Add print for SSE/NEON, use NEON rounding intrinsics if available.

In SSE, by adding/subtracting 2^MantissaBits, we force rounding according to the
current rounding mode.

For NEON, we use the provided intrinsics for rint/floor/ceil if
available (armv8).

Related to #1969.

4 files changed, 140 insertions, 149 deletions

diff --git a/Eigen/src/Core/arch/NEON/PacketMath.h b/Eigen/src/Core/arch/NEON/PacketMath.h
index f77a18a4f..ec6ea90c5 100644
--- a/Eigen/src/Core/arch/NEON/PacketMath.h
+++ b/Eigen/src/Core/arch/NEON/PacketMath.h
@@ -196,6 +196,7 @@ struct packet_traits<float> : default_packet_traits
     HasDiv   = 1,
     HasFloor = 1,
     HasCeil = 1,
+    HasRint = 1,
 
     HasSin  = EIGEN_FAST_MATH,
     HasCos  = EIGEN_FAST_MATH,
@@ -3182,63 +3183,88 @@ template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet2l pselect(const Packet2l
 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet2ul pselect(const Packet2ul& mask, const Packet2ul& a, const Packet2ul& b)
 { return vbslq_u64(mask, a, b); }
 
+// Use armv8 rounding intinsics if available.
+#if EIGEN_ARCH_ARMV8
+template<> EIGEN_STRONG_INLINE Packet2f print<Packet2f>(const Packet2f& a)
+{ return vrndn_f32(a); }
+
+template<> EIGEN_STRONG_INLINE Packet4f print<Packet4f>(const Packet4f& a)
+{ return vrndnq_f32(a); }
 
 template<> EIGEN_STRONG_INLINE Packet2f pfloor<Packet2f>(const Packet2f& a)
-{
-  const Packet2f cst_1 = pset1<Packet2f>(1.0f);
-  // Round to nearest.
-  Packet2f tmp = vcvt_f32_s32(vcvt_s32_f32(a));
-  // If greater, subtract one.
-  Packet2ui mask = vcgt_f32(tmp, a);
-  mask = vand_u32(mask, vreinterpret_u32_f32(cst_1));
-  tmp = vsub_f32(tmp, vreinterpret_f32_u32(mask));
-  // Handle saturation cases.
-  const Packet2f cst_max = pset1<Packet2f>(static_cast<float>(NumTraits<int32_t>::highest()));
-  return pselect(pcmp_lt(pabs(a), cst_max), tmp, a);
+{ return vrndm_f32(a); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pfloor<Packet4f>(const Packet4f& a)
+{ return vrndmq_f32(a); }
+
+template<> EIGEN_STRONG_INLINE Packet2f pceil<Packet2f>(const Packet2f& a)
+{ return vrndp_f32(a); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pceil<Packet4f>(const Packet4f& a)
+{ return vrndpq_f32(a); }
+
+#else
+
+template<> EIGEN_STRONG_INLINE Packet4f print(const Packet4f& a) {
+  // Adds and subtracts signum(a) * 2^23 to force rounding.
+  const Packet4f offset = 
+    pselect(pcmp_lt(a, pzero(a)), 
+      pset1<Packet4f>(-static_cast<float>(1<<23)),
+      pset1<Packet4f>(+static_cast<float>(1<<23)));
+  return psub(padd(a, offset), offset);
+}
+
+template<> EIGEN_STRONG_INLINE Packet2f print(const Packet2f& a) {
+  // Adds and subtracts signum(a) * 2^23 to force rounding.
+  const Packet2f offset = 
+    pselect(pcmp_lt(a, pzero(a)), 
+      pset1<Packet2f>(-static_cast<float>(1<<23)),
+      pset1<Packet2f>(+static_cast<float>(1<<23)));
+  return psub(padd(a, offset), offset);
 }
 
