Unify SSE/AVX psin functions.

It is based on the SSE version which is much more accurate, though very slightly slower.
This changeset also includes the following required changes:
 - add packet-float to packet-int type traits
 - add packet float<->int reinterpret casts
 - add faster pselect for AVX based on blendv

3 files changed, 47 insertions, 64 deletions

diff --git a/Eigen/src/Core/arch/AVX/MathFunctions.h b/Eigen/src/Core/arch/AVX/MathFunctions.h
index 42758fe07..4666ccc42 100644
--- a/Eigen/src/Core/arch/AVX/MathFunctions.h
+++ b/Eigen/src/Core/arch/AVX/MathFunctions.h
@@ -36,67 +36,7 @@ inline Packet8i pshiftleft(Packet8i v, int n)
 template <>
 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8f
 psin<Packet8f>(const Packet8f& _x) {
-  Packet8f x = _x;
-
-  // Some useful values.
-  _EIGEN_DECLARE_CONST_Packet8i(one, 1);
-  _EIGEN_DECLARE_CONST_Packet8f(one, 1.0f);
-  _EIGEN_DECLARE_CONST_Packet8f(two, 2.0f);
-  _EIGEN_DECLARE_CONST_Packet8f(one_over_four, 0.25f);
-  _EIGEN_DECLARE_CONST_Packet8f(one_over_pi, 3.183098861837907e-01f);
-  _EIGEN_DECLARE_CONST_Packet8f(neg_pi_first, -3.140625000000000e+00f);
-  _EIGEN_DECLARE_CONST_Packet8f(neg_pi_second, -9.670257568359375e-04f);
-  _EIGEN_DECLARE_CONST_Packet8f(neg_pi_third, -6.278329571784980e-07f);
-  _EIGEN_DECLARE_CONST_Packet8f(four_over_pi, 1.273239544735163e+00f);
-
-  // Map x from [-Pi/4,3*Pi/4] to z in [-1,3] and subtract the shifted period.
-  Packet8f z = pmul(x, p8f_one_over_pi);
-  Packet8f shift = _mm256_floor_ps(padd(z, p8f_one_over_four));
-  x = pmadd(shift, p8f_neg_pi_first, x);
-  x = pmadd(shift, p8f_neg_pi_second, x);
-  x = pmadd(shift, p8f_neg_pi_third, x);
-  z = pmul(x, p8f_four_over_pi);
-
-  // Make a mask for the entries that need flipping, i.e. wherever the shift
-  // is odd.
-  Packet8i shift_ints = _mm256_cvtps_epi32(shift);
-  Packet8i shift_isodd = _mm256_castps_si256(_mm256_and_ps(_mm256_castsi256_ps(shift_ints), _mm256_castsi256_ps(p8i_one)));
-  Packet8i sign_flip_mask = pshiftleft(shift_isodd, 31);
-
-  // Create a mask for which interpolant to use, i.e. if z > 1, then the mask
-  // is set to ones for that entry.
-  Packet8f ival_mask = _mm256_cmp_ps(z, p8f_one, _CMP_GT_OQ);
-
-  // Evaluate the polynomial for the interval [1,3] in z.
-  _EIGEN_DECLARE_CONST_Packet8f(coeff_right_0, 9.999999724233232e-01f);
-  _EIGEN_DECLARE_CONST_Packet8f(coeff_right_2, -3.084242535619928e-01f);
-  _EIGEN_DECLARE_CONST_Packet8f(coeff_right_4, 1.584991525700324e-02f);
-  _EIGEN_DECLARE_CONST_Packet8f(coeff_right_6, -3.188805084631342e-04f);
-  Packet8f z_minus_two = psub(z, p8f_two);
-  Packet8f z_minus_two2 = pmul(z_minus_two, z_minus_two);
-  Packet8f right = pmadd(p8f_coeff_right_6, z_minus_two2, p8f_coeff_right_4);
-  right = pmadd(right, z_minus_two2, p8f_coeff_right_2);
-  right = pmadd(right, z_minus_two2, p8f_coeff_right_0);
-
-  // Evaluate the polynomial for the interval [-1,1] in z.
-  _EIGEN_DECLARE_CONST_Packet8f(coeff_left_1, 7.853981525427295e-01f);
-  _EIGEN_DECLARE_CONST_Packet8f(coeff_left_3, -8.074536727092352e-02f);
-  _EIGEN_DECLARE_CONST_Packet8f(coeff_left_5, 2.489871967827018e-03f);
-  _EIGEN_DECLARE_CONST_Packet8f(coeff_left_7, -3.587725841214251e-05f);
-  Packet8f z2 = pmul(z, z);
-  Packet8f left = pmadd(p8f_coeff_left_7, z2, p8f_coeff_left_5);
-  left = pmadd(left, z2, p8f_coeff_left_3);
-  left = pmadd(left, z2, p8f_coeff_left_1);
-  left = pmul(left, z);
-
-  // Assemble the results, i.e. select the left and right polynomials.
-  left = _mm256_andnot_ps(ival_mask, left);
-  right = _mm256_and_ps(ival_mask, right);
-  Packet8f res = _mm256_or_ps(left, right);
-
-  // Flip the sign on the odd intervals and return the result.
-  res = _mm256_xor_ps(res, _mm256_castsi256_ps(sign_flip_mask));
-  return res;
+  return psin_float(_x);
 }
 
