ruint/
bits.rs

1use crate::Uint;
2use core::ops::{
3    BitAnd, BitAndAssign, BitOr, BitOrAssign, BitXor, BitXorAssign, Not, Shl, ShlAssign, Shr,
4    ShrAssign,
5};
6
7impl<const BITS: usize, const LIMBS: usize> Uint<BITS, LIMBS> {
8    /// Returns whether a specific bit is set.
9    ///
10    /// Returns `false` if `index` exceeds the bit width of the number.
11    #[must_use]
12    #[inline]
13    pub const fn bit(&self, index: usize) -> bool {
14        if index >= BITS {
15            return false;
16        }
17        let (limbs, bits) = (index / 64, index % 64);
18        self.limbs[limbs] & (1 << bits) != 0
19    }
20
21    /// Sets a specific bit to a value.
22    #[inline]
23    pub fn set_bit(&mut self, index: usize, value: bool) {
24        if index >= BITS {
25            return;
26        }
27        let (limbs, bits) = (index / 64, index % 64);
28        if value {
29            self.limbs[limbs] |= 1 << bits;
30        } else {
31            self.limbs[limbs] &= !(1 << bits);
32        }
33    }
34
35    /// Returns a specific byte. The byte at index `0` is the least significant
36    /// byte (little endian).
37    ///
38    /// # Panics
39    ///
40    /// Panics if `index` is greater than or equal to the byte width of the
41    /// number.
42    ///
43    /// # Examples
44    ///
45    /// ```
46    /// # use ruint::uint;
47    /// let x = uint!(0x1234567890_U64);
48    /// let bytes = [
49    ///     x.byte(0), // 0x90
50    ///     x.byte(1), // 0x78
51    ///     x.byte(2), // 0x56
52    ///     x.byte(3), // 0x34
53    ///     x.byte(4), // 0x12
54    ///     x.byte(5), // 0x00
55    ///     x.byte(6), // 0x00
56    ///     x.byte(7), // 0x00
57    /// ];
58    /// assert_eq!(bytes, x.to_le_bytes());
59    /// ```
60    ///
61    /// Panics if out of range.
62    ///
63    /// ```should_panic
64    /// # use ruint::uint;
65    /// let x = uint!(0x1234567890_U64);
66    /// let _ = x.byte(8);
67    /// ```
68    #[inline]
69    #[must_use]
70    #[track_caller]
71    pub const fn byte(&self, index: usize) -> u8 {
72        #[cfg(target_endian = "little")]
73        {
74            self.as_le_slice()[index]
75        }
76
77        #[cfg(target_endian = "big")]
78        #[allow(clippy::cast_possible_truncation)] // intentional
79        {
80            (self.limbs[index / 8] >> ((index % 8) * 8)) as u8
81        }
82    }
83
84    /// Returns a specific byte, or `None` if `index` is out of range. The byte
85    /// at index `0` is the least significant byte (little endian).
86    ///
87    /// # Examples
88    ///
89    /// ```
90    /// # use ruint::uint;
91    /// let x = uint!(0x1234567890_U64);
92    /// assert_eq!(x.checked_byte(0), Some(0x90));
93    /// assert_eq!(x.checked_byte(7), Some(0x00));
94    /// // Out of range
95    /// assert_eq!(x.checked_byte(8), None);
96    /// ```
97    #[inline]
98    #[must_use]
99    pub const fn checked_byte(&self, index: usize) -> Option<u8> {
100        if index < Self::BYTES {
101            Some(self.byte(index))
102        } else {
103            None
104        }
105    }
106
107    /// Reverses the order of bits in the integer. The least significant bit
108    /// becomes the most significant bit, second least-significant bit becomes
109    /// second most-significant bit, etc.
110    #[inline]
111    #[must_use]
112    pub fn reverse_bits(mut self) -> Self {
113        self.limbs.reverse();
114        for limb in &mut self.limbs {
115            *limb = limb.reverse_bits();
116        }
117        if BITS % 64 != 0 {
118            self >>= 64 - BITS % 64;
119        }
120        self
121    }
122
123    /// Inverts all the bits in the integer.
124    #[inline]
125    #[must_use]
126    pub const fn not(mut self) -> Self {
127        if BITS == 0 {
128            return Self::ZERO;
129        }
130
131        let mut i = 0;
132        while i < LIMBS {
133            self.limbs[i] = !self.limbs[i];
134            i += 1;
135        }
136
137        self.masked()
138    }
139
140    /// Returns the number of leading zeros in the binary representation of
141    /// `self`.
