, > +// 65 + guard bits, as we calculate in 12*7 = 84bits, which means we have > +// about 19 guard bits. If we need further precision, we may need more > +// guard bits > +// Note we place two 0 in two_over_pi, which is used to handle input less > +// than 0x1.0p23 > + > +int payne_hanek(float x, float *y) { > + union { float f; unsigned u;} ieee; > + ieee.f = x; > + unsigned u = ieee.u; > + int k = ((u & 0x7f800000) >> 23)-127; > + int ma = (u & 0x7fffff) | 0x800000; > + unsigned high, low; > + high = (ma & 0xfff000) >> 12; > + low = ma & 0xfff; > + > + // Two tune below macro, you need to fully understand the algorithm > +#define CALC_BLOCKS 7 > +#define ZERO_BITS 2 > > -int __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const > __constant int *ipio2) > -{ > - /* copied from fdlibm */ > -const float > -zero = 0.0, > -one = 1.0, > -two8 = 2.5600000000e+02, /* 0x43800000 */ > -twon8 = 3.9062500000e-03; /* 0x3b800000 */ > - > - int init_jk[3]; /* initial value for jk */ > - int jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih; > - float z,fw,f[20],fq[20],q[20]; > - init_jk[0] = 4; init_jk[1] = 7; init_jk[2] = 9; > - /* initialize jk*/ > - jk = init_jk[prec]; > - jp = jk; > - > - /* determine jx,jv,q0, note that 3>q0 */ > - jx = nx-1; > - jv = (e0-3)/8; if(jv<0) jv=0; > - q0 = e0-8*(jv+1); > - > - /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */ > - j = jv-jx; m = jx+jk; > - for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j]; > - > - /* compute q[0],q[1],...q[jk] */ > - for (i=0;i<=jk;i++) { > - for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw; > - } > - > - jz = jk; > -recompute: > - /* distill q[] into iq[] reversingly */ > - for(i=0,j=jz,z=q[jz];j>0;i++,j--) { > - fw = (float)((int)(twon8* z)); > - iq[i] = (int)(z-two8*fw); > - z = q[j-1]+fw; > - } > - > - /* compute n */ > - z = __gen_ocl_scalbnf(z,q0); /* actual value of z */ > - z -= (float)8.0*__gen_ocl_internal_floor(z*(float)0.125); /* trim off > integer >= 8 */ > - n = (int) z; > - z -= (float)n; > - ih = 0; > - if(q0>0) { /* need iq[jz-1] to determine n */ > - i = (iq[jz-1]>>(8-q0)); n += i; > - iq[jz-1] -= i<<(8-q0); > - ih = iq[jz-1]>>(7-q0); > - } > - else if(q0==0) ih = iq[jz-1]>>8; > - else if(z>=(float)0.5) ih=2; > - > - if(ih>0) { /* q > 0.5 */ > - n += 1; carry = 0; > - for(i=0;i<jz ;i++) { /* compute 1-q */ > - j = iq[i]; > - if(carry==0) { > - if(j!=0) { > - carry = 1; iq[i] = 0x100- j; > - } > - } else iq[i] = 0xff - j; > - } > - if(q0>0) { /* rare case: chance is 1 in 12 */ > - switch(q0) { > - case 1: > - iq[jz-1] &= 0x7f; break; > - case 2: > - iq[jz-1] &= 0x3f; break; > - } > - } > - if(ih==2) { > - z = one - z; > - if(carry!