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View of /branches/vis15/src/compiler/translate/translate-basis.sml

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Revision 3978 - (download) (annotate)
Wed Jun 15 19:07:40 2016 UTC (3 years, 1 month ago) by cchiw
File size: 32492 byte(s)
changed ein expressions, rewrote matchEps, added translation
(* translate-basis.sml
 *
 * This code is part of the Diderot Project (http://diderot-language.cs.uchicago.edu)
 *
 * COPYRIGHT (c) 2015 The University of Chicago
 * All rights reserved.
 *
 * Translation for basis operations in Simple AST to HighIR 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 : (HighIR.var * Var.t * SimpleTypes.meta_arg list * HighIR.var list)
          -> HighIR.assignment list

  end = struct

    structure BV = BasisVars
    structure IR = HighIR
    structure DstTy = HighTypes
    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) = [IR.ASSGN(y, IR.OP(rator, 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, SOME dim)
          in
            fn (y, _, [m]) => let
                val v = IR.Var.new("evals", ty)
                in
                  [IR.MASSGN([v, y], rator, [m])]
                end
          end
    fun eigenVal (rator, dim) = let
          val ty = DstTy.SeqTy(DstTy.vecTy dim, SOME dim)
          in
            fn (y, _, [m]) => let
                val v = IR.Var.new("evecs", ty)
                in
                  [IR.MASSGN([y, v], rator, [m])]
                end
          end

    fun assignEin (y, rator, xs) = IR.ASSGN(y, IR.EINAPP(rator, xs))

    fun simpleEOp rator (y, _, xs) = [assignEin(y, rator, xs)]

    fun dist (y, d, xs) = let
          val t0 = IR.Var.new("t0", DstTy.TensorTy[d])
          in [
            assignEin(t0, Mk.subTT[d], xs),
            assignEin(y, Mk.normT[d], [t0])]
          end

  (* build a table that maps Basis variables to their translation functions *)
    val tbl : ((IR.var * Ty.meta_arg list * IR.var list) -> IR.assignment list) VTbl.hash_table = let
          val tbl = VTbl.mkTable (128, Fail "Translate table")
          fun insert (id, def) = (case VTbl.find tbl id
                 of NONE => VTbl.insert tbl (id, def)
                  | SOME _ => raise Fail("duplicate definition of " ^ Var.nameOf id)
                (* end case *))
          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.sub_ii,             simpleOp Op.ISub),
                (BV.mul_ii,             simpleOp Op.IMul),
                (BV.div_ii,             simpleOp Op.IDiv),
                (BV.op_mod,             simpleOp Op.IMod),
                (BV.neg_i,              simpleOp Op.INeg),
                (BV.add_tt,             fn (y, [shp], xs) => let
                                          val ty1 as DstTy.TensorTy dd1 = shapeVarToTensor shp
                                          val rator = Mk.addTT(dd1)
                                          in
                                            [assignEin(y, rator, xs)]
                                          end),
                (BV.add_ff,             fn (y, [_, Ty.DIM d, Ty.SHAPE dd], xs) =>
                                          [assignEin(y, Mk.addFF(d, dd), xs)]),
                (BV.add_ft,             fn (y, [_, Ty.DIM d, Ty.SHAPE dd], [f, s]) =>
                                          [assignEin(y, Mk.addTF(d, dd), [s, f])]),
                (BV.add_tf,             fn (y, [_, Ty.DIM d, Ty.SHAPE dd], xs) =>
                                          [assignEin(y, Mk.addTF(d, dd), xs)]),
                (BV.sub_tt,             fn (y, [shp], xs) => let
                                          val ty1 as DstTy.TensorTy dd1 = shapeVarToTensor shp
                                          val rator = Mk.subTT dd1
                                          in
                                            [assignEin(y, rator, xs)]
                                          end),
                (BV.sub_ff,             fn (y, [_, Ty.DIM d, Ty.SHAPE dd], xs) =>
                                          [assignEin(y, Mk.subFF(d, dd), xs)]),
                (BV.sub_ft,             fn (y, [_, Ty.DIM d, Ty.SHAPE dd], [x1, x2]) =>
                                          [assignEin(y, Mk.subFT(d, dd), [x2, x1])]),
                (BV.sub_tf,             fn (y, [_, Ty.DIM d, Ty.SHAPE dd], xs) =>
                                          [assignEin(y, Mk.subTF(d, dd), xs)]),
                (BV.mul_rr,             fn (y, _, args) => [assignEin(y, Mk.mulRR, args)]),
