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feat(avm): back in avm context with macro - refactor context (AztecPr…
…otocol#4438) Fixes: AztecProtocol#4313
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include "mem_trace.pil"; | ||
include "alu_chip.pil"; | ||
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namespace avmMini(256); | ||
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//===== CONSTANT POLYNOMIALS ================================================== | ||
pol constant clk(i) { i }; | ||
pol constant first = [1] + [0]*; // Used mostly to toggle off the first row consisting | ||
// only in first element of shifted polynomials. | ||
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//===== CONTROL FLOW ========================================================== | ||
// Program counter | ||
pol commit pc; | ||
// Return Pointer | ||
pol commit internal_return_ptr; | ||
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pol commit sel_internal_call; | ||
pol commit sel_internal_return; | ||
pol commit sel_jump; | ||
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// Halt program execution | ||
pol commit sel_halt; | ||
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//===== TABLE SUBOP-TR ======================================================== | ||
// Boolean selectors for (sub-)operations. Only one operation is activated at | ||
// a time. | ||
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// ADD | ||
pol commit sel_op_add; | ||
// SUB | ||
pol commit sel_op_sub; | ||
// MUL | ||
pol commit sel_op_mul; | ||
// DIV | ||
pol commit sel_op_div; | ||
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// Instruction memory tag (0: uninitialized, 1: u8, 2: u16, 3: u32, 4: u64, 5: u128, 6:field) | ||
pol commit in_tag; | ||
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// Errors | ||
pol commit op_err; // Boolean flag pertaining to an operation error | ||
pol commit tag_err; // Boolean flag (foreign key to memTrace.m_tag_err) | ||
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// A helper witness being the inverse of some value | ||
// to show a non-zero equality | ||
pol commit inv; | ||
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// Intermediate register values | ||
pol commit ia; | ||
pol commit ib; | ||
pol commit ic; | ||
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// Memory operation per intermediate register | ||
pol commit mem_op_a; | ||
pol commit mem_op_b; | ||
pol commit mem_op_c; | ||
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// Read-write flag per intermediate register: Read = 0, Write = 1 | ||
pol commit rwa; | ||
pol commit rwb; | ||
pol commit rwc; | ||
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// Memory index involved into a memory operation per pertaining intermediate register | ||
// We should range constrain it to 32 bits ultimately. For first mini-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; | ||
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// 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. | ||
pol commit last; | ||
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// Relations on type constraints | ||
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sel_op_add * (1 - sel_op_add) = 0; | ||
sel_op_sub * (1 - sel_op_sub) = 0; | ||
sel_op_mul * (1 - sel_op_mul) = 0; | ||
sel_op_div * (1 - sel_op_div) = 0; | ||
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sel_internal_call * (1 - sel_internal_call) = 0; | ||
sel_internal_return * (1 - sel_internal_return) = 0; | ||
sel_jump * (1 - sel_jump) = 0; | ||
sel_halt * (1 - sel_halt) = 0; | ||
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op_err * (1 - op_err) = 0; | ||
tag_err * (1 - tag_err) = 0; // Potential optimization (boolean constraint derivation from equivalence check to memTrace)? | ||
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mem_op_a * (1 - mem_op_a) = 0; | ||
mem_op_b * (1 - mem_op_b) = 0; | ||
mem_op_c * (1 - mem_op_c) = 0; | ||
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rwa * (1 - rwa) = 0; | ||
rwb * (1 - rwb) = 0; | ||
rwc * (1 - rwc) = 0; | ||
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// TODO: Constrain rwa, rwb, rwc to u32 type and 0 <= in_tag <= 6 | ||
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// Set intermediate registers to 0 whenever tag_err occurs | ||
tag_err * ia = 0; | ||
tag_err * ib = 0; | ||
tag_err * ic = 0; | ||
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// Relation for division over the finite field | ||
// If tag_err == 1 in a division, then ib == 0 and op_err == 1. | ||
#[SUBOP_DIVISION_FF] | ||
sel_op_div * (1 - op_err) * (ic * ib - ia) = 0; | ||
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// When sel_op_div == 1, we want ib == 0 <==> op_err == 1 | ||
// This can be achieved with the 2 following relations. | ||
// inv is an extra witness to show that we can invert ib, i.e., inv = ib^(-1) | ||
