plonky2/evm/src/arithmetic/columns.rs

//! Arithmetic unit

use std::ops::Range;

pub const LIMB_BITS: usize = 16;
const EVM_REGISTER_BITS: usize = 256;

/// Return the number of LIMB_BITS limbs that are in an EVM
/// register-sized number, panicking if LIMB_BITS doesn't divide in
/// the EVM register size.
const fn n_limbs() -> usize {
    if EVM_REGISTER_BITS % LIMB_BITS != 0 {
        panic!("limb size must divide EVM register size");
    }
    let n = EVM_REGISTER_BITS / LIMB_BITS;
    if n % 2 == 1 {
        panic!("number of limbs must be even");
    }
    n
}

/// Number of LIMB_BITS limbs that are in on EVM register-sized number.
pub const N_LIMBS: usize = n_limbs();

pub const IS_ADD: usize = 0;
pub const IS_MUL: usize = IS_ADD + 1;
pub const IS_SUB: usize = IS_MUL + 1;
pub const IS_DIV: usize = IS_SUB + 1;
pub const IS_MOD: usize = IS_DIV + 1;
pub const IS_ADDMOD: usize = IS_MOD + 1;
pub const IS_SUBMOD: usize = IS_ADDMOD + 1;
pub const IS_MULMOD: usize = IS_SUBMOD + 1;
pub const IS_LT: usize = IS_MULMOD + 1;
pub const IS_GT: usize = IS_LT + 1;
pub const IS_SHL: usize = IS_GT + 1;
pub const IS_SHR: usize = IS_SHL + 1;

const START_SHARED_COLS: usize = IS_SHR + 1;

pub(crate) const ALL_OPERATIONS: [usize; 12] = [
    IS_ADD, IS_MUL, IS_SUB, IS_DIV, IS_MOD, IS_ADDMOD, IS_SUBMOD, IS_MULMOD, IS_LT, IS_GT, IS_SHL,
    IS_SHR,
];

/// Within the Arithmetic Unit, there are shared columns which can be
/// used by any arithmetic circuit, depending on which one is active
/// this cycle.
///
/// Modular arithmetic takes 9 * N_LIMBS columns which is split across
/// two rows, the first with 5 * N_LIMBS columns and the second with
/// 4 * N_LIMBS columns. (There are hence N_LIMBS "wasted columns" in
/// the second row.)
const NUM_SHARED_COLS: usize = 5 * N_LIMBS;

const GENERAL_INPUT_0: Range<usize> = START_SHARED_COLS..START_SHARED_COLS + N_LIMBS;
const GENERAL_INPUT_1: Range<usize> = GENERAL_INPUT_0.end..GENERAL_INPUT_0.end + N_LIMBS;
const GENERAL_INPUT_2: Range<usize> = GENERAL_INPUT_1.end..GENERAL_INPUT_1.end + N_LIMBS;
const GENERAL_INPUT_3: Range<usize> = GENERAL_INPUT_2.end..GENERAL_INPUT_2.end + N_LIMBS;
const AUX_INPUT_0_LO: Range<usize> = GENERAL_INPUT_3.end..GENERAL_INPUT_3.end + N_LIMBS;

// The auxiliary input columns overlap the general input columns
// because they correspond to the values in the second row for modular
// operations.
const AUX_INPUT_0_HI: Range<usize> = START_SHARED_COLS..START_SHARED_COLS + N_LIMBS;
const AUX_INPUT_1: Range<usize> = AUX_INPUT_0_HI.end..AUX_INPUT_0_HI.end + 2 * N_LIMBS;
// These auxiliary input columns are awkwardly split across two rows,
// with the first half after the general input columns and the second
// half after the auxiliary input columns.
const AUX_INPUT_2: Range<usize> = AUX_INPUT_1.end..AUX_INPUT_1.end + N_LIMBS;

// ADD takes 3 * N_LIMBS = 48 columns
pub(crate) const ADD_INPUT_0: Range<usize> = GENERAL_INPUT_0;
pub(crate) const ADD_INPUT_1: Range<usize> = GENERAL_INPUT_1;
pub(crate) const ADD_OUTPUT: Range<usize> = GENERAL_INPUT_2;

// SUB takes 3 * N_LIMBS = 48 columns
pub(crate) const SUB_INPUT_0: Range<usize> = GENERAL_INPUT_0;
pub(crate) const SUB_INPUT_1: Range<usize> = GENERAL_INPUT_1;
pub(crate) const SUB_OUTPUT: Range<usize> = GENERAL_INPUT_2;

// MUL takes 4 * N_LIMBS = 64 columns
pub(crate) const MUL_INPUT_0: Range<usize> = GENERAL_INPUT_0;
pub(crate) const MUL_INPUT_1: Range<usize> = GENERAL_INPUT_1;
pub(crate) const MUL_OUTPUT: Range<usize> = GENERAL_INPUT_2;
pub(crate) const MUL_AUX_INPUT: Range<usize> = GENERAL_INPUT_3;

// LT and GT take 4 * N_LIMBS = 64 columns
pub(crate) const CMP_INPUT_0: Range<usize> = GENERAL_INPUT_0;
pub(crate) const CMP_INPUT_1: Range<usize> = GENERAL_INPUT_1;
pub(crate) const CMP_OUTPUT: usize = GENERAL_INPUT_2.start;
pub(crate) const CMP_AUX_INPUT: Range<usize> = GENERAL_INPUT_3;

// MULMOD takes 4 * N_LIMBS + 2 * 2*N_LIMBS + N_LIMBS = 144 columns
// but split over two rows of 80 columns and 64 columns.
//
// ADDMOD, SUBMOD, MOD and DIV are currently implemented in terms of
// the general modular code, so they also take 144 columns (also split
// over two rows).
pub(crate) const MODULAR_INPUT_0: Range<usize> = GENERAL_INPUT_0;
pub(crate) const MODULAR_INPUT_1: Range<usize> = GENERAL_INPUT_1;
pub(crate) const MODULAR_MODULUS: Range<usize> = GENERAL_INPUT_2;
pub(crate) const MODULAR_OUTPUT: Range<usize> = GENERAL_INPUT_3;
pub(crate) const MODULAR_QUO_INPUT_LO: Range<usize> = AUX_INPUT_0_LO;
// NB: Last value is not used in AUX, it is used in MOD_IS_ZERO
pub(crate) const MODULAR_QUO_INPUT_HI: Range<usize> = AUX_INPUT_0_HI;
pub(crate) const MODULAR_AUX_INPUT: Range<usize> = AUX_INPUT_1.start..AUX_INPUT_1.end - 1;
pub(crate) const MODULAR_MOD_IS_ZERO: usize = AUX_INPUT_1.end - 1;
pub(crate) const MODULAR_OUT_AUX_RED: Range<usize> = AUX_INPUT_2;

#[allow(unused)] // TODO: Will be used when hooking into the CPU
pub(crate) const DIV_NUMERATOR: Range<usize> = MODULAR_INPUT_0;
#[allow(unused)] // TODO: Will be used when hooking into the CPU
pub(crate) const DIV_DENOMINATOR: Range<usize> = MODULAR_MODULUS;
#[allow(unused)] // TODO: Will be used when hooking into the CPU
pub(crate) const DIV_OUTPUT: Range<usize> = MODULAR_QUO_INPUT_LO;

pub const NUM_ARITH_COLUMNS: usize = START_SHARED_COLS + NUM_SHARED_COLS;