=0) z -= __gen_ocl_scalbnf(one,q0); > - } > - } > + unsigned result[CALC_BLOCKS]; > > - /* check if recomputation is needed */ > - if(z==zero) { > - j = 0; > - for (i=jz-1;i>=jk;i--) j |= iq[i]; > - if(j==0) { /* need recomputation */ > - for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */ > + // round down, note we need 2 bits integer precision > + int index = (k-23-2) < 0 ? (k-23-2-11)/12 : (k-23-2)/12; > > - for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */ > - f[jx+i] = (float) ipio2[jv+i]; > - for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; > - q[i] = fw; > - } > - jz += k; > - goto recompute; > - } > + for (int i = 0; i < CALC_BLOCKS; i++) { > + result[i] = low * two_over_pi[index+i+ZERO_BITS] ; > + result[i] += high * two_over_pi[index+i+1+ZERO_BITS]; > } > > - /* chop off zero terms */ > - if(z==(float)0.0) { > - jz -= 1; q0 -= 8; > - while(iq[jz]==0) { jz--; q0-=8;} > - } else { /* break z into 8-bit if necessary */ > - z = __gen_ocl_scalbnf(z,-q0); > - if(z>=two8) { > - fw = (float)((int)(twon8*z)); > - iq[jz] = (int)(z-two8*fw); > - jz += 1; q0 += 8; > - iq[jz] = (int) fw; > - } else iq[jz] = (int) z ; > + for (int i = CALC_BLOCKS-1; i > 0; i--) { > + int temp = result[i] >> 12; > + result[i] -= temp << 12; > + result[i-1] += temp; > } > +#undef CALC_BLOCKS > +#undef ZERO_BITS > > - /* convert integer "bit" chunk to floating-point value */ > - fw = __gen_ocl_scalbnf(one,q0); > - for(i=jz;i>=0;i--) { > - q[i] = fw*(float)iq[i]; fw*=twon8; > - } > + // get number of integer digits in result[0], note we only consider 12 > valid bits > + // and also it means the fraction digits in result[0] is (12-intDigit) > > - /* compute PIo2[0,...,jp]*q[jz,...,0] */ > - for(i=jz;i>=0;i--) { > - for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k]; > - fq[jz-i] = fw; > - } > + int intDigit = index*(-12) + (k-23); > > - /* compress fq[] into y[] */ > - switch(prec) { > - case 0: > - fw = 0.0; > - for (i=jz;i>=0;i--) fw += fq[i]; > - y[0] = (ih==0)? fw: -fw; > - break; > - case 1: > - case 2: > - fw = 0.0; > - for (i=jz;i>=0;i--) fw += fq[i]; > - y[0] = (ih==0)? fw: -fw; > - fw = fq[0]-fw; > - for (i=1;i<=jz;i++) fw += fq[i]; > - y[1] = (ih==0)? fw: -fw; > - break; > - case 3: /* painful */ > - for (i=jz;i>0;i--) { > - fw = fq[i-1]+fq[i]; > - fq[i] += fq[i-1]-fw; > - fq[i-1] = fw; > - } > - for (i=jz;i>1;i--) { > - fw = fq[i-1]+fq[i]; > - fq[i] += fq[i-1]-fw; > - fq[i-1] = fw; > - } > - for (fw=0.0,i=jz;i>=2;i--) fw += fq[i]; > - if(ih==0) { > - y[0] = fq[0]; y[1] = fq[1]; y[2] = fw; > - } else { > - y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw; > - } > - } > - return n&7; > + // As the integer bits may be all included in result[0], and also maybe > + // some bits in result[0], and some in result[1]. So we merge succesive > bits, > + // which makes easy coding. > > + unsigned b0 = (result[0] << 12) | result[1]; > + unsigned b1 = (result[2] << 12) | result[3]; > + unsigned b2 = (result[4] << 