The Architectures of GeneXproTools Learning Algorithms

Built-in Mathematical Functions
 
Below are listed all the 279 built-in mathematical functions available in GeneXproTools 4.0, starting with their representation in Karva Notation and their mathematical definition (for more details about their implementations, see the built-in grammars of GeneXproTools):

Basic arithmetic functions:

  • +: addition
  • -: subtraction
  • *: multiplication
  • /: division
  • Add3: addition with 3 inputs
  • Sub3: subtraction with 3 inputs
  • Mul3: multiplication with 3 inputs
  • Div3: division with 3 inputs
  • Add4: addition with 4 inputs
  • Sub4: subtraction with 4 inputs
  • Mul4: multiplication with 4 inputs
  • Div4: division with 4 inputs

Logarithmic functions:

  • Ln: natural logarithm
  • Log: logarithm of base 10
  • Log2: logarithm(x,y)

Exponential and power functions:

  • Sqrt: square root
  • Exp: exponential
  • Pow: power
  • Pow10: 10x
  • X2: x2
  • X3: x3
  • X4: x4
  • X5: x5
  • 3Rt: cube root
  • 4Rt: quartic root
  • 5Rt: quintic root
  • Logi: logistic(x)
  • Logi2: logistic(x,y)
  • Logi3: logistic(x,y,z)
  • Logi4: logistic(a,b,c,d)
  • Gau: Gaussian(x)
  • Gau2: Gaussian(x,y)
  • Gau3: Gaussian(x,y,z)
  • Gau4: Gaussian(a,b,c,d)

Rounding and other simple functions:

  • Floor: floor
  • Ceil: ceiling
  • Mod: floating-point remainder
  • Abs: absolute value
  • Inv: inverse
  • Neg: negation
  • NOT: complement
  • Nop: no operation

Minimum, maximum, and average functions:

  • Min2: minimum of 2 inputs
  • Min3: minimum of 3 inputs
  • Min4: minimum of 4 inputs
  • Max2: maximum of 2 inputs
  • Max3: maximum of 3 inputs
  • Max4: maximum of 4 inputs
  • Avg2: average of 2 inputs
  • Avg3: average of 3 inputs
  • Avg4: average of 4 inputs

Constant functions:

  • Zero: constant zero function
  • One: constant one function
  • Zero2: 0(x,y)
  • One2: 1(x,y)
  • Pi: number p 
  • E: Euler's number

Trigonometric functions (x is 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 (OR series):

  • OR1: if x < 0 OR y < 0, then 1, else 0
  • OR2: if x >= 0 OR y >= 0, then 1, else 0
  • OR3: if x <= 0 OR y <= 0, then 1, else 0
  • OR4: if x < 1 OR y < 1, then 1, else 0
  • OR5: if x >= 1 OR y >= 1, then 1, else 0
  • OR6: if x <= 1 OR y <= 1, then 1, else 0

Comparison 0/1 functions of two arguments (AND series):

  • AND1: if x < 0 AND y < 0, then 1, else 0
  • AND2: if x >= 0 AND y >= 0, then 1, else 0
  • AND3: if x <= 0 AND y <= 0, then 1, else 0
  • AND4: if x < 1 AND y < 1, then 1, else 0
  • AND5: if x >= 1 AND y >= 1, then 1, else 0
  • AND6: if x <= 1 AND y <= 1, then 1, else 0

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

  • LT2A: if x < y, then x, else y
  • GT2A: if x > y, then x, else y
  • LOE2A: if x <= y, then x, else y
  • GOE2A: if x >= y, then x, else y
  • ET2A: if x = y, then x, else y
  • NET2A: if x != y, then x, else y

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

  • LT2B: if x < y, then 1, else 0
  • GT2B: if x > y, then 1, else 0
  • LOE2B: if x <= y, then 1, else 0
  • GOE2B: if x >= y, then 1, else 0
  • ET2B: if x = y, then 1, else 0
  • NET2B: if x != y, then 1, else 0

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

  • LT2C: if x < y, then (x+y), else (x-y)
  • GT2C: if x > y, then (x+y), else (x-y)
  • LOE2C: if x <= y, then (x+y), else (x-y)
  • GOE2C: if x >= y, then (x+y), else (x-y)
  • ET2C: if x = y, then (x+y), else (x-y)
  • NET2C: if x != y, then (x+y), else (x-y)

