use of org.apache.sysml.hops.BinaryOp in project incubator-systemml by apache.
the class RewriteAlgebraicSimplificationDynamic method simplifyWeightedDivMM.
private static Hop simplifyWeightedDivMM(Hop parent, Hop hi, int pos) {
Hop hnew = null;
boolean appliedPattern = false;
// note: we do not rewrite t(X)%*%(w*(X%*%v)) where w and v are vectors (see mmchain ops)
if (HopRewriteUtils.isMatrixMultiply(hi) && (hi.getInput().get(0) instanceof BinaryOp && HopRewriteUtils.isValidOp(((BinaryOp) hi.getInput().get(0)).getOp(), LOOKUP_VALID_WDIVMM_BINARY) || hi.getInput().get(1) instanceof BinaryOp && // not applied for vector-vector mult
hi.getDim2() > 1 && HopRewriteUtils.isValidOp(((BinaryOp) hi.getInput().get(1)).getOp(), LOOKUP_VALID_WDIVMM_BINARY))) {
Hop left = hi.getInput().get(0);
Hop right = hi.getInput().get(1);
// alternative pattern: t(U) %*% (W*(U%*%t(V)))
if (right instanceof BinaryOp && HopRewriteUtils.isValidOp(((BinaryOp) right).getOp(), LOOKUP_VALID_WDIVMM_BINARY) && // prevent mv
HopRewriteUtils.isEqualSize(right.getInput().get(0), right.getInput().get(1)) && HopRewriteUtils.isOuterProductLikeMM(right.getInput().get(1)) && // BLOCKSIZE CONSTRAINT
HopRewriteUtils.isSingleBlock(right.getInput().get(1).getInput().get(0), true)) {
Hop W = right.getInput().get(0);
Hop U = right.getInput().get(1).getInput().get(0);
Hop V = right.getInput().get(1).getInput().get(1);
if (HopRewriteUtils.isTransposeOfItself(left, U)) {
if (!HopRewriteUtils.isTransposeOperation(V))
V = HopRewriteUtils.createTranspose(V);
else
V = V.getInput().get(0);
boolean mult = ((BinaryOp) right).getOp() == OpOp2.MULT;
hnew = new QuaternaryOp(hi.getName(), DataType.MATRIX, ValueType.DOUBLE, OpOp4.WDIVMM, W, U, V, new LiteralOp(-1), 1, mult, false);
hnew.setOutputBlocksizes(W.getRowsInBlock(), W.getColsInBlock());
hnew.refreshSizeInformation();
// add output transpose for efficient target indexing (redundant t() removed by other rewrites)
hnew = HopRewriteUtils.createTranspose(hnew);
appliedPattern = true;
LOG.debug("Applied simplifyWeightedDivMM1 (line " + hi.getBeginLine() + ")");
}
}
// Pattern 1e) t(U) %*% (W/(U%*%t(V) + x))
if (!appliedPattern && // DIV
HopRewriteUtils.isBinary(right, LOOKUP_VALID_WDIVMM_BINARY[1]) && // prevent mv
HopRewriteUtils.isEqualSize(right.getInput().get(0), right.getInput().get(1)) && HopRewriteUtils.isBinary(right.getInput().get(1), Hop.OpOp2.PLUS) && right.getInput().get(1).getInput().get(1).getDataType() == DataType.SCALAR && HopRewriteUtils.isOuterProductLikeMM(right.getInput().get(1).getInput().get(0)) && // BLOCKSIZE CONSTRAINT
HopRewriteUtils.isSingleBlock(right.getInput().get(1).getInput().get(0).getInput().get(0), true)) {
Hop W = right.getInput().get(0);
Hop U = right.getInput().get(1).getInput().get(0).getInput().get(0);
Hop V = right.getInput().get(1).getInput().get(0).getInput().get(1);
Hop X = right.getInput().get(1).getInput().get(1);
if (HopRewriteUtils.isTransposeOfItself(left, U)) {
if (!HopRewriteUtils.isTransposeOperation(V))
V = HopRewriteUtils.createTranspose(V);
else
V = V.getInput().get(0);
hnew = new QuaternaryOp(hi.getName(), DataType.MATRIX, ValueType.DOUBLE, OpOp4.WDIVMM, W, U, V, X, 3, false, // 3=>DIV_LEFT_EPS
false);
hnew.setOutputBlocksizes(W.getRowsInBlock(), W.getColsInBlock());
