Functions
template<typename number >
VectorizedArray< number, 1 >	type_cast (const VectorizedArray< number, 1 > &in)

template<int degree, typename CoeffsType , typename ValueType >
ValueType	horner_scheme (const std::array< CoeffsType, degree+1 > &c, const ValueType &x)

template<int degree, typename CoeffsType , typename ValueType >
ValueType	estrin_scheme (const std::array< CoeffsType, degree+1 > &c, const ValueType &x)

Variables
template<int degree, typename Number >
constexpr std::array< Number, degree+1 >	exp_pol_coeff

template<typename Number >
constexpr std::array< Number, 4 >	exp_pol_coeff< 3, Number >

template<typename Number >
constexpr std::array< Number, 5 >	exp_pol_coeff< 4, Number >

template<typename Number >
constexpr std::array< Number, 6 >	exp_pol_coeff< 5, Number >

template<typename Number >
constexpr std::array< Number, 7 >	exp_pol_coeff< 6, Number >

template<typename Number >
constexpr std::array< Number, 8 >	exp_pol_coeff< 7, Number >

template<typename Number >
constexpr std::array< Number, 9 >	exp_pol_coeff< 8, Number >

template<typename Number >
constexpr std::array< Number, 10 >	exp_pol_coeff< 9, Number >

template<typename Number >
constexpr std::array< Number, 11 >	exp_pol_coeff< 10, Number >

template<typename Number >
constexpr std::array< Number, 12 >	exp_pol_coeff< 11, Number >

template<typename Number >
constexpr Number	exp_coeff_a = numbers::signaling_nan<Number>()

template<>
constexpr double	exp_coeff_a< double > = 4503599627370496

template<>
constexpr float	exp_coeff_a< float > = 8388608

template<typename Number >
constexpr Number	exp_coeff_b = numbers::signaling_nan<Number>()

template<>
constexpr double	exp_coeff_b< double > = 4.60718241880001741e+18

template<>
constexpr float	exp_coeff_b< float > = 1065353216

template<typename Number >
constexpr Number	max_exponent = numbers::signaling_nan<Number>()

template<>
constexpr double	max_exponent< double > = 9.218868437227405312e+18

template<>
constexpr float	max_exponent< float > = 2139095040

template<typename Number >
constexpr Number	exp_max_abs_x = numbers::signaling_nan<Number>()

template<>
constexpr double	exp_max_abs_x< double > = 709.196208642

template<>
constexpr float	exp_max_abs_x< float > = 87.49823353f

Function Documentation

◆ type_cast()

template<typename number >

VectorizedArray< number, 1 > fast_transcendental::internal::type_cast ( const VectorizedArray< number, 1 > & in )

inline

The functions below provide architecture-specific specializations used as a helper by the fast_exp() implementation. Each specialization performs a two-step operation:

Static cast of each floating-point value to its corresponding integer type (float to int32_t, double to int64_t).
Reinterpretation of the resulting integer vector as a floating-point vector via bitwise casting.

Definition at line 326 of file fast_transcendental.h.

◆ horner_scheme()

template<int degree, typename CoeffsType , typename ValueType >

ValueType fast_transcendental::internal::horner_scheme	(	const std::array< CoeffsType, degree+1 > &	c,
		const ValueType &	x
	)

inline

This function computes the value of a polynomial

\[ P(x) = c_0 + c_1 x + c_2 x^2 + \dots + c_{\text{degree}} x^{\text{degree}} \]

where the coefficients \(c_i\) are provided in ascending order using Horner's scheme.

Template Parameters

degree	Degree of the polynomial.
CoeffsType	Type of the stored coefficients.
ValueType	Type of the evaluation point and result.

Parameters

c	Array of polynomial coefficients in ascending order.
x	The point at which the polynomial should be evaluated.

Returns: The value \(P(x)\).

Definition at line 356 of file fast_transcendental.h.

◆ estrin_scheme()

template<int degree, typename CoeffsType , typename ValueType >

ValueType fast_transcendental::internal::estrin_scheme	(	const std::array< CoeffsType, degree+1 > &	c,
		const ValueType &	x
	)

inline

This function computes the value of a polynomial

\[ P(x) = c_0 + c_1 x + c_2 x^2 + \dots + c_{\text{degree}} x^{\text{degree}} \]

where the coefficients \(c_i\) are provided in ascending order using Estrin's scheme.

Template Parameters

degree	Degree of the polynomial.
CoeffsType	Type of the stored coefficients.
ValueType	Type of the evaluation point and result.

Parameters

c	Array of polynomial coefficients in ascending order.
x	The point at which the polynomial should be evaluated.

Returns: The value \(P(x)\).

Definition at line 386 of file fast_transcendental.h.

