Add ndtri function, the inverse of the normal distribution function.

Eigen/src/Core/GenericPacketMath.h

@@ -83,6 +83,7 @@ struct default_packet_traits
     HasPolygamma = 0,
     HasErf = 0,
     HasErfc = 0,
+    HasNdtri = 0,
     HasI0e = 0,
     HasI1e = 0,
     HasIGamma = 0,
@@ -257,12 +258,32 @@ pldexp(const Packet &a, const Packet &exponent) { return std::ldexp(a,exponent);
 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
 pzero(const Packet& a) { return pxor(a,a); }
 
+template<> EIGEN_DEVICE_FUNC inline float pzero<float>(const float& a) {
+  EIGEN_UNUSED_VARIABLE(a);
+  return 0.;
+}
+
+template<> EIGEN_DEVICE_FUNC inline double pzero<double>(const double& a) {
+  EIGEN_UNUSED_VARIABLE(a);
+  return 0.;
+}
+
 /** \internal \returns bits of \a or \b according to the input bit mask \a mask */
 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
 pselect(const Packet& mask, const Packet& a, const Packet& b) {
   return por(pand(a,mask),pandnot(b,mask));
 }
 
+template<> EIGEN_DEVICE_FUNC inline float pselect<float>(
+    const float& mask, const float& a, const float&b) {
+  return mask == 0 ? b : a;
+}
+
+template<> EIGEN_DEVICE_FUNC inline double pselect<double>(
+    const double& mask, const double& a, const double& b) {
+  return mask == 0 ? b : a;
+}
+
 /** \internal \returns a <= b as a bit mask */
 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
 pcmp_le(const Packet& a, const Packet& b)  { return a<=b ? ptrue(a) : pzero(a); }

Eigen/src/Core/GlobalFunctions.h

@@ -76,6 +76,7 @@ namespace Eigen
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(digamma,scalar_digamma_op,derivative of lgamma,\sa ArrayBase::digamma)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(erf,scalar_erf_op,error function,\sa ArrayBase::erf)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(erfc,scalar_erfc_op,complement error function,\sa ArrayBase::erfc)
+  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(ndtri,scalar_ndtri_op,inverse normal distribution function,\sa ArrayBase::ndtri)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(exp,scalar_exp_op,exponential,\sa ArrayBase::exp)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(expm1,scalar_expm1_op,exponential of a value minus 1,\sa ArrayBase::expm1)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log,scalar_log_op,natural logarithm,\sa Eigen::log10 DOXCOMMA ArrayBase::log)

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

@@ -66,6 +66,7 @@ template<> struct packet_traits<float>  : default_packet_traits
     HasCos  = EIGEN_FAST_MATH,
     HasLog  = 1,
     HasExp  = 1,
+    HasNdtri = 1,
     HasSqrt = 1,
     HasRsqrt = 1,
     HasTanh  = EIGEN_FAST_MATH,

Eigen/src/Core/arch/AVX512/PacketMath.h

@@ -60,6 +60,9 @@ template<> struct packet_traits<float>  : default_packet_traits
 #if EIGEN_GNUC_AT_LEAST(5, 3) || (!EIGEN_COMP_GNUC_STRICT)
 #ifdef EIGEN_VECTORIZE_AVX512DQ
     HasLog = 1,
+    HasLog1p = 1,
+    HasExpm1 = 1,
+    HasNdtri = 1,
 #endif
     HasExp = 1,
     HasSqrt = EIGEN_FAST_MATH,

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

@@ -467,5 +467,60 @@ Packet pcos_float(const Packet& x)
   return psincos_float<false>(x);
 }
 
+/* polevl (modified for Eigen)
+ *
+ *      Evaluate polynomial
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int N;
+ * Scalar x, y, coef[N+1];
+ *
+ * y = polevl<decltype(x), N>( x, coef);
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Evaluates polynomial of degree N:
+ *
+ *                     2          N
+ * y  =  C  + C x + C x  +...+ C x
+ *        0    1     2          N
+ *
+ * Coefficients are stored in reverse order:
+ *
+ * coef[0] = C  , ..., coef[N] = C  .
+ *            N                   0
+ *
+ *  The function p1evl() assumes that coef[N] = 1.0 and is
+ * omitted from the array.  Its calling arguments are
+ * otherwise the same as polevl().
+ *
+ *
+ * The Eigen implementation is templatized.  For best speed, store
+ * coef as a const array (constexpr), e.g.
+ *
+ * const double coef[] = {1.0, 2.0, 3.0, ...};
+ *
+ */
+template <typename Packet, int N>
+struct ppolevl {
+  static EIGEN_STRONG_INLINE Packet run(const Packet& x, const typename unpacket_traits<Packet>::type coeff[]) {
+    EIGEN_STATIC_ASSERT((N > 0), YOU_MADE_A_PROGRAMMING_MISTAKE);
+    return pmadd(ppolevl<Packet, N-1>::run(x, coeff), x, pset1<Packet>(coeff[N]));
+  }
+};
+
+template <typename Packet>
+struct ppolevl<Packet, 0> {
+  static EIGEN_STRONG_INLINE Packet run(const Packet& x, const typename unpacket_traits<Packet>::type coeff[]) {
+    EIGEN_UNUSED_VARIABLE(x);
+    return pset1<Packet>(coeff[0]);
+  }
+};
+
 } // end namespace internal
 } // end namespace Eigen