hnew.refreshSizeInformation();
// add output transpose for efficient target indexing (redundant t() removed by other rewrites)
hnew = HopRewriteUtils.createTranspose(hnew);
appliedPattern = true;
LOG.debug("Applied simplifyWeightedDivMM1e (line " + hi.getBeginLine() + ")");
}
}
// alternative pattern: (W*(U%*%t(V))) %*% V
if (!appliedPattern && left instanceof BinaryOp && HopRewriteUtils.isValidOp(((BinaryOp) left).getOp(), LOOKUP_VALID_WDIVMM_BINARY) && // prevent mv
HopRewriteUtils.isEqualSize(left.getInput().get(0), left.getInput().get(1)) && HopRewriteUtils.isOuterProductLikeMM(left.getInput().get(1)) && // BLOCKSIZE CONSTRAINT
HopRewriteUtils.isSingleBlock(left.getInput().get(1).getInput().get(0), true)) {
Hop W = left.getInput().get(0);
Hop U = left.getInput().get(1).getInput().get(0);
Hop V = left.getInput().get(1).getInput().get(1);
if (HopRewriteUtils.isTransposeOfItself(right, V)) {
if (!HopRewriteUtils.isTransposeOperation(V))
V = right;
else
V = V.getInput().get(0);
boolean mult = ((BinaryOp) left).getOp() == OpOp2.MULT;
hnew = new QuaternaryOp(hi.getName(), DataType.MATRIX, ValueType.DOUBLE, OpOp4.WDIVMM, W, U, V, new LiteralOp(-1), 2, mult, false);
hnew.setOutputBlocksizes(W.getRowsInBlock(), W.getColsInBlock());
hnew.refreshSizeInformation();
appliedPattern = true;
LOG.debug("Applied simplifyWeightedDivMM2 (line " + hi.getBeginLine() + ")");
}
}
// Pattern 2e) (W/(U%*%t(V) + x)) %*% V
if (!appliedPattern && // DIV
HopRewriteUtils.isBinary(left, LOOKUP_VALID_WDIVMM_BINARY[1]) && // prevent mv
HopRewriteUtils.isEqualSize(left.getInput().get(0), left.getInput().get(1)) && HopRewriteUtils.isBinary(left.getInput().get(1), Hop.OpOp2.PLUS) && left.getInput().get(1).getInput().get(1).getDataType() == DataType.SCALAR && HopRewriteUtils.isOuterProductLikeMM(left.getInput().get(1).getInput().get(0)) && // BLOCKSIZE CONSTRAINT
HopRewriteUtils.isSingleBlock(left.getInput().get(1).getInput().get(0).getInput().get(0), true)) {
Hop W = left.getInput().get(0);
Hop U = left.getInput().get(1).getInput().get(0).getInput().get(0);
Hop V = left.getInput().get(1).getInput().get(0).getInput().get(1);
Hop X = left.getInput().get(1).getInput().get(1);
if (HopRewriteUtils.isTransposeOfItself(right, V)) {
if (!HopRewriteUtils.isTransposeOperation(V))
V = right;
else
V = V.getInput().get(0);
hnew = new QuaternaryOp(hi.getName(), DataType.MATRIX, ValueType.DOUBLE, OpOp4.WDIVMM, W, U, V, X, 4, false, // 4=>DIV_RIGHT_EPS
false);
hnew.setOutputBlocksizes(W.getRowsInBlock(), W.getColsInBlock());
hnew.refreshSizeInformation();
appliedPattern = true;
LOG.debug("Applied simplifyWeightedDivMM2e (line " + hi.getBeginLine() + ")");
}
}
// Pattern 3) t(U) %*% ((X!=0)*(U%*%t(V)-X))
if (!appliedPattern && // MULT
HopRewriteUtils.isBinary(right, LOOKUP_VALID_WDIVMM_BINARY[0]) && HopRewriteUtils.isBinary(right.getInput().get(1), OpOp2.MINUS) && HopRewriteUtils.isOuterProductLikeMM(right.getInput().get(1).getInput().get(0)) && right.getInput().get(1).getInput().get(1).getDataType() == DataType.MATRIX && // BLOCKSIZE CONSTRAINT
HopRewriteUtils.isSingleBlock(right.getInput().get(1).getInput().get(0).getInput().get(0), true)) {
Hop W = right.getInput().get(0);
Hop U = right.getInput().get(1).getInput().get(0).getInput().get(0);
