arithmetic_geometric_mean_fortran – DSCF-1224/arithmetic_geometric_mean

Compute arithmetic–geometric mean.

Uses

- iso_fortran_env
- ieee_arithmetic

Variables

Type	Visibility	Attributes		Name		Initial
integer,	private,	parameter	::	initial_n_iter	=	-1
integer,	private,	parameter	::	max_n_iter_real128	=	digits(0.0_real128)
integer,	private,	parameter	::	max_n_iter_real32	=	digits(0.0_real32)
integer,	private,	parameter	::	max_n_iter_real64	=	digits(0.0_real64)

Interfaces

public interface arithmetic_geometric_mean

Safe wrapper for the arithmetic-geometric mean (AGM) computation.

This interface performs lightweight AGM computation with input validation, automatic ordering. Unlike the type-bound subroutine instead, this interface does not retain intermediate calculation results, so they cannot be referenced later.

Note

If either input was NaN: returns NaN
If x and y had opposite signs (x * y .lt. 0): returns NaN
If either x or y is zero (x * y .eq. 0): returns 0
Otherwise: computes AGM using the iterative kernel

private elemental function arithmetic_geometric_mean_real32(x, y) result(agm)

Safe wrapper for the arithmetic-geometric mean (AGM) computation.

This function performs lightweight AGM computation with input validation, automatic ordering. Unlike the type-bound subroutine compute_real32 instead, this function does not retain intermediate calculation results, so they cannot be referenced later.

Note

If either input was NaN: returns NaN
If x and y had opposite signs (x * y .lt. 0): returns NaN
If either x or y is zero (x * y .eq. 0): returns 0
Otherwise: computes AGM using the iterative kernel

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real32),	intent(in)			::	x
real(kind=real32),	intent(in)			::	y

Return Value real(kind=real32)

private elemental function arithmetic_geometric_mean_real64(x, y) result(agm)

Safe wrapper for the arithmetic-geometric mean (AGM) computation.

This function performs lightweight AGM computation with input validation, automatic ordering. Unlike the type-bound subroutine compute_real64 instead, this function does not retain intermediate calculation results, so they cannot be referenced later.

Note

If either input was NaN: returns NaN
If x and y had opposite signs (x * y .lt. 0): returns NaN
If either x or y is zero (x * y .eq. 0): returns 0
Otherwise: computes AGM using the iterative kernel

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in)			::	x
real(kind=real64),	intent(in)			::	y

Return Value real(kind=real64)

private elemental function arithmetic_geometric_mean_real128(x, y) result(agm)

Safe wrapper for the arithmetic-geometric mean (AGM) computation.

This function performs lightweight AGM computation with input validation, automatic ordering. Unlike the type-bound subroutine compute_real128 instead, this function does not retain intermediate calculation results, so they cannot be referenced later.

Note

If either input was NaN: returns NaN
If x and y had opposite signs (x * y .lt. 0): returns NaN
If either x or y is zero (x * y .eq. 0): returns 0
Otherwise: computes AGM using the iterative kernel

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real128),	intent(in)			::	x
real(kind=real128),	intent(in)			::	y

Return Value real(kind=real128)

public interface arithmetic_geometric_mean_kernel

Compute arithmetic–geometric mean (AGM) using the given arithmetic mean a and geometric mean g.

This interface provides a lightweight AGM computation that returns only the final converged value without storing iteration history.
For applications that need to analyze the convergence process, use the type-bound subroutine instead, which preserves the full iteration history.

Warning

This interface assumes both inputs are positive.
No validation is performed on inputs.

Note

Convergence criterion
See is_not_converged

private elemental function arithmetic_geometric_mean_kernel_real32(a, g) result(agm)

Compute arithmetic–geometric mean (AGM) using the given arithmetic mean a and geometric mean g.

This function provides a lightweight AGM computation that returns only the final converged value without storing iteration history.
For applications that need to analyze the convergence process, use the type-bound subroutine compute_kernel_real32 instead, which preserves the full iteration history.

Warning

This function assumes both inputs are positive.
No validation is performed on inputs.

Note

Convergence criterion
See is_not_converged

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real32),	intent(in)			::	a	arithmetic mean
real(kind=real32),	intent(in)			::	g	geometric mean

Return Value real(kind=real32)

private elemental function arithmetic_geometric_mean_kernel_real64(a, g) result(agm)

Compute arithmetic–geometric mean (AGM) using the given arithmetic mean a and geometric mean g.

