elliptic_nome_fortran – DSCF-1224/elliptic_nome

public interface elliptic_nome_01

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \end{align*}$

public elemental function elliptic_nome_01_real32(k) result(q)

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \end{align*}$

Note

The elliptic modulus $k$ should satisfy ${ k }^{ 2 } \le 1/2$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real32),	intent(in)			::	k	elliptic modulus $k$

Return Value real(kind=real32)

elliptic nome $q$

public elemental function elliptic_nome_01_real64(k) result(q)

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \end{align*}$

Note

The elliptic modulus $k$ should satisfy ${ k }^{ 2 } \le 1/2$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in)			::	k	elliptic modulus $k$

Return Value real(kind=real64)

elliptic nome $q$

public elemental function elliptic_nome_01_real128(k) result(q)

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \end{align*}$

Note

The elliptic modulus $k$ should satisfy ${ k }^{ 2 } \le 1/2$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real128),	intent(in)			::	k	elliptic modulus $k$

Return Value real(kind=real128)

elliptic nome $q$

public interface elliptic_nome_05

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \end{align*}$

public elemental function elliptic_nome_05_real32(k) result(q)

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \end{align*}$

Note

The elliptic modulus $k$ should satisfy ${ k }^{ 2 } \le 1/2$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real32),	intent(in)			::	k	elliptic modulus $k$

Return Value real(kind=real32)

elliptic nome $q$

public elemental function elliptic_nome_05_real64(k) result(q)

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \end{align*}$

Note

The elliptic modulus $k$ should satisfy ${ k }^{ 2 } \le 1/2$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in)			::	k	elliptic modulus $k$

Return Value real(kind=real64)

elliptic nome $q$

public elemental function elliptic_nome_05_real128(k) result(q)

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \end{align*}$

Note

The elliptic modulus $k$ should satisfy ${ k }^{ 2 } \le 1/2$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real128),	intent(in)			::	k	elliptic modulus $k$

Return Value real(kind=real128)

elliptic nome $q$

public interface elliptic_nome_09

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \end{align*}$

public elemental function elliptic_nome_09_real32(k) result(q)

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \end{align*}$

Note

The elliptic modulus $k$ should satisfy ${ k }^{ 2 } \le 1/2$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real32),	intent(in)			::	k	elliptic modulus $k$

Return Value real(kind=real32)

elliptic nome $q$

public elemental function elliptic_nome_09_real64(k) result(q)

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \end{align*}$

Note

The elliptic modulus $k$ should satisfy ${ k }^{ 2 } \le 1/2$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in)			::	k	elliptic modulus $k$

Return Value real(kind=real64)

elliptic nome $q$

public elemental function elliptic_nome_09_real128(k) result(q)

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \end{align*}$

Note

The elliptic modulus $k$ should satisfy ${ k }^{ 2 } \le 1/2$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real128),	intent(in)			::	k	elliptic modulus $k$

Return Value real(kind=real128)

elliptic nome $q$

public interface elliptic_nome_13

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \end{align*}$

public elemental function elliptic_nome_13_real32(k) result(q)

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \end{align*}$

Note

The elliptic modulus $k$ should satisfy ${ k }^{ 2 } \le 1/2$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real32),	intent(in)			::	k	elliptic modulus $k$

Return Value real(kind=real32)

elliptic nome $q$

public elemental function elliptic_nome_13_real64(k) result(q)

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \end{align*}$

Note

The elliptic modulus $k$ should satisfy ${ k }^{ 2 } \le 1/2$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in)			::	k	elliptic modulus $k$

Return Value real(kind=real64)

elliptic nome $q$

public elemental function elliptic_nome_13_real128(k) result(q)

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \end{align*}$

Note

The elliptic modulus $k$ should satisfy ${ k }^{ 2 } \le 1/2$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real128),	intent(in)			::	k	elliptic modulus $k$

Return Value real(kind=real128)

elliptic nome $q$

public interface elliptic_nome_17

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \end{align*}$

public elemental function elliptic_nome_17_real32(k) result(q)

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \end{align*}$

Note

The elliptic modulus $k$ should satisfy ${ k }^{ 2 } \le 1/2$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real32),	intent(in)			::	k	elliptic modulus $k$

Return Value real(kind=real32)

elliptic nome $q$

public elemental function elliptic_nome_17_real64(k) result(q)

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \end{align*}$

Note

The elliptic modulus $k$ should satisfy ${ k }^{ 2 } \le 1/2$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in)			::	k	elliptic modulus $k$

Return Value real(kind=real64)

elliptic nome $q$

public elemental function elliptic_nome_17_real128(k) result(q)

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \end{align*}$

Note

The elliptic modulus $k$ should satisfy ${ k }^{ 2 } \le 1/2$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real128),	intent(in)			::	k	elliptic modulus $k$