Hop V = right.getInput().get(1).getInput().get(0).getInput().get(1);
Hop X = right.getInput().get(1).getInput().get(1);
if (// W-X constraint
HopRewriteUtils.isNonZeroIndicator(W, X) && // t(U)-U constraint
HopRewriteUtils.isTransposeOfItself(left, U)) {
if (!HopRewriteUtils.isTransposeOperation(V))
V = HopRewriteUtils.createTranspose(V);
else
V = V.getInput().get(0);
hnew = new QuaternaryOp(hi.getName(), DataType.MATRIX, ValueType.DOUBLE, OpOp4.WDIVMM, X, U, V, new LiteralOp(-1), 1, true, true);
hnew.setOutputBlocksizes(W.getRowsInBlock(), W.getColsInBlock());
hnew.refreshSizeInformation();
// add output transpose for efficient target indexing (redundant t() removed by other rewrites)
hnew = HopRewriteUtils.createTranspose(hnew);
appliedPattern = true;
LOG.debug("Applied simplifyWeightedDivMM3 (line " + hi.getBeginLine() + ")");
}
}
// Pattern 4) ((X!=0)*(U%*%t(V)-X)) %*% V
if (!appliedPattern && // MULT
HopRewriteUtils.isBinary(left, LOOKUP_VALID_WDIVMM_BINARY[0]) && HopRewriteUtils.isBinary(left.getInput().get(1), OpOp2.MINUS) && HopRewriteUtils.isOuterProductLikeMM(left.getInput().get(1).getInput().get(0)) && left.getInput().get(1).getInput().get(1).getDataType() == DataType.MATRIX && // BLOCKSIZE CONSTRAINT
HopRewriteUtils.isSingleBlock(left.getInput().get(1).getInput().get(0).getInput().get(0), true)) {
Hop W = left.getInput().get(0);
Hop U = left.getInput().get(1).getInput().get(0).getInput().get(0);
Hop V = left.getInput().get(1).getInput().get(0).getInput().get(1);
Hop X = left.getInput().get(1).getInput().get(1);
if (// W-X constraint
HopRewriteUtils.isNonZeroIndicator(W, X) && // V-t(V) constraint
HopRewriteUtils.isTransposeOfItself(right, V)) {
if (!HopRewriteUtils.isTransposeOperation(V))
V = right;
else
V = V.getInput().get(0);
hnew = new QuaternaryOp(hi.getName(), DataType.MATRIX, ValueType.DOUBLE, OpOp4.WDIVMM, X, U, V, new LiteralOp(-1), 2, true, true);
hnew.setOutputBlocksizes(W.getRowsInBlock(), W.getColsInBlock());
hnew.refreshSizeInformation();
appliedPattern = true;
LOG.debug("Applied simplifyWeightedDivMM4 (line " + hi.getBeginLine() + ")");
}
}
// Pattern 5) t(U) %*% (W*(U%*%t(V)-X))
if (!appliedPattern && // MULT
HopRewriteUtils.isBinary(right, LOOKUP_VALID_WDIVMM_BINARY[0]) && HopRewriteUtils.isBinary(right.getInput().get(1), OpOp2.MINUS) && HopRewriteUtils.isOuterProductLikeMM(right.getInput().get(1).getInput().get(0)) && right.getInput().get(1).getInput().get(1).getDataType() == DataType.MATRIX && // BLOCKSIZE CONSTRAINT
HopRewriteUtils.isSingleBlock(right.getInput().get(1).getInput().get(0).getInput().get(0), true)) {
Hop W = right.getInput().get(0);
Hop U = right.getInput().get(1).getInput().get(0).getInput().get(0);
Hop V = right.getInput().get(1).getInput().get(0).getInput().get(1);
Hop X = right.getInput().get(1).getInput().get(1);
if (// t(U)-U constraint
HopRewriteUtils.isTransposeOfItself(left, U)) {
if (!HopRewriteUtils.isTransposeOperation(V))
V = HopRewriteUtils.createTranspose(V);
else
V = V.getInput().get(0);
// note: x and w exchanged compared to patterns 1-4, 7
hnew = new QuaternaryOp(hi.getName(), DataType.MATRIX, ValueType.DOUBLE, OpOp4.WDIVMM, W, U, V, X, 1, true, true);
hnew.setOutputBlocksizes(W.getRowsInBlock(), W.getColsInBlock());
