Implement missing AVX half ops.

Minimal implementation of AVX `Eigen::half` ops to bring in line
with `bfloat16`.  Allows `packetmath_13` to pass.

Also adjusted `bfloat16` packet traits to match the supported set
of ops (e.g. Bessel is not actually implemented).

Eigen/src/Core/arch/AVX/MathFunctions.h

@@ -158,6 +158,16 @@ Packet4d prsqrt<Packet4d>(const Packet4d& _x) {
   return _mm256_div_pd(p4d_one, _mm256_sqrt_pd(_x));
 }
 
+F16_PACKET_FUNCTION(Packet8f, Packet8h, psin)
+F16_PACKET_FUNCTION(Packet8f, Packet8h, pcos)
+F16_PACKET_FUNCTION(Packet8f, Packet8h, plog)
+F16_PACKET_FUNCTION(Packet8f, Packet8h, plog1p)
+F16_PACKET_FUNCTION(Packet8f, Packet8h, pexpm1)
+F16_PACKET_FUNCTION(Packet8f, Packet8h, pexp)
+F16_PACKET_FUNCTION(Packet8f, Packet8h, ptanh)
+F16_PACKET_FUNCTION(Packet8f, Packet8h, psqrt)
+F16_PACKET_FUNCTION(Packet8f, Packet8h, prsqrt)
+
 BF16_PACKET_FUNCTION(Packet8f, Packet8bf, psin)
 BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pcos)
 BF16_PACKET_FUNCTION(Packet8f, Packet8bf, plog)

Eigen/src/Core/arch/AVX/PacketMath.h

@@ -119,22 +119,34 @@ struct packet_traits<Eigen::half> : default_packet_traits {
     AlignedOnScalar = 1,
     size = 8,
     HasHalfPacket = 0,
+
+    HasCmp    = 1,
     HasAdd    = 1,
     HasSub    = 1,
     HasMul    = 1,
     HasDiv    = 1,
+    HasSin    = EIGEN_FAST_MATH,
+    HasCos    = EIGEN_FAST_MATH,
     HasNegate = 1,
-    HasAbs    = 0,
+    HasAbs    = 1,
     HasAbs2   = 0,
-    HasMin    = 0,
+    HasMin    = 1,
-    HasMax    = 0,
+    HasMax    = 1,
-    HasConj   = 0,
+    HasConj   = 1,
     HasSetLinear = 0,
-    HasSqrt = 0,
+    HasLog    = 1,
-    HasRsqrt = 0,
+    HasLog1p  = 1,
-    HasExp = 0,
+    HasExpm1  = 1,
-    HasLog = 0,
+    HasExp    = 1,
-    HasBlend = 0
+    HasSqrt   = 1,
+    HasRsqrt  = 1,
+    HasTanh   = EIGEN_FAST_MATH,
+    HasErf    = EIGEN_FAST_MATH,
+    HasBlend  = 0,
+    HasRound  = 1,
+    HasFloor  = 1,
+    HasCeil   = 1,
+    HasRint   = 1
   };
 };
 
@@ -150,16 +162,24 @@ struct packet_traits<bfloat16> : default_packet_traits {
     size = 8,
     HasHalfPacket = 0,
 
-    HasCmp  = 1,
+    HasCmp = 1,
+    HasAdd = 1,
+    HasSub = 1,
+    HasMul = 1,
     HasDiv = 1,
     HasSin = EIGEN_FAST_MATH,
     HasCos = EIGEN_FAST_MATH,
+    HasNegate = 1,
+    HasAbs    = 1,
+    HasAbs2   = 0,
+    HasMin    = 1,
+    HasMax    = 1,
+    HasConj   = 1,
+    HasSetLinear = 0,
     HasLog = 1,
     HasLog1p  = 1,
     HasExpm1  = 1,
     HasExp = 1,
-    HasNdtri = 1,
-    HasBessel  = 1,
     HasSqrt = 1,
     HasRsqrt = 1,
     HasTanh = EIGEN_FAST_MATH,
@@ -870,8 +890,7 @@ template<> EIGEN_STRONG_INLINE Packet4d pblend(const Selector<4>& ifPacket, cons
 }
 
 // Packet math for Eigen::half
-// TODO(cantonios): add missing packet ops
+
-//    - pabs, pmin, pmax, plset, pround, print, pceil, pfloor, pcmp_lt, pcmp_le, pcmp_lt_or_nan
 template<> struct unpacket_traits<Packet8h> { typedef Eigen::half type; enum {size=8, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false}; typedef Packet8h half; };
 
 template<> EIGEN_STRONG_INLINE Packet8h pset1<Packet8h>(const Eigen::half& from) {
@@ -914,6 +933,16 @@ ploadquad<Packet8h>(const Eigen::half* from) {
   return _mm_set_epi16(b, b, b, b, a, a, a, a);
 }
 
