sp1_core_machine/operations/
add4.rs

1use slop_algebra::{AbstractField, Field};
2use sp1_derive::AlignedBorrow;
3
4use sp1_core_executor::events::ByteRecord;
5use sp1_hypercube::air::SP1AirBuilder;
6use sp1_primitives::consts::u32_to_u16_limbs;
7
8use crate::{air::WordAirBuilder, utils::u32_to_half_word};
9
10/// A set of columns needed to compute the add of four u32s as u32.
11#[derive(AlignedBorrow, Default, Debug, Clone, Copy)]
12#[repr(C)]
13pub struct Add4Operation<T> {
14    /// The result of `a + b + c + d`.
15    pub value: [T; 2],
16}
17
18impl<F: Field> Add4Operation<F> {
19    #[allow(clippy::too_many_arguments)]
20    pub fn populate(
21        &mut self,
22        record: &mut impl ByteRecord,
23        a_u32: u32,
24        b_u32: u32,
25        c_u32: u32,
26        d_u32: u32,
27    ) -> u32 {
28        let expected = a_u32.wrapping_add(b_u32).wrapping_add(c_u32).wrapping_add(d_u32);
29        let expected_limbs = u32_to_u16_limbs(expected);
30        self.value = u32_to_half_word(expected);
31        let a = u32_to_u16_limbs(a_u32);
32        let b = u32_to_u16_limbs(b_u32);
33        let c = u32_to_u16_limbs(c_u32);
34        let d = u32_to_u16_limbs(d_u32);
35
36        let base = 1u32 << 16;
37        let mut carry_limbs = [0u8; 2];
38        let mut carry = 0;
39        for i in 0..2 {
40            carry = ((a[i] as u32) + (b[i] as u32) + (c[i] as u32) + (d[i] as u32) + carry
41                - expected_limbs[i] as u32)
42                / base;
43            carry_limbs[i] = carry as u8;
44        }
45
46        // Range check.
47        record.add_u16_range_checks(&expected_limbs);
48        record.add_u8_range_checks(&carry_limbs);
49        expected
50    }
51
52    /// Evaluate the add4 operation.
53    /// Assumes that `a`, `b`, `c`, `d` are valid u32s of two u16 limbs.
54    /// Constrains that `is_real` is boolean.
55    /// If `is_real == 1` , the `value` is constrained to a valid u32 representing `a + b + c + d`.
56    #[allow(clippy::too_many_arguments)]
57    pub fn eval<AB: SP1AirBuilder>(
58        builder: &mut AB,
59        a: [AB::Expr; 2],
60        b: [AB::Expr; 2],
61        c: [AB::Expr; 2],
62        d: [AB::Expr; 2],
63        is_real: AB::Var,
64        cols: Add4Operation<AB::Var>,
65    ) {
66        builder.assert_bool(is_real);
67
68        let base = AB::F::from_canonical_u32(1 << 16);
69        let mut carry_limbs = [AB::Expr::zero(), AB::Expr::zero()];
70        let mut carry = AB::Expr::zero(); // Initialize carry to zero
71
72        // The set of constraints are
73        //  - carry is initialized to zero
74        //  - 2^16 * carry_next + value[i] = a[i] + b[i] + c[i] + d[i] + carry
75        //  - 0 <= carry < 2^8
76        //  - 0 <= value[i] < 2^16
77        // Since the carries are bounded by 2^8, no SP1Field overflows are possible.
78        // The maximum carry possible is less than 2^8, so the circuit is complete.
79        for i in 0..2 {
80            carry = (a[i].clone() + b[i].clone() + c[i].clone() + d[i].clone() - cols.value[i]
81                + carry)
82                * base.inverse();
83            carry_limbs[i] = carry.clone();
84        }
85        // Range check each limb.
86        builder.slice_range_check_u16(&cols.value, is_real);
87        builder.slice_range_check_u8(&carry_limbs, is_real);
88    }
89}
sp1_core_machine/operations/add4.rs

sp1_core_machine/operations/
add4.rs