hnew.refreshSizeInformation();
// add output transpose for efficient target indexing (redundant t() removed by other rewrites)
hnew = HopRewriteUtils.createTranspose(hnew);
appliedPattern = true;
LOG.debug("Applied simplifyWeightedDivMM5 (line " + hi.getBeginLine() + ")");
}
}
// Pattern 6) (W*(U%*%t(V)-X)) %*% V
if (!appliedPattern && // MULT
HopRewriteUtils.isBinary(left, LOOKUP_VALID_WDIVMM_BINARY[0]) && HopRewriteUtils.isBinary(left.getInput().get(1), OpOp2.MINUS) && HopRewriteUtils.isOuterProductLikeMM(left.getInput().get(1).getInput().get(0)) && left.getInput().get(1).getInput().get(1).getDataType() == DataType.MATRIX && // BLOCKSIZE CONSTRAINT
HopRewriteUtils.isSingleBlock(left.getInput().get(1).getInput().get(0).getInput().get(0), true)) {
Hop W = left.getInput().get(0);
Hop U = left.getInput().get(1).getInput().get(0).getInput().get(0);
Hop V = left.getInput().get(1).getInput().get(0).getInput().get(1);
Hop X = left.getInput().get(1).getInput().get(1);
if (// V-t(V) constraint
HopRewriteUtils.isTransposeOfItself(right, V)) {
if (!HopRewriteUtils.isTransposeOperation(V))
V = right;
else
V = V.getInput().get(0);
// note: x and w exchanged compared to patterns 1-4, 7
hnew = new QuaternaryOp(hi.getName(), DataType.MATRIX, ValueType.DOUBLE, OpOp4.WDIVMM, W, U, V, X, 2, true, true);
hnew.setOutputBlocksizes(W.getRowsInBlock(), W.getColsInBlock());
hnew.refreshSizeInformation();
appliedPattern = true;
LOG.debug("Applied simplifyWeightedDivMM6 (line " + hi.getBeginLine() + ")");
}
}
}
// Pattern 7) (W*(U%*%t(V)))
if (!appliedPattern && // MULT
HopRewriteUtils.isBinary(hi, LOOKUP_VALID_WDIVMM_BINARY[0]) && // prevent mv
HopRewriteUtils.isEqualSize(hi.getInput().get(0), hi.getInput().get(1)) && // not applied for vector-vector mult
hi.getDim2() > 1 && hi.getInput().get(0).getDataType() == DataType.MATRIX && hi.getInput().get(0).getDim2() > hi.getInput().get(0).getColsInBlock() && HopRewriteUtils.isOuterProductLikeMM(hi.getInput().get(1)) && // no mmchain
(((AggBinaryOp) hi.getInput().get(1)).checkMapMultChain() == ChainType.NONE || hi.getInput().get(1).getInput().get(1).getDim2() > 1) && // BLOCKSIZE CONSTRAINT
HopRewriteUtils.isSingleBlock(hi.getInput().get(1).getInput().get(0), true)) {
Hop W = hi.getInput().get(0);
Hop U = hi.getInput().get(1).getInput().get(0);
Hop V = hi.getInput().get(1).getInput().get(1);
// W is sparse and U/V unknown or dense; or if U/V are dense
if ((HopRewriteUtils.isSparse(W) && !HopRewriteUtils.isSparse(U) && !HopRewriteUtils.isSparse(V)) || (HopRewriteUtils.isDense(U) && HopRewriteUtils.isDense(V))) {
V = !HopRewriteUtils.isTransposeOperation(V) ? HopRewriteUtils.createTranspose(V) : V.getInput().get(0);
hnew = new QuaternaryOp(hi.getName(), DataType.MATRIX, ValueType.DOUBLE, OpOp4.WDIVMM, W, U, V, new LiteralOp(-1), 0, true, false);
hnew.setOutputBlocksizes(W.getRowsInBlock(), W.getColsInBlock());
hnew.refreshSizeInformation();
appliedPattern = true;
LOG.debug("Applied simplifyWeightedDivMM7 (line " + hi.getBeginLine() + ")");
}
}
// relink new hop into original position
if (hnew != null) {
HopRewriteUtils.replaceChildReference(parent, hi, hnew, pos);
hi = hnew;
}
return hi;
}
use of org.apache.sysml.hops.BinaryOp in project incubator-systemml by apache.
