v?Sinh

Syntax

FORTRAN:

call vssinh( n, a, y )

call vmssinh( n, a, y, mode )

call vdsinh( n, a, y )

call vmdsinh( n, a, y, mode )

call vcsinh( n, a, y )

call vmcsinh( n, a, y, mode )

call vzsinh( n, a, y )

call vmzsinh( n, a, y, mode )

C:

vsSinh( n, a, y );

vmsSinh( n, a, y, mode );

vdSinh( n, a, y );

vmdSinh( n, a, y, mode );

vcSinh( n, a, y );

vmcSinh( n, a, y, mode );

vzSinh( n, a, y );

vmzSinh( n, a, y, mode );

Include Files

FORTRAN 77: mkl_vml.f77
Fortran 90: mkl_vml.f90
C: mkl_vml_functions.h

Input Parameters

Name	Type	Description
n	FORTRAN 77: INTEGER Fortran 90: INTEGER, INTENT(IN) C: const int	Specifies the number of elements to be calculated.
a	FORTRAN 77: REAL for vssinh, vmssinh DOUBLE PRECISION for vdsinh, vmdsinh COMPLEX for vcsinh, vmcsinh DOUBLE COMPLEX for vzsinh, vmzsinh Fortran 90: REAL, INTENT(IN) for vssinh, vmssinh DOUBLE PRECISION, INTENT(IN) for vdsinh, vmdsinh COMPLEX, INTENT(IN) for vcsinh, vmcsinh DOUBLE COMPLEX, INTENT(IN) for vzsinh, vmzsinh C: const float* for vsSinh, vmsSinh const double* for vdSinh, vmdSinh const MKL_Complex8* for vcSinh, vmcSinh const MKL_Complex16* for vzSinh, vmzSinh	FORTRAN: Array that specifies the input vector a. C: Pointer to an array that contains the input vector a.
mode	FORTRAN 77: INTEGER8 Fortran 90:* INTEGER(KIND=8), INTENT(IN) C: const MKL_INT64	Overrides global VML mode setting for this function call. See vmlSetMode for possible values and their description.

Name

Type

Description

n

FORTRAN 77: INTEGER

Fortran 90: INTEGER, INTENT(IN)

C: const int

Specifies the number of elements to be calculated.

a

FORTRAN 77: REAL for vssinh, vmssinh

DOUBLE PRECISION for vdsinh, vmdsinh

COMPLEX for vcsinh, vmcsinh

DOUBLE COMPLEX for vzsinh, vmzsinh

Fortran 90: REAL, INTENT(IN) for vssinh, vmssinh

DOUBLE PRECISION, INTENT(IN) for vdsinh, vmdsinh

COMPLEX, INTENT(IN) for vcsinh, vmcsinh

DOUBLE COMPLEX, INTENT(IN) for vzsinh, vmzsinh

C: const float* for vsSinh, vmsSinh

const double* for vdSinh, vmdSinh

const MKL_Complex8* for vcSinh, vmcSinh

const MKL_Complex16* for vzSinh, vmzSinh

FORTRAN: Array that specifies the input vector a.

C: Pointer to an array that contains the input vector a.

mode

FORTRAN 77: INTEGER*8

Fortran 90: INTEGER(KIND=8), INTENT(IN)

C: const MKL_INT64

Overrides global VML mode setting for this function call. See vmlSetMode for possible values and their description.

Precision Overflow Thresholds for Real v?Sinh 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?Sinh function are beyond the scope of this document.

Output Parameters

Name	Type	Description
y	FORTRAN 77: REAL for vssinh, vmssinh DOUBLE PRECISION for vdsinh, vmdsinh COMPLEX for vcsinh, vmcsinh DOUBLE COMPLEX for vzsinh, vmzsinh Fortran 90: REAL, INTENT(OUT) for vssinh, vmssinh DOUBLE PRECISION, INTENT(OUT) for vdsinh, vmdsinh COMPLEX, INTENT(OUT) for vcsinh, vmcsinh DOUBLE COMPLEX, INTENT(OUT) for vzsinh, vmzsinh C: float* for vsSinh, vmsSinh double* for vdSinh, vmdSinh MKL_Complex8* for vcSinh, vmcSinh MKL_Complex16* for vzSinh, vmzSinh	FORTRAN: Array that specifies the output vector y. C: Pointer to an array that contains the output vector y.

Name

Type

Description

y

FORTRAN 77: REAL for vssinh, vmssinh

DOUBLE PRECISION for vdsinh, vmdsinh

COMPLEX for vcsinh, vmcsinh

DOUBLE COMPLEX for vzsinh, vmzsinh

Fortran 90: REAL, INTENT(OUT) for vssinh, vmssinh

DOUBLE PRECISION, INTENT(OUT) for vdsinh, vmdsinh

COMPLEX, INTENT(OUT) for vcsinh, vmcsinh

DOUBLE COMPLEX, INTENT(OUT) for vzsinh, vmzsinh

C: float* for vsSinh, vmsSinh

double* for vdSinh, vmdSinh

MKL_Complex8* for vcSinh, vmcSinh

MKL_Complex16* for vzSinh, vmzSinh

FORTRAN: Array that specifies the output vector y.

C: Pointer to an array that contains the output vector y.

Description

The v?Sinh function computes hyperbolic sine of vector elements.

Special Values for Real Function v?Sinh(x)
Argument	Result	VML Error Status	Exception
+0	+0
-0	-0
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?Sinh(z)
RE(z) i·IM(z)	-∞	-X	-0	+0	+X	+∞	NAN
+i·∞	-∞+i·QNAN INVALID	QNAN+i·QNAN INVALID	-0+i·QNAN INVALID	+0+i·QNAN 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		-0+i·0	+0+i·0		+∞+i·0	QNAN+i·0
-i·0	-∞-i·0		-0-i·0	+0-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	-0+i·QNAN INVALID	+0+i·QNAN INVALID	QNAN+i·QNAN INVALID	+∞+i·QNAN INVALID	QNAN+i·QNAN
+i·NAN	-∞+i·QNAN	QNAN+i·QNAN	-0+i·QNAN	+0+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 VML 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.
Sinh(CONJ(z))=CONJ(Sinh(z))
Sinh(-z)=-Sinh(z).