v?Atanh

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 12/16/2022

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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.

Name

Type

Description

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).

Parent topic: Hyperbolic Functions

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

v?Atanh