feat(avm): CMOV opcode (#5575)

Resolves #5557

Author: jeanmon

barretenberg/cpp/pil/avm/avm_main.pil

@@ -30,6 +30,7 @@ namespace avm_main(256);
 
     //===== MEMORY OPCODES ==========================================================
     pol commit sel_mov;
+    pol commit sel_cmov;
 
     //===== TABLE SUBOP-TR ========================================================
     // Boolean selectors for (sub-)operations. Only one operation is activated at
@@ -75,40 +76,45 @@ namespace avm_main(256);
     // A helper witness being the inverse of some value
     // to show a non-zero equality
     pol commit inv;
+    pol commit id_zero; // Boolean telling whether id is zero (cmov opcode)
 
     // Intermediate register values
     pol commit ia;
     pol commit ib;
     pol commit ic;
+    pol commit id;
 
     // Memory operation selector per intermediate register
     pol commit mem_op_a;
     pol commit mem_op_b;
     pol commit mem_op_c;
+    pol commit mem_op_d;
 
     // Read-write flag per intermediate register: Read = 0, Write = 1
     pol commit rwa;
     pol commit rwb;
     pol commit rwc;
+    pol commit rwd;
 
     // Indirect register values
     pol commit ind_a;
     pol commit ind_b;
     pol commit ind_c;
+    pol commit ind_d;
 
     // Indirect memory operation selector per indirect register
     pol commit ind_op_a;
     pol commit ind_op_b;
     pol commit ind_op_c;
-
+    pol commit ind_op_d;
 
     // Memory index involved into a memory operation per pertaining intermediate register
     // We should range constrain it to 32 bits ultimately. For first version of the AVM,
     // we will assume that these columns are of the right type.
     pol commit mem_idx_a;
     pol commit mem_idx_b;
     pol commit mem_idx_c;
-
+    pol commit mem_idx_d;
 
     // Track the last line of the execution trace. It does NOT correspond to the last row of the whole table
     // of size N. As this depends on the supplied bytecode, this polynomial cannot be constant.
@@ -135,27 +141,32 @@ namespace avm_main(256);
 
     // Might be removed if derived from opcode based on a lookup of constants
     sel_mov * ( 1 - sel_mov) = 0;
+    sel_cmov * ( 1 - sel_cmov) = 0;
 
     op_err * (1 - op_err) = 0;
     tag_err * (1 - tag_err) = 0; // Potential optimization (boolean constraint derivation from equivalence check to avm_mem)?
+    id_zero * (1 - id_zero) = 0;
 
     // Might be removed if derived from opcode based on a lookup of constants
     mem_op_a * (1 - mem_op_a) = 0;
     mem_op_b * (1 - mem_op_b) = 0;
     mem_op_c * (1 - mem_op_c) = 0;
+    mem_op_d * (1 - mem_op_d) = 0;
 
     rwa * (1 - rwa) = 0;
     rwb * (1 - rwb) = 0;
     rwc * (1 - rwc) = 0;
+    rwd * (1 - rwd) = 0;
 
     // Might be removed if derived from opcode based on a lookup of constants
     ind_op_a * (1 - ind_op_a) = 0;
     ind_op_b * (1 - ind_op_b) = 0;
     ind_op_c * (1 - ind_op_c) = 0;
+    ind_op_d * (1 - ind_op_d) = 0;
 
     // TODO - Constraints:
-    // - mem_idx_a, mem_idx_b, mem_idx_c to u32 type
-    // - ind_a, ind_b, ind_c to u32 type
+    // - mem_idx_a, mem_idx_b, mem_idx_c, mem_idx_d to u32 type
+    // - ind_a, ind_b, ind_c, ind_d to u32 type
     // - 0 <= r_in_tag, w_in_tag <= 6 // Maybe not needed as probably derived by the operation decomposition.
 
