to_radix_trace.cpp

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#include "barretenberg/vm2/tracegen/to_radix_trace.hpp"
 
#include <cassert>
#include <memory>
 
#include "barretenberg/numeric/uint256/uint256.hpp"
#include "barretenberg/vm2/common/aztec_constants.hpp"
#include "barretenberg/vm2/common/aztec_types.hpp"
#include "barretenberg/vm2/common/to_radix.hpp"
#include "barretenberg/vm2/generated/relations/lookups_to_radix.hpp"
#include "barretenberg/vm2/generated/relations/lookups_to_radix_mem.hpp"
#include "barretenberg/vm2/simulation/events/event_emitter.hpp"
#include "barretenberg/vm2/simulation/events/to_radix_event.hpp"
#include "barretenberg/vm2/tracegen/lib/interaction_def.hpp"
 
namespace bb::avm2::tracegen {
 
void ToRadixTraceBuilder::process(const simulation::EventEmitterInterface<simulation::ToRadixEvent>::Container& events,
                                  TraceContainer& trace)
{
    using C = Column;
 
    const auto& p_limbs_per_radix = get_p_limbs_per_radix();
 
    uint32_t row = 1; // We start from row 1 because this trace contains shifted columns.
    for (const auto& event : events) {
        FF value = event.value;
        uint32_t radix = event.radix;
        size_t radix_index = static_cast<size_t>(radix);
        uint32_t safe_limbs = static_cast<uint32_t>(p_limbs_per_radix[radix_index].size()) - 1;
 
        FF acc = 0;
        FF exponent = 1;
        bool found = false;
        bool acc_under_p = false;
 
        for (uint32_t i = 0; i < event.limbs.size(); ++i) {
            bool is_padding = i > safe_limbs;
            uint8_t limb = event.limbs[i];
            uint8_t p_limb = is_padding ? 0 : p_limbs_per_radix[radix_index][static_cast<size_t>(i)];
 
            if (limb != p_limb) {
                acc_under_p = limb < p_limb;
            }
            FF limb_p_diff = limb == p_limb ? 0 : limb > p_limb ? limb - p_limb - 1 : p_limb - limb - 1;
 
            bool is_unsafe_limb = i == safe_limbs;
            FF safety_diff = FF(i) - FF(safe_limbs);
 
            acc += exponent * limb;
 
            FF rem = value - acc;
            found = rem == 0;
 
            bool end = i == (event.limbs.size() - 1);
 
            trace.set(row,
                      { {
                          { C::to_radix_sel, 1 },
                          { C::to_radix_value, value },
                          { C::to_radix_radix, radix },
                          { C::to_radix_limb_index, i },
                          { C::to_radix_limb, limb },
                          { C::to_radix_start, i == 0 },
                          { C::to_radix_end, end },
                          { C::to_radix_not_end, !end },
                          { C::to_radix_exponent, exponent },
                          { C::to_radix_not_padding_limb, !is_padding },
                          { C::to_radix_acc, acc },
                          { C::to_radix_found, found },
                          { C::to_radix_limb_radix_diff, radix - 1 - limb },
                          { C::to_radix_rem_inverse, rem }, // Will be inverted in batch later
                          { C::to_radix_safe_limbs, safe_limbs },
                          { C::to_radix_is_unsafe_limb, is_unsafe_limb },
                          { C::to_radix_safety_diff_inverse, safety_diff }, // Will be inverted in batch later
                          { C::to_radix_p_limb, p_limb },
                          { C::to_radix_acc_under_p, acc_under_p },
                          { C::to_radix_limb_lt_p, limb < p_limb },
                          { C::to_radix_limb_eq_p, limb == p_limb },
                          { C::to_radix_limb_p_diff, limb_p_diff },
                      } });
 
            row++;
            if (is_unsafe_limb) {
                exponent = 0;
            }
            exponent *= radix;
        }
    }
 