                (BV.mul_rt,             fn (y, [shp], xs) => let
                                          val ty1 as DstTy.TensorTy dd1 = shapeVarToTensor shp
                                          val rator = Mk.mulRT(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.mulRT dd1
                                          in
                                            [assignEin(y, rator, [r, t])]
                                          end),
                (BV.mul_rf,             fn (y, [_, Ty.DIM d, Ty.SHAPE dd], xs) =>
                                          [assignEin(y, Mk.mulRF(d, dd), xs)]),
                (BV.mul_fr,             fn (y, [_, Ty.DIM d, Ty.SHAPE dd], [f, s]) =>
                                          [assignEin(y, Mk.mulRF(d, dd), [s, f])]),
                (BV.mul_ss,             fn (y, [_, Ty.DIM d], xs) =>
                                          [assignEin(y, Mk.mulSS d, xs)]),
                (BV.mul_sf,             fn (y, [_, Ty.DIM d, Ty.SHAPE dd], xs) =>
                                          [assignEin(y, Mk.mulSF(d, dd), xs)]),
                (BV.mul_fs,             fn (y, [_, Ty.DIM d, Ty.SHAPE dd], [s, f]) =>
                                          [assignEin(y, Mk.mulSF(d, dd), [f, s])]),
                (BV.mul_st,             fn (y, [_, Ty.DIM d, Ty.SHAPE dd], xs) =>
                                          [assignEin(y, Mk.mulST(d, dd), List.rev xs)]),
                (BV.mul_ts,             fn (y, [_, Ty.DIM d, Ty.SHAPE dd], xs) =>
                                          [assignEin(y, Mk.mulST(d, dd), xs)]),
                (BV.div_rr,             fn (y, _, args) => [assignEin(y, Mk.divRR, args)]),
                (BV.div_tr,             fn (y, [shp], xs) => let
                                          val ty1 as DstTy.TensorTy dd1 = shapeVarToTensor shp
                                          val rator = Mk.divTR dd1
                                          in
                                            [assignEin(y, rator, xs)]
                                          end),
                (BV.div_fr,             fn (y, [_, Ty.DIM d, Ty.SHAPE dd], xs) =>
                                          [assignEin(y, Mk.divFR(d, dd), xs)]),
                (BV.div_fs,             fn (y, [_, _, Ty.DIM d, Ty.SHAPE dd], xs) =>
                                          [assignEin(y, Mk.divFS(d, dd), xs)]),
                (BV.div_ss,             fn (y, [_, Ty.DIM d], xs) =>
                                          [assignEin(y, Mk.divSS d, xs)]),
                (BV.pow_ri,             simpleOp Op.Power),
                (BV.pow_rr,             fn (y, _, args) =>
                                            assign(y, Op.MathFn MathFns.POW, args)),
                (BV.pow_si,             fn (y, [_, Ty.DIM d1], [f, n]) => let
                                          fun getN x  = (case IR.Var.getDef x
                                                 of IR.LIT(Literal.Int n) => IntInf.toInt n
                                                  | _ => raise Fail "impossible"
                                                (* end case *))
                                          in
                                            [assignEin(y, Mk.powFI(d1, getN n), [f])]
                                          end),
                (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_t,              fn (y, [shp], xs) => let
                                          val ty1 as DstTy.TensorTy dd1 = shapeVarToTensor shp
                                          val rator = Mk.negTT dd1
                                          in
                                            [assignEin(y, rator, xs)]
                                          end),
                (BV.neg_f,              fn (y, [_, Ty.DIM d, Ty.SHAPE dd], xs) =>
                                          [assignEin(y, Mk.negFF(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) =>
                                          if (d = 2) orelse (d = 3)
                                            then [assignEin(y, Mk.grad [d], xs)]
                                            else raise Fail "unsupported gradient"),
                (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_t,          fn (y, [sv], xs) => let
                                          val DstTy.TensorTy dd1 = shapeVarToTensor sv
                                          in
                                            case (dd1,xs)
