cxx/stdlib/math_constants.txt

// Copyright 2017-2020 The Khronos Group. This work is licensed under a
// Creative Commons Attribution 4.0 International License; see
// http://creativecommons.org/licenses/by/4.0/

[[math-constants-library]]
=== Math Constants Library

OpenCL {cpp} implements math constant library.
The purpose of this library is to provide the commonly used constants for half, float and double data types.

[[header-opencl_math_constants-synopsis]]
==== Header <opencl_math_constants> Synopsis

[source]
----
namespace cl
{
template<class T> class math_constants;

#ifdef cl_khr_fp16
#define M_E_H           see below
#define M_LOG2E_H       see below
#define M_LOG10E_H      see below
#define M_LN2_H         see below
#define M_LN10_H        see below
#define M_PI_H          see below
#define M_PI_2_H        see below
#define M_PI_4_H        see below
#define M_1_PI_H        see below
#define M_2_PI_H        see below
#define M_2_SQRTPI_H    see below
#define M_SQRT2_H       see below
#define M_SQRT1_2_H     see below

template<> class math_constants<half>;
template<> class math_constants<half2>;
template<> class math_constants<half3>;
template<> class math_constants<half4>;
template<> class math_constants<half8>;
template<> class math_constants<half16>;
#endif

#define M_E_F           see below
#define M_LOG2E_F       see below
#define M_LOG10E_F      see below
#define M_LN2_F         see below
#define M_LN10_F        see below
#define M_PI_F          see below
#define M_PI_2_F        see below
#define M_PI_4_F        see below
#define M_1_PI_F        see below
#define M_2_PI_F        see below
#define M_2_SQRTPI_F    see below
#define M_SQRT2_F       see below
#define M_SQRT1_2_F     see below

template<> class math_constants<float>;
template<> class math_constants<float2>;
template<> class math_constants<float3>;
template<> class math_constants<float4>;
template<> class math_constants<float8>;
template<> class math_constants<float16>;

#ifdef cl_khr_fp64
#define M_E         see below
#define M_LOG2E     see below
#define M_LOG10E    see below
#define M_LN2       see below
#define M_LN10      see below
#define M_PI        see below
#define M_PI_2      see below
#define M_PI_4      see below
#define M_1_PI      see below
#define M_2_PI      see below
#define M_2_SQRTPI  see below
#define M_SQRT2     see below
#define M_SQRT1_2   see below

template<> class math_constants<double>;
template<> class math_constants<double2>;
template<> class math_constants<double3>;
template<> class math_constants<double4>;
template<> class math_constants<double8>;
template<> class math_constants<double16>;
#endif

template<class T>
constexpr T e_v = math_constants<T>::e();
template<class T>
constexpr T log2e_v = math_constants<T>::log2e();
template<class T>
constexpr T log10e_v = math_constants<T>::log10e();
template<class T>
constexpr T ln2_v = math_constants<T>::ln2();
template<class T>
constexpr T ln10_v = math_constants<T>::ln10();
template<class T>
constexpr T pi_v = math_constants<T>::pi();
template<class T>
constexpr T pi_2_v = math_constants<T>::pi_2();
template<class T>
constexpr T pi_4_v = math_constants<T>::pi_4();
template<class T>
constexpr T one_pi_v = math_constants<T>::one_pi();
template<class T>
constexpr T two_pi_v = math_constants<T>::two_pi();
template<class T>
constexpr T two_sqrtpi_v = math_constants<T>::two_sqrtpi();
template<class T>
constexpr T sqrt2_v = math_constants<T>::sqrt2();
template<class T>
constexpr T sqrt1_2_v = math_constants<T>::sqrt1_2();

}
----

[[class-math_constants]]
==== Class math_constants

[source]
----
namespace cl
{
template<class T>
class math_constants
{
public:
  static constexpr T e() noexcept { return T(); }
  static constexpr T log2e() noexcept { return T(); }
  static constexpr T log10e() noexcept { return T(); }
  static constexpr T ln2() noexcept { return T(); }
  static constexpr T ln10() noexcept { return T(); }
  static constexpr T pi() noexcept { return T(); }
  static constexpr T pi_2() noexcept { return T(); }
  static constexpr T pi_4() noexcept { return T(); }
  static constexpr T one_pi() noexcept { return T(); }
  static constexpr T two_pi() noexcept { return T(); }
  static constexpr T two_sqrtpi() noexcept { return T(); }
  static constexpr T sqrt2() noexcept { return T(); }
  static constexpr T sqrt1_2() noexcept { return T(); }
};

}
----

[[half-constants]]
==== Half Constants

The following constants are also available.
They are of type `half` and are accurate within the precision of the `half` type.

.Half Constants
[width="100%",cols="50%,50%",options="header"]
|====
| *Constant*
| *Description*

| `e`
| Value of e

| `log2e`
| Value of log~2~e

| `log10e`
| Value of log~10~e

| `ln2`
| Value of log~e~2

| `ln10`
| Value of log~e~10

| `pi`
| Value of {pi}

| `pi_2`
| Value of {pi} / 2

| `pi_4`
| Value of {pi} / 4

| `one_pi`
| Value of 1 / {pi}

| `two_pi`
| Value of 2 / {pi}

| `two_sqrtpi`
| Value of 2 / {sqrt}{pi}

| `sqrt2`
| Value of {sqrt}2

| `sqrt1_2`
| Value of 1 / {sqrt}2
|====

[[float-constants]]
==== Float Constants

The following constants are also available.
They are of type `float` and are accurate within the precision of the `float` type.

.Float Constants
[width="100%",cols="50%,50%",options="header"]
|====
| *Constant*
| *Description*

| `e`
| Value of e

| `log2e`
| Value of log~2~e

| `log10e`
| Value of log~10~e

| `ln2`
| Value of log~e~2

| `ln10`
| Value of log~e~10

| `pi`
| Value of {pi}

| `pi_2`
| Value of {pi} / 2

| `pi_4`
| Value of {pi} / 4

| `one_pi`
| Value of 1 / {pi}

| `two_pi`
| Value of 2 / {pi}

| `two_sqrtpi`
| Value of 2 / {sqrt}{pi}

| `sqrt2`
| Value of {sqrt}2

| `sqrt1_2`
| Value of 1 / {sqrt}2
|====

[[double-constants]]
==== Double Constants

The following constants are also available.
They are of type `double` and are accurate within the precision of the `double` type.

.Double Constants
[width="100%",cols="50%,50%",options="header"]
|====
| *Constant*
| *Description*

| `e`
| Value of e

| `log2e`
| Value of log~2~e

| `log10e`
| Value of log~10~e

| `ln2`
| Value of log~e~2

| `ln10`
| Value of log~e~10

| `pi`
| Value of {pi}

| `pi_2`
| Value of {pi} / 2

| `pi_4`
| Value of {pi} / 4

| `one_pi`
| Value of 1 / {pi}

| `two_pi`
| Value of 2 / {pi}

| `two_sqrtpi`
| Value of 2 / {sqrt}{pi}

| `sqrt2`
| Value of {sqrt}2

| `sqrt1_2`
| Value of 1 / {sqrt}2
|====