142    #[inline]
143    #[must_use]
144    pub const fn leading_zeros(&self) -> usize {
145        let mut i = LIMBS;
146        while i > 0 {
147            i -= 1;
148            if self.limbs[i] != 0 {
149                let n = LIMBS - 1 - i;
150                let skipped = n * 64;
151                let fixed = Self::MASK.leading_zeros() as usize;
152                let top = self.limbs[i].leading_zeros() as usize;
153                return skipped + top - fixed;
154            }
155        }
156
157        BITS
158    }
159
160    /// Returns the number of leading ones in the binary representation of
161    /// `self`.
162    #[inline]
163    #[must_use]
164    pub const fn leading_ones(&self) -> usize {
165        Self::not(*self).leading_zeros()
166    }
167
168    /// Returns the number of trailing zeros in the binary representation of
169    /// `self`.
170    #[inline]
171    #[must_use]
172    pub fn trailing_zeros(&self) -> usize {
173        self.as_limbs()
174            .iter()
175            .position(|&limb| limb != 0)
176            .map_or(BITS, |n| {
177                n * 64 + self.as_limbs()[n].trailing_zeros() as usize
178            })
179    }
180
181    /// Returns the number of trailing ones in the binary representation of
182    /// `self`.
183    #[inline]
184    #[must_use]
185    pub fn trailing_ones(&self) -> usize {
186        self.as_limbs()
187            .iter()
188            .position(|&limb| limb != u64::MAX)
189            .map_or(BITS, |n| {
190                n * 64 + self.as_limbs()[n].trailing_ones() as usize
191            })
192    }
193
194    /// Returns the number of ones in the binary representation of `self`.
195    #[inline]
196    #[must_use]
197    pub const fn count_ones(&self) -> usize {
198        let mut total = 0;
199
200        let mut i = 0;
201        while i < LIMBS {
202            total += self.limbs[i].count_ones() as usize;
203            i += 1;
204        }
205
206        total
207    }
208
209    /// Returns the number of zeros in the binary representation of `self`.
210    #[must_use]
211    #[inline]
212    pub const fn count_zeros(&self) -> usize {
213        BITS - self.count_ones()
214    }
215
216    /// Returns the dynamic length of this number in bits, ignoring leading
217    /// zeros.
218    ///
219    /// For the maximum length of the type, use [`Uint::BITS`](Self::BITS).
220    #[must_use]
221    #[inline]
222    pub const fn bit_len(&self) -> usize {
223        BITS - self.leading_zeros()
224    }
225
226    /// Returns the dynamic length of this number in bytes, ignoring leading
227    /// zeros.
228    ///
229    /// For the maximum length of the type, use [`Uint::BYTES`](Self::BYTES).
230    #[must_use]
231    #[inline]
232    pub const fn byte_len(&self) -> usize {
233        (self.bit_len() + 7) / 8
234    }
235
236    /// Returns the most significant 64 bits of the number and the exponent.
237    ///
238    /// Given return value $(\mathtt{bits}, \mathtt{exponent})$, the `self` can
239    /// be approximated as
240    ///
241    /// $$
242    /// \mathtt{self} ≈ \mathtt{bits} ⋅ 2^\mathtt{exponent}
243    /// $$
244    ///
245    /// If `self` is $<≥> 2^{63}$, then `exponent` will be zero and `bits` will
246    /// have leading zeros.
247    #[inline]
248    #[must_use]
249    pub fn most_significant_bits(&self) -> (u64, usize) {
250        let first_set_limb = self
251            .as_limbs()
252            .iter()
253            .rposition(|&limb| limb != 0)
254            .unwrap_or(0);
255        if first_set_limb == 0 {
256            (self.as_limbs().first().copied().unwrap_or(0), 0)
257        } else {
258            let hi = self.as_limbs()[first_set_limb];
259            let lo = self.as_limbs()[first_set_limb - 1];
260            let leading_zeros = hi.leading_zeros();
261            let bits = if leading_zeros > 0 {
262                (hi << leading_zeros) | (lo >> (64 - leading_zeros))
263            } else {
264                hi
265            };
266            let exponent = first_set_limb * 64 - leading_zeros as usize;
267            (bits, exponent)
268        }
269    }
270
271    /// Checked left shift by `rhs` bits.
272    ///
273    /// Returns $\mathtt{self} ⋅ 2^{\mathtt{rhs}}$ or [`None`] if the result
274    /// would $≥ 2^{\mathtt{BITS}}$. That is, it returns [`None`] if the bits
275    /// shifted out would be non-zero.
