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Merged in ebrevdo/eigen (pull request PR-169)

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Bugfixes to cuda tests, igamma & igammac implemented, & tests for digamma, igamma, igammac on CPU & GPU.
This commit is contained in:
Christoph Hertzberg
2016-03-16 21:59:08 +01:00
parent ab9b749b45 f1f7181f53
commit 46aa9772fc
15 changed files with 858 additions and 11 deletions
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10
Eigen/src/Core/GenericPacketMath.h
View File

@@ -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_DEVICE_FUNC EIGEN_STRONG_INLINE
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_DEVICE_FUNC EIGEN_STRONG_INLINE
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
***************************************************************************/

30
Eigen/src/Core/GlobalFunctions.h
View File

@@ -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)

68
Eigen/src/Core/MathFunctions.h
View File

@@ -946,6 +946,14 @@ T (floor)(const T& x)
return floor(x);
}
#ifdef __CUDACC__
template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
float floor(const float &x) { return ::floorf(x); }
template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
double floor(const double &x) { return ::floor(x); }
#endif
template<typename T>
EIGEN_DEVICE_FUNC
T (ceil)(const T& x)
@@ -985,6 +993,66 @@ T sqrt(const T &x)
return sqrt(x);
}
template<typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
T log(const T &x) {
EIGEN_USING_STD_MATH(log);
return log(x);
}
#ifdef __CUDACC__
template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
float log(const float &x) { return ::logf(x); }
template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
double log(const double &x) { return ::log(x); }
#endif
template<typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
T tan(const T &x) {
EIGEN_USING_STD_MATH(tan);
return tan(x);
}
#ifdef __CUDACC__
template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
float tan(const float &x) { return ::tanf(x); }
template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
double tan(const double &x) { return ::tan(x); }
#endif
template<typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
T abs(const T &x) {
EIGEN_USING_STD_MATH(abs);
return abs(x);
}
#ifdef __CUDACC__
template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
float abs(const float &x) { return ::fabsf(x); }
template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
double abs(const double &x) { return ::fabs(x); }
#endif
template<typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
T exp(const T &x) {
EIGEN_USING_STD_MATH(exp);
return exp(x);
}
#ifdef __CUDACC__
template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
float exp(const float &x) { return ::expf(x); }
template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
double exp(const double &x) { return ::exp(x); }
#endif
} // end namespace numext
namespace internal {

