Docs.rs

Struct rug::Integer[−][src]

#[repr(transparent)]

pub struct Integer { /* fields omitted */ }

An arbitrary-precision integer.

Standard arithmetic operations, bitwise operations and comparisons are supported. In standard arithmetic operations such as addition, you can mix Integer and primitive integer types; the result will be an Integer.

Internally the integer is not stored using a two’s-complement representation, however, for bitwise operations and shifts, the functionality is the same as if the representation was using two’s complement.

Examples

use rug::{Assign, Integer};
// Create an integer initialized as zero.
let mut int = Integer::new();
assert_eq!(int, 0);
assert_eq!(int.to_u32(), Some(0));
int.assign(-14);
assert_eq!(int, -14);
assert_eq!(int.to_u32(), None);
assert_eq!(int.to_i32(), Some(-14));

Arithmetic operations with mixed arbitrary and primitive types are allowed. Note that in the following example, there is only one allocation. The Integer instance is moved into the shift operation so that the result can be stored in the same instance, then that result is similarly consumed by the addition operation.

use rug::Integer;
let mut a = Integer::from(0xc);
a = (a << 80) + 0xffee;
assert_eq!(a.to_string_radix(16), "c0000000000000000ffee");
//                                  ^   ^   ^   ^   ^
//                                 80  64  48  32  16

Bitwise operations on Integer values behave as if the value uses a two’s-complement representation.

use rug::Integer;

let mut i = Integer::from(1);
i = i << 1000;
// i is now 1000000... (1000 zeros)
assert_eq!(i.significant_bits(), 1001);
assert_eq!(i.find_one(0), Some(1000));
i -= 1;
// i is now 111111... (1000 ones)
assert_eq!(i.count_ones(), Some(1000));

let a = Integer::from(0xf00d);
// -1 is all ones in two’s complement
let all_ones_xor_a = Integer::from(-1 ^ &a);
// a is unchanged as we borrowed it
let complement_a = !a;
// now a has been moved, so this would cause an error:
// assert!(a > 0);
assert_eq!(all_ones_xor_a, complement_a);
assert_eq!(complement_a, -0xf00e);
assert_eq!(format!("{:x}", complement_a), "-f00e");

To initialize a large Integer that does not fit in a primitive type, you can parse a string.

use rug::Integer;
let s1 = "123456789012345678901234567890";
let i1 = s1.parse::<Integer>().unwrap();
assert_eq!(i1.significant_bits(), 97);
let s2 = "ffff0000ffff0000ffff0000ffff0000ffff0000";
let i2 = Integer::from_str_radix(s2, 16).unwrap();
assert_eq!(i2.significant_bits(), 160);
assert_eq!(i2.count_ones(), Some(80));

Operations on two borrowed Integer values result in an incomplete-computation value that has to be assigned to a new Integer value.

use rug::Integer;
let a = Integer::from(10);
let b = Integer::from(3);
let a_b_ref = &a + &b;
let a_b = Integer::from(a_b_ref);
assert_eq!(a_b, 13);

As a special case, when an incomplete-computation value is obtained from multiplying two Integer references, it can be added to or subtracted from another Integer (or reference). This can be useful for multiply-accumulate operations.

use rug::Integer;
let mut acc = Integer::from(100);
let m1 = Integer::from(3);
let m2 = Integer::from(7);
// 100 + 3 * 7 = 121
acc += &m1 * &m2;
assert_eq!(acc, 121);
let other = Integer::from(2000);
// Do not consume any values here:
// 2000 - 3 * 7 = 1979
let sub = Integer::from(&other - &m1 * &m2);
assert_eq!(sub, 1979);

The Integer type supports various functions. Most methods have three versions:

  1. The first method consumes the operand.
  2. The second method has a “_mut” suffix and mutates the operand.
  3. The third method has a “_ref” suffix and borrows the operand. The returned item is an incomplete-computation value that can be assigned to an Integer.
use rug::Integer;

// 1. consume the operand
let a = Integer::from(-15);
let abs_a = a.abs();
assert_eq!(abs_a, 15);

// 2. mutate the operand
let mut b = Integer::from(-16);
b.abs_mut();
assert_eq!(b, 16);

// 3. borrow the operand
let c = Integer::from(-17);
let r = c.abs_ref();
let abs_c = Integer::from(r);
assert_eq!(abs_c, 17);
// c was not consumed
assert_eq!(c, -17);

Methods

impl Integer
[src]

Constructs a new arbitrary-precision Integer with value 0.

Examples

use rug::Integer;
let i = Integer::new();
assert_eq!(i, 0);

Constructs a new arbitrary-precision Integer with at least the specified capacity.

Examples

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

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);

Reserves capacity for at least additional more bits in the Integer.

If the integer already has enough excess capacity, this function does nothing.

Examples

use rug::Integer;
// 0x2000_0000 needs 30 bits.
let mut i = Integer::from(0x2000_0000);
assert_eq!(i.significant_bits(), 30);
i.reserve(290);
let capacity = i.capacity();
assert!(capacity >= 320);
i.reserve(0);
assert_eq!(i.capacity(), capacity);
i.reserve(291);
assert!(i.capacity() >= 321);

Shrinks the capacity of the Integer as much as possible.

The capacity can still be larger than the number of significant bits.

Examples

use rug::Integer;
// let i be 100 bits wide
let mut i = Integer::from_str_radix("fffff12345678901234567890", 16)
    .unwrap();
assert_eq!(i.significant_bits(), 100);
assert!(i.capacity() >= 100);
i >>= 80;
i.shrink_to_fit();
assert!(i.capacity() >= 20);

Creates an Integer from an initialized GMP integer.

Safety

  • The value must be initialized.
  • The gmp_mpfr_sys::gmp::mpz_t type can be considered as a kind of pointer, so there can be multiple copies of it. Since this function takes over ownership, no other copies of the passed value should exist.

Examples

extern crate gmp_mpfr_sys;
extern crate rug;
use gmp_mpfr_sys::gmp;
use rug::Integer;
use std::mem;
fn main() {
    let i = unsafe {
        let mut z = mem::uninitialized();
        gmp::mpz_init_set_ui(&mut z, 15);
        // z is initialized and unique
        Integer::from_raw(z)
    };
    assert_eq!(i, 15);
    // since i is an Integer now, deallocation is automatic
}

Converts an Integer into a GMP integer.

The returned object should be freed to avoid memory leaks.

Examples

extern crate gmp_mpfr_sys;
extern crate rug;
use gmp_mpfr_sys::gmp;
use rug::Integer;
fn main() {
    let i = Integer::from(15);
    let mut z = i.into_raw();
    unsafe {
        let u = gmp::mpz_get_ui(&z);
        assert_eq!(u, 15);
        // free object to prevent memory leak
        gmp::mpz_clear(&mut z);
    }
}

Returns a pointer to the inner GMP integer.

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

Examples

extern crate gmp_mpfr_sys;
extern crate rug;
use gmp_mpfr_sys::gmp;
use rug::Integer;
fn main() {
    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);
}

Returns an unsafe mutable pointer to the inner GMP integer.

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

Examples

extern crate gmp_mpfr_sys;
extern crate rug;
use gmp_mpfr_sys::gmp;
use rug::Integer;
fn main() {
    let mut i = Integer::from(15);
    let z_ptr = i.as_raw_mut();
    unsafe {
        gmp::mpz_add_ui(z_ptr, z_ptr, 20);
    }
    assert_eq!(i, 35);
}

Creates an Integer from a slice of digits of type T, where T can be any of the unsigned integer primitive types.

The resulting value cannot be negative.

Examples

use rug::integer::Order;
use rug::Integer;
let digits = [0x5678u16, 0x1234u16];
let i = Integer::from_digits(&digits, Order::Lsf);
assert_eq!(i, 0x1234_5678);

Assigns from a slice of digits of type T, where T can be any of the unsigned integer primitive types.

The resulting value cannot be negative.

Examples

use rug::integer::Order;
use rug::Integer;
let digits = [0x5678u16, 0x1234u16];
let mut i = Integer::new();
i.assign_digits(&digits, Order::Lsf);
assert_eq!(i, 0x1234_5678);

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

T can be any of the unsigned integer primitive types.

Examples

use rug::Integer;

let i: Integer = Integer::from(1) << 256;
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);

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

Examples

use rug::integer::Order;
use rug::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());

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

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

The contents of the slice can be uninitialized before this method is called; this method sets all the elements of the slice, padding with zeros if the slice is larger than required.

Panics

Panics if the slice does not have sufficient capacity.

Examples

use rug::integer::Order;
use rug::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()]);

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

use rug::integer::Order;
use rug::Integer;
use std::slice;
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);
// The dst slice points to allocated but uninitialized memory.
// All the digits will be initialized by write_digits.
unsafe {
    let ptr = digits.as_mut_ptr();
    let dst = slice::from_raw_parts_mut(ptr, len);
    i.write_digits(dst, Order::MsfBe);
    digits.set_len(len);
}

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

Creates an Integer from an f32 if it is finite, rounding towards zero.

Examples

use rug::Integer;
use std::f32;
let i = Integer::from_f32(-5.6).unwrap();
assert_eq!(i, -5);
let neg_inf = Integer::from_f32(f32::NEG_INFINITY);
assert!(neg_inf.is_none());

Creates an Integer from an f64 if it is finite, rounding towards zero.

Examples

use rug::Integer;
use std::f64;
let i = Integer::from_f64(1e20).unwrap();
assert_eq!(i, "100000000000000000000".parse::<Integer>().unwrap());
let inf = Integer::from_f64(f64::INFINITY);
assert!(inf.is_none());

Parses an Integer using the given radix.

Panics

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

Examples

use rug::Integer;
let i = Integer::from_str_radix("-ff", 16).unwrap();
assert_eq!(i, -0xff);

Parses a decimal string slice (&str) or byte slice (&[u8]) into an Integer.

Assign<Src> for Integer and From<Src> for Integer are implemented with the unwrapped returned incomplete-computation value as Src.

The string can start with an optional minus or plus sign. ASCII whitespace is ignored everywhere in the string. Underscores anywhere except before the first digit are ignored as well.

Examples

use rug::Integer;

let valid1 = Integer::parse("1223");
let i1 = Integer::from(valid1.unwrap());
assert_eq!(i1, 1223);
let valid2 = Integer::parse("123 456 789");
let i2 = Integer::from(valid2.unwrap());
assert_eq!(i2, 123_456_789);

let invalid = Integer::parse("789a");
assert!(invalid.is_err());

Parses a string slice (&str) or byte slice (&[u8]) into an Integer.

Assign<Src> for Integer and From<Src> for Integer are implemented with the unwrapped returned incomplete-computation value as Src.

The string can start with an optional minus or plus sign. ASCII whitespace is ignored everywhere in the string. Underscores anywhere except before the first digit are ignored as well.

Panics

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

Examples

use rug::Integer;

let valid1 = Integer::parse_radix("1223", 4);
let i1 = Integer::from(valid1.unwrap());
assert_eq!(i1, 3 + 4 * (2 + 4 * (2 + 4 * 1)));
let valid2 = Integer::parse_radix("1234 abcd", 16);
let i2 = Integer::from(valid2.unwrap());
assert_eq!(i2, 0x1234_abcd);

let invalid = Integer::parse_radix("123", 3);
assert!(invalid.is_err());

Converts to an i8 if the value fits.

If the compiler supports TryFrom, this conversion can also be performed using i8::try_from(&integer) or i8::try_from(integer).

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);

Converts to an i16 if the value fits.

If the compiler supports TryFrom, this conversion can also be performed using i16::try_from(&integer) or i16::try_from(integer).

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);

Converts to an i32 if the value fits.

If the compiler supports TryFrom, this conversion can also be performed using i32::try_from(&integer) or i32::try_from(integer).

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);

Converts to an i64 if the value fits.

If the compiler supports TryFrom, this conversion can also be performed using i64::try_from(&integer) or i64::try_from(integer).

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);

Converts to an i128 if the value fits.

This method is only present if the compiler supports the i128 primitive.

If the compiler supports TryFrom, this conversion can also be performed using i128::try_from(&integer) or i128::try_from(integer).

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);

Converts to an isize if the value fits.

If the compiler supports TryFrom, this conversion can also be performed using isize::try_from(&integer) or isize::try_from(integer).

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);

Converts to a u8 if the value fits.

If the compiler supports TryFrom, this conversion can also be performed using u8::try_from(&integer) or u8::try_from(integer).

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);

Converts to a u16 if the value fits.

If the compiler supports TryFrom, this conversion can also be performed using u16::try_from(&integer) or u16::try_from(integer).

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);

Converts to a u32 if the value fits.

If the compiler supports TryFrom, this conversion can also be performed using u32::try_from(&integer) or u32::try_from(integer).

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);

Converts to a u64 if the value fits.

If the compiler supports TryFrom, this conversion can also be performed using u64::try_from(&integer) or u64::try_from(integer).

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);

Converts to a u128 if the value fits.

This method is only present if the compiler supports the u128 primitive.

If the compiler supports TryFrom, this conversion can also be performed using u128::try_from(&integer) or u128::try_from(integer).

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);

Converts to a usize if the value fits.

If the compiler supports TryFrom, this conversion can also be performed using usize::try_from(&integer) or usize::try_from(integer).

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);

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

Examples

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

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

Examples

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

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

Examples

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

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

Examples

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

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

This method is only present if the compiler supports the i128 primitive.

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
);

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

Examples

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

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

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);

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

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);

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

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);

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

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);

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

This method is only present if the compiler supports the u128 primitive.

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
);

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

Examples

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

Converts to an f32, rounding towards zero.

Examples

use rug::Integer;
use std::f32;
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);

Converts to an f64, rounding towards zero.

Examples

use rug::Integer;
use std::f64;

// 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);

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));

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));

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");

Assigns from an f32 if it is finite, rounding towards zero.

Examples

use rug::Integer;
use std::f32;
let mut i = Integer::new();
let ret = i.assign_f64(-12.7);
assert!(ret.is_ok());
assert_eq!(i, -12);
let ret = i.assign_f32(f32::NAN);
assert!(ret.is_err());
assert_eq!(i, -12);

Assigns from an f64 if it is finite, rounding towards zero.

Examples

use rug::Integer;
let mut i = Integer::new();
let ret = i.assign_f64(12.7);
assert!(ret.is_ok());
assert_eq!(i, 12);
let ret = i.assign_f64(1.0 / 0.0);
assert!(ret.is_err());
assert_eq!(i, 12);

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);

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);

Returns true if the number is even.

Examples

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

Returns true if the number is odd.

Examples

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

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()));

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));

Returns true if the number is divisible by 2b.

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));

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)));

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));

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

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));

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());

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());

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());

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

Examples

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

Compares the absolute values.

Examples

use rug::Integer;
use std::cmp::Ordering;
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);

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”

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”

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);

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));

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));

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));

Sets the bit at location index to 1 if val is true or 0 if val is false.

Examples

use rug::{Assign, Integer};
let mut i = Integer::from(-1);
assert_eq!(*i.set_bit(0, false), -2);
i.assign(0xff);
assert_eq!(*i.set_bit(11, true), 0x8ff);

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));

Toggles the bit at location index.

Examples

use rug::Integer;
let mut i = Integer::from(0b100101);
i.toggle_bit(5);
assert_eq!(i, 0b101);

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));

Adds a list of Integer values.

Assign<Src> for Integer, From<Src> for Integer, AddAssign<Src> for Integer and Add<Src> for Integer are implemented with the returned incomplete-computation value as Src.

Examples

use rug::Integer;

let values = [
    Integer::from(5),
    Integer::from(1024),
    Integer::from(-100_000),
    Integer::from(-4),
];

let r = Integer::sum(values.iter());
let sum = Integer::from(r);
let expected = 5 + 1024 - 100_000 - 4;
assert_eq!(sum, expected);

Finds the dot product of a list of Integer value pairs.

Assign<Src> for Integer, From<Src> for Integer, AddAssign<Src> for Integer and Add<Src> for Integer are implemented with the returned incomplete-computation value as Src.

Examples

use rug::Integer;

let a = [Integer::from(270), Integer::from(-11)];
let b = [Integer::from(100), Integer::from(5)];

let r = Integer::dot(a.iter().zip(b.iter()));
let dot = Integer::from(r);
let expected = 270 * 100 - 11 * 5;
assert_eq!(dot, expected);

Multiplies a list of Integer values.

Assign<Src> for Integer, From<Src> for Integer, MulAssign<Src> for Integer and Mul<Src> for Integer are implemented with the returned incomplete-computation value as Src.

Examples

use rug::Integer;

let values = [
    Integer::from(5),
    Integer::from(1024),
    Integer::from(-100_000),
    Integer::from(-4),
];

let r = Integer::product(values.iter());
let product = Integer::from(r);
let expected = 5 * 1024 * -100_000 * -4;
assert_eq!(product, expected);

Computes the absolute value.

Examples

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

Computes the absolute value.

Examples

use rug::Integer;
let mut i = Integer::from(-100);
i.abs_mut();
assert_eq!(i, 100);

Computes the absolute value.

