Merged eigen/eigen into default

Eigen/src/Core/GenericPacketMath.h

@@ -216,7 +216,7 @@ pandnot(const Packet& a, const Packet& b) { return a & (~b); }
 
 /** \internal \returns ones */
 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
-ptrue(const Packet& /*a*/) { Packet b; memset(&b, 0xff, sizeof(b)); return b;}
+ptrue(const Packet& /*a*/) { Packet b; memset((void*)&b, 0xff, sizeof(b)); return b;}
 
 template <typename RealScalar>
 EIGEN_DEVICE_FUNC inline std::complex<RealScalar> ptrue(const std::complex<RealScalar>& /*a*/) {

Eigen/src/Core/arch/AVX512/Complex.h

@@ -308,18 +308,18 @@ template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<double> >(std::complex<
 template<> EIGEN_DEVICE_FUNC inline Packet4cd pgather<std::complex<double>, Packet4cd>(const std::complex<double>* from, Index stride)
 {
   return Packet4cd(_mm512_insertf64x4(_mm512_castpd256_pd512(
-            _mm256_insertf128_pd(_mm256_castpd128_pd256(pload<Packet1cd>(from+0*stride).v), pload<Packet1cd>(from+1*stride).v,1)),
+            _mm256_insertf128_pd(_mm256_castpd128_pd256(ploadu<Packet1cd>(from+0*stride).v), ploadu<Packet1cd>(from+1*stride).v,1)),
-            _mm256_insertf128_pd(_mm256_castpd128_pd256(pload<Packet1cd>(from+2*stride).v), pload<Packet1cd>(from+3*stride).v,1), 1));
+            _mm256_insertf128_pd(_mm256_castpd128_pd256(ploadu<Packet1cd>(from+2*stride).v), ploadu<Packet1cd>(from+3*stride).v,1), 1));
 }
 
 template<> EIGEN_DEVICE_FUNC inline void pscatter<std::complex<double>, Packet4cd>(std::complex<double>* to, const Packet4cd& from, Index stride)
 {
   __m512i fromi = _mm512_castpd_si512(from.v);
   double* tod = (double*)(void*)to;
-  _mm_store_pd(tod+0*stride, _mm_castsi128_pd(_mm512_extracti32x4_epi32(fromi,0)) );
+  _mm_storeu_pd(tod+0*stride, _mm_castsi128_pd(_mm512_extracti32x4_epi32(fromi,0)) );
-  _mm_store_pd(tod+2*stride, _mm_castsi128_pd(_mm512_extracti32x4_epi32(fromi,1)) );
+  _mm_storeu_pd(tod+2*stride, _mm_castsi128_pd(_mm512_extracti32x4_epi32(fromi,1)) );
-  _mm_store_pd(tod+4*stride, _mm_castsi128_pd(_mm512_extracti32x4_epi32(fromi,2)) );
+  _mm_storeu_pd(tod+4*stride, _mm_castsi128_pd(_mm512_extracti32x4_epi32(fromi,2)) );
-  _mm_store_pd(tod+6*stride, _mm_castsi128_pd(_mm512_extracti32x4_epi32(fromi,3)) );
+  _mm_storeu_pd(tod+6*stride, _mm_castsi128_pd(_mm512_extracti32x4_epi32(fromi,3)) );
 }
 
 template<> EIGEN_STRONG_INLINE std::complex<double> pfirst<Packet4cd>(const Packet4cd& a)

Eigen/src/Core/arch/AVX512/PacketMath.h

@@ -57,7 +57,7 @@ template<> struct packet_traits<float>  : default_packet_traits
     HasBlend = 0,
     HasSin = EIGEN_FAST_MATH,
     HasCos = EIGEN_FAST_MATH,
-#if EIGEN_GNUC_AT_LEAST(5, 3) || EIGEN_COMP_CLANG
+#if EIGEN_GNUC_AT_LEAST(5, 3) || (!EIGEN_COMP_GNUC_STRICT)
 #ifdef EIGEN_VECTORIZE_AVX512DQ
     HasLog = 1,
 #endif
@@ -77,7 +77,7 @@ template<> struct packet_traits<double> : default_packet_traits
     AlignedOnScalar = 1,
     size = 8,
     HasHalfPacket = 1,
-#if EIGEN_GNUC_AT_LEAST(5, 3)
+#if EIGEN_GNUC_AT_LEAST(5, 3) || (!EIGEN_COMP_GNUC_STRICT)
     HasSqrt = EIGEN_FAST_MATH,
     HasRsqrt = EIGEN_FAST_MATH,
 #endif

