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. |
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