Assign<Src> for Integer and From<Src> for Integer are implemented with the returned incomplete-computation value as 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);

Computes the signum.

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

Examples

use rug::Integer;
assert_eq!(Integer::from(-100).signum(), -1);
assert_eq!(Integer::from(0).signum(), 0);
assert_eq!(Integer::from(100).signum(), 1);

Computes the signum.

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

Examples

use rug::Integer;
let mut i = Integer::from(-100);
i.signum_mut();
assert_eq!(i, -1);

Computes the signum.

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

Assign<Src> for Integer and From<Src> for Integer are implemented with the returned incomplete-computation value as 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);

Clamps the value within the specified bounds.

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 clamped1 = too_small.clamp(&min, &max);
assert_eq!(clamped1, -10);
let in_range = Integer::from(3);
let clamped2 = in_range.clamp(&min, &max);
assert_eq!(clamped2, 3);

Clamps the value within the specified bounds.

Panics

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

Examples

use rug::Integer;
let min = -10;
let max = 10;
let mut too_small = Integer::from(-100);
too_small.clamp_mut(&min, &max);
assert_eq!(too_small, -10);
let mut in_range = Integer::from(3);
in_range.clamp_mut(&min, &max);
assert_eq!(in_range, 3);

Clamps the value within the specified bounds.

Assign<Src> for Integer and From<Src> for Integer are implemented with the returned incomplete-computation value as 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);

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

Examples

use rug::Integer;
let i = Integer::from(-1);
let keep_8 = i.keep_bits(8);
assert_eq!(keep_8, 0xff);

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

Examples

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

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

Assign<Src> for Integer and From<Src> for Integer are implemented with the returned incomplete-computation value as 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);

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

Examples

use rug::Integer;
let i = Integer::from(-1);
let i_keep_8 = i.keep_signed_bits(8);
assert_eq!(i_keep_8, -1);
let j = Integer::from(15 << 8 | 15);
let j_keep_8 = j.keep_signed_bits(8);
assert_eq!(j_keep_8, 15);

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

Examples

use rug::Integer;
let mut i = Integer::from(-1);
i.keep_signed_bits_mut(8);
assert_eq!(i, -1);
let mut j = Integer::from(15 << 8 | 15);
j.keep_signed_bits_mut(8);
assert_eq!(j, 15);

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

Assign<Src> for Integer and From<Src> for Integer are implemented with the returned incomplete-computation value as 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);

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

Examples

use rug::Integer;
let i = Integer::from(-3).next_power_of_two();
assert_eq!(i, 1);
let i = Integer::from(4).next_power_of_two();
assert_eq!(i, 4);
let i = Integer::from(7).next_power_of_two();
assert_eq!(i, 8);

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

Examples

use rug::Integer;
let mut i = Integer::from(53);
i.next_power_of_two_mut();
assert_eq!(i, 64);

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

Assign<Src> for Integer and From<Src> for Integer are implemented with the returned incomplete-computation value as 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);

Performs a division producing both the quotient and remainder.

The remainder has the same sign as the dividend.

Panics

Panics if divisor is zero.

Examples

use rug::Integer;
let dividend = Integer::from(23);
let divisor = Integer::from(-10);
let (quotient, rem) = dividend.div_rem(divisor);
assert_eq!(quotient, -2);
assert_eq!(rem, 3);

Performs a division producing both the quotient and remainder.

The remainder has the same sign as the dividend.

The quotient is stored in self and the remainder is stored in divisor.

Panics

Panics if divisor is zero.

Examples

use rug::Integer;
let mut dividend_quotient = Integer::from(-23);
let mut divisor_rem = Integer::from(10);
dividend_quotient.div_rem_mut(&mut divisor_rem);
assert_eq!(dividend_quotient, -2);
assert_eq!(divisor_rem, -3);

Performs a division producing both the quotient and remainder.

Assign<Src> for (Integer, Integer), Assign<Src> for (&mut Integer, &mut Integer) and From<Src> for (Integer, Integer) are implemented with the returned incomplete-computation value as Src.

The remainder has the same sign as the dividend.

Examples

use rug::Integer;
let dividend = Integer::from(-23);
let divisor = Integer::from(-10);
let r = dividend.div_rem_ref(&divisor);
let (quotient, rem) = <(Integer, Integer)>::from(r);
assert_eq!(quotient, 2);
assert_eq!(rem, -3);

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.

Panics

Panics if divisor is zero.

Examples

use rug::Integer;
let dividend = Integer::from(23);
let divisor = Integer::from(-10);
let (quotient, rem) = dividend.div_rem_ceil(divisor);
assert_eq!(quotient, -2);
assert_eq!(rem, 3);

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 quotient is stored in self and the remainder is stored in divisor.

Panics

Panics if divisor is zero.

Examples

use rug::Integer;
let mut dividend_quotient = Integer::from(-23);
let mut divisor_rem = Integer::from(10);
dividend_quotient.div_rem_ceil_mut(&mut divisor_rem);
assert_eq!(dividend_quotient, -2);
assert_eq!(divisor_rem, -3);

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.

Assign<Src> for (Integer, Integer), Assign<Src> for (&mut Integer, &mut Integer) and From<Src> for (Integer, Integer) are implemented with the returned incomplete-computation value as Src.

Examples

use rug::Integer;
let dividend = Integer::from(-23);
let divisor = Integer::from(-10);
let r = dividend.div_rem_ceil_ref(&divisor);
let (quotient, rem) = <(Integer, Integer)>::from(r);
assert_eq!(quotient, 3);
assert_eq!(rem, 7);

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

The remainder has the same sign as the divisor.

Panics

Panics if divisor is zero.

Examples

use rug::Integer;
let dividend = Integer::from(23);
let divisor = Integer::from(-10);
let (quotient, rem) = dividend.div_rem_floor(divisor);
assert_eq!(quotient, -3);
assert_eq!(rem, -7);

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

The remainder has the same sign as the divisor.

The quotient is stored in self and the remainder is stored in divisor.

Panics

Panics if divisor is zero.

Examples

use rug::Integer;
let mut dividend_quotient = Integer::from(-23);
let mut divisor_rem = Integer::from(10);
dividend_quotient.div_rem_floor_mut(&mut divisor_rem);
assert_eq!(dividend_quotient, -3);
assert_eq!(divisor_rem, 7);

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

The remainder has the same sign as the divisor.

Assign<Src> for (Integer, Integer), Assign<Src> for (&mut Integer, &mut Integer) and From<Src> for (Integer, Integer) are implemented with the returned incomplete-computation value as Src.

Examples

use rug::Integer;
let dividend = Integer::from(-23);
let divisor = Integer::from(-10);
let r = dividend.div_rem_floor_ref(&divisor);
let (quotient, rem) = <(Integer, Integer)>::from(r);
assert_eq!(quotient, 2);
assert_eq!(rem, -3);

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.

Panics

Panics if divisor is zero.

Examples

use rug::Integer;
// 23 / -10 -> -2 rem 3
let (q, rem) = Integer::from(23).div_rem_round((-10).into());
assert!(q == -2 && rem == 3);
// 25 / 10 -> 3 rem -5
let (q, rem) = Integer::from(25).div_rem_round(10.into());
assert!(q == 3 && rem == -5);
// -27 / 10 -> -3 rem 3
let (q, rem) = Integer::from(-27).div_rem_round(10.into());
assert!(q == -3 && rem == 3);

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.

Panics

Panics if divisor is zero.

Examples

use rug::Integer;
// -25 / -10 -> 3 rem 5
let mut dividend_quotient = Integer::from(-25);
let mut divisor_rem = Integer::from(-10);
dividend_quotient.div_rem_round_mut(&mut divisor_rem);
assert_eq!(dividend_quotient, 3);
assert_eq!(divisor_rem, 5);

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.

Assign<Src> for (Integer, Integer), Assign<Src> for (&mut Integer, &mut Integer) and From<Src> for (Integer, Integer) are implemented with the returned incomplete-computation value as Src.

Examples

use rug::Integer;
// -28 / -10 -> 3 rem 2
let dividend = Integer::from(-28);
let divisor = Integer::from(-10);
let r = dividend.div_rem_round_ref(&divisor);
let (quotient, rem) = <(Integer, Integer)>::from(r);
assert_eq!(quotient, 3);
assert_eq!(rem, 2);

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

Panics

Panics if divisor is zero.

Examples

use rug::Integer;
let dividend = Integer::from(23);
let divisor = Integer::from(-10);
let (quotient, rem) = dividend.div_rem_euc(divisor);
assert_eq!(quotient, -2);
assert_eq!(rem, 3);

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

The quotient is stored in self and the remainder is stored in divisor.

Panics

Panics if divisor is zero.

Examples

use rug::Integer;
let mut dividend_quotient = Integer::from(-23);
let mut divisor_rem = Integer::from(10);
dividend_quotient.div_rem_euc_mut(&mut divisor_rem);
assert_eq!(dividend_quotient, -3);
assert_eq!(divisor_rem, 7);

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

Assign<Src> for (Integer, Integer), Assign<Src> for (&mut Integer, &mut Integer) and From<Src> for (Integer, Integer) are implemented with the returned incomplete-computation value as Src.

Examples

use rug::Integer;
let dividend = Integer::from(-23);
let divisor = Integer::from(-10);
let r = dividend.div_rem_euc_ref(&divisor);
let (quotient, rem) = <(Integer, Integer)>::from(r);
assert_eq!(quotient, 3);
assert_eq!(rem, 7);

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);

Performs an exact division.

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

Panics

Panics if divisor is zero.

Examples

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

Performs an exact division.

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

Panics

Panics if divisor is zero.

Examples

use rug::Integer;
let mut i = Integer::from(12345 * 54321);
i.div_exact_mut(&Integer::from(12345));
assert_eq!(i, 54321);

Performs an exact division.

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

Assign<Src> for Integer and From<Src> for Integer are implemented with the returned incomplete-computation value as 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);

Performs an exact division.

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

Panics

Panics if divisor is zero.

Examples

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

Performs an exact division.

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

Panics

Panics if divisor is zero.

Examples

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

Performs an exact division.

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

Assign<Src> for Integer and From<Src> for Integer are implemented with the returned incomplete-computation value as 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);

Finds the inverse modulo modulo and returns Ok(inverse) if it exists, or Err(unchanged) if the inverse does not exist.

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

Examples

use rug::Integer;
let n = Integer::from(2);
// Modulo 4, 2 has no inverse: there is no x such that 2 * x = 1.
let inv_mod_4 = match n.invert(&Integer::from(4)) {
    Ok(_) => unreachable!(),
    Err(unchanged) => unchanged,
};
// no inverse exists, so value is unchanged
assert_eq!(inv_mod_4, 2);
let n = inv_mod_4;
// Modulo 5, the inverse of 2 is 3, as 2 * 3 = 1.
let inv_mod_5 = match n.invert(&Integer::from(5)) {
    Ok(inverse) => inverse,
    Err(_) => unreachable!(),
};
assert_eq!(inv_mod_5, 3);

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.

Examples

use rug::Integer;
let mut n = Integer::from(2);
// Modulo 4, 2 has no inverse: there is no x such that 2 * x = 1.
match n.invert_mut(&Integer::from(4)) {
    Ok(()) => unreachable!(),
    Err(()) => assert_eq!(n, 2),
}
// Modulo 5, the inverse of 2 is 3, as 2 * 3 = 1.
match n.invert_mut(&Integer::from(5)) {
    Ok(()) => assert_eq!(n, 3),
    Err(()) => unreachable!(),
}

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.

Assign<Src> for Integer and From<Src> for Integer are implemented with the unwrapped returned incomplete-computation value as 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 x such that 2 * x = 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);

Raises a number to the power of exponent modulo modulo and returns Ok(power) if an answer exists, or Err(unchanged) if it does not.

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

When the exponent is positive and the modulo is not zero, an answer always exists.

Examples

use rug::Integer;
// 7 ^ 5 = 16807
let n = Integer::from(7);
let e = Integer::from(5);
let m = Integer::from(1000);
let power = match n.pow_mod(&e, &m) {
    Ok(power) => power,
    Err(_) => unreachable!(),
};
assert_eq!(power, 807);

When the exponent is negative, an answer exists if an inverse exists.

use rug::Integer;
// 7 * 143 modulo 1000 = 1, so 7 has an inverse 143.
// 7 ^ -5 modulo 1000 = 143 ^ 5 modulo 1000 = 943.
let n = Integer::from(7);
let e = Integer::from(-5);
let m = Integer::from(1000);
let power = match n.pow_mod(&e, &m) {
    Ok(power) => power,
    Err(_) => unreachable!(),
};
assert_eq!(power, 943);

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.

Examples

use rug::{Assign, Integer};
// Modulo 1000, 2 has no inverse: there is no x such that 2 * x =  1.
let mut n = Integer::from(2);
let e = Integer::from(-5);
let m = Integer::from(1000);
match n.pow_mod_mut(&e, &m) {
    Ok(()) => unreachable!(),
    Err(()) => assert_eq!(n, 2),
}
// 7 * 143 modulo 1000 = 1, so 7 has an inverse 143.
// 7 ^ -5 modulo 1000 = 143 ^ 5 modulo 1000 = 943.
n.assign(7);
match n.pow_mod_mut(&e, &m) {
    Ok(()) => assert_eq!(n, 943),
    Err(()) => unreachable!(),
}

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.

Assign<Src> for Integer and From<Src> for Integer are implemented with the unwrapped returned incomplete-computation value as 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 x such that 2 * x =  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);

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.

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 = n.secure_pow_mod(&e, &m);
assert_eq!(power, 9);

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.

Panics

Panics if exponent ≤ 0 or if modulo is even.

Examples

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

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.

Assign<Src> for Integer and From<Src> for Integer are implemented with the returned incomplete-computation value as 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);

Raises base to the power of exponent.

Assign<Src> for Integer and From<Src> for Integer are implemented with the returned incomplete-computation value as Src.

Examples

use rug::Integer;
let p = Integer::u_pow_u(13, 12);
let i = Integer::from(p);
assert_eq!(i, 13_u64.pow(12));

Raises base to the power of exponent.

Assign<Src> for Integer and From<Src> for Integer are implemented with the returned incomplete-computation value as Src.

Examples

use rug::Integer;
let p1 = Integer::i_pow_u(-13, 13);
let i1 = Integer::from(p1);
assert_eq!(i1, (-13_i64).pow(13));
let p2 = Integer::i_pow_u(13, 13);
let i2 = Integer::from(p2);
assert_eq!(i2, (13_i64).pow(13));

Computes the nth root and truncates the result.

Panics

Panics if n is even and the value is negative.

Examples

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

Computes the nth root and truncates the result.

Panics

Panics if n is even and the value is negative.

Examples

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

Computes the nth root and truncates the result.

Assign<Src> for Integer and From<Src> for Integer are implemented with the returned incomplete-computation value as Src.

Examples

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

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 initial value of remainder is ignored.

Panics

Panics if n is even and the value is negative.

Examples

use rug::Integer;
let i = Integer::from(1004);
let (root, rem) = i.root_rem(Integer::new(), 3);
assert_eq!(root, 10);
assert_eq!(rem, 4);

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 initial value of remainder is ignored.

Panics

Panics if n is even and the value is negative.

Examples

use rug::Integer;
let mut i = Integer::from(1004);
let mut rem = Integer::new();
i.root_rem_mut(&mut rem, 3);
assert_eq!(i, 10);
assert_eq!(rem, 4);

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.

Assign<Src> for (Integer, Integer), Assign<Src> for (&mut Integer, &mut Integer) and From<Src> for (Integer, Integer) are implemented with the returned incomplete-computation value as Src.

Examples

use rug::{Assign, Integer};
let i = Integer::from(1004);
let mut root = Integer::new();
let mut rem = Integer::new();
let r = i.root_rem_ref(3);
(&mut root, &mut rem).assign(r);
assert_eq!(root, 10);
assert_eq!(rem, 4);
let r = i.root_rem_ref(3);
let (other_root, other_rem) = <(Integer, Integer)>::from(r);
assert_eq!(other_root, 10);
assert_eq!(other_rem, 4);

Computes the square.

Examples

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

Computes the square.

Examples

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

Computes the square.

Assign<Src> for Integer and From<Src> for Integer are implemented with the returned incomplete-computation value as Src.

Examples

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

Computes the square root and truncates the result.

Panics

Panics if the value is negative.

Examples

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

Computes the square root and truncates the result.

Panics

Panics if the value is negative.

Examples

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

Computes the square root and truncates the result.

Assign<Src> for Integer and From<Src> for Integer are implemented with the returned incomplete-computation value as Src.

Examples

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

Computes the square root and the remainder.

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

The initial value of remainder is ignored.

Panics

Panics if the value is negative.

Examples

use rug::Integer;
let i = Integer::from(104);
let (sqrt, rem) = i.sqrt_rem(Integer::new());
assert_eq!(sqrt, 10);
assert_eq!(rem, 4);

Computes the square root and the remainder.

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

The initial value of remainder is ignored.

Panics

Panics if the value is negative.