 template<> EIGEN_STRONG_INLINE Packet4f pfloor<Packet4f>(const Packet4f& a)
 {
   const Packet4f cst_1 = pset1<Packet4f>(1.0f);
-  // Round to nearest.
-  Packet4f tmp = vcvtq_f32_s32(vcvtq_s32_f32(a));
+  Packet4f tmp  = print<Packet4f>(a);
   // If greater, subtract one.
-  Packet4ui mask = vcgtq_f32(tmp, a);
-  mask = vandq_u32(mask, vreinterpretq_u32_f32(cst_1));
-  tmp = vsubq_f32(tmp, vreinterpretq_f32_u32(mask));
-  // Handle saturation cases.
-  const Packet4f cst_max = pset1<Packet4f>(static_cast<float>(NumTraits<int32_t>::highest()));
-  return pselect(pcmp_lt(pabs(a), cst_max), tmp, a);
+  Packet4f mask = pcmp_lt(a, tmp);
+  mask = pand(mask, cst_1);
+  return psub(tmp, mask);
 }
 
-template<> EIGEN_STRONG_INLINE Packet2f pceil<Packet2f>(const Packet2f& a)
+template<> EIGEN_STRONG_INLINE Packet2f pfloor<Packet2f>(const Packet2f& a)
 {
   const Packet2f cst_1 = pset1<Packet2f>(1.0f);
-  // Round to nearest.
-  Packet2f tmp = vcvt_f32_s32(vcvt_s32_f32(a));
-  // If smaller, add one.
-  Packet2ui mask = vclt_f32(tmp, a);
-  mask = vand_u32(mask, vreinterpret_u32_f32(cst_1));
-  tmp = vadd_f32(tmp, vreinterpret_f32_u32(mask));
-  // Handle saturation cases.
-  const Packet2f cst_max = pset1<Packet2f>(static_cast<float>(NumTraits<int32_t>::highest()));
-  return pselect(pcmp_lt(pabs(a), cst_max), tmp, a);
+  Packet2f tmp  = print<Packet2f>(a);
+  // If greater, subtract one.
+  Packet2f mask = pcmp_lt(a, tmp);
+  mask = pand(mask, cst_1);
+  return psub(tmp, mask);
 }
 
 template<> EIGEN_STRONG_INLINE Packet4f pceil<Packet4f>(const Packet4f& a)
 {
   const Packet4f cst_1 = pset1<Packet4f>(1.0f);
-  // Round to nearest.
-  Packet4f tmp = vcvtq_f32_s32(vcvtq_s32_f32(a));
+  Packet4f tmp  = print<Packet4f>(a);
+  // If smaller, add one.
+  Packet4f mask = pcmp_lt(tmp, a);
+  mask = pand(mask, cst_1);
+  return padd(tmp, mask);
+}
+
+template<> EIGEN_STRONG_INLINE Packet2f pceil<Packet2f>(const Packet2f& a)
+{
+  const Packet2f cst_1 = pset1<Packet2f>(1.0);
+  Packet2f tmp  = print<Packet2f>(a);
   // If smaller, add one.
-  Packet4ui mask = vcltq_f32(tmp, a);
-  mask = vandq_u32(mask, vreinterpretq_u32_f32(cst_1));
-  tmp = vaddq_f32(tmp, vreinterpretq_f32_u32(mask));
-  // Handle saturation cases.
-  const Packet4f cst_max = pset1<Packet4f>(static_cast<float>(NumTraits<int32_t>::highest()));
-  return pselect(pcmp_lt(pabs(a), cst_max), tmp, a);
+  Packet2f mask = pcmp_lt(tmp, a);
+  mask = pand(mask, cst_1);
+  return padd(tmp, mask);
 }
 
+#endif
+
 /**
  * Computes the integer square root
  * @remarks The calculation is performed using an algorithm which iterates through each binary digit of the result
@@ -3404,6 +3430,7 @@ template<> struct packet_traits<bfloat16> : default_packet_traits
     HasDiv       = 1,
     HasFloor     = 1,
     HasCeil      = 1,
+    HasRint      = 1,
 
     HasSin  = EIGEN_FAST_MATH,
     HasCos  = EIGEN_FAST_MATH,
@@ -3565,6 +3592,11 @@ template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4bf pselect(const Packet4
   return pselect<Packet4us>(mask, a, b);
 }
 
