Struct rug::integer::BorrowInteger

#[repr(transparent)]
pub struct BorrowInteger<'a> { /* private fields */ }

Used to get a reference to an Integer.

The struct implements Deref<Target = Integer>.

No memory is unallocated when this struct is dropped.

Examples

use rug::{integer::BorrowInteger, Integer};
let i = Integer::from(42);
let neg: BorrowInteger = i.as_neg();
// i is still valid
assert_eq!(i, 42);
assert_eq!(*neg, -42);

Implementations

impl BorrowInteger<'_>

pub const unsafe fn from_raw<'a>(raw: mpz_t) -> BorrowInteger<'a>

Create a borrow from a raw GMP integer.

Safety

• The value must be initialized.
• The mpz_t type can be considered as a kind of pointer, so there can be multiple copies of it. BorrowInteger cannot mutate the value, so there can be other copies, but none of them are allowed to mutate the value.
• The lifetime is obtained from the return type. The user must ensure the value remains valid for the duration of the lifetime.

Examples

use rug::{integer::BorrowInteger, Integer};
let i = Integer::from(42);
// Safety: i.as_raw() is a valid pointer.
let raw = unsafe { *i.as_raw() };
// Safety: i is still valid when borrow is used.
let borrow = unsafe { BorrowInteger::from_raw(raw) };
assert_eq!(i, *borrow);

Methods from Deref<Target = Integer>

pub const ZERO: Integer = Integer::new()

pub fn capacity(&self) -> usize

Returns the capacity in bits that can be stored without reallocating.

Examples

use rug::Integer;
let i = Integer::with_capacity(137);
assert!(i.capacity() >= 137);

pub fn as_raw(&self) -> *const mpz_t

Returns a pointer to the inner GMP integer.

The returned pointer will be valid for as long as self is valid.

Examples

use gmp_mpfr_sys::gmp;
use rug::Integer;
let i = Integer::from(15);
let z_ptr = i.as_raw();
unsafe {
    let u = gmp::mpz_get_ui(z_ptr);
    assert_eq!(u, 15);
}
// i is still valid
assert_eq!(i, 15);

pub fn significant_digits<T: UnsignedPrimitive>(&self) -> usize

Returns the number of digits of type T required to represent the absolute value.

T can be any unsigned integer primitive type.

Examples

use rug::Integer;

let i: Integer = Integer::from(1) << 256;
assert_eq!(i.significant_digits::<bool>(), 257);
assert_eq!(i.significant_digits::<u8>(), 33);
assert_eq!(i.significant_digits::<u16>(), 17);
assert_eq!(i.significant_digits::<u32>(), 9);
assert_eq!(i.significant_digits::<u64>(), 5);

pub fn to_digits<T: UnsignedPrimitive>(&self, order: Order) -> Vec<T>

Converts the absolute value to a Vec of digits of type T, where T can be any unsigned integer primitive type.

The Integer type also has the as_limbs method, which can be used to borrow the digits without copying them. This does come with some more constraints compared to to_digits:

1. The digit width is not optional and depends on the implementation: limb_t is typically u64 on 64-bit systems and u32 on 32-bit systems.
2. The order is not optional and is least significant digit first, with each digit in the target’s endianness, equivalent to Order::Lsf.

Examples

use rug::{integer::Order, Integer};
let i = Integer::from(0x1234_5678_9abc_def0u64);
let digits = i.to_digits::<u32>(Order::MsfBe);
assert_eq!(digits, [0x1234_5678u32.to_be(), 0x9abc_def0u32.to_be()]);

let zero = Integer::new();
let digits_zero = zero.to_digits::<u32>(Order::MsfBe);
assert!(digits_zero.is_empty());

pub fn write_digits<T: UnsignedPrimitive>(&self, digits: &mut [T], order: Order)

Writes the absolute value into a slice of digits of type T, where T can be any unsigned integer primitive type.

The slice must be large enough to hold the digits; the minimum size can be obtained using the significant_digits method.

Panics

Panics if the slice does not have sufficient capacity.

Examples

use rug::{integer::Order, Integer};
let i = Integer::from(0x1234_5678_9abc_def0u64);
let mut digits = [0xffff_ffffu32; 4];
i.write_digits(&mut digits, Order::MsfBe);
let word0 = 0x9abc_def0u32;
let word1 = 0x1234_5678u32;
assert_eq!(digits, [0, 0, word1.to_be(), word0.to_be()]);

pub unsafe fn write_digits_unaligned<T: UnsignedPrimitive>(
    &self,
    dst: *mut T,
    len: usize,
    order: Order
)

Writes the absolute value into a memory area of digits of type T, where T can be any unsigned integer primitive type.

The memory area is addressed using a pointer and a length. The len parameter is the number of digits, not the number of bytes.

The length must be large enough to hold the digits; the minimum length can be obtained using the significant_digits method.

There are no data alignment restrictions on dst, any address is allowed.

The memory locations can be uninitialized before this method is called; this method sets all len elements, padding with zeros if the length is larger than required.

Safety

To avoid undefined behavior, dst must be valid for writing len digits, that is len × size_of::<T>() bytes.

Panics

Panics if the length is less than the number of digits.

Examples

use rug::{integer::Order, Integer};
let i = Integer::from(0xfedc_ba98_7654_3210u64);
let mut digits = [0xffff_ffffu32; 4];
let ptr = digits.as_mut_ptr();
unsafe {
    let unaligned = (ptr as *mut u8).offset(2) as *mut u32;
    i.write_digits_unaligned(unaligned, 3, Order::MsfBe);
}
assert_eq!(
    digits,
    [
        0xffff_0000u32.to_be(),
        0x0000_fedcu32.to_be(),
        0xba98_7654u32.to_be(),
        0x3210_ffffu32.to_be(),
    ]
);

The following example shows how to write into uninitialized memory. In practice, the following code could be replaced by a call to the safe method to_digits.

use rug::{integer::Order, Integer};
let i = Integer::from(0x1234_5678_9abc_def0u64);
let len = i.significant_digits::<u32>();
assert_eq!(len, 2);

// The following code is equivalent to:
//     let digits = i.to_digits::<u32>(Order::MsfBe);
let mut digits = Vec::<u32>::with_capacity(len);
let ptr = digits.as_mut_ptr();
unsafe {
    i.write_digits_unaligned(ptr, len, Order::MsfBe);
    digits.set_len(len);
}

assert_eq!(digits, [0x1234_5678u32.to_be(), 0x9abc_def0u32.to_be()]);

pub fn as_limbs(&self) -> &[limb_t]

Extracts a slice of limbs used to store the value.

The slice contains the absolute value of self, with the least significant limb first.

The Integer type also implements AsRef<[limb_t]>, which is equivalent to this method.

Examples

use rug::Integer;
assert!(Integer::new().as_limbs().is_empty());
assert_eq!(Integer::from(13).as_limbs(), &[13]);
assert_eq!(Integer::from(-23).as_limbs(), &[23]);

int.as_limbs() is like a borrowing non-copy version of int.to_digits::<[limb_t]>(Order::Lsf).

use gmp_mpfr_sys::gmp::limb_t;
use rug::{integer::Order, Integer};
let int = Integer::from(0x1234_5678_9abc_def0u64);
// no copying for int_slice, which is borrowing int
let int_slice = int.as_limbs();
// digits is a copy and does not borrow int
let digits = int.to_digits::<limb_t>(Order::Lsf);
// no copying for digits_slice, which is borrowing digits
let digits_slice = &digits[..];
assert_eq!(int_slice, digits_slice);

pub fn to_i8(&self) -> Option<i8>

Converts to an i8 if the value fits.

