acir_field/
field_element.rs

1use ark_ff::PrimeField;
2use ark_ff::Zero;
3use num_bigint::BigUint;
4use serde::{Deserialize, Serialize};
5use std::borrow::Cow;
6use std::ops::{Add, AddAssign, Div, Mul, Neg, Sub, SubAssign};
7
8use crate::AcirField;
9
10/// The value 2^127, which represents the boundary between positive and negative
11/// values in i128 representation. Values greater this are treated as negative when
12/// converting to signed integers.
13const I128_SIGN_BOUNDARY: u128 = 1_u128 << 127;
14
15// XXX: Include a trait-based design with field-specific implementations.
16#[derive(Default, Clone, Copy, PartialEq, Eq, PartialOrd, Ord, Hash)]
17pub struct FieldElement<F: PrimeField>(F);
18
19impl<F: PrimeField> std::fmt::Display for FieldElement<F> {
20    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
21        // First check if the number is zero
22        //
23        let number = BigUint::from_bytes_be(&self.to_be_bytes());
24        if number == BigUint::zero() {
25            return write!(f, "0");
26        }
27        // Check if the negative version is smaller to represent
28        //
29        let minus_number = BigUint::from_bytes_be(&(self.neg()).to_be_bytes());
30        let (smaller_repr, is_negative) =
31            if minus_number.to_string().len() < number.to_string().len() {
32                (minus_number, true)
33            } else {
34                (number, false)
35            };
36        if is_negative {
37            write!(f, "-")?;
38        }
39
40        write!(f, "{smaller_repr}")
41    }
42}
43
44impl<F: PrimeField> std::fmt::Debug for FieldElement<F> {
45    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
46        std::fmt::Display::fmt(self, f)
47    }
48}
49
50impl<F: PrimeField> From<i128> for FieldElement<F> {
51    fn from(a: i128) -> FieldElement<F> {
52        // Optimized: Convert directly without string conversion
53        if a >= 0 {
54            // Positive case: convert via u128
55            FieldElement(F::from(a as u128))
56        } else {
57            // Negative case: handle i128::MIN specially to avoid overflow
58            let abs_value = a.wrapping_neg() as u128;
59            FieldElement(-F::from(abs_value))
60        }
61    }
62}
63
64impl<F: PrimeField> From<i64> for FieldElement<F> {
65    fn from(a: i64) -> Self {
66        // Optimized: Convert directly without string conversion
67        if a >= 0 {
68            FieldElement(F::from(a as u64))
69        } else {
70            // Negative case: handle i64::MIN specially to avoid overflow
71            let abs_value = a.wrapping_neg() as u64;
72            FieldElement(-F::from(abs_value))
73        }
74    }
75}
76
77impl<F: PrimeField> From<i32> for FieldElement<F> {
78    fn from(a: i32) -> Self {
79        // Optimized: Convert directly without string conversion
80        if a >= 0 {
81            FieldElement(F::from(a as u32))
82        } else {
83            // Negative case: handle i32::MIN specially to avoid overflow
84            let abs_value = a.wrapping_neg() as u32;
85            FieldElement(-F::from(abs_value))
86        }
87    }
88}
89
90impl<F: PrimeField> From<i16> for FieldElement<F> {
91    fn from(a: i16) -> Self {
92        // Optimized: Convert directly without string conversion
93        if a >= 0 {
94            FieldElement(F::from(a as u16))
95        } else {
96            // Negative case: handle i16::MIN specially to avoid overflow
97            let abs_value = a.wrapping_neg() as u16;
98            FieldElement(-F::from(abs_value))
99        }
100    }
101}
102
103impl<F: PrimeField> From<i8> for FieldElement<F> {
104    fn from(a: i8) -> Self {
105        // Optimized: Convert directly without string conversion
106        if a >= 0 {
107            FieldElement(F::from(a as u8))
108        } else {
109            // Negative case: handle i8::MIN specially to avoid overflow
110            let abs_value = a.wrapping_neg() as u8;
111            FieldElement(-F::from(abs_value))
112        }
113    }
114}
115
116impl<T: PrimeField> Serialize for FieldElement<T> {
117    fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
118    where
119        S: serde::Serializer,
120    {
121        self.to_be_bytes().serialize(serializer)
122    }
123}
124
