1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156

// 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 snarkvm_fields::PrimeField;
use snarkvm_r1cs::{ConstraintSystem, SynthesisError};

use crate::{
    bits::boolean::{AllocatedBit, Boolean},
    errors::UnsignedIntegerError,
    integers::uint::*,
    traits::{
        alloc::AllocGadget,
        integers::{Div, Integer},
        select::CondSelectGadget,
    },
};

/// Perform long division of two `UInt` objects.
/// Reference: https://en.wikipedia.org/wiki/Division_algorithm
macro_rules! div_int_impl {
    ($($gadget:ident),*) => ($(
        impl<F: PrimeField> Div<F> for $gadget {
            type ErrorType = UnsignedIntegerError;

            fn div<CS: ConstraintSystem<F>>(
                &self,
                mut cs: CS,
                other: &Self,
            ) -> Result<Self, Self::ErrorType> {
                // pseudocode:
                //
                // if D = 0 then error(DivisionByZeroException) end
                // Q := 0                  -- Initialize quotient and remainder to zero
                // R := 0
                // for i := n − 1 .. 0 do  -- Where n is number of bits in N
                //   R := R << 1           -- Left-shift R by 1 bit
                //   R(0) := N(i)          -- Set the least-significant bit of R equal to bit i of the numerator
                //   if R ≥ D then
                //     R := R − D
                //     Q(i) := 1
                //   end
                // end

                if other.eq(&Self::constant(0 as <$gadget as Integer>::IntegerType)) {
                    return Err(SynthesisError::DivisionByZero.into());
                }

                let is_constant = Boolean::constant(Self::result_is_constant(&self, &other));

                let allocated_true = Boolean::from(AllocatedBit::alloc(&mut cs.ns(|| "true"), || Ok(true)).unwrap());
                let true_bit = Boolean::conditionally_select(
                    &mut cs.ns(|| "constant_or_allocated_true"),
                    &is_constant,
                    &Boolean::constant(true),
                    &allocated_true,
                )?;

                let allocated_one = Self::alloc(&mut cs.ns(|| "one"), || Ok(1 as <$gadget as Integer>::IntegerType))?;
                let one = Self::conditionally_select(
                    &mut cs.ns(|| "constant_or_allocated_1"),
                    &is_constant,
                    &Self::constant(1 as <$gadget as Integer>::IntegerType),
                    &allocated_one,
                )?;

                let allocated_zero = Self::alloc(&mut cs.ns(|| "zero"), || Ok(0 as <$gadget as Integer>::IntegerType))?;
                let zero = Self::conditionally_select(
                    &mut cs.ns(|| "constant_or_allocated_0"),
                    &is_constant,
                    &Self::constant(0 as <$gadget as Integer>::IntegerType),
                    &allocated_zero,
                )?;

                let self_is_zero = Boolean::Constant(self.eq(&Self::constant(0 as <$gadget as Integer>::IntegerType)));
                let mut quotient = zero.clone();
                let mut remainder = zero.clone();

                for (i, bit) in self.bits.iter().rev().enumerate() {
                    // Left shift remainder by 1
                    remainder = Self::addmany(&mut cs.ns(|| format!("shift_left_{}", i)), &[
                        remainder.clone(),
                        remainder.clone(),
                    ])?;

                    // Set the least-significant bit of remainder to bit i of the numerator
                    let bit_is_true = Boolean::constant(bit.eq(&Boolean::constant(true)));
                    let new_remainder = Self::addmany(&mut cs.ns(|| format!("set_remainder_bit_{}", i)), &[
                        remainder.clone(),
                        one.clone(),
                    ])?;

                    remainder = Self::conditionally_select(
                        &mut cs.ns(|| format!("increment_or_remainder_{}", i)),
                        &bit_is_true,
                        &new_remainder,
                        &remainder,
                    )?;

                    // Greater than or equal to:
                    //   R >= D
                    //   (R == D) || (R > D)
                    //   (R == D) || ((R !=D) && ((R - D) != 0))
                    //
                    //  (R > D)                     checks subtraction overflow before evaluation
                    //  (R != D) && ((R - D) != 0)  instead evaluate subtraction and check for overflow after

                    let no_remainder = Boolean::constant(remainder.eq(&other));
                    let subtraction = remainder.sub_unsafe(&mut cs.ns(|| format!("subtract_divisor_{}", i)), &other)?;
                    let sub_is_zero = Boolean::constant(subtraction.eq(&Self::constant(0 as <$gadget as Integer>::IntegerType)));
                    let cond1 = Boolean::and(
                        &mut cs.ns(|| format!("cond_1_{}", i)),
                        &no_remainder.not(),
                        &sub_is_zero.not(),
                    )?;
                    let cond2 = Boolean::or(&mut cs.ns(|| format!("cond_2_{}", i)), &no_remainder, &cond1)?;

                    remainder = Self::conditionally_select(
                        &mut cs.ns(|| format!("subtract_or_same_{}", i)),
                        &cond2,
                        &subtraction,
                        &remainder,
                    )?;

                    let index = <$gadget as Integer>::SIZE - 1 - i as usize;
                    let bit_value = (1 as <$gadget as Integer>::IntegerType) << (index as <$gadget as Integer>::IntegerType);
                    let mut new_quotient = quotient.clone();
                    new_quotient.bits[index] = true_bit;
                    new_quotient.value = Some(new_quotient.value.unwrap() + bit_value);

                    quotient = Self::conditionally_select(
                        &mut cs.ns(|| format!("set_bit_or_same_{}", i)),
                        &cond2,
                        &new_quotient,
                        &quotient,
                    )?;
                }
                Self::conditionally_select(&mut cs.ns(|| "self_or_quotient"), &self_is_zero, self, &quotient).map_err(UnsignedIntegerError::SynthesisError)
            }
        }
    )*)
}

div_int_impl!(UInt8, UInt16, UInt32, UInt64, UInt128);