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. More...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 )

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 157 of file pfun.f90.

References pietc::u2.

◆ ahav_s()

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

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 144 of file pfun.f90.

References pietc::t, and pietc::u2.

◆ ahavh_d()

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

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 185 of file pfun.f90.

References pietc::u2.

◆ ahavh_s()

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

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 172 of file pfun.f90.

References pietc::t, and pietc::u2.

◆ atanh_d()

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

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 216 of file pfun.f90.

References pietc::o2, pietc::o3, pietc::o5, and pietc::u1.

◆ atanh_s()

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

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 198 of file pfun.f90.

References pietc::o2, pietc::t, and pietc::u1.

◆ 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 54 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 41 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 78 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 66 of file pfun.f90.

◆ hav_d()

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

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 103 of file pfun.f90.

References pietc::o2.

◆ 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 90 of file pfun.f90.

References pietc::o2, and pietc::t.

◆ havh_d()

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

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 131 of file pfun.f90.

References pietc::o2.

◆ havh_s()

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

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 118 of file pfun.f90.

References pietc::o2, and pietc::t.

◆ sech_d()

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

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 251 of file pfun.f90.

References pietc::u1, and pietc::u2.

◆ sech_s()

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

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 234 of file pfun.f90.

References pietc::u1, and pietc::u2.

◆ 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 279 of file pfun.f90.

◆ sechs_s()

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

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 267 of file pfun.f90.

◆ sinhox_d()

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

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 345 of file pfun.f90.

References pietc::u1.

◆ sinhoxm_d()

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

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 325 of file pfun.f90.

References pietc::u1.

◆ sinox_d()

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

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 311 of file pfun.f90.

References pietc::u1.

◆ 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 291 of file pfun.f90.

References pietc::u1.

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()