# HLS Math Library Accuracy - 2023.1 English

## Vitis High-Level Synthesis User Guide (UG1399)

Document ID
UG1399
Release Date
2023-07-17
Version
2023.1 English

The HLS math functions are implemented as synthesizable bit-approximate functions from the hls_math.h library. Bit-approximate HLS math library functions do not provide the same accuracy as the standard C function. To achieve the desired result, the bit-approximate implementation might use a different underlying algorithm than the standard C math library version. The accuracy of the function is specified in terms of ULP (Unit of Least Precision). This difference in accuracy has implications for both C simulation and C/RTL co-simulation.

The ULP difference is typically in the range of 1-4 ULP.

• If the standard C math library is used in the C source code, there may be a difference between the C simulation and the C/RTL co-simulation due to the fact that some functions exhibit a ULP difference from the standard C math library.
• If the HLS math library is used in the C source code, there will be no difference between the C simulation and the C/RTL co-simulation. A C simulation using the HLS math library, may however differ from a C simulation using the standard C math library.

In addition, the following seven functions might show some differences, depending on the C standard used to compile and run the C simulation:

• copysign
• fpclassify
• isinf
• isfinite
• isnan
• isnormal
• signbit

## C90 mode

Only isinf, isnan, and copysign are usually provided by the system header files, and they operate on doubles. In particular, copysign always returns a double result. This might result in unexpected results after synthesis if it must be returned to a float, because a double-to-float conversion block is introduced into the hardware.

## C99 mode (-std=c99)

All seven functions are usually provided under the expectation that the system header files will redirect them to __isnan(double) and __isnan(float). The usual GCC header files do not redirect isnormal, but implement it in terms of fpclassify.

## C++ Using math.h

All seven are provided by the system header files, and they operate on doubles.

copysign always returns a double result. This might cause unexpected results after synthesis if it must be returned to a float, because a double-to-float conversion block is introduced into the hardware.

## C++ Using cmath

Similar to C99 mode(-std=c99), except that:

• The system header files are usually different.
• The functions are properly overloaded for:
• float(). snan(double)
• isinf(double)

copysign and copysignf are handled as built-ins even when using namespace std;.

## C++ Using cmath and namespace std

No issues. AMD recommends using the following for best results:

• -std=c99 for C
• -fno-builtin for C and C++
Note: To specify the C compile options, such as -std=c99, use the Tcl command add_files with the -cflags option. Alternatively, use the Edit CFLAGs button in the Project Settings dialog box.