stdlib_specialfunctions_gamma Module


Uses


Interfaces

public interface gamma

Gamma function for integer and complex numbers

  • private impure elemental function gamma_iint8(z) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int8), intent(in) :: z

    Return Value integer(kind=int8)

  • private impure elemental function gamma_iint16(z) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int16), intent(in) :: z

    Return Value integer(kind=int16)

  • private impure elemental function gamma_iint32(z) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int32), intent(in) :: z

    Return Value integer(kind=int32)

  • private impure elemental function gamma_iint64(z) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int64), intent(in) :: z

    Return Value integer(kind=int64)

  • private impure elemental function gamma_csp(z) result(res)

    Arguments

    Type IntentOptional Attributes Name
    complex(kind=sp), intent(in) :: z

    Return Value complex(kind=sp)

  • private impure elemental function gamma_cdp(z) result(res)

    Arguments

    Type IntentOptional Attributes Name
    complex(kind=dp), intent(in) :: z

    Return Value complex(kind=dp)

public interface log_factorial

Logarithm of factorial n!, integer variable

  • private impure elemental function l_factorial_iint8(n) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int8), intent(in) :: n

    Return Value real

  • private impure elemental function l_factorial_iint16(n) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int16), intent(in) :: n

    Return Value real

  • private impure elemental function l_factorial_iint32(n) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int32), intent(in) :: n

    Return Value real

  • private impure elemental function l_factorial_iint64(n) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int64), intent(in) :: n

    Return Value real

public interface log_gamma

Logarithm of gamma function

  • private impure elemental function l_gamma_iint8(z) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int8), intent(in) :: z

    Return Value real

  • private impure elemental function l_gamma_iint16(z) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int16), intent(in) :: z

    Return Value real

  • private impure elemental function l_gamma_iint32(z) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int32), intent(in) :: z

    Return Value real

  • private impure elemental function l_gamma_iint64(z) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int64), intent(in) :: z

    Return Value real

  • private impure elemental function l_gamma_csp(z) result(res)

    Arguments

    Type IntentOptional Attributes Name
    complex(kind=sp), intent(in) :: z

    Return Value complex(kind=sp)

  • private impure elemental function l_gamma_cdp(z) result(res)

    Arguments

    Type IntentOptional Attributes Name
    complex(kind=dp), intent(in) :: z

    Return Value complex(kind=dp)

public interface log_lower_incomplete_gamma

Logarithm of lower incomplete gamma function

  • private impure elemental function l_ingamma_low_iint8sp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int8), intent(in) :: p
    real(kind=sp), intent(in) :: x

    Return Value real(kind=sp)

  • private impure elemental function l_ingamma_low_iint8dp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int8), intent(in) :: p
    real(kind=dp), intent(in) :: x

    Return Value real(kind=dp)

  • private impure elemental function l_ingamma_low_iint16sp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int16), intent(in) :: p
    real(kind=sp), intent(in) :: x

    Return Value real(kind=sp)

  • private impure elemental function l_ingamma_low_iint16dp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int16), intent(in) :: p
    real(kind=dp), intent(in) :: x

    Return Value real(kind=dp)

  • private impure elemental function l_ingamma_low_iint32sp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int32), intent(in) :: p
    real(kind=sp), intent(in) :: x

    Return Value real(kind=sp)

  • private impure elemental function l_ingamma_low_iint32dp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int32), intent(in) :: p
    real(kind=dp), intent(in) :: x

    Return Value real(kind=dp)

  • private impure elemental function l_ingamma_low_iint64sp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int64), intent(in) :: p
    real(kind=sp), intent(in) :: x

    Return Value real(kind=sp)

  • private impure elemental function l_ingamma_low_iint64dp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int64), intent(in) :: p
    real(kind=dp), intent(in) :: x

    Return Value real(kind=dp)

  • private impure elemental function l_ingamma_low_rsp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    real(kind=sp), intent(in) :: p
    real(kind=sp), intent(in) :: x

    Return Value real(kind=sp)

  • private impure elemental function l_ingamma_low_rdp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    real(kind=dp), intent(in) :: p
    real(kind=dp), intent(in) :: x

    Return Value real(kind=dp)

public interface log_upper_incomplete_gamma

Logarithm of upper incomplete gamma function

  • private impure elemental function l_ingamma_up_iint8sp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int8), intent(in) :: p
    real(kind=sp), intent(in) :: x