Variable Documentation

◆ exp_pol_coeff

template<int degree, typename Number >

constexpr std::array<Number, degree + 1> fast_transcendental::internal::exp_pol_coeff

constexpr

Initial value:

=
      []() -> std::array<Number, degree + 1> {
      static_assert(degree > 2 && degree < 12,
                    "Unsupported polynomial degree for exp_pol_coeff.");
      return std::array<Number, degree + 1>{};
    }()

Definition at line 59 of file fast_transcendental.h.

◆ exp_pol_coeff< 3, Number >

template<typename Number >

constexpr std::array<Number, 4> fast_transcendental::internal::exp_pol_coeff< 3, Number >

constexpr

Initial value:

= {
      {1.8809206555322363e-04,
       3.0316116404944521e-01,
       -2.2412622972531135e-01,
       -7.9019886953785187e-02}}

Definition at line 67 of file fast_transcendental.h.

◆ exp_pol_coeff< 4, Number >

template<typename Number >

constexpr std::array<Number, 5> fast_transcendental::internal::exp_pol_coeff< 4, Number >

constexpr

Initial value:

= {
      {-7.2868375805796964e-06,
       3.0706874220004554e-01,
       -2.4171033150558635e-01,
       -5.1666839694436362e-02,
       -1.3676523629674565e-02}}

Definition at line 74 of file fast_transcendental.h.

◆ exp_pol_coeff< 5, Number >

template<typename Number >

constexpr std::array<Number, 6> fast_transcendental::internal::exp_pol_coeff< 5, Number >

constexpr

Initial value:

= {
      {2.3053723876408911e-07,
       3.0684322094757277e-01,
       -2.4013168272249241e-01,
       -5.5876569798473615e-02,
       -8.9405772567122607e-03,
       -1.8943785491846432e-03}}

Definition at line 82 of file fast_transcendental.h.

◆ exp_pol_coeff< 6, Number >

template<typename Number >

constexpr std::array<Number, 7> fast_transcendental::internal::exp_pol_coeff< 6, Number >

constexpr

Initial value:

= {
      {-6.1646222105268035e-09,
       3.0685316242622318e-01,
       -2.4023109751048086e-01,
       -5.5478910644035311e-02,
       -9.6861881733345725e-03,
       -1.2382409419015978e-03,
       -2.1871253576104385e-04}}

Definition at line 91 of file fast_transcendental.h.

◆ exp_pol_coeff< 7, Number >

template<typename Number >

constexpr std::array<Number, 8> fast_transcendental::internal::exp_pol_coeff< 7, Number >

constexpr

Initial value:

= {
      {1.4276280848886066e-10,
       3.0685280921264796e-01,
       -2.4022632912712596e-01,
       -5.5505401662914296e-02,
       -9.6133378710895074e-03,
       -1.3431453773612783e-03,
       -1.4294822119902167e-04,
       -2.1646947017882258e-05}}

Definition at line 101 of file fast_transcendental.h.

◆ exp_pol_coeff< 8, Number >

template<typename Number >

constexpr std::array<Number, 9> fast_transcendental::internal::exp_pol_coeff< 8, Number >

constexpr

Initial value:

= {
      {-2.9146986289710858e-12,
       3.0685281970141953e-01,
       -2.4022651268062989e-01,
       -5.5504055603868258e-02,
       -9.6183855925465120e-03,
       -1.3326461166925901e-03,
       -1.5519735866800178e-04,
       -1.4147475092332136e-05,
       -1.8748679813608566e-06}}

Definition at line 112 of file fast_transcendental.h.

◆ exp_pol_coeff< 9, Number >

template<typename Number >

constexpr std::array<Number, 10> fast_transcendental::internal::exp_pol_coeff< 9, Number >

constexpr

Initial value:

= {
      {5.4337475594757437e-14,
       3.0685281943421089e-01,
       -2.4022650680203564e-01,
       -5.5504110470759059e-02,
       -9.6181181164443925e-03,
       -1.3333950497836748e-03,
       -1.5394913684739714e-04,
       -1.5370223000068715e-05,
       -1.2252831550509094e-06,
       -1.4435218373241001e-07}}

Definition at line 124 of file fast_transcendental.h.

◆ exp_pol_coeff< 10, Number >

template<typename Number >

constexpr std::array<Number, 11> fast_transcendental::internal::exp_pol_coeff< 10, Number >

constexpr

Initial value:

= {
      {7.6072080297756739e-12,
       3.0685281862960340e-01,
       -2.4022648563631835e-01,
       -5.5504349821691862e-02,
       -9.6166785909533817e-03,
       -1.3384970969245304e-03,
       -1.4276337493295606e-04,
       -3.0711077326624553e-05,
       1.1584454591775664e-05,
       -6.0984990187293866e-06,
       1.1810109241254786e-06}}

Definition at line 137 of file fast_transcendental.h.