This conversion can also be performed using

• i8::try_from(&integer)
• i8::try_from(integer)
• (&integer).checked_as::<i8>()
• integer.borrow().checked_as::<i8>()

Examples

use rug::Integer;
let fits = Integer::from(-100);
assert_eq!(fits.to_i8(), Some(-100));
let small = Integer::from(-200);
assert_eq!(small.to_i8(), None);
let large = Integer::from(200);
assert_eq!(large.to_i8(), None);

pub fn to_i16(&self) -> Option<i16>

Converts to an i16 if the value fits.

This conversion can also be performed using

• i16::try_from(&integer)
• i16::try_from(integer)
• (&integer).checked_as::<i16>()
• integer.borrow().checked_as::<i16>()

Examples

use rug::Integer;
let fits = Integer::from(-30_000);
assert_eq!(fits.to_i16(), Some(-30_000));
let small = Integer::from(-40_000);
assert_eq!(small.to_i16(), None);
let large = Integer::from(40_000);
assert_eq!(large.to_i16(), None);

pub fn to_i32(&self) -> Option<i32>

Converts to an i32 if the value fits.

This conversion can also be performed using

• i32::try_from(&integer)
• i32::try_from(integer)
• (&integer).checked_as::<i32>()
• integer.borrow().checked_as::<i32>()

Examples

use rug::Integer;
let fits = Integer::from(-50);
assert_eq!(fits.to_i32(), Some(-50));
let small = Integer::from(-123456789012345_i64);
assert_eq!(small.to_i32(), None);
let large = Integer::from(123456789012345_i64);
assert_eq!(large.to_i32(), None);

pub fn to_i64(&self) -> Option<i64>

Converts to an i64 if the value fits.

This conversion can also be performed using

• i64::try_from(&integer)
• i64::try_from(integer)
• (&integer).checked_as::<i64>()
• integer.borrow().checked_as::<i64>()

Examples

use rug::Integer;
let fits = Integer::from(-50);
assert_eq!(fits.to_i64(), Some(-50));
let small = Integer::from_str_radix("-fedcba9876543210", 16).unwrap();
assert_eq!(small.to_i64(), None);
let large = Integer::from_str_radix("fedcba9876543210", 16).unwrap();
assert_eq!(large.to_i64(), None);

pub fn to_i128(&self) -> Option<i128>

Converts to an i128 if the value fits.

This conversion can also be performed using

• i128::try_from(&integer)
• i128::try_from(integer)
• (&integer).checked_as::<i128>()
• integer.borrow().checked_as::<i128>()

Examples

use rug::Integer;
let fits = Integer::from(-50);
assert_eq!(fits.to_i128(), Some(-50));
let small: Integer = Integer::from(-1) << 130;
assert_eq!(small.to_i128(), None);
let large: Integer = Integer::from(1) << 130;
assert_eq!(large.to_i128(), None);

pub fn to_isize(&self) -> Option<isize>

Converts to an isize if the value fits.

This conversion can also be performed using

• isize::try_from(&integer)
• isize::try_from(integer)
• (&integer).checked_as::<isize>()
• integer.borrow().checked_as::<isize>()

Examples

use rug::Integer;
let fits = Integer::from(0x1000);
assert_eq!(fits.to_isize(), Some(0x1000));
let large: Integer = Integer::from(0x1000) << 128;
assert_eq!(large.to_isize(), None);

pub fn to_u8(&self) -> Option<u8>

Converts to an u8 if the value fits.

This conversion can also be performed using

• u8::try_from(&integer)
• u8::try_from(integer)
• (&integer).checked_as::<u8>()
• integer.borrow().checked_as::<u8>()

Examples

use rug::Integer;
let fits = Integer::from(200);
assert_eq!(fits.to_u8(), Some(200));
let neg = Integer::from(-1);
assert_eq!(neg.to_u8(), None);
let large = Integer::from(300);
assert_eq!(large.to_u8(), None);

pub fn to_u16(&self) -> Option<u16>

Converts to an u16 if the value fits.

This conversion can also be performed using

• u16::try_from(&integer)
• u16::try_from(integer)
• (&integer).checked_as::<u16>()
• integer.borrow().checked_as::<u16>()

Examples

use rug::Integer;
let fits = Integer::from(60_000);
assert_eq!(fits.to_u16(), Some(60_000));
let neg = Integer::from(-1);
assert_eq!(neg.to_u16(), None);
let large = Integer::from(70_000);
assert_eq!(large.to_u16(), None);

pub fn to_u32(&self) -> Option<u32>

Converts to an u32 if the value fits.

This conversion can also be performed using

• u32::try_from(&integer)
• u32::try_from(integer)
• (&integer).checked_as::<u32>()
• integer.borrow().checked_as::<u32>()

Examples

use rug::Integer;
let fits = Integer::from(1234567890);
assert_eq!(fits.to_u32(), Some(1234567890));
let neg = Integer::from(-1);
assert_eq!(neg.to_u32(), None);
let large = Integer::from(123456789012345_u64);
assert_eq!(large.to_u32(), None);

pub fn to_u64(&self) -> Option<u64>

Converts to an u64 if the value fits.

This conversion can also be performed using

• u64::try_from(&integer)
• u64::try_from(integer)
• (&integer).checked_as::<u64>()
• integer.borrow().checked_as::<u64>()

Examples

use rug::Integer;
let fits = Integer::from(123456789012345_u64);
assert_eq!(fits.to_u64(), Some(123456789012345));
let neg = Integer::from(-1);
assert_eq!(neg.to_u64(), None);
let large = "1234567890123456789012345".parse::<Integer>().unwrap();
assert_eq!(large.to_u64(), None);

pub fn to_u128(&self) -> Option<u128>

Converts to an u128 if the value fits.

This conversion can also be performed using

• u128::try_from(&integer)
• u128::try_from(integer)
• (&integer).checked_as::<u128>()
• integer.borrow().checked_as::<u128>()

Examples

use rug::Integer;
let fits = Integer::from(12345678901234567890_u128);
assert_eq!(fits.to_u128(), Some(12345678901234567890));
let neg = Integer::from(-1);
assert_eq!(neg.to_u128(), None);
let large = "1234567890123456789012345678901234567890"
    .parse::<Integer>()
    .unwrap();
assert_eq!(large.to_u128(), None);

pub fn to_usize(&self) -> Option<usize>

Converts to an usize if the value fits.

This conversion can also be performed using

• usize::try_from(&integer)
• usize::try_from(integer)
• (&integer).checked_as::<usize>()
• integer.borrow().checked_as::<usize>()

Examples

use rug::Integer;
let fits = Integer::from(0x1000);
assert_eq!(fits.to_usize(), Some(0x1000));
let neg = Integer::from(-1);
assert_eq!(neg.to_usize(), None);
let large: Integer = Integer::from(0x1000) << 128;
assert_eq!(large.to_usize(), None);

pub fn to_i8_wrapping(&self) -> i8

Converts to an i8, wrapping if the value does not fit.