276    ///
277    /// Note: This differs from [`u64::checked_shl`] which returns `None` if the
278    /// shift is larger than BITS (which is IMHO not very useful).
279    #[inline(always)]
280    #[must_use]
281    pub fn checked_shl(self, rhs: usize) -> Option<Self> {
282        match self.overflowing_shl(rhs) {
283            (value, false) => Some(value),
284            _ => None,
285        }
286    }
287
288    /// Saturating left shift by `rhs` bits.
289    ///
290    /// Returns $\mathtt{self} ⋅ 2^{\mathtt{rhs}}$ or [`Uint::MAX`] if the
291    /// result would $≥ 2^{\mathtt{BITS}}$. That is, it returns
292    /// [`Uint::MAX`] if the bits shifted out would be non-zero.
293    #[inline(always)]
294    #[must_use]
295    pub fn saturating_shl(self, rhs: usize) -> Self {
296        match self.overflowing_shl(rhs) {
297            (value, false) => value,
298            _ => Self::MAX,
299        }
300    }
301
302    /// Left shift by `rhs` bits with overflow detection.
303    ///
304    /// Returns $\mod{\mathtt{value} ⋅ 2^{\mathtt{rhs}}}_{2^{\mathtt{BITS}}}$.
305    /// If the product is $≥ 2^{\mathtt{BITS}}$ it returns `true`. That is, it
306    /// returns true if the bits shifted out are non-zero.
307    ///
308    /// Note: This differs from [`u64::overflowing_shl`] which returns `true` if
309    /// the shift is larger than `BITS` (which is IMHO not very useful).
310    #[inline]
311    #[must_use]
312    pub fn overflowing_shl(self, rhs: usize) -> (Self, bool) {
313        let (limbs, bits) = (rhs / 64, rhs % 64);
314        if limbs >= LIMBS {
315            return (Self::ZERO, self != Self::ZERO);
316        }
317
318        let word_bits = 64;
319        let mut r = Self::ZERO;
320        let mut carry = 0;
321        for i in 0..Self::LIMBS - limbs {
322            let x = self.limbs[i];
323            r.limbs[i + limbs] = (x << bits) | carry;
324            carry = (x >> (word_bits - bits - 1)) >> 1;
325        }
326        r.apply_mask();
327        (r, carry != 0)
328    }
329
330    /// Left shift by `rhs` bits.
331    ///
332    /// Returns $\mod{\mathtt{value} ⋅ 2^{\mathtt{rhs}}}_{2^{\mathtt{BITS}}}$.
333    ///
334    /// Note: This differs from [`u64::wrapping_shl`] which first reduces `rhs`
335    /// by `BITS` (which is IMHO not very useful).
336    #[inline(always)]
337    #[must_use]
338    pub fn wrapping_shl(self, rhs: usize) -> Self {
339        self.overflowing_shl(rhs).0
340    }
341
342    /// Checked right shift by `rhs` bits.
343    ///
344    /// $$
345    /// \frac{\mathtt{self}}{2^{\mathtt{rhs}}}
346    /// $$
347    ///
348    /// Returns the above or [`None`] if the division is not exact. This is the
349    /// same as
350    ///
351    /// Note: This differs from [`u64::checked_shr`] which returns `None` if the
352    /// shift is larger than BITS (which is IMHO not very useful).
353    #[inline(always)]
354    #[must_use]
355    pub fn checked_shr(self, rhs: usize) -> Option<Self> {
356        match self.overflowing_shr(rhs) {
357            (value, false) => Some(value),
358            _ => None,
359        }
360    }
361
362    /// Right shift by `rhs` bits with underflow detection.
363    ///
364    /// $$
365    /// \floor{\frac{\mathtt{self}}{2^{\mathtt{rhs}}}}
366    /// $$
367    ///
368    /// Returns the above and `false` if the division was exact, and `true` if
369    /// it was rounded down. This is the same as non-zero bits being shifted
370    /// out.
371    ///
372    /// Note: This differs from [`u64::overflowing_shr`] which returns `true` if
373    /// the shift is larger than `BITS` (which is IMHO not very useful).
374    #[inline]
375    #[must_use]
376    pub fn overflowing_shr(self, rhs: usize) -> (Self, bool) {
377        let (limbs, bits) = (rhs / 64, rhs % 64);
378        if limbs >= LIMBS {
379            return (Self::ZERO, self != Self::ZERO);
380        }
381
382        let word_bits = 64;
383        let mut r = Self::ZERO;
384        let mut carry = 0;
385        for i in 0..LIMBS - limbs {
386            let x = self.limbs[LIMBS - 1 - i];
387            r.limbs[LIMBS - 1 - i - limbs] = (x >> bits) | carry;
388            carry = (x << (word_bits - bits - 1)) << 1;
389        }
390        (r, carry != 0)
391    }
392
393    /// Right shift by `rhs` bits.