125impl<'de, T: PrimeField> Deserialize<'de> for FieldElement<T> {
126    fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>
127    where
128        D: serde::Deserializer<'de>,
129    {
130        let s: Cow<'de, [u8]> = Deserialize::deserialize(deserializer)?;
131        Ok(Self::from_be_bytes_reduce(&s))
132    }
133}
134
135impl<F: PrimeField> From<u128> for FieldElement<F> {
136    fn from(a: u128) -> FieldElement<F> {
137        FieldElement(F::from(a))
138    }
139}
140
141impl<F: PrimeField> From<usize> for FieldElement<F> {
142    fn from(a: usize) -> FieldElement<F> {
143        FieldElement::from(a as u64)
144    }
145}
146
147impl<F: PrimeField> From<u64> for FieldElement<F> {
148    fn from(a: u64) -> FieldElement<F> {
149        FieldElement(F::from(a))
150    }
151}
152
153impl<F: PrimeField> From<u32> for FieldElement<F> {
154    fn from(a: u32) -> FieldElement<F> {
155        FieldElement(F::from(a))
156    }
157}
158
159impl<F: PrimeField> From<u16> for FieldElement<F> {
160    fn from(a: u16) -> FieldElement<F> {
161        FieldElement(F::from(a))
162    }
163}
164
165impl<F: PrimeField> From<u8> for FieldElement<F> {
166    fn from(a: u8) -> FieldElement<F> {
167        FieldElement(F::from(a))
168    }
169}
170
171impl<F: PrimeField> From<bool> for FieldElement<F> {
172    fn from(boolean: bool) -> FieldElement<F> {
173        if boolean { FieldElement::one() } else { FieldElement::zero() }
174    }
175}
176
177impl<F: PrimeField> TryFrom<FieldElement<F>> for u128 {
178    type Error = ();
179
180    fn try_from(value: FieldElement<F>) -> Result<Self, Self::Error> {
181        value.try_into_u128().ok_or(())
182    }
183}
184
185impl<F: PrimeField> TryFrom<FieldElement<F>> for u64 {
186    type Error = ();
187
188    fn try_from(value: FieldElement<F>) -> Result<Self, Self::Error> {
189        value.try_to_u64().ok_or(())
190    }
191}
192
193impl<F: PrimeField> TryFrom<FieldElement<F>> for u32 {
194    type Error = ();
195
196    fn try_from(value: FieldElement<F>) -> Result<Self, Self::Error> {
197        value.try_to_u32().ok_or(())
198    }
199}
200
201impl<F: PrimeField> TryFrom<FieldElement<F>> for u16 {
202    type Error = ();
203
204    fn try_from(value: FieldElement<F>) -> Result<Self, Self::Error> {
205        value.try_to_u32().and_then(|x| x.try_into().ok()).ok_or(())
206    }
207}
208
209impl<F: PrimeField> TryFrom<FieldElement<F>> for u8 {
210    type Error = ();
211
212    fn try_from(value: FieldElement<F>) -> Result<Self, Self::Error> {
213        value.try_to_u32().and_then(|x| x.try_into().ok()).ok_or(())
214    }
215}
216
217impl<F: PrimeField> TryFrom<FieldElement<F>> for i128 {
218    type Error = ();
219
220    fn try_from(value: FieldElement<F>) -> Result<Self, Self::Error> {
221        value.try_into_i128().ok_or(())
222    }
223}
224
225impl<F: PrimeField> TryFrom<FieldElement<F>> for i64 {
226    type Error = ();
227
228    fn try_from(value: FieldElement<F>) -> Result<Self, Self::Error> {
229        value.try_into_i128().and_then(|x| x.try_into().ok()).ok_or(())
230    }
231}
232
233impl<F: PrimeField> TryFrom<FieldElement<F>> for i32 {
234    type Error = ();
235
236    fn try_from(value: FieldElement<F>) -> Result<Self, Self::Error> {
237        value.try_into_i128().and_then(|x| x.try_into().ok()).ok_or(())
238    }
239}
240
241impl<F: PrimeField> TryFrom<FieldElement<F>> for i16 {
242    type Error = ();
243
244    fn try_from(value: FieldElement<F>) -> Result<Self, Self::Error> {
245        value.try_into_i128().and_then(|x| x.try_into().ok()).ok_or(())
246    }
247}
248
249impl<F: PrimeField> TryFrom<FieldElement<F>> for i8 {
250    type Error = ();
251
252    fn try_from(value: FieldElement<F>) -> Result<Self, Self::Error> {
253        value.try_into_i128().and_then(|x| x.try_into().ok()).ok_or(())
254    }
255}
256
257impl<F: PrimeField> From<FieldElement<F>> for bool {
258    fn from(field: FieldElement<F>) -> bool {
259        !field.is_zero()
260    }
261}
262
263impl<F: PrimeField> FieldElement<F> {
264    /// Constructs a `FieldElement` from the underlying prime field representation.
265    ///
266    /// This wraps an `ark_ff::PrimeField` element into a `FieldElement`.
267    pub fn from_repr(field: F) -> Self {
268        Self(field)
269    }
270
271    /// Extracts the underlying prime field representation.
