Optimizing Logic Expressions - 2021.1 English - UG1399

During synthesis several optimizations, such as strength reduction and bit-width minimization are performed. Included in the list of automatic optimizations is expression balancing.

Expression balancing rearranges operators to construct a balanced tree and reduce latency.

• For integer operations expression balancing is on by default but may be disabled using the EXPRESSION_BALANCE pragma or directive.
• For floating-point operations, expression balancing is off by default but may be enabled.

Given the highly sequential code using assignment operators such as += and *= in the following example:

data_t foo_top (data_t a, data_t b, data_t c, data_t d)
{
 data_t sum;

 sum = 0;
 sum += a;
 sum += b;
 sum += c;
 sum += d;
 return sum;

}

Without expression balancing, and assuming each addition requires one clock cycle, the complete computation for sum requires four clock cycles shown in the following figure.

Figure 1. Adder Tree

However additions a+b and c+d can be executed in parallel allowing the latency to be reduced. After balancing the computation completes in two clock cycles as shown in the following figure. Expression balancing prohibits sharing and results in increased area.

Figure 2. Adder Tree After Balancing

For integers, you can disable expression balancing using the EXPRESSION_BALANCE optimization directive with the off option. By default, Vitis HLS does not perform the EXPRESSION_BALANCE optimization for operations of type float or double. When synthesizing float and double types, Vitis HLS maintains the order of operations performed in the C/C++ code to ensure that the results are the same as the C/C++ simulation. For example, in the following code example, all variables are of type float or double. The values of O1 and O2 are not the same even though they appear to perform the same basic calculation.

A=B*C; A=B*F;
D=E*F; D=E*C;
O1=A*D O2=A*D;

This behavior is a function of the saturation and rounding in the C/C++ standard when performing operation with types float or double. Therefore, Vitis HLS always maintains the exact order of operations when variables of type float or double are present and does not perform expression balancing by default.

You can enable expression balancing for specific operations, or you can configure the tool to enable expression balancing with float and double types using the config_compile -unsafe_math_optimizations command as follows:

1. In the Vitis HLS IDE, select Solution > Solution Settings.
2. In the Solution Settings dialog box, click the General category, select config_compile, and enable unsafe_math_optimizations.

With this setting enabled, Vitis HLS might change the order of operations to produce a more optimal design. However, the results of C/RTL co-simulation might differ from the C/C++ simulation.

The unsafe_math_optimizations feature also enables the no_signed_zeros optimization. The no_signed_zeros optimization ensures that the following expressions used with float and double types are identical:

x - 0.0 = x; 
x + 0.0 = x; 
0.0 - x = -x; 
x - x = 0.0; 
x*0.0 = 0.0;

Without the no_signed_zeros optimization the expressions above would not be equivalent due to rounding. The optimization may be optionally used without expression balancing by selecting only this option in the config_compile command.