v?Atanh

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/31/2023

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v?Atanh

Computes inverse hyperbolic tangent of vector elements.

Syntax

vsAtanh( n, a, y );

vsAtanhI(n, a, inca, y, incy);

vmsAtanh( n, a, y, mode );

vmsAtanhI(n, a, inca, y, incy, mode);

vdAtanh( n, a, y );

vdAtanhI(n, a, inca, y, incy);

vmdAtanh( n, a, y, mode );

vmdAtanhI(n, a, inca, y, incy, mode);

vcAtanh( n, a, y );

vcAtanhI(n, a, inca, y, incy);

vmcAtanh( n, a, y, mode );

vmcAtanhI(n, a, inca, y, incy, mode);

vzAtanh( n, a, y );

vzAtanhI(n, a, inca, y, incy);

vmzAtanh( n, a, y, mode );

vmzAtanhI(n, a, inca, y, incy, mode);

Include Files

mkl.h

Input Parameters

Name	Type	Description
n	const MKL_INT	Specifies the number of elements to be calculated.
a	const float* for vsAtanh, vmsAtanh const double* for vdAtanh, vmdAtanh const MKL_Complex8* for vcAtanh, vmcAtanh const MKL_Complex16* for vzAtanh, vmzAtanh	Pointer to an array that contains the input vector a.
inca, incy	const MKL_INT	Specifies increments for the elements of `a` and `y`.
mode	const MKL_INT64	Overrides global VM mode setting for this function call. See vmlSetMode for possible values and their description.

Output Parameters

Name	Type	Description
y	float* for vsAtanh, vmsAtanh double* for vdAtanh, vmdAtanh MKL_Complex8* for vcAtanh, vmcAtanh MKL_Complex16* for vzAtanh, vmzAtanh	Pointer to an array that contains the output vector y.

Name

Type

Description

float* for vsAtanh, vmsAtanh

double* for vdAtanh, vmdAtanh

MKL_Complex8* for vcAtanh, vmcAtanh

MKL_Complex16* for vzAtanh, vmzAtanh

Pointer to an array that contains 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 C

v?Atanh