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

@@ -3,7 +3,7 @@
 //
 // Copyright (C) 2007 Julien Pommier
 // Copyright (C) 2014 Pedro Gonnet (pedro.gonnet@gmail.com)
-// Copyright (C) 2009-2018 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009-2019 Gael Guennebaud <gael.guennebaud@inria.fr>
 //
 // This Source Code Form is subject to the terms of the Mozilla
 // Public License v. 2.0. If a copy of the MPL was not distributed
@@ -253,15 +253,68 @@ Packet pexp_double(const Packet _x)
   return pmax(pldexp(x,fx), _x);
 }
 
-/* The code is the rewriting of the cephes sinf/cosf functions.
+// The following code is inspired by the following stack-overflow answer:
-   Precision is excellent as long as x < 8192 (I did not bother to
+//   https://stackoverflow.com/questions/30463616/payne-hanek-algorithm-implementation-in-c/30465751#30465751
-   take into account the special handling they have for greater values
+// It has been largely optimized:
-   -- it does not return garbage for arguments over 8192, though, but
+//  - By-pass calls to frexp.
-   the extra precision is missing).
+//  - Aligned loads of required 96 bits of 2/pi. This is accomplished by
+//    (1) balancing the mantissa and exponent to the required bits of 2/pi are
+//    aligned on 8-bits, and (2) replicating the storage of the bits of 2/pi.
+//  - Avoid a branch in rounding and extraction of the remaining fractional part.
+// Overall, I measured a speed up higher than x2 on x86-64.
+inline float trig_reduce_huge (float xf, int *quadrant)
+{
+  using Eigen::numext::int32_t;
+  using Eigen::numext::uint32_t;
+  using Eigen::numext::int64_t;
+  using Eigen::numext::uint64_t;
 
-   Note that it is such that sinf((float)M_PI) = 8.74e-8, which is the
+  const double pio2_62 = 3.4061215800865545e-19;    // pi/2 * 2^-62
-   surprising but correct result.
+  const uint64_t zero_dot_five = uint64_t(1) << 61; // 0.5 in 2.62-bit fixed-point foramt
-*/
+
+  // 192 bits of 2/pi for Payne-Hanek reduction
+  // Bits are introduced by packet of 8 to enable aligned reads.
+  static const uint32_t two_over_pi [] = 
+  {
+    0x00000028, 0x000028be, 0x0028be60, 0x28be60db,
+    0xbe60db93, 0x60db9391, 0xdb939105, 0x9391054a,
+    0x91054a7f, 0x054a7f09, 0x4a7f09d5, 0x7f09d5f4,
+    0x09d5f47d, 0xd5f47d4d, 0xf47d4d37, 0x7d4d3770,
+    0x4d377036, 0x377036d8, 0x7036d8a5, 0x36d8a566,
+    0xd8a5664f, 0xa5664f10, 0x664f10e4, 0x4f10e410,
+    0x10e41000, 0xe4100000
+  };
+  
+  uint32_t xi = numext::as_uint(xf);
+  // Below, -118 = -126 + 8.
+  //   -126 is to get the exponent,
+  //   +8 is to enable alignment of 2/pi's bits on 8 bits.
+  // This is possible because the fractional part of x as only 24 meaningful bits.
+  uint32_t e = (xi >> 23) - 118;
+  // Extract the mantissa and shift it to align it wrt the exponent
+  xi = ((xi & 0x007fffffu)| 0x00800000u) << (e & 0x7);
+
+  uint32_t i = e >> 3;
+  uint32_t twoopi_1  = two_over_pi[i-1];
+  uint32_t twoopi_2  = two_over_pi[i+3];
+  uint32_t twoopi_3  = two_over_pi[i+7];
+
+  // Compute x * 2/pi in 2.62-bit fixed-point format.
+  uint64_t p;
+  p = uint64_t(xi) * twoopi_3;
+  p = uint64_t(xi) * twoopi_2 + (p >> 32);
+  p = (uint64_t(xi * twoopi_1) << 32) + p;
+
+  // Round to nearest: add 0.5 and extract integral part.
+  uint64_t q = (p + zero_dot_five) >> 62;
+  *quadrant = int(q);
+  // Now it remains to compute "r = x - q*pi/2" with high accuracy,
+  // since we have p=x/(pi/2) with high accuracy, we can more efficiently compute r as:
+  //   r = (p-q)*pi/2,
+  // where the product can be be carried out with sufficient accuracy using double precision.
+  p -= q<<62;
+  return float(double(int64_t(p)) * pio2_62);
+}
 