12) | result[5]; > + unsigned b3 = (result[6] << 12); > + > + unsigned intPart = b0 >> (24-intDigit); > + > + unsigned fract1 = ((b0 << intDigit) | (b1 >> (24-intDigit))) & 0xffffff; > + unsigned fract2 = ((b1 << intDigit) | (b2 >> (24-intDigit))) & 0xffffff; > + unsigned fract3 = ((b2 << intDigit) | (b3 >> (24-intDigit))) & 0xffffff; > + > + // larger than 0.5? which mean larger than pi/4, we need > + // transform from [0,pi/2] to [-pi/4, pi/4] through -(1.0-fract) > + int largerPiBy4 = ((fract1 & 0x800000) != 0); > + int sign = largerPiBy4 ? 1 : 0; > + intPart = largerPiBy4 ? (intPart+1) : intPart; > + > + fract1 = largerPiBy4 ? (fract1 ^ 0x00ffffff) : fract1; > + fract2 = largerPiBy4 ? (fract2 ^ 0x00ffffff) : fract2; > + fract3 = largerPiBy4 ? (fract3 ^ 0x00ffffff) : fract3; > + > + int leadingZero = (fract1 == 0); > + > + // +1 is for the hidden bit 1 in floating-point format > + int exponent = leadingZero ? -(24+1) : -(0+1); > + > + fract1 = leadingZero ? fract2 : fract1; > + fract2 = leadingZero ? fract3 : fract2; > + > + // fract1 may have leading zeros, add it > + int shift = clz(fract1)-8; > + exponent += -shift; > + > + float pio2 = 0x1.921fb6p+0; > + unsigned fdigit = ((fract1 << shift) | (fract2 >> (24-shift))) & 0xffffff; > + > + // we know that denormal number will not appear here > + ieee.u = (sign << 31) | ((exponent+127) << 23) | (fdigit & 0x7fffff); > + *y = ieee.f * pio2; > + return intPart; > } > > -__constant const int npio2_hw[32] = { > -0x3fc90f00, 0x40490f00, 0x4096cb00, 0x40c90f00, 0x40fb5300, 0x4116cb00, > -0x412fed00, 0x41490f00, 0x41623100, 0x417b5300, 0x418a3a00, 0x4196cb00, > -0x41a35c00, 0x41afed00, 0x41bc7e00, 0x41c90f00, 0x41d5a000, 0x41e23100, > -0x41eec200, 0x41fb5300, 0x4203f200, 0x420a3a00, 0x42108300, 0x4216cb00, > -0x421d1400, 0x42235c00, 0x4229a500, 0x422fed00, 0x42363600, 0x423c7e00, > -0x4242c700, 0x42490f00 > -}; > +int argumentReduceSmall(float x, float * remainder) { > + union { > + float f; > + unsigned u; > + } ieee; > > -__constant const int two_over_pi[22*9] = { > -0xA2, 0xF9, 0x83, 0x6E, 0x4E, 0x44, 0x15, 0x29, 0xFC, > -0x27, 0x57, 0xD1, 0xF5, 0x34, 0xDD, 0xC0, 0xDB, 0x62, > -0x95, 0x99, 0x3C, 0x43, 0x90, 0x41, 0xFE, 0x51, 0x63, > -0xAB, 0xDE, 0xBB, 0xC5, 0x61, 0xB7, 0x24, 0x6E, 0x3A, > -0x42, 0x4D, 0xD2, 0xE0, 0x06, 0x49, 0x2E, 0xEA, 0x09, > -0xD1, 0x92, 0x1C, 0xFE, 0x1D, 0xEB, 0x1C, 0xB1, 0x29, > -0xA7, 0x3E, 0xE8, 0x82, 0x35, 0xF5, 0x2E, 0xBB, 0x44, > -0x84, 0xE9, 0x9C, 0x70, 0x26, 0xB4, 0x5F, 0x7E, 0x41, > -0x39, 0x91, 0xD6, 0x39, 0x83, 0x53, 0x39, 0xF4, 0x9C, > -0x84, 0x5F, 0x8B, 0xBD, 0xF9, 0x28, 0x3B, 0x1F, 0xF8, > -0x97, 0xFF, 0xDE, 0x05, 0x98, 0x0F, 0xEF, 0x2F, 0x11, > -0x8B, 0x5A, 0x0A, 0x6D, 0x1F, 0x6D, 0x36, 0x7E, 0xCF, > -0x27, 0xCB, 0x09, 0xB7, 0x4F, 0x46, 0x3F, 0x66, 0x9E, > -0x5F, 0xEA, 0x2D, 0x75, 0x27, 0xBA, 