+template<> EIGEN_STRONG_INLINE Packet4bf print<Packet4bf>(const Packet4bf& a)
+{
+  return F32ToBf16(print<Packet4f>(Bf16ToF32(a)));
+}
+
 template<> EIGEN_STRONG_INLINE Packet4bf pfloor<Packet4bf>(const Packet4bf& a)
 {
   return F32ToBf16(pfloor<Packet4f>(Bf16ToF32(a)));
@@ -3751,6 +3783,7 @@ template<> struct packet_traits<double>  : default_packet_traits
     HasDiv   = 1,
     HasFloor = 1,
     HasCeil = 1,
+    HasRint = 1,
 
     HasSin  = 0,
     HasCos  = 0,
@@ -3932,33 +3965,14 @@ ptranspose(PacketBlock<Packet2d, 2>& kernel)
 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet2d pselect( const Packet2d& mask, const Packet2d& a, const Packet2d& b)
 { return vbslq_f64(vreinterpretq_u64_f64(mask), a, b); }
 
+template<> EIGEN_STRONG_INLINE Packet2d print<Packet2d>(const Packet2d& a)
+{ return vrndnq_f64(a); }
+
 template<> EIGEN_STRONG_INLINE Packet2d pfloor<Packet2d>(const Packet2d& a)
-{
-  const Packet2d cst_1 = pset1<Packet2d>(1.0);
-  // Round to nearest.
-  Packet2d tmp = vcvtq_f64_s64(vcvtq_s64_f64(a));
-  // If greater, substract 1.
-  uint64x2_t mask = vcgtq_f64(tmp, a);
-  mask = vandq_u64(mask, vreinterpretq_u64_f64(cst_1));
-  tmp = vsubq_f64(tmp, vreinterpretq_f64_u64(mask));
-  // Handle saturation cases.
-  const Packet2d cst_max = pset1<Packet2d>(static_cast<double>(NumTraits<int64_t>::highest()));
-  return pselect(pcmp_lt(pabs(a), cst_max), tmp, a);
-}
+{ return vrndmq_f64(a); }
 
 template<> EIGEN_STRONG_INLINE Packet2d pceil<Packet2d>(const Packet2d& a)
-{
-  const Packet2d cst_1 = pset1<Packet2d>(1.0);
-  // Round to nearest.
-  Packet2d tmp = vcvtq_f64_s64(vcvtq_s64_f64(a));
-  // If smaller, add one.
-  uint64x2_t mask = vcltq_f64(tmp, a);
-  mask = vandq_u64(mask, vreinterpretq_u64_f64(cst_1));
-  tmp = vaddq_f64(tmp, vreinterpretq_f64_u64(mask));
-  // Handle saturation cases.
-  const Packet2d cst_max = pset1<Packet2d>(static_cast<double>(NumTraits<int64_t>::highest()));
-  return pselect(pcmp_lt(pabs(a), cst_max), tmp, a);
-}
+{ return vrndpq_f64(a); }
 
 template<> EIGEN_STRONG_INLINE Packet2d pldexp<Packet2d>(const Packet2d& a, const Packet2d& exponent)
 { return pldexp_generic(a, exponent); }
@@ -4020,6 +4034,7 @@ struct packet_traits<Eigen::half> : default_packet_traits {
     HasDiv = 1,
     HasFloor = 1,
     HasCeil = 1,
+    HasRint = 1,
     HasSin = 0,
     HasCos = 0,
     HasLog = 0,
@@ -4231,6 +4246,30 @@ EIGEN_STRONG_INLINE Packet4hf pcmp_lt_or_nan<Packet4hf>(const Packet4hf& a, cons
 }
 