Examples

use rug::Integer;
let mut i = Integer::from(104);
let mut rem = Integer::new();
i.sqrt_rem_mut(&mut rem);
assert_eq!(i, 10);
assert_eq!(rem, 4);

Computes the square root and the remainder.

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

Assign<Src> for (Integer, Integer), Assign<Src> for (&mut Integer, &mut Integer) and From<Src> for (Integer, Integer) are implemented with the returned incomplete-computation value as 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);

Determines wheter a number is prime using some trial divisions, then reps Miller-Rabin probabilistic primality tests.

Examples

use rug::integer::IsPrime;
use rug::Integer;
let no = Integer::from(163 * 4003);
assert_eq!(no.is_probably_prime(15), IsPrime::No);
let yes = Integer::from(21_751);
assert_eq!(yes.is_probably_prime(15), IsPrime::Yes);
// 817_504_243 is actually a prime.
let probably = Integer::from(817_504_243);
assert_eq!(probably.is_probably_prime(15), IsPrime::Probably);

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

Examples

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

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

Examples

use rug::Integer;
let mut i = Integer::from(800_000_000);
i.next_prime_mut();
assert_eq!(i, 800_000_011);

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

Assign<Src> for Integer and From<Src> for Integer are implemented with the returned incomplete-computation value as 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);

Finds the greatest common divisor.

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

Examples

use rug::{Assign, Integer};
let a = Integer::new();
let mut b = Integer::new();
// gcd of 0, 0 is 0
let gcd1 = a.gcd(&b);
assert_eq!(gcd1, 0);
b.assign(10);
// gcd of 0, 10 is 10
let gcd2 = gcd1.gcd(&b);
assert_eq!(gcd2, 10);
b.assign(25);
// gcd of 10, 25 is 5
let gcd3 = gcd2.gcd(&b);
assert_eq!(gcd3, 5);

Finds the greatest common divisor.

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

Examples

use rug::{Assign, Integer};
let mut a = Integer::new();
let mut b = Integer::new();
// gcd of 0, 0 is 0
a.gcd_mut(&b);
assert_eq!(a, 0);
b.assign(10);
// gcd of 0, 10 is 10
a.gcd_mut(&b);
assert_eq!(a, 10);
b.assign(25);
// gcd of 10, 25 is 5
a.gcd_mut(&b);
assert_eq!(a, 5);

Finds the greatest common divisor.

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

Assign<Src> for Integer and From<Src> for Integer are implemented with the returned incomplete-computation value as 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);

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 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::Integer;
let a = Integer::from(4);
let b = Integer::from(6);
let (g, s, t) = a.gcd_cofactors(b, Integer::new());
assert_eq!(g, 2);
assert_eq!(s, -1);
assert_eq!(t, 1);

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 GCD is stored in self, and the two cofactors are stored in other and rop.

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::Integer;
let mut a_g = Integer::from(4);
let mut b_s = Integer::from(6);
let mut t = Integer::new();
a_g.gcd_cofactors_mut(&mut b_s, &mut t);
assert_eq!(a_g, 2);
assert_eq!(b_s, -1);
assert_eq!(t, 1);

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

Assign<Src> for (Integer, Integer, Integer), Assign<Src> for (&mut Integer, &mut Integer, &mut Integer) and From<Src> for (Integer, Integer, Integer) are implemented with the returned incomplete-computation value as Src.

In the case that only one of the two cofactors is required, Assign<Src> for (Integer, Integer), Assign<Src> for (&mut Integer, &mut Integer) and From<Src> for (Integer, Integer) are also implemented with the returned incomplete-computation value as Src.

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);

Finds the least common multiple.

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

Examples

use rug::{Assign, Integer};
let a = Integer::from(10);
let mut b = Integer::from(25);
// lcm of 10, 25 is 50
let lcm1 = a.lcm(&b);
assert_eq!(lcm1, 50);
b.assign(0);
// lcm of 50, 0 is 0
let lcm2 = lcm1.lcm(&b);
assert_eq!(lcm2, 0);

Finds the least common multiple.

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

Examples

use rug::{Assign, Integer};
let mut a = Integer::from(10);
let mut b = Integer::from(25);
// lcm of 10, 25 is 50
a.lcm_mut(&b);
assert_eq!(a, 50);
b.assign(0);
// lcm of 50, 0 is 0
a.lcm_mut(&b);
assert_eq!(a, 0);

Finds the least common multiple.

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

Assign<Src> for Integer and From<Src> for Integer are implemented with the returned incomplete-computation value as 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);

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);

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);

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);

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

Examples

use rug::Integer;
let mut i = Integer::from(Integer::u_pow_u(13, 50));
i *= 1000;
let (remove, count) = i.remove_factor(&Integer::from(13));
assert_eq!(remove, 1000);
assert_eq!(count, 50);

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

Examples

use rug::Integer;
let mut i = Integer::from(Integer::u_pow_u(13, 50));
i *= 1000;
let count = i.remove_factor_mut(&Integer::from(13));
assert_eq!(i, 1000);
assert_eq!(count, 50);

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);

Computes the factorial of n.

Assign<Src> for Integer and From<Src> for Integer are implemented with the returned incomplete-computation value as Src.

Examples

use rug::Integer;
// 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
let f = Integer::factorial(10);
let i = Integer::from(f);
assert_eq!(i, 3628800);

Computes the double factorial of n.

Assign<Src> for Integer and From<Src> for Integer are implemented with the returned incomplete-computation value as Src.

Examples

use rug::Integer;
// 10 * 8 * 6 * 4 * 2
let f = Integer::factorial_2(10);
let i = Integer::from(f);
assert_eq!(i, 3840);

Computes the m-multi factorial of n.

Assign<Src> for Integer and From<Src> for Integer are implemented with the returned incomplete-computation value as Src.

Examples

use rug::Integer;
// 10 * 7 * 4 * 1
let f = Integer::factorial_m(10, 3);
let i = Integer::from(f);
assert_eq!(i, 280);

Computes the primorial of n.

Assign<Src> for Integer and From<Src> for Integer are implemented with the returned incomplete-computation value as Src.

Examples

use rug::Integer;
// 7 * 5 * 3 * 2
let p = Integer::primorial(10);
let i = Integer::from(p);
assert_eq!(i, 210);

Computes the binomial coefficient over k.

Examples

use rug::Integer;
// 7 choose 2 is 21
let i = Integer::from(7);
let bin = i.binomial(2);
assert_eq!(bin, 21);

Computes the binomial coefficient over k.

Examples

use rug::Integer;
// 7 choose 2 is 21
let mut i = Integer::from(7);
i.binomial_mut(2);
assert_eq!(i, 21);

Computes the binomial coefficient over k.

Assign<Src> for Integer and From<Src> for Integer are implemented with the returned incomplete-computation value as Src.

Examples

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

Computes the binomial coefficient n over k.

Assign<Src> for Integer and From<Src> for Integer are implemented with the returned incomplete-computation value as Src.

Examples

use rug::Integer;
// 7 choose 2 is 21
let b = Integer::binomial_u(7, 2);
let i = Integer::from(b);
assert_eq!(i, 21);

Computes the Fibonacci number.

Assign<Src> for Integer and From<Src> for Integer are implemented with the returned incomplete-computation value as Src.

This function is meant for an isolated number. If a sequence of Fibonacci numbers is required, the first two values of the sequence should be computed with the fibonacci_2 method, then iterations should be used.

Examples

use rug::Integer;
let f = Integer::fibonacci(12);
let i = Integer::from(f);
assert_eq!(i, 144);

Computes a Fibonacci number, and the previous Fibonacci number.

Assign<Src> for (Integer, Integer), Assign<Src> for (&mut Integer, &mut Integer) and From<Src> for (Integer, Integer) are implemented with the returned incomplete-computation value as Src.

This function is meant to calculate isolated numbers. If a sequence of Fibonacci numbers is required, the first two values of the sequence should be computed with this function, then iterations should be used.

Examples

use rug::{Assign, Integer};
let f = Integer::fibonacci_2(12);
let mut pair = <(Integer, Integer)>::from(f);
assert_eq!(pair.0, 144);
assert_eq!(pair.1, 89);
// Fibonacci number F[-1] is 1
pair.assign(Integer::fibonacci_2(0));
assert_eq!(pair.0, 0);
assert_eq!(pair.1, 1);

Computes the Lucas number.

Assign<Src> for Integer and From<Src> for Integer are implemented with the returned incomplete-computation value as Src.

This function is meant for an isolated number. If a sequence of Lucas numbers is required, the first two values of the sequence should be computed with the lucas_2 method, then iterations should be used.

Examples

use rug::Integer;
let l = Integer::lucas(12);
let i = Integer::from(l);
assert_eq!(i, 322);

Computes a Lucas number, and the previous Lucas number.

Assign<Src> for (Integer, Integer), Assign<Src> for (&mut Integer, &mut Integer) and From<Src> for (Integer, Integer) are implemented with the returned incomplete-computation value as Src.

This function is meant to calculate isolated numbers. If a sequence of Lucas numbers is required, the first two values of the sequence should be computed with this function, then iterations should be used.

Examples

use rug::{Assign, Integer};
let l = Integer::lucas_2(12);
let mut pair = <(Integer, Integer)>::from(l);
assert_eq!(pair.0, 322);
assert_eq!(pair.1, 199);
pair.assign(Integer::lucas_2(0));
assert_eq!(pair.0, 2);
assert_eq!(pair.1, -1);

Generates a random number with a specified maximum number of bits.

Assign<Src> for Integer and From<Src> for Integer are implemented with the returned incomplete-computation value as Src.

Examples

use rug::rand::RandState;
use rug::{Assign, Integer};
let mut rand = RandState::new();
let mut i = Integer::from(Integer::random_bits(0, &mut rand));
assert_eq!(i, 0);
i.assign(Integer::random_bits(80, &mut rand));
assert!(i.significant_bits() <= 80);

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

Panics

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

Examples

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

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

Panics

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

Examples

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

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

Assign<Src> for Integer and From<Src> for Integer are implemented with the returned incomplete-computation value as Src.

Panics

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

Examples

use rug::rand::RandState;
use rug::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 Neg for Integer
[src]

The resulting type after applying the - operator.

Performs the unary - operation.

impl NegAssign for Integer
[src]

Peforms the negation. Read more

impl<'a> Neg for &'a Integer
[src]

The resulting type after applying the - operator.

Performs the unary - operation.

impl Add<Integer> for Integer
[src]

The resulting type after applying the + operator.

Performs the + operation.

impl<'a> Add<&'a Integer> for Integer
[src]

The resulting type after applying the + operator.

Performs the + operation.

impl<'a> Add<Integer> for &'a Integer
[src]

The resulting type after applying the + operator.

Performs the + operation.

impl<'a> Add<&'a Integer> for &'a Integer
[src]

The resulting type after applying the + operator.

Performs the + operation.

impl AddAssign<Integer> for Integer
[src]

Performs the += operation.

impl<'a> AddAssign<&'a Integer> for Integer
[src]

Performs the += operation.

impl AddFrom<Integer> for Integer
[src]

Peforms the addition. Read more

impl<'a> AddFrom<&'a Integer> for Integer
[src]

Peforms the addition. Read more

impl Sub<Integer> for Integer
[src]

The resulting type after applying the - operator.

Performs the - operation.

impl<'a> Sub<&'a Integer> for Integer
[src]

The resulting type after applying the - operator.

Performs the - operation.

impl<'a> Sub<Integer> for &'a Integer
[src]

The resulting type after applying the - operator.

Performs the - operation.

impl<'a> Sub<&'a Integer> for &'a Integer
[src]

The resulting type after applying the - operator.

Performs the - operation.

impl SubAssign<Integer> for Integer
[src]

Performs the -= operation.

impl<'a> SubAssign<&'a Integer> for Integer
[src]

Performs the -= operation.

impl SubFrom<Integer> for Integer
[src]

Peforms the subtraction. Read more

impl<'a> SubFrom<&'a Integer> for Integer
[src]

Peforms the subtraction. Read more

impl Mul<Integer> for Integer
[src]

The resulting type after applying the * operator.

Performs the * operation.

impl<'a> Mul<&'a Integer> for Integer
[src]

The resulting type after applying the * operator.

Performs the * operation.

impl<'a> Mul<Integer> for &'a Integer
[src]

The resulting type after applying the * operator.

Performs the * operation.

impl<'a> Mul<&'a Integer> for &'a Integer
[src]

The resulting type after applying the * operator.

Performs the * operation.

impl MulAssign<Integer> for Integer
[src]

Performs the *= operation.

impl<'a> MulAssign<&'a Integer> for Integer
[src]

Performs the *= operation.

impl MulFrom<Integer> for Integer
[src]

Peforms the multiplication. Read more

impl<'a> MulFrom<&'a Integer> for Integer
[src]

Peforms the multiplication. Read more

impl Div<Integer> for Integer
[src]

The resulting type after applying the / operator.

Performs the / operation.

impl<'a> Div<&'a Integer> for Integer
[src]

The resulting type after applying the / operator.

Performs the / operation.

impl<'a> Div<Integer> for &'a Integer
[src]

The resulting type after applying the / operator.

Performs the / operation.

impl<'a> Div<&'a Integer> for &'a Integer
[src]

The resulting type after applying the / operator.

Performs the / operation.

impl DivAssign<Integer> for Integer
[src]

Performs the /= operation.

impl<'a> DivAssign<&'a Integer> for Integer
[src]

Performs the /= operation.

impl DivFrom<Integer> for Integer
[src]

Peforms the division. Read more

impl<'a> DivFrom<&'a Integer> for Integer
[src]

Peforms the division. Read more

impl Rem<Integer> for Integer
[src]

The resulting type after applying the % operator.

Performs the % operation.

impl<'a> Rem<&'a Integer> for Integer
[src]

The resulting type after applying the % operator.

Performs the % operation.

impl<'a> Rem<Integer> for &'a Integer
[src]

The resulting type after applying the % operator.

Performs the % operation.

impl<'a> Rem<&'a Integer> for &'a Integer
[src]

The resulting type after applying the % operator.

Performs the % operation.

impl RemAssign<Integer> for Integer
[src]

Performs the %= operation.

impl<'a> RemAssign<&'a Integer> for Integer
[src]

Performs the %= operation.

impl RemFrom<Integer> for Integer
[src]

Peforms the remainder operation. Read more

impl<'a> RemFrom<&'a Integer> for Integer
[src]

Peforms the remainder operation. Read more

impl Not for Integer
[src]

The resulting type after applying the ! operator.

Performs the unary ! operation.

impl NotAssign for Integer
[src]

Peforms the complement. Read more

impl<'a> Not for &'a Integer
[src]

The resulting type after applying the ! operator.

Performs the unary ! operation.

impl BitAnd<Integer> for Integer
[src]

The resulting type after applying the & operator.

Performs the & operation.

impl<'a> BitAnd<&'a Integer> for Integer
[src]

The resulting type after applying the & operator.

Performs the & operation.

impl<'a> BitAnd<Integer> for &'a Integer
[src]

The resulting type after applying the & operator.

Performs the & operation.

impl<'a> BitAnd<&'a Integer> for &'a Integer
[src]

The resulting type after applying the & operator.

Performs the & operation.

impl BitAndAssign<Integer> for Integer
[src]

Performs the &= operation.

impl<'a> BitAndAssign<&'a Integer> for Integer
[src]

Performs the &= operation.

impl BitAndFrom<Integer> for Integer
[src]

Peforms the AND operation. Read more

impl<'a> BitAndFrom<&'a Integer> for Integer
[src]

Peforms the AND operation. Read more

impl BitOr<Integer> for Integer
[src]

The resulting type after applying the | operator.

Performs the | operation.

impl<'a> BitOr<&'a Integer> for Integer
[src]

The resulting type after applying the | operator.

Performs the | operation.

impl<'a> BitOr<Integer> for &'a Integer
[src]

The resulting type after applying the | operator.

Performs the | operation.

impl<'a> BitOr<&'a Integer> for &'a Integer
[src]

The resulting type after applying the | operator.

Performs the | operation.

impl BitOrAssign<Integer> for Integer
[src]

Performs the |= operation.

impl<'a> BitOrAssign<&'a Integer> for Integer
[src]

Performs the |= operation.

impl BitOrFrom<Integer> for Integer
[src]

Peforms the OR operation. Read more

impl<'a> BitOrFrom<&'a Integer> for Integer
[src]

Peforms the OR operation. Read more

impl BitXor<Integer> for Integer
[src]

The resulting type after applying the ^ operator.

Performs the ^ operation.

impl<'a> BitXor<&'a Integer> for Integer
[src]

The resulting type after applying the ^ operator.

Performs the ^ operation.

impl<'a> BitXor<Integer> for &'a Integer
[src]

The resulting type after applying the ^ operator.

Performs the ^ operation.

impl<'a> BitXor<&'a Integer> for &'a Integer
[src]

The resulting type after applying the ^ operator.

