crazy.gms : Examples of Extended Arithmetic

Description

```This example program tests and demonstrates the definition of special
(crazy) values. All GAMS operations are defined over the closed
interval from -infinity (-INF) to +infinity (INF) and the three other
special values: epsilon (EPS), missing (NA) and undefined (UNDF).
```

Small Model of Type : GAMS

Category : GAMS Model library

Main file : crazy.gms

``````\$title Examples of Extended Arithmetic  (CRAZY,SEQ=67)

\$onText
This example program tests and demonstrates the definition of special
(crazy) values. All GAMS operations are defined over the closed
interval from -infinity (-INF) to +infinity (INF) and the three other
special values: epsilon (EPS), missing (NA) and undefined (UNDF).

GAMS Development Corporation, Formulation and Language Example.

Keywords: GAMS arithmetic, GAMS language features
\$offText

* Notice that any characters are legal in a "quoted" label
Set op1 / minus-inf, "-4.000", zero   , "+2.500"
plus-inf , epsilon , missing, undefined /;

Alias (op1,op2);

* The value UNDF can not be entered, only produced by an illegal
* operation, as is shown below
Parameter a(op1) / minus-inf -inf, "-4.000" -4 , zero     0, "+2.500" 2.5
plus-inf  +inf, epsilon  eps, missing na               /;

a("undefined") = 0/0;
display a;

Parameter
b(op1,op2)  'operand 1 plus operand 2:  o1 + o2'
c(op1,op2)  'operand 1 minus operand 2: o1 - o2'
d(op1,op2)  'operand 1 to the power operand 2: o1 ** o2 (o2 is  real)'
e(op1,op2)  'operand 1 times operand 2: o1 * o2'
f(op1,op2)  'operand 1 divided by operand 2: o1 / o2'
g(op1,op2)  'operand 1 =  operand 2: o1  = o2'
h(op1,op2)  'operand 1 <= operand 2: o1 <= o2'
i(op1,op2)  'operand 1 >= operand 2: o1 >= o2'
j(op1,op2)  'operand 1 <> operand 2: o1 <> o2'
k(op1,op2)  'operand 1 <  operand 2: o1 <  o2'
l(op1,op2)  'operand 1  > operand 2: o1  > o2'
m(op1,op2)  'operand 1 or operand 2: o1 or o2'
n(op1,op2)  'operand 1 and operand 2: o1 and o2'
o(op1,op2)  'operand 1 xor operand 2: o1 xor o2'
p(op1,op2)  'operand 1 to the power operand 2: o1 ** o2  (o2 is integer)'
q(op1,op2)  'maximum of operand 1, operand 2: max(o1,o2)'
r(op1,op2)  'minimum of operand 1, operand 2: min(o1,o2)'
r1(op1,op2) 'normal random number with mean o1 and std o2: normal(o1,o2)'
s(op1,op2)  'mod of operand 1, operand 2: mod(o1,o2)'
t(op1,op2)  'round argument 1 by argument 2 places: round(o1,o2)'
t1(op1,op2) 'uniform random number between o1 and o2: uniform(o1,o2)'
u(op1,op2)  'dollar control on right hand side: u   = o1\$o2'
v(op1,op2)  'dollar control on left hand side: v\$o2 = o1'
aa(*,op1)   'single argument functions';

Scalar
looptest    'tests \$-control on loops'
sumtest     'test \$-control on sum operations'
sumt        'sum test'
prot        'prod test'
mint        'smin test'
maxt        'smax test';

b(op1,op2) = a(op1) + a(op2);
c(op1,op2) = a(op1) - a(op2);
d(op1,op2) = a(op1)**a(op2);
p(op1,op2) = power(a(op1),a(op2));
e(op1,op2) = a(op1)*a(op2);
f(op1,op2) = a(op1)/a(op2);
g(op1,op2) = a(op1)  = a(op2);
h(op1,op2) = a(op1) <= a(op2);
i(op1,op2) = a(op1) >= a(op2);
j(op1,op2) = a(op1) <> a(op2);
k(op1,op2) = a(op1) <  a(op2);
l(op1,op2) = a(op1)  > a(op2);
m(op1,op2) = a(op1) or  a(op2);
n(op1,op2) = a(op1) and a(op2);
o(op1,op2) = a(op1) xor a(op2);
q(op1,op2) = max(a(op1),a(op2));
r(op1,op2) = min(a(op1),a(op2));
r1(op1,op2)= normal(a(op1),a(op2));
s(op1,op2) = mod(a(op1),a(op2));
t(op1,op2) = round(a(op1),a(op2));
t1(op1,op2)= uniform(a(op1),a(op2));
u(op1,op2) = a(op1)\$a(op2);
v(op1,op2)\$a(op2) = a(op1);

aa("absolute",  op1) = abs   (a(op1));
aa("arctan",    op1) = arctan(a(op1));
aa("ceiling",   op1) = ceil  (a(op1));
aa("cos",       op1) = cos   (a(op1));
aa("floor",     op1) = floor (a(op1));
aa("errorf",    op1) = errorf(a(op1));
aa("exponent",  op1) = exp   (a(op1));
aa("loge",      op1) = log   (a(op1));
aa("log10",     op1) = log10 (a(op1));
aa("sine",      op1) = sin   (a(op1));
aa("sign",      op1) = sign  (a(op1));
aa("squareroot",op1) = sqrt  (a(op1));
aa("square",    op1) = sqr   (a(op1));
aa("mapval",    op1) = mapval(a(op1));
aa("truncate",  op1) = trunc (a(op1));
aa("not",       op1) = not    a(op1);

display a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,d,p,q,r,r1,s,t,t1,u,v,aa;

looptest = 0;
loop(op1\$a(op1), looptest = looptest + 10**(ord(op1) - 1));

sumtest = sum(op1\$a(op1), 10**(ord(op1) - 1));
sumt    = sum(op1, a(op1));
prot    = prod(op1, a(op1));
mint    = smin(op1, a(op1));
maxt    = smax(op1, a(op1));

option decimals = 0;
display looptest, sumtest, sumt, prot, mint, maxt;

execError = 0;
``````
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