v?Sinh

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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v?Sinh

Computes hyperbolic sine of vector elements.

Syntax

call vssinh( n, a, y )

call vssinhi(n, a, inca, y, incy)

call vmssinh( n, a, y, mode )

call vmssinhi(n, a, inca, y, incy, mode)

call vdsinh( n, a, y )

call vdsinhi(n, a, inca, y, incy)

call vmdsinh( n, a, y, mode )

call vmdsinhi(n, a, inca, y, incy, mode)

call vcsinh( n, a, y )

call vcsinhi(n, a, inca, y, incy)

call vmcsinh( n, a, y, mode )

call vmcsinhi(n, a, inca, y, incy, mode)

call vzsinh( n, a, y )

call vzsinhi(n, a, inca, y, incy)

call vmzsinh( n, a, y, mode )

call vmzsinhi(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 vdsinh, vmdsinh COMPLEX for vcsinh, vmcsinh DOUBLE COMPLEX for vzsinh, vmzsinh 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	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?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	DOUBLE PRECISION for vdsinh, vmdsinh COMPLEX for vcsinh, vmcsinh DOUBLE COMPLEX for vzsinh, vmzsinh 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	Array that specifies the output vector y.

Name

Type

Description

DOUBLE PRECISION for vdsinh, vmdsinh

COMPLEX for vcsinh, vmcsinh

DOUBLE COMPLEX for vzsinh, vmzsinh

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

Array that specifies 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	VM 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 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.
Sinh(CONJ(z))=CONJ(Sinh(z))
Sinh(-z)=-Sinh(z).

Parent topic: Hyperbolic Functions

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

v?Sinh