     //====== COMPARATOR OPCODES CONSTRAINTS =====================================
@@ -245,10 +256,36 @@ namespace avm_main(256);
     // TODO: we want to set an initial number for the reserved memory of the jump pointer
 
     //====== MEMORY OPCODES CONSTRAINTS =========================================
-    #[MOV_SAME_VALUE]
-    sel_mov * (ia - ic) = 0; // Ensure that the correct value is moved/copied.
+
+    // TODO: consolidate with zero division error handling
+
+    // When sel_cmov == 1, we need id == 0 <==> id_zero == 0
+    // This can be achieved with the 2 following relations.
+    // inv is an extra witness to show that we can invert id, i.e., inv = id^(-1)
+    // If id == 0, we have to set inv = 1 to satisfy the second relation,
+    // because id_zero == 1 from the first relation.
+    #[CMOV_CONDITION_RES_1]
+    sel_cmov * (id * inv - 1 + id_zero) = 0;
+    #[CMOV_CONDITION_RES_2]
+    sel_cmov * id_zero * (1 - inv) = 0;
+
+    // Boolean selectors telling whether we move ia to ic or ib to ic.
+    // Boolean constraints and mutual exclusivity are derived from their
+    // respective definitions based on sel_mov, sel_cmov, and id_zero.
+    pol commit sel_mov_a;
+    pol commit sel_mov_b;
+
+    // For MOV, we copy ia to ic.
+    // For CMOV, we copy ia to ic if id is NOT zero, otherwise we copy ib to ic.
+    sel_mov_a = sel_mov + sel_cmov * (1 - id_zero);
+    sel_mov_b = sel_cmov * id_zero;
+
+    #[MOV_SAME_VALUE_A]
+    sel_mov_a * (ia - ic) = 0; // Ensure that the correct value is moved/copied.
+    #[MOV_SAME_VALUE_B]
+    sel_mov_b * (ib - ic) = 0; // Ensure that the correct value is moved/copied.
     #[MOV_MAIN_SAME_TAG]
-    sel_mov * (r_in_tag - w_in_tag) = 0;
+    (sel_mov + sel_cmov) * (r_in_tag - w_in_tag) = 0;
 
     //====== Inter-table Constraints ============================================
     #[INCL_MAIN_TAG_ERR]
@@ -288,20 +325,31 @@ namespace avm_main(256);
     avm_binary.start {avm_binary.clk, avm_binary.acc_ia, avm_binary.acc_ib, avm_binary.acc_ic, avm_binary.op_id, avm_binary.in_tag};
 
     #[PERM_MAIN_MEM_A]
-    mem_op_a {clk, mem_idx_a, ia, rwa, r_in_tag, w_in_tag, sel_mov}
+    mem_op_a {clk, mem_idx_a, ia, rwa
+            , r_in_tag, w_in_tag, sel_mov_a, sel_cmov}
     is
-    avm_mem.op_a {avm_mem.clk, avm_mem.addr, avm_mem.val, avm_mem.rw, avm_mem.r_in_tag, avm_mem.w_in_tag, avm_mem.sel_mov};
+    avm_mem.op_a {avm_mem.clk, avm_mem.addr, avm_mem.val, avm_mem.rw
+                , avm_mem.r_in_tag, avm_mem.w_in_tag, avm_mem.sel_mov_a, avm_mem.sel_cmov};
 
     #[PERM_MAIN_MEM_B]
-    mem_op_b {clk, mem_idx_b, ib, rwb, r_in_tag, w_in_tag}
+    mem_op_b {clk, mem_idx_b, ib, rwb
+            , r_in_tag, w_in_tag, sel_mov_b, sel_cmov}
     is
-    avm_mem.op_b {avm_mem.clk, avm_mem.addr, avm_mem.val, avm_mem.rw, avm_mem.r_in_tag, avm_mem.w_in_tag};
+    avm_mem.op_b {avm_mem.clk, avm_mem.addr, avm_mem.val, avm_mem.rw
+                , avm_mem.r_in_tag, avm_mem.w_in_tag, avm_mem.sel_mov_b, avm_mem.sel_cmov};
 
     #[PERM_MAIN_MEM_C]
     mem_op_c {clk, mem_idx_c, ic, rwc, r_in_tag, w_in_tag}
     is
     avm_mem.op_c {avm_mem.clk, avm_mem.addr, avm_mem.val, avm_mem.rw, avm_mem.r_in_tag, avm_mem.w_in_tag};
 
