Intel® oneAPI DPC++/C++ Compiler Developer Guide and Reference
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IMF Device Library Power Functions
The IMF Device Library supports the following power and inverse power functions:
cbrt
Description: The cbrt(x) inlined function returns a cube root of x: x^(1/3).
This function is not equivalent to pow(x, 1.0/3.0) because the rational number 1/3 is not equal to the floating point number 1.0/3.0. The cbrt(x) usually gives more accurate result than pow(x, 1.0/3.0).
Special Values:
| Argument x | Result cbrt(x) |
|---|---|
| +/-∞ | +/-∞ |
| +/-0 | +/-0 |
Calling Interfaces:
Default accuracy:
float sycl::ext::intel::math::cbrt ( float x ); double sycl::ext::intel::math::cbrt ( double x );
hypot
Description: The hypot(y, x) returns a square root of sum of two squared elements: sqrt( x^2 + y^2 ).
The function calculates the length of the hypotenuse of a right triangle whose two sides have lengths x and y without undue overflow or underflow.
Special Values:
| Argument x | Argument y | Result hypot(x,y) |
|---|---|---|
| +/-0 | +/-0 | +0 |
| +/-∞ | any y | +∞ |
| any x | +/-∞ | +∞ |
Calling Interfaces:
- Default accuracy:
float sycl::ext::intel::math::hypot ( float x, float y ); double sycl::ext::intel::math::hypot ( double x, double y );
- High accuracy (HA):
float sycl::ext::intel::math::ha::hypot ( float x, float y ); double sycl::ext::intel::math::ha::hypot ( double x, double y );
- Low accuracy (LA):
float sycl::ext::intel::math::la::hypot ( float x, float y ); double sycl::ext::intel::math::la::hypot ( double x, double y );
inv
Description: The inv(x) inlined function returns the inversion of x: 1/x.
Special Values:
| Argument x | Result inv(x) |
|---|---|
| +/-0 | +/-∞ |
| +/-∞ | +/-0 |
Calling Interfaces:
Default accuracy:
float sycl::ext::intel::math::inv ( float x ); double sycl::ext::intel::math::inv ( double x );
norm
Description: The norm(dim, x) function returns the square root of the sum of squares of any number of coordinates: sqrt( x[0]^2 + x[1]^2 + ... + x[dim-1]^2 ).
This function calculates the length of the dim-D vector, where the dimension of what is passed as an argument is without undue overflow or underflow.
Special Values:
| Any x[i] | Result norm(dim, x) |
|---|---|
| +/-∞ | +∞ |
Calling Interfaces:
Default accuracy:
float sycl::ext::intel::math::norm ( int dim, float* x ); double sycl::ext::intel::math::norm ( int dim, double* x );
norm3d
Description: The norm3d(x, y, z) function returns the square root of the sum of squares of three coordinates: sqrt( x^2 + y^2 + z^2 ).
This function calculates the length of the 3-D vector without undue overflow or underflow.
Special Values:
| Any x,y,z | Result norm3d(x,y,z) |
|---|---|
| +/-∞ | +∞ |
Calling Interfaces:
Default accuracy:
float sycl::ext::intel::math::norm3d ( float x, float y, float z ); double sycl::ext::intel::math::norm3d ( double x, double y, double z );
norm4d
Description: The norm4d(w, x, y, z) function returns the square root of the sum of squares of four coordinates: sqrt( x^2 + x^2 + y^2 + z^2 ).
This function calculates the length of the 4-D vector without undue overflow or underflow.
Special Values:
| Any w,x,y,z | Result norm4d(w,x,y,z) |
|---|---|
| +/-∞ | +∞ |
Calling Interfaces:
Default accuracy:
float sycl::ext::intel::math::norm4d ( float w, float x, float y, float z ); double sycl::ext::intel::math::norm4d ( double w, double x, double y, double z );
pow
Description: The pow(x, y) returns x raised to the power of y: x^y.
Special Values:
| Argument x | Argument y | Result pow(x,y) |
|---|---|---|
| -∞ | +∞ | +∞ |
| -∞ | -∞ | +0 |
| -∞ | neg. odd int | -0 |
| -∞ | neg. even int | +0 |
| -∞ | neg. non-int | +0 |
| -∞ | pos. odd int | -∞ |
| -∞ | pos. even int | +∞ |
| -∞ | pos. non-int | +∞ |
| -∞ | +/-0 | +1 |
| -1 | +/-∞ | +1 |
| x < +0 | non-int | QNAN |
| -0 | neg. non-int | +∞ |
| +/-0 | neg. odd int | +/-∞ |
| +/-0 | neg. even int | +∞ |
| +/-0 | pos. even int | +0 |
| +/-0 | pos. non-int | +0 |
| +/-0 | +∞ | +0 |
| +/-0 | pos. odd int | +/-0 |
| +/-0 | -∞ | +∞ |
| +/-0 | -0 | +1 |
| +/-0 | +0 | +1 |
| |x| < 1 | -∞ | +∞ |
| |x| < 1 | +∞ | +0 |
| +1 | any y | +1 |
| +1 | +/-0 | +1 |
| +1 | +/-∞ | +1 |
| +1 | S/QNAN | +1 |
| |x| > 1 | -∞ | +0 |
| |x| > 1 | +∞ | +∞ |
| +∞ | +/-0 | +1 |
| +∞ | y < +0 | +0 |
| +∞ | y > +0 | +∞ |
| +∞ | -∞ | +0 |
| +∞ | +∞ | +∞ |
| any x | +0 | +1 |
| any x | -0 | +1 |
| S/QNAN | +0 | +1 |
| S/QNAN | -0 | +1 |
Useful Identities:
pow(x, y) = exp( y·log(x) ), in low accuracy and possible special values processing incompliance
Calling Interfaces:
- Default accuracy:
float sycl::ext::intel::math::pow ( float x, float y ); double sycl::ext::intel::math::pow ( double x, double y );
- High accuracy (HA):
float sycl::ext::intel::math::ha::pow ( float x, float y ); double sycl::ext::intel::math::ha::pow ( double x, double y );
- Low accuracy (LA):
float sycl::ext::intel::math::la::pow ( float x, float y ); double sycl::ext::intel::math::la::pow ( double x, double y );
- Enhanced performance:
float sycl::ext::intel::math::ep::pow ( float x, float y );
powi
Description: The powi(y, n) returns x raised to the integer power of n: x^n.