 template <>
diff --git a/Eigen/src/Core/arch/AVX/PacketMath.h b/Eigen/src/Core/arch/AVX/PacketMath.h
index a415f2f1b..0e1044aba 100644
--- a/Eigen/src/Core/arch/AVX/PacketMath.h
+++ b/Eigen/src/Core/arch/AVX/PacketMath.h
@@ -113,8 +113,17 @@ template<> struct packet_traits<int>    : default_packet_traits
 };
 */
 
-template<> struct unpacket_traits<Packet8f> { typedef float  type; typedef Packet4f half; enum {size=8, alignment=Aligned32}; };
-template<> struct unpacket_traits<Packet4d> { typedef double type; typedef Packet2d half; enum {size=4, alignment=Aligned32}; };
+template<> struct unpacket_traits<Packet8f> {
+  typedef float     type;
+  typedef Packet4f  half;
+  typedef Packet8i  integer_packet;
+  enum {size=8, alignment=Aligned32};
+};
+template<> struct unpacket_traits<Packet4d> {
+  typedef double type;
+  typedef Packet2d half;
+  enum {size=4, alignment=Aligned32};
+};
 template<> struct unpacket_traits<Packet8i> { typedef int    type; typedef Packet4i half; enum {size=8, alignment=Aligned32}; };
 
 template<> EIGEN_STRONG_INLINE Packet8f pset1<Packet8f>(const float&  from) { return _mm256_set1_ps(from); }
@@ -125,6 +134,7 @@ template<> EIGEN_STRONG_INLINE Packet8f pset1frombits<Packet8f>(unsigned int fro
 
 template<> EIGEN_STRONG_INLINE Packet8f pzero(const Packet8f& /*a*/) { return _mm256_setzero_ps(); }
 template<> EIGEN_STRONG_INLINE Packet4d pzero(const Packet4d& /*a*/) { return _mm256_setzero_pd(); }
+template<> EIGEN_STRONG_INLINE Packet8i pzero(const Packet8i& /*a*/) { return _mm256_setzero_si256(); }
 
 template<> EIGEN_STRONG_INLINE Packet8f pload1<Packet8f>(const float*  from) { return _mm256_broadcast_ss(from); }
 template<> EIGEN_STRONG_INLINE Packet4d pload1<Packet4d>(const double* from) { return _mm256_broadcast_sd(from); }
@@ -210,6 +220,16 @@ template<> EIGEN_STRONG_INLINE Packet8f pcmp_lt(const Packet8f& a, const Packet8
 template<> EIGEN_STRONG_INLINE Packet8f pcmp_eq(const Packet8f& a, const Packet8f& b) { return _mm256_cmp_ps(a,b,_CMP_EQ_OQ); }
 template<> EIGEN_STRONG_INLINE Packet8f pcmp_lt_or_nan(const Packet8f& a, const Packet8f& b) { return _mm256_cmp_ps(a, b, _CMP_NGE_UQ); }
 
