ECLiPSe distinguishes four types of numbers:
The system performs automatic type conversions in the direction
integer -> rational -> float -> breal.These conversions are done (i) to make the types of two input arguments equal and (ii) to lift the type of an input argument to the one expected by the function. The result type is the lifted input type, unless otherwise specified.
A table of predefined arithmetic functions is given below. A predefined function is evaluated by first evaluating its arguments and then calling the corresponding evaluation predicate. The evaluation predicate belonging to a compound term func(a_1,..,a_n) is the predicate func/(n+1). It receives a_1,..,a_n as its first n arguments and returns a numeric result as its last argument. This result is then used in the arithmetic computation.
This evaluation mechanism outlined above is not restricted to the predefined arithmetic functors shown in the table. In fact it works for all atoms and compound terms. It is therefore possible to define a new arithmetic operation by just defining an evaluation predicate. Similarly, many ECLiPSe built-ins return numbers in the last argument and can thus be used as evaluation predicates (e.g. arity/1, cputime/1, random/1, string_length/2, ...). Note that recursive evaluation of arguments is only done for the predefined arithmetic functions, for the others the arguments are simply passed to the evaluation predicate.
Most arithmetic errors will not be reported in is/2, but in the evaluation predicate where it occurred.
Function Description Argument Types Result Type
----------------------------------------------------------------------------
+ E unary plus number number
- E unary minus number number
abs(E) absolute value number number
sgn(E) sign value number integer
floor(E) round down number number
ceiling(E) round up number number
round(E) round to nearest number number
truncate(E) round towards zero number number
E1 + E2 addition number x number number
E1 - E2 subtraction number x number number
E1 * E2 multiplication number x number number
E1 / E2 division number x number see below
E1 // E2 integer division truncated integer x integer integer
E1 rem E2 integer remainder integer x integer integer
E1 div E2 integer division floored integer x integer integer
E1 mod E2 integer modulus integer x integer integer
gcd(E1,E2) greatest common divisor integer x integer integer
lcm(E1,E2) least common multiple integer x integer integer
E1 ^ E2 power operation number x number number
min(E1,E2) minimum of 2 values number x number number
max(E1,E2) maximum of 2 values number x number number
copysign(E1,E2) combine value and sign number x number number
nexttoward(E1,E2) next representable number number x number number
\ E bitwise complement integer integer
E1 /\ E2 bitwise conjunction integer x integer integer
E1 \/ E2 bitwise disjunction integer x integer integer
xor(E1,E2) bitwise exclusive or integer x integer integer
E1 >> E2 shift E1 right by E2 bits integer x integer integer
E1 << E2 shift E1 left by E2 bits integer x integer integer
setbit(E1,E2) set bit E2 in E1 integer x integer integer
clrbit(E1,E2) clear bit E2 in E1 integer x integer integer
getbit(E1,E2) get of bit E2 in E1 integer x integer integer
sin(E) trigonometric function number float or breal
cos(E) trigonometric function number float or breal
tan(E) trigonometric function number float or breal
asin(E) trigonometric function number float
acos(E) trigonometric function number float
atan(E) trigonometric function number float or breal
atan(E1,E2) trigonometric function number x number float or breal
exp(E) exponential function ex number float or breal
ln(E) natural logarithm number float or breal
sqrt(E) square root number float or breal
pi the constant pi --- float
e the constant e --- float
fix(E) truncate to integer number integer
integer(E) convert to integer number integer
float(E) convert to float number float
rational(E) convert to rational number rational
rationalize(E) convert to rational number rational
numerator(E) numerator of rational integer or rational integer
denominator(E) denominator of rational integer or rational integer
breal(E) convert to bounded real number breal
breal_min(E) lower bound of bounded real number float
breal_max(E) upper bound of bounded real number float
breal_from_bounds(Lo, Hi)
make bounded real from bounds number x number breal
sum(Es) sum of elements vector number
sum(Es*Es) scalar product vector*vector number
min(Es) minimum of elements vector number
max(Es) maximum of elements vector number
eval(E) eval runtime expression term number
The division operator / yields either a rational or a float result,
depending on the value of the global flag prefer_rationals. The same is
true for the result of ^ if an integer is raised to a negative integral
power.
The relation between integer divisions // and div, and remainder and modulus operations rem and mod is as follows:
X =:= (X rem Y) + (X // Y) * Y.
X =:= (X mod Y) + (X div Y) * Y.
Success:
103 is 3 + 4 * 5 ^ 2.
X is asin(sin(pi/4)). % gives X = 0.785398.
Y is 2 * 3, X is 4 + Y. % gives X = 10, Y = 6.
X is string_length("four") + 1. % gives X = 5.
[eclipse]: [user].
myconst(4.56).
user compiled 40 bytes in 0.02 seconds
yes.
[eclipse]: 5.56 is myconst + 1.
yes.
Fail:
3.14 is pi. % different values
atom is 4.
1 is 1.0.
Error:
X is _. (Error 4)
X is "s". (Error 24)
[eclipse]: X is undef(1).
calling an undefined procedure undef(1, _g63) in ...
[eclipse]: X is 3 + Y.
instantiation fault in +(3, _g45, _g53)