 template<bool ComputeSine,typename Packet>
 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
@@ -285,17 +338,6 @@ Packet psincos_float(const Packet& _x)
   PacketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
   y = psub(y_round, cst_rounding_magic); // nearest integer to x*4/pi
 
-  // Compute the sign to apply to the polynomial.
-  // sin: sign = second_bit(y_int) xor signbit(_x)
-  // cos: sign = second_bit(y_int+1)
-  Packet sign_bit = ComputeSine ? pxor(_x, preinterpret<Packet>(pshiftleft<30>(y_int)))
-                                : preinterpret<Packet>(pshiftleft<30>(padd(y_int,csti_1)));
-  sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
-
-  // Get the polynomial selection mask from the second bit of y_int
-  // We'll calculate both (sin and cos) polynomials and then select from the two.
-  Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
-
   // Reduce x by y octants to get: -Pi/4 <= x <= +Pi/4
   // using "Extended precision modular arithmetic"
   #if defined(EIGEN_HAS_SINGLE_INSTRUCTION_MADD)
@@ -332,29 +374,36 @@ Packet psincos_float(const Packet& _x)
   // The coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
   #endif
 
-  // We use huge_vals as a temporary for abs(_x) to ensure huge_vals
+  if(predux_any(pcmp_le(pset1<Packet>(huge_th),pabs(_x))))
-  // is fully initialized for the last pselect(). (prevent compiler warning)
-  Packet huge_vals = pabs(_x);
-  Packet huge_mask = pcmp_le(pset1<Packet>(huge_th),huge_vals);
-  
-  if(predux_any(huge_mask))
   {
     const int PacketSize = unpacket_traits<Packet>::size;
-    #if EIGEN_HAS_CXX11
-    alignas(Packet) float vals[PacketSize];
-    #else
     EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float vals[PacketSize];
-    #endif
+    EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float x_cpy[PacketSize];
-    pstoreu(vals, _x);
+    EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) int y_int2[PacketSize];
-    for(int k=0; k<PacketSize;++k) {
+    pstoreu(vals, pabs(_x));
+    pstoreu(x_cpy, x);
+    pstoreu(y_int2, y_int);
+    for(int k=0; k<PacketSize;++k)
+    {
       float val = vals[k];
-      if(numext::abs(val)>=huge_th)  {
+      if(val>=huge_th && (numext::isfinite)(val))
-        vals[k] = ComputeSine ? std::sin(val) : std::cos(val);
+        x_cpy[k] = trig_reduce_huge(val,&y_int2[k]);
-      }
     }
-    huge_vals = ploadu<Packet>(vals);
+    x = ploadu<Packet>(x_cpy);
+    y_int = ploadu<PacketI>(y_int2);
   }
 
+  // Compute the sign to apply to the polynomial.
+  // sin: sign = second_bit(y_int) xor signbit(_x)
+  // cos: sign = second_bit(y_int+1)
+  Packet sign_bit = ComputeSine ? pxor(_x, preinterpret<Packet>(pshiftleft<30>(y_int)))
+                                : preinterpret<Packet>(pshiftleft<30>(padd(y_int,csti_1)));
+  sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+
+  // Get the polynomial selection mask from the second bit of y_int
+  // We'll calculate both (sin and cos) polynomials and then select from the two.
+  Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
+
   Packet x2 = pmul(x,x);
 
   // Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
@@ -383,7 +432,7 @@ Packet psincos_float(const Packet& _x)
                   : pselect(poly_mask,y1,y2);
 
   // Update the sign and filter huge inputs
-  return pselect(huge_mask, huge_vals, pxor(y, sign_bit));
+  return pxor(y, sign_bit);
 }
 
 template<typename Packet>

Eigen/src/Core/util/ConfigureVectorization.h

@@ -29,10 +29,15 @@
  *
  * If we made alignment depend on whether or not EIGEN_VECTORIZE is defined, it would be impossible to link
  * vectorized and non-vectorized code.
+ * 
+ * FIXME: this code can be cleaned up once we switch to proper C++11 only.
  */
 #if (defined EIGEN_CUDACC)
   #define EIGEN_ALIGN_TO_BOUNDARY(n) __align__(n)
   #define EIGEN_ALIGNOF(x) __alignof(x)
+#elif EIGEN_HAS_ALIGNAS
+  #define EIGEN_ALIGN_TO_BOUNDARY(n) alignas(n)
+  #define EIGEN_ALIGNOF(x) alignof(x)
 #elif EIGEN_COMP_GNUC || EIGEN_COMP_PGI || EIGEN_COMP_IBM || EIGEN_COMP_ARM
   #define EIGEN_ALIGN_TO_BOUNDARY(n) __attribute__((aligned(n)))
   #define EIGEN_ALIGNOF(x) __alignof(x)
@@ -44,7 +49,7 @@
   #define EIGEN_ALIGN_TO_BOUNDARY(n) __attribute__((aligned(n)))
   #define EIGEN_ALIGNOF(x) __alignof(x)
 #else
-  #error Please tell me what is the equivalent of __attribute__((aligned(n))) and __alignof(x) for your compiler
+  #error Please tell me what is the equivalent of alignas(n) and alignof(x) for your compiler
 #endif
 
 // If the user explicitly disable vectorization, then we also disable alignment

Eigen/src/Core/util/Macros.h

@@ -129,16 +129,21 @@
   #define EIGEN_COMP_MSVC_STRICT 0
 #endif
 
-/// \internal EIGEN_COMP_IBM set to 1 if the compiler is IBM XL C++
+/// \internal EIGEN_COMP_IBM set to xlc version if the compiler is IBM XL C++
-#if defined(__IBMCPP__) || defined(__xlc__)
+// XLC   version
-  #define EIGEN_COMP_IBM 1
+// 3.1   0x0301	
+// 4.5   0x0405	
+// 5.0   0x0500
+// 12.1  0x0C01
+#if defined(__IBMCPP__) || defined(__xlc__) || defined(__ibmxl__)
+  #define EIGEN_COMP_IBM __xlC__
 #else
   #define EIGEN_COMP_IBM 0
 #endif
 
-/// \internal EIGEN_COMP_PGI set to 1 if the compiler is Portland Group Compiler
+/// \internal EIGEN_COMP_PGI set to PGI version if the compiler is Portland Group Compiler
 #if defined(__PGI)
-  #define EIGEN_COMP_PGI 1
+  #define EIGEN_COMP_PGI (__PGIC__*100+__PGIC_MINOR__)
 #else
   #define EIGEN_COMP_PGI 0
 #endif
@@ -347,9 +352,17 @@
   #define EIGEN_OS_WIN_STRICT 0
 #endif
 
-/// \internal EIGEN_OS_SUN set to 1 if the OS is SUN
+/// \internal EIGEN_OS_SUN set to __SUNPRO_C if the OS is SUN
+// compiler  solaris   __SUNPRO_C
+// version   studio
+// 5.7       10        0x570
+// 5.8       11        0x580
+// 5.9       12        0x590
+// 5.10	     12.1      0x5100
+// 5.11	     12.2      0x5110
+// 5.12	     12.3      0x5120
 #if (defined(sun) || defined(__sun)) && !(defined(__SVR4) || defined(__svr4__))
-  #define EIGEN_OS_SUN 1
+  #define EIGEN_OS_SUN __SUNPRO_C
 #else
   #define EIGEN_OS_SUN 0
 #endif
@@ -546,6 +559,22 @@
 #endif
 #endif
 
