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| 1 | +use crate::air::{Word64, WordAirBuilder, WORD64_SIZE}; |
| 2 | +use crate::bytes::event::ByteRecord; |
| 3 | + |
| 4 | +use p3_air::AirBuilder; |
| 5 | +use p3_field::{AbstractField, Field}; |
| 6 | +use sphinx_derive::AlignedBorrow; |
| 7 | + |
| 8 | +/// A set of columns needed to compute the add of two double words. |
| 9 | +#[derive(AlignedBorrow, Default, Debug, Clone, Copy)] |
| 10 | +#[repr(C)] |
| 11 | +pub struct Add64Operation<T> { |
| 12 | + /// The result of `a + b`. |
| 13 | + pub value: Word64<T>, |
| 14 | + |
| 15 | + /// Trace. |
| 16 | + pub carry: [T; WORD64_SIZE - 1], |
| 17 | +} |
| 18 | + |
| 19 | +impl<F: Field> Add64Operation<F> { |
| 20 | + pub fn populate( |
| 21 | + &mut self, |
| 22 | + record: &mut impl ByteRecord, |
| 23 | + shard: u32, |
| 24 | + channel: u32, |
| 25 | + a_u64: u64, |
| 26 | + b_u64: u64, |
| 27 | + ) -> u64 { |
| 28 | + let expected = a_u64.wrapping_add(b_u64); |
| 29 | + self.value = Word64::from(expected); |
| 30 | + let a = a_u64.to_le_bytes(); |
| 31 | + let b = b_u64.to_le_bytes(); |
| 32 | + |
| 33 | + let mut carry = [0u8; WORD64_SIZE - 1]; |
| 34 | + if u64::from(a[0]) + u64::from(b[0]) > 255 { |
| 35 | + carry[0] = 1; |
| 36 | + self.carry[0] = F::one(); |
| 37 | + } |
| 38 | + for i in 1..WORD64_SIZE - 1 { |
| 39 | + if u64::from(a[i]) + u64::from(b[i]) + u64::from(carry[i - 1]) > 255 { |
| 40 | + carry[i] = 1; |
| 41 | + self.carry[i] = F::one(); |
| 42 | + } |
| 43 | + } |
| 44 | + |
| 45 | + let base = 256u64; |
| 46 | + let overflow = u64::from( |
| 47 | + a[0].wrapping_add(b[0]) |
| 48 | + .wrapping_sub(expected.to_le_bytes()[0]), |
| 49 | + ); |
| 50 | + debug_assert_eq!(overflow.wrapping_mul(overflow.wrapping_sub(base)), 0); |
| 51 | + |
| 52 | + // Range check |
| 53 | + { |
| 54 | + record.add_u8_range_checks(shard, channel, &a); |
| 55 | + record.add_u8_range_checks(shard, channel, &b); |
| 56 | + record.add_u8_range_checks(shard, channel, &expected.to_le_bytes()); |
| 57 | + } |
| 58 | + expected |
| 59 | + } |
| 60 | + |
| 61 | + pub fn eval<AB: WordAirBuilder<F = F>>( |
| 62 | + builder: &mut AB, |
| 63 | + a: Word64<AB::Var>, |
| 64 | + b: Word64<AB::Var>, |
| 65 | + cols: Add64Operation<AB::Var>, |
| 66 | + shard: AB::Var, |
| 67 | + channel: impl Into<AB::Expr> + Clone, |
| 68 | + is_real: AB::Expr, |
| 69 | + ) { |
| 70 | + let one = AB::Expr::one(); |
| 71 | + let base = AB::F::from_canonical_u32(256); |
| 72 | + |
| 73 | + let mut builder_is_real = builder.when(is_real.clone()); |
| 74 | + |
| 75 | + // For each limb, assert that difference between the carried result and the non-carried |
| 76 | + // result is either zero or the base. |
| 77 | + let overflow_0 = a[0] + b[0] - cols.value[0]; |
| 78 | + let overflow_1 = a[1] + b[1] - cols.value[1] + cols.carry[0]; |
| 79 | + let overflow_2 = a[2] + b[2] - cols.value[2] + cols.carry[1]; |
| 80 | + let overflow_3 = a[3] + b[3] - cols.value[3] + cols.carry[2]; |
| 81 | + let overflow_4 = a[4] + b[4] - cols.value[4] + cols.carry[3]; |
| 82 | + let overflow_5 = a[5] + b[5] - cols.value[5] + cols.carry[4]; |
| 83 | + let overflow_6 = a[6] + b[6] - cols.value[6] + cols.carry[5]; |