272    ///
273    /// This returns the wrapped `ark_ff::PrimeField` element.
274    pub fn into_repr(self) -> F {
275        self.0
276    }
277
278    /// Returns true if this field element can be represented as a u128.
279    ///
280    /// A field element fits in u128 if it requires at most 128 bits to represent,
281    /// i.e., if its value is in the range [0, 2^128 - 1].
282    pub fn fits_in_u128(&self) -> bool {
283        self.num_bits() <= 128
284    }
285
286    /// Returns true if this field element can be represented as an i128.
287    ///
288    /// An i128 can represent values in the range [i128::MIN, i128::MAX], which corresponds
289    /// to field elements in [0, 2^127 - 1] (positive) and [p - 2^127, p - 1] (negative),
290    /// where p is the field modulus. The positive value 2^127 does not fit (it exceeds
291    /// i128::MAX), but the field element representing -2^127 (i.e. p - 2^127) does fit
292    /// (it is i128::MIN).
293    pub fn fits_in_i128(&self) -> bool {
294        let neg = self.neg();
295        self.num_bits() <= 127
296            || neg.num_bits() <= 127
297            || self.neg() == FieldElement::from(I128_SIGN_BOUNDARY)
298    }
299
300    /// Returns None, if the string is not a canonical
301    /// representation of a field element; less than the order
302    /// or if the hex string is invalid.
303    /// This method can be used for both hex and decimal representations.
304    pub fn try_from_str(input: &str) -> Option<FieldElement<F>> {
305        if input.contains('x') {
306            return FieldElement::from_hex(input);
307        }
308
309        let fr = F::from_str(input).ok()?;
310        Some(FieldElement(fr))
311    }
312
313    /// Assume this field element holds a signed integer of the given `bit_size` and format
314    /// it as a string. The range of valid values for this field element is `0..2^bit_size`
315    /// with `0..2^(bit_size - 1)` representing positive values and `2^(bit_size - 1)..2^bit_size`
316    /// representing negative values (as is commonly done for signed integers).
317    /// `2^(bit_size - 1)` is the lowest negative value, so for example if bit_size is 8 then
318    /// `0..127` map to `0..127`, `128` maps to `-128`, `129` maps to `-127` and `255` maps to `-1`.
319    /// If `self` falls outside of the valid range it's formatted as-is.
320    pub fn to_string_as_signed_integer(self, bit_size: u32) -> String {
321        assert!(bit_size <= 128);
322        if self.num_bits() > bit_size {
323            return self.to_string();
324        }
325
326        // Compute the maximum value that is considered a positive value
327        let max = if bit_size == 128 { i128::MAX as u128 } else { (1 << (bit_size - 1)) - 1 };
328        if self.to_u128() > max {
329            let f = FieldElement::from(2u32).pow(&bit_size.into()) - self;
330            format!("-{f}")
331        } else {
332            self.to_string()
333        }
334    }
335}
336
337impl<F: PrimeField> AcirField for FieldElement<F> {
338    fn one() -> FieldElement<F> {
339        FieldElement(F::one())
340    }
341    fn zero() -> FieldElement<F> {
342        FieldElement(F::zero())
343    }
344
345    fn is_zero(&self) -> bool {
346        self == &Self::zero()
347    }
348    fn is_one(&self) -> bool {
349        self == &Self::one()
350    }
351
352    fn pow(&self, exponent: &Self) -> Self {
353        FieldElement(self.0.pow(exponent.0.into_bigint()))
354    }
355
356    /// Maximum number of bits needed to represent a field element
357    /// This is not the amount of bits being used to represent a field element
358    /// Example, you only need 254 bits to represent a field element in BN256
359    /// But the representation uses 256 bits, so the top two bits are always zero
360    /// This method would return 254
361    fn max_num_bits() -> u32 {
362        F::MODULUS_BIT_SIZE
363    }
364
365    /// Maximum numbers of bytes needed to represent a field element
366    /// We are not guaranteed that the number of bits being used to represent a field element
367    /// will always be divisible by 8. If the case that it is not, we add one to the max number of bytes
368    /// For example, a max bit size of 254 would give a max byte size of 32.