◆ exp_pol_coeff< 11, Number >

template<typename Number >

constexpr std::array<Number, 12> fast_transcendental::internal::exp_pol_coeff< 11, Number >

constexpr

Initial value:

= {
      {3.6083394569535254e-13,
       3.0685281939395403e-01,
       -2.4022650549710606e-01,
       -5.5504128716495800e-02,
       -9.6179813320517119e-03,
       -1.3340079120703319e-03,
       -1.5221190054222076e-04,
       -1.8563222423500779e-05,
       2.5694826992914108e-06,
       -2.9577981133179920e-06,
       1.1827521620524028e-06,
       -2.1525063398151332e-07}}

Definition at line 151 of file fast_transcendental.h.

◆ exp_coeff_a

template<typename Number >

constexpr Number fast_transcendental::internal::exp_coeff_a = numbers::signaling_nan<Number>()

constexpr

This is 2^52 for double and 2^23 for float.

Definition at line 169 of file fast_transcendental.h.

◆ exp_coeff_a< double >

template<>

constexpr double fast_transcendental::internal::exp_coeff_a< double > = 4503599627370496

inlineconstexpr

Definition at line 171 of file fast_transcendental.h.

◆ exp_coeff_a< float >

template<>

constexpr float fast_transcendental::internal::exp_coeff_a< float > = 8388608

inlineconstexpr

Definition at line 173 of file fast_transcendental.h.

◆ exp_coeff_b

template<typename Number >

constexpr Number fast_transcendental::internal::exp_coeff_b = numbers::signaling_nan<Number>()

inlineconstexpr

This is 2^52 * 1023 for double and 2^23 * 127 for float.

Definition at line 179 of file fast_transcendental.h.

◆ exp_coeff_b< double >

template<>

constexpr double fast_transcendental::internal::exp_coeff_b< double > = 4.60718241880001741e+18

inlineconstexpr

Definition at line 181 of file fast_transcendental.h.

◆ exp_coeff_b< float >

template<>

constexpr float fast_transcendental::internal::exp_coeff_b< float > = 1065353216

inlineconstexpr

Definition at line 183 of file fast_transcendental.h.

◆ max_exponent

template<typename Number >

constexpr Number fast_transcendental::internal::max_exponent = numbers::signaling_nan<Number>()

inlineconstexpr

This is the maximum exponent for a floating point representation shifted to the exponent bits. In numbers this is 2^52 * 2047 for double and 2^23

255 for float.

Definition at line 191 of file fast_transcendental.h.

◆ max_exponent< double >

template<>

constexpr double fast_transcendental::internal::max_exponent< double > = 9.218868437227405312e+18

inlineconstexpr

Definition at line 193 of file fast_transcendental.h.

◆ max_exponent< float >

template<>

constexpr float fast_transcendental::internal::max_exponent< float > = 2139095040

inlineconstexpr

Definition at line 195 of file fast_transcendental.h.

◆ exp_max_abs_x

template<typename Number >

constexpr Number fast_transcendental::internal::exp_max_abs_x = numbers::signaling_nan<Number>()

inlineconstexpr

The largest |x| for which exp(x) remains a finite, representable value of type Number. For double this is approximately 308 / log10(e), and for float approximately 38 / log10(e).

Definition at line 203 of file fast_transcendental.h.

◆ exp_max_abs_x< double >

template<>

constexpr double fast_transcendental::internal::exp_max_abs_x< double > = 709.196208642

inlineconstexpr

Definition at line 205 of file fast_transcendental.h.

◆ exp_max_abs_x< float >

template<>

constexpr float fast_transcendental::internal::exp_max_abs_x< float > = 87.49823353f

inlineconstexpr

Definition at line 207 of file fast_transcendental.h.

Functions

Variables

Function Documentation

◆ type_cast()

◆ horner_scheme()

◆ estrin_scheme()

Variable Documentation

◆ exp_pol_coeff

◆ exp_pol_coeff< 3, Number >

◆ exp_pol_coeff< 4, Number >

◆ exp_pol_coeff< 5, Number >

◆ exp_pol_coeff< 6, Number >

◆ exp_pol_coeff< 7, Number >

◆ exp_pol_coeff< 8, Number >

◆ exp_pol_coeff< 9, Number >

◆ exp_pol_coeff< 10, Number >

◆ exp_pol_coeff< 11, Number >

◆ exp_coeff_a

◆ exp_coeff_a< double >

◆ exp_coeff_a< float >

◆ exp_coeff_b

◆ exp_coeff_b< double >

◆ exp_coeff_b< float >

◆ max_exponent

◆ max_exponent< double >

◆ max_exponent< float >

◆ exp_max_abs_x

◆ exp_max_abs_x< double >

◆ exp_max_abs_x< float >