the class RewriteAlgebraicSimplificationDynamic method simplifyScalarMVBinaryOperation.
private static Hop simplifyScalarMVBinaryOperation(Hop hi) {
if (// e.g., X * s
hi instanceof BinaryOp && ((BinaryOp) hi).supportsMatrixScalarOperations() && hi.getInput().get(0).getDataType() == DataType.MATRIX && hi.getInput().get(1).getDataType() == DataType.MATRIX) {
Hop right = hi.getInput().get(1);
// X * s -> X * as.scalar(s)
if (// scalar right
HopRewriteUtils.isDimsKnown(right) && right.getDim1() == 1 && right.getDim2() == 1) {
// remove link to right child and introduce cast
UnaryOp cast = HopRewriteUtils.createUnary(right, OpOp1.CAST_AS_SCALAR);
HopRewriteUtils.replaceChildReference(hi, right, cast, 1);
LOG.debug("Applied simplifyScalarMVBinaryOperation.");
}
}
return hi;
}
use of org.apache.sysml.hops.BinaryOp in project incubator-systemml by apache.
the class RewriteAlgebraicSimplificationDynamic method pushdownSumOnAdditiveBinary.
/**
* patterns: sum(A+B)->sum(A)+sum(B); sum(A-B)->sum(A)-sum(B)
*
* @param parent the parent high-level operator
* @param hi high-level operator
* @param pos position
* @return high-level operator
*/
private static Hop pushdownSumOnAdditiveBinary(Hop parent, Hop hi, int pos) {
// all patterns headed by full sum over binary operation
if (// full sum root over binaryop
hi instanceof AggUnaryOp && ((AggUnaryOp) hi).getDirection() == Direction.RowCol && ((AggUnaryOp) hi).getOp() == AggOp.SUM && hi.getInput().get(0) instanceof BinaryOp && // single parent
hi.getInput().get(0).getParent().size() == 1) {
BinaryOp bop = (BinaryOp) hi.getInput().get(0);
Hop left = bop.getInput().get(0);
Hop right = bop.getInput().get(1);
if (// dims(A) == dims(B)
HopRewriteUtils.isEqualSize(left, right) && left.getDataType() == DataType.MATRIX && right.getDataType() == DataType.MATRIX) {
OpOp2 applyOp = (// pattern a: sum(A+B)->sum(A)+sum(B)
bop.getOp() == OpOp2.PLUS || // pattern b: sum(A-B)->sum(A)-sum(B)
bop.getOp() == OpOp2.MINUS) ? bop.getOp() : null;
if (applyOp != null) {
// create new subdag sum(A) bop sum(B)
AggUnaryOp sum1 = HopRewriteUtils.createSum(left);
AggUnaryOp sum2 = HopRewriteUtils.createSum(right);
BinaryOp newBin = HopRewriteUtils.createBinary(sum1, sum2, applyOp);
// rewire new subdag
HopRewriteUtils.replaceChildReference(parent, hi, newBin, pos);
HopRewriteUtils.cleanupUnreferenced(hi, bop);
hi = newBin;
LOG.debug("Applied pushdownSumOnAdditiveBinary.");
}
}
}
return hi;
}
use of org.apache.sysml.hops.BinaryOp in project incubator-systemml by apache.
the class RewriteAlgebraicSimplificationStatic method simplifyTransposeAggBinBinaryChains.
