Initial implementation of igamma and igammac.

9 files changed, 413 insertions, 1 deletions

diff --git a/Eigen/src/Core/GenericPacketMath.h b/Eigen/src/Core/GenericPacketMath.h
index 02882bdea..ead0253df 100644
--- a/Eigen/src/Core/GenericPacketMath.h
+++ b/Eigen/src/Core/GenericPacketMath.h
@@ -78,6 +78,8 @@ struct default_packet_traits
     HasDiGamma = 0,
     HasErf = 0,
     HasErfc = 0,
+    HasIGamma = 0,
+    HasIGammac = 0,
 
     HasRound  = 0,
     HasFloor  = 0,
@@ -457,6 +459,14 @@ Packet perf(const Packet& a) { using numext::erf; return erf(a); }
 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
 Packet perfc(const Packet& a) { using numext::erfc; return erfc(a); }
 
+/** \internal \returns the incomplete gamma function igamma(\a a, \a x) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pigamma(const Packet& a, const Packet& x) { using numext::igamma; return igamma(a, x); }
+
+/** \internal \returns the complementary incomplete gamma function igammac(\a a, \a x) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pigammac(const Packet& a, const Packet& x) { using numext::igammac; return igammac(a, x); }
+
 /***************************************************************************
 * The following functions might not have to be overwritten for vectorized types
 ***************************************************************************/
diff --git a/Eigen/src/Core/GlobalFunctions.h b/Eigen/src/Core/GlobalFunctions.h
index 396da8e71..7df0fdda9 100644
--- a/Eigen/src/Core/GlobalFunctions.h
+++ b/Eigen/src/Core/GlobalFunctions.h
@@ -129,6 +129,36 @@ namespace Eigen
     );
   }
 
+  /** \returns an expression of the coefficient-wise igamma(\a a, \a x) to the given arrays.
+    *
+    * This function computes the coefficient-wise incomplete gamma function.
+    *
+    */
+  template<typename Derived,typename ExponentDerived>
+  inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_igamma_op<typename Derived::Scalar>, const Derived, const ExponentDerived>
+  igamma(const Eigen::ArrayBase<Derived>& a, const Eigen::ArrayBase<ExponentDerived>& x) 
+  {
+    return Eigen::CwiseBinaryOp<Eigen::internal::scalar_igamma_op<typename Derived::Scalar>, const Derived, const ExponentDerived>(
+      a.derived(),
+      x.derived()
+    );
+  }
+
+  /** \returns an expression of the coefficient-wise igammac(\a a, \a x) to the given arrays.
+    *
+    * This function computes the coefficient-wise complementary incomplete gamma function.
+    *
+    */
+  template<typename Derived,typename ExponentDerived>
+  inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_igammac_op<typename Derived::Scalar>, const Derived, const ExponentDerived>
+  igammac(const Eigen::ArrayBase<Derived>& a, const Eigen::ArrayBase<ExponentDerived>& x) 
+  {
+    return Eigen::CwiseBinaryOp<Eigen::internal::scalar_igammac_op<typename Derived::Scalar>, const Derived, const ExponentDerived>(
+      a.derived(),
+      x.derived()
+    );
+  }
+
   namespace internal
   {
     EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(real,scalar_real_op)
diff --git a/Eigen/src/Core/NumTraits.h b/Eigen/src/Core/NumTraits.h
index 6a596bb7d..7ddb4a867 100644
--- a/Eigen/src/Core/NumTraits.h
+++ b/Eigen/src/Core/NumTraits.h
@@ -95,6 +95,11 @@ template<typename T> struct GenericNumTraits
   static inline T infinity() {
     return numext::numeric_limits<T>::infinity();
   }
+
+  EIGEN_DEVICE_FUNC
+  static inline T quiet_NaN() {
+    return numext::numeric_limits<T>::quiet_NaN();
+  }
 };
 
 template<typename T> struct NumTraits : GenericNumTraits<T>
diff --git a/Eigen/src/Core/SpecialFunctions.h b/Eigen/src/Core/SpecialFunctions.h
index b02ad9a1f..ff2146afc 100644
--- a/Eigen/src/Core/SpecialFunctions.h
+++ b/Eigen/src/Core/SpecialFunctions.h
@@ -283,7 +283,7 @@ struct digamma_impl {
     Scalar p, q, nz, s, w, y;
     bool negative;
 
