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80 lines
3.3 KiB
80 lines
3.3 KiB
/*
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This component finds the level where the oldInsert is done.
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The rules are:
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levIns[i] == 1 if its level and all the child levels have a sibling of 0 and
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the parent level has a sibling != 0. Considere that the root level always has
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a parent with a sibling != 0.
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┌──────────────┐
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│ │
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│ │───▶ levIns[0] <== (1-done[i])
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│ │
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└──────────────┘
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▲
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│
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│
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done[0]
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done[i-1] <== levIns[i] + done[i]
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▲
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│
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│
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┌───────────┐ ┌──────────────┐
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│ │ │ │
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sibling[i-1]───▶│IsZero[i-1]│─▶│ │───▶ levIns[i] <== (1-done[i])*(1-isZero[i-1].out)
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│ │ │ │
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└───────────┘ └──────────────┘
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▲
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│
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│
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done[i]
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done[n-2] <== levIns[n-1]
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▲
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│
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│
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┌───────────┐ ┌──────────────┐
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│ │ │ │
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sibling[n-2]───▶│IsZero[n-2]│─▶│ │────▶ levIns[n-1] <== (1-isZero[n-2].out)
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│ │ │ │
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└───────────┘ └──────────────┘
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┌───────────┐
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│ │
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sibling[n-1]───▶│IsZero[n-1]│────▶ === 0
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│ │
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└───────────┘
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*/
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template SMTLevIns(nLevels) {
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signal input siblins[nLevels];
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signal output levIns[nLevels];
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signal done[nLevels-1]; // Indicates if the insLevel has aready been detecetd.
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component isZero[nLevels];
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for (var i=0; i<nLevels; i++) {
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isZero[i] = IsZero();
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isZero[i].in <== siblings[i];
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}
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// The last level must always have a sibling of 0. If not, then it cannot be inserted.
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isZero[nLevels-2].out === 1;
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levIns[nLevels-1] <== (1-isZero[nLevels-2].out);
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done[nLevels-2] <== levIns[nLevels-1];
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for (var i=nLevels-2; i>0; i--) {
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levIns[i] <== (1-done[i])*(1-isZero[i-1].out)
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done[i-1] <== levIns[i] + done[i];
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}
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levIns[0] <== (1-done[0]);
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}
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