Quantization Modes - 2024.1 English

Vitis High-Level Synthesis User Guide (UG1399)

Document ID

UG1399

Release Date

2024-07-03

Version

2024.1 English

Rounding to plus infinity	AP_RND
Rounding to zero	AP_RND_ZERO
Rounding to minus infinity	AP_RND_MIN_INF
Rounding to infinity	AP_RND_INF
Convergent rounding	AP_RND_CONV
Truncation	AP_TRN
Truncation to zero	AP_TRN_ZERO

AP_RND

Round the value to the nearest representable value for the specific ap_[u]fixed type.

ap_fixed<3, 2, AP_RND, AP_SAT> UAPFixed4 = 1.25; // Yields: 1.5
ap_fixed<3, 2, AP_RND, AP_SAT> UAPFixed4 = -1.25; // Yields: -1.0

AP_RND_ZERO

Round the value to the nearest representable value.
Round towards zero.
- For positive values, delete the redundant bits.
- For negative values, add the least significant bits to get the nearest representable value.
```
ap_fixed<3, 2, AP_RND_ZERO, AP_SAT> UAPFixed4 = 1.25; // Yields: 1.0
ap_fixed<3, 2, AP_RND_ZERO, AP_SAT> UAPFixed4 = -1.25; // Yields: -1.0
```

AP_RND_MIN_INF

Round the value to the nearest representable value.

Round towards minus infinity.

For positive values, delete the redundant bits.
For negative values, add the least significant bits.

ap_fixed<3, 2, AP_RND_MIN_INF, AP_SAT> UAPFixed4 = 1.25; // Yields: 1.0
ap_fixed<3, 2, AP_RND_MIN_INF, AP_SAT> UAPFixed4 = -1.25; // Yields: -1.5

AP_RND_INF

Round the value to the nearest representable value.
The rounding depends on the least significant bit.
- For positive values, if the least significant bit is set, round towards plus infinity. Otherwise, round towards minus infinity.
- For negative values, if the least significant bit is set, round towards minus infinity. Otherwise, round towards plus infinity.
```
ap_fixed<3, 2, AP_RND_INF, AP_SAT> UAPFixed4 = 1.25; // Yields: 1.5
ap_fixed<3, 2, AP_RND_INF, AP_SAT> UAPFixed4 = -1.25; // Yields: -1.5
```

AP_RND_CONV

Round to the nearest representable value with "ties" rounding to even, that is, the least significant bit (after rounding) is forced to zero.

A "tie" is the midpoint of two representable values and occurs when the bit following the least significant bit (after rounding) is 1 and all the bits below it are zero.

// For the following examples, bit3 of the 8-bit value becomes the
// LSB of the final 5-bit value (after rounding).
// Notes: 
//   * bit7 of the 8-bit value is the MSB (sign bit)
//   * the 3 LSBs of the 8-bit value (bit2, bit1, bit0) are treated as
//     guard, round and sticky bits.
//   * See http://pages.cs.wisc.edu/~david/courses/cs552/S12/handouts/guardbits.pdf

ap_fixed<8,3> p1 = 1.59375; // p1 = 001.10011
ap_fixed<5,3,AP_RND_CONV> rconv1 = p1; // rconv1 = 1.5 (001.10)

ap_fixed<8,3> p2 = 1.625; // p2 = 001.10100 => tie with bit3 (LSB-to-be) = 0
ap_fixed<5,3,AP_RND_CONV> rconv2 = p2; // rconv2 = 1.5 (001.10) => lsb is already zero, just truncate

ap_fixed<8,3> p3 = 1.375; // p3 = 001.01100 => tie with bit3 (LSB-to-be) = 1
ap_fixed<5,3,AP_RND_CONV> rconv3 = p3; // rconv3 = 1.5 (001.10) => lsb is made zero by rounding up

ap_fixed<8,3> p3 = 1.65625; // p3 = 001.10101
ap_fixed<5,3,AP_RND_CONV> rconv3 = p3; // rconv3 = 1.75 (001.11) => round up

AP_TRN

Always round the value towards minus infinity.

ap_fixed<3, 2, AP_TRN, AP_SAT> UAPFixed4 = 1.25; // Yields: 1.0
ap_fixed<3, 2, AP_TRN, AP_SAT> UAPFixed4 = -1.25; // Yields: -1.5

AP_TRN_ZERO

Round the value to:

For positive values, the rounding is the same as mode AP_TRN.

For negative values, round towards zero.

ap_fixed<3, 2, AP_TRN_ZERO, AP_SAT> UAPFixed4 = 1.25; // Yields: 1.0
ap_fixed<3, 2, AP_TRN_ZERO, AP_SAT> UAPFixed4 = -1.25; // Yields: -1.0