// If ib == 0, we have to set inv = 1 to satisfy the second relation, | ||
// because op_err == 1 from the first relation. | ||
#[SUBOP_DIVISION_ZERO_ERR1] | ||
sel_op_div * (ib * inv - 1 + op_err) = 0; | ||
#[SUBOP_DIVISION_ZERO_ERR2] | ||
sel_op_div * op_err * (1 - inv) = 0; | ||
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// op_err cannot be maliciously activated for a non-relevant | ||
// operation selector, i.e., op_err == 1 ==> sel_op_div || sel_op_XXX || ... | ||
// op_err * (sel_op_div + sel_op_XXX + ... - 1) == 0 | ||
// Note that the above is even a stronger constraint, as it shows | ||
// that exactly one sel_op_XXX must be true. | ||
// At this time, we have only division producing an error. | ||
#[SUBOP_ERROR_RELEVANT_OP] | ||
op_err * (sel_op_div - 1) = 0; | ||
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// TODO: constraint that we stop execution at the first error (tag_err or op_err) | ||
// An error can only happen at the last sub-operation row. | ||
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// OPEN/POTENTIAL OPTIMIZATION: Dedicated error per relevant operation? | ||
// For the division, we could lower the degree from 4 to 3 | ||
// (sel_op_div - op_div_err) * (ic * ib - ia) = 0; | ||
// Same for the relations related to the error activation: | ||
// (ib * inv - 1 + op_div_err) = 0 && op_err * (1 - inv) = 0 | ||
// This works in combination with op_div_err * (sel_op_div - 1) = 0; | ||
// Drawback is the need to paralllelize the latter. | ||
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//===== CONTROL FLOW ======================================================= | ||
//===== JUMP =============================================================== | ||
sel_jump * (pc' - ia) = 0; | ||
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//===== INTERNAL_CALL ====================================================== | ||
// - The program counter in the next row should be equal to the value loaded from the ia register | ||
// - We then write the return location (pc + 1) into the call stack (in memory) | ||
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#[RETURN_POINTER_INCREMENT] | ||
sel_internal_call * (internal_return_ptr' - (internal_return_ptr + 1)) = 0; | ||
sel_internal_call * (internal_return_ptr - mem_idx_b) = 0; | ||
sel_internal_call * (pc' - ia) = 0; | ||
sel_internal_call * ((pc + 1) - ib) = 0; | ||
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// TODO(md): Below relations may be removed through sub-op table lookup | ||
sel_internal_call * (rwb - 1) = 0; | ||
sel_internal_call * (mem_op_b - 1) = 0; | ||
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//===== INTERNAL_RETURN =================================================== | ||
// - We load the memory pointer to be the internal_return_ptr | ||
// - Constrain then next program counter to be the loaded value | ||
// - decrement the internal_return_ptr | ||
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#[RETURN_POINTER_DECREMENT] | ||
sel_internal_return * (internal_return_ptr' - (internal_return_ptr - 1)) = 0; | ||
sel_internal_return * ((internal_return_ptr - 1) - mem_idx_a) = 0; | ||
sel_internal_return * (pc' - ia) = 0; | ||
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// TODO(md): Below relations may be removed through sub-op table lookup | ||
sel_internal_return * rwa = 0; | ||
sel_internal_return * (mem_op_a - 1) = 0; | ||
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//===== CONTROL_FLOW_CONSISTENCY ============================================ | ||
pol INTERNAL_CALL_STACK_SELECTORS = (first + sel_internal_call + sel_internal_return + sel_halt); | ||
pol OPCODE_SELECTORS = (sel_op_add + sel_op_sub + sel_op_div + sel_op_mul); | ||
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// Program counter must increment if not jumping or returning | ||
#[PC_INCREMENT] | ||
(1 - first) * (1 - sel_halt) * OPCODE_SELECTORS * (pc' - (pc + 1)) = 0; | ||
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// first == 0 && sel_internal_call == 0 && sel_internal_return == 0 && sel_halt == 0 ==> internal_return_ptr == internal_return_ptr' | ||
#[INTERNAL_RETURN_POINTER_CONSISTENCY] | ||
(1 - INTERNAL_CALL_STACK_SELECTORS) * (internal_return_ptr' - internal_return_ptr) = 0; | ||
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// TODO: we want to set an initial number for the reserved memory of the jump pointer | ||
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// Inter-table Constraints | ||
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// TODO: tag_err {clk} IS memTrace.m_tag_err {memTrace.m_clk} | ||
// TODO: Map memory trace with intermediate register values whenever there is no tag error, sthg like: | ||
// mem_op_a * (1 - tag_err) {mem_idx_a, clk, ia, rwa} IS m_sub_clk == 0 && 1 - m_tag_err {m_addr, m_clk, m_val, m_rw} |
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