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// SPDX-License-Identifier: Apache-2.0
// Author: Kevin Laeufer <laeufer@cs.berkeley.edu>
package firrtl.backends.experimental.smt
import firrtl.ir
import firrtl.PrimOps
import firrtl.passes.CheckWidths.WidthTooBig
private object FirrtlExpressionSemantics {
def toSMT(e: ir.Expression): BVExpr = {
val eSMT = e match {
case ir.DoPrim(op, args, consts, _) => onPrim(op, args, consts)
case r: ir.RefLikeExpression => BVSymbol(r.serialize, getWidth(r))
case ir.UIntLiteral(value, ir.IntWidth(width)) => BVLiteral(value, width.toInt)
case ir.SIntLiteral(value, ir.IntWidth(width)) =>
val twosComplementValue = value & ((BigInt(1) << width.toInt) - 1)
BVLiteral(twosComplementValue, width.toInt)
case ir.Mux(cond, tval, fval, _) =>
val width = List(tval, fval).map(getWidth).max
BVIte(toSMT(cond), toSMT(tval, width), toSMT(fval, width))
case v: ir.ValidIf =>
throw new RuntimeException(s"Unsupported expression: ValidIf ${v.serialize}")
}
assert(
eSMT.width == getWidth(e),
"We aim to always produce a SMT expression of the same width as the firrtl expression."
)
eSMT
}
/** Ensures that the result has the desired width by appropriately extending it. */
def toSMT(e: ir.Expression, width: Int, allowNarrow: Boolean = false): BVExpr =
forceWidth(toSMT(e), isSigned(e), width, allowNarrow)
private def forceWidth(eSMT: BVExpr, eSigned: Boolean, width: Int, allowNarrow: Boolean = false): BVExpr = {
if (eSMT.width == width) { eSMT }
else if (width < eSMT.width) {
assert(allowNarrow, s"Narrowing from ${eSMT.width} bits to $width bits is not allowed!")
BVSlice(eSMT, width - 1, 0)
} else {
BVExtend(eSMT, width - eSMT.width, eSigned)
}
}
// see "Primitive Operations" section in the Firrtl Specification
private def onPrim(
op: ir.PrimOp,
args: Seq[ir.Expression],
consts: Seq[BigInt]
): BVExpr = {
(op, args, consts) match {
case (PrimOps.Add, Seq(e1, e2), _) =>
val width = args.map(getWidth).max + 1
BVOp(Op.Add, toSMT(e1, width), toSMT(e2, width))
case (PrimOps.Sub, Seq(e1, e2), _) =>
val width = args.map(getWidth).max + 1
BVOp(Op.Sub, toSMT(e1, width), toSMT(e2, width))
case (PrimOps.Mul, Seq(e1, e2), _) =>
val width = args.map(getWidth).sum
BVOp(Op.Mul, toSMT(e1, width), toSMT(e2, width))
case (PrimOps.Div, Seq(num, den), _) =>
val signed = isSigned(num)
val resWidth = if (signed) { getWidth(num) + 1 }
else { getWidth(num) }
val op = if (signed) { Op.SignedDiv }
else { Op.UnsignedDiv }
// we do the calculation on the widened values and then narrow the result if needed
val width = args.map(getWidth).max + (if (signed) 1 else 0)
val res = BVOp(op, toSMT(num, width), toSMT(den, width))
forceWidth(res, signed, resWidth, allowNarrow = true)
case (PrimOps.Rem, Seq(num, den), _) =>
val signed = isSigned(num)
val op = if (signed) Op.SignedRem else Op.UnsignedRem
val width = args.map(getWidth).max
val resWidth = args.map(getWidth).min
val res = BVOp(op, toSMT(num, width), toSMT(den, width))
forceWidth(res, signed, resWidth, allowNarrow = true)
case (PrimOps.Lt, Seq(e1, e2), _) =>
val width = args.map(getWidth).max
BVNot(BVComparison(Compare.GreaterEqual, toSMT(e1, width), toSMT(e2, width), isSigned(e1)))
case (PrimOps.Leq, Seq(e1, e2), _) =>
val width = args.map(getWidth).max
BVNot(BVComparison(Compare.Greater, toSMT(e1, width), toSMT(e2, width), isSigned(e1)))
case (PrimOps.Gt, Seq(e1, e2), _) =>
val width = args.map(getWidth).max
BVComparison(Compare.Greater, toSMT(e1, width), toSMT(e2, width), isSigned(e1))
case (PrimOps.Geq, Seq(e1, e2), _) =>
val width = args.map(getWidth).max
BVComparison(Compare.GreaterEqual, toSMT(e1, width), toSMT(e2, width), isSigned(e1))
case (PrimOps.Eq, Seq(e1, e2), _) =>
val width = args.map(getWidth).max
BVEqual(toSMT(e1, width), toSMT(e2, width))
case (PrimOps.Neq, Seq(e1, e2), _) =>
val width = args.map(getWidth).max
BVNot(BVEqual(toSMT(e1, width), toSMT(e2, width)))
case (PrimOps.Pad, Seq(e), Seq(n)) =>
val width = getWidth(e)
if (n <= width) { toSMT(e) }
else { BVExtend(toSMT(e), n.toInt - width, isSigned(e)) }
case (PrimOps.AsUInt, Seq(e), _) => checkForClockInCast(PrimOps.AsUInt, e); toSMT(e)
case (PrimOps.AsSInt, Seq(e), _) => checkForClockInCast(PrimOps.AsSInt, e); toSMT(e)
case (PrimOps.AsFixedPoint, Seq(e), _) => throw new AssertionError("Fixed-Point numbers need to be lowered!")
