plonky2/src/gates/arithmetic_u32.rs
2021-11-30 17:12:13 +01:00

428 lines
16 KiB
Rust

use std::marker::PhantomData;
use itertools::unfold;
use crate::field::extension_field::target::ExtensionTarget;
use crate::field::extension_field::Extendable;
use crate::field::field_types::{Field, RichField};
use crate::gates::gate::Gate;
use crate::iop::generator::{GeneratedValues, SimpleGenerator, WitnessGenerator};
use crate::iop::target::Target;
use crate::iop::wire::Wire;
use crate::iop::witness::{PartitionWitness, Witness};
use crate::plonk::circuit_builder::CircuitBuilder;
use crate::plonk::vars::{EvaluationTargets, EvaluationVars, EvaluationVarsBase};
/// Number of arithmetic operations performed by an arithmetic gate.
pub const NUM_U32_ARITHMETIC_OPS: usize = 3;
/// A gate to perform a basic mul-add on 32-bit values (we assume they are range-checked beforehand).
#[derive(Clone, Debug)]
pub struct U32ArithmeticGate<F: RichField + Extendable<D>, const D: usize> {
_phantom: PhantomData<F>,
}
impl<F: RichField + Extendable<D>, const D: usize> U32ArithmeticGate<F, D> {
pub fn new() -> Self {
Self {
_phantom: PhantomData,
}
}
pub fn wire_ith_multiplicand_0(i: usize) -> usize {
debug_assert!(i < NUM_U32_ARITHMETIC_OPS);
5 * i
}
pub fn wire_ith_multiplicand_1(i: usize) -> usize {
debug_assert!(i < NUM_U32_ARITHMETIC_OPS);
5 * i + 1
}
pub fn wire_ith_addend(i: usize) -> usize {
debug_assert!(i < NUM_U32_ARITHMETIC_OPS);
5 * i + 2
}
pub fn wire_ith_output_low_half(i: usize) -> usize {
debug_assert!(i < NUM_U32_ARITHMETIC_OPS);
5 * i + 3
}
pub fn wire_ith_output_high_half(i: usize) -> usize {
debug_assert!(i < NUM_U32_ARITHMETIC_OPS);
5 * i + 4
}
pub fn limb_bits() -> usize {
2
}
pub fn num_limbs() -> usize {
64 / Self::limb_bits()
}
pub fn wire_ith_output_jth_limb(i: usize, j: usize) -> usize {
debug_assert!(i < NUM_U32_ARITHMETIC_OPS);
debug_assert!(j < Self::num_limbs());
5 * NUM_U32_ARITHMETIC_OPS + Self::num_limbs() * i + j
}
}
impl<F: RichField + Extendable<D>, const D: usize> Gate<F, D> for U32ArithmeticGate<F, D> {
fn id(&self) -> String {
format!("{:?}", self)
}
fn eval_unfiltered(&self, vars: EvaluationVars<F, D>) -> Vec<F::Extension> {
let mut constraints = Vec::with_capacity(self.num_constraints());
for i in 0..NUM_U32_ARITHMETIC_OPS {
let multiplicand_0 = vars.local_wires[Self::wire_ith_multiplicand_0(i)];
let multiplicand_1 = vars.local_wires[Self::wire_ith_multiplicand_1(i)];
let addend = vars.local_wires[Self::wire_ith_addend(i)];
let computed_output = multiplicand_0 * multiplicand_1 + addend;
let output_low = vars.local_wires[Self::wire_ith_output_low_half(i)];
let output_high = vars.local_wires[Self::wire_ith_output_high_half(i)];
let base = F::Extension::from_canonical_u64(1 << 32u64);
let combined_output = output_high * base + output_low;
constraints.push(combined_output - computed_output);
let mut combined_low_limbs = F::Extension::ZERO;
let mut combined_high_limbs = F::Extension::ZERO;
let midpoint = Self::num_limbs() / 2;
let base = F::Extension::from_canonical_u64(1u64 << Self::limb_bits());
for j in (0..Self::num_limbs()).rev() {
