Module malachite_base::num::arithmetic
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Traits for arithmetic.
Modules
AddMul and AddMulAssign, traits for adding a
number and the product of two other numbers.ArithmeticCheckedShl, a trait for left-shifting a number and
checking whether the result is representable.ArithmeticCheckedShr, a trait for right-shifting a number and
checking whether the result is representable.Ceiling and CeilingAssign, traits for computing
the ceiling of a number.CheckedAbs, a trait for computing the absolute value of number and
checking whether the result is representable.CheckedAdd, a trait for adding two numbers and checking whether the
result is representable.CheckedAddMul, a trait for adding a number and the product of two
other numbers, and checking whether the result is representable.CheckedDiv, a trait for dividing two numbers and checking whether the
result is representable.CheckedMul, a trait for multiplying two numbers and checking whether
the result is representable.CheckedNeg, a trait for negating a number and checking whether the
result is representable.CheckedNextPowerOf2, a trait for getting the next-highest
power of 2, if it’s representable.CheckedPow, a trait for raising a number to the power of a u64 and
checking whether the result is representable.CheckedSquare, a trait for squaring a number and checking whether
the result is representable.CheckedSub, a trait for subtracting two numbers and checking whether
the result is representable.CheckedSubMul, a trait for subtracting the product of two numbers
from another number, and checking whether the result is representable.CoprimeWith, a trait for determining whether two numbers are coprime.DivExact and DivExactAssign, traits for
dividing two numbers when it’s known that the division is exact.Traits for simultaneously finding the quotient and remainder of two numbers, subject to various
rounding rules.
DivisibleBy, a trait for determining whether one number is divisible
by another.DivisibleByPowerOf2, a trait for determining whether a number
is divisible by $2^k$.EqModPowerOf2, a trait for determining whether one number is equal
to another modulo $2^k$.ExtendedGcd, a trait for computing the GCD (greatest common divisor)
of two numbers as well as the coefficients of Bézout’s identity $ax+by=\gcd(a,b)$.Traits for computing the factorial, double factorial, multifactorial, and subfactorial. Each
function has a trait whose implementations panic if the result cannot be represented, and a
checked trait whose implementations return
None in that case. The traits are
Factorial, DoubleFactorial,
Multifactorial, Subfactorial,
CheckedFactorial,
CheckedDoubleFactorial,
CheckedMultifactorial, and
CheckedSubfactorial.Floor and FloorAssign, traits for computing the
floor of a number.IsPowerOf2, a trait for determining whether a number is an integer
power of 2.LegendreSymbol, JacobiSymbol, and
KroneckerSymbol, traits for computing the Legendre, Jacobi, and
Kronecker symbols of two numbers.Lcm, LcmAssign, and CheckedLcm,
traits for computing the LCM (least common multiple) of two numbers.Traits for taking the base-$b$ logarithm of a number.
Traits for taking the base-2 logarithm of a number.
Traits for taking the base-$2^k$ logarithm of a number.
ModAdd and ModAddAssign, traits for adding two
numbers modulo another number.ModInverse, a trait for finding the multiplicative inverse of a number
modulo another number.ModIsReduced, a trait for checking whether a number is reduced modulo
another number.Traits for multiplying two numbers modulo another number.
ModNeg and ModNegAssign, traits for negating a
number modulo another number.Traits for finding the remainder of two numbers, subject to various rounding rules.
Traits for raising a number to a power modulo another number.
Traits for finding the remainder of a number divided by $2^k$, subject to various rounding
rules.
ModPowerOf2Add and
ModPowerOf2AddAssign, traits for adding two numbers modulo
$2^k$.ModPowerOf2Inverse, a trait for finding the multiplicative
inverse of a number modulo $2^k$.ModPowerOf2IsReduced, a trait for checking whether a number
is reduced modulo $2^k$.ModPowerOf2Mul and
ModPowerOf2MulAssign, traits for multiplying two numbers
modulo $2^k$.ModPowerOf2Neg and
ModPowerOf2NegAssign, traits for negating a number modulo
$2^k$.ModPowerOf2Pow and
ModPowerOf2PowAssign, traits for raising a number to a power
modulo $2^k$.ModPowerOf2Shl and
ModPowerOf2ShlAssign, traits for left-shifting a number
modulo $2^k$.ModPowerOf2Shr and
ModPowerOf2ShrAssign, traits for right-shifting a number
modulo $2^k$.ModPowerOf2Square and
ModPowerOf2SquareAssign, traits for squaring a number
modulo $2^k$.ModPowerOf2Sub and
ModPowerOf2SubAssign, traits for subtracting one number by
another modulo $2^k$.ModShl and ModShlAssign, traits for left-shifting
a number modulo another number.ModShr and ModShrAssign, traits for
right-shifting a number modulo another number.Traits for squaring a number modulo another number.
