Complete the coeff-wise math function table.

2025-08-11 19:29:02 +08:00 · 2016-07-20 12:14:10 +02:00 · 2016-07-20 12:14:10 +02:00 · fd057f86b3
commit fd057f86b3
parent 9e8476ef22
3 changed files with 406 additions and 38 deletions
--- a/Eigen/src/plugins/ArrayCwiseUnaryOps.h
+++ b/Eigen/src/plugins/ArrayCwiseUnaryOps.h
@ -36,7 +36,7 @@ typedef CwiseUnaryOp<internal::scalar_isfinite_op<Scalar>, const Derived> IsFini
  * Example: \include Cwise_abs.cpp
  * Output: \verbinclude Cwise_abs.out
  *
-  * \sa abs2()
+  * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_abs">Math functions</a>, abs2()
  */
 EIGEN_DEVICE_FUNC
 EIGEN_STRONG_INLINE const AbsReturnType
@ -64,7 +64,7 @@ arg() const
  * Example: \include Cwise_abs2.cpp
  * Output: \verbinclude Cwise_abs2.out
  *
-  * \sa abs(), square()
+  * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_abs2">Math functions</a>, abs(), square()
  */
 EIGEN_DEVICE_FUNC
 EIGEN_STRONG_INLINE const Abs2ReturnType
@ -81,7 +81,7 @@ abs2() const
  * Example: \include Cwise_exp.cpp
  * Output: \verbinclude Cwise_exp.out
  *
-  * \sa pow(), log(), sin(), cos()
+  * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_exp">Math functions</a>, pow(), log(), sin(), cos()
  */
 EIGEN_DEVICE_FUNC
 inline const ExpReturnType
@ -98,7 +98,7 @@ exp() const
  * Example: \include Cwise_log.cpp
  * Output: \verbinclude Cwise_log.out
  *
-  * \sa exp()
+  * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_log">Math functions</a>, exp()
  */
 EIGEN_DEVICE_FUNC
 inline const LogReturnType
@ -112,7 +112,7 @@ log() const
  * In exact arithmetic, \c x.log() is equivalent to \c (x+1).log(),
  * however, with finite precision, this function is much more accurate when \c x is close to zero.
  *
-  * \sa log()
+  * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_log1p">Math functions</a>, log()
  */
 EIGEN_DEVICE_FUNC
 inline const Log1pReturnType
@ -128,7 +128,7 @@ log1p() const
  * Example: \include Cwise_log10.cpp
  * Output: \verbinclude Cwise_log10.out
  *
-  * \sa log()
+  * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_log10">Math functions</a>, log()
  */
 EIGEN_DEVICE_FUNC
 inline const Log10ReturnType
@ -145,7 +145,7 @@ log10() const
  * Example: \include Cwise_sqrt.cpp
  * Output: \verbinclude Cwise_sqrt.out
  *
-  * \sa pow(), square()
+  * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_sqrt">Math functions</a>, pow(), square()
  */
 EIGEN_DEVICE_FUNC
 inline const SqrtReturnType
@ -195,7 +195,7 @@ sign() const
  * Example: \include Cwise_cos.cpp
  * Output: \verbinclude Cwise_cos.out
  *
-  * \sa sin(), acos()
+  * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_cos">Math functions</a>, sin(), acos()
  */
 EIGEN_DEVICE_FUNC
 inline const CosReturnType
@ -213,7 +213,7 @@ cos() const
  * Example: \include Cwise_sin.cpp
  * Output: \verbinclude Cwise_sin.out
  *
-  * \sa cos(), asin()
+  * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_sin">Math functions</a>, cos(), asin()
  */
 EIGEN_DEVICE_FUNC
 inline const SinReturnType
@ -227,7 +227,7 @@ sin() const
  * Example: \include Cwise_tan.cpp
  * Output: \verbinclude Cwise_tan.out
  *
-  * \sa cos(), sin()
+  * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_tan">Math functions</a>, cos(), sin()
  */
 EIGEN_DEVICE_FUNC
 inline const TanReturnType
@ -241,7 +241,7 @@ tan() const
  * Example: \include Cwise_atan.cpp