case (PrimOps.AsClock, Seq(e), _) => toSMT(e)
case (PrimOps.AsAsyncReset, Seq(e), _) =>
checkForClockInCast(PrimOps.AsAsyncReset, e)
throw new AssertionError(s"Asynchronous resets are not supported! Cannot cast ${e.serialize}.")
case (PrimOps.Shl, Seq(e), Seq(n)) =>
if (n == 0) { toSMT(e) }
else {
val zeros = BVLiteral(0, n.toInt)
BVConcat(toSMT(e), zeros)
}
case (PrimOps.Shr, Seq(e), Seq(n)) =>
val width = getWidth(e)
// "If n is greater than or equal to the bit-width of e,
// the resulting value will be zero for unsigned types
// and the sign bit for signed types"
if (n >= width) {
if (isSigned(e)) { BVSlice(toSMT(e), width - 1, width - 1) }
else { BV1BitZero }
} else {
BVSlice(toSMT(e), width - 1, n.toInt)
}
case (PrimOps.Dshl, Seq(e1, e2), _) =>
val width = getWidth(e1) + (1 << getWidth(e2)) - 1
BVOp(Op.ShiftLeft, toSMT(e1, width), toSMT(e2, width))
case (PrimOps.Dshr, Seq(e1, e2), _) =>
val width = getWidth(e1)
val o = if (isSigned(e1)) Op.ArithmeticShiftRight else Op.ShiftRight
BVOp(o, toSMT(e1, width), toSMT(e2, width))
case (PrimOps.Cvt, Seq(e), _) =>
if (isSigned(e)) { toSMT(e) }
else { BVConcat(BV1BitZero, toSMT(e)) }
case (PrimOps.Neg, Seq(e), _) => BVNegate(BVExtend(toSMT(e), 1, isSigned(e)))
case (PrimOps.Not, Seq(e), _) => BVNot(toSMT(e))
case (PrimOps.And, Seq(e1, e2), _) =>
val width = args.map(getWidth).max
BVAnd(toSMT(e1, width), toSMT(e2, width))
case (PrimOps.Or, Seq(e1, e2), _) =>
val width = args.map(getWidth).max
BVOr(toSMT(e1, width), toSMT(e2, width))
case (PrimOps.Xor, Seq(e1, e2), _) =>
val width = args.map(getWidth).max
BVOp(Op.Xor, toSMT(e1, width), toSMT(e2, width))
case (PrimOps.Andr, Seq(e), _) => BVReduceAnd(toSMT(e))
case (PrimOps.Orr, Seq(e), _) => BVReduceOr(toSMT(e))
case (PrimOps.Xorr, Seq(e), _) => BVReduceXor(toSMT(e))
case (PrimOps.Cat, Seq(e1, e2), _) => BVConcat(toSMT(e1), toSMT(e2))
case (PrimOps.Bits, Seq(e), Seq(hi, lo)) => BVSlice(toSMT(e), hi.toInt, lo.toInt)
case (PrimOps.Head, Seq(e), Seq(n)) =>
val width = getWidth(e)
assert(n >= 0 && n <= width)
BVSlice(toSMT(e), width - 1, width - n.toInt)
case (PrimOps.Tail, Seq(e), Seq(n)) =>
val width = getWidth(e)
assert(n >= 0 && n <= width)
assert(n < width, "While allowed by the firrtl standard, we do not support 0-bit values in this backend!")
BVSlice(toSMT(e), width - n.toInt - 1, 0)
}
}
/** For now we strictly forbid casting clocks to anything else.
* Eventually this should be replaced by a more sophisticated clock analysis pass.
*/
private def checkForClockInCast(cast: ir.PrimOp, signal: ir.Expression): Unit = {
assert(signal.tpe != ir.ClockType, s"Cannot cast (${cast.serialize}) clock expression ${signal.serialize}!")
}
private val BV1BitZero = BVLiteral(0, 1)
private def isSigned(e: ir.Expression): Boolean = e.tpe match {
case _: ir.SIntType => true
case _ => false
}
// Helper function
private def getWidth(e: ir.Expression): Int = firrtl.bitWidth(e.tpe).toInt
}
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