let this_limb = vars.local_wires[Self::wire_ith_output_jth_limb(i, j)];
let max_limb = 1 << Self::limb_bits();
let product = (0..max_limb)
.map(|x| this_limb - F::Extension::from_canonical_usize(x))
.product();
constraints.push(product);
if j < midpoint {
combined_low_limbs = base * combined_low_limbs + this_limb;
} else {
combined_high_limbs = base * combined_high_limbs + this_limb;
}
}
constraints.push(combined_low_limbs - output_low);
constraints.push(combined_high_limbs - output_high);
}
constraints
}
fn eval_unfiltered_base(&self, vars: EvaluationVarsBase<F>) -> Vec<F> {
let mut constraints = Vec::with_capacity(self.num_constraints());
for i in 0..NUM_U32_ARITHMETIC_OPS {
let multiplicand_0 = vars.local_wires[Self::wire_ith_multiplicand_0(i)];
let multiplicand_1 = vars.local_wires[Self::wire_ith_multiplicand_1(i)];
let addend = vars.local_wires[Self::wire_ith_addend(i)];
let computed_output = multiplicand_0 * multiplicand_1 + addend;
let output_low = vars.local_wires[Self::wire_ith_output_low_half(i)];
let output_high = vars.local_wires[Self::wire_ith_output_high_half(i)];
let base = F::from_canonical_u64(1 << 32u64);
let combined_output = output_high * base + output_low;
constraints.push(combined_output - computed_output);
let mut combined_low_limbs = F::ZERO;
let mut combined_high_limbs = F::ZERO;
let midpoint = Self::num_limbs() / 2;
let base = F::from_canonical_u64(1u64 << Self::limb_bits());
for j in (0..Self::num_limbs()).rev() {
let this_limb = vars.local_wires[Self::wire_ith_output_jth_limb(i, j)];
let max_limb = 1 << Self::limb_bits();
let product = (0..max_limb)
.map(|x| this_limb - F::from_canonical_usize(x))
.product();
constraints.push(product);
if j < midpoint {
combined_low_limbs = base * combined_low_limbs + this_limb;
} else {
combined_high_limbs = base * combined_high_limbs + this_limb;
}
}
constraints.push(combined_low_limbs - output_low);
constraints.push(combined_high_limbs - output_high);
}
constraints
}
fn eval_unfiltered_recursively(
&self,
builder: &mut CircuitBuilder<F, D>,
vars: EvaluationTargets<D>,
) -> Vec<ExtensionTarget<D>> {
let mut constraints = Vec::with_capacity(self.num_constraints());
for i in 0..NUM_U32_ARITHMETIC_OPS {
let multiplicand_0 = vars.local_wires[Self::wire_ith_multiplicand_0(i)];
let multiplicand_1 = vars.local_wires[Self::wire_ith_multiplicand_1(i)];
let addend = vars.local_wires[Self::wire_ith_addend(i)];
let computed_output = builder.mul_add_extension(multiplicand_0, multiplicand_1, addend);
let output_low = vars.local_wires[Self::wire_ith_output_low_half(i)];
let output_high = vars.local_wires[Self::wire_ith_output_high_half(i)];
let base: F::Extension = F::from_canonical_u64(1 << 32u64).into();
let base_target = builder.constant_extension(base);
let combined_output = builder.mul_add_extension(output_high, base_target, output_low);
constraints.push(builder.sub_extension(combined_output, computed_output));
let mut combined_low_limbs = builder.zero_extension();
let mut combined_high_limbs = builder.zero_extension();
let midpoint = Self::num_limbs() / 2;
let base = builder
.constant_extension(F::Extension::from_canonical_u64(1u64 << Self::limb_bits()));