  * Output: \verbinclude Cwise_atan.out
  *
-  * \sa tan(), asin(), acos()
+  * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_atan">Math functions</a>, tan(), asin(), acos()
  */
 EIGEN_DEVICE_FUNC
 inline const AtanReturnType
@ -255,7 +255,7 @@ atan() const
  * Example: \include Cwise_acos.cpp
  * Output: \verbinclude Cwise_acos.out
  *
-  * \sa cos(), asin()
+  * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_acos">Math functions</a>, cos(), asin()
  */
 EIGEN_DEVICE_FUNC
 inline const AcosReturnType
@ -269,7 +269,7 @@ acos() const
  * Example: \include Cwise_asin.cpp
  * Output: \verbinclude Cwise_asin.out
  *
-  * \sa sin(), acos()
+  * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_asin">Math functions</a>, sin(), acos()
  */
 EIGEN_DEVICE_FUNC
 inline const AsinReturnType
@ -283,7 +283,7 @@ asin() const
  * Example: \include Cwise_tanh.cpp
  * Output: \verbinclude Cwise_tanh.out
  *
-  * \sa tan(), sinh(), cosh()
+  * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_tanh">Math functions</a>, tan(), sinh(), cosh()
  */
 EIGEN_DEVICE_FUNC
 inline const TanhReturnType
@ -297,7 +297,7 @@ tanh() const
  * Example: \include Cwise_sinh.cpp
  * Output: \verbinclude Cwise_sinh.out
  *
-  * \sa sin(), tanh(), cosh()
+  * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_sinh">Math functions</a>, sin(), tanh(), cosh()
  */
 EIGEN_DEVICE_FUNC
 inline const SinhReturnType
@ -311,7 +311,7 @@ sinh() const
  * Example: \include Cwise_cosh.cpp
  * Output: \verbinclude Cwise_cosh.out
  *
-  * \sa tan(), sinh(), cosh()
+  * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_cosh">Math functions</a>, tan(), sinh(), cosh()
  */
 EIGEN_DEVICE_FUNC
 inline const CoshReturnType
@ -339,7 +339,7 @@ inverse() const
  * Example: \include Cwise_square.cpp
  * Output: \verbinclude Cwise_square.out
  *
-  * \sa operator/(), operator*(), abs2()
+  * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_squareE">Math functions</a>, abs2(), cube(), pow()
  */
 EIGEN_DEVICE_FUNC
 inline const SquareReturnType
@ -353,7 +353,7 @@ square() const
  * Example: \include Cwise_cube.cpp
  * Output: \verbinclude Cwise_cube.out
  *
-  * \sa square(), pow()
+  * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_cube">Math functions</a>, square(), pow()
  */
 EIGEN_DEVICE_FUNC
 inline const CubeReturnType
@ -367,7 +367,7 @@ cube() const
  * Example: \include Cwise_round.cpp
  * Output: \verbinclude Cwise_round.out
  *
-  * \sa ceil(), floor()
+  * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_round">Math functions</a>, ceil(), floor()
  */
 EIGEN_DEVICE_FUNC
 inline const RoundReturnType
@ -381,7 +381,7 @@ round() const
  * Example: \include Cwise_floor.cpp
  * Output: \verbinclude Cwise_floor.out
  *
-  * \sa ceil(), round()
+  * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_floor">Math functions</a>, ceil(), round()
  */
 EIGEN_DEVICE_FUNC
 inline const FloorReturnType
@ -395,7 +395,7 @@ floor() const
  * Example: \include Cwise_ceil.cpp
  * Output: \verbinclude Cwise_ceil.out
  *
-  * \sa floor(), round()
+  * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_ceil">Math functions</a>, floor(), round()
  */
 EIGEN_DEVICE_FUNC
 inline const CeilReturnType
@ -483,7 +483,7 @@ typedef CwiseUnaryOp<internal::scalar_erfc_op<Scalar>, const Derived> ErfcReturn
  * 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.