369    fn max_num_bytes() -> u32 {
370        let num_bytes = Self::max_num_bits() / 8;
371        if Self::max_num_bits() % 8 == 0 { num_bytes } else { num_bytes + 1 }
372    }
373
374    fn modulus() -> BigUint {
375        F::MODULUS.into()
376    }
377
378    /// This is the number of bits required to represent this specific field element
379    fn num_bits(&self) -> u32 {
380        let bigint = self.0.into_bigint();
381        let limbs = bigint.as_ref();
382        for (i, &limb) in limbs.iter().enumerate().rev() {
383            if limb != 0 {
384                return (i as u32) * 64 + (64 - limb.leading_zeros());
385            }
386        }
387        0
388    }
389
390    fn to_u128(self) -> u128 {
391        if !self.fits_in_u128() {
392            panic!("field element too large for u128");
393        }
394        let as_bigint = self.0.into_bigint();
395        let limbs = as_bigint.as_ref();
396
397        let mut result = u128::from(limbs[0]);
398        if limbs.len() > 1 {
399            let high_limb = u128::from(limbs[1]);
400            result += high_limb << 64;
401        }
402
403        result
404    }
405
406    fn try_into_u128(self) -> Option<u128> {
407        self.fits_in_u128().then(|| self.to_u128())
408    }
409
410    fn to_i128(self) -> i128 {
411        if !self.fits_in_i128() {
412            panic!("field element too large for i128");
413        }
414        // Negative integers are represented by the range [p + i128::MIN, p) while
415        // positive integers are represented by the range [0, i128::MAX).
416        // We can then differentiate positive from negative values by their MSB.
417        if self.neg().num_bits() < self.num_bits() {
418            let bytes = self.neg().to_be_bytes();
419            // wrapping_neg handles i128::MIN: bytes of 2^127 decode to i128::MIN.
420            // Because it fits in i128, we know the value is a valid i128 value
421            // so using wrapping_neg() cannot not silently miss an overflow.
422            i128::from_be_bytes(bytes[16..32].try_into().unwrap()).wrapping_neg()
423        } else {
424            let bytes = self.to_be_bytes();
425            i128::from_be_bytes(bytes[16..32].try_into().unwrap())
426        }
427    }
428
429    fn try_into_i128(self) -> Option<i128> {
430        self.fits_in_i128().then(|| self.to_i128())
431    }
432
433    fn try_to_u64(&self) -> Option<u64> {
434        (self.num_bits() <= 64).then(|| self.to_u128() as u64)
435    }
436
437    fn try_to_u32(&self) -> Option<u32> {
438        (self.num_bits() <= 32).then(|| self.to_u128() as u32)
439    }
440
441    /// Computes the inverse or returns zero if the inverse does not exist
442    /// Before using this FieldElement, please ensure that this behavior is necessary
443    fn inverse(&self) -> FieldElement<F> {
444        let inv = self.0.inverse().unwrap_or_else(F::zero);
445        FieldElement(inv)
446    }
447
448    fn to_hex(self) -> String {
449        let bytes = self.to_be_bytes();
450        hex::encode(bytes)
451    }
452
453    fn to_short_hex(self) -> String {
454        if self.is_zero() {
455            return "0x00".to_owned();
456        }
457
458        // Work directly with bytes
459        let bytes = self.to_be_bytes();
460
461        // Find the first non-zero byte
462        let first_nonzero = bytes.iter().position(|&b| b != 0).unwrap_or(bytes.len());
463        let trimmed = &bytes[first_nonzero..];
464
465        // Build the hex string directly
466        // Pre-allocate: "0x" + at least 2 chars per byte
467        let mut result = String::with_capacity(2 + trimmed.len() * 2);
468        result.push_str("0x");
469
470        // Format the first byte - use {:x} to avoid leading zero if byte >= 0x10
471        use std::fmt::Write;
472        write!(&mut result, "{:x}", trimmed[0]).unwrap();
473
474        // Ensure even length by padding if necessary
475        if !result.len().is_multiple_of(2) {
476            // Insert '0' after "0x" to make it even
477            result.insert(2, '0');
478        }
479
480        // Format remaining bytes with padding
481        for byte in &trimmed[1..] {
482            write!(&mut result, "{byte:02x}").unwrap();
483        }
484
485        result
486    }
487
488    fn from_hex(hex_str: &str) -> Option<FieldElement<F>> {
489        let value = hex_str.strip_prefix("0x").unwrap_or(hex_str);
490
491        // Decode directly, handling even length efficiently
492        let hex_as_bytes = if value.len().is_multiple_of(2) {
493            hex::decode(value).ok()?
494        } else {
495            // For odd length, prepend '0' to the string view only for decoding
496            let mut padded = String::with_capacity(value.len() + 1);
497            padded.push('0');
498            padded.push_str(value);
499            hex::decode(padded).ok()?
500        };
501
502        Some(FieldElement::from_be_bytes_reduce(&hex_as_bytes))
503    }
504
505    fn to_be_bytes(self) -> Vec<u8> {
506        let mut bytes = self.to_le_bytes();
507        bytes.reverse();
508        bytes
509    }
510
511    /// Converts the field element to a vector of bytes in little-endian order
512    fn to_le_bytes(self) -> Vec<u8> {
513        let mut bytes = Vec::new();
514        self.0.serialize_uncompressed(&mut bytes).unwrap();
515        bytes
516    }
517
518    /// Converts bytes into a FieldElement and applies a
519    /// reduction if needed.