+    #[PERM_MAIN_MEM_D]
+    mem_op_d {clk, mem_idx_d, id, rwd
+            , r_in_tag, w_in_tag, sel_cmov}
+    is
+    avm_mem.op_d {avm_mem.clk, avm_mem.addr, avm_mem.val, avm_mem.rw
+                , avm_mem.r_in_tag, avm_mem.w_in_tag, avm_mem.sel_cmov};
+
     #[PERM_MAIN_MEM_IND_A]
     ind_op_a {clk, ind_a, mem_idx_a} is avm_mem.ind_op_a {avm_mem.clk, avm_mem.addr, avm_mem.val};
 
@@ -311,6 +359,9 @@ namespace avm_main(256);
     #[PERM_MAIN_MEM_IND_C]
     ind_op_c {clk, ind_c, mem_idx_c} is avm_mem.ind_op_c {avm_mem.clk, avm_mem.addr, avm_mem.val};
 
+    #[PERM_MAIN_MEM_IND_D]
+    ind_op_d {clk, ind_d, mem_idx_d} is avm_mem.ind_op_d {avm_mem.clk, avm_mem.addr, avm_mem.val};
+
     //====== Inter-table Constraints (Range Checks) ============================================
     // TODO: Investigate optimising these range checks. Handling non-FF elements should require less range checks.
     #[LOOKUP_U8_0]

barretenberg/cpp/pil/avm/avm_mem.pil

@@ -15,20 +15,26 @@ namespace avm_mem(256);
 
     pol commit r_in_tag; // Instruction memory tag ("foreign key" pointing to avm_main.r_in_tag)
     pol commit w_in_tag; // Instruction memory tag ("foreign key" pointing to avm_main.w_in_tag)
+    pol commit skip_check_tag; // A boolean value which relaxes the consistency check in memory
+                               // trace between tag and r_in_tag. Required for CMOV opcode.
 
     // Indicator of the intermediate register pertaining to the memory operation (foreign key to avm_main.mem_op_XXX)
     pol commit op_a;
     pol commit op_b;
     pol commit op_c;
+    pol commit op_d;
 
     // Indicator of the indirect register pertaining to the memory operation (foreign key to avm_main.ind_op_XXX)
     pol commit ind_op_a;
     pol commit ind_op_b;
     pol commit ind_op_c;
+    pol commit ind_op_d;
 
-    // Selector for MOV opcode (copied from main trace for loading operation on intermediated register ia)
+    // Selectors related to MOV/CMOV opcodes (copied from main trace for loading operation on intermediated register ia/ib)
     // Boolean constraint is performed in main trace.
-    pol commit sel_mov;
+    pol commit sel_mov_a;
+    pol commit sel_mov_b;
+    pol commit sel_cmov;
 
     // Error columns
     pol commit tag_err; // Boolean (1 if r_in_tag != tag is detected)
@@ -44,20 +50,22 @@ namespace avm_mem(256);
     op_a * (1 - op_a) = 0;
     op_b * (1 - op_b) = 0;
     op_c * (1 - op_c) = 0;
+    op_d * (1 - op_d) = 0;
     ind_op_a * (1 - ind_op_a) = 0;
     ind_op_b * (1 - ind_op_b) = 0;
     ind_op_c * (1 - ind_op_c) = 0;
+    ind_op_d * (1 - ind_op_d) = 0;
 
     // TODO: addr is u32 and 0 <= tag <= 6
     //       (r_in_tag, w_in_tag will be constrained through inclusion check to main trace)
 
     // Maximum one memory operation enabled per row
-    pol MEM_SEL = op_a + op_b + op_c + ind_op_a + ind_op_b + ind_op_c;
+    pol MEM_SEL = op_a + op_b + op_c + op_d + ind_op_a + ind_op_b + ind_op_c + ind_op_d;
     MEM_SEL * (MEM_SEL - 1) = 0;
 
     // sub_clk derivation
-    pol IND_OP = ind_op_a + ind_op_b + ind_op_c;
-    sub_clk = MEM_SEL * (ind_op_b + op_b + 2 * (ind_op_c + op_c) + 3 * (1 - IND_OP + rw));
+    pol IND_OP = ind_op_a + ind_op_b + ind_op_c + ind_op_d;
+    sub_clk = MEM_SEL * (ind_op_b + op_b + 2 * (ind_op_c + op_c) + 3 * (ind_op_d + op_d) + 4 * (1 - IND_OP + rw));
     // We need the MEM_SEL factor as the right factor is not zero when all columns are zero.
 