394    ///
395    /// $$
396    /// \mathtt{wrapping\\_shr}(\mathtt{self}, \mathtt{rhs}) =
397    /// \floor{\frac{\mathtt{self}}{2^{\mathtt{rhs}}}}
398    /// $$
399    ///
400    /// Note: This differs from [`u64::wrapping_shr`] which first reduces `rhs`
401    /// by `BITS` (which is IMHO not very useful).
402    #[inline(always)]
403    #[must_use]
404    pub fn wrapping_shr(self, rhs: usize) -> Self {
405        self.overflowing_shr(rhs).0
406    }
407
408    /// Arithmetic shift right by `rhs` bits.
409    #[inline]
410    #[must_use]
411    pub fn arithmetic_shr(self, rhs: usize) -> Self {
412        if BITS == 0 {
413            return Self::ZERO;
414        }
415        let sign = self.bit(BITS - 1);
416        let mut r = self >> rhs;
417        if sign {
418            r |= Self::MAX << BITS.saturating_sub(rhs);
419        }
420        r
421    }
422
423    /// Shifts the bits to the left by a specified amount, `rhs`, wrapping the
424    /// truncated bits to the end of the resulting integer.
425    #[inline]
426    #[must_use]
427    #[allow(clippy::missing_const_for_fn)] // False positive
428    pub fn rotate_left(self, rhs: usize) -> Self {
429        if BITS == 0 {
430            return Self::ZERO;
431        }
432        let rhs = rhs % BITS;
433        (self << rhs) | (self >> (BITS - rhs))
434    }
435
436    /// Shifts the bits to the right by a specified amount, `rhs`, wrapping the
437    /// truncated bits to the beginning of the resulting integer.
438    #[inline(always)]
439    #[must_use]
440    pub fn rotate_right(self, rhs: usize) -> Self {
441        if BITS == 0 {
442            return Self::ZERO;
443        }
444        let rhs = rhs % BITS;
445        self.rotate_left(BITS - rhs)
446    }
447}
448
449impl<const BITS: usize, const LIMBS: usize> Not for Uint<BITS, LIMBS> {
450    type Output = Self;
451
452    #[inline]
453    fn not(self) -> Self::Output {
454        Self::not(self)
455    }
456}
457
458impl<const BITS: usize, const LIMBS: usize> Not for &Uint<BITS, LIMBS> {
459    type Output = Uint<BITS, LIMBS>;
460
461    #[inline]
462    fn not(self) -> Self::Output {
463        (*self).not()
464    }
465}
466
467macro_rules! impl_bit_op {
468    ($trait:ident, $fn:ident, $trait_assign:ident, $fn_assign:ident) => {
469        impl<const BITS: usize, const LIMBS: usize> $trait_assign<Uint<BITS, LIMBS>>
470            for Uint<BITS, LIMBS>
471        {
472            #[inline(always)]
473            fn $fn_assign(&mut self, rhs: Uint<BITS, LIMBS>) {
474                self.$fn_assign(&rhs);
475            }
476        }
477
478        impl<const BITS: usize, const LIMBS: usize> $trait_assign<&Uint<BITS, LIMBS>>
479            for Uint<BITS, LIMBS>
480        {
481            #[inline]
482            fn $fn_assign(&mut self, rhs: &Uint<BITS, LIMBS>) {
483                for i in 0..LIMBS {
484                    u64::$fn_assign(&mut self.limbs[i], rhs.limbs[i]);
485                }
486            }
487        }
488
489        impl<const BITS: usize, const LIMBS: usize> $trait<Uint<BITS, LIMBS>>
490            for Uint<BITS, LIMBS>
491        {
492            type Output = Uint<BITS, LIMBS>;
493
494            #[inline(always)]
495            fn $fn(mut self, rhs: Uint<BITS, LIMBS>) -> Self::Output {
496                self.$fn_assign(rhs);
497                self
498            }
499        }
500
501        impl<const BITS: usize, const LIMBS: usize> $trait<&Uint<BITS, LIMBS>>
502            for Uint<BITS, LIMBS>
503        {
504            type Output = Uint<BITS, LIMBS>;
505
506            #[inline(always)]
507            fn $fn(mut self, rhs: &Uint<BITS, LIMBS>) -> Self::Output {
508                self.$fn_assign(rhs);
509                self
510            }
511        }
512
513        impl<const BITS: usize, const LIMBS: usize> $trait<Uint<BITS, LIMBS>>
514            for &Uint<BITS, LIMBS>
515        {
516            type Output = Uint<BITS, LIMBS>;
517
518            #[inline(always)]
519            fn $fn(self, mut rhs: Uint<BITS, LIMBS>) -> Self::Output {
