eml_type_fortran – DSCF-1224/eml

All elementary functions from a single operator SupplementaryInformation.pdf

Uses

- eml_class_fortran
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Graph Key

Nodes of different colours represent the following:

Solid arrows point from a submodule to the (sub)module which it is descended from. Dashed arrows point from a module or program unit to modules which it uses.

Interfaces

public interface operator(+)

private elemental function eml_add_real64(x, y)

$x + y \mapsto x - ( - y )$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x
type(eml_real64_type),	intent(in)			::	y

Return Value type(eml_real64_type)

public interface operator(-)

private elemental module function eml_neg_real64(x)

$- x \mapsto ( \ln 1 ) - x$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private interface operator(-)

private elemental function eml_sub_real64(x, y)

$x - y \mapsto \operatorname{eml} \bigl( \ln (x) , \exp (y) \bigr)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x
type(eml_real64_type),	intent(in)			::	y

Return Value type(eml_real64_type)

public interface operator(*)

private elemental function eml_mul_real64(x, y)

$x \times y \mapsto \exp \bigl( \ln (x) + \ln (y) \bigr)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x
type(eml_real64_type),	intent(in)			::	y

Return Value type(eml_real64_type)

public interface operator(/)

private elemental function eml_div_real64(x, y)

$x / y \mapsto x \times \operatorname{inv}(y)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x
type(eml_real64_type),	intent(in)			::	y

Return Value type(eml_real64_type)

public interface operator(**)

private elemental function eml_pow_real64(x, y)

$x^y \mapsto \exp ( y \times \ln x )$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x
type(eml_real64_type),	intent(in)			::	y

Return Value type(eml_real64_type)

public interface acos

private elemental function eml_acos_real64(x)

$\arccos (x) \equiv \sqrt{-1} \ln ( x + \sqrt{ x - 1 } \sqrt{ x + 1 } )$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

public interface acosh

private elemental function eml_acosh_real64(x)

$\operatorname{arcosh} (x) \equiv \ln ( x + \sqrt{ x - 1 } \sqrt{ x + 1 } )$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

public interface asin

private elemental module function eml_asin_real64(x)

$\arcsin (x) \equiv \sqrt{-1} \ln ( \sqrt{ 1 - x^2 } - \sqrt{-1} x )$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

public interface asinh

private elemental function eml_asinh_real64(x)

$\operatorname{arsinh} (x) \equiv \ln ( x + \sqrt{ x^2 + 1 } )$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

public interface atan

private elemental function eml_atan_real64(x)

$\arctan (x) \equiv ( \sqrt{-1} / 2 ) \ln \bigl( ( \sqrt{-1} + x ) / ( \sqrt{-1} - x ) \bigr)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

public interface atanh

private elemental function eml_atanh_real64(x)

$\operatorname{artanh} \equiv ( 1 / 2 ) \ln \bigl( ( 1 + x ) / ( 1 - x ) \bigr)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

public interface avg

private elemental function eml_avg_real64(x, y)

$\operatorname{avg}(x,y) \equiv \operatorname{half}(x + y)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x
type(eml_real64_type),	intent(in)			::	y

Return Value type(eml_real64_type)

public interface cos

private elemental function eml_cos_real64(x)

$\cos (x) \equiv \cosh ( \sqrt{-1} x )$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

public interface cosh

private elemental function eml_cosh_real64(x)

$\cosh (x) \equiv \operatorname{avg} \bigl( \exp (x) , \exp (-x) \bigr)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

public interface eml

private elemental function eml_eml_real64(x, y)

$\operatorname{eml} (x,y) = \exp (x) - \ln (y)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x
type(eml_real64_type),	intent(in)			::	y

Return Value type(eml_real64_type)

public interface exp

private elemental function eml_exp_real64(x)

$\exp (x) \equiv \operatorname{eml}(x,1)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

public interface half

private elemental module function eml_half_real64(x)

$\operatorname{half}(x) \equiv x / 2$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

public interface hypot

private elemental function eml_hypot_real64(x, y)