 template <>
+EIGEN_STRONG_INLINE Packet8hf print<Packet8hf>(const Packet8hf& a)
+{ return vrndnq_f16(a); }
+
+template <>
+EIGEN_STRONG_INLINE Packet4hf print<Packet4hf>(const Packet4hf& a)
+{ return vrndn_f16(a); }
+
+template <>
+EIGEN_STRONG_INLINE Packet8hf pfloor<Packet8hf>(const Packet8hf& a)
+{ return vrndmq_f16(a); }
+
+template <>
+EIGEN_STRONG_INLINE Packet4hf pfloor<Packet4hf>(const Packet4hf& a)
+{ return vrndm_f16(a); }
+
+template <>
+EIGEN_STRONG_INLINE Packet8hf pceil<Packet8hf>(const Packet8hf& a)
+{ return vrndpq_f16(a); }
+
+template <>
+EIGEN_STRONG_INLINE Packet4hf pceil<Packet4hf>(const Packet4hf& a)
+{ return vrndp_f16(a); }
+
+template <>
 EIGEN_STRONG_INLINE Packet8hf psqrt<Packet8hf>(const Packet8hf& a) {
   return vsqrtq_f16(a);
 }
@@ -4465,62 +4504,6 @@ EIGEN_STRONG_INLINE Packet4hf pabs<Packet4hf>(const Packet4hf& a) {
 }
 
 template <>
-EIGEN_STRONG_INLINE Packet8hf pfloor<Packet8hf>(const Packet8hf& a) {
-  const Packet8hf cst_1 = pset1<Packet8hf>(Eigen::half(1.0f));
-  // Round to nearest.
-  Packet8hf tmp = vcvtq_f16_s16(vcvtq_s16_f16(a));
-  // If greater, substract one.
-  uint16x8_t mask = vcgtq_f16(tmp, a);
-  mask = vandq_u16(mask, vreinterpretq_u16_f16(cst_1));
-  tmp = vsubq_f16(tmp, vreinterpretq_f16_u16(mask));
-  // Handle saturation cases.
-  const Packet8hf cst_max = pset1<Packet8hf>(static_cast<Eigen::half>(NumTraits<int16_t>::highest()));
-  return pselect(pcmp_lt(pabs(a), cst_max), tmp, a);
-}
-
-template <>
-EIGEN_STRONG_INLINE Packet4hf pfloor<Packet4hf>(const Packet4hf& a) {
-  const Packet4hf cst_1 = pset1<Packet4hf>(Eigen::half(1.0f));
-  // Round to nearest.
-  Packet4hf tmp = vcvt_f16_s16(vcvt_s16_f16(a));
-  // If greater, substract one.
-  uint16x4_t mask = vcgt_f16(tmp, a);
-  mask = vand_u16(mask, vreinterpret_u16_f16(cst_1));
-  tmp = vsub_f16(tmp, vreinterpret_f16_u16(mask));
-  // Handle saturation cases.
-  const Packet4hf cst_max = pset1<Packet4hf>(static_cast<Eigen::half>(NumTraits<int16_t>::highest()));
-  return pselect(pcmp_lt(pabs(a), cst_max), tmp, a);
-}
-
-template <>
-EIGEN_STRONG_INLINE Packet8hf pceil<Packet8hf>(const Packet8hf& a) {
-  const Packet8hf cst_1 = pset1<Packet8hf>(Eigen::half(1.0f));
-  // Round to nearest.
-  Packet8hf tmp = vcvtq_f16_s16(vcvtq_s16_f16(a));
-  // If smaller, add one.
-  uint16x8_t mask = vcltq_f16(tmp, a);
-  mask = vandq_u16(mask, vreinterpretq_u16_f16(cst_1));
-  tmp = vaddq_f16(tmp, vreinterpretq_f16_u16(mask));
-  // Handle saturation cases.
-  const Packet8hf cst_max = pset1<Packet8hf>(static_cast<Eigen::half>(NumTraits<int16_t>::highest()));
-  return pselect(pcmp_lt(pabs(a), cst_max), tmp, a);
-}
-
-template <>
-EIGEN_STRONG_INLINE Packet4hf pceil<Packet4hf>(const Packet4hf& a) {
-  const Packet4hf cst_1 = pset1<Packet4hf>(Eigen::half(1.0f));
-  // Round to nearest.
-  Packet4hf tmp = vcvt_f16_s16(vcvt_s16_f16(a));
-  // If smaller, add one.
-  uint16x4_t mask = vclt_f16(tmp, a);
-  mask = vand_u16(mask, vreinterpret_u16_f16(cst_1));
-  tmp = vadd_f16(tmp, vreinterpret_f16_u16(mask));
-  // Handle saturation cases.
-  const Packet4hf cst_max = pset1<Packet4hf>(static_cast<Eigen::half>(NumTraits<int16_t>::highest()));
-  return pselect(pcmp_lt(pabs(a), cst_max), tmp, a);
-}
-
-template <>
 EIGEN_STRONG_INLINE Eigen::half predux<Packet8hf>(const Packet8hf& a) {
   float16x4_t a_lo, a_hi, sum;
 