                                             of ([], [arg0]) => [IR.ASSGN(y, IR.VAR arg0)]
                                              | _ => [assignEin(y, Mk.normT dd1, xs)]
                                            (* end case *)
                                          end),
                (BV.op_norm_f,          fn (y, [ _,Ty.DIM d1, Ty.SHAPE dd1], xs) => (case (dd1, xs)
                                           of ([], [arg0]) => [IR.ASSGN(y, IR.VAR arg0)]
                                            | _ => [assignEin(y, Mk.normF(d1, dd1), xs)]
                                          (* end case *))),
                (BV.op_not,             simpleOp Op.Not),
                (BV.op_cross3_tt,       simpleEOp Mk.cross3TT),
                (BV.op_cross2_tt,       simpleEOp Mk.cross2TT),
                (BV.op_cross2_ff,       simpleEOp Mk.cross2FF),
                (BV.op_cross3_ff,       simpleEOp Mk.cross3FF),
                (BV.op_outer_tt,        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.outerTT(dd1, dd2)), xs)]
                                          end),
                (BV.op_outer_tf,        fn (y, [_, Ty.DIM d, sh1, Ty.SHAPE dd2, _], xs) => let
                                          val ty1 as DstTy.TensorTy dd1 = shapeVarToTensor sh1
                                          in
                                            [assignEin(y, Mk.outerTF(d, dd1, dd2), xs)]
                                          end),
                (BV.op_outer_ft,        fn (y, [_, Ty.DIM d, Ty.SHAPE dd1, sh2, _], xs) => let
                                          val ty1 as DstTy.TensorTy dd2 = shapeVarToTensor sh2
                                          in
                                            [assignEin(y, Mk.outerFT(d, dd1, dd2), xs)]
                                          end),
                (BV.op_outer_ff,        fn (y, [_, _, Ty.DIM d, Ty.SHAPE dd1, Ty.SHAPE dd2, _], xs) =>
                                          [assignEin(y, Mk.outerFF(d, dd1, dd2), xs)]),
                (BV.op_inner_tt,        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.innerTT(dd1, dd2)), xs)]
                                          end),
                (BV.op_inner_tf,        fn (y, [_, Ty.DIM d, sh1, Ty.SHAPE dd2, _], xs) =>let
                                          val ty1 as DstTy.TensorTy dd1 = shapeVarToTensor sh1
                                          in
                                            [assignEin(y, Mk.innerTF(dd1, d, dd2), xs)]
                                          end),
                (BV.op_inner_ft,        fn (y, [_, Ty.DIM d, Ty.SHAPE dd1, sh2, _], xs) =>let
                                          val ty1 as DstTy.TensorTy dd2 = shapeVarToTensor sh2
                                          in
                                            [assignEin(y, Mk.innerFT(dd1, d, dd2), xs)]
                                          end),
                (BV.op_inner_ff,        fn (y,  [_, _, Ty.DIM d, Ty.SHAPE dd1, Ty.SHAPE dd2, _], xs) =>
                                          [assignEin(y, Mk.innerFF(dd1, d, dd2), xs)]),
                (BV.op_colon_tt,        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.colonTT(dd1, dd2), xs)]
                                          end),
                (BV.op_colon_ft,        fn (y, [_, Ty.SHAPE dd1, Ty.DIM d, Ty.SHAPE dd2, _], xs) =>
                                          [assignEin(y, Mk.colonFT(d, dd1, dd2), xs)]),
                (BV.op_colon_tf,        fn (y, [_, Ty.SHAPE dd1, Ty.DIM d, Ty.SHAPE dd2, _], xs) =>
                                          [assignEin(y, Mk.colonTF(d, dd1, dd2), xs)]),
                (BV.op_colon_ff,        fn (y, [_, Ty.SHAPE dd1, Ty.DIM d, Ty.SHAPE dd2, _], xs) =>
                                          [assignEin(y, Mk.colonFF(d, dd1, dd2), xs)]),
                (*  modulate is vector * vector pointwise multiplication *)
                (BV.fn_modulate,        fn (y, [Ty.DIM dd1], xs) =>
                                          [assignEin(y, (Mk.modulate dd1), xs)]),
                (BV.fn_normalize_t,     fn (y, [shp], xs) => let
                                          val DstTy.TensorTy dd1 = shapeVarToTensor shp
                                          in
                                            case (dd1, xs)
(* FIXME: this assignment is incorrect (there should be an absolute-value), but I don't
 * think that this case should ever arise.  Same for fn_normalize_f.