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

  • LT2D: if x < y, then (x*y), else (x/y)
  • GT2D: if x > y, then (x*y), else (x/y)
  • LOE2D: if x <= y, then (x*y), else (x/y)
  • GOE2D: if x >= y, then (x*y), else (x/y)
  • ET2D: if x = y, then (x*y), else (x/y)
  • NET2D: if x != y, then (x*y), else (x/y)

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

  • LT2E: if x < y, then (x+y), else (x*y)
  • GT2E: if x > y, then (x+y), else (x*y)
  • LOE2E: if x <= y, then (x+y), else (x*y)
  • GOE2E: if x >= y, then (x+y), else (x*y)
  • ET2E: if x = y, then (x+y), else (x*y)
  • NET2E: if x != y, then (x+y), else (x*y)

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

  • LT2F: if x < y, then (x+y), else sin(x*y)
  • GT2F: if x > y, then (x+y), else sin(x*y)
  • LOE2F: if x <= y, then (x+y), else sin(x*y)
  • GOE2F: if x >= y, then (x+y), else sin(x*y)
  • ET2F: if x = y, then (x+y), else sin(x*y)
  • NET2F: if x != y, then (x+y), else sin(x*y)

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

  • LT2G: if x < y, then (x+y), else atan(x*y)
  • GT2G: if x > y, then (x+y), else atan(x*y)
  • LOE2G: if x <= y, then (x+y), else atan(x*y)
  • GOE2G: if x >= y, then (x+y), else atan(x*y)
  • ET2G: if x = y, then (x+y), else atan(x*y)
  • NET2G: if x != y, then (x+y), else atan(x*y)

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

  • LT3A: if x < 0, then y, else z
  • GT3A: if x > 0, then y, else z
  • LOE3A: if x <= 0, then y, else z
  • GOE3A: if x >= 0, then y, else z
  • ET3A: if x = 0, then y, else z
  • NET3A: if x != 0, then y, else z

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

  • LT3B: if (x+y) < z, then (x+y), else z
  • GT3B: if (x+y) > z, then (x+y), else z
  • LOE3B: if (x+y) <= z, then (x+y), else z
  • GOE3B: if (x+y) >= z, then (x+y), else z
  • ET3B: if (x+y) = z, then (x+y), else z
  • NET3B: if (x+y) != z, then (x+y), else z

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

  • LT3C: if (x+y) < z, then (x+y), else (x+z)
  • GT3C: if (x+y) > z, then (x+y), else (x+z)
  • LOE3C: if (x+y) <= z, then (x+y), else (x+z)
  • GOE3C: if (x+y) >= z, then (x+y), else (x+z)
  • ET3C: if (x+y) = z, then (x+y), else (x+z)
  • NET3C: if (x+y) != z, then (x+y), else (x+z)

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

  • LT3D: if (x+y) < z, then (x+y), else (x-z)
  • GT3D: if (x+y) > z, then (x+y), else (x-z)
  • LOE3D: if (x+y) <= z, then (x+y), else (x-z)
  • GOE3D: if (x+y) >= z, then (x+y), else (x-z)
  • ET3D: if (x+y) = z, then (x+y), else (x-z)
  • NET3D: if (x+y) != z, then (x+y), else (x-z)

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

  • LT3E: if (x+y) < z, then (x+y), else (x*z)
  • GT3E: if (x+y) > z, then (x+y), else (x*z)
  • LOE3E: if (x+y) <= z, then (x+y), else (x*z)
  • GOE3E: if (x+y) >= z, then (x+y), else (x*z)
  • ET3E: if (x+y) = z, then (x+y), else (x*z)
  • NET3E: if (x+y) != z, then (x+y), else (x*z)

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

  • LT3F: if (x+y) < z, then (x+y), else (x/z)
  • GT3F: if (x+y) > z, then (x+y), else (x/z)
  • LOE3F: if (x+y) <= z, then (x+y), else (x/z)
  • GOE3F: if (x+y) >= z, then (x+y), else (x/z)
  • ET3F: if (x+y) = z, then (x+y), else (x/z)
  • NET3F: if (x+y) != z, then (x+y), else (x/z)