$\operatorname{hypot}(x,y) \equiv \sqrt{ x^2 + y^2 }$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x
type(eml_real64_type),	intent(in)			::	y

Return Value type(eml_real64_type)

public interface inv

private elemental function eml_inv_real64(x)

$\operatorname{inv}(x) \equiv 1 / x \mapsto \exp ( - \ln x )$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

public interface log

private elemental function eml_natural_log_real64(x)

$\ln (x) \equiv \operatorname{eml} \Bigl( 1, \exp \bigl( \operatorname{eml}(1,x) \bigr) \Bigr)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

public interface logistic_sigmoid

private elemental function eml_logistic_sigmoid_real64(x)

$\mathop{\sigma}(x) \equiv 1 / \bigl( 1 + \exp ( - x ) \bigr) \equiv 1 / \operatorname{eml} \bigl( - x , \exp ( -1 ) \bigr)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

public interface sin

private elemental function eml_sin_real64(x)

$\sin (x) \equiv \cos \bigl( x - ( \pi / 2 ) \bigr)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

public interface sinh

private elemental function eml_sinh_real64(x)

$\sinh (x) \equiv \operatorname{eml} \bigl( x , \exp ( \cosh x ) \bigr)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

public interface sqr

private elemental function eml_sqr_real64(x)

$x^2 \equiv x \times x$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

public interface sqrt

private elemental function eml_sqrt_real64(x)

$\sqrt{x} \equiv x^{1/2}$

Note

This module did not choose $\sqrt{x} \equiv \exp \bigl( \operatorname{half} ( \ln x ) \bigr)$
because the return value becomes $+ \infty$ when $x = 0$ .

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

public interface tan

private elemental function eml_tan_real64(x)

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

public interface tanh

private elemental function eml_tanh_real64(x)

$\tanh (x) \equiv \sinh (x) / \cosh (x)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private interface eml_acos

private elemental function eml_acos_real64(x)

$\arccos (x) \equiv \sqrt{-1} \ln ( x + \sqrt{ x - 1 } \sqrt{ x + 1 } )$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private interface eml_acosh

private elemental function eml_acosh_real64(x)

$\operatorname{arcosh} (x) \equiv \ln ( x + \sqrt{ x - 1 } \sqrt{ x + 1 } )$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private interface eml_add

private elemental function eml_add_real64(x, y)

$x + y \mapsto x - ( - y )$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x
type(eml_real64_type),	intent(in)			::	y

Return Value type(eml_real64_type)

private interface eml_asin

private elemental module function eml_asin_real64(x)

$\arcsin (x) \equiv \sqrt{-1} \ln ( \sqrt{ 1 - x^2 } - \sqrt{-1} x )$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private interface eml_asinh

private elemental function eml_asinh_real64(x)

$\operatorname{arsinh} (x) \equiv \ln ( x + \sqrt{ x^2 + 1 } )$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private interface eml_atan

private elemental function eml_atan_real64(x)

$\arctan (x) \equiv ( \sqrt{-1} / 2 ) \ln \bigl( ( \sqrt{-1} + x ) / ( \sqrt{-1} - x ) \bigr)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private interface eml_atanh

private elemental function eml_atanh_real64(x)

$\operatorname{artanh} \equiv ( 1 / 2 ) \ln \bigl( ( 1 + x ) / ( 1 - x ) \bigr)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private interface eml_avg

private elemental function eml_avg_real64(x, y)

$\operatorname{avg}(x,y) \equiv \operatorname{half}(x + y)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x
type(eml_real64_type),	intent(in)			::	y

Return Value type(eml_real64_type)

private interface eml_cos

private elemental function eml_cos_real64(x)

$\cos (x) \equiv \cosh ( \sqrt{-1} x )$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private interface eml_cosh

private elemental function eml_cosh_real64(x)

$\cosh (x) \equiv \operatorname{avg} \bigl( \exp (x) , \exp (-x) \bigr)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private interface eml_div

private elemental function eml_div_real64(x, y)