This conversion can also be performed using

• (&integer).wrapping_as::<i8>()
• integer.borrow().wrapping_as::<i8>()

Examples

use rug::Integer;
let large = Integer::from(0x1234);
assert_eq!(large.to_i8_wrapping(), 0x34);

pub fn to_i16_wrapping(&self) -> i16

Converts to an i16, wrapping if the value does not fit.

This conversion can also be performed using

• (&integer).wrapping_as::<i16>()
• integer.borrow().wrapping_as::<i16>()

Examples

use rug::Integer;
let large = Integer::from(0x1234_5678);
assert_eq!(large.to_i16_wrapping(), 0x5678);

pub fn to_i32_wrapping(&self) -> i32

Converts to an i32, wrapping if the value does not fit.

This conversion can also be performed using

• (&integer).wrapping_as::<i32>()
• integer.borrow().wrapping_as::<i32>()

Examples

use rug::Integer;
let large = Integer::from(0x1234_5678_9abc_def0_u64);
assert_eq!(large.to_i32_wrapping(), 0x9abc_def0_u32 as i32);

pub fn to_i64_wrapping(&self) -> i64

Converts to an i64, wrapping if the value does not fit.

This conversion can also be performed using

• (&integer).wrapping_as::<i64>()
• integer.borrow().wrapping_as::<i64>()

Examples

use rug::Integer;
let large = Integer::from_str_radix("f123456789abcdef0", 16).unwrap();
assert_eq!(large.to_i64_wrapping(), 0x1234_5678_9abc_def0);

pub fn to_i128_wrapping(&self) -> i128

Converts to an i128, wrapping if the value does not fit.

This conversion can also be performed using

• (&integer).wrapping_as::<i128>()
• integer.borrow().wrapping_as::<i128>()

Examples

use rug::Integer;
let s = "f123456789abcdef0123456789abcdef0";
let large = Integer::from_str_radix(s, 16).unwrap();
assert_eq!(
    large.to_i128_wrapping(),
    0x1234_5678_9abc_def0_1234_5678_9abc_def0
);

pub fn to_isize_wrapping(&self) -> isize

Converts to an isize, wrapping if the value does not fit.

This conversion can also be performed using

• (&integer).wrapping_as::<isize>()
• integer.borrow().wrapping_as::<isize>()

Examples

use rug::Integer;
let large: Integer = (Integer::from(0x1000) << 128) | 0x1234;
assert_eq!(large.to_isize_wrapping(), 0x1234);

pub fn to_u8_wrapping(&self) -> u8

Converts to a u8, wrapping if the value does not fit.

This conversion can also be performed using

• (&integer).wrapping_as::<u8>()
• integer.borrow().wrapping_as::<u8>()

Examples

use rug::Integer;
let neg = Integer::from(-1);
assert_eq!(neg.to_u8_wrapping(), 0xff);
let large = Integer::from(0x1234);
assert_eq!(large.to_u8_wrapping(), 0x34);

pub fn to_u16_wrapping(&self) -> u16

Converts to a u16, wrapping if the value does not fit.

This conversion can also be performed using

• (&integer).wrapping_as::<u16>()
• integer.borrow().wrapping_as::<u16>()

Examples

use rug::Integer;
let neg = Integer::from(-1);
assert_eq!(neg.to_u16_wrapping(), 0xffff);
let large = Integer::from(0x1234_5678);
assert_eq!(large.to_u16_wrapping(), 0x5678);

pub fn to_u32_wrapping(&self) -> u32

Converts to a u32, wrapping if the value does not fit.

This conversion can also be performed using

• (&integer).wrapping_as::<u32>()
• integer.borrow().wrapping_as::<u32>()

Examples

use rug::Integer;
let neg = Integer::from(-1);
assert_eq!(neg.to_u32_wrapping(), 0xffff_ffff);
let large = Integer::from(0x1234_5678_9abc_def0_u64);
assert_eq!(large.to_u32_wrapping(), 0x9abc_def0);

pub fn to_u64_wrapping(&self) -> u64

Converts to a u64, wrapping if the value does not fit.

This conversion can also be performed using

• (&integer).wrapping_as::<u64>()
• integer.borrow().wrapping_as::<u64>()

Examples

use rug::Integer;
let neg = Integer::from(-1);
assert_eq!(neg.to_u64_wrapping(), 0xffff_ffff_ffff_ffff);
let large = Integer::from_str_radix("f123456789abcdef0", 16).unwrap();
assert_eq!(large.to_u64_wrapping(), 0x1234_5678_9abc_def0);

pub fn to_u128_wrapping(&self) -> u128

Converts to a u128, wrapping if the value does not fit.

This conversion can also be performed using

• (&integer).wrapping_as::<u128>()
• integer.borrow().wrapping_as::<u128>()

Examples

use rug::Integer;
let neg = Integer::from(-1);
assert_eq!(
    neg.to_u128_wrapping(),
    0xffff_ffff_ffff_ffff_ffff_ffff_ffff_ffff
);
let s = "f123456789abcdef0123456789abcdef0";
let large = Integer::from_str_radix(s, 16).unwrap();
assert_eq!(
    large.to_u128_wrapping(),
    0x1234_5678_9abc_def0_1234_5678_9abc_def0
);

pub fn to_usize_wrapping(&self) -> usize

Converts to a usize, wrapping if the value does not fit.

This conversion can also be performed using

• (&integer).wrapping_as::<usize>()
• integer.borrow().wrapping_as::<usize>()

Examples

use rug::Integer;
let large: Integer = (Integer::from(0x1000) << 128) | 0x1234;
assert_eq!(large.to_usize_wrapping(), 0x1234);

pub fn to_f32(&self) -> f32

Converts to an f32, rounding towards zero.

This conversion can also be performed using

• (&integer).az::<f32>()
• integer.borrow().az::<f32>()

Examples

use core::f32;
use rug::Integer;
let min = Integer::from_f32(f32::MIN).unwrap();
let min_minus_one = min - 1u32;
// min_minus_one is truncated to f32::MIN
assert_eq!(min_minus_one.to_f32(), f32::MIN);
let times_two = min_minus_one * 2u32;
// times_two is too small
assert_eq!(times_two.to_f32(), f32::NEG_INFINITY);

pub fn to_f64(&self) -> f64

Converts to an f64, rounding towards zero.

This conversion can also be performed using

• (&integer).az::<f64>()
• integer.borrow().az::<f64>()

Examples

use core::f64;
use rug::Integer;

// An `f64` has 53 bits of precision.
let exact = 0x1f_ffff_ffff_ffff_u64;
let i = Integer::from(exact);
assert_eq!(i.to_f64(), exact as f64);

// large has 56 ones
let large = 0xff_ffff_ffff_ffff_u64;
// trunc has 53 ones followed by 3 zeros
let trunc = 0xff_ffff_ffff_fff8_u64;
let j = Integer::from(large);
assert_eq!(j.to_f64() as u64, trunc);

let max = Integer::from_f64(f64::MAX).unwrap();
let max_plus_one = max + 1u32;
// max_plus_one is truncated to f64::MAX
assert_eq!(max_plus_one.to_f64(), f64::MAX);
let times_two = max_plus_one * 2u32;
// times_two is too large
assert_eq!(times_two.to_f64(), f64::INFINITY);

pub fn to_f32_exp(&self) -> (f32, u32)

Converts to an f32 and an exponent, rounding towards zero.

