The Architectures of APS Learning Algorithms

The Symbols of Karva Notation
 
Below are listed of all the 70 built-in mathematical functions available in APS 3.0, starting with their representation in Karva and their definition:

Basic mathematical functions of two arguments:
  • +: addition
  • -: subtraction
  • *: multiplication
  • /: division
  • Mod: floating-point remainder
  • Pow: xy

Basic mathematical functions of one argument:

  • Sqrt: square root
  • Exp: ex
  • Pow10: 10x
  • Ln: natural logarithm
  • Log: logarithm base 10
  • Logi: logistic
  • Floor: floor
  • Ceil: ceiling
  • Abs: absolute value
  • Inv: 1/x
  • Nop: no operation
  • Neg: negation

Trigonometric functions (in radians):

  • Sin: sine
  • Cos: cosine
  • Tan: tangent
  • Csc: cosecant
  • Sec: secant
  • Cot: cotangent

Inverse trigonometric functions:

  • Asin: arcsine
  • Acos: arccosine
  • Atan: arctangent
  • Acsc: arccosecant
  • Asec: arcsecant
  • Acot: arccotangent

Hyperbolic functions:

  • Sinh: hyperbolic sine
  • Cosh: hyperbolic cosine
  • Tanh: hyperbolic tangent
  • Csch: hyperbolic cosecant
  • Sech: hyperbolic secant
  • Coth: hyperbolic cotangent

Inverse hyperbolic functions:

  • Asinh: inverse hyperbolic sine
  • Acosh: inverse hyperbolic cosine
  • Atanh: inverse hyperbolic tangent
  • Acsch: inverse hyperbolic cosecant
  • Asech: inverse hyperbolic secant
  • Acoth: inverse hyperbolic cotangent

Comparison 0/1 functions of two arguments:

  • OR1: if x < 0 OR y < 0, then 1; else 0
  • OR2: if x >= 0 OR y >= 0, then 1; else 0
  • AND1: if x < 0 AND y < 0, then 1; else 0
  • AND2: if x >= 0 AND y >= 0, then 1; else 0

Comparison IF THEN ELSE functions of two arguments (series A):

  • IFA1: if x < y, then x; else y
  • IFA2: if x > y, then x; else y
  • IFA3: if x <= y, then x; else y
  • IFA4: if x >= y, then x; else y
  • IFA5: if x = y, then x; else y
  • IFA6: if x != y, then x; else y

Comparison 0/1 IF THEN ELSE functions of two arguments (series B):

  • IFB1: if x < y, then 1; else 0
  • IFB2: if x > y, then 1; else 0
  • IFB3: if x <= y, then 1; else 0
  • IFB4: if x >= y, then 1; else 0
  • IFB5: if x = y, then 1; else 0
  • IFB6: if x != y, then 1; else 0

Comparison IF THEN ELSE functions of three arguments (series C):

  • IFC1: if x < 0, then y; else z
  • IFC2: if x > 0, then y; else z
  • IFC3: if x <= 0, then y; else z
  • IFC4: if x >= 0, then y; else z
  • IFC5: if x = 0, then y; else z
  • IFC6: if x != 0, then y; else z

Comparison IF THEN ELSE functions of four arguments (series D):

  • IFD1: if a < b, then c; else d
  • IFD2: if a > b, then c; else d
  • IFD3: if a <= b, then c; else d
  • IFD4: if a >= b, then c; else d
  • IFD5: if a = b, then c; else d
  • IFD6: if a != b, then c; else d

Dynamic UDFs are indexed and are represented by:

  • DDF0
  • DDF1
  • etc.

Static UDFs are also indexed and are represented by:

  • UDF0
  • UDF1
  • etc.
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