-    const Scalar maxnum = numext::numeric_limits<Scalar>::infinity();
+    const Scalar maxnum = NumTraits<Scalar>::infinity();
     const Scalar m_pi = 3.14159265358979323846;
 
     negative = 0;
@@ -401,6 +401,282 @@ struct erfc_impl<double> {
 };
 #endif  // EIGEN_HAS_C99_MATH
 
+/****************************************************************************
+ * Implementation of igammac (complemented incomplete gamma integral)       *
+ ****************************************************************************/
+
+template <typename Scalar>
+struct igammac_retval {
+  typedef Scalar type;
+};
+
+#ifndef EIGEN_HAS_C99_MATH
+
+template <typename Scalar>
+struct igammac_impl {
+  EIGEN_DEVICE_FUNC
+  static Scalar run(Scalar a, Scalar x) {
+    EIGEN_STATIC_ASSERT((internal::is_same<Scalar, Scalar>::value == false),
+                        THIS_TYPE_IS_NOT_SUPPORTED);
+    return Scalar(0);
+  }
+};
+
+#else
+
+template <typename Scalar> struct igamma_impl;  // predeclare igamma_impl
+
+template <typename Scalar>
+struct igammac_impl {
+  EIGEN_DEVICE_FUNC
+  static Scalar run(Scalar a, Scalar x) {
+    /*							igamc()
+     *
+     *	Incomplete gamma integral (modified for Eigen)
+     *
+     *
+     *
+     * SYNOPSIS:
+     *
+     * double a, x, y, igamc();
+     *
+     * y = igamc( a, x );
+     *
+     * DESCRIPTION:
+     *
+     * The function is defined by
+     *
+     *
+     *  igamc(a,x)   =   1 - igam(a,x)
+     *
+     *                            inf.
+     *                              -
+     *                     1       | |  -t  a-1
+     *               =   -----     |   e   t   dt.
+     *                    -      | |
+     *                   | (a)    -
+     *                             x
+     *
+     *
+     * In this implementation both arguments must be positive.
+     * The integral is evaluated by either a power series or
+     * continued fraction expansion, depending on the relative
+     * values of a and x.
+     *
+     * ACCURACY (float):
+     *
+     *                      Relative error:
+     * arithmetic   domain     # trials      peak         rms
+     *    IEEE      0,30        30000       7.8e-6      5.9e-7
+     *
+     *
+     * ACCURACY (double):
+     *
+     * Tested at random a, x.
+     *                a         x                      Relative error:
+     * arithmetic   domain   domain     # trials      peak         rms
+     *    IEEE     0.5,100   0,100      200000       1.9e-14     1.7e-15
+     *    IEEE     0.01,0.5  0,100      200000       1.4e-13     1.6e-15
+     *
+     */
+    /*
+      Cephes Math Library Release 2.2: June, 1992
+      Copyright 1985, 1987, 1992 by Stephen L. Moshier
+      Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+    */
+    const Scalar zero = 0;
+    const Scalar one = 1;
+    const Scalar two = 2;
+    const Scalar machep = NumTraits<Scalar>::epsilon();
+    const Scalar maxlog = ::log(NumTraits<Scalar>::highest());
+    const Scalar big = one / machep;
+
+    Scalar ans, ax, c, yc, r, t, y, z;
+    Scalar pk, pkm1, pkm2, qk, qkm1, qkm2;
+
+    if ((x <= zero) || ( a <= zero)) {
+      return one;
+    }
+
+    if ((x < one) || (x < a)) {
+      return (one - igamma_impl<Scalar>::run(a, x));
+    }
+
+    ax = a * ::log(x) - x - lgamma_impl<Scalar>::run(a);
+    if( ax < -maxlog ) {  // underflow
+      return zero;
+    }
+    ax = ::exp(ax);
+
+    // continued fraction
+    y = one - a;
+    z = x + y + one;
+    c = zero;
+    pkm2 = one;
+    qkm2 = x;
+    pkm1 = x + one;
+    qkm1 = z * x;
+    ans = pkm1/qkm1;
+
+    do {
+      c += one;
+      y += one;
+      z += two;
+      yc = y * c;
+      pk = pkm1 * z  -  pkm2 * yc;
+      qk = qkm1 * z  -  qkm2 * yc;