  *
-  * \sa digamma()
+  * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_lgamma">Math functions</a>, digamma()
  */
 EIGEN_DEVICE_FUNC
 inline const LgammaReturnType
@ -500,7 +500,7 @@ lgamma() const
  * the user has to provide implementations of digamma(T) for any scalar
  * type T to be supported.
  *
-  * \sa Eigen::digamma(), Eigen::polygamma(), lgamma()
+  * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_digamma">Math functions</a>, Eigen::digamma(), Eigen::polygamma(), lgamma()
  */
 EIGEN_DEVICE_FUNC
 inline const DigammaReturnType
@ -521,7 +521,7 @@ digamma() const
  * 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.
  *
-  * \sa erfc()
+  * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_erf">Math functions</a>, erfc()
  */
 EIGEN_DEVICE_FUNC
 inline const ErfReturnType
@ -542,7 +542,7 @@ erf() const
  * 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.
  *
-  * \sa erf()
+  * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_erfc">Math functions</a>, erf()
  */
 EIGEN_DEVICE_FUNC
 inline const ErfcReturnType
--- a/Eigen/src/plugins/CommonCwiseUnaryOps.h
+++ b/Eigen/src/plugins/CommonCwiseUnaryOps.h
@ -62,7 +62,7 @@ cast() const

 /** \returns an expression of the complex conjugate of \c *this.
  *
-  * \sa adjoint() */
+  * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_conj">Math functions</a>, MatrixBase::adjoint() */
 EIGEN_DEVICE_FUNC
 inline ConjugateReturnType
 conjugate() const
--- a/doc/CoeffwiseMathFunctionsTable.dox
+++ b/doc/CoeffwiseMathFunctionsTable.dox
@ -3,11 +3,11 @@ namespace Eigen {
 /** \eigenManualPage CoeffwiseMathFunctions Catalog of coefficient-wise math functions


-<span style="font-size:300%; color:red; font-weight: 900;">!WORK IN PROGRESS!</span>
+<!-- <span style="font-size:300%; color:red; font-weight: 900;">!WORK IN PROGRESS!</span> -->

 This table presents a catalog of the coefficient-wise math functions supported by %Eigen.
 In this table, \c a, \c b, refer to Array objects or expressions, and \c m refers to a linear algebra Matrix/Vector object. Standard scalar types are abbreviated as follows:
-  - \c int: \c ui32
+  - \c int: \c i32
  - \c float: \c f
  - \c double: \c d
  - \c std::complex<float>: \c cf
@ -43,7 +43,35 @@ This also means that, unless specified, if the function \c std::foo is available
  using <a href="http://en.cppreference.com/w/cpp/numeric/math/fabs">std::abs</a>; \n
  abs(a[i]);
  </td>
-  <td>SSE2, AVX (ui32,f,d)</td>
+  <td>SSE2, AVX (i32,f,d)</td>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_inverse
+  a.\link ArrayBase::inverse inverse\endlink(); \n
+  \link Eigen::inverse inverse\endlink(a); \n
+  m.\link MatrixBase::cwiseInverse cwiseInverse\endlink();
+  </td>
+  <td>inverse value (\f$ 1/a_i \f$) </td>
+  <td class="code">
+  1/a[i];
+  </td>
+  <td>All engines (f,d,fc,fd)</td>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_conj
+  a.\link ArrayBase::conjugate conjugate\endlink(); \n
+  \link Eigen::conj conj\endlink(a); \n
+  m.\link MatrixBase::conjugate conjugate();
+  </td>
+  <td><a href="https://en.wikipedia.org/wiki/Complex_conjugate">complex conjugate</a> (\f$ \bar{a_i} \f$),\n
+  no-op for real </td>
+  <td class="code">
+  using <a href="http://en.cppreference.com/w/cpp/numeric/complex/conj">std::conj</a>; \n
+  conj(a[i]);
