Contents - Index

Resident functions in MODELS


1. Resident functions

A number of numerical and logical functions are permanently defined and are available for use in a model. Their names are visible in any model, and can be used directly without being declared in a FUNCTION declaration.
The following resident functions are defined:
- numerical functions returning one value for each input argument:
abs absolute value of each argument
sqrt square root of each argument
exp exponential of each argument
ln base-e logarithm of each argument
log10 base-10 logarithm of each argument
log2 base-2 logarithm of each argument
recip 1/x for each argument x, with zero-division protection (1/0 = inf)
factorial x! for each argument x
trunc integer part of each argument
fract fractional part of each argument
round rounded value of each argument (to the nearest integer)
sign =-1 when x<0, =0 when x=0, =+1 when x>0, for each argument x
rad value conversion from degrees to radians, for each argument
deg value conversion from radians to degrees, for each argument
sin sine of each argument
cos cosine of each argument
tan tangent  of each argument
asin arc sine of each argument
acos arc cosine of each argument
atan arc tangent of each argument
sinh hyperbolic sine of each argument
cosh hyperbolic cosine of each argument
tanh hyperbolic tangent of each argument
asinh arc hyperbolic sine of each argument
acosh arc hyperbolic cosine of each argument
atanh arc hyperbolic tangent of each argument
- double-argument numerical functions returning a single value:
atan2(x1,x2) tan-1(x1/x2) with 4-quadrant range as determined by the signs of x1 and x2
binom(n,r) C(n,r) combination of r elements in a set of n = n!/(n-r)!r!
permut(n,r) P(n,r) permutation of r elements in a set of n = n!/(n-r)!
- multiple-argument numerical functions returning a single value:
min(x1,x2,...) minimum value of {­x1, x2, ...}
max(x1,x2,...) maximum value of {­x1, x2, ...}
norm(x1,x2,...) Euclidian norm =sqrt(x12+x22+...)
- no-argument numerical functions returning a single value:
random single random number between 0 and 1, uses no argument
- logical functions returning one value for each input argument:
bool value conversion of each argument from numerical to Boolean
value = 1 when argument > 0
value = 0 when argument <= 0
- multiple-argument logical functions returning a single value:
and(x1,x2,...) returns value of "x1 AND x2 AND ..."
=1 only when all the arguments are true
or(x1,x2,...) returns value of "x1 OR x2 OR ..."
=1 when one or more of the arguments are true
nand(x1,x2,...) returns value of "NOT(x1 AND x2 AND ...)"
=1 when one or more arguments are false
nor(x1,x2,...) returns value of "NOT(x1 OR x2 OR ...)"
=1 only when all the arguments are false
xor(x1,x2,...) returns value of "x1 XOR x2 XOR ..."
= 1 when only one of the arguments is true

2.  Resident simulation functions
A number of functions which are related to the time simulation of a model are permanently defined and are available for use in a model. Their names are visible in any model, and can be used directly without being declared in a FUNCTION declaration.
For those functions requiring interpolation or extrapolation (see the list of functions below), the interpolation degree "pol" is an optional argument indicating the interpolation degree 0, 1, or 2 used for evaluating the function between the available values of the element (0=discontinuous, 1=linear, 2=quadratic) (default=1).
The following resident simulation functions are defined:
deriv(x) the value of the first-order time derivative of x at the present simulation time
deriv2(x) the value of the second-order time derivative of x at the present simulation time
delay(x,d,pol) past value of x at time (t-d), including references to pre-simulation times using the history function assigned to x
prevval(x) the value of x at the previous simulation time 
backval(x,t,pol) past value of x at a time t within the last time step
backtime(x,val,pol) time at which x had the value val during the last time step
= "undefined" if not possible
predval(x,t,pol) predicted value of x at time t
predtime(x,val,pol) predicted value of time at which x will reach the value val
= "undefined" if not possible
histdef(x) a reference to the definition of the history function associated with x, used when defining the history of an element in terms of the history of another element
histval(x,t) the value of x evaluated at time t, calculated using the history function associated with x