Performs the ^ operation.

impl BitXorAssign<Integer> for Integer
[src]

Performs the ^= operation.

impl<'a> BitXorAssign<&'a Integer> for Integer
[src]

Performs the ^= operation.

impl BitXorFrom<Integer> for Integer
[src]

Peforms the XOR operation. Read more

impl<'a> BitXorFrom<&'a Integer> for Integer
[src]

Peforms the XOR operation. Read more

impl Add<i32> for Integer
[src]

The resulting type after applying the + operator.

Performs the + operation.

impl<'t> Add<&'t i32> for Integer
[src]

The resulting type after applying the + operator.

Performs the + operation.

impl<'b> Add<i32> for &'b Integer
[src]

The resulting type after applying the + operator.

Performs the + operation.

impl<'t, 'b> Add<&'t i32> for &'b Integer
[src]

The resulting type after applying the + operator.

Performs the + operation.

impl AddAssign<i32> for Integer
[src]

Performs the += operation.

impl<'t> AddAssign<&'t i32> for Integer
[src]

Performs the += operation.

impl Add<Integer> for i32
[src]

The resulting type after applying the + operator.

Performs the + operation.

impl<'b> Add<&'b Integer> for i32
[src]

The resulting type after applying the + operator.

Performs the + operation.

impl<'t> Add<Integer> for &'t i32
[src]

The resulting type after applying the + operator.

Performs the + operation.

impl<'b, 't> Add<&'b Integer> for &'t i32
[src]

The resulting type after applying the + operator.

Performs the + operation.

impl AddFrom<i32> for Integer
[src]

Peforms the addition. Read more

impl<'t> AddFrom<&'t i32> for Integer
[src]

Peforms the addition. Read more

impl Sub<i32> for Integer
[src]

The resulting type after applying the - operator.

Performs the - operation.

impl<'t> Sub<&'t i32> for Integer
[src]

The resulting type after applying the - operator.

Performs the - operation.

impl<'b> Sub<i32> for &'b Integer
[src]

The resulting type after applying the - operator.

Performs the - operation.

impl<'t, 'b> Sub<&'t i32> for &'b Integer
[src]

The resulting type after applying the - operator.

Performs the - operation.

impl SubAssign<i32> for Integer
[src]

Performs the -= operation.

impl<'t> SubAssign<&'t i32> for Integer
[src]

Performs the -= operation.

impl Sub<Integer> for i32
[src]

The resulting type after applying the - operator.

Performs the - operation.

impl<'b> Sub<&'b Integer> for i32
[src]

The resulting type after applying the - operator.

Performs the - operation.

impl<'t> Sub<Integer> for &'t i32
[src]

The resulting type after applying the - operator.

Performs the - operation.

impl<'b, 't> Sub<&'b Integer> for &'t i32
[src]

The resulting type after applying the - operator.

Performs the - operation.

impl SubFrom<i32> for Integer
[src]

Peforms the subtraction. Read more

impl<'t> SubFrom<&'t i32> for Integer
[src]

Peforms the subtraction. Read more

impl Mul<i32> for Integer
[src]

The resulting type after applying the * operator.

Performs the * operation.

impl<'t> Mul<&'t i32> for Integer
[src]

The resulting type after applying the * operator.

Performs the * operation.

impl<'b> Mul<i32> for &'b Integer
[src]

The resulting type after applying the * operator.

Performs the * operation.

impl<'t, 'b> Mul<&'t i32> for &'b Integer
[src]

The resulting type after applying the * operator.

Performs the * operation.

impl MulAssign<i32> for Integer
[src]

Performs the *= operation.

impl<'t> MulAssign<&'t i32> for Integer
[src]

Performs the *= operation.

impl Mul<Integer> for i32
[src]

The resulting type after applying the * operator.

Performs the * operation.

impl<'b> Mul<&'b Integer> for i32
[src]

The resulting type after applying the * operator.

Performs the * operation.

impl<'t> Mul<Integer> for &'t i32
[src]

The resulting type after applying the * operator.

Performs the * operation.

impl<'b, 't> Mul<&'b Integer> for &'t i32
[src]

The resulting type after applying the * operator.

Performs the * operation.

impl MulFrom<i32> for Integer
[src]

Peforms the multiplication. Read more

impl<'t> MulFrom<&'t i32> for Integer
[src]

Peforms the multiplication. Read more

impl Div<i32> for Integer
[src]

The resulting type after applying the / operator.

Performs the / operation.

impl<'t> Div<&'t i32> for Integer
[src]

The resulting type after applying the / operator.

Performs the / operation.

impl<'b> Div<i32> for &'b Integer
[src]

The resulting type after applying the / operator.

Performs the / operation.

impl<'t, 'b> Div<&'t i32> for &'b Integer
[src]

The resulting type after applying the / operator.

Performs the / operation.

impl DivAssign<i32> for Integer
[src]

Performs the /= operation.

impl<'t> DivAssign<&'t i32> for Integer
[src]

Performs the /= operation.

impl Div<Integer> for i32
[src]

The resulting type after applying the / operator.

Performs the / operation.

impl<'b> Div<&'b Integer> for i32
[src]

The resulting type after applying the / operator.

Performs the / operation.

impl<'t> Div<Integer> for &'t i32
[src]

The resulting type after applying the / operator.

Performs the / operation.

impl<'b, 't> Div<&'b Integer> for &'t i32
[src]

The resulting type after applying the / operator.

Performs the / operation.

impl DivFrom<i32> for Integer
[src]

Peforms the division. Read more

impl<'t> DivFrom<&'t i32> for Integer
[src]

Peforms the division. Read more

impl Rem<i32> for Integer
[src]

The resulting type after applying the % operator.

Performs the % operation.

impl<'t> Rem<&'t i32> for Integer
[src]

The resulting type after applying the % operator.

Performs the % operation.

impl<'b> Rem<i32> for &'b Integer
[src]

The resulting type after applying the % operator.

Performs the % operation.

impl<'t, 'b> Rem<&'t i32> for &'b Integer
[src]

The resulting type after applying the % operator.

Performs the % operation.

impl RemAssign<i32> for Integer
[src]

Performs the %= operation.

impl<'t> RemAssign<&'t i32> for Integer
[src]

Performs the %= operation.

impl Rem<Integer> for i32
[src]

The resulting type after applying the % operator.

Performs the % operation.

impl<'b> Rem<&'b Integer> for i32
[src]

The resulting type after applying the % operator.

Performs the % operation.

impl<'t> Rem<Integer> for &'t i32
[src]

The resulting type after applying the % operator.

Performs the % operation.

impl<'b, 't> Rem<&'b Integer> for &'t i32
[src]

The resulting type after applying the % operator.

Performs the % operation.

impl RemFrom<i32> for Integer
[src]

Peforms the remainder operation. Read more

impl<'t> RemFrom<&'t i32> for Integer
[src]

Peforms the remainder operation. Read more

impl Shl<i32> for Integer
[src]

The resulting type after applying the << operator.

Performs the << operation.

impl<'t> Shl<&'t i32> for Integer
[src]

The resulting type after applying the << operator.

Performs the << operation.

impl<'b> Shl<i32> for &'b Integer
[src]

The resulting type after applying the << operator.

Performs the << operation.

impl<'t, 'b> Shl<&'t i32> for &'b Integer
[src]

The resulting type after applying the << operator.

Performs the << operation.

impl ShlAssign<i32> for Integer
[src]

Performs the <<= operation.

impl<'t> ShlAssign<&'t i32> for Integer
[src]

Performs the <<= operation.

impl Shr<i32> for Integer
[src]

The resulting type after applying the >> operator.

Performs the >> operation.

impl<'t> Shr<&'t i32> for Integer
[src]

The resulting type after applying the >> operator.

Performs the >> operation.

impl<'b> Shr<i32> for &'b Integer
[src]

The resulting type after applying the >> operator.

Performs the >> operation.

impl<'t, 'b> Shr<&'t i32> for &'b Integer
[src]

The resulting type after applying the >> operator.

Performs the >> operation.

impl ShrAssign<i32> for Integer
[src]

Performs the >>= operation.

impl<'t> ShrAssign<&'t i32> for Integer
[src]

Performs the >>= operation.

impl BitAnd<i32> for Integer
[src]

The resulting type after applying the & operator.

Performs the & operation.

impl<'t> BitAnd<&'t i32> for Integer
[src]

The resulting type after applying the & operator.

Performs the & operation.

impl<'b> BitAnd<i32> for &'b Integer
[src]

The resulting type after applying the & operator.

Performs the & operation.

impl<'t, 'b> BitAnd<&'t i32> for &'b Integer
[src]

The resulting type after applying the & operator.

Performs the & operation.

impl BitAndAssign<i32> for Integer
[src]

Performs the &= operation.

impl<'t> BitAndAssign<&'t i32> for Integer
[src]

Performs the &= operation.

impl BitAnd<Integer> for i32
[src]

The resulting type after applying the & operator.

Performs the & operation.

impl<'b> BitAnd<&'b Integer> for i32
[src]

The resulting type after applying the & operator.

Performs the & operation.

impl<'t> BitAnd<Integer> for &'t i32
[src]

The resulting type after applying the & operator.

Performs the & operation.

impl<'b, 't> BitAnd<&'b Integer> for &'t i32
[src]

The resulting type after applying the & operator.

Performs the & operation.

impl BitAndFrom<i32> for Integer
[src]

Peforms the AND operation. Read more

impl<'t> BitAndFrom<&'t i32> for Integer
[src]

Peforms the AND operation. Read more

impl BitOr<i32> for Integer
[src]

The resulting type after applying the | operator.

Performs the | operation.

impl<'t> BitOr<&'t i32> for Integer
[src]

The resulting type after applying the | operator.

Performs the | operation.

impl<'b> BitOr<i32> for &'b Integer
[src]

The resulting type after applying the | operator.

Performs the | operation.

impl<'t, 'b> BitOr<&'t i32> for &'b Integer
[src]

The resulting type after applying the | operator.

Performs the | operation.

impl BitOrAssign<i32> for Integer
[src]

Performs the |= operation.

impl<'t> BitOrAssign<&'t i32> for Integer
[src]

Performs the |= operation.

impl BitOr<Integer> for i32
[src]

The resulting type after applying the | operator.

Performs the | operation.

impl<'b> BitOr<&'b Integer> for i32
[src]

The resulting type after applying the | operator.

Performs the | operation.

impl<'t> BitOr<Integer> for &'t i32
[src]

The resulting type after applying the | operator.

Performs the | operation.

impl<'b, 't> BitOr<&'b Integer> for &'t i32
[src]

The resulting type after applying the | operator.

Performs the | operation.

impl BitOrFrom<i32> for Integer
[src]

Peforms the OR operation. Read more

impl<'t> BitOrFrom<&'t i32> for Integer
[src]

Peforms the OR operation. Read more

impl BitXor<i32> for Integer
[src]

The resulting type after applying the ^ operator.

Performs the ^ operation.

impl<'t> BitXor<&'t i32> for Integer
[src]

The resulting type after applying the ^ operator.

Performs the ^ operation.

impl<'b> BitXor<i32> for &'b Integer
[src]

The resulting type after applying the ^ operator.

Performs the ^ operation.

impl<'t, 'b> BitXor<&'t i32> for &'b Integer
[src]

The resulting type after applying the ^ operator.

Performs the ^ operation.

impl BitXorAssign<i32> for Integer
[src]

Performs the ^= operation.

impl<'t> BitXorAssign<&'t i32> for Integer
[src]

Performs the ^= operation.

impl BitXor<Integer> for i32
[src]

The resulting type after applying the ^ operator.

Performs the ^ operation.

impl<'b> BitXor<&'b Integer> for i32
[src]

The resulting type after applying the ^ operator.

Performs the ^ operation.

impl<'t> BitXor<Integer> for &'t i32
[src]

The resulting type after applying the ^ operator.

Performs the ^ operation.

impl<'b, 't> BitXor<&'b Integer> for &'t i32
[src]

The resulting type after applying the ^ operator.

Performs the ^ operation.

impl BitXorFrom<i32> for Integer
[src]

Peforms the XOR operation. Read more

impl<'t> BitXorFrom<&'t i32> for Integer
[src]

Peforms the XOR operation. Read more

impl Add<u32> for Integer
[src]

The resulting type after applying the + operator.

Performs the + operation.

impl<'t> Add<&'t u32> for Integer
[src]

The resulting type after applying the + operator.

Performs the + operation.

impl<'b> Add<u32> for &'b Integer
[src]

The resulting type after applying the + operator.

Performs the + operation.

impl<'t, 'b> Add<&'t u32> for &'b Integer
[src]

The resulting type after applying the + operator.

Performs the + operation.

impl AddAssign<u32> for Integer
[src]

Performs the += operation.

impl<'t> AddAssign<&'t u32> for Integer
[src]

Performs the += operation.

impl Add<Integer> for u32
[src]

The resulting type after applying the + operator.

Performs the + operation.

impl<'b> Add<&'b Integer> for u32
[src]

The resulting type after applying the + operator.

Performs the + operation.

impl<'t> Add<Integer> for &'t u32
[src]

The resulting type after applying the + operator.

Performs the + operation.

impl<'b, 't> Add<&'b Integer> for &'t u32
[src]

The resulting type after applying the + operator.

Performs the + operation.

impl AddFrom<u32> for Integer
[src]

Peforms the addition. Read more

impl<'t> AddFrom<&'t u32> for Integer
[src]

Peforms the addition. Read more

impl Sub<u32> for Integer
[src]

The resulting type after applying the - operator.

Performs the - operation.

impl<'t> Sub<&'t u32> for Integer
[src]

The resulting type after applying the - operator.

Performs the - operation.

impl<'b> Sub<u32> for &'b Integer
[src]

The resulting type after applying the - operator.

Performs the - operation.

impl<'t, 'b> Sub<&'t u32> for &'b Integer
[src]

The resulting type after applying the - operator.

Performs the - operation.

impl SubAssign<u32> for Integer
[src]

Performs the -= operation.

impl<'t> SubAssign<&'t u32> for Integer
[src]

Performs the -= operation.

impl Sub<Integer> for u32
[src]

The resulting type after applying the - operator.

Performs the - operation.

impl<'b> Sub<&'b Integer> for u32
[src]

The resulting type after applying the - operator.

Performs the - operation.

impl<'t> Sub<Integer> for &'t u32
[src]

The resulting type after applying the - operator.

Performs the - operation.

impl<'b, 't> Sub<&'b Integer> for &'t u32
[src]

The resulting type after applying the - operator.

Performs the - operation.

impl SubFrom<u32> for Integer
[src]

Peforms the subtraction. Read more

impl<'t> SubFrom<&'t u32> for Integer
[src]

Peforms the subtraction. Read more

impl Mul<u32> for Integer
[src]

The resulting type after applying the * operator.

Performs the * operation.

impl<'t> Mul<&'t u32> for Integer
[src]

The resulting type after applying the * operator.

Performs the * operation.

impl<'b> Mul<u32> for &'b Integer
[src]

The resulting type after applying the * operator.

Performs the * operation.

impl<'t, 'b> Mul<&'t u32> for &'b Integer
[src]

The resulting type after applying the * operator.

Performs the * operation.

impl MulAssign<u32> for Integer
[src]

Performs the *= operation.

impl<'t> MulAssign<&'t u32> for Integer
[src]

Performs the *= operation.

impl Mul<Integer> for u32
[src]

The resulting type after applying the * operator.

Performs the * operation.

impl<'b> Mul<&'b Integer> for u32
[src]

The resulting type after applying the * operator.

Performs the * operation.

impl<'t> Mul<Integer> for &'t u32
[src]

The resulting type after applying the * operator.

Performs the * operation.

impl<'b, 't> Mul<&'b Integer> for &'t u32
[src]

The resulting type after applying the * operator.

Performs the * operation.

impl MulFrom<u32> for Integer
[src]

Peforms the multiplication. Read more

impl<'t> MulFrom<&'t u32> for Integer
[src]

Peforms the multiplication. Read more

impl Div<u32> for Integer
[src]

The resulting type after applying the / operator.

Performs the / operation.

impl<'t> Div<&'t u32> for Integer
[src]

The resulting type after applying the / operator.

Performs the / operation.

impl<'b> Div<u32> for &'b Integer
[src]

The resulting type after applying the / operator.

Performs the / operation.

impl<'t, 'b> Div<&'t u32> for &'b Integer
[src]

The resulting type after applying the / operator.

Performs the / operation.

impl DivAssign<u32> for Integer
[src]

Performs the /= operation.

impl<'t> DivAssign<&'t u32> for Integer
[src]

Performs the /= operation.

impl Div<Integer> for u32
[src]

The resulting type after applying the / operator.

Performs the / operation.

impl<'b> Div<&'b Integer> for u32
[src]

The resulting type after applying the / operator.

Performs the / operation.

impl<'t> Div<Integer> for &'t u32
[src]

The resulting type after applying the / operator.

Performs the / operation.

impl<'b, 't> Div<&'b Integer> for &'t u32
[src]

The resulting type after applying the / operator.

Performs the / operation.

impl DivFrom<u32> for Integer
[src]

Peforms the division. Read more

impl<'t> DivFrom<&'t u32> for Integer
[src]

Peforms the division. Read more

impl Rem<u32> for Integer
[src]

The resulting type after applying the % operator.

