Computes inverse hyperbolic tangent of vector elements.

Syntax

vsAtanh( n, a, y );

vmsAtanh( n, a, y, mode );

vdAtanh( n, a, y );

vmdAtanh( n, a, y, mode );

vcAtanh( n, a, y );

vmcAtanh( n, a, y, mode );

vzAtanh( n, a, y );

vmzAtanh( n, a, y, 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.

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.

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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