+#ifndef EIGEN_HAS_ALIGNAS
+#if EIGEN_MAX_CPP_VER>=11 && EIGEN_HAS_CXX11 &&   \
+      (     __has_feature(cxx_alignas)            \
+        ||  EIGEN_HAS_CXX14                       \
+        || (EIGEN_COMP_MSVC >= 1800)              \
+        || (EIGEN_GNUC_AT_LEAST(4,8))             \
+        || (EIGEN_COMP_CLANG>=305)                \
+        || (EIGEN_COMP_ICC>=1500)                 \
+        || (EIGEN_COMP_PGI>=1500)                 \
+        || (EIGEN_COMP_SUN>=0x5130))
+#define EIGEN_HAS_ALIGNAS 1
+#else
+#define EIGEN_HAS_ALIGNAS 0
+#endif
+#endif
+
 // Does the compiler support type_traits?
 // - full support of type traits was added only to GCC 5.1.0.
 // - 20150626 corresponds to the last release of 4.x libstdc++

Eigen/src/Core/util/Meta.h

@@ -636,8 +636,41 @@ template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
 bool not_equal_strict(const double& x,const double& y) { return std::not_equal_to<double>()(x,y); }
 #endif
 
+/** \internal extract the bits of the float \a x */
+inline unsigned int as_uint(float x)
+{
+  unsigned int ret;
+  std::memcpy(&ret, &x, sizeof(float));
+  return ret;
+}
+
 } // end namespace numext
 
 } // end namespace Eigen
 
+// Define portable (u)int{32,64} types
+#if EIGEN_HAS_CXX11
+#include <cstdint>
+namespace Eigen {
+namespace numext {
+typedef std::uint32_t uint32_t;
+typedef std::int32_t  int32_t;
+typedef std::uint64_t uint64_t;
+typedef std::int64_t  int64_t;
+}
+}
+#else
+// Without c++11, all compilers able to compile Eigen also
+// provides the C99 stdint.h header file.
+#include <stdint.h>
+namespace Eigen {
+namespace numext {
+typedef ::uint32_t uint32_t;
+typedef ::int32_t  int32_t;
+typedef ::uint64_t uint64_t;
+typedef ::int64_t  int64_t;
+}
+}
+#endif
+
 #endif // EIGEN_META_H

Eigen/src/Geometry/Transform.h

@@ -97,6 +97,9 @@ template<int Mode> struct transform_make_affine;
   *              - #AffineCompact: the transformation is stored as a (Dim)x(Dim+1) matrix.
   *              - #Projective: the transformation is stored as a (Dim+1)^2 matrix
   *                             without any assumption.
+  *              - #Isometry: same as #Affine with the additional assumption that
+  *                           the linear part represents a rotation. This assumption is exploited
+  *                           to speed up some functions such as inverse() and rotation().
   * \tparam _Options has the same meaning as in class Matrix. It allows to specify DontAlign and/or RowMajor.
   *                  These Options are passed directly to the underlying matrix type.
   *
@@ -252,11 +255,11 @@ protected:
 public:
 
   /** Default constructor without initialization of the meaningful coefficients.
-    * If Mode==Affine, then the last row is set to [0 ... 0 1] */
+    * If Mode==Affine or Mode==Isometry, then the last row is set to [0 ... 0 1] */
   EIGEN_DEVICE_FUNC inline Transform()
   {
     check_template_params();
-    internal::transform_make_affine<(int(Mode)==Affine) ? Affine : AffineCompact>::run(m_matrix);
+    internal::transform_make_affine<(int(Mode)==Affine || int(Mode)==Isometry) ? Affine : AffineCompact>::run(m_matrix);
   }
 
   EIGEN_DEVICE_FUNC inline Transform(const Transform& other)

