linearfrac#

Performs linear fraction transformation of vectors a and b with scalar parameters.

Syntax

Buffer API:

namespace oneapi::math::vm {

sycl::event linearfrac(
        sycl::queue& exec_queue,
        std::int64_t n,
        sycl::buffer<T,1>& a,
        sycl::buffer<T,1>& b,
        T scalea,
        T shifta,
        T scaleb,
        T shiftb,
        sycl::buffer<T,1>& y,
        oneapi::math::vm::mode mode = oneapi::math::vm::mode::not_defined,
        oneapi::math::vm::error_handler<T> errhandler = {});

} // namespace oneapi::math::vm

USM API:

namespace oneapi::math::vm {

sycl::event linearfrac(
        sycl::queue& exec_queue,
        std::int64_t n,
        const T *a,
        const T *b,
        T scalea,
        T shifta,
        T scaleb,
        T shiftb,
        T* y,
        std::vector<sycl::event> const & depends = {},
        oneapi::math::vm::mode mode = oneapi::math::vm::mode::not_defined,
        oneapi::math::vm::error_handler<T> errhandler = {});

} // namespace oneapi::math::vm

linearfrac supports the following precisions.

T
`float`
`double`

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 status code to oneapi::math::vm::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`

EMINand 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 ([Bibliography]):

for single precisionEMIN = -126, EMAX = 127, p = 24
for double precisionEMIN = -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.

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 a containing 1st input vector of size n.
b: The buffer b containing 2nd input vector of size n.
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
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 oneapi::math::vm::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: The pointer a to the 1st input vector of size n.
b: The pointer b to the 2nd input vector of size n.
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
depends: Vector of dependent events (to wait for input data to be ready).
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 oneapi::math::vm::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 y containing the output vector of size n.

USM API:

y: Pointer y to the output vector of size n.
return value (event): Event, signifying availability of computed output and status code(s).

Exceptions

For list of generated exceptions please refer to Exceptions

Parent topic: VM Mathematical Functions