diff --git a/Eigen/src/Core/arch/SSE/PacketMath.h b/Eigen/src/Core/arch/SSE/PacketMath.h
index 78fd99e64..b9821ad80 100755
--- a/Eigen/src/Core/arch/SSE/PacketMath.h
+++ b/Eigen/src/Core/arch/SSE/PacketMath.h
@@ -148,12 +148,11 @@ struct packet_traits<float> : default_packet_traits {
     HasErf = EIGEN_FAST_MATH,
     HasBlend = 1,
     HasCeil = 1,
-    HasFloor = 1
+    HasFloor = 1,
+    HasRint = 1,
 
 #ifdef EIGEN_VECTORIZE_SSE4_1
-    ,
-    HasRint = 1,
-    HasRound = 1
+    HasRound = 1,
 #endif
   };
 };
@@ -175,12 +174,10 @@ struct packet_traits<double> : default_packet_traits {
     HasRsqrt = 1,
     HasBlend = 1,
     HasFloor = 1,
-    HasCeil = 1
-
-#ifdef EIGEN_VECTORIZE_SSE4_1
-    ,
+    HasCeil = 1,
+    HasRint = 1,
+  #ifdef EIGEN_VECTORIZE_SSE4_1
     HasRound = 1,
-    HasRint = 1
 #endif
   };
 };
@@ -647,23 +644,17 @@ template<> EIGEN_STRONG_INLINE Packet2d pceil<Packet2d>(const Packet2d& a) { ret
 template<> EIGEN_STRONG_INLINE Packet4f pfloor<Packet4f>(const Packet4f& a) { return _mm_floor_ps(a); }
 template<> EIGEN_STRONG_INLINE Packet2d pfloor<Packet2d>(const Packet2d& a) { return _mm_floor_pd(a); }
 #else
-template<> EIGEN_STRONG_INLINE Packet4f pfloor<Packet4f>(const Packet4f& a)
-{
-  const Packet4f cst_1 = pset1<Packet4f>(1.0f);
-  Packet4i emm0 = _mm_cvttps_epi32(a);
-  Packet4f tmp  = _mm_cvtepi32_ps(emm0);
-  // If greater, subtract one.
-  Packet4f mask = _mm_cmpgt_ps(tmp, a);
-  mask = pand(mask, cst_1);
-  tmp = psub(tmp, mask);
-  // Handle saturation cases.
-  const Packet4f cst_max = pset1<Packet4f>(static_cast<float>(NumTraits<int32_t>::highest()));
-  return pselect(pcmp_lt(pabs(a), cst_max), tmp, a);
+template<> EIGEN_STRONG_INLINE Packet4f print(const Packet4f& a) {
+  // Adds and subtracts signum(a) * 2^23 to force rounding.
+  const Packet4f offset = 
+    pselect(pcmp_lt(a, pzero(a)), 
+      pset1<Packet4f>(-static_cast<float>(1<<23)),
+      pset1<Packet4f>(+static_cast<float>(1<<23)));
+  return psub(padd(a, offset), offset);
 }
 
-// Rounds to nearest integer.
-EIGEN_STRONG_INLINE Packet2d pround_to_nearest(const Packet2d& a) {
-  // Adds and subtracts signum(a) * 2^52 to force rounding to within precision.
+template<> EIGEN_STRONG_INLINE Packet2d print(const Packet2d& a) {
+  // Adds and subtracts signum(a) * 2^52 to force rounding.
   const Packet2d offset = 
     pselect(pcmp_lt(a, pzero(a)), 
       pset1<Packet2d>(-static_cast<double>(1ull<<52)),
@@ -671,10 +662,20 @@ EIGEN_STRONG_INLINE Packet2d pround_to_nearest(const Packet2d& a) {
   return psub(padd(a, offset), offset);
 }
 
