(* 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 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 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 (* 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.Add DstTy.IntTy)), (BV.add_tt, tensorOp Op.Add), (BV.add_ff, fn (y, _, [f, g]) => assign(y, Op.AddField, [f, g])), (BV.add_fr, fn (y, _, [f, s]) => assign(y, Op.OffsetField, [f, s])), (BV.add_rf, fn (y, _, [s, f]) => assign(y, Op.OffsetField, [f, s])), (BV.sub_ii, simpleOp(Op.Sub DstTy.IntTy)), (BV.sub_tt, tensorOp Op.Sub), (BV.sub_ff, fn (y, _, [f, g]) => assign(y, Op.SubField, [f, g])), (BV.sub_fr, fn (y, _, [f, s]) => let val s' = IL.Var.copy s in [ IL.ASSGN(s', IL.OP(Op.Neg DstTy.realTy, [s])), IL.ASSGN(y, IL.OP(Op.OffsetField, [f, s'])) ] end), (BV.sub_rf, fn (y, _, [s, f]) => let val f' = IL.Var.copy f in [ IL.ASSGN(f', IL.OP(Op.NegField, [f])), IL.ASSGN(y, IL.OP(Op.OffsetField, [f', s])) ] end), (BV.mul_ii, simpleOp(Op.Mul DstTy.IntTy)), (BV.mul_rr, simpleOp(Op.Mul(DstTy.realTy))), (BV.mul_rt, tensorOp Op.Scale), (BV.mul_tr, fn (y, sv, [t, r]) => tensorOp Op.Scale (y, sv, [r, t])), (BV.mul_rf, fn (y, _, [s, f]) => assign(y, Op.ScaleField, [s, f])), (BV.mul_fr, fn (y, _, [f, s]) => assign(y, Op.ScaleField, [s, f])), (BV.div_ii, simpleOp(Op.Div DstTy.IntTy)), (BV.div_rr, simpleOp(Op.Div DstTy.realTy)), (BV.div_tr, fn (y, [sv], [x, s]) => let val one = IL.Var.new("one", DstTy.realTy) val s' = IL.Var.new("sInv", DstTy.realTy) in [ IL.ASSGN(one, IL.LIT(Literal.Float(FloatLit.one))), IL.ASSGN(s', IL.OP(Op.Div DstTy.realTy, [one, s])), IL.ASSGN(y, IL.OP(Op.Scale(shapeVarToTensor sv), [s', x])) ] end), (BV.div_fr, fn (y, _, [f, s]) => let val one = IL.Var.new("one", DstTy.realTy) val s' = IL.Var.new("sInv", DstTy.realTy) in [ IL.ASSGN(one, IL.LIT(Literal.Float(FloatLit.one))), IL.ASSGN(s', IL.OP(Op.Div DstTy.realTy, [one, s])), IL.ASSGN(y, IL.OP(Op.ScaleField, [s', f])) ] end), (BV.exp_ri, simpleOp(Op.Power)), (BV.exp_rr, basisFn MathFuns.pow), (BV.curl2D, fn (y, _, xs) => assign(y, Op.CurlField 2, xs)), (BV.curl3D, fn (y, _, xs) => assign(y, Op.CurlField 3, xs)), (BV.convolve_vk, fn (y, [_, Ty.DIM d, _], xs) => assign(y, Op.Field d, xs)), (BV.convolve_kv, fn (y, [_, Ty.DIM d, _], [k, v]) => assign(y, Op.Field d, [v, k])), (BV.neg_i, simpleOp(Op.Neg DstTy.IntTy)), (BV.neg_t, tensorOp Op.Neg), (BV.neg_f, fn (y, _, xs) => assign(y, Op.NegField, xs)), (BV.op_probe, fn (y, [_, dv, sv], xs) => assign(y, Op.Probe(dimVarToTensor dv, shapeVarToTensor sv), xs)), (BV.op_D, fn (y, _, xs) => assign(y, Op.DiffField, xs)), (BV.op_Dotimes, fn (y, _, xs) => assign(y, Op.DiffField, xs)), (BV.op_norm, fn (y, [sv], xs) => (case shapeVarToTensor sv of DstTy.TensorTy[] => assign(y, Op.Abs DstTy.realTy, xs) | ty => assign(y, Op.Norm ty, xs) (* end case *))), (BV.op_not, simpleOp Op.Not), (BV.op_cross, simpleOp Op.Cross), (BV.op_outer, fn (y, [Ty.DIM d1, Ty.DIM d2], xs) => assign (y, Op.Outer(DstTy.tensorTy[d1, d2]), xs)), (BV.op_inner, fn (y, [Ty.SHAPE dd1, Ty.SHAPE dd2, _], xs) => let val ty1 = DstTy.TensorTy dd1 val ty2 = DstTy.TensorTy dd2 val rator = (case (dd1, dd2) of ([d], [d']) => Op.Dot ty1 | ([d1], [d1', d2]) => Op.MulVecMat ty2 | ([d1, d2], [d2']) => Op.MulMatVec ty1 | ([d1, d2], [d2', d3]) => Op.MulMatMat(ty1, ty2) | ([d1], [d1', d2, d3]) => Op.MulVecTen3 ty2 | ([d1, d2, d3], [d3']) => Op.MulTen3Vec ty1 | _ => raise Fail(concat[ "unsupported inner-product: ", DstTy.toString ty1, " * ", DstTy.toString ty2 ]) (* end case *)) in assign (y, rator, xs) end), (BV.op_colon, fn (y, [sh1, sh2, _], xs) => let val ty1 = shapeVarToTensor sh1 val ty2 = shapeVarToTensor sh2 in assign (y, Op.ColonMul(ty1, ty2), xs) end), (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 [ IL.ASSGN(t1, IL.OP(Op.Sub DstTy.realTy, [x, x0])), IL.ASSGN(t2, IL.OP(Op.Sub DstTy.realTy, [x1, x0])), IL.ASSGN(t3, IL.OP(Op.Div DstTy.realTy, [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), (BV.fn_modulate, vectorOp Op.Mul), (BV.fn_normalize, vectorOp Op.Normalize), (BV.fn_principleEvec, vectorOp Op.PrincipleEvec), (BV.fn_trace, fn (y, [dv], xs) => assign(y, Op.Trace(dimVarToMatrix dv), xs)), (BV.fn_transpose, fn (y, [Ty.DIM d1, Ty.DIM d2], xs) => assign(y, Op.Transpose(d1, d2), 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], []) => assign(y, Op.Identity d, [])), (BV.zero, fn (y, [sv], []) => assign(y, Op.Zero(shapeVarToTensor sv), [])), (BV.subscript, fn (y, [tv, Ty.DIM d], args) => assign(y, Op.SeqSub(DstTy.SeqTy(trType tv, d)), 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