This module is for evaluating several useful real-valued functions that are not always available in Fortran compilers. More...

Data Types
interface	ahav

interface	ahavh

interface	atanh

interface	gd

interface	gdi

interface	hav

interface	havh

interface	sech

interface	sechs

interface	sinhox

interface	sinhoxm

interface	sinox

interface	sinoxm

Functions/Subroutines
real(dp) function	ahav_d (a)
	Arc-haversine function for double precision real.

real(sp) function	ahav_s (a)
	Arc-haversine function for single precision real.

real(dp) function	ahavh_d (a)
	Hyperbolic arc-haversine for double precision real.

real(sp) function	ahavh_s (a)
	Hyperbolic arc-haversine for single precision real.

real(dp) function	atanh_d (t)
	Hyperbolic arc-tangent for double precision real.

real(sp) function	atanh_s (t)
	Hyperbolic arc-tangent for single precision real.

real(dp) function	gd_d (x)
	Gudermannian function (related to Mercator map projections)

real(sp) function	gd_s (x)
	Gudermannian function (related to Mercator map projections)

real(dp) function	gdi_d (y)
	Inverse Gudermannian function for double precision real.

real(sp) function	gdi_s (y)
	Inverse Gudermannian function for single precision real.

real(dp) function	hav_d (t)
	Haversine function for double precision real (for geometry on the sphere).

real(sp) function	hav_s (t)
	Haversine function for single precision real (for geometry on the sphere).

real(dp) function	havh_d (t)
	Hyperbolic-haversine for double precision real (for pseudosphere geometry).

real(sp) function	havh_s (t)
	Hyperbolic-haversine for single precision real (for pseudosphere geometry).

real(dp) function	sech_d (x)
	Hyperbolic secant for double precision real.

real(sp) function	sech_s (x)
	Hyperbolic secant for single precision real.

real(dp) function	sechs_d (x)
	Hyperbolic secant-squared function (logistic distribution).

real(sp) function	sechs_s (x)
	Hyperbolic secant-squared function (logistic distribution).

real(dp) function	sinhox_d (x)
	Evaluate the symmetric real function sinh(x)/x.

real(dp) function	sinhoxm_d (x)
	Evaluate the symmetric real function sinh(x)/x-1.

real(dp) function	sinox_d (x)
	Evaluate the symmetric real function sin(x)/x.

real(dp) function	sinoxm_d (x)
	Evaluate the symmetric real function sin(x)/x-1, still accurate near x=0.

Detailed Description

This module is for evaluating several useful real-valued functions that are not always available in Fortran compilers.

These have applications in map transformations, spherical and pseudo-spherical surface geometry, probability distributions, and splines.

Author: R. J. Purser

Function/Subroutine Documentation

◆ ahav_d()

real(dp) function pfun::ahav_d ( real(dp), intent(in) a )

private

Arc-haversine function for double precision real.

Parameters

[in] a double precision real argument

Returns: t arc-haversine function of a

Author: R. J. Purser

Definition at line 156 of file pfun.f90.

◆ ahav_s()

real(sp) function pfun::ahav_s ( real(sp), intent(in) a )

private

Arc-haversine function for single precision real.

Parameters

[in] a single precision real argument

Returns: t arc-haversine function of a

Author: R. J. Purser

Definition at line 143 of file pfun.f90.

◆ ahavh_d()

real(dp) function pfun::ahavh_d ( real(dp), intent(in) a )

private

Hyperbolic arc-haversine for double precision real.

Parameters

[in] a double precision real argument

Returns: t hyperbolic arc-haversine of a

Author: R. J. Purser

Definition at line 184 of file pfun.f90.

◆ ahavh_s()

real(sp) function pfun::ahavh_s ( real(sp), intent(in) a )

private

Hyperbolic arc-haversine for single precision real.

Note: The minus sign in the hyperbolic arc-haversine definition.

Parameters

[in] a single precision real argument

Returns: t hyperbolic arc-haversine of a

Author: R. J. Purser

Definition at line 171 of file pfun.f90.

◆ atanh_d()

real(dp) function pfun::atanh_d ( real(dp), intent(in) t )

private

Hyperbolic arc-tangent for double precision real.

Parameters

[in] t double precision real argument

Returns: a hyperbolic arc-tangent of t

Author: R. J. Purser

Definition at line 215 of file pfun.f90.

◆ atanh_s()

real(sp) function pfun::atanh_s ( real(sp), intent(in) t )

private

Hyperbolic arc-tangent for single precision real.

(compilers now have this)

Parameters

[in] t single precision real argument

Returns: a hyperbolic arc-tangent of t

Author: R. J. Purser

Definition at line 197 of file pfun.f90.

◆ gd_d()

real(dp) function pfun::gd_d ( real(dp), intent(in) x )

private

Gudermannian function (related to Mercator map projections)

Parameters

[in] x double precision real argument of function

Returns: y Gudermannian function of x

Author: R. J. Purser

Definition at line 53 of file pfun.f90.

◆ gd_s()

real(sp) function pfun::gd_s ( real(sp), intent(in) x )

private

Gudermannian function (related to Mercator map projections)

Parameters

[in] x single precision real argument of function

Returns: y Gudermannian function of x

Author: R. J. Purser

Definition at line 40 of file pfun.f90.

