Microsoft.Quantum.Math namespace

This namespace contains classical mathematical functions and data types.

Description

A lot of functions in this namespace offer the same functionality as the arithmetic expressions.

Operations

Name	Summary
RandomInt	> [!WARNING]
RandomIntPow2	> [!WARNING]
RandomReal	> [!WARNING]
RandomSingleQubitPauli	> [!WARNING]

Functions

Name	Summary
AbsComplex	Returns the absolute value of a complex number of type Complex.
AbsComplexPolar	Returns the absolute value of a complex number of type ComplexPolar.
AbsD	Returns the absolute value of a double-precision floating-point number.
AbsI	Returns the absolute value of an integer.
AbsL	Returns the absolute value of an integer.
AbsSquaredComplex	Returns the squared absolute value of a complex number of type Complex.
AbsSquaredComplexPolar	Returns the squared absolute value of a complex number of type ComplexPolar.
ApproximateFactorial	Returns an approximate factorial of a given number.
ArcCos	Returns the angle whose cosine is the specified number.
ArcCosh	Computes the inverse hyperbolic cosine of a number.
ArcSin	Returns the angle whose sine is the specified number.
ArcSinh	Computes the inverse hyperbolic sine of a number.
ArcTan	Returns the angle whose tangent is the specified number.
ArcTan2	Returns the angle whose tangent is the quotient of two specified numbers.
ArcTanh	Computes the inverse hyperbolic tangent of a number.
ArgComplex	Returns the phase of a complex number of type Complex.
ArgComplexPolar	Returns the phase of a complex number of type ComplexPolar.
Binom	Returns the binomial coefficient of two integers.
BitSizeI	For a non-negative integer a, returns the number of bits required to represent a.
BitSizeL	For a non-negative integer a, returns the number of bits required to represent a.
Ceiling	Returns the smallest integer greater than or equal to the specified number.
ComplexAsComplexPolar	Converts a complex number of type Complex to a complex number of type ComplexPolar.
ComplexPolarAsComplex	Converts a complex number of type ComplexPolar to a complex number of type Complex.
ContinuedFractionConvergentI	Finds the continued fraction convergent closest to fraction with the denominator less or equal to denominatorBound
ContinuedFractionConvergentL	Finds the continued fraction convergent closest to fraction with the denominator less or equal to denominatorBound
Cos	Returns the cosine of the specified angle.
Cosh	Returns the hyperbolic cosine of the specified angle.
DivRemL	Divides one BigInteger value by another, returns the result and the remainder as a tuple.
DividedByC	Returns the quotient of two inputs.
DividedByCP	Returns the quotient of two inputs.
DividedByD	Returns the quotient of two inputs.
DividedByI	Returns the quotient of two inputs.
DividedByL	Returns the quotient of two inputs.
E	Returns the natural logarithmic base to double-precision.
ExpD	Returns the natural logarithmic base raised to a specified power.
ExpModI	Returns an integer raised to a given power, with respect to a given modulus.
ExpModL	Returns an integer raised to a given power, with respect to a given modulus.
ExtendedGreatestCommonDivisorI	Returns the GCD of two integers, decomposed into a linear combination.
ExtendedGreatestCommonDivisorL	Returns the GCD of two integers, decomposed into a linear combination.
FactorialI	Returns the factorial of a given number.
FactorialL	Returns the factorial of a given integer.
Floor	Returns the smallest integer greater than or equal to the specified number.
GreatestCommonDivisorI	Computes the greatest common divisor of two integers.
GreatestCommonDivisorL	Computes the greatest common divisor of two integers.
HalfIntegerBinom	Returns a binomial coefficient of the form "½-choose-k."
IEEERemainder	Returns the remainder resulting from the division of a specified number by another specified number.
InverseModI	Returns the multiplicative inverse of a modular integer.
InverseModL	Returns $b$ such that $a \cdot b = 1 (\operatorname{mod} \texttt{modulus})$.
IsCoprimeI	Returns if two integers are co-prime.
IsCoprimeL	Returns if two integers are co-prime.
IsFinite	Returns whether a given floating-point value is a finite number.
IsInfinite	Returns whether a given floating-point value is either positive or negative infinity.
IsNaN	Returns whether a given floating-point value is not a number (i.e. is NaN).
