ark-r1cs-std/r1cs-std/src/bits/uint64.rs
r1cs-std/src/bits/uint64.rsRaw
1use algebra::{Field, FpParameters, PrimeField};
2
3use r1cs_core::{ConstraintSystem, LinearCombination, SynthesisError};
4
5use crate::{
6 boolean::{AllocatedBit, Boolean},
7 prelude::*,
8 Assignment, Vec,
9};
10
11/// Represents an interpretation of 64 `Boolean` objects as an
12/// unsigned integer.
13#[derive(Clone, Debug)]
14pub struct UInt64 {
15 // Least significant bit_gadget first
16 bits: Vec<Boolean>,
17 value: Option<u64>,
18}
19
20impl UInt64 {
21 /// Construct a constant `UInt64` from a `u64`
22 pub fn constant(value: u64) -> Self {
23 let mut bits = Vec::with_capacity(64);
24
25 let mut tmp = value;
26 for _ in 0..64 {
27 if tmp & 1 == 1 {
28 bits.push(Boolean::constant(true))
29 } else {
30 bits.push(Boolean::constant(false))
31 }
32
33 tmp >>= 1;
34 }
35
36 UInt64 {
37 bits,
38 value: Some(value),
39 }
40 }
41
42 /// Allocate a `UInt64` in the constraint system
43 pub fn alloc<ConstraintF, CS>(mut cs: CS, value: Option<u64>) -> Result<Self, SynthesisError>
44 where
45 ConstraintF: Field,
46 CS: ConstraintSystem<ConstraintF>,
47 {
48 let values = match value {
49 Some(mut val) => {
50 let mut v = Vec::with_capacity(64);
51
52 for _ in 0..64 {
53 v.push(Some(val & 1 == 1));
54 val >>= 1;
55 }
56
57 v
58 },
59 None => vec![None; 64],
60 };
61
62 let bits = values
63 .into_iter()
64 .enumerate()
65 .map(|(i, v)| {
66 Ok(Boolean::from(AllocatedBit::alloc(
67 cs.ns(|| format!("allocated bit_gadget {}", i)),
68 || v.get(),
69 )?))
70 })
71 .collect::<Result<Vec<_>, SynthesisError>>()?;
72
73 Ok(UInt64 { bits, value })
74 }
75
76 /// Turns this `UInt64` into its little-endian byte order representation.
77 pub fn to_bits_le(&self) -> Vec<Boolean> {
78 self.bits.clone()
79 }
80
81 /// Converts a little-endian byte order representation of bits into a
82 /// `UInt64`.
83 pub fn from_bits_le(bits: &[Boolean]) -> Self {
84 assert_eq!(bits.len(), 64);
85
86 let bits = bits.to_vec();
87
88 let mut value = Some(0u64);
89 for b in bits.iter().rev() {
90 value.as_mut().map(|v| *v <<= 1);
91
92 match b {
93 &Boolean::Constant(b) => {
94 if b {
95 value.as_mut().map(|v| *v |= 1);
96 }
97 },
98 &Boolean::Is(ref b) => match b.get_value() {
99 Some(true) => {
100 value.as_mut().map(|v| *v |= 1);
101 },
102 Some(false) => {},
103 None => value = None,
104 },
105 &Boolean::Not(ref b) => match b.get_value() {
106 Some(false) => {
107 value.as_mut().map(|v| *v |= 1);
108 },
109 Some(true) => {},
110 None => value = None,
111 },
112 }
113 }
114
115 Self { value, bits }
116 }
117
118 pub fn rotr(&self, by: usize) -> Self {
119 let by = by % 64;
120
121 let new_bits = self
122 .bits
123 .iter()
124 .skip(by)
125 .chain(self.bits.iter())
126 .take(64)
127 .cloned()
128 .collect();
129
130 UInt64 {
131 bits: new_bits,
132 value: self.value.map(|v| v.rotate_right(by as u32)),
133 }
134 }
135
136 /// XOR this `UInt64` with another `UInt64`
137 pub fn xor<ConstraintF, CS>(&self, mut cs: CS, other: &Self) -> Result<Self, SynthesisError>
138 where
139 ConstraintF: Field,
140 CS: ConstraintSystem<ConstraintF>,
141 {
142 let new_value = match (self.value, other.value) {
143 (Some(a), Some(b)) => Some(a ^ b),
144 _ => None,
145 };
146
147 let bits = self
148 .bits
149 .iter()
150 .zip(other.bits.iter())
151 .enumerate()
152 .map(|(i, (a, b))| Boolean::xor(cs.ns(|| format!("xor of bit_gadget {}", i)), a, b))
153 .collect::<Result<_, _>>()?;
154
155 Ok(UInt64 {
156 bits,
157 value: new_value,
158 })
159 }
160
161 /// Perform modular addition of several `UInt64` objects.
