Add rotation test (#3430)

Inspired by the example in the [Jolt inlines
doc](https://jolt.a16zcrypto.com/how/optimizations/inlines.html).

Author: georgwiese

openvm/tests/apc_builder_complex.rs

@@ -183,3 +183,11 @@ fn copy_byte() {
     ];
     assert_machine_output(program.to_vec(), "copy_byte");
 }
+
+#[test]
+fn rotate() {
+    // Rotation, implemented as `(x >> imm) | (x << (32-imm))`
+    // for imm = 1
+    let program = [srl(1, 3, 1, 0), sll(2, 3, 31, 0), or(3, 1, 2, 1)];
+    assert_machine_output(program.to_vec(), "rotate");
+}

openvm/tests/apc_snapshots/complex/rotate.txt

@@ -0,0 +1,70 @@
+Instructions:
+  SRL rd_ptr = 1, rs1_ptr = 3, rs2 = 1, rs2_as = 0
+  SLL rd_ptr = 2, rs1_ptr = 3, rs2 = 31, rs2_as = 0
+  OR rd_ptr = 3, rs1_ptr = 1, rs2 = 2, rs2_as = 1
+
+APC advantage:
+  - Main columns: 142 -> 26 (5.46x reduction)
+  - Bus interactions: 68 -> 18 (3.78x reduction)
+  - Constraints: 174 -> 5 (34.80x reduction)
+
+Symbolic machine using 26 unique main columns:
+  from_state__timestamp_0
+  reads_aux__0__base__prev_timestamp_0
+  reads_aux__0__base__timestamp_lt_aux__lower_decomp__0_0
+  writes_aux__base__prev_timestamp_0
+  writes_aux__base__timestamp_lt_aux__lower_decomp__0_0
+  writes_aux__prev_data__0_0
+  writes_aux__prev_data__1_0
+  writes_aux__prev_data__2_0
+  writes_aux__prev_data__3_0
+  a__0_0
+  a__1_0
+  a__2_0
+  a__3_0
+  b__0_0
+  b__1_0
+  b__2_0
+  b__3_0
+  writes_aux__base__prev_timestamp_1
+  writes_aux__base__timestamp_lt_aux__lower_decomp__0_1
+  writes_aux__prev_data__0_1
+  writes_aux__prev_data__1_1
+  writes_aux__prev_data__2_1
+  writes_aux__prev_data__3_1
+  a__3_1
+  a__3_2
+  is_valid
+
+// Bus 0 (EXECUTION_BRIDGE):
+mult=is_valid * -1, args=[0, from_state__timestamp_0]
+mult=is_valid * 1, args=[12, from_state__timestamp_0 + 9]
+
+// Bus 1 (MEMORY):
+mult=is_valid * -1, args=[1, 3, b__0_0, b__1_0, b__2_0, b__3_0, reads_aux__0__base__prev_timestamp_0]
+mult=is_valid * -1, args=[1, 1, writes_aux__prev_data__0_0, writes_aux__prev_data__1_0, writes_aux__prev_data__2_0, writes_aux__prev_data__3_0, writes_aux__base__prev_timestamp_0]
+mult=is_valid * -1, args=[1, 2, writes_aux__prev_data__0_1, writes_aux__prev_data__1_1, writes_aux__prev_data__2_1, writes_aux__prev_data__3_1, writes_aux__base__prev_timestamp_1]
+mult=is_valid * 1, args=[1, 1, a__0_0, a__1_0, a__2_0, a__3_0, from_state__timestamp_0 + 6]
+mult=is_valid * 1, args=[1, 2, 0, 0, 0, a__3_1, from_state__timestamp_0 + 7]
+mult=is_valid * 1, args=[1, 3, a__0_0, a__1_0, a__2_0, a__3_2, from_state__timestamp_0 + 8]
+
+// Bus 3 (VARIABLE_RANGE_CHECKER):
+mult=is_valid * 1, args=[reads_aux__0__base__timestamp_lt_aux__lower_decomp__0_0, 17]
+mult=is_valid * 1, args=[15360 * reads_aux__0__base__prev_timestamp_0 + 15360 * reads_aux__0__base__timestamp_lt_aux__lower_decomp__0_0 + 15360 - 15360 * from_state__timestamp_0, 12]
+mult=is_valid * 1, args=[writes_aux__base__timestamp_lt_aux__lower_decomp__0_0, 17]
+mult=is_valid * 1, args=[15360 * writes_aux__base__prev_timestamp_0 + 15360 * writes_aux__base__timestamp_lt_aux__lower_decomp__0_0 - (15360 * from_state__timestamp_0 + 15360), 12]
+mult=is_valid * 1, args=[7864320 * a__3_1 - 1006632960 * b__0_0, 7]
+mult=is_valid * 1, args=[writes_aux__base__timestamp_lt_aux__lower_decomp__0_1, 17]
+mult=is_valid * 1, args=[15360 * writes_aux__base__prev_timestamp_1 + 15360 * writes_aux__base__timestamp_lt_aux__lower_decomp__0_1 - (15360 * from_state__timestamp_0 + 61440), 12]
+
+// Bus 6 (BITWISE_LOOKUP):
+mult=is_valid * 1, args=[a__3_0, a__3_1, 2 * a__3_2 - (a__3_0 + a__3_1), 1]
+mult=is_valid * 1, args=[a__0_0, a__1_0, 0, 0]
+mult=is_valid * 1, args=[a__2_0, 0, 0, 0]
+
+// Algebraic constraints:
+(b__0_0 + 256 * b__1_0 + 65536 * b__2_0 + 16777216 * b__3_0 - (2 * a__0_0 + 512 * a__1_0 + 131072 * a__2_0 + 33554432 * a__3_0)) * (b__0_0 + 256 * b__1_0 + 65536 * b__2_0 + 16777216 * b__3_0 - (2 * a__0_0 + 512 * a__1_0 + 131072 * a__2_0 + 33554432 * a__3_0 + 1)) = 0
+(b__1_0 + 256 * b__2_0 + 65536 * b__3_0 - (2 * a__1_0 + 512 * a__2_0 + 131072 * a__3_0)) * (b__1_0 + 256 * b__2_0 + 65536 * b__3_0 - (2 * a__1_0 + 512 * a__2_0 + 131072 * a__3_0 + 1)) = 0
+(b__2_0 + 256 * b__3_0 - (2 * a__2_0 + 512 * a__3_0)) * (b__2_0 + 256 * b__3_0 - (2 * a__2_0 + 512 * a__3_0 + 1)) = 0
+(b__3_0 - 2 * a__3_0) * (b__3_0 - (2 * a__3_0 + 1)) = 0
+is_valid * (is_valid - 1) = 0