v?Atanh

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

v?Atanh

vsAtanh vdAtanh vcAtanh vzAtanh vmsAtanh vmdAtanh vmcAtanh vmzAtanh 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`		Specifies the number of elements to be calculated.
`a`	Fortran 77: DOUBLE PRECISION for `vdatanh` , `vmdatanh`Fortran 77: COMPLEX for `vcatanh` , `vmcatanh`Fortran 77: DOUBLE COMPLEX for `vzatanh` , `vmzatanh`Fortran 90: REAL , INTENT(IN) for `vsatanh` , `vmsatanh`Fortran 90: DOUBLE PRECISION , INTENT(IN) for `vdatanh` , `vmdatanh`Fortran 90: COMPLEX , INTENT(IN) for `vcatanh` , `vmcatanh`Fortran 90: 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 (Sets a new mode for VM functions according to the mode parameter and stores the previous VM mode to oldmode.) for possible values and their description.

Output Parameters

Name	Type	Description
`y`	Fortran 77: DOUBLE PRECISION for `vdatanh` , `vmdatanh`Fortran 77: COMPLEX for `vcatanh` , `vmcatanh`Fortran 77: DOUBLE COMPLEX for `vzatanh` , `vmzatanh`Fortran 90: REAL , INTENT(OUT) for `vsatanh` , `vmsatanh`Fortran 90: DOUBLE PRECISION , INTENT(OUT) for `vdatanh` , `vmdatanh`Fortran 90: COMPLEX , INTENT(OUT) for `vcatanh` , `vmcatanh`Fortran 90: 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) .

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

v?Atanh

Syntax

Include Files

Input Parameters

Output Parameters

Description