162 pub fn addmany<ConstraintF, CS>(mut cs: CS, operands: &[Self]) -> Result<Self, SynthesisError>
163 where
164 ConstraintF: PrimeField,
165 CS: ConstraintSystem<ConstraintF>,
166 {
167 // Make some arbitrary bounds for ourselves to avoid overflows
168 // in the scalar field
169 assert!(ConstraintF::Params::MODULUS_BITS >= 128);
170
171 assert!(operands.len() >= 1);
172 assert!(operands.len() <= 10);
173
174 if operands.len() == 1 {
175 return Ok(operands[0].clone());
176 }
177
178 // Compute the maximum value of the sum so we allocate enough bits for
179 // the result
180 let mut max_value = (operands.len() as u128) * u128::from(u64::max_value());
181
182 // Keep track of the resulting value
183 let mut result_value = Some(0u64 as u128);
184
185 // This is a linear combination that we will enforce to be "zero"
186 let mut lc = LinearCombination::zero();
187
188 let mut all_constants = true;
189
190 // Iterate over the operands
191 for op in operands {
192 // Accumulate the value
193 match op.value {
194 Some(val) => {
195 result_value.as_mut().map(|v| *v += u128::from(val));
196 },
197 None => {
198 // If any of our operands have unknown value, we won't
199 // know the value of the result
200 result_value = None;
201 },
202 }
203
204 // Iterate over each bit_gadget of the operand and add the operand to
205 // the linear combination
206 let mut coeff = ConstraintF::one();
207 for bit in &op.bits {
208 match *bit {
209 Boolean::Is(ref bit) => {
210 all_constants = false;
211
212 // Add coeff * bit_gadget
213 lc += (coeff, bit.get_variable());
214 },
215 Boolean::Not(ref bit) => {
216 all_constants = false;
217
218 // Add coeff * (1 - bit_gadget) = coeff * ONE - coeff * bit_gadget
219 lc = lc + (coeff, CS::one()) - (coeff, bit.get_variable());
220 },
221 Boolean::Constant(bit) => {
222 if bit {
223 lc += (coeff, CS::one());
224 }
225 },
226 }
227
228 coeff.double_in_place();
229 }
230 }
231
232 // The value of the actual result is modulo 2^64
233 let modular_value = result_value.map(|v| v as u64);
234
235 if all_constants && modular_value.is_some() {
236 // We can just return a constant, rather than
237 // unpacking the result into allocated bits.
238
239 return Ok(UInt64::constant(modular_value.unwrap()));
240 }
241
242 // Storage area for the resulting bits
243 let mut result_bits = vec![];
244
245 // Allocate each bit_gadget of the result
246 let mut coeff = ConstraintF::one();
247 let mut i = 0;
248 while max_value != 0 {
249 // Allocate the bit_gadget
250 let b = AllocatedBit::alloc(cs.ns(|| format!("result bit_gadget {}", i)), || {
251 result_value.map(|v| (v >> i) & 1 == 1).get()
252 })?;
253
254 // Subtract this bit_gadget from the linear combination to ensure the sums
255 // balance out
256 lc = lc - (coeff, b.get_variable());
257
258 result_bits.push(b.into());
259
260 max_value >>= 1;
261 i += 1;
262 coeff.double_in_place();
263 }
264
265 // Enforce that the linear combination equals zero
266 cs.enforce(|| "modular addition", |lc| lc, |lc| lc, |_| lc);
267
268 // Discard carry bits that we don't care about
269 result_bits.truncate(64);
270
271 Ok(UInt64 {
272 bits: result_bits,
273 value: modular_value,
274 })
275 }
276}
277
278impl<ConstraintF: Field> ToBytesGadget<ConstraintF> for UInt64 {
