Developer Reference

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linearfrac

Computes the element-wise linear fractional transformation of vectors
a
and
b
with scalar parameters.

Description

The
linearfrac(a,b,scalea,shifta,scaleb,shiftb)
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
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,
linearfrac
sets the VM Error Status to
status::accuracy_warning
. 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:
  • ifscalea=0, there are no limitations for the values of
    a[i]
    and
    shifta
    .
  • ifscaleb=0, there are no limitations for the values of
    b[i]
    and
    shiftb
    .

API

Syntax
Buffer API
namespace oneapi::mkl::vm { sycl::event linearfrac(sycl::queue & exec_queue, std::int64_t n, sycl::buffer<T> & a, sycl::buffer<T> & b, T scalea, T shifta, T scaleb, T shiftb, sycl::buffer<T> & y, oneapi::mkl::vm::mode mode = oneapi::mkl::vm::mode::not_defined, oneapi::mkl::vm::error_handler<T> errhandler = {}); }
namespace oneapi::mkl::vm { sycl::event linearfrac(sycl::queue & exec_queue, sycl::buffer<T> & a, oneapi::mkl::slice sa, sycl::buffer<T> & b, oneapi::mkl::slice sb, T scalea, T shifta, T scaleb, T shiftb, sycl::buffer<T> & y, oneapi::mkl::slice sy, oneapi::mkl::vm::mode mode = oneapi::mkl::vm::mode::not_defined, oneapi::mkl::vm::error_handler<T> errhandler = {}); }
USM API
namespace oneapi::mkl::vm { sycl::event linearfrac(sycl::queue & exec_queue, std::int64_t n, T const * a, T const * b, T scalea, T shifta, T scaleb, T shiftb, T * y, std::vector<cl::sycl::event> const & depends = {}, oneapi::mkl::vm::mode mode = oneapi::mkl::vm::mode::not_defined, oneapi::mkl::vm::error_handler<T> errhandler = {}); }
namespace oneapi::mkl::vm { sycl::event linearfrac(sycl::queue & exec_queue, T const * a, oneapi::mkl::slice sa, T const * b, oneapi::mkl::slice sb, T scalea, T shifta, T scaleb, T shiftb, T * y, oneapi::mkl::slice sy, std::vector<cl::sycl::event> const & depends = {}, oneapi::mkl::vm::mode mode = oneapi::mkl::vm::mode::not_defined, oneapi::mkl::vm::error_handler<T> errhandler = {}); }
linearfrac
supports the following precisions and devices:
T
Devices supported
float
Host, CPU, and GPU
double
Host, CPU, and GPU
Input Parameters
Buffer API
exec_queue
The queue where the routine should be executed.
n
Specifies the number of elements to be calculated.
a
The buffer containing the 1st input vector.
sa
Slice selector for
a
. See Data Types for a description of the oneMKL slice type.
b
The buffer containing the 2nd input vector.
sb
Slice selector for
b
. See Data Types for a description of the oneMKL slice type.
scalea
Constant value for scaling multipliers of vector
a
shifta
Constant value for shifting addend of vector
a
scaleb
Constant value for scaling multipliers of vector
b
shiftb
Constant value for shifting addend of vector
b
sy
Slice selector for
y
. See Data Types for a description of the oneMKL slice type.
mode
Overrides the global VM mode setting for this function call. See set_mode function for possible values and their description. This is an optional parameter. The default value is
mode::not_defined
.
errhandler
Sets local error handling mode for this function call. See the create_error_handler function for arguments and their descriptions. This is an optional parameter. The local error handler is disabled by default.
USM API
exec_queue
The queue where the routine should be executed.
n
Specifies the number of elements to be calculated.
a
Pointer to the 1st input vector.
sa
Slice selector for
a
. See Data Types for a description of the oneMKL slice type.
b
Pointer to the 2nd input vector.
sb
Slice selector for
b
. See Data Types for a description of the oneMKL slice type.
scalea
Constant value for scaling multipliers of vector
a
shifta
Constant value for shifting addend of vector
a
scaleb
Constant value for scaling multipliers of vector
b
shiftb
Constant value for shifting addend of vector
b
sy
Slice selector for
y
. See Data Types for a description of the oneMKL slice type.
depends
Vector of dependent events (to wait for input data to be ready). This is an optional parameter. The default is an empty vector.
mode
Overrides the global VM mode setting for this function call. See the set_mode function for possible values and their description. This is an optional parameter. The default value is
mode::not_defined
.
errhandler
Sets local error handling mode for this function call. See the create_error_handler function for arguments and their descriptions. This is an optional parameter. The local error handler is disabled by default.
Output Parameters
Buffer API
y
The buffer containing the output vector.
return value (event)
Computation end event.
USM API
y
Pointer to the output vector.
return value (event)
Computation end event.

Examples

An example of how to use
linearfrac
can be found in the oneMKL installation directory, under:
examples/dpcpp/vml/source/vllinearfrac.cpp

Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.