Struct fvm_shared::smooth::EPSILON
source · pub struct EPSILON { /* private fields */ }
Methods from Deref<Target = BigInt>§
pub const ZERO: BigInt = _
sourcepub fn to_bytes_be(&self) -> (Sign, Vec<u8>)
pub fn to_bytes_be(&self) -> (Sign, Vec<u8>)
sourcepub fn to_bytes_le(&self) -> (Sign, Vec<u8>)
pub fn to_bytes_le(&self) -> (Sign, Vec<u8>)
sourcepub fn to_u32_digits(&self) -> (Sign, Vec<u32>)
pub fn to_u32_digits(&self) -> (Sign, Vec<u32>)
Returns the sign and the u32
digits representation of the BigInt
ordered least
significant digit first.
§Examples
use num_bigint::{BigInt, Sign};
assert_eq!(BigInt::from(-1125).to_u32_digits(), (Sign::Minus, vec![1125]));
assert_eq!(BigInt::from(4294967295u32).to_u32_digits(), (Sign::Plus, vec![4294967295]));
assert_eq!(BigInt::from(4294967296u64).to_u32_digits(), (Sign::Plus, vec![0, 1]));
assert_eq!(BigInt::from(-112500000000i64).to_u32_digits(), (Sign::Minus, vec![830850304, 26]));
assert_eq!(BigInt::from(112500000000i64).to_u32_digits(), (Sign::Plus, vec![830850304, 26]));
sourcepub fn to_u64_digits(&self) -> (Sign, Vec<u64>)
pub fn to_u64_digits(&self) -> (Sign, Vec<u64>)
Returns the sign and the u64
digits representation of the BigInt
ordered least
significant digit first.
§Examples
use num_bigint::{BigInt, Sign};
assert_eq!(BigInt::from(-1125).to_u64_digits(), (Sign::Minus, vec![1125]));
assert_eq!(BigInt::from(4294967295u32).to_u64_digits(), (Sign::Plus, vec![4294967295]));
assert_eq!(BigInt::from(4294967296u64).to_u64_digits(), (Sign::Plus, vec![4294967296]));
assert_eq!(BigInt::from(-112500000000i64).to_u64_digits(), (Sign::Minus, vec![112500000000]));
assert_eq!(BigInt::from(112500000000i64).to_u64_digits(), (Sign::Plus, vec![112500000000]));
assert_eq!(BigInt::from(1u128 << 64).to_u64_digits(), (Sign::Plus, vec![0, 1]));
sourcepub fn iter_u32_digits(&self) -> U32Digits<'_> ⓘ
pub fn iter_u32_digits(&self) -> U32Digits<'_> ⓘ
Returns an iterator of u32
digits representation of the BigInt
ordered least
significant digit first.
§Examples
use num_bigint::BigInt;
assert_eq!(BigInt::from(-1125).iter_u32_digits().collect::<Vec<u32>>(), vec![1125]);
assert_eq!(BigInt::from(4294967295u32).iter_u32_digits().collect::<Vec<u32>>(), vec![4294967295]);
assert_eq!(BigInt::from(4294967296u64).iter_u32_digits().collect::<Vec<u32>>(), vec![0, 1]);
assert_eq!(BigInt::from(-112500000000i64).iter_u32_digits().collect::<Vec<u32>>(), vec![830850304, 26]);
assert_eq!(BigInt::from(112500000000i64).iter_u32_digits().collect::<Vec<u32>>(), vec![830850304, 26]);
sourcepub fn iter_u64_digits(&self) -> U64Digits<'_> ⓘ
pub fn iter_u64_digits(&self) -> U64Digits<'_> ⓘ
Returns an iterator of u64
digits representation of the BigInt
ordered least
significant digit first.
