v?Acosh

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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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.

Name

Type

Description

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)).

Parent topic: Hyperbolic Functions

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

v?Acosh