| 84 | + let overflow_7 = a[7] + b[7] - cols.value[7] + cols.carry[6]; |
| 85 | + builder_is_real.assert_zero(overflow_0.clone() * (overflow_0.clone() - base)); |
| 86 | + builder_is_real.assert_zero(overflow_1.clone() * (overflow_1.clone() - base)); |
| 87 | + builder_is_real.assert_zero(overflow_2.clone() * (overflow_2.clone() - base)); |
| 88 | + builder_is_real.assert_zero(overflow_3.clone() * (overflow_3.clone() - base)); |
| 89 | + builder_is_real.assert_zero(overflow_4.clone() * (overflow_4.clone() - base)); |
| 90 | + builder_is_real.assert_zero(overflow_5.clone() * (overflow_5.clone() - base)); |
| 91 | + builder_is_real.assert_zero(overflow_6.clone() * (overflow_6.clone() - base)); |
| 92 | + builder_is_real.assert_zero(overflow_7.clone() * (overflow_7.clone() - base)); |
| 93 | + |
| 94 | + // If the carry is one, then the overflow must be the base. |
| 95 | + builder_is_real.assert_zero(cols.carry[0] * (overflow_0.clone() - base)); |
| 96 | + builder_is_real.assert_zero(cols.carry[1] * (overflow_1.clone() - base)); |
| 97 | + builder_is_real.assert_zero(cols.carry[2] * (overflow_2.clone() - base)); |
| 98 | + builder_is_real.assert_zero(cols.carry[3] * (overflow_3.clone() - base)); |
| 99 | + builder_is_real.assert_zero(cols.carry[4] * (overflow_4.clone() - base)); |
| 100 | + builder_is_real.assert_zero(cols.carry[5] * (overflow_5.clone() - base)); |
| 101 | + builder_is_real.assert_zero(cols.carry[6] * (overflow_6.clone() - base)); |
| 102 | + |
| 103 | + // If the carry is not one, then the overflow must be zero. |
| 104 | + builder_is_real.assert_zero((cols.carry[0] - one.clone()) * overflow_0.clone()); |
| 105 | + builder_is_real.assert_zero((cols.carry[1] - one.clone()) * overflow_1.clone()); |
| 106 | + builder_is_real.assert_zero((cols.carry[2] - one.clone()) * overflow_2.clone()); |
| 107 | + builder_is_real.assert_zero((cols.carry[3] - one.clone()) * overflow_3.clone()); |
| 108 | + builder_is_real.assert_zero((cols.carry[4] - one.clone()) * overflow_4.clone()); |
| 109 | + builder_is_real.assert_zero((cols.carry[5] - one.clone()) * overflow_5.clone()); |
| 110 | + builder_is_real.assert_zero((cols.carry[6] - one.clone()) * overflow_6.clone()); |
| 111 | + |
| 112 | + // Assert that the carry is either zero or one. |
| 113 | + builder_is_real.assert_bool(cols.carry[0]); |
| 114 | + builder_is_real.assert_bool(cols.carry[1]); |
| 115 | + builder_is_real.assert_bool(cols.carry[2]); |
| 116 | + builder_is_real.assert_bool(cols.carry[3]); |
| 117 | + builder_is_real.assert_bool(cols.carry[4]); |
| 118 | + builder_is_real.assert_bool(cols.carry[5]); |
| 119 | + builder_is_real.assert_bool(cols.carry[6]); |
| 120 | + builder_is_real.assert_bool(is_real.clone()); |
| 121 | + |
| 122 | + // Range check each byte. |
| 123 | + { |
| 124 | + builder.slice_range_check_u8(&a.0, shard, channel.clone(), is_real.clone()); |
| 125 | + builder.slice_range_check_u8(&b.0, shard, channel.clone(), is_real.clone()); |
| 126 | + builder.slice_range_check_u8(&cols.value.0, shard, channel, is_real); |
| 127 | + } |
| 128 | + } |
| 129 | +} |
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