520    fn from_be_bytes_reduce(bytes: &[u8]) -> FieldElement<F> {
521        FieldElement(F::from_be_bytes_mod_order(bytes))
522    }
523
524    /// Converts bytes in little-endian order into a FieldElement and applies a
525    /// reduction if needed.
526    fn from_le_bytes_reduce(bytes: &[u8]) -> FieldElement<F> {
527        FieldElement(F::from_le_bytes_mod_order(bytes))
528    }
529
530    /// Returns the closest number of bytes to the bits specified
531    /// This method truncates
532    fn fetch_nearest_bytes(&self, num_bits: usize) -> Vec<u8> {
533        fn nearest_bytes(num_bits: usize) -> usize {
534            num_bits.div_ceil(8) * 8
535        }
536
537        let num_bytes = nearest_bytes(num_bits);
538        let num_elements = num_bytes / 8;
539
540        let bytes = self.to_le_bytes();
541
542        bytes[0..num_elements].to_vec()
543    }
544}
545
546impl<F: PrimeField> Neg for FieldElement<F> {
547    type Output = FieldElement<F>;
548
549    fn neg(self) -> Self::Output {
550        FieldElement(-self.0)
551    }
552}
553
554impl<F: PrimeField> Mul for FieldElement<F> {
555    type Output = FieldElement<F>;
556    fn mul(mut self, rhs: FieldElement<F>) -> Self::Output {
557        self.0.mul_assign(&rhs.0);
558        FieldElement(self.0)
559    }
560}
561impl<F: PrimeField> Div for FieldElement<F> {
562    type Output = FieldElement<F>;
563    #[allow(clippy::suspicious_arithmetic_impl)]
564    fn div(self, rhs: FieldElement<F>) -> Self::Output {
565        self * rhs.inverse()
566    }
567}
568impl<F: PrimeField> Add for FieldElement<F> {
569    type Output = FieldElement<F>;
570    fn add(mut self, rhs: FieldElement<F>) -> Self::Output {
571        self.add_assign(rhs);
572        FieldElement(self.0)
573    }
574}
575impl<F: PrimeField> AddAssign for FieldElement<F> {
576    fn add_assign(&mut self, rhs: FieldElement<F>) {
577        self.0.add_assign(&rhs.0);
578    }
579}
580
581impl<F: PrimeField> Sub for FieldElement<F> {
582    type Output = FieldElement<F>;
583    fn sub(mut self, rhs: FieldElement<F>) -> Self::Output {
584        self.sub_assign(rhs);
585        FieldElement(self.0)
586    }
587}
588impl<F: PrimeField> SubAssign for FieldElement<F> {
589    fn sub_assign(&mut self, rhs: FieldElement<F>) {
590        self.0.sub_assign(&rhs.0);
591    }
592}
593
594#[cfg(test)]
595mod tests {
596    use super::{AcirField, FieldElement};
597    use proptest::prelude::*;
598    use std::ops::Neg;
599
600    #[test]
601    fn requires_zero_bit_to_hold_zero() {
602        let field = FieldElement::<ark_bn254::Fr>::zero();
603        assert_eq!(field.num_bits(), 0);
604    }
605
606    #[test]
607    fn requires_one_bit_to_hold_one() {
608        let field = FieldElement::<ark_bn254::Fr>::one();
609        assert_eq!(field.num_bits(), 1);
610    }
611
612    proptest! {
613        #[test]
614        fn num_bits_agrees_with_ilog2(num in 1u128..) {
615            let field = FieldElement::<ark_bn254::Fr>::from(num);
616            prop_assert_eq!(field.num_bits(), num.ilog2() + 1);
617        }
618    }
619
620    #[test]
621    fn test_fits_in_u128() {
622        let field = FieldElement::<ark_bn254::Fr>::from(u128::MAX);
623        assert_eq!(field.num_bits(), 128);
624        assert!(field.fits_in_u128());
625        let big_field = field + FieldElement::one();
626        assert_eq!(big_field.num_bits(), 129);
627        assert!(!big_field.fits_in_u128());
628    }
629
630    #[test]
631    fn test_to_u128_basic() {
632        type F = FieldElement<ark_bn254::Fr>;
633
634        // Test zero
635        assert_eq!(F::zero().to_u128(), 0);
636
637        // Test small values
638        assert_eq!(F::from(1_u128).to_u128(), 1);
639        assert_eq!(F::from(42_u128).to_u128(), 42);
640        assert_eq!(F::from(1000_u128).to_u128(), 1000);
641
642        // Test u128::MAX
643        assert_eq!(F::from(u128::MAX).to_u128(), u128::MAX);
644
645        // Test power of 2 boundaries
646        assert_eq!(F::from(1_u128 << 127).to_u128(), 1_u128 << 127);
647        assert_eq!(F::from((1_u128 << 127) - 1).to_u128(), (1_u128 << 127) - 1);
648    }
649
650    #[test]
651    #[should_panic(expected = "field element too large for u128")]
652    fn test_to_u128_panics_on_overflow() {
653        type F = FieldElement<ark_bn254::Fr>;
654
655        // Create a field element larger than u128::MAX
656        let too_large = F::from(u128::MAX) + F::one();
657        too_large.to_u128(); // Should panic
658    }
659
660    #[test]
661    fn test_try_into_u128() {
