[Beignet] [PATCH 3/5] GBE: Improve atan precision

[Ruiling Song]

Signed-off-by: Ruiling Song <ruiling.song at intel.com>
---
 backend/src/ocl_stdlib.tmpl.h |   85 ++++++++++++++++++++++++++++++++---------
 1 file changed, 68 insertions(+), 17 deletions(-)

diff --git a/backend/src/ocl_stdlib.tmpl.h b/backend/src/ocl_stdlib.tmpl.h
index 24613cd..ecbca20 100755
--- a/backend/src/ocl_stdlib.tmpl.h
+++ b/backend/src/ocl_stdlib.tmpl.h
@@ -2330,24 +2330,75 @@ INLINE_OVERLOADABLE float __gen_ocl_internal_acospi(float x) {
   return __gen_ocl_internal_acos(x) / M_PI_F;
 }
 INLINE_OVERLOADABLE float __gen_ocl_internal_atan(float x) {
-  float a = 0, c = 1;
-  if (x <= -1) {
-    a = - M_PI_2_F;
-    x = 1 / x;
-    c = -1;
-  }
-  if (x >= 1) {
-    a = M_PI_2_F;
-    x = 1 / x;
-    c = -1;
-  }
-  a += c*x;
-  int i;
-  int sign;
-  for(i=3, sign=-1; i<63; i+=2, sign=-sign) {
-    a += c*sign*__gen_ocl_pow(x,i)/i;
+  /* copied from fdlibm */
+  float atanhi[4];
+  atanhi[0] = 4.6364760399e-01; /* atan(0.5)hi 0x3eed6338 */
+  atanhi[1] = 7.8539812565e-01; /* atan(1.0)hi 0x3f490fda */
+  atanhi[2] = 9.8279368877e-01; /* atan(1.5)hi 0x3f7b985e */
+  atanhi[3] = 1.5707962513e+00; /* atan(inf)hi 0x3fc90fda */
+
+  float atanlo[4];
+  atanlo[0] = 5.0121582440e-09; /* atan(0.5)lo 0x31ac3769 */
+  atanlo[1] =  3.7748947079e-08; /* atan(1.0)lo 0x33222168 */
+  atanlo[2] =  3.4473217170e-08; /* atan(1.5)lo 0x33140fb4 */
+  atanlo[3] =  7.5497894159e-08; /* atan(inf)lo 0x33a22168 */
+
+  float aT[11];
+  aT[0] = 3.3333334327e-01; /* 0x3eaaaaaa */
+  aT[1] =  -2.0000000298e-01; /* 0xbe4ccccd */
+  aT[2] =   1.4285714924e-01; /* 0x3e124925 */
+  aT[3] =  -1.1111110449e-01; /* 0xbde38e38 */
+  aT[4] =   9.0908870101e-02; /* 0x3dba2e6e */
+  aT[5] =  -7.6918758452e-02; /* 0xbd9d8795 */
+  aT[6] =   6.6610731184e-02; /* 0x3d886b35 */
+  aT[7] =  -5.8335702866e-02; /* 0xbd6ef16b */
+  aT[8] =   4.9768779427e-02; /* 0x3d4bda59 */
+  aT[9] =  -3.6531571299e-02; /* 0xbd15a221 */
+  aT[10] =   1.6285819933e-02; /* 0x3c8569d7 */
+  const float one = 1.0, huge = 1.0e30;
+
+  float w,s1,s2,z;
+  int ix,hx,id;
+
+  GEN_OCL_GET_FLOAT_WORD(hx,x);
+  ix = hx&0x7fffffff;
+  if(ix>=0x50800000) {  /* if |x| >= 2^34 */
+      if(ix>0x7f800000)
+    return x+x;   /* NaN */
+      if(hx>0) return  atanhi[3]+atanlo[3];
+      else     return -atanhi[3]-atanlo[3];
+  } if (ix < 0x3ee00000) {  /* |x| < 0.4375 */
+      if (ix < 0x31000000) {  /* |x| < 2^-29 */
+    if(huge+x>one) return x;  /* raise inexact */
+      }
+      id = -1;
+  } else {
+  x = __gen_ocl_fabs(x);
+  if (ix < 0x3f980000) {    /* |x| < 1.1875 */
+      if (ix < 0x3f300000) {  /* 7/16 <=|x|<11/16 */
+    id = 0; x = ((float)2.0*x-one)/((float)2.0+x);
+      } else {      /* 11/16<=|x|< 19/16 */
+    id = 1; x  = (x-one)/(x+one);
+      }
+  } else {
+      if (ix < 0x401c0000) {  /* |x| < 2.4375 */
+    id = 2; x  = (x-(float)1.5)/(one+(float)1.5*x);
+      } else {      /* 2.4375 <= |x| < 2^66 */
+    id = 3; x  = -(float)1.0/x;
+      }
+  }}
+    /* end of argument reduction */
+  z = x*x;
+  w = z*z;
+    /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
+  s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
+  s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
+  if (id<0) return x - x*(s1+s2);
+  else {
+      z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
+      return (hx<0)? -z:z;
   }
-  return a;
+
 }
 INLINE_OVERLOADABLE float __gen_ocl_internal_atanpi(float x) {
   return __gen_ocl_internal_atan(x) / M_PI_F;
-- 
1.7.9.5