v?Cosh

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 10/15/2026

Version

Public

v?Cosh

vsCosh vdCosh vcCosh vzCosh vmsCosh vmdCosh vmcCosh vmzCosh Computes hyperbolic cosine of vector elements.

Syntax

call vscosh(n, a, y)
call vscoshi(n, a, inca, y, incy)
call vmscosh(n, a, y, mode)
call vmscoshi(n, a, inca, y, incy, mode)
call vdcosh(n, a, y)
call vdcoshi(n, a, inca, y, incy)
call vmdcosh(n, a, y, mode)
call vmdcoshi(n, a, inca, y, incy, mode)
call vccosh(n, a, y)
call vccoshi(n, a, inca, y, incy)
call vmccosh(n, a, y, mode)
call vmccoshi(n, a, inca, y, incy, mode)
call vzcosh(n, a, y)
call vzcoshi(n, a, inca, y, incy)
call vmzcosh(n, a, y, mode)
call vmzcoshi(n, a, inca, y, incy, mode)

Include Files

mkl_vml.f90

Input Parameters

Name	Type	Description
`n`		Specifies the number of elements to be calculated.
`a`	Fortran 77: DOUBLE PRECISION for `vdcosh` , `vmdcosh`Fortran 77: COMPLEX for `vccosh` , `vmccosh`Fortran 77: DOUBLE COMPLEX for `vzcosh` , `vmzcosh`Fortran 90: REAL , INTENT(IN) for `vscosh` , `vmscosh`Fortran 90: DOUBLE PRECISION , INTENT(IN) for `vdcosh` , `vmdcosh`Fortran 90: COMPLEX , INTENT(IN) for `vccosh` , `vmccosh`Fortran 90: DOUBLE COMPLEX , INTENT(IN) for `vzcosh` , `vmzcosh`	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.

Precision Overflow Thresholds for Real v?Cosh Function

Data Type	Threshold Limitations on Input Parameters
single precision	`-Ln(FLT_MAX)-Ln2 <a[i] < Ln(FLT_MAX)+Ln2`
double precision	`-Ln(DBL_MAX)-Ln2 <a[i] < Ln(DBL_MAX)+Ln2`

Precision overflow thresholds for the complex v?Cosh function are beyond the scope of this document.

Output Parameters

Name	Type	Description
`y`	Fortran 77: DOUBLE PRECISION for `vdcosh` , `vmdcosh`Fortran 77: COMPLEX for `vccosh` , `vmccosh`Fortran 77: DOUBLE COMPLEX for `vzcosh` , `vmzcosh`Fortran 90: REAL , INTENT(OUT) for `vscosh` , `vmscosh`Fortran 90: DOUBLE PRECISION , INTENT(OUT) for `vdcosh` , `vmdcosh`Fortran 90: COMPLEX , INTENT(OUT) for `vccosh` , `vmccosh`Fortran 90: DOUBLE COMPLEX , INTENT(OUT) for `vzcosh` , `vmzcosh`	Array that specifies the output vector `y` .

Description

The v?Cosh function computes hyperbolic cosine of vector elements.

Special Values for Real Function v?Cosh(x)

Argument	Result	VM Error Status	Exception
+0	+1
-0	+1
X > overflow	∞	VML_STATUS_OVERFLOW	OVERFLOW
X < -overflow	∞	VML_STATUS_OVERFLOW	OVERFLOW
∞	∞
∞	∞
QNAN	QNAN
SNAN	QNAN		INVALID

See Special Value Notations for the conventions used in the table below.

Special Values for Complex Function v?Cosh(z)

RE(z) i · IM(z)	∞	-X	-0	+0	+X	∞	NAN
+i · ∞	∞ +i · QNAN INVALID	QNAN+i · QNAN INVALID	QNAN-i · 0 INVALID	QNAN+i · 0 INVALID	QNAN+i · QNAN INVALID	∞ +i · QNAN INVALID	QNAN+i · QNAN
+i · Y	∞ · Cos(Y)- i · ∞ · Sin(Y)					∞ · CIS(Y)	QNAN+i · QNAN
+i · 0	∞ -i · 0		+1-i · 0	+1+i · 0		∞ +i · 0	QNAN+i · 0
-i · 0	∞ +i · 0		+1+i · 0	+1-i · 0		∞ -i · 0	QNAN-i · 0
-i · Y	∞ · Cos(Y)- i · ∞ · Sin(Y)					∞ · CIS(Y)	QNAN+i · QNAN
-i · ∞	∞ +i · QNAN INVALID	QNAN+i · QNAN INVALID	QNAN+i · 0 INVALID	QNAN-i · 0 INVALID	QNAN+i · QNAN INVALID	∞ +i · QNAN INVALID	QNAN+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 the INVALID exception when the real or imaginary part of the argument is SNAN
raises the OVERFLOW exception and sets the VM Error Status to VML_STATUS_OVERFLOW in the case of overflow, that is, when \(RE(z)\) , \(IM(z)\) are finite non-zero numbers, but the real or imaginary part of the exact result is so large that it does not meet the target precision.
\(Cosh(CONJ(z))=CONJ(Cosh(z))\)
\(Cosh(-z)=Cosh(z)\) .

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

v?Cosh

Syntax

Include Files

Input Parameters

Output Parameters

Description