0xC7, 0xEB, 0xE5, > -0xF1, 0x7B, 0x3D, 0x07, 0x39, 0xF7, 0x8A, 0x52, 0x92, > -0xEA, 0x6B, 0xFB, 0x5F, 0xB1, 0x1F, 0x8D, 0x5D, 0x08, > -0x56, 0x03, 0x30, 0x46, 0xFC, 0x7B, 0x6B, 0xAB, 0xF0, > -0xCF, 0xBC, 0x20, 0x9A, 0xF4, 0x36, 0x1D, 0xA9, 0xE3, > -0x91, 0x61, 0x5E, 0xE6, 0x1B, 0x08, 0x65, 0x99, 0x85, > -0x5F, 0x14, 0xA0, 0x68, 0x40, 0x8D, 0xFF, 0xD8, 0x80, > -0x4D, 0x73, 0x27, 0x31, 0x06, 0x06, 0x15, 0x56, 0xCA, > -0x73, 0xA8, 0xC9, 0x60, 0xE2, 0x7B, 0xC0, 0x8C, 0x6B, > -}; > + float twoByPi = 2.0f/3.14159265f; > + float piBy2_1h = (float) 0xc90/0x1.0p11, > + piBy2_1l = (float) 0xfda/0x1.0p23, > + piBy2_2h = (float) 0xa22/0x1.0p35, > + piBy2_2l = (float) 0x168/0x1.0p47, > + piBy2_3h = (float) 0xc23/0x1.0p59, > + piBy2_3l = (float) 0x4c4/0x1.0p71; > > + float y = (float)(int)(twoByPi * x + 0.5f); > + ieee.f = y; > + ieee.u = ieee.u & 0xfffff000; > > -int __ieee754_rem_pio2f(float x, float *y) { > - /* copied from fdlibm */ > - float z,w,t,r,fn; > - float tx[3]; > - > -const float half_value = 5.0000000e-1; > -const float zero = 0.0000000000; > -const float two8 = 2.5600000000e+02; > -const float invpio2 = 6.3661980629e-01; > -const float pio2_1 = 1.5707855225e+00; > -const float pio2_1t = 1.0804334124e-05; > -const float pio2_2 = 1.0804273188e-05; > -const float pio2_2t = 6.0770999344e-11; > -const float pio2_3 = 6.0770943833e-11; > -const float pio2_3t = 6.1232342629e-17; > - int e0,i,j,nx,n,ix,hx; > + float yh = ieee.f; > + float yl = y - yh; > + float rem = x - yh*piBy2_1h - yh*piBy2_1l - yl*piBy2_1h - yl*piBy2_1l; > + rem = rem - yh*piBy2_2h - yh*piBy2_2l + yl*piBy2_2h + yl*piBy2_2l; > + rem = rem - yh*piBy2_3h - yh*piBy2_3l - yl*piBy2_3h - yl*piBy2_3l; > > - GEN_OCL_GET_FLOAT_WORD(hx,x); > - ix = hx&0x7fffffff; > - if(ix<=0x3f490fd8) /* |x| ~<= pi/4 , no need for reduction */ > - {y[0] = x; y[1] = 0; return 0;} > - if(ix<0x4016cbe4) { /* |x| < 3pi/4, special case with n=+-1 */ > - if(hx>0) { > - z = x - pio2_1; > - if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */ > - y[0] = z - pio2_1t; > - y[1] = (z-y[0])-pio2_1t; > - } else { /* near pi/2, use 24+24+24 bit pi */ > - z -= pio2_2; > - y[0] = z - pio2_2t; > - y[1] = (z-y[0])-pio2_2t; > - } > - return 1; > - } else { /* negative x */ > - z = x + pio2_1; > - if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */ > - y[0] = z + pio2_1t; > - y[1] = (z-y[0])+pio2_1t; > - } else { /* near pi/2, use 24+24+24 bit pi */ > - z += pio2_2; > - y[0] = z + pio2_2t; > - y[1] = (z-y[0])+pio2_2t; > - } > - return -1; > - } > - } > - if(ix<=0x43490f80) { /* |x| ~<= 2^7*(pi/2), medium size */ > - t = __gen_ocl_fabs(x); > - n = (int) (t*invpio2+half_value); > - fn = (float)n; > - r = t-fn*pio2_1; > - w = fn*pio2_1t; /* 1st round good to 40 bit */ > - if(n<32&&(ix&0xffffff00)!