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

@@ -44,6 +44,7 @@ template<> struct packet_traits<float> : default_packet_traits
     HasPolygamma = 1,
     HasErf = 1,
     HasErfc = 1,
+    HasNdtri = 1,
     HasI0e = 1,
     HasI1e = 1,
     HasIGamma = 1,
@@ -78,6 +79,7 @@ template<> struct packet_traits<double> : default_packet_traits
     HasPolygamma = 1,
     HasErf = 1,
     HasErfc = 1,
+    HasNdtri = 1,
     HasI0e = 1,
     HasI1e = 1,
     HasIGamma = 1,

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

@@ -111,6 +111,9 @@ template<> struct packet_traits<float>  : default_packet_traits
     HasCos  = EIGEN_FAST_MATH,
     HasLog  = 1,
     HasExp  = 1,
+    HasLog1p = 1,
+    HasExpm1 = 1,
+    HasNdtri = 1,
     HasSqrt = 1,
     HasRsqrt = 1,
     HasTanh  = EIGEN_FAST_MATH,

Eigen/src/Core/arch/SYCL/InteropHeaders.h

@@ -54,6 +54,7 @@ struct sycl_packet_traits : default_packet_traits {
     HasPolygamma = 0,
     HasErf = 0,
     HasErfc = 0,
+    HasNdtri = 0,
     HasIGamma = 0,
     HasIGammac = 0,
     HasBetaInc = 0,

Eigen/src/Core/util/ForwardDeclarations.h

@@ -214,6 +214,7 @@ template<typename Scalar> struct scalar_lgamma_op;
 template<typename Scalar> struct scalar_digamma_op;
 template<typename Scalar> struct scalar_erf_op;
 template<typename Scalar> struct scalar_erfc_op;
+template<typename Scalar> struct scalar_ndtri_op;
 template<typename Scalar> struct scalar_igamma_op;
 template<typename Scalar> struct scalar_igammac_op;
 template<typename Scalar> struct scalar_zeta_op;

Eigen/src/plugins/ArrayCwiseUnaryOps.h

@@ -536,14 +536,12 @@ typedef CwiseUnaryOp<internal::scalar_lgamma_op<Scalar>, const Derived> LgammaRe
 typedef CwiseUnaryOp<internal::scalar_digamma_op<Scalar>, const Derived> DigammaReturnType;
 typedef CwiseUnaryOp<internal::scalar_erf_op<Scalar>, const Derived> ErfReturnType;
 typedef CwiseUnaryOp<internal::scalar_erfc_op<Scalar>, const Derived> ErfcReturnType;
+typedef CwiseUnaryOp<internal::scalar_ndtri_op<Scalar>, const Derived> NdtriReturnType;
 
 /** \cpp11 \returns an expression of the coefficient-wise ln(|gamma(*this)|).
   *
   * \specialfunctions_module
   *
-  * Example: \include Cwise_lgamma.cpp
-  * Output: \verbinclude Cwise_lgamma.out
-  *
   * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types,
   * or float/double in non c++11 mode, the user has to provide implementations of lgamma(T) for any scalar
   * type T to be supported.
@@ -579,9 +577,6 @@ digamma() const
   *
   * \specialfunctions_module
   *
-  * Example: \include Cwise_erf.cpp
-  * Output: \verbinclude Cwise_erf.out
-  *
   * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types,
   * or float/double in non c++11 mode, the user has to provide implementations of erf(T) for any scalar
   * type T to be supported.
@@ -600,9 +595,6 @@ erf() const
   *
   * \specialfunctions_module
   *
-  * Example: \include Cwise_erfc.cpp
-  * Output: \verbinclude Cwise_erfc.out
-  *
   * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types,
   * or float/double in non c++11 mode, the user has to provide implementations of erfc(T) for any scalar
   * type T to be supported.
@@ -615,3 +607,21 @@ erfc() const
 {
   return ErfcReturnType(derived());
 }
+
+/** \cpp11 \returns an expression of the coefficient-wise Complementary error
+  * function of *this.
+  *
+  * \specialfunctions_module
+  *
+  * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types,
+  * or float/double in non c++11 mode, the user has to provide implementations of ndtri(T) for any scalar
+  * type T to be supported.
+  *
+  * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_ndtri">Math functions</a>, erf()
+  */
+EIGEN_DEVICE_FUNC
+inline const NdtriReturnType
+ndtri() const
+{
+  return NdtriReturnType(derived());
+}