# Fixed-Point Identifier Summary - 2021.2 English

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

Document ID
UG1399
Release Date
2021-12-15
Version
2021.2 English

The following table shows the quantization and overflow modes.

Tip: Quantization and overflow modes that do more than the default behavior of standard hardware arithmetic (wrap and truncate) result in operators with more associated hardware. It costs logic (LUTs) to implement the more advanced modes, such as round to minus infinity or saturate symmetrically.
Table 1. Fixed-Point Identifier Summary
Identifier Description
W Word length in bits
I The number of bits used to represent the integer value, that is, the number of integer bits to the left of the binary point. When this value is negative, it represents the number of implicit sign bits (for signed representation), or the number of implicit zero bits (for unsigned representation) to the right of the binary point. For example,
``````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``````
Q Quantization mode: This dictates the behavior when greater precision is generated than can be defined by smallest fractional bit in the variable used to store the result.
ap_fixed Types Description
AP_RND Round to plus infinity
AP_RND_ZERO Round to zero
AP_RND_MIN_INF Round to minus infinity
AP_RND_INF Round to infinity
AP_RND_CONV Convergent rounding
AP_TRN Truncation to minus infinity (default)
AP_TRN_ZERO Truncation to zero
O

Overflow mode: This dictates the behavior when the result of an operation exceeds the maximum (or minimum in the case of negative numbers) possible value that can be stored in the variable used to store the result.

ap_fixed Types Description
AP_SAT 1 Saturation
AP_SAT_ZERO 1 Saturation to zero
AP_SAT_SYM 1 Symmetrical saturation
AP_WRAP Wrap around (default)
AP_WRAP_SM Sign magnitude wrap around
N This defines the number of saturation bits in overflow wrap modes.
1. Using the AP_SAT* modes can result in higher resource usage as extra logic will be needed to perform saturation and this extra cost can be as high as 20% additional LUT usage.