§Examples
use num_bigint::BigInt;
assert_eq!(BigInt::from(-1125).iter_u64_digits().collect::<Vec<u64>>(), vec![1125u64]);
assert_eq!(BigInt::from(4294967295u32).iter_u64_digits().collect::<Vec<u64>>(), vec![4294967295u64]);
assert_eq!(BigInt::from(4294967296u64).iter_u64_digits().collect::<Vec<u64>>(), vec![4294967296u64]);
assert_eq!(BigInt::from(-112500000000i64).iter_u64_digits().collect::<Vec<u64>>(), vec![112500000000u64]);
assert_eq!(BigInt::from(112500000000i64).iter_u64_digits().collect::<Vec<u64>>(), vec![112500000000u64]);
assert_eq!(BigInt::from(1u128 << 64).iter_u64_digits().collect::<Vec<u64>>(), vec![0, 1]);
sourcepub fn to_signed_bytes_be(&self) -> Vec<u8> ⓘ
pub fn to_signed_bytes_be(&self) -> Vec<u8> ⓘ
sourcepub fn to_signed_bytes_le(&self) -> Vec<u8> ⓘ
pub fn to_signed_bytes_le(&self) -> Vec<u8> ⓘ
sourcepub fn to_str_radix(&self, radix: u32) -> String
pub fn to_str_radix(&self, radix: u32) -> String
Returns the integer formatted as a string in the given radix.
radix
must be in the range 2...36
.
§Examples
use num_bigint::BigInt;
let i = BigInt::parse_bytes(b"ff", 16).unwrap();
assert_eq!(i.to_str_radix(16), "ff");
sourcepub fn to_radix_be(&self, radix: u32) -> (Sign, Vec<u8>)
pub fn to_radix_be(&self, radix: u32) -> (Sign, Vec<u8>)
Returns the integer in the requested base in big-endian digit order.
The output is not given in a human readable alphabet but as a zero
based u8
number.
radix
must be in the range 2...256
.
§Examples
use num_bigint::{BigInt, Sign};
assert_eq!(BigInt::from(-0xFFFFi64).to_radix_be(159),
(Sign::Minus, vec![2, 94, 27]));
// 0xFFFF = 65535 = 2*(159^2) + 94*159 + 27
sourcepub fn to_radix_le(&self, radix: u32) -> (Sign, Vec<u8>)
pub fn to_radix_le(&self, radix: u32) -> (Sign, Vec<u8>)
Returns the integer in the requested base in little-endian digit order.
The output is not given in a human readable alphabet but as a zero
based u8
number.
radix
must be in the range 2...256
.
§Examples
use num_bigint::{BigInt, Sign};
assert_eq!(BigInt::from(-0xFFFFi64).to_radix_le(159),
(Sign::Minus, vec![27, 94, 2]));
// 0xFFFF = 65535 = 27 + 94*159 + 2*(159^2)
sourcepub fn magnitude(&self) -> &BigUint
pub fn magnitude(&self) -> &BigUint
Returns the magnitude of the BigInt
as a BigUint
.
§Examples
use num_bigint::{BigInt, BigUint};
use num_traits::Zero;
assert_eq!(BigInt::from(1234).magnitude(), &BigUint::from(1234u32));
assert_eq!(BigInt::from(-4321).magnitude(), &BigUint::from(4321u32));
assert!(BigInt::ZERO.magnitude().is_zero());
sourcepub fn bits(&self) -> u64
pub fn bits(&self) -> u64
Determines the fewest bits necessary to express the BigInt
,
not including the sign.
sourcepub fn to_biguint(&self) -> Option<BigUint>
pub fn to_biguint(&self) -> Option<BigUint>
pub fn checked_add(&self, v: &BigInt) -> Option<BigInt>
pub fn checked_sub(&self, v: &BigInt) -> Option<BigInt>
pub fn checked_mul(&self, v: &BigInt) -> Option<BigInt>
pub fn checked_div(&self, v: &BigInt) -> Option<BigInt>
sourcepub fn modpow(&self, exponent: &BigInt, modulus: &BigInt) -> BigInt
pub fn modpow(&self, exponent: &BigInt, modulus: &BigInt) -> BigInt
Returns (self ^ exponent) mod modulus
Note that this rounds like mod_floor
, not like the %
operator,
which makes a difference when given a negative self
or modulus
.