662        type F = FieldElement<ark_bn254::Fr>;
663
664        // Valid conversions
665        assert_eq!(F::zero().try_into_u128(), Some(0));
666        assert_eq!(F::from(42_u128).try_into_u128(), Some(42));
667        assert_eq!(F::from(u128::MAX).try_into_u128(), Some(u128::MAX));
668
669        // Invalid conversion
670        let too_large = F::from(u128::MAX) + F::one();
671        assert_eq!(too_large.try_into_u128(), None);
672    }
673
674    #[test]
675    fn test_fits_in_i128() {
676        type F = FieldElement<ark_bn254::Fr>;
677
678        // Positive values that fit
679        assert!(F::zero().fits_in_i128());
680        assert!(F::from(1_i128).fits_in_i128());
681        assert!(F::from(42_i128).fits_in_i128());
682        assert!(F::from(i128::MAX).fits_in_i128());
683
684        // Negative values that fit
685        assert!(F::from(-1_i128).fits_in_i128());
686        assert!(F::from(-42_i128).fits_in_i128());
687        assert!(F::from(i128::MIN + 1).fits_in_i128());
688        assert!(F::from(i128::MIN).fits_in_i128());
689
690        // Boundary: 2^127 - 1 fits (i128::MAX)
691        assert!(F::from((1_u128 << 127) - 1).fits_in_i128());
692
693        // Boundary: the positive field element 2^127 does NOT fit (exceeds i128::MAX).
694        // This is distinct from F::from(i128::MIN), which is the field element p - 2^127.
695        assert!(!F::from(1_u128 << 127).fits_in_i128());
696
697        // Values that don't fit
698        let too_large = F::from(u128::MAX);
699        assert!(!too_large.fits_in_i128());
700    }
701
702    #[test]
703    fn test_to_i128_positive() {
704        type F = FieldElement<ark_bn254::Fr>;
705
706        // Test positive values
707        assert_eq!(F::zero().to_i128(), 0);
708        assert_eq!(F::from(1_i128).to_i128(), 1);
709        assert_eq!(F::from(42_i128).to_i128(), 42);
710        assert_eq!(F::from(1000_i128).to_i128(), 1000);
711        assert_eq!(F::from(i128::MAX).to_i128(), i128::MAX);
712    }
713
714    #[test]
715    fn test_to_i128_negative() {
716        type F = FieldElement<ark_bn254::Fr>;
717
718        // Test negative values
719        assert_eq!(F::from(-1_i128).to_i128(), -1);
720        assert_eq!(F::from(-42_i128).to_i128(), -42);
721        assert_eq!(F::from(-1000_i128).to_i128(), -1000);
722
723        // Test boundary values
724        assert_eq!(F::from(-i128::MAX).to_i128(), -i128::MAX);
725        assert_eq!(F::from(i128::MIN + 1).to_i128(), i128::MIN + 1);
726        assert_eq!(F::from(i128::MIN).to_i128(), i128::MIN);
727    }
728
729    #[test]
730    fn test_to_i128_roundtrip() {
731        type F = FieldElement<ark_bn254::Fr>;
732
733        // Test roundtrip for various values
734        let test_values = vec![
735            0_i128,
736            1,
737            -1,
738            42,
739            -42,
740            i128::MAX,
741            i128::MAX - 1,
742            i128::MIN,
743            i128::MIN + 1,
744            -i128::MAX,
745        ];
746
747        for value in test_values {
748            let field = F::from(value);
749            assert!(field.fits_in_i128(), "Value {value} should fit in i128");
750            assert_eq!(field.to_i128(), value, "Roundtrip failed for {value}");
751        }
752    }
753
754    #[test]
755    #[should_panic(expected = "field element too large for i128")]
756    fn test_to_i128_panics_on_positive_overflow() {
757        type F = FieldElement<ark_bn254::Fr>;
758
759        // 2^127 is too large (exceeds i128::MAX)
760        let too_large = F::from(1_u128 << 127);
761        too_large.to_i128(); // Should panic
762    }
763
764    #[test]
765    #[should_panic(expected = "field element too large for i128")]
766    fn test_to_i128_panics_on_large_value() {
767        type F = FieldElement<ark_bn254::Fr>;
768
769        // Large positive value that doesn't fit
770        let too_large = F::from(u128::MAX);
771        too_large.to_i128(); // Should panic
772    }
773
774    #[test]
775    fn test_try_into_i128() {
776        type F = FieldElement<ark_bn254::Fr>;
777        // Valid positive conversions
778        assert_eq!(F::zero().try_into_i128(), Some(0));
779        assert_eq!(F::from(42_i128).try_into_i128(), Some(42));
780        assert_eq!(F::from(i128::MAX).try_into_i128(), Some(i128::MAX));
781        assert_eq!(F::from(-i128::MAX).try_into_i128(), Some(-i128::MAX));
782
783        // Valid negative conversions
784        assert_eq!(F::from(-1_i128).try_into_i128(), Some(-1));
785        assert_eq!(F::from(-42_i128).try_into_i128(), Some(-42));
