Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

ID 766686
Date 3/22/2024
Public

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v?Atanh

Computes inverse hyperbolic tangent of vector elements.

Syntax

call vsatanh( n, a, y )

call vsatanhi(n, a, inca, y, incy)

call vmsatanh( n, a, y, mode )

call vmsatanhi(n, a, inca, y, incy, mode)

call vdatanh( n, a, y )

call vdatanhi(n, a, inca, y, incy)

call vmdatanh( n, a, y, mode )

call vmdatanhi(n, a, inca, y, incy, mode)

call vcatanh( n, a, y )

call vcatanhi(n, a, inca, y, incy)

call vmcatanh( n, a, y, mode )

call vmcatanhi(n, a, inca, y, incy, mode)

call vzatanh( n, a, y )

call vzatanhi(n, a, inca, y, incy)

call vmzatanh( n, a, y, mode )

call vmzatanhi(n, a, inca, y, incy, mode)

Include Files

  • mkl_vml.f90

Input Parameters

Name

Type

Description

n

INTEGER, INTENT(IN)

Specifies the number of elements to be calculated.

a

DOUBLE PRECISION for vdatanh, vmdatanh

COMPLEX for vcatanh, vmcatanh

DOUBLE COMPLEX for vzatanh, vmzatanh

REAL, INTENT(IN) for vsatanh, vmsatanh

DOUBLE PRECISION, INTENT(IN) for vdatanh, vmdatanh

COMPLEX, INTENT(IN) for vcatanh, vmcatanh

DOUBLE COMPLEX, INTENT(IN) for vzatanh, vmzatanh

Array that specifies the input vector a.

inca, incy

INTEGER, INTENT(IN)

Specifies increments for the elements of a and y.

mode

INTEGER(KIND=8), INTENT(IN)

Overrides global VM mode setting for this function call. See vmlSetMode for possible values and their description.

Output Parameters

Name

Type

Description

y

DOUBLE PRECISION for vdatanh, vmdatanh

COMPLEX for vcatanh, vmcatanh

DOUBLE COMPLEX for vzatanh, vmzatanh

REAL, INTENT(OUT) for vsatanh, vmsatanh

DOUBLE PRECISION, INTENT(OUT) for vdatanh, vmdatanh

COMPLEX, INTENT(OUT) for vcatanh, vmcatanh

DOUBLE COMPLEX, INTENT(OUT) for vzatanh, vmzatanh

Array that specifies the output vector y.

Description

The v?Atanh function computes inverse hyperbolic tangent of vector elements.

Special Values for Real Function v?Atanh(x)
Argument Result VM Error Status Exception
+1 + VML_STATUS_SING ZERODIVIDE
-1 - VML_STATUS_SING ZERODIVIDE
|X| > 1 QNAN VML_STATUS_ERRDOM INVALID
+ QNAN VML_STATUS_ERRDOM INVALID
- QNAN VML_STATUS_ERRDOM INVALID
QNAN QNAN    
SNAN QNAN   INVALID

See Special Value Notations for the conventions used in the table below.

Special Values for Complex Function v?Atanh(z)

RE(z)

i·IM(z)

-

 

-X

 

-0

 

+0

 

+X

 

+

 

NAN

 

+i· -0+i·π/2 -0+i·π/2 -0+i·π/2 +0+i·π/2 +0+i·π/2 +0+i·π/2 +0+i·π/2
+i·Y -0+i·π/2         +0+i·π/2

QNAN+i·QNAN

+i·0 -0+i·π/2   -0+i·0 +0+i·0   +0+i·π/2

QNAN+i·QNAN

-i·0 -0-i·π/2   -0-i·0 +0-i·0   +0-i·π/2

QNAN-i·QNAN

-i·Y -0-i·π/2         +0-i·π/2

QNAN+i·QNAN

-i· -0-i·π/2 -0-i·π/2 -0-i·π/2 +0-i·π/2 +0-i·π/2 +0-i·π/2 +0-i·π/2
+i·NAN

-0+i·QNAN

QNAN+i·QNAN

-0+i·QNAN

+0+i·QNAN

QNAN+i·QNAN

+0+i·QNAN

QNAN+i·QNAN

Notes:

  • Atanh(+-1+-i*0)=+-+-i*0, and ZERODIVIDE exception is raised

  • raises INVALID exception when real or imaginary part of the argument is SNAN

  • Atanh(CONJ(z))=CONJ(Atanh(z))

  • Atanh(-z)=-Atanh(z).