The result will be in the interval [0, modulus)
for modulus > 0
,
or in the interval (modulus, 0]
for modulus < 0
Panics if the exponent is negative or the modulus is zero.
sourcepub fn modinv(&self, modulus: &BigInt) -> Option<BigInt>
pub fn modinv(&self, modulus: &BigInt) -> Option<BigInt>
Returns the modular multiplicative inverse if it exists, otherwise None
.
This solves for x
such that self * x ≡ 1 (mod modulus)
.
Note that this rounds like mod_floor
, not like the %
operator,
which makes a difference when given a negative self
or modulus
.
The solution will be in the interval [0, modulus)
for modulus > 0
,
or in the interval (modulus, 0]
for modulus < 0
,
and it exists if and only if gcd(self, modulus) == 1
.
use num_bigint::BigInt;
use num_integer::Integer;
use num_traits::{One, Zero};
let m = BigInt::from(383);
// Trivial cases
assert_eq!(BigInt::zero().modinv(&m), None);
assert_eq!(BigInt::one().modinv(&m), Some(BigInt::one()));
let neg1 = &m - 1u32;
assert_eq!(neg1.modinv(&m), Some(neg1));
// Positive self and modulus
let a = BigInt::from(271);
let x = a.modinv(&m).unwrap();
assert_eq!(x, BigInt::from(106));
assert_eq!(x.modinv(&m).unwrap(), a);
assert_eq!((&a * x).mod_floor(&m), BigInt::one());
// Negative self and positive modulus
let b = -&a;
let x = b.modinv(&m).unwrap();
assert_eq!(x, BigInt::from(277));
assert_eq!((&b * x).mod_floor(&m), BigInt::one());
// Positive self and negative modulus
let n = -&m;
let x = a.modinv(&n).unwrap();
assert_eq!(x, BigInt::from(-277));
assert_eq!((&a * x).mod_floor(&n), &n + 1);
// Negative self and modulus
let x = b.modinv(&n).unwrap();
assert_eq!(x, BigInt::from(-106));
assert_eq!((&b * x).mod_floor(&n), &n + 1);
sourcepub fn sqrt(&self) -> BigInt
pub fn sqrt(&self) -> BigInt
Returns the truncated principal square root of self
–
see num_integer::Roots::sqrt()
.
sourcepub fn cbrt(&self) -> BigInt
pub fn cbrt(&self) -> BigInt
Returns the truncated principal cube root of self
–
see num_integer::Roots::cbrt()
.
sourcepub fn nth_root(&self, n: u32) -> BigInt
pub fn nth_root(&self, n: u32) -> BigInt
Returns the truncated principal n
th root of self
–
See num_integer::Roots::nth_root()
.
sourcepub fn trailing_zeros(&self) -> Option<u64>
pub fn trailing_zeros(&self) -> Option<u64>
Returns the number of least-significant bits that are zero,
or None
if the entire number is zero.
