v?Cosh

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 12/16/2022

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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.

Name

Type

Description

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).

Parent topic: Hyperbolic Functions

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Developer Reference for Intel® oneAPI Math Kernel Library for C

v?Cosh