 *)
                                             of ([], [x]) => [IR.ASSGN(y, IR.VAR x)]
                                              | (_, [_]) => [assignEin(y, Mk.normalizeTT dd1, xs@xs)]
                                            (* end case *)
                                          end),
                (BV.fn_normalize_f,     fn (y, [ _,Ty.DIM d1, Ty.SHAPE dd1], xs) => (case (dd1, xs)
                                           of ([], [arg0]) => [IR.ASSGN(y, IR.VAR arg0)]
                                            | (_, [arg0]) => [assignEin(y, Mk.normalizeFF(d1, dd1), xs@xs)]
                                          (* end case *))),
                (BV.fn_trace_t,         fn (y, [Ty.DIM d], xs) =>
                                          [assignEin(y, (Mk.traceT d), xs)]),
                (BV.fn_trace_f,         fn (y, [_, Ty.DIM d, Ty.SHAPE dd], xs) =>
                                          [assignEin(y, Mk.traceF(d, dd), xs)]),
                (BV.fn_transpose_t,     fn (y, [Ty.DIM d1, Ty.DIM d2], xs) =>
                                          [assignEin(y, (Mk.transposeT [d1, d2]), xs)]),
                (BV.fn_transpose_f,     fn (y, [_, Ty.DIM d1, Ty.DIM d2, Ty.DIM d3], xs) =>
                                          [assignEin(y, (Mk.transposeF (d1, d2, d3)), xs)]),
                (BV.fn_det2_t,          simpleEOp (Mk.det2T)),
                (BV.fn_det3_t,          simpleEOp (Mk.det3T)),
                (BV.fn_det2_f,          simpleEOp (Mk.det2F)),
                (BV.fn_det3_f,          simpleEOp (Mk.det3F)),
                (BV.fn_sqrt_r,          fn (y, _, xs) =>
                                          [assignEin(y, Mk.sqrtR, xs)]),
                (BV.fn_sqrt_s,          fn (y, [_, Ty.DIM d1], xs) =>
                                          [assignEin(y, Mk.sqrtF d1, xs)]),
                (BV.fn_cos_r,           fn (y, _, xs) =>
                                          [assignEin(y, Mk.cosR, xs)]),
                (BV.fn_cos_s,           fn (y, [_, Ty.DIM d1], xs) =>
                                          [assignEin(y, Mk.cosF d1, xs)]),
                (BV.fn_acos_r,           fn (y, _, xs) =>
                                          [assignEin(y, Mk.acosR, xs)]),
                (BV.fn_acos_s,          fn (y, [_, Ty.DIM d1], xs) =>
                                          [assignEin(y, Mk.acosF d1, xs)]),
                (BV.fn_sin_r,           fn (y, _, xs) =>
                                          [assignEin(y, Mk.sinR, xs)]),
                (BV.fn_sin_s,           fn (y, [_, Ty.DIM d1], xs) =>
                                          [assignEin(y, Mk.sinF d1, xs)]),
                (BV.fn_asin_r,          fn (y, _, xs) =>
                                          [assignEin(y, Mk.asinR, xs)]),
                (BV.fn_asin_s,          fn (y, [_, Ty.DIM d1], xs) =>
                                          [assignEin(y, Mk.asinF d1, xs)]),
                (BV.fn_tan_r,           fn (y, _, xs) =>
                                          [assignEin(y, Mk.tanR, xs)]),
                (BV.fn_tan_s,           fn (y, [_, Ty.DIM d1], xs) =>
                                          [assignEin(y, Mk.tanF d1, xs)]),
                (BV.fn_atan_r,          fn (y, _, xs) =>
                                          [assignEin(y, Mk.atanR, xs)]),
                (BV.fn_atan_s,          fn (y, [_, Ty.DIM d1], xs) =>
                                          [assignEin(y, Mk.atanF d1, xs)]),
                (BV.fn_exp_r,           fn (y, _, xs) =>
                                          [assignEin(y, Mk.expT, xs)]),
                (BV.fn_exp_s,           fn (y, [_, Ty.DIM d1], xs) =>
                                          [assignEin(y, Mk.expF d1, xs)]),
                (BV.fn_inside,          fn (y, [_, Ty.DIM d, _], xs) => assign(y, Op.Inside d, xs)),
(* FIXME:
                (BV.clamp_trr,          fn (y, [sv, dv], [x, lo, hi]) => let
					  in [
					  ] end),
*)
                (BV.clamp_ttt,          tensorOp Op.Clamp),
                (BV.lerp3,              tensorOp Op.Lerp),
                (BV.lerp5,              fn (y, [sv], [a, b, x0, x, x1]) => let
                                          val t1 = IR.Var.new("t1", DstTy.realTy)
                                          val t2 = IR.Var.new("t2", DstTy.realTy)
                                          val t3 = IR.Var.new("t3", DstTy.realTy)
                                          in [
                                            assignEin(t1, Mk.subRR, [x, x0]),
                                            assignEin(t2, Mk.subRR, [x1, x0]),
                                            assignEin(t3, Mk.divRR, [t1, t2]),
