example: Projected / Repeated columns usage (#6)

* example: Add example of Projected column usage

* example: Add example of Repeated column usage

* example: Add example of ZeroPadded column usage

examples/Cargo.toml

@@ -92,6 +92,18 @@ path = "acc-shifted.rs"
 name = "acc-packed"
 path = "acc-packed.rs"
 
+[[example]]
+name = "acc-projected"
+path = "acc-projected.rs"
+
+[[example]]
+name = "acc-repeated"
+path = "acc-repeated.rs"
+
+[[example]]
+name = "acc-zeropadded"
+path = "acc-zeropadded.rs"
+
 [lints.clippy]
 needless_range_loop = "allow"
 

examples/acc-projected.rs

@@ -0,0 +1,248 @@
+use binius_circuits::{builder::ConstraintSystemBuilder, unconstrained::unconstrained};
+use binius_core::{constraint_system::validate::validate_witness, oracle::ProjectionVariant};
+use binius_field::{arch::OptimalUnderlier, BinaryField128b, BinaryField8b};
+
+type U = OptimalUnderlier;
+type F128 = BinaryField128b;
+type F8 = BinaryField8b;
+
+#[derive(Clone)]
+struct U8U128ProjectionInfo {
+	log_size: usize,
+	decimal: usize,
+	binary: Vec<F128>,
+	variant: ProjectionVariant,
+}
+
+// The idea behind projection is that data from a column of some given field (F8)
+// can be interpreted as a data of some or greater field (F128) and written to another column with equal or smaller length,
+// which depends on LOG_SIZE and values of projection. Also two possible variants of projections are available, which
+// has significant impact on input data processing.
+// In the following example we have input column with bytes (u8) projected to the output column with u128 values.
+fn projection(
+	builder: &mut ConstraintSystemBuilder<U, F128>,
+	projection_info: U8U128ProjectionInfo,
+	namespace: &str,
+) {
+	builder.push_namespace(format!("projection {}", namespace));
+
+	let input =
+		unconstrained::<U, F128, F8>(builder, "in", projection_info.clone().log_size).unwrap();
+
+	let projected = builder
+		.add_projected(
+			"projected",
+			input,
+			projection_info.clone().binary,
+			projection_info.clone().variant,
+		)
+		.unwrap();
+
+	if let Some(witness) = builder.witness() {
+		let input_values = witness.get::<F8>(input).unwrap().as_slice::<u8>();
+		let mut projected_witness = witness.new_column::<F128>(projected);
+		let projected_values = projected_witness.as_mut_slice::<F128>();
+
+		assert_eq!(projected_values.len(), projection_info.expected_projection_len());
+
+		match projection_info.variant {
+			ProjectionVariant::FirstVars => {
+				// Quite elaborated regularity, on my opinion
+				for idx in 0..projected_values.len() {
+					projected_values[idx] = F128::new(
+						input_values[(idx
+							* 2usize.pow(projection_info.clone().binary.len() as u32))
+							+ projection_info.clone().decimal] as u128,
+					);
+				}
+			}