279 #[inline]
280 fn to_bytes<CS: ConstraintSystem<ConstraintF>>(
281 &self,
282 _cs: CS,
283 ) -> Result<Vec<UInt8>, SynthesisError> {
284 let value_chunks = match self.value.map(|val| {
285 use algebra::bytes::ToBytes;
286 let mut bytes = [0u8; 8];
287 val.write(bytes.as_mut()).unwrap();
288 bytes
289 }) {
290 Some(chunks) => [
291 Some(chunks[0]),
292 Some(chunks[1]),
293 Some(chunks[2]),
294 Some(chunks[3]),
295 Some(chunks[4]),
296 Some(chunks[5]),
297 Some(chunks[6]),
298 Some(chunks[7]),
299 ],
300 None => [None, None, None, None, None, None, None, None],
301 };
302 let mut bytes = Vec::new();
303 for (i, chunk8) in self.to_bits_le().chunks(8).enumerate() {
304 let byte = UInt8 {
305 bits: chunk8.to_vec(),
306 value: value_chunks[i],
307 };
308 bytes.push(byte);
309 }
310
311 Ok(bytes)
312 }
313}
314
315impl PartialEq for UInt64 {
316 fn eq(&self, other: &Self) -> bool {
317 self.value.is_some() && other.value.is_some() && self.value == other.value
318 }
319}
320
321impl Eq for UInt64 {}
322
323impl<ConstraintF: Field> ConditionalEqGadget<ConstraintF> for UInt64 {
324 fn conditional_enforce_equal<CS: ConstraintSystem<ConstraintF>>(
325 &self,
326 mut cs: CS,
327 other: &Self,
328 condition: &Boolean,
329 ) -> Result<(), SynthesisError> {
330 for (i, (a, b)) in self.bits.iter().zip(&other.bits).enumerate() {
331 a.conditional_enforce_equal(
332 &mut cs.ns(|| format!("uint64_equal_{}", i)),
333 b,
334 condition,
335 )?;
336 }
337 Ok(())
338 }
339
340 fn cost() -> usize {
341 64 * <Boolean as ConditionalEqGadget<ConstraintF>>::cost()
342 }
343}
344
345#[cfg(test)]
346mod test {
347 use super::UInt64;
348 use crate::{bits::boolean::Boolean, test_constraint_system::TestConstraintSystem, Vec};
349 use algebra::{bls12_381::Fr, One, Zero};
350 use r1cs_core::ConstraintSystem;
351 use rand::{Rng, SeedableRng};
352 use rand_xorshift::XorShiftRng;
353
354 #[test]
355 fn test_uint64_from_bits() {
356 let mut rng = XorShiftRng::seed_from_u64(1231275789u64);
357
358 for _ in 0..1000 {
359 let v = (0..64)
360 .map(|_| Boolean::constant(rng.gen()))
361 .collect::<Vec<_>>();
362
363 let b = UInt64::from_bits_le(&v);
364
365 for (i, bit_gadget) in b.bits.iter().enumerate() {
366 match bit_gadget {
367 &Boolean::Constant(bit_gadget) => {
368 assert!(bit_gadget == ((b.value.unwrap() >> i) & 1 == 1));
369 },
370 _ => unreachable!(),
371 }
372 }
373
374 let expected_to_be_same = b.to_bits_le();
375
376 for x in v.iter().zip(expected_to_be_same.iter()) {
377 match x {
378 (&Boolean::Constant(true), &Boolean::Constant(true)) => {},
379 (&Boolean::Constant(false), &Boolean::Constant(false)) => {},
380 _ => unreachable!(),
381 }
382 }
383 }
384 }
385
386 #[test]
387 fn test_uint64_xor() {
388 let mut rng = XorShiftRng::seed_from_u64(1231275789u64);
389
390 for _ in 0..1000 {
391 let mut cs = TestConstraintSystem::<Fr>::new();
392
393 let a: u64 = rng.gen();
394 let b: u64 = rng.gen();
395 let c: u64 = rng.gen();
396
397 let mut expected = a ^ b ^ c;
398
399 let a_bit = UInt64::alloc(cs.ns(|| "a_bit"), Some(a)).unwrap();
400 let b_bit = UInt64::constant(b);
401 let c_bit = UInt64::alloc(cs.ns(|| "c_bit"), Some(c)).unwrap();
402
403 let r = a_bit.xor(cs.ns(|| "first xor"), &b_bit).unwrap();
404 let r = r.xor(cs.ns(|| "second xor"), &c_bit).unwrap();
