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# Common Math Functions (HOC)

These math functions return a double precision value and take a double precision argument. The exception is `atan2()` which has two double precision arguments.

Diagnostics:

  Arguments that are out of range give an argument domain diagnostic.

  These functions call the library routines supplied by the compiler.

`abs`()

  absolute value

  see `Vector.abs()` for the `Vector` class.

`int`()

  returns the integer part of its argument (truncates toward 0).

`sqrt`()

  square root

  see `Vector.sqrt()` for the `Vector` class.

`exp`()
  Description:

    returns the exponential function to the base e

    When exp is used in model descriptions, it is often the case that the cvode variable step integrator extrapolates voltages to values which return out of range values for the exp (often used in rate functions). There were so many of these false warnings that it was deemed better to turn off the warning message when Cvode is active. In any case the return value is exp(700). This message is not turned off at the interpreter level or when cvode is not active.

        for i=690, 710 print i, exp(i)

`log`()

  logarithm to the base e see `Vector.log()` for the `Vector` class.

`log10`()

  logarithm to the base 10

  see `Vector.log10()` for the `Vector` class.

`cos`()

  trigonometric function of radian argument.

  see `Vector.sin()`

`sin`()

  trigonometric function of radian argument.

  see `Vector.sin()` for the `Vector` class.

`tanh`()

  hyperbolic tangent. see `Vector.tanh()` for the `Vector` class.

`atan`()

  returns the arc-tangent of y/x in the range -PI/2 to PI/2. (x > 0)

`atan2`()
  Syntax:
    `radians = atan2(y, x)`
  Description:
    returns the arc-tangent of y/x in the range -PI < radians <= PI. y and x can be any double precision value, including 0. If both are 0 the value returned is 0. Imagine a right triangle with base x and height y. The result is the angle in radians between the base and hypotenuse

  Example:

  >     atan2(0,0)
  >     for i=-1,1 { print atan2(i*1e-6, 10) }
  >     for i=-1,1 { print atan2(i*1e-6, -10) }
  >     for i=-1,1 { print atan2(10, i*1e-6) }
  >     for i=-1,1 { print atan2(-10, i*1e-6) }
  >     atan2(10,10)
  >     atan2(10,-10)
  >     atan2(-10,10)
  >     atan2(-10,-10)

`erf`()

  normalized error function

  \[{\rm erf}(z) = \frac{2}{\sqrt{\pi}} \int_{0}^{z} e^{-t^2} dt\]

`erfc`()

  returns `1.0 - erf(z)` but on sun machines computed by other methods that avoid cancellation for large z.

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