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Warning
The SpinalHDL fixed point support is only partially used/tested, if you find any bugs with it or you think that some functionality is missing, please create a github issue. Also, please do not use undocumented features in production code.
Description¶
The UFix and SFix types correspond to a vector of bits that can be used for fixed point arithmetic.
Declaration¶
The syntax to declare a fixed point number is as follows:
Unsigned Fixed Point¶
Syntax | bit width | resolution | max | min |
|---|---|---|---|---|
UFix(peak:ExpNumber, resolution:ExpNumber) | peak-resolution | 2^resolution | 2^peak-2^resolution | 0 |
UFix(peak:ExpNumber, width:BitCount) | width | 2^(peak-width) | 2^peak-2^(peak-width) | 0 |
Signed Fixed Point¶
Syntax | bit width | resolution | max | min |
|---|---|---|---|---|
SFix(peak:ExpNumber, resolution:ExpNumber) | peak-resolution+1 | 2^resolution | 2^peak-2^resolution | -(2^peak) |
SFix(peak:ExpNumber, width:BitCount) | width | 2^(peak-width-1) | 2^peak-2^(peak-width-1) | -(2^peak) |
Format¶
The chosen format follows the usual way of defining fixed point number format using Q notation. More information there).
For example Q8.2 will mean an fixed point of 8+2 bits, where 8 bit are used for the natural part and 2 bits for the fractional part.If the fixed point number is signed, one more bit is used for the sign.
The resolution is defined as being the smallest power of two that can be represented in this number.
Examples¶
Assignments¶
Valid Assignments¶
An assignment to a fixed point value is valid when there is no bit loss. Any bit loss will result in an error.
If the source fixed point value is too big, the .truncated function will allow you toresize the source number to match the destination size.
Example¶
From a Scala constant¶
Scala BigInts or Doubles can be used as constants when assigning to UFix or SFix signals.
Example¶
Raw value¶
The integer representation of the fixed point number can be read or written using theraw property.
Example¶
Operators¶
The following operators are available for the UFix type
Arithmetic¶
Operator | Description | Returned resolution | Returned amplitude |
|---|---|---|---|
x + y | Addition | Min(x.resolution, y.resolution) | Max(x.amplitude, y.amplitude) |
x - y | Subtraction | Min(x.resolution, y.resolution) | Max(x.amplitude, y.amplitude) |
x * y | Multiplication | x.resolution * y.resolution) | x.amplitude * y.amplitude |
x >> y | Arithmetic shift right, y : Int | x.amplitude >> y | x.resolution >> y |
x << y | Arithmetic shift left, y : Int | x.amplitude << y | x.resolution << y |
x >> y | Arithmetic shift right, y : Int | x.amplitude >> y | x.resolution |
x << y | Arithmetic shift left, y : Int | x.amplitude << y | x.resolution |
Comparison¶
Operator | Description | Return type |
|---|---|---|
x y | Equality | Bool |
x =/= y | Inequality | Bool |
x > y | Greater than | Bool |
x >= y | Greater than or equal | Bool |
x > y | Less than | Bool |
x >= y | Less than or equal | Bool |
Type cast¶
Operator | Description | Return |
|---|---|---|
x.asBits | Binary cast to Bits | Bits(w(x) bits) |
x.asUInt | Binary cast to UInt | UInt(w(x) bits) |
Pcsx2 pc windows 64bit. x.asSInt | Binary cast to SInt | SInt(w(x) bits) |
x.asBools | Cast into a array of Bool | Vec(Bool,width(x)) |
x.toUInt | Return the corresponding UInt (with truncation) | UInt |
x.toSInt | Return the corresponding SInt (with truncation) | SInt |
x.toUFix | Return the corresponding UFix | UFix |
x.toSFix | Return the corresponding SFix | SFix |
Misc¶
Name | Return | Description |
|---|---|---|
x.maxValue | Return the maximum value storable | Double |
x.minValue | Return the minimum value storable | Double |
x.resolution | x.amplitude * y.amplitude | Double |