Operators

An expression can be formed using operators and functions acting on operands.

Table 2.4: Real Operators in MAD-9

Operator	Meaning	result type	operand type(s)
Real operators with one operand
+ X	unary plus, returns X	real	real
- X	unary minus, returns the negative of X	real	real
Real operators with two operands
X + Y	add X to Y	real	real,real
X - Y	subtract Y from X	real	real,real
X * Y	multiply X by Y	real	real,real
X / Y	divide X by Y	real	real,real
X ^ Y	power, return X raised to the power Y ( $\mathtt{Y} > 0$)	real	real,real

Table 2.5: Real Functions in MAD-9

Function	Meaning	result type	argument type(s)
Real functions with no arguments
RANF()	random number, uniform distribution in [0,1)	real	-
GAUSS()	random number, Gaussian distribution with $\sigma=1$	real	-
USER0()	random number, user-defined distribution	real	-
SI()	arc length from start of ring to the entry of the current element. This function is only available in the EALIGN command	real	-
SC()	arc length from start of ring to the centre of the current element. This function is only available in the EALIGN command	real	-
SO()	arc length from start of ring to the exit of current the element. This function is only available in the EALIGN command	real	-
Real functions with one argument
TRUNC(X)	truncate X towards zero (discard fractional part)	real	real
ROUND(X)	round X to nearest integer	real	real
FLOOR(X)	return largest integer not greater than X	real	real
CEIL(X)	return smallest integer not less than X	real	real
SIGN(X)	return sign of X (+1 for X positive, -1 for X negative, 0 for X zero)	real	real
SQRT(X)	return square root of X	real	real
LOG(X)	return natural logarithm of X	real	real
EXP(X)	return exponential to the base $e$ of X	real	real
SIN(X)	return trigonometric sine of X	real	real
COS(X)	return trigonometric cosine of X	real	real
ABS(X)	return absolute value of X	real	real
TAN(X)	return trigonometric tangent of X	real	real
ASIN(X)	return inverse trigonometric sine of X	real	real
ACOS(X)	return inverse trigonometric cosine of X	real	real
ATAN(X)	return inverse trigonometric tangent of X	real	real
TGAUSS(X)	random number, Gaussian distribution with $\sigma$=1, truncated at X	real	real
USER1(X)	random number, user-defined distribution with one parameter	real	real
EVAL(X)	evaluate the argument immediately and transmit it as a constant	real	real
Real functions with two arguments
ATAN2(X,Y)	return inverse trigonometric tangent of Y/X	real	real,real
MAX(X,Y)	return the larger of X, Y	real	real,real
MIN(X,Y)	return the smaller of X, Y	real	real,real
MOD(X,Y)	return the largest value less than Y which differs from X by a multiple of Y	real	real,real
USER2(X,Y)	random number, user-defined distribution with two parameters	real	real,real

Table 2.6: Real Functions of Arrays in MAD-9

Function	Meaning	result type	operand type
VMAX(X,Y)	return largest array component	real	real array
VMIN(X,Y)	return smallest array component	real	real array
VRMS(X,Y)	return rms value of an array	real	real array
VABSMAX(X,Y)	return absolute largest array component	real	real array

Care must be used when an ordinary expression contains a random generator. It may be re-evaluated at unpredictable times, generating a new value. However, the use of a random generator in an assignment expression is safe. Examples:

D:DRIFT,L=0.01*RANF();    // a drift space with random length,
                          // may change during execution.
P=EVAL(0.001*TGAUSS(X));  // Evaluated once and stored as a constant.