[Beignet] [PATCH 4/5] GBE: Improve precision of atan2

[Ruiling Song]

Signed-off-by: Ruiling Song <ruiling.song at intel.com>
---
 backend/src/ocl_stdlib.tmpl.h |   95 +++++++++++++++++++++++++++++++++--------
 1 file changed, 78 insertions(+), 17 deletions(-)

diff --git a/backend/src/ocl_stdlib.tmpl.h b/backend/src/ocl_stdlib.tmpl.h
index ecbca20..ca53ab8 100755
--- a/backend/src/ocl_stdlib.tmpl.h
+++ b/backend/src/ocl_stdlib.tmpl.h
@@ -2414,25 +2414,86 @@ INLINE_OVERLOADABLE float __gen_ocl_internal_erfc(float x) {
 #define sqrt native_sqrt
 INLINE_OVERLOADABLE float rsqrt(float x) { return native_rsqrt(x); }
 INLINE_OVERLOADABLE float __gen_ocl_internal_atan2(float y, float x) {
-  uint hx = *(uint *)(&x), ix = hx & 0x7FFFFFFF;
-  uint hy = *(uint *)(&y), iy = hy & 0x7FFFFFFF;
-  if (ix > 0x7F800000 || iy > 0x7F800000)
-    return nan(0u);
-  if (ix == 0) {
-    if (y > 0)
-      return M_PI_2_F;
-    if (y < 0)
-      return - M_PI_2_F;
-    return nan(0u);
-  } else {
-    float z = __gen_ocl_internal_atan(y / x);
-    if (x > 0)
-      return z;
-    if (y >= 0)
-      return M_PI_F + z;
-    return - M_PI_F + z;
+  /* copied from fdlibm */
+  float z;
+  int k,m,hx,hy,ix,iy;
+  const float
+  tiny  = 1.0e-30,
+  zero  = 0.0,
+  pi_o_4  = 7.8539818525e-01, /* 0x3f490fdb */
+  pi_o_2  = 1.5707963705e+00, /* 0x3fc90fdb */
+  pi      = 3.1415927410e+00, /* 0x40490fdb */
+  pi_lo   = -8.7422776573e-08; /* 0xb3bbbd2e */
+
+  GEN_OCL_GET_FLOAT_WORD(hx,x);
+  ix = hx&0x7fffffff;
+  GEN_OCL_GET_FLOAT_WORD(hy,y);
+  iy = hy&0x7fffffff;
+
+  if((ix>0x7f800000)||
+     (iy>0x7f800000)) /* x or y is NaN */
+     return x+y;
+  if(hx==0x3f800000) return z=__gen_ocl_internal_atan(y);   /* x=1.0 */
+  m = ((hy>>31)&1)|((hx>>30)&2);  /* 2*sign(x)+sign(y) */
+
+    /* when y = 0 */
+  if(iy==0) {
+      switch(m) {
+    case 0:
+    case 1: return y;   /* atan(+-0,+anything)=+-0 */
+    case 2: return  pi+tiny;/* atan(+0,-anything) = pi */
+    case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
+      }
+  }
+    /* when x = 0 */
+  if(ix==0) return (hy<0)?  -pi_o_2-tiny: pi_o_2+tiny;
+
+  /* both are denorms. Gen does not support denorm, so we convert to normal float number*/
+  if(ix <= 0x7fffff && iy <= 0x7fffff) {
+    x = (float)(ix) * (1.0f - ((hx>>30) & 0x2));
+    y = (float)(iy) * (1.0f - ((hy>>30) & 0x2));
+  }
+
+    /* when x is INF */
+  if(ix==0x7f800000) {
+      if(iy==0x7f800000) {
+    switch(m) {
+        case 0: return  pi_o_4+tiny;/* atan(+INF,+INF) */
+        case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
+        case 2: return  (float)3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
+        case 3: return (float)-3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
+    }
+      } else {
+    switch(m) {
+        case 0: return  zero  ; /* atan(+...,+INF) */
+        case 1: return -zero  ; /* atan(-...,+INF) */
+        case 2: return  pi+tiny  ;  /* atan(+...,-INF) */
+        case 3: return -pi-tiny  ;  /* atan(-...,-INF) */
+    }
+      }
+  }
+    /* when y is INF */
+  if(iy==0x7f800000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
+
+    /* compute y/x */
+  k = (iy-ix)>>23;
+  if(k > 60) z=pi_o_2+(float)0.5*pi_lo;   /* |y/x| >  2**60 */
+  else if(hx<0&&k<-60) z=0.0;   /* |y|/x < -2**60 */
+  else z=__gen_ocl_internal_atan(__gen_ocl_fabs(y/x)); /* safe to do y/x */
+  switch (m) {
+      case 0: return       z  ; /* atan(+,+) */
+      case 1: {
+              uint zh;
+          GEN_OCL_GET_FLOAT_WORD(zh,z);
+          GEN_OCL_SET_FLOAT_WORD(z,zh ^ 0x80000000);
+        }
+        return       z  ; /* atan(-,+) */
+      case 2: return  pi-(z-pi_lo);/* atan(+,-) */
+      default: /* case 3 */
+            return  (z-pi_lo)-pi;/* atan(-,-) */
   }
 }
+
 INLINE_OVERLOADABLE float __gen_ocl_internal_atan2pi(float y, float x) {
   uint ix = as_uint(x), iy = as_uint(y),
        pos_zero = 0, neg_zero = 0x80000000u,
-- 
1.7.9.5