From 53c77061f08d220db9955b91b30f65e5d13c6277 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Mon, 24 Oct 2016 15:50:27 +0200
Subject: 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.

---
 test/nullary.cpp | 38 +++++++++++++++++++++++---------------
 1 file changed, 23 insertions(+), 15 deletions(-)

(limited to 'test/nullary.cpp')

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);
   }
-- 
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