infer static parameters even when more complicated arithmetic is involved

compiler/ast.nim

@@ -1581,7 +1581,7 @@ proc hasPattern*(s: PSym): bool {.inline.} =
   result = isRoutine(s) and s.ast.sons[patternPos].kind != nkEmpty
 
 iterator items*(n: PNode): PNode =
-  for i in 0.. <n.len: yield n.sons[i]
+  for i in 0.. <n.safeLen: yield n.sons[i]
 
 iterator pairs*(n: PNode): tuple[i: int, n: PNode] =
   for i in 0.. <n.len: yield (i, n.sons[i])
@@ -1624,6 +1624,16 @@ proc toObject*(typ: PType): PType =
   if result.kind == tyRef:
     result = result.lastSon
 
+proc findUnresolvedStatic*(n: PNode): PNode =
+  if n.kind == nkSym and n.typ.kind == tyStatic and n.typ.n == nil:
+    return n
+
+  for son in n:
+    let n = son.findUnresolvedStatic
+    if n != nil: return n
+
+  return nil
+
 when false:
   proc containsNil*(n: PNode): bool =
     # only for debugging

compiler/msgs.nim

@@ -109,6 +109,7 @@ type
     errXCannotBeClosure, errXMustBeCompileTime,
     errCannotInferTypeOfTheLiteral,
     errCannotInferReturnType,
+    errCannotInferStaticParam,
     errGenericLambdaNotAllowed,
     errProcHasNoConcreteType,
     errCompilerDoesntSupportTarget,
@@ -373,6 +374,7 @@ const
     errXMustBeCompileTime: "'$1' can only be used in compile-time context",
     errCannotInferTypeOfTheLiteral: "cannot infer the type of the $1",
     errCannotInferReturnType: "cannot infer the return type of the proc",
+    errCannotInferStaticParam: "cannot infer the value of the static param `$1`",
     errGenericLambdaNotAllowed: "A nested proc can have generic parameters only when " &
                                 "it is used as an operand to another routine and the types " &
                                 "of the generic paramers can be inferred from the expected signature.",

compiler/semdata.nim

@@ -318,23 +318,14 @@ proc makeRangeWithStaticExpr*(c: PContext, n: PNode): PType =
   let intType = getSysType(tyInt)
   result = newTypeS(tyRange, c)
   result.sons = @[intType]
-  if n.typ.n == nil: result.flags.incl tfUnresolved
+  if n.typ != nil and n.typ.n == nil:
+    result.flags.incl tfUnresolved
   result.n = newNode(nkRange, n.info, @[
     newIntTypeNode(nkIntLit, 0, intType),
     makeStaticExpr(c, n.nMinusOne)])
 
 template rangeHasUnresolvedStatic*(t: PType): bool =
-  # this accepts the ranges's node
+  tfUnresolved in t.flags
-  t.n != nil and t.n.len > 1 and t.n[1].kind == nkStaticExpr
-
-proc findUnresolvedStaticInRange*(t: PType): (PType, int) =
-  assert t.kind == tyRange
-  # XXX: This really needs to become more sophisticated
-  let upperBound = t.n[1]
-  if upperBound[0].kind == nkCall:
-    return (upperBound[0][1].typ, 1)
-  else:
-    return (upperBound.typ, 0)
 
 proc errorType*(c: PContext): PType =
   ## creates a type representing an error state

compiler/semexprs.nim

@@ -627,6 +627,7 @@ proc evalAtCompileTime(c: PContext, n: PNode): PNode =
 
 proc semStaticExpr(c: PContext, n: PNode): PNode =
   let a = semExpr(c, n.sons[0])
+  if a.findUnresolvedStatic != nil: return a
   result = evalStaticExpr(c.module, c.cache, a, c.p.owner)
   if result.isNil:
     localError(n.info, errCannotInterpretNodeX, renderTree(n))

compiler/semtypes.nim

@@ -195,6 +195,7 @@ proc semRangeAux(c: PContext, n: PNode, prev: PType): PType =
   for i in 0..1:
     if hasGenericArguments(range[i]):
       result.n.addSon makeStaticExpr(c, range[i])
+      result.flags.incl tfUnresolved
     else:
       result.n.addSon semConstExpr(c, range[i])
 

compiler/semtypinst.nim

@@ -445,7 +445,7 @@ proc replaceTypeVarsTAux(cl: var TReplTypeVars, t: PType): PType =
     elif t.sons[0].kind != tyNone:
       result = makeTypeDesc(cl.c, replaceTypeVarsT(cl, t.sons[0]))
 
