v?Cosh

Syntax

call vscosh( n, a, y )

call vmscosh( n, a, y, mode )

call vdcosh( n, a, y )

call vmdcosh( n, a, y, mode )

call vccosh( n, a, y )

call vmccosh( n, a, y, mode )

call vzcosh( n, a, y )

call vmzcosh( n, a, y, 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 vdcosh, vmdcosh COMPLEX for vccosh, vmccosh DOUBLE COMPLEX for vzcosh, vmzcosh REAL, INTENT(IN) for vscosh, vmscosh DOUBLE PRECISION, INTENT(IN) for vdcosh, vmdcosh COMPLEX, INTENT(IN) for vccosh, vmccosh DOUBLE COMPLEX, INTENT(IN) for vzcosh, vmzcosh	Array that specifies the input vector a.
mode	INTEGER(KIND=8), INTENT(IN)	Overrides global VM mode setting for this function call. See vmlSetMode for possible values and their description.

Name

Type

Description

n

INTEGER, INTENT(IN)

Specifies the number of elements to be calculated.

a

DOUBLE PRECISION for vdcosh, vmdcosh

COMPLEX for vccosh, vmccosh

DOUBLE COMPLEX for vzcosh, vmzcosh

REAL, INTENT(IN) for vscosh, vmscosh

DOUBLE PRECISION, INTENT(IN) for vdcosh, vmdcosh

COMPLEX, INTENT(IN) for vccosh, vmccosh

DOUBLE COMPLEX, INTENT(IN) for vzcosh, vmzcosh

Array that specifies the input vector a.

mode

INTEGER(KIND=8), INTENT(IN)

Overrides global VM mode setting for this function call. See vmlSetMode 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	DOUBLE PRECISION for vdcosh, vmdcosh COMPLEX for vccosh, vmccosh DOUBLE COMPLEX for vzcosh, vmzcosh REAL, INTENT(OUT) for vscosh, vmscosh DOUBLE PRECISION, INTENT(OUT) for vdcosh, vmdcosh COMPLEX, INTENT(OUT) for vccosh, vmccosh DOUBLE COMPLEX, INTENT(OUT) for vzcosh, vmzcosh	Array that specifies the output vector y.

Name

Type

Description

y

DOUBLE PRECISION for vdcosh, vmdcosh

COMPLEX for vccosh, vmccosh

DOUBLE COMPLEX for vzcosh, vmzcosh

REAL, INTENT(OUT) for vscosh, vmscosh

DOUBLE PRECISION, INTENT(OUT) for vdcosh, vmdcosh

COMPLEX, INTENT(OUT) for vccosh, vmccosh

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).