+  </td>
+  <td>All engines (fc,fd)</td>
 </tr>
 <tr>
 <th colspan="4">Exponential functions</th>
@ -67,12 +95,12 @@ This also means that, unless specified, if the function \c std::foo is available
  a.\link ArrayBase::log log\endlink(); \n
  \link Eigen::log log\endlink(a);
  </td>
-  <td>natural (base \f$ e \f$) logarithm (\f$ ln({a_i}) \f$)</td>
+  <td>natural (base \f$ e \f$) logarithm (\f$ \ln({a_i}) \f$)</td>
  <td class="code">
  using <a href="http://en.cppreference.com/w/cpp/numeric/math/log">std::log</a>; \n
  log(a[i]);
  </td>
-  <td>SSE2, AVX (f,d)</td>
+  <td>SSE2, AVX (f)</td>
 </tr>
 <tr>
  <td class="code">
@ -80,23 +108,298 @@ This also means that, unless specified, if the function \c std::foo is available
  a.\link ArrayBase::log1p log1p\endlink(); \n
  \link Eigen::log1p log1p\endlink(a);
  </td>
-  <td>natural (base \f$ e \f$) logarithm of 1 plus \n the given number (\f$ ln({1+a_i}) \f$)</td>
+  <td>natural (base \f$ e \f$) logarithm of 1 plus \n the given number (\f$ \ln({1+a_i}) \f$)</td>
  <td>built-in generic implementation based on \c log,\n
  plus \c using <a href="http://en.cppreference.com/w/cpp/numeric/math/log1p">\c std::log1p </a>; \cpp11</td>
  <td></td>
 </tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_log10
+  a.\link ArrayBase::log10 log10\endlink(); \n
+  \link Eigen::log10 log10\endlink(a);
+  </td>
+  <td>base 10 logarithm (\f$ \log_{10}({a_i}) \f$)</td>
+  <td class="code">
+  using <a href="http://en.cppreference.com/w/cpp/numeric/math/log10">std::log10</a>; \n
+  log10(a[i]);
+  </td>
+  <td></td>
+</tr>
 <tr>
 <th colspan="4">Power functions</th>
 </tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_pow
+  a.\link ArrayBase::pow pow\endlink(b); \n
+  \link Eigen::pow pow\endlink(a,b);
+  </td>
+  <td>raises a number to the given power (\f$ a_i ^ {b_i} \f$) \n \c a and \c b can be either an array or scalar.</td>
+  <td class="code">
+  using <a href="http://en.cppreference.com/w/cpp/numeric/math/pow">std::pow</a>; \n
+  pow(a[i],b[i]);\n
+  (plus builtin for integer types)</td>
+  <td></td>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_sqrt
+  a.\link ArrayBase::sqrt sqrt\endlink(); \n
+  \link Eigen::sqrt sqrt\endlink(a);\n
+  m.\link MatrixBase::cwiseSqrt cwiseSqrt\endlink();
+  </td>
+  <td>computes square root (\f$ \sqrt a_i \f$)</td>
+  <td class="code">
+  using <a href="http://en.cppreference.com/w/cpp/numeric/math/sqrt">std::sqrt</a>; \n
+  sqrt(a[i]);</td>
+  <td>SSE2, AVX (f,d)</td>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_rsqrt
+  a.\link ArrayBase::rsqrt rsqrt\endlink(); \n
+  \link Eigen::rsqrt rsqrt\endlink(a);
+  </td>
+  <td><a href="https://en.wikipedia.org/wiki/Fast_inverse_square_root">reciprocal square root</a> (\f$ 1/{\sqrt a_i} \f$)</td>
+  <td class="code">
+  using <a href="http://en.cppreference.com/w/cpp/numeric/math/sqrt">std::sqrt</a>; \n
+  1/sqrt(a[i]); \n
+  </td>
+  <td>SSE2, AVX, AltiVec, ZVector (f,d)\n
+  (approx + 1 Newton iteration)</td>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_square
+  a.\link ArrayBase::square square\endlink(); \n
+  \link Eigen::square square\endlink(a);
+  </td>
+  <td>computes square power (\f$ a_i^2 \f$)</td>
+  <td class="code">
+  a[i]*a[i]</td>
+  <td>All (i32,f,d,cf,cd)</td>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_cube
