Module arithmetic

Traits for arithmetic.

Modules

abs

Abs, AbsAssign, and UnsignedAbs, traits for getting the absolute value of a number.

abs_diff

AbsDiff and AbsDiffAssign, traits for getting the absolute value of the difference between two numbers.

add_mul

AddMul and AddMulAssign, traits for adding a number and the product of two other numbers.

arithmetic_checked_shl

ArithmeticCheckedShl, a trait for left-shifting a number and checking whether the result is representable.

arithmetic_checked_shr

ArithmeticCheckedShr, a trait for right-shifting a number and checking whether the result is representable.

binomial_coefficient

Traits for computing the binomial coefficient of two numbers. There is a trait whose implementations panic if the result cannot be represented, and a checked trait whose implementations return None in that case: BinomialCoefficient and CheckedBinomialCoefficient.

ceiling

Ceiling and CeilingAssign, traits for computing the ceiling of a number.

checked_abs

CheckedAbs, a trait for computing the absolute value of number and checking whether the result is representable.

checked_add

CheckedAdd, a trait for adding two numbers and checking whether the result is representable.

checked_add_mul

CheckedAddMul, a trait for adding a number and the product of two other numbers, and checking whether the result is representable.

checked_div

CheckedDiv, a trait for dividing two numbers and checking whether the result is representable.

checked_mul

CheckedMul, a trait for multiplying two numbers and checking whether the result is representable.

checked_neg

CheckedNeg, a trait for negating a number and checking whether the result is representable.

checked_next_power_of_2

CheckedNextPowerOf2, a trait for getting the next-highest power of 2, if it’s representable.

checked_pow

CheckedPow, a trait for raising a number to the power of a u64 and checking whether the result is representable.

checked_square

CheckedSquare, a trait for squaring a number and checking whether the result is representable.

checked_sub

CheckedSub, a trait for subtracting two numbers and checking whether the result is representable.

checked_sub_mul

CheckedSubMul, a trait for subtracting the product of two numbers from another number, and checking whether the result is representable.

coprime_with

CoprimeWith, a trait for determining whether two numbers are coprime.

div_exact

DivExact and DivExactAssign, traits for dividing two numbers when it’s known that the division is exact.

div_mod

Traits for simultaneously finding the quotient and remainder of two numbers, subject to various rounding rules.

div_round

DivRound and DivExactAssign, traits for dividing two numbers according to a specified RoundingMode.

divisible_by

DivisibleBy, a trait for determining whether one number is divisible by another.

divisible_by_power_of_2

DivisibleByPowerOf2, a trait for determining whether a number is divisible by $2^k$.

eq_mod

EqMod, a trait for determining whether one number is equal by another modulo a third.

eq_mod_power_of_2

EqModPowerOf2, a trait for determining whether one number is equal to another modulo $2^k$.

extended_gcd

ExtendedGcd, a trait for computing the GCD (greatest common divisor) of two numbers as well as the coefficients of Bézout’s identity $ax+by=\gcd(a,b)$.

factorial

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

Floor and FloorAssign, traits for computing the floor of a number.

gcd

Gcd and GcdAssign, traits for computing the GCD (greatest common divisor) of two numbers.

is_power_of_2

IsPowerOf2, a trait for determining whether a number is an integer power of 2.

kronecker_symbol

LegendreSymbol, JacobiSymbol, and KroneckerSymbol, traits for computing the Legendre, Jacobi, and Kronecker symbols of two numbers.

lcm

Lcm, LcmAssign, and CheckedLcm, traits for computing the LCM (least common multiple) of two numbers.

log_base

Traits for taking the base-$b$ logarithm of a number.

log_base_2

Traits for taking the base-2 logarithm of a number.

log_base_power_of_2

Traits for taking the base-$2^k$ logarithm of a number.

mod_add

ModAdd and ModAddAssign, traits for adding two numbers modulo another number.

mod_inverse

ModInverse, a trait for finding the multiplicative inverse of a number modulo another number.

mod_is_reduced

ModIsReduced, a trait for checking whether a number is reduced modulo another number.

mod_mul

Traits for multiplying two numbers modulo another number.

mod_neg

ModNeg and ModNegAssign, traits for negating a number modulo another number.

mod_op

Traits for finding the remainder of two numbers, subject to various rounding rules.

mod_pow

Traits for raising a number to a power modulo another number.