    // Batch invert the columns.
    trace.invert_columns({ { C::to_radix_safety_diff_inverse, C::to_radix_rem_inverse } });
}
 
void ToRadixTraceBuilder::process_with_memory(
    const simulation::EventEmitterInterface<simulation::ToRadixMemoryEvent>::Container& events, TraceContainer& trace)
{
    using C = Column;
 
    uint32_t row = 1; // We start from row 1 because this trace contains shifted columns.
    for (const auto& event : events) {
        // Helpers
        uint8_t num_limbs_is_zero = event.num_limbs == 0 ? 1 : 0;
        FF num_limbs_inv = event.num_limbs == 0 ? FF(0) : FF(event.num_limbs); // Will be inverted in batch later
        uint8_t value_is_zero = event.value == FF(0) ? 1 : 0;
        FF value_inv = event.value == FF(0) ? FF(0) : event.value; // Will be inverted in batch later
 
        // Error Handling - Out of Memory Access
        uint64_t dst_addr = static_cast<uint64_t>(event.dst_addr);
        uint64_t write_addr_upper_bound = dst_addr + event.num_limbs;
        bool write_out_of_range = write_addr_upper_bound > AVM_MEMORY_SIZE;
 
        // Error Handling - Radix Range
        bool invalid_radix = (event.radix < 2 || event.radix > 256);
        bool invalid_bitwise_radix = event.is_output_bits && event.radix != 2;
 
        // Error Handling - Num Limbs and Value
        bool invalid_num_limbs = event.num_limbs == 0 && !(event.value == FF(0));
 
        // Common values for the first row
        trace.set(row,
                  { {
                      { C::to_radix_mem_sel, 1 },
                      { C::to_radix_mem_start, 1 },
                      // Unconditional Inputs
                      { C::to_radix_mem_execution_clk, event.execution_clk },
                      { C::to_radix_mem_space_id, event.space_id },
                      { C::to_radix_mem_dst_addr, dst_addr },
                      { C::to_radix_mem_value_to_decompose, event.value },
                      { C::to_radix_mem_radix, event.radix },
                      { C::to_radix_mem_num_limbs, event.num_limbs },
                      { C::to_radix_mem_is_output_bits, event.is_output_bits ? 1 : 0 },
                      // Helpers
                      { C::to_radix_mem_max_mem_size, static_cast<uint64_t>(AVM_MEMORY_SIZE) },
                      { C::to_radix_mem_write_addr_upper_bound, write_addr_upper_bound },
                      { C::to_radix_mem_two, 2 },
                      { C::to_radix_mem_two_five_six, 256 },
                      { C::to_radix_mem_sel_num_limbs_is_zero, num_limbs_is_zero },
                      { C::to_radix_mem_num_limbs_inv, num_limbs_inv },
                      { C::to_radix_mem_sel_value_is_zero, value_is_zero },
                      { C::to_radix_mem_value_inv, value_inv },
                  } });
 
        // Input validation errors
        if (write_out_of_range || invalid_radix || invalid_bitwise_radix || invalid_num_limbs) {
            trace.set(row,
                      { {
                          { C::to_radix_mem_last, 1 },
                          { C::to_radix_mem_input_validation_error, 1 },
                          { C::to_radix_mem_err, 1 },
                          { C::to_radix_mem_sel_dst_out_of_range_err, write_out_of_range },
                          { C::to_radix_mem_sel_radix_lt_2_err, event.radix < 2 },
                          { C::to_radix_mem_sel_radix_gt_256_err, event.radix > 256 },
                          { C::to_radix_mem_sel_invalid_bitwise_radix, invalid_bitwise_radix ? 1 : 0 },
                          { C::to_radix_mem_sel_invalid_num_limbs_err, invalid_num_limbs ? 1 : 0 },
                      } });
            row++;
            continue;
        }
 
        // At this point, a decomposition has happened, so we can process the limbs
 
        // Compute found for the given decomposition
        FF acc = 0;
        FF exponent = 1;
        std::vector<bool> found(event.limbs.size(), false);
        for (size_t i = 0; i < event.limbs.size(); ++i) {
            // Limbs are BE, we compute found in LE since the to_radix subtrace is little endian
            size_t reverse_index = event.limbs.size() - i - 1;
            FF limb_value = event.limbs[reverse_index].as_ff();
            acc += exponent * limb_value;
            exponent *= event.radix;
            found[reverse_index] = acc == event.value;
        }
 
        // Num limbs = 0 short circuit
        if (event.num_limbs == 0) {
            trace.set(row,
                      { {
                          { C::to_radix_mem_last, 1 },
                      } });
            row++;
            continue;
        }
 
