Mathematical Functions¶

High-performance mathematical operations and transcendental functions.

A¶

• function compiletime::abs(T) Compile-time absolute value.
• function acos(const T1 &) Returns the arc cosine of x. The returned angle is in the range 0 through \(\pi\) .
• function asin(const T1 &) Returns the arc sine of x. The returned angle is in the range \(-\pi/2\) through \(\pi/2\) .
• function atan2(const T1 &, const T2 &) Returns the arc tangent of y/x using the signs of both arguments to determine the correct quadrant. The result is in the range \([-\pi, \pi]\) .
• function atan2deg(const T1 &, const T2 &) Returns the arc tangent of y/x (expressed in degrees) using the signs of both arguments to determine the correct quadrant. The result is in the range [-180, 180].
• function atan(const T1 &) Returns the arc tangent of x. The returned angle is in the range \(-\pi/2\) through \(\pi/2\) .
• function atandeg(const T1 &) Returns the arc tangent of x, expressed in degrees. The returned angle is in the range -90 through 90.

C¶

• function cabs(const T1 &) Returns the absolute value (magnitude) of the complex number x
• function cabssqr(const T1 &) Returns the squared absolute value (magnitude squared) of the complex number x
• function carg(const T1 &) Returns the phase angle (argument) of the complex number x
• function cartesian(const T1 &) Converts a complex number from polar to cartesian representation
• function catmullrom(M, T, T, T, T) Catmull-Rom spline interpolation.
• function cbrt(const T1 &) Returns the cube root of x.
• function ccos(const T1 &) Returns the cosine of the complex number x
• function ccosh(const T1 &) Returns the hyperbolic cosine of the complex number x
• function cexp10(const T1 &) Returns 10 raised to the complex number x
• function cexp2(const T1 &) Returns 2 raised to the complex number x
• function cexp(const T1 &) Returns e raised to the complex number x
• function clog10(const T1 &) Returns the common (base-10) logarithm of the complex number x
• function clog2(const T1 &) Returns the binary (base-2) logarithm of the complex number x
• function clog(const T1 &) Returns the natural logarithm of the complex number x
• function cos2x(const T &, const T &) Returns cos(2x) from already computed sin(x) and cos(x).
• function cos3x(const T &, const T &) Returns cos(3x) from already computed sin(x) and cos(x).
• function cos(const T1 &) Returns the trigonometric cosine of x, evaluated in radians.
• function cosdeg(const T1 &) Returns the trigonometric cosine of the angle expressed in degrees.
• function cosh(const T1 &) Returns the hyperbolic cosine of x.
• function coshsinh(const T1 &) Computes cosh and sinh of x in a single pass and interleaves the results.
• function cosine(M, T, T) Cosine interpolation.
• function cossin(const T1 &) Returns the trigonometric cosine of the even elements of x and sine of the odd elements.
• function cossindeg(const T1 &) Returns the trigonometric cosine of the even elements and sine of the odd elements of x, where x is a vector of angles expressed in degrees.
• function compiletime::cos(T) Compile-time cosine, derived from sin .
• function coth(const T1 &) Returns the hyperbolic cotangent of x.
• function csin(const T1 &) Returns the sine of the complex number x
• function csinh(const T1 &) Returns the hyperbolic sine of the complex number x
• function csqr(const T1 &) Returns square of the complex number x
• function csqrt(const T1 &) Returns square root of the complex number x
• function cubic(M, T, T, T, T) Cubic interpolation.

E¶

• function exp10(const T1 &) Returns 10 raised to the given power x.
• function exp2(const T1 &) Returns 2 raised to the given power x.
• function exp_fmadd(const T1 &, const T2 &, const T3 &) Returns exp(x * m + a).
• function exp(const T1 &) Returns e raised to the given power x.

F¶

• function factorial_approx(const T1 &) Returns the approximate factorial of an argument.
• variable factorial_table Lookup table of exact factorial values for 0 <= n <= 20.
• function factorial(int) Returns the exact factorial of an argument.
• function fastcos(const T1 &) Returns a fast (lower-precision) approximation of the trigonometric cosine of x.
• function fastcosdeg(const T1 &) Returns a fast (lower-precision) approximation of the trigonometric cosine of the angle expressed in degrees.
• function fastsin(const T1 &) Returns a fast (lower-precision) approximation of the trigonometric sine of x.
• function fastsindeg(const T1 &) Returns a fast (lower-precision) approximation of the trigonometric sine of the angle expressed in degrees.

G¶

• function gamma(const T1 &) Returns the approximate gamma function of an argument.

L¶

• function linear(M, T, T) Linear interpolation.
• function log10(const T1 &) Returns the common (base-10) logarithm of x.
• function log2(const T1 &) Returns the binary (base-2) logarithm of x.
• function log_fmadd(const T1 &, const T2 &, const T3 &) Returns log(x) * m + a.
• function logb(const T1 &) Returns the unbiased exponent of x as a floating-point value (equivalent to std::logb).
• function log(const T1 &) Returns the natural logarithm of x.
• function logm(const T1 &, const T2 &) Returns log(x) * m.
• function logn(const T1 &, const T2 &) Returns the logarithm of x with base y.

M¶

• function modzerobessel(const T1 &) Computes the modified zeroth-order Bessel function of the first kind. This function calculates I₀(x), the modified Bessel function of the first kind with order zero, for the given input value.
• function compiletime::mulsign(T, T) Compile-time multiplication by sign of a second value.

N¶

• function nearest(M, T, T) Nearest-neighbor interpolation.

P¶

• function polar(const T1 &) Converts a complex number to its polar representation (magnitude, phase)
• function pow(const T1 &, const T2 &) Returns x raised to the given power y.

R¶

• function root(const T1 &, const T2 &) Returns the real y-th root of x.

S¶

• function compiletime::select(bool, T, T) Compile-time conditional select between two values.
• function sin2x(const T &, const T &) Returns sin(2x) from already computed sin(x) and cos(x).
• function sin3x(const T &, const T &) Returns sin(3x) from already computed sin(x) and cos(x).
• function sinc(const T1 &) Returns the (normalized) sinc function of x.
• function sin(const T1 &) Returns the trigonometric sine of x, evaluated in radians.
• function sincos(const T1 &) Returns the trigonometric sine of the even elements of x and cosine of the odd elements.
• function sincosdeg(const T1 &) Returns the trigonometric sine of the even elements and cosine of the odd elements of x, where x is a vector of angles expressed in degrees.
• function sindeg(const T1 &) Returns the trigonometric sine of the angle expressed in degrees.
• function sinh(const T1 &) Returns the hyperbolic sine of x.
• function sinhcosh(const T1 &) Computes sinh and cosh of x in a single pass and interleaves the results.
• function compiletime::sin(T) Compile-time sine, accurate to better than 1e-4.
• function sqrt(const T1 &) Returns the positive square root of x. \(\sqrt{x}\)

T¶

• function tan(const T1 &) Computes the tangent of the input (in radians).
• function tandeg(const T1 &) Computes the tangent of the input (in degrees).
• function tanh(const T1 &) Returns the hyperbolic tangent of x.
• function compiletime::trunc(T) Compile-time truncation toward zero.