*Result*- Output: a number.
*Expression*- An arithmetic expression.

ECLiPSe distinguishes four types of numbers:

**integers**e.g. 12345- Integers can be of arbitrary magnitude. Integers that fit into the word size of the machine are handled more efficiently.
**rationals**e.g. 3_4- Rational numbers represent the corresponding mathematical notion (the ratio of two integers). The operations defined on rationals give precise (rational) results.
**floats**e.g. 3.1415- Floats are an imprecise approximation of real numbers. They are represented as IEEE double precision floats. Floating point operations are typically subject to rounding errors. Undefined operations produce infinity results if possible, otherwise exceptions (not NaNs).
**bounded reals (breal)**e.g. 3.1415__3.1416- Bounded reals are a safe representation of real numbers, characterised by a lower and upper bound in floating point format. Operations on breals are safe in the sense that the resulting bounds always enclose the precise result (interval arithmetic).

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 numberThe 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.

- is(-, +) is det

*(4) instantiation fault*- Expression is uninstantiated
*(21) undefined arithmetic expression*- An evaluation predicate in the expression is not defined.
*(24) number expected*- Expression is not a valid arithmetic expression.

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)