◆ gdi_d()

real(dp) function pfun::gdi_d ( real(dp), intent(in) y )

private

Inverse Gudermannian function for double precision real.

Parameters

[in] y double precision real argument

Returns: x inverse Gudermannian function of y

Author: R. J. Purser

Definition at line 77 of file pfun.f90.

◆ gdi_s()

real(sp) function pfun::gdi_s ( real(sp), intent(in) y )

private

Inverse Gudermannian function for single precision real.

Parameters

[in] y single precision real argument

Returns: x inverse Gudermannian function of y

Author: R. J. Purser

Definition at line 65 of file pfun.f90.

◆ hav_d()

real(dp) function pfun::hav_d ( real(dp), intent(in) t )

private

Haversine function for double precision real (for geometry on the sphere).

Parameters

[in] t double precision real argument

Returns: a haversine function of t

Author: R. J. Purser

Definition at line 102 of file pfun.f90.

◆ hav_s()

real(sp) function pfun::hav_s ( real(sp), intent(in) t )

private

Haversine function for single precision real (for geometry on the sphere).

Parameters

[in] t single precision real argument

Returns: a haversine function of t

Author: R. J. Purser

Definition at line 89 of file pfun.f90.

◆ havh_d()

real(dp) function pfun::havh_d ( real(dp), intent(in) t )

private

Hyperbolic-haversine for double precision real (for pseudosphere geometry).

Parameters

[in] t double precision real argument

Returns: a hyperbolic-haversine function of t

Author: R. J. Purser

Definition at line 130 of file pfun.f90.

◆ havh_s()

real(sp) function pfun::havh_s ( real(sp), intent(in) t )

private

Hyperbolic-haversine for single precision real (for pseudosphere geometry).

Note: The minus sign in the hyperbolic-haversine definition.

Parameters

[in] t single precision real argument

Returns: a hyperbolic-haversine function of t

Author: R. J. Purser

Definition at line 117 of file pfun.f90.

◆ sech_d()

real(dp) function pfun::sech_d ( real(dp), intent(in) x )

private

Hyperbolic secant for double precision real.

Parameters

[in] x double precision real argument

Returns: r hyperbolic secant of x

Author: R. J. Purser

Definition at line 250 of file pfun.f90.

◆ sech_s()

real(sp) function pfun::sech_s ( real(sp), intent(in) x )

private

Hyperbolic secant for single precision real.

Parameters

[in] x single precision real argument

Returns: r hyperbolic secant of x

Author: R. J. Purser

Definition at line 233 of file pfun.f90.

◆ sechs_d()

real(dp) function pfun::sechs_d ( real(dp), intent(in) x )

private

Hyperbolic secant-squared function (logistic distribution).

Parameters

[in] x double precision real argument

Returns: r sech-squared of x

Author: R. J. Purser

Definition at line 278 of file pfun.f90.

◆ sechs_s()

real(sp) function pfun::sechs_s ( real(sp), intent(in) x )

private

Hyperbolic secant-squared function (logistic distribution).

Parameters

[in] x single precision real argument

Returns: r sech-squared of x

Author: R. J. Purser

Definition at line 266 of file pfun.f90.

◆ sinhox_d()

real(dp) function pfun::sinhox_d ( real(dp), intent(in) x )

private

Evaluate the symmetric real function sinh(x)/x.

Parameters

[in] x double precision real argument

Returns: r sinh(x)/x

Author: R. J. Purser

Definition at line 344 of file pfun.f90.

◆ sinhoxm_d()

real(dp) function pfun::sinhoxm_d ( real(dp), intent(in) x )

private

Evaluate the symmetric real function sinh(x)/x-1.

still accurate near x=0.

Parameters

[in] x double precision real argument

Returns: r sinh(x)-1

Author: R. J. Purser

Definition at line 324 of file pfun.f90.

◆ sinox_d()

real(dp) function pfun::sinox_d ( real(dp), intent(in) x )

private

Evaluate the symmetric real function sin(x)/x.

Parameters

[in] x double precision real argument

Returns: r sin(x)/x

Author: R. J. Purser

Definition at line 310 of file pfun.f90.

◆ sinoxm_d()

real(dp) function pfun::sinoxm_d ( real(dp), intent(in) x )

private

Evaluate the symmetric real function sin(x)/x-1, still accurate near x=0.

Parameters

[in] x double precision real argument

Returns: r sin(x)/x-1

Author: R. J. Purser

Definition at line 290 of file pfun.f90.

Data Types

Functions/Subroutines

Detailed Description

Function/Subroutine Documentation

◆ ahav_d()

◆ ahav_s()

◆ ahavh_d()

◆ ahavh_s()

◆ atanh_d()

◆ atanh_s()

◆ gd_d()

◆ gd_s()

◆ gdi_d()

◆ gdi_s()

◆ hav_d()

◆ hav_s()

◆ havh_d()

◆ havh_s()

◆ sech_d()

◆ sech_s()

◆ sechs_d()

◆ sechs_s()

◆ sinhox_d()

◆ sinhoxm_d()

◆ sinox_d()

◆ sinoxm_d()