+      if( qk != zero ) {
+        r = pk/qk;
+        t = ::abs( (ans - r)/r );
+        ans = r;
+      } else  {
+        t = one;
+      }
+      pkm2 = pkm1;
+      pkm1 = pk;
+      qkm2 = qkm1;
+      qkm1 = qk;
+      if (::abs(pk) > big) {
+        pkm2 *= machep;
+        pkm1 *= machep;
+        qkm2 *= machep;
+        qkm1 *= machep;
+      }
+    } while( t > machep );
+
+    return ( ans * ax );
+  }
+};
+
+#endif  // EIGEN_HAS_C99_MATH
+
+/****************************************************************************
+ * Implementation of igamma (incomplete gamma integral)                     *
+ ****************************************************************************/
+
+template <typename Scalar>
+struct igamma_retval {
+  typedef Scalar type;
+};
+
+#ifndef EIGEN_HAS_C99_MATH
+
+template <typename Scalar>
+struct igamma_impl {
+  EIGEN_DEVICE_FUNC
+  static Scalar run(Scalar a, Scalar x) {
+    EIGEN_STATIC_ASSERT((internal::is_same<Scalar, Scalar>::value == false),
+                        THIS_TYPE_IS_NOT_SUPPORTED);
+    return Scalar(0);
+  }
+};
+
+#else
+
+template <typename Scalar>
+struct igamma_impl {
+  EIGEN_DEVICE_FUNC
+  static Scalar run(Scalar a, Scalar x) {
+    /*							igam()
+     *	Incomplete gamma integral
+     *
+     *
+     *
+     * SYNOPSIS:
+     *
+     * double a, x, y, igam();
+     *
+     * y = igam( a, x );
+     *
+     * DESCRIPTION:
+     *
+     * The function is defined by
+     *
+     *                           x
+     *                            -
+     *                   1       | |  -t  a-1
+     *  igam(a,x)  =   -----     |   e   t   dt.
+     *                  -      | |
+     *                 | (a)    -
+     *                           0
+     *
+     *
+     * In this implementation both arguments must be positive.
+     * The integral is evaluated by either a power series or
+     * continued fraction expansion, depending on the relative
+     * values of a and x.
+     *
+     * ACCURACY (double):
+     *
+     *                      Relative error:
+     * arithmetic   domain     # trials      peak         rms
+     *    IEEE      0,30       200000       3.6e-14     2.9e-15
+     *    IEEE      0,100      300000       9.9e-14     1.5e-14
+     *
+     *
+     * ACCURACY (float):
+     *
+     *                      Relative error:
+     * arithmetic   domain     # trials      peak         rms
+     *    IEEE      0,30        20000       7.8e-6      5.9e-7
+     *
+     */
+    /*
+      Cephes Math Library Release 2.2: June, 1992
+      Copyright 1985, 1987, 1992 by Stephen L. Moshier
+      Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+    */
+
+
+    /* left tail of incomplete gamma function:
+     *
+     *          inf.      k
+     *   a  -x   -       x
+     *  x  e     >   ----------
+     *           -     -
+     *          k=0   | (a+k+1)
+     *
+     */
+    const Scalar zero = 0;
+    const Scalar one = 1;
+    const Scalar machep = NumTraits<Scalar>::epsilon();
+    const Scalar maxlog = ::log(NumTraits<Scalar>::highest());
+
+    double ans, ax, c, r;
+
+    if( (x <= zero) || ( a <= zero) ) {
+      return zero;
+    }
+
+    if( (x > one) && (x > a ) ) {
+      return (one - igammac_impl<Scalar>::run(a,x));
+    }
+
+    /* Compute  x**a * exp(-x) / gamma(a)  */
+    ax = a * ::log(x) - x - lgamma_impl<Scalar>::run(a);
+    if( ax < -maxlog ) {
+      // underflow
+      return zero;
+    }
+    ax = ::exp(ax);
+
+    /* power series */
+    r = a;
+    c = one;
+    ans = one;
+
+    do {
+      r += one;
+      c *= x/r;
+      ans += c;
+    } while( c/ans > machep );
+
+    return( ans * ax/a );
+  }
+};
+
+#endif  // EIGEN_HAS_C99_MATH
+
 }  // end namespace internal
 