+  a.\link ArrayBase::cube cube\endlink(); \n
+  \link Eigen::cube cube\endlink(a);
+  </td>
+  <td>computes cubic power (\f$ a_i^3 \f$)</td>
+  <td class="code">
+  a[i]*a[i]*a[i]</td>
+  <td>All (i32,f,d,cf,cd)</td>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_abs2
+  a.\link ArrayBase::abs2 abs2\endlink(); \n
+  \link Eigen::abs2 abs2\endlink(a);\n
+  m.\link MatrixBase::cwiseAbs2 cwiseAbs2\endlink();
+  </td>
+  <td>computes the squared absolute value (\f$ |a_i|^2 \f$)</td>
+  <td class="code">
+  real:    a[i]*a[i] \n
+  complex:  real(a[i])*real(a[i]) \n
+  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; + imag(a[i])*imag(a[i])</td>
+  <td>All (i32,f,d)</td>
+</tr>
 <tr>
 <th colspan="4">Trigonometric functions</th>
 </tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_sin
+  a.\link ArrayBase::sin sin\endlink(); \n
+  \link Eigen::sin sin\endlink(a);
+  </td>
+  <td>computes sine</td>
+  <td class="code">
+  using <a href="http://en.cppreference.com/w/cpp/numeric/math/sin">std::sin</a>; \n
+  sin(a[i]);</td>
+  <td>SSE2, AVX (f)</td>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_cos
+  a.\link ArrayBase::cos cos\endlink(); \n
+  \link Eigen::cos cos\endlink(a);
+  </td>
+  <td>computes cosine</td>
+  <td class="code">
+  using <a href="http://en.cppreference.com/w/cpp/numeric/math/cos">std::cos</a>; \n
+  cos(a[i]);</td>
+  <td>SSE2, AVX (f)</td>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_tan
+  a.\link ArrayBase::tan tan\endlink(); \n
+  \link Eigen::tan tan\endlink(a);
+  </td>
+  <td>computes tangent</td>
+  <td class="code">
+  using <a href="http://en.cppreference.com/w/cpp/numeric/math/tan">std::tan</a>; \n
+  tan(a[i]);</td>
+  <td></td>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_asin
+  a.\link ArrayBase::asin asin\endlink(); \n
+  \link Eigen::asin asin\endlink(a);
+  </td>
+  <td>computes arc sine (\f$ \sin^{-1} a_i \f$)</td>
+  <td class="code">
+  using <a href="http://en.cppreference.com/w/cpp/numeric/math/asin">std::asin</a>; \n
+  asin(a[i]);</td>
+  <td></td>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_acos
+  a.\link ArrayBase::acos acos\endlink(); \n
+  \link Eigen::acos acos\endlink(a);
+  </td>
+  <td>computes arc cosine  (\f$ \cos^{-1} a_i \f$)</td>
+  <td class="code">
+  using <a href="http://en.cppreference.com/w/cpp/numeric/math/acos">std::acos</a>; \n
+  acos(a[i]);</td>
+  <td></td>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_atan
+  a.\link ArrayBase::atan tan\endlink(); \n
+  \link Eigen::atan atan\endlink(a);
+  </td>
+  <td>computes arc tangent (\f$ \tan^{-1} a_i \f$)</td>
+  <td class="code">
+  using <a href="http://en.cppreference.com/w/cpp/numeric/math/atan">std::atan</a>; \n
+  atan(a[i]);</td>
+  <td></td>
+</tr>
 <tr>
 <th colspan="4">Hyperbolic functions</th>
 </tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_sinh
+  a.\link ArrayBase::sinh sinh\endlink(); \n
+  \link Eigen::sinh sinh\endlink(a);
+  </td>
+  <td>computes hyperbolic sine</td>
+  <td class="code">
+  using <a href="http://en.cppreference.com/w/cpp/numeric/math/sinh">std::sinh</a>; \n
+  sinh(a[i]);</td>
+  <td></td>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_cosh
+  a.\link ArrayBase::cosh cohs\endlink(); \n
+  \link Eigen::cosh cosh\endlink(a);
