[Beignet] [PATCH] libocl: Reimplement trigonometric functions.
Zhigang Gong
zhigang.gong at linux.intel.com
Wed Jan 7 00:22:24 PST 2015
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 <ruiling.song at intel.com>
> ---
> 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
>
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