This function provides a lightweight AGM computation that returns only the final converged value without storing iteration history.
For applications that need to analyze the convergence process, use the type-bound subroutine compute_kernel_real64 instead, which preserves the full iteration history.

Warning

This function assumes both inputs are positive.
No validation is performed on inputs.

Note

Convergence criterion
See is_not_converged

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in)			::	a	arithmetic mean
real(kind=real64),	intent(in)			::	g	geometric mean

Return Value real(kind=real64)

private elemental function arithmetic_geometric_mean_kernel_real128(a, g) result(agm)

Compute arithmetic–geometric mean (AGM) using the given arithmetic mean a and geometric mean g.

This function provides a lightweight AGM computation that returns only the final converged value without storing iteration history.
For applications that need to analyze the convergence process, use the type-bound subroutine compute_kernel_real128 instead, which preserves the full iteration history.

Warning

This function assumes both inputs are positive.
No validation is performed on inputs.

Note

Convergence criterion
See is_not_converged

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real128),	intent(in)			::	a	arithmetic mean
real(kind=real128),	intent(in)			::	g	geometric mean

Return Value real(kind=real128)

private interface compute_step

Compute arithmetic and geometric mean using the given prev_a and prev_g.

Warning

This interface assumes both inputs are positive.
No validation is performed on inputs.

private elemental subroutine compute_step_real32(prev_a, prev_g, next_a, next_g)

Compute arithmetic and geometric mean using the given prev_a and prev_g.

Warning

This subroutine assumes both inputs are positive.
No validation is performed on inputs.

Arguments

Type	Intent		Name
real(kind=real32),	intent(in)	::	prev_a	previous arithmetic mean
real(kind=real32),	intent(in)	::	prev_g	previous geometric mean
real(kind=real32),	intent(out)	::	next_a	next arithmetic mean
real(kind=real32),	intent(out)	::	next_g	next geometric mean

private elemental subroutine compute_step_real64(prev_a, prev_g, next_a, next_g)

Compute arithmetic and geometric mean using the given prev_a and prev_g.

Warning

This subroutine assumes both inputs are positive.
No validation is performed on inputs.

Arguments

Type	Intent		Name
real(kind=real64),	intent(in)	::	prev_a	previous arithmetic mean
real(kind=real64),	intent(in)	::	prev_g	previous geometric mean
real(kind=real64),	intent(out)	::	next_a	next arithmetic mean
real(kind=real64),	intent(out)	::	next_g	next geometric mean

private elemental subroutine compute_step_real128(prev_a, prev_g, next_a, next_g)

Compute arithmetic and geometric mean using the given prev_a and prev_g.

Warning

This subroutine assumes both inputs are positive.
No validation is performed on inputs.

Arguments

Type	Intent		Name
real(kind=real128),	intent(in)	::	prev_a	previous arithmetic mean
real(kind=real128),	intent(in)	::	prev_g	previous geometric mean
real(kind=real128),	intent(out)	::	next_a	next arithmetic mean
real(kind=real128),	intent(out)	::	next_g	next geometric mean

public interface gap

private elemental function gap_final_real32(agm) result(gap_final)

Extract the final gap (arithmetic mean - geometric mean).

Warning

This function assumes the AGM computation has been performed via the compute method.
If called on an uninitialized or improperly computed AGM object, the result may be NaN or undefined.

Arguments

Type	Intent	Optional	Attributes		Name
type(arithmetic_geometric_mean_real32_type),	intent(in)			::	agm

Return Value real(kind=real32)

private elemental function gap_final_real64(agm) result(gap_final)

Extract the final gap (arithmetic mean - geometric mean).

Warning

This function assumes the AGM computation has been performed via the compute method.
If called on an uninitialized or improperly computed AGM object, the result may be NaN or undefined.

Arguments

Type	Intent	Optional	Attributes		Name
type(arithmetic_geometric_mean_real64_type),	intent(in)			::	agm

Return Value real(kind=real64)

private elemental function gap_final_real128(agm) result(gap_final)

Extract the final gap (arithmetic mean - geometric mean).

Warning

This function assumes the AGM computation has been performed via the compute method.
If called on an uninitialized or improperly computed AGM object, the result may be NaN or undefined.