+template<> EIGEN_STRONG_INLINE Packet8h ptrue(const Packet8h& a) {
+ return _mm_cmpeq_epi32(a, a);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8h pabs(const Packet8h& a) {
+  const __m128i sign_mask = _mm_set1_epi16(static_cast<numext::uint16_t>(0x8000));
+  return _mm_andnot_si128(sign_mask, a);
+}
+
 EIGEN_STRONG_INLINE Packet8f half2float(const Packet8h& a) {
 #ifdef EIGEN_HAS_FP16_C
   return _mm256_cvtph_ps(a);
@@ -951,8 +980,21 @@ EIGEN_STRONG_INLINE Packet8h float2half(const Packet8f& a) {
 #endif
 }
 
-template<> EIGEN_STRONG_INLINE Packet8h ptrue(const Packet8h& a) {
+template <>
- return _mm_cmpeq_epi32(a, a);
+EIGEN_STRONG_INLINE Packet8h pmin<Packet8h>(const Packet8h& a,
+                                            const Packet8h& b) {
+  return float2half(pmin<Packet8f>(half2float(a), half2float(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8h pmax<Packet8h>(const Packet8h& a,
+                                            const Packet8h& b) {
+  return float2half(pmax<Packet8f>(half2float(a), half2float(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8h plset<Packet8h>(const half& a) {
+  return float2half(plset<Packet8f>(static_cast<float>(a)));
 }
 
 template<> EIGEN_STRONG_INLINE Packet8h por(const Packet8h& a,const Packet8h& b) {
@@ -974,13 +1016,36 @@ template<> EIGEN_STRONG_INLINE Packet8h pselect(const Packet8h& mask, const Pack
   return _mm_blendv_epi8(b, a, mask);
 }
 
+template<> EIGEN_STRONG_INLINE Packet8h pround<Packet8h>(const Packet8h& a) {
+  return float2half(pround<Packet8f>(half2float(a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8h print<Packet8h>(const Packet8h& a) {
+  return float2half(print<Packet8f>(half2float(a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8h pceil<Packet8h>(const Packet8h& a) {
+  return float2half(pceil<Packet8f>(half2float(a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8h pfloor<Packet8h>(const Packet8h& a) {
+  return float2half(pfloor<Packet8f>(half2float(a)));
+}
+
 template<> EIGEN_STRONG_INLINE Packet8h pcmp_eq(const Packet8h& a,const Packet8h& b) {
-  Packet8f af = half2float(a);
+  return Pack16To8(pcmp_eq(half2float(a), half2float(b)));
-  Packet8f bf = half2float(b);
+}
-  Packet8f rf = pcmp_eq(af, bf);
+
-  // Pack the 32-bit flags into 16-bits flags.
+template<> EIGEN_STRONG_INLINE Packet8h pcmp_le(const Packet8h& a,const Packet8h& b) {
-  return _mm_packs_epi32(_mm256_extractf128_si256(_mm256_castps_si256(rf), 0),
+  return Pack16To8(pcmp_le(half2float(a), half2float(b)));
-                         _mm256_extractf128_si256(_mm256_castps_si256(rf), 1));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8h pcmp_lt(const Packet8h& a,const Packet8h& b) {
+  return Pack16To8(pcmp_lt(half2float(a), half2float(b)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8h pcmp_lt_or_nan(const Packet8h& a,const Packet8h& b) {
+  return Pack16To8(pcmp_lt_or_nan(half2float(a), half2float(b)));
 }
 
 template<> EIGEN_STRONG_INLINE Packet8h pconj(const Packet8h& a) { return a; }
@@ -1148,6 +1213,8 @@ ptranspose(PacketBlock<Packet8h,4>& kernel) {
   kernel.packet[3] = pload<Packet8h>(out[3]);
 }
 
+// BFloat16 implementation.
+
 EIGEN_STRONG_INLINE Packet8f Bf16ToF32(const Packet8bf& a) {
 #ifdef EIGEN_VECTORIZE_AVX2
   __m256i extend = _mm256_cvtepu16_epi32(a);
@@ -1262,7 +1329,8 @@ template<> EIGEN_STRONG_INLINE Packet8bf ptrue(const Packet8bf& a) {
 
 template <>
 EIGEN_STRONG_INLINE Packet8bf pabs(const Packet8bf& a) {
-  return F32ToBf16(pabs<Packet8f>(Bf16ToF32(a)));
+  const __m128i sign_mask = _mm_set1_epi16(static_cast<numext::uint16_t>(0x8000));
+  return _mm_andnot_si128(sign_mask, a);
 }
 
 template <>

Eigen/src/Core/arch/Default/Half.h

@@ -56,6 +56,13 @@
   #define EIGEN_CONSTEXPR
 #endif
 
+#define F16_PACKET_FUNCTION(PACKET_F, PACKET_F16, METHOD)           \
+  template <>                                                       \
+  EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED  \
+  PACKET_F16 METHOD<PACKET_F16>(const PACKET_F16& _x) {            \
+    return float2half(METHOD<PACKET_F>(half2float(_x)));            \
+  }
+
 namespace Eigen {
 
 struct half;

test/packetmath.cpp

@@ -556,7 +556,7 @@ void packetmath_real() {
     VERIFY((numext::isnan)(data2[0]));
     // TODO(rmlarsen): Re-enable for bfloat16.
     if (!internal::is_same<Scalar, bfloat16>::value) {
-      VERIFY_IS_EQUAL(std::exp(small), data2[1]);
+      VERIFY_IS_APPROX(std::exp(small), data2[1]);
     }
 