/**
* Patterns: t(t(A)%*%t(B)+C) -> B%*%A+t(C)
*
* @param parent parent high-level operator
* @param hi high-level operator
* @param pos position
* @return high-level operator
*/
private static Hop simplifyTransposeAggBinBinaryChains(Hop parent, Hop hi, int pos) {
if (HopRewriteUtils.isTransposeOperation(hi) && // basic binary
hi.getInput().get(0) instanceof BinaryOp && ((BinaryOp) hi.getInput().get(0)).supportsMatrixScalarOperations()) {
Hop left = hi.getInput().get(0).getInput().get(0);
Hop C = hi.getInput().get(0).getInput().get(1);
// check matrix mult and both inputs transposes w/ single consumer
if (left instanceof AggBinaryOp && C.getDataType().isMatrix() && HopRewriteUtils.isTransposeOperation(left.getInput().get(0)) && left.getInput().get(0).getParent().size() == 1 && HopRewriteUtils.isTransposeOperation(left.getInput().get(1)) && left.getInput().get(1).getParent().size() == 1) {
Hop A = left.getInput().get(0).getInput().get(0);
Hop B = left.getInput().get(1).getInput().get(0);
AggBinaryOp abop = HopRewriteUtils.createMatrixMultiply(B, A);
ReorgOp rop = HopRewriteUtils.createTranspose(C);
BinaryOp bop = HopRewriteUtils.createBinary(abop, rop, OpOp2.PLUS);
HopRewriteUtils.replaceChildReference(parent, hi, bop, pos);
hi = bop;
LOG.debug("Applied simplifyTransposeAggBinBinaryChains (line " + hi.getBeginLine() + ").");
}
}
return hi;
}
use of org.apache.sysml.hops.BinaryOp in project incubator-systemml by apache.
the class RewriteAlgebraicSimplificationStatic method simplifyBushyBinaryOperation.
/**
* (X*(Y*(Z%*%v))) -> (X*Y)*(Z%*%v)
* (X+(Y+(Z%*%v))) -> (X+Y)+(Z%*%v)
*
* Note: Restriction ba() at leaf and root instead of data at leaf to not reorganize too
* eagerly, which would loose additional rewrite potential. This rewrite has two goals
* (1) enable XtwXv, and increase piggybacking potential by creating bushy trees.
*
* @param parent parent high-level operator
* @param hi high-level operator
* @param pos position
* @return high-level operator
*/
private static Hop simplifyBushyBinaryOperation(Hop parent, Hop hi, int pos) {
if (hi instanceof BinaryOp && parent instanceof AggBinaryOp) {
BinaryOp bop = (BinaryOp) hi;
Hop left = bop.getInput().get(0);
Hop right = bop.getInput().get(1);
OpOp2 op = bop.getOp();
if (left.getDataType() == DataType.MATRIX && right.getDataType() == DataType.MATRIX && HopRewriteUtils.isValidOp(op, LOOKUP_VALID_ASSOCIATIVE_BINARY)) {
boolean applied = false;
if (right instanceof BinaryOp) {
BinaryOp bop2 = (BinaryOp) right;
Hop left2 = bop2.getInput().get(0);
Hop right2 = bop2.getInput().get(1);
OpOp2 op2 = bop2.getOp();
if (op == op2 && right2.getDataType() == DataType.MATRIX && (right2 instanceof AggBinaryOp)) {
// (X*(Y*op()) -> (X*Y)*op()
BinaryOp bop3 = HopRewriteUtils.createBinary(left, left2, op);
BinaryOp bop4 = HopRewriteUtils.createBinary(bop3, right2, op);
HopRewriteUtils.replaceChildReference(parent, bop, bop4, pos);
HopRewriteUtils.cleanupUnreferenced(bop, bop2);
hi = bop4;
applied = true;
LOG.debug("Applied simplifyBushyBinaryOperation1");
}
}
if (!applied && left instanceof BinaryOp) {
BinaryOp bop2 = (BinaryOp) left;
Hop left2 = bop2.getInput().get(0);
Hop right2 = bop2.getInput().get(1);
OpOp2 op2 = bop2.getOp();
if (op == op2 && left2.getDataType() == DataType.MATRIX && (left2 instanceof AggBinaryOp) && // X not vector, or Y vector
(right2.getDim2() > 1 || right.getDim2() == 1) && // X not vector, or Y vector
(right2.getDim1() > 1 || right.getDim1() == 1)) {
// ((op()*X)*Y) -> op()*(X*Y)
BinaryOp bop3 = HopRewriteUtils.createBinary(right2, right, op);
BinaryOp bop4 = HopRewriteUtils.createBinary(left2, bop3, op);
HopRewriteUtils.replaceChildReference(parent, bop, bop4, pos);
HopRewriteUtils.cleanupUnreferenced(bop, bop2);
hi = bop4;
LOG.debug("Applied simplifyBushyBinaryOperation2");
}
}
}
}
return hi;
}
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