v?Exp

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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Public

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v?Exp

Computes an exponential of vector elements.

Syntax

call vsexp( n, a, y )

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

call vmsexp( n, a, y, mode )

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

call vdexp( n, a, y )

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

call vmdexp( n, a, y, mode )

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

call vcexp( n, a, y )

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

call vmcexp( n, a, y, mode )

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

call vzexp( n, a, y )

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

call vmzexp( n, a, y, mode )

call vmzexpi(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 vdexp, vmdexp COMPLEX for vcexp, vmcexp DOUBLE COMPLEX for vzexp, vmzexp REAL, INTENT(IN) for vsexp, vmsexp DOUBLE PRECISION, INTENT(IN) for vdexp, vmdexp COMPLEX, INTENT(IN) for vcexp, vmcexp DOUBLE COMPLEX, INTENT(IN) for vzexp, vmzexp	Array, 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?Exp Function
Data Type	Threshold Limitations on Input Parameters
single precision	`a[i] < Ln( FLT_MAX )`
double precision	`a[i] < Ln( DBL_MAX )`

Precision overflow thresholds for the complex v?Exp function are beyond the scope of this document.

Output Parameters

Name	Type	Description
y	DOUBLE PRECISION for vdexp, vmdexp COMPLEX for vcexp, vmcexp DOUBLE COMPLEX for vzexp, vmzexp REAL, INTENT(OUT) for vsexp, vmsexp DOUBLE PRECISION, INTENT(OUT) for vdexp, vmdexp COMPLEX, INTENT(OUT) for vcexp, vmcexp DOUBLE COMPLEX, INTENT(OUT) for vzexp, vmzexp	Array, specifies the output vector y.

Name

Type

Description

DOUBLE PRECISION for vdexp, vmdexp

COMPLEX for vcexp, vmcexp

DOUBLE COMPLEX for vzexp, vmzexp

REAL, INTENT(OUT) for vsexp, vmsexp

DOUBLE PRECISION, INTENT(OUT) for vdexp, vmdexp

COMPLEX, INTENT(OUT) for vcexp, vmcexp

DOUBLE COMPLEX, INTENT(OUT) for vzexp, vmzexp

Array, specifies the output vector y.

Description

The v?Exp function computes an exponential of vector elements.

Special Values for Real Function v?Exp(x)
Argument	Result	VM Error Status	Exception
+0	+1
-0	+1
X > overflow	+∞	VML_STATUS_OVERFLOW	OVERFLOW
X < underflow	+0	VML_STATUS_UNDERFLOW	UNDERFLOW
+∞	+∞
-∞	+0
QNAN	QNAN
SNAN	QNAN		INVALID

See Special Value Notations for the conventions used in the table below.

Special Values for Complex Function v?Exp(z)
RE(z) i·IM(z)	-∞	-X	-0	+0	+X	+∞	NAN
+i·∞	+0+i·0	QNAN+i·QNAN INVALID	QNAN+i·QNAN INVALID	QNAN+i·QNAN INVALID	QNAN+i·QNAN INVALID	+∞+i·QNAN INVALID	QNAN+i·QNAN INVALID
+i·Y	+0·CIS(Y)					+∞·CIS(Y)	QNAN+i·QNAN
+i·0	+0·CIS(0)		+1+i·0	+1+i·0		+∞+i·0	QNAN+i·0
-i·0	+0·CIS(0)		+1-i·0	+1-i·0		+∞-i·0	QNAN-i·0
-i·Y	+0·CIS(Y)					+∞·CIS(Y)	QNAN+i·QNAN
-i·∞	+0-i·0	QNAN+i·QNAN INVALID	QNAN+i·QNAN INVALID	QNAN+i·QNAN INVALID	QNAN+i·QNAN INVALID	+∞+i·QNAN INVALID	QNAN+i·QNAN INVALID
+i·NAN	+0+i·0	QNAN+i·QNAN INVALID	QNAN+i·QNAN INVALID	QNAN+i·QNAN INVALID	QNAN+i·QNAN INVALID	+∞+i·QNAN	QNAN+i·QNAN

Notes:

raises the INVALID exception when real or imaginary part of the argument is SNAN
raises the INVALID exception on argument z=-∞+i·QNAN
raises the OVERFLOW exception and sets the VM Error Status to VML_STATUS_OVERFLOW in the case of overflow, that is, when both RE(z) and 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.

Parent topic: Exponential and Logarithmic Functions

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

v?Exp