Trait Implementations§
Auto Trait Implementations§
impl Freeze for EPSILON
impl RefUnwindSafe for EPSILON
impl Send for EPSILON
impl Sync for EPSILON
impl Unpin for EPSILON
impl UnwindSafe for EPSILON
Blanket Implementations§
source§impl<T> BorrowMut<T> for Twhere
T: ?Sized,
impl<T> BorrowMut<T> for Twhere
T: ?Sized,
source§fn borrow_mut(&mut self) -> &mut T
fn borrow_mut(&mut self) -> &mut T
source§impl<T> FmtForward for T
impl<T> FmtForward for T
source§fn fmt_binary(self) -> FmtBinary<Self>where
Self: Binary,
fn fmt_binary(self) -> FmtBinary<Self>where
Self: Binary,
self
to use its Binary
implementation when Debug
-formatted.source§fn fmt_display(self) -> FmtDisplay<Self>where
Self: Display,
fn fmt_display(self) -> FmtDisplay<Self>where
Self: Display,
self
to use its Display
implementation when
Debug
-formatted.source§fn fmt_lower_exp(self) -> FmtLowerExp<Self>where
Self: LowerExp,
fn fmt_lower_exp(self) -> FmtLowerExp<Self>where
Self: LowerExp,
self
to use its LowerExp
implementation when
Debug
-formatted.source§fn fmt_lower_hex(self) -> FmtLowerHex<Self>where
Self: LowerHex,
fn fmt_lower_hex(self) -> FmtLowerHex<Self>where
Self: LowerHex,
self
to use its LowerHex
implementation when
Debug
-formatted.source§fn fmt_octal(self) -> FmtOctal<Self>where
Self: Octal,
fn fmt_octal(self) -> FmtOctal<Self>where
Self: Octal,
self
to use its Octal
implementation when Debug
-formatted.source§fn fmt_pointer(self) -> FmtPointer<Self>where
Self: Pointer,
fn fmt_pointer(self) -> FmtPointer<Self>where
Self: Pointer,
self
to use its Pointer
implementation when
Debug
-formatted.source§fn fmt_upper_exp(self) -> FmtUpperExp<Self>where
Self: UpperExp,
fn fmt_upper_exp(self) -> FmtUpperExp<Self>where
Self: UpperExp,
self
to use its UpperExp
implementation when
Debug
-formatted.source§fn fmt_upper_hex(self) -> FmtUpperHex<Self>where
Self: UpperHex,
fn fmt_upper_hex(self) -> FmtUpperHex<Self>where
Self: UpperHex,
self
to use its UpperHex
implementation when
Debug
-formatted.source§impl<T> IntoEither for T
impl<T> IntoEither for T
source§fn into_either(self, into_left: bool) -> Either<Self, Self>
fn into_either(self, into_left: bool) -> Either<Self, Self>
self
into a Left
variant of Either<Self, Self>
if into_left
is true
.
Converts self
into a Right
variant of Either<Self, Self>
otherwise. Read moresource§fn into_either_with<F>(self, into_left: F) -> Either<Self, Self>
fn into_either_with<F>(self, into_left: F) -> Either<Self, Self>
self
into a Left
variant of Either<Self, Self>
if into_left(&self)
returns true
.
Converts self
into a Right
variant of Either<Self, Self>
otherwise. Read moresource§impl<T> Pipe for Twhere
T: ?Sized,
impl<T> Pipe for Twhere
T: ?Sized,
source§fn pipe<R>(self, func: impl FnOnce(Self) -> R) -> Rwhere
Self: Sized,
fn pipe<R>(self, func: impl FnOnce(Self) -> R) -> Rwhere
Self: Sized,
source§fn pipe_ref<'a, R>(&'a self, func: impl FnOnce(&'a Self) -> R) -> Rwhere
R: 'a,
fn pipe_ref<'a, R>(&'a self, func: impl FnOnce(&'a Self) -> R) -> Rwhere
R: 'a,
self
and passes that borrow into the pipe function. Read moresource§fn pipe_ref_mut<'a, R>(&'a mut self, func: impl FnOnce(&'a mut Self) -> R) -> Rwhere
R: 'a,
fn pipe_ref_mut<'a, R>(&'a mut self, func: impl FnOnce(&'a mut Self) -> R) -> Rwhere
R: 'a,
self
