Warning
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 your code.
UFix/SFix¶
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 can be found on the Wikipedia page about the Q number format.
For example Q8.2 will mean a fixed-point number of 8+2 bits, where 8 bits 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.
Note
To make representing power-of-two numbers less error prone, there is a numeric type in spinal.core
called ExpNumber
, which is used for the fixed-point type constructors.
A convenience wrapper exists for this type, in the form of the exp
function (used in the code samples on this page).
Examples¶
// Unsigned Fixed-Point
val UQ_8_2 = UFix(peak = 8 exp, resolution = -2 exp) // bit width = 8 - (-2) = 10 bits
val UQ_8_2 = UFix(8 exp, -2 exp)
val UQ_8_2 = UFix(peak = 8 exp, width = 10 bits)
val UQ_8_2 = UFix(8 exp, 10 bits)
// Signed Fixed-Point
val Q_8_2 = SFix(peak = 8 exp, resolution = -2 exp) // bit width = 8 - (-2) + 1 = 11 bits
val Q_8_2 = SFix(8 exp, -2 exp)
val Q_8_2 = SFix(peak = 8 exp, width = 11 bits)
val Q_8_2 = SFix(8 exp, 11 bits)
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 to resize the source number to match the destination size.
Example¶
val i16_m2 = SFix(16 exp, -2 exp)
val i16_0 = SFix(16 exp, 0 exp)
val i8_m2 = SFix( 8 exp, -2 exp)
val o16_m2 = SFix(16 exp, -2 exp)
val o16_m0 = SFix(16 exp, 0 exp)
val o14_m2 = SFix(14 exp, -2 exp)
o16_m2 := i16_m2 // OK
o16_m0 := i16_m2 // Not OK, Bit loss
o14_m2 := i16_m2 // Not OK, Bit loss
o16_m0 := i16_m2.truncated // OK, as it is resized
o14_m2 := i16_m2.truncated // OK, as it is resized
Raw value¶
The integer representation of the fixed-point number can be read or written by using the raw
property.
Example¶
val UQ_8_2 = UFix(8 exp, 10 bits)
UQ_8_2.raw := 4 // Assign the value corresponding to 1.0
UQ_8_2.raw := U(17) // Assign the value corresponding to 4.25
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) |
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 |