The returned f32 is in the range 0.5 ≤ x < 1. If the value is zero, (0.0, 0) is returned.

Examples

use rug::Integer;
let zero = Integer::new();
let (d0, exp0) = zero.to_f32_exp();
assert_eq!((d0, exp0), (0.0, 0));
let fifteen = Integer::from(15);
let (d15, exp15) = fifteen.to_f32_exp();
assert_eq!((d15, exp15), (15.0 / 16.0, 4));

pub fn to_f64_exp(&self) -> (f64, u32)

Converts to an f64 and an exponent, rounding towards zero.

The returned f64 is in the range 0.5 ≤ x < 1. If the value is zero, (0.0, 0) is returned.

Examples

use rug::Integer;
let zero = Integer::new();
let (d0, exp0) = zero.to_f64_exp();
assert_eq!((d0, exp0), (0.0, 0));
let fifteen = Integer::from(15);
let (d15, exp15) = fifteen.to_f64_exp();
assert_eq!((d15, exp15), (15.0 / 16.0, 4));

pub fn to_string_radix(&self, radix: i32) -> String

Returns a string representation of the number for the specified radix.

Panics

Panics if radix is less than 2 or greater than 36.

Examples

use rug::{Assign, Integer};
let mut i = Integer::new();
assert_eq!(i.to_string_radix(10), "0");
i.assign(-10);
assert_eq!(i.to_string_radix(16), "-a");
i.assign(0x1234cdef);
assert_eq!(i.to_string_radix(4), "102031030313233");
i.assign(Integer::parse_radix("123456789aAbBcCdDeEfF", 16).unwrap());
assert_eq!(i.to_string_radix(16), "123456789aabbccddeeff");

pub fn as_neg(&self) -> BorrowInteger<'_>

Borrows a negated copy of the Integer.

The returned object implements Deref<Target = Integer>.

This method performs a shallow copy and negates it, and negation does not change the allocated data.

Examples

use rug::Integer;
let i = Integer::from(42);
let neg_i = i.as_neg();
assert_eq!(*neg_i, -42);
// methods taking &self can be used on the returned object
let reneg_i = neg_i.as_neg();
assert_eq!(*reneg_i, 42);
assert_eq!(*reneg_i, i);

pub fn as_abs(&self) -> BorrowInteger<'_>

Borrows an absolute copy of the Integer.

The returned object implements Deref<Target = Integer>.

This method performs a shallow copy and possibly negates it, and negation does not change the allocated data.

Examples

use rug::Integer;
let i = Integer::from(-42);
let abs_i = i.as_abs();
assert_eq!(*abs_i, 42);
// methods taking &self can be used on the returned object
let reabs_i = abs_i.as_abs();
assert_eq!(*reabs_i, 42);
assert_eq!(*reabs_i, *abs_i);

pub fn as_rational(&self) -> BorrowRational<'_>

Borrows a copy of the Integer as a Rational number.

The returned object implements Deref<Target = Rational>.

Examples

use rug::Integer;
let i = Integer::from(42);
let r = i.as_rational();
assert_eq!(*r, (42, 1));
// methods taking &self can be used on the returned object
let recip_r = r.as_recip();
assert_eq!(*recip_r, (1, 42));

pub fn is_even(&self) -> bool

Returns true if the number is even.

Examples

use rug::Integer;
assert!(!(Integer::from(13).is_even()));
assert!(Integer::from(-14).is_even());

pub fn is_odd(&self) -> bool

Returns true if the number is odd.

Examples

use rug::Integer;
assert!(Integer::from(13).is_odd());
assert!(!Integer::from(-14).is_odd());

pub fn is_divisible(&self, divisor: &Self) -> bool

Returns true if the number is divisible by divisor. Unlike other division functions, divisor can be zero.

Examples

use rug::Integer;
let i = Integer::from(230);
assert!(i.is_divisible(&Integer::from(10)));
assert!(!i.is_divisible(&Integer::from(100)));
assert!(!i.is_divisible(&Integer::new()));

pub fn is_divisible_u(&self, divisor: u32) -> bool

Returns true if the number is divisible by divisor. Unlike other division functions, divisor can be zero.

Examples

use rug::Integer;
let i = Integer::from(230);
assert!(i.is_divisible_u(23));
assert!(!i.is_divisible_u(100));
assert!(!i.is_divisible_u(0));

pub fn is_divisible_2pow(&self, b: u32) -> bool

Returns true if the number is divisible by 2^b.

Examples

use rug::Integer;
let i = Integer::from(15 << 17);
assert!(i.is_divisible_2pow(16));
assert!(i.is_divisible_2pow(17));
assert!(!i.is_divisible_2pow(18));

pub fn is_congruent(&self, c: &Self, divisor: &Self) -> bool

Returns true if the number is congruent to c mod divisor, that is, if there exists a q such that self = c + q × divisor. Unlike other division functions, divisor can be zero.

Examples

use rug::Integer;
let n = Integer::from(105);
let divisor = Integer::from(10);
assert!(n.is_congruent(&Integer::from(5), &divisor));
assert!(n.is_congruent(&Integer::from(25), &divisor));
assert!(!n.is_congruent(&Integer::from(7), &divisor));
// n is congruent to itself if divisor is 0
assert!(n.is_congruent(&n, &Integer::from(0)));

pub fn is_congruent_u(&self, c: u32, divisor: u32) -> bool

Returns true if the number is congruent to c mod divisor, that is, if there exists a q such that self = c + q × divisor. Unlike other division functions, divisor can be zero.

Examples

use rug::Integer;
let n = Integer::from(105);
assert!(n.is_congruent_u(3335, 10));
assert!(!n.is_congruent_u(107, 10));
// n is congruent to itself if divisor is 0
assert!(n.is_congruent_u(105, 0));

pub fn is_congruent_2pow(&self, c: &Self, b: u32) -> bool

Returns true if the number is congruent to c mod 2^b, that is, if there exists a q such that self = c + q × 2^b.

Examples

use rug::Integer;
let n = Integer::from(13 << 17 | 21);
assert!(n.is_congruent_2pow(&Integer::from(7 << 17 | 21), 17));
assert!(!n.is_congruent_2pow(&Integer::from(13 << 17 | 22), 17));

pub fn is_perfect_power(&self) -> bool

Returns true if the number is a perfect power.

Examples

use rug::Integer;
// 0 is 0 to the power of anything
assert!(Integer::from(0).is_perfect_power());
// 25 is 5 to the power of 2
assert!(Integer::from(25).is_perfect_power());
// -243 is -3 to the power of 5
assert!(Integer::from(243).is_perfect_power());

assert!(!Integer::from(24).is_perfect_power());
assert!(!Integer::from(-100).is_perfect_power());

pub fn is_perfect_square(&self) -> bool

Returns true if the number is a perfect square.