+template<> EIGEN_STRONG_INLINE Packet8i pcmp_eq(const Packet8i& a, const Packet8i& b) {
+#ifdef EIGEN_VECTORIZE_AVX2
+  return _mm256_cmpeq_epi32(a,b);
+#else
+  __m128i lo = _mm_cmpeq_epi32(_mm256_extractf128_si256(a, 0), _mm256_extractf128_si256(b, 0));
+  __m128i hi = _mm_cmpeq_epi32(_mm256_extractf128_si256(a, 1), _mm256_extractf128_si256(b, 1));
+  return _mm256_insertf128_si256(_mm256_castsi128_si256(lo), (hi), 1);
+#endif
+}
+
 template<> EIGEN_STRONG_INLINE Packet8f pround<Packet8f>(const Packet8f& a) { return _mm256_round_ps(a, _MM_FROUND_CUR_DIRECTION); }
 template<> EIGEN_STRONG_INLINE Packet4d pround<Packet4d>(const Packet4d& a) { return _mm256_round_pd(a, _MM_FROUND_CUR_DIRECTION); }
 
@@ -231,6 +251,21 @@ template<> EIGEN_STRONG_INLINE Packet4d pxor<Packet4d>(const Packet4d& a, const
 template<> EIGEN_STRONG_INLINE Packet8f pandnot<Packet8f>(const Packet8f& a, const Packet8f& b) { return _mm256_andnot_ps(b,a); }
 template<> EIGEN_STRONG_INLINE Packet4d pandnot<Packet4d>(const Packet4d& a, const Packet4d& b) { return _mm256_andnot_pd(b,a); }
 
+template<> EIGEN_STRONG_INLINE Packet8f pselect<Packet8f>(const Packet8f& mask, const Packet8f& a, const Packet8f& b)
+{ return _mm256_blendv_ps(b,a,mask); }
+template<> EIGEN_STRONG_INLINE Packet4d pselect<Packet4d>(const Packet4d& mask, const Packet4d& a, const Packet4d& b)
+{ return _mm256_blendv_pd(b,a,mask); }
+
+template<> EIGEN_STRONG_INLINE Packet8i pshiftleft<Packet8i>(const Packet8i& a, int n) {
+#ifdef EIGEN_VECTORIZE_AVX2
+  return _mm256_slli_epi32(a, n);
+#else
+  __m128i lo = _mm_slli_epi32(_mm256_extractf128_si256(a, 0), n);
+  __m128i hi = _mm_slli_epi32(_mm256_extractf128_si256(a, 1), n);
+  return _mm256_insertf128_si256(_mm256_castsi128_si256(lo), (hi), 1);
+#endif
+}
+
 template<> EIGEN_STRONG_INLINE Packet8f pload<Packet8f>(const float*   from) { EIGEN_DEBUG_ALIGNED_LOAD return _mm256_load_ps(from); }
 template<> EIGEN_STRONG_INLINE Packet4d pload<Packet4d>(const double*  from) { EIGEN_DEBUG_ALIGNED_LOAD return _mm256_load_pd(from); }
 template<> EIGEN_STRONG_INLINE Packet8i pload<Packet8i>(const int*     from) { EIGEN_DEBUG_ALIGNED_LOAD return _mm256_load_si256(reinterpret_cast<const __m256i*>(from)); }
diff --git a/Eigen/src/Core/arch/AVX/TypeCasting.h b/Eigen/src/Core/arch/AVX/TypeCasting.h
index 83bfdc604..7d2e1e67f 100644
--- a/Eigen/src/Core/arch/AVX/TypeCasting.h
+++ b/Eigen/src/Core/arch/AVX/TypeCasting.h
@@ -37,13 +37,21 @@ struct type_casting_traits<int, float> {
 
 
 template<> EIGEN_STRONG_INLINE Packet8i pcast<Packet8f, Packet8i>(const Packet8f& a) {
-  return _mm256_cvtps_epi32(a);
+  return _mm256_cvttps_epi32(a);
 }
 
 template<> EIGEN_STRONG_INLINE Packet8f pcast<Packet8i, Packet8f>(const Packet8i& a) {
   return _mm256_cvtepi32_ps(a);
 }
 
+template<> EIGEN_STRONG_INLINE Packet8i preinterpret<Packet8i,Packet8f>(const Packet8f& a) {
+  return _mm256_castps_si256(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8f preinterpret<Packet8f,Packet8i>(const Packet8i& a) {
+  return _mm256_castsi256_ps(a);
+}
+
 } // end namespace internal
 
 } // end namespace Eigen