-  of tyUserTypeClass:
+  of tyUserTypeClass, tyStatic:
     result = t
 
   of tyGenericInst, tyUserTypeClassInst:
@@ -502,8 +502,9 @@ proc initTypeVars*(p: PContext, pt: TIdTable, info: TLineInfo;
   result.owner = owner
 
 proc replaceTypesInBody*(p: PContext, pt: TIdTable, n: PNode;
-                         owner: PSym): PNode =
+                         owner: PSym, allowMetaTypes = false): PNode =
   var cl = initTypeVars(p, pt, n.info, owner)
+  cl.allowMetaTypes = allowMetaTypes
   pushInfoContext(n.info)
   result = replaceTypeVarsN(cl, n)
   popInfoContext()

compiler/sigmatch.nim

@@ -681,16 +681,125 @@ proc maybeSkipDistinct(t: PType, callee: PSym): PType =
   else:
     result = t
 
-proc tryResolvingStaticExpr(c: var TCandidate, n: PNode): PNode =
+proc tryResolvingStaticExpr(c: var TCandidate, n: PNode,
+                            allowUnresolved = false): PNode =
   # Consider this example:
   #   type Value[N: static[int]] = object
   #   proc foo[N](a: Value[N], r: range[0..(N-1)])
   # Here, N-1 will be initially nkStaticExpr that can be evaluated only after
   # N is bound to a concrete value during the matching of the first param.
   # This proc is used to evaluate such static expressions.
-  let instantiated = replaceTypesInBody(c.c, c.bindings, n, nil)
+  let instantiated = replaceTypesInBody(c.c, c.bindings, n, nil,
+                                        allowMetaTypes = allowUnresolved)
   result = c.c.semExpr(c.c, instantiated)
 
+proc inferStaticParam*(lhs: PNode, rhs: BiggestInt): PType =
+  # This is a simple integer arithimetic equation solver,
+  # capable of deriving the value of a static parameter in
+  # expressions such as (N + 5) / 2 = rhs
+  #
+  # Preconditions:
+  #
+  #   * The input of this proc must be semantized 
+  #     - all templates should be expanded
+  #     - aby constant folding possible should already be performed
+  #
+  #   * There must be exactly one unresolved static parameter
+  #
+  # Result:
+  #
+  #   The proc will return the inferred static type with the `n` field
+  #   populated with the inferred value.
+  #
+  #   `nil` will be returned if the inference was not possible
+  #
+  if lhs.kind in nkCallKinds and lhs[0].kind == nkSym:
+    case lhs[0].sym.magic
+    of mUnaryLt:
+      return inferStaticParam(lhs[1], rhs + 1)
+
+    of mAddI, mAddU, mInc, mSucc:
+      if lhs[1].kind == nkIntLit:
+        return inferStaticParam(lhs[2], rhs - lhs[1].intVal)
+      elif lhs[2].kind == nkIntLit:
+        return inferStaticParam(lhs[1], rhs - lhs[2].intVal)
+    
+    of mDec, mSubI, mSubU, mPred:
+      if lhs[1].kind == nkIntLit:
+        return inferStaticParam(lhs[2], lhs[1].intVal - rhs)
+      elif lhs[2].kind == nkIntLit:
+        return inferStaticParam(lhs[1], rhs + lhs[2].intVal)
+    
+    of mMulI, mMulU:
+      if lhs[1].kind == nkIntLit:
+        if rhs mod lhs[1].intVal == 0:
+          return inferStaticParam(lhs[2], rhs div lhs[1].intVal)
+      elif lhs[2].kind == nkIntLit:
+        if rhs mod lhs[2].intVal == 0:
+          return inferStaticParam(lhs[1], rhs div lhs[2].intVal)
+    
+    of mDivI, mDivU:
+      if lhs[1].kind == nkIntLit:
+        if lhs[1].intVal mod rhs == 0:
+          return inferStaticParam(lhs[2], lhs[1].intVal div rhs)
+      elif lhs[2].kind == nkIntLit:
+        return inferStaticParam(lhs[1], lhs[2].intVal * rhs)
+    
+    of mShlI:
+      if lhs[2].kind == nkIntLit:
+        return inferStaticParam(lhs[1], rhs shr lhs[2].intVal)
+    
+    of mShrI:
+      if lhs[2].kind == nkIntLit:
+        return inferStaticParam(lhs[1], rhs shl lhs[2].intVal)
+    
+    of mUnaryMinusI:
+      return inferStaticParam(lhs[1], -rhs)
+    
+    of mUnaryPlusI, mToInt, mToBiggestInt:
+      return inferStaticParam(lhs[1], rhs)
+    
+    else: discard
+  
+  elif lhs.kind == nkSym and lhs.typ.kind == tyStatic and lhs.typ.n == nil:
+    lhs.typ.n = newIntNode(nkIntLit, rhs)
+    return lhs.typ
+  
+  return nil
+
+proc failureToInferStaticParam(n: PNode) =
+  let staticParam = n.findUnresolvedStatic
+  let name = if staticParam != nil: staticParam.sym.name.s
+             else: "unknown"
+  localError(n.info, errCannotInferStaticParam, name)
+
+proc inferStaticsInRange(c: var TCandidate,
+                         inferred, concrete: PType): TTypeRelation =
+  let lowerBound = tryResolvingStaticExpr(c, inferred.n[0],
+                                          allowUnresolved = true)
+  let upperBound = tryResolvingStaticExpr(c, inferred.n[1],
+                                          allowUnresolved = true)
+  
+  template doInferStatic(c: var TCandidate, e: PNode, r: BiggestInt) =
+    var exp = e
+    var rhs = r
+    var inferred = inferStaticParam(exp, rhs)
+    if inferred != nil:
+      put(c.bindings, inferred, inferred)
+      return isGeneric
+    else:
+      failureToInferStaticParam exp
+
+  if lowerBound.kind == nkIntLit:
+    if upperBound.kind == nkIntLit:
+      if lengthOrd(concrete) == upperBound.intVal - lowerBound.intVal + 1:
+        return isGeneric
+      else:
+        return isNone
+    doInferStatic(c, upperBound, lengthOrd(concrete) + lowerBound.intVal - 1)
+  elif upperBound.kind == nkIntLit:
+    doInferStatic(c, lowerBound, upperBound.intVal + 1 - lengthOrd(concrete))
+
 template subtypeCheck() =
   if result <= isSubrange and f.lastSon.skipTypes(abstractInst).kind in {tyRef, tyPtr, tyVar}:
     result = isNone
@@ -894,34 +1003,10 @@ proc typeRel(c: var TCandidate, f, aOrig: PType, doBind = true): TTypeRelation =
                           a.sons[1].skipTypes({tyTypeDesc}))
       if result < isGeneric: return isNone
       