$x / y \mapsto x \times \operatorname{inv}(y)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x
type(eml_real64_type),	intent(in)			::	y

Return Value type(eml_real64_type)

private interface eml_exp

private elemental function eml_exp_real64(x)

$\exp (x) \equiv \operatorname{eml}(x,1)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private interface eml_half

private elemental module function eml_half_real64(x)

$\operatorname{half}(x) \equiv x / 2$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private interface eml_hypot

private elemental function eml_hypot_real64(x, y)

$\operatorname{hypot}(x,y) \equiv \sqrt{ x^2 + y^2 }$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x
type(eml_real64_type),	intent(in)			::	y

Return Value type(eml_real64_type)

private interface eml_inv

private elemental function eml_inv_real64(x)

$\operatorname{inv}(x) \equiv 1 / x \mapsto \exp ( - \ln x )$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private interface eml_log

private elemental function eml_natural_log_real64(x)

$\ln (x) \equiv \operatorname{eml} \Bigl( 1, \exp \bigl( \operatorname{eml}(1,x) \bigr) \Bigr)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private interface eml_logistic_sigmoid

private elemental function eml_logistic_sigmoid_real64(x)

$\mathop{\sigma}(x) \equiv 1 / \bigl( 1 + \exp ( - x ) \bigr) \equiv 1 / \operatorname{eml} \bigl( - x , \exp ( -1 ) \bigr)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private interface eml_mul

private elemental function eml_mul_real64(x, y)

$x \times y \mapsto \exp \bigl( \ln (x) + \ln (y) \bigr)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x
type(eml_real64_type),	intent(in)			::	y

Return Value type(eml_real64_type)

private interface eml_neg

private elemental module function eml_neg_real64(x)

$- x \mapsto ( \ln 1 ) - x$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private interface eml_pow

private elemental function eml_pow_real64(x, y)

$x^y \mapsto \exp ( y \times \ln x )$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x
type(eml_real64_type),	intent(in)			::	y

Return Value type(eml_real64_type)

private interface eml_sin

private elemental function eml_sin_real64(x)

$\sin (x) \equiv \cos \bigl( x - ( \pi / 2 ) \bigr)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private interface eml_sinh

private elemental function eml_sinh_real64(x)

$\sinh (x) \equiv \operatorname{eml} \bigl( x , \exp ( \cosh x ) \bigr)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private interface eml_sqr

private elemental function eml_sqr_real64(x)

$x^2 \equiv x \times x$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private interface eml_sqrt

private elemental function eml_sqrt_real64(x)

$\sqrt{x} \equiv x^{1/2}$

Note

This module did not choose $\sqrt{x} \equiv \exp \bigl( \operatorname{half} ( \ln x ) \bigr)$
because the return value becomes $+ \infty$ when $x = 0$ .

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private interface eml_sub

private elemental function eml_sub_real64(x, y)

$x - y \mapsto \operatorname{eml} \bigl( \ln (x) , \exp (y) \bigr)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x
type(eml_real64_type),	intent(in)			::	y

Return Value type(eml_real64_type)

private interface eml_tan

private elemental function eml_tan_real64(x)

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private interface eml_tanh

private elemental function eml_tanh_real64(x)

$\tanh (x) \equiv \sinh (x) / \cosh (x)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

Derived Types

type, public, extends(eml_real64_class) :: eml_real64_type

Type-Bound Procedures

generic, public :: set_p1 => set_p1_real64
procedure, private, pass, non_overridable :: set_iu_real64
procedure, private, pass, non_overridable :: set_m1_real64
procedure, private, pass, non_overridable :: set_p2_real64
procedure, private, pass, non_overridable :: set_pi_real64
generic, public :: set_iu => set_iu_real64
generic, public :: set_m1 => set_m1_real64
generic, public :: set_p2 => set_p2_real64
generic, public :: set_pi => set_pi_real64

Functions

private elemental function eml_acos_real64(x)