+			ProjectionVariant::LastVars => {
+				// decimal representation of the binary values is used as a simple offset
+				for idx in 0..projected_values.len() {
+					projected_values[idx] =
+						F128::new(input_values[projection_info.clone().decimal + idx] as u128);
+				}
+			}
+		};
+	}
+	builder.pop_namespace();
+}
+
+impl U8U128ProjectionInfo {
+	fn new(
+		log_size: usize,
+		decimal: usize,
+		binary: Vec<F128>,
+		variant: ProjectionVariant,
+	) -> U8U128ProjectionInfo {
+		assert!(log_size >= binary.len());
+
+		if variant == ProjectionVariant::LastVars {
+			// Pad with zeroes to LOG_SIZE len iterator.
+			// In this case we interpret binary values in a reverse order, meaning that the very first
+			// element is elder byte, so zeroes must be explicitly appended
+			let mut binary_clone = binary.clone();
+			let mut zeroes = vec![F128::new(0u128); log_size - binary.len()];
+			binary_clone.append(&mut zeroes);
+
+			let coefficients = (0..binary_clone.len())
+				.map(|degree| F128::new(2usize.pow(degree as u32) as u128))
+				.collect::<Vec<F128>>();
+
+			let value = binary_clone
+				.iter()
+				.zip(coefficients.iter().rev())
+				.fold(F128::new(0u128), |acc, (byte, coefficient)| acc + (*byte) * (*coefficient));
+
+			assert_eq!(decimal as u128, value.val());
+		}
+
+		U8U128ProjectionInfo {
+			log_size,
+			decimal,
+			binary,
+			variant,
+		}
+	}
+
+	fn expected_projection_len(&self) -> usize {
+		2usize.pow((self.log_size - self.binary.len()) as u32)
+	}
+}
+
+fn main() {
+	let allocator = bumpalo::Bump::new();
+	let mut builder = ConstraintSystemBuilder::<U, F128>::new_with_witness(&allocator);
+
+	let projection_data = U8U128ProjectionInfo::new(
+		4usize,
+		9usize,
+		vec![
+			F128::from(1u128),
+			F128::from(0u128),
+			F128::from(0u128),
+			F128::from(1u128),
+		],
+		ProjectionVariant::FirstVars,
+	);
+	projection(&mut builder, projection_data, "test_1");
+
+	let projection_data = U8U128ProjectionInfo::new(
+		16usize,
+		34816usize,
+		vec![
+			F128::from(1u128),
+			F128::from(0u128),
+			F128::from(0u128),
+			F128::from(0u128),
+			F128::from(1u128),
+		],
+		ProjectionVariant::LastVars,
+	);
+	projection(&mut builder, projection_data, "test_2");
+
+	let projection_data = U8U128ProjectionInfo::new(
+		4usize,
+		15usize,
+		vec![
+			F128::from(1u128),
+			F128::from(1u128),
+			F128::from(1u128),
+			F128::from(1u128),
+		],
+		ProjectionVariant::LastVars,
+	);
+	projection(&mut builder, projection_data, "test_3");
+
+	let projection_data = U8U128ProjectionInfo::new(
+		6usize,
+		60usize,
+		vec![
+			F128::from(1u128),
+			F128::from(1u128),
+			F128::from(1u128),
+			F128::from(1u128),
+		],
+		ProjectionVariant::LastVars,
+	);
+	/*
+		With projection_data defined above we have 2^LOG_SIZE = 2^6 bytes in the input,