 namespace numext {
@@ -429,8 +705,21 @@ EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(erfc, Scalar)
   return EIGEN_MATHFUNC_IMPL(erfc, Scalar)::run(x);
 }
 
+template <typename Scalar>
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(igamma, Scalar)
+    igamma(const Scalar& a, const Scalar& x) {
+  return EIGEN_MATHFUNC_IMPL(igamma, Scalar)::run(a, x);
+}
+
+template <typename Scalar>
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(igammac, Scalar)
+    igammac(const Scalar& a, const Scalar& x) {
+  return EIGEN_MATHFUNC_IMPL(igammac, Scalar)::run(a, x);
+}
+
 }  // end namespace numext
 
+
 }  // end namespace Eigen
 
 #endif  // EIGEN_SPECIAL_FUNCTIONS_H
diff --git a/Eigen/src/Core/arch/CUDA/MathFunctions.h b/Eigen/src/Core/arch/CUDA/MathFunctions.h
index a2c06a817..6e84d3af8 100644
--- a/Eigen/src/Core/arch/CUDA/MathFunctions.h
+++ b/Eigen/src/Core/arch/CUDA/MathFunctions.h
@@ -116,6 +116,24 @@ double2 perfc<double2>(const double2& a)
   return make_double2(erfc(a.x), erfc(a.y));
 }
 
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+float4 pigamma<float4>(const float4& a, const float4& x)
+{
+  using numext::pigamma;
+  return make_float4(
+    pigamma(a.x, x.x),
+    pigamma(a.y, x.y),
+    pigamma(a.z, x.z),
+    pigamma(a.w, x.w));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+double2 pigammac<double2>(const double2& a, const double& x)
+{
+  using numext::pigammac;
+  return make_double2(pigammac(a.x, x.x), pigammac(a.y, x.y));
+}
+
 
 #endif
 
diff --git a/Eigen/src/Core/arch/CUDA/PacketMath.h b/Eigen/src/Core/arch/CUDA/PacketMath.h
index d3d9f910e..d2563030b 100644
--- a/Eigen/src/Core/arch/CUDA/PacketMath.h
+++ b/Eigen/src/Core/arch/CUDA/PacketMath.h
@@ -43,6 +43,8 @@ template<> struct packet_traits<float> : default_packet_traits
     HasDiGamma = 1,
     HasErf = 1,
     HasErfc = 1,
+    HasIgamma = 1,
+    HasIGammac = 1,
 
     HasBlend = 0,
   };
@@ -67,6 +69,8 @@ template<> struct packet_traits<double> : default_packet_traits
     HasDiGamma = 1,
     HasErf = 1,
     HasErfc = 1,
+    HasIGamma = 1,
+    HasIGammac = 1,
 
     HasBlend = 0,
   };
diff --git a/Eigen/src/Core/functors/BinaryFunctors.h b/Eigen/src/Core/functors/BinaryFunctors.h
index 4962d625c..5cdfff845 100644
--- a/Eigen/src/Core/functors/BinaryFunctors.h
+++ b/Eigen/src/Core/functors/BinaryFunctors.h
@@ -337,6 +337,55 @@ template<> struct functor_traits<scalar_boolean_or_op> {
   };
 };
 