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

  • LT3G: if (x+y) < z, then (x*y), else (x+z)
  • GT3G: if (x+y) > z, then (x*y), else (x+z)
  • LOE3G: if (x+y) <= z, then (x*y), else (x+z)
  • GOE3G: if (x+y) >= z, then (x*y), else (x+z)
  • ET3G: if (x+y) = z, then (x*y), else (x+z)
  • NET3G: if (x+y) != z, then (x*y), else (x+z)

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

  • LT3H: if (x+y) < z, then (x*y), else (x-z)
  • GT3H: if (x+y) > z, then (x*y), else (x-z)
  • LOE3H: if (x+y) <= z, then (x*y), else (x-z)
  • GOE3H: if (x+y) >= z, then (x*y), else (x-z)
  • ET3H: if (x+y) = z, then (x*y), else (x-z)
  • NET3H: if (x+y) != z, then (x*y), else (x-z)

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

  • LT3I: if (x+y) < z, then (x*y), else (x*z)
  • GT3I: if (x+y) > z, then (x*y), else (x*z)
  • LOE3I: if (x+y) <= z, then (x*y), else (x*z)
  • GOE3I: if (x+y) >= z, then (x*y), else (x*z)
  • ET3I: if (x+y) = z, then (x*y), else (x*z)
  • NET3I: if (x+y) != z, then (x*y), else (x*z)

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

  • LT3J: if (x+y) < z, then (x*y), else (x/z)
  • GT3J: if (x+y) > z, then (x*y), else (x/z)
  • LOE3J: if (x+y) <= z, then (x*y), else (x/z)
  • GOE3J: if (x+y) >= z, then (x*y), else (x/z)
  • ET3J: if (x+y) = z, then (x*y), else (x/z)
  • NET3J: if (x+y) != z, then (x*y), else (x/z)

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

  • LT3K: if (x+y) < z, then (x+y+z), else sin(x*y*z)
  • GT3K: if (x+y) > z, then (x+y+z), else sin(x*y*z)
  • LOE3K: if (x+y) <= z, then (x+y+z), else sin(x*y*z)
  • GOE3K: if (x+y) >= z, then (x+y+z), else sin(x*y*z)
  • ET3K: if (x+y) = z, then (x+y+z), else sin(x*y*z)
  • NET3K: if (x+y) != z, then (x+y+z), else sin(x*y*z)

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

  • LT3L: if (x+y) < z, then (x+y+z), else atan(x*y*z)
  • GT3L: if (x+y) > z, then (x+y+z), else atan(x*y*z)
  • LOE3L: if (x+y) <= z, then (x+y+z), else atan(x*y*z)
  • GOE3L: if (x+y) >= z, then (x+y+z), else atan(x*y*z)
  • ET3L: if (x+y) = z, then (x+y+z), else atan(x*y*z)
  • NET3L: if (x+y) != z, then (x+y+z), else atan(x*y*z)

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

  • LT4A: if a < b, then c, else d
  • GT4A: if a > b, then c, else d
  • LOE4A: if a <= b, then c, else d
  • GOE4A: if a >= b, then c, else d
  • ET4A: if a = b, then c, else d
  • NET4A: if a != b, then c, else d

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

  • LT4B: if (a+b) < (c+d), then c, else d
  • GT4B: if (a+b) > (c+d), then c, else d
  • LOE4B: if (a+b) <= (c+d), then c, else d
  • GOE4B: if (a+b) >= (c+d), then c, else d
  • ET4B: if (a+b) = (c+d), then c, else d
  • NET4B: if (a+b) != (c+d), then c, else d

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

  • LT4C: if (a+b) < (c+d), then (a+b), else (c+d)
  • GT4C: if (a+b) > (c+d), then (a+b), else (c+d)
  • LOE4C: if (a+b) <= (c+d), then (a+b), else (c+d)
  • GOE4C: if (a+b) >= (c+d), then (a+b), else (c+d)
  • ET4C: if (a+b) = (c+d), then (a+b), else (c+d)
  • NET4C: if (a+b) != (c+d), then (a+b), else (c+d)

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

  • LT4D: if (a+b) < (c+d), then (a+b), else (c-d)
  • GT4D: if (a+b) > (c+d), then (a+b), else (c-d)
  • LOE4D: if (a+b) <= (c+d), then (a+b), else (c-d)
  • GOE4D: if (a+b) >= (c+d), then (a+b), else (c-d)
  • ET4D: if (a+b) = (c+d), then (a+b), else (c-d)
  • NET4D: if (a+b) != (c+d), then (a+b), else (c-d)