$\arccos (x) \equiv \sqrt{-1} \ln ( x + \sqrt{ x - 1 } \sqrt{ x + 1 } )$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private elemental function eml_acosh_real64(x)

$\operatorname{arcosh} (x) \equiv \ln ( x + \sqrt{ x - 1 } \sqrt{ x + 1 } )$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private elemental function eml_add_real64(x, y)

$x + y \mapsto x - ( - y )$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x
type(eml_real64_type),	intent(in)			::	y

Return Value type(eml_real64_type)

private elemental module function eml_asin_real64(x)

$\arcsin (x) \equiv \sqrt{-1} \ln ( \sqrt{ 1 - x^2 } - \sqrt{-1} x )$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private elemental function eml_asinh_real64(x)

$\operatorname{arsinh} (x) \equiv \ln ( x + \sqrt{ x^2 + 1 } )$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private elemental function eml_atan_real64(x)

$\arctan (x) \equiv ( \sqrt{-1} / 2 ) \ln \bigl( ( \sqrt{-1} + x ) / ( \sqrt{-1} - x ) \bigr)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private elemental function eml_atanh_real64(x)

$\operatorname{artanh} \equiv ( 1 / 2 ) \ln \bigl( ( 1 + x ) / ( 1 - x ) \bigr)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private elemental function eml_avg_real64(x, y)

$\operatorname{avg}(x,y) \equiv \operatorname{half}(x + y)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x
type(eml_real64_type),	intent(in)			::	y

Return Value type(eml_real64_type)

private elemental function eml_cos_real64(x)

$\cos (x) \equiv \cosh ( \sqrt{-1} x )$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private elemental function eml_cosh_real64(x)

$\cosh (x) \equiv \operatorname{avg} \bigl( \exp (x) , \exp (-x) \bigr)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private elemental function eml_div_real64(x, y)

$x / y \mapsto x \times \operatorname{inv}(y)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x
type(eml_real64_type),	intent(in)			::	y

Return Value type(eml_real64_type)

private elemental function eml_eml_real64(x, y)

$\operatorname{eml} (x,y) = \exp (x) - \ln (y)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x
type(eml_real64_type),	intent(in)			::	y

Return Value type(eml_real64_type)

private elemental function eml_exp_real64(x)

$\exp (x) \equiv \operatorname{eml}(x,1)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private elemental module function eml_half_real64(x)

$\operatorname{half}(x) \equiv x / 2$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private elemental function eml_hypot_real64(x, y)

$\operatorname{hypot}(x,y) \equiv \sqrt{ x^2 + y^2 }$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x
type(eml_real64_type),	intent(in)			::	y

Return Value type(eml_real64_type)

private elemental function eml_inv_real64(x)

$\operatorname{inv}(x) \equiv 1 / x \mapsto \exp ( - \ln x )$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private elemental function eml_logistic_sigmoid_real64(x)

$\mathop{\sigma}(x) \equiv 1 / \bigl( 1 + \exp ( - x ) \bigr) \equiv 1 / \operatorname{eml} \bigl( - x , \exp ( -1 ) \bigr)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private elemental function eml_mul_real64(x, y)

$x \times y \mapsto \exp \bigl( \ln (x) + \ln (y) \bigr)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x
type(eml_real64_type),	intent(in)			::	y

Return Value type(eml_real64_type)

private elemental function eml_natural_log_real64(x)

$\ln (x) \equiv \operatorname{eml} \Bigl( 1, \exp \bigl( \operatorname{eml}(1,x) \bigr) \Bigr)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private elemental module function eml_neg_real64(x)

$- x \mapsto ( \ln 1 ) - x$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private elemental function eml_pow_real64(x, y)

$x^y \mapsto \exp ( y \times \ln x )$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x
type(eml_real64_type),	intent(in)			::	y

Return Value type(eml_real64_type)

private elemental function eml_sin_real64(x)

$\sin (x) \equiv \cos \bigl( x - ( \pi / 2 ) \bigr)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private elemental function eml_sinh_real64(x)

