Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

ID 766686
Date 11/07/2023
Public

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Document Table of Contents

v?Cosh

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

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.

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.

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.

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).