foreng_math_misc

Miscellaneous Mathematic functions

Uses

- foreng_env
- foreng_math_trig

Interfaces

factorial nth_root exp_series

Functions

factorial_int16 factorial_int32 factorial_int64 factorial_int128 exp_series_r32 exp_series_r64 sind_series nth_root_r32 nth_root_r64 fibonacci_loop

Interfaces

public interface factorial

Compute $x!$

public recursive function factorial_int16(x) result(x_fact)

Recursively compute the factorial of a 16-bit integer. The max value that can be passed is 7 If x is less than 0 or greater 7, the function will return 0

Arguments

Type Intent Optional Attributes Name

integer(kind=int16), intent(in) :: x
$0 \leq x \leq 7$

Return Value integer(kind=int16)

$x!$
public recursive function factorial_int32(x) result(x_fact)

Recursively compute the factorial of a 32-bit integer. The max value that can be passed is 16 If x is less than 0 or greater 16, the function will return 0

Arguments

Type Intent Optional Attributes Name

integer(kind=int32), intent(in) :: x
$0 \leq x \leq 16$

Return Value integer(kind=int32)

$x!$
public recursive function factorial_int64(x) result(x_fact)

Recursively compute the factorial of a 64-bit integer. The max value that can be passed is 20 If x is less than 0 or greater 20, the function will return 0

Arguments

Type Intent Optional Attributes Name

integer(kind=int64), intent(in) :: x
$0 \leq x \leq 20$

Return Value integer(kind=int64)

$x!$
public recursive function factorial_int128(x) result(x_fact)

Recursively compute the factorial of a 128-bit integer [supported on gfortran]. The max value that can be passed is 33 If x is less than 0 or greater 33, the function will return 0

Arguments

Type Intent Optional Attributes Name

integer(kind=int128), intent(in) :: x
$0 \leq x \leq 33$

Return Value integer(kind=int128)

$x!$

public interface nth_root

Compute $\sqrt[n]{x}$

public function nth_root_r32(x_, n_) result(root_)

Arguments

Type Intent Optional Attributes Name

real(kind=real32), intent(in) :: x_

integer, intent(in) :: n_

Return Value real(kind=real32)
public function nth_root_r64(x_, n_) result(root_)

Arguments

Type Intent Optional Attributes Name

real(kind=real64), intent(in) :: x_

integer, intent(in) :: n_

Return Value real(kind=real64)

public interface exp_series

Compute $e^x$ using a truncated taylor series

public function exp_series_r32(x) result(exp)

Compute $e^x$ using a taylor series with 12 terms

Arguments

Type Intent Optional Attributes Name

real(kind=real32), intent(in) :: x

Return Value real
public function exp_series_r64(x) result(exp)

Calculate $e^x$ using a taylor series with 20 terms

Arguments

Type Intent Optional Attributes Name

real(kind=real64), intent(in) :: x

Return Value real(kind=real64)

Functions

public recursive function factorial_int16(x) result(x_fact)

Recursively compute the factorial of a 16-bit integer. The max value that can be passed is 7 If x is less than 0 or greater 7, the function will return 0

Arguments

Type	Intent	Optional	Attributes		Name
integer(kind=int16),	intent(in)			::	x	$0 \leq x \leq 7$

Return Value integer(kind=int16)

$x!$

public recursive function factorial_int32(x) result(x_fact)

Recursively compute the factorial of a 32-bit integer. The max value that can be passed is 16 If x is less than 0 or greater 16, the function will return 0

Arguments

Type	Intent	Optional	Attributes		Name
integer(kind=int32),	intent(in)			::	x	$0 \leq x \leq 16$

Return Value integer(kind=int32)

$x!$

public recursive function factorial_int64(x) result(x_fact)

Recursively compute the factorial of a 64-bit integer. The max value that can be passed is 20 If x is less than 0 or greater 20, the function will return 0

Arguments

Type	Intent	Optional	Attributes		Name
integer(kind=int64),	intent(in)			::	x	$0 \leq x \leq 20$

Return Value integer(kind=int64)

$x!$

public recursive function factorial_int128(x) result(x_fact)

Recursively compute the factorial of a 128-bit integer [supported on gfortran]. The max value that can be passed is 33 If x is less than 0 or greater 33, the function will return 0

Arguments

Type	Intent	Optional	Attributes		Name
integer(kind=int128),	intent(in)			::	x	$0 \leq x \leq 33$

Return Value integer(kind=int128)

$x!$

public function exp_series_r32(x) result(exp)

Compute $e^x$ using a taylor series with 12 terms

Arguments

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

Return Value real

public function exp_series_r64(x) result(exp)

Calculate $e^x$ using a taylor series with 20 terms

Arguments

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

Return Value real(kind=real64)

public function sind_series(x_, n_) result(sin_x)

Compute sine using a truncated taylor series

Arguments

Type	Intent	Optional	Attributes		Name
real,	intent(in)			::	x_	Angle in degrees
integer,	intent(in)			::	n_	Number of terms to use

Return Value real

public function nth_root_r32(x_, n_) result(root_)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real32),	intent(in)			::	x_
integer,	intent(in)			::	n_

Return Value real(kind=real32)

public function nth_root_r64(x_, n_) result(root_)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in)			::	x_
integer,	intent(in)			::	n_

Return Value real(kind=real64)

public function fibonacci_loop(n) result(f_n)

Update current F number Update previous two numbers

Arguments

Type	Intent	Optional	Attributes		Name
integer(kind=int64),	intent(in)			::	n	Nth fibonacci to compute

foreng_math_misc Module

Contents

Interfaces

Functions

Uses

Contents

Interfaces

Functions

Interfaces

public interface factorial

public recursive function factorial_int16(x) result(x_fact)

Arguments

Return Value integer(kind=int16)

public recursive function factorial_int32(x) result(x_fact)

Arguments

Return Value integer(kind=int32)

public recursive function factorial_int64(x) result(x_fact)

Arguments

Return Value integer(kind=int64)

public recursive function factorial_int128(x) result(x_fact)

Arguments

Return Value integer(kind=int128)

public interface nth_root

public function nth_root_r32(x_, n_) result(root_)

Arguments

Return Value real(kind=real32)

public function nth_root_r64(x_, n_) result(root_)

Arguments

Return Value real(kind=real64)

public interface exp_series

public function exp_series_r32(x) result(exp)

Arguments

Return Value real

public function exp_series_r64(x) result(exp)

Arguments

Return Value real(kind=real64)

Functions

public recursive function factorial_int16(x) result(x_fact)

Arguments

Return Value integer(kind=int16)

public recursive function factorial_int32(x) result(x_fact)

Arguments

Return Value integer(kind=int32)

public recursive function factorial_int64(x) result(x_fact)

Arguments

Return Value integer(kind=int64)

public recursive function factorial_int128(x) result(x_fact)

Arguments

Return Value integer(kind=int128)

public function exp_series_r32(x) result(exp)

Arguments

Return Value real

public function exp_series_r64(x) result(exp)

Arguments

Return Value real(kind=real64)

public function sind_series(x_, n_) result(sin_x)

Arguments

Return Value real

public function nth_root_r32(x_, n_) result(root_)

Arguments

Return Value real(kind=real32)

public function nth_root_r64(x_, n_) result(root_)

Arguments

Return Value real(kind=real64)

public function fibonacci_loop(n) result(f_n)

Arguments

Return Value integer(kind=int64)