mod_power_of_2

Traits for finding the remainder of a number divided by $2^k$, subject to various rounding rules.

mod_power_of_2_add

ModPowerOf2Add and ModPowerOf2AddAssign, traits for adding two numbers modulo $2^k$.

mod_power_of_2_inverse

ModPowerOf2Inverse, a trait for finding the multiplicative inverse of a number modulo $2^k$.

mod_power_of_2_is_reduced

ModPowerOf2IsReduced, a trait for checking whether a number is reduced modulo $2^k$.

mod_power_of_2_mul

ModPowerOf2Mul and ModPowerOf2MulAssign, traits for multiplying two numbers modulo $2^k$.

mod_power_of_2_neg

ModPowerOf2Neg and ModPowerOf2NegAssign, traits for negating a number modulo $2^k$.

mod_power_of_2_pow

ModPowerOf2Pow and ModPowerOf2PowAssign, traits for raising a number to a power modulo $2^k$.

mod_power_of_2_shl

ModPowerOf2Shl and ModPowerOf2ShlAssign, traits for left-shifting a number modulo $2^k$.

mod_power_of_2_shr

ModPowerOf2Shr and ModPowerOf2ShrAssign, traits for right-shifting a number modulo $2^k$.

mod_power_of_2_square

ModPowerOf2Square and ModPowerOf2SquareAssign, traits for squaring a number modulo $2^k$.

mod_power_of_2_sub

ModPowerOf2Sub and ModPowerOf2SubAssign, traits for subtracting one number by another modulo $2^k$.

mod_shl

ModShl and ModShlAssign, traits for left-shifting a number modulo another number.

mod_shr

ModShr and ModShrAssign, traits for right-shifting a number modulo another number.

mod_square

Traits for squaring a number modulo another number.

mod_sub

ModSub and ModSubAssign, traits for subtracting two numbers modulo another number.

neg

NegAssign, a trait for negating a number in place.

next_power_of_2

NextPowerOf2 and NextPowerOf2Assign, traits for getting the next-highest power of 2.

overflowing_abs

OverflowingAbs and OverflowingAbsAssign, traits for taking the absolute value of a number and returning a boolean indicating whether an overflow occurred.

overflowing_add

OverflowingAdd and OverflowingAddAssign, traits for adding two numbers and returning a boolean indicating whether an overflow occurred.

overflowing_add_mul

OverflowingAddMul and OverflowingAddMulAssign, traits for adding the product of two other numbers to a number and returning a boolean indicating whether an overflow occurred.

overflowing_div

OverflowingDiv and OverflowingDivAssign, traits for dividing two numbers and returning a boolean indicating whether an overflow occurred.

overflowing_mul

OverflowingMul and OverflowingMulAssign, traits for multiplying two numbers and returning a boolean indicating whether an overflow occurred.

overflowing_neg

OverflowingNeg and OverflowingNegAssign, traits for negating a number and returning a boolean indicating whether an overflow occurred.

overflowing_pow

OverflowingPow and OverflowingPowAssign, traits for raising a number to a power and returning a boolean indicating whether an overflow occurred.

overflowing_square

OverflowingSquare and OverflowingSquareAssign, traits for squaring a number and returning a boolean indicating whether an overflow occurred.

overflowing_sub

OverflowingSub and OverflowingSubAssign, traits for subtracting two numbers and returning a boolean indicating whether an overflow occurred.

overflowing_sub_mul

OverflowingSubMul and OverflowingSubMulAssign, traits for subtracting the product of two other numbers from a number and returning a boolean indicating whether an overflow occurred.

parity

Parity, a trait for determining whether a number is even or odd.

pow

Pow and PowAssign, traits for raising a number to a power.

power_of_2

PowerOf2, a trait for computing a power of 2.

primorial

Traits for computing the primorial and the product of the first $n$ primes. There is a trait whose implementations panic if the result cannot be represented, and a checked trait whose implementations return None in that case: Primorial and CheckedPrimorial.

reciprocal

Reciprocal and ReciprocalAssign, traits for computing the reciprocal (multiplicative inverse) of a number.

root

Traits for taking the $n$th root of a number.

rotate

RotateLeft, RotateLeftAssign, RotateRight, and RotateRightAssign, traits for rotating a number’s bits.

round_to_multiple

RoundToMultiple and RoundToMultipleAssign, traits for rounding a number to a multiple of another number.

