Microsoft.Quantum.Math namespace

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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.