Special Values:
| Argument x | Argument n | Result powi(x,n) |
|---|---|---|
| -∞ | neg. odd int | -0 |
| -∞ | neg. even int | +0 |
| -∞ | pos. odd int | -∞ |
| -∞ | pos. even int | +∞ |
| -∞ | 0 | +1 |
| +/-0 | neg. odd int | +/-∞ |
| +/-0 | neg. even int | +∞ |
| +/-0 | pos. even int | +0 |
| +/-0 | pos. odd int | +/-0 |
| +/-0 | 0 | +1 |
| +1 | any n | +1 |
| +1 | 0 | +1 |
| +∞ | 0 | +1 |
| +∞ | n < 0 | +0 |
| +∞ | n > 0 | +∞ |
| any x | 0 | +1 |
| S/QNAN | 0 | +1 |
Calling Interfaces:
Default accuracy:
float sycl::ext::intel::math::powi ( float x, int n ); double sycl::ext::intel::math::powi ( double x, int n );
rcbrt
Description: The rcbrt(x) inlined function returns the inverse cube root of x: x^(-1/3).
This function is not equivalent to pow(x, -1.0/3.0) because the rational number -1/3 is not equal to the floating point number -1.0/3.0. The rcbrt(x) usually gives more accurate result than pow(x, -1.0/3.0).
Special Values:
| Argument x | Result rcbrt(x) |
|---|---|
| +/-0 | +/-∞ |
| +/-∞ | +/-0 |
Calling Interfaces:
Default accuracy:
float sycl::ext::intel::math::rcbrt ( float x ); double sycl::ext::intel::math::rcbrt ( double x );
rhypot
Description: The rhypot(y, x) returns an inverse square root of sum of two squared elements: 1 / sqrt( x^2 + y^2 ).
The function calculates 1.0 over the length of the hypotenuse of a right triangle whose two sides have lengths x and y without undue overflow or underflow.
Special Values:
| Argument x | Argument y | Result rhypot(x,y) |
|---|---|---|
| +/-0 | +/-0 | +∞ |
| +/-∞ | any y | +0 |
| any x | +/-∞ | +0 |
Calling Interfaces:
Default accuracy:
float sycl::ext::intel::math::rhypot ( float x, float y ); double sycl::ext::intel::math::rhypot ( double x, double y );
rnorm
Description: The rnorm(dim, x) function returns the inverse square root of the sum of squares of any number of coordinates: 1 / sqrt( x[0]^2 + x[1]^2 + ... + x[dim-1]^2 ).
This function calculates one over the length of the dim-D vector, dimension of which is passed as an argument without undue overflow or underflow.
Special Values:
| Any x[i] | Result rnorm(dim, x) |
|---|---|
| +/-∞ | +0 |
Calling Interfaces:
Default accuracy:
float sycl::ext::intel::math::rnorm ( int dim, float* x ); double sycl::ext::intel::math::rnorm ( int dim, double* x );
rnorm3d
Description: The rnorm3d(x, y, z) function returns the inverse square root of the sum of squares of three coordinates: 1 / sqrt( x^2 + y^2 + z^2 ).
This function calculates one over the length of the 3-D vector without undue overflow or underflow.
Special Values:
| Any x,y,z | Result rnorm3d(x,y,z) |
|---|---|
| +/-∞ | +0 |
Calling Interfaces:
Default accuracy:
float sycl::ext::intel::math::rnorm3d ( float x, float y, float z ); double sycl::ext::intel::math::rnorm3d ( double x, double y, double z );
rnorm4d
Description: The rnorm4d(w, x, y, z) function returns the inverse square root of the sum of squares of four coordinates: 1 / sqrt( w^2 + x^2 + y^2 + z^2 ).
This function calculates one over the length of the 4-D vector without undue overflow or underflow.
Special Values:
| Any w,x,y,z | Result rnorm4d(w,x,y,z) |
|---|---|
| +/-∞ | +0 |
Calling Interfaces:
Default accuracy:
float sycl::ext::intel::math::rnorm4d ( float w, float x, float y, float z ); double sycl::ext::intel::math::rnorm4d ( double w, double x, double y, double z );
rsqrt
Description: The rsqrt(x) inlined function returns inverse square root of x: x^(-1/2).
Special Values:
| Argument x | Result rsqrt(x) |
|---|---|
| -∞ | QNAN |
| x < +0 | QNAN |
| +/-0 | +/-∞ |
| +∞ | +0 |
Calling Interfaces:
Default accuracy:
float sycl::ext::intel::math::rsqrt ( float x ); double sycl::ext::intel::math::rsqrt ( double x );
sqrt
Description: The sqrt(x) inlined function returns square root of x: x^(1/2).
Special Values:
| Argument x | Result sqrt(x) |
|---|---|
| -∞ | QNAN |
| x < +0 | QNAN |
| +/-0 | +/-0 |
| +∞ | +∞ |
Calling Interfaces:
Default accuracy:
float sycl::ext::intel::math::sqrt ( float x ); double sycl::ext::intel::math::sqrt ( double x );