v?Acosh

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

v?Acosh

vsAcosh vdAcosh vcAcosh vzAcosh vmsAcosh vmdAcosh vmcAcosh vmzAcosh 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`	Fortran 77: DOUBLE PRECISION for `vdacosh` , `vmdacosh`Fortran 77: COMPLEX for `vcacosh` , `vmcacosh`Fortran 77: DOUBLE COMPLEX for `vzacosh` , `vmzacosh`Fortran 90: REAL , INTENT(IN) for `vsacosh` , `vmsacosh`Fortran 90: DOUBLE PRECISION , INTENT(IN) for `vdacosh` , `vmdacosh`Fortran 90: COMPLEX , INTENT(IN) for `vcacosh` , `vmcacosh`Fortran 90: 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 (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 `vdacosh` , `vmdacosh`Fortran 77: COMPLEX for `vcacosh` , `vmcacosh`Fortran 77: DOUBLE COMPLEX for `vzacosh` , `vmzacosh`Fortran 90: REAL , INTENT(OUT) for `vsacosh` , `vmsacosh`Fortran 90: DOUBLE PRECISION , INTENT(OUT) for `vdacosh` , `vmdacosh`Fortran 90: COMPLEX , INTENT(OUT) for `vcacosh` , `vmcacosh`Fortran 90: 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
\(Acosh(CONJ(z))=CONJ(Acosh(z))\) .

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

v?Acosh

Syntax

Include Files

Input Parameters

Output Parameters

Description