Replace M_LOG2E and M_LN2 with custom macros.

For these to exist we would need to define `_USE_MATH_DEFINES` before
`cmath` or `math.h` is first included.  However, we don't
control the include order for projects outside Eigen, so even defining
the macro in `Eigen/Core` does not fix the issue for projects that
end up including `<cmath>` before Eigen does (explicitly or transitively).

To fix this, we define `EIGEN_LOG2E` and `EIGEN_LN2` ourselves.

Eigen/src/Core/GenericPacketMath.h

@@ -668,7 +668,7 @@ Packet plog10(const Packet& a) { EIGEN_USING_STD(log10); return log10(a); }
 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
 Packet plog2(const Packet& a) {
   typedef typename internal::unpacket_traits<Packet>::type Scalar;
-  return pmul(pset1<Packet>(Scalar(M_LOG2E)), plog(a)); 
+  return pmul(pset1<Packet>(Scalar(EIGEN_LOG2E)), plog(a)); 
 }
 
 /** \internal \returns the square-root of \a a (coeff-wise) */

Eigen/src/Core/MathFunctions.h

@@ -10,9 +10,11 @@
 #ifndef EIGEN_MATHFUNCTIONS_H
 #define EIGEN_MATHFUNCTIONS_H
 
-// source: http://www.geom.uiuc.edu/~huberty/math5337/groupe/digits.html
 // TODO this should better be moved to NumTraits
+// Source: WolframAlpha
 #define EIGEN_PI    3.141592653589793238462643383279502884197169399375105820974944592307816406L
+#define EIGEN_LOG2E 1.442695040888963407359924681001892137426645954152985934135449406931109219L
+#define EIGEN_LN2   0.693147180559945309417232121458176568075500134360255254120680009493393621L
 
 namespace Eigen {
 

Eigen/src/Core/arch/Default/BFloat16.h

@@ -513,7 +513,7 @@ EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 log10(const bfloat16& a) {
   return bfloat16(::log10f(float(a)));
 }
 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 log2(const bfloat16& a) {
-  return bfloat16(static_cast<float>(M_LOG2E) * ::logf(float(a)));
+  return bfloat16(static_cast<float>(EIGEN_LOG2E) * ::logf(float(a)));
 }
 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 sqrt(const bfloat16& a) {
     return bfloat16(::sqrtf(float(a)));

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

@@ -132,10 +132,10 @@ Packet plog_impl_float(const Packet _x)
 
   // Add the logarithm of the exponent back to the result of the interpolation.
   if (base2) {
-    const Packet cst_log2e = pset1<Packet>(static_cast<float>(M_LOG2E));
+    const Packet cst_log2e = pset1<Packet>(static_cast<float>(EIGEN_LOG2E));
     x = pmadd(x, cst_log2e, e);
   } else {
-    const Packet cst_ln2 = pset1<Packet>(static_cast<float>(M_LN2));
+    const Packet cst_ln2 = pset1<Packet>(static_cast<float>(EIGEN_LN2));
     x = pmadd(e, cst_ln2, x);
   }
 
@@ -253,10 +253,10 @@ Packet plog_impl_double(const Packet _x)
 
   // Add the logarithm of the exponent back to the result of the interpolation.
   if (base2) {
-    const Packet cst_log2e = pset1<Packet>(M_LOG2E);
+    const Packet cst_log2e = pset1<Packet>(EIGEN_LOG2E);
     x = pmadd(x, cst_log2e, e);
   } else {
-    const Packet cst_ln2 = pset1<Packet>(M_LN2);
+    const Packet cst_ln2 = pset1<Packet>(EIGEN_LN2);
     x = pmadd(e, cst_ln2, x);
   }
 

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

@@ -623,7 +623,7 @@ EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half log10(const half& a) {
   return half(::log10f(float(a)));
 }
 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half log2(const half& a) {
-  return half(static_cast<float>(M_LOG2E) * ::logf(float(a)));
+  return half(static_cast<float>(EIGEN_LOG2E) * ::logf(float(a)));
 }
 
 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half sqrt(const half& a) {

Eigen/src/Core/functors/UnaryFunctors.h

@@ -403,7 +403,7 @@ struct functor_traits<scalar_log10_op<Scalar> >
   */
 template<typename Scalar> struct scalar_log2_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_log2_op)
-  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return Scalar(M_LOG2E) * std::log(a); }
+  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return Scalar(EIGEN_LOG2E) * std::log(a); }
   template <typename Packet>
   EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::plog2(a); }
 };

test/packetmath.cpp

@@ -495,7 +495,7 @@ void packetmath() {
 // c++11 has std::log2 for real, but not for complex types.
 template <typename Scalar>
 Scalar log2(Scalar x) {
-  return Scalar(M_LOG2E) * std::log(x);
+  return Scalar(EIGEN_LOG2E) * std::log(x);
 }
 
 template <typename Scalar, typename Packet>