Performs the % operation.

impl<'t> Rem<&'t u32> for Integer
[src]

The resulting type after applying the % operator.

Performs the % operation.

impl<'b> Rem<u32> for &'b Integer
[src]

The resulting type after applying the % operator.

Performs the % operation.

impl<'t, 'b> Rem<&'t u32> for &'b Integer
[src]

The resulting type after applying the % operator.

Performs the % operation.

impl RemAssign<u32> for Integer
[src]

Performs the %= operation.

impl<'t> RemAssign<&'t u32> for Integer
[src]

Performs the %= operation.

impl Rem<Integer> for u32
[src]

The resulting type after applying the % operator.

Performs the % operation.

impl<'b> Rem<&'b Integer> for u32
[src]

The resulting type after applying the % operator.

Performs the % operation.

impl<'t> Rem<Integer> for &'t u32
[src]

The resulting type after applying the % operator.

Performs the % operation.

impl<'b, 't> Rem<&'b Integer> for &'t u32
[src]

The resulting type after applying the % operator.

Performs the % operation.

impl RemFrom<u32> for Integer
[src]

Peforms the remainder operation. Read more

impl<'t> RemFrom<&'t u32> for Integer
[src]

Peforms the remainder operation. Read more

impl Shl<u32> for Integer
[src]

The resulting type after applying the << operator.

Performs the << operation.

impl<'t> Shl<&'t u32> for Integer
[src]

The resulting type after applying the << operator.

Performs the << operation.

impl<'b> Shl<u32> for &'b Integer
[src]

The resulting type after applying the << operator.

Performs the << operation.

impl<'t, 'b> Shl<&'t u32> for &'b Integer
[src]

The resulting type after applying the << operator.

Performs the << operation.

impl ShlAssign<u32> for Integer
[src]

Performs the <<= operation.

impl<'t> ShlAssign<&'t u32> for Integer
[src]

Performs the <<= operation.

impl Shr<u32> for Integer
[src]

The resulting type after applying the >> operator.

Performs the >> operation.

impl<'t> Shr<&'t u32> for Integer
[src]

The resulting type after applying the >> operator.

Performs the >> operation.

impl<'b> Shr<u32> for &'b Integer
[src]

The resulting type after applying the >> operator.

Performs the >> operation.

impl<'t, 'b> Shr<&'t u32> for &'b Integer
[src]

The resulting type after applying the >> operator.

Performs the >> operation.

impl ShrAssign<u32> for Integer
[src]

Performs the >>= operation.

impl<'t> ShrAssign<&'t u32> for Integer
[src]

Performs the >>= operation.

impl Pow<u32> for Integer
[src]

The resulting type after the power operation.

Performs the power operation. Read more

impl<'t> Pow<&'t u32> for Integer
[src]

The resulting type after the power operation.

Performs the power operation. Read more

impl<'b> Pow<u32> for &'b Integer
[src]

The resulting type after the power operation.

Performs the power operation. Read more

impl<'t, 'b> Pow<&'t u32> for &'b Integer
[src]

The resulting type after the power operation.

Performs the power operation. Read more

impl PowAssign<u32> for Integer
[src]

Peforms the power operation. Read more

impl<'t> PowAssign<&'t u32> for Integer
[src]

Peforms the power operation. Read more

impl BitAnd<u32> for Integer
[src]

The resulting type after applying the & operator.

Performs the & operation.

impl<'t> BitAnd<&'t u32> for Integer
[src]

The resulting type after applying the & operator.

Performs the & operation.

impl<'b> BitAnd<u32> for &'b Integer
[src]

The resulting type after applying the & operator.

Performs the & operation.

impl<'t, 'b> BitAnd<&'t u32> for &'b Integer
[src]

The resulting type after applying the & operator.

Performs the & operation.

impl BitAndAssign<u32> for Integer
[src]

Performs the &= operation.

impl<'t> BitAndAssign<&'t u32> for Integer
[src]

Performs the &= operation.

impl BitAnd<Integer> for u32
[src]

The resulting type after applying the & operator.

Performs the & operation.

impl<'b> BitAnd<&'b Integer> for u32
[src]

The resulting type after applying the & operator.

Performs the & operation.

impl<'t> BitAnd<Integer> for &'t u32
[src]

The resulting type after applying the & operator.

Performs the & operation.

impl<'b, 't> BitAnd<&'b Integer> for &'t u32
[src]

The resulting type after applying the & operator.

Performs the & operation.

impl BitAndFrom<u32> for Integer
[src]

Peforms the AND operation. Read more

impl<'t> BitAndFrom<&'t u32> for Integer
[src]

Peforms the AND operation. Read more

impl BitOr<u32> for Integer
[src]

The resulting type after applying the | operator.

Performs the | operation.

impl<'t> BitOr<&'t u32> for Integer
[src]

The resulting type after applying the | operator.

Performs the | operation.

impl<'b> BitOr<u32> for &'b Integer
[src]

The resulting type after applying the | operator.

Performs the | operation.

impl<'t, 'b> BitOr<&'t u32> for &'b Integer
[src]

The resulting type after applying the | operator.

Performs the | operation.

impl BitOrAssign<u32> for Integer
[src]

Performs the |= operation.

impl<'t> BitOrAssign<&'t u32> for Integer
[src]

Performs the |= operation.

impl BitOr<Integer> for u32
[src]

The resulting type after applying the | operator.

Performs the | operation.

impl<'b> BitOr<&'b Integer> for u32
[src]

The resulting type after applying the | operator.

Performs the | operation.

impl<'t> BitOr<Integer> for &'t u32
[src]

The resulting type after applying the | operator.

Performs the | operation.

impl<'b, 't> BitOr<&'b Integer> for &'t u32
[src]

The resulting type after applying the | operator.

Performs the | operation.

impl BitOrFrom<u32> for Integer
[src]

Peforms the OR operation. Read more

impl<'t> BitOrFrom<&'t u32> for Integer
[src]

Peforms the OR operation. Read more

impl BitXor<u32> for Integer
[src]

The resulting type after applying the ^ operator.

Performs the ^ operation.

impl<'t> BitXor<&'t u32> for Integer
[src]

The resulting type after applying the ^ operator.

Performs the ^ operation.

impl<'b> BitXor<u32> for &'b Integer
[src]

The resulting type after applying the ^ operator.

Performs the ^ operation.

impl<'t, 'b> BitXor<&'t u32> for &'b Integer
[src]

The resulting type after applying the ^ operator.

Performs the ^ operation.

impl BitXorAssign<u32> for Integer
[src]

Performs the ^= operation.

impl<'t> BitXorAssign<&'t u32> for Integer
[src]

Performs the ^= operation.

impl BitXor<Integer> for u32
[src]

The resulting type after applying the ^ operator.

Performs the ^ operation.

impl<'b> BitXor<&'b Integer> for u32
[src]

The resulting type after applying the ^ operator.

Performs the ^ operation.

impl<'t> BitXor<Integer> for &'t u32
[src]

The resulting type after applying the ^ operator.

Performs the ^ operation.

impl<'b, 't> BitXor<&'b Integer> for &'t u32
[src]

The resulting type after applying the ^ operator.

Performs the ^ operation.

impl BitXorFrom<u32> for Integer
[src]

Peforms the XOR operation. Read more

impl<'t> BitXorFrom<&'t u32> for Integer
[src]

Peforms the XOR operation. Read more

impl<T> Sum<T> for Integer where
    Integer: AddAssign<T>, 
[src]

Method which takes an iterator and generates Self from the elements by "summing up" the items. Read more

impl<T> Product<T> for Integer where
    Integer: MulAssign<T>, 
[src]

Method which takes an iterator and generates Self from the elements by multiplying the items. Read more

impl Eq for Integer
[src]

impl Ord for Integer
[src]

This method returns an Ordering between self and other. Read more

Compares and returns the maximum of two values. Read more

Compares and returns the minimum of two values. Read more

impl PartialEq for Integer
[src]

This method tests for self and other values to be equal, and is used by ==. Read more

This method tests for !=.

impl PartialOrd for Integer
[src]

This method returns an ordering between self and other values if one exists. Read more

This method tests less than (for self and other) and is used by the < operator. Read more

This method tests less than or equal to (for self and other) and is used by the <= operator. Read more

This method tests greater than (for self and other) and is used by the > operator. Read more

This method tests greater than or equal to (for self and other) and is used by the >= operator. Read more

impl PartialEq<i8> for Integer
[src]

This method tests for self and other values to be equal, and is used by ==. Read more

This method tests for !=.

impl PartialEq<Integer> for i8
[src]

This method tests for self and other values to be equal, and is used by ==. Read more

This method tests for !=.

impl PartialOrd<i8> for Integer
[src]

This method returns an ordering between self and other values if one exists. Read more

This method tests less than (for self and other) and is used by the < operator. Read more

This method tests less than or equal to (for self and other) and is used by the <= operator. Read more

This method tests greater than (for self and other) and is used by the > operator. Read more

This method tests greater than or equal to (for self and other) and is used by the >= operator. Read more

impl PartialOrd<Integer> for i8
[src]

This method returns an ordering between self and other values if one exists. Read more

This method tests less than (for self and other) and is used by the < operator. Read more

This method tests less than or equal to (for self and other) and is used by the <= operator. Read more

This method tests greater than (for self and other) and is used by the > operator. Read more

This method tests greater than or equal to (for self and other) and is used by the >= operator. Read more

impl PartialEq<i16> for Integer
[src]

This method tests for self and other values to be equal, and is used by ==. Read more

This method tests for !=.

impl PartialEq<Integer> for i16
[src]

This method tests for self and other values to be equal, and is used by ==. Read more

This method tests for !=.

impl PartialOrd<i16> for Integer
[src]

This method returns an ordering between self and other values if one exists. Read more

This method tests less than (for self and other) and is used by the < operator. Read more

This method tests less than or equal to (for self and other) and is used by the <= operator. Read more

This method tests greater than (for self and other) and is used by the > operator. Read more

This method tests greater than or equal to (for self and other) and is used by the >= operator. Read more

impl PartialOrd<Integer> for i16
[src]

This method returns an ordering between self and other values if one exists. Read more

This method tests less than (for self and other) and is used by the < operator. Read more

This method tests less than or equal to (for self and other) and is used by the <= operator. Read more

This method tests greater than (for self and other) and is used by the > operator. Read more

This method tests greater than or equal to (for self and other) and is used by the >= operator. Read more

impl PartialEq<i32> for Integer
[src]

This method tests for self and other values to be equal, and is used by ==. Read more

This method tests for !=.

impl PartialEq<Integer> for i32
[src]

This method tests for self and other values to be equal, and is used by ==. Read more

This method tests for !=.

impl PartialOrd<i32> for Integer
[src]

This method returns an ordering between self and other values if one exists. Read more

This method tests less than (for self and other) and is used by the < operator. Read more

This method tests less than or equal to (for self and other) and is used by the <= operator. Read more

This method tests greater than (for self and other) and is used by the > operator. Read more

This method tests greater than or equal to (for self and other) and is used by the >= operator. Read more

impl PartialOrd<Integer> for i32
[src]

This method returns an ordering between self and other values if one exists. Read more

This method tests less than (for self and other) and is used by the < operator. Read more

This method tests less than or equal to (for self and other) and is used by the <= operator. Read more

This method tests greater than (for self and other) and is used by the > operator. Read more

This method tests greater than or equal to (for self and other) and is used by the >= operator. Read more

impl PartialEq<i64> for Integer
[src]

This method tests for self and other values to be equal, and is used by ==. Read more

This method tests for !=.

impl PartialEq<Integer> for i64
[src]

This method tests for self and other values to be equal, and is used by ==. Read more

This method tests for !=.

impl PartialOrd<i64> for Integer
[src]

This method returns an ordering between self and other values if one exists. Read more

This method tests less than (for self and other) and is used by the < operator. Read more

This method tests less than or equal to (for self and other) and is used by the <= operator. Read more

This method tests greater than (for self and other) and is used by the > operator. Read more

This method tests greater than or equal to (for self and other) and is used by the >= operator. Read more

impl PartialOrd<Integer> for i64
[src]

This method returns an ordering between self and other values if one exists. Read more

This method tests less than (for self and other) and is used by the < operator. Read more

This method tests less than or equal to (for self and other) and is used by the <= operator. Read more

This method tests greater than (for self and other) and is used by the > operator. Read more

This method tests greater than or equal to (for self and other) and is used by the >= operator. Read more

impl PartialEq<i128> for Integer
[src]

This method tests for self and other values to be equal, and is used by ==. Read more

This method tests for !=.

impl PartialEq<Integer> for i128
[src]

This method tests for self and other values to be equal, and is used by ==. Read more

This method tests for !=.

impl PartialOrd<i128> for Integer
[src]

This method returns an ordering between self and other values if one exists. Read more

This method tests less than (for self and other) and is used by the < operator. Read more

This method tests less than or equal to (for self and other) and is used by the <= operator. Read more

This method tests greater than (for self and other) and is used by the > operator. Read more

This method tests greater than or equal to (for self and other) and is used by the >= operator. Read more

impl PartialOrd<Integer> for i128
[src]

This method returns an ordering between self and other values if one exists. Read more

This method tests less than (for self and other) and is used by the < operator. Read more

This method tests less than or equal to (for self and other) and is used by the <= operator. Read more

This method tests greater than (for self and other) and is used by the > operator. Read more

This method tests greater than or equal to (for self and other) and is used by the >= operator. Read more

impl PartialEq<isize> for Integer
[src]

This method tests for self and other values to be equal, and is used by ==. Read more

This method tests for !=.

impl PartialEq<Integer> for isize
[src]

This method tests for self and other values to be equal, and is used by ==. Read more

This method tests for !=.

impl PartialOrd<isize> for Integer
[src]

This method returns an ordering between self and other values if one exists. Read more

This method tests less than (for self and other) and is used by the < operator. Read more

This method tests less than or equal to (for self and other) and is used by the <= operator. Read more

This method tests greater than (for self and other) and is used by the > operator. Read more

This method tests greater than or equal to (for self and other) and is used by the >= operator. Read more

impl PartialOrd<Integer> for isize
[src]

This method returns an ordering between self and other values if one exists. Read more

This method tests less than (for self and other) and is used by the < operator. Read more

This method tests less than or equal to (for self and other) and is used by the <= operator. Read more

This method tests greater than (for self and other) and is used by the > operator. Read more

This method tests greater than or equal to (for self and other) and is used by the >= operator. Read more

impl PartialEq<u8> for Integer
[src]

This method tests for self and other values to be equal, and is used by ==. Read more

This method tests for !=.

impl PartialEq<Integer> for u8
[src]

This method tests for self and other values to be equal, and is used by ==. Read more

This method tests for !=.

impl PartialOrd<u8> for Integer
[src]

This method returns an ordering between self and other values if one exists. Read more

This method tests less than (for self and other) and is used by the < operator. Read more

This method tests less than or equal to (for self and other) and is used by the <= operator. Read more

This method tests greater than (for self and other) and is used by the > operator. Read more

This method tests greater than or equal to (for self and other) and is used by the >= operator. Read more

impl PartialOrd<Integer> for u8
[src]

This method returns an ordering between self and other values if one exists. Read more

This method tests less than (for self and other) and is used by the < operator. Read more

This method tests less than or equal to (for self and other) and is used by the <= operator. Read more

This method tests greater than (for self and other) and is used by the > operator. Read more

This method tests greater than or equal to (for self and other) and is used by the >= operator. Read more

impl PartialEq<u16> for Integer
[src]

This method tests for self and other values to be equal, and is used by ==. Read more

This method tests for !=.

impl PartialEq<Integer> for u16
[src]

This method tests for self and other values to be equal, and is used by ==. Read more

This method tests for !=.

impl PartialOrd<u16> for Integer
[src]

This method returns an ordering between self and other values if one exists. Read more

This method tests less than (for self and other) and is used by the < operator. Read more

This method tests less than or equal to (for self and other) and is used by the <= operator. Read more

This method tests greater than (for self and other) and is used by the > operator. Read more

This method tests greater than or equal to (for self and other) and is used by the >= operator. Read more

impl PartialOrd<Integer> for u16
[src]

This method returns an ordering between self and other values if one exists. Read more

This method tests less than (for self and other) and is used by the < operator. Read more

This method tests less than or equal to (for self and other) and is used by the <= operator. Read more

This method tests greater than (for self and other) and is used by the > operator. Read more

This method tests greater than or equal to (for self and other) and is used by the >= operator. Read more

impl PartialEq<u32> for Integer
[src]

This method tests for self and other values to be equal, and is used by ==. Read more

This method tests for !=.

impl PartialEq<Integer> for u32
[src]

This method tests for self and other values to be equal, and is used by ==. Read more

This method tests for !=.

impl PartialOrd<u32> for Integer
[src]

This method returns an ordering between self and other values if one exists. Read more

This method tests less than (for self and other) and is used by the < operator. Read more

This method tests less than or equal to (for self and other) and is used by the <= operator. Read more