+		the size of projection is computed as follows: 2.pow(LOG_SIZE - binary.len()) = 2.pow(6 - 4) = 4.
+		the index of the input byte to use as projection is computed as follows (according to
+		a LastVars projection variant regularity):
+
+		idx + decimal, e.g.:
+
+		0 + 60
+		1 + 60
+		2 + 60
+		3 + 60
+
+		where idx is [0..4].
+
+		Memory layout:
+
+		input: [a5, a2, b1, 60, 91, ed, 5e, fb, ae, 1c, b2, 14, 92, 73, 92, c8, 56, 6d, fa, de, a8, 46, 77, 48, e1, cc, 90, 75, 78, d5, 19, be, 0c, 86, 39, 28, 0c, cc, e9, 4e, 46, d9, 84, 65, 4a, a2, b4, 64, eb, 59, 7b, fd, 3f, 0e, 2d, ea, 06, 42, a9, ea, (19), (8f), (19), (52)], len: 64
+		output: [
+			BinaryField128b(0x00000000000000000000000000000019),
+			BinaryField128b(0x0000000000000000000000000000008f),
+			BinaryField128b(0x00000000000000000000000000000019),
+			BinaryField128b(0x00000000000000000000000000000052)
+		]
+	*/
+	projection(&mut builder, projection_data, "test_4");
+
+	let projection_data = U8U128ProjectionInfo::new(
+		4usize,
+		15usize,
+		vec![
+			F128::from(1u128),
+			F128::from(1u128),
+			F128::from(1u128),
+			F128::from(1u128),
+		],
+		ProjectionVariant::FirstVars,
+	);
+	projection(&mut builder, projection_data, "test_5");
+
+	let projection_data = U8U128ProjectionInfo::new(
+		6usize,
+		13usize,
+		vec![
+			F128::from(1u128),
+			F128::from(0u128),
+			F128::from(1u128),
+			F128::from(1u128),
+		],
+		ProjectionVariant::FirstVars,
+	);
+	/*
+		With projection_data defined above we have 2^LOG_SIZE = 2^6 bytes in the input,
+		the size of projection is computed as follows: 2.pow(LOG_SIZE - binary.len()) = 2.pow(6 - 4) = 4.
+		the index of the input byte to use as projection is computed as follows:
+
+		idx * 2usize.pow(binary.len()) + decimal, e.g.:
+
+		0 * 2.pow(4) + 13 = 13, so input[13]
+		1 * 2.pow(4) + 13 = 29, so input[29]
+		2 * 2.pow(4) + 13 = 45, so input[45]
+		3 * 2.pow(4) + 13 = 61, so input[61]
+
+		where idx is [0..4] according to a FirstVars projection variant regularity.
+
+		Memory layout:
+
+		input: [18, d8, 58, d3, 24, f1, 8b, ec, 74, 1c, ab, 78, 13, (3e), 57, d7, 36, 15, 54, 50, 9a, cb, 98, 90, 58, cb, 79, 05, 83, (72), ea, 4d, f6, 3d, f3, 2f, af, e3, 32, 11, c9, 97, fb, ba, 24, (36), e9, 38, 7e, c7, a9, 68, bf, 31, 51, cf, 7b, 12, 20, 53, d8, (df), d7, cc], len: 64
+
+		output: BinaryField128b(0x0000000000000000000000000000003e)
+		output: BinaryField128b(0x00000000000000000000000000000072)
+		output: BinaryField128b(0x00000000000000000000000000000036)
+		output: BinaryField128b(0x000000000000000000000000000000df)
+	*/
+	projection(&mut builder, projection_data, "test_6");
+
+	let witness = builder.take_witness().unwrap();
+	let cs = builder.build().unwrap();
+
+	validate_witness(&cs, &[], &witness).unwrap();
+}