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

  • LT4E: if (a+b) < (c+d), then (a+b), else (c*d)
  • GT4E: if (a+b) > (c+d), then (a+b), else (c*d)
  • LOE4E: if (a+b) <= (c+d), then (a+b), else (c*d)
  • GOE4E: if (a+b) >= (c+d), then (a+b), else (c*d)
  • ET4E: if (a+b) = (c+d), then (a+b), else (c*d)
  • NET4E: if (a+b) != (c+d), then (a+b), else (c*d)

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

  • LT4F: if (a+b) < (c+d), then (a+b), else (c/d)
  • GT4F: if (a+b) > (c+d), then (a+b), else (c/d)
  • LOE4F: if (a+b) <= (c+d), then (a+b), else (c/d)
  • GOE4F: if (a+b) >= (c+d), then (a+b), else (c/d)
  • ET4F: if (a+b) = (c+d), then (a+b), else (c/d)
  • NET4F: if (a+b) != (c+d), then (a+b), else (c/d)

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

  • LT4G: if (a+b) < (c+d), then (a*b), else (c+d)
  • GT4G: if (a+b) > (c+d), then (a*b), else (c+d)
  • LOE4G: if (a+b) <= (c+d), then (a*b), else (c+d)
  • GOE4G: if (a+b) >= (c+d), then (a*b), else (c+d)
  • ET4G: if (a+b) = (c+d), then (a*b), else (c+d)
  • NET4G: if (a+b) != (c+d), then (a*b), else (c+d)

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

  • LT4H: if (a+b) < (c+d), then (a*b), else (c-d)
  • GT4H: if (a+b) > (c+d), then (a*b), else (c-d)
  • LOE4H: if (a+b) <= (c+d), then (a*b), else (c-d)
  • GOE4H: if (a+b) >= (c+d), then (a*b), else (c-d)
  • ET4H: if (a+b) = (c+d), then (a*b), else (c-d)
  • NET4H: if (a+b) != (c+d), then (a*b), else (c-d)

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

  • LT4I: if (a+b) < (c+d), then (a*b), else (c*d)
  • GT4I: if (a+b) > (c+d), then (a*b), else (c*d)
  • LOE4I: if (a+b) <= (c+d), then (a*b), else (c*d)
  • GOE4I: if (a+b) >= (c+d), then (a*b), else (c*d)
  • ET4I: if (a+b) = (c+d), then (a*b), else (c*d)
  • NET4I: if (a+b) != (c+d), then (a*b), else (c*d)

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

  • LT4J: if (a+b) < (c+d), then (a*b), else (c/d)
  • GT4J: if (a+b) > (c+d), then (a*b), else (c/d)
  • LOE4J: if (a+b) <= (c+d), then (a*b), else (c/d)
  • GOE4J: if (a+b) >= (c+d), then (a*b), else (c/d)
  • ET4J: if (a+b) = (c+d), then (a*b), else (c/d)
  • NET4J: if (a+b) != (c+d), then (a*b), else (c/d)

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

  • LT4K: if (a+b) < (c+d), then sin(a*b), else sin(c*d)
  • GT4K: if (a+b) > (c+d), then sin(a*b), else sin(c*d)
  • LOE4K: if (a+b) <= (c+d), then sin(a*b), else sin(c*d)
  • GOE4K: if (a+b) >= (c+d), then sin(a*b), else sin(c*d)
  • ET4K: if (a+b) = (c+d), then sin(a*b), else sin(c*d)
  • NET4K: if (a+b) != (c+d), then sin(a*b), else sin(c*d)

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

  • LT4L: if (a+b) < (c+d), then atan(a*b), else atan(c*d)
  • GT4L: if (a+b) > (c+d), then atan(a*b), else atan(c*d)
  • LOE4L: if (a+b) <= (c+d), then atan(a*b), else atan(c*d)
  • GOE4L: if (a+b) >= (c+d), then atan(a*b), else atan(c*d)
  • ET4L: if (a+b) = (c+d), then atan(a*b), else atan(c*d)
  • NET4L: if (a+b) != (c+d), then atan(a*b), else atan(c*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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