        // Truncation error (still does decomposition)
        bool truncation_error = event.num_limbs != 0 && !found.at(0);
 
        if (truncation_error) {
            trace.set(row,
                      { {
                          { C::to_radix_mem_last, 1 },
                          { C::to_radix_mem_err, 1 },
                          { C::to_radix_mem_sel_truncation_error, 1 },
                          // Decomposition
                          { C::to_radix_mem_sel_should_decompose, 1 },
                          { C::to_radix_mem_limb_index_to_lookup, event.num_limbs - 1 },
                          { C::to_radix_mem_limb_value, event.limbs.at(0).as_ff() },
                          { C::to_radix_mem_value_found, 0 },
                      } });
 
            row++;
            continue;
        }
 
        uint32_t remaining_limbs = static_cast<uint32_t>(event.num_limbs);
 
        // Base case
        for (uint32_t i = 0; i < event.num_limbs; ++i) {
            MemoryValue limb_value = event.limbs.at(i);
            bool last = i == (event.num_limbs - 1);
 
            trace.set(row,
                      { {
                          { C::to_radix_mem_sel, 1 },
                          { C::to_radix_mem_num_limbs, remaining_limbs },
                          { C::to_radix_mem_num_limbs_minus_one_inv,
                            remaining_limbs - 1 == 0 ? 0 : FF(remaining_limbs - 1) }, // Will be inverted in batch later
                          { C::to_radix_mem_last, last ? 1 : 0 },
                          // Decomposition
                          { C::to_radix_mem_sel_should_decompose, 1 },
                          { C::to_radix_mem_value_to_decompose, event.value },
                          { C::to_radix_mem_limb_index_to_lookup, remaining_limbs - 1 },
                          { C::to_radix_mem_radix, event.radix },
                          { C::to_radix_mem_limb_value, limb_value.as_ff() },
                          { C::to_radix_mem_value_found, found.at(i) ? 1 : 0 },
                          // Memory write
                          { C::to_radix_mem_sel_should_write_mem, 1 },
                          { C::to_radix_mem_execution_clk, event.execution_clk },
                          { C::to_radix_mem_space_id, event.space_id },
                          { C::to_radix_mem_dst_addr, dst_addr },
                          { C::to_radix_mem_output_tag, static_cast<uint8_t>(limb_value.get_tag()) },
                          { C::to_radix_mem_is_output_bits, event.is_output_bits ? 1 : 0 },
                      } });
 
            remaining_limbs--; // Decrement the number of limbs
            dst_addr++;        // Increment the destination address for the next limb
 
            row++;
        }
    }
 
    // Batch invert the columns.
    trace.invert_columns(
        { { C::to_radix_mem_num_limbs_inv, C::to_radix_mem_value_inv, C::to_radix_mem_num_limbs_minus_one_inv } });
}
 
const InteractionDefinition ToRadixTraceBuilder::interactions =
    InteractionDefinition()
        .add<lookup_to_radix_limb_range_settings, InteractionType::LookupIntoIndexedByClk>()
        .add<lookup_to_radix_limb_less_than_radix_range_settings, InteractionType::LookupIntoIndexedByClk>()
        .add<lookup_to_radix_fetch_safe_limbs_settings, InteractionType::LookupIntoIndexedByClk>()
        .add<lookup_to_radix_fetch_p_limb_settings, InteractionType::LookupIntoPDecomposition>()
        .add<lookup_to_radix_limb_p_diff_range_settings, InteractionType::LookupIntoIndexedByClk>()
        // Mem Aware To Radix
        // GT checks
        .add<lookup_to_radix_mem_check_dst_addr_in_range_settings, InteractionType::LookupGeneric>(Column::gt_sel)
        .add<lookup_to_radix_mem_check_radix_lt_2_settings, InteractionType::LookupGeneric>(Column::gt_sel)
        .add<lookup_to_radix_mem_check_radix_gt_256_settings, InteractionType::LookupGeneric>(Column::gt_sel)
        // Dispatch to To Radix
        .add<lookup_to_radix_mem_input_output_to_radix_settings, InteractionType::LookupGeneric>();
 
} // namespace bb::avm2::tracegen