# Scientific calculator functions

CE
Clear Entry - clear the command line.

AC
Clear All - clear display and memory.

### Mathematical constant

pi
mathematical constant π = 3.14...

e
Euler's number e = 2.71828...

### Exponents and Logarithms

sqrt (x)
Compute the square root of x. x must be positive.

cbrt (x)
Compute the real cube root of x. x must be positive.

nthrt (x, n)
Compute the real (non-complex) n-th root of x. x must be positive.

x^2
raise x to power 2.

x^3
raise x to power 3.

x^Y
raise x to power Y.

ln (x)
Compute the natural logarithm of x.

log (x)
Compute the base-10 logarithm of x.

exp (x)
Compute e^x of x.

### Trigonometry

deg (x)
Convert radians of x to degrees.

Convert degrees of x to radians.

sin (x)
Compute the sine of x.

cos (x)
Compute the cosine of x.

tan (x)
Compute the tangent of x.

asin (x)
Compute the inverse sine of x.

acos (x)
Compute the inverse cosine of x.

atan (x)
Compute the inverse tangent of x.

cot (x)
Compute the cotangent of x.

acot (x)
Compute the inverse cotangent of x.

sec (x)
Compute the secant of x.

asec (x)
Compute the inverse secant of x.

sinc (x)
Compute the normalized sinc function of x. sinc (x) = sin (π * x) / π * x.

si (x)
Compute the unnormalized sinc function of x. si (x) = sin (x) / x.

atan2 (y, x)
Returns the angle whose tangent is the quotient of y and x.
This function is equivalent to arg complex (x, y).

### Hyperbolic Functions

sinh (x)
Compute the hyperbolic sine of x.

asinh (x)
Compute the inverse hyperbolic sine of x.

sech (x)
Compute the hyperbolic secant of x.

asech (x)
Compute the inverse hyperbolic secant of x.

csch (x)
Compute the hyperbolic cosecant of x.

acsch (x)
Compute the inverse hyperbolic cosecant of x.

cosh (x)
Compute the hyperbolic cosine of x.

acosh (x)
Compute the inverse hyperbolic cosine of x.

coth (x)
Compute the hyperbolic cotangent of x.

acoth (x)
Compute the inverse hyperbolic cotangent of x.

tanh (x)
Compute hyperbolic tangent of x.

atanh (x)
Compute the inverse hyperbolic tangent of x.

### Algebra Functions

abs (x)
Returns the absolute value of x.
div (x, n)
Returns the quotient of the integer division x / n.
mod (x, n)
Returns the remainder of dividing two integers. Floating point numbers will be rounded to integer before computation.
rem (x, n)
Returns the IEEE-remainder of dividing two specified numbers.
gcd (a, b)
Returns the greatest common divisor of the integers a and b.
lcm (a, b)
Returns the least common multiple of the integers a and b.
hypot (a, ..., n)

Computes the square root of the sum of the squares of a number serie.

$$\displaystyle h=\sqrt{a^2+b^2+...n^2}$$

### Bit calculation

The bits of a binary number are numbered by LSB 0 (least significant bit). This means that the least significant bit is 0.

bitand (a, b)
Logical AND operation of all bits of two integers.
bitor (a, b)
Logical OR operation of all bits of two integers.
bitxor (a, b)
Logical exclusive OR combination of all bits of two integers.
bitcmp (a, n)
Inversion of the bits of the integer a. The number of bits involved is specified in n.
bitset (a, n)
Sets a bit of the integer a to 1. n is the number of the bit (LSB 0).
bitclr (a, n)
Sets a bit of the integer a to 0. n is the number of the bit (LSB 0).
bitshl (a, n)
Shifts the bits of the integers a to the left. n is the number of shifted digits.
bitshr (a, n)
Shifts the bits of the integers a to the right. n is the number of shifted digits.
bitget (a, n)
Return the bit value at position n of the unsigned integers in a.

### Combinatorics

ncr (n, k)
Returns the number of possible combinations that can be obtained by taking a sample (k) of items from a larger set (n) without repetition.
npr (n, k)
Returns the number of possible variations k from the total n without repetition.

### Special Functions

sig (x)

Compute the sigmoid function. A sigmoid function, or S-function, is a mathematical function with an S-shaped graph.

$$\displaystyle sig(x)=\frac{1}{1+e^{-x}}=\frac{e^x}{1+e^x}$$

dsig (x)

Compute the derivative of the sigmoid function.

$$\displaystyle dsig(x)=1-sig(x)= 1-\frac{1}{1+e^{-x}}$$

logit (y)

Compute logit, the inverse function of the logistic sigmoid function.

$$\displaystyle sig^{-1}(y)= -ln\left(\frac{1}{y}-1\right) = ln\left(\frac{y}{1-y}\right)$$

softsign (x)

Compute softsign function. The function is used in the activation function of the neural network.

$$\displaystyle softsign (x)= \frac{x}{1+|x|}$$

### Utilities

ceil (a)
Return the smallest integer not less than x. This is equivalent to rounding towards positive infinity.
floor (a)
Return the largest integer not greater than x. This is equivalent to rounding towards negative infinity.
round (a)
Return the integer nearest to x.
roundb (a)
Return the integer nearest to x. If there are two nearest integers, return the even one (banker’s rounding).
trunc (a)
Truncate fractional portion of x and return the integer portion. This is equivalent to rounding towards zero.