+  </td>
+  <td>computes hyperbolic cosine</td>
+  <td class="code">
+  using <a href="http://en.cppreference.com/w/cpp/numeric/math/cosh">std::cosh</a>; \n
+  cosh(a[i]);</td>
+  <td></td>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_tanh
+  a.\link ArrayBase::tanh tanh\endlink(); \n
+  \link Eigen::tanh tanh\endlink(a);
+  </td>
+  <td>computes hyperbolic tangent</td>
+  <td class="code">
+  using <a href="http://en.cppreference.com/w/cpp/numeric/math/tanh">std::tanh</a>; \n
+  tanh(a[i]);</td>
+  <td></td>
+</tr>
+<tr>
+<th colspan="4">Nearest integer floating point operations</th>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_ceil
+  a.\link ArrayBase::ceil ceil\endlink(); \n
+  \link Eigen::ceil ceil\endlink(a);
+  </td>
+  <td>nearest integer not less than the given value</td>
+  <td class="code">
+  using <a href="http://en.cppreference.com/w/cpp/numeric/math/ceil">std::ceil</a>; \n
+  ceil(a[i]);</td>
+  <td>SSE4,AVX,ZVector (f,d)</td>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_floor
+  a.\link ArrayBase::floor floor\endlink(); \n
+  \link Eigen::floor floor\endlink(a);
+  </td>
+  <td>nearest integer not greater than the given value</td>
+  <td class="code">
+  using <a href="http://en.cppreference.com/w/cpp/numeric/math/floor">std::floor</a>; \n
+  floor(a[i]);</td>
+  <td>SSE4,AVX,ZVector (f,d)</td>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_round
+  a.\link ArrayBase::round round\endlink(); \n
+  \link Eigen::round round\endlink(a);
+  </td>
+  <td>nearest integer, \n rounding away from zero in halfway cases</td>
+  <td>built-in generic implementation \n based on \c floor and \c ceil,\n
+  plus \c using <a href="http://en.cppreference.com/w/cpp/numeric/math/round">\c std::round </a>; \cpp11</td>
+  <td>SSE4,AVX,ZVector (f,d)</td>
+</tr>
+<tr>
+<th colspan="4">Floating point manipulation functions</th>
+</tr>
+<tr>
+<th colspan="4">Classification and comparison</th>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_isfinite
+  a.\link ArrayBase::isfinite isfinite\endlink(); \n
+  \link Eigen::isfinite isfinite\endlink(a);
+  </td>
+  <td>checks if the given number has finite value</td>
+  <td>built-in generic implementation,\n
+  plus \c using <a href="http://en.cppreference.com/w/cpp/numeric/math/isfinite">\c std::isfinite </a>; \cpp11</td>
+  <td></td>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_isinf
+  a.\link ArrayBase::isinf isinf\endlink(); \n
+  \link Eigen::isinf isinf\endlink(a);
+  </td>
+  <td>checks if the given number is infinite</td>
+  <td>built-in generic implementation,\n
+  plus \c using <a href="http://en.cppreference.com/w/cpp/numeric/math/isinf">\c std::isinf </a>; \cpp11</td>
+  <td></td>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_isnan
+  a.\link ArrayBase::isnan isnan\endlink(); \n
+  \link Eigen::isnan isnan\endlink(a);
+  </td>
+  <td>checks if the given number is not a number</td>
+  <td>built-in generic implementation,\n
+  plus \c using <a href="http://en.cppreference.com/w/cpp/numeric/math/isnan">\c std::isnan </a>; \cpp11</td>
+  <td></td>
+</tr>
 <tr>
 <th colspan="4">Error and gamma functions</th>
 </tr>
+<tr> <td colspan="4">  Require \c #include \c <unsupported/Eigen/SpecialFunctions> </td></tr>
 <tr>
  <td class="code">
  \anchor cwisetable_erf
