Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

ID 766686
Date 7/13/2023
Public

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Document Table of Contents

v?Acosh

Computes inverse hyperbolic cosine (nonnegative) of vector elements.

Syntax

call vsacosh( n, a, y )

call vsacoshi(n, a, inca, y, incy)

call vmsacosh( n, a, y, mode )

call vmsacoshi(n, a, inca, y, incy, mode)

call vdacosh( n, a, y )

call vdacoshi(n, a, inca, y, incy)

call vmdacosh( n, a, y, mode )

call vmdacoshi(n, a, inca, y, incy, mode)

call vcacosh( n, a, y )

call vcacoshi(n, a, inca, y, incy)

call vmcacosh( n, a, y, mode )

call vmcacoshi(n, a, inca, y, incy, mode)

call vzacosh( n, a, y )

call vzacoshi(n, a, inca, y, incy)

call vmzacosh( n, a, y, mode )

call vmzacoshi(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 vdacosh, vmdacosh

COMPLEX for vcacosh, vmcacosh

DOUBLE COMPLEX for vzacosh, vmzacosh

REAL, INTENT(IN) for vsacosh, vmsacosh

DOUBLE PRECISION, INTENT(IN) for vdacosh, vmdacosh

COMPLEX, INTENT(IN) for vcacosh, vmcacosh

DOUBLE COMPLEX, INTENT(IN) for vzacosh, vmzacosh

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 vdacosh, vmdacosh

COMPLEX for vcacosh, vmcacosh

DOUBLE COMPLEX for vzacosh, vmzacosh

REAL, INTENT(OUT) for vsacosh, vmsacosh

DOUBLE PRECISION, INTENT(OUT) for vdacosh, vmdacosh

COMPLEX, INTENT(OUT) for vcacosh, vmcacosh

DOUBLE COMPLEX, INTENT(OUT) for vzacosh, vmzacosh

Array that specifies the output vector y.

Description

The v?Acosh function computes inverse hyperbolic cosine (nonnegative) of vector elements.

Special Values for Real Function v?Acosh(x)
Argument Result VM Error Status Exception
+1 +0    
X < +1 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?Acosh(z)

RE(z)

i·IM(z)

-

 

-X

 

-0

 

+0

 

+X

 

+

 

NAN

 

+i· ++i·π/2 ++i·π/2 ++i·π/2 ++i·π/2 ++i·π/4

++i·QNAN

+i·Y ++i·π         ++i·0

QNAN+i·QNAN

+i·0 ++i·π   +0+i·π/2 +0+i·π/2   ++i·0

QNAN+i·QNAN

-i·0 ++i·π   +0+i·π/2 +0+i·π/2   ++i·0

QNAN+i·QNAN

-i·Y ++i·π         ++i·0

QNAN+i·QNAN

-i· +-i·π/2 +-i·π/2 +-i·π/2 +-i·π/2 +-i·π/4

++i·QNAN

+i·NAN

++i·QNAN

QNAN+i·QNAN

QNAN+i·QNAN

QNAN+i·QNAN

QNAN+i·QNAN

++i·QNAN

QNAN+i·QNAN

Notes:

  • raises INVALID exception when real or imaginary part of the argument is SNAN

  • Acosh(CONJ(z))=CONJ(Acosh(z)).