HIP complex math API

HIP complex math API#

HIP provides built-in support for complex number operations through specialized types and functions, available for both single-precision (float) and double-precision (double) calculations. All complex types and functions are available on both host and device.

For any complex number z, the form is:

\[z = x + yi\]

where x is the real part and y is the imaginary part.

Complex Number Types#

A brief overview of the specialized data types used to represent complex numbers in HIP, available in both single and double precision formats.

Type

Description

hipFloatComplex
Complex number using single-precision (float) values
(note: hipComplex is an alias of hipFloatComplex)

hipDoubleComplex

Complex number using double-precision (double) values

Complex Number Functions#

Note

Changes have been made to small vector constructors for hipComplex and hipFloatComplex initialization, such as float2 and int4. If your code previously relied on a single value to initialize all components within a vector or complex type, you might need to update your code.

A comprehensive collection of functions for creating and manipulating complex numbers, organized by functional categories for easy reference.

Type Construction#

Functions for creating complex number objects and extracting their real and imaginary components.

Function

Description
hipFloatComplex
make_hipFloatComplex(
float a,
float b
)
Creates a complex number
(note: make_hipComplex is an alias of make_hipFloatComplex)
\(z = a + bi\)
float
hipCrealf(
hipFloatComplex z
)
Returns real part of z
\(\Re(z) = x\)
float
hipCimagf(
hipFloatComplex z
)
Returns imaginary part of z
\(\Im(z) = y\)

Function

Description
hipDoubleComplex
make_hipDoubleComplex(
double a,
double b
)
Creates a complex number
\(z = a + bi\)
double
hipCreal(
hipDoubleComplex z
)
Returns real part of z
\(\Re(z) = x\)
double
hipCimag(
hipDoubleComplex z
)
Returns imaginary part of z
\(\Im(z) = y\)

Basic Arithmetic#

Operations for performing standard arithmetic with complex numbers, including addition, subtraction, multiplication, division, and fused multiply-add.

Function

Description
hipFloatComplex
hipCaddf(
hipFloatComplex p,
hipFloatComplex q
)
Addition of two single-precision complex values
\((a + bi) + (c + di) = (a + c) + (b + d)i\)
hipFloatComplex
hipCsubf(
hipFloatComplex p,
hipFloatComplex q
)
Subtraction of two single-precision complex values
\((a + bi) - (c + di) = (a - c) + (b - d)i\)
hipFloatComplex
hipCmulf(
hipFloatComplex p,
hipFloatComplex q
)
Multiplication of two single-precision complex values
\((a + bi)(c + di) = (ac - bd) + (bc + ad)i\)
hipFloatComplex
hipCdivf(
hipFloatComplex p,
hipFloatComplex q
)
Division of two single-precision complex values
\(\frac{a + bi}{c + di} = \frac{(ac + bd) + (bc - ad)i}{c^2 + d^2}\)
hipFloatComplex
hipCfmaf(
hipComplex p,
hipComplex q,
hipComplex r
)
Fused multiply-add of three single-precision complex values
\((a + bi)(c + di) + (e + fi)\)

Function

Description
hipDoubleComplex
hipCadd(
hipDoubleComplex p,
hipDoubleComplex q
)
Addition of two double-precision complex values
\((a + bi) + (c + di) = (a + c) + (b + d)i\)
hipDoubleComplex
hipCsub(
hipDoubleComplex p,
hipDoubleComplex q
)
Subtraction of two double-precision complex values
\((a + bi) - (c + di) = (a - c) + (b - d)i\)
hipDoubleComplex
hipCmul(
hipDoubleComplex p,
hipDoubleComplex q
)
Multiplication of two double-precision complex values
\((a + bi)(c + di) = (ac - bd) + (bc + ad)i\)
hipDoubleComplex
hipCdiv(
hipDoubleComplex p,
hipDoubleComplex q
)
Division of two double-precision complex values
\(\frac{a + bi}{c + di} = \frac{(ac + bd) + (bc - ad)i}{c^2 + d^2}\)
hipDoubleComplex
hipCfma(
hipDoubleComplex p,
hipDoubleComplex q,
hipDoubleComplex r
)
Fused multiply-add of three double-precision complex values
\((a + bi)(c + di) + (e + fi)\)

Complex Operations#

Functions for complex-specific calculations, including conjugate determination and magnitude (absolute value) computation.

Function

Description
hipFloatComplex
hipConjf(
hipFloatComplex z
)
Complex conjugate
\(\overline{a + bi} = a - bi\)
float
hipCabsf(
hipFloatComplex z
)
Absolute value (magnitude)
\(|a + bi| = \sqrt{a^2 + b^2}\)
float
hipCsqabsf(
hipFloatComplex z
)
Squared absolute value
\(|a + bi|^2 = a^2 + b^2\)

Function

Description
hipDoubleComplex
hipConj(
hipDoubleComplex z
)
Complex conjugate
\(\overline{a + bi} = a - bi\)
double
hipCabs(
hipDoubleComplex z
)
Absolute value (magnitude)
\(|a + bi| = \sqrt{a^2 + b^2}\)
double
hipCsqabs(
hipDoubleComplex z
)
Squared absolute value
\(|a + bi|^2 = a^2 + b^2\)

Type Conversion#

Utility functions for conversion between single-precision and double-precision complex number formats.

Function

Description
hipFloatComplex
hipComplexDoubleToFloat(
hipDoubleComplex z
)

Converts double-precision to single-precision complex
hipDoubleComplex
hipComplexFloatToDouble(
hipFloatComplex z
)

Converts single-precision to double-precision complex

Example Usage#

The following example demonstrates using complex numbers to compute the Discrete Fourier Transform (DFT) of a simple signal on the GPU. The DFT converts a signal from the time domain to the frequency domain. The kernel function computeDFT shows various HIP complex math operations in action:

  • Creating complex numbers with make_hipFloatComplex

  • Performing complex multiplication with hipCmulf

  • Accumulating complex values with hipCaddf

The example also demonstrates proper use of complex number handling on both host and device, including memory allocation, transfer, and validation of results between CPU and GPU implementations.

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