     // Remark: lastAccess == 1 on first row and therefore any relation with the
@@ -106,6 +114,10 @@ namespace avm_mem(256);
     #[MEM_ZERO_INIT]
     lastAccess * (1 - rw') * val' = 0;
 
+    // Skip check tag
+     #[SKIP_CHECK_TAG]
+    skip_check_tag = sel_cmov * (op_d + op_a * (1-sel_mov_a) + op_b * (1-sel_mov_b));
+
     // Memory tag consistency check for load operations, i.e., rw == 0.
     // We want to prove that r_in_tag == tag <==> tag_err == 0
     // We want to show that we can invert (r_in_tag - tag) when tag_err == 1,
@@ -120,10 +132,13 @@ namespace avm_mem(256);
     // The new column one_min_inv is set to 1 - (r_in_tag - tag)^(-1) when tag_err == 1
     // but must be set to 0 when tags are matching and tag_err = 0
     #[MEM_IN_TAG_CONSISTENCY_1]
-    (1 - rw) * ((r_in_tag - tag) * (1 - one_min_inv) - tag_err) = 0;
+    (1 - skip_check_tag) * (1 - rw) * ((r_in_tag - tag) * (1 - one_min_inv) - tag_err) = 0;
     #[MEM_IN_TAG_CONSISTENCY_2]
     (1 - tag_err) * one_min_inv = 0;
 
+    #[NO_TAG_ERR_WRITE_OR_SKIP]
+    (skip_check_tag + rw) * tag_err = 0;
+
     // Correctness of two above checks MEM_IN_TAG_CONSISTENCY_1/2 (assuming rw == 0):
     // r_in_tag == tag ==> tag_err == 0 (first relation)
     // tag_err == 0 ==> one_min_inv == 0 by second relation. First relation ==> r_in_tag - tag == 0
@@ -140,18 +155,20 @@ namespace avm_mem(256);
     ind_op_a * (r_in_tag - 3) = 0;
     ind_op_b * (r_in_tag - 3) = 0;
     ind_op_c * (r_in_tag - 3) = 0;
+    ind_op_d * (r_in_tag - 3) = 0;
 
     // Indirect operation is always a load
     ind_op_a * rw = 0;
     ind_op_b * rw = 0;
     ind_op_c * rw = 0;
+    ind_op_d * rw = 0;
 
-    //====== MOV Opcode Tag Constraint =====================================
+    //====== MOV/CMOV Opcode Tag Constraint =====================================
     // The following constraint ensures that the r_in_tag is set to tag for
-    // the load operation pertaining to Ia.
-    // The permutation check #[PERM_MAIN_MEM_A] guarantees that the r_in_tag
-    // value load operation for Ia is copied back in the main trace.
+    // the load operation pertaining to Ia resp. Ib.
+    // The permutation check #[PERM_MAIN_MEM_A/B] guarantees that the r_in_tag
+    // value load operation for Ia/Ib is copied back in the main trace.
     // Constraint #[MOV_MAIN_SAME_TAG] copies r_in_tag to w_in_tag in the main
     // trace. Then, #[PERM_MAIN_MEM_C] copies w_in_tag for store operation from Ic.
     #[MOV_SAME_TAG]
-    sel_mov * tag_err = 0; // Equivalent to sel_mov * (r_in_tag - tag) = 0
+    (sel_mov_a + sel_mov_b) * tag_err = 0; // Equivalent to (sel_mov_a + sel_mov_b) * (r_in_tag - tag) = 0