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// Copyright (C) 2019-2021 Aleo Systems Inc.
// This file is part of the snarkVM library.
// The snarkVM library is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
// The snarkVM library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
// You should have received a copy of the GNU General Public License
// along with the snarkVM library. If not, see <https://www.gnu.org/licenses/>.
use std::iter;
use snarkvm_fields::{FieldParameters, PrimeField};
use snarkvm_r1cs::{Assignment, ConstraintSystem, LinearCombination};
use crate::{
bits::boolean::{AllocatedBit, Boolean},
errors::SignedIntegerError,
integers::int::*,
traits::{
alloc::AllocGadget,
bits::{RippleCarryAdder, SignExtend},
integers::{Integer, Mul},
select::CondSelectGadget,
},
};
macro_rules! mul_int_impl {
($($gadget: ident)*) => ($(
/// Bitwise multiplication of two signed integer objects.
impl<F: PrimeField> Mul<F> for $gadget {
type ErrorType = SignedIntegerError;
fn mul<CS: ConstraintSystem<F>>(&self, mut cs: CS, other: &Self) -> Result<Self, Self::ErrorType> {
// pseudocode:
//
// res = 0;
// for (i, bit) in other.bits.enumerate() {
// shifted_self = self << i;
//
// if bit {
// res += shifted_self;
// }
// }
// return res
// Conditionally select constant result
let is_constant = Boolean::constant(Self::result_is_constant(&self, &other));
let allocated_false = Boolean::from(AllocatedBit::alloc(&mut cs.ns(|| "false"), || Ok(false)).unwrap());
let false_bit = Boolean::conditionally_select(
&mut cs.ns(|| "constant_or_allocated_false"),
&is_constant,
&Boolean::constant(false),
&allocated_false,
)?;
// Sign extend to double precision
let size = <$gadget as Integer>::SIZE * 2;
let a = Boolean::sign_extend(&self.bits, size);
let b = Boolean::sign_extend(&other.bits, size);
let mut bits = vec![false_bit; size];
// Compute double and add algorithm
let mut to_add = Vec::new();
let mut a_shifted = Vec::new();
for (i, b_bit) in b.iter().enumerate() {
// double
a_shifted.extend(iter::repeat(false_bit).take(i));
a_shifted.extend(a.iter());
a_shifted.truncate(size);
// conditionally add
to_add.reserve(a_shifted.len());
for (j, a_bit) in a_shifted.iter().enumerate() {
let selected_bit = Boolean::conditionally_select(
&mut cs.ns(|| format!("select product bit {} {}", i, j)),
b_bit,
a_bit,
&false_bit,
)?;
to_add.push(selected_bit);
}
bits = bits.add_bits(
&mut cs.ns(|| format!("add bit {}", i)),
&to_add
)?;
let _carry = bits.pop();
to_add.clear();
a_shifted.clear();
}
drop(to_add);
drop(a_shifted);
// Compute the maximum value of the sum
let max_bits = <$gadget as Integer>::SIZE;
// Truncate the bits to the size of the integer
bits.truncate(max_bits);
// Make some arbitrary bounds for ourselves to avoid overflows
// in the scalar field
assert!(F::Parameters::MODULUS_BITS >= max_bits as u32);
// Accumulate the value
let result_value = match (self.value, other.value) {
(Some(a), Some(b)) => {
// check for multiplication overflow here
let val = match a.checked_mul(b) {
Some(val) => val,
None => return Err(SignedIntegerError::Overflow)
};
Some(val)
},
_ => {
// If any of the operands have unknown value, we won't
// know the value of the result
None
}
};
// This is a linear combination that we will enforce to be zero
let mut lc = LinearCombination::zero();
let mut all_constants = true;
// Iterate over each bit_gadget of result and add each bit to
// the linear combination
let mut coeff = F::one();
for bit in bits {
match bit {
Boolean::Is(ref bit) => {
all_constants = false;
// Add the coeff * bit_gadget
lc += (coeff, bit.get_variable());
}
Boolean::Not(ref bit) => {
all_constants = false;
// Add coeff * (1 - bit_gadget) = coeff * ONE - coeff * bit_gadget
lc = lc + (coeff, CS::one()) - (coeff, bit.get_variable());
}
Boolean::Constant(bit) => {
if bit {
lc += (coeff, CS::one());
}
}
}
coeff.double_in_place();
}
// The value of the actual result is modulo 2 ^ $size
let modular_value = result_value.map(|v| v as <$gadget as Integer>::IntegerType);
if all_constants && modular_value.is_some() {
// We can just return a constant, rather than
// unpacking the result into allocated bits.