+template<> EIGEN_STRONG_INLINE Packet4f pfloor<Packet4f>(const Packet4f& a)
+{
+  const Packet4f cst_1 = pset1<Packet4f>(1.0f);
+  Packet4f tmp  = print<Packet4f>(a);
+  // If greater, subtract one.
+  Packet4f mask = _mm_cmpgt_ps(tmp, a);
+  mask = pand(mask, cst_1);
+  return psub(tmp, mask);
+}
+
 template<> EIGEN_STRONG_INLINE Packet2d pfloor<Packet2d>(const Packet2d& a)
 {
   const Packet2d cst_1 = pset1<Packet2d>(1.0);
-  Packet2d tmp  = pround_to_nearest(a);
+  Packet2d tmp  = print<Packet2d>(a);
   // If greater, subtract one.
   Packet2d mask = _mm_cmpgt_pd(tmp, a);
   mask = pand(mask, cst_1);
@@ -684,21 +685,17 @@ template<> EIGEN_STRONG_INLINE Packet2d pfloor<Packet2d>(const Packet2d& a)
 template<> EIGEN_STRONG_INLINE Packet4f pceil<Packet4f>(const Packet4f& a)
 {
   const Packet4f cst_1 = pset1<Packet4f>(1.0f);
-  Packet4i emm0 = _mm_cvttps_epi32(a);
-  Packet4f tmp  = _mm_cvtepi32_ps(emm0);
+  Packet4f tmp  = print<Packet4f>(a);
   // If smaller, add one.
   Packet4f mask = _mm_cmplt_ps(tmp, a);
   mask = pand(mask, cst_1);
-  tmp = padd(tmp, mask);
-  // Handle saturation cases.
-  const Packet4f cst_max = pset1<Packet4f>(static_cast<float>(NumTraits<int32_t>::highest()));
-  return pselect(pcmp_lt(pabs(a), cst_max), tmp, a);
+  return padd(tmp, mask);
 }
 
 template<> EIGEN_STRONG_INLINE Packet2d pceil<Packet2d>(const Packet2d& a)
 {
   const Packet2d cst_1 = pset1<Packet2d>(1.0);
-  Packet2d tmp  = pround_to_nearest(a);
+  Packet2d tmp  = print<Packet2d>(a);
   // If smaller, add one.
   Packet2d mask = _mm_cmplt_pd(tmp, a);
   mask = pand(mask, cst_1);
diff --git a/Eigen/src/Core/util/Macros.h b/Eigen/src/Core/util/Macros.h
index b39c6ca43..ac514cbb4 100644
--- a/Eigen/src/Core/util/Macros.h
+++ b/Eigen/src/Core/util/Macros.h
@@ -265,6 +265,14 @@
   #define EIGEN_ARCH_ARM_OR_ARM64 0
 #endif
 
+/// \internal EIGEN_ARCH_ARMV8 set to 1 if the architecture is armv8 or greater.
+#if EIGEN_ARCH_ARM_OR_ARM64 && defined(__ARM_ARCH) && __ARM_ARCH >= 8
+#define EIGEN_ARCH_ARMV8 1
+#else
+#define EIGEN_ARCH_ARMV8 0
+#endif
+
+
 /// \internal EIGEN_HAS_ARM64_FP16 set to 1 if the architecture provides an IEEE
 /// compliant Arm fp16 type
 #if EIGEN_ARCH_ARM64
diff --git a/test/packetmath.cpp b/test/packetmath.cpp
index ceafb9002..76ac47554 100644
--- a/test/packetmath.cpp
+++ b/test/packetmath.cpp
@@ -577,6 +577,9 @@ void packetmath_real() {
       values.push_back(Scalar(-1.5) + val);  // Bug 1785.
       val = val / Scalar(2);
     }
+    values.push_back(NumTraits<Scalar>::infinity());
+    values.push_back(-NumTraits<Scalar>::infinity());
+    values.push_back(NumTraits<Scalar>::quiet_NaN());
     
     for (size_t k=0; k<values.size(); ++k) {
       data1[0] = values[k];