Return Value real(kind=real128)

elliptic nome $q$

public interface elliptic_nome_21

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \end{align*}$

public elemental function elliptic_nome_21_real32(k) result(q)

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \end{align*}$

Note

The elliptic modulus $k$ should satisfy ${ k }^{ 2 } \le 1/2$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real32),	intent(in)			::	k	elliptic modulus $k$

Return Value real(kind=real32)

elliptic nome $q$

public elemental function elliptic_nome_21_real64(k) result(q)

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \end{align*}$

Note

The elliptic modulus $k$ should satisfy ${ k }^{ 2 } \le 1/2$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in)			::	k	elliptic modulus $k$

Return Value real(kind=real64)

elliptic nome $q$

public elemental function elliptic_nome_21_real128(k) result(q)

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \end{align*}$

Note

The elliptic modulus $k$ should satisfy ${ k }^{ 2 } \le 1/2$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real128),	intent(in)			::	k	elliptic modulus $k$

Return Value real(kind=real128)

elliptic nome $q$

public interface elliptic_nome_25

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \\ & + 268616 { \varepsilon }^{ 25 } \end{align*}$

public elemental function elliptic_nome_25_real32(k) result(q)

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \\ & + 268616 { \varepsilon }^{ 25 } \end{align*}$

Note

The elliptic modulus $k$ should satisfy ${ k }^{ 2 } \le 1/2$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real32),	intent(in)			::	k	elliptic modulus $k$

Return Value real(kind=real32)

elliptic nome $q$

public elemental function elliptic_nome_25_real64(k) result(q)

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \\ & + 268616 { \varepsilon }^{ 25 } \end{align*}$

Note

The elliptic modulus $k$ should satisfy ${ k }^{ 2 } \le 1/2$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in)			::	k	elliptic modulus $k$

Return Value real(kind=real64)

elliptic nome $q$

public elemental function elliptic_nome_25_real128(k) result(q)

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \\ & + 268616 { \varepsilon }^{ 25 } \end{align*}$

Note

The elliptic modulus $k$ should satisfy ${ k }^{ 2 } \le 1/2$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real128),	intent(in)			::	k	elliptic modulus $k$

Return Value real(kind=real128)

elliptic nome $q$

public interface elliptic_nome_29

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \\ & + 268616 { \varepsilon }^{ 25 } \\ & + 3567400 { \varepsilon }^{ 29 } \end{align*}$

public elemental function elliptic_nome_29_real32(k) result(q)

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \\ & + 268616 { \varepsilon }^{ 25 } \\ & + 3567400 { \varepsilon }^{ 29 } \end{align*}$

Note

The elliptic modulus $k$ should satisfy ${ k }^{ 2 } \le 1/2$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real32),	intent(in)			::	k	elliptic modulus $k$

Return Value real(kind=real32)

elliptic nome $q$

public elemental function elliptic_nome_29_real64(k) result(q)

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \\ & + 268616 { \varepsilon }^{ 25 } \\ & + 3567400 { \varepsilon }^{ 29 } \end{align*}$

Note

The elliptic modulus $k$ should satisfy ${ k }^{ 2 } \le 1/2$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in)			::	k	elliptic modulus $k$

Return Value real(kind=real64)

elliptic nome $q$

public elemental function elliptic_nome_29_real128(k) result(q)

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \\ & + 268616 { \varepsilon }^{ 25 } \\ & + 3567400 { \varepsilon }^{ 29 } \end{align*}$

Note

The elliptic modulus $k$ should satisfy ${ k }^{ 2 } \le 1/2$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real128),	intent(in)			::	k	elliptic modulus $k$

Return Value real(kind=real128)

elliptic nome $q$

public interface elliptic_nome_33

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \\ & + 268616 { \varepsilon }^{ 25 } \\ & + 3567400 { \varepsilon }^{ 29 } \\ & + 48555069 { \varepsilon }^{ 33 } \end{align*}$

public elemental function elliptic_nome_33_real32(k) result(q)

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \\ & + 268616 { \varepsilon }^{ 25 } \\ & + 3567400 { \varepsilon }^{ 29 } \\ & + 48555069 { \varepsilon }^{ 33 } \end{align*}$

Note

The elliptic modulus $k$ should satisfy ${ k }^{ 2 } \le 1/2$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real32),	intent(in)			::	k	elliptic modulus $k$

Return Value real(kind=real32)

elliptic nome $q$

public elemental function elliptic_nome_33_real64(k) result(q)

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \\ & + 268616 { \varepsilon }^{ 25 } \\ & + 3567400 { \varepsilon }^{ 29 } \\ & + 48555069 { \varepsilon }^{ 33 } \end{align*}$