$\sinh (x) \equiv \operatorname{eml} \bigl( x , \exp ( \cosh x ) \bigr)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private elemental function eml_sqr_real64(x)

$x^2 \equiv x \times x$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private elemental function eml_sqrt_real64(x)

$\sqrt{x} \equiv x^{1/2}$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private elemental function eml_sub_real64(x, y)

$x - y \mapsto \operatorname{eml} \bigl( \ln (x) , \exp (y) \bigr)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x
type(eml_real64_type),	intent(in)			::	y

Return Value type(eml_real64_type)

private elemental function eml_tan_real64(x)

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

private elemental function eml_tanh_real64(x)

$\tanh (x) \equiv \sinh (x) / \cosh (x)$

Arguments

Type	Intent	Optional	Attributes		Name
type(eml_real64_type),	intent(in)			::	x

Return Value type(eml_real64_type)

Subroutines

private elemental subroutine set_iu_real64(self)

$\sqrt{-1} \mapsto - \exp \Bigl( \operatorname{half} \bigl( \log ( -1 ) \bigr) \Bigr)$

Arguments

Type	Intent	Optional	Attributes		Name
class(eml_real64_type),	intent(inout)			::	self

private elemental subroutine set_m1_real64(self)

$-1 \mapsto \ln (1) - 1$

Arguments

Type	Intent	Optional	Attributes		Name
class(eml_real64_type),	intent(inout)			::	self

private elemental module subroutine set_p2_real64(self)

$2 \mapsto 1 - ( -1 )$

Arguments

Type	Intent	Optional	Attributes		Name
class(eml_real64_type),	intent(inout)			::	self

private elemental subroutine set_pi_real64(self)

$\pi \mapsto \sqrt{ - {\bigl( \ln ( -1 ) \bigr)}^2 }$

Arguments

Type	Intent	Optional	Attributes		Name
class(eml_real64_type),	intent(inout)			::	self

eml_type_fortran Module

Contents

Interfaces

Derived Types

Functions

Subroutines

Uses

Interfaces

public interface operator(+)

private elemental function eml_add_real64(x, y)

Arguments

Return Value type(eml_real64_type)

public interface operator(-)

private elemental module function eml_neg_real64(x)

Arguments

Return Value type(eml_real64_type)

private interface operator(-)

private elemental function eml_sub_real64(x, y)

Arguments

Return Value type(eml_real64_type)

public interface operator(*)

private elemental function eml_mul_real64(x, y)

Arguments

Return Value type(eml_real64_type)

public interface operator(/)

private elemental function eml_div_real64(x, y)

Arguments

Return Value type(eml_real64_type)

public interface operator(**)

private elemental function eml_pow_real64(x, y)

Arguments

Return Value type(eml_real64_type)

public interface acos

private elemental function eml_acos_real64(x)

Arguments

Return Value type(eml_real64_type)

public interface acosh

private elemental function eml_acosh_real64(x)

Arguments

Return Value type(eml_real64_type)

public interface asin

private elemental module function eml_asin_real64(x)

Arguments

Return Value type(eml_real64_type)

public interface asinh

private elemental function eml_asinh_real64(x)

Arguments

Return Value type(eml_real64_type)

public interface atan

private elemental function eml_atan_real64(x)

Arguments

Return Value type(eml_real64_type)

public interface atanh

private elemental function eml_atanh_real64(x)

Arguments

Return Value type(eml_real64_type)

public interface avg

private elemental function eml_avg_real64(x, y)

Arguments

Return Value type(eml_real64_type)

public interface cos

private elemental function eml_cos_real64(x)

Arguments

Return Value type(eml_real64_type)

public interface cosh

private elemental function eml_cosh_real64(x)

Arguments

Return Value type(eml_real64_type)

public interface eml

private elemental function eml_eml_real64(x, y)

Arguments

Return Value type(eml_real64_type)

public interface exp

private elemental function eml_exp_real64(x)

Arguments

Return Value type(eml_real64_type)

public interface half

private elemental module function eml_half_real64(x)

Arguments

Return Value type(eml_real64_type)