                                            IR.ASSGN(y, IR.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_abs_i,           simpleOp (Op.Abs DstTy.IntTy)),
                (BV.fn_abs_r,           simpleOp (Op.Abs DstTy.realTy)),
                (BV.fn_max_i,           simpleOp (Op.Max DstTy.IntTy)),
                (BV.fn_max_r,           simpleOp (Op.Max DstTy.realTy)),
                (BV.fn_min_i,           simpleOp (Op.Min DstTy.IntTy)),
                (BV.fn_min_r,           simpleOp (Op.Min DstTy.realTy)),
                (BV.kn_bspln3,          kernel Kernel.bspln3),
                (BV.kn_bspln5,          kernel Kernel.bspln5),
                (BV.kn_ctmr,            kernel Kernel.ctmr),
                (BV.kn_c4hexic,         kernel Kernel.c4hexic),
                (BV.kn_tent,            kernel Kernel.tent),
                (BV.i2r,                simpleOp Op.IntToReal),
                (BV.identity,           fn (y, [Ty.DIM d], xs) =>
                                          [assignEin(y, Mk.identity d, xs)]),
(* FIXME: eventually zero should be implemented by Ein
                (BV.zero,               fn (y, [Ty.SHAPE dd], []) =>
                                          [assignEin(y, Mk.zeros dd, [])]),
*)
                (BV.zero,               fn (y, [sv], []) =>
                                          assign(y, Op.Zero(shapeVarToTensor sv), [])),
                (BV.nan,                fn (y, [Ty.SHAPE dd], []) => let
                                            val nan = IR.LIT(Literal.Real(RealLit.nan))
                                            fun mk (y, [], stms) = IR.ASSGN(y, nan) :: stms
                                              | mk (y, d::dd, stms) = let
                                                  val ty = shapeVarToTensor(Ty.SHAPE dd)
                                                  val zs = List.tabulate(d, fn _ => IR.Var.new("_nan", ty))
                                                  in
                                                    IR.ASSGN(y, IR.CONS(zs, IR.Var.ty y)) ::
                                                      List.foldl (fn (z, stms) => mk(z, dd, stms)) stms zs
                                                  end
                                            in
                                              List.rev (mk (y, dd, []))
                                            end),
              (* sequence operations *)
                (BV.subscript,          fn (y, [tv, Ty.DIM d], args) =>
                                          assign(y,
                                            Op.Subscript(DstTy.SeqTy(trType tv, SOME d)),
                                            args)),
                (BV.dynSubscript,       fn (y, [tv], args) =>
                                          assign(y, Op.Subscript(DstTy.SeqTy(trType tv, NONE)), args)),
                (BV.at_Td,              fn (y, [tv], args) => assign(y, Op.Prepend(trType tv), args)),
                (BV.at_dT,              fn (y, [tv], args) => assign(y, Op.Append(trType tv), args)),
                (BV.at_dd,              fn (y, [tv], args) => assign(y, Op.Concat(trType tv), args)),
                (BV.range,              fn (y, _, args) => assign(y, Op.Range, args)),
                (BV.fn_length,          fn (y, [tv], [s]) => assign(y, Op.Length(trType tv), [s])),
              (* image operations *)
                (BV.fn_size,            fn (y, [Ty.DIM d, _], [img]) => let
                                          val DstTy.ImageTy info = IR.Var.ty img
                                        (* we extract each dimension separately and then build the sequence value *)
                                          val dims = List.tabulate(d, fn i => IR.Var.new("i"^Int.toString i, DstTy.IntTy))
                                          fun mkStms ([], _, stms) = stms (* in reverse order! *)
                                            | mkStms (d::dr, i, stms) = mkStms (dr, i+1,
                                                IR.ASSGN(d, IR.OP(Op.ImageDim(info, i), [img])) :: stms)
                                          in
                                            List.revAppend (mkStms (dims, 0, []), [
                                                IR.ASSGN(y, IR.SEQ(dims, DstTy.SeqTy(DstTy.intTy, SOME d)))
                                              ])
                                          end),
                (BV.image_border,       fn (y, _, args as [img, _]) => let
                                          val DstTy.ImageTy info = IR.Var.ty img
                                          in
                                            assign(y, Op.BorderCtlDefault info, args)
                                          end),
                (BV.image_clamp,        fn (y, _, args as [img]) => let