786        assert_eq!(F::from(i128::MIN + 1).try_into_i128(), Some(i128::MIN + 1));
787        assert_eq!(F::from(i128::MAX - 1).try_into_i128(), Some(i128::MAX - 1));
788        assert_eq!(F::from(1_i128 << 126).try_into_i128(), Some(1_i128 << 126));
789        assert_eq!(F::from(-((1_i128 << 126) - 1)).try_into_i128(), Some(-((1_i128 << 126) - 1)));
790        // i128::MIN (= -2^127) fits: its field representation is p - 2^127, which is
791        // the same field element as F::from(1_u128 << 127).neg().
792        assert_eq!(F::from(i128::MIN).try_into_i128(), Some(i128::MIN));
793        assert_eq!(F::from(1_u128 << 127).neg().try_into_i128(), Some(i128::MIN));
794        // Invalid conversions
795        assert_eq!(F::from(1_u128 << 127).try_into_i128(), None);
796        assert_eq!(F::from(u128::MAX).try_into_i128(), None);
797        // A few other invalid values
798        assert_eq!(F::from((1_u128 << 127) + 1).try_into_i128(), None);
799        assert_eq!(F::from((1_u128 << 127) + 1000).try_into_i128(), None);
800        assert_eq!(F::from((1_u128 << 127) + 1).neg().try_into_i128(), None);
801        assert_eq!(F::from((1_u128 << 127) + 100).try_into_i128(), None);
802        assert_eq!(F::from((1_u128 << 127) + 100).neg().try_into_i128(), None);
803    }
804
805    #[test]
806    fn serialize_fixed_test_vectors() {
807        // Serialized field elements from of 0, -1, -2, -3
808        let hex_strings = vec![
809            "0000000000000000000000000000000000000000000000000000000000000000",
810            "30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000000",
811            "30644e72e131a029b85045b68181585d2833e84879b9709143e1f593efffffff",
812            "30644e72e131a029b85045b68181585d2833e84879b9709143e1f593effffffe",
813        ];
814
815        for (i, string) in hex_strings.into_iter().enumerate() {
816            let minus_i_field_element = -FieldElement::<ark_bn254::Fr>::from(i as i128);
817            assert_eq!(minus_i_field_element.to_hex(), string);
818        }
819    }
820
821    #[test]
822    fn max_num_bits_smoke() {
823        let max_num_bits_bn254 = FieldElement::<ark_bn254::Fr>::max_num_bits();
824        assert_eq!(max_num_bits_bn254, 254);
825    }
826
827    proptest! {
828        #[test]
829        fn test_endianness_prop(value in any::<u64>()) {
830            let field = FieldElement::<ark_bn254::Fr>::from(value);
831            // Test serialization consistency
832            let le_bytes = field.to_le_bytes();
833            let be_bytes = field.to_be_bytes();
834
835            let mut reversed_le = le_bytes.clone();
836            reversed_le.reverse();
837            prop_assert_eq!(&be_bytes, &reversed_le, "BE bytes should be reverse of LE bytes");
838
839            // Test deserialization consistency
840            let from_le = FieldElement::from_le_bytes_reduce(&le_bytes);
841            let from_be = FieldElement::from_be_bytes_reduce(&be_bytes);
842            prop_assert_eq!(from_le, from_be, "Deserialization should be consistent between LE and BE");
843            prop_assert_eq!(from_le, field, "Deserialized value should match original");
844        }
845    }
846
847    #[test]
848    fn test_endianness() {
849        let field = FieldElement::<ark_bn254::Fr>::from(0x1234_5678_u32);
850        let le_bytes = field.to_le_bytes();
851        let be_bytes = field.to_be_bytes();
852
853        // Check that the bytes are reversed between BE and LE
854        let mut reversed_le = le_bytes.clone();
855        reversed_le.reverse();
856        assert_eq!(&be_bytes, &reversed_le);
857
858        // Verify we can reconstruct the same field element from either byte order
859        let from_le = FieldElement::from_le_bytes_reduce(&le_bytes);
860        let from_be = FieldElement::from_be_bytes_reduce(&be_bytes);
861        assert_eq!(from_le, from_be);
862        assert_eq!(from_le, field);
863
864        // Additional test with a larger number to ensure proper byte handling
865        let large_field = FieldElement::<ark_bn254::Fr>::from(0x0123_4567_89AB_CDEF_u64); // cSpell:disable-line
866        let large_le = large_field.to_le_bytes();
867        let reconstructed = FieldElement::from_le_bytes_reduce(&large_le);
868        assert_eq!(reconstructed, large_field);
869    }
870
871    proptest! {
872        // This currently panics due to the fact that we allow inputs which are greater than the field modulus,
873        // automatically reducing them to fit within the canonical range.