LargestFixedPoint	Returns the largest representable number for specific fixed point dimensions.
Lg	Computes the base-2 logarithm of a number.
Log	Returns the natural (base $e$) logarithm of a specified number.
Log10	Returns the base-10 logarithm of a specified number.
LogFactorialD	Returns the approximate natural logarithm of the factorial of a given integer.
LogGammaD	Returns the natural logarithm of the gamma function (aka the log-gamma function).
LogOf2	Returns the natural logarithm of 2.
Max	Given an array of integers, returns the largest element.
MaxD	Returns the larger of two specified numbers.
MaxI	Returns the larger of two specified numbers.
MaxL	Returns the larger of two specified numbers.
Min	Given an array of integers, returns the smallest element.
MinD	Returns the smaller of two specified numbers.
MinI	Returns the smaller of two specified numbers.
MinL	Returns the smaller of two specified numbers.
MinusC	Returns the difference between two inputs.
MinusCP	Returns the difference between two inputs.
MinusD	Returns the difference between two inputs.
MinusI	Returns the difference between two inputs.
MinusL	Returns the difference between two inputs.
ModI	Returns the modulus of a number with respect to another number.
ModL	Returns the modulus of a number with respect to another number.
ModPowL	Performs modular division on a number raised to the power of another number.
ModulusI	Computes the canonical residue of value modulo modulus.
ModulusL	Computes the canonical residue of value modulo modulus.
NaN	Returns a value that is not a number (i.e. NaN).
NegationC	Returns the unary negation of an input.
NegationCP	Returns the unary negation of an input.
NegationD	Returns the unary negation of an input.
NegationI	Returns the unary negation of an input.
NegationL	Returns the unary negation of an input.
PI	Represents the ratio of the circumference of a circle to its diameter.
PNorm	Returns the p-norm of a vector of real numbers.
PNormalized	Normalizes a vector of real numbers according to the p-norm for a given p.
PlusA	Returns the sum (concatenation) of two inputs.
PlusC	Returns the sum of two inputs.
PlusCP	Returns the sum of two inputs.
PlusD	Returns the sum of two inputs.
PlusI	Returns the sum of two inputs.
PlusL	Returns the sum of two inputs.
PowC	Returns a number raised to a given power.
PowCP	Returns a number raised to a given power.
PowD	Returns the number x raised to the power y.
PowI	Returns a number raised to a given power.
PowL	Returns a number raised to a given power.
RealMod	Computes the modulus between two real numbers.
Round	Returns the nearest integer to the specified number.
SignD	Returns an integer that indicates the sign of a number.
SignI	Returns an integer that indicates the sign of a number.
SignL	Returns an integer that indicates the sign of a number.
Sin	Returns the sine of the specified angle.
Sinh	Returns the hyperbolic sine of the specified angle.
SmallestFixedPoint	Returns the smallest representable number for specific fixed point dimensions.
Sqrt	Returns the square root of a specified number.
SquaredNorm	Returns the squared 2-norm of a vector.
Tan	Returns the tangent of the specified angle.
Tanh	Returns the hyperbolic tangent of the specified angle.
TimesC	Returns the product of two inputs.
TimesCP	Returns the product of two inputs.
TimesD	Returns the product of two inputs.
TimesI	Returns the product of two inputs.
TimesL	Returns the product of two inputs.
Truncate	Returns the integral part of a number.
_ContinuedFractionConvergentI	Internal recursive call to calculate the GCD with a bound
_ContinuedFractionConvergentL	Internal recursive call to calculate the GCD with a bound
_ExtendedGreatestCommonDivisorI	Internal recursive call to calculate the GCD.
_ExtendedGreatestCommonDivisorL	Internal recursive call to calculate the GCD.

User-defined types

Name	Summary
BigFraction	Represents a rational number of the form p/q. Integer p is the first element of the tuple and q is the second element of the tuple.
Complex	Represents a complex number by its real and imaginary components. The first element of the tuple is the real component, the second one - the imaginary component.
ComplexPolar	Represents a complex number in polar form.
Fraction	Represents a rational number of the form p/q. Integer p is the first element of the tuple and q is the second element of the tuple.