-      proc inferStaticRange(c: var TCandidate, inferred, concrete: PType) =
+      if fRange.rangeHasUnresolvedStatic:
-        var (staticT, offset) = inferred.findUnresolvedStaticInRange
+        return inferStaticsInRange(c, fRange, a)
-        var
-          replacementT = newTypeWithSons(c.c, tyStatic, @[tyInt.getSysType])
-          concreteUpperBound = concrete.n[1].intVal
-        # we must correct for the off-by-one discrepancy between
-        # ranges and static params:
-        replacementT.n = newIntNode(nkIntLit, concreteUpperBound + offset)
-        if tfInferrableStatic in staticT.flags:
-          staticT.n = replacementT.n
-        put(c.bindings, staticT, replacementT)
-
-      if rangeHasUnresolvedStatic(fRange):
-        if tfUnresolved in fRange.flags:
-          # This is a range from an array instantiated with a generic
-          # static param. We must extract the static param here and bind
-          # it to the size of the currently supplied array.
-          inferStaticRange(c, fRange, aRange)
-          return isGeneric
-
-        let len = tryResolvingStaticExpr(c, fRange.n[1])
-        if len.kind == nkIntLit and len.intVal+1 == lengthOrd(a):
-          return # if we get this far, the result is already good
-        else:
-          return isNone
       elif c.c.inTypeClass > 0 and aRange.rangeHasUnresolvedStatic:
-        inferStaticRange(c, aRange, fRange)
+        return inferStaticsInRange(c, aRange, f)
-        return isGeneric
       elif lengthOrd(fRange) != lengthOrd(a):
         result = isNone
     else: discard

compiler/types.nim

@@ -63,7 +63,7 @@ const
   abstractVarRange* = {tyGenericInst, tyRange, tyVar, tyDistinct, tyOrdinal,
                        tyTypeDesc, tyAlias, tyInferred}
   abstractInst* = {tyGenericInst, tyDistinct, tyOrdinal, tyTypeDesc, tyAlias,
-                   tyInferred} + tyTypeClasses
+                   tyInferred}
   skipPtrs* = {tyVar, tyPtr, tyRef, tyGenericInst, tyTypeDesc, tyAlias,
                tyInferred}
   # typedescX is used if we're sure tyTypeDesc should be included (or skipped)

doc/manual/generics.txt

@@ -367,8 +367,8 @@ operator and also when types dependent on them are being matched:
     MyConcept[M, N: static[int]; T] = concept x
       x.foo(SquareMatrix[N, T]) is array[M, int]
 
-Nim may include a simple linear equation solver in the future to help us
+The Nim compiler includes a simple linear equation solver, allowing it to
-infer static params when arithmetic is involved.
+infer static params in some situations where integer arithmetic is involved.
 
 Just like in regular type classes, Nim discriminates between ``bind once``
 and ``bind many`` types when matching the concept. You can add the ``distinct``