Fix a bug in the implementation of Carmack's fast sqrt algorithm in Eigen (enabled by EIGEN_FAST_MATH), which causes the vectorized parts of the computation to return -0.0 instead of NaN for negative arguments.

Benchmark speed in Giga-sqrts/s
Intel(R) Xeon(R) CPU E5-1650 v3 @ 3.50GHz
-----------------------------------------
                    SSE        AVX
Fast=1              2.529G     4.380G
Fast=0              1.944G     1.898G
Fast=1 fixed        2.214G     3.739G

This table illustrates the worst case in terms speed impact: It was measured by repeatedly computing the sqrt of an n=4096 float vector that fits in L1 cache. For large vectors the operation becomes memory bound and the differences between the different versions almost negligible.

1 files changed, 14 insertions, 17 deletions

diff --git a/test/packetmath.cpp b/test/packetmath.cpp
index 1394d9f2b..c3d3e1521 100644
--- a/test/packetmath.cpp
+++ b/test/packetmath.cpp
@@ -193,7 +193,7 @@ template<typename Scalar> void packetmath()
     internal::pstore(data2+3*PacketSize, A3);
     VERIFY(areApprox(ref, data2, 4*PacketSize) && "internal::pbroadcast4");
   }
-  
+
   {
     for (int i=0; i<PacketSize*2; ++i)
       ref[i] = data1[i/PacketSize];
@@ -203,9 +203,9 @@ template<typename Scalar> void packetmath()
     internal::pstore(data2+1*PacketSize, A1);
     VERIFY(areApprox(ref, data2, 2*PacketSize) && "internal::pbroadcast2");
   }
- 
+
   VERIFY(internal::isApprox(data1[0], internal::pfirst(internal::pload<Packet>(data1))) && "internal::pfirst");
- 
+
   if(PacketSize>1)
   {
     for(int offset=0;offset<4;++offset)
@@ -315,7 +315,7 @@ template<typename Scalar> void packetmath_real()
   CHECK_CWISE1_IF(PacketTraits::HasRound, numext::round, internal::pround);
   CHECK_CWISE1_IF(PacketTraits::HasCeil, numext::ceil, internal::pceil);
   CHECK_CWISE1_IF(PacketTraits::HasFloor, numext::floor, internal::pfloor);
-  
+
   for (int i=0; i<size; ++i)
   {
     data1[i] = internal::random<Scalar>(-1,1);
@@ -440,12 +440,9 @@ template<typename Scalar> void packetmath_real()
     data1[0] = Scalar(-1.0f);
     h.store(data2, internal::plog(h.load(data1)));
     VERIFY((numext::isnan)(data2[0]));
-#if !EIGEN_FAST_MATH
     h.store(data2, internal::psqrt(h.load(data1)));
     VERIFY((numext::isnan)(data2[0]));
     VERIFY((numext::isnan)(data2[1]));
-#endif
-
   }
 }
 
@@ -459,7 +456,7 @@ template<typename Scalar> void packetmath_notcomplex()
   EIGEN_ALIGN_MAX Scalar data1[PacketTraits::size*4];
   EIGEN_ALIGN_MAX Scalar data2[PacketTraits::size*4];
   EIGEN_ALIGN_MAX Scalar ref[PacketTraits::size*4];
-  
+
   Array<Scalar,Dynamic,1>::Map(data1, PacketTraits::size*4).setRandom();
 
   ref[0] = data1[0];
@@ -478,7 +475,7 @@ template<typename Scalar> void packetmath_notcomplex()
   for (int i=0; i<PacketSize; ++i)
     ref[0] = (std::max)(ref[0],data1[i]);
   VERIFY(internal::isApprox(ref[0], internal::predux_max(internal::pload<Packet>(data1))) && "internal::predux_max");
-  
+
   for (int i=0; i<PacketSize; ++i)
     ref[i] = data1[0]+Scalar(i);
   internal::pstore(data2, internal::plset<Packet>(data1[0]));
@@ -490,12 +487,12 @@ template<typename Scalar,bool ConjLhs,bool ConjRhs> void test_conj_helper(Scalar
   typedef internal::packet_traits<Scalar> PacketTraits;
   typedef typename PacketTraits::type Packet;
   const int PacketSize = PacketTraits::size;
-  
+
   internal::conj_if<ConjLhs> cj0;
   internal::conj_if<ConjRhs> cj1;
   internal::conj_helper<Scalar,Scalar,ConjLhs,ConjRhs> cj;
   internal::conj_helper<Packet,Packet,ConjLhs,ConjRhs> pcj;
-  
+
   for(int i=0;i<PacketSize;++i)
   {
     ref[i] = cj0(data1[i]) * cj1(data2[i]);
@@ -503,7 +500,7 @@ template<typename Scalar,bool ConjLhs,bool ConjRhs> void test_conj_helper(Scalar
   }
   internal::pstore(pval,pcj.pmul(internal::pload<Packet>(data1),internal::pload<Packet>(data2)));
   VERIFY(areApprox(ref, pval, PacketSize) && "conj_helper pmul");
-  
+
   for(int i=0;i<PacketSize;++i)
   {
     Scalar tmp = ref[i];
@@ -531,12 +528,12 @@ template<typename Scalar> void packetmath_complex()
     data1[i] = internal::random<Scalar>() * Scalar(1e2);
     data2[i] = internal::random<Scalar>() * Scalar(1e2);
   }
-  
+
   test_conj_helper<Scalar,false,false> (data1,data2,ref,pval);
   test_conj_helper<Scalar,false,true>  (data1,data2,ref,pval);
   test_conj_helper<Scalar,true,false>  (data1,data2,ref,pval);
   test_conj_helper<Scalar,true,true>   (data1,data2,ref,pval);
-  
+
   {
     for(int i=0;i<PacketSize;++i)
       ref[i] = Scalar(std::imag(data1[i]),std::real(data1[i]));
@@ -556,9 +553,9 @@ template<typename Scalar> void packetmath_scatter_gather()
   for (int i=0; i<PacketSize; ++i) {
     data1[i] = internal::random<Scalar>()/RealScalar(PacketSize);
   }
-  
+
   int stride = internal::random<int>(1,20);
-  
+
   EIGEN_ALIGN_MAX Scalar buffer[PacketSize*20];
   memset(buffer, 0, 20*sizeof(Packet));
   Packet packet = internal::pload<Packet>(data1);
@@ -594,7 +591,7 @@ void test_packetmath()
     CALL_SUBTEST_1( packetmath_notcomplex<float>() );
     CALL_SUBTEST_2( packetmath_notcomplex<double>() );
     CALL_SUBTEST_3( packetmath_notcomplex<int>() );
-    
+
     CALL_SUBTEST_1( packetmath_real<float>() );
     CALL_SUBTEST_2( packetmath_real<double>() );