Eigen/src/LU/FullPivLU.h

@@ -18,6 +18,7 @@ template<typename _MatrixType> struct traits<FullPivLU<_MatrixType> >
 {
   typedef MatrixXpr XprKind;
   typedef SolverStorage StorageKind;
+  typedef int StorageIndex;
   enum { Flags = 0 };
 };
 
@@ -64,7 +65,6 @@ template<typename _MatrixType> class FullPivLU
     typedef SolverBase<FullPivLU> Base;
 
     EIGEN_GENERIC_PUBLIC_INTERFACE(FullPivLU)
-    // FIXME StorageIndex defined in EIGEN_GENERIC_PUBLIC_INTERFACE should be int
     enum {
       MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
       MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
@@ -529,8 +529,8 @@ void FullPivLU<MatrixType>::computeInPlace()
       m_nonzero_pivots = k;
       for(Index i = k; i < size; ++i)
       {
-        m_rowsTranspositions.coeffRef(i) = i;
+        m_rowsTranspositions.coeffRef(i) = internal::convert_index<StorageIndex>(i);
-        m_colsTranspositions.coeffRef(i) = i;
+        m_colsTranspositions.coeffRef(i) = internal::convert_index<StorageIndex>(i);
       }
       break;
     }
@@ -541,8 +541,8 @@ void FullPivLU<MatrixType>::computeInPlace()
     // Now that we've found the pivot, we need to apply the row/col swaps to
     // bring it to the location (k,k).
 
-    m_rowsTranspositions.coeffRef(k) = row_of_biggest_in_corner;
+    m_rowsTranspositions.coeffRef(k) = internal::convert_index<StorageIndex>(row_of_biggest_in_corner);
-    m_colsTranspositions.coeffRef(k) = col_of_biggest_in_corner;
+    m_colsTranspositions.coeffRef(k) = internal::convert_index<StorageIndex>(col_of_biggest_in_corner);
     if(k != row_of_biggest_in_corner) {
       m_lu.row(k).swap(m_lu.row(row_of_biggest_in_corner));
       ++number_of_transpositions;

Eigen/src/LU/PartialPivLU.h

@@ -19,6 +19,7 @@ template<typename _MatrixType> struct traits<PartialPivLU<_MatrixType> >
 {
   typedef MatrixXpr XprKind;
   typedef SolverStorage StorageKind;
+  typedef int StorageIndex;
   typedef traits<_MatrixType> BaseTraits;
   enum {
     Flags = BaseTraits::Flags & RowMajorBit,
@@ -80,7 +81,6 @@ template<typename _MatrixType> class PartialPivLU
     typedef _MatrixType MatrixType;
     typedef SolverBase<PartialPivLU> Base;
     EIGEN_GENERIC_PUBLIC_INTERFACE(PartialPivLU)
-    // FIXME StorageIndex defined in EIGEN_GENERIC_PUBLIC_INTERFACE should be int
     enum {
       MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
       MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime

test/geo_transformations.cpp

@@ -612,6 +612,62 @@ template<typename Scalar, int Dim, int Options> void transform_products()
   VERIFY_IS_APPROX((ac*p).matrix(), a_m*p_m);
 }
 