Examples

use rug::Integer;
assert!(Integer::from(0).is_perfect_square());
assert!(Integer::from(1).is_perfect_square());
assert!(Integer::from(4).is_perfect_square());
assert!(Integer::from(9).is_perfect_square());

assert!(!Integer::from(15).is_perfect_square());
assert!(!Integer::from(-9).is_perfect_square());

pub fn is_power_of_two(&self) -> bool

Returns true if the number is a power of two.

Examples

use rug::Integer;
assert!(Integer::from(1).is_power_of_two());
assert!(Integer::from(4).is_power_of_two());
assert!(Integer::from(1 << 30).is_power_of_two());

assert!(!Integer::from(7).is_power_of_two());
assert!(!Integer::from(0).is_power_of_two());
assert!(!Integer::from(-1).is_power_of_two());

pub fn cmp0(&self) -> Ordering

Returns the same result as self.cmp(&0.into()), but is faster.

Examples

use core::cmp::Ordering;
use rug::Integer;
assert_eq!(Integer::from(-5).cmp0(), Ordering::Less);
assert_eq!(Integer::from(0).cmp0(), Ordering::Equal);
assert_eq!(Integer::from(5).cmp0(), Ordering::Greater);

pub fn cmp_abs(&self, other: &Self) -> Ordering

Compares the absolute values.

Examples

use core::cmp::Ordering;
use rug::Integer;
let a = Integer::from(-10);
let b = Integer::from(4);
assert_eq!(a.cmp(&b), Ordering::Less);
assert_eq!(a.cmp_abs(&b), Ordering::Greater);

pub fn significant_bits(&self) -> u32

Returns the number of bits required to represent the absolute value.

Examples

use rug::Integer;

assert_eq!(Integer::from(0).significant_bits(), 0);  //    “”
assert_eq!(Integer::from(1).significant_bits(), 1);  //   “1”
assert_eq!(Integer::from(4).significant_bits(), 3);  // “100”
assert_eq!(Integer::from(7).significant_bits(), 3);  // “111”
assert_eq!(Integer::from(-1).significant_bits(), 1); //   “1”
assert_eq!(Integer::from(-4).significant_bits(), 3); // “100”
assert_eq!(Integer::from(-7).significant_bits(), 3); // “111”

pub fn signed_bits(&self) -> u32

Returns the number of bits required to represent the value using a two’s-complement representation.

For non-negative numbers, this method returns one more than the significant_bits method, since an extra zero is needed before the most significant bit.

Examples

use rug::Integer;

assert_eq!(Integer::from(-5).signed_bits(), 4); // “1011”
assert_eq!(Integer::from(-4).signed_bits(), 3); //  “100”
assert_eq!(Integer::from(-3).signed_bits(), 3); //  “101”
assert_eq!(Integer::from(-2).signed_bits(), 2); //   “10”
assert_eq!(Integer::from(-1).signed_bits(), 1); //    “1”
assert_eq!(Integer::from(0).signed_bits(), 1);  //    “0”
assert_eq!(Integer::from(1).signed_bits(), 2);  //   “01”
assert_eq!(Integer::from(2).signed_bits(), 3);  //  “010”
assert_eq!(Integer::from(3).signed_bits(), 3);  //  “011”
assert_eq!(Integer::from(4).signed_bits(), 4);  // “0100”

pub fn count_ones(&self) -> Option<u32>

Returns the number of one bits if the value ≥ 0.

Examples

use rug::Integer;
assert_eq!(Integer::from(0).count_ones(), Some(0));
assert_eq!(Integer::from(15).count_ones(), Some(4));
assert_eq!(Integer::from(-1).count_ones(), None);

pub fn count_zeros(&self) -> Option<u32>

Returns the number of zero bits if the value < 0.

Examples

use rug::Integer;
assert_eq!(Integer::from(0).count_zeros(), None);
assert_eq!(Integer::from(1).count_zeros(), None);
assert_eq!(Integer::from(-1).count_zeros(), Some(0));
assert_eq!(Integer::from(-2).count_zeros(), Some(1));
assert_eq!(Integer::from(-7).count_zeros(), Some(2));
assert_eq!(Integer::from(-8).count_zeros(), Some(3));

pub fn find_zero(&self, start: u32) -> Option<u32>

Returns the location of the first zero, starting at start. If the bit at location start is zero, returns start.

use rug::Integer;
// -2 is ...11111110
assert_eq!(Integer::from(-2).find_zero(0), Some(0));
assert_eq!(Integer::from(-2).find_zero(1), None);
// 15 is ...00001111
assert_eq!(Integer::from(15).find_zero(0), Some(4));
assert_eq!(Integer::from(15).find_zero(20), Some(20));

pub fn find_one(&self, start: u32) -> Option<u32>

Returns the location of the first one, starting at start. If the bit at location start is one, returns start.

use rug::Integer;
// 1 is ...00000001
assert_eq!(Integer::from(1).find_one(0), Some(0));
assert_eq!(Integer::from(1).find_one(1), None);
// -16 is ...11110000
assert_eq!(Integer::from(-16).find_one(0), Some(4));
assert_eq!(Integer::from(-16).find_one(20), Some(20));

pub fn get_bit(&self, index: u32) -> bool

Returns true if the bit at location index is 1 or false if the bit is 0.

Examples

use rug::Integer;
let i = Integer::from(0b100101);
assert!(i.get_bit(0));
assert!(!i.get_bit(1));
assert!(i.get_bit(5));
let neg = Integer::from(-1);
assert!(neg.get_bit(1000));

pub fn hamming_dist(&self, other: &Self) -> Option<u32>

Retuns the Hamming distance if the two numbers have the same sign.

The Hamming distance is the number of different bits.

Examples

use rug::Integer;
let i = Integer::from(-1);
assert_eq!(Integer::from(0).hamming_dist(&i), None);
assert_eq!(Integer::from(-1).hamming_dist(&i), Some(0));
// -1 is ...11111111 and -13 is ...11110011
assert_eq!(Integer::from(-13).hamming_dist(&i), Some(2));

pub fn abs_ref(&self) -> AbsIncomplete<'_>

Computes the absolute value.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Integer
• From<Src> for Integer
• Complete<Completed = Integer> for Src

Examples

use rug::Integer;
let i = Integer::from(-100);
let r = i.abs_ref();
let abs = Integer::from(r);
assert_eq!(abs, 100);
assert_eq!(i, -100);

pub fn signum_ref(&self) -> SignumIncomplete<'_>

Computes the signum.

• 0 if the value is zero
• 1 if the value is positive
• −1 if the value is negative

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Integer
• From<Src> for Integer
• Complete<Completed = Integer> for Src

Examples

use rug::Integer;
let i = Integer::from(-100);
let r = i.signum_ref();
let signum = Integer::from(r);
assert_eq!(signum, -1);
assert_eq!(i, -100);

pub fn clamp_ref<'min, 'max, Min, Max>(
    &self,
    min: &'min Min,
    max: &'max Max
) -> ClampIncomplete<'_, 'min, 'max, Min, Max> where
    Self: PartialOrd<Min> + PartialOrd<Max> + for<'a> Assign<&'a Min> + for<'a> Assign<&'a Max>, 

Clamps the value within the specified bounds.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Integer
• From<Src> for Integer
• Complete<Completed = Integer> for Src

Panics

Panics if the maximum value is less than the minimum value.

