Visible to Intel only — GUID: GUID-024E7D7C-03CD-4EC4-8D47-1E7A9EFF84F1
Visible to Intel only — GUID: GUID-024E7D7C-03CD-4EC4-8D47-1E7A9EFF84F1
v?LinearFrac
Performs linear fraction transformation of vectors a and b with scalar parameters.
Syntax
call vslinearfrac( n, a, b, scalea, shifta, scaleb, shiftb, y )
call vslinearfraci(n, a, inca, b, incb, scalea, shifta, scaleb, shiftb, y, incy)
call vmslinearfrac( n, a, b, scalea, shifta, scaleb, shiftb, y, mode )
call vmslinearfraci(n, a, inca, b, incb, scalea, shifta, scaleb, shiftb, y, incy, mode)
call vdlinearfrac( n, a, b, scalea, shifta, scaleb, shiftb, y )
call vdlinearfraci(n, a, inca, b, incb, scalea, shifta, scaleb, shiftb, y, incy)
call vmdlinearfrac( n, a, b, scalea, shifta, scaleb, shiftb, y, mode )
call vmdlinearfraci(n, a, inca, b, incb, scalea, shifta, scaleb, shiftb, 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 vdlinearfrac, vmdlinearfrac REAL, INTENT(IN) for vslinearfrac, vmslinearfrac DOUBLE PRECISION, INTENT(IN) for vdlinearfrac, vmdlinearfrac |
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. |
scalea, scaleb |
DOUBLE PRECISION for vdlinearfrac, vmdlinearfrac REAL, INTENT(IN) for vslinearfrac, vmslinearfrac DOUBLE PRECISION, INTENT(IN) for vdlinearfrac, vmdlinearfrac |
Constant values for scaling multipliers of vectors a and b. |
shifta, shiftb |
DOUBLE PRECISION for vdlinearfrac, vmdlinearfrac REAL, INTENT(IN) for vslinearfrac, vmslinearfrac DOUBLE PRECISION, INTENT(IN) for vdlinearfrac, vmdlinearfrac |
Constant values for shifting addends of vectors a and b. |
mode |
INTEGER(KIND=8), INTENT(IN) |
Overrides global VM mode setting for this function call. See vmlSetMode for possible values and their description. |
Output Parameters
Name |
Type |
Description |
---|---|---|
y |
DOUBLE PRECISION for vdlinearfrac, vmdlinearfrac REAL, INTENT(OUT) for vslinearfrac, vmslinearfrac DOUBLE PRECISION, INTENT(OUT) for vdlinearfrac, vmdlinearfrac |
Array that specifies the output vector y. |
Description
The v?LinearFrac function performs a linear fraction transformation of vector a by vector b with scalar parameters: scaling multipliers scalea, scaleb and shifting addends shifta, shiftb:
y[i]=(scalea·a[i]+shifta)/(scaleb·b[i]+shiftb), i=1,2 … n
The v?LinearFrac function is implemented in the EP accuracy mode only, therefore no special values are defined for this function. If used in HA or LA mode, v?LinearFrac sets the VM Error Status to VML_STATUS_ACCURACYWARNING (see the Values of the VM Status table). Correctness is guaranteed within the threshold limitations defined for each input parameter (see the table below); otherwise, the behavior is unspecified.
Threshold Limitations on Input Parameters |
---|
2EMIN/2≤ |scalea| ≤ 2(EMAX-2)/2 |
2EMIN/2≤ |scaleb| ≤ 2(EMAX-2)/2 |
|shifta| ≤ 2EMAX-2 |
|shiftb| ≤ 2EMAX-2 |
2EMIN/2≤a[i] ≤ 2(EMAX-2)/2 |
2EMIN/2≤b[i] ≤ 2(EMAX-2)/2 |
a[i] ≠ - (shifta/scalea)*(1-δ1), |δ1| ≤ 21-(p-1)/2 |
b[i] ≠ - (shiftb/scaleb)*(1-δ2), |δ2| ≤ 21-(p-1)/2 |
EMIN and EMAX are the minimum and maximum exponents and p is the number of significant bits (precision) for the corresponding data type according to the ANSI/IEEE Standard 754-2008 ([IEEE754]):
for single precision EMIN = -126, EMAX = 127, p = 24
for double precision EMIN = -1022, EMAX = 1023, p = 53
The thresholds become less strict for common cases with scalea=0 and/or scaleb=0:
if scalea=0, there are no limitations for the values of a[i] and shifta.
if scaleb=0, there are no limitations for the values of b[i] and shiftb.
To use the v?linearfrac to shift vector a by a scalar value, set scaleb to 0. Note that even if scaleb is 0, b must be declared.
To use the v?linearfrac to compute shifta/(scaleb·b[i]+shiftb), set scalea to 0. Note that even if scalea is 0, a must be declared.