(* translate-basis.sml * * COPYRIGHT (c) 2010 The Diderot Project (http://diderot-language.cs.uchicago.edu) * All rights reserved. * * Translation for basis operations in Simple AST to HighIL code *) structure TranslateBasis : sig (* translate(lhs, f, mvs, args) translates the application of f (specialized * to the instantiated meta variables mvs) to a list of SSA assignments in * reverse order. *) val translate : (HighIL.var * Var.var * SimpleTypes.meta_arg list * HighIL.var list) -> HighIL.assignment list end = struct structure BV = BasisVars structure IL = HighIL structure DstTy = HighILTypes structure Op = HighOps structure Ty = SimpleTypes structure VTbl = Var.Tbl structure mk= mkOperators fun trType (Ty.TY ty) = TranslateTy.tr ty | trType _ = raise Fail "expected type" fun dimVarToInt (Ty.DIM d) = d | dimVarToInt _ = raise Fail "expected dim" fun dimVarToTensor dv = DstTy.tensorTy[dimVarToInt dv] fun dimVarToMatrix dv = let val d = dimVarToInt dv in DstTy.tensorTy[d, d] (* square matrix type *) end fun shapeVarToTensor (Ty.SHAPE shp) = DstTy.tensorTy shp | shapeVarToTensor _ = raise Fail "expected shape" fun assign (y, rator, xs) = [IL.ASSGN(y, IL.OP(rator, xs))] fun basisFn name (y, [], xs) = [IL.ASSGN(y, IL.APPLY(name, xs))] fun simpleOp rator (y, [], xs) = assign (y, rator, xs) fun tensorOp rator (y, [sv], xs) = assign (y, rator(shapeVarToTensor sv), xs) fun vectorOp rator (y, [dv], xs) = assign (y, rator(dimVarToTensor dv), xs) fun kernel h (y, [], []) = assign(y, Op.Kernel(h, 0), []) (* utility functions for synthesizing eigenvector/eigenvalue code *) fun eigenVec (rator, dim) = let val ty = DstTy.SeqTy(DstTy.realTy, dim) in fn (y, _, [m]) => let val v = IL.Var.new("evals", ty) in [IL.MASSGN([v, y], rator, [m])] end end fun eigenVal (rator, dim) = let val ty = DstTy.SeqTy(DstTy.vecTy dim, dim) in fn (y, _, [m]) => let val v = IL.Var.new("evecs", ty) in [IL.MASSGN([y, v], rator, [m])] end end fun assignEin (y, rator, xs) = IL.ASSGN(y, IL.EINAPP(rator, xs)) fun simpleEOp rator (y, _,xs) = [assignEin(y, rator, xs)] fun mkNorm (shape,A) =let val RTy=DstTy.TensorTy [] val b=IL.Var.new("dot" ,RTy) val c=IL.Var.new("sqrt" ,RTy) val rator=(case shape of [_]=>mk.innerProduct(shape,shape) | [_,_]=>mk.doubleDot(shape,shape) | _ => raise Fail "unsupported norm" (*end case*)) val dot=assignEin(b,rator, [A,A]) val rator= IL.OP(Op.Sqrt, [b]) in (c,rator,dot) end (* shape is an int list, DIM is in int|variable, k-level of differntiation *) (* build a table that maps Basis variables to their translation functions *) val tbl : ((IL.var * Ty.meta_arg list * IL.var list) -> IL.assignment list) VTbl.hash_table = let val tbl = VTbl.mkTable (128, Fail "Translate table") val insert = VTbl.insert tbl in List.app