added pil examples

privacy-scaling-explorations · Oct 30, 2023 · 8803c3a · 8803c3a
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diff --git a/examples/fibonacci.pil b/examples/fibonacci.pil
@@ -0,0 +1,54 @@
+// each step instance is a row
+
+constant %NUM_STEPS = 10; // pragma_num_steps
+
+// each circuit is a namespace
+namespace Fibonacci(%NUM_STEPS); // apply num_steps to the circuit
+    // declare internal and forward signals
+    col witness a, b, c, n;
+
+    // convert TraceWitness StepInstance to the following fixed columns
+    col fixed fibo_first_step = [1, 0, 0, 0, 0, 0, 0, 0, 0, 0];
+    col fixed fibo_step = [0, 1, 1, 1, 1, 1, 1, 0, 0, 0];
+    col fixed padding = [0, 0, 0, 0, 0, 0, 0, 1, 1, 1];
+
+    // need this fixed column in all circuits to disable next in the last row, because they rotate to the first row
+    // also need it for pragma_last_step
+    col fixed ISLAST(i) { match i {
+        %NUM_STEPS - 1 => 1,
+        _ => 0,
+    } };
+
+    // need this fixed column for pragma_first_step
+    col fixed ISFIRST(i) { match i { 
+        0 => 1, 
+        _ => 0,
+    } };
+
+    // fibo_first_step setup
+    fibo_first_step * (a - 1) = 0;
+    fibo_first_step * (b - 1) = 0;
+    fibo_first_step * (a + b - c) = 0;
+    fibo_first_step * (b - a') = 0;
+    fibo_first_step * (c - b') = 0;
+    fibo_first_step * (n - n') = 0;
+
+    // fibo_step setup
+    fibo_step * (a + b - c) = 0;
+    fibo_step * (b - a') = 0;
+    fibo_step * (c - b') = 0;
+    fibo_step * (n - n') = 0;
+
+    // padding setup
+    // Note that (1 - ISLAST) is multiplied to the step type of the last step instance for transition constraints only
+    (1 - ISLAST) * padding * (b - b') = 0;
+    (1 - ISLAST) * padding * (n - n') = 0;
+
+    // circuit setup
+    // pragma_num_steps is already applied at the top
+    ISFIRST * (1 - fibo_first_step) = 0; // pragma_first_step
+    ISLAST * (1 - padding) = 0; // pragma_last_step
+    public out = b(%NUM_STEPS-1); // expose last
+
+    // trace input for first step instance
+    ISFIRST * (n - 7) = 0;
diff --git a/examples/mimc7.pil b/examples/mimc7.pil
@@ -0,0 +1,151 @@
+// don't need a supercircuit concepts, as variables among different circuits (namespaces) can be freely referred to each other
+constant %NUM_STEPS = 91;
+
+namespace Mimc7Circuit(%NUM_STEPS);
+    col witness x, k, c, xkc, y, row, out;
+
+    // can technically loop these as well but should write them all out as a general solution to convert them from TraceWitness StepInstance
+    col fixed mimc7_first_step = [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
+    col fixed mimc7_step = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0];
+    col fixed mimc7_last_step = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1];
+
+    col fixed ISLAST(i) { match i {
+        %NUM_STEPS - 1 => 1,
+        _ => 0,
+    } };
+
+    col fixed ISFIRST(i) { match i { 
+        0 => 1, 
+        _ => 0,
+    } };
+
+    // mimc7_first_step setup
+    mimc7_first_step * (x + k + c - xkc) = 0;
+    mimc7_first_step * (xkc * xkc * xkc * xkc * xkc * xkc * xkc - y) = 0;
+    mimc7_first_step * (y - x') = 0;
+    mimc7_first_step * (k - k') = 0;
+    mimc7_first_step * (Mimc7Circuit.row - 0) = 0;
+    mimc7_first_step * (row + 1 - row') = 0;
+    // convert the following from Lookup, mimc7_first_step is applied here so that we only do the lookup at this step type
+    mimc7_first_step {row, c} in {Mimc7Constants.lookup_row, Mimc7Constants.lookup_c};
+
+    // mimc7_step setup
+    mimc7_step * (x + k + c - xkc) = 0;
+    mimc7_step * (xkc * xkc * xkc * xkc * xkc * xkc * xkc - y) = 0;
+    mimc7_step * (y - x') = 0;
+    mimc7_step * (k - k') = 0;
+    mimc7_step * (row + 1 - row') = 0;
+    mimc7_step {row, c} in {Mimc7Constants.lookup_row, Mimc7Constants.lookup_c};
+
+    // mimc7_last_step setup
+    mimc7_last_step * (x + k - out) = 0;
+
+    // circuit setup
+    // pragma_num_steps is already applied at the top
+    ISFIRST * (1 - mimc7_first_step) = 0; // pragma_first_step
+    ISLAST * (1 - mimc7_last_step) = 0; // pragma_last_step
+
+    // trace input for first step instance
+    // x = 1, k = 2
+    ISFIRST * (x - 1) = 0;
+    ISFIRST * (k - 2) = 0;
+
+
+namespace Mimc7Constants(%NUM_STEPS);
+    // obtain these from the FixedAssignments struct
+    // can technically loop this as well but should write them all out as a general solution for converting from FixedAssignments
+    col fixed lookup_row = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90];
+    col fixed lookup_c = [
+        0,
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+        13602139229813231349386885113156901793661719180900395818909719758150455500533
+    ];
+    // there's only lookup, not lookup table abstraction in PIL, so the two fixed columns are good enough