Std.Math
The Std.Math namespace contains the following functions and operations:
| Name | Description |
|---|---|
| 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 a large 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 approximate binomial coefficient of two integers. |
| BitSizeI | For a non-negative integer a, returns the number of bits required to represent a. NOTE: This function returns the smallest n such that a < 2^n. |
| BitSizeL | For a non-negative integer a, returns the number of bits required to represent a. NOTE: This function returns the smallest n such that a < 2^n. |
| Ceiling | Returns the smallest integer greater than or equal to the specified number. For example: Ceiling(3.1) = 4; Ceiling(-3.7) = -3 |
| 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. The polar representation of a complex number is c = rโ ๐^(t๐). |
| ContinuedFractionConvergentI | Finds the continued fraction convergent closest to fraction with the denominator less or equal to denominatorBound Using process similar to this: https://nrich.maths.org/1397 |
| ContinuedFractionConvergentL | Finds the continued fraction convergent closest to fraction with the denominator less or equal to denominatorBound Using process similar to this: https://nrich.maths.org/1397 |
| Cos | Returns the cosine of the specified angle. |
| Cosh | Returns the hyperbolic cosine of the specified angle. |
| DividedByC | Returns the quotient of two inputs of type Complex. |
| DividedByCP | Returns the quotient of two inputs of type ComplexPolar. |
| DivRemI | Divides one Integer value by another, returns the result and the remainder as a tuple. |
| DivRemL | Divides one BigInteger value by another, returns the result and the remainder as a tuple. |
| E | Returns a double-precision approximation of the mathematical constant ๐ โ 2.7182818284590452354 |
| ExpModI | Returns an integer raised to a given power, with respect to a given modulus. I.e. (expBase^power) % modulus. |
| ExpModL | Returns an integer raised to a given power, with respect to a given modulus. I.e. (expBase^power) % modulus. |
| ExtendedGreatestCommonDivisorI | Returns a tuple (u,v) such that ua+vb=GCD(a,b) Note: GCD is always positive except that GCD(0,0)=0. |
| ExtendedGreatestCommonDivisorL | Returns a tuple (u,v) such that ua+vb=GCD(a,b) Note: GCD is always positive except that GCD(0,0)=0. |
| FactorialI | Returns the factorial of a given number. |
| FactorialL | Returns the factorial of a given number. |
| Floor | Returns the largest integer less than or equal to the specified number. For example: Floor(3.7) = 3; Floor(-3.1) = -4 |
| GreatestCommonDivisorI | Computes the greatest common divisor of two integers. Note: GCD is always positive except that GCD(0,0)=0. |
| GreatestCommonDivisorL | Computes the greatest common divisor of two integers. Note: GCD is always positive except that GCD(0,0)=0. |
| HammingWeightI | Returns the number of 1 bits in the binary representation of integer n. |
| InverseModI | Returns the multiplicative inverse of a modular integer. |
| InverseModL | Returns the multiplicative inverse of a modular integer. |
| IsCoprimeI | Returns if two integers are co-prime. |
| IsCoprimeL | Returns if two integers are co-prime. |
| 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 a double-precision approximation of the constant ใ2 โ 0.6931471805599453 |
| 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 of type Complex. |
| MinusCP | Returns the difference between two inputs of type ComplexPolar. |
| ModulusI | Computes the canonical residue of value modulo modulus. The result is always in the range 0..modulus-1 even for negative numbers. |
| ModulusL | Computes the canonical residue of value modulo modulus. The result is always in the range 0..modulus-1 even for negative numbers. |
| NegationC | Returns the unary negation of an input of type Complex. |
| NegationCP | Returns the unary negation of an input of type ComplexPolar |
| PI | Returns a double-precision approximation of the matematical constant ๐ โ 3.14159265358979323846 |
| PlusC | Returns the sum of two inputs of type Complex. |
| PlusCP | Returns the sum of two inputs of type ComplexPolar. |
| PNorm | Returns the L(p) norm of a vector of Doubles. That is, given an array x of type Double[], this returns the p-norm $|xฬ|โ$= (โ(xแตข)แต)ยนแแต. |
| PNormalized | Normalizes a vector of Doubles in the L(p) norm. That is, given an array x of type Double[], this returns an array where all elements are divided by the p-norm $|xฬ|โ$. Function leaves array with norm 0 unchanged. |
| PowC | Returns a number raised to a given power of type Complex. Note that this is a multi-valued function, but only one value is returned. |
| PowCP | Returns a number raised to a given power of type ComplexPolar. Note that this is a multi-valued function, but only one value is returned. |
| RealMod | Computes the modulus between two real numbers. |
| Round | Returns the nearest integer to the specified number. For example: Round(3.7) = 4; Round(-3.7) = -4 |
| SignD | Returns -1, 0 or +1 that indicates the sign of a number. |
| SignI | Returns -1, 0 or +1 that indicates the sign of a number. |
| SignL | Returns -1, 0 or +1 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 of type Complex. |
| TimesCP | Returns the product of two inputs of type ComplexPolar. |
| TrailingZeroCountI | For a non-zero integer a, returns the number of trailing zero bits in the binary representation of a. |
| TrailingZeroCountL | For a non-zero integer a, returns the number of trailing zero bits in the binary representation of a. |
| Truncate | Returns the integral part of a number. For example: Truncate(3.7) = 3; Truncate(-3.7) = -3 |