Performs linear fraction transformation of vectors a and b with scalar parameters.
FORTRAN:
call vslinearfrac( n, a, b, scalea, shifta, scaleb, shiftb, y )
call vmslinearfrac( n, a, b, scalea, shifta, scaleb, shiftb, y, mode )
call vdlinearfrac( n, a, b, scalea, shifta, scaleb, shiftb, y )
call vmdlinearfrac( n, a, b, scalea, shifta, scaleb, shiftb, y, mode )
C:
vsLinearFrac( n, a, b, scalea, shifta, scaleb, shiftb, y );
vmsLinearFrac( n, a, b, scalea, shifta, scaleb, shiftb, y, mode );
vdLinearFrac( n, a, b, scalea, shifta, scaleb, shiftb, y )
vmdLinearFrac( n, a, b, scalea, shifta, scaleb, shiftb, y, mode );
Name |
Type |
Description |
|---|---|---|
n |
FORTRAN 77: INTEGER Fortran 90: INTEGER, INTENT(IN) C: const int |
Specifies the number of elements to be calculated. |
a, b |
FORTRAN 77: REAL for vslinearfrac DOUBLE PRECISION for vdlinearfrac Fortran 90: REAL, INTENT(IN) for vslinearfrac DOUBLE PRECISION, INTENT(IN) for vdlinearfrac C: const float* for vsLinearFrac const double* for vdLinearFrac |
FORTRAN: Arrays that specify the input vectors a and b. C: Pointers to arrays that contain the input vectors a and b. |
scalea, scaleb |
FORTRAN 77: REAL for vslinearfrac DOUBLE PRECISION for vdlinearfrac Fortran 90: REAL, INTENT(IN) for vslinearfrac DOUBLE PRECISION, INTENT(IN) for vdlinearfrac C: const float* for vsLinearFrac const double* for vdLinearFrac |
Constant values for shifting addends of vectors a and b. |
shifta, shiftb |
FORTRAN 77: REAL for vslinearfrac DOUBLE PRECISION for vdlinearfrac Fortran 90: REAL, INTENT(IN) for vslinearfrac DOUBLE PRECISION, INTENT(IN) for vdlinearfrac C: const float* for vsLinearFrac const double* for vdLinearFrac |
Constant values for scaling multipliers of vectors a and b. |
mode |
FORTRAN 77: INTEGER*8 Fortran 90: INTEGER(KIND=8), INTENT(IN) C: const MKL_INT64 |
Overrides global VML mode setting for this function call. See vmlSetMode for possible values and their description. |
Name |
Type |
Description |
|---|---|---|
y |
FORTRAN 77: REAL for vslinearfrac DOUBLE PRECISION for vdlinearfrac Fortran 90: REAL, INTENT(OUT) for vslinearfrac DOUBLE PRECISION, INTENT(OUT) for vdlinearfrac C: float* for vsLinearFrac double* for vdLinearFrac |
FORTRAN: Array that specifies the output vector y. C: Pointer to an array that contains the output vector y. |
The v?LinearFrac function performs linear fraction transformation of vectors 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. 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 maximum and minimum exponents and p is the number of significant bits (precision) for corresponding data type according to the ANSI/IEEE Std 754-2008 standard ([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