and passes that borrow into the pipe function. Read moresource§fn pipe_borrow<'a, B, R>(&'a self, func: impl FnOnce(&'a B) -> R) -> R
fn pipe_borrow<'a, B, R>(&'a self, func: impl FnOnce(&'a B) -> R) -> R
source§fn pipe_borrow_mut<'a, B, R>(
&'a mut self,
func: impl FnOnce(&'a mut B) -> R,
) -> R
fn pipe_borrow_mut<'a, B, R>( &'a mut self, func: impl FnOnce(&'a mut B) -> R, ) -> R
source§fn pipe_as_ref<'a, U, R>(&'a self, func: impl FnOnce(&'a U) -> R) -> R
fn pipe_as_ref<'a, U, R>(&'a self, func: impl FnOnce(&'a U) -> R) -> R
self
, then passes self.as_ref()
into the pipe function.source§fn pipe_as_mut<'a, U, R>(&'a mut self, func: impl FnOnce(&'a mut U) -> R) -> R
fn pipe_as_mut<'a, U, R>(&'a mut self, func: impl FnOnce(&'a mut U) -> R) -> R
self
, then passes self.as_mut()
into the pipe
function.source§fn pipe_deref<'a, T, R>(&'a self, func: impl FnOnce(&'a T) -> R) -> R
fn pipe_deref<'a, T, R>(&'a self, func: impl FnOnce(&'a T) -> R) -> R
self
, then passes self.deref()
into the pipe function.source§impl<T> Pointable for T
impl<T> Pointable for T
source§impl<T> Tap for T
impl<T> Tap for T
source§fn tap_borrow<B>(self, func: impl FnOnce(&B)) -> Self
fn tap_borrow<B>(self, func: impl FnOnce(&B)) -> Self
Borrow<B>
of a value. Read moresource§fn tap_borrow_mut<B>(self, func: impl FnOnce(&mut B)) -> Self
fn tap_borrow_mut<B>(self, func: impl FnOnce(&mut B)) -> Self
BorrowMut<B>
of a value. Read moresource§fn tap_ref<R>(self, func: impl FnOnce(&R)) -> Self
fn tap_ref<R>(self, func: impl FnOnce(&R)) -> Self
AsRef<R>
view of a value. Read moresource§fn tap_ref_mut<R>(self, func: impl FnOnce(&mut R)) -> Self
fn tap_ref_mut<R>(self, func: impl FnOnce(&mut R)) -> Self
AsMut<R>
view of a value. Read moresource§fn tap_deref<T>(self, func: impl FnOnce(&T)) -> Self
fn tap_deref<T>(self, func: impl FnOnce(&T)) -> Self
Deref::Target
of a value. Read moresource§fn tap_deref_mut<T>(self, func: impl FnOnce(&mut T)) -> Self
fn tap_deref_mut<T>(self, func: impl FnOnce(&mut T)) -> Self
Deref::Target
of a value. Read moresource§fn tap_dbg(self, func: impl FnOnce(&Self)) -> Self
fn tap_dbg(self, func: impl FnOnce(&Self)) -> Self
.tap()
only in debug builds, and is erased in release builds.source§fn tap_mut_dbg(self, func: impl FnOnce(&mut Self)) -> Self
fn tap_mut_dbg(self, func: impl FnOnce(&mut Self)) -> Self
.tap_mut()
only in debug builds, and is erased in release
builds.source§fn tap_borrow_dbg<B>(self, func: impl FnOnce(&B)) -> Self
fn tap_borrow_dbg<B>(self, func: impl FnOnce(&B)) -> Self
.tap_borrow()
only in debug builds, and is erased in release
builds.source§fn tap_borrow_mut_dbg<B>(self, func: impl FnOnce(&mut B)) -> Self
fn tap_borrow_mut_dbg<B>(self, func: impl FnOnce(&mut B)) -> Self
.tap_borrow_mut()
only in debug builds, and is erased in release
builds.source§fn tap_ref_dbg<R>(self, func: impl FnOnce(&R)) -> Self
fn tap_ref_dbg<R>(self, func: impl FnOnce(&R)) -> Self
.tap_ref()
only in debug builds, and is erased in release
builds.source§fn tap_ref_mut_dbg<R>(self, func: impl FnOnce(&mut R)) -> Self
fn tap_ref_mut_dbg<R>(self, func: impl FnOnce(&mut R)) -> Self
.tap_ref_mut()
only in debug builds, and is erased in release
builds.source§fn tap_deref_dbg<T>(self, func: impl FnOnce(&T)) -> Self
fn tap_deref_dbg<T>(self, func: impl FnOnce(&T)) -> Self
.tap_deref()
only in debug builds, and is erased in release
builds.