405
406 assert!(cs.is_satisfied());
407
408 assert!(r.value == Some(expected));
409
410 for b in r.bits.iter() {
411 match b {
412 &Boolean::Is(ref b) => {
413 assert!(b.get_value().unwrap() == (expected & 1 == 1));
414 },
415 &Boolean::Not(ref b) => {
416 assert!(!b.get_value().unwrap() == (expected & 1 == 1));
417 },
418 &Boolean::Constant(b) => {
419 assert!(b == (expected & 1 == 1));
420 },
421 }
422
423 expected >>= 1;
424 }
425 }
426 }
427
428 #[test]
429 fn test_uint64_addmany_constants() {
430 let mut rng = XorShiftRng::seed_from_u64(1231275789u64);
431
432 for _ in 0..1000 {
433 let mut cs = TestConstraintSystem::<Fr>::new();
434
435 let a: u64 = rng.gen();
436 let b: u64 = rng.gen();
437 let c: u64 = rng.gen();
438
439 let a_bit = UInt64::constant(a);
440 let b_bit = UInt64::constant(b);
441 let c_bit = UInt64::constant(c);
442
443 let mut expected = a.wrapping_add(b).wrapping_add(c);
444
445 let r = UInt64::addmany(cs.ns(|| "addition"), &[a_bit, b_bit, c_bit]).unwrap();
446
447 assert!(r.value == Some(expected));
448
449 for b in r.bits.iter() {
450 match b {
451 &Boolean::Is(_) => panic!(),
452 &Boolean::Not(_) => panic!(),
453 &Boolean::Constant(b) => {
454 assert!(b == (expected & 1 == 1));
455 },
456 }
457
458 expected >>= 1;
459 }
460 }
461 }
462
463 #[test]
464 fn test_uint64_addmany() {
465 let mut rng = XorShiftRng::seed_from_u64(1231275789u64);
466
467 for _ in 0..1000 {
468 let mut cs = TestConstraintSystem::<Fr>::new();
469
470 let a: u64 = rng.gen();
471 let b: u64 = rng.gen();
472 let c: u64 = rng.gen();
473 let d: u64 = rng.gen();
474
475 let mut expected = (a ^ b).wrapping_add(c).wrapping_add(d);
476
477 let a_bit = UInt64::alloc(cs.ns(|| "a_bit"), Some(a)).unwrap();
478 let b_bit = UInt64::constant(b);
479 let c_bit = UInt64::constant(c);
480 let d_bit = UInt64::alloc(cs.ns(|| "d_bit"), Some(d)).unwrap();
481
482 let r = a_bit.xor(cs.ns(|| "xor"), &b_bit).unwrap();
483 let r = UInt64::addmany(cs.ns(|| "addition"), &[r, c_bit, d_bit]).unwrap();
484
485 assert!(cs.is_satisfied());
486
487 assert!(r.value == Some(expected));
488
489 for b in r.bits.iter() {
490 match b {
491 &Boolean::Is(ref b) => {
492 assert!(b.get_value().unwrap() == (expected & 1 == 1));
493 },
494 &Boolean::Not(ref b) => {
495 assert!(!b.get_value().unwrap() == (expected & 1 == 1));
496 },
497 &Boolean::Constant(_) => unreachable!(),
498 }
499
500 expected >>= 1;
501 }
502
503 // Flip a bit_gadget and see if the addition constraint still works
504 if cs.get("addition/result bit_gadget 0/boolean").is_zero() {
505 cs.set("addition/result bit_gadget 0/boolean", Fr::one());
506 } else {
507 cs.set("addition/result bit_gadget 0/boolean", Fr::zero());
508 }
509
510 assert!(!cs.is_satisfied());
511 }
512 }
513
514 #[test]
515 fn test_uint64_rotr() {
516 let mut rng = XorShiftRng::seed_from_u64(1231275789u64);
517
518 let mut num = rng.gen();
519
520 let a = UInt64::constant(num);
521
522 for i in 0..64 {
523 let b = a.rotr(i);
524
525 assert!(b.value.unwrap() == num);
526
527 let mut tmp = num;
528 for b in &b.bits {
529 match b {
530 &Boolean::Constant(b) => {
531 assert_eq!(b, tmp & 1 == 1);
532 },
533 _ => unreachable!(),
534 }
535
536 tmp >>= 1;
537 }
538
539 num = num.rotate_right(1);
540 }
541 }
542}