return Ok(Self::constant(modular_value.unwrap()));
}
// Storage area for the resulting bits
let mut result_bits = Vec::with_capacity(max_bits);
// Allocate each bit_gadget of the result
let mut coeff = F::one();
for i in 0..max_bits {
// get bit value
let mask = 1 << i as <$gadget as Integer>::IntegerType;
// Allocate the bit_gadget
let b = AllocatedBit::alloc(cs.ns(|| format!("result bit_gadget {}", i)), || {
result_value.map(|v| (v & mask) == mask).get()
})?;
// Subtract this bit_gadget from the linear combination to ensure that the sums
// balance out
lc = lc - (coeff, b.get_variable());
result_bits.push(b.into());
coeff.double_in_place();
}
// Enforce that the linear combination equals zero
cs.enforce(|| "modular multiplication", |lc| lc, |lc| lc, |_| lc);
// Discard carry bits we don't care about
result_bits.truncate(<$gadget as Integer>::SIZE);
Ok(Self {
bits: result_bits,
value: modular_value,
})
}
fn mul_unsafe<CS: ConstraintSystem<F>>(&self, mut cs: CS, other: &Self) -> Result<Self, Self::ErrorType> {
// the pseudocode is the same as with Mul::mul, just without the early return on overflow
// Conditionally select constant result
let is_constant = Boolean::constant(Self::result_is_constant(&self, &other));
let allocated_false = Boolean::from(AllocatedBit::alloc(&mut cs.ns(|| "false"), || Ok(false)).unwrap());
let false_bit = Boolean::conditionally_select(
&mut cs.ns(|| "constant_or_allocated_false"),
&is_constant,
&Boolean::constant(false),
&allocated_false,
)?;
// Sign extend to double precision
let size = <$gadget as Integer>::SIZE * 2;
let a = Boolean::sign_extend(&self.bits, size);
let b = Boolean::sign_extend(&other.bits, size);
let mut bits = vec![false_bit; size];
// Compute double and add algorithm
let mut to_add = Vec::new();
let mut a_shifted = Vec::new();
for (i, b_bit) in b.iter().enumerate() {
// double
a_shifted.extend(iter::repeat(false_bit).take(i));
a_shifted.extend(a.iter());
a_shifted.truncate(size);
// conditionally add
to_add.reserve(a_shifted.len());
for (j, a_bit) in a_shifted.iter().enumerate() {
let selected_bit = Boolean::conditionally_select(
&mut cs.ns(|| format!("select product bit {} {}", i, j)),
b_bit,
a_bit,
&false_bit,
)?;
to_add.push(selected_bit);
}
bits = bits.add_bits(
&mut cs.ns(|| format!("add bit {}", i)),
&to_add
)?;
let _carry = bits.pop();
to_add.clear();
a_shifted.clear();
}
drop(to_add);
drop(a_shifted);
// Compute the maximum value of the sum
let max_bits = <$gadget as Integer>::SIZE;
// Truncate the bits to the size of the integer
bits.truncate(max_bits);
// Make some arbitrary bounds for ourselves to avoid overflows
// in the scalar field
assert!(F::Parameters::MODULUS_BITS >= max_bits as u32);
// Accumulate the value
let result_value = match (self.value, other.value) {
(Some(a), Some(b)) => {
Some(a.wrapping_mul(b))
},
_ => {
// If any of the operands have unknown value, we won't
// know the value of the result
None
}
};
// This is a linear combination that we will enforce to be zero
let mut lc = LinearCombination::zero();
let mut all_constants = true;
// Iterate over each bit_gadget of result and add each bit to
// the linear combination
let mut coeff = F::one();
for bit in bits {
match bit {
Boolean::Is(ref bit) => {
all_constants = false;
// Add the coeff * bit_gadget
lc += (coeff, bit.get_variable());
}
Boolean::Not(ref bit) => {
all_constants = false;
// Add coeff * (1 - bit_gadget) = coeff * ONE - coeff * bit_gadget
lc = lc + (coeff, CS::one()) - (coeff, bit.get_variable());
}
Boolean::Constant(bit) => {
if bit {
lc += (coeff, CS::one());
}
}
}
coeff.double_in_place();
}
// The value of the actual result is modulo 2 ^ $size
let modular_value = result_value.map(|v| v as <$gadget as Integer>::IntegerType);
if all_constants && modular_value.is_some() {
// We can just return a constant, rather than
// unpacking the result into allocated bits.
return Ok(Self::constant(modular_value.unwrap()));
}
// Storage area for the resulting bits
let mut result_bits = Vec::with_capacity(max_bits);
// Allocate each bit_gadget of the result
let mut coeff = F::one();
for i in 0..max_bits {
// get bit value
let mask = 1 << i as <$gadget as Integer>::IntegerType;
// Allocate the bit_gadget
let b = AllocatedBit::alloc(cs.ns(|| format!("result bit_gadget {}", i)), || {
result_value.map(|v| (v & mask) == mask).get()
})?;
// Subtract this bit_gadget from the linear combination to ensure that the sums
// balance out
lc = lc - (coeff, b.get_variable());
result_bits.push(b.into());
coeff.double_in_place();
}
// Enforce that the linear combination equals zero
cs.enforce(|| "modular multiplication", |lc| lc, |lc| lc, |_| lc);
// Discard carry bits we don't care about
result_bits.truncate(<$gadget as Integer>::SIZE);
Ok(Self {
bits: result_bits,
value: modular_value,
})
}
}
)*)
}
mul_int_impl!(Int8 Int16 Int32 Int64 Int128);