Developer Reference for Intel® oneAPI Math Kernel Library for Fortran
v?Sinh
vsSinh vdSinh vcSinh vzSinh vmsSinh vmdSinh vmcSinh vmzSinh 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 |
Fotran 77: DOUBLE PRECISION for vdsinh , vmdsinhFotran 77: COMPLEX for vcsinh , vmcsinhFotran 77: DOUBLE COMPLEX for vzsinh , vmzsinhFotran 90: REAL , INTENT(IN) for vssinh , vmssinhFotran 90: DOUBLE PRECISION , INTENT(IN) for vdsinh , vmdsinhFotran 90: COMPLEX , INTENT(IN) for vcsinh , vmcsinhFotran 90: 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 (Sets a new mode for VM functions according to the mode parameter and stores the previous VM mode to oldmode.) 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: DOUBLE PRECISION for vdsinh , vmdsinhFortran 77: COMPLEX for vcsinh , vmcsinhFortran 77: DOUBLE COMPLEX for vzsinh , vmzsinhFortran 90: REAL , INTENT(OUT) for vssinh , vmssinhFortran 90: DOUBLE PRECISION , INTENT(OUT) for vdsinh , vmdsinhFortran 90: COMPLEX , INTENT(OUT) for vcsinh , vmcsinhFortran 90: 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 · ∞ |
INVALID |
QNAN+i · QNAN INVALID |
-0+i · QNAN INVALID |
+0+i · QNAN INVALID |
QNAN+i · QNAN INVALID |
INVALID |
QNAN+i · QNAN |
+i · Y |
|
|
QNAN+i · QNAN |
||||
+i · 0 |
|
-0+i · 0 |
+0+i · 0 |
|
QNAN+i · 0 |
||
-i · 0 |
|
-0-i · 0 |
+0-i · 0 |
|
QNAN-i · 0 |
||
-i · Y |
|
|
QNAN+i · QNAN |
||||
-i · ∞ |
INVALID |
QNAN+i · QNAN INVALID |
-0+i · QNAN INVALID |
+0+i · QNAN INVALID |
QNAN+i · QNAN INVALID |
INVALID |
QNAN+i · QNAN |
+i · NAN |
|
QNAN+i · QNAN |
-0+i · QNAN |
+0+i · QNAN |
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.
\(Sinh(CONJ(z))=CONJ(Sinh(z))\)
\(Sinh(-z)=-Sinh(z)\) .