+template<typename Scalar, int Mode, int Options> void transformations_no_scale()
+{
+     /* this test covers the following files:
+     Cross.h Quaternion.h, Transform.h
+  */
+  typedef Matrix<Scalar,3,1> Vector3;
+  typedef Matrix<Scalar,4,1> Vector4;
+  typedef Quaternion<Scalar> Quaternionx;
+  typedef AngleAxis<Scalar> AngleAxisx;
+  typedef Transform<Scalar,3,Mode,Options> Transform3;
+  typedef Translation<Scalar,3> Translation3;
+  typedef Matrix<Scalar,4,4> Matrix4;
+
+  Vector3 v0 = Vector3::Random(),
+          v1 = Vector3::Random();
+
+  Transform3 t0, t1, t2;
+
+  Scalar a = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI));
+
+  Quaternionx q1, q2;
+
+  q1 = AngleAxisx(a, v0.normalized());
+
+  t0 = Transform3::Identity();
+  VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity());
+
+  t0.setIdentity();
+  t1.setIdentity();
+  v1 = Vector3::Ones();
+  t0.linear() = q1.toRotationMatrix();
+  t0.pretranslate(v0);
+  t1.linear() = q1.conjugate().toRotationMatrix();
+  t1.translate(-v0);
+
+  VERIFY((t0 * t1).matrix().isIdentity(test_precision<Scalar>()));
+
+  t1.fromPositionOrientationScale(v0, q1, v1);
+  VERIFY_IS_APPROX(t1.matrix(), t0.matrix());
+  VERIFY_IS_APPROX(t1*v1, t0*v1);
+
+  // translation * vector
+  t0.setIdentity();
+  t0.translate(v0);
+  VERIFY_IS_APPROX((t0 * v1).template head<3>(), Translation3(v0) * v1);
+
+  // Conversion to matrix.
+  Transform3 t3;
+  t3.linear() = q1.toRotationMatrix();
+  t3.translation() = v1;
+  Matrix4 m3 = t3.matrix();
+  VERIFY((m3 * m3.inverse()).isIdentity(test_precision<Scalar>()));
+  // Verify implicit last row is initialized.
+  VERIFY_IS_APPROX(Vector4(m3.row(3)), Vector4(0.0, 0.0, 0.0, 1.0));
+}
+
 EIGEN_DECLARE_TEST(geo_transformations)
 {
   for(int i = 0; i < g_repeat; i++) {
@@ -625,7 +681,7 @@ EIGEN_DECLARE_TEST(geo_transformations)
     CALL_SUBTEST_3(( transformations<double,Projective,AutoAlign>() ));
     CALL_SUBTEST_3(( transformations<double,Projective,DontAlign>() ));
     CALL_SUBTEST_3(( transform_alignment<double>() ));
-    
+
     CALL_SUBTEST_4(( transformations<float,Affine,RowMajor|AutoAlign>() ));
     CALL_SUBTEST_4(( non_projective_only<float,Affine,RowMajor>() ));
     
@@ -641,5 +697,8 @@ EIGEN_DECLARE_TEST(geo_transformations)
 
     CALL_SUBTEST_8(( transform_associativity<double,2,ColMajor>(Rotation2D<double>(internal::random<double>()*double(EIGEN_PI))) ));
     CALL_SUBTEST_8(( transform_associativity<double,3,ColMajor>(Quaterniond::UnitRandom()) ));
+
+    CALL_SUBTEST_9(( transformations_no_scale<double,Affine,AutoAlign>() ));
+    CALL_SUBTEST_9(( transformations_no_scale<double,Isometry,AutoAlign>() ));
   }
 }

test/lu.cpp

@@ -18,6 +18,8 @@ typename MatrixType::RealScalar matrix_l1_norm(const MatrixType& m) {
 
 template<typename MatrixType> void lu_non_invertible()
 {
+  STATIC_CHECK(( internal::is_same<typename FullPivLU<MatrixType>::StorageIndex,int>::value ));
+
   typedef typename MatrixType::RealScalar RealScalar;
   /* this test covers the following files:
      LU.h
@@ -191,6 +193,8 @@ template<typename MatrixType> void lu_partial_piv()
   m1.setRandom();
   PartialPivLU<MatrixType> plu(m1);
 
+  STATIC_CHECK(( internal::is_same<typename PartialPivLU<MatrixType>::StorageIndex,int>::value ));
+
   VERIFY_IS_APPROX(m1, plu.reconstructedMatrix());
 
   m3 = MatrixType::Random(size,size);

test/packetmath.cpp

@@ -568,6 +568,7 @@ template<typename Scalar,typename Packet> void packetmath_real()
       h.store(data2, internal::plog(h.load(data1)));
       VERIFY((numext::isinf)(data2[0]));
     }
+    if(PacketTraits::HasSqrt)
     {
       packet_helper<PacketTraits::HasSqrt,Packet> h;
       data1[0] = Scalar(-1.0f);