for j in (0..Self::num_limbs()).rev() {
let this_limb = vars.local_wires[Self::wire_ith_output_jth_limb(i, j)];
let max_limb = 1 << Self::limb_bits();
let mut product = builder.one_extension();
for x in 0..max_limb {
let x_target =
builder.constant_extension(F::Extension::from_canonical_usize(x));
let diff = builder.sub_extension(this_limb, x_target);
product = builder.mul_extension(product, diff);
}
constraints.push(product);
if j < midpoint {
combined_low_limbs =
builder.mul_add_extension(base, combined_low_limbs, this_limb);
} else {
combined_high_limbs =
builder.mul_add_extension(base, combined_high_limbs, this_limb);
}
}
constraints.push(builder.sub_extension(combined_low_limbs, output_low));
constraints.push(builder.sub_extension(combined_high_limbs, output_high));
}
constraints
}
fn generators(
&self,
gate_index: usize,
_local_constants: &[F],
) -> Vec<Box<dyn WitnessGenerator<F>>> {
(0..NUM_U32_ARITHMETIC_OPS)
.map(|i| {
let g: Box<dyn WitnessGenerator<F>> = Box::new(
U32ArithmeticGenerator {
gate_index,
i,
_phantom: PhantomData,
}
.adapter(),
);
g
})
.collect::<Vec<_>>()
}
fn num_wires(&self) -> usize {
NUM_U32_ARITHMETIC_OPS * (5 + Self::num_limbs())
}
fn num_constants(&self) -> usize {
0
}
fn degree(&self) -> usize {
1 << Self::limb_bits()
}
fn num_constraints(&self) -> usize {
NUM_U32_ARITHMETIC_OPS * (3 + Self::num_limbs())
}
}
#[derive(Clone, Debug)]
struct U32ArithmeticGenerator<F: RichField + Extendable<D>, const D: usize> {
gate_index: usize,
i: usize,
_phantom: PhantomData<F>,
}
impl<F: RichField + Extendable<D>, const D: usize> SimpleGenerator<F>
for U32ArithmeticGenerator<F, D>
{
fn dependencies(&self) -> Vec<Target> {
let local_target = |input| Target::wire(self.gate_index, input);
vec![
local_target(U32ArithmeticGate::<F, D>::wire_ith_multiplicand_0(self.i)),
local_target(U32ArithmeticGate::<F, D>::wire_ith_multiplicand_1(self.i)),
local_target(U32ArithmeticGate::<F, D>::wire_ith_addend(self.i)),
]
}
fn run_once(&self, witness: &PartitionWitness<F>, out_buffer: &mut GeneratedValues<F>) {
let local_wire = |input| Wire {
gate: self.gate_index,
input,
};
let get_local_wire = |input| witness.get_wire(local_wire(input));
let multiplicand_0 =
get_local_wire(U32ArithmeticGate::<F, D>::wire_ith_multiplicand_0(self.i));
let multiplicand_1 =
get_local_wire(U32ArithmeticGate::<F, D>::wire_ith_multiplicand_1(self.i));
let addend = get_local_wire(U32ArithmeticGate::<F, D>::wire_ith_addend(self.i));
let output = multiplicand_0 * multiplicand_1 + addend;
let mut output_u64 = output.to_canonical_u64();
let output_high_u64 = output_u64 >> 32;
let output_low_u64 = output_u64 & ((1 << 32) - 1);
let output_high = F::from_canonical_u64(output_high_u64);
let output_low = F::from_canonical_u64(output_low_u64);
let output_high_wire =
local_wire(U32ArithmeticGate::<F, D>::wire_ith_output_high_half(self.i));
let output_low_wire =
local_wire(U32ArithmeticGate::<F, D>::wire_ith_output_low_half(self.i));
out_buffer.set_wire(output_high_wire, output_high);
out_buffer.set_wire(output_low_wire, output_low);
