Fix PPC rand and other failures.

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

diff --git a/Eigen/src/Core/arch/AltiVec/PacketMath.h b/Eigen/src/Core/arch/AltiVec/PacketMath.h
index 414f05c..a4b134c 100644
--- a/Eigen/src/Core/arch/AltiVec/PacketMath.h
+++ b/Eigen/src/Core/arch/AltiVec/PacketMath.h
@@ -105,6 +105,7 @@
 static const Packet16uc p16uc_DUPLICATE16_ODD = {2, 3, 2, 3, 6, 7, 6, 7, 10, 11, 10, 11, 14, 15, 14, 15};
 
 static Packet16uc p16uc_QUADRUPLICATE16_HI = {0, 1, 0, 1, 0, 1, 0, 1, 2, 3, 2, 3, 2, 3, 2, 3};
+static Packet16uc p16uc_QUADRUPLICATE16 = {0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3};
 
 static Packet16uc p16uc_MERGEE16 = {0, 1, 16, 17, 4, 5, 20, 21, 8, 9, 24, 25, 12, 13, 28, 29};
 static Packet16uc p16uc_MERGEO16 = {2, 3, 18, 19, 6, 7, 22, 23, 10, 11, 26, 27, 14, 15, 30, 31};
@@ -1716,6 +1717,26 @@
   return vec_mergeh(p, p);
 }
 
+template <>
+EIGEN_STRONG_INLINE Packet16c ploadquad<Packet16c>(const signed char* from) {
+  Packet16c p;
+  if ((std::ptrdiff_t(from) % 16) == 0)
+    p = pload<Packet16c>(from);
+  else
+    p = ploadu<Packet16c>(from);
+  return vec_perm(p, p, p16uc_QUADRUPLICATE16);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16uc ploadquad<Packet16uc>(const unsigned char* from) {
+  Packet16uc p;
+  if ((std::ptrdiff_t(from) % 16) == 0)
+    p = pload<Packet16uc>(from);
+  else
+    p = ploadu<Packet16uc>(from);
+  return vec_perm(p, p, p16uc_QUADRUPLICATE16);
+}
+
 template <typename Packet>
 EIGEN_STRONG_INLINE void pstoreu_common(__UNPACK_TYPE__(Packet) * to, const Packet& from) {
   EIGEN_DEBUG_UNALIGNED_STORE

test/array_for_matrix.cpp

diff --git a/test/array_for_matrix.cpp b/test/array_for_matrix.cpp
index afe6894..6d7d0dd 100644
--- a/test/array_for_matrix.cpp
+++ b/test/array_for_matrix.cpp
@@ -19,12 +19,18 @@
   Index cols = m.cols();
 
   MatrixType m1 = MatrixType::Random(rows, cols), m2 = MatrixType::Random(rows, cols), m3(rows, cols);
-
   ColVectorType cv1 = ColVectorType::Random(rows);
   RowVectorType rv1 = RowVectorType::Random(cols);
 
   Scalar s1 = internal::random<Scalar>(), s2 = internal::random<Scalar>();
 
+  // Prevent overflows for integer types.
+  if (Eigen::NumTraits<Scalar>::IsInteger) {
+    constexpr Scalar kMaxVal = Scalar(10000);
+    m1.array() = m1.array() - kMaxVal * (m1.array() / kMaxVal);
+    m2.array() = m2.array() - kMaxVal * (m2.array() / kMaxVal);
+  }
+
   // scalar addition
   VERIFY_IS_APPROX(m1.array() + s1, s1 + m1.array());
   VERIFY_IS_APPROX((m1.array() + s1).matrix(), MatrixType::Constant(rows, cols, s1) + m1);

test/main.h

diff --git a/test/main.h b/test/main.h
index 771725f..bce6736 100644
--- a/test/main.h
+++ b/test/main.h
@@ -176,11 +176,6 @@
 #define DEBUG
 #endif
 