Arguments

Type	Intent	Optional	Attributes		Name
type(arithmetic_geometric_mean_real128_type),	intent(in)			::	agm

Return Value real(kind=real128)

private elemental function gap_selectable_real32(agm, i) result(gap_selectable)

Extract the gap (arithmetic mean - geometric mean) at a specific iteration.

Warning

This function assumes the AGM computation has been performed via the compute method.
If called on an uninitialized or improperly computed AGM object, the result may be NaN or undefined.

The iteration index i must be valid: 0 <= i <= n_iter.
No bounds checking is performed; invalid indices may cause undefined behavior.

Arguments

Type	Intent	Optional	Attributes		Name
type(arithmetic_geometric_mean_real32_type),	intent(in)			::	agm
integer,	intent(in)			::	i

Return Value real(kind=real32)

private elemental function gap_selectable_real64(agm, i) result(gap_selectable)

Extract the gap (arithmetic mean - geometric mean) at a specific iteration.

Warning

This function assumes the AGM computation has been performed via the compute method.
If called on an uninitialized or improperly computed AGM object, the result may be NaN or undefined.

The iteration index i must be valid: 0 <= i <= n_iter.
No bounds checking is performed; invalid indices may cause undefined behavior.

Arguments

Type	Intent	Optional	Attributes		Name
type(arithmetic_geometric_mean_real64_type),	intent(in)			::	agm
integer,	intent(in)			::	i

Return Value real(kind=real64)

private elemental function gap_selectable_real128(agm, i) result(gap_selectable)

Extract the gap (arithmetic mean - geometric mean) at a specific iteration.

Warning

This function assumes the AGM computation has been performed via the compute method.
If called on an uninitialized or improperly computed AGM object, the result may be NaN or undefined.

The iteration index i must be valid: 0 <= i <= n_iter.
No bounds checking is performed; invalid indices may cause undefined behavior.

Arguments

Type	Intent	Optional	Attributes		Name
type(arithmetic_geometric_mean_real128_type),	intent(in)			::	agm
integer,	intent(in)			::	i

Return Value real(kind=real128)

private interface initialize

Initialize components: n_iter, list_a and list_g

private elemental subroutine initialize_real32(agm)

Initialize components: n_iter, list_a and list_g

Arguments

Type	Intent	Optional	Attributes		Name
type(arithmetic_geometric_mean_real32_type),	intent(inout)			::	agm

private elemental subroutine initialize_real64(agm)

Initialize components: n_iter, list_a and list_g

Arguments

Type	Intent	Optional	Attributes		Name
type(arithmetic_geometric_mean_real64_type),	intent(inout)			::	agm

private elemental subroutine initialize_real128(agm)

Initialize components: n_iter, list_a and list_g

Arguments

Type	Intent	Optional	Attributes		Name
type(arithmetic_geometric_mean_real128_type),	intent(inout)			::	agm

private interface is_not_converged

Check if the arithmetic-geometric mean iteration has not yet converged.

Note

Convergence criterion
Returns .true. if the absolute difference between the arithmetic mean a and geometric mean g exceeds the machine epsilon relative to the smaller value, as determined by spacing(min(a, g)).

Mathematically: |a - g| > spacing(min(a, g))

Appendix
This interface is designed for internal use within the AGM iteration where both values are guaranteed to be positive and converging.

private elemental function is_not_converged_real32(a, g) result(stat)

Check if the arithmetic-geometric mean iteration has not yet converged.

Note

Mathematically: |a - g| > spacing(min(a, g))

Appendix
This function is designed for internal use within the AGM iteration where both values are guaranteed to be positive and converging.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real32),	intent(in)			::	a	arithmetic mean
real(kind=real32),	intent(in)			::	g	geometric mean

Return Value logical

private elemental function is_not_converged_real64(a, g) result(stat)

Check if the arithmetic-geometric mean iteration has not yet converged.

Note

Mathematically: |a - g| > spacing(min(a, g))

Appendix
This function is designed for internal use within the AGM iteration where both values are guaranteed to be positive and converging.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in)			::	a	arithmetic mean
real(kind=real64),	intent(in)			::	g	geometric mean

Return Value logical

private elemental function is_not_converged_real128(a, g) result(stat)

Check if the arithmetic-geometric mean iteration has not yet converged.