     data1[0] = -small;
@@ -564,21 +564,21 @@ void packetmath_real() {
     h.store(data2, internal::pexp(h.load(data1)));
     // TODO(rmlarsen): Re-enable for bfloat16.
     if (!internal::is_same<Scalar, bfloat16>::value) {
-      VERIFY_IS_EQUAL(std::exp(-small), data2[0]);
+      VERIFY_IS_APPROX(std::exp(-small), data2[0]);
     }
     VERIFY_IS_EQUAL(std::exp(Scalar(0)), data2[1]);
 
     data1[0] = (std::numeric_limits<Scalar>::min)();
     data1[1] = -(std::numeric_limits<Scalar>::min)();
     h.store(data2, internal::pexp(h.load(data1)));
-    VERIFY_IS_EQUAL(std::exp((std::numeric_limits<Scalar>::min)()), data2[0]);
+    VERIFY_IS_APPROX(std::exp((std::numeric_limits<Scalar>::min)()), data2[0]);
-    VERIFY_IS_EQUAL(std::exp(-(std::numeric_limits<Scalar>::min)()), data2[1]);
+    VERIFY_IS_APPROX(std::exp(-(std::numeric_limits<Scalar>::min)()), data2[1]);
 
     data1[0] = std::numeric_limits<Scalar>::denorm_min();
     data1[1] = -std::numeric_limits<Scalar>::denorm_min();
     h.store(data2, internal::pexp(h.load(data1)));
-    VERIFY_IS_EQUAL(std::exp(std::numeric_limits<Scalar>::denorm_min()), data2[0]);
+    VERIFY_IS_APPROX(std::exp(std::numeric_limits<Scalar>::denorm_min()), data2[0]);
-    VERIFY_IS_EQUAL(std::exp(-std::numeric_limits<Scalar>::denorm_min()), data2[1]);
+    VERIFY_IS_APPROX(std::exp(-std::numeric_limits<Scalar>::denorm_min()), data2[1]);
   }
 
   if (PacketTraits::HasTanh) {
@@ -618,7 +618,7 @@ void packetmath_real() {
       test::packet_helper<PacketTraits::HasLog, Packet> h;
       h.store(data2, internal::plog(h.load(data1)));
       VERIFY((numext::isnan)(data2[0]));
-      VERIFY_IS_EQUAL(std::log(std::numeric_limits<Scalar>::epsilon()), data2[1]);
+      VERIFY_IS_APPROX(std::log(std::numeric_limits<Scalar>::epsilon()), data2[1]);
 
       data1[0] = -std::numeric_limits<Scalar>::epsilon();
       data1[1] = Scalar(0);
@@ -629,7 +629,7 @@ void packetmath_real() {
       data1[0] = (std::numeric_limits<Scalar>::min)();
       data1[1] = -(std::numeric_limits<Scalar>::min)();
       h.store(data2, internal::plog(h.load(data1)));
-      VERIFY_IS_EQUAL(std::log((std::numeric_limits<Scalar>::min)()), data2[0]);
+      VERIFY_IS_APPROX(std::log((std::numeric_limits<Scalar>::min)()), data2[0]);
       VERIFY((numext::isnan)(data2[1]));
 
       // Note: 32-bit arm always flushes denorms to zero.
@@ -672,8 +672,10 @@ void packetmath_real() {
       VERIFY((numext::isnan)(data2[0]));
       VERIFY((numext::isnan)(data2[1]));
     }
-    // TODO(rmlarsen): Re-enable for bfloat16.
+    // TODO(rmlarsen): Re-enable for half and bfloat16.
-    if (PacketTraits::HasCos && !internal::is_same<Scalar, bfloat16>::value) {
+    if (PacketTraits::HasCos
+        && !internal::is_same<Scalar, half>::value
+        && !internal::is_same<Scalar, bfloat16>::value) {
       test::packet_helper<PacketTraits::HasCos, Packet> h;
       for (Scalar k = Scalar(1); k < Scalar(10000) / std::numeric_limits<Scalar>::epsilon(); k *= Scalar(2)) {
         for (int k1 = 0; k1 <= 1; ++k1) {
@@ -1074,12 +1076,7 @@ EIGEN_DECLARE_TEST(packetmath) {
     CALL_SUBTEST_10(test::runner<uint64_t>::run());
     CALL_SUBTEST_11(test::runner<std::complex<float> >::run());
     CALL_SUBTEST_12(test::runner<std::complex<double> >::run());
-#if defined(EIGEN_VECTORIZE_AVX)
-    // AVX half packets not fully implemented.
-    CALL_SUBTEST_13((packetmath<half, internal::packet_traits<half>::type>()));
-#else
     CALL_SUBTEST_13(test::runner<half>::run());
-#endif
     CALL_SUBTEST_14((packetmath<bool, internal::packet_traits<bool>::type>()));
     CALL_SUBTEST_15(test::runner<bfloat16>::run());
     g_first_pass = false;