This method tests greater than (for self and other) and is used by the > operator. Read more

This method tests greater than or equal to (for self and other) and is used by the >= operator. Read more

impl PartialOrd<Integer> for u32
[src]

This method returns an ordering between self and other values if one exists. Read more

This method tests less than (for self and other) and is used by the < operator. Read more

This method tests less than or equal to (for self and other) and is used by the <= operator. Read more

This method tests greater than (for self and other) and is used by the > operator. Read more

This method tests greater than or equal to (for self and other) and is used by the >= operator. Read more

impl PartialEq<u64> for Integer
[src]

This method tests for self and other values to be equal, and is used by ==. Read more

This method tests for !=.

impl PartialEq<Integer> for u64
[src]

This method tests for self and other values to be equal, and is used by ==. Read more

This method tests for !=.

impl PartialOrd<u64> for Integer
[src]

This method returns an ordering between self and other values if one exists. Read more

This method tests less than (for self and other) and is used by the < operator. Read more

This method tests less than or equal to (for self and other) and is used by the <= operator. Read more

This method tests greater than (for self and other) and is used by the > operator. Read more

This method tests greater than or equal to (for self and other) and is used by the >= operator. Read more

impl PartialOrd<Integer> for u64
[src]

This method returns an ordering between self and other values if one exists. Read more

This method tests less than (for self and other) and is used by the < operator. Read more

This method tests less than or equal to (for self and other) and is used by the <= operator. Read more

This method tests greater than (for self and other) and is used by the > operator. Read more

This method tests greater than or equal to (for self and other) and is used by the >= operator. Read more

impl PartialEq<u128> for Integer
[src]

This method tests for self and other values to be equal, and is used by ==. Read more

This method tests for !=.

impl PartialEq<Integer> for u128
[src]

This method tests for self and other values to be equal, and is used by ==. Read more

This method tests for !=.

impl PartialOrd<u128> for Integer
[src]

This method returns an ordering between self and other values if one exists. Read more

This method tests less than (for self and other) and is used by the < operator. Read more

This method tests less than or equal to (for self and other) and is used by the <= operator. Read more

This method tests greater than (for self and other) and is used by the > operator. Read more

This method tests greater than or equal to (for self and other) and is used by the >= operator. Read more

impl PartialOrd<Integer> for u128
[src]

This method returns an ordering between self and other values if one exists. Read more

This method tests less than (for self and other) and is used by the < operator. Read more

This method tests less than or equal to (for self and other) and is used by the <= operator. Read more

This method tests greater than (for self and other) and is used by the > operator. Read more

This method tests greater than or equal to (for self and other) and is used by the >= operator. Read more

impl PartialEq<usize> for Integer
[src]

This method tests for self and other values to be equal, and is used by ==. Read more

This method tests for !=.

impl PartialEq<Integer> for usize
[src]

This method tests for self and other values to be equal, and is used by ==. Read more

This method tests for !=.

impl PartialOrd<usize> for Integer
[src]

This method returns an ordering between self and other values if one exists. Read more

This method tests less than (for self and other) and is used by the < operator. Read more

This method tests less than or equal to (for self and other) and is used by the <= operator. Read more

This method tests greater than (for self and other) and is used by the > operator. Read more

This method tests greater than or equal to (for self and other) and is used by the >= operator. Read more

impl PartialOrd<Integer> for usize
[src]

This method returns an ordering between self and other values if one exists. Read more

This method tests less than (for self and other) and is used by the < operator. Read more

This method tests less than or equal to (for self and other) and is used by the <= operator. Read more

This method tests greater than (for self and other) and is used by the > operator. Read more

This method tests greater than or equal to (for self and other) and is used by the >= operator. Read more

impl PartialEq<f32> for Integer
[src]

This method tests for self and other values to be equal, and is used by ==. Read more

This method tests for !=.

impl PartialEq<Integer> for f32
[src]

This method tests for self and other values to be equal, and is used by ==. Read more

This method tests for !=.

impl PartialOrd<f32> for Integer
[src]

This method returns an ordering between self and other values if one exists. Read more

This method tests less than (for self and other) and is used by the < operator. Read more

This method tests less than or equal to (for self and other) and is used by the <= operator. Read more

This method tests greater than (for self and other) and is used by the > operator. Read more

This method tests greater than or equal to (for self and other) and is used by the >= operator. Read more

impl PartialOrd<Integer> for f32
[src]

This method returns an ordering between self and other values if one exists. Read more

This method tests less than (for self and other) and is used by the < operator. Read more

This method tests less than or equal to (for self and other) and is used by the <= operator. Read more

This method tests greater than (for self and other) and is used by the > operator. Read more

This method tests greater than or equal to (for self and other) and is used by the >= operator. Read more

impl PartialEq<f64> for Integer
[src]

This method tests for self and other values to be equal, and is used by ==. Read more

This method tests for !=.

impl PartialEq<Integer> for f64
[src]

This method tests for self and other values to be equal, and is used by ==. Read more

This method tests for !=.

impl PartialOrd<f64> for Integer
[src]

This method returns an ordering between self and other values if one exists. Read more

This method tests less than (for self and other) and is used by the < operator. Read more

This method tests less than or equal to (for self and other) and is used by the <= operator. Read more

This method tests greater than (for self and other) and is used by the > operator. Read more

This method tests greater than or equal to (for self and other) and is used by the >= operator. Read more

impl PartialOrd<Integer> for f64
[src]

This method returns an ordering between self and other values if one exists. Read more

This method tests less than (for self and other) and is used by the < operator. Read more

This method tests less than or equal to (for self and other) and is used by the <= operator. Read more

This method tests greater than (for self and other) and is used by the > operator. Read more

This method tests greater than or equal to (for self and other) and is used by the >= operator. Read more

impl DivRounding for Integer
[src]

The resulting type from the division operation.

Performs division, rounding the quotient towards zero.

Performs division, rounding the quotient up.

Performs division, rounding the quotient down.

Performs Euclidean division, rounding the quotient so that the remainder cannot be negative. Read more

impl<'i> DivRounding<&'i Integer> for Integer
[src]

The resulting type from the division operation.

Performs division, rounding the quotient towards zero.

Performs division, rounding the quotient up.

Performs division, rounding the quotient down.

Performs Euclidean division, rounding the quotient so that the remainder cannot be negative. Read more

impl<'i> DivRounding<Integer> for &'i Integer
[src]

The resulting type from the division operation.

Performs division, rounding the quotient towards zero.

Performs division, rounding the quotient up.

Performs division, rounding the quotient down.

Performs Euclidean division, rounding the quotient so that the remainder cannot be negative. Read more

impl<'i> DivRounding for &'i Integer
[src]

The resulting type from the division operation.

Performs division, rounding the quotient towards zero.

Performs division, rounding the quotient up.

Performs division, rounding the quotient down.

Performs Euclidean division, rounding the quotient so that the remainder cannot be negative. Read more

impl DivRoundingAssign for Integer
[src]

Performs division, rounding the quotient towards zero.

Performs division, rounding the quotient up.

Performs division, rounding the quotient down.

Performs Euclidean division, rounding the quotient so that the remainder cannot be negative. Read more

impl<'i> DivRoundingAssign<&'i Integer> for Integer
[src]

Performs division, rounding the quotient towards zero.

Performs division, rounding the quotient up.

Performs division, rounding the quotient down.

Performs Euclidean division, rounding the quotient so that the remainder cannot be negative. Read more

impl DivRoundingFrom for Integer
[src]

Performs division, rounding the quotient towards zero.

Performs division, rounding the quotient up.

Performs division, rounding the quotient down.

Performs Euclidean division, rounding the quotient so that the remainder cannot be negative. Read more

impl<'i> DivRoundingFrom<&'i Integer> for Integer
[src]

Performs division, rounding the quotient towards zero.

Performs division, rounding the quotient up.

Performs division, rounding the quotient down.

Performs Euclidean division, rounding the quotient so that the remainder cannot be negative. Read more

impl RemRounding for Integer
[src]

The resulting type from the remainder operation.

Finds the remainder when the quotient is rounded towards zero.

Finds the remainder when the quotient is rounded up.

Finds the remainder when the quotient is rounded down.

Finds the positive remainder from Euclidean division.

impl<'i> RemRounding<&'i Integer> for Integer
[src]

The resulting type from the remainder operation.

Finds the remainder when the quotient is rounded towards zero.

Finds the remainder when the quotient is rounded up.

Finds the remainder when the quotient is rounded down.

Finds the positive remainder from Euclidean division.

impl<'i> RemRounding<Integer> for &'i Integer
[src]

The resulting type from the remainder operation.

Finds the remainder when the quotient is rounded towards zero.

Finds the remainder when the quotient is rounded up.

Finds the remainder when the quotient is rounded down.

Finds the positive remainder from Euclidean division.

impl<'i> RemRounding for &'i Integer
[src]

The resulting type from the remainder operation.

Finds the remainder when the quotient is rounded towards zero.

Finds the remainder when the quotient is rounded up.

Finds the remainder when the quotient is rounded down.

Finds the positive remainder from Euclidean division.

impl RemRoundingAssign for Integer
[src]

Finds the remainder when the quotient is rounded towards zero.

Finds the remainder when the quotient is rounded up.

Finds the remainder when the quotient is rounded down.

Finds the positive remainder from Euclidean division.

impl<'i> RemRoundingAssign<&'i Integer> for Integer
[src]

Finds the remainder when the quotient is rounded towards zero.

Finds the remainder when the quotient is rounded up.

Finds the remainder when the quotient is rounded down.

Finds the positive remainder from Euclidean division.

impl RemRoundingFrom for Integer
[src]

Finds the remainder when the quotient is rounded towards zero.

Finds the remainder when the quotient is rounded up.

Finds the remainder when the quotient is rounded down.

Finds the positive remainder from Euclidean division.

impl<'i> RemRoundingFrom<&'i Integer> for Integer
[src]

Finds the remainder when the quotient is rounded towards zero.

Finds the remainder when the quotient is rounded up.

Finds the remainder when the quotient is rounded down.

Finds the positive remainder from Euclidean division.

impl DivRounding<i32> for Integer
[src]

The resulting type from the division operation.

Performs division, rounding the quotient towards zero.

Performs division, rounding the quotient up.

Performs division, rounding the quotient down.

Performs Euclidean division, rounding the quotient so that the remainder cannot be negative. Read more

impl<'t> DivRounding<&'t i32> for Integer
[src]

The resulting type from the division operation.

Performs division, rounding the quotient towards zero.

Performs division, rounding the quotient up.

Performs division, rounding the quotient down.

Performs Euclidean division, rounding the quotient so that the remainder cannot be negative. Read more

impl<'i> DivRounding<i32> for &'i Integer
[src]

The resulting type from the division operation.

Performs division, rounding the quotient towards zero.

Performs division, rounding the quotient up.

Performs division, rounding the quotient down.

Performs Euclidean division, rounding the quotient so that the remainder cannot be negative. Read more

impl<'t, 'i> DivRounding<&'t i32> for &'i Integer
[src]

The resulting type from the division operation.

Performs division, rounding the quotient towards zero.

Performs division, rounding the quotient up.

Performs division, rounding the quotient down.

Performs Euclidean division, rounding the quotient so that the remainder cannot be negative. Read more

impl DivRoundingAssign<i32> for Integer
[src]

Performs division, rounding the quotient towards zero.

Performs division, rounding the quotient up.

Performs division, rounding the quotient down.

Performs Euclidean division, rounding the quotient so that the remainder cannot be negative. Read more

impl<'t> DivRoundingAssign<&'t i32> for Integer
[src]

Performs division, rounding the quotient towards zero.

Performs division, rounding the quotient up.

Performs division, rounding the quotient down.

Performs Euclidean division, rounding the quotient so that the remainder cannot be negative. Read more

impl DivRounding<Integer> for i32
[src]

The resulting type from the division operation.

Performs division, rounding the quotient towards zero.

Performs division, rounding the quotient up.

Performs division, rounding the quotient down.

Performs Euclidean division, rounding the quotient so that the remainder cannot be negative. Read more

impl<'i> DivRounding<&'i Integer> for i32
[src]

The resulting type from the division operation.

Performs division, rounding the quotient towards zero.

Performs division, rounding the quotient up.

Performs division, rounding the quotient down.

Performs Euclidean division, rounding the quotient so that the remainder cannot be negative. Read more

impl<'t> DivRounding<Integer> for &'t i32
[src]

The resulting type from the division operation.

Performs division, rounding the quotient towards zero.

Performs division, rounding the quotient up.

Performs division, rounding the quotient down.

Performs Euclidean division, rounding the quotient so that the remainder cannot be negative. Read more

impl<'i, 't> DivRounding<&'i Integer> for &'t i32
[src]

The resulting type from the division operation.

Performs division, rounding the quotient towards zero.

Performs division, rounding the quotient up.

Performs division, rounding the quotient down.

Performs Euclidean division, rounding the quotient so that the remainder cannot be negative. Read more

impl DivRoundingFrom<i32> for Integer
[src]

Performs division, rounding the quotient towards zero.

Performs division, rounding the quotient up.

Performs division, rounding the quotient down.

Performs Euclidean division, rounding the quotient so that the remainder cannot be negative. Read more

impl<'t> DivRoundingFrom<&'t i32> for Integer
[src]

Performs division, rounding the quotient towards zero.

Performs division, rounding the quotient up.

Performs division, rounding the quotient down.

Performs Euclidean division, rounding the quotient so that the remainder cannot be negative. Read more

impl RemRounding<i32> for Integer
[src]

The resulting type from the remainder operation.

Finds the remainder when the quotient is rounded towards zero.

Finds the remainder when the quotient is rounded up.

Finds the remainder when the quotient is rounded down.

Finds the positive remainder from Euclidean division.

impl<'t> RemRounding<&'t i32> for Integer
[src]

The resulting type from the remainder operation.

Finds the remainder when the quotient is rounded towards zero.

Finds the remainder when the quotient is rounded up.

Finds the remainder when the quotient is rounded down.

Finds the positive remainder from Euclidean division.

impl<'i> RemRounding<i32> for &'i Integer
[src]

The resulting type from the remainder operation.

Finds the remainder when the quotient is rounded towards zero.

Finds the remainder when the quotient is rounded up.

Finds the remainder when the quotient is rounded down.

Finds the positive remainder from Euclidean division.

impl<'t, 'i> RemRounding<&'t i32> for &'i Integer
[src]

The resulting type from the remainder operation.

Finds the remainder when the quotient is rounded towards zero.

Finds the remainder when the quotient is rounded up.

Finds the remainder when the quotient is rounded down.

Finds the positive remainder from Euclidean division.

impl RemRoundingAssign<i32> for Integer
[src]

Finds the remainder when the quotient is rounded towards zero.

Finds the remainder when the quotient is rounded up.

Finds the remainder when the quotient is rounded down.

Finds the positive remainder from Euclidean division.

impl<'t> RemRoundingAssign<&'t i32> for Integer
[src]

Finds the remainder when the quotient is rounded towards zero.

Finds the remainder when the quotient is rounded up.

Finds the remainder when the quotient is rounded down.

Finds the positive remainder from Euclidean division.

impl RemRounding<Integer> for i32
[src]

The resulting type from the remainder operation.

Finds the remainder when the quotient is rounded towards zero.

Finds the remainder when the quotient is rounded up.

Finds the remainder when the quotient is rounded down.

Finds the positive remainder from Euclidean division.

impl<'i> RemRounding<&'i Integer> for i32
[src]

The resulting type from the remainder operation.

Finds the remainder when the quotient is rounded towards zero.

Finds the remainder when the quotient is rounded up.

Finds the remainder when the quotient is rounded down.

Finds the positive remainder from Euclidean division.

impl<'t> RemRounding<Integer> for &'t i32
[src]

The resulting type from the remainder operation.

Finds the remainder when the quotient is rounded towards zero.

Finds the remainder when the quotient is rounded up.

Finds the remainder when the quotient is rounded down.

Finds the positive remainder from Euclidean division.

impl<'i, 't> RemRounding<&'i Integer> for &'t i32
[src]

The resulting type from the remainder operation.

Finds the remainder when the quotient is rounded towards zero.

Finds the remainder when the quotient is rounded up.

Finds the remainder when the quotient is rounded down.

Finds the positive remainder from Euclidean division.

impl RemRoundingFrom<i32> for Integer
[src]

Finds the remainder when the quotient is rounded towards zero.

Finds the remainder when the quotient is rounded up.

Finds the remainder when the quotient is rounded down.

Finds the positive remainder from Euclidean division.

impl<'t> RemRoundingFrom<&'t i32> for Integer
[src]

Finds the remainder when the quotient is rounded towards zero.

Finds the remainder when the quotient is rounded up.

Finds the remainder when the quotient is rounded down.

Finds the positive remainder from Euclidean division.

impl DivRounding<u32> for Integer
[src]

The resulting type from the division operation.

Performs division, rounding the quotient towards zero.

Performs division, rounding the quotient up.

Performs division, rounding the quotient down.