let num_limbs = U32ArithmeticGate::<F, D>::num_limbs();
let limb_base = 1 << U32ArithmeticGate::<F, D>::limb_bits();
let output_limbs_u64 = unfold((), move |_| {
let ret = output_u64 % limb_base;
output_u64 /= limb_base;
Some(ret)
})
.take(num_limbs);
let output_limbs_f = output_limbs_u64.map(F::from_canonical_u64);
for (j, output_limb) in output_limbs_f.enumerate() {
let wire = local_wire(U32ArithmeticGate::<F, D>::wire_ith_output_jth_limb(
self.i, j,
));
out_buffer.set_wire(wire, output_limb);
}
}
}
#[cfg(test)]
mod tests {
use std::marker::PhantomData;
use anyhow::Result;
use rand::Rng;
use crate::field::extension_field::quartic::QuarticExtension;
use crate::field::field_types::Field;
use crate::field::goldilocks_field::GoldilocksField;
use crate::gates::arithmetic_u32::{U32ArithmeticGate, NUM_U32_ARITHMETIC_OPS};
use crate::gates::gate::Gate;
use crate::gates::gate_testing::{test_eval_fns, test_low_degree};
use crate::hash::hash_types::HashOut;
use crate::plonk::vars::EvaluationVars;
#[test]
fn low_degree() {
test_low_degree::<GoldilocksField, _, 4>(U32ArithmeticGate::<GoldilocksField, 4> {
_phantom: PhantomData,
})
}
#[test]
fn eval_fns() -> Result<()> {
test_eval_fns::<GoldilocksField, _, 4>(U32ArithmeticGate::<GoldilocksField, 4> {
_phantom: PhantomData,
})
}
#[test]
fn test_gate_constraint() {
type F = GoldilocksField;
type FF = QuarticExtension<GoldilocksField>;
const D: usize = 4;
fn get_wires(
multiplicands_0: Vec<u64>,
multiplicands_1: Vec<u64>,
addends: Vec<u64>,
) -> Vec<FF> {
let mut v0 = Vec::new();
let mut v1 = Vec::new();
let limb_bits = U32ArithmeticGate::<F, D>::limb_bits();
let num_limbs = U32ArithmeticGate::<F, D>::num_limbs();
let limb_base = 1 << limb_bits;
for c in 0..NUM_U32_ARITHMETIC_OPS {
let m0 = multiplicands_0[c];
let m1 = multiplicands_1[c];
let a = addends[c];
let mut output = m0 * m1 + a;
let output_low = output & ((1 << 32) - 1);
let output_high = output >> 32;
let mut output_limbs = Vec::with_capacity(num_limbs);
for _i in 0..num_limbs {
output_limbs.push(output % limb_base);
output /= limb_base;
}
let mut output_limbs_f: Vec<_> = output_limbs
.into_iter()
.map(F::from_canonical_u64)
.collect();
v0.push(F::from_canonical_u64(m0));
v0.push(F::from_canonical_u64(m1));
v0.push(F::from_canonical_u64(a));
v0.push(F::from_canonical_u64(output_low));
v0.push(F::from_canonical_u64(output_high));
v1.append(&mut output_limbs_f);
}
v0.iter()
.chain(v1.iter())
.map(|&x| x.into())
.collect::<Vec<_>>()
}
let mut rng = rand::thread_rng();
let multiplicands_0: Vec<_> = (0..NUM_U32_ARITHMETIC_OPS)
.map(|_| rng.gen::<u32>() as u64)
.collect();
let multiplicands_1: Vec<_> = (0..NUM_U32_ARITHMETIC_OPS)
.map(|_| rng.gen::<u32>() as u64)
.collect();
let addends: Vec<_> = (0..NUM_U32_ARITHMETIC_OPS)
.map(|_| rng.gen::<u32>() as u64)
.collect();
let gate = U32ArithmeticGate::<F, D> {
_phantom: PhantomData,
};
let vars = EvaluationVars {
local_constants: &[],
local_wires: &get_wires(multiplicands_0, multiplicands_1, addends),
public_inputs_hash: &HashOut::rand(),
};
assert!(
gate.eval_unfiltered(vars).iter().all(|x| x.is_zero()),
"Gate constraints are not satisfied."
);
}
}