v?Atanh

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 10/15/2026

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