874        #[test]
875        #[should_panic(expected = "serialized field element is not equal to input")]
876        fn recovers_original_hex_string(hex in "[0-9a-f]{64}") {
877            let fe: FieldElement::<ark_bn254::Fr> = FieldElement::from_hex(&hex).expect("should accept any 32 byte hex string");
878            let output_hex = fe.to_hex();
879
880            prop_assert_eq!(hex, output_hex, "serialized field element is not equal to input");
881        }
882
883        #[test]
884        fn accepts_odd_length_hex_strings(hex in "(?:0x)[0-9a-fA-F]+") {
885            // Here we inject a "0" immediately after the "0x" (if it exists) to construct an equivalent
886            // hex string with the opposite parity length.
887            let insert_index = if hex.starts_with("0x") { 2 } else { 0 };
888            let mut opposite_parity_string = hex.clone();
889            opposite_parity_string.insert(insert_index, '0');
890
891            let fe_1: FieldElement::<ark_bn254::Fr> = FieldElement::from_hex(&hex).unwrap();
892            let fe_2: FieldElement::<ark_bn254::Fr> = FieldElement::from_hex(&opposite_parity_string).unwrap();
893
894            prop_assert_eq!(fe_1, fe_2, "equivalent hex strings with opposite parity deserialized to different values");
895        }
896    }
897
898    #[test]
899    fn test_to_hex() {
900        type F = FieldElement<ark_bn254::Fr>;
901        assert_eq!(
902            F::zero().to_hex(),
903            "0000000000000000000000000000000000000000000000000000000000000000"
904        );
905        assert_eq!(
906            F::one().to_hex(),
907            "0000000000000000000000000000000000000000000000000000000000000001"
908        );
909        assert_eq!(
910            F::from(0x123_u128).to_hex(),
911            "0000000000000000000000000000000000000000000000000000000000000123"
912        );
913        assert_eq!(
914            F::from(0x1234_u128).to_hex(),
915            "0000000000000000000000000000000000000000000000000000000000001234"
916        );
917    }
918
919    #[test]
920    fn test_to_short_hex() {
921        type F = FieldElement<ark_bn254::Fr>;
922        assert_eq!(F::zero().to_short_hex(), "0x00");
923        assert_eq!(F::one().to_short_hex(), "0x01");
924        assert_eq!(F::from(0x123_u128).to_short_hex(), "0x0123");
925        assert_eq!(F::from(0x1234_u128).to_short_hex(), "0x1234");
926    }
927
928    #[test]
929    fn to_string_as_signed_integer() {
930        type F = FieldElement<ark_bn254::Fr>;
931        assert_eq!(F::zero().to_string_as_signed_integer(8), "0");
932        assert_eq!(F::one().to_string_as_signed_integer(8), "1");
933        assert_eq!(F::from(127_u128).to_string_as_signed_integer(8), "127");
934        assert_eq!(F::from(128_u128).to_string_as_signed_integer(8), "-128");
935        assert_eq!(F::from(129_u128).to_string_as_signed_integer(8), "-127");
936        assert_eq!(F::from(255_u128).to_string_as_signed_integer(8), "-1");
937        assert_eq!(F::from(32767_u128).to_string_as_signed_integer(16), "32767");
938        assert_eq!(F::from(32768_u128).to_string_as_signed_integer(16), "-32768");
939        assert_eq!(F::from(65535_u128).to_string_as_signed_integer(16), "-1");
940    }
941}
acir_field/field_element.rs

acir_field/
field_element.rs