Examples

use rug::Integer;
let min = -10;
let max = 10;
let too_small = Integer::from(-100);
let r1 = too_small.clamp_ref(&min, &max);
let clamped1 = Integer::from(r1);
assert_eq!(clamped1, -10);
let in_range = Integer::from(3);
let r2 = in_range.clamp_ref(&min, &max);
let clamped2 = Integer::from(r2);
assert_eq!(clamped2, 3);

pub fn keep_bits_ref(&self, n: u32) -> KeepBitsIncomplete<'_>

Keeps the n least significant bits only, producing a result that is greater or equal to 0.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Integer
• From<Src> for Integer
• Complete<Completed = Integer> for Src

Examples

use rug::Integer;
let i = Integer::from(-1);
let r = i.keep_bits_ref(8);
let eight_bits = Integer::from(r);
assert_eq!(eight_bits, 0xff);

pub fn keep_signed_bits_ref(&self, n: u32) -> KeepSignedBitsIncomplete<'_>

Keeps the n least significant bits only, producing a negative result if the nth least significant bit is one.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Integer
• From<Src> for Integer
• Complete<Completed = Integer> for Src

Examples

use rug::Integer;
let i = Integer::from(-1);
let r = i.keep_signed_bits_ref(8);
let eight_bits = Integer::from(r);
assert_eq!(eight_bits, -1);

pub fn next_power_of_two_ref(&self) -> NextPowerOfTwoIncomplete<'_>

Finds the next power of two, or 1 if the number ≤ 0.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Integer
• From<Src> for Integer
• Complete<Completed = Integer> for Src

Examples

use rug::Integer;
let i = Integer::from(53);
let r = i.next_power_of_two_ref();
let next = Integer::from(r);
assert_eq!(next, 64);

pub fn div_rem_ref<'a>(&'a self, divisor: &'a Self) -> DivRemIncomplete<'_>

Performs a division producing both the quotient and remainder.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for (Integer, Integer)
• Assign<Src> for (&mut Integer, &mut Integer)
• From<Src> for (Integer, Integer)
• Complete<Completed = (Integer, Integer)> for Src

The remainder has the same sign as the dividend.

Examples

use rug::{Complete, Integer};
let dividend = Integer::from(-23);
let divisor = Integer::from(-10);
let (quotient, rem) = dividend.div_rem_ref(&divisor).complete();
assert_eq!(quotient, 2);
assert_eq!(rem, -3);

pub fn div_rem_ceil_ref<'a>(
    &'a self,
    divisor: &'a Self
) -> DivRemCeilIncomplete<'_>

Performs a division producing both the quotient and remainder, with the quotient rounded up.

The sign of the remainder is the opposite of the divisor’s sign.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for (Integer, Integer)
• Assign<Src> for (&mut Integer, &mut Integer)
• From<Src> for (Integer, Integer)
• Complete<Completed = (Integer, Integer)> for Src

Examples

use rug::{Complete, Integer};
let dividend = Integer::from(-23);
let divisor = Integer::from(-10);
let (quotient, rem) = dividend.div_rem_ceil_ref(&divisor).complete();
assert_eq!(quotient, 3);
assert_eq!(rem, 7);

pub fn div_rem_floor_ref<'a>(
    &'a self,
    divisor: &'a Self
) -> DivRemFloorIncomplete<'_>

Performs a division producing both the quotient and remainder, with the quotient rounded down.

The remainder has the same sign as the divisor.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for (Integer, Integer)
• Assign<Src> for (&mut Integer, &mut Integer)
• From<Src> for (Integer, Integer)
• Complete<Completed = (Integer, Integer)> for Src

Examples

use rug::{Complete, Integer};
let dividend = Integer::from(-23);
let divisor = Integer::from(-10);
let (quotient, rem) = dividend.div_rem_floor_ref(&divisor).complete();
assert_eq!(quotient, 2);
assert_eq!(rem, -3);

pub fn div_rem_round_ref<'a>(
    &'a self,
    divisor: &'a Self
) -> DivRemRoundIncomplete<'_>

Performs a division producing both the quotient and remainder, with the quotient rounded to the nearest integer.

When the quotient before rounding lies exactly between two integers, it is rounded away from zero.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for (Integer, Integer)
• Assign<Src> for (&mut Integer, &mut Integer)
• From<Src> for (Integer, Integer)
• Complete<Completed = (Integer, Integer)> for Src

Examples

use rug::{Complete, Integer};
// -28 / -10 → 3 rem 2
let dividend = Integer::from(-28);
let divisor = Integer::from(-10);
let (quotient, rem) = dividend.div_rem_round_ref(&divisor).complete();
assert_eq!(quotient, 3);
assert_eq!(rem, 2);

pub fn div_rem_euc_ref<'a>(
    &'a self,
    divisor: &'a Self
) -> DivRemEucIncomplete<'_>

Performs Euclidan division producing both the quotient and remainder, with a positive remainder.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for (Integer, Integer)
• Assign<Src> for (&mut Integer, &mut Integer)
• From<Src> for (Integer, Integer)
• Complete<Completed = (Integer, Integer)> for Src

Examples

use rug::{Complete, Integer};
let dividend = Integer::from(-23);
let divisor = Integer::from(-10);
let (quotient, rem) = dividend.div_rem_euc_ref(&divisor).complete();
assert_eq!(quotient, 3);
assert_eq!(rem, 7);

pub fn mod_u(&self, modulo: u32) -> u32

Returns the modulo, or the remainder of Euclidean division by a u32.

The result is always zero or positive.

Panics

Panics if modulo is zero.

Examples

use rug::Integer;
let pos = Integer::from(23);
assert_eq!(pos.mod_u(1), 0);
assert_eq!(pos.mod_u(10), 3);
assert_eq!(pos.mod_u(100), 23);
let neg = Integer::from(-23);
assert_eq!(neg.mod_u(1), 0);
assert_eq!(neg.mod_u(10), 7);
assert_eq!(neg.mod_u(100), 77);

pub fn div_exact_ref<'a>(&'a self, divisor: &'a Self) -> DivExactIncomplete<'_>

Performs an exact division.

This is much faster than normal division, but produces correct results only when the division is exact.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Integer
• From<Src> for Integer
• Complete<Completed = Integer> for Src

Examples

use rug::Integer;
let i = Integer::from(12345 * 54321);
let divisor = Integer::from(12345);
let r = i.div_exact_ref(&divisor);
let quotient = Integer::from(r);
assert_eq!(quotient, 54321);

pub fn div_exact_u_ref(&self, divisor: u32) -> DivExactUIncomplete<'_>

Performs an exact division.

This is much faster than normal division, but produces correct results only when the division is exact.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Integer
• From<Src> for Integer
• Complete<Completed = Integer> for Src

Examples

use rug::Integer;
let i = Integer::from(12345 * 54321);
let r = i.div_exact_u_ref(12345);
assert_eq!(Integer::from(r), 54321);

pub fn invert_ref<'a>(
    &'a self,
    modulo: &'a Self
) -> Option<InvertIncomplete<'a>>

Finds the inverse modulo modulo if an inverse exists.