+/** \internal
+  * \brief Template functor to compute the incomplete gamma function igamma(a, x)
+  *
+  * \sa class CwiseBinaryOp, Cwise::igamma
+  */
+template<typename Scalar> struct scalar_igamma_op {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_igamma_op)
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& x) const {
+    using numext::igamma; return igamma(a, x);
+  }
+  template<typename Packet>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& x) const {
+    return internal::pigammac(a, x);
+  }
+};
+template<typename Scalar>
+struct functor_traits<scalar_igamma_op<Scalar> > {
+  enum {
+    // Guesstimate
+    Cost = 20 * NumTraits<Scalar>::MulCost + 10 * NumTraits<Scalar>::AddCost,
+    PacketAccess = packet_traits<Scalar>::HasIGamma
+  };
+};
+
+
+/** \internal
+  * \brief Template functor to compute the complementary incomplete gamma function igammac(a, x)
+  *
+  * \sa class CwiseBinaryOp, Cwise::igammac
+  */
+template<typename Scalar> struct scalar_igammac_op {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_igammac_op)
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& x) const {
+    using numext::igammac; return igammac(a, x);
+  }
+  template<typename Packet>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& x) const
+  {
+    return internal::pigammac(a, x);
+  }
+};
+template<typename Scalar>
+struct functor_traits<scalar_igammac_op<Scalar> > {
+  enum {
+    // Guesstimate
+    Cost = 20 * NumTraits<Scalar>::MulCost + 10 * NumTraits<Scalar>::AddCost,
+    PacketAccess = packet_traits<Scalar>::HasIGammac
+  };
+};
 
 
 //---------- binary functors bound to a constant, thus appearing as a unary functor ----------
diff --git a/Eigen/src/Core/util/ForwardDeclarations.h b/Eigen/src/Core/util/ForwardDeclarations.h
index f09632375..a102e5457 100644
--- a/Eigen/src/Core/util/ForwardDeclarations.h
+++ b/Eigen/src/Core/util/ForwardDeclarations.h
@@ -206,6 +206,8 @@ template<typename Scalar> struct scalar_add_op;
 template<typename Scalar> struct scalar_constant_op;
 template<typename Scalar> struct scalar_identity_op;
 template<typename Scalar,bool iscpx> struct scalar_sign_op;
+template<typename Scalar> struct scalar_igamma_op;
+template<typename Scalar> struct scalar_igammac_op;
 
 template<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_product_op;
 template<typename LhsScalar,typename RhsScalar> struct scalar_multiple2_op;
diff --git a/Eigen/src/Core/util/Meta.h b/Eigen/src/Core/util/Meta.h
index 6b35179f2..24e8a6d8a 100644
--- a/Eigen/src/Core/util/Meta.h
+++ b/Eigen/src/Core/util/Meta.h
@@ -148,6 +148,7 @@ template<typename T> struct numeric_limits
   static T (max)() { assert(false && "Highest not supported for this type"); }
   static T (min)() { assert(false && "Lowest not supported for this type"); }
   static T infinity() { assert(false && "Infinity not supported for this type"); }
+  static T quiet_NaN() { assert(false && "quiet_NaN not supported for this type"); }
 };
 template<> struct numeric_limits<float>
 {
@@ -159,6 +160,8 @@ template<> struct numeric_limits<float>
   static float (min)() { return FLT_MIN; }
   EIGEN_DEVICE_FUNC
   static float infinity() { return CUDART_INF_F; }
+  EIGEN_DEVICE_FUNC
+  static float quiet_NaN() { return CUDART_NAN_F; }
 };
 template<> struct numeric_limits<double>
 {
@@ -170,6 +173,8 @@ template<> struct numeric_limits<double>
   static double (min)() { return DBL_MIN; }
   EIGEN_DEVICE_FUNC
   static double infinity() { return CUDART_INF; }
+  EIGEN_DEVICE_FUNC
+  static double quiet_NaN() { return CUDART_NAN; }
 };
 template<> struct numeric_limits<int>
 {