# math

functions
abs            erf            log            tanh
atan           erfc           log10
atan2          exp            sin
cos            int            sqrt

The above math functions return a double precision value and take a double precision argument. The exception is atan2 with two double precision arguments.

## DIAGNOSTICS

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

These functions call the library routines supplied by the compiler.

# sin

math


see sin for the Vector class.

# cos

math


see sin

# atan

math

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

# atan2

math


## 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

## EXAMPLES

execute following 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)


# tanh

math

hyperbolic tangent. see tanh for the Vector class.

# log

math

logarithm to the base e see log for the Vector class.

# log10

math

logarithm to the base 10

see log10 for the Vector class.

# exp

math


## 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)


# sqrt

math

square root

see sqrt for the Vector class.

# int

math

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

# abs

math

absolute value

see abs for the Vector class.

# erf

math

normalized error function @eqn ${\rm erf}(z) = \frac{2}{\sqrt{\pi}} \int_{0}^{z} e^{-t^2} dt$ @endeqn

# erfc

math

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

neuron/general/function/sin.hel : May 13 2012