520                rhs.$fn_assign(self);
521                rhs
522            }
523        }
524
525        impl<const BITS: usize, const LIMBS: usize> $trait<&Uint<BITS, LIMBS>>
526            for &Uint<BITS, LIMBS>
527        {
528            type Output = Uint<BITS, LIMBS>;
529
530            #[inline(always)]
531            fn $fn(self, rhs: &Uint<BITS, LIMBS>) -> Self::Output {
532                self.clone().$fn(rhs)
533            }
534        }
535    };
536}
537
538impl_bit_op!(BitOr, bitor, BitOrAssign, bitor_assign);
539impl_bit_op!(BitAnd, bitand, BitAndAssign, bitand_assign);
540impl_bit_op!(BitXor, bitxor, BitXorAssign, bitxor_assign);
541
542impl<const BITS: usize, const LIMBS: usize> Shl<Self> for Uint<BITS, LIMBS> {
543    type Output = Self;
544
545    #[inline(always)]
546    fn shl(self, rhs: Self) -> Self::Output {
547        // This check shortcuts, and prevents panics on the `[0]` later
548        if BITS == 0 {
549            return self;
550        }
551        // Rationale: if BITS is larger than 2**64 - 1, it means we're running
552        // on a 128-bit platform with 2.3 exabytes of memory. In this case,
553        // the code produces incorrect output.
554        #[allow(clippy::cast_possible_truncation)]
555        self.wrapping_shl(rhs.as_limbs()[0] as usize)
556    }
557}
558
559impl<const BITS: usize, const LIMBS: usize> Shl<&Self> for Uint<BITS, LIMBS> {
560    type Output = Self;
561
562    #[inline(always)]
563    fn shl(self, rhs: &Self) -> Self::Output {
564        self << *rhs
565    }
566}
567
568impl<const BITS: usize, const LIMBS: usize> Shr<Self> for Uint<BITS, LIMBS> {
569    type Output = Self;
570
571    #[inline(always)]
572    fn shr(self, rhs: Self) -> Self::Output {
573        // This check shortcuts, and prevents panics on the `[0]` later
574        if BITS == 0 {
575            return self;
576        }
577        // Rationale: if BITS is larger than 2**64 - 1, it means we're running
578        // on a 128-bit platform with 2.3 exabytes of memory. In this case,
579        // the code produces incorrect output.
580        #[allow(clippy::cast_possible_truncation)]
581        self.wrapping_shr(rhs.as_limbs()[0] as usize)
582    }
583}
584
585impl<const BITS: usize, const LIMBS: usize> Shr<&Self> for Uint<BITS, LIMBS> {
586    type Output = Self;
587
588    #[inline(always)]
589    fn shr(self, rhs: &Self) -> Self::Output {
590        self >> *rhs
591    }
592}
593
594impl<const BITS: usize, const LIMBS: usize> ShlAssign<Self> for Uint<BITS, LIMBS> {
595    #[inline(always)]
596    fn shl_assign(&mut self, rhs: Self) {
597        *self = *self << rhs;
598    }
599}
600
601impl<const BITS: usize, const LIMBS: usize> ShlAssign<&Self> for Uint<BITS, LIMBS> {
602    #[inline(always)]
603    fn shl_assign(&mut self, rhs: &Self) {
604        *self = *self << rhs;
605    }
606}
607
608impl<const BITS: usize, const LIMBS: usize> ShrAssign<Self> for Uint<BITS, LIMBS> {
609    #[inline(always)]
610    fn shr_assign(&mut self, rhs: Self) {
611        *self = *self >> rhs;
612    }
613}
614
615impl<const BITS: usize, const LIMBS: usize> ShrAssign<&Self> for Uint<BITS, LIMBS> {
616    #[inline(always)]
617    fn shr_assign(&mut self, rhs: &Self) {
618        *self = *self >> rhs;
619    }
620}
621
622macro_rules! impl_shift {
623    (@main $u:ty) => {
624        impl<const BITS: usize, const LIMBS: usize> Shl<$u> for Uint<BITS, LIMBS> {
625            type Output = Self;
626
627            #[inline(always)]
628            #[allow(clippy::cast_possible_truncation)]
629            fn shl(self, rhs: $u) -> Self::Output {
630                self.wrapping_shl(rhs as usize)
631            }
632        }
633
634        impl<const BITS: usize, const LIMBS: usize> Shr<$u> for Uint<BITS, LIMBS> {
635            type Output = Self;
636
637            #[inline(always)]
638            #[allow(clippy::cast_possible_truncation)]
639            fn shr(self, rhs: $u) -> Self::Output {
640                self.wrapping_shr(rhs as usize)
641            }
642        }
643    };
644