examples/acc-repeated.rs

@@ -0,0 +1,124 @@
+use binius_circuits::{builder::ConstraintSystemBuilder, unconstrained::unconstrained};
+use binius_core::constraint_system::validate::validate_witness;
+use binius_field::{
+	arch::OptimalUnderlier, packed::set_packed_slice, BinaryField128b, BinaryField1b,
+	BinaryField8b, PackedBinaryField128x1b,
+};
+
+type U = OptimalUnderlier;
+type F128 = BinaryField128b;
+type F8 = BinaryField8b;
+type F1 = BinaryField1b;
+
+// FIXME: Following gadgets are unconstrained. Only for demonstrative purpose, don't use in production
+
+const LOG_SIZE: usize = 8;
+
+// The idea of 'Repeated' column is that one can just copy data from initial column multiple times,
+// so new column is X times bigger than original one. The following gadget operates over bytes, e.g.
+// it creates column with some input bytes written and then creates one more 'Repeated' column
+// where the same bytes are copied multiple times.
+fn bytes_repeat_gadget(builder: &mut ConstraintSystemBuilder<U, F128>) {
+	builder.push_namespace("bytes_repeat_gadget");
+
+	let bytes = unconstrained::<U, F128, F8>(builder, "input", LOG_SIZE).unwrap();
+
+	let repeat_times_log = 4usize;
+	let repeating = builder
+		.add_repeating("repeating", bytes, repeat_times_log)
+		.unwrap();
+
+	if let Some(witness) = builder.witness() {
+		let input_values = witness.get::<F8>(bytes).unwrap().as_slice::<u8>();
+
+		let mut repeating_witness = witness.new_column::<F8>(repeating);
+		let repeating_values = repeating_witness.as_mut_slice::<u8>();
+
+		let repeat_times = 2usize.pow(repeat_times_log as u32);
+		assert_eq!(2usize.pow(LOG_SIZE as u32), input_values.len());
+		assert_eq!(input_values.len() * repeat_times, repeating_values.len());
+
+		for idx in 0..repeat_times {
+			let start = idx * input_values.len();
+			let end = start + input_values.len();
+			repeating_values[start..end].copy_from_slice(input_values);
+		}
+	}
+
+	builder.pop_namespace();
+}
+
+// Bit-oriented repeating is more elaborated due to a specifics of memory layout in Binius.
+// In the following example, we use LOG_SIZE=8, which gives 2.pow(8) = 32 bytes written in the memory
+// layout. This gives 32 * 8 = 256 bits of input information. Having that Repeated' column
+// is instantiated with 'repeat_times_log = 2', this means that we have to repeat our bytes
+// 2.pow(repeat_times_log) = 4 times ultimately. For setting bit values we use PackedBinaryField128x1b,
+// so for 32 bytes (256 bits) of input data we use 2 PackedBinaryField128x1b elements. Considering 4
+// repetitions Binius creates column with 8 PackedBinaryField128x1b elements totally.
+// Proper writing bits requires separate iterating over PackedBinaryField128x1b elements and input bytes
+// with extracting particular bit values from the input and setting appropriate bit in a given PackedBinaryField128x1b.
+fn bits_repeat_gadget(builder: &mut ConstraintSystemBuilder<U, F128>) {
+	builder.push_namespace("bits_repeat_gadget");
+
+	let bits = unconstrained::<U, F128, F1>(builder, "input", LOG_SIZE).unwrap();
+	let repeat_times_log = 2usize;
+
+	// Binius will create column with appropriate height for us
+	let repeating = builder
+		.add_repeating("repeating", bits, repeat_times_log)
+		.unwrap();
+
+	if let Some(witness) = builder.witness() {
+		let input_values = witness.get::<F1>(bits).unwrap().as_slice::<u8>();
+		let mut repeating_witness = witness.new_column::<F1>(repeating);
+		let output_values = repeating_witness.packed();
+
+		// this performs writing input bits exactly 1 time. Depending on number of repetitions we
+		// need to call this multiple times, providing offset for output values (PackedBinaryField128x1b elements)
+		fn write_input(
+			input_values: &[u8],
+			output_values: &mut [PackedBinaryField128x1b],
+			output_packed_offset: usize,
+		) {
+			let mut output_index = output_packed_offset;
+			for (input_index, _) in (0..input_values.len()).enumerate() {
+				let byte = input_values[input_index];
+
+				set_packed_slice(output_values, output_index, F1::from(byte));
+				set_packed_slice(output_values, output_index + 1, F1::from((byte >> 1) & 0x01));
+				set_packed_slice(output_values, output_index + 2, F1::from((byte >> 2) & 0x01));
+				set_packed_slice(output_values, output_index + 3, F1::from((byte >> 3) & 0x01));
+				set_packed_slice(output_values, output_index + 4, F1::from((byte >> 4) & 0x01));
+				set_packed_slice(output_values, output_index + 5, F1::from((byte >> 5) & 0x01));
+				set_packed_slice(output_values, output_index + 6, F1::from((byte >> 6) & 0x01));
+				set_packed_slice(output_values, output_index + 7, F1::from((byte >> 7) & 0x01));
+
+				output_index += 8;
+			}
+		}
+
+		let repeat_times = 2u32.pow(repeat_times_log as u32);
+
+		let mut offset = 0;
+		for _ in 0..repeat_times {
+			write_input(input_values, output_values, offset);
+			offset += input_values.len() * 8;
+		}
+	}
+
+	builder.pop_namespace();
+}
+
+fn main() {
+	let allocator = bumpalo::Bump::new();
+
+	let mut builder = ConstraintSystemBuilder::<U, F128>::new_with_witness(&allocator);
+
+	bytes_repeat_gadget(&mut builder);
+	bits_repeat_gadget(&mut builder);
+
+	let witness = builder.take_witness().unwrap();
+	let cs = builder.build().unwrap();
+
+	validate_witness(&cs, &[], &witness).unwrap();
+}