    Return Value real(kind=sp)

  • private impure elemental function l_ingamma_up_iint8dp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int8), intent(in) :: p
    real(kind=dp), intent(in) :: x

    Return Value real(kind=dp)

  • private impure elemental function l_ingamma_up_iint16sp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int16), intent(in) :: p
    real(kind=sp), intent(in) :: x

    Return Value real(kind=sp)

  • private impure elemental function l_ingamma_up_iint16dp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int16), intent(in) :: p
    real(kind=dp), intent(in) :: x

    Return Value real(kind=dp)

  • private impure elemental function l_ingamma_up_iint32sp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int32), intent(in) :: p
    real(kind=sp), intent(in) :: x

    Return Value real(kind=sp)

  • private impure elemental function l_ingamma_up_iint32dp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int32), intent(in) :: p
    real(kind=dp), intent(in) :: x

    Return Value real(kind=dp)

  • private impure elemental function l_ingamma_up_iint64sp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int64), intent(in) :: p
    real(kind=sp), intent(in) :: x

    Return Value real(kind=sp)

  • private impure elemental function l_ingamma_up_iint64dp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int64), intent(in) :: p
    real(kind=dp), intent(in) :: x

    Return Value real(kind=dp)

  • private impure elemental function l_ingamma_up_rsp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    real(kind=sp), intent(in) :: p
    real(kind=sp), intent(in) :: x

    Return Value real(kind=sp)

  • private impure elemental function l_ingamma_up_rdp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    real(kind=dp), intent(in) :: p
    real(kind=dp), intent(in) :: x

    Return Value real(kind=dp)

public interface lower_incomplete_gamma

Lower incomplete gamma function

  • private impure elemental function ingamma_low_iint8sp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int8), intent(in) :: p
    real(kind=sp), intent(in) :: x

    Return Value real(kind=sp)

  • private impure elemental function ingamma_low_iint8dp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int8), intent(in) :: p
    real(kind=dp), intent(in) :: x

    Return Value real(kind=dp)

  • private impure elemental function ingamma_low_iint16sp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int16), intent(in) :: p
    real(kind=sp), intent(in) :: x

    Return Value real(kind=sp)

  • private impure elemental function ingamma_low_iint16dp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int16), intent(in) :: p
    real(kind=dp), intent(in) :: x

    Return Value real(kind=dp)

  • private impure elemental function ingamma_low_iint32sp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int32), intent(in) :: p
    real(kind=sp), intent(in) :: x

    Return Value real(kind=sp)

  • private impure elemental function ingamma_low_iint32dp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int32), intent(in) :: p
    real(kind=dp), intent(in) :: x

    Return Value real(kind=dp)

  • private impure elemental function ingamma_low_iint64sp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int64), intent(in) :: p
    real(kind=sp), intent(in) :: x

    Return Value real(kind=sp)

  • private impure elemental function ingamma_low_iint64dp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int64), intent(in) :: p
    real(kind=dp), intent(in) :: x

    Return Value real(kind=dp)

  • private impure elemental function ingamma_low_rsp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    real(kind=sp), intent(in) :: p
    real(kind=sp), intent(in) :: x

    Return Value real(kind=sp)

  • private impure elemental function ingamma_low_rdp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    real(kind=dp), intent(in) :: p
    real(kind=dp), intent(in) :: x

    Return Value real(kind=dp)

public interface regularized_gamma_p

Regularized (normalized) lower incomplete gamma function, P

  • private impure elemental function regamma_p_iint8sp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int8), intent(in) :: p
    real(kind=sp), intent(in) :: x

    Return Value real(kind=sp)

  • private impure elemental function regamma_p_iint8dp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int8), intent(in) :: p
    real(kind=dp), intent(in) :: x

    Return Value real(kind=dp)

  • private impure elemental function regamma_p_iint16sp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int16), intent(in) :: p
    real(kind=sp), intent(in) :: x

    Return Value real(kind=sp)

  • private impure elemental function regamma_p_iint16dp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int16), intent(in) :: p
    real(kind=dp), intent(in) :: x

    Return Value real(kind=dp)

  • private impure elemental function regamma_p_iint32sp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int32), intent(in) :: p
    real(kind=sp), intent(in) :: x

    Return Value real(kind=sp)

  • private impure elemental function regamma_p_iint32dp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int32), intent(in) :: p
    real(kind=dp), intent(in) :: x