ModSub and ModSubAssign, traits for subtracting
two numbers modulo another number.NextPowerOf2 and NextPowerOf2Assign,
traits for getting the next-highest power of 2.OverflowingAbs and
OverflowingAbsAssign, traits for taking the absolute value
of a number and returning a boolean indicating whether an overflow occurred.OverflowingAdd and
OverflowingAddAssign, traits for adding two numbers and
returning a boolean indicating whether an overflow occurred.OverflowingAddMul and
OverflowingAddMulAssign, traits for adding the product of
two other numbers to a number and returning a boolean indicating whether an overflow occurred.OverflowingDiv and
OverflowingDivAssign, traits for dividing two numbers and
returning a boolean indicating whether an overflow occurred.OverflowingMul and
OverflowingMulAssign, traits for multiplying two numbers and
returning a boolean indicating whether an overflow occurred.OverflowingNeg and
OverflowingNegAssign, traits for negating a number and
returning a boolean indicating whether an overflow occurred.OverflowingPow and
OverflowingPowAssign, traits for raising a number to a power
and returning a boolean indicating whether an overflow occurred.OverflowingSquare and
OverflowingSquareAssign, traits for squaring a number and
returning a boolean indicating whether an overflow occurred.OverflowingSub and
OverflowingSubAssign, traits for subtracting two numbers and
returning a boolean indicating whether an overflow occurred.OverflowingSubMul and
OverflowingSubMulAssign, traits for subtracting the
product of two other numbers from a number and returning a boolean indicating whether an
overflow occurred.PowerOf2, a trait for computing a power of 2.Traits for taking the $n$th root of a number.
RoundToMultiple and
RoundToMultipleAssign, traits for rounding a number to a
multiple of another number.RoundToMultipleOfPowerOf2 and
RoundToMultipleOfPowerOf2Assign, traits for
rounding a number to a multiple of a power of 2.SaturatingAbs and
SaturatingAbsAssign, traits for taking the absolute value of a
number and saturating at numeric bounds instead of overflowing.SaturatingAdd and
SaturatingAddAssign, traits for adding two numbers and
saturating at numeric bounds instead of overflowing.SaturatingAddMul and
SaturatingAddMulAssign, traits for adding the product of
two numbers to a number and saturating at numeric bounds instead of overflowing.SaturatingMul and
SaturatingMulAssign, traits for multiplying two numbers and
saturating at numeric bounds instead of overflowing.SaturatingNeg and
SaturatingNegAssign, traits for negating a number and
saturating at numeric bounds instead of overflowing.SaturatingPow and
SaturatingPowAssign, traits for raising a number to a power
and saturating at numeric bounds instead of overflowing.SaturatingSquare and
SaturatingSquareAssign, traits for squaring a number and
saturating at numeric bounds instead of overflowing.SaturatingSub and
SaturatingSubAssign, traits for subtracting two numbers and
saturating at numeric bounds instead of overflowing.SaturatingSubMul and
SaturatingSubMulAssign, traits for subtracting a number by
the product of two numbers and saturating at numeric bounds instead of overflowing.ShlRound and ShlRoundAssign, traits for
multiplying a number by a power of 2 and rounding according to a specified
RoundingMode.ShrRound and ShrRoundAssign, traits for
dividing a number by a power of 2 and rounding according to a specified
RoundingMode.Traits for taking the square root of a number.
Square and SquareAssign, traits for squaring a
number.SubMul and SubMulAssign, traits for subtracting
the product of two numbers from a number.Various traits for performing arithmetic operations on numbers.
WrappingAbs and WrappingAbsAssign,
traits for computing the absolute value of a number and wrapping at the boundary of the type.WrappingAdd and WrappingAddAssign,
traits for adding two numbers and wrapping at the boundary of the type.WrappingAddMul and
WrappingAddMulAssign, traits for adding the product of two
numbers to a third and wrapping at the boundary of the type.WrappingDiv and WrappingDivAssign,
traits for dividing two numbers and wrapping at the boundary of the type.WrappingMul and WrappingMulAssign,
traits for multiplying two numbers and wrapping at the boundary of the type.WrappingNeg and WrappingNegAssign for
negating a number and wrapping at the boundary of the type.WrappingPow and WrappingPowAssign,
traits for raising a number to a power and wrapping at the boundary of the type.WrappingSquare and
WrappingSquareAssign, traits for squaring a number and wrapping
at the boundary of the type.WrappingSub and WrappingSubAssign,
traits for subtracting two numbers and wrapping at the boundary of the type.WrappingSubMul and
WrappingSubMulAssign, traits for subtracting a number by the
product of two other numbers and wrapping at the boundary of the type.XMulYToZZ, a trait for multiplying two numbers and returning the result
as a double-width number.XXAddYYToZZ, a trait for adding two double-width numbers and returning
the result as a double-width number.XXDivModYToQR, a trait for dividing a double-width number by a
single-width number and returning the quotient and remainder.XXSubYYToZZ, a trait for subtracting two double-width numbers and
returning the result as a double-width number.XXXAddYYYToZZZ, a trait for adding two triple-width numbers and
returning the result as a triple-width number.XXXSubYYYToZZZ, a trait for subtracting two triple-width numbers
and returning the result as a triple-width number.XXXXAddYYYYToZZZZ, a trait for adding two quadruple-width
numbers and returning the result as a quadruple-width number.