bug #698: rewrite LinSpaced for integer scalar types to avoid overflow and guarantee an even spacing when possible.

Otherwise, the "high" bound is implicitly lowered to the largest value allowing for an even distribution.
This changeset also disable vectorization for this integer path.

1 files changed, 23 insertions, 15 deletions

diff --git a/test/nullary.cpp b/test/nullary.cpp
index 35f24de47..162e84210 100644
--- a/test/nullary.cpp
+++ b/test/nullary.cpp
@@ -57,23 +57,31 @@ void testVectorType(const VectorType& base)
     VERIFY_IS_APPROX(m,n);
   }
 
-  VectorType n(size);
-  for (int i=0; i<size; ++i)
-    n(i) = size==1 ? low : (low + ((high-low)*Scalar(i))/(size-1));
-  VERIFY_IS_APPROX(m,n);
-
-  // random access version
-  m = VectorType::LinSpaced(size,low,high);
-  VERIFY_IS_APPROX(m,n);
+  if((!NumTraits<Scalar>::IsInteger) || ((high-low)>=size && (Index(high-low)%(size-1))==0) || (Index(high-low+1)<size && (size%Index(high-low+1))==0))
+  {
+    VectorType n(size);
+    if((!NumTraits<Scalar>::IsInteger) || (high-low>=size))
+      for (int i=0; i<size; ++i)
+        n(i) = size==1 ? low : (low + ((high-low)*Scalar(i))/(size-1));
+    else
+      for (int i=0; i<size; ++i)
+        n(i) = size==1 ? low : low + Scalar((double(high-low+1)*double(i))/double(size));
+    VERIFY_IS_APPROX(m,n);
 
-  VERIFY( internal::isApprox(m(m.size()-1),high) );
-  VERIFY( size==1 || internal::isApprox(m(0),low) );
+    // random access version
+    m = VectorType::LinSpaced(size,low,high);
+    VERIFY_IS_APPROX(m,n);
+    VERIFY( internal::isApprox(m(m.size()-1),high) );
+    VERIFY( size==1 || internal::isApprox(m(0),low) );
 
-  // sequential access version
-  m = VectorType::LinSpaced(Sequential,size,low,high);
-  VERIFY_IS_APPROX(m,n);
+    // sequential access version
+    m = VectorType::LinSpaced(Sequential,size,low,high);
+    VERIFY_IS_APPROX(m,n);
+    VERIFY( internal::isApprox(m(m.size()-1),high) );
+  }
 
-  VERIFY( internal::isApprox(m(m.size()-1),high) );
+  Scalar tol_factor = (high>=0) ? (1+NumTraits<Scalar>::dummy_precision()) : (1-NumTraits<Scalar>::dummy_precision());
+  VERIFY( m(m.size()-1) <= high*tol_factor );
   VERIFY( size==1 || internal::isApprox(m(0),low) );
 
   // check whether everything works with row and col major vectors
@@ -96,7 +104,7 @@ void testVectorType(const VectorType& base)
   VERIFY_IS_APPROX( ScalarMatrix::LinSpaced(1,low,high), ScalarMatrix::Constant(high) );
 
   // regression test for bug 526 (linear vectorized transversal)
-  if (size > 1) {
+  if (size > 1 && (!NumTraits<Scalar>::IsInteger)) {
     m.tail(size-1).setLinSpaced(low, high);
     VERIFY_IS_APPROX(m(size-1), high);
   }