    Return Value real(kind=dp)

  • private impure elemental function regamma_p_iint64sp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int64), intent(in) :: p
    real(kind=sp), intent(in) :: x

    Return Value real(kind=sp)

  • private impure elemental function regamma_p_iint64dp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int64), intent(in) :: p
    real(kind=dp), intent(in) :: x

    Return Value real(kind=dp)

  • private impure elemental function regamma_p_rsp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    real(kind=sp), intent(in) :: p
    real(kind=sp), intent(in) :: x

    Return Value real(kind=sp)

  • private impure elemental function regamma_p_rdp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    real(kind=dp), intent(in) :: p
    real(kind=dp), intent(in) :: x

    Return Value real(kind=dp)

public interface regularized_gamma_q

Regularized (normalized) upper incomplete gamma function, Q

  • private impure elemental function regamma_q_iint8sp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int8), intent(in) :: p
    real(kind=sp), intent(in) :: x

    Return Value real(kind=sp)

  • private impure elemental function regamma_q_iint8dp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int8), intent(in) :: p
    real(kind=dp), intent(in) :: x

    Return Value real(kind=dp)

  • private impure elemental function regamma_q_iint16sp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int16), intent(in) :: p
    real(kind=sp), intent(in) :: x

    Return Value real(kind=sp)

  • private impure elemental function regamma_q_iint16dp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int16), intent(in) :: p
    real(kind=dp), intent(in) :: x

    Return Value real(kind=dp)

  • private impure elemental function regamma_q_iint32sp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int32), intent(in) :: p
    real(kind=sp), intent(in) :: x

    Return Value real(kind=sp)

  • private impure elemental function regamma_q_iint32dp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int32), intent(in) :: p
    real(kind=dp), intent(in) :: x

    Return Value real(kind=dp)

  • private impure elemental function regamma_q_iint64sp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int64), intent(in) :: p
    real(kind=sp), intent(in) :: x

    Return Value real(kind=sp)

  • private impure elemental function regamma_q_iint64dp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int64), intent(in) :: p
    real(kind=dp), intent(in) :: x

    Return Value real(kind=dp)

  • private impure elemental function regamma_q_rsp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    real(kind=sp), intent(in) :: p
    real(kind=sp), intent(in) :: x

    Return Value real(kind=sp)

  • private impure elemental function regamma_q_rdp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    real(kind=dp), intent(in) :: p
    real(kind=dp), intent(in) :: x

    Return Value real(kind=dp)

public interface upper_incomplete_gamma

Upper incomplete gamma function

  • private impure elemental function ingamma_up_iint8sp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int8), intent(in) :: p
    real(kind=sp), intent(in) :: x

    Return Value real(kind=sp)

  • private impure elemental function ingamma_up_iint8dp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int8), intent(in) :: p
    real(kind=dp), intent(in) :: x

    Return Value real(kind=dp)

  • private impure elemental function ingamma_up_iint16sp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int16), intent(in) :: p
    real(kind=sp), intent(in) :: x

    Return Value real(kind=sp)

  • private impure elemental function ingamma_up_iint16dp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int16), intent(in) :: p
    real(kind=dp), intent(in) :: x

    Return Value real(kind=dp)

  • private impure elemental function ingamma_up_iint32sp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int32), intent(in) :: p
    real(kind=sp), intent(in) :: x

    Return Value real(kind=sp)

  • private impure elemental function ingamma_up_iint32dp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int32), intent(in) :: p
    real(kind=dp), intent(in) :: x

    Return Value real(kind=dp)

  • private impure elemental function ingamma_up_iint64sp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int64), intent(in) :: p
    real(kind=sp), intent(in) :: x

    Return Value real(kind=sp)

  • private impure elemental function ingamma_up_iint64dp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    integer(kind=int64), intent(in) :: p
    real(kind=dp), intent(in) :: x

    Return Value real(kind=dp)

  • private impure elemental function ingamma_up_rsp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    real(kind=sp), intent(in) :: p
    real(kind=sp), intent(in) :: x

    Return Value real(kind=sp)

  • private impure elemental function ingamma_up_rdp(p, x) result(res)

    Arguments

    Type IntentOptional Attributes Name
    real(kind=dp), intent(in) :: p
    real(kind=dp), intent(in) :: x

    Return Value real(kind=dp)