round_to_multiple_of_power_of_2

RoundToMultipleOfPowerOf2 and RoundToMultipleOfPowerOf2Assign, traits for rounding a number to a multiple of a power of 2.

saturating_abs

SaturatingAbs and SaturatingAbsAssign, traits for taking the absolute value of a number and saturating at numeric bounds instead of overflowing.

saturating_add

SaturatingAdd and SaturatingAddAssign, traits for adding two numbers and saturating at numeric bounds instead of overflowing.

saturating_add_mul

SaturatingAddMul and SaturatingAddMulAssign, traits for adding the product of two numbers to a number and saturating at numeric bounds instead of overflowing.

saturating_mul

SaturatingMul and SaturatingMulAssign, traits for multiplying two numbers and saturating at numeric bounds instead of overflowing.

saturating_neg

SaturatingNeg and SaturatingNegAssign, traits for negating a number and saturating at numeric bounds instead of overflowing.

saturating_pow

SaturatingPow and SaturatingPowAssign, traits for raising a number to a power and saturating at numeric bounds instead of overflowing.

saturating_square

SaturatingSquare and SaturatingSquareAssign, traits for squaring a number and saturating at numeric bounds instead of overflowing.

saturating_sub

SaturatingSub and SaturatingSubAssign, traits for subtracting two numbers and saturating at numeric bounds instead of overflowing.

saturating_sub_mul

SaturatingSubMul and SaturatingSubMulAssign, traits for subtracting a number by the product of two numbers and saturating at numeric bounds instead of overflowing.

shl_round

ShlRound and ShlRoundAssign, traits for multiplying a number by a power of 2 and rounding according to a specified RoundingMode.

shr_round

ShrRound and ShrRoundAssign, traits for dividing a number by a power of 2 and rounding according to a specified RoundingMode.

sign

Sign, a trait for determining the sign of a number.

sqrt

Traits for taking the square root of a number.

square

Square and SquareAssign, traits for squaring a number.

sub_mul

SubMul and SubMulAssign, traits for subtracting the product of two numbers from a number.

traits

Various traits for performing arithmetic operations on numbers.

wrapping_abs

WrappingAbs and WrappingAbsAssign, traits for computing the absolute value of a number and wrapping at the boundary of the type.

wrapping_add

WrappingAdd and WrappingAddAssign, traits for adding two numbers and wrapping at the boundary of the type.

wrapping_add_mul

WrappingAddMul and WrappingAddMulAssign, traits for adding the product of two numbers to a third and wrapping at the boundary of the type.

wrapping_div

WrappingDiv and WrappingDivAssign, traits for dividing two numbers and wrapping at the boundary of the type.

wrapping_mul

WrappingMul and WrappingMulAssign, traits for multiplying two numbers and wrapping at the boundary of the type.

wrapping_neg

WrappingNeg and WrappingNegAssign for negating a number and wrapping at the boundary of the type.

wrapping_pow

WrappingPow and WrappingPowAssign, traits for raising a number to a power and wrapping at the boundary of the type.

wrapping_square

WrappingSquare and WrappingSquareAssign, traits for squaring a number and wrapping at the boundary of the type.

wrapping_sub

WrappingSub and WrappingSubAssign, traits for subtracting two numbers and wrapping at the boundary of the type.

wrapping_sub_mul

WrappingSubMul and WrappingSubMulAssign, traits for subtracting a number by the product of two other numbers and wrapping at the boundary of the type.

x_mul_y_to_zz

XMulYToZZ, a trait for multiplying two numbers and returning the result as a double-width number.

xx_add_yy_to_zz

XXAddYYToZZ, a trait for adding two double-width numbers and returning the result as a double-width number.

xx_div_mod_y_to_qr

XXDivModYToQR, a trait for dividing a double-width number by a single-width number and returning the quotient and remainder.

xx_sub_yy_to_zz

XXSubYYToZZ, a trait for subtracting two double-width numbers and returning the result as a double-width number.

xxx_add_yyy_to_zzz

XXXAddYYYToZZZ, a trait for adding two triple-width numbers and returning the result as a triple-width number.

xxx_sub_yyy_to_zzz

XXXSubYYYToZZZ, a trait for subtracting two triple-width numbers and returning the result as a triple-width number.

xxxx_add_yyyy_to_zzzz

XXXXAddYYYYToZZZZ, a trait for adding two quadruple-width numbers and returning the result as a quadruple-width number.