Performs Euclidean division, rounding the quotient so that the remainder cannot be negative. Read more

impl<'t> DivRounding<&'t u32> for Integer
[src]

The resulting type from the division operation.

Performs division, rounding the quotient towards zero.

Performs division, rounding the quotient up.

Performs division, rounding the quotient down.

Performs Euclidean division, rounding the quotient so that the remainder cannot be negative. Read more

impl<'i> DivRounding<u32> for &'i Integer
[src]

The resulting type from the division operation.

Performs division, rounding the quotient towards zero.

Performs division, rounding the quotient up.

Performs division, rounding the quotient down.

Performs Euclidean division, rounding the quotient so that the remainder cannot be negative. Read more

impl<'t, 'i> DivRounding<&'t u32> for &'i Integer
[src]

The resulting type from the division operation.

Performs division, rounding the quotient towards zero.

Performs division, rounding the quotient up.

Performs division, rounding the quotient down.

Performs Euclidean division, rounding the quotient so that the remainder cannot be negative. Read more

impl DivRoundingAssign<u32> for Integer
[src]

Performs division, rounding the quotient towards zero.

Performs division, rounding the quotient up.

Performs division, rounding the quotient down.

Performs Euclidean division, rounding the quotient so that the remainder cannot be negative. Read more

impl<'t> DivRoundingAssign<&'t u32> for Integer
[src]

Performs division, rounding the quotient towards zero.

Performs division, rounding the quotient up.

Performs division, rounding the quotient down.

Performs Euclidean division, rounding the quotient so that the remainder cannot be negative. Read more

impl DivRounding<Integer> for u32
[src]

The resulting type from the division operation.

Performs division, rounding the quotient towards zero.

Performs division, rounding the quotient up.

Performs division, rounding the quotient down.

Performs Euclidean division, rounding the quotient so that the remainder cannot be negative. Read more

impl<'i> DivRounding<&'i Integer> for u32
[src]

The resulting type from the division operation.

Performs division, rounding the quotient towards zero.

Performs division, rounding the quotient up.

Performs division, rounding the quotient down.

Performs Euclidean division, rounding the quotient so that the remainder cannot be negative. Read more

impl<'t> DivRounding<Integer> for &'t u32
[src]

The resulting type from the division operation.

Performs division, rounding the quotient towards zero.

Performs division, rounding the quotient up.

Performs division, rounding the quotient down.

Performs Euclidean division, rounding the quotient so that the remainder cannot be negative. Read more

impl<'i, 't> DivRounding<&'i Integer> for &'t u32
[src]

The resulting type from the division operation.

Performs division, rounding the quotient towards zero.

Performs division, rounding the quotient up.

Performs division, rounding the quotient down.

Performs Euclidean division, rounding the quotient so that the remainder cannot be negative. Read more

impl DivRoundingFrom<u32> for Integer
[src]

Performs division, rounding the quotient towards zero.

Performs division, rounding the quotient up.

Performs division, rounding the quotient down.

Performs Euclidean division, rounding the quotient so that the remainder cannot be negative. Read more

impl<'t> DivRoundingFrom<&'t u32> for Integer
[src]

Performs division, rounding the quotient towards zero.

Performs division, rounding the quotient up.

Performs division, rounding the quotient down.

Performs Euclidean division, rounding the quotient so that the remainder cannot be negative. Read more

impl RemRounding<u32> for Integer
[src]

The resulting type from the remainder operation.

Finds the remainder when the quotient is rounded towards zero.

Finds the remainder when the quotient is rounded up.

Finds the remainder when the quotient is rounded down.

Finds the positive remainder from Euclidean division.

impl<'t> RemRounding<&'t u32> for Integer
[src]

The resulting type from the remainder operation.

Finds the remainder when the quotient is rounded towards zero.

Finds the remainder when the quotient is rounded up.

Finds the remainder when the quotient is rounded down.

Finds the positive remainder from Euclidean division.

impl<'i> RemRounding<u32> for &'i Integer
[src]

The resulting type from the remainder operation.

Finds the remainder when the quotient is rounded towards zero.

Finds the remainder when the quotient is rounded up.

Finds the remainder when the quotient is rounded down.

Finds the positive remainder from Euclidean division.

impl<'t, 'i> RemRounding<&'t u32> for &'i Integer
[src]

The resulting type from the remainder operation.

Finds the remainder when the quotient is rounded towards zero.

Finds the remainder when the quotient is rounded up.

Finds the remainder when the quotient is rounded down.

Finds the positive remainder from Euclidean division.

impl RemRoundingAssign<u32> for Integer
[src]

Finds the remainder when the quotient is rounded towards zero.

Finds the remainder when the quotient is rounded up.

Finds the remainder when the quotient is rounded down.

Finds the positive remainder from Euclidean division.

impl<'t> RemRoundingAssign<&'t u32> for Integer
[src]

Finds the remainder when the quotient is rounded towards zero.

Finds the remainder when the quotient is rounded up.

Finds the remainder when the quotient is rounded down.

Finds the positive remainder from Euclidean division.

impl RemRounding<Integer> for u32
[src]

The resulting type from the remainder operation.

Finds the remainder when the quotient is rounded towards zero.

Finds the remainder when the quotient is rounded up.

Finds the remainder when the quotient is rounded down.

Finds the positive remainder from Euclidean division.

impl<'i> RemRounding<&'i Integer> for u32
[src]

The resulting type from the remainder operation.

Finds the remainder when the quotient is rounded towards zero.

Finds the remainder when the quotient is rounded up.

Finds the remainder when the quotient is rounded down.

Finds the positive remainder from Euclidean division.

impl<'t> RemRounding<Integer> for &'t u32
[src]

The resulting type from the remainder operation.

Finds the remainder when the quotient is rounded towards zero.

Finds the remainder when the quotient is rounded up.

Finds the remainder when the quotient is rounded down.

Finds the positive remainder from Euclidean division.

impl<'i, 't> RemRounding<&'i Integer> for &'t u32
[src]

The resulting type from the remainder operation.

Finds the remainder when the quotient is rounded towards zero.

Finds the remainder when the quotient is rounded up.

Finds the remainder when the quotient is rounded down.

Finds the positive remainder from Euclidean division.

impl RemRoundingFrom<u32> for Integer
[src]

Finds the remainder when the quotient is rounded towards zero.

Finds the remainder when the quotient is rounded up.

Finds the remainder when the quotient is rounded down.

Finds the positive remainder from Euclidean division.

impl<'t> RemRoundingFrom<&'t u32> for Integer
[src]

Finds the remainder when the quotient is rounded towards zero.

Finds the remainder when the quotient is rounded up.

Finds the remainder when the quotient is rounded down.

Finds the positive remainder from Euclidean division.

impl Serialize for Integer
[src]

Serialize this value into the given Serde serializer. Read more

impl<'de> Deserialize<'de> for Integer
[src]

Deserialize this value from the given Serde deserializer. Read more

impl Default for Integer
[src]

Returns the "default value" for a type. Read more

impl Clone for Integer
[src]

Returns a copy of the value. Read more

Performs copy-assignment from source. Read more

impl Drop for Integer
[src]

Executes the destructor for this type. Read more

impl Hash for Integer
[src]

Feeds this value into the given [Hasher]. Read more

Feeds a slice of this type into the given [Hasher]. Read more

impl Assign for Integer
[src]

Peforms the assignement. Read more

impl<'a> Assign<&'a Integer> for Integer
[src]

Peforms the assignement. Read more

impl<'a> From<&'a Integer> for Integer
[src]

Performs the conversion.

impl TryFrom<Integer> for i8
[src]

🔬 This is a nightly-only experimental API. (try_from)

The type returned in the event of a conversion error.

🔬 This is a nightly-only experimental API. (try_from)

Performs the conversion.

impl<'a> TryFrom<&'a Integer> for i8
[src]

🔬 This is a nightly-only experimental API. (try_from)

The type returned in the event of a conversion error.

🔬 This is a nightly-only experimental API. (try_from)

Performs the conversion.

impl TryFrom<Integer> for i16
[src]

🔬 This is a nightly-only experimental API. (try_from)

The type returned in the event of a conversion error.

🔬 This is a nightly-only experimental API. (try_from)

Performs the conversion.

impl<'a> TryFrom<&'a Integer> for i16
[src]

🔬 This is a nightly-only experimental API. (try_from)

The type returned in the event of a conversion error.

🔬 This is a nightly-only experimental API. (try_from)

Performs the conversion.

impl TryFrom<Integer> for i32
[src]

🔬 This is a nightly-only experimental API. (try_from)

The type returned in the event of a conversion error.

🔬 This is a nightly-only experimental API. (try_from)

Performs the conversion.

impl<'a> TryFrom<&'a Integer> for i32
[src]

🔬 This is a nightly-only experimental API. (try_from)

The type returned in the event of a conversion error.

🔬 This is a nightly-only experimental API. (try_from)

Performs the conversion.

impl TryFrom<Integer> for i64
[src]

🔬 This is a nightly-only experimental API. (try_from)

The type returned in the event of a conversion error.

🔬 This is a nightly-only experimental API. (try_from)

Performs the conversion.

impl<'a> TryFrom<&'a Integer> for i64
[src]

🔬 This is a nightly-only experimental API. (try_from)

The type returned in the event of a conversion error.

🔬 This is a nightly-only experimental API. (try_from)

Performs the conversion.

impl TryFrom<Integer> for i128
[src]

🔬 This is a nightly-only experimental API. (try_from)

The type returned in the event of a conversion error.

🔬 This is a nightly-only experimental API. (try_from)

Performs the conversion.

impl<'a> TryFrom<&'a Integer> for i128
[src]

🔬 This is a nightly-only experimental API. (try_from)

The type returned in the event of a conversion error.

🔬 This is a nightly-only experimental API. (try_from)

Performs the conversion.

impl TryFrom<Integer> for isize
[src]

🔬 This is a nightly-only experimental API. (try_from)

The type returned in the event of a conversion error.

🔬 This is a nightly-only experimental API. (try_from)

Performs the conversion.

impl<'a> TryFrom<&'a Integer> for isize
[src]

🔬 This is a nightly-only experimental API. (try_from)

The type returned in the event of a conversion error.

🔬 This is a nightly-only experimental API. (try_from)

Performs the conversion.

impl TryFrom<Integer> for u8
[src]

🔬 This is a nightly-only experimental API. (try_from)

The type returned in the event of a conversion error.

🔬 This is a nightly-only experimental API. (try_from)

Performs the conversion.

impl<'a> TryFrom<&'a Integer> for u8
[src]

🔬 This is a nightly-only experimental API. (try_from)

The type returned in the event of a conversion error.

🔬 This is a nightly-only experimental API. (try_from)

Performs the conversion.

impl TryFrom<Integer> for u16
[src]

🔬 This is a nightly-only experimental API. (try_from)

The type returned in the event of a conversion error.

🔬 This is a nightly-only experimental API. (try_from)

Performs the conversion.

impl<'a> TryFrom<&'a Integer> for u16
[src]

🔬 This is a nightly-only experimental API. (try_from)

The type returned in the event of a conversion error.

🔬 This is a nightly-only experimental API. (try_from)

Performs the conversion.

impl TryFrom<Integer> for u32
[src]

🔬 This is a nightly-only experimental API. (try_from)

The type returned in the event of a conversion error.

🔬 This is a nightly-only experimental API. (try_from)

Performs the conversion.

impl<'a> TryFrom<&'a Integer> for u32
[src]

🔬 This is a nightly-only experimental API. (try_from)

The type returned in the event of a conversion error.

🔬 This is a nightly-only experimental API. (try_from)

Performs the conversion.

impl TryFrom<Integer> for u64
[src]

🔬 This is a nightly-only experimental API. (try_from)

The type returned in the event of a conversion error.

🔬 This is a nightly-only experimental API. (try_from)

Performs the conversion.

impl<'a> TryFrom<&'a Integer> for u64
[src]

🔬 This is a nightly-only experimental API. (try_from)

The type returned in the event of a conversion error.

🔬 This is a nightly-only experimental API. (try_from)

Performs the conversion.

impl TryFrom<Integer> for u128
[src]

🔬 This is a nightly-only experimental API. (try_from)

The type returned in the event of a conversion error.

🔬 This is a nightly-only experimental API. (try_from)

Performs the conversion.

impl<'a> TryFrom<&'a Integer> for u128
[src]

🔬 This is a nightly-only experimental API. (try_from)

The type returned in the event of a conversion error.

🔬 This is a nightly-only experimental API. (try_from)

Performs the conversion.

impl TryFrom<Integer> for usize
[src]

🔬 This is a nightly-only experimental API. (try_from)

The type returned in the event of a conversion error.

🔬 This is a nightly-only experimental API. (try_from)

Performs the conversion.

impl<'a> TryFrom<&'a Integer> for usize
[src]

🔬 This is a nightly-only experimental API. (try_from)

The type returned in the event of a conversion error.

🔬 This is a nightly-only experimental API. (try_from)

Performs the conversion.

impl Assign<i8> for Integer
[src]

Peforms the assignement. Read more

impl From<i8> for Integer
[src]

Performs the conversion.

impl<'a> Assign<&'a i8> for Integer
[src]

Peforms the assignement. Read more

impl Assign<i16> for Integer
[src]

Peforms the assignement. Read more

impl From<i16> for Integer
[src]

Performs the conversion.

impl<'a> Assign<&'a i16> for Integer
[src]

Peforms the assignement. Read more

impl Assign<i32> for Integer
[src]

Peforms the assignement. Read more

impl From<i32> for Integer
[src]

Performs the conversion.

impl<'a> Assign<&'a i32> for Integer
[src]

Peforms the assignement. Read more

impl Assign<i64> for Integer
[src]

Peforms the assignement. Read more

impl From<i64> for Integer
[src]

Performs the conversion.

impl<'a> Assign<&'a i64> for Integer
[src]

Peforms the assignement. Read more

impl Assign<i128> for Integer
[src]

Peforms the assignement. Read more

impl From<i128> for Integer
[src]

Performs the conversion.

impl<'a> Assign<&'a i128> for Integer
[src]

Peforms the assignement. Read more

impl Assign<isize> for Integer
[src]

Peforms the assignement. Read more

impl From<isize> for Integer
[src]

Performs the conversion.

impl<'a> Assign<&'a isize> for Integer
[src]

Peforms the assignement. Read more

impl Assign<u8> for Integer
[src]

Peforms the assignement. Read more

impl From<u8> for Integer
[src]

Performs the conversion.

impl<'a> Assign<&'a u8> for Integer
[src]

Peforms the assignement. Read more

impl Assign<u16> for Integer
[src]

Peforms the assignement. Read more

impl From<u16> for Integer
[src]

Performs the conversion.

impl<'a> Assign<&'a u16> for Integer
[src]

Peforms the assignement. Read more

impl Assign<u32> for Integer
[src]

Peforms the assignement. Read more

impl From<u32> for Integer
[src]

Performs the conversion.

impl<'a> Assign<&'a u32> for Integer
[src]

Peforms the assignement. Read more

impl Assign<u64> for Integer
[src]

Peforms the assignement. Read more

impl From<u64> for Integer
[src]

Performs the conversion.

impl<'a> Assign<&'a u64> for Integer
[src]

Peforms the assignement. Read more

impl Assign<u128> for Integer
[src]

Peforms the assignement. Read more

impl From<u128> for Integer
[src]

Performs the conversion.

impl<'a> Assign<&'a u128> for Integer
[src]

Peforms the assignement. Read more

impl Assign<usize> for Integer
[src]

Peforms the assignement. Read more

impl From<usize> for Integer
[src]

Performs the conversion.

impl<'a> Assign<&'a usize> for Integer
[src]

Peforms the assignement. Read more

impl FromStr for Integer
[src]

The associated error which can be returned from parsing.

Parses a string s to return a value of this type. Read more

impl Display for Integer
[src]

Formats the value using the given formatter. Read more

impl Debug for Integer
[src]

Formats the value using the given formatter. Read more

impl Binary for Integer
[src]

Formats the value using the given formatter.

impl Octal for Integer
[src]

Formats the value using the given formatter.

impl LowerHex for Integer
[src]

Formats the value using the given formatter.

impl UpperHex for Integer
[src]

Formats the value using the given formatter.

impl Send for Integer
[src]

impl Sync for Integer
[src]

impl PartialEq<Integer> for Rational
[src]

This method tests for self and other values to be equal, and is used by ==. Read more

This method tests for !=.

impl PartialEq<Rational> for Integer
[src]

This method tests for self and other values to be equal, and is used by ==. Read more

This method tests for !=.

impl PartialOrd<Integer> for Rational
[src]

This method returns an ordering between self and other values if one exists. Read more

This method tests less than (for self and other) and is used by the < operator. Read more

This method tests less than or equal to (for self and other) and is used by the <= operator. Read more

This method tests greater than (for self and other) and is used by the > operator. Read more

This method tests greater than or equal to (for self and other) and is used by the >= operator. Read more

impl PartialOrd<Rational> for Integer
[src]

This method returns an ordering between self and other values if one exists. Read more

This method tests less than (for self and other) and is used by the < operator. Read more

This method tests less than or equal to (for self and other) and is used by the <= operator. Read more

This method tests greater than (for self and other) and is used by the > operator. Read more

This method tests greater than or equal to (for self and other) and is used by the >= operator. Read more

impl Add<Integer> for Float
[src]

The resulting type after applying the + operator.

