Overview of Arbitrary Precision Fixed-Point Data Types - 2021.2 English

Fixed-point data types model the data as an integer and fraction bits with the format ap_fixed<W,I,Q> as explained in the table below. In the following example, the Vitis HLS ap_fixed type is used to define an 18-bit variable with 6 bits specified as representing the numbers above the binary point, and 12 bits implied to represent the value after the decimal point. The variable is specified as signed and the quantization mode is set to round to plus infinity. Because the overflow mode is not specified, the default wrap-around mode is used for overflow.

#include <ap_fixed.h>
...
ap_fixed<18,6,AP_RND > my_type;
...

When performing calculations where the variables have different number of bits or different precision, the binary point is automatically aligned.

The behavior of the C++ simulations performed using fixed-point matches the resulting hardware. This allows you to analyze the bit-accurate, quantization, and overflow behaviors using fast C-level simulation.

Fixed-point types are a useful replacement for floating point types which require many clock cycle to complete. Unless the entire range of the floating-point type is required, the same accuracy can often be implemented with a fixed-point type resulting in the same accuracy with smaller and faster hardware.

A summary of the ap_fixed type identifiers is provided in the following table.

ap_fixed<2, 0> a = -0.5;    // a can be -0.5,

ap_ufixed<1, 0> x = 0.5;    // 1-bit representation. x can be 0 or 0.5
ap_ufixed<1, -1> y = 0.25;  // 1-bit representation. y can be 0 or 0.25
const ap_fixed<1, -7> z = 1.0/256;  // 1-bit representation for z = 2^-8

The default maximum width allowed for ap_[u]fixed data types is 1024 bits. This default may be overridden by defining the macro AP_INT_MAX_W with a positive integer value less than or equal to 4096 before inclusion of the ap_int.h header file.