insert [ (BV.lt_ii, simpleOp(Op.LT DstTy.IntTy)), (BV.lt_rr, simpleOp(Op.LT DstTy.realTy)), (BV.lte_ii, simpleOp(Op.LTE DstTy.IntTy)), (BV.lte_rr, simpleOp(Op.LTE DstTy.realTy)), (BV.gte_ii, simpleOp(Op.GTE DstTy.IntTy)), (BV.gte_rr, simpleOp(Op.GTE(DstTy.realTy))), (BV.gt_ii, simpleOp(Op.GT DstTy.IntTy)), (BV.gt_rr, simpleOp(Op.GT(DstTy.realTy))), (BV.equ_bb, simpleOp(Op.EQ DstTy.BoolTy)), (BV.equ_ii, simpleOp(Op.EQ DstTy.IntTy)), (BV.equ_ss, simpleOp(Op.EQ DstTy.StringTy)), (BV.equ_rr, simpleOp(Op.EQ(DstTy.realTy))), (BV.neq_bb, simpleOp(Op.NEQ DstTy.BoolTy)), (BV.neq_ii, simpleOp(Op.NEQ DstTy.IntTy)), (BV.neq_ss, simpleOp(Op.NEQ DstTy.StringTy)), (BV.neq_rr, simpleOp(Op.NEQ(DstTy.realTy))), (BV.add_ii, simpleOp Op.IAdd), (BV.add_tt, fn (y, [shp], xs) => let val ty1 as DstTy.TensorTy dd1 = shapeVarToTensor shp val rator =mk.addTen(dd1) in [assignEin(y, rator,xs)] end), (BV.add_ff, fn (y, [_,Ty.DIM d, Ty.SHAPE dd], xs) => [assignEin(y, mk.addField(d, dd),xs)]), (BV.add_fr, fn (y, [_,Ty.DIM d], [f,s]) => [assignEin(y, mk.addTenField(d),[s,f])]), (BV.add_rf, fn (y, [_,Ty.DIM d], xs) => [assignEin(y, mk.addTenField(d),xs)]), (BV.sub_ii, simpleOp Op.ISub), (BV.sub_tt, fn (y, [shp], xs) => let val ty1 as DstTy.TensorTy dd1 = shapeVarToTensor shp val rator =mk.subTen(dd1) in [assignEin(y, rator,xs)] end), (BV.sub_ff, fn (y, [_,Ty.DIM d, Ty.SHAPE dd], xs) => [assignEin(y, mk.subField(d, dd),xs)]), (BV.sub_fr, fn (y, [_,Ty.DIM d], xs) => [assignEin(y, mk.subFieldTen(d),xs)]), (BV.sub_rf, fn (y, [_,Ty.DIM d], xs) => [assignEin(y, mk.subTenField(d),xs)]), (BV.mul_ii, simpleOp Op.IMul), (BV.mul_rr, fn (y,_,args) => [assignEin(y, mk.prodScalar,args)]), (BV.mul_rt, fn (y, [shp], xs) => let val ty1 as DstTy.TensorTy dd1 = shapeVarToTensor shp val rator =mk.scaleTen(dd1) in [assignEin(y, rator,xs)] end), (BV.mul_tr, fn (y, [shp], [t, r]) => let val ty1 as DstTy.TensorTy dd1 = shapeVarToTensor shp val rator = mk.scaleTen dd1 in [assignEin(y, rator,[r,t])] end), (BV.mul_rf, fn (y, [_,Ty.DIM d, Ty.SHAPE dd], xs) => [assignEin(y, mk.scaleField(d, dd),xs)]), (BV.mul_fr, fn (y, [_,Ty.DIM d, Ty.SHAPE dd], [f, s]) => [assignEin(y, mk.scaleField(d, dd),[s,f])]), (BV.mul_ss, fn (y, [_,Ty.DIM d], xs) => [assignEin(y, mk.mulFieldss d,xs)]), (BV.mul_sf, fn (y, [_,Ty.DIM d, Ty.SHAPE dd], xs) => [assignEin(y, mk.mulFieldsf(d,dd),xs)]), (BV.mul_fs, fn (y, [_,Ty.DIM d, Ty.SHAPE dd], [f,s]) => [assignEin(y, mk.mulFieldsf(d,dd),[s,f])]), (BV.div_ii, simpleOp Op.IDiv), (BV.div_rr, fn (y,_,args) => [assignEin(y, mk.divScalar,args)]), (BV.div_tr, fn (y, [shp], xs) => let val ty1 as DstTy.TensorTy dd1 = shapeVarToTensor shp val rator =mk.divTen(dd1) in [assignEin(y, rator,xs)] end), (BV.div_fr, fn (y, [_,Ty.DIM d, Ty.SHAPE