Algebraic and Transcendental Functions

Algebraic functions

Function	Description
sq(x)	$x^2$
sqrt(x)	$\sqrt{x}$
qb(x)	$x³$
qbrt(x)	$\sqrt[3]{x}$

Polynomial "poly" (Horner scheme)

The poly() function can be used to efficiently calculate a polynomial by applying the Horner scheme. In the implementation, the explicit exponentiation of $x$ is avoided by the clever bracketing of terms.

$$p(x) = a_N \cdot x^n + ... + a_1 \cdot x + a_0 = ((a_N \cdot x + a_{N-1}) \cdot x ... + a_1) \cdot x + a_0$$

px1 = poly(x, an, ...a1, a0);
A_Coef = [an, ...a1, a0];
px2 = poly(x, A_Coef);

In the second form, the coefficients $a_N ... a_0$ are passed as a vector.

Transcendent functions

Function	Description
log(x)	$log_{10}(x)$, logarithm of x to the base 10
lg2(x)	$log_{2}(x)$, logarithm of x to the base 2
ln(x)	$ln(x)$, natural logarithm
ln1p(x)	$ln(1 + x)$, (better resolution for x close to 0)
pow(x,y) x^y	$x^y$, exponentiation of x with y
exp10(x)	$10^x$, exponentiation of 10 with x
exp2(x)	$2^x$, exponentiation of 2 with x
exp(x)	$e^x$, exponentiation of the Euler constant e with x
expm1(x)	$e^x - 1$, (better resolution for x near 0)

Trigonometric and arc functions

All angle arguments must be passed in radians. Accordingly, angles are also returned in radians

Function	Description
sin(x)	sine of x
cos(x)	cosine of x
tan(x)	tangent of x
asin(x)	arc sine of x
acos(x)	arc cosine of x
atan(x)	arc tangent of x
atanYX(y,x)	Inverse tangent of anticathete y and anticathete x Function also ensured for x = 0 Correct result for all quadrants in the range $[-\pi, \pi]$

Angle conversion

Function	Description
rad2deg(x)	Conversion of the angle x from radians to degrees
deg2rad(x)	Conversion of the angle x from radians to radians

Hyperbolic and area functions

Function	Description
sinh(x)	hyperbolic sine of x
cosh(x)	Cosine hyperbolic of x
tanh(x)	hyperbolic tangent of x
asinh(x)	area sine hyperbolic of x
acosh(x)	area-cosine hyperbolic of x
atanh(x)	area-tangent hyperbolic of x