Note

Mathematically: |a - g| > spacing(min(a, g))

Appendix
This function is designed for internal use within the AGM iteration where both values are guaranteed to be positive and converging.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real128),	intent(in)			::	a	arithmetic mean
real(kind=real128),	intent(in)			::	g	geometric mean

Return Value logical

public interface max

private elemental function max_final_real32(agm) result(max_final)

Extract the final arithmetic-geometric mean from completed AGM calculations.
Specifically, this function returns the larger of the two final values.

Warning

This function assumes the AGM computation has been performed via the compute method.
If called on an uninitialized or improperly computed AGM object, the result may be NaN or undefined.

Arguments

Type	Intent	Optional	Attributes		Name
type(arithmetic_geometric_mean_real32_type),	intent(in)			::	agm

Return Value real(kind=real32)

private elemental function max_final_real64(agm) result(max_final)

Extract the final arithmetic-geometric mean from completed AGM calculations.
Specifically, this function returns the larger of the two final values.

Warning

This function assumes the AGM computation has been performed via the compute method.
If called on an uninitialized or improperly computed AGM object, the result may be NaN or undefined.

Arguments

Type	Intent	Optional	Attributes		Name
type(arithmetic_geometric_mean_real64_type),	intent(in)			::	agm

Return Value real(kind=real64)

private elemental function max_final_real128(agm) result(max_final)

Extract the final arithmetic-geometric mean from completed AGM calculations.
Specifically, this function returns the larger of the two final values.

Warning

This function assumes the AGM computation has been performed via the compute method.
If called on an uninitialized or improperly computed AGM object, the result may be NaN or undefined.

Arguments

Type	Intent	Optional	Attributes		Name
type(arithmetic_geometric_mean_real128_type),	intent(in)			::	agm

Return Value real(kind=real128)

private elemental function max_selectable_real32(agm, i) result(max_selectable)

Extract the arithmetic-geometric mean value at a specific iteration.
Specifically, this function returns the larger of the two values.

Warning

This function assumes the AGM computation has been performed via the compute method.
If called on an uninitialized or improperly computed AGM object, the result may be NaN or undefined.

The iteration index i must be valid: 0 <= i <= n_iter.
No bounds checking is performed; invalid indices may cause undefined behavior.

Arguments

Type	Intent	Optional	Attributes		Name
type(arithmetic_geometric_mean_real32_type),	intent(in)			::	agm
integer,	intent(in)			::	i

Return Value real(kind=real32)

private elemental function max_selectable_real64(agm, i) result(max_selectable)

Extract the arithmetic-geometric mean value at a specific iteration.
Specifically, this function returns the larger of the two values.

Warning

This function assumes the AGM computation has been performed via the compute method.
If called on an uninitialized or improperly computed AGM object, the result may be NaN or undefined.

The iteration index i must be valid: 0 <= i <= n_iter.
No bounds checking is performed; invalid indices may cause undefined behavior.

Arguments

Type	Intent	Optional	Attributes		Name
type(arithmetic_geometric_mean_real64_type),	intent(in)			::	agm
integer,	intent(in)			::	i

Return Value real(kind=real64)

private elemental function max_selectable_real128(agm, i) result(max_selectable)

Extract the arithmetic-geometric mean value at a specific iteration.
Specifically, this function returns the larger of the two values.

Warning

This function assumes the AGM computation has been performed via the compute method.
If called on an uninitialized or improperly computed AGM object, the result may be NaN or undefined.

The iteration index i must be valid: 0 <= i <= n_iter.
No bounds checking is performed; invalid indices may cause undefined behavior.

Arguments

Type	Intent	Optional	Attributes		Name
type(arithmetic_geometric_mean_real128_type),	intent(in)			::	agm
integer,	intent(in)			::	i

Return Value real(kind=real128)

public interface min

private elemental function min_final_real32(agm) result(min_final)

Extract the final arithmetic-geometric mean from completed AGM calculations.
Specifically, this function returns the smaller of the two final values.

Warning

This function assumes the AGM computation has been performed via the compute method.
If called on an uninitialized or improperly computed AGM object, the result may be NaN or undefined.

Arguments

Type	Intent	Optional	Attributes		Name
type(arithmetic_geometric_mean_real32_type),	intent(in)			::	agm

Return Value real(kind=real32)

private elemental function min_final_real64(agm) result(min_final)

Extract the final arithmetic-geometric mean from completed AGM calculations.
Specifically, this function returns the smaller of the two final values.

Warning

This function assumes the AGM computation has been performed via the compute method.
If called on an uninitialized or improperly computed AGM object, the result may be NaN or undefined.