645    (@ref $u:ty) => {
646        impl<const BITS: usize, const LIMBS: usize> Shl<&$u> for Uint<BITS, LIMBS> {
647            type Output = Self;
648
649            #[inline(always)]
650            fn shl(self, rhs: &$u) -> Self::Output {
651                <Self>::shl(self, *rhs)
652            }
653        }
654
655        impl<const BITS: usize, const LIMBS: usize> Shr<&$u> for Uint<BITS, LIMBS> {
656            type Output = Self;
657
658            #[inline(always)]
659            fn shr(self, rhs: &$u) -> Self::Output {
660                <Self>::shr(self, *rhs)
661            }
662        }
663    };
664
665    (@assign $u:ty) => {
666        impl<const BITS: usize, const LIMBS: usize> ShlAssign<$u> for Uint<BITS, LIMBS> {
667            #[inline(always)]
668            fn shl_assign(&mut self, rhs: $u) {
669                *self = *self << rhs;
670            }
671        }
672
673        impl<const BITS: usize, const LIMBS: usize> ShrAssign<$u> for Uint<BITS, LIMBS> {
674            #[inline(always)]
675            fn shr_assign(&mut self, rhs: $u) {
676                *self = *self >> rhs;
677            }
678        }
679    };
680
681    ($u:ty) => {
682        impl_shift!(@main $u);
683        impl_shift!(@ref $u);
684        impl_shift!(@assign $u);
685        impl_shift!(@assign &$u);
686    };
687
688    ($u:ty, $($tail:ty),*) => {
689        impl_shift!($u);
690        impl_shift!($($tail),*);
691    };
692}
693
694impl_shift!(usize, u8, u16, u32, isize, i8, i16, i32);
695
696// Only when losslessy castable to usize.
697#[cfg(target_pointer_width = "64")]
698impl_shift!(u64, i64);
699
700#[cfg(test)]
701mod tests {
702    use super::*;
703    use crate::{aliases::U128, const_for, nlimbs};
704    use core::cmp::min;
705    use proptest::proptest;
706
707    #[test]
708    fn test_leading_zeros() {
709        assert_eq!(Uint::<0, 0>::ZERO.leading_zeros(), 0);
710        assert_eq!(Uint::<1, 1>::ZERO.leading_zeros(), 1);
711        assert_eq!(Uint::<1, 1>::ONE.leading_zeros(), 0);
712        const_for!(BITS in NON_ZERO {
713            const LIMBS: usize = nlimbs(BITS);
714            type U = Uint::<BITS, LIMBS>;
715            assert_eq!(U::ZERO.leading_zeros(), BITS);
716            assert_eq!(U::MAX.leading_zeros(), 0);
717            assert_eq!(U::ONE.leading_zeros(), BITS - 1);
718            proptest!(|(value: U)| {
719                let zeros = value.leading_zeros();
720                assert!(zeros <= BITS);
721                assert!(zeros < BITS || value == U::ZERO);
722                if zeros < BITS {
723                    let (left, overflow) = value.overflowing_shl(zeros);
724                    assert!(!overflow);
725                    assert!(left.leading_zeros() == 0 || value == U::ZERO);
726                    assert!(left.bit(BITS - 1));
727                    assert_eq!(value >> (BITS - zeros), Uint::ZERO);
728                }
729            });
730        });
731        proptest!(|(value: u128)| {
732            let uint = U128::from(value);
733            assert_eq!(uint.leading_zeros(), value.leading_zeros() as usize);
734        });
735    }
736
737    #[test]
738    fn test_leading_ones() {
739        assert_eq!(Uint::<0, 0>::ZERO.leading_ones(), 0);
740        assert_eq!(Uint::<1, 1>::ZERO.leading_ones(), 0);
741        assert_eq!(Uint::<1, 1>::ONE.leading_ones(), 1);
742    }
743
744    #[test]
745    fn test_most_significant_bits() {
746        const_for!(BITS in NON_ZERO {
747            const LIMBS: usize = nlimbs(BITS);
748            type U = Uint::<BITS, LIMBS>;
749            proptest!(|(value: u64)| {
750                let value = if U::LIMBS <= 1 { value & U::MASK } else { value };
751                assert_eq!(U::from(value).most_significant_bits(), (value, 0));
752            });
753        });
754        proptest!(|(mut limbs: [u64; 2])| {
755            if limbs[1] == 0 {
756                limbs[1] = 1;
757            }
758            let (bits, exponent) = U128::from_limbs(limbs).most_significant_bits();
759            assert!(bits >= 1_u64 << 63);
