v?Cosh
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. |
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.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.
RE(z) i · IM(z) | - ∞ | -X | -0 | +0 | +X | + ∞ | NAN |
---|---|---|---|---|---|---|---|
+i · ∞ | + ∞ +i· QNANINVALID | QNAN+i · QNANINVALID | QNAN-i · 0INVALID | QNAN+i · 0INVALID | QNAN+i · QNANINVALID | + ∞ +i· QNAN INVALID | QNAN+i · QNAN |
+i · Y | + ∞ · Cos(Y)- i· ∞ · Sin(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) | + ∞ · | QNAN+i · QNAN | ||||
-i · ∞ | + ∞ +i· QNANINVALID | QNAN+i · QNANINVALID | QNAN+i · 0INVALID | QNAN-i · 0INVALID | QNAN+i · QNANINVALID | + ∞ +i· QNANINVALID | 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 theINVALIDexception when the real or imaginary part of the argument isSNAN
- raises theOVERFLOWexception and sets the VM Error Status toVML_STATUS_OVERFLOWin the case of overflow, that is, whenRE(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).