Arguments

Type	Intent	Optional	Attributes		Name
type(arithmetic_geometric_mean_real64_type),	intent(in)			::	agm

Return Value real(kind=real64)

private elemental function min_final_real128(agm) result(min_final)

Extract the final arithmetic-geometric mean from completed AGM calculations.
Specifically, this function returns the smaller of the two final values.

Warning

This function assumes the AGM computation has been performed via the compute method.
If called on an uninitialized or improperly computed AGM object, the result may be NaN or undefined.

Arguments

Type	Intent	Optional	Attributes		Name
type(arithmetic_geometric_mean_real128_type),	intent(in)			::	agm

Return Value real(kind=real128)

private elemental function min_selectable_real32(agm, i) result(min_selectable)

Extract the arithmetic-geometric mean value at a specific iteration.
Specifically, this function returns the smaller of the two values.

Warning

This function assumes the AGM computation has been performed via the compute method.
If called on an uninitialized or improperly computed AGM object, the result may be NaN or undefined.

The iteration index i must be valid: 0 <= i <= n_iter.
No bounds checking is performed; invalid indices may cause undefined behavior.

Arguments

Type	Intent	Optional	Attributes		Name
type(arithmetic_geometric_mean_real32_type),	intent(in)			::	agm
integer,	intent(in)			::	i

Return Value real(kind=real32)

private elemental function min_selectable_real64(agm, i) result(min_selectable)

Extract the arithmetic-geometric mean value at a specific iteration.
Specifically, this function returns the smaller of the two values.

Warning

This function assumes the AGM computation has been performed via the compute method.
If called on an uninitialized or improperly computed AGM object, the result may be NaN or undefined.

The iteration index i must be valid: 0 <= i <= n_iter.
No bounds checking is performed; invalid indices may cause undefined behavior.

Arguments

Type	Intent	Optional	Attributes		Name
type(arithmetic_geometric_mean_real64_type),	intent(in)			::	agm
integer,	intent(in)			::	i

Return Value real(kind=real64)

private elemental function min_selectable_real128(agm, i) result(min_selectable)

Extract the arithmetic-geometric mean value at a specific iteration.
Specifically, this function returns the smaller of the two values.

Warning

This function assumes the AGM computation has been performed via the compute method.
If called on an uninitialized or improperly computed AGM object, the result may be NaN or undefined.

The iteration index i must be valid: 0 <= i <= n_iter.
No bounds checking is performed; invalid indices may cause undefined behavior.

Arguments

Type	Intent	Optional	Attributes		Name
type(arithmetic_geometric_mean_real128_type),	intent(in)			::	agm
integer,	intent(in)			::	i

Return Value real(kind=real128)

Derived Types

type, private, abstract :: arithmetic_geometric_mean_base_type

Components

Type	Visibility	Attributes		Name		Initial
integer,	private		::	n_iter_	=	initial_n_iter	the number of iterations performed during AGM calculation

Type-Bound Procedures

procedure, public, pass :: n_iter

type, public, extends(arithmetic_geometric_mean_base_type) :: arithmetic_geometric_mean_real128_type

Components

Type	Visibility	Attributes		Name		Initial
real(kind=real128),	private		::	list_a(0:max_n_iter_real128)			history of the arithmetic mean
real(kind=real128),	private		::	list_g(0:max_n_iter_real128)			history of the geometric mean

Type-Bound Procedures

generic, public :: compute => compute_real128
generic, private :: compute_kernel => compute_kernel_real128
procedure, private, pass :: compute_kernel_real128
procedure, private, pass :: compute_real128
procedure, public, pass :: n_iter

type, public, extends(arithmetic_geometric_mean_base_type) :: arithmetic_geometric_mean_real32_type

Components

Type	Visibility	Attributes		Name		Initial
real(kind=real32),	private		::	list_a(0:max_n_iter_real32)			history of the arithmetic mean
real(kind=real32),	private		::	list_g(0:max_n_iter_real32)			history of the geometric mean

Type-Bound Procedures

generic, public :: compute => compute_real32
generic, private :: compute_kernel => compute_kernel_real32
procedure, private, pass :: compute_kernel_real32
procedure, private, pass :: compute_real32
procedure, public, pass :: n_iter

type, public, extends(arithmetic_geometric_mean_base_type) :: arithmetic_geometric_mean_real64_type

