v?Pow

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 12/16/2022

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v?Pow

Computes a to the power b for elements of two vectors.

Syntax

call vspow( n, a, b, y )

call vspowi(n, a, inca, b, incb, y, incy)

call vmspow( n, a, b, y, mode )

call vmspowi(n, a, inca, b, incb, y, incy, mode)

call vdpow( n, a, b, y )

call vdpowi(n, a, inca, b, incb, y, incy)

call vmdpow( n, a, b, y, mode )

call vmdpowi(n, a, inca, b, incb, y, incy, mode)

call vcpow( n, a, b, y )

call vcpowi(n, a, inca, b, incb, y, incy)

call vmcpow( n, a, b, y, mode )

call vmcpowi(n, a, inca, b, incb, y, incy, mode)

call vzpow( n, a, b, y )

call vzpowi(n, a, inca, b, incb, y, incy)

call vmzpow( n, a, b, y, mode )

call vmzpowi(n, a, inca, b, incb, 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`, `b`	DOUBLE PRECISION for vdpow, vmdpow COMPLEX for vcpow, vmcpow DOUBLE COMPLEX for vzpow, vmzpow REAL, INTENT(IN) for vspow, vmspow DOUBLE PRECISION, INTENT(IN) for vdpow, vmdpow COMPLEX, INTENT(IN) for vcpow, vmcpow DOUBLE COMPLEX, INTENT(IN) for vzpow, vmzpow	Arrays that specify the input vectors a and b.
inca, incb, incy	INTEGER, INTENT(IN)	Specifies increments for the elements of `a`, `b`, 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?Pow Function
Data Type	Threshold Limitations on Input Parameters
single precision	`abs(a[i]) < ( FLT_MAX )^1/b[i]`
double precision	`abs(a[i]) < ( DBL_MAX )^1/b[i]`

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

Output Parameters

Name	Type	Description
`y`	DOUBLE PRECISION for vdpow, vmdpow COMPLEX for vcpow, vmcpow DOUBLE COMPLEX for vzpow, vmzpow REAL, INTENT(OUT) for vspow, vmspow DOUBLE PRECISION, INTENT(OUT) for vdpow, vmdpow COMPLEX, INTENT(OUT) for vcpow, vmcpow DOUBLE COMPLEX, INTENT(OUT) for vzpow, vmzpow	Array that specifies the output vector y.

Name

Type

Description

y

DOUBLE PRECISION for vdpow, vmdpow

COMPLEX for vcpow, vmcpow

DOUBLE COMPLEX for vzpow, vmzpow

REAL, INTENT(OUT) for vspow, vmspow

DOUBLE PRECISION, INTENT(OUT) for vdpow, vmdpow

COMPLEX, INTENT(OUT) for vcpow, vmcpow

DOUBLE COMPLEX, INTENT(OUT) for vzpow, vmzpow

Array that specifies the output vector y.

Description

The v?Pow function computes a to the power b for elements of two vectors.

The real function v(s/d)Pow has certain limitations on the input range of a and b parameters. Specifically, if a[i] is positive, then b[i] may be arbitrary. For negative a[i], the value of b[i] must be an integer (either positive or negative).

The complex function v(c/z)Pow has no input range limitations.

Special values for Real Function v?Pow(x,y)
Argument 1 (X)	Argument 2 (Y)	Result	VM Error Status	Exception
+0	neg. odd integer	+∞	VML_STATUS_ERRDOM	ZERODIVIDE
-0	neg. odd integer	-∞	VML_STATUS_ERRDOM	ZERODIVIDE
+0	neg. even integer	+∞	VML_STATUS_ERRDOM	ZERODIVIDE
-0	neg. even integer	+∞	VML_STATUS_ERRDOM	ZERODIVIDE
+0	neg. non-integer	+∞	VML_STATUS_ERRDOM	ZERODIVIDE
-0	neg. non-integer	+∞	VML_STATUS_ERRDOM	ZERODIVIDE
-0	pos. odd integer	+0
-0	pos. odd integer	-0
+0	pos. even integer	+0
-0	pos. even integer	+0
+0	pos. non-integer	+0
-0	pos. non-integer	+0
-1	+∞	+1
-1	-∞	+1
+1	any value	+1
+1	+0	+1
+1	-0	+1
+1	+∞	+1
+1	-∞	+1
+1	QNAN	+1
any value	+0	+1
+0	+0	+1
-0	+0	+1
+∞	+0	+1
-∞	+0	+1
QNAN	+0	+1
any value	-0	+1
+0	-0	+1
-0	-0	+1
+∞	-0	+1
-∞	-0	+1
QNAN	-0	+1
X < +0	non-integer	QNAN	VML_STATUS_ERRDOM	INVALID
\|X\| < 1	-∞	+∞
+0	-∞	+∞	VML_STATUS_ERRDOM	ZERODIVIDE
-0	-∞	+∞	VML_STATUS_ERRDOM	ZERODIVIDE
\|X\| > 1	-∞	+0
+∞	-∞	+0
-∞	-∞	+0
\|X\| < 1	+∞	+0
+0	+∞	+0
-0	+∞	+0
\|X\| > 1	+∞	+∞
+∞	+∞	+∞
-∞	+∞	+∞
-∞	neg. odd integer	-0
-∞	neg. even integer	+0
-∞	neg. non-integer	+0
-∞	pos. odd integer	-∞
-∞	pos. even integer	+∞
-∞	pos. non-integer	+∞
+∞	X < +0	+0
+∞	X > +0	+∞
Big finite value*	Big finite value*	+/-∞	VML_STATUS_OVERFLOW	OVERFLOW
QNAN	QNAN	QNAN
QNAN	SNAN	QNAN		INVALID
SNAN	QNAN	QNAN		INVALID
SNAN	SNAN	QNAN		INVALID

The complex double precision versions of this function, vzPow and vmzPow, are implemented in the EP accuracy mode only. If used in HA or LA mode, vzPow and vmzPow set the VM Error Status to VML_STATUS_ACCURACYWARNING (see the Values of the VM Status table).

* Overflow in a real function is supported only in the HA/LA accuracy modes. The overflow occurs when x and y are finite numbers, but the result is too large to fit the target precision. In this case, the function:

Returns ∞ in the result.
Raises the OVERFLOW exception.
Sets the VM Error Status to VML_STATUS_OVERFLOW.

Overflow in a complex function occurs (supported in the HA/LA accuracy modes only) when all RE(x), RE(y), IM(x), IM(y) arguments are finite numbers, but the real or imaginary part of the computed result is so large that it does not fit the target precision. In this case, the function returns ∞ in that part of the result, raises the OVERFLOW exception, and sets the VM Error Status to VML_STATUS_OVERFLOW (overriding any possible VML_STATUS_ACCURACYWARNING status).

Parent topic: Power and Root Functions

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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