Floating-Point Data Type - Floating-Point Data Type - 2026.1 English - UG1483

IEEE-754 Standard for Floating-Point Data Type

One Sign bit (S), X exponent bits, and Y fraction bits represents floating-point data, as shown in the following figure. The Sign bit is always the most-significant bit (MSB).

Figure 1. Floating-Point Data

According to the IEEE-754 standard, a floating-point value is represented and stored in the normalized form. In the normalized form the exponent value E is a biased/normalized value. The normalized exponent, E, equals the sum of the actual exponent value and the exponent bias. In the normalized form, Y-1 bits store the fraction value. The F0 fraction bit is always hidden and its value is assumed to be 1.

S represents the value of the sign of the number. If S is 0 then the value is a positive floating-point number; otherwise it is negative. The X bits that follow store the normalized exponent value E. The last Y-1 bits store the fraction/mantissa value in the normalized form.

The following equation shows the exponent bias calculation for the given exponent width:

Figure 2. Exponent Bias

In the preceding equation, X is the exponent bit width.

According to the IEEE standard, 32 bits represents a single precision floating-point data. The normalized exponent and fraction/mantissa are allocated 8 and 24 bits, respectively. The exponent bias for single precision is 127.

Similarly, a total of 64 bits represents a double precision floating-point data. This uses a total of 64 bits where the exponent bit width is 11 and the fraction bit width is 53. The exponent bias value for double precision is 1023.

The following equation shows the normalized floating-point number:

Figure 3. Normalized Floating Point Value

The actual value of exponent (E_actual) = E - Exponent_bias. Considering 1 as the value for the hidden bit F0 and the E_actual value, you can calculate a floating-point number as follows:

Figure 4. Floating Point Number Calculation

Floating-Point Data Representation in Model Composer

The HDL Gateway In block supports Boolean, Fixed-point, and Floating-point data types as shown in the following figure. You can select either a Single, Double, or Custom precision type after specifying the floating-point data type.

For example, if you specify an Exponent width of 9 and a Fraction width of 31. The floating-point data value is stored in a total of 40 bits as follows:

• The MSB bit is for sign representation
• The following 9 bits store the biased exponent value
• The 30 LSB bits store the fractional value

Figure 5. Floating-point Precision

If you select Single precision, the total bit width is assumed to be 32, 8 bits for the exponent and 24 bits for the fraction. This is in compliance with the IEEE-754 standard. Similarly when you select Double precision, the total bit width is assumed to be 64 bits. That is, 11 bits for the exponent and 53 bits for the fraction part.

When you select Custom precision, the Exponent width and Fraction width fields activate. You can then specify values for these fields (8 and 24 are the default values). The total bit width for Custom precision data is the summation of the number of exponent bits and the number of fraction bits. Similar to fraction bit width for Single precision and Double precision data types the fraction bit width for Custom precision data type must include the hidden bit F0.

Displaying the Data Type on Output Signals

As the following figure shows, after successful rate and type propagation, the floating-point data type displays on the output of each HDL block. To display the signal data type as shown in the following figure, select Debug > Diagnostics > Information Overlays > Port Data Types.

A floating-point data type uses the format: XFloat_<exponent_bit_width>_<fraction_bit_width>.

Single and Double precision data types use the string "XFloat_8_24" and "XFloat_11_53", respectively.

If for a Custom precision data type you specify the exponent bit width 9 and the fraction bit width 31, then it displays as "XFloat_9_31". A total of 40 bits store the floating-point data value. Because floating-point data is stored in a normalized form, the fractional value is stored in 30 bits.

In Model Composer the fixed-point data type uses the format XFix_<total_data_width>_<binary_point_width>. For example, a fixed-point data type with the data width of 40 and binary point width of 31 is displays as XFix_40_31.

Vitis Model Composer uses the exponent bit width and the fraction bit width to configure and generate an instance of the Floating-Point Operator core.

Rate and Type Propagation

During data rate and type propagation across a Model Composer HDL block that supports floating-point data, the following design rules are verified. The tool issues an appropriate error if it detects one of the following violations:

1. A signal carrying floating-point data connects to the port of an HDL block that doesn't support the floating-point data type.
2. The data input (both A and B, where applicable) and the data output of an HDL block are not the same floating-point data type. The DRC checks occur between the two inputs of a block as well as between an input and an output of the block.

   If you specify a Custom precision floating-point data type, the exponent bit width and the fraction bit width of the two ports are compared. This is to determine if they are of the same data type.

   Note: This check does not included the Convert and Relational blocks. The Convert block supports Float-to-float data type conversion between two different floating-point data types. The Relational block output is always the Boolean data type because it gives a true or false result for a comparison operation.
3. The data inputs are of the fixed-point data type, and the data output is expected to be floating-point, and vice versa.
   Note: This check does not included the Convert and Relational blocks. The Convert block supports Fixed-to-float as well as Float-to-fixed data type conversion. The Relational block output is always the Boolean data type because it gives a true or false result for a comparison operation.
4. You select Custom precision for the Output Type of blocks, that support the floating-point data type. For example, blocks such as AddSub, Mult, CMult, and MUX, only support Full output precision if the data inputs are of the floating-point data type.
5. The AddSub block uses the Carry In port or Carry Out port when the operation on a floating-point data type is specified.
6. The Floating-Point Operator IP core gives an error for DRC rules defined for the IP.