Note

The elliptic modulus $k$ should satisfy ${ k }^{ 2 } \le 1/2$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in)			::	k	elliptic modulus $k$

Return Value real(kind=real64)

elliptic nome $q$

public elemental function elliptic_nome_33_real128(k) result(q)

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \\ & + 268616 { \varepsilon }^{ 25 } \\ & + 3567400 { \varepsilon }^{ 29 } \\ & + 48555069 { \varepsilon }^{ 33 } \end{align*}$

Note

The elliptic modulus $k$ should satisfy ${ k }^{ 2 } \le 1/2$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real128),	intent(in)			::	k	elliptic modulus $k$

Return Value real(kind=real128)

elliptic nome $q$

public interface elliptic_nome_auto

public elemental function elliptic_nome_auto_real32(k) result(q)

Calculate the elliptic nome $q$ for the given elliptic modulus $k$

Note

The elliptic modulus $k$ should satisfy ${ k }^{ 2 } \le 1/2$ .
If the calculation does not converge, it returns NaN.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real32),	intent(in)			::	k	elliptic modulus $k$

Return Value real(kind=real32)

elliptic nome $q$

public elemental function elliptic_nome_auto_real64(k) result(q)

Calculate the elliptic nome $q$ for the given elliptic modulus $k$

Note

The elliptic modulus $k$ should satisfy ${ k }^{ 2 } \le 1/2$ .
If the calculation does not converge, it returns NaN.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in)			::	k	elliptic modulus $k$

Return Value real(kind=real64)

elliptic nome $q$

public elemental function elliptic_nome_auto_real128(k) result(q)

Calculate the elliptic nome $q$ for the given elliptic modulus $k$

Note

The elliptic modulus $k$ should satisfy ${ k }^{ 2 } \le 1/2$ .
If the calculation does not converge, it returns NaN.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real128),	intent(in)			::	k	elliptic modulus $k$

Return Value real(kind=real128)

elliptic nome $q$

elliptic_nome_fortran Module

Contents

Interfaces

Uses

Interfaces

public interface elliptic_nome_01

public elemental function elliptic_nome_01_real32(k) result(q)

Arguments

Return Value real(kind=real32)

public elemental function elliptic_nome_01_real64(k) result(q)

Arguments

Return Value real(kind=real64)

public elemental function elliptic_nome_01_real128(k) result(q)

Arguments

Return Value real(kind=real128)

public interface elliptic_nome_05

public elemental function elliptic_nome_05_real32(k) result(q)

Arguments

Return Value real(kind=real32)

public elemental function elliptic_nome_05_real64(k) result(q)

Arguments

Return Value real(kind=real64)

public elemental function elliptic_nome_05_real128(k) result(q)

Arguments

Return Value real(kind=real128)

public interface elliptic_nome_09

public elemental function elliptic_nome_09_real32(k) result(q)

Arguments

Return Value real(kind=real32)

public elemental function elliptic_nome_09_real64(k) result(q)

Arguments

Return Value real(kind=real64)

public elemental function elliptic_nome_09_real128(k) result(q)

Arguments

Return Value real(kind=real128)

public interface elliptic_nome_13

public elemental function elliptic_nome_13_real32(k) result(q)

Arguments

Return Value real(kind=real32)

public elemental function elliptic_nome_13_real64(k) result(q)

Arguments

Return Value real(kind=real64)

public elemental function elliptic_nome_13_real128(k) result(q)

Arguments

Return Value real(kind=real128)

public interface elliptic_nome_17

public elemental function elliptic_nome_17_real32(k) result(q)

Arguments

Return Value real(kind=real32)

public elemental function elliptic_nome_17_real64(k) result(q)

Arguments

Return Value real(kind=real64)

public elemental function elliptic_nome_17_real128(k) result(q)

Arguments

Return Value real(kind=real128)

public interface elliptic_nome_21

public elemental function elliptic_nome_21_real32(k) result(q)

Arguments

Return Value real(kind=real32)

public elemental function elliptic_nome_21_real64(k) result(q)

Arguments

Return Value real(kind=real64)

public elemental function elliptic_nome_21_real128(k) result(q)

Arguments

Return Value real(kind=real128)

public interface elliptic_nome_25

public elemental function elliptic_nome_25_real32(k) result(q)

Arguments

Return Value real(kind=real32)

public elemental function elliptic_nome_25_real64(k) result(q)

Arguments

Return Value real(kind=real64)

public elemental function elliptic_nome_25_real128(k) result(q)

Arguments

Return Value real(kind=real128)

public interface elliptic_nome_29

public elemental function elliptic_nome_29_real32(k) result(q)

Arguments

Return Value real(kind=real32)

public elemental function elliptic_nome_29_real64(k) result(q)