The inverse exists if the modulo is not zero, and self and the modulo are co-prime, that is their GCD is 1.

The following are implemented with the unwrapped returned incomplete-computation value as Src:

• Assign<Src> for Integer
• From<Src> for Integer
• Complete<Completed = Integer> for Src

Examples

use rug::Integer;
let two = Integer::from(2);
let four = Integer::from(4);
let five = Integer::from(5);

// Modulo 4, 2 has no inverse, there is no i such that 2 × i = 1.
// For this conversion, if no inverse exists, the Integer
// created is left unchanged as 0.
assert!(two.invert_ref(&four).is_none());

// Modulo 5, the inverse of 2 is 3, as 2 × 3 = 1.
let r = two.invert_ref(&five).unwrap();
let inverse = Integer::from(r);
assert_eq!(inverse, 3);

pub fn pow_mod_ref<'a>(
    &'a self,
    exponent: &'a Self,
    modulo: &'a Self
) -> Option<PowModIncomplete<'a>>

Raises a number to the power of exponent modulo modulo if an answer exists.

If the exponent is negative, then the number must have an inverse for an answer to exist.

The following are implemented with the unwrapped returned incomplete-computation value as Src:

• Assign<Src> for Integer
• From<Src> for Integer
• Complete<Completed = Integer> for Src

Examples

use rug::Integer;
let two = Integer::from(2);
let thousand = Integer::from(1000);
let minus_five = Integer::from(-5);
let seven = Integer::from(7);

// Modulo 1000, 2 has no inverse: there is no i such that 2 × i = 1.
assert!(two.pow_mod_ref(&minus_five, &thousand).is_none());

// 7 × 143 modulo 1000 = 1, so 7 has an inverse 143.
// 7 ^ -5 modulo 1000 = 143 ^ 5 modulo 1000 = 943.
let r = seven.pow_mod_ref(&minus_five, &thousand).unwrap();
let power = Integer::from(r);
assert_eq!(power, 943);

pub fn secure_pow_mod_ref<'a>(
    &'a self,
    exponent: &'a Self,
    modulo: &'a Self
) -> SecurePowModIncomplete<'a>

Raises a number to the power of exponent modulo modulo, with resilience to side-channel attacks.

The exponent must be greater than zero, and the modulo must be odd.

This method is intended for cryptographic purposes where resilience to side-channel attacks is desired. The function is designed to take the same time and use the same cache access patterns for same-sized arguments, assuming that the arguments are placed at the same position and the machine state is identical when starting.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Integer
• From<Src> for Integer
• Complete<Completed = Integer> for Src

Panics

Panics if exponent ≤ 0 or if modulo is even.

Examples

use rug::Integer;
// 7 ^ 4 mod 13 = 9
let n = Integer::from(7);
let e = Integer::from(4);
let m = Integer::from(13);
let power = Integer::from(n.secure_pow_mod_ref(&e, &m));
assert_eq!(power, 9);

pub fn root_ref(&self, n: u32) -> RootIncomplete<'_>

Computes the nth root and truncates the result.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Integer
• From<Src> for Integer
• Complete<Completed = Integer> for Src

Examples

use rug::Integer;
let i = Integer::from(1004);
assert_eq!(Integer::from(i.root_ref(3)), 10);

pub fn root_rem_ref(&self, n: u32) -> RootRemIncomplete<'_>

Computes the nth root and returns the truncated root and the remainder.

The remainder is the original number minus the truncated root raised to the power of n.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for (Integer, Integer)
• Assign<Src> for (&mut Integer, &mut Integer)
• From<Src> for (Integer, Integer)
• Complete<Completed = (Integer, Integer)> for Src

Examples

use rug::{Assign, Complete, Integer};
let i = Integer::from(1004);
let mut root = Integer::new();
let mut rem = Integer::new();
// 1004 = 10^3 + 5
(&mut root, &mut rem).assign(i.root_rem_ref(3));
assert_eq!(root, 10);
assert_eq!(rem, 4);
// 1004 = 3^6 + 275
let (other_root, other_rem) = i.root_rem_ref(6).complete();
assert_eq!(other_root, 3);
assert_eq!(other_rem, 275);

pub fn square_ref(&self) -> MulIncomplete<'_>

Computes the square.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Integer
• From<Src> for Integer
• Complete<Completed = Integer> for Src
• AddAssign<Src> for Integer
• Add<Src> for Integer, Add<Integer> for Src
• SubAssign<Src> for Integer, SubFrom<Src> for Integer
• Sub<Src> for Integer, Sub<Integer> for Src

i.square_ref() produces the exact same result as &i * &i.

Examples

use rug::Integer;
let i = Integer::from(13);
assert_eq!(Integer::from(i.square_ref()), 169);

pub fn sqrt_ref(&self) -> SqrtIncomplete<'_>

Computes the square root and truncates the result.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Integer
• From<Src> for Integer
• Complete<Completed = Integer> for Src

Examples

use rug::Integer;
let i = Integer::from(104);
assert_eq!(Integer::from(i.sqrt_ref()), 10);

pub fn sqrt_rem_ref(&self) -> SqrtRemIncomplete<'_>

Computes the square root and the remainder.

The remainder is the original number minus the truncated root squared.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for (Integer, Integer)
• Assign<Src> for (&mut Integer, &mut Integer)
• From<Src> for (Integer, Integer)
• Complete<Completed = (Integer, Integer)> for Src

Examples

use rug::{Assign, Integer};
let i = Integer::from(104);
let mut sqrt = Integer::new();
let mut rem = Integer::new();
let r = i.sqrt_rem_ref();
(&mut sqrt, &mut rem).assign(r);
assert_eq!(sqrt, 10);
assert_eq!(rem, 4);
let r = i.sqrt_rem_ref();
let (other_sqrt, other_rem) = <(Integer, Integer)>::from(r);
assert_eq!(other_sqrt, 10);
assert_eq!(other_rem, 4);

pub fn is_probably_prime(&self, reps: u32) -> IsPrime

Determines wheter a number is prime.

This function uses some trial divisions, a Baille-PSW probable prime test, then reps − 24 Miller-Rabin probabilistic primality tests.

Examples

use rug::{integer::IsPrime, Integer};
let no = Integer::from(163 * 4003);
assert_eq!(no.is_probably_prime(30), IsPrime::No);
let yes = Integer::from(817_504_243);
assert_eq!(yes.is_probably_prime(30), IsPrime::Yes);
// 16_412_292_043_871_650_369 is actually a prime.
let probably = Integer::from(16_412_292_043_871_650_369_u64);
assert_eq!(probably.is_probably_prime(30), IsPrime::Probably);

pub fn next_prime_ref(&self) -> NextPrimeIncomplete<'_>

Identifies primes using a probabilistic algorithm; the chance of a composite passing will be extremely small.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Integer
• From<Src> for Integer
• Complete<Completed = Integer> for Src

Examples

use rug::Integer;
let i = Integer::from(800_000_000);
let r = i.next_prime_ref();
let prime = Integer::from(r);
assert_eq!(prime, 800_000_011);

pub fn gcd_ref<'a>(&'a self, other: &'a Self) -> GcdIncomplete<'_>

Finds the greatest common divisor.

