IMF Device Library 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

NOTE:

The special values processing rules of inlined functions inv may be affected by the -f[no-]fast-math compiler switch.

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

NOTE:

Special values processing rules of inlined functions rsqrt may be affected by -f[no-]fast-math compiler switch.

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
+∞	+∞

NOTE:

Special values processing rules of inlined functions sqrt may be affected by -f[no-]fast-math compiler switch.

Calling Interfaces:

Default accuracy:

float       sycl::ext::intel::math::sqrt ( float x );
double      sycl::ext::intel::math::sqrt ( double x );

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