Performs the + operation.

impl<'a> Add<&'a Integer> for Float
[src]

The resulting type after applying the + operator.

Performs the + operation.

impl<'a> Add<&'a Integer> for &'a Float
[src]

The resulting type after applying the + operator.

Performs the + operation.

impl AddAssign<Integer> for Float
[src]

Performs the += operation.

impl<'a> AddAssign<&'a Integer> for Float
[src]

Performs the += operation.

impl AddAssignRound<Integer> for Float
[src]

The rounding method.

The direction from rounding.

Performs the addition. Read more

impl<'a> AddAssignRound<&'a Integer> for Float
[src]

The rounding method.

The direction from rounding.

Performs the addition. Read more

impl<'a> Add<Integer> for &'a Float
[src]

The resulting type after applying the + operator.

Performs the + operation.

impl Add<Float> for Integer
[src]

The resulting type after applying the + operator.

Performs the + operation.

impl<'a> Add<&'a Float> for Integer
[src]

The resulting type after applying the + operator.

Performs the + operation.

impl<'a> Add<Float> for &'a Integer
[src]

The resulting type after applying the + operator.

Performs the + operation.

impl<'a> Add<&'a Float> for &'a Integer
[src]

The resulting type after applying the + operator.

Performs the + operation.

impl AddFrom<Integer> for Float
[src]

Peforms the addition. Read more

impl<'a> AddFrom<&'a Integer> for Float
[src]

Peforms the addition. Read more

impl AddFromRound<Integer> for Float
[src]

The rounding method.

The direction from rounding.

Performs the addition. Read more

impl<'a> AddFromRound<&'a Integer> for Float
[src]

The rounding method.

The direction from rounding.

Performs the addition. Read more

impl Sub<Integer> for Float
[src]

The resulting type after applying the - operator.

Performs the - operation.

impl<'a> Sub<&'a Integer> for Float
[src]

The resulting type after applying the - operator.

Performs the - operation.

impl<'a> Sub<&'a Integer> for &'a Float
[src]

The resulting type after applying the - operator.

Performs the - operation.

impl SubAssign<Integer> for Float
[src]

Performs the -= operation.

impl<'a> SubAssign<&'a Integer> for Float
[src]

Performs the -= operation.

impl SubAssignRound<Integer> for Float
[src]

The rounding method.

The direction from rounding.

Performs the subtraction. Read more

impl<'a> SubAssignRound<&'a Integer> for Float
[src]

The rounding method.

The direction from rounding.

Performs the subtraction. Read more

impl<'a> Sub<Integer> for &'a Float
[src]

The resulting type after applying the - operator.

Performs the - operation.

impl Sub<Float> for Integer
[src]

The resulting type after applying the - operator.

Performs the - operation.

impl<'a> Sub<&'a Float> for Integer
[src]

The resulting type after applying the - operator.

Performs the - operation.

impl<'a> Sub<Float> for &'a Integer
[src]

The resulting type after applying the - operator.

Performs the - operation.

impl<'a> Sub<&'a Float> for &'a Integer
[src]

The resulting type after applying the - operator.

Performs the - operation.

impl SubFrom<Integer> for Float
[src]

Peforms the subtraction. Read more

impl<'a> SubFrom<&'a Integer> for Float
[src]

Peforms the subtraction. Read more

impl SubFromRound<Integer> for Float
[src]

The rounding method.

The direction from rounding.

Performs the subtraction. Read more

impl<'a> SubFromRound<&'a Integer> for Float
[src]

The rounding method.

The direction from rounding.

Performs the subtraction. Read more

impl Mul<Integer> for Float
[src]

The resulting type after applying the * operator.

Performs the * operation.

impl<'a> Mul<&'a Integer> for Float
[src]

The resulting type after applying the * operator.

Performs the * operation.

impl<'a> Mul<&'a Integer> for &'a Float
[src]

The resulting type after applying the * operator.

Performs the * operation.

impl MulAssign<Integer> for Float
[src]

Performs the *= operation.

impl<'a> MulAssign<&'a Integer> for Float
[src]

Performs the *= operation.

impl MulAssignRound<Integer> for Float
[src]

The rounding method.

The direction from rounding.

Performs the multiplication. Read more

impl<'a> MulAssignRound<&'a Integer> for Float
[src]

The rounding method.

The direction from rounding.

Performs the multiplication. Read more

impl<'a> Mul<Integer> for &'a Float
[src]

The resulting type after applying the * operator.

Performs the * operation.

impl Mul<Float> for Integer
[src]

The resulting type after applying the * operator.

Performs the * operation.

impl<'a> Mul<&'a Float> for Integer
[src]

The resulting type after applying the * operator.

Performs the * operation.

impl<'a> Mul<Float> for &'a Integer
[src]

The resulting type after applying the * operator.

Performs the * operation.

impl<'a> Mul<&'a Float> for &'a Integer
[src]

The resulting type after applying the * operator.

Performs the * operation.

impl MulFrom<Integer> for Float
[src]

Peforms the multiplication. Read more

impl<'a> MulFrom<&'a Integer> for Float
[src]

Peforms the multiplication. Read more

impl MulFromRound<Integer> for Float
[src]

The rounding method.

The direction from rounding.

Performs the multiplication. Read more

impl<'a> MulFromRound<&'a Integer> for Float
[src]

The rounding method.

The direction from rounding.

Performs the multiplication. Read more

impl Div<Integer> for Float
[src]

The resulting type after applying the / operator.

Performs the / operation.

impl<'a> Div<&'a Integer> for Float
[src]

The resulting type after applying the / operator.

Performs the / operation.

impl<'a> Div<&'a Integer> for &'a Float
[src]

The resulting type after applying the / operator.

Performs the / operation.

impl DivAssign<Integer> for Float
[src]

Performs the /= operation.

impl<'a> DivAssign<&'a Integer> for Float
[src]

Performs the /= operation.

impl DivAssignRound<Integer> for Float
[src]

The rounding method.

The direction from rounding.

Performs the division. Read more

impl<'a> DivAssignRound<&'a Integer> for Float
[src]

The rounding method.

The direction from rounding.

Performs the division. Read more

impl<'a> Div<Integer> for &'a Float
[src]

The resulting type after applying the / operator.

Performs the / operation.

impl Div<Float> for Integer
[src]

The resulting type after applying the / operator.

Performs the / operation.

impl<'a> Div<&'a Float> for Integer
[src]

The resulting type after applying the / operator.

Performs the / operation.

impl<'a> Div<Float> for &'a Integer
[src]

The resulting type after applying the / operator.

Performs the / operation.

impl<'a> Div<&'a Float> for &'a Integer
[src]

The resulting type after applying the / operator.

Performs the / operation.

impl DivFrom<Integer> for Float
[src]

Peforms the division. Read more

impl<'a> DivFrom<&'a Integer> for Float
[src]

Peforms the division. Read more

impl DivFromRound<Integer> for Float
[src]

The rounding method.

The direction from rounding.

Performs the division. Read more

impl<'a> DivFromRound<&'a Integer> for Float
[src]

The rounding method.

The direction from rounding.

Performs the division. Read more

impl Pow<Integer> for Float
[src]

The resulting type after the power operation.

Performs the power operation. Read more

impl<'a> Pow<&'a Integer> for Float
[src]

The resulting type after the power operation.

Performs the power operation. Read more

impl<'a> Pow<&'a Integer> for &'a Float
[src]

The resulting type after the power operation.

Performs the power operation. Read more

impl PowAssign<Integer> for Float
[src]

Peforms the power operation. Read more

impl<'a> PowAssign<&'a Integer> for Float
[src]

Peforms the power operation. Read more

impl PowAssignRound<Integer> for Float
[src]

The rounding method.

The direction from rounding.

Performs the power operation. Read more

impl<'a> PowAssignRound<&'a Integer> for Float
[src]

The rounding method.

The direction from rounding.

Performs the power operation. Read more

impl<'a> Pow<Integer> for &'a Float
[src]

The resulting type after the power operation.

Performs the power operation. Read more

impl PartialEq<Integer> for Float
[src]

This method tests for self and other values to be equal, and is used by ==. Read more

This method tests for !=.

impl PartialEq<Float> for Integer
[src]

This method tests for self and other values to be equal, and is used by ==. Read more

This method tests for !=.

impl PartialOrd<Float> for Integer
[src]

This method returns an ordering between self and other values if one exists. Read more

This method tests less than (for self and other) and is used by the < operator. Read more

This method tests less than or equal to (for self and other) and is used by the <= operator. Read more

This method tests greater than (for self and other) and is used by the > operator. Read more

This method tests greater than or equal to (for self and other) and is used by the >= operator. Read more

impl PartialOrd<Integer> for Float
[src]

This method returns an ordering between self and other values if one exists. Read more

This method tests less than (for self and other) and is used by the < operator. Read more

This method tests less than or equal to (for self and other) and is used by the <= operator. Read more

This method tests greater than (for self and other) and is used by the > operator. Read more

This method tests greater than or equal to (for self and other) and is used by the >= operator. Read more

impl<'a> AssignRound<&'a Integer> for Float
[src]

The rounding method.

The direction from rounding.

Peforms the assignment. Read more

impl AssignRound<Integer> for Float
[src]

The rounding method.

The direction from rounding.

Peforms the assignment. Read more

impl Pow<Integer> for Complex
[src]

The resulting type after the power operation.

Performs the power operation. Read more

impl<'a> Pow<&'a Integer> for Complex
[src]

The resulting type after the power operation.

Performs the power operation. Read more

impl<'a> Pow<&'a Integer> for &'a Complex
[src]

The resulting type after the power operation.

Performs the power operation. Read more

impl PowAssign<Integer> for Complex
[src]

Peforms the power operation. Read more

impl<'a> PowAssign<&'a Integer> for Complex
[src]

Peforms the power operation. Read more

impl PowAssignRound<Integer> for Complex
[src]

The rounding method.

The direction from rounding.

Performs the power operation. Read more

impl<'a> PowAssignRound<&'a Integer> for Complex
[src]

The rounding method.

The direction from rounding.

Performs the power operation. Read more

impl<'a> Pow<Integer> for &'a Complex
[src]

The resulting type after the power operation.

Performs the power operation. Read more

impl Add<Integer> for Complex
[src]

The resulting type after applying the + operator.

Performs the + operation.

impl<'a> Add<&'a Integer> for Complex
[src]

The resulting type after applying the + operator.

Performs the + operation.

impl<'a> Add<&'a Integer> for &'a Complex
[src]

The resulting type after applying the + operator.

Performs the + operation.

impl AddAssign<Integer> for Complex
[src]

Performs the += operation.

impl<'a> AddAssign<&'a Integer> for Complex
[src]

Performs the += operation.

impl AddAssignRound<Integer> for Complex
[src]

The rounding method.

The direction from rounding.

Performs the addition. Read more

impl<'a> AddAssignRound<&'a Integer> for Complex
[src]

The rounding method.

The direction from rounding.

Performs the addition. Read more

impl<'a> Add<Integer> for &'a Complex
[src]

The resulting type after applying the + operator.

Performs the + operation.

impl Add<Complex> for Integer
[src]

The resulting type after applying the + operator.

Performs the + operation.

impl<'a> Add<&'a Complex> for Integer
[src]

The resulting type after applying the + operator.

Performs the + operation.

impl<'a> Add<Complex> for &'a Integer
[src]

The resulting type after applying the + operator.

Performs the + operation.

impl<'a> Add<&'a Complex> for &'a Integer
[src]

The resulting type after applying the + operator.

Performs the + operation.

impl AddFrom<Integer> for Complex
[src]

Peforms the addition. Read more

impl<'a> AddFrom<&'a Integer> for Complex
[src]

Peforms the addition. Read more

impl AddFromRound<Integer> for Complex
[src]

The rounding method.

The direction from rounding.

Performs the addition. Read more

impl<'a> AddFromRound<&'a Integer> for Complex
[src]

The rounding method.

The direction from rounding.

Performs the addition. Read more

impl Sub<Integer> for Complex
[src]

The resulting type after applying the - operator.

Performs the - operation.

impl<'a> Sub<&'a Integer> for Complex
[src]

The resulting type after applying the - operator.

Performs the - operation.

impl<'a> Sub<&'a Integer> for &'a Complex
[src]

The resulting type after applying the - operator.

Performs the - operation.

impl SubAssign<Integer> for Complex
[src]

Performs the -= operation.

impl<'a> SubAssign<&'a Integer> for Complex
[src]

Performs the -= operation.

impl SubAssignRound<Integer> for Complex
[src]

The rounding method.

The direction from rounding.

Performs the subtraction. Read more

impl<'a> SubAssignRound<&'a Integer> for Complex
[src]

The rounding method.

The direction from rounding.

Performs the subtraction. Read more

impl<'a> Sub<Integer> for &'a Complex
[src]

The resulting type after applying the - operator.

Performs the - operation.

impl Sub<Complex> for Integer
[src]

The resulting type after applying the - operator.

Performs the - operation.

impl<'a> Sub<&'a Complex> for Integer
[src]

The resulting type after applying the - operator.

Performs the - operation.

impl<'a> Sub<Complex> for &'a Integer
[src]

The resulting type after applying the - operator.

Performs the - operation.

impl<'a> Sub<&'a Complex> for &'a Integer
[src]

The resulting type after applying the - operator.

Performs the - operation.

impl SubFrom<Integer> for Complex
[src]

Peforms the subtraction. Read more

impl<'a> SubFrom<&'a Integer> for Complex
[src]

Peforms the subtraction. Read more

impl SubFromRound<Integer> for Complex
[src]

The rounding method.

The direction from rounding.

Performs the subtraction. Read more

impl<'a> SubFromRound<&'a Integer> for Complex
[src]

The rounding method.

The direction from rounding.

Performs the subtraction. Read more

impl Mul<Integer> for Complex
[src]

The resulting type after applying the * operator.

Performs the * operation.

impl<'a> Mul<&'a Integer> for Complex
[src]

The resulting type after applying the * operator.

Performs the * operation.

impl<'a> Mul<&'a Integer> for &'a Complex
[src]

The resulting type after applying the * operator.

Performs the * operation.

impl MulAssign<Integer> for Complex
[src]

Performs the *= operation.

impl<'a> MulAssign<&'a Integer> for Complex
[src]

Performs the *= operation.

impl MulAssignRound<Integer> for Complex
[src]

The rounding method.

The direction from rounding.

Performs the multiplication. Read more

impl<'a> MulAssignRound<&'a Integer> for Complex
[src]

The rounding method.

The direction from rounding.

Performs the multiplication. Read more

impl<'a> Mul<Integer> for &'a Complex
[src]

The resulting type after applying the * operator.

Performs the * operation.

impl Mul<Complex> for Integer
[src]

The resulting type after applying the * operator.

Performs the * operation.

impl<'a> Mul<&'a Complex> for Integer
[src]

The resulting type after applying the * operator.

Performs the * operation.

impl<'a> Mul<Complex> for &'a Integer
[src]

The resulting type after applying the * operator.

Performs the * operation.

impl<'a> Mul<&'a Complex> for &'a Integer
[src]

The resulting type after applying the * operator.

Performs the * operation.

impl MulFrom<Integer> for Complex
[src]

Peforms the multiplication. Read more

impl<'a> MulFrom<&'a Integer> for Complex
[src]

Peforms the multiplication. Read more

impl MulFromRound<Integer> for Complex
[src]

The rounding method.

The direction from rounding.

Performs the multiplication. Read more

impl<'a> MulFromRound<&'a Integer> for Complex
[src]

The rounding method.

The direction from rounding.

Performs the multiplication. Read more

impl Div<Integer> for Complex
[src]

The resulting type after applying the / operator.

Performs the / operation.

impl<'a> Div<&'a Integer> for Complex
[src]

The resulting type after applying the / operator.

Performs the / operation.

impl<'a> Div<&'a Integer> for &'a Complex
[src]

The resulting type after applying the / operator.

Performs the / operation.

impl DivAssign<Integer> for Complex
[src]

Performs the /= operation.

impl<'a> DivAssign<&'a Integer> for Complex
[src]

Performs the /= operation.

impl DivAssignRound<Integer> for Complex
[src]

The rounding method.

The direction from rounding.

Performs the division. Read more

impl<'a> DivAssignRound<&'a Integer> for Complex
[src]

The rounding method.

The direction from rounding.

Performs the division. Read more

impl<'a> Div<Integer> for &'a Complex
[src]

The resulting type after applying the / operator.

Performs the / operation.

impl PartialEq<Integer> for Complex
[src]

This method tests for self and other values to be equal, and is used by ==. Read more

This method tests for !=.

impl PartialEq<Complex> for Integer
[src]

This method tests for self and other values to be equal, and is used by ==. Read more

This method tests for !=.