760            assert_eq!(exponent, 64 - limbs[1].leading_zeros() as usize);
761        });
762    }
763
764    #[test]
765    fn test_checked_shl() {
766        assert_eq!(
767            Uint::<65, 2>::from_limbs([0x0010_0000_0000_0000, 0]).checked_shl(1),
768            Some(Uint::<65, 2>::from_limbs([0x0020_0000_0000_0000, 0]))
769        );
770        assert_eq!(
771            Uint::<127, 2>::from_limbs([0x0010_0000_0000_0000, 0]).checked_shl(64),
772            Some(Uint::<127, 2>::from_limbs([0, 0x0010_0000_0000_0000]))
773        );
774    }
775
776    #[test]
777    #[allow(
778        clippy::cast_lossless,
779        clippy::cast_possible_truncation,
780        clippy::cast_possible_wrap
781    )]
782    fn test_small() {
783        const_for!(BITS in [1, 2, 8, 16, 32, 63, 64] {
784            type U = Uint::<BITS, 1>;
785            proptest!(|(a: U, b: U)| {
786                assert_eq!(a | b, U::from_limbs([a.limbs[0] | b.limbs[0]]));
787                assert_eq!(a & b, U::from_limbs([a.limbs[0] & b.limbs[0]]));
788                assert_eq!(a ^ b, U::from_limbs([a.limbs[0] ^ b.limbs[0]]));
789            });
790            proptest!(|(a: U, s in 0..BITS)| {
791                assert_eq!(a << s, U::from_limbs([a.limbs[0] << s & U::MASK]));
792                assert_eq!(a >> s, U::from_limbs([a.limbs[0] >> s]));
793            });
794        });
795        proptest!(|(a: Uint::<32, 1>, s in 0_usize..=34)| {
796            assert_eq!(a.reverse_bits(), Uint::from((a.limbs[0] as u32).reverse_bits() as u64));
797            assert_eq!(a.rotate_left(s), Uint::from((a.limbs[0] as u32).rotate_left(s as u32) as u64));
798            assert_eq!(a.rotate_right(s), Uint::from((a.limbs[0] as u32).rotate_right(s as u32) as u64));
799            if s < 32 {
800                let arr_shifted = (((a.limbs[0] as i32) >> s) as u32) as u64;
801                assert_eq!(a.arithmetic_shr(s), Uint::from_limbs([arr_shifted]));
802            }
803        });
804        proptest!(|(a: Uint::<64, 1>, s in 0_usize..=66)| {
805            assert_eq!(a.reverse_bits(), Uint::from(a.limbs[0].reverse_bits()));
806            assert_eq!(a.rotate_left(s), Uint::from(a.limbs[0].rotate_left(s as u32)));
807            assert_eq!(a.rotate_right(s), Uint::from(a.limbs[0].rotate_right(s as u32)));
808            if s < 64 {
809                let arr_shifted = ((a.limbs[0] as i64) >> s) as u64;
810                assert_eq!(a.arithmetic_shr(s), Uint::from_limbs([arr_shifted]));
811            }
812        });
813    }
814
815    #[test]
816    fn test_shift_reverse() {
817        const_for!(BITS in SIZES {
818            const LIMBS: usize = nlimbs(BITS);
819            type U = Uint::<BITS, LIMBS>;
820            proptest!(|(value: U, shift in 0..=BITS + 2)| {
821                let left = (value << shift).reverse_bits();
822                let right = value.reverse_bits() >> shift;
823                assert_eq!(left, right);
824            });
825        });
826    }
827
828    #[test]
829    fn test_rotate() {
830        const_for!(BITS in SIZES {
831            const LIMBS: usize = nlimbs(BITS);
832            type U = Uint::<BITS, LIMBS>;
833            proptest!(|(value: U, shift in  0..=BITS + 2)| {
834                let rotated = value.rotate_left(shift).rotate_right(shift);
835                assert_eq!(value, rotated);
836            });
837        });
838    }
839
840    #[test]
841    fn test_arithmetic_shr() {
842        const_for!(BITS in SIZES {
843            const LIMBS: usize = nlimbs(BITS);
844            type U = Uint::<BITS, LIMBS>;
845            proptest!(|(value: U, shift in  0..=BITS + 2)| {
846                let shifted = value.arithmetic_shr(shift);
847                assert_eq!(shifted.leading_ones(), match value.leading_ones() {
848                    0 => 0,
849                    n => min(BITS, n + shift)
850                });
851            });
852        });
853    }
854
855    #[test]
856    fn test_overflowing_shr() {
857        // Test: Single limb right shift from 40u64 by 1 bit.