5
Eigen/src/Core/NumTraits.h
View File

@@ -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>

344
Eigen/src/Core/SpecialFunctions.h
View File

@@ -283,8 +283,8 @@ struct digamma_impl {
Scalar p, q, nz, s, w, y;
bool negative;
const Scalar maxnum = numext::numeric_limits<Scalar>::infinity();
const Scalar m_pi = 3.14159265358979323846;
const Scalar maxnum = NumTraits<Scalar>::infinity();
const Scalar m_pi = EIGEN_PI;
negative = 0;
nz = 0.0;
@@ -296,7 +296,7 @@ struct digamma_impl {
if (x <= zero) {
negative = one;
q = x;
p = ::floor(q);
p = numext::floor(q);
if (p == q) {
return maxnum;
}
@@ -309,7 +309,7 @@ struct digamma_impl {
p += one;
nz = q - p;
}
nz = m_pi / ::tan(m_pi * nz);
nz = m_pi / numext::tan(m_pi * nz);
}
else {
nz = zero;
@@ -327,7 +327,7 @@ struct digamma_impl {
y = digamma_impl_maybe_poly<Scalar>::run(s);
y = ::log(s) - (half / s) - y - w;
y = numext::log(s) - (half / s) - y - w;
return (negative) ? y - nz : y;
}
@@ -401,6 +401,327 @@ 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 igamma_helper {
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
static Scalar machep() { assert(false && "machep not supported for this type"); return 0.0; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
static Scalar big() { assert(false && "big not supported for this type"); return 0.0; }
};
template <>
struct igamma_helper<float> {
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
static float machep() {
return NumTraits<float>::epsilon() / 2; // 1.0 - machep == 1.0
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
static float big() {
// use epsneg (1.0 - epsneg == 1.0)
return 1.0 / (NumTraits<float>::epsilon() / 2);
}
};
template <>
struct igamma_helper<double> {
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
static double machep() {
return NumTraits<double>::epsilon() / 2; // 1.0 - machep == 1.0
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
static double big() {
return 1.0 / NumTraits<double>::epsilon();
}
};
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 = igamma_helper<Scalar>::machep();
const Scalar maxlog = numext::log(NumTraits<Scalar>::highest());
const Scalar big = igamma_helper<Scalar>::big();
const Scalar biginv = 1 / big;
const Scalar nan = NumTraits<Scalar>::quiet_NaN();
const Scalar inf = NumTraits<Scalar>::infinity();
Scalar ans, ax, c, yc, r, t, y, z;
Scalar pk, pkm1, pkm2, qk, qkm1, qkm2;
if ((x < zero) || ( a <= zero)) {
// domain error
return nan;
}
if ((x < one) || (x < a)) {
return (one - igamma_impl<Scalar>::run(a, x));
}
if (x == inf) return zero; // std::isinf crashes on CUDA
/* Compute x**a * exp(-x) / gamma(a) */
ax = a * numext::log(x) - x - lgamma_impl<Scalar>::run(a);
if (ax < -maxlog) { // underflow
return zero;
}
ax = numext::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;
while (true) {
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 = numext::abs((ans - r) / r);
ans = r;
} else {
t = one;
}
pkm2 = pkm1;
pkm1 = pk;
qkm2 = qkm1;
qkm1 = qk;
if (abs(pk) > big) {
pkm2 *= biginv;
pkm1 *= biginv;
qkm2 *= biginv;
qkm1 *= biginv;
}
if (t <= machep) break;
}
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 = igamma_helper<Scalar>::machep();
const Scalar maxlog = numext::log(NumTraits<Scalar>::highest());
const Scalar nan = NumTraits<Scalar>::quiet_NaN();
double ans, ax, c, r;
if (x == zero) return zero;
if ((x < zero) || ( a <= zero)) { // domain error
return nan;
}
if ((x > one) && (x > a)) {
return (one - igammac_impl<Scalar>::run(a, x));
}
/* Compute x**a * exp(-x) / gamma(a) */
ax = a * numext::log(x) - x - lgamma_impl<Scalar>::run(a);
if (ax < -maxlog) {
// underflow
return zero;
}
ax = numext::exp(ax);
/* power series */
r = a;
c = one;
ans = one;
while (true) {
r += one;
c *= x/r;
ans += c;
if (c/ans <= machep) break;
}
return (ans * ax / a);
}
};
#endif // EIGEN_HAS_C99_MATH
} // end namespace internal
namespace numext {
@@ -429,8 +750,21 @@ 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

36
Eigen/src/Core/arch/CUDA/MathFunctions.h
View File

@@ -117,6 +117,42 @@ double2 perfc<double2>(const double2& a)
}
template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
float4 pigamma<float4>(const float4& a, const float4& x)
{
using numext::igamma;
return make_float4(
igamma(a.x, x.x),
igamma(a.y, x.y),
igamma(a.z, x.z),
igamma(a.w, x.w));
}
template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
double2 pigamma<double2>(const double2& a, const double2& x)
{
using numext::igamma;
return make_double2(igamma(a.x, x.x), igamma(a.y, x.y));
}
template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
float4 pigammac<float4>(const float4& a, const float4& x)
{
using numext::igammac;
return make_float4(
igammac(a.x, x.x),
igammac(a.y, x.y),
igammac(a.z, x.z),
igammac(a.w, x.w));
}
template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
double2 pigammac<double2>(const double2& a, const double2& x)
{
using numext::igammac;
return make_double2(igammac(a.x, x.x), igammac(a.y, x.y));
}
#endif
} // end namespace internal

5
Eigen/src/Core/arch/CUDA/PacketMath.h
View File

@@ -42,6 +42,8 @@ template<> struct packet_traits<float> : default_packet_traits
HasDiGamma = 1,
HasErf = 1,
HasErfc = 1,
HasIgamma = 1,
HasIGammac = 1,
HasBlend = 0,
};
@@ -66,6 +68,8 @@ template<> struct packet_traits<double> : default_packet_traits
HasDiGamma = 1,
HasErf = 1,
HasErfc = 1,
HasIGamma = 1,
HasIGammac = 1,
HasBlend = 0,
};
@@ -308,7 +312,6 @@ template<> EIGEN_DEVICE_FUNC inline double2 pabs<double2>(const double2& a) {
return make_double2(fabs(a.x), fabs(a.y));
}
EIGEN_DEVICE_FUNC inline void
ptranspose(PacketBlock<float4,4>& kernel) {
double tmp = kernel.packet[0].y;

49
Eigen/src/Core/functors/BinaryFunctors.h
View File

@@ -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 ----------

2
Eigen/src/Core/util/ForwardDeclarations.h
View File

@@ -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;

5
Eigen/src/Core/util/Meta.h
View File

@@ -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>
{