The result is always positive except when both inputs are zero.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Integer
• From<Src> for Integer
• Complete<Completed = Integer> for Src

Examples

use rug::Integer;
let a = Integer::from(100);
let b = Integer::from(125);
let r = a.gcd_ref(&b);
// gcd of 100, 125 is 25
assert_eq!(Integer::from(r), 25);

pub fn gcd_u_ref(&self, other: u32) -> GcdUIncomplete<'_>

Finds the greatest common divisor.

The result is always positive except when both inputs are zero.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Integer
• From<Src> for Integer
• From<Src> for Option<u32>
• Complete<Completed = Integer> for Src

The last item above is useful to obtain the result as a u32 if it fits. If other > 0 , the result always fits. If the result does not fit, it is equal to the absolute value of self.

Examples

use rug::Integer;
let i = Integer::from(100);
let r = i.gcd_u_ref(125);
// gcd of 100, 125 is 25
assert_eq!(Integer::from(r), 25);
let r = i.gcd_u_ref(125);
assert_eq!(Option::<u32>::from(r), Some(25));

pub fn gcd_cofactors_ref<'a>(
    &'a self,
    other: &'a Self
) -> GcdCofactorsIncomplete<'_>

Finds the greatest common divisor (GCD) of the two inputs (self and other), and two cofactors to obtain the GCD from the two inputs.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for (Integer, Integer, Integer)
• Assign<Src> for (&mut Integer, &mut Integer, &mut Integer)
• From<Src> for (Integer, Integer, Integer)
• Complete<Completed = (Integer, Integer, Integer)> for Src

In the case that only one of the two cofactors is required, the following are also implemented:

• Assign<Src> for (Integer, Integer)
• Assign<Src> for (&mut Integer, &mut Integer)
• From<Src> for (Integer, Integer)

The GCD is always positive except when both inputs are zero. If the inputs are a and b, then the GCD is g and the cofactors are s and t such that

a × s + b × t = g

The values s and t are chosen such that normally, |s| < |b| / (2g) and |t| < |a| / (2g), and these relations define s and t uniquely. There are a few exceptional cases:

• If |a| = |b|, then s = 0, t = sgn(b).
• Otherwise, if b = 0 or |b| = 2g, then s = sgn(a), and if a = 0 or |a| = 2g, then t = sgn(b).

Examples

use rug::{Assign, Integer};
let a = Integer::from(4);
let b = Integer::from(6);
let r = a.gcd_cofactors_ref(&b);
let mut g = Integer::new();
let mut s = Integer::new();
let mut t = Integer::new();
(&mut g, &mut s, &mut t).assign(r);
assert_eq!(a, 4);
assert_eq!(b, 6);
assert_eq!(g, 2);
assert_eq!(s, -1);
assert_eq!(t, 1);

In the case that only one of the two cofactors is required, this can be achieved as follows:

use rug::{Assign, Integer};
let a = Integer::from(4);
let b = Integer::from(6);

// no t required
let (mut g1, mut s1) = (Integer::new(), Integer::new());
(&mut g1, &mut s1).assign(a.gcd_cofactors_ref(&b));
assert_eq!(g1, 2);
assert_eq!(s1, -1);

// no s required
let (mut g2, mut t2) = (Integer::new(), Integer::new());
(&mut g2, &mut t2).assign(b.gcd_cofactors_ref(&a));
assert_eq!(g2, 2);
assert_eq!(t2, 1);

pub fn lcm_ref<'a>(&'a self, other: &'a Self) -> LcmIncomplete<'_>

Finds the least common multiple.

The result is always positive except when one or both inputs are zero.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Integer
• From<Src> for Integer
• Complete<Completed = Integer> for Src

Examples

use rug::Integer;
let a = Integer::from(100);
let b = Integer::from(125);
let r = a.lcm_ref(&b);
// lcm of 100, 125 is 500
assert_eq!(Integer::from(r), 500);

pub fn lcm_u_ref(&self, other: u32) -> LcmUIncomplete<'_>

Finds the least common multiple.

The result is always positive except when one or both inputs are zero.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Integer
• From<Src> for Integer
• Complete<Completed = Integer> for Src

Examples

use rug::Integer;
let i = Integer::from(100);
let r = i.lcm_u_ref(125);
// lcm of 100, 125 is 500
assert_eq!(Integer::from(r), 500);

pub fn jacobi(&self, n: &Self) -> i32

Calculates the Jacobi symbol (self/n).

Examples

use rug::{Assign, Integer};
let m = Integer::from(10);
let mut n = Integer::from(13);
assert_eq!(m.jacobi(&n), 1);
n.assign(15);
assert_eq!(m.jacobi(&n), 0);
n.assign(17);
assert_eq!(m.jacobi(&n), -1);

pub fn legendre(&self, p: &Self) -> i32

Calculates the Legendre symbol (self/p).

Examples

use rug::{Assign, Integer};
let a = Integer::from(5);
let mut p = Integer::from(7);
assert_eq!(a.legendre(&p), -1);
p.assign(11);
assert_eq!(a.legendre(&p), 1);

pub fn kronecker(&self, n: &Self) -> i32

Calculates the Jacobi symbol (self/n) with the Kronecker extension.

Examples

use rug::{Assign, Integer};
let k = Integer::from(3);
let mut n = Integer::from(16);
assert_eq!(k.kronecker(&n), 1);
n.assign(17);
assert_eq!(k.kronecker(&n), -1);
n.assign(18);
assert_eq!(k.kronecker(&n), 0);

pub fn remove_factor_ref<'a>(
    &'a self,
    factor: &'a Self
) -> RemoveFactorIncomplete<'a>

Removes all occurrences of factor, and counts the number of occurrences removed.

Examples

use rug::{Assign, Integer};
let mut i = Integer::from(Integer::u_pow_u(13, 50));
i *= 1000;
let factor = Integer::from(13);
let r = i.remove_factor_ref(&factor);
let (mut j, mut count) = (Integer::new(), 0);
(&mut j, &mut count).assign(r);
assert_eq!(count, 50);
assert_eq!(j, 1000);

pub fn binomial_ref(&self, k: u32) -> BinomialIncomplete<'_>

Computes the binomial coefficient over k.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Integer
• From<Src> for Integer
• Complete<Completed = Integer> for Src

Examples

use rug::{Complete, Integer};
// 7 choose 2 is 21
let i = Integer::from(7);
assert_eq!(i.binomial_ref(2).complete(), 21);

pub fn random_below_ref<'a>(
    &'a self,
    rng: &'a mut dyn MutRandState
) -> RandomBelowIncomplete<'a>

Generates a non-negative random number below the given boundary value.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Integer
• From<Src> for Integer
• Complete<Completed = Integer> for Src

Panics

Panics if the boundary value is less than or equal to zero.

Examples

use rug::{rand::RandState, Integer};
let mut rand = RandState::new();
let bound = Integer::from(15);
let i = Integer::from(bound.random_below_ref(&mut rand));
println!("0 ≤ {} < {}", i, bound);
assert!(i < bound);

Trait Implementations

impl<'a> Debug for BorrowInteger<'a>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Deref for BorrowInteger<'_>

type Target = Integer

The resulting type after dereferencing.

fn deref(&self) -> &Integer

Dereferences the value.