858        // Expects resulting integer: 20 with no fractional part.
859        assert_eq!(
860            Uint::<64, 1>::from_limbs([40u64]).overflowing_shr(1),
861            (Uint::<64, 1>::from(20), false)
862        );
863
864        // Test: Single limb right shift from 41u64 by 1 bit.
865        // Expects resulting integer: 20 with a detected fractional part.
866        assert_eq!(
867            Uint::<64, 1>::from_limbs([41u64]).overflowing_shr(1),
868            (Uint::<64, 1>::from(20), true)
869        );
870
871        // Test: Two limbs right shift from 0x0010_0000_0000_0000 and 0 by 1 bit.
872        // Expects resulting limbs: [0x0080_0000_0000_000, 0] with no fractional part.
873        assert_eq!(
874            Uint::<65, 2>::from_limbs([0x0010_0000_0000_0000, 0]).overflowing_shr(1),
875            (Uint::<65, 2>::from_limbs([0x0008_0000_0000_0000, 0]), false)
876        );
877
878        // Test: Shift beyond single limb capacity with MAX value.
879        // Expects the highest possible value in 256-bit representation with a detected
880        // fractional part.
881        assert_eq!(
882            Uint::<256, 4>::MAX.overflowing_shr(65),
883            (
884                Uint::<256, 4>::from_str_radix(
885                    "7fffffffffffffffffffffffffffffffffffffffffffffff",
886                    16
887                )
888                .unwrap(),
889                true
890            )
891        );
892        // Test: Large 4096-bit integer right shift by 34 bits.
893        // Expects a specific value with no fractional part.
894        assert_eq!(
895            Uint::<4096, 64>::from_str_radix("3ffffffffffffffffffffffffffffc00000000", 16,)
896                .unwrap()
897                .overflowing_shr(34),
898            (
899                Uint::<4096, 64>::from_str_radix("fffffffffffffffffffffffffffff", 16).unwrap(),
900                false
901            )
902        );
903        // Test: Extremely large 4096-bit integer right shift by 100 bits.
904        // Expects a specific value with no fractional part.
905        assert_eq!(
906            Uint::<4096, 64>::from_str_radix(
907                "fffffffffffffffffffffffffffff0000000000000000000000000",
908                16,
909            )
910            .unwrap()
911            .overflowing_shr(100),
912            (
913                Uint::<4096, 64>::from_str_radix("fffffffffffffffffffffffffffff", 16).unwrap(),
914                false
915            )
916        );
917        // Test: Complex 4096-bit integer right shift by 1 bit.
918        // Expects a specific value with no fractional part.
919        assert_eq!(
920            Uint::<4096, 64>::from_str_radix(
921                "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffff0bdbfe",
922                16,
923            )
924            .unwrap()
925            .overflowing_shr(1),
926            (
927                Uint::<4096, 64>::from_str_radix(
928                    "7fffffffffffffffffffffffffffffffffffffffffffffffffffffffff85edff",
929                    16
930                )
931                .unwrap(),
932                false
933            )
934        );
935        // Test: Large 4096-bit integer right shift by 1000 bits.
936        // Expects a specific value with no fractional part.
937        assert_eq!(
938            Uint::<4096, 64>::from_str_radix(
939                "fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
940                16,
941            )
942            .unwrap()
943            .overflowing_shr(1000),
944            (
945                Uint::<4096, 64>::from_str_radix(
946                    "fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
947                    16
948                )
949                .unwrap(),
950                false
951            )
952        );
953        // Test: MAX 4096-bit integer right shift by 34 bits.
954        // Expects a specific value with a detected fractional part.
955        assert_eq!(
956            Uint::<4096, 64>::MAX
957            .overflowing_shr(34),
958            (
959                Uint::<4096, 64>::from_str_radix(
960                    "3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
961                    16
962                )
963                .unwrap(),
964                true
965            )
966        );
967    }
968}
ruint/bits.rs

ruint/
bits.rs
