Developer Reference for Intel® oneAPI Math Kernel Library for C

ID 766684
Date 3/22/2024
Public

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Document Table of Contents

v?Cosh

Computes hyperbolic cosine of vector elements.

Syntax

vsCosh( n, a, y );

vsCoshI(n, a, inca, y, incy);

vmsCosh( n, a, y, mode );

vmsCoshI(n, a, inca, y, incy, mode);

vdCosh( n, a, y );

vdCoshI(n, a, inca, y, incy);

vmdCosh( n, a, y, mode );

vmdCoshI(n, a, inca, y, incy, mode);

vcCosh( n, a, y );

vcCoshI(n, a, inca, y, incy);

vmcCosh( n, a, y, mode );

vmcCoshI(n, a, inca, y, incy, mode);

vzCosh( n, a, y );

vzCoshI(n, a, inca, y, incy);

vmzCosh( n, a, y, mode );

vmzCoshI(n, a, inca, y, incy, mode);

Include Files

  • mkl.h

Input Parameters

Name

Type

Description

n

const MKL_INT

Specifies the number of elements to be calculated.

a

const float* for vsCosh, vmsCosh

const double* for vdCosh, vmdCosh

const MKL_Complex8* for vcCosh, vmcCosh

const MKL_Complex16* for vzCosh, vmzCosh

Pointer to an array that contains the input vector a.

inca, incy

const MKL_INT

Specifies increments for the elements of a and y.

mode

const MKL_INT64

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

float* for vsCosh, vmsCosh

double* for vdCosh, vmdCosh

MKL_Complex8* for vcCosh, vmcCosh

MKL_Complex16* for vzCosh, vmzCosh

Pointer to an array that contains 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).