=npio2_hw[n-1]) { > - y[0] = r-w; /* quick check no cancellation */ > - } else { > - uint high; > - j = ix>>23; > - y[0] = r-w; > - GEN_OCL_GET_FLOAT_WORD(high,y[0]); > - i = j-((high>>23)&0xff); > - if(i>8) { /* 2nd iteration needed, good to 57 */ > - t = r; > - w = fn*pio2_2; > - r = t-w; > - w = fn*pio2_2t-((t-r)-w); > - y[0] = r-w; > - GEN_OCL_GET_FLOAT_WORD(high,y[0]); > - i = j-((high>>23)&0xff); > - if(i>25) { /* 3rd iteration need, 74 bits acc */ > - t = r; /* will cover all possible cases */ > - w = fn*pio2_3; > - r = t-w; > - w = fn*pio2_3t-((t-r)-w); > - y[0] = r-w; > - } > - } > - } > - y[1] = (r-y[0])-w; > - if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} > - else return n; > - } > - /* > - * all other (large) arguments > - */ > - if(ix>=0x7f800000) { /* x is inf or NaN */ > - y[0]=y[1]=x-x; return 0; > - } > - /* set z = scalbn(|x|,ilogb(x)-7) */ > - e0 = (ix>>23)-134; /* e0 = ilogb(z)-7; */ > - GEN_OCL_SET_FLOAT_WORD(z, ix - ((int)(e0<<23))); > - for(i=0;i<2;i++) { > - tx[i] = (float)((int)(z)); > - z = (z-tx[i])*two8; > + *remainder = rem; > + return (int)y; > +} > + > + > +int __ieee754_rem_pio2f(float x, float *y) { > + if (x < 4000.0f) { > + return argumentReduceSmall(x, y); > + } else { > + return payne_hanek(x, y); > } > - tx[2] = z; > - nx = 3; > - while(tx[nx-1]==zero) nx--; /* skip zero term */ > - n = __kernel_rem_pio2f(tx,y,e0,nx,2,two_over_pi); > - if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} > - return n; > } > > -OVERLOADABLE float __kernel_sinf(float x, float y, int iy) > +OVERLOADABLE float __kernel_sinf(float x) > { > /* copied from fdlibm */ > -const float > -half_value = 5.0000000000e-01,/* 0x3f000000 */ > -S1 = -1.6666667163e-01, /* 0xbe2aaaab */ > -S2 = 8.3333337680e-03, /* 0x3c088889 */ > -S3 = -1.9841270114e-04, /* 0xb9500d01 */ > -S4 = 2.7557314297e-06, /* 0x3638ef1b */ > -S5 = -2.5050759689e-08, /* 0xb2d72f34 */ > -S6 = 1.5896910177e-10; /* 0x2f2ec9d3 */ > + const float > + half_value = 5.0000000000e-01,/* 0x3f000000 */ > + S1 = -1.6666667163e-01, /* 0xbe2aaaab */ > + S2 = 8.3333337680e-03, /* 0x3c088889 */ > + S3 = -1.9841270114e-04, /* 0xb9500d01 */ > + S4 = 2.7557314297e-06, /* 0x3638ef1b */ > + S5 = -2.5050759689e-08, /* 0xb2d72f34 */ > + S6 = 1.5896910177e-10; /* 0x2f2ec9d3 */ > float z,r,v; > - int ix; > - GEN_OCL_GET_FLOAT_WORD(ix,x); > - ix &= 0x7fffffff; /* high word of x */ > - if(ix<0x32000000) /* |x| < 2**-27 */ > - {if((int)x==0) return x;} /* generate inexact */ > z = x*x; > v = z*x; > r = S2+z*(S3+z*(S4+z*(S5+z*S6))); > - if(iy==0) return x+v*(S1+z*r); > - else return x-((z*(half_value*y-v*r)-y)-v*S1); > + return x+v*(S1+z*r); > } > > float __kernel_cosf(float x, float y) > @@ -746,19 +568,10 @@ float __kernel_cosf(float x, float y) > C4 = -2.7557314297e-07, /* 0xb493f27c */ > C5 = 2.0875723372e-09, /* 0x310f74f6 */ > C6 = -1.1359647598e-11; /* 0xad47d74e */ > - const float pio2_hi = 0x1.92p0, pio2_mid = 0x1.fb4p-12, pio2_low = > 0x1.4442d2p-24; > float a,hz,z,r,qx; > int ix; > GEN_OCL_GET_FLOAT_WORD(ix,x); > ix &= 0x7fffffff; /* ix = |x|'s high word*/ > - if(ix<0x32000000) { /* if x < 2**27 */ > - if(((int)x)==0) return one; /* generate inexact */ > - } > - > - if(x < 0.0f) { x= -x; y = -y; } > - if(ix > 0x3f490fdb) { /* |x|>pi/4*/ > - return -__kernel_sinf(x-pio2_hi-pio2_mid-pio2_low, y, 1); > - } > z = x*x; > r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6))))); > if(ix < 0x3e99999a) /* if |x| < 0.3 */ > @@ -775,29 +588,26 @@ OVERLOADABLE float sin(float x) { > if (__ocl_math_fastpath_flag) > return __gen_ocl_internal_fastpath_sin(x); > > - /* copied from fdlibm */ > - float y[2],z=0.0; > + float y,z=0.0; > int n, ix; > > + float negative = x < 0.0f? -1.0f : 1.0f; > + x = negative * x; > + > GEN_OCL_GET_FLOAT_WORD(ix,x); > > - /* |x| ~< pi/4 */ > ix &= 0x7fffffff; > - if(ix <= 0x3f490fd8) return __kernel_sinf(x,z,0); > > /* sin(Inf or NaN) is NaN */ > - else if (ix>=0x7f800000) return x-x; > + if (ix>=0x7f800000) return x-x; > > /* argument reduction needed */ > else { > - n = __ieee754_rem_pio2f(x,y); > - switch(n&3) { > - case 0: return __kernel_sinf(y[0],y[1],1); > - case 1: return __kernel_cosf(y[0],y[1]); > - case 2: return -__kernel_sinf(y[0],y[1],1); > - default: > - return -__kernel_cosf(y[0],y[1]); > - } > + n = __ieee754_rem_pio2f(x,&y); > + float s = __kernel_sinf(y); > + float c = __kernel_cosf(y,0.0f); > + float ret = (n&1) ? negative*c : negative*s; > + return (n&3)> 1? -1.0f*ret : ret; > } > } > > @@ -805,29 +615,32 @@ OVERLOADABLE float cos(float x) { > if (__ocl_math_fastpath_flag) > return __gen_ocl_internal_fastpath_cos(x); > > - /* copied from fdlibm */ > - float y[2],z=0.0; > + float y,z=0.0; > int n, ix; > - > + x = __gen_ocl_fabs(x); > GEN_OCL_GET_FLOAT_WORD(ix,x); > > - /* |x| ~< pi/4 */ > ix &= 0x7fffffff; > - if(ix <= 0x3f490fd8) return __kernel_cosf(x,z); > > /* cos(Inf or NaN) is NaN */ > - else if (ix>=0x7f800000) return x-x; > + if (ix>=0x7f800000) return x-x; > > /* argument reduction needed */ > else { > - n = __ieee754_rem_pio2f(x,y); > - switch(n&3) { > - case 0: return __kernel_cosf(y[0],y[1]); > - case 1: return -__kernel_sinf(y[0],y[1],1); > - case 2: return -__kernel_cosf(y[0],y[1]); > - default: > - return __kernel_sinf(y[0],y[1],1); > - } > + n = __ieee754_rem_pio2f(x,&y); > + n &= 3; > + float c = __kernel_cosf(y, 0.0f); > + float s = __kernel_sinf(y); > + float v = (n&1) ? s : c; > + /* n&3 return > + 0 cos(y) > + 1 -sin(y) > + 2 -cos(y) > + 3 sin(y) > + */ > + int mask = (n>>1) ^ n; > + float sign = (mask&1) ? -1.0f : 1.0f; > + return sign * v; > } > } > > @@ -908,46 +721,27 @@ float __kernel_tanf(float x, float y, int iy) > > OVERLOADABLE float tan(float x) > { > - > if (__ocl_math_fastpath_flag) > return __gen_ocl_internal_fastpath_tan(x); > > - /* copied from fdlibm */ > - const float pio2_hi = 0x1.92p-0, pio2_mid = 0x1.fb4p-12, pio2_low = > 0x1.4442d2p-24; > - const float pio4 = 7.8539812565e-01; > - float y[2],z=0.0; > - int n, ix; > + float y,z=0.0; > + int n, ix; > + float negative = x < 0.0f? -1.0f : 1.0f; > + x = negative * x; > > - GEN_OCL_GET_FLOAT_WORD(ix,x); > + GEN_OCL_GET_FLOAT_WORD(ix,x); > > - /* |x| ~< pi/4 */ > - ix &= 0x7fffffff; > - if(ix <= 0x3f490fda) return __kernel_tanf(x,z,1); > + ix &= 0x7fffffff; > > /* tan(Inf or NaN) is NaN */ > - else if (ix>=0x7f800000) return x-x; /* NaN */ > + if (ix>=0x7f800000) return x-x; /* NaN */ > > /* argument reduction needed */ > - else { > - n = __ieee754_rem_pio2f(x,y); > - > - x = y[0]; > - float m = y[1]; > - int iy = 1-((n&1)<<1); > - GEN_OCL_GET_FLOAT_WORD(ix,x); > - float sign = 1.0f; > - if(ix < 0) { > - x = -x; m = -m; > - sign = -1.0f; > - } > - > - if(x > pio4) {/* reduce x to less than pi/4 through (pi/2-x) */ > - float t = __kernel_tanf(pio2_hi-x+pio2_mid+pio2_low, -m, 1); > - if(iy == -1) return sign*(-t); else return sign*1/t; > - } else > - return __kernel_tanf(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even > + else { > + n = __ieee754_rem_pio2f(x,&y); > + return negative * __kernel_tanf(y,0.0f,1-((n&1)<<1)); /* 1 -- n even > -1 -- n odd */ > - } > + } > } > > OVERLOADABLE float __gen_ocl_internal_cospi(float x) { > @@ -967,13 +761,13 @@ OVERLOADABLE float __gen_ocl_internal_cospi(float x) { > return __kernel_cosf(m*M_PI_F, 0.0f); > case 1: > case 2: > - return __kernel_sinf((0.5f-m)*M_PI_F, 0.0f, 0); > + return __kernel_sinf((0.5f-m)*M_PI_F); > case 3: > case 4: > return -__kernel_cosf((m-1.0f)*M_PI_F, 0.0f); > case 5: > case 6: > - return __kernel_sinf((m-1.5f)*M_PI_F, 0.0f, 0); > + return __kernel_sinf((m-1.5f)*M_PI_F); > default: > return __kernel_cosf((2.0f-m)*M_PI_F, 0.0f); > } > @@ -994,18 +788,18 @@ OVERLOADABLE float __gen_ocl_internal_sinpi(float x) { > > switch(ix) { > case 0: > - return sign*__kernel_sinf(m*M_PI_F, 0.0f, 0); > + return sign*__kernel_sinf(m*M_PI_F); > case 1: > case 2: > return sign*__kernel_cosf((m-0.5f)*M_PI_F, 0.0f); > case 3: > case 4: > - return -sign*__kernel_sinf((m-1.0f)*M_PI_F, 0.0f, 0); > + return -sign*__kernel_sinf((m-1.0f)*M_PI_F); > case 5: > case 6: > return -sign*__kernel_cosf((m-1.5f)*M_PI_F, 0.0f); > default: > - return -sign*__kernel_sinf((2.0f-m)*M_PI_F, 0.0f, 0); > + return -sign*__kernel_sinf((2.0f-m)*M_PI_F); > } > > } > -- > 1.7.10.4 > > _______________________________________________ > Beignet mailing list > [email protected] > http://lists.freedesktop.org/mailman/listinfo/beignet _______________________________________________ Beignet mailing list [email protected] http://lists.freedesktop.org/mailman/listinfo/beignet