@ -124,24 +427,89 @@ This also means that, unless specified, if the function \c std::foo is available
  <td></td>
 </tr>
 <tr>
-<th colspan="4">Nearest integer floating point operations</th>
+  <td class="code">
+  \anchor cwisetable_lgamma
+  a.\link ArrayBase::lgamma lgamma\endlink(); \n
+  \link Eigen::lgamma lgamma\endlink(a);
+  </td>
+  <td>natural logarithm of the gamma function</td>
+  <td class="code">
+  using <a href="http://en.cppreference.com/w/cpp/numeric/math/lgamma">std::lgamma</a>; \cpp11 \n
+  lgamma(a[i]);
+  </td>
+  <td></td>
 </tr>
 <tr>
-<th colspan="4">Floating point manipulation functions</th>
+  <td class="code">
+  \anchor cwisetable_digamma
+  a.\link ArrayBase::digamma digamma\endlink(); \n
+  \link Eigen::digamma digamma\endlink(a);
+  </td>
+  <td><a href="https://en.wikipedia.org/wiki/Digamma_function">logarithmic derivative of the gamma function</a></td>
+  <td>
+  built-in for float and double
+  </td>
+  <td></td>
 </tr>
 <tr>
-<th colspan="4">Classification and comparison</th>
+  <td class="code">
+  \anchor cwisetable_igamma
+  \link Eigen::igamma igamma\endlink(a,x);
+  </td>
+  <td><a href="https://en.wikipedia.org/wiki/Incomplete_gamma_function">lower incomplete gamma integral</a>
+  \n \f$ \gamma(a_i,x_i)= \frac{1}{|a_i|} \int_{0}^{x_i}e^{\text{-}t} t^{a_i-1} \mathrm{d} t \f$</td>
+  <td>
+  built-in for float and double,\n but requires \cpp11
+  </td>
+  <td></td>
 </tr>
 <tr>
-<th colspan="4">Miscellaneous</th>
+  <td class="code">
+  \anchor cwisetable_igammac
+  \link Eigen::igammac igammac\endlink(a,x);
+  </td>
+  <td><a href="https://en.wikipedia.org/wiki/Incomplete_gamma_function">upper incomplete gamma integral</a>
+  \n \f$ \Gamma(a_i,x_i) = \frac{1}{|a_i|} \int_{x_i}^{\infty}e^{\text{-}t} t^{a_i-1} \mathrm{d} t \f$</td>
+  <td>
+  built-in for float and double,\n but requires \cpp11
+  </td>
+  <td></td>
+</tr>
+<tr>
+<th colspan="4">Special functions</th>
+</tr>
+<tr> <td colspan="4">  Require \c #include \c <unsupported/Eigen/SpecialFunctions> </td></tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_polygamma
+  \link Eigen::polygamma polygamma\endlink(n,x);
+  </td>
+  <td><a href="https://en.wikipedia.org/wiki/Polygamma_function">n-th derivative of digamma at x</a></td>
+  <td>
+  built-in generic based on\n <a href="#cwisetable_lgamma">\c lgamma </a>,
+  <a href="#cwisetable_digamma"> \c digamma </a>
+  and <a href="#cwisetable_zeta">\c zeta </a>.
+  </td>
+  <td></td>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_betainc
+  \link Eigen::betainc betainc\endlink(a,b,x);
+  </td>
+  <td><a href="https://en.wikipedia.org/wiki/Beta_function#Incomplete_beta_function">Incomplete beta function</a></td>
+  <td>
+  built-in for float and double,\n but requires \cpp11
+  </td>
+  <td></td>
 </tr>
 <tr>
  <td class="code">
  \anchor cwisetable_zeta
-  a.\link ArrayBase::zeta zeta\endlink(b); \n
  \link Eigen::zeta zeta\endlink(a,b);
  </td>
-  <td><a href="https://en.wikipedia.org/wiki/Hurwitz_zeta_function">Hurwitz zeta function</a> \n \f$ \zeta(a_i,b_i)=\sum_{k=0}^{\infty}(b_i+k)^{\text{-}a_i} \f$</td>
+  <td><a href="https://en.wikipedia.org/wiki/Hurwitz_zeta_function">Hurwitz zeta function</a>
+  \n \f$ \zeta(a_i,b_i)=\sum_{k=0}^{\infty}(b_i+k)^{\text{-}a_i} \f$</td>
  <td>
  built-in for float and double
  </td>