dd], xs) => [assignEin(y, mk.divideField(d, dd),xs)]), (BV.div_ss, fn (y, [_,Ty.DIM d], xs) => [assignEin(y, mk.divFieldss d,xs)]), (BV.exp_ri, simpleOp(Op.Power)), (BV.exp_rr, basisFn MathFuns.pow), (BV.curl2D, simpleEOp mk.curl2d), (BV.curl3D, simpleEOp mk.curl3d), (BV.convolve_vk, fn (y, [_, Ty.DIM d, Ty.SHAPE dd], xs) => [assignEin(y, mk.conv(d, dd),xs)]), (BV.convolve_kv, fn (y, [_, Ty.DIM d, Ty.SHAPE dd], [k, v]) => [assignEin(y, mk.conv(d, dd),[v,k])]), (BV.neg_i, simpleOp Op.INeg), (BV.neg_t, fn (y, [shp], xs) => let val ty1 as DstTy.TensorTy dd1 = shapeVarToTensor shp val rator =mk.negTen(dd1) in [assignEin(y, rator,xs)] end), (BV.neg_f, fn (y, [_,Ty.DIM d, Ty.SHAPE dd], xs) => [assignEin(y, mk.negField(d, dd),xs)]), (BV.op_probe, fn (y, [_, Ty.DIM d, Ty.SHAPE dd], xs) => [assignEin(y, (mk.probe(dd,d)),xs)]), (BV.op_D, fn (y, [_, Ty.DIM d], xs) => [assignEin(y, mk.grad([d]),xs)]), (BV.op_Dotimes, fn (y, [_, Ty.DIM d1, Ty.SHAPE dd, Ty.DIM d2], xs) => [assignEin(y, mk.dotimes(d1, dd@[d2]),xs)]), (BV.op_Ddot, fn (y, [_, Ty.DIM d1, Ty.SHAPE dd, Ty.DIM d2], xs) => [assignEin(y, mk.divergence(d1, dd),xs)] ), (BV.op_norm, fn (y, [sv], [x]) => (case shapeVarToTensor sv of DstTy.TensorTy[] => assign(y, Op.Abs DstTy.realTy, [x]) | DstTy.TensorTy dd=> let val RTy=DstTy.TensorTy [] val (_,sqrtop,dot)= mkNorm (dd,x) in [dot ,IL.ASSGN (y,sqrtop)] end | ty => assign(y, Op.Norm ty, [x]) (* end case *))), (BV.op_not, simpleOp Op.Not), (BV.op_cross, simpleEOp mk.crossProduct), (BV.op_crossField, simpleEOp mk.crossProductField), (BV.op_outer, fn (y, [Ty.DIM d1, Ty.DIM d2], xs) => [assignEin(y, (mk.outerProduct(d1, d2)), xs)]), (* Any Shape fields (BV.op_outerField, fn (y, [_, Ty.DIM d1, Ty.SHAPE dd1, Ty.SHAPE dd2], xs)=> [assignEin(y, mk.outerField(d1, dd1, dd2), xs)]), *) (BV.op_outerField, fn (y, [_, Ty.DIM d1], xs)=> [assignEin(y, mk.outerField(d1), xs)]), (BV.op_inner, fn (y, [sh1, sh2, _], xs) => let val ty1 as DstTy.TensorTy dd1 = shapeVarToTensor sh1 val ty2 as DstTy.TensorTy dd2 = shapeVarToTensor sh2 in [assignEin(y, (mk.innerProduct(dd1,dd2)),xs)] end), (BV.op_innerField, fn (y, [_,Ty.SHAPE dd1,Ty.DIM d,Ty.SHAPE dd2,_], xs) => [assignEin(y, mk.innerProductField(dd1,d,dd2),xs)]), (BV.op_colon, fn (y, [sh1, sh2, _], xs) => let val ty1 as DstTy.TensorTy dd1 = shapeVarToTensor sh1 val ty2 as DstTy.TensorTy dd2 = shapeVarToTensor sh2 in [assignEin(y, (mk.doubleDot(dd1,dd2)),xs)] end), (BV.op_colonField, fn (y, [_,Ty.SHAPE dd1,_,Ty.SHAPE dd2, _], xs) => [assignEin(y, (mk.doubleDotField(dd1,dd2)),xs)]), (BV.fn_inside, fn (y, [_, Ty.DIM d, _], xs) => assign(y, Op.Inside d, xs)), (BV.clamp_rrr, simpleOp (Op.Clamp DstTy.realTy)), (BV.clamp_vvv, vectorOp Op.Clamp), (BV.lerp3, tensorOp Op.Lerp), (BV.lerp5, fn (y, [sv], [a, b, x0, x, x1]) => let val t1 = IL.Var.new("t1", DstTy.realTy) val t2 = IL.Var.new("t2", DstTy.realTy) val t3 = IL.Var.new("t3", DstTy.realTy) in [ assignEin(t1, mk.subScalar,[x,x0]), assignEin(t2, mk.subScalar,[x1,x0]), assignEin(t3, mk.divScalar,[t1,t2]), IL.ASSGN(y, IL.OP(Op.Lerp(shapeVarToTensor sv), [a, b, t3])) ] end), (BV.evals2x2, eigenVal (Op.Eigen2x2, 2)), (BV.evals3x3, eigenVal (Op.Eigen3x3, 3)), (BV.evecs2x2, eigenVec (Op.Eigen2x2, 2)), (BV.evecs3x3, eigenVec (Op.Eigen3x3, 3)), (BV.fn_max, simpleOp Op.Max), (BV.fn_min, simpleOp Op.Min), (* modulate is vector * vector pointwise multiplication *) (BV.fn_modulate, fn (y,[Ty.DIM dd1], xs) => [assignEin(y, (mk.modulate dd1),xs)]), (* vectorOp Op.Normalize),*) (BV.fn_normalize, vectorOp Op.Normalize), (* fn (y, [Ty.DIM i], [x]) =>let val (c,sqrtop,dot)= mkNorm ([i],x) val d = IL.Var.new ("int", DstTy.intTy) val e=IL.Var.new("divide" ,DstTy.TensorTy []) in [dot ,IL.ASSGN (c,sqrtop), IL.ASSGN (d, IL.LIT(Literal.Int 1)), assignEin(e,mk.divScalar,[d,c]), assignEin(y,mk.scaleTen [i],[e,x])] end)*) (BV.fn_principleEvec, vectorOp Op.PrincipleEvec), (BV.fn_trace, fn (y, [Ty.DIM d], xs) => [assignEin(y,(mk.trace d), xs)]), (BV.fn_traceField, fn (y, [_,Ty.DIM d,Ty.SHAPE dd], xs) => [assignEin(y,mk.traceField(d,dd), xs)]), (BV.fn_transpose, fn (y, [Ty.DIM d1, Ty.DIM d2], xs) => [assignEin(y, (mk.transpose [d1,d2]), xs)]), (BV.fn_transposeField, fn (y, [_,Ty.DIM d1, Ty.DIM d2,Ty.DIM d3], xs) => [assignEin(y, (mk.transposeField (d1,d2,d3)), xs)]), (BV.kn_bspln3, kernel Kernel.bspln3), (BV.kn_bspln5, kernel Kernel.bspln5), (BV.kn_ctmr, kernel Kernel.ctmr), (BV.kn_c2ctmr, kernel Kernel.ctmr), (BV.kn_c4hexic, kernel Kernel.c4hexic), (BV.kn_tent, kernel Kernel.tent), (BV.kn_c1tent, kernel Kernel.tent), (BV.i2r, simpleOp Op.IntToReal), (BV.identity, fn (y, [Ty.DIM d], xs) => [assignEin(y, (mk.identity d), xs)]), (BV.zero, fn (y, [sv], []) => assign(y, Op.Zero(shapeVarToTensor sv), [])), (BV.subscript, fn (y, [ty, Ty.DIM d], xs) => assign (y, Op.SeqSub(DstTy.SeqTy(trType ty, d)), xs)) (*, (BV.dynSubscript, fn (y, [tv], args) => assign(y, Op.SeqSub(DstTy.DynSeqTy(pruneTy tv)), args)) *) ]; (* add C math functions *) List.app (fn (n, x) => insert(x, basisFn n)) BV.mathFns; tbl end fun translate (y, f, mvs, xs) = (case VTbl.find tbl f of SOME transFn => transFn(y, mvs, xs) | NONE => raise Fail("TranslateBasis.translate: unknown basis function " ^ Var.uniqueNameOf f) (* end case *)) handle ex => (print(concat["translate (", IL.Var.toString y, ", ", Var.uniqueNameOf f, ", ...)\n"]); raise ex) end
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The output has ended thus: nt(concat["translate (", IL.Var.toString y, ", ", Var.uniqueNameOf f, ", ...)\n"]); raise ex) end