                                          val DstTy.ImageTy info = IR.Var.ty img
                                          in
                                            assign(y, Op.BorderCtlClamp info, args)
                                          end),
                (BV.image_mirror,       fn (y, _, args as [img]) => let
                                          val DstTy.ImageTy info = IR.Var.ty img
                                          in
                                            assign(y, Op.BorderCtlMirror info, args)
                                          end),
                (BV.image_wrap,         fn (y, _, args as [img]) => let
                                          val DstTy.ImageTy info = IR.Var.ty img
                                          in
                                            assign(y, Op.BorderCtlWrap info, args)
                                          end),
                (BV.dist2_t,           fn (y, _, xs) => dist(y, 2, xs)),
                (BV.dist3_t,           fn (y, _, xs) => dist(y, 3, xs)),
              (* reduction operators *)
                (BV.red_all,            fn (y, _, args as [e, v, k]) =>
                                          assign(y, Op.R_All(IR.Var.ty v), args)),
                (BV.red_exists,         fn (y, _, args as [e, v, k]) =>
                                          assign(y, Op.R_Exists(IR.Var.ty v), args)),
                (BV.red_max,            fn (y, _, args as [e, v, k]) =>
                                          assign(y, Op.R_Max(IR.Var.ty v), args)),
                (BV.red_mean,           fn (y, _, args as [e, v, k]) =>
                                          assign(y, Op.R_Mean(IR.Var.ty v), args)),
                (BV.red_min,            fn (y, _, args as [e, v, k]) =>
                                          assign(y, Op.R_Min(IR.Var.ty v), args)),
                (BV.red_product,        fn (y, _, args as [e, v, k]) =>
                                          assign(y, Op.R_Product(IR.Var.ty v),args)),
                (BV.red_sum,            fn (y, _, args as [e, v, k]) =>
                                          assign(y, Op.R_Sum(IR.Var.ty v), args)),
                (BV.red_variance,       fn (y, _, args as [e, v, k]) =>
                                          assign(y, Op.R_Variance(IR.Var.ty v), args)),
              (* spatial queries *)
                (BV.fn_sphere_im,       fn (y, [tv], args as [p, s]) =>
                                          assign(y, Op.SphereQuery(IR.Var.ty p, trType tv), args)),
                (BV.fn_sphere1_r,       fn (y, [tv], args as [p, s]) =>
                                          assign(y, Op.SphereQuery(IR.Var.ty p, trType tv), args)),
                (BV.fn_sphere2_t,       fn (y, [tv], args as [p, s]) =>
                                          assign(y, Op.SphereQuery(IR.Var.ty p, trType tv), args)),
                (BV.fn_sphere3_t,       fn (y, [tv], args as [p, s]) =>
                                          assign(y, Op.SphereQuery(IR.Var.ty p, trType tv), args)),
              (* math functions that have not been lifted *)
                (BV.fn_atan2_rr,        fn (y, _, args) =>
                                          assign(y, Op.MathFn MathFns.ATAN2, args)),
                (BV.fn_ceil_r,          fn (y, _, args) =>
                                          assign(y, Op.MathFn MathFns.CEIL, args)),
                (BV.fn_floor_r,         fn (y, _, args) =>
                                          assign(y, Op.MathFn MathFns.FLOOR, args)),
                (BV.fn_fmod_rr,         fn (y, _, args) =>
                                          assign(y, Op.MathFn MathFns.FMOD, args)),
                (BV.fn_erf_r,           fn (y, _, args) =>
                                          assign(y, Op.MathFn MathFns.ERF, args)),
                (BV.fn_erfc_r,          fn (y, _, args) =>
                                          assign(y, Op.MathFn MathFns.ERFC, args)),
                (BV.fn_log_r,           fn (y, _, args) =>
                                          assign(y, Op.MathFn MathFns.LOG, args)),
                (BV.fn_log10_r,         fn (y, _, args) =>
                                          assign(y, Op.MathFn MathFns.LOG10, args)),
                (BV.fn_log2_r,          fn (y, _, args) =>
                                          assign(y, Op.MathFn MathFns.LOG2, args)),
                (BV.fn_pow_rr,          fn (y, _, args) =>
                                          assign(y, Op.MathFn MathFns.POW, args))
              ];
            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 (", IR.Var.toString y, ", ",
Var.uniqueNameOf f, ", ...)\n"]); raise ex)

  end

root@smlnj-gforge.cs.uchicago.edu
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