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SpinalHDL Core
There is a newer version: 1.12.0
package spinal.core

/* Example UQ(8,8) means 8 bit width with 8 bit decimal 0 bit integer */
object UQ {
  def apply(width: Int, fraction: Int): QFormat = new QFormat(width, fraction,false)
}

/* Example SQ(8,7) means 8 bit width with 7 bit decimal, 0 bit integer, 1 sign bit*/
object SQ {
  def apply(width: Int, fraction: Int): QFormat = new QFormat(width, fraction,true)
}

case class QFormat(width: Int, fraction: Int, signed: Boolean) {
  val nonFraction: Int = width - fraction
  val amplify: Int = if(signed) (nonFraction - 1) else nonFraction
  val numeric: Int = if(signed) (width - 1) else width
  val capcity: Double = scala.math.pow(2, width)
  val halfCapcity: Double = capcity/2
  val resolution: Double  = 1/scala.math.pow(2, fraction)
  val minValue: Double = if(signed) - halfCapcity*resolution else 0
  val maxValue: Double = if(signed) (halfCapcity - 1)*resolution else (capcity -1)*resolution

  def alignHex: Int = scala.math.ceil(width/4.0).toInt
  def alignOct: Int = scala.math.ceil(width/3.0).toInt
  /*
  *  Float  (B=2 / p=24): Eps = 2^(-24) = 5.9604644775390625E-8
  *  Double (B=2 / p=53): Eps = 2^(-53) = 1.1102230246251565E-16*/
  val epsInDouble: Double = scala.math.pow(2, amplify - 53)

  def *(right: QFormat): QFormat = {
    QFormat(this.width + right.width, this.fraction + right.fraction, this.signed | right.signed)
  }

  def +(right: QFormat): QFormat = {
    val fraction = scala.math.max(this.fraction, right.fraction)
    val noneFraction = scala.math.max(this.nonFraction, right.nonFraction)
    QFormat(noneFraction + fraction, fraction, this.signed | right.signed)
  }

  def -(right: QFormat): QFormat = this.+(- right)

  def unary_- : QFormat = {
    if(signed) this else QFormat(this.width+1, this.fraction, true)
  }

//  /* SQ(10,5) >>>  4 = SQ(10,9)*/
//  /* SQ(11,0) >>> 10 = SQ(11,10)*/
//  def >>>(n: Int): QFormat = {
//    val newFrac  = this.fraction + n
//    val newWidth = if(this.amplify > n) this.width else (this.width + n - this.amplify )
//    this.copy(newWidth, newFrac)
//  }
//
//  /* SQ(10,9) <<<  4 = SQ(10,5)*/
//  /* SQ(3,2)  <<< 10 = SQ(11,0)*/
//  def <<<(n: Int): QFormat = {
//    val newFrac  = if(this.fraction>n) (this.fraction - n) else 0
//    val newWidth = if(this.fraction>n) this.width else (this.width + n - this.fraction)
//    this.copy(newWidth, newFrac)
//  }

  /* SQ(10,5) >> 4 = SQ(6,1)*/
  /* SQ(10,5) >> 6 = SQ(4,0)*/
  def >>(n: Int): QFormat = {
    val newFrac  = if(this.fraction>n) (this.fraction - n) else 0
    val newWidth = if(this.width > n) this.width - n else  0
    this.copy(newWidth, newFrac)
  }

  /* SQ(6,1) << 4 = SQ(10,5)*/
  /* SQ(4,0) << 6 = SQ(10,6)*/
  def <<(n: Int): QFormat = {
    this.copy(this.width + n, this.fraction + n)
  }

  def *(x: Double): QFormat = {
    val zoom = spinal.core.log2Up(scala.math.ceil(x).toInt)
    val newWidth = width + zoom
    this.copy(newWidth, fraction)
  }

  /*SQ(8,7)*4 => SQ(10,7)*/
  def *(x: Int): QFormat = this.*(x.toDouble)

  override def toString : String = {
    if(signed) s"SQ($width, $fraction)" else s"UQ($width, $fraction)"
  }

  def verbose : String = {
    s"""${getClass().getName.split('.').last} : Q($width,$fraction,${if(signed) "signed" else "unsigned"})
resolution: $resolution
maxValue  : $maxValue
minValue  : $minValue"""
  }
}