Components

Type	Visibility	Attributes		Name		Initial
real(kind=real64),	private		::	list_a(0:max_n_iter_real64)			history of the arithmetic mean
real(kind=real64),	private		::	list_g(0:max_n_iter_real64)			history of the geometric mean

Type-Bound Procedures

generic, public :: compute => compute_real64
generic, private :: compute_kernel => compute_kernel_real64
procedure, private, pass :: compute_kernel_real64
procedure, private, pass :: compute_real64
procedure, public, pass :: n_iter

Functions

public elemental function n_iter(agm)

return the number of iterations performed during AGM calculation

Arguments

Type	Intent	Optional	Attributes		Name
class(arithmetic_geometric_mean_base_type),	intent(in)			::	agm

Return Value integer

private elemental function is_not_converged_real128(a, g) result(stat)

Check if the arithmetic-geometric mean iteration has not yet converged.

Type	Intent		Name
class(arithmetic_geometric_mean_real128_type),	intent(inout)	::	agm
real(kind=real128),	intent(in)	::	init_a	initial value: arithmetic mean
real(kind=real128),	intent(in)	::	init_g	initial value: geometric mean

Type	Intent		Name
class(arithmetic_geometric_mean_real32_type),	intent(inout)	::	agm
real(kind=real32),	intent(in)	::	init_a	initial value: arithmetic mean
real(kind=real32),	intent(in)	::	init_g	initial value: geometric mean

Type	Intent		Name
class(arithmetic_geometric_mean_real64_type),	intent(inout)	::	agm
real(kind=real64),	intent(in)	::	init_a	initial value: arithmetic mean
real(kind=real64),	intent(in)	::	init_g	initial value: geometric mean

arithmetic_geometric_mean_fortran Module

Contents

Variables

Interfaces

Derived Types

Functions

Subroutines

Uses

Variables

Interfaces

public interface arithmetic_geometric_mean

private elemental function arithmetic_geometric_mean_real32(x, y) result(agm)

Arguments

Return Value real(kind=real32)

private elemental function arithmetic_geometric_mean_real64(x, y) result(agm)

Arguments

Return Value real(kind=real64)

private elemental function arithmetic_geometric_mean_real128(x, y) result(agm)

Arguments

Return Value real(kind=real128)

public interface arithmetic_geometric_mean_kernel

private elemental function arithmetic_geometric_mean_kernel_real32(a, g) result(agm)

Arguments

Return Value real(kind=real32)

private elemental function arithmetic_geometric_mean_kernel_real64(a, g) result(agm)

Arguments

Return Value real(kind=real64)

private elemental function arithmetic_geometric_mean_kernel_real128(a, g) result(agm)

Arguments

Return Value real(kind=real128)

private interface compute_step

private elemental subroutine compute_step_real32(prev_a, prev_g, next_a, next_g)

Arguments

private elemental subroutine compute_step_real64(prev_a, prev_g, next_a, next_g)

Arguments

private elemental subroutine compute_step_real128(prev_a, prev_g, next_a, next_g)

Arguments

public interface gap

private elemental function gap_final_real32(agm) result(gap_final)

Arguments

Return Value real(kind=real32)

private elemental function gap_final_real64(agm) result(gap_final)

Arguments

Return Value real(kind=real64)

private elemental function gap_final_real128(agm) result(gap_final)

Arguments

Return Value real(kind=real128)

private elemental function gap_selectable_real32(agm, i) result(gap_selectable)

Arguments

Return Value real(kind=real32)

private elemental function gap_selectable_real64(agm, i) result(gap_selectable)

Arguments

Return Value real(kind=real64)

private elemental function gap_selectable_real128(agm, i) result(gap_selectable)

Arguments

Return Value real(kind=real128)

private interface initialize

private elemental subroutine initialize_real32(agm)

Arguments

private elemental subroutine initialize_real64(agm)

Arguments

private elemental subroutine initialize_real128(agm)

Arguments

private interface is_not_converged

private elemental function is_not_converged_real32(a, g) result(stat)

Arguments

Return Value logical

private elemental function is_not_converged_real64(a, g) result(stat)

Arguments

Return Value logical

private elemental function is_not_converged_real128(a, g) result(stat)

Arguments

Return Value logical

public interface max

private elemental function max_final_real32(agm) result(max_final)

Arguments

Return Value real(kind=real32)

private elemental function max_final_real64(agm) result(max_final)

Arguments

Return Value real(kind=real64)