-// bounds integer values for AltiVec
-#if defined(__ALTIVEC__) || defined(__VSX__)
-#define EIGEN_MAKING_DOCS
-#endif
-
 #define DEFAULT_REPEAT 10
 
 namespace Eigen {

test/product.h

diff --git a/test/product.h b/test/product.h
index 8d46846..31f577f 100644
--- a/test/product.h
+++ b/test/product.h
@@ -53,7 +53,7 @@
                  MatrixType::Flags & RowMajorBit ? ColMajor : RowMajor>
       OtherMajorMatrixType;
 
-  // Wwe want a tighter epsilon for not-approx tests.  Otherwise, for certain
+  // We want a tighter epsilon for not-approx tests.  Otherwise, for certain
   // low-precision types (e.g. bfloat16), the bound ends up being relatively large
   // (e.g. 0.12), causing flaky tests.
   RealScalar not_approx_epsilon = RealScalar(0.1) * NumTraits<RealScalar>::dummy_precision();
@@ -69,6 +69,15 @@
   ColSquareMatrixType square2 = ColSquareMatrixType::Random(cols, cols), res2 = ColSquareMatrixType::Random(cols, cols);
   RowVectorType v1 = RowVectorType::Random(rows);
   ColVectorType vc2 = ColVectorType::Random(cols), vcres(cols);
+
+  // Prevent overflows for integer types.
+  if (Eigen::NumTraits<Scalar>::IsInteger) {
+    constexpr Scalar kMaxVal = Scalar(10000);
+    m1.array() = m1.array() - kMaxVal * (m1.array() / kMaxVal);
+    m2.array() = m2.array() - kMaxVal * (m2.array() / kMaxVal);
+    v1.array() = v1.array() - kMaxVal * (v1.array() / kMaxVal);
+  }
+
   OtherMajorMatrixType tm1 = m1;
 
   Scalar s1 = internal::random<Scalar>();

test/redux.cpp

diff --git a/test/redux.cpp b/test/redux.cpp
index 8a8138d..872e44f 100644
--- a/test/redux.cpp
+++ b/test/redux.cpp
@@ -30,6 +30,12 @@
 
   Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> m2(rows, rows);
   m2.setRandom();
+  // Prevent overflows for integer types.
+  if (Eigen::NumTraits<Scalar>::IsInteger) {
+    constexpr Scalar kMaxVal = Scalar(10000);
+    m1.array() = m1.array() - kMaxVal * (m1.array() / kMaxVal);
+    m2.array() = m2.array() - kMaxVal * (m2.array() / kMaxVal);
+  }
 
   VERIFY_IS_MUCH_SMALLER_THAN(MatrixType::Zero(rows, cols).sum(), Scalar(1));
   VERIFY_IS_APPROX(

test/stl_iterators.cpp

diff --git a/test/stl_iterators.cpp b/test/stl_iterators.cpp
index 7a62673..4b60e68 100644
--- a/test/stl_iterators.cpp
+++ b/test/stl_iterators.cpp
@@ -463,6 +463,13 @@
   // check rows/cols iterators with STL algorithms
   {
     RowVectorType row = RowVectorType::Random(cols);
+    VectorType col = VectorType::Random(rows);
+    // Prevent overflows for integer types.
+    if (Eigen::NumTraits<Scalar>::IsInteger) {
+      constexpr Scalar kMaxVal = Scalar(1000);
+      row.array() = row.array() - kMaxVal * (row.array() / kMaxVal);
+      col.array() = col.array() - kMaxVal * (col.array() / kMaxVal);
+    }
     A.rowwise() = row;
     VERIFY(std::all_of(A.rowwise().begin(), A.rowwise().end(), [&row](typename ColMatrixType::RowXpr x) {
       return internal::isApprox(x.squaredNorm(), row.squaredNorm());
@@ -471,7 +478,6 @@
       return internal::isApprox(x.squaredNorm(), row.squaredNorm());
     }));
 
-    VectorType col = VectorType::Random(rows);
     A.colwise() = col;
     VERIFY(std::all_of(A.colwise().begin(), A.colwise().end(), [&col](typename ColMatrixType::ColXpr x) {
       return internal::isApprox(x.squaredNorm(), col.squaredNorm());